Changeset 1c5b54 in git for doc/singular.idx
- Timestamp:
- Jan 12, 2018, 7:07:33 PM (6 years ago)
- Branches:
- (u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
- Children:
- a959dfcb571533a94c05b115085bd177e3b7f8fa
- Parents:
- ce4b2fb5302493784ac68ec931cfb54f96e899ff
- File:
-
- 1 edited
-
doc/singular.idx (modified) (7 diffs)
Legend:
- Unmodified
- Added
- Removed
-
doc/singular.idx
rce4b2f r1c5b54 1 1 ! sing_36.htm#IDX101 2 2 != sing_36.htm#IDX95 3 != sing_ 95.htm#SEC1353 != sing_100.htm#SEC140 4 4 " sing_36.htm#IDX104 5 5 # sing_36.htm#IDX118 6 6 $ sing_36.htm#IDX119 7 7 % sing_36.htm#IDX91 8 % sing_76.htm#SEC116 9 % sing_93.htm#SEC133 10 % sing_105.htm#SEC145 11 % sing_142.htm#SEC182 8 % sing_81.htm#SEC121 9 % sing_98.htm#SEC138 10 % sing_110.htm#SEC150 11 % sing_147.htm#SEC187 12 % sing_155.htm#SEC195 12 13 && sing_36.htm#IDX102 13 && sing_ 96.htm#SEC13614 && sing_101.htm#SEC141 14 15 ( sing_36.htm#IDX80 15 () sing_1 26.htm#IDX13016 () sing_131.htm#IDX130 16 17 ) sing_36.htm#IDX81 17 18 * bigintmat operations sing_36.htm#IDX89 18 * sing_ 76.htm#SEC11619 * sing_8 2.htm#SEC12220 * sing_ 88.htm#SEC12821 * sing_9 3.htm#SEC13322 * sing_10 1.htm#SEC14123 * sing_1 05.htm#SEC14524 * sing_13 2.htm#SEC17225 * sing_1 37.htm#SEC17726 * sing_14 2.htm#SEC18227 * sing_15 0.htm#SEC19019 * sing_81.htm#SEC121 20 * sing_87.htm#SEC127 21 * sing_93.htm#SEC133 22 * sing_98.htm#SEC138 23 * sing_106.htm#SEC146 24 * sing_110.htm#SEC150 25 * sing_137.htm#SEC177 26 * sing_142.htm#SEC182 27 * sing_147.htm#SEC187 28 * sing_155.htm#SEC195 28 29 ** sing_36.htm#IDX93 29 30 + bigintmat operations sing_36.htm#IDX85 30 + sing_ 76.htm#SEC11631 + sing_8 2.htm#SEC12232 + sing_ 88.htm#SEC12833 + sing_9 3.htm#SEC13334 + sing_10 1.htm#SEC14135 + sing_1 05.htm#SEC14536 + sing_12 1.htm#SEC16137 + sing_13 2.htm#SEC17238 + sing_1 37.htm#SEC17739 + sing_14 2.htm#SEC18240 + sing_15 0.htm#SEC19041 + sing_16 4.htm#SEC20442 + sing_17 0.htm#SEC21043 + sing_1 75.htm#SEC21531 + sing_81.htm#SEC121 32 + sing_87.htm#SEC127 33 + sing_93.htm#SEC133 34 + sing_98.htm#SEC138 35 + sing_106.htm#SEC146 36 + sing_110.htm#SEC150 37 + sing_126.htm#SEC166 38 + sing_137.htm#SEC177 39 + sing_142.htm#SEC182 40 + sing_147.htm#SEC187 41 + sing_155.htm#SEC195 42 + sing_169.htm#SEC209 43 + sing_175.htm#SEC215 44 + sing_180.htm#SEC220 44 45 ++ sing_36.htm#IDX86 45 46 - bigintmat operations sing_36.htm#IDX87 46 - sing_ 76.htm#SEC11647 - sing_8 2.htm#SEC12248 - sing_9 3.htm#SEC13349 - sing_10 1.htm#SEC14150 - sing_1 05.htm#SEC14551 - sing_13 2.htm#SEC17252 - sing_14 2.htm#SEC18253 - sing_15 0.htm#SEC19054 - sing_1 75.htm#SEC21547 - sing_81.htm#SEC121 48 - sing_87.htm#SEC127 49 - sing_98.htm#SEC138 50 - sing_106.htm#SEC146 51 - sing_110.htm#SEC150 52 - sing_137.htm#SEC177 53 - sing_147.htm#SEC187 54 - sing_155.htm#SEC195 55 - sing_180.htm#SEC220 55 56 -- sing_36.htm#IDX88 56 57 --MPhost sing_19.htm#IDX66 … … 78 79 --ticks-per-sec sing_19.htm#IDX62 79 80 --user-option sing_19.htm#IDX58 80 -> sing_15 4.htm#SEC19481 -> sing_159.htm#SEC199 81 82 -MPhost Command line options 82 83 -MPport Command line options … … 116 117 .singularrc file, no loading Command line options sing_19.htm#IDX46 117 118 / sing_36.htm#IDX90 118 / sing_105.htm#SEC145 119 / sing_132.htm#SEC172 120 / sing_142.htm#SEC182 121 / sing_150.htm#SEC190 122 / sing_175.htm#SEC215 119 / sing_76.htm#SEC116 120 / sing_110.htm#SEC150 121 / sing_137.htm#SEC177 122 / sing_147.htm#SEC187 123 / sing_155.htm#SEC195 124 / sing_180.htm#SEC220 123 125 // sing_36.htm#IDX107 124 126 // sing_36.htm#IDX109 125 127 // sing_36.htm#IDX110 126 128 : sing_36.htm#IDX114 127 : sing_1 05.htm#SEC145129 : sing_110.htm#SEC150 128 130 :: sing_36.htm#IDX115 129 :: sing_14 4.htm#SEC184131 :: sing_149.htm#SEC189 130 132 ; sing_36.htm#IDX111 131 133 < sing_36.htm#IDX100 132 < sing_15 0.htm#SEC190133 < sing_1 75.htm#SEC215134 < sing_24 1.htm#SEC281134 < sing_155.htm#SEC195 135 < sing_180.htm#SEC220 136 < sing_247.htm#SEC287 135 137 <= sing_36.htm#IDX99 136 <= sing_ 95.htm#SEC135137 <= sing_14 2.htm#SEC182138 <= sing_15 0.htm#SEC190139 <= sing_17 0.htm#SEC210140 <= sing_1 75.htm#SEC215138 <= sing_100.htm#SEC140 139 <= sing_147.htm#SEC187 140 <= sing_155.htm#SEC195 141 <= sing_175.htm#SEC215 142 <= sing_180.htm#SEC220 141 143 <> sing_36.htm#IDX96 142 <> sing_ 95.htm#SEC135143 <> sing_13 2.htm#SEC172144 <> sing_14 2.htm#SEC182145 <> sing_15 0.htm#SEC190146 <> sing_16 4.htm#SEC204147 <> sing_17 0.htm#SEC210148 <> sing_1 75.htm#SEC215144 <> sing_100.htm#SEC140 145 <> sing_137.htm#SEC177 146 <> sing_147.htm#SEC187 147 <> sing_155.htm#SEC195 148 <> sing_169.htm#SEC209 149 <> sing_175.htm#SEC215 150 <> sing_180.htm#SEC220 149 151 = sing_36.htm#IDX77 150 152 == sing_36.htm#IDX94 151 == sing_ 95.htm#SEC135152 == sing_13 2.htm#SEC172153 == sing_14 2.htm#SEC182154 == sing_15 0.htm#SEC190155 == sing_16 4.htm#SEC204156 == sing_17 0.htm#SEC210157 == sing_1 75.htm#SEC215153 == sing_100.htm#SEC140 154 == sing_137.htm#SEC177 155 == sing_147.htm#SEC187 156 == sing_155.htm#SEC195 157 == sing_169.htm#SEC209 158 == sing_175.htm#SEC215 159 == sing_180.htm#SEC220 158 160 > sing_36.htm#IDX98 159 > sing_15 0.htm#SEC190160 > sing_1 75.htm#SEC215161 > sing_155.htm#SEC195 162 > sing_180.htm#SEC220 161 163 >= sing_36.htm#IDX97 162 >= sing_ 95.htm#SEC135163 >= sing_14 2.htm#SEC182164 >= sing_15 0.htm#SEC190165 >= sing_17 0.htm#SEC210166 >= sing_1 75.htm#SEC215164 >= sing_100.htm#SEC140 165 >= sing_147.htm#SEC187 166 >= sing_155.htm#SEC195 167 >= sing_175.htm#SEC215 168 >= sing_180.htm#SEC220 167 169 ? sing_36.htm#IDX106 168 ? sing_25 1.htm#IDX148169 AG codes sing_8 32.htm#SEC884170 AGcode_L sing_17 81.htm#SEC185760329171 AGcode_Omega sing_17 82.htm#SEC185856285172 ASCII sing_ 881.htm#SEC957 26816173 ASCII links sing_11 2.htm#SEC152170 ? sing_259.htm#IDX148 171 AG codes sing_851.htm#SEC903 172 AGcode_L sing_1795.htm#SEC1871 60329 173 AGcode_Omega sing_1796.htm#SEC1872 56285 174 ASCII sing_901.htm#SEC977 26816 175 ASCII links sing_117.htm#SEC157 174 176 ASSUME sing_64.htm#SEC101 175 A_L sing_1480.htm#SEC1556 16721 176 A_Z sing_880.htm#SEC956 50866 177 Access to elements of a user defined type Access to elements of a user defined type sing_180.htm#SEC220 178 Adj_div sing_1776.htm#SEC1852 44919 179 Adjoint ideal sing_1357.htm#IDX592 180 Alexander polynomial sing_1451.htm#IDX616 181 Algebraic Geometry codes sing_1775.htm#IDX764 182 Algebraic dependence Algebraic dependence sing_813.htm#SEC865 183 Algebraic geometry sing_1332.htm#SEC1408 184 AltVarEnd sing_726.htm#SEC778 11020 185 AltVarStart sing_725.htm#SEC777 21592 186 Ann sing_1271.htm#SEC1347 61560 187 Appel function sing_555.htm#IDX349 188 Appel hypergeometric function sing_555.htm#IDX350 189 Applications sing_830.htm#SEC882 190 ArnoldAction sing_1573.htm#SEC1649 26958 191 Assignments for user defined types Assignments for user defined types sing_182.htm#SEC222 192 AssocTanToEnv sing_917.htm#SEC993 39826 193 Atkin sing_1864.htm#SEC1940 sprintf 177 A_L sing_1494.htm#SEC1570 16721 178 A_Z sing_900.htm#SEC976 50866 179 Access to elements of a user defined type Access to elements of a user defined type sing_185.htm#SEC225 180 Adj_div sing_1790.htm#SEC1866 44919 181 Adjoint ideal sing_1371.htm#IDX618 182 Alexander polynomial sing_1465.htm#IDX642 183 Algebraic Geometry codes sing_1789.htm#IDX790 184 Algebraic dependence Algebraic dependence sing_830.htm#SEC882 185 Algebraic geometry sing_1346.htm#SEC1422 186 AltVarEnd sing_743.htm#SEC795 11020 187 AltVarStart sing_742.htm#SEC794 21592 188 Ann sing_1285.htm#SEC1361 61560 189 Appel function sing_563.htm#IDX351 190 Appel hypergeometric function sing_563.htm#IDX352 191 Applications sing_849.htm#SEC901 192 Arnold, classification. sing_2317.htm#IDX946 193 Arnold, classification. sing_2318.htm#IDX947 194 ArnoldAction sing_1587.htm#SEC1663 26958 195 Assignments for user defined types Assignments for user defined types sing_187.htm#SEC227 196 AssocTanToEnv sing_937.htm#SEC1013 46214 197 Atkin sing_1878.htm#SEC1954 sprintf 194 198 Authors sing_1.htm#IDX16 195 BINresol sing_1370.htm#SEC1446 52996 199 Automatic Deduction of Geometric Theorems sing_920.htm#IDX426 200 BINresol sing_1384.htm#SEC1460 52996 196 201 Background sing_3.htm#SEC5 197 Basic programming sing_788.htm#SEC840 198 Basic programming sing_788.htm#SEC840 199 BelongSemig sing_2295.htm#SEC2371 22405 200 BerlekampMassey sing_2345.htm#SEC2421 2172 201 Bern sing_2268.htm#SEC2344 64051 202 Bernstein operator sing_532.htm#IDX331 203 Bernstein-Sato polynomial sing_497.htm#IDX312 204 Bernstein-Sato polynomial sing_532.htm#IDX328 205 Bernstein-Sato polynomial sing_1514.htm#IDX647 206 Bernstein-Sato polynomial sing_1518.htm#IDX664 207 Bernstein-Sato polynomial for variety sing_588.htm#IDX353 208 Betti number Syzygies and resolutions sing_847.htm#SEC904 209 BettiNumsH sing_2375.htm#SEC2451 18661 210 BettiNumsS sing_2378.htm#SEC2454 14964 211 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_857.htm#SEC914 212 BlowingUp sing_1493.htm#SEC1569 43153 213 Blowupcenter sing_1373.htm#SEC1449 3423 214 BorelCheck sing_1448.htm#SEC1524 48787 215 Bott's formula sing_2510.htm#IDX979 216 Branches of space curve singularities Branches of space curve singularities sing_821.htm#SEC873 217 Briancon-Maisonobe algorithm sing_532.htm#IDX337 218 Brieskorn lattice sing_1514.htm#IDX643 219 Brieskorn lattice sing_1515.htm#IDX654 220 Brieskorn lattice sing_1516.htm#IDX657 221 Brieskorn lattice sing_1517.htm#IDX660 222 Brieskorn lattice sing_1518.htm#IDX663 223 Brieskorn lattice sing_1519.htm#IDX667 224 Brieskorn lattice sing_1520.htm#IDX671 225 Brieskorn lattice sing_1521.htm#IDX677 226 Brieskorn lattice sing_1522.htm#IDX685 227 Brieskorn lattice sing_1523.htm#IDX691 228 Brieskorn lattice sing_1524.htm#IDX699 229 Brieskorn lattice sing_1525.htm#IDX709 230 Brieskorn lattice sing_1536.htm#IDX715 231 Brieskorn lattice sing_1538.htm#IDX726 232 Brieskorn lattice sing_1566.htm#IDX753 233 Brill-Noether algorithm sing_1775.htm#IDX765 234 BrillNoether sing_1778.htm#SEC1854 39919 235 Buchberger algorithm for toric ideals Buchberger algorithm sing_858.htm#SEC915 236 Budur-Mustata-Saito approach sing_588.htm#IDX357 237 Building Singular sing_2567.htm#SEC2657 238 C programming language Major differences to the C programming language sing_401.htm#SEC441 239 C, module ordering sing_840.htm#IDX411 240 CGS sing_903.htm#IDX426 241 CM_regularity sing_1435.htm#SEC1511 33865 242 CMtype sing_1604.htm#SEC1680 24849 243 CRHT-ideal sing_864.htm#SEC928 244 CSMA sing_2291.htm#SEC2367 49080 202 Basic programming sing_805.htm#SEC857 203 Basic programming sing_805.htm#SEC857 204 BelongSemig sing_2313.htm#SEC2389 22405 205 BerlekampMassey sing_2368.htm#SEC2444 2172 206 Bern sing_2286.htm#SEC2362 64051 207 Bernstein operator sing_540.htm#IDX333 208 Bernstein-Sato polynomial sing_505.htm#IDX314 209 Bernstein-Sato polynomial sing_540.htm#IDX330 210 Bernstein-Sato polynomial sing_1528.htm#IDX673 211 Bernstein-Sato polynomial sing_1532.htm#IDX690 212 Bernstein-Sato polynomial for variety sing_596.htm#IDX355 213 Betti sing_2497.htm#SEC2573 21134 214 Betti number Syzygies and resolutions sing_867.htm#SEC924 215 BettiNumsH sing_2398.htm#SEC2474 18661 216 BettiNumsN sing_2403.htm#SEC2479 44681 217 BettiNumsS sing_2401.htm#SEC2477 14964 218 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_877.htm#SEC934 219 BlowingUp sing_1507.htm#SEC1583 43153 220 Blowupcenter sing_1387.htm#SEC1463 3423 221 BorelCheck sing_1462.htm#SEC1538 48787 222 Bott's formula sing_2692.htm#IDX1047 223 Branches of space curve singularities Branches of space curve singularities sing_838.htm#SEC890 224 Briancon-Maisonobe algorithm sing_540.htm#IDX339 225 Brieskorn lattice sing_1528.htm#IDX669 226 Brieskorn lattice sing_1529.htm#IDX680 227 Brieskorn lattice sing_1530.htm#IDX683 228 Brieskorn lattice sing_1531.htm#IDX686 229 Brieskorn lattice sing_1532.htm#IDX689 230 Brieskorn lattice sing_1533.htm#IDX693 231 Brieskorn lattice sing_1534.htm#IDX697 232 Brieskorn lattice sing_1535.htm#IDX703 233 Brieskorn lattice sing_1536.htm#IDX711 234 Brieskorn lattice sing_1537.htm#IDX717 235 Brieskorn lattice sing_1538.htm#IDX725 236 Brieskorn lattice sing_1539.htm#IDX735 237 Brieskorn lattice sing_1550.htm#IDX741 238 Brieskorn lattice sing_1552.htm#IDX752 239 Brieskorn lattice sing_1580.htm#IDX779 240 Brill-Noether algorithm sing_1789.htm#IDX791 241 BrillNoether sing_1792.htm#SEC1868 39919 242 Buchberger algorithm for toric ideals Buchberger algorithm sing_878.htm#SEC935 243 Budur-Mustata-Saito approach sing_596.htm#IDX359 244 Building Singular sing_2749.htm#SEC2838 245 C programming language Major differences to the C programming language sing_409.htm#SEC449 246 C, module ordering sing_859.htm#IDX413 247 CGS sing_922.htm#IDX435 248 CM_regularity sing_1449.htm#SEC1525 33865 249 CMtype sing_1618.htm#SEC1694 24849 250 CRHT-ideal sing_884.htm#SEC948 251 CSMA sing_2309.htm#SEC2385 49080 245 252 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 246 Castelnuovo-Mumford regularity sing_1435.htm#IDX608 253 Canonical Forms sing_920.htm#IDX424 254 Castelnuovo-Mumford regularity sing_1449.htm#IDX634 247 255 Category string sing_51.htm#SEC88 248 CenCharDec sing_6 82.htm#SEC73444505249 Center sing_14 12.htm#SEC148825541250 CenterBO sing_14 19.htm#SEC149534701251 CentralQuot sing_6 80.htm#SEC73256490252 CentralSaturation sing_6 81.htm#SEC73331585256 CenCharDec sing_699.htm#SEC751 44505 257 Center sing_1426.htm#SEC1502 25541 258 CenterBO sing_1433.htm#SEC1509 34701 259 CentralQuot sing_697.htm#SEC749 56490 260 CentralSaturation sing_698.htm#SEC750 31585 253 261 Change of rings sing_9.htm#SEC15 254 Characteristic sets sing_8 48.htm#SEC905255 CharacteristicExponents CharacteristicExponents sing_1 499.htm#SEC157521795256 ChernClass sing_2 523.htm#SEC259932965257 ChernRootsDual sing_22 47.htm#SEC232340100258 ChernRootsHom sing_22 56.htm#SEC233248446259 ChernRootsProd sing_22 49.htm#SEC232513967260 ChernRootsSum sing_22 45.htm#SEC232157286261 ChernRootsSymm sing_22 58.htm#SEC233459304262 ChernRootsWedge sing_22 59.htm#SEC23357239263 Chevalley-Rosenlicht theorem sing_13 51.htm#IDX577264 Chevalley-Rosenlicht theorem sing_13 52.htm#IDX580265 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2 514.htm#IDX984266 ChowRing sing_2 514.htm#SEC259057977267 Classification of hypersurface singularities Classification of hypersurface singularities sing_8 22.htm#SEC874268 Classification of singularities sing_2 497.htm#IDX962269 Code Codes and the decoding problem sing_8 63.htm#SEC921270 Codes and the decoding problem Codes and the decoding problem sing_8 63.htm#SEC920271 Coding theory sing_17 74.htm#SEC1850272 Coefficient rings Notes for Singular users sing_2 565.htm#SEC2649262 Characteristic sets sing_868.htm#SEC925 263 CharacteristicExponents CharacteristicExponents sing_1513.htm#SEC1589 21795 264 ChernClass sing_2705.htm#SEC2781 32965 265 ChernRootsDual sing_2265.htm#SEC2341 40100 266 ChernRootsHom sing_2274.htm#SEC2350 48446 267 ChernRootsProd sing_2267.htm#SEC2343 13967 268 ChernRootsSum sing_2263.htm#SEC2339 57286 269 ChernRootsSymm sing_2276.htm#SEC2352 59304 270 ChernRootsWedge sing_2277.htm#SEC2353 7239 271 Chevalley-Rosenlicht theorem sing_1365.htm#IDX603 272 Chevalley-Rosenlicht theorem sing_1366.htm#IDX606 273 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2696.htm#IDX1052 274 ChowRing sing_2696.htm#SEC2772 57977 275 Classification of hypersurface singularities Classification of hypersurface singularities sing_839.htm#SEC891 276 Classification of singularities sing_2665.htm#IDX1023 277 Code Codes and the decoding problem sing_883.htm#SEC941 278 Codes and the decoding problem Codes and the decoding problem sing_883.htm#SEC940 279 Coding theory sing_1788.htm#SEC1864 280 Coefficient rings Notes for Singular users sing_2747.htm#SEC2831 273 281 Command line options Command line options sing_19.htm#SEC26 274 Commands Functions and system variables sing_201.htm#SEC241 275 Commands for user defined types Commands for user defined types sing_181.htm#SEC221 276 Commutative Algebra sing_801.htm#SEC853 277 Commutative algebra sing_1089.htm#SEC1165 278 CompDecomp sing_494.htm#SEC546 9959 279 CompInt sing_2297.htm#SEC2373 7518 280 CompleteHomog sing_2235.htm#SEC2311 42123 281 ComplexValue sing_2367.htm#SEC2443 45546 282 Comprehensive Groebner System sing_903.htm#IDX429 283 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_797.htm#SEC849 284 ConsLevels sing_911.htm#SEC987 45986 285 ConsLevelsToLevels sing_912.htm#SEC988 56302 286 ContactMatrix sing_1501.htm#SEC1577 40767 287 Conti-Traverso algorithm sing_853.htm#SEC910 282 Commands Functions and system variables sing_206.htm#SEC246 283 Commands for user defined types Commands for user defined types sing_186.htm#SEC226 284 Commutative Algebra sing_818.htm#SEC870 285 Commutative algebra sing_1101.htm#SEC1177 286 CompDecomp sing_502.htm#SEC554 9959 287 CompInt sing_2315.htm#SEC2391 7518 288 CompleteHomog sing_2253.htm#SEC2329 42123 289 ComplexValue sing_2390.htm#SEC2466 45546 290 Comprehensive Groebner System sing_922.htm#IDX438 291 Comprehensive Groebner Systems sing_920.htm#IDX422 292 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_814.htm#SEC866 293 ConsLevels sing_930.htm#SEC1006 23520 294 ConsLevelsToLevels sing_931.htm#SEC1007 32625 295 Constructible sets sing_920.htm#IDX430 296 ContactMatrix sing_1515.htm#SEC1591 40767 297 Conti-Traverso algorithm sing_873.htm#SEC930 288 298 Contributors sing_1.htm#IDX15 289 Control structures sing_3 69.htm#SEC409290 Control theory System and Control theory sing_18 08.htm#SEC1884291 Cooper philosophy sing_8 64.htm#SEC926292 Cornacchia sing_18 54.htm#SEC193063434293 CornacchiaModified sing_18 55.htm#SEC193159790294 Crep sing_9 06.htm#SEC982 35724295 Critical points sing_8 16.htm#SEC868296 CurveParam sing_1 495.htm#SEC1571 359297 CurveRes sing_1 494.htm#SEC157048848298 Curves sing_13 57.htm#IDX589299 Control structures sing_377.htm#SEC417 300 Control theory System and Control theory sing_1822.htm#SEC1898 301 Cooper philosophy sing_884.htm#SEC946 302 Cornacchia sing_1868.htm#SEC1944 63434 303 CornacchiaModified sing_1869.htm#SEC1945 59790 304 Crep sing_925.htm#SEC1001 17485 305 Critical points sing_833.htm#SEC885 306 CurveParam sing_1509.htm#SEC1585 53605 307 CurveRes sing_1508.htm#SEC1584 48848 308 Curves sing_1371.htm#IDX615 299 309 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 300 Cyclic code sing_1 789.htm#IDX772301 Cyclic roots sing_ 794.htm#SEC846302 D-integration sing_5 55.htm#IDX346303 D-localization sing_5 55.htm#IDX342304 D-localization sing_7 60.htm#IDX380305 D-module purityfiltration_lib sing_ 497.htm#IDX310306 D-module sing_5 32.htm#IDX325307 D-module sing_5 55.htm#IDX339308 D-module sing_5 88.htm#IDX351309 D-module sing_7 38.htm#IDX365310 D-module sing_7 60.htm#IDX377311 D-module structure sing_5 32.htm#IDX326312 D-module structure sing_5 88.htm#IDX352313 D-restriction sing_5 55.htm#IDX344314 DBM links sing_1 17.htm#SEC157310 Cyclic code sing_1803.htm#IDX798 311 Cyclic roots sing_811.htm#SEC863 312 D-integration sing_563.htm#IDX348 313 D-localization sing_563.htm#IDX344 314 D-localization sing_777.htm#IDX382 315 D-module purityfiltration_lib sing_505.htm#IDX312 316 D-module sing_540.htm#IDX327 317 D-module sing_563.htm#IDX341 318 D-module sing_596.htm#IDX353 319 D-module sing_755.htm#IDX367 320 D-module sing_777.htm#IDX379 321 D-module structure sing_540.htm#IDX328 322 D-module structure sing_596.htm#IDX354 323 D-restriction sing_563.htm#IDX346 324 DBM links sing_122.htm#SEC162 315 325 DISPLAY environment variable The online help system sing_16.htm#IDX28 316 DLoc sing_5 58.htm#SEC6105981317 DLoc0 sing_56 0.htm#SEC61214327326 DLoc sing_566.htm#SEC618 5981 327 DLoc0 sing_568.htm#SEC620 14327 318 328 Data types sing_72.htm#SEC112 319 Data types (plural) sing_4 14.htm#IDX296329 Data types (plural) sing_422.htm#IDX298 320 330 Debugging tools sing_63.htm#SEC100 321 331 Decker, Wolfram sing_1.htm#IDX17 322 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_179.htm#SEC219 323 Decoding sing_1789.htm#IDX774 324 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_862.htm#SEC919 325 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_867.htm#SEC937 326 Definition of a user defined type Definition of a user defined type sing_178.htm#SEC218 327 Deformations sing_819.htm#SEC871 328 Deformations, T1 and T2 sing_818.htm#SEC870 329 Degree sing_1336.htm#SEC1412 47790 330 Delta sing_1420.htm#SEC1496 33497 331 DeltaList sing_1421.htm#SEC1497 65148 332 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_184.htm#SEC224 333 Decoding sing_1803.htm#IDX800 334 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_882.htm#SEC939 335 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_887.htm#SEC957 336 Definition of a user defined type Definition of a user defined type sing_183.htm#SEC223 337 Deformations sing_836.htm#SEC888 338 Deformations, T1 and T2 sing_835.htm#SEC887 339 Deg sing_2500.htm#SEC2576 35419 340 Degree sing_2501.htm#SEC2577 48523 341 DegreePure sing_1350.htm#SEC1426 33003 342 Degrees sing_2502.htm#SEC2578 50349 343 Delta sing_1434.htm#SEC1510 33497 344 DeltaList sing_1435.htm#SEC1511 65148 332 345 Demo mode sing_24.htm#SEC35 333 Depth sing_8 08.htm#SEC860334 Determinacy sing_2 500.htm#IDX966335 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_8 56.htm#SEC913336 Distributed computing sing_9 31.htm#IDX478337 Dlocalization sing_7 61.htm#SEC81322140346 Depth sing_825.htm#SEC877 347 Determinacy sing_2668.htm#IDX1027 348 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_876.htm#SEC933 349 Distributed computing sing_951.htm#IDX496 350 Dlocalization sing_778.htm#SEC830 22140 338 351 Documentation Tool sing_60.htm#SEC97 339 Dp, global ordering sing_838.htm#IDX394 340 Ds, local ordering sing_839.htm#IDX404 341 DsingularLocus sing_765.htm#SEC817 46495 352 Dp, global ordering sing_857.htm#IDX396 353 Ds, local ordering sing_858.htm#IDX406 354 DsingularLocus sing_782.htm#SEC834 46495 355 Dynamic Geometry sing_920.htm#IDX427 342 356 Dynamic loading sing_71.htm#SEC111 343 Dynamic modules sing_ 796.htm#SEC848344 ECPP sing_1 898.htm#SEC197455777345 ECoef sing_13 79.htm#SEC145514154346 EOrdlist sing_13 77.htm#SEC145336329347 ERROR sing_23 0.htm#SEC270357 Dynamic modules sing_813.htm#SEC865 358 ECPP sing_1912.htm#SEC1988 55777 359 ECoef sing_1393.htm#SEC1469 14154 360 EOrdlist sing_1391.htm#SEC1467 36329 361 ERROR sing_236.htm#SEC276 348 362 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 349 Edatalist sing_13 76.htm#SEC145261593350 Edelman-Reiner sing_21 85.htm#IDX855363 Edatalist sing_1390.htm#SEC1466 61593 364 Edelman-Reiner sing_2196.htm#IDX881 351 365 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 352 366 Editing input sing_18.htm#SEC25 353 Elimination sing_8 04.htm#SEC856367 Elimination sing_821.htm#SEC873 354 368 Emacs Emacs user interface sing_21.htm#SEC28 355 369 Emacs, Singular demo mode sing_24.htm#SEC35 … … 361 375 Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30 362 376 Emacs, user interface Emacs user interface sing_21.htm#SEC28 363 Emaxcont sing_1381.htm#SEC1457 47312 364 Enumerative geometry sing_2510.htm#IDX977 365 Equal sing_1335.htm#SEC1411 19984 366 Eresol sing_1371.htm#SEC1447 12842 367 EulerAff sing_2292.htm#SEC2368 54325 368 EulerProj sing_2293.htm#SEC2369 13537 369 Evaluation of logical expressions Evaluation of logical expressions sing_403.htm#SEC443 370 Examples sing_786.htm#SEC838 377 Emaxcont sing_1395.htm#SEC1471 47312 378 Enumerative geometry sing_2692.htm#IDX1045 379 Envelope sing_920.htm#IDX429 380 Equal sing_1349.htm#SEC1425 19984 381 Eresol sing_1385.htm#SEC1461 12842 382 EulerAff sing_2310.htm#SEC2386 54325 383 EulerProj sing_2311.htm#SEC2387 13537 384 Evaluation of logical expressions Evaluation of logical expressions sing_411.htm#SEC451 385 Examples sing_803.htm#SEC855 371 386 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 372 Exp for matrices sing_13 53.htm#IDX581373 Experimental libraries Experimental libraries sing_22 29.htm#SEC2305374 Ext sing_11 49.htm#SEC122521909375 Ext, computation of sing_8 07.htm#SEC859376 Ext_R sing_11 48.htm#SEC122453310377 Exterior sing_7 12.htm#SEC76423593378 Extra weight vector sing_8 43.htm#SEC895379 Factorization sing_8 09.htm#SEC861380 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_9 18.htm#SEC994 61191381 Feynman graph sing_11 25.htm#IDX514382 Finite fields sing_8 03.htm#SEC855387 Exp for matrices sing_1367.htm#IDX607 388 Experimental libraries Experimental libraries sing_2240.htm#SEC2316 389 Ext sing_1161.htm#SEC1237 21909 390 Ext, computation of sing_824.htm#SEC876 391 Ext_R sing_1160.htm#SEC1236 53310 392 Exterior sing_729.htm#SEC781 23593 393 Extra weight vector sing_862.htm#SEC914 394 Factorization sing_826.htm#SEC878 395 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_938.htm#SEC1014 18153 396 Feynman graph sing_1137.htm#IDX529 397 Finite fields sing_820.htm#SEC872 383 398 First steps sing_6.htm#SEC12 384 Fitzgerald-Lax method Fitzgerald-Lax method sing_866.htm#SEC934 399 Fitzgerald-Lax method Fitzgerald-Lax method sing_886.htm#SEC954 400 Float sing_250.htm#SEC290 385 401 Flow control sing_40.htm#SEC70 386 402 Formal Checker sing_59.htm#SEC96 387 Formatting output sing_793.htm#SEC845 388 Free resolution sing_805.htm#SEC857 389 Free resolution, graded Handling graded modules sing_806.htm#SEC858 390 FultonA sing_2290.htm#SEC2366 33688 391 Functions sing_202.htm#SEC242 392 Future benefits of Singular 4 Notes for Singular users sing_2565.htm#SEC2655 393 G-algebra sing_478.htm#SEC518 394 G-algebra sing_478.htm#SEC520 395 G-algebra, setup sing_478.htm#SEC522 396 GBWeight sing_561.htm#SEC613 24641 397 GBsolve sing_1688.htm#SEC1764 16830 398 GIT sing_2386.htm#IDX949 399 GKZsystem sing_678.htm#SEC730 20528 400 GKdim sing_651.htm#SEC703 9814 403 Formatting output sing_810.htm#SEC862 404 Free resolution sing_822.htm#SEC874 405 Free resolution, graded Handling graded modules sing_823.htm#SEC875 406 FultonA sing_2308.htm#SEC2384 33688 407 Functions sing_207.htm#SEC247 408 Future benefits of Singular 4 Notes for Singular users sing_2747.htm#SEC2836 409 G-algebra sing_486.htm#SEC526 410 G-algebra sing_486.htm#SEC528 411 G-algebra, setup sing_486.htm#SEC530 412 GBWeight sing_569.htm#SEC621 24641 413 GBsolve sing_1702.htm#SEC1778 16830 414 GIT-Fans sing_845.htm#SEC897 415 GITcone sing_2417.htm#SEC2493 64643 416 GITfan sing_2418.htm#SEC2494 32549 417 GITfanFromOrbitCones GITfanFromOrbitCones sing_2419.htm#SEC2495 63104 418 GITfanParallel sing_2420.htm#SEC2496 53071 419 GITfanParallelSymmetric GITfanParallelSymmetric sing_2435.htm#SEC2511 30232 420 GITfanSymmetric sing_2434.htm#SEC2510 25831 421 GKZfan sing_2421.htm#SEC2497 sprintf 422 GKZsystem sing_695.htm#SEC747 20528 423 GKdim sing_668.htm#SEC720 9814 401 424 GMP sing_1.htm#IDX3 402 GMP sing_2 569.htm#SEC2659403 GND.lib sing_2 393.htm#SEC2469404 GND_lib sing_2 393.htm#SEC2469405 GTZmod sing_1 197.htm#SEC127330091406 GTZopt sing_12 04.htm#SEC128014642407 G_a -Invariants sing_8 25.htm#SEC877408 Gamma sing_1 386.htm#SEC14623820409 Gauss-Manin connection Gauss-Manin connection sing_8 49.htm#SEC906410 Gauss-Manin connection sing_15 66.htm#IDX752411 Gauss-Manin connection sing_16 13.htm#IDX755412 Gauss-Manin system sing_15 14.htm#IDX642413 Gauss-Manin system sing_15 15.htm#IDX653414 Gauss-Manin system sing_15 16.htm#IDX656415 Gauss-Manin system sing_15 17.htm#IDX659416 Gauss-Manin system sing_15 18.htm#IDX662417 Gauss-Manin system sing_15 19.htm#IDX666418 Gauss-Manin system sing_15 20.htm#IDX670419 Gauss-Manin system sing_15 21.htm#IDX676420 Gauss-Manin system sing_15 22.htm#IDX684421 Gauss-Manin system sing_15 23.htm#IDX690422 Gauss-Manin system sing_15 24.htm#IDX698423 Gauss-Manin system sing_15 25.htm#IDX708424 Gauss-Manin system sing_15 36.htm#IDX714425 Gauss-Manin system sing_15 38.htm#IDX725425 GMP sing_2751.htm#SEC2840 426 GND.lib sing_2442.htm#SEC2518 427 GND_lib sing_2442.htm#SEC2518 428 GTZmod sing_1211.htm#SEC1287 30091 429 GTZopt sing_1218.htm#SEC1294 14642 430 G_a -Invariants sing_842.htm#SEC894 431 Gamma sing_1400.htm#SEC1476 3820 432 Gauss-Manin connection Gauss-Manin connection sing_869.htm#SEC926 433 Gauss-Manin connection sing_1580.htm#IDX778 434 Gauss-Manin connection sing_1627.htm#IDX781 435 Gauss-Manin system sing_1528.htm#IDX668 436 Gauss-Manin system sing_1529.htm#IDX679 437 Gauss-Manin system sing_1530.htm#IDX682 438 Gauss-Manin system sing_1531.htm#IDX685 439 Gauss-Manin system sing_1532.htm#IDX688 440 Gauss-Manin system sing_1533.htm#IDX692 441 Gauss-Manin system sing_1534.htm#IDX696 442 Gauss-Manin system sing_1535.htm#IDX702 443 Gauss-Manin system sing_1536.htm#IDX710 444 Gauss-Manin system sing_1537.htm#IDX716 445 Gauss-Manin system sing_1538.htm#IDX724 446 Gauss-Manin system sing_1539.htm#IDX734 447 Gauss-Manin system sing_1550.htm#IDX740 448 Gauss-Manin system sing_1552.htm#IDX751 426 449 General command syntax General command syntax sing_35.htm#SEC59 427 450 General concepts sing_12.htm#SEC18 428 General purpose sing_8 74.htm#SEC950451 General purpose sing_894.htm#SEC970 429 452 General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41 430 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_480.htm#SEC530 431 Generalized Newton identities Generalized Newton identities sing_865.htm#SEC931 432 Geometric genus sing_1357.htm#IDX593 433 German Umlaute sing_399.htm#IDX283 453 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_488.htm#SEC538 454 Generalized Newton identities Generalized Newton identities sing_885.htm#SEC951 455 Geometric Invariant Theory Geometric Invariant Theory sing_844.htm#SEC896 456 Geometric genus sing_1371.htm#IDX619 457 German Umlaute sing_407.htm#IDX285 434 458 Getting started sing_5.htm#SEC11 435 Global orderings sing_838.htm#SEC890 436 GoettscheF sing_2373.htm#SEC2449 27881 437 Graded commutative algebras Graded commutative algebras (SCA) sing_482.htm#SEC534 438 Grassmannian sing_2515.htm#SEC2591 43898 439 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2515.htm#IDX985 459 Global orderings sing_857.htm#SEC909 460 Goettsche's formula sing_2395.htm#IDX984 461 GoettscheF sing_2396.htm#SEC2472 27881 462 Graded commutative algebras Graded commutative algebras (SCA) sing_490.htm#SEC542 463 Grassmannian sing_2697.htm#SEC2773 43898 464 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2697.htm#IDX1053 440 465 Greuel, Gert-Martin sing_1.htm#IDX18 441 Groebner Bases Computing Groebner and Standard Bases sing_797.htm#SEC849 442 Groebner bases in G-algebras Groebner bases in G-algebras sing_479.htm#SEC523 443 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_485.htm#SEC537 444 Groebner bases, decodeGB sing_1789.htm#IDX776 445 Groebner bases, slim sing_800.htm#SEC852 446 Groebner basis conversion Groebner basis conversion sing_799.htm#SEC851 447 Groebner cover sing_902.htm#IDX422 448 Groebner cover sing_909.htm#IDX435 449 Groebner cover sing_910.htm#IDX441 450 Groebner fan sing_2052.htm#IDX793 451 Groebner walk sing_1140.htm#IDX535 452 Groebner walk sing_1142.htm#IDX537 453 Groebner walk sing_2507.htm#IDX973 454 Groebner walk sing_2508.htm#IDX974 455 Groebnerwalk sing_1136.htm#IDX531 456 Groebnerwalk sing_2432.htm#IDX958 457 Groebnerwalk sing_2506.htm#IDX972 458 Groebnerwalk sing_2549.htm#IDX1001 459 Gromov-Witten invariants sing_1125.htm#IDX511 460 Gromov-Witten invariants sing_1131.htm#IDX520 461 Gromov-Witten invariants sing_1132.htm#IDX524 462 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2540.htm#IDX997 463 Gromov-Witten invariants, multiple covers sing_2539.htm#IDX996 464 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2541.htm#IDX998 465 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2542.htm#IDX999 466 Gromov-Witten invariants. sing_2510.htm#IDX980 467 Gweights sing_706.htm#SEC758 651 468 H2basis sing_1571.htm#SEC1647 3414 469 HHnormalForm sing_2305.htm#SEC2381 33972 470 Hamburger-Noether expansion sing_1451.htm#IDX612 471 Hamburger-Noether expansion sing_1539.htm#IDX734 472 Hamburger-Noether expansions sing_1776.htm#IDX766 473 Handling graded modules Handling graded modules sing_806.htm#SEC858 474 Hcode sing_1473.htm#SEC1549 26628 466 Groebner Bases Computing Groebner and Standard Bases sing_814.htm#SEC866 467 Groebner Cover sing_920.htm#IDX423 468 Groebner bases in G-algebras Groebner bases in G-algebras sing_487.htm#SEC531 469 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_493.htm#SEC545 470 Groebner bases, decodeGB sing_1803.htm#IDX802 471 Groebner bases, slim sing_817.htm#SEC869 472 Groebner basis conversion Groebner basis conversion sing_816.htm#SEC868 473 Groebner cover sing_921.htm#IDX431 474 Groebner cover sing_928.htm#IDX450 475 Groebner cover sing_929.htm#IDX457 476 Groebner fan sing_2066.htm#IDX819 477 Groebner walk sing_1152.htm#IDX550 478 Groebner walk sing_1154.htm#IDX552 479 Groebner walk sing_2689.htm#IDX1041 480 Groebner walk sing_2690.htm#IDX1042 481 Groebnerwalk sing_1148.htm#IDX546 482 Groebnerwalk sing_2534.htm#IDX994 483 Groebnerwalk sing_2688.htm#IDX1040 484 Groebnerwalk sing_2731.htm#IDX1069 485 Gromov-Witten invariants sing_1137.htm#IDX526 486 Gromov-Witten invariants sing_1143.htm#IDX535 487 Gromov-Witten invariants sing_1144.htm#IDX539 488 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2722.htm#IDX1065 489 Gromov-Witten invariants, multiple covers sing_2721.htm#IDX1064 490 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2723.htm#IDX1066 491 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2724.htm#IDX1067 492 Gromov-Witten invariants. sing_2692.htm#IDX1048 493 Gweights sing_723.htm#SEC775 651 494 H2basis sing_1585.htm#SEC1661 3414 495 HHnormalForm sing_2326.htm#SEC2402 33972 496 Hamburger-Noether expansion sing_1465.htm#IDX638 497 Hamburger-Noether expansion sing_1553.htm#IDX760 498 Hamburger-Noether expansions sing_1790.htm#IDX792 499 Handling graded modules Handling graded modules sing_823.htm#SEC875 500 Hcode sing_1487.htm#SEC1563 26628 475 501 Help string sing_45.htm#SEC82 476 Hensel sing_2 35.htm#SEC275477 Hilbert function sing_3 48.htm#IDX188478 Hilbert function sing_8 46.htm#SEC900479 Hilbert series sing_8 46.htm#SEC900480 Hilbert-driven GB algorithm Groebner basis conversion sing_ 799.htm#SEC851481 HilbertClassPoly sing_18 61.htm#SEC1937sprintf482 HilbertSeries sing_16 66.htm#SEC174221249483 HilbertWeights sing_16 67.htm#SEC1743sprintf484 Hom sing_11 52.htm#SEC122861434485 HomJJ sing_12 27.htm#SEC13031525486 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_8 55.htm#SEC912502 Hensel sing_241.htm#SEC281 503 Hilbert function sing_356.htm#IDX188 504 Hilbert function sing_866.htm#SEC920 505 Hilbert series sing_866.htm#SEC920 506 Hilbert-driven GB algorithm Groebner basis conversion sing_816.htm#SEC868 507 HilbertClassPoly sing_1875.htm#SEC1951 sprintf 508 HilbertSeries sing_1680.htm#SEC1756 21249 509 HilbertWeights sing_1681.htm#SEC1757 sprintf 510 Hom sing_1164.htm#SEC1240 61434 511 HomJJ sing_1241.htm#SEC1317 1525 512 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_875.htm#SEC932 487 513 How to enter and exit How to enter and exit sing_14.htm#SEC20 488 514 How to use this manual How to use this manual sing_4.htm#SEC6 489 Hurwitz numbers sing_1131.htm#IDX523 490 Hurwitz numbers sing_1132.htm#IDX527 491 Hypersurface singularities, classification of Classification of hypersurface singularities sing_822.htm#SEC874 492 IN sing_272.htm#IDX149 493 Ideal membership sing_845.htm#IDX416 515 Hurwitz numbers sing_1143.htm#IDX538 516 Hurwitz numbers sing_1144.htm#IDX542 517 Hypersurface singularities, classification of Classification of hypersurface singularities sing_839.htm#SEC891 518 I-regular function sing_928.htm#IDX456 519 IN sing_280.htm#IDX149 520 Ideal membership sing_865.htm#IDX418 494 521 Identifiers, syntax of sing_37.htm#SEC65 495 ImageGroup sing_16 69.htm#SEC174528808496 ImageVariety sing_16 68.htm#SEC174415252497 Imap, option sing_3 07.htm#IDX175522 ImageGroup sing_1683.htm#SEC1759 28808 523 ImageVariety sing_1682.htm#SEC1758 15252 524 Imap, option sing_315.htm#IDX175 498 525 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 499 Incl sing_13 34.htm#SEC14107621500 Index sing_2 574.htm#SEC2664526 Incl sing_1348.htm#SEC1424 7621 527 Index sing_2756.htm#SEC2845 501 528 Info string sing_52.htm#SEC89 502 InterDiv sing_14 02.htm#SEC147846142529 InterDiv sing_1416.htm#SEC1492 46142 503 530 Interactive use sing_13.htm#SEC19 504 531 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 505 IntersectWithSub sing_ 683.htm#SEC73556289506 Intersection theory sing_2 510.htm#IDX976507 IntersectionMatrix sing_15 00.htm#SEC157629351532 IntersectWithSub sing_700.htm#SEC752 56289 533 Intersection theory sing_2692.htm#IDX1044 534 IntersectionMatrix sing_1514.htm#SEC1590 29351 508 535 Introduction sing_2.htm#SEC4 509 Invariant Theory sing_824.htm#SEC876 510 Invariant theory sing_1618.htm#SEC1694 511 InvariantQ sing_1671.htm#SEC1747 53256 512 InvariantRing sing_1670.htm#SEC1746 22928 513 Invariants of a finite group Invariants of a finite group sing_826.htm#SEC878 514 Invariants of plane curve singularities Invariants of plane curve singularities sing_820.htm#SEC872 515 IsSCA sing_727.htm#SEC779 58445 516 J-marked schemes sing_1442.htm#IDX610 517 J-marked schemes, Borel ideals sing_1447.htm#IDX611 518 JMBTest.lib sing_1442.htm#SEC1518 519 JMBTest_lib sing_1442.htm#SEC1518 520 JMSConst.lib sing_1447.htm#SEC1523 521 JMSConst_lib sing_1447.htm#SEC1523 522 JMarkedScheme sing_1449.htm#SEC1525 60696 523 Jacobi sing_1871.htm#SEC1947 29843 524 Jacobson form sing_1826.htm#IDX777 525 Jacobson normal form sing_1826.htm#IDX778 526 Janet basis sing_2505.htm#IDX970 527 Janet division, Janet basis sing_2504.htm#IDX969 528 JuReTopDim sing_1344.htm#SEC1420 sprintf 529 JuReZeroDim sing_1345.htm#SEC1421 sprintf 530 KScoef sing_1564.htm#SEC1640 sprintf 531 KSconvert sing_1562.htm#SEC1638 3585 532 KSker sing_1561.htm#SEC1637 40166 533 KSlinear sing_1563.htm#SEC1639 19896 534 KSpencerKernel sing_1611.htm#SEC1687 12490 535 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2412.htm#SEC2488 20741 536 Kernel of module homomorphisms Kernel of module homomorphisms sing_812.htm#SEC864 537 KoszulHomology sing_1161.htm#SEC1237 sprintf 538 LETTERPLACE sing_483.htm#SEC535 539 LIB sing_276.htm#SEC316 536 Invariant Theory sing_841.htm#SEC893 537 Invariant theory sing_1632.htm#SEC1708 538 InvariantQ sing_1685.htm#SEC1761 53256 539 InvariantRing sing_1684.htm#SEC1760 22928 540 Invariants of a finite group Invariants of a finite group sing_843.htm#SEC895 541 Invariants of plane curve singularities Invariants of plane curve singularities sing_837.htm#SEC889 542 IsSCA sing_744.htm#SEC796 58445 543 J-marked schemes sing_1456.htm#IDX636 544 J-marked schemes, Borel ideals sing_1461.htm#IDX637 545 JMBTest.lib sing_1456.htm#SEC1532 546 JMBTest_lib sing_1456.htm#SEC1532 547 JMSConst.lib sing_1461.htm#SEC1537 548 JMSConst_lib sing_1461.htm#SEC1537 549 JMarkedScheme sing_1463.htm#SEC1539 60696 550 Jacobi sing_1885.htm#SEC1961 29843 551 Jacobson form sing_1840.htm#IDX803 552 Jacobson normal form sing_1840.htm#IDX804 553 Janet basis sing_2687.htm#IDX1038 554 Janet division, Janet basis sing_2686.htm#IDX1037 555 JuReTopDim sing_1358.htm#SEC1434 sprintf 556 JuReZeroDim sing_1359.htm#SEC1435 sprintf 557 KScoef sing_1578.htm#SEC1654 sprintf 558 KSconvert sing_1576.htm#SEC1652 3585 559 KSker sing_1575.htm#SEC1651 40166 560 KSlinear sing_1577.htm#SEC1653 19896 561 KSpencerKernel sing_1625.htm#SEC1701 12490 562 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2461.htm#SEC2537 20741 563 Ker sing_2506.htm#SEC2582 58279 564 Kernel of module homomorphisms Kernel of module homomorphisms sing_829.htm#SEC881 565 KoszulHomology sing_1173.htm#SEC1249 sprintf 566 Kronecker modules sing_2395.htm#IDX986 567 L, ordering sing_863.htm#SEC915 568 LETTERPLACE sing_491.htm#SEC543 569 LIB sing_284.htm#SEC324 540 570 LIB commands sing_53.htm#SEC90 541 LIBs sing_8 70.htm#SEC946542 LLL sing_35 0.htm#IDX220543 LOT algorithm sing_5 32.htm#IDX338544 LU-decomposition of a matrix of numbers sing_28 1.htm#SEC321545 Laurent series sing_11 29.htm#IDX519546 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_8 28.htm#SEC880547 Left ideal membership Groebner bases in G-algebras sing_4 79.htm#SEC526548 Left normal form Groebner bases in G-algebras sing_4 79.htm#SEC525549 LengthSym sing_7 37.htm#SEC78916591550 LengthSymElement sing_7 36.htm#SEC78828292551 Letterplace sing_4 83.htm#SEC535552 Lexicographic Groebner bases, computation of Groebner basis conversion sing_ 799.htm#SEC851571 LIBs sing_890.htm#SEC966 572 LLL sing_358.htm#IDX220 573 LOT algorithm sing_540.htm#IDX340 574 LU-decomposition of a matrix of numbers sing_289.htm#SEC329 575 Laurent series sing_1141.htm#IDX534 576 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_847.htm#SEC899 577 Left ideal membership Groebner bases in G-algebras sing_487.htm#SEC534 578 Left normal form Groebner bases in G-algebras sing_487.htm#SEC533 579 LengthSym sing_754.htm#SEC806 16591 580 LengthSymElement sing_753.htm#SEC805 28292 581 Letterplace sing_491.htm#SEC543 582 Lexicographic Groebner bases, computation of Groebner basis conversion sing_816.htm#SEC868 553 583 Libraries Writing procedures and libraries sing_48.htm#SEC85 554 Libraries sing_ 789.htm#SEC841584 Libraries sing_806.htm#SEC858 555 585 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 556 Library versioning Notes for Singular users sing_2 565.htm#SEC2653557 Lie algebra sing_13 52.htm#IDX578558 Lie group sing_13 55.htm#IDX583559 Lie group sing_13 56.htm#IDX586560 Limitations sing_ 399.htm#SEC439561 Linear algebra sing_10 29.htm#SEC1105562 Linear code sing_1 789.htm#IDX773563 LinearActionQ sing_16 73.htm#SEC174962218564 LinearCombinationQ sing_16 74.htm#SEC175059373565 LinearizeAction sing_16 72.htm#SEC174860266586 Library versioning Notes for Singular users sing_2747.htm#SEC2834 587 Lie algebra sing_1366.htm#IDX604 588 Lie group sing_1369.htm#IDX609 589 Lie group sing_1370.htm#IDX612 590 Limitations sing_407.htm#SEC447 591 Linear algebra sing_1041.htm#SEC1117 592 Linear code sing_1803.htm#IDX799 593 LinearActionQ sing_1687.htm#SEC1763 62218 594 LinearCombinationQ sing_1688.htm#SEC1764 59373 595 LinearizeAction sing_1686.htm#SEC1762 60266 566 596 Loading a library sing_62.htm#SEC99 567 Local orderings sing_839.htm#SEC891 568 Log for matrices sing_1354.htm#IDX582 569 Long coefficients sing_791.htm#SEC843 570 M, ordering sing_841.htm#SEC893 571 MVComplex sing_2321.htm#SEC2397 62126 572 MacdonaldF sing_2376.htm#SEC2452 12751 573 Macintosh installation Macintosh installation instructions sing_2573.htm#SEC2663 574 Mathematical background Mathematical background sing_844.htm#SEC896 575 Mathematical background (plural) Mathematical background (plural) sing_477.htm#SEC517 576 Matrix orderings sing_841.htm#SEC893 577 Max sing_1580.htm#SEC1656 23 578 Maximus sing_1444.htm#SEC1520 10010 579 Maxord sing_1385.htm#SEC1461 14124 580 MillerRabin sing_1881.htm#SEC1957 15740 581 Milnor number Milnor and Tjurina number sing_815.htm#SEC867 582 Milnor number sing_2499.htm#IDX965 583 Min sing_1581.htm#SEC1657 29622 584 MinMult sing_2296.htm#SEC2372 39835 585 MinimalDecomposition MinimalDecomposition sing_1675.htm#SEC1751 24161 586 Minimum distance sing_1789.htm#IDX775 587 Minimus sing_1443.htm#SEC1519 61721 588 Miscellaneous libraries Miscellaneous libraries sing_2156.htm#SEC2232 589 ModEqn sing_1574.htm#SEC1650 59394 590 Modular techniques sing_931.htm#IDX475 591 Module orderings sing_840.htm#SEC892 597 Local orderings sing_858.htm#SEC910 598 Loci sing_920.htm#IDX428 599 Log for matrices sing_1368.htm#IDX608 600 Long coefficients sing_808.htm#SEC860 601 M, ordering sing_860.htm#SEC912 602 MVComplex sing_2344.htm#SEC2420 62126 603 Macdonald's formula sing_2395.htm#IDX985 604 MacdonaldF sing_2399.htm#SEC2475 12751 605 Macintosh installation Macintosh installation instructions sing_2755.htm#SEC2844 606 Mathematical background Mathematical background sing_864.htm#SEC916 607 Mathematical background (plural) Mathematical background (plural) sing_485.htm#SEC525 608 Matrix orderings sing_860.htm#SEC912 609 Max sing_1594.htm#SEC1670 23 610 Maximus sing_1458.htm#SEC1534 10010 611 Maxord sing_1399.htm#SEC1475 14124 612 MillerRabin sing_1895.htm#SEC1971 15740 613 Milnor number Milnor and Tjurina number sing_832.htm#SEC884 614 Milnor number sing_2667.htm#IDX1026 615 Min sing_1595.htm#SEC1671 29622 616 MinMult sing_2314.htm#SEC2390 39835 617 MinimalDecomposition MinimalDecomposition sing_1689.htm#SEC1765 24161 618 Minimum distance sing_1803.htm#IDX801 619 Minimus sing_1457.htm#SEC1533 61721 620 Miscellaneous libraries Miscellaneous libraries sing_2167.htm#SEC2243 621 ModEqn sing_1588.htm#SEC1664 59394 622 Modular techniques sing_951.htm#IDX493 623 Module orderings sing_859.htm#SEC911 592 624 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 593 Monodromy sing_15 66.htm#IDX750594 Monomial orderings sing_8 35.htm#SEC887625 Monodromy sing_1580.htm#IDX776 626 Monomial orderings sing_854.htm#SEC906 595 627 Monomial orderings, Term orderings sing_31.htm#SEC44 596 Morse lemma sing_2498.htm#IDX963 597 MultiplicitySequence MultiplicitySequence sing_1498.htm#SEC1574 1309 598 NF sing_326.htm#SEC366 599 NF sing_469.htm#SEC509 600 NFMora sing_1947.htm#SEC2023 40670 601 NPos sing_1217.htm#SEC1293 15702 602 NPos_test sing_1215.htm#SEC1291 48172 603 NSplaces sing_1777.htm#SEC1853 48675 628 Mori dream spaces sing_2241.htm#IDX941 629 Morse lemma addnondegeneratevariables sing_2666.htm#IDX1024 630 Morse lemma sing_2669.htm#IDX1028 631 MultiplicitySequence MultiplicitySequence sing_1512.htm#SEC1588 1309 632 NF sing_334.htm#SEC374 633 NF sing_477.htm#SEC517 634 NFMora sing_1961.htm#SEC2037 40670 635 NPos sing_1231.htm#SEC1307 15702 636 NPos_test sing_1229.htm#SEC1305 48172 637 NSplaces sing_1791.htm#SEC1867 48675 604 638 NTL sing_1.htm#IDX4 605 639 Names sing_37.htm#SEC65 606 640 Names in procedures sing_46.htm#SEC83 607 641 Names, indexed sing_37.htm#SEC65 608 New libraries depending on Singular 4 Notes for Singular users sing_2565.htm#SEC2651 609 New orderings for modules Notes for Singular users sing_2565.htm#SEC2654 610 Newton non-degenerate sing_1553.htm#IDX748 611 Newton polygon sing_1552.htm#IDX747 612 Newton polygon sing_1553.htm#IDX749 613 Newton polygons sing_2552.htm#IDX1004 614 Newton polytope sing_2052.htm#IDX792 615 NoetherPosition sing_1211.htm#SEC1287 18735 616 Non-commutative LIBs Non-commutative libraries sing_489.htm#SEC541 617 Non-commutative algebra Non-commutative algebra sing_827.htm#SEC879 618 Non-commutative algebra sing_861.htm#SEC918 619 Non-commutative libraries Non-commutative libraries sing_489.htm#SEC541 620 Non-commutative subsystem Non-commutative subsystem sing_412.htm#SEC452 621 Nonhyp sing_1374.htm#SEC1450 sprintf 622 Normal form sing_845.htm#IDX415 623 Normalization sing_811.htm#SEC863 624 Notes for Singular users Notes for Singular users sing_2565.htm#SEC2648 625 Notes for developers Notes for developers sing_2566.htm#SEC2656 626 NullCone sing_1676.htm#SEC1752 64635 627 NumIrrDecom sing_1348.htm#SEC1424 sprintf 628 NumLocalDim sing_1337.htm#SEC1413 1739 629 NumPrimDecom sing_1350.htm#SEC1426 34134 630 Oaku-Takayama algorithm sing_532.htm#IDX336 642 New orderings for modules Notes for Singular users sing_2747.htm#SEC2835 643 Newton non-degenerate sing_1567.htm#IDX774 644 Newton polygon sing_1566.htm#IDX773 645 Newton polygon sing_1567.htm#IDX775 646 Newton polygons sing_2734.htm#IDX1072 647 Newton polytope sing_2066.htm#IDX818 648 Newton step sing_2670.htm#IDX1032 649 NoetherPosition sing_1225.htm#SEC1301 18735 650 Non-commutative LIBs Non-commutative libraries sing_497.htm#SEC549 651 Non-commutative algebra Non-commutative algebra sing_846.htm#SEC898 652 Non-commutative algebra sing_881.htm#SEC938 653 Non-commutative libraries Non-commutative libraries sing_497.htm#SEC549 654 Non-commutative subsystem Non-commutative subsystem sing_420.htm#SEC460 655 Nonhyp sing_1388.htm#SEC1464 sprintf 656 Normalization sing_828.htm#SEC880 657 Notes for Singular users Notes for Singular users sing_2747.htm#SEC2830 658 Notes for developers Notes for developers sing_2748.htm#SEC2837 659 NullCone sing_1690.htm#SEC1766 64635 660 NumIrrDecom sing_1362.htm#SEC1438 sprintf 661 NumLocalDim sing_1351.htm#SEC1427 1739 662 NumPrimDecom sing_1364.htm#SEC1440 34134 663 Oaku-Takayama algorithm sing_540.htm#IDX338 631 664 Objects sing_38.htm#SEC66 632 Orlik-Solomon sing_2186.htm#IDX856 633 Output, formatting of sing_793.htm#SEC845 634 PBW sing_511.htm#IDX324 635 PBW basis sing_478.htm#SEC519 636 PBW_eqDeg sing_529.htm#SEC581 23181 637 PBW_maxDeg sing_530.htm#SEC582 59566 638 PBW_maxMonom sing_531.htm#SEC583 1155 639 PEsolve sing_1686.htm#SEC1762 9229 640 PH_ais sing_2208.htm#SEC2284 49473 641 PH_nais sing_2209.htm#SEC2285 46271 642 PLURAL sing_413.htm#SEC453 643 PLURAL LIBs Non-commutative libraries sing_489.htm#SEC541 644 PPolyH sing_2374.htm#SEC2450 25241 645 PPolyS sing_2377.htm#SEC2453 13817 646 ParToVar sing_2369.htm#SEC2445 13991 647 Parallelization Parallelization with ssi links sing_795.htm#SEC847 648 Parallelization sing_931.htm#IDX476 665 Orlik-Solomon sing_2197.htm#IDX882 666 Output sing_2516.htm#IDX992 667 Output sing_2613.htm#IDX999 668 Output sing_2615.htm#IDX1000 669 Output sing_2616.htm#IDX1001 670 Output sing_2617.htm#IDX1002 671 Output sing_2618.htm#IDX1003 672 Output sing_2619.htm#IDX1004 673 Output sing_2620.htm#IDX1005 674 Output sing_2621.htm#IDX1006 675 Output sing_2622.htm#IDX1007 676 Output sing_2623.htm#IDX1008 677 Output sing_2624.htm#IDX1009 678 Output sing_2625.htm#IDX1010 679 Output sing_2626.htm#IDX1011 680 Output sing_2627.htm#IDX1012 681 Output sing_2628.htm#IDX1013 682 Output sing_2629.htm#IDX1014 683 Output sing_2630.htm#IDX1015 684 Output sing_2631.htm#IDX1016 685 Output sing_2632.htm#IDX1017 686 Output sing_2633.htm#IDX1018 687 Output sing_2634.htm#IDX1019 688 Output sing_2635.htm#IDX1020 689 Output sing_2636.htm#IDX1021 690 Output sing_2637.htm#IDX1022 691 Output, formatting of sing_810.htm#SEC862 692 PBW sing_519.htm#IDX326 693 PBW basis sing_486.htm#SEC527 694 PBW_eqDeg sing_537.htm#SEC589 23181 695 PBW_maxDeg sing_538.htm#SEC590 59566 696 PBW_maxMonom sing_539.htm#SEC591 1155 697 PEsolve sing_1700.htm#SEC1776 9229 698 PH_ais sing_2219.htm#SEC2295 49473 699 PH_nais sing_2220.htm#SEC2296 46271 700 PLURAL sing_421.htm#SEC461 701 PLURAL LIBs Non-commutative libraries sing_497.htm#SEC549 702 PPolyH sing_2397.htm#SEC2473 25241 703 PPolyN sing_2402.htm#SEC2478 39067 704 PPolyS sing_2400.htm#SEC2476 13817 705 ParToVar sing_2392.htm#SEC2468 13991 706 Parallelization Parallelization with ssi links sing_812.htm#SEC864 707 Parallelization sing_951.htm#IDX494 649 708 Parameter list sing_44.htm#SEC81 650 Parameters sing_792.htm#SEC844 651 Parametrization sing_1357.htm#IDX590 652 Parametrization, image. sing_1367.htm#IDX602 653 PartC sing_2286.htm#SEC2362 54120 654 PartitionVar sing_2366.htm#SEC2442 41350 655 Path names Notes for Singular users sing_2565.htm#SEC2652 656 PerfectPowerTest sing_1844.htm#SEC1920 17450 657 Perturbation walk sing_1141.htm#IDX536 709 Parameters sing_809.htm#SEC861 710 Parametric Polynomial Systems sing_920.htm#IDX425 711 Parametrization sing_1371.htm#IDX616 712 Parametrization, image. sing_1381.htm#IDX628 713 PartC sing_2304.htm#SEC2380 54120 714 PartitionVar sing_2389.htm#SEC2465 41350 715 Path names Notes for Singular users sing_2747.htm#SEC2833 716 PerfectPowerTest sing_1858.htm#SEC1934 17450 717 Perturbation walk sing_1153.htm#IDX551 658 718 Pfister, Gerhard sing_1.htm#IDX19 659 Pipe links sing_1 16.htm#SEC156660 PocklingtonLehmer sing_18 83.htm#SEC195913634661 Poincare polynomial sing_2 198.htm#IDX880662 Polar curves sing_8 17.htm#SEC869663 PollardRho sing_18 84.htm#SEC196049602664 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_22 11.htm#IDX896665 PolyBoRi, Boolean Groebner Basis sing_22 13.htm#IDX897666 PolyBoRi, Boolean Groebner Basis sing_22 14.htm#IDX898667 PolyBoRi, Boolean Groebner Basis sing_22 15.htm#IDX899668 PolyBoRi, Boolean Groebner Basis sing_22 16.htm#IDX900669 PolyBoRi, Boolean Groebner Basis sing_22 17.htm#IDX901670 PolyBoRi, Boolean Groebner Basis sing_22 18.htm#IDX902671 PolyBoRi, Boolean Groebner Basis sing_22 19.htm#IDX903672 PolyBoRi, Boolean Groebner Basis sing_22 20.htm#IDX904673 PolyBoRi, Boolean Groebner Basis sing_22 21.htm#IDX905674 PolyBoRi, Boolean Groebner Basis sing_22 22.htm#IDX906675 PolyBoRi, Boolean Groebner Basis sing_22 23.htm#IDX907676 PolyBoRi, Boolean Groebner Basis sing_22 24.htm#IDX908677 PolyBoRi, Boolean Groebner Basis sing_22 25.htm#IDX909678 PolyBoRi, Boolean Groebner Basis sing_22 27.htm#IDX911679 PolyBoRi, zero-supressed decision diagram sing_22 26.htm#IDX910680 Polybori, Boolean Groebner Basis sing_22 28.htm#IDX912681 Polynomial data sing_8 33.htm#SEC885682 Pottier algorithm sing_8 54.htm#SEC911719 Pipe links sing_121.htm#SEC161 720 PocklingtonLehmer sing_1897.htm#SEC1973 13634 721 Poincare polynomial sing_2209.htm#IDX906 722 Polar curves sing_834.htm#SEC886 723 PollardRho sing_1898.htm#SEC1974 49602 724 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2222.htm#IDX922 725 PolyBoRi, Boolean Groebner Basis sing_2224.htm#IDX923 726 PolyBoRi, Boolean Groebner Basis sing_2225.htm#IDX924 727 PolyBoRi, Boolean Groebner Basis sing_2226.htm#IDX925 728 PolyBoRi, Boolean Groebner Basis sing_2227.htm#IDX926 729 PolyBoRi, Boolean Groebner Basis sing_2228.htm#IDX927 730 PolyBoRi, Boolean Groebner Basis sing_2229.htm#IDX928 731 PolyBoRi, Boolean Groebner Basis sing_2230.htm#IDX929 732 PolyBoRi, Boolean Groebner Basis sing_2231.htm#IDX930 733 PolyBoRi, Boolean Groebner Basis sing_2232.htm#IDX931 734 PolyBoRi, Boolean Groebner Basis sing_2233.htm#IDX932 735 PolyBoRi, Boolean Groebner Basis sing_2234.htm#IDX933 736 PolyBoRi, Boolean Groebner Basis sing_2235.htm#IDX934 737 PolyBoRi, Boolean Groebner Basis sing_2236.htm#IDX935 738 PolyBoRi, Boolean Groebner Basis sing_2238.htm#IDX937 739 PolyBoRi, zero-supressed decision diagram sing_2237.htm#IDX936 740 Polybori, Boolean Groebner Basis sing_2239.htm#IDX938 741 Polynomial data sing_852.htm#SEC904 742 Pottier algorithm sing_874.htm#SEC931 683 743 Preface sing_1.htm#SEC1 684 Prep sing_9 07.htm#SEC983 49657685 Primary decomposition Primary decomposition sing_8 10.htm#SEC862686 PrimdecA sing_1 193.htm#SEC1269248687 PrimdecB sing_1 194.htm#SEC12709653744 Prep sing_926.htm#SEC1002 61895 745 Primary decomposition Primary decomposition sing_827.htm#SEC879 746 PrimdecA sing_1207.htm#SEC1283 248 747 PrimdecB sing_1208.htm#SEC1284 9653 688 748 Procedure definition Procedure definition sing_43.htm#SEC78 689 749 Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84 690 750 Procedures sing_42.htm#SEC77 691 751 Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14 692 Procedures and libraries sing_ 789.htm#SEC841752 Procedures and libraries sing_806.htm#SEC858 693 753 Procedures in a library Procedures in a library sing_54.htm#SEC91 694 Product orderings 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References (plural) sing_481.htm#SEC531 710 Release Notes sing_2561.htm#SEC2637 711 ResTree sing_1403.htm#SEC1479 58727 763 Qso3Casimir sing_694.htm#SEC746 40212 764 Quotient sing_1742.htm#SEC1818 24888 765 QuotientEquations sing_1589.htm#SEC1665 18230 766 Rational curves sing_1371.htm#IDX617 767 ReJunkUseHomo sing_1357.htm#SEC1433 10186 768 ReesAlgebra sing_1324.htm#SEC1400 59951 769 References sing_889.htm#SEC963 770 References (plural) sing_489.htm#SEC539 771 Release Notes sing_2743.htm#SEC2819 772 Res sing_2496.htm#SEC2572 92 773 ResTree sing_1417.htm#SEC1493 58727 712 774 Resolution sing_11.htm#SEC17 713 Resolution of singularities Resolution of singularities sing_8 23.htm#SEC875714 Resolution, free sing_8 05.htm#SEC857715 ReynoldsImage sing_16 77.htm#SEC175335172716 ReynoldsOperator sing_16 78.htm#SEC175414986717 RiemannRochBN sing_22 31.htm#SEC230720085718 RiemannRochHess sing_24 31.htm#SEC2507sprintf719 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_8 29.htm#SEC881720 Ring-dependent options Notes for Singular users sing_2 565.htm#SEC2650775 Resolution of singularities Resolution of singularities sing_840.htm#SEC892 776 Resolution, free sing_822.htm#SEC874 777 ReynoldsImage sing_1691.htm#SEC1767 35172 778 ReynoldsOperator sing_1692.htm#SEC1768 14986 779 RiemannRochBN sing_2249.htm#SEC2325 20085 780 RiemannRochHess sing_2480.htm#SEC2556 sprintf 781 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_848.htm#SEC900 782 Ring-dependent options Notes for Singular users sing_2747.htm#SEC2832 721 783 Rings and orderings sing_28.htm#SEC39 722 784 Rings and standard bases Rings and standard bases sing_7.htm#SEC13 723 785 Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 724 SCA Graded commutative algebras (SCA) sing_4 82.htm#SEC534786 SCA Graded commutative algebras (SCA) sing_490.htm#SEC542 725 787 SDB breakpoint Source code debugger sing_66.htm#SEC106 726 788 SDB debugger Source code debugger sing_66.htm#SEC106 727 SDLoc sing_5 59.htm#SEC6119512728 SINGULAR libraries sing_8 70.htm#SEC946789 SDLoc sing_567.htm#SEC619 9512 790 SINGULAR libraries sing_890.htm#SEC966 729 791 SINGULARHIST sing_18.htm#SEC25 730 SScontinue sing_1013.htm#SEC1089 38390 731 SSres sing_1011.htm#SEC1087 4648 732 SSsyz sing_1012.htm#SEC1088 34610 733 SV-decoding algorithm sing_1784.htm#IDX769 734 SV-decoding algorithm, preprocessing sing_1783.htm#IDX768 735 Sannfs sing_535.htm#SEC587 42932 736 SannfsBFCT sing_544.htm#SEC596 59702 737 SannfsVar sing_591.htm#SEC643 37522 738 Sannfslog sing_536.htm#SEC588 49313 739 Saturation sing_802.htm#SEC854 740 Saturation sing_1122.htm#IDX505 792 SV-decoding algorithm sing_1798.htm#IDX795 793 SV-decoding algorithm, preprocessing sing_1797.htm#IDX794 794 Sannfs sing_543.htm#SEC595 42932 795 SannfsBFCT sing_552.htm#SEC604 59702 796 SannfsVar sing_599.htm#SEC651 37522 797 Sannfslog sing_544.htm#SEC596 49313 798 Saturation sing_819.htm#SEC871 799 Saturation sing_1134.htm#IDX520 741 800 Sch@"onemann, Hans sing_1.htm#IDX20 742 Schoof sing_1895.htm#SEC1971 49281 743 Schreyer ordering sing_1006.htm#IDX492 744 Schreyer resolution sing_1006.htm#IDX493 745 Schubert calculus sing_2510.htm#IDX978 746 SchubertClass sing_2547.htm#SEC2623 62336 747 SchurCh sing_2283.htm#SEC2359 58575 748 SchurS sing_2282.htm#SEC2358 46004 749 Scontinue sing_1010.htm#SEC1086 11534 750 SegreA sing_2289.htm#SEC2365 55776 751 Semigroup sing_1491.htm#SEC1567 22323 752 Setting up a G-algebra sing_478.htm#SEC522 753 ShanksMestre sing_1894.htm#SEC1970 12973 754 SimplifyIdeal sing_1679.htm#SEC1755 sprintf 755 Singular sing_350.htm#IDX255 756 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2563.htm#SEC2646 801 Schoof sing_1909.htm#SEC1985 49281 802 Schubert calculus sing_2692.htm#IDX1046 803 SchubertClass sing_2729.htm#SEC2805 62336 804 SchurCh sing_2301.htm#SEC2377 58575 805 SchurS sing_2300.htm#SEC2376 46004 806 SegreA sing_2307.htm#SEC2383 55776 807 Semigroup sing_1505.htm#SEC1581 22323 808 SetDeg sing_2499.htm#SEC2575 40547 809 Setting up a G-algebra sing_486.htm#SEC530 810 ShanksMestre sing_1908.htm#SEC1984 12973 811 SimplifyIdeal sing_1693.htm#SEC1769 sprintf 812 Singular sing_358.htm#IDX257 813 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2745.htm#SEC2828 757 814 Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36 758 815 Singular, demo mode sing_24.htm#SEC35 … … 760 817 Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38 761 818 Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 762 Singular2bertini sing_1341.htm#SEC1417 7552 763 SingularLib sing_350.htm#IDX257 764 Singularities sing_1450.htm#SEC1526 765 Singularity Theory sing_814.htm#SEC866 766 Skeletons for parallelization sing_931.htm#IDX477 767 Smith form sing_1826.htm#IDX779 768 Smith normal form sing_1826.htm#IDX780 769 SolowayStrassen sing_1882.htm#SEC1958 22680 770 Solving systems of polynomial equations Solving systems of polynomial equations sing_831.htm#SEC883 819 Singular2bertini sing_1355.htm#SEC1431 7552 820 SingularLib sing_358.htm#IDX259 821 Singularities sing_1464.htm#SEC1540 822 Singularity Theory sing_831.htm#SEC883 823 Skeletons for parallelization sing_951.htm#IDX495 824 Smith form sing_1840.htm#IDX805 825 Smith normal form sing_1840.htm#IDX806 826 SolowayStrassen sing_1896.htm#SEC1972 22680 827 Solving systems of polynomial equations Solving systems of polynomial equations sing_850.htm#SEC902 828 Source sing_2488.htm#SEC2564 10351 771 829 Source code debugger, invocation Command line options sing_19.htm#IDX33 772 Space curve singularities, branches of Branches of space curve singularities sing_8 21.htm#SEC873830 Space curve singularities, branches of Branches of space curve singularities sing_838.htm#SEC890 773 831 Special characters sing_36.htm#SEC64 774 Splitting lemma sing_2498.htm#IDX964 775 Sres sing_1008.htm#SEC1084 60186 776 Ssi file links sing_114.htm#SEC154 777 Ssi links sing_113.htm#SEC153 778 Ssi tcp links sing_115.htm#SEC155 779 Ssyz sing_1009.htm#SEC1085 56541 780 StabEqn sing_1576.htm#SEC1652 28539 781 StabEqnId sing_1577.htm#SEC1653 27955 782 StabOrder sing_1578.htm#SEC1654 55603 783 Standard Bases Computing Groebner and Standard Bases sing_797.htm#SEC849 784 Standard bases sing_845.htm#SEC897 785 StartOrderingV sing_1445.htm#SEC1521 58927 832 Splitting lemma addnondegeneratevariables sing_2666.htm#IDX1025 833 Splitting lemma sing_2669.htm#IDX1029 834 Ssi file links sing_119.htm#SEC159 835 Ssi links sing_118.htm#SEC158 836 Ssi tcp links sing_120.htm#SEC160 837 StabEqn sing_1590.htm#SEC1666 28539 838 StabEqnId sing_1591.htm#SEC1667 27955 839 StabOrder sing_1592.htm#SEC1668 55603 840 Standard Bases Computing Groebner and Standard Bases sing_814.htm#SEC866 841 Standard bases sing_865.htm#SEC917 842 StartOrderingV sing_1459.htm#SEC1535 58927 786 843 Startup sequence sing_20.htm#SEC27 787 StringF sing_15 65.htm#SEC164111590788 SymGroup sing_7 35.htm#SEC78756676789 Symbolic-numerical solving Symbolic-numerical solving sing_8 31.htm#SEC883790 Symbolic-numerical solving sing_16 83.htm#SEC1759791 System and Control theory System and Control theory sing_18 08.htm#SEC1884792 System dependent limitations System dependent limitations sing_40 0.htm#SEC440793 System variables sing_3 86.htm#SEC426794 Syzygies and resolutions Syzygies and resolutions sing_8 47.htm#SEC901795 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_48 0.htm#SEC527796 T1 sing_8 18.htm#SEC870797 T2 sing_8 18.htm#SEC870844 StringF sing_1579.htm#SEC1655 11590 845 SymGroup sing_752.htm#SEC804 56676 846 Symbolic-numerical solving Symbolic-numerical solving sing_850.htm#SEC902 847 Symbolic-numerical solving sing_1697.htm#SEC1773 848 System and Control theory System and Control theory sing_1822.htm#SEC1898 849 System dependent limitations System dependent limitations sing_408.htm#SEC448 850 System variables sing_394.htm#SEC434 851 Syzygies and resolutions Syzygies and resolutions sing_867.htm#SEC921 852 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_488.htm#SEC535 853 T1 sing_835.htm#SEC887 854 T2 sing_835.htm#SEC887 798 855 TRACE Tracing of procedures sing_65.htm#SEC102 799 TRACE sing_395.htm#SEC435 800 T_1 sing_1598.htm#SEC1674 59277 801 T_12 sing_1600.htm#SEC1676 12923 802 T_2 sing_1599.htm#SEC1675 55781 803 Teaching sing_1840.htm#SEC1916 856 TRACE sing_403.htm#SEC443 857 T_1 sing_1612.htm#SEC1688 59277 858 T_12 sing_1614.htm#SEC1690 12923 859 T_2 sing_1613.htm#SEC1689 55781 860 Target sing_2487.htm#SEC2563 16006 861 Teaching sing_1854.htm#SEC1930 804 862 Template for writing a library sing_55.htm#SEC92 805 TestGRRes sing_24 11.htm#SEC24878315806 TestJMark sing_14 46.htm#SEC152241314863 TestGRRes sing_2460.htm#SEC2536 8315 864 TestJMark sing_1460.htm#SEC1536 41314 807 865 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 808 The Tran algorithm sing_11 38.htm#IDX533809 The fractal walk algorithm sing_11 37.htm#IDX532810 The fractal walk algorithm sing_2 509.htm#IDX975866 The Tran algorithm sing_1150.htm#IDX548 867 The fractal walk algorithm sing_1149.htm#IDX547 868 The fractal walk algorithm sing_2691.htm#IDX1043 811 869 The online help system The online help system sing_16.htm#SEC22 812 Tjurina sing_1 596.htm#SEC167211249813 Tjurina number Milnor and Tjurina number sing_8 15.htm#SEC867814 Tjurina number sing_12 32.htm#IDX560870 Tjurina sing_1610.htm#SEC1686 11249 871 Tjurina number Milnor and Tjurina number sing_832.htm#SEC884 872 Tjurina number sing_1246.htm#IDX577 815 873 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 816 Tor sing_11 63.htm#SEC1239sprintf817 Toric ideals and integer programming Toric ideals and integer programming sing_8 50.htm#SEC907818 Tricks and pitfalls sing_ 398.htm#SEC438819 Tropical Geometry sing_ 1992.htm#SEC2068874 Tor sing_1175.htm#SEC1251 sprintf 875 Toric ideals and integer programming Toric ideals and integer programming sing_870.htm#SEC927 876 Tricks and pitfalls sing_406.htm#SEC446 877 Tropical Geometry sing_2006.htm#SEC2082 820 878 Type casting Type conversion and casting sing_39.htm#SEC69 821 879 Type conversion Type conversion and casting sing_39.htm#SEC68 822 880 Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98 823 U_D_O sing_10 78.htm#SEC115426192824 Unix installation Unix installation instructions sing_2 571.htm#SEC2661825 UpOneMatrix sing_7 24.htm#SEC77663020826 UpperMonomials sing_15 79.htm#SEC165520941827 UseBertini sing_13 40.htm#SEC141643362828 User defined types sing_1 77.htm#SEC217829 V-filtration sing_15 14.htm#IDX645830 V-filtration sing_15 20.htm#IDX673831 V-filtration sing_15 21.htm#IDX679832 V-filtration sing_15 22.htm#IDX687833 V-filtration sing_15 23.htm#IDX693834 V-filtration sing_15 24.htm#IDX701835 V-filtration sing_15 25.htm#IDX711836 V-filtration sing_15 36.htm#IDX717837 V-filtration sing_15 38.htm#IDX728838 VarToPar sing_23 68.htm#SEC244410508881 U_D_O sing_1090.htm#SEC1166 26192 882 Unix installation Unix installation instructions sing_2753.htm#SEC2842 883 UpOneMatrix sing_741.htm#SEC793 63020 884 UpperMonomials sing_1593.htm#SEC1669 20941 885 UseBertini sing_1354.htm#SEC1430 43362 886 User defined types sing_182.htm#SEC222 887 V-filtration sing_1528.htm#IDX671 888 V-filtration sing_1534.htm#IDX699 889 V-filtration sing_1535.htm#IDX705 890 V-filtration sing_1536.htm#IDX713 891 V-filtration sing_1537.htm#IDX719 892 V-filtration sing_1538.htm#IDX727 893 V-filtration sing_1539.htm#IDX737 894 V-filtration sing_1550.htm#IDX743 895 V-filtration sing_1552.htm#IDX754 896 VarToPar sing_2391.htm#SEC2467 10508 839 897 Variables, indexed sing_37.htm#SEC65 840 Version number Version schema for Singular sing_2 564.htm#SEC2647841 Version schema for Singular Version schema for Singular sing_2 564.htm#SEC2647898 Version number Version schema for Singular sing_2746.htm#SEC2829 899 Version schema for Singular Version schema for Singular sing_2746.htm#SEC2829 842 900 Version string sing_50.htm#SEC87 843 Visualization sing_17 46.htm#SEC1822844 WLemma sing_9 20.htm#SEC996 3921845 WP, global ordering sing_8 38.htm#IDX398846 WSemigroup sing_1 496.htm#SEC157257449847 Weierstrass sing_17 79.htm#SEC185558220848 Weierstrass semigroup sing_17 75.htm#IDX763849 Weyl sing_7 09.htm#SEC76129212850 Weyl algebra sing_5 32.htm#IDX330851 Weyl algebra sing_5 88.htm#IDX355852 Weyl closure sing_7 60.htm#IDX383853 WeylClosure sing_7 62.htm#SEC81423845854 WeylClosure1 sing_7 63.htm#SEC81515759855 Wibmer's Lemma sing_9 20.htm#IDX473856 Windows installation Windows installation instructions sing_2 572.htm#SEC2662857 WitSet sing_13 47.htm#SEC142339803858 WitSupSet sing_13 46.htm#SEC142247758859 Ws, local ordering sing_8 39.htm#IDX410860 XLsolve sing_1 689.htm#SEC176534970901 Visualization sing_1760.htm#SEC1836 902 WLemma sing_940.htm#SEC1016 7302 903 WP, global ordering sing_857.htm#IDX400 904 WSemigroup sing_1510.htm#SEC1586 57449 905 Weierstrass sing_1793.htm#SEC1869 58220 906 Weierstrass semigroup sing_1789.htm#IDX789 907 Weyl sing_726.htm#SEC778 29212 908 Weyl algebra sing_540.htm#IDX332 909 Weyl algebra sing_596.htm#IDX357 910 Weyl closure sing_777.htm#IDX385 911 WeylClosure sing_779.htm#SEC831 23845 912 WeylClosure1 sing_780.htm#SEC832 15759 913 Wibmer's Lemma sing_940.htm#IDX491 914 Windows installation Windows installation instructions sing_2754.htm#SEC2843 915 WitSet sing_1361.htm#SEC1437 39803 916 WitSupSet sing_1360.htm#SEC1436 47758 917 Ws, local ordering sing_858.htm#IDX412 918 XLsolve sing_1703.htm#SEC1779 34970 861 919 ZZ sing_28.htm#SEC39 862 920 ZZ/m sing_28.htm#SEC39 863 921 ZZ/p sing_28.htm#SEC39 864 ZZsolve sing_1 690.htm#SEC176618657922 ZZsolve sing_1704.htm#SEC1780 18657 865 923 [ sing_36.htm#IDX83 866 [] sing_1 37.htm#SEC177867 [] sing_15 0.htm#SEC190868 [] sing_17 0.htm#SEC210869 [] sing_1 75.htm#SEC215924 [] sing_142.htm#SEC182 925 [] sing_155.htm#SEC195 926 [] sing_175.htm#SEC215 927 [] sing_180.htm#SEC220 870 928 \ sing_36.htm#IDX112 871 929 ] sing_36.htm#IDX84 872 930 ^ sing_36.htm#IDX92 873 ^ sing_ 76.htm#SEC116874 ^ sing_ 88.htm#SEC128875 ^ sing_14 2.htm#SEC182876 ^ sing_15 0.htm#SEC190931 ^ sing_81.htm#SEC121 932 ^ sing_93.htm#SEC133 933 ^ sing_147.htm#SEC187 934 ^ sing_155.htm#SEC195 877 935 _ sing_36.htm#IDX116 878 936 ` sing_36.htm#IDX105 879 a, ordering sing_843.htm#SEC895 880 absFactorize sing_1091.htm#SEC1167 52546 881 absFactorizeBCG sing_1092.htm#SEC1168 55510 882 absPrimdecGTZ sing_1290.htm#SEC1366 46393 883 absPrimdecGTZE sing_1291.htm#SEC1367 48005 884 absValue sing_882.htm#SEC958 54595 885 absfact.lib sing_1090.htm#SEC1166 886 absfact_lib sing_1090.htm#SEC1166 887 absolute factorization. sing_1090.htm#IDX504 888 abstract variety, projective space, Grassmannian printVariety sing_2511.htm#IDX981 889 abstract variety, projective space, Grassmannian sing_2512.htm#IDX982 890 abstractR sing_1429.htm#SEC1505 22284 891 actionIsProper sing_1659.htm#SEC1735 52474 892 addNvarsTo sing_1005.htm#SEC1081 63123 893 addRat sing_781.htm#SEC833 4768 894 addSheaf sing_2530.htm#SEC2606 27062 895 addcol sing_1047.htm#SEC1123 52204 896 addcores sing_974.htm#SEC1050 41254 897 addrow sing_1048.htm#SEC1124 47055 898 addvarsTo sing_1004.htm#SEC1080 17717 899 ademRelations sing_641.htm#SEC693 30263 900 adjoint sing_1072.htm#SEC1148 56619 901 adjointIdeal sing_1358.htm#SEC1434 11455 902 adjunction divisor sing_1776.htm#IDX767 903 admissibleSub sing_700.htm#SEC752 6583 904 afaces sing_2387.htm#SEC2463 41634 905 affine code Fitzgerald-Lax method sing_866.htm#SEC935 906 ainvar.lib sing_1656.htm#SEC1732 907 ainvar_lib sing_1656.htm#SEC1732 908 aksaka.lib sing_1841.htm#SEC1917 909 aksaka_lib sing_1841.htm#SEC1917 910 alexanderpolynomial sing_1454.htm#SEC1530 36814 911 alexpoly.lib sing_1451.htm#SEC1527 912 alexpoly_lib sing_1451.htm#SEC1527 913 algDependent sing_1097.htm#SEC1173 20789 914 alg_kernel sing_1098.htm#SEC1174 307 915 algebra.lib sing_1093.htm#SEC1169 916 algebra_containment sing_1094.htm#SEC1170 47912 917 algebra_lib sing_1093.htm#SEC1169 918 algebraic dependence sing_730.htm#IDX361 919 algebraic field extension sing_1304.htm#IDX567 920 algebraicDependence sing_1317.htm#SEC1393 38500 921 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_857.htm#SEC914 922 algorithm of Conti and Traverso sing_853.htm#SEC910 923 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_856.htm#SEC913 924 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_855.htm#SEC912 925 algorithm of Pottier sing_854.htm#SEC911 926 align sing_203.htm#SEC243 927 all.lib sing_875.htm#SEC951 928 allDoubleExt sing_747.htm#SEC799 43457 929 allExtOfLeft sing_744.htm#SEC796 6405 930 allExtOfRight sing_745.htm#SEC797 56781 931 allPositive sing_508.htm#SEC560 1409 932 all_lib sing_875.htm#SEC951 937 a, ordering sing_862.htm#SEC914 938 absFactorize sing_1103.htm#SEC1179 52546 939 absFactorizeBCG sing_1104.htm#SEC1180 55510 940 absPrimdecGTZ sing_1304.htm#SEC1380 46393 941 absPrimdecGTZE sing_1305.htm#SEC1381 48005 942 absValue sing_902.htm#SEC978 54595 943 absfact.lib sing_1102.htm#SEC1178 944 absfact_lib sing_1102.htm#SEC1178 945 absolute factorization. sing_1102.htm#IDX519 946 abstract variety, projective space, Grassmannian printVariety sing_2693.htm#IDX1049 947 abstract variety, projective space, Grassmannian sing_2694.htm#IDX1050 948 abstractR sing_1443.htm#SEC1519 22284 949 actionIsProper sing_1673.htm#SEC1749 52474 950 addLeftFractions sing_2653.htm#SEC2729 38826 951 addModules sing_2508.htm#SEC2584 51193 952 addNvarsTo sing_1025.htm#SEC1101 63123 953 addRat sing_798.htm#SEC850 4768 954 addSheaf sing_2712.htm#SEC2788 27062 955 addcol sing_1059.htm#SEC1135 52204 956 addcores sing_994.htm#SEC1070 41254 957 addnondegeneratevariables addnondegeneratevariables sing_2669.htm#SEC2745 40483 958 addrow sing_1060.htm#SEC1136 47055 959 addvarsTo sing_1024.htm#SEC1100 17717 960 ademRelations sing_658.htm#SEC710 30263 961 adjoint sing_1084.htm#SEC1160 56619 962 adjointIdeal sing_1372.htm#SEC1448 11455 963 adjunction divisor sing_1790.htm#IDX793 964 admissibleSub sing_717.htm#SEC769 6583 965 afaces sing_2413.htm#SEC2489 28045 966 affine code Fitzgerald-Lax method sing_886.htm#SEC955 967 ainvar.lib sing_1670.htm#SEC1746 968 ainvar_lib sing_1670.htm#SEC1746 969 aksaka.lib sing_1855.htm#SEC1931 970 aksaka_lib sing_1855.htm#SEC1931 971 alexanderpolynomial sing_1468.htm#SEC1544 36814 972 alexpoly.lib sing_1465.htm#SEC1541 973 alexpoly_lib sing_1465.htm#SEC1541 974 algDependent sing_1109.htm#SEC1185 20789 975 alg_kernel sing_1110.htm#SEC1186 307 976 algebra.lib sing_1105.htm#SEC1181 977 algebra_containment sing_1106.htm#SEC1182 47912 978 algebra_lib sing_1105.htm#SEC1181 979 algebraic dependence sing_747.htm#IDX363 980 algebraic field extension sing_1318.htm#IDX586 981 algebraicDependence sing_1331.htm#SEC1407 38500 982 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_877.htm#SEC934 983 algorithm of Conti and Traverso sing_873.htm#SEC930 984 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_876.htm#SEC933 985 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_875.htm#SEC932 986 algorithm of Pottier sing_874.htm#SEC931 987 alias General command syntax sing_35.htm#SEC59 988 align sing_208.htm#SEC248 989 all.lib sing_895.htm#SEC971 990 allDoubleExt sing_764.htm#SEC816 43457 991 allExtOfLeft sing_761.htm#SEC813 6405 992 allExtOfRight sing_762.htm#SEC814 56781 993 allPositive sing_516.htm#SEC568 1409 994 all_lib sing_895.htm#SEC971 933 995 allowing net access Command line options sing_19.htm#IDX41 934 allprint sing_922.htm#SEC998 5195 935 allreal sing_1984.htm#SEC2060 57232 936 allrealst sing_1982.htm#SEC2058 40962 937 allsquarefree sing_1558.htm#SEC1634 45545 938 ambientDimension sing_1997.htm#SEC2073 18907 939 and Evaluation of logical expressions sing_96.htm#SEC136 940 and sing_403.htm#SEC443 941 annPoly sing_556.htm#SEC608 18228 942 annRat sing_557.htm#SEC609 62662 943 annRatSyz sing_770.htm#SEC822 15672 944 annfs sing_533.htm#SEC585 38155 945 annfs0 sing_545.htm#SEC597 26476 946 annfs2 sing_546.htm#SEC598 47962 947 annfsBMI sing_542.htm#SEC594 2532 948 annfsParamBM sing_541.htm#SEC593 43587 949 annfsRB sing_547.htm#SEC599 31892 950 annfspecial sing_534.htm#SEC586 27566 951 annihilator of polynomial sing_555.htm#IDX340 952 annihilator of rational function sing_555.htm#IDX341 953 annihilator of rational function sing_760.htm#IDX386 954 annil sing_1199.htm#SEC1275 48744 955 appelF1 sing_574.htm#SEC626 63146 956 appelF2 sing_575.htm#SEC627 22460 957 appelF4 sing_576.htm#SEC628 6847 958 appendWeight2Ord sing_702.htm#SEC754 21488 959 apply sing_370.htm#SEC410 960 applyAdF sing_524.htm#SEC576 40329 961 arcpoint.lib sing_1464.htm#SEC1540 962 arcpoint_lib sing_1464.htm#SEC1540 963 areZeroElements sing_2473.htm#SEC2549 14728 996 allprint sing_942.htm#SEC1018 5195 997 allreal sing_1998.htm#SEC2074 57232 998 allrealst sing_1996.htm#SEC2072 40962 999 allsquarefree sing_1572.htm#SEC1648 45545 1000 ambientDimension sing_2011.htm#SEC2087 18907 1001 and Evaluation of logical expressions sing_101.htm#SEC141 1002 and sing_411.htm#SEC451 1003 annPoly sing_564.htm#SEC616 18228 1004 annRat sing_565.htm#SEC617 62662 1005 annRatSyz sing_787.htm#SEC839 15672 1006 annfs sing_541.htm#SEC593 38155 1007 annfs0 sing_553.htm#SEC605 26476 1008 annfs2 sing_554.htm#SEC606 47962 1009 annfsBMI sing_550.htm#SEC602 2532 1010 annfsParamBM sing_549.htm#SEC601 43587 1011 annfsRB sing_555.htm#SEC607 31892 1012 annfspecial sing_542.htm#SEC594 27566 1013 annihilator of polynomial sing_563.htm#IDX342 1014 annihilator of rational function sing_563.htm#IDX343 1015 annihilator of rational function sing_777.htm#IDX388 1016 annil sing_1213.htm#SEC1289 48744 1017 appelF1 sing_582.htm#SEC634 63146 1018 appelF2 sing_583.htm#SEC635 22460 1019 appelF4 sing_584.htm#SEC636 6847 1020 appendWeight2Ord sing_719.htm#SEC771 21488 1021 apply sing_378.htm#SEC418 1022 applyAdF sing_532.htm#SEC584 40329 1023 applyPermutationToIntvec applyPermutationToIntvec sing_2438.htm#SEC2514 28900 1024 arcpoint.lib sing_1478.htm#SEC1554 1025 arcpoint_lib sing_1478.htm#SEC1554 1026 areEqualLeftFractions areEqualLeftFractions sing_2655.htm#SEC2731 29498 1027 areZeroElements sing_2575.htm#SEC2651 14728 964 1028 argument, default sing_44.htm#SEC81 965 1029 argument, optional sing_44.htm#SEC81 966 arr.lib sing_2157.htm#SEC2233 967 arr2multarr sing_2190.htm#SEC2266 15063 968 arrBoolean sing_2179.htm#SEC2255 63256 969 arrBoundedChambers sing_2200.htm#SEC2276 18347 970 arrBraid sing_2180.htm#SEC2256 34093 971 arrCenter sing_2167.htm#SEC2243 24565 972 arrCentered sing_2169.htm#SEC2245 15904 973 arrCentral sing_2168.htm#SEC2244 14086 974 arrCentralize sing_2170.htm#SEC2246 53235 975 arrChambers sing_2199.htm#SEC2275 44578 976 arrCharPoly sing_2197.htm#SEC2273 44129 977 arrCone sing_2173.htm#SEC2249 38068 978 arrCoordChange sing_2171.htm#SEC2247 61430 979 arrCoordNormalize sing_2172.htm#SEC2248 46273 980 arrDecone sing_2174.htm#SEC2250 54637 981 arrDer sing_2187.htm#SEC2263 48815 982 arrEdelmanReiner sing_2185.htm#SEC2261 59091 983 arrEssentialize sing_2178.htm#SEC2254 6667 984 arrExponents sing_2189.htm#SEC2265 1948 985 arrFlats sing_2194.htm#SEC2270 64792 986 arrIsEssential sing_2177.htm#SEC2253 34363 987 arrIsFree sing_2188.htm#SEC2264 3860 988 arrLastVar sing_2166.htm#SEC2242 25835 989 arrLattice sing_2195.htm#SEC2271 58951 990 arrLocalize sing_2175.htm#SEC2251 56070 991 arrOrlikSolomon sing_2186.htm#SEC2262 31686 992 arrPoincare sing_2198.htm#SEC2274 412 993 arrPrintMatrix sing_2162.htm#SEC2238 21204 994 arrRandom sing_2183.htm#SEC2259 59986 995 arrRandomCentral sing_2184.htm#SEC2260 43698 996 arrRestrict sing_2176.htm#SEC2252 sprintf 997 arrSet sing_2158.htm#SEC2234 53769 998 arrSwapVar sing_2165.htm#SEC2241 44919 999 arrTypeB sing_2181.htm#SEC2257 22358 1000 arrTypeD sing_2182.htm#SEC2258 26495 1001 arr_lib sing_2157.htm#SEC2233 1002 arrange sing_549.htm#SEC601 50350 1003 arrangement sing_2158.htm#IDX798 1004 arrangement sing_2159.htm#IDX803 1005 arrangement sing_2190.htm#IDX865 1006 arrangement sing_2191.htm#IDX868 1007 ask sing_1849.htm#SEC1925 3862 1008 assPrimes sing_1108.htm#SEC1184 sprintf 1009 assign sing_2158.htm#IDX800 1010 assignment,custom Assignments for user defined types sing_182.htm#SEC222 1011 associated tangent FamElemsAtEnvCompPoints sing_917.htm#IDX466 1012 associated tangent sing_918.htm#IDX470 1013 assprimeszerodim.lib assprimeszerodim_lib sing_1106.htm#SEC1182 1014 assprimeszerodim_lib assprimeszerodim_lib sing_1106.htm#SEC1182 1015 atkins.lib sing_1850.htm#SEC1926 1016 atkins_lib sing_1850.htm#SEC1926 1017 attrib sing_204.htm#SEC244 1018 autonom sing_1813.htm#SEC1889 57044 1019 autonomDim sing_1814.htm#SEC1890 30055 1020 awalk1 sing_1139.htm#SEC1215 11044 1021 awalk2 sing_1140.htm#SEC1216 8955 1022 b-function sing_497.htm#IDX313 1023 bFactor sing_579.htm#SEC631 15179 1024 babyGiant sing_1879.htm#SEC1955 41113 1025 backward sing_2355.htm#SEC2431 11225 1026 bareiss sing_205.htm#SEC245 1027 base2str sing_878.htm#SEC954 sprintf 1030 arr.lib sing_2168.htm#SEC2244 1031 arr2multarr sing_2201.htm#SEC2277 15063 1032 arrBoolean sing_2190.htm#SEC2266 63256 1033 arrBoundedChambers sing_2211.htm#SEC2287 18347 1034 arrBraid sing_2191.htm#SEC2267 34093 1035 arrCenter sing_2178.htm#SEC2254 24565 1036 arrCentered sing_2180.htm#SEC2256 15904 1037 arrCentral sing_2179.htm#SEC2255 14086 1038 arrCentralize sing_2181.htm#SEC2257 53235 1039 arrChambers sing_2210.htm#SEC2286 44578 1040 arrCharPoly sing_2208.htm#SEC2284 44129 1041 arrCone sing_2184.htm#SEC2260 38068 1042 arrCoordChange sing_2182.htm#SEC2258 61430 1043 arrCoordNormalize sing_2183.htm#SEC2259 46273 1044 arrDecone sing_2185.htm#SEC2261 54637 1045 arrDer sing_2198.htm#SEC2274 48815 1046 arrEdelmanReiner sing_2196.htm#SEC2272 59091 1047 arrEssentialize sing_2189.htm#SEC2265 6667 1048 arrExponents sing_2200.htm#SEC2276 1948 1049 arrFlats sing_2205.htm#SEC2281 64792 1050 arrIsEssential sing_2188.htm#SEC2264 34363 1051 arrIsFree sing_2199.htm#SEC2275 3860 1052 arrLastVar sing_2177.htm#SEC2253 25835 1053 arrLattice sing_2206.htm#SEC2282 58951 1054 arrLocalize sing_2186.htm#SEC2262 56070 1055 arrOrlikSolomon sing_2197.htm#SEC2273 31686 1056 arrPoincare sing_2209.htm#SEC2285 412 1057 arrPrintMatrix sing_2173.htm#SEC2249 21204 1058 arrRandom sing_2194.htm#SEC2270 59986 1059 arrRandomCentral sing_2195.htm#SEC2271 43698 1060 arrRestrict sing_2187.htm#SEC2263 sprintf 1061 arrSet sing_2169.htm#SEC2245 53769 1062 arrSwapVar sing_2176.htm#SEC2252 44919 1063 arrTypeB sing_2192.htm#SEC2268 22358 1064 arrTypeD sing_2193.htm#SEC2269 26495 1065 arr_lib sing_2168.htm#SEC2244 1066 arrange sing_557.htm#SEC609 50350 1067 arrangement sing_2169.htm#IDX824 1068 arrangement sing_2170.htm#IDX829 1069 arrangement sing_2201.htm#IDX891 1070 arrangement sing_2202.htm#IDX894 1071 ask sing_1863.htm#SEC1939 3862 1072 assPrimes sing_1120.htm#SEC1196 sprintf 1073 assign sing_2169.htm#IDX826 1074 assignment,custom Assignments for user defined types sing_187.htm#SEC227 1075 associated tangent FamElemsAtEnvCompPoints sing_937.htm#IDX484 1076 associated tangent sing_938.htm#IDX488 1077 assprimeszerodim.lib assprimeszerodim_lib sing_1118.htm#SEC1194 1078 assprimeszerodim_lib assprimeszerodim_lib sing_1118.htm#SEC1194 1079 atkins.lib sing_1864.htm#SEC1940 1080 atkins_lib sing_1864.htm#SEC1940 1081 attrib sing_209.htm#SEC249 1082 autGenWeights sing_2244.htm#SEC2320 32642 1083 autGradAlg sing_2243.htm#SEC2319 21136 1084 autKS sing_2242.htm#SEC2318 51607 1085 autX sing_2247.htm#SEC2323 43261 1086 autXhat sing_2246.htm#SEC2322 35932 1087 autgradalg.lib sing_2241.htm#SEC2317 1088 autgradalg_lib sing_2241.htm#SEC2317 1089 automorphism group sing_2241.htm#IDX942 1090 automorphisms sing_2241.htm#IDX939 1091 autonom sing_1827.htm#SEC1903 57044 1092 autonomDim sing_1828.htm#SEC1904 30055 1093 awalk1 sing_1151.htm#SEC1227 11044 1094 awalk2 sing_1152.htm#SEC1228 8955 1095 b-function sing_505.htm#IDX315 1096 bFactor sing_587.htm#SEC639 15179 1097 babyGiant sing_1893.htm#SEC1969 41113 1098 backward sing_2378.htm#SEC2454 11225 1099 bareiss sing_210.htm#SEC250 1100 base2str sing_898.htm#SEC974 sprintf 1028 1101 basering sing_28.htm#IDX76 1029 basering sing_83.htm#SEC123 1030 basicinvariants sing_1470.htm#SEC1546 32136 1031 belongSemigroup sing_1111.htm#SEC1187 19983 1032 bernstein sing_1518.htm#SEC1594 5605 1033 bernsteinBM sing_537.htm#SEC589 57689 1034 bernsteinLift sing_538.htm#SEC590 22885 1035 bertini2Singular sing_1342.htm#SEC1418 58501 1036 betti sing_206.htm#SEC246 1037 betti (plural) sing_447.htm#SEC487 1038 bfct sing_498.htm#SEC550 29858 1039 bfctAnn sing_500.htm#SEC552 36658 1040 bfctBound sing_769.htm#SEC821 5630 1041 bfctIdeal sing_502.htm#SEC554 41018 1042 bfctOneGB sing_501.htm#SEC553 9696 1043 bfctSyz sing_499.htm#SEC551 26796 1044 bfctVarAnn sing_590.htm#SEC642 51667 1045 bfctVarIn sing_589.htm#SEC641 9274 1046 bfun.lib sing_497.htm#SEC549 1047 bfun_lib sing_497.htm#SEC549 1048 bigint sing_73.htm#SEC113 1049 bigint declarations sing_74.htm#SEC114 1050 bigint expressions sing_75.htm#SEC115 1051 bigint operations sing_76.htm#SEC116 1052 bigint related functions bigint related functions sing_77.htm#SEC117 1053 bigintmat sing_78.htm#SEC118 1054 bigintmat declarations bigintmat declarations sing_79.htm#SEC119 1055 bigintmat expressions bigintmat expressions sing_80.htm#SEC120 1056 bigintmat operations bigintmat operations sing_82.htm#SEC122 1057 bigintmat type cast sing_81.htm#SEC121 1058 bimodules sing_490.htm#IDX301 1059 bimodules.lib sing_490.htm#SEC542 1060 bimodules_lib sing_490.htm#SEC542 1061 binary_add sing_1902.htm#SEC1978 42817 1062 binomial sing_883.htm#SEC959 23208 1063 binomials2intmat sing_1265.htm#SEC1341 58804 1064 birational map, image, inverse. sing_1359.htm#IDX596 1065 bistd sing_491.htm#SEC543 45237 1066 bisyzygies sing_490.htm#IDX302 1067 bitrinity sing_492.htm#SEC544 3516 1068 blackbox sing_186.htm#SEC226 1069 blackbox sing_194.htm#SEC234 1102 basering sing_88.htm#SEC128 1103 basicinvariants sing_1484.htm#SEC1560 32136 1104 belongSemigroup sing_1123.htm#SEC1199 19983 1105 bernstein sing_1532.htm#SEC1608 5605 1106 bernsteinBM sing_545.htm#SEC597 57689 1107 bernsteinLift sing_546.htm#SEC598 22885 1108 bertini sing_1347.htm#IDX590 1109 bertini sing_1352.htm#IDX597 1110 bertini2Singular sing_1356.htm#SEC1432 58501 1111 betti sing_211.htm#SEC251 1112 betti (plural) sing_455.htm#SEC495 1113 betti number sing_2395.htm#IDX983 1114 bfct sing_506.htm#SEC558 29858 1115 bfctAnn sing_508.htm#SEC560 36658 1116 bfctBound sing_786.htm#SEC838 5630 1117 bfctIdeal sing_510.htm#SEC562 41018 1118 bfctOneGB sing_509.htm#SEC561 9696 1119 bfctSyz sing_507.htm#SEC559 26796 1120 bfctVarAnn sing_598.htm#SEC650 51667 1121 bfctVarIn sing_597.htm#SEC649 9274 1122 bfun.lib sing_505.htm#SEC557 1123 bfun_lib sing_505.htm#SEC557 1124 bigint sing_78.htm#SEC118 1125 bigint declarations sing_79.htm#SEC119 1126 bigint expressions sing_80.htm#SEC120 1127 bigint operations sing_81.htm#SEC121 1128 bigint related functions bigint related functions sing_82.htm#SEC122 1129 bigintToBinary sing_2436.htm#SEC2512 59742 1130 bigintmat sing_83.htm#SEC123 1131 bigintmat declarations bigintmat declarations sing_84.htm#SEC124 1132 bigintmat expressions bigintmat expressions sing_85.htm#SEC125 1133 bigintmat operations bigintmat operations sing_87.htm#SEC127 1134 bigintmat type cast sing_86.htm#SEC126 1135 bimodules sing_498.htm#IDX303 1136 bimodules.lib sing_498.htm#SEC550 1137 bimodules_lib sing_498.htm#SEC550 1138 binaryToBigint sing_2437.htm#SEC2513 sprintf 1139 binary_add sing_1916.htm#SEC1992 42817 1140 binomial sing_903.htm#SEC979 23208 1141 binomials2intmat sing_1279.htm#SEC1355 58804 1142 birational map, image, inverse. sing_1373.htm#IDX622 1143 bistd sing_499.htm#SEC551 45237 1144 bisyzygies sing_498.htm#IDX304 1145 bitrinity sing_500.htm#SEC552 3516 1146 blackbox sing_191.htm#SEC231 1147 blackbox sing_199.htm#SEC239 1070 1148 block sing_40.htm#SEC70 1071 block sing_369.htm#SEC409 1072 blowUp sing_1410.htm#SEC1486 34819 1073 blowUp2 sing_1411.htm#SEC1487 65264 1074 blowUpBO sing_1417.htm#SEC1493 58146 1075 blowup0 sing_1116.htm#SEC1192 44451 1076 boolean sing_2179.htm#IDX842 1077 boolean expressions sing_95.htm#SEC135 1078 boolean operations sing_96.htm#SEC136 1079 boolean_constant sing_2213.htm#SEC2289 52873 1080 boolean_ideal sing_2217.htm#SEC2293 53515 1081 boolean_poly sing_2214.htm#SEC2290 41652 1082 boolean_poly_ring sing_2212.htm#SEC2288 sprintf 1083 boolean_set sing_2218.htm#SEC2294 58235 1084 boolean_std sing_2211.htm#SEC2287 5921 1085 borderBasis sing_2502.htm#SEC2578 33172 1086 boundBuFou sing_1979.htm#SEC2055 26589 1087 boundDes sing_1981.htm#SEC2057 35149 1088 boundaryLatticePoints boundaryLatticePoints sing_2070.htm#SEC2146 6238 1089 boundposDes sing_1980.htm#SEC2056 58854 1090 bracket sing_350.htm#IDX197 1091 bracket sing_406.htm#SEC446 1092 bracket sing_448.htm#SEC488 1093 braid sing_2180.htm#IDX844 1094 branchTo procs with different argument types sing_155.htm#SEC195 1095 break sing_371.htm#SEC411 1096 break point sing_385.htm#SEC425 1097 breakpoint sing_372.htm#SEC412 1098 brillnoether.lib sing_2230.htm#SEC2306 1099 brillnoether_lib sing_2230.htm#SEC2306 1100 brnoeth.lib sing_1775.htm#SEC1851 1101 brnoeth_lib sing_1775.htm#SEC1851 1149 block sing_377.htm#SEC417 1150 blowUp sing_1424.htm#SEC1500 34819 1151 blowUp2 sing_1425.htm#SEC1501 65264 1152 blowUpBO sing_1431.htm#SEC1507 58146 1153 blowup0 sing_1128.htm#SEC1204 44451 1154 boolean sing_2190.htm#IDX868 1155 boolean expressions sing_100.htm#SEC140 1156 boolean operations sing_101.htm#SEC141 1157 boolean_constant sing_2224.htm#SEC2300 52873 1158 boolean_ideal sing_2228.htm#SEC2304 53515 1159 boolean_poly sing_2225.htm#SEC2301 41652 1160 boolean_poly_ring sing_2223.htm#SEC2299 sprintf 1161 boolean_set sing_2229.htm#SEC2305 58235 1162 boolean_std sing_2222.htm#SEC2298 5921 1163 border basis sing_2683.htm#IDX1033 1164 borderBasis sing_2684.htm#SEC2760 33172 1165 boundBuFou sing_1993.htm#SEC2069 26589 1166 boundDes sing_1995.htm#SEC2071 35149 1167 boundaryLatticePoints boundaryLatticePoints sing_2081.htm#SEC2157 6238 1168 boundposDes sing_1994.htm#SEC2070 58854 1169 bounds sing_2671.htm#SEC2747 50218 1170 boxSet sing_2673.htm#SEC2749 8552 1171 bracket sing_358.htm#IDX197 1172 bracket sing_414.htm#SEC454 1173 bracket sing_456.htm#SEC496 1174 braid sing_2191.htm#IDX870 1175 branchTo procs with different argument types sing_160.htm#SEC200 1176 break sing_379.htm#SEC419 1177 break point sing_393.htm#SEC433 1178 breakpoint sing_380.htm#SEC420 1179 brillnoether.lib sing_2248.htm#SEC2324 1180 brillnoether_lib sing_2248.htm#SEC2324 1181 brnoeth.lib sing_1789.htm#SEC1865 1182 brnoeth_lib sing_1789.htm#SEC1865 1102 1183 browser, command line option Command line options sing_19.htm#IDX44 1103 browser, setting the sing_35 0.htm#IDX1931184 browser, setting the sing_358.htm#IDX193 1104 1185 browsers The online help system sing_16.htm#IDX21 1105 browsers, setting the sing_350.htm#IDX192 1106 bubblesort sing_1852.htm#SEC1928 63278 1107 busadj sing_1070.htm#SEC1146 36301 1108 bvar sing_2225.htm#SEC2301 52773 1109 c, module ordering sing_840.htm#IDX413 1110 cProj sing_2272.htm#SEC2348 24037 1111 calculateI sing_1384.htm#SEC1460 31107 1112 calculate_max_sum sing_1921.htm#SEC1997 4706 1113 calculate_ordering sing_1899.htm#SEC1975 42616 1114 cancelunit, option sing_307.htm#IDX171 1115 canonMap sing_1144.htm#SEC1220 47599 1116 canonical sing_902.htm#IDX424 1117 canonical form sing_911.htm#IDX447 1118 canonical form sing_912.htm#IDX449 1119 canonical, discussion of parametric ideal sing_910.htm#IDX443 1120 canonicalizeCone sing_1998.htm#SEC2074 6251 1121 canonize sing_1821.htm#SEC1897 54090 1122 cantoradd sing_1935.htm#SEC2011 55304 1123 cantormult sing_1938.htm#SEC2014 57569 1124 cantorred sing_1936.htm#SEC2012 46502 1125 cardGroup sing_1113.htm#SEC1189 5553 1126 case No case or switch statement sing_404.htm#SEC444 1127 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2556.htm#SEC2632 55393 1186 browsers, setting the sing_358.htm#IDX192 1187 bubblesort sing_1866.htm#SEC1942 63278 1188 busadj sing_1082.htm#SEC1158 36301 1189 bvar sing_2236.htm#SEC2312 52773 1190 c, module ordering sing_859.htm#IDX415 1191 cProj sing_2290.htm#SEC2366 24037 1192 calculateI sing_1398.htm#SEC1474 31107 1193 calculate_max_sum sing_1935.htm#SEC2011 4706 1194 calculate_ordering sing_1913.htm#SEC1989 42616 1195 cancelunit, option sing_315.htm#IDX171 1196 canonMap sing_1156.htm#SEC1232 47599 1197 canoncial form sing_925.htm#IDX445 1198 canoncial form sing_926.htm#IDX447 1199 canoncial form sing_927.htm#IDX449 1200 canonical sing_921.htm#IDX433 1201 canonical sing_929.htm#IDX459 1202 canonical form sing_930.htm#IDX464 1203 canonical form sing_931.htm#IDX466 1204 canonicalizeCone sing_2012.htm#SEC2088 6251 1205 canonize sing_1835.htm#SEC1911 54090 1206 cantoradd sing_1949.htm#SEC2025 55304 1207 cantormult sing_1952.htm#SEC2028 57569 1208 cantorred sing_1950.htm#SEC2026 46502 1209 cardGroup sing_1125.htm#SEC1201 5553 1210 case No case or switch statement sing_412.htm#SEC452 1211 catNets sing_2613.htm#SEC2689 24760 1212 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2738.htm#SEC2814 55393 1128 1213 cdd sing_1.htm#IDX10 1129 1214 cddlib sing_1.htm#IDX11 1130 center sing_511.htm#IDX320 65108 1131 center sing_517.htm#SEC569 1132 center sing_2167.htm#IDX824 1133 center sing_2168.htm#IDX825 1134 center sing_2169.htm#IDX827 1135 center sing_2170.htm#IDX829 1136 centerRed sing_516.htm#SEC568 59910 1137 centerVS sing_515.htm#SEC567 27548 1138 central sing_2161.htm#IDX810 1139 central sing_2168.htm#IDX826 1140 central sing_2170.htm#IDX828 1141 central sing_2184.htm#IDX853 1142 central.lib sing_511.htm#SEC563 1143 central1st sing_2356.htm#SEC2432 29090 1144 central2nd sing_2357.htm#SEC2433 37545 1145 central_lib sing_511.htm#SEC563 1146 centralize sing_511.htm#IDX323 1147 centralizeSet sing_512.htm#SEC564 55737 1148 centralizer sing_511.htm#IDX321 65261 1149 centralizer sing_518.htm#SEC570 1150 centralizerRed sing_514.htm#SEC566 8209 1151 centralizerVS sing_513.htm#SEC565 22925 1152 cf_class sing_204.htm#IDX132 1153 cgs sing_877.htm#SEC953 57776 1154 cgsdr sing_903.htm#SEC979 11367 1155 chAll sing_2242.htm#SEC2318 2690 1156 chAllInv sing_2243.htm#SEC2319 57760 1157 chDual sing_2248.htm#SEC2324 17745 1158 chHE sing_2244.htm#SEC2320 63916 1159 chHom sing_2257.htm#SEC2333 54776 1160 chNum sing_2238.htm#SEC2314 54415 1161 chNumbers sing_2239.htm#SEC2315 42134 1162 chNumbersProj sing_2276.htm#SEC2352 28837 1163 chProd sing_2250.htm#SEC2326 40209 1164 chProdE sing_2251.htm#SEC2327 33460 1165 chProdL sing_2252.htm#SEC2328 44795 1166 chProdLP sing_2253.htm#SEC2329 8881 1167 chProdM sing_2254.htm#SEC2330 64514 1168 chProdMP sing_2255.htm#SEC2331 17103 1169 chProj sing_2273.htm#SEC2349 32311 1170 chSum sing_2246.htm#SEC2322 21088 1171 chSymm sing_2260.htm#SEC2336 24066 1172 chSymm2L sing_2261.htm#SEC2337 51625 1173 chSymm2LP sing_2262.htm#SEC2338 26099 1174 chWedge sing_2263.htm#SEC2339 57678 1175 chWedge2L sing_2264.htm#SEC2340 46597 1176 chWedge2LP sing_2265.htm#SEC2341 8876 1177 chaincrit sing_1949.htm#SEC2025 9502 1178 chambers sing_2199.htm#IDX881 1179 chambers sing_2200.htm#IDX882 1180 changeDenominator sing_1237.htm#SEC1313 21094 1181 changechar sing_979.htm#SEC1055 65454 1182 changeord sing_980.htm#SEC1056 55156 1183 changeordTo sing_1003.htm#SEC1079 41903 1184 changes sing_2562.htm#SEC2638 1185 changevar sing_981.htm#SEC1057 32829 1186 char sing_207.htm#SEC247 1187 charInfo sing_572.htm#SEC624 11034 1188 charVariety sing_571.htm#SEC623 18306 1189 char_series sing_208.htm#SEC248 1190 characteristic exponents sing_1458.htm#IDX620 1191 characteristic exponents sing_1459.htm#IDX625 1192 characteristic exponents sing_1460.htm#IDX628 1193 characteristic exponents sing_1461.htm#IDX632 1194 characteristic exponents sing_1545.htm#IDX738 1195 characteristic polynomial sing_2197.htm#IDX879 1196 characteristic variety sing_555.htm#IDX348 1197 characteristic variety sing_760.htm#IDX382 1198 charexp2conductor sing_1461.htm#SEC1537 sprintf 1199 charexp2generators sing_1459.htm#SEC1535 16838 1200 charexp2inter sing_1460.htm#SEC1536 39881 1201 charexp2multseq sing_1458.htm#SEC1534 334 1202 charexp2poly sing_1462.htm#SEC1538 sprintf 1203 charpoly sing_1071.htm#SEC1147 29561 1204 charstr sing_209.htm#SEC249 1205 checkFactor sing_548.htm#SEC600 55900 1206 checkRoot sing_543.htm#SEC595 37045 1207 chern sing_2237.htm#SEC2313 4916 1208 chern.lib sing_2232.htm#SEC2308 1209 chernCharPoly sing_2279.htm#SEC2355 31610 1210 chernPoly sing_2278.htm#SEC2354 31316 1211 chern_lib sing_2232.htm#SEC2308 1212 chineseRem sing_1870.htm#SEC1946 38560 1213 chinrem sing_210.htm#SEC250 1214 chinrempoly sing_2492.htm#SEC2568 42312 1215 chinrestp sing_1929.htm#SEC2005 24779 1216 cimonom.lib sing_2294.htm#SEC2370 1217 cimonom_lib sing_2294.htm#SEC2370 1218 cisimplicial.lib sing_1109.htm#SEC1185 1219 cisimplicial_lib sing_1109.htm#SEC1185 1220 classify sing_1471.htm#SEC1547 4953 1221 classify.lib sing_1469.htm#SEC1545 1222 classifyCeq sing_1488.htm#SEC1564 42719 1223 classifyMapGerms.lib classifyMapGerms_lib sing_2306.htm#SEC2382 1224 classifyMapGerms_lib classifyMapGerms_lib sing_2306.htm#SEC2382 1225 classifySimpleMaps sing_2312.htm#SEC2388 62176 1226 classifySimpleMaps1 sing_2313.htm#SEC2389 24789 1227 classify_aeq.lib sing_2298.htm#SEC2374 1228 classify_aeq_lib sing_2298.htm#SEC2374 1229 classify_lib sing_1469.htm#SEC1545 1230 classifyceq.lib sing_1487.htm#IDX635 1231 classifyceq_lib sing_1487.htm#IDX636 1232 classifyci.lib sing_1489.htm#IDX637 1233 classifyci_lib sing_1489.htm#IDX638 1234 classifyicis sing_1490.htm#SEC1566 37651 1235 classpoly sing_2277.htm#SEC2353 45724 1236 cleanTmp sing_2148.htm#SEC2224 14108 1237 cleanunit sing_1382.htm#SEC1458 sprintf 1238 cleardenom sing_211.htm#SEC251 1239 close sing_212.htm#SEC252 1240 closed_points sing_1785.htm#SEC1861 47269 1241 closetex sing_1752.htm#SEC1828 42334 1242 closureFrac sing_1230.htm#SEC1306 9252 1243 coDim sing_2308.htm#SEC2384 60680 1244 coDimMap sing_2307.htm#SEC2383 2002 1245 coHom sing_753.htm#SEC805 51043 1246 codim sing_1583.htm#SEC1659 14253 1247 codimension sing_1999.htm#SEC2075 32207 1248 coding theory sing_832.htm#SEC884 1249 coef sing_213.htm#SEC253 1250 coefficient sing_2160.htm#IDX806 1251 coefficient sing_2161.htm#IDX809 1252 coefficient sing_2162.htm#IDX813 1253 coefficient field sing_139.htm#SEC179 1215 center sing_519.htm#IDX322 65108 1216 center sing_525.htm#SEC577 1217 center sing_2178.htm#IDX850 1218 center sing_2179.htm#IDX851 1219 center sing_2180.htm#IDX853 1220 center sing_2181.htm#IDX855 1221 centerRed sing_524.htm#SEC576 59910 1222 centerVS sing_523.htm#SEC575 27548 1223 central sing_2172.htm#IDX836 1224 central sing_2179.htm#IDX852 1225 central sing_2181.htm#IDX854 1226 central sing_2195.htm#IDX879 1227 central.lib sing_519.htm#SEC571 1228 central1st sing_2379.htm#SEC2455 29090 1229 central2nd sing_2380.htm#SEC2456 37545 1230 central_lib sing_519.htm#SEC571 1231 centralize sing_519.htm#IDX325 1232 centralizeSet sing_520.htm#SEC572 55737 1233 centralizer sing_519.htm#IDX323 65261 1234 centralizer sing_526.htm#SEC578 1235 centralizerRed sing_522.htm#SEC574 8209 1236 centralizerVS sing_521.htm#SEC573 22925 1237 cf_class sing_209.htm#IDX132 1238 cgs sing_897.htm#SEC973 57776 1239 cgsdr sing_922.htm#SEC998 44460 1240 chAll sing_2260.htm#SEC2336 2690 1241 chAllInv sing_2261.htm#SEC2337 57760 1242 chDual sing_2266.htm#SEC2342 17745 1243 chHE sing_2262.htm#SEC2338 63916 1244 chHom sing_2275.htm#SEC2351 54776 1245 chNum sing_2256.htm#SEC2332 54415 1246 chNumbers sing_2257.htm#SEC2333 42134 1247 chNumbersProj sing_2294.htm#SEC2370 28837 1248 chProd sing_2268.htm#SEC2344 40209 1249 chProdE sing_2269.htm#SEC2345 33460 1250 chProdL sing_2270.htm#SEC2346 44795 1251 chProdLP sing_2271.htm#SEC2347 8881 1252 chProdM sing_2272.htm#SEC2348 64514 1253 chProdMP sing_2273.htm#SEC2349 17103 1254 chProj sing_2291.htm#SEC2367 32311 1255 chSum sing_2264.htm#SEC2340 21088 1256 chSymm sing_2278.htm#SEC2354 24066 1257 chSymm2L sing_2279.htm#SEC2355 51625 1258 chSymm2LP sing_2280.htm#SEC2356 26099 1259 chWedge sing_2281.htm#SEC2357 57678 1260 chWedge2L sing_2282.htm#SEC2358 46597 1261 chWedge2LP sing_2283.htm#SEC2359 8876 1262 chaincrit sing_1963.htm#SEC2039 9502 1263 chambers sing_2210.htm#IDX907 1264 chambers sing_2211.htm#IDX908 1265 changeDenominator sing_1251.htm#SEC1327 21094 1266 changechar sing_999.htm#SEC1075 65454 1267 changeord sing_1000.htm#SEC1076 55156 1268 changeordTo sing_1023.htm#SEC1099 41903 1269 changes sing_2744.htm#SEC2820 1270 changevar sing_1001.htm#SEC1077 32829 1271 char sing_212.htm#SEC252 1272 charInfo sing_580.htm#SEC632 11034 1273 charVariety sing_579.htm#SEC631 18306 1274 char_series sing_213.htm#SEC253 1275 characteristic exponents sing_1472.htm#IDX646 1276 characteristic exponents sing_1473.htm#IDX651 1277 characteristic exponents sing_1474.htm#IDX654 1278 characteristic exponents sing_1475.htm#IDX658 1279 characteristic exponents sing_1559.htm#IDX764 1280 characteristic polynomial sing_2208.htm#IDX905 1281 characteristic variety sing_563.htm#IDX350 1282 characteristic variety sing_777.htm#IDX384 1283 charexp2conductor sing_1475.htm#SEC1551 sprintf 1284 charexp2generators sing_1473.htm#SEC1549 16838 1285 charexp2inter sing_1474.htm#SEC1550 39881 1286 charexp2multseq sing_1472.htm#SEC1548 334 1287 charexp2poly sing_1476.htm#SEC1552 sprintf 1288 charpoly sing_1083.htm#SEC1159 29561 1289 charstr sing_214.htm#SEC254 1290 checkFactor sing_556.htm#SEC608 55900 1291 checkRoot sing_551.htm#SEC603 37045 1292 chern sing_2255.htm#SEC2331 4916 1293 chern.lib sing_2250.htm#SEC2326 1294 chernCharPoly sing_2297.htm#SEC2373 31610 1295 chernPoly sing_2296.htm#SEC2372 31316 1296 chern_lib sing_2250.htm#SEC2326 1297 chineseRem sing_1884.htm#SEC1960 38560 1298 chinrem sing_215.htm#SEC255 1299 chinrempoly sing_2639.htm#SEC2715 42312 1300 chinrestp sing_1943.htm#SEC2019 24779 1301 cimonom.lib sing_2312.htm#SEC2388 1302 cimonom_lib sing_2312.htm#SEC2388 1303 cisimplicial.lib sing_1121.htm#SEC1197 1304 cisimplicial_lib sing_1121.htm#SEC1197 1305 classification sing_2316.htm#IDX945 1306 classify sing_1485.htm#SEC1561 4953 1307 classify.lib sing_1483.htm#SEC1559 1308 classify2.lib sing_2316.htm#SEC2392 1309 classify2_lib sing_2316.htm#SEC2392 1310 classifyCeq sing_1502.htm#SEC1578 42719 1311 classifyMapGerms.lib classifyMapGerms_lib sing_2328.htm#SEC2404 1312 classifyMapGerms_lib classifyMapGerms_lib sing_2328.htm#SEC2404 1313 classifySimpleMaps sing_2334.htm#SEC2410 62176 1314 classifySimpleMaps1 sing_2335.htm#SEC2411 24789 1315 classifyUnimodalMaps classifyUnimodalMaps sing_2336.htm#SEC2412 63464 1316 classify_aeq.lib sing_2319.htm#SEC2395 1317 classify_aeq_lib sing_2319.htm#SEC2395 1318 classify_lib sing_1483.htm#SEC1559 1319 classifyceq.lib sing_1501.htm#IDX661 1320 classifyceq_lib sing_1501.htm#IDX662 1321 classifyci.lib sing_1503.htm#IDX663 1322 classifyci_lib sing_1503.htm#IDX664 1323 classifyicis sing_1504.htm#SEC1580 37651 1324 classpoly sing_2295.htm#SEC2371 45724 1325 cleanTmp sing_2159.htm#SEC2235 14108 1326 cleanunit sing_1396.htm#SEC1472 sprintf 1327 cleardenom sing_216.htm#SEC256 1328 close sing_217.htm#SEC257 1329 closed_points sing_1799.htm#SEC1875 47269 1330 closetex sing_1766.htm#SEC1842 42334 1331 closureFrac sing_1244.htm#SEC1320 9252 1332 coDim sing_2330.htm#SEC2406 60680 1333 coDimMap sing_2329.htm#SEC2405 2002 1334 coHom sing_770.htm#SEC822 51043 1335 codim sing_1597.htm#SEC1673 14253 1336 codimension sing_2013.htm#SEC2089 32207 1337 coding theory sing_851.htm#SEC903 1338 coef sing_218.htm#SEC258 1339 coefficient sing_2171.htm#IDX832 1340 coefficient sing_2172.htm#IDX835 1341 coefficient sing_2173.htm#IDX839 1342 coefficient field sing_144.htm#SEC184 1254 1343 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 1255 coefficients, long sing_791.htm#SEC843 1256 coeffmod sing_1847.htm#SEC1923 23531 1257 coeffs sing_214.htm#SEC254 1258 colength of derivations curveColengthDerivations sing_2318.htm#IDX925 1259 collectDiv sing_1427.htm#SEC1503 50348 1260 colrank sing_1819.htm#SEC1895 52290 1261 colred sing_1054.htm#SEC1130 1693 1262 commRing sing_784.htm#SEC836 30892 1263 comma sing_405.htm#SEC445 1264 command,custom Commands for user defined types sing_181.htm#SEC221 1265 command-line option, setting value of sing_350.htm#IDX279 1266 command-line option, value of sing_350.htm#IDX277 1267 command-line options, print all values of sing_350.htm#IDX276 1344 coefficients, long sing_808.htm#SEC860 1345 coeffmod sing_1861.htm#SEC1937 23531 1346 coeffs sing_219.htm#SEC259 1347 coker sing_2504.htm#SEC2580 35639 1348 colength of derivations curveColengthDerivations sing_2341.htm#IDX961 1349 collectDiv sing_1441.htm#SEC1517 50348 1350 colrank sing_1833.htm#SEC1909 52290 1351 colred sing_1066.htm#SEC1142 1693 1352 commRing sing_801.htm#SEC853 30892 1353 comma sing_413.htm#SEC453 1354 command,custom Commands for user defined types sing_186.htm#SEC226 1355 command-line option, setting value of sing_358.htm#IDX281 1356 command-line option, value of sing_358.htm#IDX279 1357 command-line options, print all values of sing_358.htm#IDX278 1268 1358 command-line options, short help Command line options sing_19.htm#IDX38 1269 commands (plural) sing_4 46.htm#IDX3001359 commands (plural) sing_454.htm#IDX302 1270 1360 comment sing_36.htm#IDX108 1271 compareTasks sing_1018.htm#SEC1094 45157 1272 completeReduction sing_1661.htm#SEC1737 57157 1361 compareMatrix sing_2512.htm#SEC2588 49930 1362 compareModules sing_2507.htm#SEC2583 3692 1363 compareTasks sing_1030.htm#SEC1106 45157 1364 compareVectors sing_2532.htm#SEC2608 12881 1365 completeReduction sing_1675.htm#SEC1751 57157 1273 1366 complex sing_28.htm#IDX75 1274 complexSingType sing_1485.htm#SEC1561 34483 1275 compregb.lib sing_876.htm#SEC952 1276 compregb_lib sing_876.htm#SEC952 1277 comprehensive Groebner system sing_876.htm#IDX419 1278 compress sing_1031.htm#SEC1107 61998 1279 computeConstant sing_1129.htm#SEC1205 55024 1280 computeGromovWitten sing_1132.htm#SEC1208 18834 1281 computeN sing_1431.htm#SEC1507 61628 1282 computeV sing_1430.htm#SEC1506 40316 1283 computemcm sing_1389.htm#SEC1465 36956 1284 concat sing_1032.htm#SEC1108 16653 1285 conductor sing_1238.htm#IDX561 1286 conductor sing_1461.htm#IDX631 1287 conductor sing_2316.htm#IDX919 1288 conductor, degree sing_1545.htm#IDX741 1289 cone sing_183.htm#SEC223 1290 cone sing_2173.htm#IDX833 1291 cone sing_2174.htm#IDX835 1292 coneLink sing_2002.htm#SEC2078 13635 1293 coneViaInequalities sing_2001.htm#SEC2077 25661 1294 coneViaPoints sing_2000.htm#SEC2076 3386 1295 conic, parametrization, rational point. sing_1366.htm#IDX601 1296 conicWithTangents sing_2124.htm#SEC2200 60752 1297 constructH sing_1390.htm#SEC1466 59577 1298 constructblwup sing_1391.htm#SEC1467 19326 1299 constructible set sing_911.htm#IDX445 1300 constructible sets sing_912.htm#IDX448 1301 constructlastblwup sing_1392.htm#SEC1468 7639 1302 constructor sing_2190.htm#IDX866 1303 constructor sing_2191.htm#IDX869 1304 contact matrix sing_1460.htm#IDX627 1305 containedQ sing_1740.htm#SEC1816 46718 1306 containsAsFace sing_2003.htm#SEC2079 25159 1307 containsInCollection containsInCollection sing_2036.htm#SEC2112 14368 1308 containsInSupport sing_2004.htm#SEC2080 32493 1309 containsPositiveVector containsPositiveVector sing_2005.htm#SEC2081 27042 1310 containsRelatively sing_2006.htm#SEC2082 17126 1311 content sing_953.htm#SEC1029 9095 1312 contentSB, option sing_307.htm#IDX172 1313 continue Behavior of continue sing_373.htm#SEC413 1314 continue sing_407.htm#SEC447 1315 contraHom sing_754.htm#SEC806 24706 1316 contract sing_215.htm#SEC255 1317 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2537.htm#IDX994 1318 contributionBundle sing_2537.htm#SEC2613 32874 1319 contributors sing_350.htm#IDX200 1320 control sing_1811.htm#SEC1887 44498 1321 control.lib sing_1810.htm#SEC1886 1322 controlDim sing_1812.htm#SEC1888 2417 1323 controlExample sing_1824.htm#SEC1900 2678 1324 control_Matrix sing_1513.htm#SEC1589 sprintf 1325 control_lib sing_1810.htm#SEC1886 1326 convertdata sing_1387.htm#SEC1463 54629 1327 convexHull sing_2007.htm#SEC2083 56690 1328 convexIntersection sing_2008.htm#SEC2084 63587 1329 convloc sing_552.htm#SEC604 19122 1330 coordinate change sing_2170.htm#IDX830 1331 coordinate change sing_2171.htm#IDX831 1332 coordinate change sing_2172.htm#IDX832 1333 coordinates sing_1967.htm#IDX783 1334 coords sing_1967.htm#SEC2043 29362 1335 copyTask sing_1017.htm#SEC1093 65331 1367 complexClassify sing_2317.htm#SEC2393 22796 1368 complexSingType sing_1499.htm#SEC1575 34483 1369 complexType sing_2318.htm#SEC2394 55772 1370 compregb.lib sing_896.htm#SEC972 1371 compregb_lib sing_896.htm#SEC972 1372 comprehensive Groebner system sing_896.htm#IDX421 1373 compress sing_1043.htm#SEC1119 61998 1374 computeAfaceOrbits sing_2423.htm#SEC2499 28683 1375 computeConstant sing_1141.htm#SEC1217 55024 1376 computeGromovWitten sing_1144.htm#SEC1220 18834 1377 computeN sing_1445.htm#SEC1521 61628 1378 computeV sing_1444.htm#SEC1520 40316 1379 computemcm sing_1403.htm#SEC1479 36956 1380 concat sing_1044.htm#SEC1120 16653 1381 conductor sing_1252.htm#IDX578 1382 conductor sing_1475.htm#IDX657 1383 conductor sing_2339.htm#IDX955 1384 conductor, degree sing_1559.htm#IDX767 1385 cone sing_188.htm#SEC228 1386 cone sing_2184.htm#IDX859 1387 cone sing_2185.htm#IDX861 1388 coneLink sing_2016.htm#SEC2092 13635 1389 coneViaInequalities sing_2015.htm#SEC2091 25661 1390 coneViaPoints sing_2014.htm#SEC2090 3386 1391 conic, parametrization, rational point. sing_1380.htm#IDX627 1392 conicWithTangents sing_2135.htm#SEC2211 60752 1393 constructH sing_1404.htm#SEC1480 59577 1394 constructblwup sing_1405.htm#SEC1481 19326 1395 constructible set sing_930.htm#IDX462 1396 constructible sets sing_931.htm#IDX465 1397 constructlastblwup sing_1406.htm#SEC1482 7639 1398 constructor sing_2201.htm#IDX892 1399 constructor sing_2202.htm#IDX895 1400 contact matrix sing_1474.htm#IDX653 1401 containedQ sing_1754.htm#SEC1830 46718 1402 containsAsFace sing_2017.htm#SEC2093 25159 1403 containsInCollection containsInCollection sing_2050.htm#SEC2126 14368 1404 containsInSupport sing_2018.htm#SEC2094 32493 1405 containsPositiveVector containsPositiveVector sing_2019.htm#SEC2095 27042 1406 containsRelatively sing_2020.htm#SEC2096 17126 1407 content sing_973.htm#SEC1049 9095 1408 contentSB, option sing_315.htm#IDX172 1409 continue Behavior of continue sing_381.htm#SEC421 1410 continue sing_415.htm#SEC455 1411 contraHom sing_771.htm#SEC823 54270 1412 contract sing_220.htm#SEC260 1413 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2719.htm#IDX1062 1414 contributionBundle sing_2719.htm#SEC2795 32874 1415 contributors sing_358.htm#IDX200 1416 control sing_1825.htm#SEC1901 44498 1417 control.lib sing_1824.htm#SEC1900 1418 controlDim sing_1826.htm#SEC1902 2417 1419 controlExample sing_1838.htm#SEC1914 2678 1420 control_Matrix sing_1527.htm#SEC1603 sprintf 1421 control_lib sing_1824.htm#SEC1900 1422 convertLeftToRightFraction convertLeftToRightFraction sing_2652.htm#SEC2728 4318 1423 convertRightToLeftFraction convertRightToLeftFraction sing_2651.htm#SEC2727 19389 1424 convertdata sing_1401.htm#SEC1477 54629 1425 convexHull sing_2021.htm#SEC2097 56690 1426 convexIntersection sing_2022.htm#SEC2098 63587 1427 convloc sing_560.htm#SEC612 19122 1428 coordinate change sing_2181.htm#IDX856 1429 coordinate change sing_2182.htm#IDX857 1430 coordinate change sing_2183.htm#IDX858 1431 coordinates sing_1981.htm#IDX809 1432 coords sing_1981.htm#SEC2057 29362 1433 copyTask sing_1029.htm#SEC1105 65331 1336 1434 copyright sing_1.htm#IDX1 1337 corank sing_1472.htm#SEC1548 33709 1338 cornerMonomials sing_1268.htm#SEC1344 33995 1339 countPoints sing_1892.htm#SEC1968 58566 1340 coverings sing_1131.htm#IDX522 1341 coverings sing_1132.htm#IDX526 1342 cpu sing_350.htm#IDX202 1343 cpu sing_350.htm#IDX273 1344 createBO sing_1418.htm#SEC1494 32669 1345 createGradedRingHomomorphism createGradedRingHomomorphism sing_2449.htm#SEC2525 62177 1346 createGroup sing_2442.htm#SEC2518 28500 1347 createQuotientGroup sing_2443.htm#SEC2519 26374 1348 createTask sing_1015.htm#SEC1091 48404 1349 createTorsionFreeGroup createTorsionFreeGroup sing_2444.htm#SEC2520 51944 1350 createlist sing_1400.htm#SEC1476 61781 1351 crypto.lib sing_1865.htm#SEC1941 1352 crypto_lib sing_1865.htm#SEC1941 1353 cup sing_1145.htm#SEC1221 57972 1354 cupproduct sing_1146.htm#SEC1222 43349 1355 curve singularities sing_1451.htm#IDX614 1356 curve singularities sing_1539.htm#IDX736 1357 curve singularity sing_2314.htm#IDX914 1358 curveColengthDerivations curveColengthDerivations sing_2318.htm#SEC2394 2078 1359 curveConductorMult sing_2316.htm#SEC2392 15897 1360 curveDeligneNumber sing_2317.htm#SEC2393 12294 1361 curveDeltaInv sing_2315.htm#SEC2391 16375 1362 curveInv.lib sing_2314.htm#SEC2390 1363 curveInv_lib sing_2314.htm#SEC2390 1364 curvepar.lib sing_1492.htm#SEC1568 1365 curvepar_lib sing_1492.htm#SEC1568 1366 custom assignment Assignments for user defined types sing_182.htm#SEC222 1367 custom command Commands for user defined types sing_181.htm#SEC221 1368 custom type Definition of a user defined type sing_178.htm#SEC218 1369 customstd.lib sing_2202.htm#SEC2278 1370 customstd_lib sing_2202.htm#SEC2278 1371 cycleLength sing_2061.htm#SEC2137 16898 1372 cyclePoints sing_2065.htm#SEC2141 54460 1373 cyclic sing_940.htm#SEC1016 21375 1374 cyclic code Codes and the decoding problem sing_863.htm#SEC922 1375 cyclotomic sing_1626.htm#SEC1702 33749 1376 datetime sing_216.htm#SEC256 50127 1377 dbprint sing_217.htm#SEC257 1378 deRham.lib sing_2319.htm#SEC2395 1379 deRhamCohom sing_569.htm#SEC621 58222 1380 deRhamCohomIdeal sing_570.htm#SEC622 42169 1381 deRhamCohomology sing_2320.htm#SEC2396 41947 1382 deRham_lib sing_2319.htm#SEC2395 1383 debugLib, option sing_307.htm#IDX176 1384 debug_log sing_1482.htm#SEC1558 62043 1435 corank sing_1486.htm#SEC1562 33709 1436 cornerMonomials sing_1282.htm#SEC1358 33995 1437 countPoints sing_1906.htm#SEC1982 58566 1438 coverings sing_1143.htm#IDX537 1439 coverings sing_1144.htm#IDX541 1440 cpu sing_358.htm#IDX202 1441 cpu sing_358.htm#IDX275 1442 createBO sing_1432.htm#SEC1508 32669 1443 createGradedRingHomomorphism createGradedRingHomomorphism sing_2551.htm#SEC2627 62177 1444 createGroup sing_2544.htm#SEC2620 28500 1445 createQuotientGroup sing_2545.htm#SEC2621 26374 1446 createTask sing_1027.htm#SEC1103 48404 1447 createTorsionFreeGroup createTorsionFreeGroup sing_2546.htm#SEC2622 51944 1448 createlist sing_1414.htm#SEC1490 61781 1449 cring sing_73.htm#SEC113 1450 cring declarations sing_74.htm#SEC114 1451 cring expressions sing_75.htm#SEC115 1452 cring operations sing_76.htm#SEC116 1453 cring related functions cring related functions sing_77.htm#SEC117 1454 crossprod sing_221.htm#SEC261 1455 crypto.lib sing_1879.htm#SEC1955 1456 crypto_lib sing_1879.htm#SEC1955 1457 cup sing_1157.htm#SEC1233 57972 1458 cupproduct sing_1158.htm#SEC1234 43349 1459 curve singularities sing_1465.htm#IDX640 1460 curve singularities sing_1553.htm#IDX762 1461 curve singularity sing_2337.htm#IDX950 1462 curveColengthDerivations curveColengthDerivations sing_2341.htm#SEC2417 2078 1463 curveConductorMult sing_2339.htm#SEC2415 15897 1464 curveDeligneNumber sing_2340.htm#SEC2416 12294 1465 curveDeltaInv sing_2338.htm#SEC2414 16375 1466 curveInv.lib sing_2337.htm#SEC2413 1467 curveInv_lib sing_2337.htm#SEC2413 1468 curvepar.lib sing_1506.htm#SEC1582 1469 curvepar_lib sing_1506.htm#SEC1582 1470 custom assignment Assignments for user defined types sing_187.htm#SEC227 1471 custom command Commands for user defined types sing_186.htm#SEC226 1472 custom type Definition of a user defined type sing_183.htm#SEC223 1473 customstd.lib sing_2213.htm#SEC2289 1474 customstd_lib sing_2213.htm#SEC2289 1475 cycleLength sing_2072.htm#SEC2148 16898 1476 cyclePoints sing_2076.htm#SEC2152 54460 1477 cyclic sing_960.htm#SEC1036 21375 1478 cyclic code Codes and the decoding problem sing_883.htm#SEC942 1479 cyclotomic sing_1640.htm#SEC1716 33749 1480 datetime sing_222.htm#SEC262 50127 1481 dbprint sing_223.htm#SEC263 1482 deRham.lib sing_2342.htm#SEC2418 1483 deRhamCohom sing_577.htm#SEC629 58222 1484 deRhamCohomIdeal sing_578.htm#SEC630 42169 1485 deRhamCohomology sing_2343.htm#SEC2419 41947 1486 deRham_lib sing_2342.htm#SEC2418 1487 debugLib, option sing_315.htm#IDX176 1488 debug_log sing_1496.htm#SEC1572 62043 1385 1489 debugger Source code debugger sing_66.htm#SEC103 1386 1490 debugging library code Source code debugger sing_66.htm#SEC103 1387 dec1var sing_1198.htm#SEC1274 36098 1388 decimal sing_1866.htm#SEC1942 56066 1389 decode sing_1802.htm#SEC1878 64330 1390 decodeCode sing_1804.htm#SEC1880 28262 1391 decodeRandom sing_1803.htm#SEC1879 40118 1392 decodeRandomFL sing_1807.htm#SEC1883 35423 1393 decodeSV sing_1784.htm#SEC1860 37975 1394 decodegb.lib sing_1789.htm#SEC1865 1395 decodegb_lib sing_1789.htm#SEC1865 1396 decoding, decoding problem Codes and the decoding problem sing_863.htm#SEC923 1397 decoef sing_1832.htm#SEC1908 60284 1398 decone sing_2173.htm#IDX834 1399 decone sing_2174.htm#IDX836 1400 def sing_83.htm#SEC123 1401 def declarations sing_84.htm#SEC124 1402 defRes, option sing_307.htm#IDX177 1491 dec1var sing_1212.htm#SEC1288 36098 1492 decimal sing_1880.htm#SEC1956 56066 1493 decode sing_1816.htm#SEC1892 64330 1494 decodeCode sing_1818.htm#SEC1894 28262 1495 decodeRandom sing_1817.htm#SEC1893 40118 1496 decodeRandomFL sing_1821.htm#SEC1897 35423 1497 decodeSV sing_1798.htm#SEC1874 37975 1498 decodegb.lib sing_1803.htm#SEC1879 1499 decodegb_lib sing_1803.htm#SEC1879 1500 decoding, decoding problem Codes and the decoding problem sing_883.htm#SEC943 1501 decoef sing_1846.htm#SEC1922 60284 1502 decomposition of modules sing_1205.htm#IDX566 1503 decomposition, numerical sing_1352.htm#IDX595 1504 decone sing_2184.htm#IDX860 1505 decone sing_2185.htm#IDX862 1506 def sing_88.htm#SEC128 1507 def declarations sing_89.htm#SEC129 1508 defRes, option sing_315.htm#IDX177 1403 1509 default argument sing_44.htm#SEC81 1404 defineHomogeneous sing_2482.htm#SEC2558 55072 1405 defined sing_218.htm#SEC258 1406 defl sing_1349.htm#SEC1425 11825 1407 deform sing_1584.htm#SEC1660 5250 1408 deform.lib sing_1503.htm#SEC1579 1409 deform_lib sing_1503.htm#SEC1579 1410 defring sing_982.htm#SEC1058 1814 1411 defringp sing_984.htm#SEC1060 42905 1412 defrings sing_983.htm#SEC1059 1034 1413 deg sing_219.htm#SEC259 1414 degBound sing_387.htm#SEC427 1415 degree Miscellaneous oddities sing_220.htm#SEC260 1416 degree sing_410.htm#IDX290 1417 degree lexicographical ordering sing_838.htm#IDX393 1418 degree of a polynomial Miscellaneous oddities sing_410.htm#IDX294 1419 degree reverse lexicographical ordering sing_838.htm#IDX391 1420 degreeDivisor sing_2330.htm#SEC2406 31751 1421 degreeFormalDivisor sing_2338.htm#SEC2414 42503 1422 degreepart sing_1692.htm#SEC1768 53036 1423 delete sing_121.htm#SEC161 1424 delete sing_221.htm#SEC261 1425 delete sing_268.htm#SEC308 1426 deleteGenerator sing_584.htm#SEC636 24917 1427 deleteSublist sing_884.htm#SEC960 20406 1428 deligne number curveColengthDerivations sing_2314.htm#IDX916 1429 deligne number sing_2317.htm#IDX921 1430 deligne number sing_2318.htm#IDX923 1431 delta sing_1551.htm#SEC1627 56952 1432 delta invariant sing_1232.htm#IDX559 1433 delta invariant sing_1551.htm#IDX746 1434 delta invariant sing_2315.htm#IDX917 1435 delta invariant. sing_1224.htm#IDX552 1436 delta invariant. sing_1225.htm#IDX555 1437 delta invariant. sing_1226.htm#IDX558 1438 deltaLoc sing_1232.htm#SEC1308 35192 1439 denom_list sing_350.htm#IDX204 1440 denominator sing_222.htm#SEC262 1441 depth sing_1147.htm#SEC1223 17777 1442 depthIdeal sing_1208.htm#SEC1284 54782 1443 derivate sing_1658.htm#SEC1734 15409 1444 derivation sing_2187.htm#IDX857 1445 desingularization sing_2393.htm#IDX952 59041 1446 desingularization sing_2394.htm#SEC2470 1447 det sing_223.htm#SEC263 1448 det_B sing_1073.htm#SEC1149 60143 1449 detadj sing_1567.htm#SEC1643 5914 1450 determinacy sing_2500.htm#SEC2576 44818 1451 determinecenter sing_1372.htm#SEC1448 44496 1452 detropicalise sing_2142.htm#SEC2218 38025 1453 develop sing_1541.htm#SEC1617 48457 1454 diag sing_1033.htm#SEC1109 56759 1455 diagInvariants sing_1247.htm#SEC1323 62096 1456 diag_test sing_1069.htm#SEC1145 31469 1457 diff sing_224.htm#SEC264 1458 diffRat sing_783.htm#SEC835 36134 1459 difpoly2tex sing_1833.htm#SEC1909 6451 1460 dim sing_225.htm#SEC265 1461 dim (plural) sing_449.htm#SEC489 1462 dimGradedPart sing_1440.htm#SEC1516 11262 1463 dimH sing_1439.htm#SEC1515 38534 1464 dimMon sing_1188.htm#SEC1264 39971 1465 dimStack sing_2535.htm#SEC2611 47772 1466 dim_slocus sing_1585.htm#SEC1661 47218 1467 dimension sing_2009.htm#SEC2085 35262 1468 dimension, moduli space of stable maps, rational curves dimStack sing_2535.htm#IDX992 1469 dimensionOfLocalization dimensionOfLocalization sing_2381.htm#SEC2457 25632 1470 direct_boolean_poly sing_2215.htm#SEC2291 49893 1471 direct_from_boolean_poly direct_from_boolean_poly sing_2221.htm#SEC2297 36941 1472 disc sing_1853.htm#SEC1929 45279 1473 discr sing_1607.htm#SEC1683 9642 1474 discrepancy sing_1425.htm#SEC1501 5597 1475 discrim sing_919.htm#SEC995 21370 1476 discussion of parametric ideal sing_902.htm#IDX425 1477 disjoint sing_903.htm#IDX427 1478 disp_zdd sing_2228.htm#SEC2304 41439 1479 displayCohom sing_1441.htm#SEC1517 22633 1480 displayHNE sing_1544.htm#SEC1620 29845 1481 displayInvariants sing_1546.htm#SEC1622 13678 1482 displayMultsequence sing_1548.htm#SEC1624 16668 1483 displayPuiseuxExpansion displayPuiseuxExpansion sing_2117.htm#SEC2193 560 1484 displayTropicalLifting displayTropicalLifting sing_2115.htm#SEC2191 28144 1485 distributed computing sing_933.htm#IDX481 1486 distributed computing sing_973.htm#IDX483 1487 distributed computing sing_1014.htm#IDX496 1488 div Miscellaneous oddities sing_76.htm#SEC116 1489 div sing_93.htm#SEC133 1490 div sing_410.htm#IDX287 1491 divideUnits sing_1829.htm#SEC1905 26711 1492 dividelist sing_1399.htm#SEC1475 34210 1493 division sing_226.htm#SEC266 1494 division sing_904.htm#IDX430 1495 division sing_905.htm#IDX432 1496 division (plural) sing_450.htm#SEC490 1497 divisor sing_1932.htm#SEC2008 47231 1498 divisorplus sing_2324.htm#SEC2400 34248 1499 divisors negativeformaldivisor sing_2323.htm#IDX926 1500 divisors sing_2324.htm#IDX927 1501 divisors sing_2325.htm#IDX928 1502 divisors sing_2326.htm#IDX929 1503 divisors sing_2327.htm#IDX930 1504 divisors sing_2328.htm#IDX931 1505 divisors sing_2329.htm#IDX932 1506 divisors sing_2330.htm#IDX933 1507 divisors sing_2331.htm#IDX934 1508 divisors sing_2332.htm#IDX935 1509 divisors sing_2333.htm#IDX936 1510 divisors sing_2334.htm#IDX937 1511 divisors sing_2335.htm#IDX938 1512 divisors sing_2336.htm#IDX939 1513 divisors sing_2337.htm#IDX940 1514 divisors sing_2338.htm#IDX941 1515 divisors, polyhedra sing_2339.htm#IDX942 1516 divisors, polyhedra sing_2340.htm#IDX943 1517 divisors, polyhedra sing_2341.htm#IDX944 1518 divisors.lib sing_2322.htm#SEC2398 1519 divisors_lib sing_2322.htm#SEC2398 1520 dmod.lib sing_532.htm#SEC584 1521 dmodAction sing_778.htm#SEC830 9763 1522 dmodActionRat sing_779.htm#SEC831 6277 1523 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_771.htm#SEC823 44337 1524 dmod_lib sing_532.htm#SEC584 1525 dmodapp.lib sing_555.htm#SEC607 1526 dmodapp_lib sing_555.htm#SEC607 1527 dmodloc.lib sing_760.htm#IDX375 1528 dmodloc_lib sing_760.htm#IDX376 1529 dmodoublext sing_755.htm#SEC807 60637 1530 dmodvar.lib sing_588.htm#SEC640 1531 dmodvar_lib sing_588.htm#SEC640 1532 double sing_1937.htm#SEC2013 34697 1533 doubleExt sing_746.htm#SEC798 56896 1534 downloading Download instructions sing_2570.htm#SEC2660 1535 dp, global ordering sing_838.htm#IDX392 1536 drawNewtonSubdivision drawNewtonSubdivision sing_2120.htm#SEC2196 50904 1537 drawTropicalCurve sing_2119.htm#SEC2195 10441 1538 ds, local ordering sing_839.htm#IDX402 1539 dsum sing_1034.htm#SEC1110 1303 1540 dualCone sing_2010.htm#SEC2086 61460 1541 dualConic sing_2144.htm#SEC2220 31080 1542 dualPart sing_2285.htm#SEC2361 13279 1543 dualPartition sing_2548.htm#SEC2624 24739 1544 dualPolytope sing_2049.htm#SEC2125 32081 1545 dualSheaf sing_2526.htm#SEC2602 633 1546 dual_code sing_1786.htm#SEC1862 57229 1547 dump sing_227.htm#SEC267 1548 dynamic geometry sing_913.htm#IDX452 1549 dynamic geometry sing_914.htm#IDX455 1550 ecart sing_1940.htm#SEC2016 32475 1551 echo sing_388.htm#SEC428 1552 eexgcdN sing_1867.htm#SEC1943 53237 1553 effective sing_2332.htm#SEC2408 53028 1554 egcdMain sing_1733.htm#SEC1809 25359 1555 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2071.htm#SEC2147 38271 1556 ehrhartRing sing_1243.htm#SEC1319 16966 1557 eigenvals sing_1081.htm#SEC1157 11228 1558 eigenvalue sing_320.htm#SEC360 1559 eigenvalue sing_1081.htm#IDX502 1560 eigenvalues sing_1326.htm#SEC1402 2182 1561 elemSymmId sing_941.htm#SEC1017 sprintf 1562 elim sing_1118.htm#SEC1194 62585 1563 elim.lib sing_1115.htm#SEC1191 1564 elim1 sing_1119.htm#SEC1195 15653 1565 elim2 sing_1120.htm#SEC1196 44749 1566 elimRing sing_1117.htm#SEC1193 12194 1567 elimWeight sing_703.htm#SEC755 54297 1568 elim_lib sing_1115.htm#SEC1191 1569 eliminate sing_228.htm#SEC268 1570 eliminate (plural) sing_451.htm#SEC491 1571 eliminateNC sing_698.htm#SEC750 3777 1572 elimination sing_697.htm#IDX360 1573 elimlinearpart sing_1693.htm#SEC1769 14251 1574 elimpart sing_1694.htm#SEC1770 10258 1575 elimpartanyr sing_1695.htm#SEC1771 39751 1576 elimrep sing_1380.htm#SEC1456 23641 1577 elliptic curve sing_1128.htm#IDX518 1578 elliptic curves sing_1125.htm#IDX512 1579 elliptic curves sing_1131.htm#IDX521 1580 elliptic curves sing_1132.htm#IDX525 1581 ellipticAdd sing_1888.htm#SEC1964 13279 1582 ellipticAllPoints sing_1893.htm#SEC1969 60770 1583 ellipticMult sing_1889.htm#SEC1965 1558 1584 ellipticNF sing_2068.htm#SEC2144 5045 1585 ellipticNFDB sing_2069.htm#SEC2145 27917 1586 ellipticRandomCurve sing_1890.htm#SEC1966 36980 1587 ellipticRandomPoint sing_1891.htm#SEC1967 6866 1588 ellipticcovers.lib sing_1125.htm#IDX506 1589 ellipticcovers_lib sing_1125.htm#IDX507 1590 else sing_378.htm#SEC418 1591 embedMat sing_729.htm#SEC781 17119 1592 emptyFan sing_2037.htm#SEC2113 7396 1593 encode sing_1794.htm#SEC1870 56687 1594 endomorphism filtration sing_1525.htm#IDX712 1595 endvfilt sing_1525.htm#SEC1601 26670 1596 engine sing_585.htm#SEC637 30876 1597 envelop FamElemsAtEnvCompPoints sing_915.htm#SEC991 9501 1598 envelop sing_915.htm#IDX458 1599 envelop sing_916.htm#IDX461 1600 envelop sing_917.htm#IDX465 1601 envelop sing_918.htm#IDX469 1602 envelope sing_452.htm#SEC492 1603 enveloping algebra sing_350.htm#IDX208 1604 enveloping algebra sing_490.htm#IDX304 1510 defineHomogeneous sing_2584.htm#SEC2660 55072 1511 defined sing_224.htm#SEC264 1512 defl sing_1363.htm#SEC1439 11825 1513 deform sing_1598.htm#SEC1674 5250 1514 deform.lib sing_1517.htm#SEC1593 1515 deform_lib sing_1517.htm#SEC1593 1516 defring sing_1002.htm#SEC1078 1814 1517 defringp sing_1004.htm#SEC1080 42905 1518 defrings sing_1003.htm#SEC1079 1034 1519 deg sing_225.htm#SEC265 1520 degBound sing_395.htm#SEC435 1521 degree Miscellaneous oddities sing_226.htm#SEC266 1522 degree sing_418.htm#IDX292 1523 degree lexicographical ordering sing_857.htm#IDX395 1524 degree of a polynomial Miscellaneous oddities sing_418.htm#IDX296 1525 degree reverse lexicographical ordering sing_857.htm#IDX393 1526 degreeDivisor sing_2353.htm#SEC2429 31751 1527 degreeFormalDivisor sing_2361.htm#SEC2437 42503 1528 degreepart sing_1706.htm#SEC1782 53036 1529 delete sing_126.htm#SEC166 1530 delete sing_227.htm#SEC267 1531 delete sing_276.htm#SEC316 1532 deleteGenerator sing_592.htm#SEC644 24917 1533 deleteSublist sing_904.htm#SEC980 20406 1534 deligne number curveColengthDerivations sing_2337.htm#IDX952 1535 deligne number sing_2340.htm#IDX957 1536 deligne number sing_2341.htm#IDX959 1537 delta sing_1565.htm#SEC1641 56952 1538 delta invariant sing_1246.htm#IDX576 1539 delta invariant sing_1565.htm#IDX772 1540 delta invariant sing_2338.htm#IDX953 1541 delta invariant. sing_1238.htm#IDX569 1542 delta invariant. sing_1239.htm#IDX572 1543 delta invariant. sing_1240.htm#IDX575 1544 deltaLoc sing_1246.htm#SEC1322 35192 1545 denom_list sing_358.htm#IDX204 1546 denominator sing_228.htm#SEC268 1547 depth sing_1159.htm#SEC1235 17777 1548 depthIdeal sing_1222.htm#SEC1298 54782 1549 derivate sing_1672.htm#SEC1748 15409 1550 derivation sing_2198.htm#IDX883 1551 desingularization sing_2442.htm#IDX988 59041 1552 desingularization sing_2443.htm#SEC2519 1553 det sing_229.htm#SEC269 1554 det_B sing_1085.htm#SEC1161 60143 1555 detadj sing_1581.htm#SEC1657 5914 1556 determinacy sing_2668.htm#SEC2744 44818 1557 determinecenter sing_1386.htm#SEC1462 44496 1558 detropicalise sing_2153.htm#SEC2229 38025 1559 develop sing_1555.htm#SEC1631 48457 1560 diag sing_1045.htm#SEC1121 56759 1561 diagInvariants sing_1261.htm#SEC1337 62096 1562 diag_test sing_1081.htm#SEC1157 31469 1563 diff sing_230.htm#SEC270 1564 diffRat sing_800.htm#SEC852 36134 1565 difpoly2tex sing_1847.htm#SEC1923 6451 1566 dim sing_231.htm#SEC271 1567 dim (plural) sing_457.htm#SEC497 1568 dimGradedPart sing_1454.htm#SEC1530 11262 1569 dimH sing_1453.htm#SEC1529 38534 1570 dimMon sing_1202.htm#SEC1278 39971 1571 dimStack sing_2717.htm#SEC2793 47772 1572 dim_slocus sing_1599.htm#SEC1675 47218 1573 dimension sing_2023.htm#SEC2099 35262 1574 dimension, moduli space of stable maps, rational curves dimStack sing_2717.htm#IDX1060 1575 dimensionOfLocalization dimensionOfLocalization sing_2406.htm#SEC2482 25632 1576 direct_boolean_poly sing_2226.htm#SEC2302 49893 1577 direct_from_boolean_poly direct_from_boolean_poly sing_2232.htm#SEC2308 36941 1578 disc sing_1867.htm#SEC1943 45279 1579 discr sing_1621.htm#SEC1697 9642 1580 discrepancy sing_1439.htm#SEC1515 5597 1581 discrim sing_939.htm#SEC1015 44091 1582 discussion of parametric ideal sing_921.htm#IDX434 1583 discussion of parametric ideal sing_929.htm#IDX460 1584 disjoint sing_922.htm#IDX436 1585 disp_zdd sing_2239.htm#SEC2315 41439 1586 displayCohom sing_1455.htm#SEC1531 22633 1587 displayHNE sing_1558.htm#SEC1634 29845 1588 displayInvariants sing_1560.htm#SEC1636 13678 1589 displayMultsequence sing_1562.htm#SEC1638 16668 1590 displayPuiseuxExpansion displayPuiseuxExpansion sing_2128.htm#SEC2204 560 1591 displayTropicalLifting displayTropicalLifting sing_2126.htm#SEC2202 28144 1592 distributed computing sing_953.htm#IDX499 1593 distributed computing sing_993.htm#IDX501 1594 distributed computing sing_1026.htm#IDX511 1595 div Miscellaneous oddities sing_81.htm#SEC121 1596 div sing_98.htm#SEC138 1597 div sing_155.htm#SEC195 1598 div sing_418.htm#IDX289 1599 divideUnits sing_1843.htm#SEC1919 26711 1600 dividelist sing_1413.htm#SEC1489 34210 1601 division sing_232.htm#SEC272 1602 division sing_923.htm#IDX439 1603 division sing_924.htm#IDX441 1604 division (plural) sing_458.htm#SEC498 1605 divisor sing_1946.htm#SEC2022 47231 1606 divisorplus sing_2347.htm#SEC2423 34248 1607 divisors negativeformaldivisor sing_2346.htm#IDX962 1608 divisors sing_2347.htm#IDX963 1609 divisors sing_2348.htm#IDX964 1610 divisors sing_2349.htm#IDX965 1611 divisors sing_2350.htm#IDX966 1612 divisors sing_2351.htm#IDX967 1613 divisors sing_2352.htm#IDX968 1614 divisors sing_2353.htm#IDX969 1615 divisors sing_2354.htm#IDX970 1616 divisors sing_2355.htm#IDX971 1617 divisors sing_2356.htm#IDX972 1618 divisors sing_2357.htm#IDX973 1619 divisors sing_2358.htm#IDX974 1620 divisors sing_2359.htm#IDX975 1621 divisors sing_2360.htm#IDX976 1622 divisors sing_2361.htm#IDX977 1623 divisors, polyhedra sing_2362.htm#IDX978 1624 divisors, polyhedra sing_2363.htm#IDX979 1625 divisors, polyhedra sing_2364.htm#IDX980 1626 divisors.lib sing_2345.htm#SEC2421 1627 divisors_lib sing_2345.htm#SEC2421 1628 dmod.lib sing_540.htm#SEC592 1629 dmodAction sing_795.htm#SEC847 9763 1630 dmodActionRat sing_796.htm#SEC848 6277 1631 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_788.htm#SEC840 44337 1632 dmod_lib sing_540.htm#SEC592 1633 dmodapp.lib sing_563.htm#SEC615 1634 dmodapp_lib sing_563.htm#SEC615 1635 dmodloc.lib sing_777.htm#IDX377 1636 dmodloc_lib sing_777.htm#IDX378 1637 dmodoublext sing_772.htm#SEC824 60637 1638 dmodvar.lib sing_596.htm#SEC648 1639 dmodvar_lib sing_596.htm#SEC648 1640 double sing_1951.htm#SEC2027 34697 1641 doubleExt sing_763.htm#SEC815 56896 1642 downloading Download instructions sing_2752.htm#SEC2841 1643 dp, global ordering sing_857.htm#IDX394 1644 drawNewtonSubdivision drawNewtonSubdivision sing_2131.htm#SEC2207 50904 1645 drawTropicalCurve sing_2130.htm#SEC2206 10441 1646 ds, local ordering sing_858.htm#IDX404 1647 dsum sing_1046.htm#SEC1122 1303 1648 dualCone sing_2024.htm#SEC2100 61460 1649 dualConic sing_2155.htm#SEC2231 31080 1650 dualPart sing_2303.htm#SEC2379 13279 1651 dualPartition sing_2730.htm#SEC2806 24739 1652 dualPolytope sing_2063.htm#SEC2139 32081 1653 dualSheaf sing_2708.htm#SEC2784 633 1654 dual_code sing_1800.htm#SEC1876 57229 1655 dump sing_233.htm#SEC273 1656 dynamic geometry sing_932.htm#IDX469 1657 dynamic geometry sing_933.htm#IDX472 1658 ecart sing_1954.htm#SEC2030 32475 1659 echo sing_396.htm#SEC436 1660 eexgcdN sing_1881.htm#SEC1957 53237 1661 effective sing_2355.htm#SEC2431 53028 1662 egcdMain sing_1747.htm#SEC1823 25359 1663 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2082.htm#SEC2158 38271 1664 ehrhartRing sing_1257.htm#SEC1333 16966 1665 eigenvals sing_1093.htm#SEC1169 11228 1666 eigenvalue sing_328.htm#SEC368 1667 eigenvalue sing_1093.htm#IDX517 1668 eigenvalues sing_1340.htm#SEC1416 2182 1669 elemSymmId sing_961.htm#SEC1037 sprintf 1670 elim sing_1130.htm#SEC1206 62585 1671 elim.lib sing_1127.htm#SEC1203 1672 elim1 sing_1131.htm#SEC1207 15653 1673 elim2 sing_1132.htm#SEC1208 44749 1674 elimRing sing_1129.htm#SEC1205 12194 1675 elimWeight sing_720.htm#SEC772 54297 1676 elim_lib sing_1127.htm#SEC1203 1677 eliminate sing_234.htm#SEC274 1678 eliminate (plural) sing_459.htm#SEC499 1679 eliminateNC sing_715.htm#SEC767 3777 1680 elimination sing_714.htm#IDX362 1681 elimlinearpart sing_1707.htm#SEC1783 14251 1682 elimpart sing_1708.htm#SEC1784 10258 1683 elimpartanyr sing_1709.htm#SEC1785 39751 1684 elimrep sing_1394.htm#SEC1470 23641 1685 elliptic curve sing_1140.htm#IDX533 1686 elliptic curves sing_1137.htm#IDX527 1687 elliptic curves sing_1143.htm#IDX536 1688 elliptic curves sing_1144.htm#IDX540 1689 ellipticAdd sing_1902.htm#SEC1978 13279 1690 ellipticAllPoints sing_1907.htm#SEC1983 60770 1691 ellipticMult sing_1903.htm#SEC1979 1558 1692 ellipticNF sing_2079.htm#SEC2155 5045 1693 ellipticNFDB sing_2080.htm#SEC2156 27917 1694 ellipticRandomCurve sing_1904.htm#SEC1980 36980 1695 ellipticRandomPoint sing_1905.htm#SEC1981 6866 1696 ellipticcovers.lib sing_1137.htm#IDX521 1697 ellipticcovers_lib sing_1137.htm#IDX522 1698 else sing_386.htm#SEC426 1699 embedMat sing_746.htm#SEC798 17119 1700 emptyFan sing_2051.htm#SEC2127 7396 1701 encode sing_1808.htm#SEC1884 56687 1702 endomorphism filtration sing_1539.htm#IDX738 1703 endvfilt sing_1539.htm#SEC1615 26670 1704 engine sing_593.htm#SEC645 30876 1705 ensureLeftNcfrac sing_2601.htm#SEC2677 64571 1706 ensureRightNcfrac sing_2602.htm#SEC2678 14107 1707 envelop FamElemsAtEnvCompPoints sing_934.htm#SEC1010 27362 1708 envelop sing_934.htm#IDX475 1709 envelop sing_935.htm#IDX478 1710 envelop sing_937.htm#IDX483 1711 envelop sing_938.htm#IDX487 1712 envelope sing_460.htm#SEC500 1713 enveloping algebra sing_358.htm#IDX208 1714 enveloping algebra sing_498.htm#IDX306 1605 1715 environment variable, DISPLAY The online help system sing_16.htm#IDX29 1606 equalJinI sing_14 68.htm#SEC1544185021607 equalMultiDeg sing_2 475.htm#SEC2551370901608 equations sing_20 11.htm#SEC208778961609 equiRadical sing_12 84.htm#SEC136088841610 equidim sing_1 286.htm#SEC1362385411611 equidimMax sing_1 287.htm#SEC1363492891612 equidimMaxEHV sing_1 288.htm#SEC1364426501613 equidimZ sing_1 299.htm#SEC1375496101614 equising.lib sing_15 08.htm#SEC15841615 equising_lib sing_15 08.htm#SEC15841616 equisingular Tjurina number sing_14 51.htm#IDX6191617 equisingularity ideal sing_15 10.htm#IDX6391618 equisingularity stratum sing_15 11.htm#IDX6401716 equalJinI sing_1482.htm#SEC1558 18502 1717 equalMultiDeg sing_2577.htm#SEC2653 37090 1718 equations sing_2025.htm#SEC2101 7896 1719 equiRadical sing_1298.htm#SEC1374 8884 1720 equidim sing_1300.htm#SEC1376 38541 1721 equidimMax sing_1301.htm#SEC1377 49289 1722 equidimMaxEHV sing_1302.htm#SEC1378 42650 1723 equidimZ sing_1313.htm#SEC1389 49610 1724 equising.lib sing_1522.htm#SEC1598 1725 equising_lib sing_1522.htm#SEC1598 1726 equisingular Tjurina number sing_1465.htm#IDX645 1727 equisingularity ideal sing_1524.htm#IDX665 1728 equisingularity stratum sing_1525.htm#IDX666 1619 1729 error recovery sing_15.htm#SEC21 1620 errorInsert sing_1797.htm#SEC1873 59470 1621 errorRand sing_1798.htm#SEC1874 5727 1622 errormap sing_2362.htm#SEC2438 7782 1623 esIdeal sing_1510.htm#SEC1586 60477 1624 esStratum sing_1511.htm#SEC1587 50094 1625 essential sing_2177.htm#IDX839 1626 essential sing_2178.htm#IDX840 1627 eta sing_2063.htm#SEC2139 60729 1628 euler sing_1846.htm#SEC1922 10519 1629 eulerChProj sing_2275.htm#SEC2351 28549 1630 eval sing_229.htm#SEC269 1631 evaluateFormalDivisor evaluateFormalDivisor sing_2334.htm#SEC2410 3535 1632 evaluatePDivisor sing_2340.htm#SEC2416 18855 1633 evaluate_reynolds sing_1631.htm#SEC1707 46353 1634 evalutateIntegral sing_1130.htm#SEC1206 sprintf 1635 example sing_231.htm#SEC271 1636 example sing_2179.htm#IDX841 1637 example sing_2180.htm#IDX843 1638 example sing_2181.htm#IDX845 1639 example sing_2182.htm#IDX847 1640 example sing_2183.htm#IDX849 1641 example sing_2184.htm#IDX851 1642 example sing_2185.htm#IDX854 1643 execute sing_232.htm#SEC272 1644 exit sing_382.htm#SEC422 1645 exp2pt sing_1834.htm#SEC1910 19621 1646 expo sing_1858.htm#SEC1934 8833 1647 exponents sing_2189.htm#IDX862 1648 export sing_375.htm#SEC415 1649 exportNuminvs sing_1251.htm#SEC1327 10423 1650 exportto sing_376.htm#SEC416 1651 expp sing_2546.htm#SEC2622 15751 1730 errorInsert sing_1811.htm#SEC1887 59470 1731 errorRand sing_1812.htm#SEC1888 5727 1732 errormap sing_2385.htm#SEC2461 7782 1733 esIdeal sing_1524.htm#SEC1600 60477 1734 esStratum sing_1525.htm#SEC1601 50094 1735 essential sing_2188.htm#IDX865 1736 essential sing_2189.htm#IDX866 1737 eta sing_2074.htm#SEC2150 60729 1738 euler sing_1860.htm#SEC1936 10519 1739 eulerChProj sing_2293.htm#SEC2369 28549 1740 eval sing_235.htm#SEC275 1741 evalJacobianAtBox sing_2679.htm#SEC2755 42716 1742 evalPolyAtBox sing_2678.htm#SEC2754 43040 1743 evaluateFormalDivisor evaluateFormalDivisor sing_2357.htm#SEC2433 3535 1744 evaluatePDivisor sing_2363.htm#SEC2439 18855 1745 evaluateProduct sing_2433.htm#SEC2509 54515 1746 evaluate_reynolds sing_1645.htm#SEC1721 46353 1747 evalutateIntegral sing_1142.htm#SEC1218 sprintf 1748 example sing_237.htm#SEC277 1749 example sing_2190.htm#IDX867 1750 example sing_2191.htm#IDX869 1751 example sing_2192.htm#IDX871 1752 example sing_2193.htm#IDX873 1753 example sing_2194.htm#IDX875 1754 example sing_2195.htm#IDX877 1755 example sing_2196.htm#IDX880 1756 execute sing_238.htm#SEC278 1757 exit sing_390.htm#SEC430 1758 exp2pt sing_1848.htm#SEC1924 19621 1759 expo sing_1872.htm#SEC1948 8833 1760 exponents sing_2200.htm#IDX888 1761 export sing_383.htm#SEC423 1762 exportNuminvs sing_1265.htm#SEC1341 10423 1763 exportto sing_384.htm#SEC424 1764 expp sing_2728.htm#SEC2804 15751 1652 1765 expression list sing_72.htm#IDX128 1653 expression list sing_4 14.htm#IDX2971654 ext-module purityfiltration_lib sing_7 38.htm#IDX3661655 extcurve sing_17 80.htm#SEC185667301656 extdevelop sing_15 42.htm#SEC1618510441657 extendGC sing_9 10.htm#SEC986 191351658 extendWeyl sing_7 72.htm#SEC824499541659 extendedTensor sing_7 04.htm#SEC75649751660 extendpoly sing_9 09.htm#SEC985 291131661 extendring sing_ 985.htm#SEC1061 647811662 extension of rings sing_13 04.htm#IDX5681663 exterior basis sing_10 60.htm#IDX4991664 exterior power sing_10 62.htm#IDX5011665 exteriorBasis sing_10 60.htm#SEC1136sprintf1666 exteriorPower sing_10 62.htm#SEC1138201731667 extgcd sing_23 3.htm#SEC2731668 fVector sing_20 40.htm#SEC211637151669 fVectorP sing_20 72.htm#SEC2148318431670 facFirstShift sing_ 691.htm#SEC74364691671 facFirstWeyl sing_ 687.htm#SEC739424121672 facGBIdeal sing_12 69.htm#SEC134599241673 facShift sing_ 690.htm#SEC742212531674 facSubWeyl sing_ 689.htm#SEC74196301675 facWeyl sing_ 686.htm#SEC738323311676 faceContaining sing_20 12.htm#SEC2088648041677 facetVertexLatticeDistances facetVertexLatticeDistances sing_20 73.htm#SEC2149607141678 facetWidth sing_20 74.htm#SEC2150628101679 facetWidths sing_20 75.htm#SEC215155031680 facets sing_20 13.htm#SEC208981121681 facstd sing_2 34.htm#SEC2741682 factmodd sing_2 35.htm#SEC2751683 factor sing_3 14.htm#SEC3541684 factorH sing_ 899.htm#SEC975 248141685 factorLenstraECM sing_1 897.htm#SEC1973549511686 factorMain sing_17 34.htm#SEC1810651521687 factorgroup sing_2 465.htm#SEC2541599141688 factorial sing_ 885.htm#SEC961 328711689 factorization sing_3 15.htm#SEC3551690 factorization sing_1 090.htm#IDX5031691 factorize sing_2 36.htm#SEC2761692 factorize sing_3 14.htm#SEC3541766 expression list sing_422.htm#IDX299 1767 ext-module purityfiltration_lib sing_755.htm#IDX368 1768 extcurve sing_1794.htm#SEC1870 6730 1769 extdevelop sing_1556.htm#SEC1632 51044 1770 extendGC sing_929.htm#SEC1005 25229 1771 extendWeyl sing_789.htm#SEC841 49954 1772 extendedTensor sing_721.htm#SEC773 4975 1773 extendpoly sing_928.htm#SEC1004 29201 1774 extendring sing_1005.htm#SEC1081 64781 1775 extension of rings sing_1318.htm#IDX587 1776 exterior basis sing_1072.htm#IDX514 1777 exterior power sing_1074.htm#IDX516 1778 exteriorBasis sing_1072.htm#SEC1148 sprintf 1779 exteriorPower sing_1074.htm#SEC1150 20173 1780 extgcd sing_239.htm#SEC279 1781 fVector sing_2054.htm#SEC2130 3715 1782 fVectorP sing_2083.htm#SEC2159 31843 1783 facFirstShift sing_708.htm#SEC760 6469 1784 facFirstWeyl sing_704.htm#SEC756 42412 1785 facGBIdeal sing_1283.htm#SEC1359 9924 1786 facShift sing_707.htm#SEC759 21253 1787 facSubWeyl sing_706.htm#SEC758 9630 1788 facWeyl sing_703.htm#SEC755 32331 1789 faceContaining sing_2026.htm#SEC2102 64804 1790 facetVertexLatticeDistances facetVertexLatticeDistances sing_2084.htm#SEC2160 60714 1791 facetWidth sing_2085.htm#SEC2161 62810 1792 facetWidths sing_2086.htm#SEC2162 5503 1793 facets sing_2027.htm#SEC2103 8112 1794 facstd sing_240.htm#SEC280 1795 factmodd sing_241.htm#SEC281 1796 factor sing_322.htm#SEC362 1797 factorH sing_919.htm#SEC995 24814 1798 factorLenstraECM sing_1911.htm#SEC1987 54951 1799 factorMain sing_1748.htm#SEC1824 65152 1800 factorgroup sing_2567.htm#SEC2643 59914 1801 factorial sing_905.htm#SEC981 32871 1802 factorization sing_323.htm#SEC363 1803 factorization sing_1102.htm#IDX518 1804 factorize sing_242.htm#SEC282 1805 factorize sing_322.htm#SEC362 1693 1806 factory sing_1.htm#IDX2 1694 fan sing_18 4.htm#SEC2241695 fan sing_20 52.htm#IDX7881696 fanViaCones sing_20 38.htm#SEC2114164181697 farey sing_2 37.htm#SEC2771698 fareypoly sing_23 43.htm#SEC2419123891699 fastExpt sing_18 42.htm#SEC1918439121700 fastHC, option sing_3 07.htm#IDX1531701 fastelim sing_1 696.htm#SEC177274091702 fetch sing_2 38.htm#SEC2781703 fetch (plural) sing_4 53.htm#SEC4931704 fetchall sing_ 986.htm#SEC1062 75371705 ffmodStd sing_23 47.htm#SEC2423506801706 ffmodstd.lib sing_23 42.htm#SEC24181707 ffmodstd_lib sing_23 42.htm#SEC24181708 ffsolve sing_16 85.htm#SEC1761204321709 ffsolve.lib sing_16 84.htm#SEC17601710 ffsolve_lib sing_16 84.htm#SEC17601711 fglm sing_2 39.htm#SEC2791712 fglm sing_3 47.htm#IDX1871713 fglm_solve sing_17 12.htm#SEC1788513981714 fglmquot sing_24 0.htm#SEC2801715 fibonacci sing_ 886.htm#SEC962 247501716 field sing_1 39.htm#SEC1791807 fan sing_189.htm#SEC229 1808 fan sing_2066.htm#IDX814 1809 fanViaCones sing_2052.htm#SEC2128 16418 1810 farey sing_243.htm#SEC283 1811 fareypoly sing_2366.htm#SEC2442 12389 1812 fastExpt sing_1856.htm#SEC1932 43912 1813 fastHC, option sing_315.htm#IDX153 1814 fastelim sing_1710.htm#SEC1786 7409 1815 fetch sing_244.htm#SEC284 1816 fetch (plural) sing_461.htm#SEC501 1817 fetchall sing_1006.htm#SEC1082 7537 1818 ffmodStd sing_2370.htm#SEC2446 50680 1819 ffmodstd.lib sing_2365.htm#SEC2441 1820 ffmodstd_lib sing_2365.htm#SEC2441 1821 ffsolve sing_1699.htm#SEC1775 20432 1822 ffsolve.lib sing_1698.htm#SEC1774 1823 ffsolve_lib sing_1698.htm#SEC1774 1824 fglm sing_245.htm#SEC285 1825 fglm sing_355.htm#IDX187 1826 fglm_solve sing_1726.htm#SEC1802 51398 1827 fglmquot sing_246.htm#SEC286 1828 fibonacci sing_906.htm#SEC982 24750 1829 field sing_144.htm#SEC184 1717 1830 file, .singularrc sing_20.htm#IDX71 1718 filecmd sing_241.htm#SEC281 1719 filtration purityfiltration_lib sing_738.htm#IDX367 1720 finalCharts sing_1404.htm#SEC1480 37296 1721 find sing_242.htm#SEC282 1722 findAuto sing_645.htm#SEC697 51205 1723 findInvo sing_643.htm#SEC695 18177 1724 findInvoDiag sing_644.htm#SEC696 7365 1725 findOrientedBoundary findOrientedBoundary sing_2064.htm#SEC2140 24110 1726 findTorsion sing_1823.htm#SEC1899 29572 1727 find_first_primitive_root find_first_primitive_root sing_1901.htm#SEC1977 33327 1728 find_index sing_1905.htm#SEC1981 62564 1729 findifs.lib sing_1830.htm#SEC1906 1730 findifs_example sing_1831.htm#SEC1907 33849 1731 findifs_lib sing_1830.htm#SEC1906 1732 findimAlgebra sing_713.htm#SEC765 64612 1733 finduni sing_243.htm#SEC283 1734 findvars sing_1697.htm#SEC1773 54503 1735 finite field sing_139.htm#SEC179 1736 finite field sing_1684.htm#IDX761 1737 finiteDiagInvariants finiteDiagInvariants sing_1246.htm#SEC1322 3508 1738 finitediff.lib sing_2348.htm#IDX945 1739 finitediff_lib sing_2348.htm#IDX946 1740 finitenessTest sing_1104.htm#SEC1180 40633 1741 finvar.lib sing_1619.htm#SEC1695 1742 finvar_lib sing_1619.htm#SEC1695 1743 first index is 1 sing_409.htm#SEC449 1744 firstoct sing_1745.htm#SEC1821 11498 1745 fitting sing_1150.htm#SEC1226 20661 1746 fixed points, moduli space of stable maps, graph fixedPoints sing_2536.htm#IDX993 1747 fixedPoints sing_2536.htm#SEC2612 25366 1748 fl2poly sing_582.htm#SEC634 51682 1749 flatten sing_1035.htm#SEC1111 55617 1750 flatteningStrat sing_1151.htm#SEC1227 15622 1751 floating point sing_995.htm#IDX486 1752 for sing_377.htm#SEC417 1753 formaldivisorplus sing_2335.htm#SEC2411 31959 1754 forward sing_2354.htm#SEC2430 15383 1755 fourier sing_577.htm#SEC629 5326 1756 fouriersystem sing_2365.htm#SEC2441 43681 1757 fpadim.lib sing_593.htm#SEC645 1758 fpadim_lib sing_593.htm#SEC645 1759 fprintf sing_244.htm#SEC284 13662 1760 frandwalk sing_2509.htm#SEC2585 25555 1761 free sing_2188.htm#IDX859 1762 free sing_2189.htm#IDX861 1763 free associative algebra, tensor algebra Free associative algebras sing_484.htm#SEC536 1764 freeGBasis sing_628.htm#SEC680 43055 1765 freegb.lib sing_624.htm#SEC676 1766 freegb_lib sing_624.htm#SEC676 1767 freemodule sing_245.htm#SEC285 1768 freerank sing_943.htm#SEC1019 52218 1769 from_boolean_constant from_boolean_constant sing_2219.htm#SEC2295 44881 1770 from_boolean_ideal sing_2223.htm#SEC2299 62698 1771 from_boolean_poly sing_2220.htm#SEC2296 27864 1772 from_boolean_set sing_2224.htm#SEC2300 60615 1773 frwalk sing_246.htm#SEC286 1774 full representation sing_909.htm#IDX440 1775 full representation sing_910.htm#IDX444 1776 fullFan sing_2039.htm#SEC2115 7534 1777 fullSerreRelations sing_639.htm#SEC691 27691 1778 fullSpace sing_1994.htm#SEC2070 19485 1779 furtherInvar sing_1663.htm#SEC1739 19209 1780 further_hn_proc sing_1559.htm#SEC1635 63500 1781 fwalk sing_1137.htm#SEC1213 15070 1782 galois field sing_139.htm#SEC179 1783 gauss_col sing_1045.htm#SEC1121 36252 1784 gauss_nf sing_1076.htm#SEC1152 51060 1785 gauss_row sing_1046.htm#SEC1122 58877 1786 gaussred sing_1074.htm#SEC1150 29001 1787 gaussred_pivot sing_1075.htm#SEC1151 25477 1788 gcd sing_247.htm#SEC287 1789 gcdMon sing_1177.htm#SEC1253 42448 1790 gcddivisor sing_1933.htm#SEC2009 1276 1791 gen sing_248.htm#SEC288 1792 genMDSMat sing_1800.htm#SEC1876 3347 1793 genSymId sing_1323.htm#SEC1399 17521 1794 general error-locator polynomial sing_864.htm#SEC929 1795 general neron. sing_2393.htm#IDX953 1796 general weighted lexicographical ordering sing_839.htm#IDX408 1797 general weighted reverse lexicographical ordering Local orderings sing_839.htm#IDX405 1798 general.lib sing_879.htm#SEC955 1799 generalOrder sing_1958.htm#SEC2034 42536 1800 general_lib sing_879.htm#SEC955 1801 generateG sing_1896.htm#SEC1972 51697 1802 generators sing_1459.htm#IDX623 1803 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2014.htm#SEC2090 4454 1804 generatorsOfSpan sing_2015.htm#SEC2091 40297 1805 generic representation sing_909.htm#IDX439 1806 genericid sing_961.htm#SEC1037 29731 1807 genericity sing_1820.htm#SEC1896 16822 1808 genericmat sing_1036.htm#SEC1112 35016 1809 genoutput sing_1393.htm#SEC1469 18973 1810 genus sing_1228.htm#SEC1304 sprintf 1811 geometric invariant theory sing_2386.htm#IDX950 1812 geometrical locus FamElemsAtEnvCompPoints sing_913.htm#IDX450 1813 geometrical locus sing_914.htm#IDX453 1814 geometrical locus sing_915.htm#IDX456 1815 geometrical locus sing_916.htm#IDX459 1816 geometrical locus sing_917.htm#IDX463 1817 geometrical locus sing_918.htm#IDX467 1818 getArguments sing_1026.htm#SEC1102 14254 1819 getCommand sing_1025.htm#SEC1101 32181 1820 getCone sing_2041.htm#SEC2117 41394 1821 getGradingGroup sing_2440.htm#SEC2516 18137 1822 getLattice sing_2441.htm#SEC2517 7775 1823 getLinearForms sing_2016.htm#SEC2092 47590 1824 getModuleGrading sing_2451.htm#SEC2527 43451 1825 getMultiplicity sing_2017.htm#SEC2093 639 1826 getOneVar sing_1236.htm#SEC1312 55402 1827 getResult sing_1027.htm#SEC1103 51722 1828 getSmallest sing_1235.htm#SEC1311 1623 1829 getState sing_1028.htm#SEC1104 36453 1830 getVariableWeights sing_2439.htm#SEC2515 9591 1831 getcores sing_976.htm#SEC1052 30785 1832 getdump sing_249.htm#SEC289 1833 getenv sing_350.htm#IDX211 1834 gfan.lib sing_1993.htm#SEC2069 1835 gfan_lib sing_1993.htm#SEC2069 1831 filecmd sing_247.htm#SEC287 1832 filtration purityfiltration_lib sing_755.htm#IDX369 1833 finalCharts sing_1418.htm#SEC1494 37296 1834 find sing_248.htm#SEC288 1835 findAuto sing_662.htm#SEC714 51205 1836 findInvo sing_660.htm#SEC712 18177 1837 findInvoDiag sing_661.htm#SEC713 7365 1838 findOrientedBoundary findOrientedBoundary sing_2075.htm#SEC2151 24110 1839 findTorsion sing_1837.htm#SEC1913 29572 1840 find_first_primitive_root find_first_primitive_root sing_1915.htm#SEC1991 33327 1841 find_index sing_1919.htm#SEC1995 62564 1842 findifs.lib sing_1844.htm#SEC1920 1843 findifs_example sing_1845.htm#SEC1921 33849 1844 findifs_lib sing_1844.htm#SEC1920 1845 findimAlgebra sing_730.htm#SEC782 64612 1846 finduni sing_249.htm#SEC289 1847 findvars sing_1711.htm#SEC1787 54503 1848 finite field sing_144.htm#SEC184 1849 finite field sing_1698.htm#IDX787 1850 finiteDiagInvariants finiteDiagInvariants sing_1260.htm#SEC1336 3508 1851 finitediff.lib sing_2371.htm#IDX981 1852 finitediff_lib sing_2371.htm#IDX982 1853 finitenessTest sing_1116.htm#SEC1192 40633 1854 finvar.lib sing_1633.htm#SEC1709 1855 finvar_lib sing_1633.htm#SEC1709 1856 first index is 1 sing_417.htm#SEC457 1857 firstoct sing_1759.htm#SEC1835 11498 1858 fitting sing_1162.htm#SEC1238 20661 1859 fixed points, moduli space of stable maps, graph fixedPoints sing_2718.htm#IDX1061 1860 fixedPoints sing_2718.htm#SEC2794 25366 1861 fl2poly sing_590.htm#SEC642 51682 1862 flatten sing_1047.htm#SEC1123 55617 1863 flatteningStrat sing_1163.htm#SEC1239 15622 1864 floating point sing_1015.htm#IDX504 1865 for sing_385.htm#SEC425 1866 formaldivisorplus sing_2358.htm#SEC2434 31959 1867 forward sing_2377.htm#SEC2453 15383 1868 fourier sing_585.htm#SEC637 5326 1869 fouriersystem sing_2388.htm#SEC2464 43681 1870 fpadim.lib sing_601.htm#SEC653 1871 fpadim_lib sing_601.htm#SEC653 1872 fpaprops.lib sing_632.htm#SEC684 1873 fpaprops_lib sing_632.htm#SEC684 1874 fprintf sing_251.htm#SEC291 13662 1875 fracStatus sing_2647.htm#SEC2723 14582 1876 frandwalk sing_2691.htm#SEC2767 25555 1877 free sing_2199.htm#IDX885 1878 free sing_2200.htm#IDX887 1879 free associative algebra, tensor algebra Free associative algebras sing_492.htm#SEC544 1880 freeGBasis sing_646.htm#SEC698 43055 1881 freeModule sing_2484.htm#SEC2560 34173 1882 freeModule2Module sing_2513.htm#SEC2589 15296 1883 freegb.lib sing_641.htm#SEC693 1884 freegb_lib sing_641.htm#SEC693 1885 freemodule sing_252.htm#SEC292 1886 freerank sing_963.htm#SEC1039 52218 1887 fres sing_253.htm#SEC293 1888 from_boolean_constant from_boolean_constant sing_2230.htm#SEC2306 44881 1889 from_boolean_ideal sing_2234.htm#SEC2310 62698 1890 from_boolean_poly sing_2231.htm#SEC2307 27864 1891 from_boolean_set sing_2235.htm#SEC2311 60615 1892 frwalk sing_254.htm#SEC294 1893 full representation sing_928.htm#IDX455 1894 full representation sing_929.htm#IDX461 1895 fullDimImages sing_2414.htm#SEC2490 20094 1896 fullFan sing_2053.htm#SEC2129 7534 1897 fullSerreRelations sing_656.htm#SEC708 27691 1898 fullSpace sing_2008.htm#SEC2084 19485 1899 furtherInvar sing_1677.htm#SEC1753 19209 1900 further_hn_proc sing_1573.htm#SEC1649 63500 1901 fwalk sing_1149.htm#SEC1225 15070 1902 galois field sing_144.htm#SEC184 1903 gauss_col sing_1057.htm#SEC1133 36252 1904 gauss_nf sing_1088.htm#SEC1164 51060 1905 gauss_row sing_1058.htm#SEC1134 58877 1906 gaussred sing_1086.htm#SEC1162 29001 1907 gaussred_pivot sing_1087.htm#SEC1163 25477 1908 gcd sing_255.htm#SEC295 1909 gcdMon sing_1191.htm#SEC1267 42448 1910 gcddivisor sing_1947.htm#SEC2023 1276 1911 gen sing_256.htm#SEC296 1912 genMDSMat sing_1814.htm#SEC1890 3347 1913 genSymId sing_1337.htm#SEC1413 17521 1914 general error-locator polynomial sing_884.htm#SEC949 1915 general neron. sing_2442.htm#IDX989 1916 general weighted lexicographical ordering sing_858.htm#IDX410 1917 general weighted reverse lexicographical ordering Local orderings sing_858.htm#IDX407 1918 general.lib sing_899.htm#SEC975 1919 generalOrder sing_1972.htm#SEC2048 42536 1920 general_lib sing_899.htm#SEC975 1921 generateG sing_1910.htm#SEC1986 51697 1922 generators sing_1473.htm#IDX649 1923 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2028.htm#SEC2104 4454 1924 generatorsOfSpan sing_2029.htm#SEC2105 40297 1925 generic representation sing_928.htm#IDX454 1926 genericid sing_981.htm#SEC1057 29731 1927 genericity sing_1834.htm#SEC1910 16822 1928 genericmat sing_1048.htm#SEC1124 35016 1929 genoutput sing_1407.htm#SEC1483 18973 1930 genus sing_1242.htm#SEC1318 sprintf 1931 geometrical locus FamElemsAtEnvCompPoints sing_932.htm#IDX467 1932 geometrical locus sing_933.htm#IDX470 1933 geometrical locus sing_934.htm#IDX473 1934 geometrical locus sing_935.htm#IDX476 1935 geometrical locus sing_936.htm#IDX479 1936 geometrical locus sing_937.htm#IDX481 1937 geometrical locus sing_938.htm#IDX485 1938 getArguments sing_1038.htm#SEC1114 14254 1939 getCommand sing_1037.htm#SEC1113 32181 1940 getCone sing_2055.htm#SEC2131 41394 1941 getGradingGroup sing_2542.htm#SEC2618 18137 1942 getLattice sing_2543.htm#SEC2619 7775 1943 getLinearForms sing_2030.htm#SEC2106 47590 1944 getModuleGrading sing_2553.htm#SEC2629 43451 1945 getMultiplicity sing_2031.htm#SEC2107 639 1946 getOneVar sing_1250.htm#SEC1326 55402 1947 getResult sing_1039.htm#SEC1115 51722 1948 getSmallest sing_1249.htm#SEC1325 1623 1949 getState sing_1040.htm#SEC1116 36453 1950 getVariableWeights sing_2541.htm#SEC2617 9591 1951 getcores sing_996.htm#SEC1072 30785 1952 getdump sing_257.htm#SEC297 1953 getenv sing_358.htm#IDX211 1954 gfan.lib sing_2007.htm#SEC2083 1955 gfan_lib sing_2007.htm#SEC2083 1836 1956 gfanlib sing_1.htm#IDX9 1837 gitCone sing_2388.htm#SEC2464 23853 1838 gitFan sing_2389.htm#SEC2465 sprintf 1839 gitfan sing_2386.htm#IDX948 1840 gitfan.lib sing_2386.htm#SEC2462 1841 gitfan_lib sing_2386.htm#SEC2462 1842 gkdim.lib sing_650.htm#SEC702 1843 gkdim_lib sing_650.htm#SEC702 1844 gkzFan sing_2390.htm#SEC2466 35496 1845 global sing_204.htm#IDX133 1846 global Bernstein-Sato polynomial sing_497.htm#IDX311 1847 global Bernstein-Sato polynomial sing_532.htm#IDX329 1848 global Bernstein-Sato polynomial for variety sing_588.htm#IDX354 1849 globalSections sing_2329.htm#SEC2405 55191 1850 gmscoeffs sing_1517.htm#SEC1593 13182 1851 gmsnf sing_1516.htm#SEC1592 44676 1852 gmspoly.lib sing_1536.htm#SEC1612 1853 gmspoly_lib sing_1536.htm#SEC1612 1854 gmsring sing_1515.htm#SEC1591 59438 1855 gmssing.lib sing_1514.htm#SEC1590 1856 gmssing_lib sing_1514.htm#SEC1590 1857 goettsche.lib sing_2372.htm#SEC2448 1858 goettsche_lib sing_2372.htm#SEC2448 1859 good basis sing_1514.htm#IDX651 1860 good basis sing_1524.htm#IDX706 1861 good basis sing_1536.htm#IDX722 1862 good basis sing_1538.htm#IDX733 1863 goodBasis sing_1538.htm#SEC1614 41606 1864 gorensteinIndex sing_2076.htm#SEC2152 52919 1865 gorensteinVector sing_2077.htm#SEC2153 50407 1866 graal.lib sing_2379.htm#SEC2455 1867 graalMixed sing_2380.htm#SEC2456 6401 1868 graal_lib sing_2379.htm#SEC2455 1869 gradeNumber sing_742.htm#SEC794 29956 1870 graded Weyl algebra sing_497.htm#IDX314 1871 graded module, graded piece sing_1440.htm#IDX609 1872 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2395.htm#IDX954 1873 graded modules, handling of Handling graded modules sing_806.htm#SEC858 1874 gradedModules.lib sing_2395.htm#SEC2471 1875 gradedModules_lib sing_2395.htm#SEC2471 1876 gradiator sing_2484.htm#SEC2560 53802 1877 graph sing_1126.htm#IDX516 1878 graph sing_1127.htm#IDX517 1879 graph sing_2531.htm#IDX988 1880 graph sing_2532.htm#IDX989 1881 graphics.lib sing_1747.htm#SEC1823 1882 graphics_lib sing_1747.htm#SEC1823 1957 gitCone sing_2441.htm#SEC2517 23853 1958 gitfan.lib sing_2411.htm#SEC2487 1959 gitfan_lib sing_2411.htm#SEC2487 1960 gkdim.lib sing_667.htm#SEC719 1961 gkdim_lib sing_667.htm#SEC719 1962 global sing_209.htm#IDX133 1963 global Bernstein-Sato polynomial sing_505.htm#IDX313 1964 global Bernstein-Sato polynomial sing_540.htm#IDX331 1965 global Bernstein-Sato polynomial for variety sing_596.htm#IDX356 1966 globalSections sing_2352.htm#SEC2428 55191 1967 gmscoeffs sing_1531.htm#SEC1607 13182 1968 gmsnf sing_1530.htm#SEC1606 44676 1969 gmspoly.lib sing_1550.htm#SEC1626 1970 gmspoly_lib sing_1550.htm#SEC1626 1971 gmsring sing_1529.htm#SEC1605 59438 1972 gmssing.lib sing_1528.htm#SEC1604 1973 gmssing_lib sing_1528.htm#SEC1604 1974 goettsche.lib sing_2395.htm#SEC2471 1975 goettsche_lib sing_2395.htm#SEC2471 1976 good basis sing_1528.htm#IDX677 1977 good basis sing_1538.htm#IDX732 1978 good basis sing_1550.htm#IDX748 1979 good basis sing_1552.htm#IDX759 1980 goodBasis sing_1552.htm#SEC1628 41606 1981 gorensteinIndex sing_2087.htm#SEC2163 52919 1982 gorensteinVector sing_2088.htm#SEC2164 50407 1983 graal.lib sing_2404.htm#SEC2480 1984 graalMixed sing_2405.htm#SEC2481 6401 1985 graal_lib sing_2404.htm#SEC2480 1986 gradeNumber sing_759.htm#SEC811 29956 1987 graded Weyl algebra sing_505.htm#IDX316 1988 graded algebra sing_2241.htm#IDX940 1989 graded module, graded piece sing_1454.htm#IDX635 1990 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2444.htm#IDX990 1991 graded modules, handling of Handling graded modules sing_823.htm#SEC875 1992 graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2481.htm#IDX991 1993 gradedModules.lib sing_2444.htm#SEC2520 1994 gradedModules_lib sing_2444.htm#SEC2520 1995 gradiator sing_2586.htm#SEC2662 53802 1996 graph sing_1138.htm#IDX531 1997 graph sing_1139.htm#IDX532 1998 graph sing_2713.htm#IDX1056 1999 graph sing_2714.htm#IDX1057 2000 graphics.lib sing_1761.htm#SEC1837 2001 graphics_lib sing_1761.htm#SEC1837 1883 2002 graphviz sing_1.htm#IDX13 1884 graver4ti2 sing_1321.htm#SEC1397 39635 1885 grconcat sing_2418.htm#SEC2494 16754 1886 grdeg sing_2398.htm#SEC2474 22879 1887 grgens sing_2407.htm#SEC2483 12823 1888 grgroebner sing_2417.htm#SEC2493 29288 1889 grlift sing_2415.htm#SEC2491 21656 1890 grlifting sing_2422.htm#SEC2498 51177 1891 grlifting2 sing_2423.htm#SEC2499 59011 1892 grlifting3 sing_2425.htm#SEC2501 6369 1893 grneg sing_2428.htm#SEC2504 64584 1894 grobcov sing_902.htm#SEC978 27432 1895 grobcov.lib sing_900.htm#SEC976 1896 grobcov_lib sing_900.htm#SEC976 1897 grobj sing_2396.htm#SEC2472 18115 1898 groebner sing_250.htm#SEC290 5130 1899 groebner sing_798.htm#SEC850 1900 groebner basis computations sing_250.htm#IDX147 1901 groebnerComplex sing_2155.htm#SEC2231 2421 1902 groebnerCone sing_2149.htm#SEC2225 58776 1903 groebnerFan sing_2154.htm#SEC2230 48157 1904 groebnerFanP sing_2057.htm#SEC2133 5802 1905 gromovWitten sing_1131.htm#SEC1207 28559 1906 grorder sing_2409.htm#SEC2485 20857 1907 ground field sing_139.htm#SEC179 1908 group_reynolds sing_1627.htm#SEC1703 35079 1909 grpower sing_2405.htm#SEC2481 3960 1910 grpres sing_2408.htm#SEC2484 18145 1911 grprod sing_2416.htm#SEC2492 41525 1912 grrange sing_2427.htm#SEC2503 41835 1913 grres sing_2414.htm#SEC2490 35795 1914 grrndmap sing_2420.htm#SEC2496 4054 1915 grrndmap2 sing_2421.htm#SEC2497 50536 1916 grrndmat sing_2419.htm#SEC2495 42634 1917 grshift sing_2400.htm#SEC2476 1415 1918 grsum sing_2404.htm#SEC2480 60602 1919 grsyz sing_2413.htm#SEC2489 61843 1920 grtest sing_2397.htm#SEC2473 62577 1921 grtranspose sing_2406.htm#SEC2482 13865 1922 grtranspose1 sing_2410.htm#SEC2486 3637 1923 grtwist sing_2402.htm#SEC2478 10498 1924 grtwists sing_2403.htm#SEC2479 56638 1925 grview sing_2399.htm#SEC2475 6878 1926 grwalk.lib sing_1136.htm#SEC1212 1927 grwalk_lib sing_1136.htm#SEC1212 1928 grzero sing_2401.htm#SEC2477 4212 1929 gwalk sing_1142.htm#SEC1218 38238 1930 hStarVector sing_2078.htm#SEC2154 60821 1931 hVector sing_2079.htm#SEC2155 46486 1932 h_increasing_knapsack h_increasing_knapsack sing_1919.htm#SEC1995 62968 1933 hardware platform sing_350.htm#IDX269 1934 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_999.htm#SEC1075 54609 1935 hasCommutativeVars sing_996.htm#SEC1072 3152 1936 hasGlobalOrdering sing_997.htm#SEC1073 34053 1937 hasMixedOrdering sing_998.htm#SEC1074 29738 1938 hasNumericCoeffs sing_995.htm#SEC1071 14522 1939 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1000.htm#SEC1076 56211 1940 headStand sing_1058.htm#SEC1134 14413 1941 heightZ sing_1298.htm#SEC1374 16800 1942 help sing_251.htm#SEC291 2003 graver4ti2 sing_1335.htm#SEC1411 39635 2004 grconcat sing_2467.htm#SEC2543 16754 2005 grdeg sing_2447.htm#SEC2523 22879 2006 grgens sing_2456.htm#SEC2532 12823 2007 grgroebner sing_2466.htm#SEC2542 29288 2008 grlift sing_2464.htm#SEC2540 21656 2009 grlifting sing_2471.htm#SEC2547 51177 2010 grlifting2 sing_2472.htm#SEC2548 59011 2011 grlifting3 sing_2474.htm#SEC2550 6369 2012 grneg sing_2477.htm#SEC2553 64584 2013 grobcov sing_921.htm#SEC997 44826 2014 grobcov.lib sing_920.htm#SEC996 2015 grobcov_lib sing_920.htm#SEC996 2016 grobj sing_2445.htm#SEC2521 18115 2017 groebner sing_258.htm#SEC298 53038 2018 groebner sing_815.htm#SEC867 2019 groebner basis computations sing_258.htm#IDX147 2020 groebnerComplex sing_2166.htm#SEC2242 2421 2021 groebnerCone sing_2160.htm#SEC2236 58776 2022 groebnerFan sing_2165.htm#SEC2241 48157 2023 gromovWitten sing_1143.htm#SEC1219 28559 2024 grorder sing_2458.htm#SEC2534 20857 2025 ground field sing_144.htm#SEC184 2026 groupActionOnHashes sing_2429.htm#SEC2505 406 2027 groupActionOnQImage sing_2428.htm#SEC2504 53270 2028 group_reynolds sing_1641.htm#SEC1717 35079 2029 grpower sing_2454.htm#SEC2530 3960 2030 grpres sing_2457.htm#SEC2533 18145 2031 grprod sing_2465.htm#SEC2541 41525 2032 grrange sing_2476.htm#SEC2552 41835 2033 grres sing_2463.htm#SEC2539 35795 2034 grrndmap sing_2469.htm#SEC2545 4054 2035 grrndmap2 sing_2470.htm#SEC2546 50536 2036 grrndmat sing_2468.htm#SEC2544 42634 2037 grshift sing_2449.htm#SEC2525 1415 2038 grsum sing_2453.htm#SEC2529 60602 2039 grsyz sing_2462.htm#SEC2538 61843 2040 grtest sing_2446.htm#SEC2522 62577 2041 grtranspose sing_2455.htm#SEC2531 13865 2042 grtranspose1 sing_2459.htm#SEC2535 3637 2043 grtwist sing_2451.htm#SEC2527 10498 2044 grtwists sing_2452.htm#SEC2528 56638 2045 grview sing_2448.htm#SEC2524 6878 2046 grwalk.lib sing_1148.htm#SEC1224 2047 grwalk_lib sing_1148.htm#SEC1224 2048 grzero sing_2450.htm#SEC2526 4212 2049 gwalk sing_1154.htm#SEC1230 38238 2050 hStarVector sing_2089.htm#SEC2165 60821 2051 hVector sing_2090.htm#SEC2166 46486 2052 h_increasing_knapsack h_increasing_knapsack sing_1933.htm#SEC2009 62968 2053 hardware platform sing_358.htm#IDX271 2054 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1019.htm#SEC1095 54609 2055 hasCommutativeVars sing_1016.htm#SEC1092 3152 2056 hasGlobalOrdering sing_1017.htm#SEC1093 34053 2057 hasLeftDenom sing_2595.htm#SEC2671 47260 2058 hasMixedOrdering sing_1018.htm#SEC1094 29738 2059 hasNumericCoeffs sing_1015.htm#SEC1091 14522 2060 hasRightDenom sing_2596.htm#SEC2672 34279 2061 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1020.htm#SEC1096 56211 2062 hashToCone sing_2439.htm#SEC2515 6929 2063 hashesToFan sing_2440.htm#SEC2516 26774 2064 headStand sing_1070.htm#SEC1146 14413 2065 heightZ sing_1312.htm#SEC1388 16800 2066 help sing_259.htm#SEC299 1943 2067 help browsers The online help system sing_16.htm#IDX22 1944 2068 help browsers, dummy The online help system sing_16.htm#IDX25 … … 1947 2071 help browsers, html The online help system sing_16.htm#IDX23 1948 2072 help browsers, setting command to use The online help system sing_16.htm#IDX30 1949 help browsers, setting the sing_35 0.htm#IDX1942073 help browsers, setting the sing_358.htm#IDX194 1950 2074 help, accessing over the net Command line options sing_19.htm#IDX42 1951 2075 help, online help system The online help system sing_16.htm#SEC22 1952 hermiteNormalForm sing_2485.htm#SEC2561 37225 1953 hess.lib sing_2430.htm#SEC2506 1954 hess_lib sing_2430.htm#SEC2506 1955 hessenberg sing_350.htm#IDX217 24168 1956 hessenberg sing_1080.htm#SEC1156 1957 highcorner sing_252.htm#SEC292 1958 hilb sing_253.htm#SEC293 1959 hilbPoly sing_959.htm#SEC1035 36118 1960 hilbert4ti2 sing_1320.htm#SEC1396 13993 1961 hilbertBasis sing_2080.htm#SEC2156 35423 1962 hilbertSeries sing_2487.htm#SEC2563 60148 1963 hilbvec sing_1698.htm#SEC1774 9204 1964 hnexpansion sing_1540.htm#SEC1616 46990 1965 hnoether.lib sing_1539.htm#SEC1615 1966 hnoether_lib sing_1539.htm#SEC1615 1967 holonomic rank sing_760.htm#IDX378 1968 holonomicRank sing_764.htm#SEC816 41306 1969 hom_kernel sing_1158.htm#SEC1234 32604 1970 homog sing_254.htm#SEC294 1971 homog_part sing_2543.htm#SEC2619 20875 1972 homog_parts sing_2544.htm#SEC2620 12854 1973 homogeneitySpace sing_2151.htm#SEC2227 48243 1974 homogfacFirstQWeyl sing_693.htm#SEC745 32751 1975 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_695.htm#SEC747 9014 1976 homogfacNthQWeyl sing_692.htm#SEC744 55267 1977 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_694.htm#SEC746 62161 1978 homolog.lib sing_1143.htm#SEC1219 1979 homolog_lib sing_1143.htm#SEC1219 1980 homology sing_1153.htm#SEC1229 15040 1981 howto, download Download instructions sing_2570.htm#SEC2660 1982 howto, install on Macintosh Macintosh installation instructions sing_2573.htm#SEC2663 1983 howto, install on Unix Unix installation instructions sing_2571.htm#SEC2661 1984 howto, install on Windows Windows installation instructions sing_2572.htm#SEC2662 1985 hres sing_255.htm#SEC295 2076 hermiteNormalForm sing_2587.htm#SEC2663 37225 2077 hess.lib sing_2479.htm#SEC2555 2078 hess_lib sing_2479.htm#SEC2555 2079 hessenberg sing_358.htm#IDX217 24168 2080 hessenberg sing_1092.htm#SEC1168 2081 highcorner sing_260.htm#SEC300 2082 hilb sing_261.htm#SEC301 2083 hilbPoly sing_979.htm#SEC1055 36118 2084 hilbert4ti2 sing_1334.htm#SEC1410 13993 2085 hilbertBasis sing_2091.htm#SEC2167 35423 2086 hilbertSeries sing_2589.htm#SEC2665 60148 2087 hilbvec sing_1712.htm#SEC1788 9204 2088 hnexpansion sing_1554.htm#SEC1630 46990 2089 hnoether.lib sing_1553.htm#SEC1629 2090 hnoether_lib sing_1553.htm#SEC1629 2091 holonomic rank sing_777.htm#IDX380 2092 holonomicRank sing_781.htm#SEC833 41306 2093 hom sing_2525.htm#SEC2601 40032 2094 hom_kernel sing_1170.htm#SEC1246 32604 2095 homog sing_262.htm#SEC302 2096 homog_part sing_2725.htm#SEC2801 20875 2097 homog_parts sing_2726.htm#SEC2802 12854 2098 homogeneitySpace sing_2162.htm#SEC2238 48243 2099 homogfacFirstQWeyl sing_710.htm#SEC762 32751 2100 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_712.htm#SEC764 9014 2101 homogfacNthQWeyl sing_709.htm#SEC761 19238 2102 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_711.htm#SEC763 2523 2103 homolog.lib sing_1155.htm#SEC1231 2104 homolog_lib sing_1155.htm#SEC1231 2105 homology sing_1165.htm#SEC1241 15040 2106 homomorphism sing_2509.htm#SEC2585 27115 2107 howto, download Download instructions sing_2752.htm#SEC2841 2108 howto, install on Macintosh Macintosh installation instructions sing_2755.htm#SEC2844 2109 howto, install on Unix Unix installation instructions sing_2753.htm#SEC2842 2110 howto, install on Windows Windows installation instructions sing_2754.htm#SEC2843 2111 hres sing_263.htm#SEC303 1986 2112 html, default help The online help system sing_16.htm#IDX24 1987 hyperel.lib sing_1926.htm#SEC2002 1988 hyperel_lib sing_1926.htm#SEC2002 1989 hyperplane sing_2158.htm#IDX799 1990 hyperplane arrangement sing_532.htm#IDX335 1991 hypersurface singularity sing_1566.htm#IDX751 1992 iMult sing_1231.htm#SEC1307 22059 1993 id2mod sing_955.htm#SEC1031 32918 1994 ideal sing_85.htm#SEC125 1995 ideal declarations sing_86.htm#SEC126 1996 ideal declarations (plural) ideal declarations (plural) sing_416.htm#SEC456 1997 ideal expressions sing_87.htm#SEC127 1998 ideal expressions (plural) ideal expressions (plural) sing_417.htm#SEC457 1999 ideal operations sing_88.htm#SEC128 2000 ideal operations (plural) ideal operations (plural) sing_418.htm#SEC458 2001 ideal related functions ideal related functions sing_89.htm#SEC129 2002 ideal related functions (plural) ideal related functions (plural) sing_419.htm#SEC459 2003 ideal, toric sing_851.htm#SEC908 2004 idealSplit sing_1705.htm#SEC1781 4673 2005 ideals Miscellaneous oddities sing_410.htm#IDX291 2006 idealsimplify sing_1467.htm#SEC1543 38569 2007 identifier Identifier resolution sing_411.htm#SEC451 2008 identifyvar sing_1375.htm#SEC1451 59662 2009 if sing_378.htm#SEC418 2010 imageLattice sing_2453.htm#SEC2529 15740 2011 image_of_variety sing_1655.htm#SEC1731 43711 2012 imap sing_256.htm#SEC296 2013 imap (plural) sing_454.htm#SEC494 2014 imapall sing_987.htm#SEC1063 16023 2015 impart sing_257.htm#SEC297 2016 importfrom sing_379.htm#SEC419 2017 inCenter sing_521.htm#SEC573 22152 2018 inCentralizer sing_522.htm#SEC574 49000 2019 inForm sing_564.htm#SEC616 5283 2020 inSubring sing_1096.htm#SEC1172 24817 2021 indSet sing_1203.htm#SEC1279 32828 2022 indepSet sing_258.htm#SEC298 2113 hyperel.lib sing_1940.htm#SEC2016 2114 hyperel_lib sing_1940.htm#SEC2016 2115 hyperplane sing_2169.htm#IDX825 2116 hyperplane arrangement sing_540.htm#IDX337 2117 hypersurface singularity sing_1580.htm#IDX777 2118 iMult sing_1245.htm#SEC1321 22059 2119 id sing_2482.htm#SEC2558 47592 2120 id2mod sing_975.htm#SEC1051 32918 2121 ideal sing_90.htm#SEC130 2122 ideal declarations sing_91.htm#SEC131 2123 ideal declarations (plural) ideal declarations (plural) sing_424.htm#SEC464 2124 ideal expressions sing_92.htm#SEC132 2125 ideal expressions (plural) ideal expressions (plural) sing_425.htm#SEC465 2126 ideal operations sing_93.htm#SEC133 2127 ideal operations (plural) ideal operations (plural) sing_426.htm#SEC466 2128 ideal related functions ideal related functions sing_94.htm#SEC134 2129 ideal related functions (plural) ideal related functions (plural) sing_427.htm#SEC467 2130 ideal, toric sing_871.htm#SEC928 2131 idealSplit sing_1719.htm#SEC1795 4673 2132 ideals Miscellaneous oddities sing_418.htm#IDX293 2133 idealsimplify sing_1481.htm#SEC1557 38569 2134 identifier Identifier resolution sing_419.htm#SEC459 2135 identifyvar sing_1389.htm#SEC1465 59662 2136 if sing_386.htm#SEC426 2137 image sing_2505.htm#SEC2581 43481 2138 imageLattice sing_2555.htm#SEC2631 15740 2139 image_of_variety sing_1669.htm#SEC1745 43711 2140 imap sing_264.htm#SEC304 2141 imap (plural) sing_462.htm#SEC502 2142 imapall sing_1007.htm#SEC1083 16023 2143 impart sing_265.htm#SEC305 2144 importfrom sing_387.htm#SEC427 2145 inCenter sing_529.htm#SEC581 22152 2146 inCentralizer sing_530.htm#SEC582 49000 2147 inForm sing_572.htm#SEC624 5283 2148 inSubring sing_1108.htm#SEC1184 24817 2149 indSet sing_1217.htm#SEC1293 32828 2150 indepSet sing_266.htm#SEC306 2023 2151 indexed names sing_36.htm#IDX82 2024 2152 indexed names sing_37.htm#SEC65 2025 2153 indices, multi sing_37.htm#SEC65 2026 inequalities sing_20 18.htm#SEC2094101222027 infRedTail, option sing_3 07.htm#IDX1542154 inequalities sing_2032.htm#SEC2108 10122 2155 infRedTail, option sing_315.htm#IDX154 2028 2156 info The online help system sing_16.htm#SEC23 2029 iniD sing_1 395.htm#SEC1471350842030 init_debug sing_14 74.htm#SEC1550298632031 initial sing_21 52.htm#SEC222886782032 initial form sing_ 497.htm#IDX3162033 initial ideal sing_ 497.htm#IDX3152034 initial ideal approach sing_ 497.htm#IDX3192035 initial ideal approach sing_5 88.htm#IDX3582036 initialForm sing_21 29.htm#SEC2205577932037 initialIdeal sing_21 30.htm#SEC2206222052038 initialIdealW sing_5 63.htm#SEC615360862039 initialMalgrange sing_5 62.htm#SEC614268462040 injective_knapsack sing_19 20.htm#SEC199676192041 inout.lib sing_9 21.htm#SEC9972042 inout_lib sing_9 21.htm#SEC9972157 iniD sing_1409.htm#SEC1485 35084 2158 init_debug sing_1488.htm#SEC1564 29863 2159 initial sing_2163.htm#SEC2239 8678 2160 initial form sing_505.htm#IDX318 2161 initial ideal sing_505.htm#IDX317 2162 initial ideal approach sing_505.htm#IDX321 2163 initial ideal approach sing_596.htm#IDX360 2164 initialForm sing_2140.htm#SEC2216 57793 2165 initialIdeal sing_2141.htm#SEC2217 22205 2166 initialIdealW sing_571.htm#SEC623 36086 2167 initialMalgrange sing_570.htm#SEC622 26846 2168 injective_knapsack sing_1934.htm#SEC2010 7619 2169 inout.lib sing_941.htm#SEC1017 2170 inout_lib sing_941.htm#SEC1017 2043 2171 input sing_41.htm#SEC71 2044 insert sing_12 1.htm#SEC1612045 insert sing_2 59.htm#SEC2992046 insertCone sing_20 42.htm#SEC2118138582047 insertGenerator sing_5 83.htm#SEC635139512048 instructions, Macintosh installation Macintosh installation instructions sing_2 573.htm#SEC26632049 instructions, Unix installation Unix installation instructions sing_2 571.htm#SEC26612050 instructions, Windows installation Windows installation instructions sing_2 572.htm#SEC26622051 instructions, downloading Download instructions sing_2 570.htm#SEC26602052 int sing_9 0.htm#SEC1302053 int declarations sing_9 1.htm#SEC1312054 int expressions sing_9 2.htm#SEC1322055 int 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sing_2 463.htm#SEC2539sprintf2078 integralbasis.lib sing_11 64.htm#SEC12402079 integralbasis_lib sing_11 64.htm#SEC12402080 integration of D-module sing_5 55.htm#IDX3472172 insert sing_126.htm#SEC166 2173 insert sing_267.htm#SEC307 2174 insertCone sing_2056.htm#SEC2132 13858 2175 insertGenerator sing_591.htm#SEC643 13951 2176 instructions, Macintosh installation Macintosh installation instructions sing_2755.htm#SEC2844 2177 instructions, Unix installation Unix installation instructions sing_2753.htm#SEC2842 2178 instructions, Windows installation Windows installation instructions sing_2754.htm#SEC2843 2179 instructions, downloading Download instructions sing_2752.htm#SEC2841 2180 int sing_95.htm#SEC135 2181 int declarations sing_96.htm#SEC136 2182 int expressions sing_97.htm#SEC137 2183 int operations sing_98.htm#SEC138 2184 int related functions int related functions sing_99.htm#SEC139 2185 intInverse sing_2564.htm#SEC2640 sprintf 2186 intPart sing_1888.htm#SEC1964 48360 2187 intRank sing_2556.htm#SEC2632 1830 2188 intRoot sing_1889.htm#SEC1965 54582 2189 intRoots sing_588.htm#SEC640 24538 2190 intStrategy, option sing_315.htm#IDX155 2191 intclMonIdeal sing_1258.htm#SEC1334 22338 2192 intclToricRing sing_1254.htm#SEC1330 62143 2193 integer division Miscellaneous oddities sing_418.htm#IDX288 2194 integer programming sing_879.htm#SEC936 2195 integral sing_2700.htm#SEC2776 62683 2196 integral basis sing_1177.htm#IDX553 2197 integral basis sing_1372.htm#IDX620 2198 integral closure sing_1238.htm#IDX568 2199 integral closure sing_1239.htm#IDX571 2200 integral closure sing_1240.htm#IDX574 2201 integral closure sing_1253.htm#IDX580 2202 integralBasis sing_1177.htm#SEC1253 38114 2203 integralIdeal sing_575.htm#SEC627 29194 2204 integralModule sing_576.htm#SEC628 58078 2205 integralSection sing_2565.htm#SEC2641 sprintf 2206 integralbasis.lib sing_1176.htm#SEC1252 2207 integralbasis_lib sing_1176.htm#SEC1252 2208 integration of D-module sing_563.htm#IDX349 2081 2209 interface, Emacs Emacs user interface sing_21.htm#SEC28 2082 interiorLatticePoints interiorLatticePoints sing_2081.htm#SEC2157 49868 2083 internalfunctions sing_1475.htm#SEC1551 61230 2084 interpolate sing_1711.htm#SEC1787 51502 2085 interpolation sing_260.htm#SEC300 2086 interred sing_261.htm#SEC301 2087 intersect sing_262.htm#SEC302 2088 intersect (plural) sing_455.htm#SEC495 2089 intersectElim, option sing_307.htm#IDX173 2090 intersectLattices sing_2459.htm#SEC2535 41354 2091 intersectMon sing_1180.htm#SEC1256 44572 2092 intersectSyz, option sing_307.htm#IDX174 2093 intersectZ sing_1300.htm#SEC1376 sprintf 2094 intersection sing_1549.htm#SEC1625 46938 2095 intersection lattice sing_2194.htm#IDX874 2096 intersection lattice sing_2195.htm#IDX875 2097 intersection multiplicity sing_1460.htm#IDX629 2098 intersection multiplicity sing_1549.htm#IDX744 2099 intersectionDiv sing_1423.htm#SEC1499 29017 2100 intersectionValRingIdeals intersectionValRingIdeals sing_1249.htm#SEC1325 38773 2101 intersectionValRings intersectionValRings sing_1248.htm#SEC1324 35761 2102 intmat sing_97.htm#SEC137 2103 intmat declarations sing_98.htm#SEC138 2104 intmat expressions sing_99.htm#SEC139 2105 intmat operations sing_101.htm#SEC141 2106 intmat related functions intmat related functions sing_102.htm#SEC142 2107 intmat type cast sing_100.htm#SEC140 2108 intmat2mons sing_1264.htm#SEC1340 21150 2109 intprog.lib sing_1166.htm#SEC1242 2110 intprog_lib sing_1166.htm#SEC1242 2111 intvec sing_103.htm#SEC143 2112 intvec declarations sing_104.htm#SEC144 2113 intvec expressions sing_105.htm#SEC145 2114 intvec operations sing_106.htm#SEC146 2115 intvec related functions intvec related functions sing_107.htm#SEC147 2116 invariant sing_2317.htm#IDX922 2117 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1624.htm#IDX757 2118 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1625.htm#IDX758 2119 invariantRing sing_1657.htm#SEC1733 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involut_lib sing_642.htm#SEC694 2139 involution sing_647.htm#SEC699 34280 2140 invunit sing_1568.htm#SEC1644 62398 2141 iostruct sing_1822.htm#SEC1898 60444 2142 irrRealizationDim sing_2111.htm#SEC2187 7814 2143 irred_secondary_char0 irred_secondary_char0 sing_1646.htm#SEC1722 2943 2144 irred_secondary_no_molien irred_secondary_no_molien sing_1649.htm#SEC1725 55905 2145 irreddecMon sing_1189.htm#SEC1265 20160 2146 irreducible power series sing_1550.htm#IDX745 2147 irreducible secondary invariant irred_secondary_char0 sing_1646.htm#IDX759 2148 isAface sing_2391.htm#SEC2467 47756 2149 isAntiEndo sing_649.htm#SEC701 19156 2150 isBounded sing_2082.htm#SEC2158 28183 2151 isCI sing_204.htm#IDX139 58425 2152 isCI sing_1114.htm#SEC1190 2153 isCM sing_204.htm#IDX140 50469 2154 isCM sing_1154.htm#SEC1230 2155 isCMcod2 sing_1603.htm#SEC1679 2563 2156 isCanonical sing_2083.htm#SEC2159 51109 2157 isCartan sing_523.htm#SEC575 39541 2158 isCentral sing_720.htm#SEC772 54650 2159 isCommutative 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sing_496.htm#SEC548 36558 2203 isUpperTriangular sing_701.htm#SEC753 40655 2204 isVar sing_640.htm#SEC692 43851 2205 isVeryAmple sing_2091.htm#SEC2167 64652 2206 isWeyl sing_723.htm#SEC775 28994 2207 isZeroElement sing_2472.htm#SEC2548 514 2208 is_NND sing_1553.htm#SEC1629 26564 2209 is_NP sing_1212.htm#SEC1288 43891 2210 is_active sing_1586.htm#SEC1662 6867 2211 is_bijective sing_1101.htm#SEC1177 49512 2212 is_cenBimodule sing_756.htm#SEC808 35450 2213 is_cenSubbimodule sing_757.htm#SEC809 26181 2214 is_ci sing_1587.htm#SEC1663 35370 2215 is_complex sing_1037.htm#SEC1113 1234 2216 is_fix_injective sing_1924.htm#SEC2000 11663 2217 is_h_injective sing_1923.htm#SEC1999 36696 2218 is_injective sing_1099.htm#SEC1175 15776 2219 is_irred sing_1550.htm#SEC1626 51150 2220 is_is sing_1588.htm#SEC1664 64105 2221 is_nested sing_1213.htm#SEC1289 9200 2222 is_prime sing_1904.htm#SEC1980 29018 2223 is_primitive_root sing_1900.htm#SEC1976 42838 2224 is_pure sing_748.htm#SEC800 59105 2225 is_reg sing_1589.htm#SEC1665 18146 2226 is_regs sing_1590.htm#SEC1666 50242 2227 is_surjective sing_1100.htm#SEC1176 57044 2228 is_zero sing_944.htm#SEC1020 24341 2229 isartinianMon sing_1186.htm#SEC1262 1103 2230 isgenericMon sing_1187.htm#SEC1263 14444 2231 ishyper sing_1927.htm#SEC2003 65518 2232 isirreducibleMon sing_1185.htm#SEC1261 22428 2233 isoncurve sing_1928.htm#SEC2004 16384 2234 isparam sing_1991.htm#SEC2067 56395 2235 isprimaryMon sing_1184.htm#SEC1260 57367 2236 isprimeMon sing_1183.htm#SEC1259 9124 2237 isuni sing_1976.htm#SEC2052 39427 2238 iv2lp sing_618.htm#SEC670 53390 2239 iv2lpList sing_619.htm#SEC671 38626 2240 iv2lpMat sing_620.htm#SEC672 41720 2241 ivDHilbert sing_594.htm#SEC646 18825 2242 ivDHilbertSickle sing_595.htm#SEC647 16102 2243 ivDimCheck sing_596.htm#SEC648 42112 2244 ivHilbert sing_597.htm#SEC649 34233 2245 ivKDim sing_598.htm#SEC650 40986 2246 ivL2lpI sing_617.htm#SEC669 45855 2247 ivMis2Base sing_599.htm#SEC651 57812 2248 ivMis2Dim sing_600.htm#SEC652 15557 2249 ivOrdMisLex sing_601.htm#SEC653 40656 2250 ivSickle sing_602.htm#SEC654 48016 2251 ivSickleDim sing_604.htm#SEC656 57209 2252 ivSickleHil sing_603.htm#SEC655 1967 2253 jInvariant sing_2123.htm#SEC2199 2369 2254 jOft sing_1859.htm#SEC1935 25716 2255 jacob sing_263.htm#SEC303 2256 jacoblift sing_1569.htm#SEC1645 40125 2257 jacobson sing_1828.htm#SEC1904 59267 2258 jacobson.lib sing_1826.htm#SEC1902 2259 jacobson_lib sing_1826.htm#SEC1902 2260 janet sing_264.htm#SEC304 2261 jet sing_265.htm#SEC305 2262 jordan sing_1085.htm#SEC1161 16602 2263 jordanbasis sing_1086.htm#SEC1162 12736 2264 jordanmatrix sing_1087.htm#SEC1163 2886 2265 jordannf sing_1088.htm#SEC1164 20535 2266 jungfib sing_1408.htm#SEC1484 5432 2267 jungnormal sing_1407.htm#SEC1483 43561 2268 jungresolve sing_1406.htm#SEC1482 45004 2269 katsura sing_942.htm#SEC1018 45913 2270 kbase sing_266.htm#SEC306 2271 kbase (plural) sing_456.htm#SEC496 2272 keepring sing_380.htm#SEC420 2273 kernel sing_267.htm#SEC307 2274 kernelLattice sing_2455.htm#SEC2531 36320 2275 kill sing_268.htm#SEC308 2276 killTask sing_1016.htm#SEC1092 39317 2277 killall sing_888.htm#SEC964 34661 2278 killattrib sing_269.htm#SEC309 2279 kmemory sing_887.htm#SEC963 52193 2280 kohom sing_1159.htm#SEC1235 50086 2281 kontrahom sing_1160.htm#SEC1236 58549 2282 koszul sing_270.htm#SEC310 2283 kskernel.lib sing_1560.htm#SEC1636 2284 kskernel_lib sing_1560.htm#SEC1636 2210 interiorLatticePoints interiorLatticePoints sing_2092.htm#SEC2168 49868 2211 internalfunctions sing_1489.htm#SEC1565 61230 2212 interpolate sing_1725.htm#SEC1801 51502 2213 interpolation sing_268.htm#SEC308 2214 interpret sing_2527.htm#SEC2603 48499 2215 interpretElem sing_2530.htm#SEC2606 51740 2216 interpretInv sing_2528.htm#SEC2604 6149 2217 interpretList sing_2531.htm#SEC2607 64061 2218 interred sing_269.htm#SEC309 2219 intersect sing_270.htm#SEC310 2220 intersect (plural) sing_463.htm#SEC503 2221 intersectElim, option sing_315.htm#IDX173 2222 intersectLattices sing_2561.htm#SEC2637 41354 2223 intersectMon sing_1194.htm#SEC1270 44572 2224 intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2427.htm#SEC2503 19444 2225 intersectSyz, option sing_315.htm#IDX174 2226 intersectZ sing_1314.htm#SEC1390 sprintf 2227 intersection sing_1563.htm#SEC1639 46938 2228 intersection lattice sing_2205.htm#IDX900 2229 intersection lattice sing_2206.htm#IDX901 2230 intersection multiplicity sing_1474.htm#IDX655 2231 intersection multiplicity sing_1563.htm#IDX770 2232 intersectionDiv sing_1437.htm#SEC1513 29017 2233 intersectionValRingIdeals intersectionValRingIdeals sing_1263.htm#SEC1339 38773 2234 intersectionValRings intersectionValRings sing_1262.htm#SEC1338 35761 2235 interval arithmetic sing_2670.htm#IDX1031 2236 intmat sing_102.htm#SEC142 2237 intmat declarations sing_103.htm#SEC143 2238 intmat expressions sing_104.htm#SEC144 2239 intmat operations sing_106.htm#SEC146 2240 intmat related functions intmat related functions sing_107.htm#SEC147 2241 intmat type cast sing_105.htm#SEC145 2242 intmat2mons sing_1278.htm#SEC1354 21150 2243 intprog.lib sing_1178.htm#SEC1254 2244 intprog_lib sing_1178.htm#SEC1254 2245 intvec sing_108.htm#SEC148 2246 intvec declarations sing_109.htm#SEC149 2247 intvec expressions sing_110.htm#SEC150 2248 intvec operations sing_111.htm#SEC151 2249 intvec related functions intvec related functions sing_112.htm#SEC152 2250 invariant sing_2340.htm#IDX958 2251 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1638.htm#IDX783 2252 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1639.htm#IDX784 2253 invariantRing sing_1671.htm#SEC1747 18582 2254 invariant_algebra_perm invariant_algebra_perm sing_1639.htm#SEC1715 63525 2255 invariant_algebra_reynolds invariant_algebra_reynolds sing_1638.htm#SEC1714 35705 2256 invariant_basis sing_1646.htm#SEC1722 18343 2257 invariant_basis_reynolds invariant_basis_reynolds sing_1647.htm#SEC1723 54788 2258 invariant_ring sing_1634.htm#SEC1710 8059 2259 invariant_ring_random invariant_ring_random sing_1635.htm#SEC1711 6986 2260 invariants curveColengthDerivations sing_1559.htm#SEC1635 57499 2261 invariants sing_2337.htm#IDX951 2262 invariants sing_2341.htm#IDX960 2263 inverse sing_1076.htm#SEC1152 27411 2264 inverse of a matrix via its LU-decomposition sing_290.htm#SEC330 2265 inverseFourier sing_586.htm#SEC638 65140 2266 inverse_B sing_1077.htm#SEC1153 17616 2267 inverse_L sing_1078.htm#SEC1154 49271 2268 inverse_modulus sing_1917.htm#SEC1993 60822 2269 invertBirMap sing_1373.htm#SEC1449 16086 2270 invertLeftFraction sing_2657.htm#SEC2733 51903 2271 invertNcfrac sing_2605.htm#SEC2681 50842 2272 invertNumberMain sing_1749.htm#SEC1825 62615 2273 involut.lib sing_659.htm#SEC711 2274 involut_lib sing_659.htm#SEC711 2275 involution sing_664.htm#SEC716 34280 2276 invunit sing_1582.htm#SEC1658 62398 2277 iostruct sing_1836.htm#SEC1912 60444 2278 irrRealizationDim sing_2122.htm#SEC2198 7814 2279 irred_secondary_char0 irred_secondary_char0 sing_1660.htm#SEC1736 2943 2280 irred_secondary_no_molien irred_secondary_no_molien sing_1663.htm#SEC1739 55905 2281 irreddecMon sing_1203.htm#SEC1279 20160 2282 irreducible power series sing_1564.htm#IDX771 2283 irreducible secondary invariant irred_secondary_char0 sing_1660.htm#IDX785 2284 isAface sing_2412.htm#SEC2488 25344 2285 isAntiEndo sing_666.htm#SEC718 19156 2286 isBounded sing_2093.htm#SEC2169 28183 2287 isCI sing_209.htm#IDX139 58425 2288 isCI sing_1126.htm#SEC1202 2289 isCM sing_209.htm#IDX140 50469 2290 isCM sing_1166.htm#SEC1242 2291 isCMcod2 sing_1617.htm#SEC1693 2563 2292 isCanonical sing_2094.htm#SEC2170 51109 2293 isCartan sing_531.htm#SEC583 39541 2294 isCentral sing_737.htm#SEC789 54650 2295 isCommutative sing_739.htm#SEC791 60728 2296 isCompatible sing_2057.htm#SEC2133 57323 2297 isCompressed sing_2095.htm#SEC2171 2849 2298 isDenom sing_2609.htm#SEC2685 55537 2299 isEqualDivisor sing_2351.htm#SEC2427 17569 2300 isEquising sing_1526.htm#SEC1602 1424 2301 isFlat sing_1167.htm#SEC1243 14706 2302 isFsat sing_581.htm#SEC633 28225 2303 isFullSpace sing_2033.htm#SEC2109 27433 2304 isGorenstein sing_2096.htm#SEC2172 24010 2305 isGradedRingHomomorphism isGradedRingHomomorphism sing_2550.htm#SEC2626 39551 2306 isGroup sing_2548.htm#SEC2624 55744 2307 isGroupHomomorphism sing_2549.htm#SEC2625 65475 2308 isHolonomic sing_559.htm#SEC611 30274 2309 isHomg sing_209.htm#IDX135 2310 isHomogeneous sing_2576.htm#SEC2652 3034 2311 isInS sing_2646.htm#SEC2722 30907 2312 isInt sing_594.htm#SEC646 9879 2313 isIntegralSurjective isIntegralSurjective sing_2562.htm#SEC2638 sprintf 2314 isInvertibleLeftFraction isInvertibleLeftFraction sing_2656.htm#SEC2732 623 2315 isInvertibleNcfrac sing_2604.htm#SEC2680 48367 2316 isInvolution sing_665.htm#SEC717 13601 2317 isLatticeEmpty sing_2097.htm#SEC2173 48517 2318 isLocalizationRegular isLocalizationRegular sing_2408.htm#SEC2484 11221 2319 isLocallyFree sing_1168.htm#SEC1244 46389 2320 isMonomial sing_1189.htm#SEC1265 57615 2321 isNC sing_738.htm#SEC790 57151 2322 isNormal sing_2098.htm#SEC2174 64236 2323 isOnCurve sing_1901.htm#SEC1977 36324 2324 isOneFraction sing_2659.htm#SEC2735 55015 2325 isOneNcfrac sing_2598.htm#SEC2674 12754 2326 isOrigin sing_2034.htm#SEC2110 13977 2327 isPositive sing_2573.htm#SEC2649 50852 2328 isPrimitiveSublattice isPrimitiveSublattice sing_2563.htm#SEC2639 sprintf 2329 isPure sing_2058.htm#SEC2134 44002 2330 isPureTensor sing_503.htm#SEC555 21323 2331 isQuotientRing sing_1021.htm#SEC1097 sprintf 2332 isRational sing_562.htm#SEC614 57398 2333 isReflexive sing_2099.htm#SEC2175 3991 2334 isReg sing_1169.htm#SEC1245 40920 2335 isSB sing_209.htm#IDX134 2336 isSimplicial sing_2035.htm#SEC2111 57789 2337 isSmooth sing_2100.htm#SEC2176 37647 2338 isSubModule sing_1022.htm#SEC1098 sprintf 2339 isSublattice sing_2554.htm#SEC2630 10501 2340 isSymmetric sing_1338.htm#SEC1414 61363 2341 isTame sing_1551.htm#SEC1627 31925 2342 isTerminal sing_2101.htm#SEC2177 29416 2343 isTorsionFree sing_2572.htm#SEC2648 52228 2344 isTwoSidedGB sing_504.htm#SEC556 36558 2345 isUpperTriangular sing_718.htm#SEC770 40655 2346 isVar sing_657.htm#SEC709 43851 2347 isVeryAmple sing_2102.htm#SEC2178 64652 2348 isWeyl sing_740.htm#SEC792 28994 2349 isZeroElement sing_2574.htm#SEC2650 514 2350 isZeroFraction sing_2658.htm#SEC2734 1926 2351 isZeroNcfrac sing_2597.htm#SEC2673 6841 2352 is_NND sing_1567.htm#SEC1643 26564 2353 is_NP sing_1226.htm#SEC1302 43891 2354 is_active sing_1600.htm#SEC1676 6867 2355 is_bijective sing_1113.htm#SEC1189 49512 2356 is_cenBimodule sing_773.htm#SEC825 35450 2357 is_cenSubbimodule sing_774.htm#SEC826 26181 2358 is_ci sing_1601.htm#SEC1677 35370 2359 is_complex sing_1049.htm#SEC1125 1234 2360 is_fix_injective sing_1938.htm#SEC2014 11663 2361 is_h_injective sing_1937.htm#SEC2013 36696 2362 is_injective sing_1111.htm#SEC1187 15776 2363 is_irred sing_1564.htm#SEC1640 51150 2364 is_is sing_1602.htm#SEC1678 64105 2365 is_nested sing_1227.htm#SEC1303 9200 2366 is_prime sing_1918.htm#SEC1994 29018 2367 is_primitive_root sing_1914.htm#SEC1990 42838 2368 is_pure sing_765.htm#SEC817 59105 2369 is_reg sing_1603.htm#SEC1679 18146 2370 is_regs sing_1604.htm#SEC1680 50242 2371 is_surjective sing_1112.htm#SEC1188 57044 2372 is_zero sing_964.htm#SEC1040 24341 2373 isartinianMon sing_1200.htm#SEC1276 1103 2374 isgenericMon sing_1201.htm#SEC1277 14444 2375 ishyper sing_1941.htm#SEC2017 65518 2376 isirreducibleMon sing_1199.htm#SEC1275 22428 2377 isoncurve sing_1942.htm#SEC2018 16384 2378 isparam sing_2005.htm#SEC2081 56395 2379 isprimaryMon sing_1198.htm#SEC1274 57367 2380 isprimeMon sing_1197.htm#SEC1273 9124 2381 isuni sing_1990.htm#SEC2066 39427 2382 iv2lp sing_626.htm#SEC678 59849 2383 iv2lpList sing_627.htm#SEC679 18518 2384 iv2lpMat sing_628.htm#SEC680 21612 2385 ivDHilbert sing_609.htm#SEC661 56709 2386 ivDHilbertSickle sing_610.htm#SEC662 43194 2387 ivDimCheck sing_611.htm#SEC663 258 2388 ivHilbert sing_612.htm#SEC664 37184 2389 ivKDim sing_613.htm#SEC665 26109 2390 ivL2lpI sing_625.htm#SEC677 2454 2391 ivMis2Base sing_614.htm#SEC666 57812 2392 ivMis2Dim sing_615.htm#SEC667 42072 2393 ivOrdMisLex sing_616.htm#SEC668 27789 2394 ivSickle sing_617.htm#SEC669 42888 2395 ivSickleDim sing_619.htm#SEC671 64347 2396 ivSickleHil sing_618.htm#SEC670 41396 2397 ivmatGaussian sing_2677.htm#SEC2753 37718 2398 ivmatInit sing_2674.htm#SEC2750 22774 2399 ivmatSet sing_2675.htm#SEC2751 53480 2400 jInvariant sing_2134.htm#SEC2210 2369 2401 jOft sing_1873.htm#SEC1949 25716 2402 jacob sing_271.htm#SEC311 2403 jacoblift sing_1583.htm#SEC1659 40125 2404 jacobson sing_1842.htm#SEC1918 59267 2405 jacobson.lib sing_1840.htm#SEC1916 2406 jacobson_lib sing_1840.htm#SEC1916 2407 janet sing_272.htm#SEC312 2408 janet basis sing_2683.htm#IDX1034 2409 jet sing_273.htm#SEC313 2410 jordan sing_1097.htm#SEC1173 16602 2411 jordanbasis sing_1098.htm#SEC1174 12736 2412 jordanmatrix sing_1099.htm#SEC1175 2886 2413 jordannf sing_1100.htm#SEC1176 20535 2414 jungfib sing_1422.htm#SEC1498 5432 2415 jungnormal sing_1421.htm#SEC1497 43561 2416 jungresolve sing_1420.htm#SEC1496 45004 2417 katsura sing_962.htm#SEC1038 45913 2418 kbase sing_274.htm#SEC314 2419 kbase (plural) sing_464.htm#SEC504 2420 keepring sing_388.htm#SEC428 2421 kerHom sing_2526.htm#SEC2602 53906 2422 kernel sing_275.htm#SEC315 2423 kernelLattice sing_2557.htm#SEC2633 36320 2424 kill sing_276.htm#SEC316 2425 killTask sing_1028.htm#SEC1104 39317 2426 killall sing_908.htm#SEC984 34661 2427 killattrib sing_277.htm#SEC317 2428 kmemory sing_907.htm#SEC983 52193 2429 kohom sing_1171.htm#SEC1247 50086 2430 kontrahom sing_1172.htm#SEC1248 58549 2431 koszul sing_278.htm#SEC318 2432 kskernel.lib sing_1574.htm#SEC1650 2433 kskernel_lib sing_1574.htm#SEC1650 2285 2434 l-adic numbers sing_32.htm#SEC46 2286 laguerre sing_271.htm#SEC311 2287 laguerre_solve sing_1707.htm#SEC1783 10155 2288 lastvarGeneral sing_1957.htm#SEC2033 28645 2289 latex.lib sing_1751.htm#SEC1827 2290 latex_lib sing_1751.htm#SEC1827 2291 lattice sing_2195.htm#IDX877 2292 latticeArea sing_2066.htm#SEC2142 53771 2293 latticeBasis sing_2456.htm#SEC2532 43162 2294 latticeCodegree sing_2092.htm#SEC2168 25482 2295 latticeDegree sing_2093.htm#SEC2169 52881 2296 latticePoints sing_2094.htm#SEC2170 41965 2297 latticeVolume sing_2095.htm#SEC2171 42234 2298 laxfrT sing_2352.htm#SEC2428 60899 2299 laxfrX sing_2353.htm#SEC2429 57254 2300 lazy, option sing_307.htm#IDX156 2301 lcm sing_945.htm#SEC1021 44755 2302 lcmMon sing_1178.htm#SEC1254 52749 2303 lcmN sing_1868.htm#SEC1944 52355 2304 lcmofall sing_1388.htm#SEC1464 56889 2305 lead sing_272.htm#SEC312 2306 leadcoef sing_273.htm#SEC313 2307 leadexp sing_274.htm#SEC314 2308 leadmonom sing_275.htm#SEC315 2309 leadmonomial sing_1943.htm#SEC2019 8195 2310 left annihilator ideal sing_532.htm#IDX327 2311 leftInverse sing_1817.htm#SEC1893 41469 2312 leftKernel sing_1815.htm#SEC1891 9292 2313 length, option sing_307.htm#IDX157 2314 letplaceGBasis sing_626.htm#SEC678 33757 2315 letterplace correspondence Letterplace correspondence sing_486.htm#SEC538 2316 lex_solve sing_1713.htm#SEC1789 48692 2317 lexicographical ordering sing_838.htm#IDX388 2435 laguerre sing_279.htm#SEC319 2436 laguerre_solve sing_1721.htm#SEC1797 10155 2437 lastvarGeneral sing_1971.htm#SEC2047 28645 2438 latex.lib sing_1765.htm#SEC1841 2439 latex_lib sing_1765.htm#SEC1841 2440 lattice sing_2206.htm#IDX903 2441 latticeArea sing_2077.htm#SEC2153 53771 2442 latticeBasis sing_2558.htm#SEC2634 43162 2443 latticeCodegree sing_2103.htm#SEC2179 25482 2444 latticeDegree sing_2104.htm#SEC2180 52881 2445 latticePoints sing_2105.htm#SEC2181 41965 2446 latticeVolume sing_2106.htm#SEC2182 42234 2447 laxfrT sing_2375.htm#SEC2451 60899 2448 laxfrX sing_2376.htm#SEC2452 57254 2449 lazy, option sing_315.htm#IDX156 2450 lcm sing_965.htm#SEC1041 44755 2451 lcmMon sing_1192.htm#SEC1268 52749 2452 lcmN sing_1882.htm#SEC1958 52355 2453 lcmofall sing_1402.htm#SEC1478 56889 2454 lead sing_280.htm#SEC320 2455 leadcoef sing_281.htm#SEC321 2456 leadexp sing_282.htm#SEC322 2457 leadmonom sing_283.htm#SEC323 2458 leadmonomial sing_1957.htm#SEC2033 8195 2459 left annihilator ideal sing_540.htm#IDX329 2460 leftInverse sing_1831.htm#SEC1907 41469 2461 leftKernel sing_1829.htm#SEC1905 9292 2462 leftOre sing_2649.htm#SEC2725 44669 2463 length sing_2672.htm#SEC2748 9547 2464 length, option sing_315.htm#IDX157 2465 letplaceGBasis sing_643.htm#SEC695 33757 2466 letterplace correspondence Letterplace correspondence sing_494.htm#SEC546 2467 lex_solve sing_1727.htm#SEC1803 48692 2468 lexicographical ordering sing_857.htm#IDX390 2318 2469 lib2doc sing_60.htm#SEC97 2319 libSingular sing_2 569.htm#SEC26592470 libSingular sing_2751.htm#SEC2840 2320 2471 libcdd sing_1.htm#IDX12 2321 2472 libfac sing_1.htm#IDX6 2322 2473 libparse sing_69.htm#SEC109 2323 library sing_22 10.htm#IDX8922324 library sing_2386.htm#IDX9472474 library sing_2221.htm#IDX918 2475 library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2411.htm#IDX987 2325 2476 library, info string sing_55.htm#IDX124 2326 library, polybori.lib sing_22 10.htm#IDX8892477 library, polybori.lib sing_2221.htm#IDX915 2327 2478 library, template sing_55.htm#SEC92 2328 2479 library, template.lib sing_55.htm#IDX122 2329 lieBracket sing_637.htm#SEC689 50745 2330 lift sing_277.htm#SEC317 2331 lift sing_490.htm#IDX303 2332 lift (plural) sing_457.htm#SEC497 2333 lift_kbase sing_1506.htm#SEC1582 10906 2334 lift_rel_kb sing_1507.htm#SEC1583 13673 2335 liftenvelope sing_493.htm#SEC545 58802 2336 liftstd sing_278.htm#SEC318 2337 liftstd (plural) sing_458.htm#SEC498 2338 linReduce sing_505.htm#SEC557 57527 2339 linReduceIdeal sing_506.htm#SEC558 19076 2340 linSyzSolve sing_507.htm#SEC559 26185 2341 linalg.lib sing_1063.htm#SEC1139 2342 linalg_lib sing_1063.htm#SEC1139 2343 linealityDimension sing_2022.htm#SEC2098 30751 2344 linealitySpace sing_2023.htm#SEC2099 14489 2345 linear algebra sing_205.htm#SEC245 2346 linear algebra sing_281.htm#SEC321 2347 linear algebra sing_282.htm#SEC322 2348 linear algebra sing_283.htm#SEC323 2349 linear code, dual sing_1786.htm#IDX770 2350 linear code, systematic sing_1787.htm#IDX771 2351 linear interreduction sing_497.htm#IDX318 2352 linearCombinations sing_526.htm#SEC578 20514 2353 linearMapKernel sing_525.htm#SEC577 43761 2354 linear_relations sing_1055.htm#SEC1131 45983 2355 linearlyEquivalent sing_2331.htm#SEC2407 28351 2356 linearpart sing_1699.htm#SEC1775 2162 2357 linesHypersurface sing_2540.htm#SEC2616 9129 2358 link Parallelization with ssi links sing_108.htm#SEC148 2359 link sing_795.htm#SEC847 2360 link declarations sing_109.htm#SEC149 2361 link expressions sing_110.htm#SEC150 2362 link related functions link related functions sing_111.htm#SEC151 2363 list sing_118.htm#SEC158 2364 list declarations sing_119.htm#SEC159 2365 list expressions sing_120.htm#SEC160 2366 list operations sing_121.htm#SEC161 2367 list related functions list related functions sing_122.htm#SEC162 2368 listvar sing_279.htm#SEC319 2369 lll sing_2488.htm#SEC2564 35827 2370 load sing_381.htm#SEC421 2371 loadLib, option sing_307.htm#IDX178 2372 loadProc, option sing_307.htm#IDX179 2373 locAtZero sing_1233.htm#SEC1309 5687 2374 locNormal sing_1169.htm#SEC1245 52237 2375 local methods sing_1168.htm#IDX541 2376 local methods sing_1169.htm#IDX544 2480 lieBracket sing_650.htm#SEC702 50745 2481 lift sing_285.htm#SEC325 2482 lift sing_498.htm#IDX305 2483 lift (plural) sing_465.htm#SEC505 2484 lift_kbase sing_1520.htm#SEC1596 10906 2485 lift_rel_kb sing_1521.htm#SEC1597 13673 2486 liftenvelope sing_501.htm#SEC553 58802 2487 liftstd sing_286.htm#SEC326 2488 liftstd (plural) sing_466.htm#SEC506 2489 linReduce sing_513.htm#SEC565 57527 2490 linReduceIdeal sing_514.htm#SEC566 19076 2491 linSyzSolve sing_515.htm#SEC567 26185 2492 linalg.lib sing_1075.htm#SEC1151 2493 linalg_lib sing_1075.htm#SEC1151 2494 linealityDimension sing_2036.htm#SEC2112 30751 2495 linealitySpace sing_2037.htm#SEC2113 14489 2496 linear algebra sing_210.htm#SEC250 2497 linear algebra sing_289.htm#SEC329 2498 linear algebra sing_290.htm#SEC330 2499 linear algebra sing_291.htm#SEC331 2500 linear code, dual sing_1800.htm#IDX796 2501 linear code, systematic sing_1801.htm#IDX797 2502 linear interreduction sing_505.htm#IDX320 2503 linearCombinations sing_534.htm#SEC586 20514 2504 linearMapKernel sing_533.htm#SEC585 43761 2505 linear_relations sing_1067.htm#SEC1143 45983 2506 linearlyEquivalent sing_2354.htm#SEC2430 28351 2507 linearpart sing_1713.htm#SEC1789 2162 2508 linesHypersurface sing_2722.htm#SEC2798 9129 2509 link Parallelization with ssi links sing_113.htm#SEC153 2510 link sing_812.htm#SEC864 2511 link declarations sing_114.htm#SEC154 2512 link expressions sing_115.htm#SEC155 2513 link related functions link related functions sing_116.htm#SEC156 2514 list sing_123.htm#SEC163 2515 list declarations sing_124.htm#SEC164 2516 list expressions sing_125.htm#SEC165 2517 list operations sing_126.htm#SEC166 2518 list related functions list related functions sing_127.htm#SEC167 2519 listvar sing_287.htm#SEC327 2520 lll sing_2590.htm#SEC2666 35827 2521 load sing_389.htm#SEC429 2522 loadLib, option sing_315.htm#IDX178 2523 loadProc, option sing_315.htm#IDX179 2524 locAtZero sing_1247.htm#SEC1323 5687 2525 locNormal sing_1181.htm#SEC1257 52237 2526 locStatus sing_2644.htm#SEC2720 54575 2527 local methods sing_1180.htm#IDX556 2528 local methods sing_1181.htm#IDX559 2377 2529 local names sing_46.htm#SEC83 2378 local rings, computing in Rings associated to monomial orderings sing_790.htm#SEC842 2379 local weighted lexicographical ordering sing_839.htm#IDX409 2380 local weighted reverse lexicographical ordering Local orderings sing_839.htm#IDX406 2381 localInvar sing_1662.htm#SEC1738 38478 2382 localization Rings associated to monomial orderings sing_790.htm#SEC842 2383 localization sing_2175.htm#IDX837 2384 localization of D-module sing_555.htm#IDX343 2385 localization of D-module sing_760.htm#IDX381 2386 locally closed set sing_909.htm#IDX437 2387 locally closed set sing_911.htm#IDX446 2388 localstd sing_1953.htm#SEC2029 25562 2389 locnormal.lib sing_1168.htm#SEC1244 2390 locnormal_lib sing_1168.htm#SEC1244 2391 locstd sing_1591.htm#SEC1667 25864 2392 locus FamElemsAtEnvCompPoints sing_913.htm#SEC989 49563 2393 locus sing_913.htm#IDX451 2394 locus sing_914.htm#IDX454 2395 locus sing_915.htm#IDX457 2396 locus sing_916.htm#IDX460 2397 locus sing_917.htm#IDX464 2398 locus sing_918.htm#IDX468 2399 locusdg sing_914.htm#SEC990 62891 2400 locusto sing_916.htm#SEC992 17047 2401 log2 sing_1843.htm#SEC1919 40703 2402 logarithmic annihilator ideal sing_532.htm#IDX332 2403 logg sing_2545.htm#SEC2621 38736 2404 lp, global ordering sing_838.htm#IDX387 2405 lp2iv sing_621.htm#SEC673 26909 2406 lp2ivId sing_622.htm#SEC674 15628 2407 lp2lstr sing_633.htm#SEC685 24713 2408 lpDHilbert sing_605.htm#SEC657 11075 2409 lpDHilbertSickle sing_606.htm#SEC658 46653 2410 lpDimCheck sing_608.htm#SEC660 50239 2411 lpHilbert sing_607.htm#SEC659 53685 2412 lpId2ivLi sing_623.htm#SEC675 29846 2413 lpKDim sing_609.htm#SEC661 53650 2414 lpMis2Base sing_610.htm#SEC662 10826 2415 lpMis2Dim sing_611.htm#SEC663 47442 2416 lpMult sing_630.htm#SEC682 58898 2417 lpNF sing_627.htm#SEC679 55144 2418 lpOrdMisLex sing_612.htm#SEC664 21260 2419 lpPower sing_632.htm#SEC684 7325 2420 lpSickle sing_613.htm#SEC665 19646 2421 lpSickleDim sing_615.htm#SEC667 50163 2422 lpSickleHil sing_614.htm#SEC666 19038 2423 lprint sing_923.htm#SEC999 5285 2424 lres sing_280.htm#SEC320 2425 ls, local ordering sing_839.htm#IDX400 2426 lst2str sing_634.htm#SEC686 10088 2427 lsum sing_1135.htm#SEC1211 50315 2428 ludecomp sing_281.htm#SEC321 2429 luinverse sing_282.htm#SEC322 2430 lusolve sing_283.htm#SEC323 2431 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1915.htm#SEC1991 57945 2432 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1914.htm#SEC1990 33857 2433 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1913.htm#SEC1989 7880 2434 magnitude sing_1837.htm#SEC1913 37967 2435 makeDivisor sing_2323.htm#SEC2399 3414 2436 makeFormalDivisor sing_2333.htm#SEC2409 54579 2437 makeGraph sing_1126.htm#SEC1202 21758 2438 makeGraphVE sing_2531.htm#SEC2607 sprintf 2439 makeHeisenberg sing_711.htm#SEC763 2050 2440 makeLetterplaceRing sing_625.htm#SEC677 41789 2441 makeMalgrange sing_592.htm#SEC644 41377 2442 makeModElimRing sing_728.htm#SEC780 56092 2443 makePDivisor sing_2339.htm#SEC2415 45273 2444 makeQsl2 sing_675.htm#SEC727 3997 2445 makeQsl3 sing_676.htm#SEC728 41249 2446 makeQso3 sing_674.htm#SEC726 58910 2447 makeSheaf sing_2519.htm#SEC2595 10497 2448 makeUe6 sing_671.htm#SEC723 58585 2449 makeUe7 sing_672.htm#SEC724 61849 2450 makeUe8 sing_673.htm#SEC725 64987 2451 makeUf4 sing_670.htm#SEC722 8408 2452 makeUg2 sing_669.htm#SEC721 34512 2453 makeUgl sing_655.htm#SEC707 3543 2454 makeUsl sing_654.htm#SEC706 24536 2455 makeUsl2 sing_653.htm#SEC705 42637 2456 makeUso10 sing_661.htm#SEC713 6936 2457 makeUso11 sing_662.htm#SEC714 35873 2458 makeUso12 sing_663.htm#SEC715 19319 2459 makeUso5 sing_656.htm#SEC708 34378 2460 makeUso6 sing_657.htm#SEC709 65009 2461 makeUso7 sing_658.htm#SEC710 49142 2462 makeUso8 sing_659.htm#SEC711 33275 2463 makeUso9 sing_660.htm#SEC712 16896 2464 makeUsp1 sing_664.htm#SEC716 44522 2465 makeUsp2 sing_665.htm#SEC717 18017 2466 makeUsp3 sing_666.htm#SEC718 57445 2467 makeUsp4 sing_667.htm#SEC719 51690 2468 makeUsp5 sing_668.htm#SEC720 35951 2469 makeVariety sing_2511.htm#SEC2587 23915 2470 makeWeyl sing_710.htm#SEC762 8554 2471 map sing_123.htm#SEC163 2472 map (plural) sing_420.htm#SEC460 2473 map declarations sing_124.htm#SEC164 2474 map declarations (plural) map declarations (plural) sing_421.htm#SEC461 2475 map expressions sing_125.htm#SEC165 2476 map expressions (plural) map expressions (plural) sing_422.htm#SEC462 2477 map operations sing_126.htm#IDX129 2478 map operations (plural) map operations (plural) sing_423.htm#IDX298 2479 map related functions map related functions sing_127.htm#IDX131 2480 map related functions (plural) map related functions (plural) sing_424.htm#IDX299 2481 mapIsFinite sing_1103.htm#SEC1179 60897 2482 mapToRatNormCurve sing_1363.htm#SEC1439 8877 2483 mapall sing_988.htm#SEC1064 14907 2484 mappingcone sing_2424.htm#SEC2500 48219 2485 mappingcone3 sing_2426.htm#SEC2502 58973 2486 markov4ti2 sing_1319.htm#SEC1395 9163 2487 mat2arr sing_2160.htm#SEC2236 20840 2488 mat2carr sing_2161.htm#SEC2237 13777 2489 mat_rk sing_1077.htm#SEC1153 32196 2490 matbil sing_1964.htm#SEC2040 1611 2491 mathematical objects Representation of mathematical objects sing_834.htm#SEC886 2492 mathinit sing_1749.htm#SEC1825 16793 2493 matmult sing_1965.htm#SEC2041 60088 2494 matrix sing_128.htm#SEC168 2495 matrix sing_2160.htm#IDX805 2496 matrix sing_2161.htm#IDX808 2497 matrix sing_2162.htm#IDX812 2498 matrix declarations sing_129.htm#SEC169 2499 matrix diagonalization sing_1826.htm#IDX781 2500 matrix expressions sing_130.htm#SEC170 2501 matrix operations sing_132.htm#SEC172 2502 matrix related functions matrix related functions sing_133.htm#SEC173 2503 matrix type cast sing_131.htm#SEC171 2504 matrix.lib sing_1030.htm#SEC1106 2505 matrixExp sing_1353.htm#SEC1429 53063 2506 matrixLog sing_1354.htm#SEC1430 26235 2507 matrixT1 sing_1605.htm#SEC1681 15051 2508 matrix_lib sing_1030.htm#SEC1106 2509 matrixpres sing_2429.htm#SEC2505 60645 2510 matrixsystem sing_2363.htm#SEC2439 62950 2511 max sing_284.htm#SEC324 23624 2512 maxEord sing_1378.htm#SEC1454 64032 2513 maxExp sing_204.htm#IDX136 2514 maxIntRoot sing_777.htm#SEC829 37127 2515 maxZeros sing_1356.htm#SEC1432 35964 2516 maxabs sing_1983.htm#SEC2059 64510 2517 maxcoef sing_946.htm#SEC1022 50577 2518 maxdeg sing_947.htm#SEC1023 39794 2519 maxdeg1 sing_948.htm#SEC1024 21545 2520 maxideal sing_285.htm#SEC325 2521 maximalFace sing_2096.htm#SEC2172 35224 2522 maximalGroebnerCone sing_2150.htm#SEC2226 62935 2523 maximalValue sing_2097.htm#SEC2173 32783 2524 maximum sing_1856.htm#SEC1932 2355 2525 maximum number of zeroes sing_1356.htm#IDX588 2530 local rings, computing in Rings associated to monomial orderings sing_807.htm#SEC859 2531 local weighted lexicographical ordering sing_858.htm#IDX411 2532 local weighted reverse lexicographical ordering Local orderings sing_858.htm#IDX408 2533 localInvar sing_1676.htm#SEC1752 38478 2534 localization Rings associated to monomial orderings sing_807.htm#SEC859 2535 localization sing_2186.htm#IDX863 2536 localization of D-module sing_563.htm#IDX345 2537 localization of D-module sing_777.htm#IDX383 2538 locally closed set sing_925.htm#IDX444 2539 locally closed set sing_926.htm#IDX446 2540 locally closed set sing_927.htm#IDX448 2541 locally closed set sing_928.htm#IDX452 2542 locally closed set sing_930.htm#IDX463 2543 localstd sing_1967.htm#SEC2043 25562 2544 locnormal.lib sing_1180.htm#SEC1256 2545 locnormal_lib sing_1180.htm#SEC1256 2546 locstd sing_1605.htm#SEC1681 25864 2547 locus FamElemsAtEnvCompPoints sing_932.htm#SEC1008 22530 2548 locus sing_932.htm#IDX468 2549 locus sing_933.htm#IDX471 2550 locus sing_934.htm#IDX474 2551 locus sing_935.htm#IDX477 2552 locus sing_936.htm#IDX480 2553 locus sing_937.htm#IDX482 2554 locus sing_938.htm#IDX486 2555 locusdg sing_933.htm#SEC1009 6077 2556 locusto sing_935.htm#SEC1011 730 2557 log2 sing_1857.htm#SEC1933 40703 2558 logarithmic annihilator ideal sing_540.htm#IDX334 2559 logg sing_2727.htm#SEC2803 38736 2560 lp, global ordering sing_857.htm#IDX389 2561 lp2iv sing_629.htm#SEC681 17398 2562 lp2ivId sing_630.htm#SEC682 16290 2563 lp2lstr sing_651.htm#SEC703 24713 2564 lpCalcSubstDegBound sing_639.htm#SEC691 46179 2565 lpCalcSubstDegBounds lpCalcSubstDegBounds sing_640.htm#SEC692 56500 2566 lpDHilbert sing_607.htm#SEC659 10461 2567 lpDHilbertSickle sing_608.htm#SEC660 41445 2568 lpDimCheck sing_604.htm#SEC656 9807 2569 lpGkDim sing_636.htm#SEC688 10351 2570 lpGlDimBound sing_637.htm#SEC689 53074 2571 lpHilbert sing_606.htm#SEC658 44093 2572 lpId2ivLi sing_631.htm#SEC683 13273 2573 lpIsPrime sing_635.htm#SEC687 27562 2574 lpIsSemiPrime sing_634.htm#SEC686 27642 2575 lpKDim sing_603.htm#SEC655 18278 2576 lpMis2Base sing_605.htm#SEC657 10826 2577 lpMis2Dim sing_602.htm#SEC654 39947 2578 lpMult sing_647.htm#SEC699 58898 2579 lpNF sing_644.htm#SEC696 2851 2580 lpNoetherian sing_633.htm#SEC685 43125 2581 lpOrdMisLex sing_620.htm#SEC672 30943 2582 lpPower sing_649.htm#SEC701 7325 2583 lpSickle sing_621.htm#SEC673 288 2584 lpSickleDim sing_623.htm#SEC675 61018 2585 lpSickleHil sing_622.htm#SEC674 55268 2586 lpSubstitute sing_638.htm#SEC690 54386 2587 lprint sing_943.htm#SEC1019 5285 2588 lres sing_288.htm#SEC328 2589 ls, local ordering sing_858.htm#IDX402 2590 lst2str sing_652.htm#SEC704 10088 2591 lsum sing_1147.htm#SEC1223 50315 2592 ludecomp sing_289.htm#SEC329 2593 luinverse sing_290.htm#SEC330 2594 lusolve sing_291.htm#SEC331 2595 mRes sing_2494.htm#SEC2570 58702 2596 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1929.htm#SEC2005 57945 2597 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1928.htm#SEC2004 33857 2598 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1927.htm#SEC2003 7880 2599 magnitude sing_1851.htm#SEC1927 37967 2600 makeDivisor sing_2346.htm#SEC2422 3414 2601 makeFormalDivisor sing_2356.htm#SEC2432 54579 2602 makeGraph sing_1138.htm#SEC1214 21758 2603 makeGraphVE sing_2713.htm#SEC2789 sprintf 2604 makeHeisenberg sing_728.htm#SEC780 2050 2605 makeIdeal sing_2486.htm#SEC2562 57829 2606 makeLetterplaceRing sing_642.htm#SEC694 1592 2607 makeMalgrange sing_600.htm#SEC652 41377 2608 makeMatrix sing_2485.htm#SEC2561 64348 2609 makeModElimRing sing_745.htm#SEC797 56092 2610 makePDivisor sing_2362.htm#SEC2438 45273 2611 makeQsl2 sing_692.htm#SEC744 3997 2612 makeQsl3 sing_693.htm#SEC745 41249 2613 makeQso3 sing_691.htm#SEC743 58910 2614 makeSheaf sing_2701.htm#SEC2777 10497 2615 makeUe6 sing_688.htm#SEC740 58585 2616 makeUe7 sing_689.htm#SEC741 61849 2617 makeUe8 sing_690.htm#SEC742 64987 2618 makeUf4 sing_687.htm#SEC739 8408 2619 makeUg2 sing_686.htm#SEC738 34512 2620 makeUgl sing_672.htm#SEC724 3543 2621 makeUsl sing_671.htm#SEC723 24536 2622 makeUsl2 sing_670.htm#SEC722 42637 2623 makeUso10 sing_678.htm#SEC730 6936 2624 makeUso11 sing_679.htm#SEC731 35873 2625 makeUso12 sing_680.htm#SEC732 19319 2626 makeUso5 sing_673.htm#SEC725 34378 2627 makeUso6 sing_674.htm#SEC726 65009 2628 makeUso7 sing_675.htm#SEC727 49142 2629 makeUso8 sing_676.htm#SEC728 33275 2630 makeUso9 sing_677.htm#SEC729 16896 2631 makeUsp1 sing_681.htm#SEC733 44522 2632 makeUsp2 sing_682.htm#SEC734 18017 2633 makeUsp3 sing_683.htm#SEC735 57445 2634 makeUsp4 sing_684.htm#SEC736 51690 2635 makeUsp5 sing_685.htm#SEC737 35951 2636 makeVariety sing_2693.htm#SEC2769 23915 2637 makeVector sing_2514.htm#SEC2590 9049 2638 makeWeyl sing_727.htm#SEC779 8554 2639 map sing_128.htm#SEC168 2640 map (plural) sing_428.htm#SEC468 2641 map declarations sing_129.htm#SEC169 2642 map declarations (plural) map declarations (plural) sing_429.htm#SEC469 2643 map expressions sing_130.htm#SEC170 2644 map expressions (plural) map expressions (plural) sing_430.htm#SEC470 2645 map operations sing_131.htm#IDX129 2646 map operations (plural) map operations (plural) sing_431.htm#IDX300 2647 map related functions map related functions sing_132.htm#IDX131 2648 map related functions (plural) map related functions (plural) sing_432.htm#IDX301 2649 mapIsFinite sing_1115.htm#SEC1191 60897 2650 mapToRatNormCurve sing_1377.htm#SEC1453 8877 2651 mapall sing_1008.htm#SEC1084 14907 2652 mappingcone sing_2473.htm#SEC2549 48219 2653 mappingcone3 sing_2475.htm#SEC2551 58973 2654 markov4ti2 sing_1333.htm#SEC1409 9163 2655 mat2arr sing_2171.htm#SEC2247 20840 2656 mat2carr sing_2172.htm#SEC2248 13777 2657 mat_rk sing_1089.htm#SEC1165 32196 2658 matbil sing_1978.htm#SEC2054 1611 2659 mathematical objects Representation of mathematical objects sing_853.htm#SEC905 2660 mathinit sing_1763.htm#SEC1839 16793 2661 matmult sing_1979.htm#SEC2055 60088 2662 matrix sing_133.htm#SEC173 2663 matrix sing_2171.htm#IDX831 2664 matrix sing_2172.htm#IDX834 2665 matrix sing_2173.htm#IDX838 2666 matrix declarations sing_134.htm#SEC174 2667 matrix diagonalization sing_1840.htm#IDX807 2668 matrix expressions sing_135.htm#SEC175 2669 matrix operations sing_137.htm#SEC177 2670 matrix related functions matrix related functions sing_138.htm#SEC178 2671 matrix type cast sing_136.htm#SEC176 2672 matrix.lib sing_1042.htm#SEC1118 2673 matrixExp sing_1367.htm#SEC1443 53063 2674 matrixLog sing_1368.htm#SEC1444 26235 2675 matrixT1 sing_1619.htm#SEC1695 15051 2676 matrix_lib sing_1042.htm#SEC1118 2677 matrixpres sing_2478.htm#SEC2554 60645 2678 matrixsystem sing_2386.htm#SEC2462 62950 2679 max sing_292.htm#SEC332 23624 2680 maxEord sing_1392.htm#SEC1468 64032 2681 maxExp sing_209.htm#IDX136 2682 maxIntRoot sing_794.htm#SEC846 37127 2683 maxZeros sing_1370.htm#SEC1446 35964 2684 maxabs sing_1997.htm#SEC2073 64510 2685 maxcoef sing_966.htm#SEC1042 50577 2686 maxdeg sing_967.htm#SEC1043 39794 2687 maxdeg1 sing_968.htm#SEC1044 21545 2688 maxideal sing_293.htm#SEC333 2689 maximalFace sing_2107.htm#SEC2183 35224 2690 maximalGroebnerCone sing_2161.htm#SEC2237 62935 2691 maximalValue sing_2108.htm#SEC2184 32783 2692 maximum sing_1870.htm#SEC1946 2355 2693 maximum number of zeroes sing_1370.htm#IDX614 2526 2694 mdouble sing_56.htm#SEC93 56685 2527 mem, option sing_307.htm#IDX180 2528 membershipMon sing_1179.htm#SEC1255 40876 2529 memory sing_286.htm#SEC326 2530 memory managment sing_286.htm#SEC326 2531 merkle_hellman_decryption merkle_hellman_decryption sing_1917.htm#SEC1993 49106 2532 merkle_hellman_encryption merkle_hellman_encryption sing_1916.htm#SEC1992 13645 2533 midpoint sing_2359.htm#SEC2435 29391 2534 milnor sing_1592.htm#SEC1668 23173 2535 milnorcode sing_1476.htm#SEC1552 13849 2536 milnornumber sing_2499.htm#SEC2575 21855 2537 min sing_287.htm#SEC327 56342 2538 minAssChar sing_1278.htm#SEC1354 18758 2539 minAssCharE sing_1279.htm#SEC1355 31570 2540 minAssGTZ sing_1276.htm#SEC1352 41315 2541 minAssGTZE sing_1277.htm#SEC1353 50867 2542 minAssZ sing_1296.htm#SEC1372 54152 2543 minEcart sing_1946.htm#SEC2022 34890 2544 minIntRoot sing_553.htm#SEC605 3288 2545 minIntRoot2 sing_776.htm#SEC828 46494 2546 minMult sing_1110.htm#SEC1186 31978 2547 minbase sing_288.htm#SEC328 2548 minbaseMon sing_1176.htm#SEC1252 1501 2549 mindeg sing_949.htm#SEC1025 16307 2550 mindeg1 sing_950.htm#SEC1026 39698 2551 mindist sing_1801.htm#SEC1877 55281 2552 minimal display time, setting the sing_350.htm#IDX282 2553 minimalFace sing_2098.htm#SEC2174 40971 2554 minimalValue sing_2099.htm#SEC2175 31262 2555 minipoly sing_1082.htm#SEC1158 4927 2556 minkowskiSum sing_2100.htm#SEC2176 3969 2557 minor sing_289.htm#SEC329 2558 minpoly sing_389.htm#SEC429 2559 minres sing_290.htm#SEC330 2560 minres (plural) sing_459.htm#SEC499 2561 mirror symmetry sing_1125.htm#IDX509 2562 mixed Hodge structure sing_1514.htm#IDX644 2563 mixed Hodge structure sing_1520.htm#IDX672 2564 mixed Hodge structure sing_1521.htm#IDX678 2565 mixed Hodge structure sing_1522.htm#IDX686 2566 mixed Hodge structure sing_1523.htm#IDX692 2567 mixed Hodge structure sing_1524.htm#IDX700 2568 mixed Hodge structure sing_1525.htm#IDX710 2569 mixed Hodge structure sing_1536.htm#IDX716 2570 mixed Hodge structure sing_1538.htm#IDX727 2571 mod sing_76.htm#SEC116 2572 mod sing_93.htm#SEC133 2573 mod sing_142.htm#SEC182 2574 mod2id sing_954.htm#SEC1030 27927 2575 mod2str sing_635.htm#SEC687 35236 2576 modBorder sing_2503.htm#SEC2579 19224 2577 modDec sing_1195.htm#SEC1271 48578 2578 modJanet sing_2505.htm#SEC2581 8550 2579 modNPos sing_1218.htm#SEC1294 17130 2580 modNormal sing_1171.htm#SEC1247 39654 2581 modNpos_test sing_1216.htm#SEC1292 34326 2582 modStd sing_1173.htm#SEC1249 4500 2583 modVStd sing_2310.htm#SEC2386 38529 2584 modVStd0 sing_2311.htm#SEC2387 46080 2585 modWalk sing_2433.htm#SEC2509 sprintf 2586 mod_versal sing_1505.htm#SEC1581 63927 2587 modality sing_1484.htm#SEC1560 49951 2588 modfWalk sing_2435.htm#SEC2511 sprintf 2589 modfrWalk sing_2436.htm#SEC2512 sprintf 2590 modnormal.lib sing_1170.htm#SEC1246 2591 modnormal_lib sing_1170.htm#SEC1246 2592 modrWalk sing_2434.htm#SEC2510 sprintf 2593 modregCM sing_1222.htm#SEC1298 5049 2594 modsatiety sing_1220.htm#SEC1296 44506 2595 modstd.lib sing_1172.htm#SEC1248 2596 modstd_lib sing_1172.htm#SEC1248 2597 modular sing_932.htm#SEC1008 16950 2598 modular methods sing_1168.htm#IDX542 2599 modular methods sing_1170.htm#IDX547 2600 modular methods. sing_1169.htm#IDX545 2601 modular techniques. sing_1171.htm#IDX549 2602 modular.lib sing_931.htm#SEC1007 2603 modular_lib sing_931.htm#SEC1007 2604 modular_lib sing_931.htm#IDX474 2605 module sing_134.htm#SEC174 2606 module (plural) sing_425.htm#SEC465 2607 module declarations sing_135.htm#SEC175 2608 module declarations (plural) module declarations (plural) sing_426.htm#SEC466 2609 module expressions sing_136.htm#SEC176 2610 module expressions (plural) module expressions (plural) sing_427.htm#SEC467 2611 module operations sing_137.htm#SEC177 2612 module operations (plural) module operations (plural) sing_428.htm#SEC468 2613 module ordering C sing_840.htm#IDX412 2614 module ordering c sing_840.htm#IDX414 2615 module related functions module related functions sing_138.htm#SEC178 2616 module related functions (plural) module related functions (plural) sing_429.htm#SEC469 2617 module_containment sing_1095.htm#SEC1171 31620 2618 moduliSpace sing_2533.htm#SEC2609 37013 2619 modulo sing_291.htm#SEC331 2620 modulo (plural) sing_460.htm#SEC500 2621 moduloSlim sing_718.htm#SEC770 52636 2622 modwalk.lib sing_2432.htm#IDX955 2623 modwalk_lib sing_2432.htm#IDX956 2624 moebius sing_2196.htm#SEC2272 61319 2625 moebius function sing_2196.htm#IDX878 2626 molien sing_1628.htm#SEC1704 63561 2627 mondromy.lib sing_1566.htm#SEC1642 2628 mondromy_lib sing_1566.htm#SEC1642 2629 monitor sing_292.htm#SEC332 2630 monodromy sing_1514.htm#IDX648 40112 2631 monodromy sing_1519.htm#SEC1595 2632 monodromy sing_1519.htm#IDX668 2633 monodromy sing_1524.htm#IDX703 2634 monodromy sing_1536.htm#IDX719 2635 monodromy sing_1538.htm#IDX730 2636 monodromyB sing_1570.htm#SEC1646 46517 2637 monomial sing_293.htm#SEC333 2638 monomial ordering sing_997.htm#IDX488 2639 monomial orderings General definitions for orderings sing_790.htm#SEC842 2640 monomial orderings sing_837.htm#SEC889 2641 monomial orderings introduction Introduction to orderings sing_836.htm#SEC888 2642 monomialInIdeal sing_774.htm#SEC826 4687 2643 monomialLcm sing_1944.htm#SEC2020 36233 2644 monomialabortstd sing_2203.htm#SEC2279 14901 2645 monomialideal.lib sing_1174.htm#SEC1250 2646 monomialideal_lib sing_1174.htm#SEC1250 2647 monomials and precedence Miscellaneous oddities sing_410.htm#IDX288 2648 mons2intmat sing_1263.htm#SEC1339 15555 2649 morsesplit sing_1477.htm#SEC1553 3417 2650 mp_res_mat sing_1710.htm#SEC1786 44453 2651 mplot sing_1750.htm#SEC1826 21740 2652 mpresmat sing_294.htm#SEC334 2653 mprimdec.lib sing_1191.htm#SEC1267 2654 mprimdec_lib sing_1191.htm#SEC1267 2655 mregular.lib sing_1206.htm#SEC1282 2656 mregular_lib sing_1206.htm#SEC1282 2657 mres sing_295.htm#SEC335 2658 mres (plural) sing_461.htm#SEC501 2659 mstd sing_296.htm#SEC336 2695 mem, option sing_315.htm#IDX180 2696 membershipMon sing_1193.htm#SEC1269 40876 2697 memory sing_294.htm#SEC334 2698 memory managment sing_294.htm#SEC334 2699 merkle_hellman_decryption merkle_hellman_decryption sing_1931.htm#SEC2007 49106 2700 merkle_hellman_encryption merkle_hellman_encryption sing_1930.htm#SEC2006 13645 2701 midpoint sing_2382.htm#SEC2458 29391 2702 milnor sing_1606.htm#SEC1682 23173 2703 milnorcode sing_1490.htm#SEC1566 13849 2704 milnornumber sing_2667.htm#SEC2743 21855 2705 min sing_295.htm#SEC335 56342 2706 minAssChar sing_1292.htm#SEC1368 18758 2707 minAssCharE sing_1293.htm#SEC1369 31570 2708 minAssGTZ sing_1290.htm#SEC1366 41315 2709 minAssGTZE sing_1291.htm#SEC1367 50867 2710 minAssZ sing_1310.htm#SEC1386 54152 2711 minEcart sing_1960.htm#SEC2036 34890 2712 minIntRoot sing_561.htm#SEC613 3288 2713 minIntRoot2 sing_793.htm#SEC845 46494 2714 minMult sing_1122.htm#SEC1198 31978 2715 minbase sing_296.htm#SEC336 2716 minbaseMon sing_1190.htm#SEC1266 1501 2717 mindeg sing_969.htm#SEC1045 16307 2718 mindeg1 sing_970.htm#SEC1046 39698 2719 mindist sing_1815.htm#SEC1891 55281 2720 minimal display time, setting the sing_358.htm#IDX284 2721 minimalAfaceOrbits sing_2424.htm#SEC2500 2467 2722 minimalAfaces sing_2415.htm#SEC2491 47736 2723 minimalFace sing_2109.htm#SEC2185 40971 2724 minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2426.htm#SEC2502 11756 2725 minimalValue sing_2110.htm#SEC2186 31262 2726 minipoly sing_1094.htm#SEC1170 4927 2727 minkowskiSum sing_2111.htm#SEC2187 3969 2728 minor sing_297.htm#SEC337 2729 minpoly sing_397.htm#SEC437 2730 minres sing_298.htm#SEC338 2731 minres (plural) sing_467.htm#SEC507 2732 mirror symmetry sing_1137.htm#IDX524 2733 mixed Hodge structure sing_1528.htm#IDX670 2734 mixed Hodge structure sing_1534.htm#IDX698 2735 mixed Hodge structure sing_1535.htm#IDX704 2736 mixed Hodge structure sing_1536.htm#IDX712 2737 mixed Hodge structure sing_1537.htm#IDX718 2738 mixed Hodge structure sing_1538.htm#IDX726 2739 mixed Hodge structure sing_1539.htm#IDX736 2740 mixed Hodge structure sing_1550.htm#IDX742 2741 mixed Hodge structure sing_1552.htm#IDX753 2742 mod sing_81.htm#SEC121 2743 mod sing_98.htm#SEC138 2744 mod sing_147.htm#SEC187 2745 mod sing_155.htm#SEC195 2746 mod2id sing_974.htm#SEC1050 27927 2747 mod2str sing_653.htm#SEC705 35236 2748 modBorder sing_2685.htm#SEC2761 19224 2749 modDec sing_1209.htm#SEC1285 48578 2750 modIntersect sing_1187.htm#SEC1263 43699 2751 modJanet sing_2687.htm#SEC2763 8550 2752 modNPos sing_1232.htm#SEC1308 17130 2753 modNormal sing_1183.htm#SEC1259 39654 2754 modNpos_test sing_1230.htm#SEC1306 34326 2755 modSagbiAlg sing_2327.htm#SEC2403 25025 2756 modStd sing_1185.htm#SEC1261 7824 2757 modSyz sing_1186.htm#SEC1262 37065 2758 modVStd sing_2332.htm#SEC2408 38529 2759 modVStd0 sing_2333.htm#SEC2409 46080 2760 modWalk sing_2535.htm#SEC2611 sprintf 2761 mod_versal sing_1519.htm#SEC1595 63927 2762 modality sing_1498.htm#SEC1574 49951 2763 modfWalk sing_2537.htm#SEC2613 sprintf 2764 modfrWalk sing_2538.htm#SEC2614 sprintf 2765 modnormal.lib sing_1182.htm#SEC1258 2766 modnormal_lib sing_1182.htm#SEC1258 2767 modrWalk sing_2536.htm#SEC2612 sprintf 2768 modregCM sing_1236.htm#SEC1312 5049 2769 modsatiety sing_1234.htm#SEC1310 44506 2770 modstd.lib sing_1184.htm#SEC1260 2771 modstd_lib sing_1184.htm#SEC1260 2772 modular sing_952.htm#SEC1028 16950 2773 modular methods sing_1180.htm#IDX557 2774 modular methods sing_1182.htm#IDX562 2775 modular methods. sing_1181.htm#IDX560 2776 modular techniques. sing_1183.htm#IDX564 2777 modular.lib sing_951.htm#SEC1027 2778 modular_lib sing_951.htm#SEC1027 2779 modular_lib sing_951.htm#IDX492 2780 module sing_139.htm#SEC179 2781 module (plural) sing_433.htm#SEC473 2782 module declarations sing_140.htm#SEC180 2783 module declarations (plural) module declarations (plural) sing_434.htm#SEC474 2784 module expressions sing_141.htm#SEC181 2785 module expressions (plural) module expressions (plural) sing_435.htm#SEC475 2786 module operations sing_142.htm#SEC182 2787 module operations (plural) module operations (plural) sing_436.htm#SEC476 2788 module ordering C sing_859.htm#IDX414 2789 module ordering c sing_859.htm#IDX416 2790 module related functions module related functions sing_143.htm#SEC183 2791 module related functions (plural) module related functions (plural) sing_437.htm#SEC477 2792 module_containment sing_1107.htm#SEC1183 31620 2793 modules.lib sing_2481.htm#SEC2557 2794 modules_lib sing_2481.htm#SEC2557 2795 moduliSpace sing_2715.htm#SEC2791 37013 2796 modulo sing_299.htm#SEC339 2797 modulo (plural) sing_468.htm#SEC508 2798 moduloSlim sing_735.htm#SEC787 52636 2799 modwalk.lib sing_2534.htm#SEC2610 2800 modwalk_lib sing_2534.htm#SEC2610 2801 moebius sing_2207.htm#SEC2283 61319 2802 moebius function sing_2207.htm#IDX904 2803 molien sing_1642.htm#SEC1718 63561 2804 mondromy.lib sing_1580.htm#SEC1656 2805 mondromy_lib sing_1580.htm#SEC1656 2806 monitor sing_300.htm#SEC340 2807 monodromy sing_1528.htm#IDX674 40112 2808 monodromy sing_1533.htm#SEC1609 2809 monodromy sing_1533.htm#IDX694 2810 monodromy sing_1538.htm#IDX729 2811 monodromy sing_1550.htm#IDX745 2812 monodromy sing_1552.htm#IDX756 2813 monodromyB sing_1584.htm#SEC1660 46517 2814 monomial sing_301.htm#SEC341 2815 monomial ordering sing_1017.htm#IDX506 2816 monomial orderings General definitions for orderings sing_807.htm#SEC859 2817 monomial orderings sing_856.htm#SEC908 2818 monomial orderings introduction Introduction to orderings sing_855.htm#SEC907 2819 monomialInIdeal sing_791.htm#SEC843 4687 2820 monomialLcm sing_1958.htm#SEC2034 36233 2821 monomialabortstd sing_2214.htm#SEC2290 14901 2822 monomialideal.lib sing_1188.htm#SEC1264 2823 monomialideal_lib sing_1188.htm#SEC1264 2824 monomials and precedence Miscellaneous oddities sing_418.htm#IDX290 2825 mons2intmat sing_1277.htm#SEC1353 15555 2826 morsesplit sing_1491.htm#SEC1567 3417 2827 movingCone sing_2422.htm#SEC2498 39892 2828 mp_res_mat sing_1724.htm#SEC1800 44453 2829 mplot sing_1764.htm#SEC1840 21740 2830 mpresmat sing_302.htm#SEC342 2831 mprimdec.lib sing_1205.htm#SEC1281 2832 mprimdec_lib sing_1205.htm#SEC1281 2833 mregular.lib sing_1220.htm#SEC1296 2834 mregular_lib sing_1220.htm#SEC1296 2835 mres sing_303.htm#SEC343 2836 mres (plural) sing_469.htm#SEC509 2837 mstd sing_304.htm#SEC344 2660 2838 msum sing_58.htm#SEC95 53344 2661 2839 mtriple sing_57.htm#SEC94 55390 2662 mult Miscellaneous oddities sing_ 297.htm#SEC3372663 mult sing_41 0.htm#IDX2892664 multBound sing_39 0.htm#SEC4302665 multRat sing_7 82.htm#SEC834440472666 multarr2arr sing_2 191.htm#SEC2267447312667 multarrMultRestrict sing_2 193.htm#SEC2269417422668 multarrRestrict sing_2 192.htm#SEC2268sprintf2669 multcol sing_10 49.htm#SEC1125218992670 multdivisor sing_23 25.htm#SEC2401651392671 multformaldivisor sing_23 37.htm#SEC2413322382672 multi sing_19 31.htm#SEC2007184732840 mult Miscellaneous oddities sing_305.htm#SEC345 2841 mult sing_418.htm#IDX291 2842 multBound sing_398.htm#SEC438 2843 multRat sing_799.htm#SEC851 44047 2844 multarr2arr sing_2202.htm#SEC2278 44731 2845 multarrMultRestrict sing_2204.htm#SEC2280 41742 2846 multarrRestrict sing_2203.htm#SEC2279 sprintf 2847 multcol sing_1061.htm#SEC1137 21899 2848 multdivisor sing_2348.htm#SEC2424 65139 2849 multformaldivisor sing_2360.htm#SEC2436 32238 2850 multi sing_1945.htm#SEC2021 18473 2673 2851 multi indices sing_37.htm#SEC65 2674 multiDeg sing_2467.htm#SEC2543 7049 2675 multiDegBasis sing_2468.htm#SEC2544 3320 2676 multiDegGroebner sing_2476.htm#SEC2552 1040 2677 multiDegModulo sing_2478.htm#SEC2554 27244 2678 multiDegPartition sing_2469.htm#SEC2545 9577 2679 multiDegResolution sing_2479.htm#SEC2555 38535 2680 multiDegSyzygy sing_2477.htm#SEC2553 54075 2681 multiDegTensor sing_2480.htm#SEC2556 45108 2682 multiDegTor sing_2481.htm#SEC2557 sprintf 2683 multiarrangement sing_2187.htm#IDX858 2684 multiarrangement sing_2188.htm#IDX860 2685 multiarrangement sing_2189.htm#IDX863 2686 multiarrangement sing_2190.htm#IDX864 2687 multiarrangement sing_2191.htm#IDX867 2688 multiarrangement sing_2192.htm#IDX870 2689 multiarrangement sing_2193.htm#IDX872 2690 multidimensional_knapsack multidimensional_knapsack sing_1909.htm#SEC1985 15647 2691 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2437.htm#IDX961 2692 multigrading.lib sing_2437.htm#IDX959 2693 multigrading_lib sing_2437.htm#IDX960 2694 multipleCover sing_2539.htm#SEC2615 55988 2695 multiplicities, sequence of sing_1545.htm#IDX742 2696 multiplicity sing_2316.htm#IDX920 2697 multiplicity sequence sing_1458.htm#IDX621 2698 multiplicity sequence sing_1461.htm#IDX633 2699 multiplicity sequence sing_1547.htm#IDX743 2700 multiplylist sing_1398.htm#SEC1474 34999 2701 multivariate equations sing_1684.htm#IDX760 2702 multrow sing_1050.htm#SEC1126 871 2703 multseq2charexp sing_1457.htm#SEC1533 sprintf 2704 multsequence sing_1547.htm#SEC1623 35117 2705 nBoundaryLatticePoints nBoundaryLatticePoints sing_2101.htm#SEC2177 49670 2706 nHilbertBasis sing_2102.htm#SEC2178 173 2707 nInteriorLatticePoints nInteriorLatticePoints sing_2103.htm#SEC2179 42152 2708 nLatticePoints sing_2104.htm#SEC2180 5977 2709 naccache_stern_decryption naccache_stern_decryption sing_1912.htm#SEC1988 31429 2710 naccache_stern_encryption naccache_stern_encryption sing_1911.htm#SEC1987 60034 2711 naccache_stern_generation naccache_stern_generation sing_1910.htm#SEC1986 2559 2712 nameof sing_298.htm#SEC338 2713 names sing_299.htm#SEC339 2714 nashmult sing_1465.htm#SEC1541 8491 2715 nblocks sing_350.htm#IDX221 2716 ncExt_R sing_751.htm#SEC803 14357 2717 ncHilb.lib sing_2489.htm#SEC2565 2718 ncHilb_lib sing_2489.htm#SEC2565 2719 ncHom sing_752.htm#SEC804 45033 2720 ncRelations sing_719.htm#SEC771 7225 2721 nc_algebra sing_462.htm#SEC502 2722 nc_hilb sing_350.htm#IDX223 2723 ncalg.lib sing_652.htm#SEC704 2724 ncalg_lib sing_652.htm#SEC704 2725 ncalgebra sing_463.htm#SEC503 2726 ncdecomp.lib sing_679.htm#SEC731 2727 ncdecomp_lib sing_679.htm#SEC731 2728 ncdetection sing_646.htm#SEC698 24994 2729 ncfactor sing_685.htm#SEC737 53809 2730 ncfactor.lib sing_684.htm#SEC736 2731 ncfactor_lib sing_684.htm#SEC736 2732 nchilb sing_2490.htm#SEC2566 9026 2733 nchomolog.lib sing_750.htm#IDX371 2734 nchomolog_lib sing_750.htm#IDX372 2735 ncols sing_300.htm#SEC340 2736 ncones sing_2046.htm#SEC2122 48316 2737 ncpreim.lib sing_697.htm#SEC749 2738 ncpreim_lib sing_697.htm#SEC749 2739 nctools.lib sing_705.htm#SEC757 2740 nctools_lib sing_705.htm#SEC757 2741 ndcond sing_708.htm#SEC760 1006 2742 negatedCone sing_2024.htm#SEC2100 38527 2743 negative degree lexicographical ordering sing_839.htm#IDX403 2744 negative degree reverse lexicographical ordering Local orderings sing_839.htm#IDX401 2745 negative lexicographical ordering sing_839.htm#IDX399 2746 negativedivisor sing_2326.htm#SEC2402 8274 2747 negativeformaldivisor negativeformaldivisor sing_2336.htm#SEC2412 55026 2852 multiDeg sing_2569.htm#SEC2645 7049 2853 multiDegBasis sing_2570.htm#SEC2646 3320 2854 multiDegGroebner sing_2578.htm#SEC2654 1040 2855 multiDegModulo sing_2580.htm#SEC2656 27244 2856 multiDegPartition sing_2571.htm#SEC2647 9577 2857 multiDegResolution sing_2581.htm#SEC2657 38535 2858 multiDegSyzygy sing_2579.htm#SEC2655 54075 2859 multiDegTensor sing_2582.htm#SEC2658 45108 2860 multiDegTor sing_2583.htm#SEC2659 sprintf 2861 multiarrangement sing_2198.htm#IDX884 2862 multiarrangement sing_2199.htm#IDX886 2863 multiarrangement sing_2200.htm#IDX889 2864 multiarrangement sing_2201.htm#IDX890 2865 multiarrangement sing_2202.htm#IDX893 2866 multiarrangement sing_2203.htm#IDX896 2867 multiarrangement sing_2204.htm#IDX898 2868 multidimensional_knapsack multidimensional_knapsack sing_1923.htm#SEC1999 15647 2869 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2539.htm#IDX997 2870 multigrading.lib sing_2539.htm#IDX995 2871 multigrading_lib sing_2539.htm#IDX996 2872 multipleCover sing_2721.htm#SEC2797 55988 2873 multiplicities, sequence of sing_1559.htm#IDX768 2874 multiplicity sing_2339.htm#IDX956 2875 multiplicity sequence sing_1472.htm#IDX647 2876 multiplicity sequence sing_1475.htm#IDX659 2877 multiplicity sequence sing_1561.htm#IDX769 2878 multiplyLeftFractions multiplyLeftFractions sing_2654.htm#SEC2730 57489 2879 multiplylist sing_1412.htm#SEC1488 34999 2880 multivariate equations sing_1698.htm#IDX786 2881 multrow sing_1062.htm#SEC1138 871 2882 multseq2charexp sing_1471.htm#SEC1547 sprintf 2883 multsequence sing_1561.htm#SEC1637 35117 2884 nBoundaryLatticePoints nBoundaryLatticePoints sing_2112.htm#SEC2188 49670 2885 nHilbertBasis sing_2113.htm#SEC2189 173 2886 nInteriorLatticePoints nInteriorLatticePoints sing_2114.htm#SEC2190 42152 2887 nLatticePoints sing_2115.htm#SEC2191 5977 2888 naccache_stern_decryption naccache_stern_decryption sing_1926.htm#SEC2002 31429 2889 naccache_stern_encryption naccache_stern_encryption sing_1925.htm#SEC2001 60034 2890 naccache_stern_generation naccache_stern_generation sing_1924.htm#SEC2000 2559 2891 nameof sing_306.htm#SEC346 2892 names sing_307.htm#SEC347 2893 nashmult sing_1479.htm#SEC1555 8491 2894 nblocks sing_358.htm#IDX221 2895 ncExt_R sing_768.htm#SEC820 14357 2896 ncHilb.lib sing_2591.htm#SEC2667 2897 ncHilb_lib sing_2591.htm#SEC2667 2898 ncHom sing_769.htm#SEC821 45033 2899 ncRelations sing_736.htm#SEC788 7225 2900 nc_algebra sing_470.htm#SEC510 2901 nc_hilb sing_358.htm#IDX223 2902 ncalg.lib sing_669.htm#SEC721 2903 ncalg_lib sing_669.htm#SEC721 2904 ncalgebra sing_471.htm#SEC511 2905 ncdecomp.lib sing_696.htm#SEC748 2906 ncdecomp_lib sing_696.htm#SEC748 2907 ncdetection sing_663.htm#SEC715 24994 2908 ncfactor sing_702.htm#SEC754 53809 2909 ncfactor.lib sing_701.htm#SEC753 2910 ncfactor_lib sing_701.htm#SEC753 2911 ncfrac.lib sing_2594.htm#SEC2670 2912 ncfrac_lib sing_2594.htm#SEC2670 2913 nchilb sing_2592.htm#SEC2668 40517 2914 nchomolog.lib sing_767.htm#IDX373 2915 nchomolog_lib sing_767.htm#IDX374 2916 ncloc.lib sing_2608.htm#SEC2684 2917 ncloc_lib sing_2608.htm#SEC2684 2918 ncols sing_308.htm#SEC348 2919 ncones sing_2060.htm#SEC2136 48316 2920 ncpreim.lib sing_714.htm#SEC766 2921 ncpreim_lib sing_714.htm#SEC766 2922 nctools.lib sing_722.htm#SEC774 2923 nctools_lib sing_722.htm#SEC774 2924 ndcond sing_725.htm#SEC777 1006 2925 negateNcfrac sing_2603.htm#SEC2679 23626 2926 negatedCone sing_2038.htm#SEC2114 38527 2927 negative degree lexicographical ordering sing_858.htm#IDX405 2928 negative degree reverse lexicographical ordering Local orderings sing_858.htm#IDX403 2929 negative lexicographical ordering sing_858.htm#IDX401 2930 negativedivisor sing_2349.htm#SEC2425 8274 2931 negativeformaldivisor negativeformaldivisor sing_2359.htm#SEC2435 55026 2932 net sing_2612.htm#IDX998 sprintf 2933 net sing_2614.htm#SEC2690 2748 2934 net access Command line options sing_19.htm#IDX40 2749 newTest sing_1851.htm#SEC1927 36655 2750 newline sing_166.htm#SEC206 2751 news sing_2562.htm#SEC2638 2752 newstruct sing_177.htm#SEC217 2753 newstruct sing_2210.htm#IDX894 2754 newtonDiag sing_958.htm#SEC1034 56652 2755 newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2555.htm#SEC2631 22052 2756 newtonPolytope sing_2050.htm#SEC2126 56291 2757 newtonPolytopeLP sing_2055.htm#SEC2131 36186 2758 newtonPolytopeP sing_2054.htm#SEC2130 29927 2759 newtonpoly sing_1552.htm#SEC1628 31930 2760 nf_icis sing_1593.htm#SEC1669 49093 2761 nfmodStd sing_2493.htm#SEC2569 46077 2762 nfmodSyz sing_2495.htm#SEC2571 55942 2763 nfmodstd.lib sing_2491.htm#SEC2567 2764 nfmodstd_lib sing_2491.htm#SEC2567 2765 nfmodsyz.lib sing_2494.htm#SEC2570 2766 nfmodsyz_lib sing_2494.htm#SEC2570 2767 nilpotent Lie algebras sing_1351.htm#IDX573 2768 nmaxcones sing_2045.htm#SEC2121 660 2769 noether sing_391.htm#SEC431 2770 noether.lib sing_1214.htm#SEC1290 2771 noetherNormal sing_1102.htm#SEC1178 44522 2772 noether_lib sing_1214.htm#SEC1290 2773 non-english special characters sing_399.htm#IDX284 2774 nonMonomials sing_1267.htm#SEC1343 16309 2775 nonZeroEntry sing_1105.htm#SEC1181 933 2776 none, option sing_307.htm#IDX150 2777 norTest sing_1234.htm#SEC1310 sprintf 2778 norm sing_1930.htm#SEC2006 31143 2779 normal sing_1224.htm#SEC1300 61073 2780 normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2538.htm#IDX995 2781 normal.lib sing_1223.htm#SEC1299 2782 normalBundle sing_2538.htm#SEC2614 sprintf 2783 normalC sing_1226.htm#SEC1302 34842 2784 normalConductor sing_1238.htm#SEC1314 26085 2785 normalFan sing_2105.htm#SEC2181 39216 2786 normalFanL sing_2056.htm#SEC2132 55096 2787 normalForm sing_2327.htm#SEC2403 34962 2788 normalI sing_1311.htm#SEC1387 7516 2789 normalP sing_1225.htm#SEC1301 36584 2790 normalToricRing sing_1241.htm#SEC1317 29638 2791 normalToricRingFromBinomials normalToricRingFromBinomials sing_1242.htm#SEC1318 2301 2792 normal_lib sing_1223.htm#SEC1299 2793 normalform sing_1481.htm#SEC1557 5550 2794 normalform sing_2305.htm#IDX913 2935 netBigInt sing_2620.htm#SEC2696 63523 2936 netBigIntMat sing_2615.htm#SEC2691 36296 2937 netBigIntMatShort sing_2616.htm#SEC2692 30702 2938 netCoefficientRing sing_2617.htm#SEC2693 6081 2939 netIdeal sing_2618.htm#SEC2694 64434 2940 netInt sing_2619.htm#SEC2695 19545 2941 netIntMat sing_2621.htm#SEC2697 34242 2942 netIntMatShort sing_2622.htm#SEC2698 21160 2943 netIntVector sing_2623.htm#SEC2699 17568 2944 netIntVectorShort sing_2624.htm#SEC2700 16105 2945 netList sing_2626.htm#SEC2702 29178 2946 netMap sing_2627.htm#SEC2703 19115 2947 netMap2 sing_2628.htm#SEC2704 44053 2948 netMatrix sing_2516.htm#SEC2592 29311 2949 netNumber sing_2625.htm#SEC2701 24930 2950 netPoly sing_2631.htm#SEC2707 7938 2951 netPrimePower sing_2632.htm#SEC2708 54219 2952 netRing sing_2633.htm#SEC2709 42246 2953 netString sing_2634.htm#SEC2710 43247 2954 netVector sing_2515.htm#SEC2591 32453 2955 netmatrix sing_2629.htm#SEC2705 4023 2956 netmatrixShort sing_2630.htm#SEC2706 24709 2957 nets.lib sing_2612.htm#SEC2688 2958 nets_lib sing_2612.htm#SEC2688 2959 netvector sing_2635.htm#SEC2711 39957 2960 netvectorShort sing_2636.htm#SEC2712 22053 2961 newTest sing_1865.htm#SEC1941 36655 2962 newline sing_171.htm#SEC211 2963 news sing_2744.htm#SEC2820 2964 newstruct sing_182.htm#SEC222 2965 newstruct sing_2221.htm#IDX920 2966 newtonDiag sing_978.htm#SEC1054 56652 2967 newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2737.htm#SEC2813 22052 2968 newtonPolytope sing_2064.htm#SEC2140 56291 2969 newtonPolytopeLP sing_2069.htm#SEC2145 36186 2970 newtonPolytopeP sing_2068.htm#SEC2144 29927 2971 newtonpoly sing_1566.htm#SEC1642 31930 2972 nf_icis sing_1607.htm#SEC1683 49093 2973 nfmodStd sing_2640.htm#SEC2716 46077 2974 nfmodSyz sing_2642.htm#SEC2718 55942 2975 nfmodstd.lib sing_2638.htm#SEC2714 2976 nfmodstd_lib sing_2638.htm#SEC2714 2977 nfmodsyz.lib sing_2641.htm#SEC2717 2978 nfmodsyz_lib sing_2641.htm#SEC2717 2979 nilpotent Lie algebras sing_1365.htm#IDX599 2980 nmaxcones sing_2059.htm#SEC2135 660 2981 noether sing_399.htm#SEC439 2982 noether.lib sing_1228.htm#SEC1304 2983 noetherNormal sing_1114.htm#SEC1190 44522 2984 noether_lib sing_1228.htm#SEC1304 2985 non-english special characters sing_407.htm#IDX286 2986 nonMonomials sing_1281.htm#SEC1357 16309 2987 nonZeroEntry sing_1117.htm#SEC1193 933 2988 none, option sing_315.htm#IDX150 2989 norTest sing_1248.htm#SEC1324 sprintf 2990 norm sing_1944.htm#SEC2020 31143 2991 normaform (up to a bound) sing_358.htm#IDX246 2992 normal sing_1238.htm#SEC1314 61073 2993 normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2720.htm#IDX1063 2994 normal form sing_865.htm#IDX417 2995 normal.lib sing_1237.htm#SEC1313 2996 normalBundle sing_2720.htm#SEC2796 sprintf 2997 normalC sing_1240.htm#SEC1316 34842 2998 normalConductor sing_1252.htm#SEC1328 26085 2999 normalFan sing_2116.htm#SEC2192 39216 3000 normalForm sing_2350.htm#SEC2426 34962 3001 normalI sing_1325.htm#SEC1401 7516 3002 normalP sing_1239.htm#SEC1315 36584 3003 normalToricRing sing_1255.htm#SEC1331 29638 3004 normalToricRingFromBinomials normalToricRingFromBinomials sing_1256.htm#SEC1332 2301 3005 normal_lib sing_1237.htm#SEC1313 3006 normalform sing_1495.htm#SEC1571 5550 3007 normalform sing_2326.htm#IDX948 2795 3008 normaliz sing_1.htm#IDX14 18426 2796 normaliz sing_1254.htm#SEC1330 2797 normaliz.lib sing_1239.htm#SEC1315 2798 normaliz_lib sing_1239.htm#SEC1315 2799 normalization sing_1168.htm#IDX540 2800 normalization sing_1169.htm#IDX543 2801 normalization sing_1170.htm#IDX546 2802 normalization sing_1171.htm#IDX548 2803 normalization sing_1224.htm#IDX550 2804 normalization sing_1225.htm#IDX553 2805 normalization sing_1226.htm#IDX556 2806 normalization sing_1238.htm#IDX562 2807 normalization sing_1239.htm#IDX564 2808 normalization sing_2315.htm#IDX918 2809 normalization. sing_1165.htm#IDX539 2810 normalization. sing_1358.htm#IDX595 2811 normalize sing_951.htm#SEC1027 44788 2812 not sing_96.htm#SEC136 2813 notBuckets, option sing_307.htm#IDX160 2814 notRegularity, option sing_307.htm#IDX158 2815 notSugar, option sing_307.htm#IDX159 2816 notWarnSB, option sing_307.htm#IDX181 2817 npar sing_1836.htm#SEC1912 5753 2818 npars sing_301.htm#SEC341 2819 nrRootsDeterm sing_1961.htm#SEC2037 sprintf 2820 nrRootsProbab sing_1960.htm#SEC2036 sprintf 2821 nres sing_302.htm#SEC342 2822 nres (plural) sing_464.htm#SEC504 2823 nrows sing_303.htm#SEC343 2824 nrroots sing_1990.htm#SEC2066 54867 2825 nsatiety sing_1219.htm#SEC1295 53333 2826 nselect sing_1121.htm#SEC1197 34057 2827 nt_solve sing_1725.htm#SEC1801 33061 2828 ntsolve.lib sing_1724.htm#SEC1800 2829 ntsolve_lib sing_1724.htm#SEC1800 2830 number sing_139.htm#SEC179 2831 number sing_2164.htm#IDX818 2832 number declarations sing_140.htm#SEC180 2833 number expressions sing_141.htm#SEC181 2834 number operations sing_142.htm#SEC182 2835 number related functions number related functions sing_143.htm#SEC183 2836 numberOfConesOfDimension numberOfConesOfDimension sing_2047.htm#SEC2123 5905 2837 number_e sing_889.htm#SEC965 59152 2838 number_pi sing_890.htm#SEC966 15492 2839 numerAlg.lib sing_1333.htm#IDX569 2840 numerAlg_lib sing_1333.htm#IDX570 2841 numerDecom.lib sing_1338.htm#IDX571 2842 numerDecom_lib sing_1338.htm#IDX572 2843 numerator sing_304.htm#SEC344 2844 nvars sing_305.htm#SEC345 2845 oneDimBelongSemigroup oneDimBelongSemigroup sing_1112.htm#SEC1188 34399 3009 normaliz sing_1268.htm#SEC1344 3010 normaliz.lib sing_1253.htm#SEC1329 3011 normaliz_lib sing_1253.htm#SEC1329 3012 normalization sing_1180.htm#IDX555 3013 normalization sing_1181.htm#IDX558 3014 normalization sing_1182.htm#IDX561 3015 normalization sing_1183.htm#IDX563 3016 normalization sing_1238.htm#IDX567 3017 normalization sing_1239.htm#IDX570 3018 normalization sing_1240.htm#IDX573 3019 normalization sing_1252.htm#IDX579 3020 normalization sing_1253.htm#IDX581 3021 normalization sing_2338.htm#IDX954 3022 normalization. sing_1177.htm#IDX554 3023 normalization. sing_1372.htm#IDX621 3024 normalize sing_971.htm#SEC1047 44788 3025 normalizeMonoidal sing_2660.htm#SEC2736 33071 3026 normalizeRational sing_2661.htm#SEC2737 55177 3027 not sing_101.htm#SEC141 3028 notBuckets, option sing_315.htm#IDX160 3029 notRegularity, option sing_315.htm#IDX158 3030 notSugar, option sing_315.htm#IDX159 3031 notWarnSB, option sing_315.htm#IDX181 3032 npar sing_1850.htm#SEC1926 5753 3033 npars sing_309.htm#SEC349 3034 nrRootsDeterm sing_1975.htm#SEC2051 sprintf 3035 nrRootsProbab sing_1974.htm#SEC2050 sprintf 3036 nres sing_310.htm#SEC350 3037 nres (plural) sing_472.htm#SEC512 3038 nrows sing_311.htm#SEC351 3039 nrroots sing_2004.htm#SEC2080 54867 3040 nsatiety sing_1233.htm#SEC1309 53333 3041 nselect sing_1133.htm#SEC1209 34057 3042 nt_solve sing_1739.htm#SEC1815 33061 3043 ntsolve.lib sing_1738.htm#SEC1814 3044 ntsolve_lib sing_1738.htm#SEC1814 3045 number sing_144.htm#SEC184 3046 number sing_2175.htm#IDX844 3047 number declarations sing_145.htm#SEC185 3048 number expressions sing_146.htm#SEC186 3049 number operations sing_147.htm#SEC187 3050 number related functions number related functions sing_148.htm#SEC188 3051 numberOfConesOfDimension numberOfConesOfDimension sing_2061.htm#SEC2137 5905 3052 number_e sing_909.htm#SEC985 59152 3053 number_pi sing_910.htm#SEC986 15492 3054 numerAlg.lib sing_1347.htm#IDX588 3055 numerAlg_lib sing_1347.htm#IDX589 3056 numerAlg_lib sing_1352.htm#IDX598 3057 numerDecom.lib sing_1352.htm#IDX592 3058 numerDecom_lib sing_1347.htm#IDX591 3059 numerDecom_lib sing_1352.htm#IDX593 3060 numerator sing_312.htm#SEC352 3061 numerical irreducible decomposition sing_1352.htm#IDX594 3062 nvars sing_313.htm#SEC353 3063 olga.lib sing_2643.htm#SEC2719 3064 olga_lib sing_2643.htm#SEC2719 3065 oneDimBelongSemigroup oneDimBelongSemigroup sing_1124.htm#SEC1200 34399 3066 oneNcfrac sing_2600.htm#SEC2676 35654 2846 3067 online help The online help system sing_16.htm#SEC22 2847 open sing_3 06.htm#SEC3462848 opentex sing_17 53.htm#SEC1829542362849 operatorBM sing_5 39.htm#SEC591548752850 operatorModulo sing_54 0.htm#SEC592260642851 oppose sing_4 65.htm#SEC5052852 opposite sing_4 66.htm#SEC5062853 opposite polynomial sing_35 0.htm#IDX2312854 opposite ring sing_35 0.htm#IDX2282855 option sing_3 07.htm#SEC3473068 open sing_314.htm#SEC354 3069 opentex sing_1767.htm#SEC1843 54236 3070 operatorBM sing_547.htm#SEC599 54875 3071 operatorModulo sing_548.htm#SEC600 26064 3072 oppose sing_473.htm#SEC513 3073 opposite sing_474.htm#SEC514 3074 opposite polynomial sing_358.htm#IDX231 3075 opposite ring sing_358.htm#IDX228 3076 option sing_315.htm#SEC355 2856 3077 option(warn) sing_70.htm#SEC110 2857 optionIsSet sing_994.htm#SEC1070 57325 2858 or Evaluation of logical expressions sing_96.htm#SEC136 2859 or sing_403.htm#SEC443 2860 orbit sing_1351.htm#IDX575 2861 orbit sing_1352.htm#IDX579 2862 orbit sing_1355.htm#IDX584 2863 orbit sing_1356.htm#IDX587 2864 orbitCones sing_2392.htm#SEC2468 5522 2865 orbit_variety sing_1652.htm#SEC1728 22665 2866 orbitparam.lib sing_1351.htm#SEC1427 2867 orbitparam_lib sing_1351.htm#SEC1427 2868 ord sing_308.htm#SEC348 2869 ord_test sing_989.htm#SEC1065 36532 2870 order ideal, border basis sing_2502.htm#IDX967 2871 order ideal, border basis sing_2503.htm#IDX968 2872 orderings General definitions for orderings sing_837.htm#SEC889 2873 orderings introduction Introduction to orderings sing_836.htm#SEC888 2874 orderings, M sing_841.htm#SEC893 2875 orderings, a sing_843.htm#SEC895 2876 orderings, global sing_838.htm#SEC890 2877 orderings, local sing_839.htm#SEC891 2878 orderings, product sing_842.htm#SEC894 2879 ordstr sing_309.htm#SEC349 2880 origin sing_1995.htm#SEC2071 31408 2881 orthogonalize sing_1068.htm#SEC1144 63711 2882 outer sing_1038.htm#SEC1114 64048 3078 optionIsSet sing_1014.htm#SEC1090 57325 3079 or Evaluation of logical expressions sing_101.htm#SEC141 3080 or sing_411.htm#SEC451 3081 orbit sing_1365.htm#IDX601 3082 orbit sing_1366.htm#IDX605 3083 orbit sing_1369.htm#IDX610 3084 orbit sing_1370.htm#IDX613 3085 orbitConeOrbits sing_2425.htm#SEC2501 60979 3086 orbitCones sing_2416.htm#SEC2492 60528 3087 orbit_variety sing_1666.htm#SEC1742 22665 3088 orbitparam.lib sing_1365.htm#SEC1441 3089 orbitparam_lib sing_1365.htm#SEC1441 3090 ord sing_316.htm#SEC356 3091 ord_test sing_1009.htm#SEC1085 36532 3092 order ideal, border basis sing_2684.htm#IDX1035 3093 order ideal, border basis sing_2685.htm#IDX1036 3094 orderings General definitions for orderings sing_856.htm#SEC908 3095 orderings introduction Introduction to orderings sing_855.htm#SEC907 3096 orderings, L sing_863.htm#SEC915 3097 orderings, M sing_860.htm#SEC912 3098 orderings, a sing_862.htm#SEC914 3099 orderings, global sing_857.htm#SEC909 3100 orderings, local sing_858.htm#SEC910 3101 orderings, product sing_861.htm#SEC913 3102 ordstr sing_317.htm#SEC357 3103 origin sing_2009.htm#SEC2085 31408 3104 orthogonalize sing_1080.htm#SEC1156 63711 3105 outer sing_1050.htm#SEC1126 64048 2883 3106 output sing_41.htm#SEC71 2884 3107 p-adic numbers sing_32.htm#SEC46 2885 pFactor sing_1885.htm#SEC1961 31504 2886 pIntersect sing_503.htm#SEC555 44055 2887 pIntersectSyz sing_504.htm#SEC556 45608 2888 package sing_144.htm#SEC184 2889 package declarations package declarations sing_145.htm#SEC185 2890 package related functions package related functions sing_146.htm#SEC186 2891 pairset sing_1950.htm#SEC2026 38258 2892 par sing_310.htm#SEC350 2893 par2varRing sing_873.htm#SEC949 44769 2894 paraConic sing_1366.htm#SEC1442 9828 2895 paraPlaneCurve sing_1360.htm#SEC1436 34094 2896 parallel skeletons sing_933.htm#IDX480 2897 parallel.lib sing_933.htm#SEC1009 2898 parallelTestAND sing_937.htm#SEC1013 1415 2899 parallelTestOR sing_938.htm#SEC1014 14920 2900 parallelWaitAll sing_936.htm#SEC1012 2017 2901 parallelWaitFirst sing_935.htm#SEC1011 32 2902 parallelWaitN sing_934.htm#SEC1010 38878 2903 parallel_lib sing_933.htm#SEC1009 2904 parallelization sing_933.htm#IDX479 2905 parallelization sing_973.htm#IDX482 2906 parallelization sing_1014.htm#IDX495 2907 param sing_1543.htm#SEC1619 57220 2908 parameter, as numbers sing_139.htm#SEC179 2909 parameterSubstitute sing_2145.htm#SEC2221 63147 2910 parametric annihilator sing_532.htm#IDX333 2911 parametric annihilator for variety sing_588.htm#IDX356 2912 parametric ideal sing_902.htm#IDX423 2913 parametric ideal sing_909.htm#IDX436 2914 parametric ideal sing_909.htm#IDX438 2915 parametric ideal sing_910.htm#IDX442 2916 parametrization sing_1351.htm#IDX576 2917 parametrization sing_1355.htm#IDX585 2918 parametrization sing_1543.htm#IDX737 2919 parametrizeOrbit sing_1355.htm#SEC1431 26969 2920 paraplanecurves.lib sing_1357.htm#SEC1433 2921 paraplanecurves_lib sing_1357.htm#SEC1433 2922 pardeg sing_311.htm#SEC351 2923 parstr sing_312.htm#SEC352 2924 part sing_2284.htm#SEC2360 31485 2925 partOver sing_2287.htm#SEC2363 25555 2926 partUnder sing_2288.htm#SEC2364 13123 2927 partial_molien sing_1630.htm#SEC1706 21772 2928 partitions sing_1133.htm#SEC1209 48089 2929 partitions sing_1133.htm#IDX528 2930 path integral sing_1125.htm#IDX515 2931 pause sing_930.htm#SEC1006 2273 2932 pdivi sing_904.htm#SEC980 39081 2933 pdivi sing_905.htm#IDX433 2934 pdivisorplus sing_2341.htm#SEC2417 47486 2935 permcol sing_1051.htm#SEC1127 12886 2936 permrow sing_1052.htm#SEC1128 26561 2937 permutations sing_1134.htm#IDX529 2938 permute sing_1134.htm#SEC1210 40893 2939 permute_L sing_1788.htm#SEC1864 10716 2940 perron sing_731.htm#SEC783 3782 2941 perron.lib sing_730.htm#SEC782 2942 perron_lib sing_730.htm#SEC782 2943 phindex.lib sing_2205.htm#IDX885 2944 phindex_lib sing_2205.htm#IDX886 2945 picksFormula sing_2067.htm#SEC2143 14656 2946 pid sing_350.htm#IDX240 2947 plainInvariants sing_1502.htm#SEC1578 40916 2948 planeCur sing_2303.htm#SEC2379 sprintf 2949 plot sing_1766.htm#SEC1842 46610 2950 plotRot sing_1770.htm#SEC1846 57150 2951 plotRotated sing_1769.htm#SEC1845 33009 2952 plotRotatedDirect sing_1772.htm#SEC1848 18202 2953 plotRotatedList sing_1771.htm#SEC1847 41668 2954 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1773.htm#SEC1849 38856 2955 plural sing_996.htm#IDX487 2956 pmat sing_924.htm#SEC1000 3857 2957 pnormalf sing_905.htm#SEC981 34068 2958 pointid.lib sing_1266.htm#SEC1342 2959 pointid_lib sing_1266.htm#SEC1342 2960 polSol sing_766.htm#SEC818 323 2961 polSolFiniteRank sing_767.htm#SEC819 30875 2962 pollTask sing_1024.htm#SEC1100 53950 2963 poly sing_147.htm#SEC187 2964 poly (plural) sing_430.htm#SEC470 2965 poly declarations sing_148.htm#SEC188 2966 poly declarations (plural) poly declarations (plural) sing_431.htm#SEC471 2967 poly expressions sing_149.htm#SEC189 2968 poly expressions (plural) poly expressions (plural) sing_432.htm#SEC472 2969 poly operations sing_150.htm#SEC190 2970 poly operations (plural) poly operations (plural) sing_433.htm#SEC473 2971 poly related functions poly related functions sing_151.htm#SEC191 2972 poly related functions (plural) poly related functions (plural) sing_434.htm#SEC474 2973 poly.lib sing_939.htm#SEC1015 2974 poly2list sing_581.htm#SEC633 4960 2975 poly2zdd sing_2226.htm#SEC2302 61839 2976 polyInterpolation sing_2344.htm#SEC2420 45866 2977 polyVars sing_773.htm#SEC825 43882 2978 poly_lib sing_939.htm#SEC1015 2979 polybori sing_2210.htm#IDX890 2980 polybori.lib sing_2210.htm#IDX887 2981 polybori.lib sing_2210.htm#IDX891 2982 polybori_lib sing_2210.htm#IDX888 2983 polymake sing_2052.htm#IDX791 2984 polymake.lib sing_2052.htm#SEC2128 2985 polymakePolytope sing_2053.htm#SEC2129 47302 2986 polymake_lib sing_2052.htm#SEC2128 2987 polynomial solutions sing_760.htm#IDX384 2988 polynomial, opposite sing_350.htm#IDX232 2989 polytope sing_185.htm#SEC225 2990 polytope sing_2052.htm#IDX787 2991 polytopeViaInequalities polytopeViaInequalities sing_2025.htm#SEC2101 52084 2992 polytopeViaPoints sing_2026.htm#SEC2102 281 2993 pos_def sing_1079.htm#SEC1155 4994 2994 poset sing_2195.htm#IDX876 2995 positiveOrthant sing_1996.htm#SEC2072 42102 2996 posweight sing_1610.htm#SEC1686 3364 2997 powSumSym sing_2241.htm#SEC2317 2339 2998 power sing_1039.htm#SEC1115 23365 2999 powerN sing_1869.htm#SEC1945 20170 3000 powerX sing_1878.htm#SEC1954 47971 3001 power_products sing_1644.htm#SEC1720 54629 3002 powerpolyX sing_1848.htm#SEC1924 37247 3003 powersums sing_1971.htm#SEC2047 59049 3004 preComp sing_1202.htm#SEC1278 16160 3005 preimage sing_313.htm#SEC353 3006 preimage sing_697.htm#IDX359 3007 preimage (plural) sing_467.htm#SEC507 3008 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_992.htm#IDX485 3009 preimageLattice sing_2457.htm#SEC2533 37348 3010 preimageLoc sing_992.htm#SEC1068 33315 3011 preimageNC sing_699.htm#SEC751 16037 3012 prepEmbDiv sing_1428.htm#SEC1504 36708 3013 prepMat sing_1681.htm#SEC1757 39868 3014 prepRealclassify sing_1486.htm#SEC1562 10994 3015 prepSV sing_1783.htm#SEC1859 50095 3016 prepareAss sing_1285.htm#SEC1361 21802 3017 presentTree sing_1415.htm#SEC1491 10731 3018 presolve.lib sing_1691.htm#SEC1767 3019 presolve_lib sing_1691.htm#SEC1767 3020 primL sing_1873.htm#SEC1949 14513 3021 primList sing_1872.htm#SEC1948 6802 3022 primRoot sing_1325.htm#SEC1401 14210 3023 primTest sing_1201.htm#SEC1277 8105 3024 primary_char0 sing_1634.htm#SEC1710 61413 3025 primary_char0_no_molien primary_char0_no_molien sing_1636.htm#SEC1712 50477 3026 primary_char0_no_molien_random primary_char0_no_molien_random sing_1641.htm#SEC1717 8422 3027 primary_char0_random primary_char0_random sing_1639.htm#SEC1715 5996 3028 primary_charp sing_1635.htm#SEC1711 37863 3029 primary_charp_no_molien primary_charp_no_molien sing_1637.htm#SEC1713 32282 3030 primary_charp_no_molien_random primary_charp_no_molien_random sing_1642.htm#SEC1718 11498 3031 primary_charp_random primary_charp_random sing_1640.htm#SEC1716 24739 3032 primary_charp_without primary_charp_without sing_1638.htm#SEC1714 49585 3033 primary_charp_without_random primary_charp_without_random sing_1643.htm#SEC1719 36998 3034 primary_invariants sing_1622.htm#SEC1698 5500 3035 primary_invariants_random primary_invariants_random sing_1623.htm#SEC1699 28958 3036 primdec.lib sing_1270.htm#SEC1346 3037 primdecGTZ sing_1272.htm#SEC1348 6091 3038 primdecGTZE sing_1273.htm#SEC1349 64882 3039 primdecMon sing_1190.htm#SEC1266 3856 3040 primdecSY sing_1274.htm#SEC1350 6547 3041 primdecSYE sing_1275.htm#SEC1351 52788 3042 primdecZ sing_1294.htm#SEC1370 48194 3043 primdecZM sing_1295.htm#SEC1371 17214 3044 primdec_lib sing_1270.htm#SEC1346 3045 primdecint.lib sing_1293.htm#SEC1369 3046 primdecint_lib sing_1293.htm#SEC1369 3047 prime sing_314.htm#SEC354 3048 primeClosure sing_1229.htm#SEC1305 43589 3049 primecoeffs sing_896.htm#SEC972 46153 3050 primefactors sing_315.htm#SEC355 3051 primes sing_891.htm#SEC967 24408 3052 primitiv.lib sing_1301.htm#SEC1377 3053 primitiv_lib sing_1301.htm#SEC1377 3054 primitive sing_1302.htm#SEC1378 36163 3055 primitive element sing_1302.htm#IDX566 3056 primitiveSpan sing_2464.htm#SEC2540 sprintf 3057 primitive_extra sing_1303.htm#SEC1379 49025 3058 primparam sing_1497.htm#SEC1573 35357 3059 principal intersection sing_497.htm#IDX317 3060 print sing_316.htm#SEC356 3061 print sing_2162.htm#IDX811 3062 printGraph sing_1127.htm#SEC1203 45041 3063 printGraphG sing_2532.htm#SEC2608 48742 3064 printGroup sing_2445.htm#SEC2521 6791 3065 printMoebius sing_2201.htm#SEC2277 45828 3066 printSheaf sing_2520.htm#SEC2596 31762 3067 printStack sing_2534.htm#SEC2610 3692 3068 printTask sing_1019.htm#SEC1095 54549 3069 printVariety sing_2512.htm#SEC2588 2846 3070 printf sing_317.htm#SEC357 2294 3071 printlevel sing_392.htm#SEC432 3072 proc sing_152.htm#SEC192 3073 proc declaration sing_153.htm#SEC193 3074 proc expression sing_154.htm#SEC194 3108 pFactor sing_1899.htm#SEC1975 31504 3109 pIntersect sing_511.htm#SEC563 44055 3110 pIntersectSyz sing_512.htm#SEC564 45608 3111 package sing_149.htm#SEC189 3112 package declarations package declarations sing_150.htm#SEC190 3113 package related functions package related functions sing_151.htm#SEC191 3114 pairset sing_1964.htm#SEC2040 38258 3115 par sing_318.htm#SEC358 3116 par2varRing sing_893.htm#SEC969 44769 3117 paraConic sing_1380.htm#SEC1456 9828 3118 paraPlaneCurve sing_1374.htm#SEC1450 34094 3119 parallel skeletons sing_953.htm#IDX498 3120 parallel.lib sing_953.htm#SEC1029 3121 parallelTestAND sing_957.htm#SEC1033 1415 3122 parallelTestOR sing_958.htm#SEC1034 14920 3123 parallelWaitAll sing_956.htm#SEC1032 2017 3124 parallelWaitFirst sing_955.htm#SEC1031 32 3125 parallelWaitN sing_954.htm#SEC1030 38878 3126 parallel_lib sing_953.htm#SEC1029 3127 parallelization sing_953.htm#IDX497 3128 parallelization sing_993.htm#IDX500 3129 parallelization sing_1026.htm#IDX510 3130 param sing_1557.htm#SEC1633 57220 3131 parameter, as numbers sing_144.htm#SEC184 3132 parameterSubstitute sing_2156.htm#SEC2232 63147 3133 parametric annihilator sing_540.htm#IDX335 3134 parametric annihilator for variety sing_596.htm#IDX358 3135 parametric ideal sing_921.htm#IDX432 3136 parametric ideal sing_928.htm#IDX451 3137 parametric ideal sing_928.htm#IDX453 3138 parametric ideal sing_929.htm#IDX458 3139 parametrization sing_1365.htm#IDX602 3140 parametrization sing_1369.htm#IDX611 3141 parametrization sing_1557.htm#IDX763 3142 parametrizeOrbit sing_1369.htm#SEC1445 26969 3143 paraplanecurves.lib sing_1371.htm#SEC1447 3144 paraplanecurves_lib sing_1371.htm#SEC1447 3145 pardeg sing_319.htm#SEC359 3146 parstr sing_320.htm#SEC360 3147 part sing_2302.htm#SEC2378 31485 3148 partOver sing_2305.htm#SEC2381 25555 3149 partUnder sing_2306.htm#SEC2382 13123 3150 partial_molien sing_1644.htm#SEC1720 21772 3151 partitions sing_1145.htm#SEC1221 48089 3152 partitions sing_1145.htm#IDX543 3153 path integral sing_1137.htm#IDX530 3154 pause sing_950.htm#SEC1026 2273 3155 pdivi sing_923.htm#SEC999 21786 3156 pdivi sing_924.htm#IDX442 3157 pdivisorplus sing_2364.htm#SEC2440 47486 3158 permcol sing_1063.htm#SEC1139 12886 3159 permrow sing_1064.htm#SEC1140 26561 3160 permutationFromIntvec permutationFromIntvec sing_2431.htm#SEC2507 6533 3161 permutationToIntvec sing_2432.htm#SEC2508 1989 3162 permutations sing_1146.htm#IDX544 3163 permute sing_1146.htm#SEC1222 40893 3164 permute_L sing_1802.htm#SEC1878 10716 3165 perron sing_748.htm#SEC800 3782 3166 perron.lib sing_747.htm#SEC799 3167 perron_lib sing_747.htm#SEC799 3168 phindex.lib sing_2216.htm#IDX911 3169 phindex_lib sing_2216.htm#IDX912 3170 picksFormula sing_2078.htm#SEC2154 14656 3171 pid sing_358.htm#IDX240 3172 plainInvariants sing_1516.htm#SEC1592 40916 3173 planeCur sing_2324.htm#SEC2400 sprintf 3174 plot sing_1780.htm#SEC1856 46610 3175 plotRot sing_1784.htm#SEC1860 57150 3176 plotRotated sing_1783.htm#SEC1859 33009 3177 plotRotatedDirect sing_1786.htm#SEC1862 18202 3178 plotRotatedList sing_1785.htm#SEC1861 41668 3179 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1787.htm#SEC1863 38856 3180 plural sing_1016.htm#IDX505 3181 pmat sing_944.htm#SEC1020 3857 3182 pnormalf sing_924.htm#SEC1000 26174 3183 pointid.lib sing_1280.htm#SEC1356 3184 pointid_lib sing_1280.htm#SEC1356 3185 polSol sing_783.htm#SEC835 323 3186 polSolFiniteRank sing_784.htm#SEC836 30875 3187 pollTask sing_1036.htm#SEC1112 53950 3188 poly sing_152.htm#SEC192 3189 poly (plural) sing_438.htm#SEC478 3190 poly declarations sing_153.htm#SEC193 3191 poly declarations (plural) poly declarations (plural) sing_439.htm#SEC479 3192 poly expressions sing_154.htm#SEC194 3193 poly expressions (plural) poly expressions (plural) sing_440.htm#SEC480 3194 poly operations sing_155.htm#SEC195 3195 poly operations (plural) poly operations (plural) sing_441.htm#SEC481 3196 poly related functions poly related functions sing_156.htm#SEC196 3197 poly related functions (plural) poly related functions (plural) sing_442.htm#SEC482 3198 poly.lib sing_959.htm#SEC1035 3199 poly2list sing_589.htm#SEC641 4960 3200 poly2zdd sing_2237.htm#SEC2313 61839 3201 polyInterpolation sing_2367.htm#SEC2443 45866 3202 polyVars sing_790.htm#SEC842 43882 3203 poly_lib sing_959.htm#SEC1035 3204 polybori sing_2221.htm#IDX916 3205 polybori.lib sing_2221.htm#IDX913 3206 polybori.lib sing_2221.htm#IDX917 3207 polybori_lib sing_2221.htm#IDX914 3208 polymake sing_2066.htm#IDX817 3209 polymake.lib sing_2066.htm#SEC2142 3210 polymakePolytope sing_2067.htm#SEC2143 47302 3211 polymake_lib sing_2066.htm#SEC2142 3212 polynomial solutions sing_777.htm#IDX386 3213 polynomial, opposite sing_358.htm#IDX232 3214 polytope sing_190.htm#SEC230 3215 polytope sing_2066.htm#IDX813 3216 polytopeViaInequalities polytopeViaInequalities sing_2039.htm#SEC2115 52084 3217 polytopeViaPoints sing_2040.htm#SEC2116 281 3218 pos_def sing_1091.htm#SEC1167 4994 3219 poset sing_2206.htm#IDX902 3220 positiveOrthant sing_2010.htm#SEC2086 42102 3221 posweight sing_1624.htm#SEC1700 3364 3222 powSumSym sing_2259.htm#SEC2335 2339 3223 power sing_1051.htm#SEC1127 23365 3224 powerN sing_1883.htm#SEC1959 20170 3225 powerX sing_1892.htm#SEC1968 47971 3226 power_products sing_1658.htm#SEC1734 54629 3227 powerpolyX sing_1862.htm#SEC1938 37247 3228 powersums sing_1985.htm#SEC2061 59049 3229 preComp sing_1216.htm#SEC1292 16160 3230 preimage sing_321.htm#SEC361 3231 preimage sing_714.htm#IDX361 3232 preimage (plural) sing_475.htm#SEC515 3233 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1012.htm#IDX503 3234 preimageLattice sing_2559.htm#SEC2635 37348 3235 preimageLoc sing_1012.htm#SEC1088 33315 3236 preimageNC sing_716.htm#SEC768 16037 3237 prepEmbDiv sing_1442.htm#SEC1518 36708 3238 prepMat sing_1695.htm#SEC1771 39868 3239 prepRealclassify sing_1500.htm#SEC1576 10994 3240 prepSV sing_1797.htm#SEC1873 50095 3241 prepareAss sing_1299.htm#SEC1375 21802 3242 presentTree sing_1429.htm#SEC1505 10731 3243 presentation sing_2517.htm#SEC2593 40323 3244 presolve.lib sing_1705.htm#SEC1781 3245 presolve_lib sing_1705.htm#SEC1781 3246 primL sing_1887.htm#SEC1963 14513 3247 primList sing_1886.htm#SEC1962 6802 3248 primRoot sing_1339.htm#SEC1415 14210 3249 primTest sing_1215.htm#SEC1291 8105 3250 primary decomposition sing_1284.htm#IDX583 3251 primary decomposition sing_1307.htm#IDX584 3252 primary decomposition of modules sing_1205.htm#IDX565 3253 primary decomposition, numerical sing_1352.htm#IDX596 3254 primary_char0 sing_1648.htm#SEC1724 61413 3255 primary_char0_no_molien primary_char0_no_molien sing_1650.htm#SEC1726 50477 3256 primary_char0_no_molien_random primary_char0_no_molien_random sing_1655.htm#SEC1731 8422 3257 primary_char0_random primary_char0_random sing_1653.htm#SEC1729 5996 3258 primary_charp sing_1649.htm#SEC1725 37863 3259 primary_charp_no_molien primary_charp_no_molien sing_1651.htm#SEC1727 32282 3260 primary_charp_no_molien_random primary_charp_no_molien_random sing_1656.htm#SEC1732 11498 3261 primary_charp_random primary_charp_random sing_1654.htm#SEC1730 24739 3262 primary_charp_without primary_charp_without sing_1652.htm#SEC1728 49585 3263 primary_charp_without_random primary_charp_without_random sing_1657.htm#SEC1733 36998 3264 primary_invariants sing_1636.htm#SEC1712 5500 3265 primary_invariants_random primary_invariants_random sing_1637.htm#SEC1713 28958 3266 primdec.lib sing_1284.htm#SEC1360 3267 primdecGTZ sing_1286.htm#SEC1362 6091 3268 primdecGTZE sing_1287.htm#SEC1363 64882 3269 primdecMon sing_1204.htm#SEC1280 3856 3270 primdecSY sing_1288.htm#SEC1364 6547 3271 primdecSYE sing_1289.htm#SEC1365 52788 3272 primdecZ sing_1308.htm#SEC1384 48194 3273 primdecZM sing_1309.htm#SEC1385 17214 3274 primdec_lib sing_1284.htm#SEC1360 3275 primdecint.lib sing_1307.htm#SEC1383 3276 primdecint_lib sing_1307.htm#SEC1383 3277 prime sing_322.htm#SEC362 3278 primeClosure sing_1243.htm#SEC1319 43589 3279 primecoeffs sing_916.htm#SEC992 46153 3280 primefactors sing_323.htm#SEC363 3281 primes sing_911.htm#SEC987 24408 3282 primitiv.lib sing_1315.htm#SEC1391 3283 primitiv_lib sing_1315.htm#SEC1391 3284 primitive sing_1316.htm#SEC1392 36163 3285 primitive element sing_1316.htm#IDX585 3286 primitiveSpan sing_2566.htm#SEC2642 sprintf 3287 primitive_extra sing_1317.htm#SEC1393 49025 3288 primparam sing_1511.htm#SEC1587 35357 3289 principal intersection sing_505.htm#IDX319 3290 print sing_324.htm#SEC364 3291 print sing_2173.htm#IDX837 3292 printBetti sing_2498.htm#SEC2574 28941 3293 printFreeModule sing_2490.htm#SEC2566 13316 3294 printGraph sing_1139.htm#SEC1215 45041 3295 printGraphG sing_2714.htm#SEC2790 48742 3296 printGroup sing_2547.htm#SEC2623 6791 3297 printHom sing_2493.htm#SEC2569 7070 3298 printMatrix sing_2489.htm#SEC2565 15522 3299 printModule sing_2492.htm#SEC2568 sprintf 3300 printMoebius sing_2212.htm#SEC2288 45828 3301 printResolution sing_2491.htm#SEC2567 29278 3302 printSheaf sing_2702.htm#SEC2778 31762 3303 printStack sing_2716.htm#SEC2792 3692 3304 printTask sing_1031.htm#SEC1107 54549 3305 printVariety sing_2694.htm#SEC2770 2846 3306 printf sing_325.htm#SEC365 2294 3307 printlevel sing_400.htm#SEC440 3308 proc sing_157.htm#SEC197 3309 proc declaration sing_158.htm#SEC198 3310 proc expression sing_159.htm#SEC199 3075 3311 procedure, ASCII help sing_56.htm#IDX125 3076 3312 procedure, ASCII/Texinfo help sing_58.htm#IDX127 … … 3078 3314 procedures, help string sing_45.htm#SEC82 3079 3315 procedures, static Procedure definition sing_43.htm#SEC78 3080 procs with different argument types procs with different argument types sing_1 55.htm#SEC1953081 prodcrit sing_19 48.htm#SEC2024562313082 product sing_ 892.htm#SEC968 544313083 product variety, abstract variety sing_2 513.htm#IDX9833084 productVariety sing_2 513.htm#SEC2589541913085 productgroup sing_2 466.htm#SEC2542559373086 progress watch sing_3 07.htm#IDX1633087 projectLattice sing_2 458.htm#SEC2534284633088 projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2 517.htm#IDX9873089 projective dimension purityfiltration_lib sing_7 38.htm#IDX3683316 procs with different argument types procs with different argument types sing_160.htm#SEC200 3317 prodcrit sing_1962.htm#SEC2038 56231 3318 product sing_912.htm#SEC988 54431 3319 product variety, abstract variety sing_2695.htm#IDX1051 3320 productVariety sing_2695.htm#SEC2771 54191 3321 productgroup sing_2568.htm#SEC2644 55937 3322 progress watch sing_315.htm#IDX163 3323 projectLattice sing_2560.htm#SEC2636 28463 3324 projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2699.htm#IDX1055 3325 projective dimension purityfiltration_lib sing_755.htm#IDX370 3090 3326 projective limes sing_32.htm#SEC46 3091 projective space, abstract variety sing_2 516.htm#IDX9863092 projectiveBundle sing_2 517.htm#SEC2593137913093 projectiveDimension sing_7 39.htm#SEC79181653094 projectiveSpace sing_2 516.htm#SEC2592217293327 projective space, abstract variety sing_2698.htm#IDX1054 3328 projectiveBundle sing_2699.htm#SEC2775 13791 3329 projectiveDimension sing_756.htm#SEC808 8165 3330 projectiveSpace sing_2698.htm#SEC2774 21729 3095 3331 prompt sing_15.htm#SEC21 3096 prompt, option sing_307.htm#IDX182 3097 propagator sing_1125.htm#IDX513 42460 3098 propagator sing_1128.htm#SEC1204 3099 prot, option sing_307.htm#IDX161 3100 protocol of computations sing_307.htm#IDX162 3101 proximitymatrix sing_1456.htm#SEC1532 58403 3102 prune sing_318.htm#SEC358 3103 prwalk sing_2507.htm#SEC2583 46963 3104 psigncnd sing_1744.htm#SEC1820 57734 3105 puiseux2generators sing_1555.htm#SEC1631 64508 3106 puiseuxExpansion sing_2116.htm#SEC2192 46277 3107 pure tensor sing_490.htm#IDX305 3108 purelist sing_749.htm#SEC801 15517 3109 purity purityfiltration_lib sing_738.htm#IDX370 3110 purityFiltration sing_740.htm#SEC792 5742 3111 purityTriang sing_741.htm#SEC793 3665 3112 purityfiltration.lib purityfiltration_lib sing_738.htm#IDX363 3113 purityfiltration_lib purityfiltration_lib sing_738.htm#IDX364 3114 pushForward sing_2483.htm#SEC2559 26697 3115 pwalk sing_1141.htm#SEC1217 61187 3116 pyobject sing_186.htm#SEC226 3117 pyobject sing_2210.htm#IDX893 3118 pyobject declarations pyobject declarations sing_187.htm#SEC227 3119 pyobject expressions pyobject expressions sing_188.htm#SEC228 3120 pyobject operations sing_189.htm#SEC229 3121 pyobject related functions pyobject related functions sing_190.htm#SEC230 3122 pyramid sing_2360.htm#SEC2436 7421 3123 python_eval sing_191.htm#SEC231 3124 python_import sing_192.htm#SEC232 3125 python_run sing_193.htm#SEC233 3126 qbase sing_1974.htm#SEC2050 8633 3127 qepcad sing_2370.htm#SEC2446 39171 3128 qepcadsystem sing_2371.htm#SEC2447 31977 3129 qhmatrix sing_1608.htm#SEC1684 61813 3130 qhmoduli.lib sing_1572.htm#SEC1648 3131 qhmoduli_lib sing_1572.htm#SEC1648 3132 qhspectrum sing_1595.htm#SEC1671 13732 3133 qhweight sing_319.htm#SEC359 3134 qmatrix.lib sing_732.htm#SEC784 3135 qmatrix_lib sing_732.htm#SEC784 3136 qminor sing_734.htm#SEC786 52670 3137 qrds sing_320.htm#SEC360 3138 qring Miscellaneous oddities sing_161.htm#SEC201 3139 qring sing_410.htm#IDX293 3140 qring (plural) sing_435.htm#SEC475 3141 qring declaration sing_165.htm#SEC205 3142 qring declaration (plural) qring declaration (plural) sing_436.htm#SEC476 3143 qring related functions (plural) qring related functions (plural) sing_437.htm#SEC477 3144 qring ring ideal 'factor ring' sing_1001.htm#IDX491 3145 qringNF, option sing_307.htm#IDX164 3146 qslimgb sing_872.htm#SEC948 51999 3147 quadraticSieve sing_1886.htm#SEC1962 58557 3148 quantMat sing_733.htm#SEC785 56227 3149 quickclass sing_1478.htm#SEC1554 14018 3150 quit sing_382.htm#SEC422 3151 quotSheaf sing_2529.htm#SEC2605 49619 3152 quote sing_321.htm#SEC361 3153 quotient sing_322.htm#SEC362 3154 quotient (plural) sing_468.htm#SEC508 3155 quotientLatticeBasis quotientLatticeBasis sing_2027.htm#SEC2103 15613 3156 quotientMain sing_1736.htm#SEC1812 39870 3157 quotientMon sing_1181.htm#SEC1257 57149 3158 quotients sing_2386.htm#IDX951 3159 rHRR sing_2281.htm#SEC2357 20131 3160 rJanet sing_2504.htm#SEC2580 30716 3161 rMacaulay sing_925.htm#SEC1001 45499 3162 rad_con sing_952.htm#SEC1028 21777 3163 radical sing_1282.htm#SEC1358 1407 3164 radicalEHV sing_1283.htm#SEC1359 33703 3165 radicalMemberShip sing_2138.htm#SEC2214 28527 3166 radicalMon sing_1182.htm#SEC1258 64912 3167 radicalZ sing_1297.htm#SEC1373 5783 3168 randcharpoly sing_1968.htm#SEC2044 37737 3169 randlinpoly sing_1970.htm#SEC2046 22330 3170 random sing_323.htm#SEC363 3171 random sing_350.htm#IDX244 3172 random sing_2183.htm#IDX850 3173 random sing_2184.htm#IDX852 3174 random number generator, seed sing_350.htm#IDX242 3175 random.lib sing_960.htm#SEC1036 3176 randomBinomial sing_972.htm#SEC1048 17913 3177 randomCheck sing_1799.htm#SEC1875 20973 3178 randomLast sing_971.htm#SEC1047 2046 3179 randomPoint sing_2028.htm#SEC2104 22561 3180 randomPolyInT sing_2147.htm#SEC2223 2264 3181 random_lib sing_960.htm#SEC1036 3182 randomid sing_962.htm#SEC1038 7815 3183 randommat sing_963.htm#SEC1039 33569 3184 rank sing_204.htm#IDX137 3185 rank sing_324.htm#SEC364 3186 rankSheaf sing_2521.htm#SEC2597 11850 3187 ratSol sing_768.htm#SEC820 62488 3188 ratgb.lib sing_758.htm#IDX373 3189 ratgb_lib sing_758.htm#IDX374 3190 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1360.htm#IDX597 3191 rational normal curve, projection. sing_1361.htm#IDX598 3192 rational normal curve, projection. sing_1364.htm#IDX599 3193 rational normal curve, projection. sing_1365.htm#IDX600 3194 rational solutions sing_760.htm#IDX385 3195 rational univariate projection sing_1968.htm#IDX784 3196 rationalCurve sing_2541.htm#SEC2617 61201 3197 rationalPointConic sing_1362.htm#SEC1438 9761 3198 ratstd sing_759.htm#SEC811 61346 3199 rays sing_2029.htm#SEC2105 44445 3200 re2squ sing_1339.htm#SEC1415 24350 3201 read sing_325.htm#SEC365 3202 readNmzData sing_1257.htm#SEC1333 18957 3203 reading, option sing_307.htm#IDX183 3332 prompt, option sing_315.htm#IDX182 3333 propagator sing_1137.htm#IDX528 42460 3334 propagator sing_1140.htm#SEC1216 3335 prot, option sing_315.htm#IDX161 3336 protocol of computations sing_315.htm#IDX162 3337 proximitymatrix sing_1470.htm#SEC1546 58403 3338 prune sing_326.htm#SEC366 3339 pruneModule sing_2524.htm#SEC2600 51453 3340 prwalk sing_2689.htm#SEC2765 46963 3341 psigncnd sing_1758.htm#SEC1834 57734 3342 puiseux2generators sing_1569.htm#SEC1645 64508 3343 puiseuxExpansion sing_2127.htm#SEC2203 46277 3344 pure tensor sing_498.htm#IDX307 3345 purelist sing_766.htm#SEC818 15517 3346 purity purityfiltration_lib sing_755.htm#IDX372 3347 purityFiltration sing_757.htm#SEC809 5742 3348 purityTriang sing_758.htm#SEC810 3665 3349 purityfiltration.lib purityfiltration_lib sing_755.htm#IDX365 3350 purityfiltration_lib purityfiltration_lib sing_755.htm#IDX366 3351 pushForward sing_2585.htm#SEC2661 26697 3352 pwalk sing_1153.htm#SEC1229 61187 3353 pyobject sing_191.htm#SEC231 3354 pyobject sing_2221.htm#IDX919 3355 pyobject declarations pyobject declarations sing_192.htm#SEC232 3356 pyobject expressions pyobject expressions sing_193.htm#SEC233 3357 pyobject operations sing_194.htm#SEC234 3358 pyobject related functions pyobject related functions sing_195.htm#SEC235 3359 pyramid sing_2383.htm#SEC2459 7421 3360 python_eval sing_196.htm#SEC236 3361 python_import sing_197.htm#SEC237 3362 python_run sing_198.htm#SEC238 3363 qbase sing_1988.htm#SEC2064 8633 3364 qepcad sing_2393.htm#SEC2469 39171 3365 qepcadsystem sing_2394.htm#SEC2470 31977 3366 qhmatrix sing_1622.htm#SEC1698 61813 3367 qhmoduli.lib sing_1586.htm#SEC1662 3368 qhmoduli_lib sing_1586.htm#SEC1662 3369 qhspectrum sing_1609.htm#SEC1685 13732 3370 qhweight sing_327.htm#SEC367 3371 qmatrix.lib sing_749.htm#SEC801 3372 qmatrix_lib sing_749.htm#SEC801 3373 qminor sing_751.htm#SEC803 52670 3374 qrds sing_328.htm#SEC368 3375 qring Miscellaneous oddities sing_166.htm#SEC206 3376 qring sing_418.htm#IDX295 3377 qring (plural) sing_443.htm#SEC483 3378 qring declaration sing_170.htm#SEC210 3379 qring declaration (plural) qring declaration (plural) sing_444.htm#SEC484 3380 qring related functions (plural) qring related functions (plural) sing_445.htm#SEC485 3381 qring ring ideal 'factor ring' sing_1021.htm#IDX509 3382 qringNF, option sing_315.htm#IDX164 3383 qslimgb sing_892.htm#SEC968 51999 3384 quadraticSieve sing_1900.htm#SEC1976 58557 3385 quantMat sing_750.htm#SEC802 56227 3386 quickclass sing_1492.htm#SEC1568 14018 3387 quit sing_390.htm#SEC430 3388 quotSheaf sing_2711.htm#SEC2787 49619 3389 quote sing_329.htm#SEC369 3390 quotient sing_330.htm#SEC370 3391 quotient (plural) sing_476.htm#SEC516 3392 quotientLatticeBasis quotientLatticeBasis sing_2041.htm#SEC2117 15613 3393 quotientMain sing_1750.htm#SEC1826 39870 3394 quotientMon sing_1195.htm#SEC1271 57149 3395 rHRR sing_2299.htm#SEC2375 20131 3396 rJanet sing_2686.htm#SEC2762 30716 3397 rMacaulay sing_945.htm#SEC1021 45499 3398 rad_con sing_972.htm#SEC1048 21777 3399 radical sing_1296.htm#SEC1372 1407 3400 radicalEHV sing_1297.htm#SEC1373 33703 3401 radicalMemberShip sing_2149.htm#SEC2225 28527 3402 radicalMon sing_1196.htm#SEC1272 64912 3403 radicalZ sing_1311.htm#SEC1387 5783 3404 randcharpoly sing_1982.htm#SEC2058 37737 3405 randlinpoly sing_1984.htm#SEC2060 22330 3406 random sing_331.htm#SEC371 3407 random sing_358.htm#IDX244 3408 random sing_2194.htm#IDX876 3409 random sing_2195.htm#IDX878 3410 random number generator, seed sing_358.htm#IDX242 3411 random.lib sing_980.htm#SEC1056 3412 randomBinomial sing_992.htm#SEC1068 17913 3413 randomCheck sing_1813.htm#SEC1889 20973 3414 randomLast sing_991.htm#SEC1067 2046 3415 randomPoint sing_2042.htm#SEC2118 22561 3416 randomPolyInT sing_2158.htm#SEC2234 2264 3417 random_lib sing_980.htm#SEC1056 3418 randomid sing_982.htm#SEC1058 7815 3419 randommat sing_983.htm#SEC1059 33569 3420 rank sing_209.htm#IDX137 3421 rank sing_332.htm#SEC372 3422 rankSheaf sing_2703.htm#SEC2779 11850 3423 ratSol sing_785.htm#SEC837 62488 3424 ratgb.lib sing_775.htm#IDX375 3425 ratgb_lib sing_775.htm#IDX376 3426 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1374.htm#IDX623 3427 rational normal curve, projection. sing_1375.htm#IDX624 3428 rational normal curve, projection. sing_1378.htm#IDX625 3429 rational normal curve, projection. sing_1379.htm#IDX626 3430 rational solutions sing_777.htm#IDX387 3431 rational univariate projection sing_1982.htm#IDX810 3432 rationalCurve sing_2723.htm#SEC2799 61201 3433 rationalPointConic sing_1376.htm#SEC1452 9761 3434 ratstd sing_776.htm#SEC828 61346 3435 rays sing_2043.htm#SEC2119 44445 3436 rcolon sing_2593.htm#SEC2669 1208 3437 re2squ sing_1353.htm#SEC1429 24350 3438 read sing_333.htm#SEC373 3439 readNmzData sing_1271.htm#SEC1347 18957 3440 reading, option sing_315.htm#IDX183 3204 3441 readline sing_1.htm#IDX5 3205 3442 real sing_28.htm#IDX74 3206 real roots, univariate polynomial sing_1975.htm#IDX786 3207 real roots, univariate projection sing_1959.htm#IDX782 3208 real roots,sign conditions sing_1742.htm#IDX762 3209 realclassify sing_2497.htm#SEC2573 60279 3210 realclassify.lib sing_2496.htm#SEC2572 3211 realclassify_lib sing_2496.htm#SEC2572 3212 realizationDim sing_2110.htm#SEC2186 37756 3213 realizationDimPoly sing_2112.htm#SEC2188 3611 3214 realizationMatroids.lib realizationMatroids_lib sing_2109.htm#SEC2185 3215 realizationMatroids_lib realizationMatroids_lib sing_2109.htm#SEC2185 3216 realmorsesplit sing_2498.htm#SEC2574 16318 3217 realpoly sing_1306.htm#SEC1382 9453 3218 realrad sing_1308.htm#SEC1384 43381 3219 realrad.lib sing_1305.htm#SEC1381 3220 realrad_lib sing_1305.htm#SEC1381 3221 realzero sing_1307.htm#SEC1383 12712 3222 recursive_boolean_poly recursive_boolean_poly sing_2216.htm#SEC2292 17045 3223 recursive_from_boolean_poly recursive_from_boolean_poly sing_2222.htm#SEC2298 37794 3224 redSB, option sing_307.htm#IDX165 3225 redTail, option sing_307.htm#IDX167 3226 redThrough, option sing_307.htm#IDX168 3227 redefine, option sing_307.htm#IDX184 3228 reduce sing_326.htm#SEC366 3229 reduce sing_511.htm#IDX322 3230 reduce sing_904.htm#IDX431 3231 reduce sing_905.htm#IDX434 3232 reduce (plural) sing_469.htm#SEC509 3233 reduced sing_903.htm#IDX428 3234 reduced standard basis sing_307.htm#IDX166 3235 reduction sing_1660.htm#SEC1736 31048 3236 reesclos.lib sing_1309.htm#SEC1385 3237 reesclos_lib sing_1309.htm#SEC1385 3238 reference sing_194.htm#SEC234 3239 reference declarations reference declarations sing_195.htm#SEC235 3240 reference expressions reference expressions sing_196.htm#SEC236 3241 reference operations reference and shared operations sing_199.htm#SEC239 3242 reference related functions reference and shared related functions sing_200.htm#SEC240 3243 regCM sing_1221.htm#SEC1297 25488 3244 regIdeal sing_1207.htm#SEC1283 3827 3245 regMonCurve sing_1210.htm#SEC1286 41311 3246 regularity Syzygies and resolutions sing_327.htm#SEC367 3247 regularity sing_847.htm#SEC904 3248 reiffen sing_550.htm#SEC602 32856 3249 rel_orbit_variety sing_1653.htm#SEC1729 34278 3250 relations sing_730.htm#IDX362 3251 relativeInteriorPoint relativeInteriorPoint sing_2030.htm#SEC2106 30097 3252 relative_orbit_variety relative_orbit_variety sing_1654.htm#SEC1730 32995 3253 relweight sing_1609.htm#SEC1685 10658 3254 remainder sing_1729.htm#SEC1805 1191 3255 remainderMain sing_1737.htm#SEC1813 3532 3256 removeCone sing_2048.htm#SEC2124 33877 3257 removepower sing_1466.htm#SEC1542 47644 3258 repart sing_328.htm#SEC368 3259 replace sing_1838.htm#SEC1914 50075 3260 representation, math objects Representation of mathematical objects sing_834.htm#SEC886 3261 res sing_329.htm#SEC369 53499 3262 resbinomial.lib sing_1369.htm#IDX603 3263 resbinomial_lib sing_1369.htm#IDX604 3264 reservedName sing_330.htm#SEC370 3265 resfunction sing_1383.htm#SEC1459 59312 3266 resgraph.lib sing_1401.htm#SEC1477 3267 resgraph_lib sing_1401.htm#SEC1477 3268 resjung.lib sing_1405.htm#SEC1481 3269 resjung_lib sing_1405.htm#SEC1481 3270 reslist sing_1397.htm#SEC1473 64950 3271 resolution purityfiltration_lib sing_156.htm#SEC196 3272 resolution sing_738.htm#IDX369 3273 resolution (plural) sing_438.htm#SEC478 3274 resolution declarations resolution declarations sing_157.htm#SEC197 3275 resolution declarations (plural) resolution declarations (plural) sing_439.htm#SEC479 3276 resolution expressions resolution expressions sing_158.htm#SEC198 3277 resolution expressions (plural) resolution expressions (plural) sing_440.htm#SEC480 3278 resolution graph sing_1451.htm#IDX617 3279 resolution related functions resolution related functions sing_159.htm#SEC199 3280 resolution related functions (plural) resolution related functions (plural) sing_441.htm#SEC481 3281 resolution, La Scala's method sing_280.htm#SEC320 3282 resolution, computation of sing_329.htm#IDX186 3283 resolution, hilbert-driven sing_255.htm#SEC295 3284 resolutionInLocalization resolutionInLocalization sing_2385.htm#SEC2461 31106 3285 resolutiongraph sing_1452.htm#SEC1528 32697 3286 resolve sing_1413.htm#SEC1489 27374 3287 resolve.lib sing_1409.htm#SEC1485 3288 resolve_lib sing_1409.htm#SEC1485 3289 resources.lib sing_973.htm#SEC1049 3290 resources_lib sing_973.htm#SEC1049 3291 restriction sing_2176.htm#IDX838 3292 restriction sing_2192.htm#IDX871 3293 restriction sing_2193.htm#IDX873 3294 restriction of sing_555.htm#IDX345 3295 restrictionIdeal sing_565.htm#SEC617 49796 3296 restrictionModule sing_566.htm#SEC618 62461 3297 resultant sing_294.htm#SEC334 3298 resultant sing_331.htm#SEC371 3299 reszeta.lib sing_1422.htm#SEC1498 3300 reszeta_lib sing_1422.htm#SEC1498 3301 return sing_383.htm#SEC423 3302 return type of procedures Return type of procedures sing_408.htm#SEC448 3303 returnSB, option sing_307.htm#IDX152 3304 reverse sing_1989.htm#SEC2065 35880 3305 reverse lexicographical ordering sing_838.htm#IDX390 3306 reynolds_molien sing_1629.htm#SEC1705 45316 3307 rho sing_1880.htm#SEC1956 51414 3308 rightInverse sing_1818.htm#SEC1894 6558 3309 rightKernel sing_1816.htm#SEC1892 46603 3310 rightModulo sing_717.htm#SEC769 12618 3311 rightNF sing_716.htm#SEC768 42610 3312 rightNFWeyl sing_785.htm#SEC837 35828 3313 rightStd sing_715.htm#SEC767 5740 3314 ring sing_160.htm#SEC200 3315 ring sing_901.htm#IDX420 3316 ring (plural) sing_442.htm#SEC482 3317 ring coefficients hasTransExtensionCoefficient sing_999.htm#IDX489 3318 ring coefficients sing_1000.htm#IDX490 3319 ring declarations sing_162.htm#SEC202 3320 ring declarations (plural) ring declarations (plural) sing_443.htm#SEC483 3321 ring operations sing_164.htm#SEC204 3322 ring operations (plural) ring operations (plural) sing_444.htm#SEC484 3323 ring related functions ring related functions sing_163.htm#SEC203 3324 ring related functions (plural) ring related functions (plural) sing_445.htm#SEC485 3325 ring, opposite sing_350.htm#IDX229 3326 ring.lib sing_978.htm#SEC1054 3327 ring_cf sing_204.htm#IDX138 3328 ring_lib sing_978.htm#SEC1054 3329 ring_list sing_333.htm#SEC373 3330 ring_variable sing_2163.htm#IDX815 3331 ring_variable sing_2164.htm#IDX817 3332 ring_variable sing_2165.htm#IDX821 3333 ring_variable sing_2166.htm#IDX823 3334 ringlist sing_332.htm#SEC372 3335 ringlist (plural) sing_470.htm#SEC510 3336 rings sing_901.htm#IDX421 3337 ringtensor sing_990.htm#SEC1066 56648 3338 ringweights sing_991.htm#SEC1067 33307 3339 rinvar.lib sing_1665.htm#SEC1741 3340 rinvar_lib sing_1665.htm#SEC1741 3341 rmNmzFiles sing_1262.htm#SEC1338 32601 3342 rm_unitcol sing_1057.htm#SEC1133 5591 3343 rm_unitrow sing_1056.htm#SEC1132 35694 3344 rmx sing_1763.htm#SEC1839 17675 3345 rncAntiCanonicalMap sing_1361.htm#SEC1437 41965 3346 rncItProjEven sing_1365.htm#SEC1441 18200 3347 rncItProjOdd sing_1364.htm#SEC1440 61976 3348 root of Bernstein-Sato polynomial sing_532.htm#IDX334 3349 rootofUnity sing_993.htm#SEC1069 21365 3350 roots sing_1730.htm#SEC1806 18436 3351 rootsMain sing_1738.htm#SEC1814 54934 3352 rootsModp sing_1862.htm#SEC1938 47315 3353 rootsmr.lib sing_1959.htm#SEC2035 3354 rootsmr_lib sing_1959.htm#SEC2035 3355 rootsur.lib sing_1975.htm#SEC2051 3356 rootsur_lib sing_1975.htm#SEC2051 3357 round sing_1860.htm#SEC1936 9248 3358 rowShift sing_204.htm#IDX141 3359 rowShift sing_206.htm#SEC246 3360 rowred sing_1053.htm#SEC1129 63416 3361 rp, global ordering sing_838.htm#IDX389 3362 rstandard.lib sing_2501.htm#SEC2577 3363 rstandard_lib sing_2501.htm#SEC2577 3364 rswalk sing_2551.htm#SEC2627 50903 3365 rtimer sing_396.htm#SEC436 3366 rvalue No rvalue of increments and assignments sing_402.htm#SEC442 3367 rvar sing_334.htm#SEC374 3368 rwalk sing_2508.htm#SEC2584 42525 3369 rwalk.lib sing_2506.htm#SEC2582 3370 rwalk_lib sing_2506.htm#SEC2582 3371 s_res sing_1007.htm#SEC1083 47429 3372 sa_poly_reduce sing_520.htm#SEC572 60856 3373 sa_reduce sing_519.htm#SEC571 55799 3374 sagbi sing_1315.htm#SEC1391 46653 3375 sagbi.lib sing_1312.htm#SEC1388 3376 sagbiAlg sing_2299.htm#SEC2375 sprintf 3377 sagbiMod sing_2300.htm#SEC2376 sprintf 3378 sagbiPart sing_1316.htm#SEC1392 56066 3379 sagbiReduce sing_1314.htm#SEC1390 19036 3380 sagbiSPoly sing_1313.htm#SEC1389 17365 3381 sagbi_lib sing_1312.htm#SEC1388 3382 salida sing_1394.htm#SEC1470 9839 3383 sameComponent sing_1942.htm#SEC2018 13540 3384 sameQ sing_1741.htm#SEC1817 45579 3385 sat sing_1122.htm#SEC1198 6266 3386 satiety sing_1209.htm#SEC1285 34323 3387 satstd sing_2204.htm#SEC2280 63657 3388 sba sing_335.htm#SEC375 3389 scalarProd sing_509.htm#SEC561 54488 3390 scheme sing_2351.htm#SEC2427 15722 3391 schreyer.lib sing_1006.htm#SEC1082 3392 schreyer_lib sing_1006.htm#SEC1082 3393 schubert.lib sing_2510.htm#SEC2586 3394 schubert_lib sing_2510.htm#SEC2586 3443 real root isolation sing_2670.htm#IDX1030 3444 real roots, univariate polynomial sing_1989.htm#IDX812 3445 real roots, univariate projection sing_1973.htm#IDX808 3446 real roots,sign conditions sing_1756.htm#IDX788 3447 realclassify sing_2665.htm#SEC2741 51416 3448 realclassify.lib sing_2664.htm#SEC2740 3449 realclassify_lib sing_2664.htm#SEC2740 3450 realizationDim sing_2121.htm#SEC2197 37756 3451 realizationDimPoly sing_2123.htm#SEC2199 3611 3452 realizationMatroids.lib realizationMatroids_lib sing_2120.htm#SEC2196 3453 realizationMatroids_lib realizationMatroids_lib sing_2120.htm#SEC2196 3454 realmorsesplit sing_2666.htm#SEC2742 16318 3455 realpoly sing_1320.htm#SEC1396 9453 3456 realrad sing_1322.htm#SEC1398 43381 3457 realrad.lib sing_1319.htm#SEC1395 3458 realrad_lib sing_1319.htm#SEC1395 3459 realzero sing_1321.htm#SEC1397 12712 3460 recursive_boolean_poly recursive_boolean_poly sing_2227.htm#SEC2303 17045 3461 recursive_from_boolean_poly recursive_from_boolean_poly sing_2233.htm#SEC2309 37794 3462 redSB, option sing_315.htm#IDX165 3463 redTail, option sing_315.htm#IDX167 3464 redThrough, option sing_315.htm#IDX168 3465 redefine, option sing_315.htm#IDX184 3466 reduce sing_334.htm#SEC374 3467 reduce sing_519.htm#IDX324 3468 reduce sing_923.htm#IDX440 3469 reduce sing_924.htm#IDX443 3470 reduce (plural) sing_477.htm#SEC517 3471 reduce (up to a bound) sing_358.htm#IDX245 3472 reduceIntChain sing_2529.htm#SEC2605 17776 3473 reduced sing_922.htm#IDX437 3474 reduced standard basis sing_315.htm#IDX166 3475 reduction sing_1674.htm#SEC1750 31048 3476 reesclos.lib sing_1323.htm#SEC1399 3477 reesclos_lib sing_1323.htm#SEC1399 3478 reference sing_199.htm#SEC239 3479 reference declarations reference declarations sing_200.htm#SEC240 3480 reference expressions reference expressions sing_201.htm#SEC241 3481 reference operations reference and shared operations sing_204.htm#SEC244 3482 reference related functions reference and shared related functions sing_205.htm#SEC245 3483 regCM sing_1235.htm#SEC1311 25488 3484 regIdeal sing_1221.htm#SEC1297 3827 3485 regMonCurve sing_1224.htm#SEC1300 41311 3486 regularity Syzygies and resolutions sing_335.htm#SEC375 3487 regularity sing_867.htm#SEC924 3488 reiffen sing_558.htm#SEC610 32856 3489 rel_orbit_variety sing_1667.htm#SEC1743 34278 3490 relations sing_747.htm#IDX364 3491 relativeInteriorPoint relativeInteriorPoint sing_2044.htm#SEC2120 30097 3492 relative_orbit_variety relative_orbit_variety sing_1668.htm#SEC1744 32995 3493 relweight sing_1623.htm#SEC1699 10658 3494 remainder sing_1743.htm#SEC1819 1191 3495 remainderMain sing_1751.htm#SEC1827 3532 3496 removeCone sing_2062.htm#SEC2138 33877 3497 removepower sing_1480.htm#SEC1556 47644 3498 repart sing_336.htm#SEC376 3499 replace sing_1852.htm#SEC1928 50075 3500 representation, math objects Representation of mathematical objects sing_853.htm#SEC905 3501 res sing_337.htm#SEC377 10393 3502 resbinomial.lib sing_1383.htm#IDX629 3503 resbinomial_lib sing_1383.htm#IDX630 3504 reservedName sing_338.htm#SEC378 3505 resfunction sing_1397.htm#SEC1473 59312 3506 resgraph.lib sing_1415.htm#SEC1491 3507 resgraph_lib sing_1415.htm#SEC1491 3508 resjung.lib sing_1419.htm#SEC1495 3509 resjung_lib sing_1419.htm#SEC1495 3510 reslist sing_1411.htm#SEC1487 64950 3511 resolution purityfiltration_lib sing_161.htm#SEC201 3512 resolution sing_755.htm#IDX371 3513 resolution (plural) sing_446.htm#SEC486 3514 resolution declarations resolution declarations sing_162.htm#SEC202 3515 resolution declarations (plural) resolution declarations (plural) sing_447.htm#SEC487 3516 resolution expressions resolution expressions sing_163.htm#SEC203 3517 resolution expressions (plural) resolution expressions (plural) sing_448.htm#SEC488 3518 resolution graph sing_1465.htm#IDX643 3519 resolution related functions resolution related functions sing_164.htm#SEC204 3520 resolution related functions (plural) resolution related functions (plural) sing_449.htm#SEC489 3521 resolution, La Scala's method sing_288.htm#SEC328 3522 resolution, computation of sing_337.htm#IDX186 3523 resolution, hilbert-driven sing_263.htm#SEC303 3524 resolutionInLocalization resolutionInLocalization sing_2410.htm#SEC2486 31106 3525 resolutiongraph sing_1466.htm#SEC1542 32697 3526 resolve sing_1427.htm#SEC1503 27374 3527 resolve.lib sing_1423.htm#SEC1499 3528 resolve_lib sing_1423.htm#SEC1499 3529 resources.lib sing_993.htm#SEC1069 3530 resources_lib sing_993.htm#SEC1069 3531 restriction sing_2187.htm#IDX864 3532 restriction sing_2203.htm#IDX897 3533 restriction sing_2204.htm#IDX899 3534 restriction of sing_563.htm#IDX347 3535 restrictionIdeal sing_573.htm#SEC625 49796 3536 restrictionModule sing_574.htm#SEC626 62461 3537 resultant sing_302.htm#SEC342 3538 resultant sing_339.htm#SEC379 3539 reszeta.lib sing_1436.htm#SEC1512 3540 reszeta_lib sing_1436.htm#SEC1512 3541 return sing_391.htm#SEC431 3542 return type of procedures Return type of procedures sing_416.htm#SEC456 3543 returnSB, option sing_315.htm#IDX152 3544 reverse sing_2003.htm#SEC2079 35880 3545 reverse lexicographical ordering sing_857.htm#IDX392 3546 reynolds_molien sing_1643.htm#SEC1719 45316 3547 rho sing_1894.htm#SEC1970 51414 3548 rightInverse sing_1832.htm#SEC1908 6558 3549 rightKernel sing_1830.htm#SEC1906 46603 3550 rightModulo sing_734.htm#SEC786 12618 3551 rightNF sing_733.htm#SEC785 42610 3552 rightNFWeyl sing_802.htm#SEC854 35828 3553 rightOre sing_2650.htm#SEC2726 56918 3554 rightStd sing_732.htm#SEC784 5740 3555 ring sing_165.htm#SEC205 3556 ring (plural) sing_450.htm#SEC490 3557 ring coefficients hasTransExtensionCoefficient sing_1019.htm#IDX507 3558 ring coefficients sing_1020.htm#IDX508 3559 ring declarations sing_167.htm#SEC207 3560 ring declarations (plural) ring declarations (plural) sing_451.htm#SEC491 3561 ring operations sing_169.htm#SEC209 3562 ring operations (plural) ring operations (plural) sing_452.htm#SEC492 3563 ring related functions ring related functions sing_168.htm#SEC208 3564 ring related functions (plural) ring related functions (plural) sing_453.htm#SEC493 3565 ring, opposite sing_358.htm#IDX229 3566 ring.lib sing_998.htm#SEC1074 3567 ring_cf sing_209.htm#IDX138 3568 ring_lib sing_998.htm#SEC1074 3569 ring_list sing_341.htm#SEC381 3570 ring_variable sing_2174.htm#IDX841 3571 ring_variable sing_2175.htm#IDX843 3572 ring_variable sing_2176.htm#IDX847 3573 ring_variable sing_2177.htm#IDX849 3574 ringlist sing_340.htm#SEC380 3575 ringlist (plural) sing_478.htm#SEC518 3576 ringtensor sing_1010.htm#SEC1086 56648 3577 ringweights sing_1011.htm#SEC1087 33307 3578 rinvar.lib sing_1679.htm#SEC1755 3579 rinvar_lib sing_1679.htm#SEC1755 3580 rmNmzFiles sing_1276.htm#SEC1352 32601 3581 rm_unitcol sing_1069.htm#SEC1145 5591 3582 rm_unitrow sing_1068.htm#SEC1144 35694 3583 rmx sing_1777.htm#SEC1853 17675 3584 rncAntiCanonicalMap sing_1375.htm#SEC1451 41965 3585 rncItProjEven sing_1379.htm#SEC1455 18200 3586 rncItProjOdd sing_1378.htm#SEC1454 61976 3587 root of Bernstein-Sato polynomial sing_540.htm#IDX336 3588 rootIsolation sing_2681.htm#SEC2757 34513 3589 rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2680.htm#SEC2756 42387 3590 rootIsolationPrimdec rootIsolationPrimdec sing_2682.htm#SEC2758 35485 3591 rootisolation.lib sing_2670.htm#SEC2746 3592 rootisolation_lib sing_2670.htm#SEC2746 3593 rootofUnity sing_1013.htm#SEC1089 21365 3594 roots sing_1744.htm#SEC1820 18436 3595 rootsMain sing_1752.htm#SEC1828 54934 3596 rootsModp sing_1876.htm#SEC1952 47315 3597 rootsmr.lib sing_1973.htm#SEC2049 3598 rootsmr_lib sing_1973.htm#SEC2049 3599 rootsur.lib sing_1989.htm#SEC2065 3600 rootsur_lib sing_1989.htm#SEC2065 3601 round sing_1874.htm#SEC1950 9248 3602 rowShift sing_209.htm#IDX141 3603 rowShift sing_211.htm#SEC251 3604 rowred sing_1065.htm#SEC1141 63416 3605 rp, global ordering sing_857.htm#IDX391 3606 rstandard.lib sing_2683.htm#SEC2759 3607 rstandard_lib sing_2683.htm#SEC2759 3608 rswalk sing_2733.htm#SEC2809 50903 3609 rtimer sing_404.htm#SEC444 3610 rvalue No rvalue of increments and assignments sing_410.htm#SEC450 3611 rvar sing_342.htm#SEC382 3612 rwalk sing_2690.htm#SEC2766 42525 3613 rwalk.lib sing_2688.htm#SEC2764 3614 rwalk_lib sing_2688.htm#SEC2764 3615 sRes sing_2495.htm#SEC2571 23381 3616 sa_poly_reduce sing_528.htm#SEC580 60856 3617 sa_reduce sing_527.htm#SEC579 55799 3618 sagbi sing_1329.htm#SEC1405 46653 3619 sagbi basis sing_2327.htm#IDX949 3620 sagbi.lib sing_1326.htm#SEC1402 3621 sagbiAlg sing_2320.htm#SEC2396 sprintf 3622 sagbiMod sing_2321.htm#SEC2397 sprintf 3623 sagbiPart sing_1330.htm#SEC1406 56066 3624 sagbiReduce sing_1328.htm#SEC1404 19036 3625 sagbiSPoly sing_1327.htm#SEC1403 17365 3626 sagbi_lib sing_1326.htm#SEC1402 3627 salida sing_1408.htm#SEC1484 9839 3628 sameComponent sing_1956.htm#SEC2032 13540 3629 sameQ sing_1755.htm#SEC1831 45579 3630 sat sing_1134.htm#SEC1210 6266 3631 satiety sing_1223.htm#SEC1299 34323 3632 satstd sing_2215.htm#SEC2291 16128 3633 sba sing_343.htm#SEC383 3634 scalarProd sing_517.htm#SEC569 54488 3635 scheme sing_2374.htm#SEC2450 15722 3636 schubert.lib sing_2692.htm#SEC2768 3637 schubert_lib sing_2692.htm#SEC2768 3395 3638 sdb, source code debugger Source code debugger sing_66.htm#SEC103 3396 second degree sing_9 19.htm#IDX4713397 secondary fan sing_20 52.htm#IDX7893398 secondary polytope sing_20 52.htm#IDX7903399 secondary Fan sing_2060.htm#SEC2136 432053400 secondary Polytope sing_2059.htm#SEC2135 484513401 secondary_ and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1650.htm#SEC1726 370583402 secondary_char 0 sing_1645.htm#SEC1721 310293403 secondary_ charp sing_1647.htm#SEC1723 163643404 secondary_no _molien sing_1648.htm#SEC1724 36163405 se condary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1651.htm#SEC1727 316753406 se gre sing_2236.htm#SEC2312 440353407 select sing_1123.htm#SEC1199 170963408 se lect1 sing_1124.htm#SEC1200 326173409 semaphore sing_350.htm#IDX247 443423410 semaphore sing_977.htm#SEC10533411 sem aphores sing_973.htm#IDX4843412 semi CMcod2 sing_1606.htm#SEC1682 159053413 semi Group sing_2301.htm#SEC2377sprintf3414 semi Mod sing_2302.htm#SEC2378 sprintf3415 semi div sing_1934.htm#SEC2010 581073416 semigroup sing_1455.htm#SEC1531 290453417 semigroup sing_1459.htm#IDX6243418 semigroup of values sing_1545.htm#IDX7393419 se migroupGenerator sing_2031.htm#SEC2107 594463420 sep sing_1292.htm#SEC1368 sprintf3421 separat eHNE sing_1556.htm#SEC1632 120523422 se parator sing_1192.htm#SEC1268 330003423 se rreRelations sing_638.htm#SEC690 339943424 set sing_2158.htm#IDX8013425 set BaseMultigrading sing_2438.htm#SEC2514 65753426 setL etterplaceAttributes setLetterplaceAttributes sing_629.htm#SEC681 57593427 set LinearForms sing_2032.htm#SEC2108 627313428 setM oduleGrading sing_2450.htm#SEC2526 590183429 set Multiplicity sing_2033.htm#SEC2109 275373430 setNmz DataPath sing_1259.htm#SEC1335 181233431 setNmz ExecPath sing_1255.htm#SEC1331 389933432 setNmz Filename sing_1258.htm#SEC1334 202063433 set NmzOption sing_1252.htm#SEC1328 90123434 set UniformizingParameter setUniformizingParameter sing_2553.htm#SEC2629 636353435 set _is_injective sing_1922.htm#SEC1998 84293436 set cores sing_975.htm#SEC1051 497043437 set env sing_350.htm#IDX2503438 set globalrings sing_901.htm#SEC977 333793439 s etinitials sing_2361.htm#SEC2437 247923440 s etring sing_336.htm#SEC3763441 sh sing_350.htm#IDX2523442 shared sing_194.htm#SEC2343443 shared declarations sing_197.htm#SEC2373444 shared expressions sing_198.htm#SEC2383445 sh ared operations reference and shared operations sing_199.htm#SEC2393446 sh ared related functions reference and shared related functions sing_200.htm#SEC2403447 sheaf cohomology sing_1432.htm#IDX6053448 sheafCoh sing_1438.htm#SEC1514 645013449 sheaf CohBGG sing_1436.htm#SEC1512 134393450 sheaf CohBGG2 sing_1437.htm#SEC1513 33383451 sh eafcoh.lib sing_1432.htm#SEC15083452 sh eafcoh_lib sing_1432.htm#SEC15083453 sh iftPoly sing_631.htm#SEC683 652233454 sho rt sing_393.htm#SEC4333455 show sing_926.htm#SEC1002 155993456 show BO sing_1414.htm#SEC1490 200893457 show DataTypes sing_1416.htm#SEC1492 42703458 show NmzOptions sing_1253.htm#SEC1329 649553459 show Numinvs sing_1250.htm#SEC1326 189343460 s howgrades sing_743.htm#SEC795 480813461 s howrecursive sing_927.htm#SEC1003 61273462 si ckle sing_616.htm#SEC668 171663463 signa l handler sing_2569.htm#SEC26593464 signature Brieskorn sing_1615.htm#SEC1691 262833465 signature L sing_2206.htm#SEC2282 654933466 signature Lqf sing_2207.htm#SEC2283 188113467 sign atureNemethi sing_1617.htm#SEC1693 219813468 sign aturePuiseux sing_1616.htm#SEC1692 233983469 signc nd sing_1743.htm#SEC1819 401473470 si gncond.lib sing_1742.htm#SEC18183471 si gncond_lib sing_1742.htm#SEC18183472 simple solver sing_1687.htm#SEC1763 134183473 simplex sing_337.htm#SEC3773474 simpl exOut sing_1714.htm#SEC1790 560993475 simplify sing_338.htm#SEC3783476 si mplifyRat sing_780.htm#SEC832 526583477 sing .lib sing_1582.htm#SEC16583478 sing4ti2 .lib sing_1318.htm#SEC13943479 sing 4ti2_lib sing_1318.htm#SEC13943480 sing _lib sing_1582.htm#SEC16583481 singular locus of D-module sing_760.htm#IDX3793482 singularities sing_1514.htm#IDX6413483 singularities sing_1515.htm#IDX6523484 singularities sing_1516.htm#IDX6553485 singularities sing_1517.htm#IDX6583486 singularities sing_1518.htm#IDX6613487 singularities sing_1519.htm#IDX6653488 singularities sing_1520.htm#IDX6693489 singularities sing_1521.htm#IDX6753490 singularities sing_1522.htm#IDX6833491 singularities sing_1523.htm#IDX6893492 singularities sing_1524.htm#IDX6973493 singularities sing_1525.htm#IDX7073494 singularities sing_1613.htm#IDX7543495 singularities, resolution of Resolution of singularities sing_8 23.htm#SEC8753496 singularity sing_14 79.htm#SEC1555230023639 second degree sing_939.htm#IDX489 3640 secondary fan sing_2066.htm#IDX815 3641 secondary polytope sing_2066.htm#IDX816 3642 secondaryPolytope sing_2071.htm#SEC2147 48451 3643 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1664.htm#SEC1740 37058 3644 secondary_char0 sing_1659.htm#SEC1735 31029 3645 secondary_charp sing_1661.htm#SEC1737 16364 3646 secondary_no_molien sing_1662.htm#SEC1738 3616 3647 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1665.htm#SEC1741 31675 3648 segre sing_2254.htm#SEC2330 44035 3649 select sing_1135.htm#SEC1211 17096 3650 select1 sing_1136.htm#SEC1212 32617 3651 semaphore sing_358.htm#IDX249 44342 3652 semaphore sing_997.htm#SEC1073 3653 semaphores sing_993.htm#IDX502 3654 semiCMcod2 sing_1620.htm#SEC1696 15905 3655 semiGroup sing_2322.htm#SEC2398 sprintf 3656 semiMod sing_2323.htm#SEC2399 sprintf 3657 semidiv sing_1948.htm#SEC2024 58107 3658 semigroup sing_1469.htm#SEC1545 29045 3659 semigroup sing_1473.htm#IDX650 3660 semigroup of values sing_1559.htm#IDX765 3661 semigroupGenerator sing_2045.htm#SEC2121 59446 3662 sep sing_1306.htm#SEC1382 sprintf 3663 separateHNE sing_1570.htm#SEC1646 12052 3664 separator sing_1206.htm#SEC1282 33000 3665 serreRelations sing_655.htm#SEC707 33994 3666 set sing_2169.htm#IDX827 3667 setBaseMultigrading sing_2540.htm#SEC2616 6575 3668 setLetterplaceAttributes setLetterplaceAttributes sing_645.htm#SEC697 5759 3669 setLinearForms sing_2046.htm#SEC2122 62731 3670 setModuleGrading sing_2552.htm#SEC2628 59018 3671 setMultiplicity sing_2047.htm#SEC2123 27537 3672 setNmzDataPath sing_1273.htm#SEC1349 18123 3673 setNmzExecPath sing_1269.htm#SEC1345 38993 3674 setNmzFilename sing_1272.htm#SEC1348 20206 3675 setNmzOption sing_1266.htm#SEC1342 9012 3676 setUniformizingParameter setUniformizingParameter sing_2735.htm#SEC2811 63635 3677 set_is_injective sing_1936.htm#SEC2012 8429 3678 setcores sing_995.htm#SEC1071 49704 3679 setenv sing_358.htm#IDX252 3680 setinitials sing_2384.htm#SEC2460 24792 3681 setring sing_344.htm#SEC384 3682 sh sing_358.htm#IDX254 3683 shared sing_199.htm#SEC239 3684 shared declarations sing_202.htm#SEC242 3685 shared expressions sing_203.htm#SEC243 3686 shared operations reference and shared operations sing_204.htm#SEC244 3687 shared related functions reference and shared related functions sing_205.htm#SEC245 3688 sheaf cohomology sing_1446.htm#IDX631 3689 sheafCoh sing_1452.htm#SEC1528 64501 3690 sheafCohBGG sing_1450.htm#SEC1526 13439 3691 sheafCohBGG2 sing_1451.htm#SEC1527 3338 3692 sheafcoh.lib sing_1446.htm#SEC1522 3693 sheafcoh_lib sing_1446.htm#SEC1522 3694 shiftPoly sing_648.htm#SEC700 65223 3695 short sing_401.htm#SEC441 3696 show sing_946.htm#SEC1022 15599 3697 showBO sing_1428.htm#SEC1504 20089 3698 showDataTypes sing_1430.htm#SEC1506 4270 3699 showNmzOptions sing_1267.htm#SEC1343 64955 3700 showNuminvs sing_1264.htm#SEC1340 18934 3701 showgrades sing_760.htm#SEC812 48081 3702 showrecursive sing_947.htm#SEC1023 6127 3703 sickle sing_624.htm#SEC676 54811 3704 signal handler sing_2751.htm#SEC2840 3705 signatureBrieskorn sing_1629.htm#SEC1705 26283 3706 signatureL sing_2217.htm#SEC2293 65493 3707 signatureLqf sing_2218.htm#SEC2294 18811 3708 signatureNemethi sing_1631.htm#SEC1707 21981 3709 signaturePuiseux sing_1630.htm#SEC1706 23398 3710 signcnd sing_1757.htm#SEC1833 40147 3711 signcond.lib sing_1756.htm#SEC1832 3712 signcond_lib sing_1756.htm#SEC1832 3713 simplePrune sing_2533.htm#SEC2609 sprintf 3714 simplesolver sing_1701.htm#SEC1777 13418 3715 simplex sing_345.htm#SEC385 3716 simplexOut sing_1728.htm#SEC1804 56099 3717 simplify sing_346.htm#SEC386 3718 simplifyRat sing_797.htm#SEC849 52658 3719 sing.lib sing_1596.htm#SEC1672 3720 sing4ti2.lib sing_1332.htm#SEC1408 3721 sing4ti2_lib sing_1332.htm#SEC1408 3722 sing_lib sing_1596.htm#SEC1672 3723 singular locus of D-module sing_777.htm#IDX381 3724 singularities sing_1528.htm#IDX667 3725 singularities sing_1529.htm#IDX678 3726 singularities sing_1530.htm#IDX681 3727 singularities sing_1531.htm#IDX684 3728 singularities sing_1532.htm#IDX687 3729 singularities sing_1533.htm#IDX691 3730 singularities sing_1534.htm#IDX695 3731 singularities sing_1535.htm#IDX701 3732 singularities sing_1536.htm#IDX709 3733 singularities sing_1537.htm#IDX715 3734 singularities sing_1538.htm#IDX723 3735 singularities sing_1539.htm#IDX733 3736 singularities sing_1627.htm#IDX780 3737 singularities sing_2316.htm#IDX944 3738 singularities, resolution of Resolution of singularities sing_840.htm#SEC892 3739 singularity sing_1493.htm#SEC1569 23002 3497 3740 singularrc sing_20.htm#IDX73 3498 size Miscellaneous oddities sing_339.htm#SEC379 3499 size sing_410.htm#IDX292 3500 skewmat sing_1040.htm#SEC1116 2167 3501 sleep sing_345.htm#SEC385 3502 slimgb sing_340.htm#SEC380 3503 slimgb sing_800.htm#SEC852 3504 slimgb (plural) sing_471.htm#SEC511 3505 slocus sing_1594.htm#SEC1670 27853 3506 smith sing_1827.htm#SEC1903 61915 3507 smithNormalForm sing_2486.htm#SEC2562 7174 3508 solutionsMod2 sing_1877.htm#SEC1953 53360 3509 solve sing_919.htm#IDX472 3078 3510 solve sing_1708.htm#SEC1784 3511 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_283.htm#SEC323 3512 solve.lib sing_1706.htm#SEC1782 3513 solveTInitialFormPar solveTInitialFormPar sing_2141.htm#SEC2217 36670 3514 solve_IP sing_1167.htm#SEC1243 59518 3515 solve_lib sing_1706.htm#SEC1782 3516 solvelinearpart sing_1701.htm#SEC1777 42872 3517 sort sing_893.htm#SEC969 58207 3518 sortIntvec sing_587.htm#SEC639 60798 3519 sortandmap sing_1702.htm#SEC1778 10314 3520 sortier sing_1664.htm#SEC1740 3555 3521 sortvars sing_1703.htm#SEC1779 61778 3522 sortvec sing_341.htm#SEC381 3741 size Miscellaneous oddities sing_347.htm#SEC387 3742 size sing_418.htm#IDX294 3743 skewmat sing_1052.htm#SEC1128 2167 3744 sleep sing_353.htm#SEC393 3745 slimgb sing_348.htm#SEC388 3746 slimgb sing_817.htm#SEC869 3747 slimgb (plural) sing_479.htm#SEC519 3748 slocus sing_1608.htm#SEC1684 27853 3749 smith sing_1841.htm#SEC1917 61915 3750 smithNormalForm sing_2588.htm#SEC2664 7174 3751 solutionsMod2 sing_1891.htm#SEC1967 53360 3752 solve sing_939.htm#IDX490 3078 3753 solve sing_1722.htm#SEC1798 3754 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_291.htm#SEC331 3755 solve.lib sing_1720.htm#SEC1796 3756 solveTInitialFormPar solveTInitialFormPar sing_2152.htm#SEC2228 36670 3757 solve_IP sing_1179.htm#SEC1255 59518 3758 solve_lib sing_1720.htm#SEC1796 3759 solvelinearpart sing_1715.htm#SEC1791 42872 3760 sort sing_913.htm#SEC989 58207 3761 sortIntvec sing_595.htm#SEC647 60798 3762 sortandmap sing_1716.htm#SEC1792 10314 3763 sortier sing_1678.htm#SEC1754 3555 3764 sortvars sing_1717.htm#SEC1793 61778 3765 sortvec sing_349.htm#SEC389 3766 source sing_2511.htm#SEC2587 63163 3523 3767 source code debugger, sdb Source code debugger sing_66.htm#SEC103 3524 spaceCur sing_2304.htm#SEC2380 sprintf 3525 spadd sing_1528.htm#SEC1604 48739 3526 span sing_2034.htm#SEC2110 64343 3527 sparseHomogIdeal sing_969.htm#SEC1045 22631 3528 sparseInterpolation sing_2346.htm#SEC2422 28771 3529 sparseid sing_964.htm#SEC1040 20824 3530 sparsemat sing_966.htm#SEC1042 17653 3531 sparsematrix sing_965.htm#SEC1041 41031 3532 sparsepoly sing_967.htm#SEC1043 21649 3533 sparsetriag sing_968.htm#SEC1044 50657 3534 spcurve.lib sing_1602.htm#SEC1678 3535 spcurve_lib sing_1602.htm#SEC1678 3536 special characters, non-english sing_399.htm#IDX285 3537 spectral pairs sing_1514.htm#IDX650 3538 spectral pairs sing_1521.htm#IDX682 3539 spectral pairs sing_1523.htm#IDX696 3540 spectral pairs sing_1524.htm#IDX705 3541 spectral pairs sing_1536.htm#IDX721 3542 spectral pairs sing_1538.htm#IDX732 3543 spectralNeg sing_1424.htm#SEC1500 36691 3544 spectrum sing_1514.htm#IDX649 47545 3545 spectrum sing_1520.htm#SEC1596 3546 spectrum sing_1520.htm#IDX674 3547 spectrum sing_1521.htm#IDX681 3548 spectrum sing_1522.htm#IDX688 3549 spectrum sing_1523.htm#IDX695 3550 spectrum sing_1524.htm#IDX704 3551 spectrum sing_1536.htm#IDX720 3552 spectrum sing_1538.htm#IDX731 3553 spectrum sing_1613.htm#IDX756 3554 spectrum.lib sing_1612.htm#SEC1688 3555 spectrum_lib sing_1612.htm#SEC1688 3556 spectrumnd sing_1613.htm#SEC1689 29943 3557 spgamma sing_1535.htm#SEC1611 59653 3558 spgeomgenus sing_1534.htm#SEC1610 57796 3559 spissemicont sing_1531.htm#SEC1607 23679 3560 split sing_928.htm#SEC1004 29794 3561 splitPolygon sing_2062.htm#SEC2138 706 3562 splitring sing_1304.htm#SEC1380 56404 3563 splitting sing_1200.htm#SEC1276 34734 3564 spmilnor sing_1533.htm#SEC1609 32933 3565 spmul sing_1530.htm#SEC1606 43607 3566 spnf sing_1083.htm#SEC1159 57309 3567 spoly sing_1945.htm#SEC2021 35454 3568 sppairs sing_1521.htm#SEC1597 49513 3569 sppnf sing_1526.htm#SEC1602 16650 3570 sppprint sing_1527.htm#SEC1603 43682 3571 spprint sing_1084.htm#SEC1160 18671 3572 sprintf sing_343.htm#SEC383 55889 3573 spsemicont sing_1532.htm#SEC1608 61169 3574 spsub sing_1529.htm#SEC1605 54296 3575 sqfrNorm sing_1731.htm#SEC1807 20546 3576 sqfrNormMain sing_1739.htm#SEC1815 9890 3577 sqr sing_1857.htm#SEC1933 sprintf 3578 sqrfree sing_342.htm#SEC382 3579 squareRoot sing_1876.htm#SEC1952 17446 3580 squarefree sing_1557.htm#SEC1633 48485 3581 sres sing_344.htm#SEC384 3582 ssi Parallelization with ssi links sing_795.htm#SEC847 3583 stack, moduli space of stable maps sing_2534.htm#IDX991 3584 stack, moduli space of stable maps, rational curves moduliSpace sing_2533.htm#IDX990 3585 staircase sing_1748.htm#SEC1824 49781 3586 standard sing_1952.htm#SEC2028 14067 3587 standard bases. sing_2203.htm#IDX883 3588 standard bases. sing_2204.htm#IDX884 3589 standard.lib sing_871.htm#IDX417 3590 standard_lib sing_871.htm#IDX418 3591 startNmz sing_1261.htm#SEC1337 21925 3592 startTasks sing_1020.htm#SEC1096 16715 3768 spaceCur sing_2325.htm#SEC2401 sprintf 3769 spadd sing_1542.htm#SEC1618 48739 3770 span sing_2048.htm#SEC2124 64343 3771 sparseHomogIdeal sing_989.htm#SEC1065 22631 3772 sparseInterpolation sing_2369.htm#SEC2445 28771 3773 sparseid sing_984.htm#SEC1060 20824 3774 sparsemat sing_986.htm#SEC1062 17653 3775 sparsematrix sing_985.htm#SEC1061 41031 3776 sparsepoly sing_987.htm#SEC1063 21649 3777 sparsetriag sing_988.htm#SEC1064 50657 3778 spcurve.lib sing_1616.htm#SEC1692 3779 spcurve_lib sing_1616.htm#SEC1692 3780 special characters, non-english sing_407.htm#IDX287 3781 spectral pairs sing_1528.htm#IDX676 3782 spectral pairs sing_1535.htm#IDX708 3783 spectral pairs sing_1537.htm#IDX722 3784 spectral pairs sing_1538.htm#IDX731 3785 spectral pairs sing_1550.htm#IDX747 3786 spectral pairs sing_1552.htm#IDX758 3787 spectralNeg sing_1438.htm#SEC1514 36691 3788 spectrum sing_1528.htm#IDX675 47545 3789 spectrum sing_1534.htm#SEC1610 3790 spectrum sing_1534.htm#IDX700 3791 spectrum sing_1535.htm#IDX707 3792 spectrum sing_1536.htm#IDX714 3793 spectrum sing_1537.htm#IDX721 3794 spectrum sing_1538.htm#IDX730 3795 spectrum sing_1550.htm#IDX746 3796 spectrum sing_1552.htm#IDX757 3797 spectrum sing_1627.htm#IDX782 3798 spectrum.lib sing_1626.htm#SEC1702 3799 spectrum_lib sing_1626.htm#SEC1702 3800 spectrumnd sing_1627.htm#SEC1703 29943 3801 spgamma sing_1549.htm#SEC1625 59653 3802 spgeomgenus sing_1548.htm#SEC1624 57796 3803 spissemicont sing_1545.htm#SEC1621 23679 3804 split sing_948.htm#SEC1024 29794 3805 splitPolygon sing_2073.htm#SEC2149 706 3806 splitring sing_1318.htm#SEC1394 56404 3807 splitting sing_1214.htm#SEC1290 34734 3808 spmilnor sing_1547.htm#SEC1623 32933 3809 spmul sing_1544.htm#SEC1620 43607 3810 spnf sing_1095.htm#SEC1171 57309 3811 spoly sing_1959.htm#SEC2035 35454 3812 sppairs sing_1535.htm#SEC1611 49513 3813 sppnf sing_1540.htm#SEC1616 16650 3814 sppprint sing_1541.htm#SEC1617 43682 3815 spprint sing_1096.htm#SEC1172 18671 3816 sprintf sing_351.htm#SEC391 55889 3817 spsemicont sing_1546.htm#SEC1622 61169 3818 spsub sing_1543.htm#SEC1619 54296 3819 sqfrNorm sing_1745.htm#SEC1821 20546 3820 sqfrNormMain sing_1753.htm#SEC1829 9890 3821 sqr sing_1871.htm#SEC1947 sprintf 3822 sqrfree sing_350.htm#SEC390 3823 squareRoot sing_1890.htm#SEC1966 17446 3824 squarefree sing_1571.htm#SEC1647 48485 3825 sres sing_352.htm#SEC392 3826 ssi Parallelization with ssi links sing_812.htm#SEC864 3827 stabilizer sing_2245.htm#SEC2321 36692 3828 stack, moduli space of stable maps sing_2716.htm#IDX1059 3829 stack, moduli space of stable maps, rational curves moduliSpace sing_2715.htm#IDX1058 3830 stackNets sing_2637.htm#SEC2713 30974 3831 staircase sing_1762.htm#SEC1838 49781 3832 standard sing_1966.htm#SEC2042 14067 3833 standard bases, saturation sing_2215.htm#IDX910 3834 standard bases. sing_2214.htm#IDX909 3835 standard.lib sing_891.htm#IDX419 3836 standard_lib sing_891.htm#IDX420 3837 startNmz sing_1275.htm#SEC1351 21925 3838 startTasks sing_1032.htm#SEC1108 16715 3593 3839 static procedures Procedure definition sing_43.htm#SEC78 3594 status sing_345.htm#SEC385 3595 std sing_346.htm#SEC386 3596 std sing_798.htm#SEC850 3597 std (plural) sing_472.htm#SEC512 3598 stdfglm sing_347.htm#SEC387 256 3599 stdhilb sing_348.htm#SEC388 63138 3600 stopTask sing_1021.htm#SEC1097 6801 3601 stratify sing_1682.htm#SEC1758 56744 3602 stratify.lib sing_1680.htm#SEC1756 3603 stratify_lib sing_1680.htm#SEC1756 3604 string Miscellaneous oddities sing_166.htm#SEC206 3605 string sing_410.htm#IDX295 3606 string sing_916.htm#IDX462 3607 string declarations sing_167.htm#SEC207 3608 string expressions sing_168.htm#SEC208 3609 string operations sing_170.htm#SEC210 3610 string related functions string related functions sing_171.htm#SEC211 3611 string type cast sing_169.htm#SEC209 3612 stripHNE sing_1554.htm#SEC1630 19265 3613 sturm sing_1985.htm#SEC2061 54353 3614 sturmha sing_1987.htm#SEC2063 12467 3615 sturmhaseq sing_1988.htm#SEC2064 59133 3616 sturmquery sing_1963.htm#SEC2039 10805 3617 sturmseq sing_1986.htm#SEC2062 23005 3618 submat sing_1041.htm#SEC1117 37665 3619 subrInterred sing_957.htm#SEC1033 10165 3620 subset_sum01 sing_1906.htm#SEC1982 60620 3621 subset_sum02 sing_1907.htm#SEC1983 37340 3622 subst sing_349.htm#SEC389 3623 subst (plural) sing_473.htm#SEC513 3624 substitute sing_956.htm#SEC1032 28919 3625 sugarCrit, option sing_307.htm#IDX169 3626 sum sing_894.htm#SEC970 555 3627 sum_of_powers sing_2240.htm#SEC2316 12170 3628 sumlist sing_1396.htm#SEC1472 59918 3629 sumofquotients sing_2542.htm#SEC2618 4569 3630 super-commutative algebras Graded commutative algebras (SCA) sing_482.htm#SEC534 3631 superCommutative sing_714.htm#SEC766 45528 3632 super_increasing_knapsack super_increasing_knapsack sing_1918.htm#SEC1994 9177 3633 surf.lib sing_1765.htm#SEC1841 3634 surf_lib sing_1765.htm#SEC1841 3635 surfacesignature.lib surfacesignature_lib sing_1614.htm#SEC1690 3636 surfacesignature_lib surfacesignature_lib sing_1614.htm#SEC1690 3840 status sing_353.htm#SEC393 3841 std sing_354.htm#SEC394 3842 std sing_815.htm#SEC867 3843 std (plural) sing_480.htm#SEC520 3844 stdfglm sing_355.htm#SEC395 256 3845 stdhilb sing_356.htm#SEC396 63138 3846 stdlocus sing_936.htm#SEC1012 25619 3847 stopTask sing_1033.htm#SEC1109 6801 3848 storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2430.htm#SEC2506 64428 3849 stratify sing_1696.htm#SEC1772 56744 3850 stratify.lib sing_1694.htm#SEC1770 3851 stratify_lib sing_1694.htm#SEC1770 3852 string Miscellaneous oddities sing_171.htm#SEC211 3853 string sing_418.htm#IDX297 3854 string declarations sing_172.htm#SEC212 3855 string expressions sing_173.htm#SEC213 3856 string operations sing_175.htm#SEC215 3857 string related functions string related functions sing_176.htm#SEC216 3858 string type cast sing_174.htm#SEC214 3859 stripHNE sing_1568.htm#SEC1644 19265 3860 sturm sing_1999.htm#SEC2075 54353 3861 sturmha sing_2001.htm#SEC2077 12467 3862 sturmhaseq sing_2002.htm#SEC2078 59133 3863 sturmquery sing_1977.htm#SEC2053 10805 3864 sturmseq sing_2000.htm#SEC2076 23005 3865 submat sing_1053.htm#SEC1129 37665 3866 subquotient sing_2503.htm#SEC2579 40364 3867 subrInterred sing_977.htm#SEC1053 10165 3868 subset_sum01 sing_1920.htm#SEC1996 60620 3869 subset_sum02 sing_1921.htm#SEC1997 37340 3870 subst sing_357.htm#SEC397 3871 subst (plural) sing_481.htm#SEC521 3872 substitute sing_976.htm#SEC1052 28919 3873 sugarCrit, option sing_315.htm#IDX169 3874 sum sing_914.htm#SEC990 555 3875 sum_of_powers sing_2258.htm#SEC2334 12170 3876 sumlist sing_1410.htm#SEC1486 59918 3877 sumofquotients sing_2724.htm#SEC2800 4569 3878 super-commutative algebras Graded commutative algebras (SCA) sing_490.htm#SEC542 3879 superCommutative sing_731.htm#SEC783 45528 3880 super_increasing_knapsack super_increasing_knapsack sing_1932.htm#SEC2008 9177 3881 surf.lib sing_1779.htm#SEC1855 3882 surf_lib sing_1779.htm#SEC1855 3883 surfacesignature.lib surfacesignature_lib sing_1628.htm#SEC1704 3884 surfacesignature_lib surfacesignature_lib sing_1628.htm#SEC1704 3637 3885 surfer sing_1.htm#IDX8 14287 3638 surfer sing_17 67.htm#SEC18433886 surfer sing_1781.htm#SEC1857 3639 3887 surfex sing_1.htm#IDX7 3640 surfex.lib sing_1768.htm#SEC1844 3641 surfex_lib sing_1768.htm#SEC1844 3642 suspend sing_345.htm#SEC385 3643 swalk sing_2550.htm#SEC2626 16794 3644 swalk.lib sing_2549.htm#SEC2625 3645 swalk_lib sing_2549.htm#SEC2625 3646 swap sing_1483.htm#SEC1559 15408 3647 swap sing_2165.htm#IDX819 3648 switch No case or switch statement sing_404.htm#SEC444 3649 switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2558.htm#SEC2634 1827 3650 syModStd sing_1328.htm#SEC1404 50246 3651 symNsym sing_2234.htm#SEC2310 55230 3652 sym_gauss sing_1067.htm#SEC1143 5121 3653 symm sing_2233.htm#SEC2309 64628 3654 symmStd sing_1327.htm#SEC1403 39353 3655 symmat sing_1042.htm#SEC1118 61294 3656 symmetric basis sing_1059.htm#IDX498 3657 symmetric power sing_1061.htm#IDX500 3658 symmetricBasis sing_1059.htm#SEC1135 sprintf 3659 symmetricPower sing_1061.htm#SEC1137 6542 3660 symmetricPowerSheaf sing_2528.htm#SEC2604 56922 3661 symmfunc sing_1972.htm#SEC2048 45575 3662 symodstd.lib sing_1322.htm#SEC1398 3663 symodstd_lib sing_1322.htm#SEC1398 3664 symsignature sing_1962.htm#SEC2038 10520 3665 syndrome sing_1795.htm#SEC1871 14057 3666 sysBin sing_1793.htm#SEC1869 41948 3667 sysCRHT sing_1790.htm#SEC1866 58930 3668 sysCRHTMindist sing_1791.htm#SEC1867 13692 3669 sysFL sing_1806.htm#SEC1882 53040 3670 sysNewton sing_1792.htm#SEC1868 19704 3671 sysQE sing_1796.htm#SEC1872 61026 3672 sys_code sing_1787.htm#SEC1863 20220 3673 system sing_350.htm#SEC390 3674 system, -- sing_350.htm#IDX275 3675 system, --long_option_name sing_350.htm#IDX278 3676 system, --long_option_name=value sing_350.htm#IDX280 3677 system, HC sing_350.htm#IDX215 3678 system, LLL sing_350.htm#IDX219 3679 system, Singular sing_350.htm#IDX256 3680 system, SingularLib sing_350.htm#IDX258 3681 system, absFact sing_350.htm#IDX190 3682 system, alarm sing_350.htm#IDX189 3683 system, blackbox sing_350.htm#IDX191 3684 system, bracket sing_350.htm#IDX196 3685 system, browsers sing_350.htm#IDX195 3686 system, btest sing_350.htm#IDX198 3687 system, complexNearZero sing_350.htm#IDX199 3688 system, contributors sing_350.htm#IDX201 3689 system, cpu sing_350.htm#IDX203 3690 system, cpu sing_350.htm#IDX274 3691 system, denom_list sing_350.htm#IDX205 3692 system, eigenvals sing_350.htm#IDX206 3693 system, env sing_350.htm#IDX207 3694 system, executable sing_350.htm#IDX209 3695 system, freegb sing_350.htm#IDX210 3696 system, getPrecDigits sing_350.htm#IDX213 3697 system, getenv sing_350.htm#IDX212 3698 system, gmsnf sing_350.htm#IDX214 3699 system, hessenberg sing_350.htm#IDX216 3700 system, install sing_350.htm#IDX218 3701 system, nblocks sing_350.htm#IDX222 3702 system, nc_hilb sing_350.htm#IDX224 3703 system, neworder sing_350.htm#IDX225 3704 system, newstruct sing_350.htm#IDX226 3705 system, opp sing_350.htm#IDX227 3706 system, oppose sing_350.htm#IDX230 3707 system, pcvBasis sing_350.htm#IDX239 3708 system, pcvCV2P sing_350.htm#IDX237 3709 system, pcvDim sing_350.htm#IDX238 3710 system, pcvLAddL sing_350.htm#IDX233 3711 system, pcvMinDeg sing_350.htm#IDX235 3712 system, pcvP2CV sing_350.htm#IDX236 3713 system, pcvPMulL sing_350.htm#IDX234 3714 system, pid sing_350.htm#IDX241 3715 system, random sing_350.htm#IDX243 3716 system, reserve sing_350.htm#IDX245 3717 system, reservedLink sing_350.htm#IDX246 3718 system, semaphore sing_350.htm#IDX248 3719 system, semic sing_350.htm#IDX249 3720 system, setenv sing_350.htm#IDX251 3721 system, sh sing_350.htm#IDX253 3722 system, shrinktest sing_350.htm#IDX254 3723 system, spadd sing_350.htm#IDX259 3724 system, spectrum sing_350.htm#IDX260 3725 system, spmul sing_350.htm#IDX261 3726 system, std_syz sing_350.htm#IDX262 3727 system, stest sing_350.htm#IDX263 3728 system, tensorModuleMult sing_350.htm#IDX264 3729 system, twostd sing_350.htm#IDX265 3730 system, uname sing_350.htm#IDX268 3731 system, version sing_350.htm#IDX271 3732 system, with sing_350.htm#IDX272 3733 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2382.htm#SEC2458 63094 3734 syz sing_351.htm#SEC391 3735 syz (plural) sing_474.htm#SEC514 3736 syzygy sing_1006.htm#IDX494 3737 tDetropicalise sing_2143.htm#SEC2219 23532 3738 tInitialForm sing_2127.htm#SEC2203 24484 3739 tInitialFormPar sing_2139.htm#SEC2215 9584 3740 tInitialFormParMax sing_2140.htm#SEC2216 7829 3741 tInitialIdeal sing_2128.htm#SEC2204 17937 3742 tab sing_929.htm#SEC1005 60407 3743 tail sing_1941.htm#SEC2017 13066 3744 tame polynomial sing_1536.htm#IDX713 3745 tame 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system, semic sing_358.htm#IDX251 3969 system, setenv sing_358.htm#IDX253 3970 system, sh sing_358.htm#IDX255 3971 system, shrinktest sing_358.htm#IDX256 3972 system, spadd sing_358.htm#IDX261 3973 system, spectrum sing_358.htm#IDX262 3974 system, spmul sing_358.htm#IDX263 3975 system, std_syz sing_358.htm#IDX264 3976 system, stest sing_358.htm#IDX265 3977 system, tensorModuleMult sing_358.htm#IDX266 3978 system, twostd sing_358.htm#IDX267 3979 system, uname sing_358.htm#IDX270 3980 system, version sing_358.htm#IDX273 3981 system, with sing_358.htm#IDX274 3982 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2407.htm#SEC2483 63094 3983 syz sing_359.htm#SEC399 3984 syz (plural) sing_482.htm#SEC522 3985 tDetropicalise sing_2154.htm#SEC2230 23532 3986 tInitialForm sing_2138.htm#SEC2214 24484 3987 tInitialFormPar sing_2150.htm#SEC2226 9584 3988 tInitialFormParMax sing_2151.htm#SEC2227 7829 3989 tInitialIdeal sing_2139.htm#SEC2215 17937 3990 tab sing_949.htm#SEC1025 60407 3991 tail sing_1955.htm#SEC2031 13066 3992 tame polynomial sing_1550.htm#IDX739 3993 tame polynomial sing_1551.htm#IDX749 3994 tame polynomial sing_1552.htm#IDX750 3995 tangentGens sing_1366.htm#SEC1442 37797 3996 tangentcone sing_1615.htm#SEC1691 20056 3997 target sing_2510.htm#SEC2586 18743 3998 task sing_1026.htm#IDX512 3999 tasks.lib sing_1026.htm#SEC1102 4000 tasks_lib sing_1026.htm#SEC1102 4001 tau_es sing_1523.htm#SEC1599 17043 4002 tau_es2 sing_1477.htm#SEC1553 38083 4003 tdCf sing_2287.htm#SEC2363 21522 4004 tdFactor sing_2289.htm#SEC2365 37910 4005 tdProj sing_2292.htm#SEC2368 38406 4006 tdTerms sing_2288.htm#SEC2364 30166 4007 teachstd.lib sing_1953.htm#SEC2029 4008 teachstd_lib sing_1953.htm#SEC2029 3760 4009 template.lib sing_55.htm#IDX120 3761 4010 template.lib sing_55.htm#IDX123 3762 4011 template_lib sing_55.htm#SEC92 3763 4012 template_lib sing_55.htm#IDX121 3764 tensor sing_490.htm#IDX309 65451 3765 tensor sing_1043.htm#SEC1119 3766 tensorMod 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sing_1756.htm#SEC1832 6682 3786 texmap sing_1757.htm#SEC1833 35265 3787 texname sing_1758.htm#SEC1834 1008 3788 texobj sing_1759.htm#SEC1835 2107 3789 texpoly sing_1760.htm#SEC1836 64109 3790 texproc sing_1761.htm#SEC1837 23626 3791 texring sing_1762.htm#SEC1838 38275 3792 the first alternative algorithm sing_1139.htm#IDX534 3793 three_elements sing_1925.htm#SEC2001 513 3794 timeFactorize sing_898.htm#SEC974 49531 3795 timeStd sing_897.htm#SEC973 31506 3796 timer sing_394.htm#SEC434 3797 timer resolution, setting the sing_350.htm#IDX281 3798 timestep sing_2364.htm#SEC2440 38225 3799 tjurina sing_1597.htm#SEC1673 9100 3800 tmatrix sing_1524.htm#SEC1600 57332 3801 todd sing_2266.htm#SEC2342 25618 3802 toddE sing_2267.htm#SEC2343 17823 3803 toddPoly sing_2280.htm#SEC2356 65066 3804 tolessvars sing_1700.htm#SEC1776 56590 3805 topChernClass sing_2524.htm#SEC2600 17374 3806 topological invariants sing_1451.htm#IDX615 3807 topological invariants sing_1458.htm#IDX622 3808 topological 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4017 tensorMatrix sing_2518.htm#SEC2594 31437 4018 tensorMod sing_1174.htm#SEC1250 21961 4019 tensorModFreemod sing_2520.htm#SEC2596 11852 4020 tensorModule sing_2519.htm#SEC2595 58772 4021 tensorProduct sing_2523.htm#SEC2599 sprintf 4022 tensorSheaf sing_2709.htm#SEC2785 24072 4023 term orderings General definitions for orderings sing_856.htm#SEC908 4024 term orderings introduction Introduction to orderings sing_855.htm#SEC907 4025 testFraction sing_2648.htm#SEC2724 28466 4026 testLocData sing_2645.htm#SEC2721 50986 4027 testNCfac sing_705.htm#SEC757 60394 4028 testNcfrac sing_2606.htm#SEC2682 34186 4029 testNcfracExamples sing_2607.htm#SEC2683 15399 4030 testNcloc sing_2610.htm#SEC2686 62706 4031 testNclocExamples sing_2611.htm#SEC2687 14584 4032 testOlga sing_2662.htm#SEC2738 53953 4033 testOlgaExamples sing_2663.htm#SEC2739 62869 4034 testParametrization sing_1381.htm#SEC1457 18686 4035 testPointConic sing_1382.htm#SEC1458 25315 4036 testPrimary sing_1294.htm#SEC1370 34254 4037 testPrimaryE sing_1295.htm#SEC1371 20693 4038 tex sing_1768.htm#SEC1844 12226 4039 texDrawBasic sing_2145.htm#SEC2221 3635 4040 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2147.htm#SEC2223 42021 4041 texDrawTriangulation texDrawTriangulation sing_2148.htm#SEC2224 18865 4042 texDrawTropical sing_2146.htm#SEC2222 58447 4043 texMatrix sing_2144.htm#SEC2220 1334 4044 texNumber sing_2142.htm#SEC2218 12628 4045 texPolynomial sing_2143.htm#SEC2219 41136 4046 texcoef sing_1849.htm#SEC1925 28189 4047 texdemo sing_1769.htm#SEC1845 13008 4048 texfactorize sing_1770.htm#SEC1846 6682 4049 texmap sing_1771.htm#SEC1847 35265 4050 texname sing_1772.htm#SEC1848 1008 4051 texobj sing_1773.htm#SEC1849 2107 4052 texpoly sing_1774.htm#SEC1850 64109 4053 texproc sing_1775.htm#SEC1851 23626 4054 texring sing_1776.htm#SEC1852 38275 4055 the first alternative algorithm sing_1151.htm#IDX549 4056 three_elements sing_1939.htm#SEC2015 513 4057 timeFactorize sing_918.htm#SEC994 49531 4058 timeStd sing_917.htm#SEC993 31506 4059 timer sing_402.htm#SEC442 4060 timer resolution, setting the sing_358.htm#IDX283 4061 timestep sing_2387.htm#SEC2463 38225 4062 tjurina sing_1611.htm#SEC1687 9100 4063 tmatrix sing_1538.htm#SEC1614 57332 4064 todd sing_2284.htm#SEC2360 25618 4065 toddE sing_2285.htm#SEC2361 17823 4066 toddPoly sing_2298.htm#SEC2374 65066 4067 tolessvars sing_1714.htm#SEC1790 56590 4068 topChernClass sing_2706.htm#SEC2782 17374 4069 topological invariants sing_1465.htm#IDX641 4070 topological invariants sing_1472.htm#IDX648 4071 topological invariants sing_1473.htm#IDX652 4072 topological invariants sing_1474.htm#IDX656 4073 topological invariants sing_1475.htm#IDX660 4074 toric ideals sing_871.htm#SEC928 4075 toric ring sing_1253.htm#IDX582 4076 toric.lib sing_1343.htm#SEC1419 4077 toric_ideal sing_1344.htm#SEC1420 5760 4078 toric_lib sing_1343.htm#SEC1419 4079 toric_std sing_1345.htm#SEC1421 26141 4080 torusInvariants sing_1259.htm#SEC1335 911 4081 total divisors 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sing_1137.htm#IDX523 4105 tropical geometry sing_2734.htm#IDX1070 4106 tropical mirror symmetry sing_1137.htm#IDX525 4107 tropical polynomials sing_2124.htm#IDX823 4108 tropical varieties sing_2734.htm#IDX1071 4109 tropical.lib sing_2124.htm#IDX820 4110 tropicalCurve sing_2129.htm#SEC2205 16865 4111 tropicalJInvariant sing_2132.htm#SEC2208 40395 4112 tropicalLifting sing_2125.htm#SEC2201 7052 4113 tropicalLinkNewton sing_2742.htm#SEC2818 63886 4114 tropicalNewton.lib sing_2734.htm#SEC2810 4115 tropicalNewton_lib sing_2734.htm#SEC2810 4116 tropicalPointNewton sing_2739.htm#SEC2815 18572 4117 tropicalSubst sing_2157.htm#SEC2233 49846 4118 tropicalVariety sing_2164.htm#SEC2240 39087 4119 tropicalVarietyNewton tropicalVarietyNewton sing_2741.htm#SEC2817 28532 4120 tropical_lib sing_2124.htm#IDX821 4121 tropicalise sing_2136.htm#SEC2212 49739 4122 tropicaliseSet sing_2137.htm#SEC2213 35136 4123 truncate sing_1447.htm#SEC1523 13545 4124 truncateFast sing_1448.htm#SEC1524 5124 4125 truncated module sing_1447.htm#IDX632 4126 truncated module sing_1448.htm#IDX633 4127 tst_ncfactor sing_713.htm#SEC765 3339 4128 twalk sing_1150.htm#SEC1226 35753 4129 two-sided sing_498.htm#IDX309 4130 two-sided Groebner basis sing_498.htm#IDX310 4131 twostd sing_358.htm#IDX268 4132 twostd sing_483.htm#SEC523 4133 type sing_362.htm#SEC402 4134 type B sing_2192.htm#IDX872 4135 type D sing_2193.htm#IDX874 4136 type,custom Definition of a user defined type sing_183.htm#SEC223 4137 type2arr sing_2170.htm#SEC2246 62624 4138 typecasting sing_2170.htm#IDX828 4139 typecasting sing_2171.htm#IDX830 4140 typecasting sing_2172.htm#IDX833 4141 typeof sing_363.htm#SEC403 4142 u sing_2373.htm#SEC2449 12154 4143 uname sing_358.htm#IDX269 4144 unbounded_knapsack sing_1922.htm#SEC1998 17226 4145 unipotent groups sing_1365.htm#IDX600 4146 uniquePoint sing_2049.htm#SEC2125 893 4147 unitMatrix sing_2676.htm#SEC2752 33014 4148 unitmat sing_1056.htm#SEC1132 12862 4149 univariate sing_364.htm#SEC404 4150 univarpoly 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