Changeset a719149 in git
- Timestamp:
- Mar 19, 2016, 9:49:56 PM (8 years ago)
- Branches:
- (u'spielwiese', 'fe61d9c35bf7c61f2b6cbf1b56e25e2f08d536cc')
- Children:
- 485fc1841a6e561a3943c6679fc121708c19e9a2
- Parents:
- 44982519aa89e921c7d8cb3634a92a3d3b22444b
- Files:
-
- 2 edited
-
doc/singular.idx (modified) (4 diffs)
-
emacs/hlp-cmpl.el (modified) (13 diffs)
Legend:
- Unmodified
- Added
- Removed
-
doc/singular.idx
r449825 ra719149 1 ! sing_36.htm#IDX10 22 != sing_36.htm#IDX9 63 != sing_95.htm#SEC13 44 " sing_36.htm#IDX10 55 # sing_36.htm#IDX11 96 $ sing_36.htm#IDX1 207 % sing_36.htm#IDX9 28 % sing_76.htm#SEC11 59 % sing_93.htm#SEC13 210 % sing_105.htm#SEC14 411 && sing_36.htm#IDX10 312 && sing_96.htm#SEC13 513 ( sing_36.htm#IDX8 114 ) sing_36.htm#IDX8 215 * bigintmat operations sing_36.htm#IDX 9016 * sing_76.htm#SEC11 517 * sing_82.htm#SEC12 118 * sing_88.htm#SEC12 719 * sing_93.htm#SEC13 220 * sing_101.htm#SEC14 021 * sing_105.htm#SEC14 422 ** sing_36.htm#IDX9 423 + bigintmat operations sing_36.htm#IDX8 624 + sing_76.htm#SEC11 525 + sing_82.htm#SEC12 126 + sing_88.htm#SEC12 727 + sing_93.htm#SEC13 228 + sing_101.htm#SEC14 029 + sing_105.htm#SEC14 430 ++ sing_36.htm#IDX8 731 - bigintmat operations sing_36.htm#IDX8 832 - sing_76.htm#SEC11 533 - sing_82.htm#SEC12 134 - sing_93.htm#SEC13 235 - sing_101.htm#SEC14 036 - sing_105.htm#SEC14 437 -- sing_36.htm#IDX8 938 --MPhost sing_19.htm#IDX6 739 --MPport sing_19.htm#IDX6 61 ! sing_36.htm#IDX101 2 != sing_36.htm#IDX95 3 != sing_95.htm#SEC135 4 " sing_36.htm#IDX104 5 # sing_36.htm#IDX118 6 $ sing_36.htm#IDX119 7 % sing_36.htm#IDX91 8 % sing_76.htm#SEC116 9 % sing_93.htm#SEC133 10 % sing_105.htm#SEC145 11 && sing_36.htm#IDX102 12 && sing_96.htm#SEC136 13 ( sing_36.htm#IDX80 14 ) sing_36.htm#IDX81 15 * bigintmat operations sing_36.htm#IDX89 16 * sing_76.htm#SEC116 17 * sing_82.htm#SEC122 18 * sing_88.htm#SEC128 19 * sing_93.htm#SEC133 20 * sing_101.htm#SEC141 21 * sing_105.htm#SEC145 22 ** sing_36.htm#IDX93 23 + bigintmat operations sing_36.htm#IDX85 24 + sing_76.htm#SEC116 25 + sing_82.htm#SEC122 26 + sing_88.htm#SEC128 27 + sing_93.htm#SEC133 28 + sing_101.htm#SEC141 29 + sing_105.htm#SEC145 30 ++ sing_36.htm#IDX86 31 - bigintmat operations sing_36.htm#IDX87 32 - sing_76.htm#SEC116 33 - sing_82.htm#SEC122 34 - sing_93.htm#SEC133 35 - sing_101.htm#SEC141 36 - sing_105.htm#SEC145 37 -- sing_36.htm#IDX88 38 --MPhost sing_19.htm#IDX66 39 --MPport sing_19.htm#IDX65 40 40 --allow-net sing_19.htm#IDX39 41 --batch sing_19.htm#IDX6 541 --batch sing_19.htm#IDX64 42 42 --browser sing_19.htm#IDX43 43 43 --echo sing_19.htm#IDX35 44 --emacs sing_19.htm#IDX6 845 --emacs-dir sing_19.htm#IDX6 946 --emacs-load sing_19.htm#IDX 7047 --execute sing_19.htm#IDX5 744 --emacs sing_19.htm#IDX67 45 --emacs-dir sing_19.htm#IDX68 46 --emacs-load sing_19.htm#IDX69 47 --execute sing_19.htm#IDX56 48 48 --help sing_19.htm#IDX37 49 --min-time sing_19.htm#IDX6 249 --min-time sing_19.htm#IDX61 50 50 --no-out sing_19.htm#IDX49 51 51 --no-rc sing_19.htm#IDX45 … … 55 55 --no-warn sing_19.htm#IDX48 56 56 --quiet sing_19.htm#IDX53 57 --random sing_19.htm#IDX6 157 --random sing_19.htm#IDX60 58 58 --sdb sing_19.htm#IDX32 59 --singular sing_19.htm#IDX71 60 --ticks-per-sec sing_19.htm#IDX63 61 --user-option sing_19.htm#IDX59 62 --verbose sing_19.htm#IDX54 63 -> sing_154.htm#SEC193 59 --singular sing_19.htm#IDX70 60 --ticks-per-sec sing_19.htm#IDX62 61 --user-option sing_19.htm#IDX58 62 -> sing_154.htm#SEC194 64 63 -MPhost Command line options 65 64 -MPport Command line options 66 65 -allow-net Command line options 67 -b Command line options sing_19.htm#IDX6 466 -b Command line options sing_19.htm#IDX63 68 67 -batch Command line options 69 68 -browser Command line options 70 -c Command line options sing_19.htm#IDX5 669 -c Command line options sing_19.htm#IDX55 71 70 -d Command line options sing_19.htm#IDX31 72 71 -e Command line options sing_19.htm#IDX34 … … 87 86 -q Command line options sing_19.htm#IDX52 88 87 -quiet Command line options 89 -r Command line options sing_19.htm#IDX 6088 -r Command line options sing_19.htm#IDX59 90 89 -random Command line options 91 90 -sdb Command line options 92 91 -singular Command line options 93 92 -ticks-per-sec Command line options 94 -u Command line options sing_19.htm#IDX5 893 -u Command line options sing_19.htm#IDX57 95 94 -user-option Command line options 96 -v Command line options sing_19.htm#IDX55 97 -verbose Command line options 98 .. sing_36.htm#IDX114 99 .singularrc file sing_20.htm#IDX73 95 -v Command line options sing_19.htm#IDX54 96 .. sing_36.htm#IDX113 97 .singularrc file sing_20.htm#IDX72 100 98 .singularrc file, no loading Command line options sing_19.htm#IDX46 101 / sing_36.htm#IDX9 1102 / sing_105.htm#SEC14 4103 // sing_36.htm#IDX10 8104 // sing_36.htm#IDX1 10105 // sing_36.htm#IDX11 1106 : sing_36.htm#IDX11 5107 : sing_105.htm#SEC14 4108 :: sing_36.htm#IDX11 6109 :: sing_144.htm#SEC18 3110 ; sing_36.htm#IDX11 2111 < sing_36.htm#IDX10 1112 < sing_298.htm#SEC33 7113 <= sing_36.htm#IDX 100114 <= sing_95.htm#SEC13 4115 <> sing_36.htm#IDX9 7116 <> sing_95.htm#SEC13 4117 = sing_36.htm#IDX7 8118 == sing_36.htm#IDX9 5119 == sing_95.htm#SEC13 4120 > sing_36.htm#IDX9 9121 >= sing_36.htm#IDX9 8122 >= sing_95.htm#SEC13 4123 ? sing_36.htm#IDX10 7124 ? sing_308.htm#IDX14 4125 AG codes sing_887.htm#SEC93 8126 AGcode_L sing_182 6.htm#SEC1901127 AGcode_Omega sing_18 27.htm#SEC1902128 ASCII sing_936.htm#SEC101 1129 ASCII links sing_112.htm#SEC15 1130 ASSUME sing_64.htm#SEC10 0131 A_L sing_152 5.htm#SEC1600132 A_Z sing_935.htm#SEC101 0133 Access to elements of a user defined type Access to elements of a user defined type sing_180.htm#SEC2 19134 Adj_div sing_182 1.htm#SEC1896135 Adjoint ideal sing_140 2.htm#IDX535136 Alexander polynomial sing_149 6.htm#IDX559137 Algebraic Geometry codes sing_182 0.htm#IDX707138 Algebraic dependence Algebraic dependence sing_868.htm#SEC9 19139 Algebraic geometry sing_13 77.htm#SEC1452140 AltVarEnd sing_781.htm#SEC83 2141 AltVarStart sing_780.htm#SEC83 1142 Ann sing_131 6.htm#SEC1391143 Appel function sing_611.htm#IDX3 40144 Appel hypergeometric function sing_611.htm#IDX34 1145 Applications sing_885.htm#SEC93 6146 ArnoldAction sing_16 18.htm#SEC1693147 Assignments for user defined types Assignments for user defined types sing_182.htm#SEC22 1148 Atkin sing_19 09.htm#SEC198499 / sing_36.htm#IDX90 100 / sing_105.htm#SEC145 101 // sing_36.htm#IDX107 102 // sing_36.htm#IDX109 103 // sing_36.htm#IDX110 104 : sing_36.htm#IDX114 105 : sing_105.htm#SEC145 106 :: sing_36.htm#IDX115 107 :: sing_144.htm#SEC184 108 ; sing_36.htm#IDX111 109 < sing_36.htm#IDX100 110 < sing_298.htm#SEC338 111 <= sing_36.htm#IDX99 112 <= sing_95.htm#SEC135 113 <> sing_36.htm#IDX96 114 <> sing_95.htm#SEC135 115 = sing_36.htm#IDX77 116 == sing_36.htm#IDX94 117 == sing_95.htm#SEC135 118 > sing_36.htm#IDX98 119 >= sing_36.htm#IDX97 120 >= sing_95.htm#SEC135 121 ? sing_36.htm#IDX106 122 ? sing_308.htm#IDX143 123 AG codes sing_887.htm#SEC939 124 AGcode_L sing_1829.htm#SEC1905 125 AGcode_Omega sing_1830.htm#SEC1906 126 ASCII sing_936.htm#SEC1012 127 ASCII links sing_112.htm#SEC152 128 ASSUME sing_64.htm#SEC101 129 A_L sing_1528.htm#SEC1604 130 A_Z sing_935.htm#SEC1011 131 Access to elements of a user defined type Access to elements of a user defined type sing_180.htm#SEC220 132 Adj_div sing_1824.htm#SEC1900 133 Adjoint ideal sing_1405.htm#IDX535 134 Alexander polynomial sing_1499.htm#IDX559 135 Algebraic Geometry codes sing_1823.htm#IDX707 136 Algebraic dependence Algebraic dependence sing_868.htm#SEC920 137 Algebraic geometry sing_1380.htm#SEC1456 138 AltVarEnd sing_781.htm#SEC833 139 AltVarStart sing_780.htm#SEC832 140 Ann sing_1319.htm#SEC1395 141 Appel function sing_611.htm#IDX339 142 Appel hypergeometric function sing_611.htm#IDX340 143 Applications sing_885.htm#SEC937 144 ArnoldAction sing_1621.htm#SEC1697 145 Assignments for user defined types Assignments for user defined types sing_182.htm#SEC222 146 Atkin sing_1912.htm#SEC1988 149 147 Authors sing_1.htm#IDX16 150 BINresol sing_141 5.htm#SEC1490148 BINresol sing_1418.htm#SEC1494 151 149 Background sing_3.htm#SEC5 152 Basic programming sing_843.htm#SEC894 153 Basic programming sing_843.htm#SEC894 154 BelongSemig sing_2225.htm#SEC2300 155 Bern sing_2203.htm#SEC2278 156 Bernstein operator sing_588.htm#IDX322 157 Bernstein-Sato polynomial sing_553.htm#IDX303 158 Bernstein-Sato polynomial sing_588.htm#IDX319 159 Bernstein-Sato polynomial sing_1559.htm#IDX590 160 Bernstein-Sato polynomial sing_1563.htm#IDX607 161 Bernstein-Sato polynomial for variety sing_644.htm#IDX344 162 Betti number Syzygies and resolutions sing_902.htm#SEC958 163 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_912.htm#SEC968 164 BlowingUp sing_1538.htm#SEC1613 165 Blowupcenter sing_1418.htm#SEC1493 166 BorelCheck sing_1493.htm#SEC1568 167 Branches of space curve singularities Branches of space curve singularities sing_876.htm#SEC927 168 Briancon-Maisonobe algorithm sing_588.htm#IDX328 169 Brieskorn lattice sing_1559.htm#IDX586 170 Brieskorn lattice sing_1560.htm#IDX597 171 Brieskorn lattice sing_1561.htm#IDX600 172 Brieskorn lattice sing_1562.htm#IDX603 173 Brieskorn lattice sing_1563.htm#IDX606 174 Brieskorn lattice sing_1564.htm#IDX610 175 Brieskorn lattice sing_1565.htm#IDX614 176 Brieskorn lattice sing_1566.htm#IDX620 177 Brieskorn lattice sing_1567.htm#IDX628 178 Brieskorn lattice sing_1568.htm#IDX634 179 Brieskorn lattice sing_1569.htm#IDX642 180 Brieskorn lattice sing_1570.htm#IDX652 181 Brieskorn lattice sing_1581.htm#IDX658 182 Brieskorn lattice sing_1583.htm#IDX669 183 Brieskorn lattice sing_1611.htm#IDX696 184 Brill-Noether algorithm sing_1820.htm#IDX708 185 BrillNoether sing_1823.htm#SEC1898 186 Buchberger algorithm for toric ideals Buchberger algorithm sing_913.htm#SEC969 187 Budur-Mustata-Saito approach sing_644.htm#IDX348 188 Building Singular sing_2456.htm#SEC2543 189 C programming language Major differences to the C programming language sing_457.htm#SEC496 190 C, module ordering sing_895.htm#IDX402 191 CGS, disjoint, reduced, Comprehensive Groebner System cgsdr sing_957.htm#IDX412 192 CM_regularity sing_1480.htm#SEC1555 33865 193 CMtype sing_1649.htm#SEC1724 194 CRHT-ideal sing_919.htm#SEC982 195 Castelnuovo-Mumford regularity sing_1480.htm#IDX551 196 Category string sing_51.htm#SEC87 197 CenCharDec sing_738.htm#SEC789 198 Center sing_1457.htm#SEC1532 199 CenterBO sing_1464.htm#SEC1539 200 CentralQuot sing_736.htm#SEC787 201 CentralSaturation sing_737.htm#SEC788 150 Basic programming sing_843.htm#SEC895 151 Basic programming sing_843.htm#SEC895 152 BelongSemig sing_2230.htm#SEC2306 153 BerlekampMassey sing_2256.htm#SEC2332 154 Bern sing_2208.htm#SEC2284 155 Bernstein operator sing_588.htm#IDX321 156 Bernstein-Sato polynomial sing_553.htm#IDX302 157 Bernstein-Sato polynomial sing_588.htm#IDX318 158 Bernstein-Sato polynomial sing_1562.htm#IDX590 159 Bernstein-Sato polynomial sing_1566.htm#IDX607 160 Bernstein-Sato polynomial for variety sing_644.htm#IDX343 161 Betti number Syzygies and resolutions sing_902.htm#SEC959 162 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_912.htm#SEC969 163 BlowingUp sing_1541.htm#SEC1617 164 Blowupcenter sing_1421.htm#SEC1497 165 BorelCheck sing_1496.htm#SEC1572 166 Branches of space curve singularities Branches of space curve singularities sing_876.htm#SEC928 167 Briancon-Maisonobe algorithm sing_588.htm#IDX327 168 Brieskorn lattice sing_1562.htm#IDX586 169 Brieskorn lattice sing_1563.htm#IDX597 170 Brieskorn lattice sing_1564.htm#IDX600 171 Brieskorn lattice sing_1565.htm#IDX603 172 Brieskorn lattice sing_1566.htm#IDX606 173 Brieskorn lattice sing_1567.htm#IDX610 174 Brieskorn lattice sing_1568.htm#IDX614 175 Brieskorn lattice sing_1569.htm#IDX620 176 Brieskorn lattice sing_1570.htm#IDX628 177 Brieskorn lattice sing_1571.htm#IDX634 178 Brieskorn lattice sing_1572.htm#IDX642 179 Brieskorn lattice sing_1573.htm#IDX652 180 Brieskorn lattice sing_1584.htm#IDX658 181 Brieskorn lattice sing_1586.htm#IDX669 182 Brieskorn lattice sing_1614.htm#IDX696 183 Brill-Noether algorithm sing_1823.htm#IDX708 184 BrillNoether sing_1826.htm#SEC1902 185 Buchberger algorithm for toric ideals Buchberger algorithm sing_913.htm#SEC970 186 Budur-Mustata-Saito approach sing_644.htm#IDX347 187 Building Singular sing_2470.htm#SEC2559 188 C programming language Major differences to the C programming language sing_457.htm#SEC497 189 C, module ordering sing_895.htm#IDX401 190 CGS, disjoint, reduced, Comprehensive Groebner System cgsdr sing_957.htm#IDX411 191 CM_regularity sing_1483.htm#SEC1559 33865 192 CMtype sing_1652.htm#SEC1728 193 CRHT-ideal sing_919.htm#SEC983 194 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 195 Castelnuovo-Mumford regularity sing_1483.htm#IDX551 196 Category string sing_51.htm#SEC88 197 CenCharDec sing_738.htm#SEC790 198 Center sing_1460.htm#SEC1536 199 CenterBO sing_1467.htm#SEC1543 200 CentralQuot sing_736.htm#SEC788 201 CentralSaturation sing_737.htm#SEC789 202 202 Change of rings sing_9.htm#SEC15 203 Characteristic sets sing_903.htm#SEC9 59204 CharacteristicExponents CharacteristicExponents sing_154 4.htm#SEC1619205 ChernRootsDual sing_218 4.htm#SEC2259206 ChernRootsHom sing_219 1.htm#SEC2266207 ChernRootsProd sing_218 6.htm#SEC2261208 ChernRootsSum sing_218 2.htm#SEC2257209 ChernRootsSymm sing_219 3.htm#SEC2268210 ChernRootsWedge sing_219 4.htm#SEC2269211 Chevalley-Rosenlicht theorem sing_139 6.htm#IDX520212 Chevalley-Rosenlicht theorem sing_1 397.htm#IDX523213 Classification of hypersurface singularities Classification of hypersurface singularities sing_877.htm#SEC92 8214 Classification of singularities sing_2 393.htm#IDX891215 Code Codes and the decoding problem sing_918.htm#SEC97 5216 Codes and the decoding problem Codes and the decoding problem sing_918.htm#SEC97 4217 Coding theory sing_18 19.htm#SEC1894218 Coefficient rings Notes for Singular users sing_24 54.htm#SEC2535203 Characteristic sets sing_903.htm#SEC960 204 CharacteristicExponents CharacteristicExponents sing_1547.htm#SEC1623 205 ChernRootsDual sing_2187.htm#SEC2263 206 ChernRootsHom sing_2196.htm#SEC2272 207 ChernRootsProd sing_2189.htm#SEC2265 208 ChernRootsSum sing_2185.htm#SEC2261 209 ChernRootsSymm sing_2198.htm#SEC2274 210 ChernRootsWedge sing_2199.htm#SEC2275 211 Chevalley-Rosenlicht theorem sing_1399.htm#IDX520 212 Chevalley-Rosenlicht theorem sing_1400.htm#IDX523 213 Classification of hypersurface singularities Classification of hypersurface singularities sing_877.htm#SEC929 214 Classification of singularities sing_2404.htm#IDX891 215 Code Codes and the decoding problem sing_918.htm#SEC976 216 Codes and the decoding problem Codes and the decoding problem sing_918.htm#SEC975 217 Coding theory sing_1822.htm#SEC1898 218 Coefficient rings Notes for Singular users sing_2468.htm#SEC2551 219 219 Command line options Command line options sing_19.htm#SEC26 220 Commands Functions and system variables sing_258.htm#SEC29 7221 Commands for user defined types Commands for user defined types sing_181.htm#SEC22 0222 Commutative Algebra sing_856.htm#SEC90 7223 Commutative algebra sing_113 5.htm#SEC1210224 CompDecomp sing_550.htm#SEC60 1225 CompInt sing_22 27.htm#SEC2302226 CompleteHomog sing_217 2.htm#SEC2247227 ComplexValue sing_22 67.htm#SEC2342228 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_852.htm#SEC90 3229 ConsLevels sing_964.htm#SEC10 39230 ContactMatrix sing_154 6.htm#SEC1621231 Conti-Traverso algorithm sing_908.htm#SEC96 4220 Commands Functions and system variables sing_258.htm#SEC298 221 Commands for user defined types Commands for user defined types sing_181.htm#SEC221 222 Commutative Algebra sing_856.htm#SEC908 223 Commutative algebra sing_1138.htm#SEC1214 224 CompDecomp sing_550.htm#SEC602 225 CompInt sing_2232.htm#SEC2308 226 CompleteHomog sing_2175.htm#SEC2251 227 ComplexValue sing_2278.htm#SEC2354 228 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_852.htm#SEC904 229 ConsLevels sing_964.htm#SEC1040 230 ContactMatrix sing_1549.htm#SEC1625 231 Conti-Traverso algorithm sing_908.htm#SEC965 232 232 Contributors sing_1.htm#IDX15 233 Control structures sing_425.htm#SEC46 4234 Control theory System and Control theory sing_185 3.htm#SEC1928235 Cooper philosophy sing_919.htm#SEC98 0236 Cornacchia sing_1 899.htm#SEC1974237 CornacchiaModified sing_190 0.htm#SEC1975238 Crep sing_960.htm#SEC103 5239 Critical points sing_871.htm#SEC92 2240 CurveParam sing_154 0.htm#SEC1615241 CurveRes sing_15 39.htm#SEC1614242 Curves sing_140 2.htm#IDX532243 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC3 5244 Cyclic code sing_183 4.htm#IDX715245 Cyclic roots sing_849.htm#SEC90 0246 D-integration sing_611.htm#IDX33 7247 D-localization sing_611.htm#IDX33 3248 D-localization sing_815.htm#IDX37 1249 D-module purityfiltration_lib sing_553.htm#IDX30 1250 D-module sing_588.htm#IDX31 6251 D-module sing_611.htm#IDX3 30252 D-module sing_644.htm#IDX34 2253 D-module sing_793.htm#IDX35 6254 D-module sing_815.htm#IDX36 8255 D-module structure sing_588.htm#IDX31 7256 D-module structure sing_644.htm#IDX34 3257 D-restriction sing_611.htm#IDX33 5258 DBM links sing_117.htm#SEC15 6233 Control structures sing_425.htm#SEC465 234 Control theory System and Control theory sing_1856.htm#SEC1932 235 Cooper philosophy sing_919.htm#SEC981 236 Cornacchia sing_1902.htm#SEC1978 237 CornacchiaModified sing_1903.htm#SEC1979 238 Crep sing_960.htm#SEC1036 239 Critical points sing_871.htm#SEC923 240 CurveParam sing_1543.htm#SEC1619 241 CurveRes sing_1542.htm#SEC1618 242 Curves sing_1405.htm#IDX532 243 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 244 Cyclic code sing_1837.htm#IDX715 245 Cyclic roots sing_849.htm#SEC901 246 D-integration sing_611.htm#IDX336 247 D-localization sing_611.htm#IDX332 248 D-localization sing_815.htm#IDX370 249 D-module purityfiltration_lib sing_553.htm#IDX300 250 D-module sing_588.htm#IDX315 251 D-module sing_611.htm#IDX329 252 D-module sing_644.htm#IDX341 253 D-module sing_793.htm#IDX355 254 D-module sing_815.htm#IDX367 255 D-module structure sing_588.htm#IDX316 256 D-module structure sing_644.htm#IDX342 257 D-restriction sing_611.htm#IDX334 258 DBM links sing_117.htm#SEC157 259 259 DISPLAY environment variable The online help system sing_16.htm#IDX28 260 DLoc sing_614.htm#SEC66 5261 DLoc0 sing_616.htm#SEC66 7262 Data types sing_72.htm#SEC11 1263 Data types (plural) sing_470.htm#IDX28 7264 Debugging tools sing_63.htm#SEC 99260 DLoc sing_614.htm#SEC666 261 DLoc0 sing_616.htm#SEC668 262 Data types sing_72.htm#SEC112 263 Data types (plural) sing_470.htm#IDX286 264 Debugging tools sing_63.htm#SEC100 265 265 Decker, Wolfram sing_1.htm#IDX17 266 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_179.htm#SEC218 267 Decoding sing_1834.htm#IDX717 268 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_917.htm#SEC973 269 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_922.htm#SEC991 270 Definition of a user defined type Definition of a user defined type sing_178.htm#SEC217 271 Deformations sing_874.htm#SEC925 272 Deformations, T1 and T2 sing_873.htm#SEC924 273 Degree sing_1381.htm#SEC1456 274 Delta sing_1465.htm#SEC1540 275 DeltaList sing_1466.htm#SEC1541 276 Demo mode sing_24.htm#SEC34 277 Depth sing_863.htm#SEC914 278 Determinacy sing_2396.htm#IDX895 279 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_911.htm#SEC967 280 Distributed computing sing_980.htm#IDX426 281 Dlocalization sing_816.htm#SEC867 282 Documentation Tool sing_60.htm#SEC96 283 Dp, global ordering sing_893.htm#IDX385 284 Ds, local ordering sing_894.htm#IDX395 285 DsingularLocus sing_820.htm#SEC871 286 Dynamic loading sing_71.htm#SEC110 287 Dynamic modules sing_851.htm#SEC902 288 ECPP sing_1943.htm#SEC2018 289 ECoef sing_1424.htm#SEC1499 290 EOrdlist sing_1422.htm#SEC1497 291 ERROR sing_287.htm#SEC326 292 Edatalist sing_1421.htm#SEC1496 293 Edelman-Reiner sing_2150.htm#IDX826 294 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC36 266 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_179.htm#SEC219 267 Decoding sing_1837.htm#IDX717 268 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_917.htm#SEC974 269 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_922.htm#SEC992 270 Definition of a user defined type Definition of a user defined type sing_178.htm#SEC218 271 Deformations sing_874.htm#SEC926 272 Deformations, T1 and T2 sing_873.htm#SEC925 273 Degree sing_1384.htm#SEC1460 274 Delta sing_1468.htm#SEC1544 275 DeltaList sing_1469.htm#SEC1545 276 Demo mode sing_24.htm#SEC35 277 Depth sing_863.htm#SEC915 278 Determinacy sing_2407.htm#IDX895 279 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_911.htm#SEC968 280 Distributed computing sing_980.htm#IDX425 281 Dlocalization sing_816.htm#SEC868 282 Documentation Tool sing_60.htm#SEC97 283 Dp, global ordering sing_893.htm#IDX384 284 Ds, local ordering sing_894.htm#IDX394 285 DsingularLocus sing_820.htm#SEC872 286 Dynamic loading sing_71.htm#SEC111 287 Dynamic modules sing_851.htm#SEC903 288 ECPP sing_1946.htm#SEC2022 289 ECoef sing_1427.htm#SEC1503 290 EOrdlist sing_1425.htm#SEC1501 291 ERROR sing_287.htm#SEC327 292 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 293 Edatalist sing_1424.htm#SEC1500 294 Edelman-Reiner sing_2153.htm#IDX826 295 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 295 296 Editing input sing_18.htm#SEC25 296 Elimination sing_859.htm#SEC91 0297 Elimination sing_859.htm#SEC911 297 298 Emacs Emacs user interface sing_21.htm#SEC28 298 Emacs, Singular demo mode sing_24.htm#SEC3 4299 Emacs, Singular demo mode sing_24.htm#SEC35 299 300 Emacs, a quick guide A quick guide to Emacs sing_22.htm#SEC29 300 Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC3 5301 Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC3 6302 Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC3 7301 Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC36 302 Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC37 303 Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC38 303 304 Emacs, overview A quick guide to Emacs sing_22.htm#SEC29 304 305 Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30 305 306 Emacs, user interface Emacs user interface sing_21.htm#SEC28 306 Emaxcont sing_142 6.htm#SEC1501307 Equal sing_138 0.htm#SEC1455308 Eresol sing_141 6.htm#SEC1491309 Evaluation of logical expressions Evaluation of logical expressions sing_459.htm#SEC49 8310 Examples sing_841.htm#SEC89 2311 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC 39312 Exp for matrices sing_1 398.htm#IDX524313 Experimental libraries Experimental libraries sing_212 1.htm#SEC2196314 Ext sing_119 5.htm#SEC1270315 Ext, computation of sing_862.htm#SEC91 3316 Ext_R sing_119 4.htm#SEC1269317 Exterior sing_767.htm#SEC81 8318 Extra weight vector sing_898.htm#SEC9 49319 Factorization sing_864.htm#SEC91 5320 Feynman graph sing_117 1.htm#IDX461321 Finite fields sing_858.htm#SEC9 09307 Emaxcont sing_1429.htm#SEC1505 308 Equal sing_1383.htm#SEC1459 309 Eresol sing_1419.htm#SEC1495 310 Evaluation of logical expressions Evaluation of logical expressions sing_459.htm#SEC499 311 Examples sing_841.htm#SEC893 312 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 313 Exp for matrices sing_1401.htm#IDX524 314 Experimental libraries Experimental libraries sing_2124.htm#SEC2200 315 Ext sing_1198.htm#SEC1274 316 Ext, computation of sing_862.htm#SEC914 317 Ext_R sing_1197.htm#SEC1273 318 Exterior sing_767.htm#SEC819 319 Extra weight vector sing_898.htm#SEC950 320 Factorization sing_864.htm#SEC916 321 Feynman graph sing_1174.htm#IDX461 322 Finite fields sing_858.htm#SEC910 322 323 First steps sing_6.htm#SEC12 323 Fitzgerald-Lax method Fitzgerald-Lax method sing_921.htm#SEC98 8324 Flow control sing_40.htm#SEC 69325 Formal Checker sing_59.htm#SEC9 5326 Formatting output sing_848.htm#SEC 899327 Free resolution sing_860.htm#SEC91 1328 Free resolution, graded Handling graded modules sing_861.htm#SEC91 2329 Functions sing_259.htm#SEC29 8330 Future benefits of Singular 4 Notes for Singular users sing_24 54.htm#SEC2541331 G-algebra sing_534.htm#SEC57 3332 G-algebra sing_534.htm#SEC57 5333 G-algebra, setup sing_534.htm#SEC57 7334 GBWeight sing_617.htm#SEC66 8335 GBsolve sing_173 3.htm#SEC1808336 GIT sing_22 79.htm#IDX877337 GKZsystem sing_734.htm#SEC78 5338 GKdim sing_707.htm#SEC75 8324 Fitzgerald-Lax method Fitzgerald-Lax method sing_921.htm#SEC989 325 Flow control sing_40.htm#SEC70 326 Formal Checker sing_59.htm#SEC96 327 Formatting output sing_848.htm#SEC900 328 Free resolution sing_860.htm#SEC912 329 Free resolution, graded Handling graded modules sing_861.htm#SEC913 330 Functions sing_259.htm#SEC299 331 Future benefits of Singular 4 Notes for Singular users sing_2468.htm#SEC2557 332 G-algebra sing_534.htm#SEC574 333 G-algebra sing_534.htm#SEC576 334 G-algebra, setup sing_534.htm#SEC578 335 GBWeight sing_617.htm#SEC669 336 GBsolve sing_1736.htm#SEC1812 337 GIT sing_2290.htm#IDX877 338 GKZsystem sing_734.htm#SEC786 339 GKdim sing_707.htm#SEC759 339 340 GMP sing_1.htm#IDX3 340 GND.lib sing_22 86.htm#SEC2361341 GND_lib sing_22 86.htm#SEC2361342 GTZmod sing_124 3.htm#SEC1318343 GTZopt sing_125 0.htm#SEC1325344 G_a -Invariants sing_880.htm#SEC93 1345 Gamma sing_143 1.htm#SEC1506346 Gauss-Manin connection Gauss-Manin connection sing_904.htm#SEC96 0347 Gauss-Manin connection sing_161 1.htm#IDX695348 Gauss-Manin connection sing_16 58.htm#IDX698349 Gauss-Manin system sing_15 59.htm#IDX585350 Gauss-Manin system sing_156 0.htm#IDX596351 Gauss-Manin system sing_156 1.htm#IDX599352 Gauss-Manin system sing_156 2.htm#IDX602353 Gauss-Manin system sing_156 3.htm#IDX605354 Gauss-Manin system sing_156 4.htm#IDX609355 Gauss-Manin system sing_156 5.htm#IDX613356 Gauss-Manin system sing_156 6.htm#IDX619357 Gauss-Manin system sing_15 67.htm#IDX627358 Gauss-Manin system sing_15 68.htm#IDX633359 Gauss-Manin system sing_15 69.htm#IDX641360 Gauss-Manin system sing_157 0.htm#IDX651361 Gauss-Manin system sing_158 1.htm#IDX657362 Gauss-Manin system sing_158 3.htm#IDX668363 General command syntax General command syntax sing_35.htm#SEC5 8341 GND.lib sing_2297.htm#SEC2373 342 GND_lib sing_2297.htm#SEC2373 343 GTZmod sing_1246.htm#SEC1322 344 GTZopt sing_1253.htm#SEC1329 345 G_a -Invariants sing_880.htm#SEC932 346 Gamma sing_1434.htm#SEC1510 347 Gauss-Manin connection Gauss-Manin connection sing_904.htm#SEC961 348 Gauss-Manin connection sing_1614.htm#IDX695 349 Gauss-Manin connection sing_1661.htm#IDX698 350 Gauss-Manin system sing_1562.htm#IDX585 351 Gauss-Manin system sing_1563.htm#IDX596 352 Gauss-Manin system sing_1564.htm#IDX599 353 Gauss-Manin system sing_1565.htm#IDX602 354 Gauss-Manin system sing_1566.htm#IDX605 355 Gauss-Manin system sing_1567.htm#IDX609 356 Gauss-Manin system sing_1568.htm#IDX613 357 Gauss-Manin system sing_1569.htm#IDX619 358 Gauss-Manin system sing_1570.htm#IDX627 359 Gauss-Manin system sing_1571.htm#IDX633 360 Gauss-Manin system sing_1572.htm#IDX641 361 Gauss-Manin system sing_1573.htm#IDX651 362 Gauss-Manin system sing_1584.htm#IDX657 363 Gauss-Manin system sing_1586.htm#IDX668 364 General command syntax General command syntax sing_35.htm#SEC59 364 365 General concepts sing_12.htm#SEC18 365 General purpose sing_929.htm#SEC100 4366 General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC4 0367 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_536.htm#SEC58 5368 Generalized Newton identities Generalized Newton identities sing_920.htm#SEC98 5369 Geometric genus sing_140 2.htm#IDX536370 German Umlaute sing_455.htm#IDX27 4366 General purpose sing_929.htm#SEC1005 367 General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41 368 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_536.htm#SEC586 369 Generalized Newton identities Generalized Newton identities sing_920.htm#SEC986 370 Geometric genus sing_1405.htm#IDX536 371 German Umlaute sing_455.htm#IDX273 371 372 Getting started sing_5.htm#SEC11 372 Global orderings sing_893.htm#SEC94 4373 Graded commutative algebras Graded commutative algebras (SCA) sing_538.htm#SEC5 89373 Global orderings sing_893.htm#SEC945 374 Graded commutative algebras Graded commutative algebras (SCA) sing_538.htm#SEC590 374 375 Greuel, Gert-Martin sing_1.htm#IDX18 375 Groebner Bases Computing Groebner and Standard Bases sing_852.htm#SEC90 3376 Groebner bases in G-algebras Groebner bases in G-algebras sing_535.htm#SEC57 8377 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_541.htm#SEC59 2378 Groebner bases, decodeGB sing_183 4.htm#IDX719379 Groebner bases, slim sing_855.htm#SEC90 6380 Groebner basis conversion Groebner basis conversion sing_854.htm#SEC90 5381 Groebner cover, parametric ideal, canonical, discussion of extend sing_956.htm#IDX41 1382 Groebner cover, parametric ideal, canonical, discussion of sing_963.htm#IDX41 5383 Groebner fan sing_20 38.htm#IDX736384 Groebner walk sing_118 6.htm#IDX480385 Groebner walk sing_11 88.htm#IDX482386 Groebner walk sing_23 86.htm#IDX888387 Groebner walk sing_23 87.htm#IDX889388 Gromov-Witten invariants sing_117 1.htm#IDX458389 Gromov-Witten invariants sing_11 77.htm#IDX467390 Gromov-Witten invariants sing_11 78.htm#IDX471391 Gweights sing_761.htm#SEC81 2392 H2basis sing_161 6.htm#SEC1691393 Hamburger-Noether expansion sing_149 6.htm#IDX555394 Hamburger-Noether expansion sing_158 4.htm#IDX677395 Hamburger-Noether expansions sing_182 1.htm#IDX709396 Handling graded modules Handling graded modules sing_861.htm#SEC91 2397 Hcode sing_15 18.htm#SEC1593398 Help string sing_45.htm#SEC8 1399 Hensel sing_292.htm#SEC33 1400 Hilbert function sing_404.htm#IDX18 4401 Hilbert function sing_901.htm#SEC95 4402 Hilbert series sing_901.htm#SEC95 4403 Hilbert-driven GB algorithm Groebner basis conversion sing_854.htm#SEC90 5404 HilbertClassPoly sing_190 6.htm#SEC1981405 HilbertSeries sing_171 1.htm#SEC1786406 HilbertWeights sing_171 2.htm#SEC1787407 Hom sing_1 198.htm#SEC1273408 HomJJ sing_127 3.htm#SEC1348409 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_910.htm#SEC96 6376 Groebner Bases Computing Groebner and Standard Bases sing_852.htm#SEC904 377 Groebner bases in G-algebras Groebner bases in G-algebras sing_535.htm#SEC579 378 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_541.htm#SEC593 379 Groebner bases, decodeGB sing_1837.htm#IDX719 380 Groebner bases, slim sing_855.htm#SEC907 381 Groebner basis conversion Groebner basis conversion sing_854.htm#SEC906 382 Groebner cover, parametric ideal, canonical, discussion of extend sing_956.htm#IDX410 383 Groebner cover, parametric ideal, canonical, discussion of sing_963.htm#IDX414 384 Groebner fan sing_2041.htm#IDX736 385 Groebner walk sing_1189.htm#IDX480 386 Groebner walk sing_1191.htm#IDX482 387 Groebner walk sing_2397.htm#IDX888 388 Groebner walk sing_2398.htm#IDX889 389 Gromov-Witten invariants sing_1174.htm#IDX458 390 Gromov-Witten invariants sing_1180.htm#IDX467 391 Gromov-Witten invariants sing_1181.htm#IDX471 392 Gweights sing_761.htm#SEC813 393 H2basis sing_1619.htm#SEC1695 394 Hamburger-Noether expansion sing_1499.htm#IDX555 395 Hamburger-Noether expansion sing_1587.htm#IDX677 396 Hamburger-Noether expansions sing_1824.htm#IDX709 397 Handling graded modules Handling graded modules sing_861.htm#SEC913 398 Hcode sing_1521.htm#SEC1597 399 Help string sing_45.htm#SEC82 400 Hensel sing_292.htm#SEC332 401 Hilbert function sing_404.htm#IDX183 402 Hilbert function sing_901.htm#SEC955 403 Hilbert series sing_901.htm#SEC955 404 Hilbert-driven GB algorithm Groebner basis conversion sing_854.htm#SEC906 405 HilbertClassPoly sing_1909.htm#SEC1985 406 HilbertSeries sing_1714.htm#SEC1790 407 HilbertWeights sing_1715.htm#SEC1791 408 Hom sing_1201.htm#SEC1277 409 HomJJ sing_1276.htm#SEC1352 410 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_910.htm#SEC967 410 411 How to enter and exit How to enter and exit sing_14.htm#SEC20 411 412 How to use this manual How to use this manual sing_4.htm#SEC6 412 Hurwitz numbers sing_11 77.htm#IDX470413 Hurwitz numbers sing_11 78.htm#IDX474414 Hypersurface singularities, classification of Classification of hypersurface singularities sing_877.htm#SEC92 8415 IN sing_329.htm#IDX14 5416 Ideal membership sing_900.htm#IDX40 7417 Identifiers, syntax of sing_37.htm#SEC6 4418 ImageGroup sing_171 4.htm#SEC1789419 ImageVariety sing_171 3.htm#SEC1788420 Imap, option sing_364.htm#IDX17 1421 Implemented algorithms Implemented algorithms sing_33.htm#SEC4 6422 Incl sing_13 79.htm#SEC1454423 Index sing_24 62.htm#SEC2549424 Info string sing_52.htm#SEC8 8425 InterDiv sing_14 47.htm#SEC1522413 Hurwitz numbers sing_1180.htm#IDX470 414 Hurwitz numbers sing_1181.htm#IDX474 415 Hypersurface singularities, classification of Classification of hypersurface singularities sing_877.htm#SEC929 416 IN sing_329.htm#IDX144 417 Ideal membership sing_900.htm#IDX406 418 Identifiers, syntax of sing_37.htm#SEC65 419 ImageGroup sing_1717.htm#SEC1793 420 ImageVariety sing_1716.htm#SEC1792 421 Imap, option sing_364.htm#IDX170 422 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 423 Incl sing_1382.htm#SEC1458 424 Index sing_2476.htm#SEC2565 425 Info string sing_52.htm#SEC89 426 InterDiv sing_1450.htm#SEC1526 426 427 Interactive use sing_13.htm#SEC19 427 428 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 428 IntersectWithSub sing_739.htm#SEC79 0429 IntersectionMatrix sing_154 5.htm#SEC1620429 IntersectWithSub sing_739.htm#SEC791 430 IntersectionMatrix sing_1548.htm#SEC1624 430 431 Introduction sing_2.htm#SEC4 431 Invariant Theory sing_879.htm#SEC93 0432 Invariant theory sing_166 3.htm#SEC1738433 InvariantQ sing_171 6.htm#SEC1791434 InvariantRing sing_171 5.htm#SEC1790435 Invariants of a finite group Invariants of a finite group sing_881.htm#SEC93 2436 Invariants of plane curve singularities Invariants of plane curve singularities sing_875.htm#SEC92 6437 IsSCA sing_782.htm#SEC83 3438 J-marked schemes sing_14 87.htm#IDX553439 J-marked schemes, Borel ideals sing_149 2.htm#IDX554440 JMBTest.lib sing_14 87.htm#SEC1562441 JMBTest_lib sing_14 87.htm#SEC1562442 JMSConst.lib sing_149 2.htm#SEC1567443 JMSConst_lib sing_149 2.htm#SEC1567444 JMarkedScheme sing_149 4.htm#SEC1569445 Jacobi sing_191 6.htm#SEC1991446 Jacobson form sing_187 1.htm#IDX720447 Jacobson normal form sing_187 1.htm#IDX721448 JuReTopDim sing_13 89.htm#SEC1464449 JuReZeroDim sing_139 0.htm#SEC1465450 KScoef sing_16 09.htm#SEC1684451 KSconvert sing_16 07.htm#SEC1682452 KSker sing_160 6.htm#SEC1681453 KSlinear sing_16 08.htm#SEC1683454 KSpencerKernel sing_165 6.htm#SEC1731455 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_23 05.htm#SEC2380456 Kernel of module homomorphisms Kernel of module homomorphisms sing_867.htm#SEC91 8457 KoszulHomology sing_12 07.htm#SEC1282458 LETTERPLACE sing_539.htm#SEC59 0459 LIB sing_333.htm#SEC37 2460 LIB commands sing_53.htm#SEC 89461 LIBs sing_925.htm#SEC100 0462 LLL sing_406.htm#IDX21 4463 LOT algorithm sing_588.htm#IDX32 9464 LU-decomposition of a matrix of numbers sing_338.htm#SEC37 7465 Laurent series sing_117 5.htm#IDX466466 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_883.htm#SEC93 4467 Left ideal membership Groebner bases in G-algebras sing_535.htm#SEC58 1468 Left normal form Groebner bases in G-algebras sing_535.htm#SEC58 0469 LengthSym sing_792.htm#SEC84 3470 LengthSymElement sing_791.htm#SEC84 2471 Letterplace sing_539.htm#SEC59 0472 Lexicographic Groebner bases, computation of Groebner basis conversion sing_854.htm#SEC90 5473 Libraries Writing procedures and libraries sing_48.htm#SEC8 4474 Libraries sing_844.htm#SEC89 5475 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC8 5476 Library versioning Notes for Singular users sing_24 54.htm#SEC2539477 Lie algebra sing_1 397.htm#IDX521478 Lie group sing_140 0.htm#IDX526479 Lie group sing_140 1.htm#IDX529480 Limitations sing_455.htm#SEC49 4481 Linear algebra sing_107 5.htm#SEC1150482 Linear code sing_183 4.htm#IDX716483 LinearActionQ sing_17 18.htm#SEC1793484 LinearCombinationQ sing_17 19.htm#SEC1794485 LinearizeAction sing_17 17.htm#SEC1792486 Loading a library sing_62.htm#SEC9 8487 Local orderings sing_894.htm#SEC94 5488 Log for matrices sing_1 399.htm#IDX525489 Long coefficients sing_846.htm#SEC89 7490 M, ordering sing_896.htm#SEC94 7491 MVComplex sing_2 399.htm#SEC2474492 Macintosh installation Macintosh installation instructions sing_24 61.htm#SEC2548493 Mathematical background Mathematical background sing_899.htm#SEC95 0494 Mathematical background (plural) Mathematical background (plural) sing_533.htm#SEC57 2495 Matrix orderings sing_896.htm#SEC94 7496 Max sing_162 5.htm#SEC1700497 Maximus sing_14 89.htm#SEC1564498 Maxord sing_143 0.htm#SEC1505499 MillerRabin sing_192 6.htm#SEC2001500 Milnor number Milnor and Tjurina number sing_870.htm#SEC92 1501 Milnor number sing_2 395.htm#IDX894502 Min sing_162 6.htm#SEC1701503 MinMult sing_22 26.htm#SEC2301504 MinimalDecomposition MinimalDecomposition sing_172 0.htm#SEC1795505 Minimum distance sing_183 4.htm#IDX718506 Minimus sing_14 88.htm#SEC1563507 Miscellaneous libraries Miscellaneous libraries sing_209 6.htm#SEC2171508 ModEqn sing_16 19.htm#SEC1694509 Modular techniques sing_980.htm#IDX42 3510 Module orderings sing_895.htm#SEC94 6432 Invariant Theory sing_879.htm#SEC931 433 Invariant theory sing_1666.htm#SEC1742 434 InvariantQ sing_1719.htm#SEC1795 435 InvariantRing sing_1718.htm#SEC1794 436 Invariants of a finite group Invariants of a finite group sing_881.htm#SEC933 437 Invariants of plane curve singularities Invariants of plane curve singularities sing_875.htm#SEC927 438 IsSCA sing_782.htm#SEC834 439 J-marked schemes sing_1490.htm#IDX553 440 J-marked schemes, Borel ideals sing_1495.htm#IDX554 441 JMBTest.lib sing_1490.htm#SEC1566 442 JMBTest_lib sing_1490.htm#SEC1566 443 JMSConst.lib sing_1495.htm#SEC1571 444 JMSConst_lib sing_1495.htm#SEC1571 445 JMarkedScheme sing_1497.htm#SEC1573 446 Jacobi sing_1919.htm#SEC1995 447 Jacobson form sing_1874.htm#IDX720 448 Jacobson normal form sing_1874.htm#IDX721 449 JuReTopDim sing_1392.htm#SEC1468 450 JuReZeroDim sing_1393.htm#SEC1469 451 KScoef sing_1612.htm#SEC1688 452 KSconvert sing_1610.htm#SEC1686 453 KSker sing_1609.htm#SEC1685 454 KSlinear sing_1611.htm#SEC1687 455 KSpencerKernel sing_1659.htm#SEC1735 456 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2316.htm#SEC2392 457 Kernel of module homomorphisms Kernel of module homomorphisms sing_867.htm#SEC919 458 KoszulHomology sing_1210.htm#SEC1286 459 LETTERPLACE sing_539.htm#SEC591 460 LIB sing_333.htm#SEC373 461 LIB commands sing_53.htm#SEC90 462 LIBs sing_925.htm#SEC1001 463 LLL sing_406.htm#IDX213 464 LOT algorithm sing_588.htm#IDX328 465 LU-decomposition of a matrix of numbers sing_338.htm#SEC378 466 Laurent series sing_1178.htm#IDX466 467 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_883.htm#SEC935 468 Left ideal membership Groebner bases in G-algebras sing_535.htm#SEC582 469 Left normal form Groebner bases in G-algebras sing_535.htm#SEC581 470 LengthSym sing_792.htm#SEC844 471 LengthSymElement sing_791.htm#SEC843 472 Letterplace sing_539.htm#SEC591 473 Lexicographic Groebner bases, computation of Groebner basis conversion sing_854.htm#SEC906 474 Libraries Writing procedures and libraries sing_48.htm#SEC85 475 Libraries sing_844.htm#SEC896 476 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 477 Library versioning Notes for Singular users sing_2468.htm#SEC2555 478 Lie algebra sing_1400.htm#IDX521 479 Lie group sing_1403.htm#IDX526 480 Lie group sing_1404.htm#IDX529 481 Limitations sing_455.htm#SEC495 482 Linear algebra sing_1078.htm#SEC1154 483 Linear code sing_1837.htm#IDX716 484 LinearActionQ sing_1721.htm#SEC1797 485 LinearCombinationQ sing_1722.htm#SEC1798 486 LinearizeAction sing_1720.htm#SEC1796 487 Loading a library sing_62.htm#SEC99 488 Local orderings sing_894.htm#SEC946 489 Log for matrices sing_1402.htm#IDX525 490 Long coefficients sing_846.htm#SEC898 491 M, ordering sing_896.htm#SEC948 492 MVComplex sing_2410.htm#SEC2486 493 Macintosh installation Macintosh installation instructions sing_2475.htm#SEC2564 494 Mathematical background Mathematical background sing_899.htm#SEC951 495 Mathematical background (plural) Mathematical background (plural) sing_533.htm#SEC573 496 Matrix orderings sing_896.htm#SEC948 497 Max sing_1628.htm#SEC1704 498 Maximus sing_1492.htm#SEC1568 499 Maxord sing_1433.htm#SEC1509 500 MillerRabin sing_1929.htm#SEC2005 501 Milnor number Milnor and Tjurina number sing_870.htm#SEC922 502 Milnor number sing_2406.htm#IDX894 503 Min sing_1629.htm#SEC1705 504 MinMult sing_2231.htm#SEC2307 505 MinimalDecomposition MinimalDecomposition sing_1723.htm#SEC1799 506 Minimum distance sing_1837.htm#IDX718 507 Minimus sing_1491.htm#SEC1567 508 Miscellaneous libraries Miscellaneous libraries sing_2099.htm#SEC2175 509 ModEqn sing_1622.htm#SEC1698 510 Modular techniques sing_980.htm#IDX422 511 Module orderings sing_895.htm#SEC947 511 512 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 512 Monodromy sing_161 1.htm#IDX693513 Monomial orderings sing_890.htm#SEC94 1514 Monomial orderings, Term orderings sing_31.htm#SEC4 3515 Morse lemma sing_2 394.htm#IDX892516 MultiplicitySequence MultiplicitySequence sing_154 3.htm#SEC1618517 NF sing_383.htm#SEC42 2518 NF sing_525.htm#SEC56 4519 NFMora sing_199 2.htm#SEC2067520 NPos sing_126 3.htm#SEC1338521 NPos_test sing_126 1.htm#SEC1336522 NSplaces sing_182 2.htm#SEC1897513 Monodromy sing_1614.htm#IDX693 514 Monomial orderings sing_890.htm#SEC942 515 Monomial orderings, Term orderings sing_31.htm#SEC44 516 Morse lemma sing_2405.htm#IDX892 517 MultiplicitySequence MultiplicitySequence sing_1546.htm#SEC1622 518 NF sing_383.htm#SEC423 519 NF sing_525.htm#SEC565 520 NFMora sing_1995.htm#SEC2071 521 NPos sing_1266.htm#SEC1342 522 NPos_test sing_1264.htm#SEC1340 523 NSplaces sing_1825.htm#SEC1901 523 524 NTL sing_1.htm#IDX4 524 Names sing_37.htm#SEC6 4525 Names in procedures sing_46.htm#SEC8 2526 Names, indexed sing_37.htm#SEC6 4527 New libraries depending on Singular 4 Notes for Singular users sing_24 54.htm#SEC2537528 New orderings for modules Notes for Singular users sing_24 54.htm#SEC2540529 Newton non-degenerate sing_1 598.htm#IDX691530 Newton polygon sing_1 597.htm#IDX690531 Newton polygon sing_1 598.htm#IDX692532 Newton polytope sing_20 38.htm#IDX735533 NoetherPosition sing_12 57.htm#SEC1332534 Non-commutative LIBs Non-commutative libraries sing_545.htm#SEC59 6535 Non-commutative algebra Non-commutative algebra sing_882.htm#SEC93 3536 Non-commutative algebra sing_916.htm#SEC97 2537 Non-commutative libraries Non-commutative libraries sing_545.htm#SEC59 6538 Non-commutative subsystem Non-commutative subsystem sing_468.htm#SEC50 7539 Nonhyp sing_14 19.htm#SEC1494540 Normal form sing_900.htm#IDX40 6541 Normalization sing_866.htm#SEC91 7542 Notes for Singular users Notes for Singular users sing_24 54.htm#SEC2534543 Notes for developers Notes for developers sing_24 55.htm#SEC2542544 NullCone sing_172 1.htm#SEC1796545 NumIrrDecom sing_139 3.htm#SEC1468546 NumLocalDim sing_138 2.htm#SEC1457547 NumPrimDecom sing_139 5.htm#SEC1470548 Oaku-Takayama algorithm sing_588.htm#IDX32 7549 Objects sing_38.htm#SEC6 5550 Orlik-Solomon sing_215 1.htm#IDX827551 Output, formatting of sing_848.htm#SEC 899552 PBW sing_567.htm#IDX31 5553 PBW basis sing_534.htm#SEC57 4554 PBW_eqDeg sing_585.htm#SEC63 6555 PBW_maxDeg sing_586.htm#SEC63 7556 PBW_maxMonom sing_587.htm#SEC63 8557 PEsolve sing_173 1.htm#SEC1806558 PH_ais sing_210 0.htm#SEC2175559 PH_nais sing_210 1.htm#SEC2176560 PLURAL sing_469.htm#SEC50 8561 PLURAL LIBs Non-commutative libraries sing_545.htm#SEC59 6562 ParToVar sing_22 69.htm#SEC2344563 Parallelization Parallelization with ssi links sing_850.htm#SEC90 1564 Parallelization sing_980.htm#IDX42 4565 Parameter list sing_44.htm#SEC8 0566 Parameters sing_847.htm#SEC89 8567 Parametrization sing_140 2.htm#IDX533568 Parametrization, image. sing_141 2.htm#IDX545569 PartC sing_222 1.htm#SEC2296570 PartitionVar sing_22 66.htm#SEC2341571 Path names Notes for Singular users sing_24 54.htm#SEC2538572 PerfectPowerTest sing_18 89.htm#SEC1964573 Perturbation walk sing_11 87.htm#IDX481525 Names sing_37.htm#SEC65 526 Names in procedures sing_46.htm#SEC83 527 Names, indexed sing_37.htm#SEC65 528 New libraries depending on Singular 4 Notes for Singular users sing_2468.htm#SEC2553 529 New orderings for modules Notes for Singular users sing_2468.htm#SEC2556 530 Newton non-degenerate sing_1601.htm#IDX691 531 Newton polygon sing_1600.htm#IDX690 532 Newton polygon sing_1601.htm#IDX692 533 Newton polytope sing_2041.htm#IDX735 534 NoetherPosition sing_1260.htm#SEC1336 535 Non-commutative LIBs Non-commutative libraries sing_545.htm#SEC597 536 Non-commutative algebra Non-commutative algebra sing_882.htm#SEC934 537 Non-commutative algebra sing_916.htm#SEC973 538 Non-commutative libraries Non-commutative libraries sing_545.htm#SEC597 539 Non-commutative subsystem Non-commutative subsystem sing_468.htm#SEC508 540 Nonhyp sing_1422.htm#SEC1498 541 Normal form sing_900.htm#IDX405 542 Normalization sing_866.htm#SEC918 543 Notes for Singular users Notes for Singular users sing_2468.htm#SEC2550 544 Notes for developers Notes for developers sing_2469.htm#SEC2558 545 NullCone sing_1724.htm#SEC1800 546 NumIrrDecom sing_1396.htm#SEC1472 547 NumLocalDim sing_1385.htm#SEC1461 548 NumPrimDecom sing_1398.htm#SEC1474 549 Oaku-Takayama algorithm sing_588.htm#IDX326 550 Objects sing_38.htm#SEC66 551 Orlik-Solomon sing_2154.htm#IDX827 552 Output, formatting of sing_848.htm#SEC900 553 PBW sing_567.htm#IDX314 554 PBW basis sing_534.htm#SEC575 555 PBW_eqDeg sing_585.htm#SEC637 556 PBW_maxDeg sing_586.htm#SEC638 557 PBW_maxMonom sing_587.htm#SEC639 558 PEsolve sing_1734.htm#SEC1810 559 PH_ais sing_2103.htm#SEC2179 560 PH_nais sing_2104.htm#SEC2180 561 PLURAL sing_469.htm#SEC509 562 PLURAL LIBs Non-commutative libraries sing_545.htm#SEC597 563 ParToVar sing_2280.htm#SEC2356 564 Parallelization Parallelization with ssi links sing_850.htm#SEC902 565 Parallelization sing_980.htm#IDX423 566 Parameter list sing_44.htm#SEC81 567 Parameters sing_847.htm#SEC899 568 Parametrization sing_1405.htm#IDX533 569 Parametrization, image. sing_1415.htm#IDX545 570 PartC sing_2226.htm#SEC2302 571 PartitionVar sing_2277.htm#SEC2353 572 Path names Notes for Singular users sing_2468.htm#SEC2554 573 PerfectPowerTest sing_1892.htm#SEC1968 574 Perturbation walk sing_1190.htm#IDX481 574 575 Pfister, Gerhard sing_1.htm#IDX19 575 Pipe links sing_116.htm#SEC15 5576 PocklingtonLehmer sing_19 28.htm#SEC2003577 Poincare polynomial sing_216 3.htm#IDX851578 Polar curves sing_872.htm#SEC92 3579 PollardRho sing_19 29.htm#SEC2004580 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_210 3.htm#IDX752581 PolyBoRi, Boolean Groebner Basis sing_210 5.htm#IDX753582 PolyBoRi, Boolean Groebner Basis sing_210 6.htm#IDX754583 PolyBoRi, Boolean Groebner Basis sing_21 07.htm#IDX755584 PolyBoRi, Boolean Groebner Basis sing_21 08.htm#IDX756585 PolyBoRi, Boolean Groebner Basis sing_21 09.htm#IDX757586 PolyBoRi, Boolean Groebner Basis sing_211 0.htm#IDX758587 PolyBoRi, Boolean Groebner Basis sing_211 1.htm#IDX759588 PolyBoRi, Boolean Groebner Basis sing_211 2.htm#IDX760589 PolyBoRi, Boolean Groebner Basis sing_211 3.htm#IDX761590 PolyBoRi, Boolean Groebner Basis sing_211 4.htm#IDX762591 PolyBoRi, Boolean Groebner Basis sing_211 5.htm#IDX763592 PolyBoRi, Boolean Groebner Basis sing_211 6.htm#IDX764593 PolyBoRi, Boolean Groebner Basis sing_21 17.htm#IDX765594 PolyBoRi, Boolean Groebner Basis sing_21 19.htm#IDX767595 PolyBoRi, zero-supressed decision diagram sing_21 18.htm#IDX766596 Polybori, Boolean Groebner Basis sing_212 0.htm#IDX768597 Polynomial data sing_888.htm#SEC9 39598 Pottier algorithm sing_909.htm#SEC96 5576 Pipe links sing_116.htm#SEC156 577 PocklingtonLehmer sing_1931.htm#SEC2007 578 Poincare polynomial sing_2166.htm#IDX851 579 Polar curves sing_872.htm#SEC924 580 PollardRho sing_1932.htm#SEC2008 581 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2106.htm#IDX752 582 PolyBoRi, Boolean Groebner Basis sing_2108.htm#IDX753 583 PolyBoRi, Boolean Groebner Basis sing_2109.htm#IDX754 584 PolyBoRi, Boolean Groebner Basis sing_2110.htm#IDX755 585 PolyBoRi, Boolean Groebner Basis sing_2111.htm#IDX756 586 PolyBoRi, Boolean Groebner Basis sing_2112.htm#IDX757 587 PolyBoRi, Boolean Groebner Basis sing_2113.htm#IDX758 588 PolyBoRi, Boolean Groebner Basis sing_2114.htm#IDX759 589 PolyBoRi, Boolean Groebner Basis sing_2115.htm#IDX760 590 PolyBoRi, Boolean Groebner Basis sing_2116.htm#IDX761 591 PolyBoRi, Boolean Groebner Basis sing_2117.htm#IDX762 592 PolyBoRi, Boolean Groebner Basis sing_2118.htm#IDX763 593 PolyBoRi, Boolean Groebner Basis sing_2119.htm#IDX764 594 PolyBoRi, Boolean Groebner Basis sing_2120.htm#IDX765 595 PolyBoRi, Boolean Groebner Basis sing_2122.htm#IDX767 596 PolyBoRi, zero-supressed decision diagram sing_2121.htm#IDX766 597 Polybori, Boolean Groebner Basis sing_2123.htm#IDX768 598 Polynomial data sing_888.htm#SEC940 599 Pottier algorithm sing_909.htm#SEC966 599 600 Preface sing_1.htm#SEC1 600 Prep sing_961.htm#SEC103 6601 Primary decomposition Primary decomposition sing_865.htm#SEC91 6602 PrimdecA sing_12 39.htm#SEC1314603 PrimdecB sing_124 0.htm#SEC1315604 Procedure definition Procedure definition sing_43.htm#SEC7 7605 Procedure-specific commands Procedure-specific commands sing_47.htm#SEC8 3606 Procedures sing_42.htm#SEC7 6601 Prep sing_961.htm#SEC1037 602 Primary decomposition Primary decomposition sing_865.htm#SEC917 603 PrimdecA sing_1242.htm#SEC1318 604 PrimdecB sing_1243.htm#SEC1319 605 Procedure definition Procedure definition sing_43.htm#SEC78 606 Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84 607 Procedures sing_42.htm#SEC77 607 608 Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14 608 Procedures and libraries sing_844.htm#SEC89 5609 Procedures in a library Procedures in a library sing_54.htm#SEC9 0610 Product orderings sing_897.htm#SEC94 8611 Programming sing_842.htm#SEC89 3612 PtoCrep sing_962.htm#SEC103 7613 Puiseux expansion sing_149 6.htm#IDX556614 Puiseux expansion sing_158 4.htm#IDX678615 Puiseux pairs Invariants of plane curve singularities sing_875.htm#SEC92 6616 Puiseux pairs sing_159 0.htm#IDX683617 Qso3Casimir sing_733.htm#SEC78 4618 Quotient sing_177 3.htm#SEC1848619 QuotientEquations sing_162 0.htm#SEC1695620 Rational curves sing_140 2.htm#IDX534621 ReJunkUseHomo sing_13 88.htm#SEC1463622 ReesAlgebra sing_135 5.htm#SEC1430623 References sing_924.htm#SEC99 7624 References (plural) sing_537.htm#SEC58 6625 Release Notes sing_24 50.htm#SEC2525626 ResTree sing_14 48.htm#SEC1523609 Procedures and libraries sing_844.htm#SEC896 610 Procedures in a library Procedures in a library sing_54.htm#SEC91 611 Product orderings sing_897.htm#SEC949 612 Programming sing_842.htm#SEC894 613 PtoCrep sing_962.htm#SEC1038 614 Puiseux expansion sing_1499.htm#IDX556 615 Puiseux expansion sing_1587.htm#IDX678 616 Puiseux pairs Invariants of plane curve singularities sing_875.htm#SEC927 617 Puiseux pairs sing_1593.htm#IDX683 618 Qso3Casimir sing_733.htm#SEC785 619 Quotient sing_1776.htm#SEC1852 620 QuotientEquations sing_1623.htm#SEC1699 621 Rational curves sing_1405.htm#IDX534 622 ReJunkUseHomo sing_1391.htm#SEC1467 623 ReesAlgebra sing_1358.htm#SEC1434 624 References sing_924.htm#SEC998 625 References (plural) sing_537.htm#SEC587 626 Release Notes sing_2464.htm#SEC2540 627 ResTree sing_1451.htm#SEC1527 627 628 Resolution sing_11.htm#SEC17 628 Resolution of singularities Resolution of singularities sing_878.htm#SEC9 29629 Resolution, free sing_860.htm#SEC91 1630 ReynoldsImage sing_172 2.htm#SEC1797631 ReynoldsOperator sing_172 3.htm#SEC1798632 RiemannRochBN sing_21 68.htm#SEC2243633 RiemannRochHess sing_23 24.htm#SEC2399634 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_884.htm#SEC93 5635 Ring-dependent options Notes for Singular users sing_24 54.htm#SEC2536636 Rings and orderings sing_28.htm#SEC3 8629 Resolution of singularities Resolution of singularities sing_878.htm#SEC930 630 Resolution, free sing_860.htm#SEC912 631 ReynoldsImage sing_1725.htm#SEC1801 632 ReynoldsOperator sing_1726.htm#SEC1802 633 RiemannRochBN sing_2171.htm#SEC2247 634 RiemannRochHess sing_2335.htm#SEC2411 635 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_884.htm#SEC936 636 Ring-dependent options Notes for Singular users sing_2468.htm#SEC2552 637 Rings and orderings sing_28.htm#SEC39 637 638 Rings and standard bases Rings and standard bases sing_7.htm#SEC13 638 639 Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 639 SCA Graded commutative algebras (SCA) sing_538.htm#SEC5 89640 SDB breakpoint Source code debugger sing_66.htm#SEC10 5641 SDB debugger Source code debugger sing_66.htm#SEC10 5642 SDLoc sing_615.htm#SEC66 6643 SINGULAR libraries sing_925.htm#SEC100 0640 SCA Graded commutative algebras (SCA) sing_538.htm#SEC590 641 SDB breakpoint Source code debugger sing_66.htm#SEC106 642 SDB debugger Source code debugger sing_66.htm#SEC106 643 SDLoc sing_615.htm#SEC667 644 SINGULAR libraries sing_925.htm#SEC1001 644 645 SINGULARHIST sing_18.htm#SEC25 645 SV-decoding algorithm sing_1829.htm#IDX712 646 SV-decoding algorithm, preprocessing sing_1828.htm#IDX711 647 Sannfs sing_591.htm#SEC642 648 SannfsBFCT sing_600.htm#SEC651 649 SannfsVar sing_647.htm#SEC698 650 Sannfslog sing_592.htm#SEC643 651 Saturation sing_857.htm#SEC908 646 SScontinue sing_1062.htm#SEC1138 647 SSres sing_1060.htm#SEC1136 648 SSsyz sing_1061.htm#SEC1137 649 SV-decoding algorithm sing_1832.htm#IDX712 650 SV-decoding algorithm, preprocessing sing_1831.htm#IDX711 651 Sannfs sing_591.htm#SEC643 652 SannfsBFCT sing_600.htm#SEC652 653 SannfsVar sing_647.htm#SEC699 654 Sannfslog sing_592.htm#SEC644 655 Saturation sing_857.htm#SEC909 656 Saturation sing_1171.htm#IDX452 657 Saturation sing_2463.htm#SEC2539 652 658 Sch@"onemann, Hans sing_1.htm#IDX20 653 Schoof sing_194 0.htm#SEC2015654 Schreyer ordering sing_1055.htm#IDX4 40655 Schreyer resolution sing_1055.htm#IDX44 1656 SchurCh sing_22 18.htm#SEC2293657 SchurS sing_22 17.htm#SEC2292658 Scontinue sing_1059.htm#SEC113 4659 Semigroup sing_153 6.htm#SEC1611660 Setting up a G-algebra sing_534.htm#SEC57 7661 ShanksMestre sing_19 39.htm#SEC2014662 SimplifyIdeal sing_172 4.htm#SEC1799663 Singular sing_406.htm#IDX24 6664 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_24 52.htm#SEC2532665 Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC3 5666 Singular, demo mode sing_24.htm#SEC3 4667 Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC3 6668 Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC3 7659 Schoof sing_1943.htm#SEC2019 660 Schreyer ordering sing_1055.htm#IDX439 661 Schreyer resolution sing_1055.htm#IDX440 662 SchurCh sing_2223.htm#SEC2299 663 SchurS sing_2222.htm#SEC2298 664 Scontinue sing_1059.htm#SEC1135 665 Semigroup sing_1539.htm#SEC1615 666 Setting up a G-algebra sing_534.htm#SEC578 667 ShanksMestre sing_1942.htm#SEC2018 668 SimplifyIdeal sing_1727.htm#SEC1803 669 Singular sing_406.htm#IDX245 670 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2466.htm#SEC2548 671 Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36 672 Singular, demo mode sing_24.htm#SEC35 673 Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 674 Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38 669 675 Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 670 Singular2bertini sing_138 6.htm#SEC1461671 SingularLib sing_406.htm#IDX24 8672 Singularities sing_149 5.htm#SEC1570673 Singularity Theory sing_869.htm#SEC92 0674 Skeletons for parallelization sing_980.htm#IDX42 5675 Smith form sing_187 1.htm#IDX722676 Smith normal form sing_187 1.htm#IDX723677 SolowayStrassen sing_19 27.htm#SEC2002678 Solving systems of polynomial equations Solving systems of polynomial equations sing_886.htm#SEC93 7676 Singular2bertini sing_1389.htm#SEC1465 677 SingularLib sing_406.htm#IDX247 678 Singularities sing_1498.htm#SEC1574 679 Singularity Theory sing_869.htm#SEC921 680 Skeletons for parallelization sing_980.htm#IDX424 681 Smith form sing_1874.htm#IDX722 682 Smith normal form sing_1874.htm#IDX723 683 SolowayStrassen sing_1930.htm#SEC2006 684 Solving systems of polynomial equations Solving systems of polynomial equations sing_886.htm#SEC938 679 685 Source code debugger, invocation Command line options sing_19.htm#IDX33 680 Space curve singularities, branches of Branches of space curve singularities sing_876.htm#SEC92 7681 Special characters sing_36.htm#SEC6 3682 Splitting lemma sing_2 394.htm#IDX893683 Sres sing_1057.htm#SEC113 2684 Ssi file links sing_114.htm#SEC15 3685 Ssi links sing_113.htm#SEC15 2686 Ssi tcp links sing_115.htm#SEC15 4687 Ssyz sing_1058.htm#SEC113 3688 StabEqn sing_162 1.htm#SEC1696689 StabEqnId sing_162 2.htm#SEC1697690 StabOrder sing_162 3.htm#SEC1698691 Standard Bases Computing Groebner and Standard Bases sing_852.htm#SEC90 3692 Standard bases sing_900.htm#SEC95 1693 StartOrderingV sing_149 0.htm#SEC1565686 Space curve singularities, branches of Branches of space curve singularities sing_876.htm#SEC928 687 Special characters sing_36.htm#SEC64 688 Splitting lemma sing_2405.htm#IDX893 689 Sres sing_1057.htm#SEC1133 690 Ssi file links sing_114.htm#SEC154 691 Ssi links sing_113.htm#SEC153 692 Ssi tcp links sing_115.htm#SEC155 693 Ssyz sing_1058.htm#SEC1134 694 StabEqn sing_1624.htm#SEC1700 695 StabEqnId sing_1625.htm#SEC1701 696 StabOrder sing_1626.htm#SEC1702 697 Standard Bases Computing Groebner and Standard Bases sing_852.htm#SEC904 698 Standard bases sing_900.htm#SEC952 699 StartOrderingV sing_1493.htm#SEC1569 694 700 Startup sequence sing_20.htm#SEC27 695 StringF sing_161 0.htm#SEC1685696 SymGroup sing_790.htm#SEC84 1697 Symbolic-numerical solving Symbolic-numerical solving sing_886.htm#SEC93 7698 Symbolic-numerical solving sing_17 28.htm#SEC1803699 System and Control theory System and Control theory sing_185 3.htm#SEC1928700 System dependent limitations System dependent limitations sing_456.htm#SEC49 5701 System variables sing_442.htm#SEC48 1702 Syzygies and resolutions Syzygies and resolutions sing_902.htm#SEC95 5703 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_536.htm#SEC58 2704 T1 sing_873.htm#SEC92 4705 T2 sing_873.htm#SEC92 4706 TRACE Tracing of procedures sing_65.htm#SEC10 1707 TRACE sing_451.htm#SEC49 0708 T_1 sing_164 3.htm#SEC1718709 T_12 sing_164 5.htm#SEC1720710 T_2 sing_164 4.htm#SEC1719711 Teaching sing_188 5.htm#SEC1960712 Template for writing a library sing_55.htm#SEC9 1713 TestGRRes sing_23 04.htm#SEC2379714 TestJMark sing_149 1.htm#SEC1566715 The SINGULAR language The SINGULAR language sing_34.htm#SEC5 5716 The Tran algorithm sing_118 4.htm#IDX478717 The fractal walk algorithm sing_118 3.htm#IDX477718 The fractal walk algorithm sing_23 88.htm#IDX890701 StringF sing_1613.htm#SEC1689 702 SymGroup sing_790.htm#SEC842 703 Symbolic-numerical solving Symbolic-numerical solving sing_886.htm#SEC938 704 Symbolic-numerical solving sing_1731.htm#SEC1807 705 System and Control theory System and Control theory sing_1856.htm#SEC1932 706 System dependent limitations System dependent limitations sing_456.htm#SEC496 707 System variables sing_442.htm#SEC482 708 Syzygies and resolutions Syzygies and resolutions sing_902.htm#SEC956 709 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_536.htm#SEC583 710 T1 sing_873.htm#SEC925 711 T2 sing_873.htm#SEC925 712 TRACE Tracing of procedures sing_65.htm#SEC102 713 TRACE sing_451.htm#SEC491 714 T_1 sing_1646.htm#SEC1722 715 T_12 sing_1648.htm#SEC1724 716 T_2 sing_1647.htm#SEC1723 717 Teaching sing_1888.htm#SEC1964 718 Template for writing a library sing_55.htm#SEC92 719 TestGRRes sing_2315.htm#SEC2391 720 TestJMark sing_1494.htm#SEC1570 721 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 722 The Tran algorithm sing_1187.htm#IDX478 723 The fractal walk algorithm sing_1186.htm#IDX477 724 The fractal walk algorithm sing_2399.htm#IDX890 719 725 The online help system The online help system sing_16.htm#SEC22 720 Tjurina sing_164 1.htm#SEC1716721 Tjurina number Milnor and Tjurina number sing_870.htm#SEC92 1722 Tjurina number sing_12 78.htm#IDX505723 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC3 7724 Tor sing_12 09.htm#SEC1284725 Toric ideals and integer programming Toric ideals and integer programming sing_905.htm#SEC96 1726 Tricks and pitfalls sing_454.htm#SEC49 3727 Tropical Geometry sing_20 37.htm#SEC2112728 Type casting Type conversion and casting sing_39.htm#SEC6 8729 Type conversion Type conversion and casting sing_39.htm#SEC6 7730 Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC9 7731 U_D_O sing_112 4.htm#SEC1199732 Unix installation Unix installation instructions sing_24 59.htm#SEC2546733 UpOneMatrix sing_779.htm#SEC83 0734 UpperMonomials sing_162 4.htm#SEC1699735 UseBertini sing_138 5.htm#SEC1460736 User defined types sing_177.htm#SEC21 6737 V-filtration sing_15 59.htm#IDX588738 V-filtration sing_156 5.htm#IDX616739 V-filtration sing_156 6.htm#IDX622740 V-filtration sing_15 67.htm#IDX630741 V-filtration sing_15 68.htm#IDX636742 V-filtration sing_15 69.htm#IDX644743 V-filtration sing_157 0.htm#IDX654744 V-filtration sing_158 1.htm#IDX660745 V-filtration sing_158 3.htm#IDX671746 VarToPar sing_22 68.htm#SEC2343747 Variables, indexed sing_37.htm#SEC6 4748 Version number Version schema for Singular sing_24 53.htm#SEC2533749 Version schema for Singular Version schema for Singular sing_24 53.htm#SEC2533750 Version string sing_50.htm#SEC8 6751 Visualization sing_179 1.htm#SEC1866752 WP, global ordering sing_893.htm#IDX38 9753 WSemigroup sing_154 1.htm#SEC1616754 Weierstrass sing_182 4.htm#SEC1899755 Weierstrass semigroup sing_182 0.htm#IDX706756 Weyl sing_764.htm#SEC81 5757 Weyl algebra sing_588.htm#IDX32 1758 Weyl algebra sing_644.htm#IDX34 6759 Weyl closure sing_815.htm#IDX37 4760 WeylClosure sing_817.htm#SEC86 8761 WeylClosure1 sing_818.htm#SEC8 69762 Windows installation Windows installation instructions sing_24 60.htm#SEC2547763 WitSet sing_139 2.htm#SEC1467764 WitSupSet sing_139 1.htm#SEC1466765 Ws, local ordering sing_894.htm#IDX40 1766 XLsolve sing_173 4.htm#SEC1809767 ZZsolve sing_173 5.htm#SEC1810768 [ sing_36.htm#IDX8 4769 \ sing_36.htm#IDX11 3770 ] sing_36.htm#IDX8 5771 ^ sing_36.htm#IDX9 3772 ^ sing_76.htm#SEC11 5773 ^ sing_88.htm#SEC12 7774 _ sing_36.htm#IDX11 7775 ` sing_36.htm#IDX10 6776 a, ordering sing_898.htm#SEC9 49777 absFactorize sing_11 37.htm#SEC1212778 absFactorizeBCG sing_11 38.htm#SEC1213779 absPrimdecGTZ sing_133 5.htm#SEC1410780 absPrimdecGTZE sing_133 6.htm#SEC1411781 absValue sing_937.htm#SEC101 2782 absfact.lib sing_113 6.htm#SEC1211783 absfact_lib sing_113 6.htm#SEC1211784 absolute factorization. sing_113 6.htm#IDX452785 abstractR sing_147 4.htm#SEC1549786 actionIsProper sing_170 4.htm#SEC1779787 addNvarsTo sing_1054.htm#SEC11 29788 addRat sing_836.htm#SEC88 7789 addcol sing_109 3.htm#SEC1168790 addcores sing_1023.htm#SEC109 8791 addrow sing_109 4.htm#SEC1169792 addvarsTo sing_1053.htm#SEC112 8793 ademRelations sing_697.htm#SEC74 8794 adjoint sing_11 18.htm#SEC1193795 adjointIdeal sing_140 3.htm#SEC1478796 adjunction divisor sing_182 1.htm#IDX710797 admissibleSub sing_755.htm#SEC80 6798 afaces sing_22 80.htm#SEC2355799 affine code Fitzgerald-Lax method sing_921.htm#SEC9 89800 ainvar.lib sing_170 1.htm#SEC1776801 ainvar_lib sing_170 1.htm#SEC1776802 aksaka.lib sing_188 6.htm#SEC1961803 aksaka_lib sing_188 6.htm#SEC1961804 alexanderpolynomial sing_1 499.htm#SEC1574805 alexpoly.lib sing_149 6.htm#SEC1571806 alexpoly_lib sing_149 6.htm#SEC1571807 algDependent sing_114 3.htm#SEC1218808 alg_kernel sing_114 4.htm#SEC1219809 algebra.lib sing_11 39.htm#SEC1214810 algebra_containment sing_114 0.htm#SEC1215811 algebra_lib sing_11 39.htm#SEC1214812 algebraic dependence sing_785.htm#IDX35 2813 algebraic field extension sing_13 49.htm#IDX510814 algebraicDependence sing_136 2.htm#SEC1437815 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_912.htm#SEC96 8816 algorithm of Conti and Traverso sing_908.htm#SEC96 4817 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_911.htm#SEC96 7818 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_910.htm#SEC96 6819 algorithm of Pottier sing_909.htm#SEC96 5820 align sing_260.htm#SEC 299821 all.lib sing_930.htm#SEC100 5822 allDoubleExt sing_802.htm#SEC85 3823 allExtOfLeft sing_799.htm#SEC85 0824 allExtOfRight sing_800.htm#SEC85 1825 allPositive sing_564.htm#SEC61 5826 all_lib sing_930.htm#SEC100 5726 Tjurina sing_1644.htm#SEC1720 727 Tjurina number Milnor and Tjurina number sing_870.htm#SEC922 728 Tjurina number sing_1281.htm#IDX505 729 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 730 Tor sing_1212.htm#SEC1288 731 Toric ideals and integer programming Toric ideals and integer programming sing_905.htm#SEC962 732 Tricks and pitfalls sing_454.htm#SEC494 733 Tropical Geometry sing_2040.htm#SEC2116 734 Type casting Type conversion and casting sing_39.htm#SEC69 735 Type conversion Type conversion and casting sing_39.htm#SEC68 736 Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98 737 U_D_O sing_1127.htm#SEC1203 738 Unix installation Unix installation instructions sing_2473.htm#SEC2562 739 UpOneMatrix sing_779.htm#SEC831 740 UpperMonomials sing_1627.htm#SEC1703 741 UseBertini sing_1388.htm#SEC1464 742 User defined types sing_177.htm#SEC217 743 V-filtration sing_1562.htm#IDX588 744 V-filtration sing_1568.htm#IDX616 745 V-filtration sing_1569.htm#IDX622 746 V-filtration sing_1570.htm#IDX630 747 V-filtration sing_1571.htm#IDX636 748 V-filtration sing_1572.htm#IDX644 749 V-filtration sing_1573.htm#IDX654 750 V-filtration sing_1584.htm#IDX660 751 V-filtration sing_1586.htm#IDX671 752 VarToPar sing_2279.htm#SEC2355 753 Variables, indexed sing_37.htm#SEC65 754 Version number Version schema for Singular sing_2467.htm#SEC2549 755 Version schema for Singular Version schema for Singular sing_2467.htm#SEC2549 756 Version string sing_50.htm#SEC87 757 Visualization sing_1794.htm#SEC1870 758 WP, global ordering sing_893.htm#IDX388 759 WSemigroup sing_1544.htm#SEC1620 760 Weierstrass sing_1827.htm#SEC1903 761 Weierstrass semigroup sing_1823.htm#IDX706 762 Weyl sing_764.htm#SEC816 763 Weyl algebra sing_588.htm#IDX320 764 Weyl algebra sing_644.htm#IDX345 765 Weyl closure sing_815.htm#IDX373 766 WeylClosure sing_817.htm#SEC869 767 WeylClosure1 sing_818.htm#SEC870 768 Windows installation Windows installation instructions sing_2474.htm#SEC2563 769 WitSet sing_1395.htm#SEC1471 770 WitSupSet sing_1394.htm#SEC1470 771 Ws, local ordering sing_894.htm#IDX400 772 XLsolve sing_1737.htm#SEC1813 773 ZZsolve sing_1738.htm#SEC1814 774 [ sing_36.htm#IDX83 775 \ sing_36.htm#IDX112 776 ] sing_36.htm#IDX84 777 ^ sing_36.htm#IDX92 778 ^ sing_76.htm#SEC116 779 ^ sing_88.htm#SEC128 780 _ sing_36.htm#IDX116 781 ` sing_36.htm#IDX105 782 a, ordering sing_898.htm#SEC950 783 absFactorize sing_1140.htm#SEC1216 784 absFactorizeBCG sing_1141.htm#SEC1217 785 absPrimdecGTZ sing_1338.htm#SEC1414 786 absPrimdecGTZE sing_1339.htm#SEC1415 787 absValue sing_937.htm#SEC1013 788 absfact.lib sing_1139.htm#SEC1215 789 absfact_lib sing_1139.htm#SEC1215 790 absolute factorization. sing_1139.htm#IDX451 791 abstractR sing_1477.htm#SEC1553 792 actionIsProper sing_1707.htm#SEC1783 793 addNvarsTo sing_1054.htm#SEC1130 794 addRat sing_836.htm#SEC888 795 addcol sing_1096.htm#SEC1172 796 addcores sing_1023.htm#SEC1099 797 addrow sing_1097.htm#SEC1173 798 addvarsTo sing_1053.htm#SEC1129 799 ademRelations sing_697.htm#SEC749 800 adjoint sing_1121.htm#SEC1197 801 adjointIdeal sing_1406.htm#SEC1482 802 adjunction divisor sing_1824.htm#IDX710 803 admissibleSub sing_755.htm#SEC807 804 afaces sing_2291.htm#SEC2367 805 affine code Fitzgerald-Lax method sing_921.htm#SEC990 806 ainvar.lib sing_1704.htm#SEC1780 807 ainvar_lib sing_1704.htm#SEC1780 808 aksaka.lib sing_1889.htm#SEC1965 809 aksaka_lib sing_1889.htm#SEC1965 810 alexanderpolynomial sing_1502.htm#SEC1578 811 alexpoly.lib sing_1499.htm#SEC1575 812 alexpoly_lib sing_1499.htm#SEC1575 813 algDependent sing_1146.htm#SEC1222 814 alg_kernel sing_1147.htm#SEC1223 815 algebra.lib sing_1142.htm#SEC1218 816 algebra_containment sing_1143.htm#SEC1219 817 algebra_lib sing_1142.htm#SEC1218 818 algebraic dependence sing_785.htm#IDX351 819 algebraic field extension sing_1352.htm#IDX510 820 algebraicDependence sing_1365.htm#SEC1441 821 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_912.htm#SEC969 822 algorithm of Conti and Traverso sing_908.htm#SEC965 823 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_911.htm#SEC968 824 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_910.htm#SEC967 825 algorithm of Pottier sing_909.htm#SEC966 826 align sing_260.htm#SEC300 827 all.lib sing_930.htm#SEC1006 828 allDoubleExt sing_802.htm#SEC854 829 allExtOfLeft sing_799.htm#SEC851 830 allExtOfRight sing_800.htm#SEC852 831 allPositive sing_564.htm#SEC616 832 all_lib sing_930.htm#SEC1006 827 833 allowing net access Command line options sing_19.htm#IDX41 828 allprint sing_971.htm#SEC104 6829 allreal sing_20 29.htm#SEC2104830 allrealst sing_20 27.htm#SEC2102831 allsquarefree sing_160 3.htm#SEC1678832 ambientDimension sing_187.htm#SEC22 6833 and Evaluation of logical expressions sing_96.htm#SEC13 5834 and sing_459.htm#SEC49 8835 annPoly sing_612.htm#SEC66 3836 annRat sing_613.htm#SEC66 4837 annRatSyz sing_825.htm#SEC87 6838 annfs sing_589.htm#SEC64 0839 annfs0 sing_601.htm#SEC65 2840 annfs2 sing_602.htm#SEC65 3841 annfsBMI sing_598.htm#SEC6 49842 annfsParamBM sing_597.htm#SEC64 8843 annfsRB sing_603.htm#SEC65 4844 annfspecial sing_590.htm#SEC64 1845 annihilator of polynomial sing_611.htm#IDX33 1846 annihilator of rational function sing_611.htm#IDX33 2847 annihilator of rational function sing_815.htm#IDX37 7848 annil sing_124 5.htm#SEC1320849 appelF1 sing_630.htm#SEC68 1850 appelF2 sing_631.htm#SEC68 2851 appelF4 sing_632.htm#SEC68 3852 appendWeight2Ord sing_757.htm#SEC80 8853 apply sing_426.htm#SEC46 5854 applyAdF sing_580.htm#SEC63 1855 arcpoint.lib sing_15 09.htm#SEC1584856 arcpoint_lib sing_15 09.htm#SEC1584857 areZeroElements sing_23 66.htm#SEC2441858 argument, default sing_44.htm#SEC8 0859 argument, optional sing_44.htm#SEC8 0860 arr.lib sing_212 2.htm#SEC2197861 arr2multarr sing_215 5.htm#SEC2230862 arrBoolean sing_214 4.htm#SEC2219863 arrBoundedChambers sing_216 5.htm#SEC2240864 arrBraid sing_214 5.htm#SEC2220865 arrCenter sing_213 2.htm#SEC2207866 arrCentered sing_213 4.htm#SEC2209867 arrCentral sing_213 3.htm#SEC2208868 arrCentralize sing_213 5.htm#SEC2210869 arrChambers sing_216 4.htm#SEC2239870 arrCharPoly sing_216 2.htm#SEC2237871 arrCone sing_21 38.htm#SEC2213872 arrCoordChange sing_213 6.htm#SEC2211873 arrCoordNormalize sing_21 37.htm#SEC2212874 arrDecone sing_21 39.htm#SEC2214875 arrDer sing_215 2.htm#SEC2227876 arrEdelmanReiner sing_215 0.htm#SEC2225877 arrEssentialize sing_214 3.htm#SEC2218878 arrExponents sing_215 4.htm#SEC2229879 arrFlats sing_21 59.htm#SEC2234880 arrIsEssential sing_214 2.htm#SEC2217881 arrIsFree sing_215 3.htm#SEC2228882 arrLastVar sing_213 1.htm#SEC2206883 arrLattice sing_216 0.htm#SEC2235884 arrLocalize sing_214 0.htm#SEC2215885 arrOrlikSolomon sing_215 1.htm#SEC2226886 arrPoincare sing_216 3.htm#SEC2238887 arrPrintMatrix sing_21 27.htm#SEC2202888 arrRandom sing_21 48.htm#SEC2223889 arrRandomCentral sing_21 49.htm#SEC2224890 arrRestrict sing_214 1.htm#SEC2216891 arrSet sing_212 3.htm#SEC2198892 arrSwapVar sing_213 0.htm#SEC2205893 arrTypeB sing_214 6.htm#SEC2221894 arrTypeD sing_21 47.htm#SEC2222895 arr_lib sing_212 2.htm#SEC2197896 arrange sing_605.htm#SEC65 6897 arrangement sing_212 3.htm#IDX769898 arrangement sing_212 4.htm#IDX774899 arrangement sing_215 5.htm#IDX836900 arrangement sing_215 6.htm#IDX839901 ask sing_189 4.htm#SEC1969902 assPrimes sing_115 4.htm#SEC1229903 assign sing_212 3.htm#IDX771904 assignment,custom Assignments for user defined types sing_182.htm#SEC22 1905 assprimeszerodim.lib assprimeszerodim_lib sing_115 2.htm#SEC1227906 assprimeszerodim_lib assprimeszerodim_lib sing_115 2.htm#SEC1227907 atkins.lib sing_189 5.htm#SEC1970908 atkins_lib sing_189 5.htm#SEC1970909 attrib sing_261.htm#SEC30 0910 autonom sing_18 58.htm#SEC1933911 autonomDim sing_18 59.htm#SEC1934912 awalk1 sing_118 5.htm#SEC1260913 awalk2 sing_118 6.htm#SEC1261914 b-function sing_553.htm#IDX30 4915 bFactor sing_635.htm#SEC68 6916 babyGiant sing_192 4.htm#SEC1999917 backward sing_22 55.htm#SEC2330918 bareiss sing_262.htm#SEC30 1919 base2str sing_933.htm#SEC100 8920 basering sing_28.htm#IDX7 7921 basering sing_83.htm#SEC12 2922 basicinvariants sing_151 5.htm#SEC1590923 belongSemigroup sing_11 57.htm#SEC1232924 bernstein sing_156 3.htm#SEC1638925 bernsteinBM sing_593.htm#SEC64 4926 bernsteinLift sing_594.htm#SEC64 5927 bertini2Singular sing_13 87.htm#SEC1462928 betti sing_263.htm#SEC30 2929 betti (plural) sing_503.htm#SEC54 2930 bfct sing_554.htm#SEC60 5931 bfctAnn sing_556.htm#SEC60 7932 bfctBound sing_824.htm#SEC87 5933 bfctIdeal sing_558.htm#SEC6 09934 bfctOneGB sing_557.htm#SEC60 8935 bfctSyz sing_555.htm#SEC60 6936 bfctVarAnn sing_646.htm#SEC69 7937 bfctVarIn sing_645.htm#SEC69 6938 bfun.lib sing_553.htm#SEC60 4939 bfun_lib sing_553.htm#SEC60 4940 bigint sing_73.htm#SEC11 2941 bigint declarations sing_74.htm#SEC11 3942 bigint expressions sing_75.htm#SEC11 4943 bigint operations sing_76.htm#SEC11 5944 bigint related functions bigint related functions sing_77.htm#SEC11 6945 bigintmat sing_78.htm#SEC11 7946 bigintmat declarations bigintmat declarations sing_79.htm#SEC11 8947 bigintmat expressions bigintmat expressions sing_80.htm#SEC1 19948 bigintmat operations bigintmat operations sing_82.htm#SEC12 1949 bigintmat type cast sing_81.htm#SEC12 0950 bimodules sing_546.htm#IDX29 2951 bimodules.lib sing_546.htm#SEC59 7952 bimodules_lib sing_546.htm#SEC59 7953 binary_add sing_19 47.htm#SEC2022954 binomial sing_938.htm#SEC101 3955 binomials2intmat sing_131 0.htm#SEC138558804956 birational map, image, inverse. sing_140 4.htm#IDX539957 bistd sing_547.htm#SEC59 8958 bisyzygies sing_546.htm#IDX29 3959 bitrinity sing_548.htm#SEC 599960 blackbox sing_243.htm#SEC28 2961 blackbox sing_251.htm#SEC29 0962 block sing_40.htm#SEC 69963 block sing_425.htm#SEC46 4964 blowUp sing_145 5.htm#SEC1530965 blowUp2 sing_145 6.htm#SEC1531966 blowUpBO sing_146 2.htm#SEC1537967 blowup0 sing_116 2.htm#SEC1237968 boolean sing_214 4.htm#IDX813969 boolean expressions sing_95.htm#SEC13 4970 boolean operations sing_96.htm#SEC13 5971 boolean_constant sing_210 5.htm#SEC218052873972 boolean_ideal sing_21 09.htm#SEC218453515973 boolean_poly sing_210 6.htm#SEC218141652974 boolean_poly_ring sing_210 4.htm#SEC2179sprintf975 boolean_set sing_211 0.htm#SEC218558235976 boolean_std sing_210 3.htm#SEC21785921977 boundBuFou sing_202 4.htm#SEC2099978 boundDes sing_202 6.htm#SEC2101979 boundaryLatticePoints boundaryLatticePoints sing_24 11.htm#SEC2486980 boundposDes sing_202 5.htm#SEC2100981 bracket sing_406.htm#IDX19 2982 bracket sing_462.htm#SEC50 1983 bracket sing_504.htm#SEC54 3984 braid sing_214 5.htm#IDX815985 branchTo procs with different argument types sing_155.htm#SEC19 4986 break sing_427.htm#SEC46 6987 break point sing_441.htm#SEC48 0988 breakpoint sing_428.htm#SEC46 7989 brillnoether.lib sing_21 67.htm#SEC2242990 brillnoether_lib sing_21 67.htm#SEC2242991 brnoeth.lib sing_182 0.htm#SEC1895992 brnoeth_lib sing_182 0.htm#SEC1895834 allprint sing_971.htm#SEC1047 835 allreal sing_2032.htm#SEC2108 836 allrealst sing_2030.htm#SEC2106 837 allsquarefree sing_1606.htm#SEC1682 838 ambientDimension sing_187.htm#SEC227 839 and Evaluation of logical expressions sing_96.htm#SEC136 840 and sing_459.htm#SEC499 841 annPoly sing_612.htm#SEC664 842 annRat sing_613.htm#SEC665 843 annRatSyz sing_825.htm#SEC877 844 annfs sing_589.htm#SEC641 845 annfs0 sing_601.htm#SEC653 846 annfs2 sing_602.htm#SEC654 847 annfsBMI sing_598.htm#SEC650 848 annfsParamBM sing_597.htm#SEC649 849 annfsRB sing_603.htm#SEC655 850 annfspecial sing_590.htm#SEC642 851 annihilator of polynomial sing_611.htm#IDX330 852 annihilator of rational function sing_611.htm#IDX331 853 annihilator of rational function sing_815.htm#IDX376 854 annil sing_1248.htm#SEC1324 855 appelF1 sing_630.htm#SEC682 856 appelF2 sing_631.htm#SEC683 857 appelF4 sing_632.htm#SEC684 858 appendWeight2Ord sing_757.htm#SEC809 859 apply sing_426.htm#SEC466 860 applyAdF sing_580.htm#SEC632 861 arcpoint.lib sing_1512.htm#SEC1588 862 arcpoint_lib sing_1512.htm#SEC1588 863 areZeroElements sing_2377.htm#SEC2453 864 argument, default sing_44.htm#SEC81 865 argument, optional sing_44.htm#SEC81 866 arr.lib sing_2125.htm#SEC2201 867 arr2multarr sing_2158.htm#SEC2234 868 arrBoolean sing_2147.htm#SEC2223 869 arrBoundedChambers sing_2168.htm#SEC2244 870 arrBraid sing_2148.htm#SEC2224 871 arrCenter sing_2135.htm#SEC2211 872 arrCentered sing_2137.htm#SEC2213 873 arrCentral sing_2136.htm#SEC2212 874 arrCentralize sing_2138.htm#SEC2214 875 arrChambers sing_2167.htm#SEC2243 876 arrCharPoly sing_2165.htm#SEC2241 877 arrCone sing_2141.htm#SEC2217 878 arrCoordChange sing_2139.htm#SEC2215 879 arrCoordNormalize sing_2140.htm#SEC2216 880 arrDecone sing_2142.htm#SEC2218 881 arrDer sing_2155.htm#SEC2231 882 arrEdelmanReiner sing_2153.htm#SEC2229 883 arrEssentialize sing_2146.htm#SEC2222 884 arrExponents sing_2157.htm#SEC2233 885 arrFlats sing_2162.htm#SEC2238 886 arrIsEssential sing_2145.htm#SEC2221 887 arrIsFree sing_2156.htm#SEC2232 888 arrLastVar sing_2134.htm#SEC2210 889 arrLattice sing_2163.htm#SEC2239 890 arrLocalize sing_2143.htm#SEC2219 891 arrOrlikSolomon sing_2154.htm#SEC2230 892 arrPoincare sing_2166.htm#SEC2242 893 arrPrintMatrix sing_2130.htm#SEC2206 894 arrRandom sing_2151.htm#SEC2227 895 arrRandomCentral sing_2152.htm#SEC2228 896 arrRestrict sing_2144.htm#SEC2220 897 arrSet sing_2126.htm#SEC2202 898 arrSwapVar sing_2133.htm#SEC2209 899 arrTypeB sing_2149.htm#SEC2225 900 arrTypeD sing_2150.htm#SEC2226 901 arr_lib sing_2125.htm#SEC2201 902 arrange sing_605.htm#SEC657 903 arrangement sing_2126.htm#IDX769 904 arrangement sing_2127.htm#IDX774 905 arrangement sing_2158.htm#IDX836 906 arrangement sing_2159.htm#IDX839 907 ask sing_1897.htm#SEC1973 908 assPrimes sing_1157.htm#SEC1233 909 assign sing_2126.htm#IDX771 910 assignment,custom Assignments for user defined types sing_182.htm#SEC222 911 assprimeszerodim.lib assprimeszerodim_lib sing_1155.htm#SEC1231 912 assprimeszerodim_lib assprimeszerodim_lib sing_1155.htm#SEC1231 913 atkins.lib sing_1898.htm#SEC1974 914 atkins_lib sing_1898.htm#SEC1974 915 attrib sing_261.htm#SEC301 916 autonom sing_1861.htm#SEC1937 917 autonomDim sing_1862.htm#SEC1938 918 awalk1 sing_1188.htm#SEC1264 919 awalk2 sing_1189.htm#SEC1265 920 b-function sing_553.htm#IDX303 921 bFactor sing_635.htm#SEC687 922 babyGiant sing_1927.htm#SEC2003 923 backward sing_2266.htm#SEC2342 924 bareiss sing_262.htm#SEC302 925 base2str sing_933.htm#SEC1009 926 basering sing_28.htm#IDX76 927 basering sing_83.htm#SEC123 928 basicinvariants sing_1518.htm#SEC1594 929 belongSemigroup sing_1160.htm#SEC1236 930 bernstein sing_1566.htm#SEC1642 931 bernsteinBM sing_593.htm#SEC645 932 bernsteinLift sing_594.htm#SEC646 933 bertini2Singular sing_1390.htm#SEC1466 934 betti sing_263.htm#SEC303 935 betti (plural) sing_503.htm#SEC543 936 bfct sing_554.htm#SEC606 937 bfctAnn sing_556.htm#SEC608 938 bfctBound sing_824.htm#SEC876 939 bfctIdeal sing_558.htm#SEC610 940 bfctOneGB sing_557.htm#SEC609 941 bfctSyz sing_555.htm#SEC607 942 bfctVarAnn sing_646.htm#SEC698 943 bfctVarIn sing_645.htm#SEC697 944 bfun.lib sing_553.htm#SEC605 945 bfun_lib sing_553.htm#SEC605 946 bigint sing_73.htm#SEC113 947 bigint declarations sing_74.htm#SEC114 948 bigint expressions sing_75.htm#SEC115 949 bigint operations sing_76.htm#SEC116 950 bigint related functions bigint related functions sing_77.htm#SEC117 951 bigintmat sing_78.htm#SEC118 952 bigintmat declarations bigintmat declarations sing_79.htm#SEC119 953 bigintmat expressions bigintmat expressions sing_80.htm#SEC120 954 bigintmat operations bigintmat operations sing_82.htm#SEC122 955 bigintmat type cast sing_81.htm#SEC121 956 bimodules sing_546.htm#IDX291 957 bimodules.lib sing_546.htm#SEC598 958 bimodules_lib sing_546.htm#SEC598 959 binary_add sing_1950.htm#SEC2026 960 binomial sing_938.htm#SEC1014 961 binomials2intmat sing_1313.htm#SEC1389 58804 962 birational map, image, inverse. sing_1407.htm#IDX539 963 bistd sing_547.htm#SEC599 964 bisyzygies sing_546.htm#IDX292 965 bitrinity sing_548.htm#SEC600 966 blackbox sing_243.htm#SEC283 967 blackbox sing_251.htm#SEC291 968 block sing_40.htm#SEC70 969 block sing_425.htm#SEC465 970 blowUp sing_1458.htm#SEC1534 971 blowUp2 sing_1459.htm#SEC1535 972 blowUpBO sing_1465.htm#SEC1541 973 blowup0 sing_1165.htm#SEC1241 974 boolean sing_2147.htm#IDX813 975 boolean expressions sing_95.htm#SEC135 976 boolean operations sing_96.htm#SEC136 977 boolean_constant sing_2108.htm#SEC2184 52873 978 boolean_ideal sing_2112.htm#SEC2188 53515 979 boolean_poly sing_2109.htm#SEC2185 41652 980 boolean_poly_ring sing_2107.htm#SEC2183 sprintf 981 boolean_set sing_2113.htm#SEC2189 58235 982 boolean_std sing_2106.htm#SEC2182 5921 983 boundBuFou sing_2027.htm#SEC2103 984 boundDes sing_2029.htm#SEC2105 985 boundaryLatticePoints boundaryLatticePoints sing_2422.htm#SEC2498 986 boundposDes sing_2028.htm#SEC2104 987 bracket sing_406.htm#IDX191 988 bracket sing_462.htm#SEC502 989 bracket sing_504.htm#SEC544 990 braid sing_2148.htm#IDX815 991 branchTo procs with different argument types sing_155.htm#SEC195 992 break sing_427.htm#SEC467 993 break point sing_441.htm#SEC481 994 breakpoint sing_428.htm#SEC468 995 brillnoether.lib sing_2170.htm#SEC2246 996 brillnoether_lib sing_2170.htm#SEC2246 997 brnoeth.lib sing_1823.htm#SEC1899 998 brnoeth_lib sing_1823.htm#SEC1899 993 999 browser, command line option Command line options sing_19.htm#IDX44 994 browser, setting the sing_406.htm#IDX18 81000 browser, setting the sing_406.htm#IDX187 995 1001 browsers The online help system sing_16.htm#IDX21 996 browsers, setting the sing_406.htm#IDX18 7997 bubblesort sing_1 897.htm#SEC1972998 busadj sing_111 6.htm#SEC1191999 bvar sing_21 17.htm#SEC2192527731000 c, module ordering sing_895.htm#IDX40 41001 cProj sing_22 07.htm#SEC22821002 calculateI sing_14 29.htm#SEC15041003 calculate_max_sum sing_196 6.htm#SEC20411004 calculate_ordering sing_194 4.htm#SEC20191005 cancelunit, option sing_364.htm#IDX16 71006 canonMap sing_119 0.htm#SEC12651007 canonicalizeCone sing_188.htm#SEC22 71008 canonize sing_186 6.htm#SEC19411009 cantoradd sing_198 0.htm#SEC20551010 cantormult sing_198 3.htm#SEC20581011 cantorred sing_198 1.htm#SEC20561012 cardGroup sing_11 59.htm#SEC12341013 case No case or switch statement sing_460.htm#SEC 4991002 browsers, setting the sing_406.htm#IDX186 1003 bubblesort sing_1900.htm#SEC1976 1004 busadj sing_1119.htm#SEC1195 1005 bvar sing_2120.htm#SEC2196 52773 1006 c, module ordering sing_895.htm#IDX403 1007 cProj sing_2212.htm#SEC2288 1008 calculateI sing_1432.htm#SEC1508 1009 calculate_max_sum sing_1969.htm#SEC2045 1010 calculate_ordering sing_1947.htm#SEC2023 1011 cancelunit, option sing_364.htm#IDX166 1012 canonMap sing_1193.htm#SEC1269 1013 canonicalizeCone sing_188.htm#SEC228 1014 canonize sing_1869.htm#SEC1945 1015 cantoradd sing_1983.htm#SEC2059 1016 cantormult sing_1986.htm#SEC2062 1017 cantorred sing_1984.htm#SEC2060 1018 cardGroup sing_1162.htm#SEC1238 1019 case No case or switch statement sing_460.htm#SEC500 1014 1020 cdd sing_1.htm#IDX10 1015 1021 cddlib sing_1.htm#IDX11 1016 center sing_567.htm#IDX311 1017 center sing_573.htm#SEC624 1018 center sing_2132.htm#IDX795 1019 center sing_2133.htm#IDX796 1020 center sing_2134.htm#IDX798 1021 center sing_2135.htm#IDX800 1022 centerRed sing_572.htm#SEC623 1023 centerVS sing_571.htm#SEC622 1024 central sing_2126.htm#IDX781 1025 central sing_2133.htm#IDX797 1026 central sing_2135.htm#IDX799 1027 central sing_2149.htm#IDX824 1028 central.lib sing_567.htm#SEC618 1029 central1st sing_2256.htm#SEC2331 1030 central2nd sing_2257.htm#SEC2332 1031 central_lib sing_567.htm#SEC618 1032 centralize sing_567.htm#IDX314 1033 centralizeSet sing_568.htm#SEC619 1034 centralizer sing_567.htm#IDX312 1035 centralizer sing_574.htm#SEC625 1036 centralizerRed sing_570.htm#SEC621 1037 centralizerVS sing_569.htm#SEC620 1038 cgs sing_932.htm#SEC1007 1039 cgsdr sing_957.htm#SEC1032 1040 chAll sing_2179.htm#SEC2254 1041 chAllInv sing_2180.htm#SEC2255 1042 chDual sing_2185.htm#SEC2260 1043 chHE sing_2181.htm#SEC2256 1044 chHom sing_2192.htm#SEC2267 1045 chNum sing_2175.htm#SEC2250 1046 chNumbers sing_2176.htm#SEC2251 1047 chNumbersProj sing_2211.htm#SEC2286 1048 chProd sing_2187.htm#SEC2262 1049 chProdE sing_2188.htm#SEC2263 1050 chProdL sing_2189.htm#SEC2264 1051 chProdLP sing_2190.htm#SEC2265 1052 chProj sing_2208.htm#SEC2283 1053 chSum sing_2183.htm#SEC2258 1054 chSymm sing_2195.htm#SEC2270 1055 chSymm2L sing_2196.htm#SEC2271 1056 chSymm2LP sing_2197.htm#SEC2272 1057 chWedge sing_2198.htm#SEC2273 1058 chWedge2L sing_2199.htm#SEC2274 1059 chWedge2LP sing_2200.htm#SEC2275 1060 chaincrit sing_1994.htm#SEC2069 1061 chambers sing_2164.htm#IDX852 1062 chambers sing_2165.htm#IDX853 1063 changeDenominator sing_1283.htm#SEC1358 1064 changechar sing_1028.htm#SEC1103 1065 changeord sing_1029.htm#SEC1104 1066 changeordTo sing_1052.htm#SEC1127 1067 changes sing_2451.htm#SEC2526 1068 changevar sing_1030.htm#SEC1105 1069 char sing_264.htm#SEC303 1070 charInfo sing_628.htm#SEC679 1071 charVariety sing_627.htm#SEC678 1072 char_series sing_265.htm#SEC304 1073 characteristic exponents sing_1503.htm#IDX563 1074 characteristic exponents sing_1504.htm#IDX568 1075 characteristic exponents sing_1505.htm#IDX571 1076 characteristic exponents sing_1506.htm#IDX575 1077 characteristic exponents sing_1590.htm#IDX681 1078 characteristic polynomial sing_2162.htm#IDX850 1079 characteristic variety sing_611.htm#IDX339 1080 characteristic variety sing_815.htm#IDX373 1081 charexp2conductor sing_1506.htm#SEC1581 1082 charexp2generators sing_1504.htm#SEC1579 1083 charexp2inter sing_1505.htm#SEC1580 1084 charexp2multseq sing_1503.htm#SEC1578 1085 charexp2poly sing_1507.htm#SEC1582 1086 charpoly sing_1117.htm#SEC1192 1087 charstr sing_266.htm#SEC305 1088 checkFactor sing_604.htm#SEC655 1089 checkRoot sing_599.htm#SEC650 1090 chern sing_2174.htm#SEC2249 1091 chern.lib sing_2169.htm#SEC2244 1092 chernCharPoly sing_2214.htm#SEC2289 1093 chernPoly sing_2213.htm#SEC2288 1094 chern_lib sing_2169.htm#SEC2244 1095 chineseRem sing_1915.htm#SEC1990 1096 chinrem sing_267.htm#SEC306 1097 chinrempoly sing_2383.htm#SEC2458 1098 chinrestp sing_1974.htm#SEC2049 1099 cimonom.lib sing_2224.htm#SEC2299 1100 cimonom_lib sing_2224.htm#SEC2299 1101 cisimplicial.lib sing_1155.htm#SEC1230 1102 cisimplicial_lib sing_1155.htm#SEC1230 1103 classify sing_1516.htm#SEC1591 1104 classify.lib sing_1514.htm#SEC1589 1105 classifyCeq sing_1533.htm#SEC1608 1106 classify_lib sing_1514.htm#SEC1589 1107 classifyceq.lib sing_1532.htm#IDX578 1108 classifyceq_lib sing_1532.htm#IDX579 1109 classifyci.lib sing_1534.htm#IDX580 1110 classifyci_lib sing_1534.htm#IDX581 1111 classifyicis sing_1535.htm#SEC1610 1112 classpoly sing_2212.htm#SEC2287 1113 cleanTmp sing_2095.htm#SEC2170 1114 cleanunit sing_1427.htm#SEC1502 1115 cleardenom sing_268.htm#SEC307 1116 close sing_269.htm#SEC308 1117 closed_points sing_1830.htm#SEC1905 1118 closetex sing_1797.htm#SEC1872 1119 closureFrac sing_1276.htm#SEC1351 1120 coHom sing_808.htm#SEC859 1121 codim sing_1628.htm#SEC1703 1122 codimension sing_189.htm#SEC228 1123 coding theory sing_887.htm#SEC938 1124 coef sing_270.htm#SEC309 1125 coefficient sing_2125.htm#IDX777 1126 coefficient sing_2126.htm#IDX780 1127 coefficient sing_2127.htm#IDX784 1128 coefficient field sing_139.htm#SEC178 1129 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC44 1130 coefficients, long sing_846.htm#SEC897 1131 coeffmod sing_1892.htm#SEC1967 1132 coeffs sing_271.htm#SEC310 1133 collectDiv sing_1472.htm#SEC1547 1134 colrank sing_1864.htm#SEC1939 1135 colred sing_1100.htm#SEC1175 1136 commRing sing_839.htm#SEC890 1137 comma sing_461.htm#SEC500 1138 command,custom Commands for user defined types sing_181.htm#SEC220 1139 command-line option, setting value of sing_406.htm#IDX270 1140 command-line option, value of sing_406.htm#IDX268 1141 command-line options, print all values of sing_406.htm#IDX267 1022 center sing_567.htm#IDX310 1023 center sing_573.htm#SEC625 1024 center sing_2135.htm#IDX795 1025 center sing_2136.htm#IDX796 1026 center sing_2137.htm#IDX798 1027 center sing_2138.htm#IDX800 1028 centerRed sing_572.htm#SEC624 1029 centerVS sing_571.htm#SEC623 1030 central sing_2129.htm#IDX781 1031 central sing_2136.htm#IDX797 1032 central sing_2138.htm#IDX799 1033 central sing_2152.htm#IDX824 1034 central.lib sing_567.htm#SEC619 1035 central1st sing_2267.htm#SEC2343 1036 central2nd sing_2268.htm#SEC2344 1037 central_lib sing_567.htm#SEC619 1038 centralize sing_567.htm#IDX313 1039 centralizeSet sing_568.htm#SEC620 1040 centralizer sing_567.htm#IDX311 1041 centralizer sing_574.htm#SEC626 1042 centralizerRed sing_570.htm#SEC622 1043 centralizerVS sing_569.htm#SEC621 1044 cgs sing_932.htm#SEC1008 1045 cgsdr sing_957.htm#SEC1033 1046 chAll sing_2182.htm#SEC2258 1047 chAllInv sing_2183.htm#SEC2259 1048 chDual sing_2188.htm#SEC2264 1049 chHE sing_2184.htm#SEC2260 1050 chHom sing_2197.htm#SEC2273 1051 chNum sing_2178.htm#SEC2254 1052 chNumbers sing_2179.htm#SEC2255 1053 chNumbersProj sing_2216.htm#SEC2292 1054 chProd sing_2190.htm#SEC2266 1055 chProdE sing_2191.htm#SEC2267 1056 chProdL sing_2192.htm#SEC2268 1057 chProdLP sing_2193.htm#SEC2269 1058 chProdM sing_2194.htm#SEC2270 1059 chProdMP sing_2195.htm#SEC2271 1060 chProj sing_2213.htm#SEC2289 1061 chSum sing_2186.htm#SEC2262 1062 chSymm sing_2200.htm#SEC2276 1063 chSymm2L sing_2201.htm#SEC2277 1064 chSymm2LP sing_2202.htm#SEC2278 1065 chWedge sing_2203.htm#SEC2279 1066 chWedge2L sing_2204.htm#SEC2280 1067 chWedge2LP sing_2205.htm#SEC2281 1068 chaincrit sing_1997.htm#SEC2073 1069 chambers sing_2167.htm#IDX852 1070 chambers sing_2168.htm#IDX853 1071 changeDenominator sing_1286.htm#SEC1362 1072 changechar sing_1028.htm#SEC1104 1073 changeord sing_1029.htm#SEC1105 1074 changeordTo sing_1052.htm#SEC1128 1075 changes sing_2465.htm#SEC2541 1076 changevar sing_1030.htm#SEC1106 1077 char sing_264.htm#SEC304 1078 charInfo sing_628.htm#SEC680 1079 charVariety sing_627.htm#SEC679 1080 char_series sing_265.htm#SEC305 1081 characteristic exponents sing_1506.htm#IDX563 1082 characteristic exponents sing_1507.htm#IDX568 1083 characteristic exponents sing_1508.htm#IDX571 1084 characteristic exponents sing_1509.htm#IDX575 1085 characteristic exponents sing_1593.htm#IDX681 1086 characteristic polynomial sing_2165.htm#IDX850 1087 characteristic variety sing_611.htm#IDX338 1088 characteristic variety sing_815.htm#IDX372 1089 charexp2conductor sing_1509.htm#SEC1585 1090 charexp2generators sing_1507.htm#SEC1583 1091 charexp2inter sing_1508.htm#SEC1584 1092 charexp2multseq sing_1506.htm#SEC1582 1093 charexp2poly sing_1510.htm#SEC1586 1094 charpoly sing_1120.htm#SEC1196 1095 charstr sing_266.htm#SEC306 1096 checkFactor sing_604.htm#SEC656 1097 checkRoot sing_599.htm#SEC651 1098 chern sing_2177.htm#SEC2253 1099 chern.lib sing_2172.htm#SEC2248 1100 chernCharPoly sing_2219.htm#SEC2295 1101 chernPoly sing_2218.htm#SEC2294 1102 chern_lib sing_2172.htm#SEC2248 1103 chineseRem sing_1918.htm#SEC1994 1104 chinrem sing_267.htm#SEC307 1105 chinrempoly sing_2394.htm#SEC2470 1106 chinrestp sing_1977.htm#SEC2053 1107 cimonom.lib sing_2229.htm#SEC2305 1108 cimonom_lib sing_2229.htm#SEC2305 1109 cisimplicial.lib sing_1158.htm#SEC1234 1110 cisimplicial_lib sing_1158.htm#SEC1234 1111 classify sing_1519.htm#SEC1595 1112 classify.lib sing_1517.htm#SEC1593 1113 classifyCeq sing_1536.htm#SEC1612 1114 classify_lib sing_1517.htm#SEC1593 1115 classifyceq.lib sing_1535.htm#IDX578 1116 classifyceq_lib sing_1535.htm#IDX579 1117 classifyci.lib sing_1537.htm#IDX580 1118 classifyci_lib sing_1537.htm#IDX581 1119 classifyicis sing_1538.htm#SEC1614 1120 classpoly sing_2217.htm#SEC2293 1121 cleanTmp sing_2098.htm#SEC2174 1122 cleanunit sing_1430.htm#SEC1506 1123 cleardenom sing_268.htm#SEC308 1124 close sing_269.htm#SEC309 1125 closed_points sing_1833.htm#SEC1909 1126 closetex sing_1800.htm#SEC1876 1127 closureFrac sing_1279.htm#SEC1355 1128 coHom sing_808.htm#SEC860 1129 codim sing_1631.htm#SEC1707 1130 codimension sing_189.htm#SEC229 1131 coding theory sing_887.htm#SEC939 1132 coef sing_270.htm#SEC310 1133 coefficient sing_2128.htm#IDX777 1134 coefficient sing_2129.htm#IDX780 1135 coefficient sing_2130.htm#IDX784 1136 coefficient field sing_139.htm#SEC179 1137 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 1138 coefficients, long sing_846.htm#SEC898 1139 coeffmod sing_1895.htm#SEC1971 1140 coeffs sing_271.htm#SEC311 1141 collectDiv sing_1475.htm#SEC1551 1142 colrank sing_1867.htm#SEC1943 1143 colred sing_1103.htm#SEC1179 1144 commRing sing_839.htm#SEC891 1145 comma sing_461.htm#SEC501 1146 command,custom Commands for user defined types sing_181.htm#SEC221 1147 command-line option, setting value of sing_406.htm#IDX269 1148 command-line option, value of sing_406.htm#IDX267 1149 command-line options, print all values of sing_406.htm#IDX266 1142 1150 command-line options, short help Command line options sing_19.htm#IDX38 1143 commands (plural) sing_502.htm#IDX29 11144 comment sing_36.htm#IDX10 91145 compareTasks sing_106 4.htm#SEC11391146 completeReduction sing_170 6.htm#SEC17811147 complex sing_28.htm#IDX7 61148 complexSingType sing_153 0.htm#SEC16051149 compregb.lib sing_931.htm#SEC100 61150 compregb_lib sing_931.htm#SEC100 61151 comprehensive Groebner system sing_931.htm#IDX4 101152 compress sing_10 77.htm#SEC11521153 computeConstant sing_117 5.htm#SEC12501154 computeGromovWitten sing_11 78.htm#SEC12531155 computeN sing_147 6.htm#SEC15511156 computeV sing_147 5.htm#SEC15501157 computemcm sing_143 4.htm#SEC15091158 concat sing_10 78.htm#SEC11531159 conductor sing_150 6.htm#IDX5741160 conductor, degree sing_159 0.htm#IDX6841161 cone sing_183.htm#SEC22 21162 cone sing_21 38.htm#IDX8041163 cone sing_21 39.htm#IDX8061164 cone related functions cone related functions sing_186.htm#SEC22 51165 coneLink sing_190.htm#SEC2 291166 coneViaInequalities sing_185.htm#SEC22 41167 coneViaPoints sing_184.htm#SEC22 31168 conic, parametrization, rational point. sing_141 1.htm#IDX5441169 conicWithTangents sing_207 1.htm#SEC21461170 constructH sing_143 5.htm#SEC15101171 constructblwup sing_143 6.htm#SEC15111172 constructlastblwup sing_14 37.htm#SEC15121173 constructor sing_215 5.htm#IDX8371174 constructor sing_215 6.htm#IDX8401175 contact matrix sing_150 5.htm#IDX5701176 containedQ sing_178 5.htm#SEC18601177 containsAsFace sing_191.htm#SEC23 01178 containsInCollection containsInCollection sing_223.htm#SEC26 21179 containsInSupport sing_192.htm#SEC23 11180 containsPositiveVector containsPositiveVector sing_193.htm#SEC23 21181 containsRelatively sing_194.htm#SEC23 31182 content sing_1002.htm#SEC107 71183 contentSB, option sing_364.htm#IDX16 81184 continue Behavior of continue sing_429.htm#SEC46 81185 continue sing_463.htm#SEC50 21186 contraHom sing_809.htm#SEC86 01187 contract sing_272.htm#SEC31 11188 contributors sing_406.htm#IDX19 51189 control sing_185 6.htm#SEC19311190 control.lib sing_185 5.htm#SEC19301191 controlDim sing_18 57.htm#SEC19321192 controlExample sing_18 69.htm#SEC19441193 control_Matrix sing_15 58.htm#SEC16331194 control_lib sing_185 5.htm#SEC19301195 convertdata sing_143 2.htm#SEC15071196 convex geometry sing_24 00.htm#SEC24751197 convexHull sing_195.htm#SEC23 41198 convexIntersection sing_196.htm#SEC23 51199 convloc sing_608.htm#SEC6 591200 coordinate change sing_213 5.htm#IDX8011201 coordinate change sing_213 6.htm#IDX8021202 coordinate change sing_21 37.htm#IDX8031203 coordinates sing_201 2.htm#IDX7261204 coords sing_201 2.htm#SEC20871205 copyTask sing_106 3.htm#SEC11381151 commands (plural) sing_502.htm#IDX290 1152 comment sing_36.htm#IDX108 1153 compareTasks sing_1067.htm#SEC1143 1154 completeReduction sing_1709.htm#SEC1785 1155 complex sing_28.htm#IDX75 1156 complexSingType sing_1533.htm#SEC1609 1157 compregb.lib sing_931.htm#SEC1007 1158 compregb_lib sing_931.htm#SEC1007 1159 comprehensive Groebner system sing_931.htm#IDX409 1160 compress sing_1080.htm#SEC1156 1161 computeConstant sing_1178.htm#SEC1254 1162 computeGromovWitten sing_1181.htm#SEC1257 1163 computeN sing_1479.htm#SEC1555 1164 computeV sing_1478.htm#SEC1554 1165 computemcm sing_1437.htm#SEC1513 1166 concat sing_1081.htm#SEC1157 1167 conductor sing_1509.htm#IDX574 1168 conductor, degree sing_1593.htm#IDX684 1169 cone sing_183.htm#SEC223 1170 cone sing_2141.htm#IDX804 1171 cone sing_2142.htm#IDX806 1172 cone related functions cone related functions sing_186.htm#SEC226 1173 coneLink sing_190.htm#SEC230 1174 coneViaInequalities sing_185.htm#SEC225 1175 coneViaPoints sing_184.htm#SEC224 1176 conic, parametrization, rational point. sing_1414.htm#IDX544 1177 conicWithTangents sing_2074.htm#SEC2150 1178 constructH sing_1438.htm#SEC1514 1179 constructblwup sing_1439.htm#SEC1515 1180 constructlastblwup sing_1440.htm#SEC1516 1181 constructor sing_2158.htm#IDX837 1182 constructor sing_2159.htm#IDX840 1183 contact matrix sing_1508.htm#IDX570 1184 containedQ sing_1788.htm#SEC1864 1185 containsAsFace sing_191.htm#SEC231 1186 containsInCollection containsInCollection sing_223.htm#SEC263 1187 containsInSupport sing_192.htm#SEC232 1188 containsPositiveVector containsPositiveVector sing_193.htm#SEC233 1189 containsRelatively sing_194.htm#SEC234 1190 content sing_1002.htm#SEC1078 1191 contentSB, option sing_364.htm#IDX167 1192 continue Behavior of continue sing_429.htm#SEC469 1193 continue sing_463.htm#SEC503 1194 contraHom sing_809.htm#SEC861 1195 contract sing_272.htm#SEC312 1196 contributors sing_406.htm#IDX194 1197 control sing_1859.htm#SEC1935 1198 control.lib sing_1858.htm#SEC1934 1199 controlDim sing_1860.htm#SEC1936 1200 controlExample sing_1872.htm#SEC1948 1201 control_Matrix sing_1561.htm#SEC1637 1202 control_lib sing_1858.htm#SEC1934 1203 convertdata sing_1435.htm#SEC1511 1204 convex geometry sing_2411.htm#SEC2487 1205 convexHull sing_195.htm#SEC235 1206 convexIntersection sing_196.htm#SEC236 1207 convloc sing_608.htm#SEC660 1208 coordinate change sing_2138.htm#IDX801 1209 coordinate change sing_2139.htm#IDX802 1210 coordinate change sing_2140.htm#IDX803 1211 coordinates sing_2015.htm#IDX726 1212 coords sing_2015.htm#SEC2091 1213 copyTask sing_1066.htm#SEC1142 1206 1214 copyright sing_1.htm#IDX1 1207 corank sing_1517.htm#SEC1592 1208 cornerMonomials sing_1313.htm#SEC1388 1209 countPoints sing_1937.htm#SEC2012 1210 coverings sing_1177.htm#IDX469 1211 coverings sing_1178.htm#IDX473 1212 cpu sing_406.htm#IDX197 1213 cpu sing_406.htm#IDX264 1214 createBO sing_1463.htm#SEC1538 1215 createGradedRingHomomorphism createGradedRingHomomorphism sing_2342.htm#SEC2417 1216 createGroup sing_2335.htm#SEC2410 1217 createQuotientGroup sing_2336.htm#SEC2411 1218 createTask sing_1061.htm#SEC1136 1219 createTorsionFreeGroup createTorsionFreeGroup sing_2337.htm#SEC2412 1220 createlist sing_1445.htm#SEC1520 1221 crypto.lib sing_1910.htm#SEC1985 1222 crypto_lib sing_1910.htm#SEC1985 1223 cup sing_1191.htm#SEC1266 1224 cupproduct sing_1192.htm#SEC1267 1225 curve singularities sing_1496.htm#IDX557 1226 curve singularities sing_1584.htm#IDX679 1227 curvepar.lib sing_1537.htm#SEC1612 1228 curvepar_lib sing_1537.htm#SEC1612 1229 custom assignment Assignments for user defined types sing_182.htm#SEC221 1230 custom command Commands for user defined types sing_181.htm#SEC220 1231 custom type Definition of a user defined type sing_178.htm#SEC217 1232 cycleLength sing_2047.htm#SEC2122 1233 cyclePoints sing_2051.htm#SEC2126 1234 cyclic sing_989.htm#SEC1064 1235 cyclic code Codes and the decoding problem sing_918.htm#SEC976 1236 cyclotomic sing_1671.htm#SEC1746 1237 datetime sing_273.htm#SEC312 1238 dbprint sing_274.htm#SEC313 1239 deRham.lib sing_2397.htm#IDX896 1240 deRhamCohom sing_625.htm#SEC676 1241 deRhamCohomIdeal sing_626.htm#SEC677 1242 deRhamCohomology sing_2398.htm#SEC2473 1243 deRham_lib sing_2397.htm#IDX897 1244 debugLib, option sing_364.htm#IDX172 1245 debug_log sing_1527.htm#SEC1602 1246 debugger Source code debugger sing_66.htm#SEC102 1247 debugging library code Source code debugger sing_66.htm#SEC102 1248 dec1var sing_1244.htm#SEC1319 1249 decimal sing_1911.htm#SEC1986 1250 decode sing_1847.htm#SEC1922 1251 decodeCode sing_1849.htm#SEC1924 1252 decodeRandom sing_1848.htm#SEC1923 1253 decodeRandomFL sing_1852.htm#SEC1927 1254 decodeSV sing_1829.htm#SEC1904 1255 decodegb.lib sing_1834.htm#SEC1909 1256 decodegb_lib sing_1834.htm#SEC1909 1257 decoding, decoding problem Codes and the decoding problem sing_918.htm#SEC977 1258 decoef sing_1877.htm#SEC1952 1259 decone sing_2138.htm#IDX805 1260 decone sing_2139.htm#IDX807 1261 def sing_83.htm#SEC122 1262 def declarations sing_84.htm#SEC123 1263 defRes, option sing_364.htm#IDX173 1264 default argument sing_44.htm#SEC80 1265 defineHomogeneous sing_2375.htm#SEC2450 1266 defined sing_275.htm#SEC314 1267 defl sing_1394.htm#SEC1469 1268 deform sing_1629.htm#SEC1704 1269 deform.lib sing_1548.htm#SEC1623 1270 deform_lib sing_1548.htm#SEC1623 1271 defring sing_1031.htm#SEC1106 1272 defringp sing_1033.htm#SEC1108 1273 defrings sing_1032.htm#SEC1107 1274 deg sing_276.htm#SEC315 1275 degBound sing_443.htm#SEC482 1276 degree Miscellaneous oddities sing_277.htm#SEC316 1277 degree sing_466.htm#IDX281 1278 degree lexicographical ordering sing_893.htm#IDX384 1279 degree of a polynomial Miscellaneous oddities sing_466.htm#IDX285 1280 degree reverse lexicographical ordering sing_893.htm#IDX382 1281 degreeDivisor sing_2236.htm#SEC2311 1282 degreeFormalDivisor sing_2244.htm#SEC2319 1283 degreepart sing_1737.htm#SEC1812 1284 delete sing_278.htm#SEC317 1285 delete sing_325.htm#SEC364 1286 deleteGenerator sing_640.htm#SEC691 1287 deleteSublist sing_939.htm#SEC1014 1288 delta sing_1596.htm#SEC1671 1289 delta invariant sing_1278.htm#IDX504 1290 delta invariant sing_1596.htm#IDX689 1291 delta invariant. sing_1270.htm#IDX497 1292 delta invariant. sing_1271.htm#IDX500 1293 delta invariant. sing_1272.htm#IDX503 1294 deltaLoc sing_1278.htm#SEC1353 1295 denom_list sing_406.htm#IDX199 1296 denominator sing_279.htm#SEC318 1297 depth sing_1193.htm#SEC1268 1298 depthIdeal sing_1254.htm#SEC1329 1299 derivate sing_1703.htm#SEC1778 1300 derivation sing_2152.htm#IDX828 1301 desingularization sing_2286.htm#IDX880 1302 desingularization sing_2287.htm#SEC2362 1303 det sing_280.htm#SEC319 1304 det_B sing_1119.htm#SEC1194 1305 detadj sing_1612.htm#SEC1687 1306 determinacy sing_2396.htm#SEC2471 1307 determinecenter sing_1417.htm#SEC1492 1308 detropicalise sing_2089.htm#SEC2164 1309 develop sing_1586.htm#SEC1661 1310 diag sing_1079.htm#SEC1154 1311 diagInvariants sing_1292.htm#SEC1367 62096 1312 diag_test sing_1115.htm#SEC1190 1313 diff sing_281.htm#SEC320 1314 diffRat sing_838.htm#SEC889 1315 difpoly2tex sing_1878.htm#SEC1953 1316 dim sing_282.htm#SEC321 1317 dim (plural) sing_505.htm#SEC544 1318 dimGradedPart sing_1485.htm#SEC1560 11262 1319 dimH sing_1484.htm#SEC1559 38534 1320 dimMon sing_1234.htm#SEC1309 1321 dim_slocus sing_1630.htm#SEC1705 1322 dimension sing_197.htm#SEC236 1323 dimensionOfLocalization dimensionOfLocalization sing_2274.htm#SEC2349 1324 direct_boolean_poly sing_2107.htm#SEC2182 49893 1325 direct_from_boolean_poly direct_from_boolean_poly sing_2113.htm#SEC2188 36941 1326 disc sing_1898.htm#SEC1973 1327 discr sing_1652.htm#SEC1727 1328 discrepancy sing_1470.htm#SEC1545 1329 disp_zdd sing_2120.htm#SEC2195 41439 1330 displayCohom sing_1486.htm#SEC1561 22633 1331 displayHNE sing_1589.htm#SEC1664 1332 displayInvariants sing_1591.htm#SEC1666 1333 displayMultsequence sing_1593.htm#SEC1668 1334 displayPuiseuxExpansion displayPuiseuxExpansion sing_2064.htm#SEC2139 1335 displayTropicalLifting displayTropicalLifting sing_2062.htm#SEC2137 1336 distributed computing sing_982.htm#IDX429 1337 distributed computing sing_1022.htm#IDX431 1338 distributed computing sing_1060.htm#IDX444 1339 div Miscellaneous oddities sing_76.htm#SEC115 1340 div sing_93.htm#SEC132 1341 div sing_466.htm#IDX278 1342 divideUnits sing_1874.htm#SEC1949 1343 dividelist sing_1444.htm#SEC1519 1344 division sing_283.htm#SEC322 1345 division (plural) sing_506.htm#SEC545 1346 division, pdivi, reduce sing_959.htm#IDX414 1347 division, reduce sing_958.htm#IDX413 1348 divisor sing_1977.htm#SEC2052 1349 divisorplus sing_2230.htm#SEC2305 1350 divisors negativeformaldivisor sing_2229.htm#IDX854 1351 divisors sing_2230.htm#IDX855 1352 divisors sing_2231.htm#IDX856 1353 divisors sing_2232.htm#IDX857 1354 divisors sing_2233.htm#IDX858 1355 divisors sing_2234.htm#IDX859 1356 divisors sing_2235.htm#IDX860 1357 divisors sing_2236.htm#IDX861 1358 divisors sing_2237.htm#IDX862 1359 divisors sing_2238.htm#IDX863 1360 divisors sing_2239.htm#IDX864 1361 divisors sing_2240.htm#IDX865 1362 divisors sing_2241.htm#IDX866 1363 divisors sing_2242.htm#IDX867 1364 divisors sing_2243.htm#IDX868 1365 divisors sing_2244.htm#IDX869 1366 divisors, polyhedra sing_2245.htm#IDX870 1367 divisors, polyhedra sing_2246.htm#IDX871 1368 divisors, polyhedra sing_2247.htm#IDX872 1369 divisors.lib sing_2228.htm#SEC2303 1370 divisors_lib sing_2228.htm#SEC2303 1371 dmod.lib sing_588.htm#SEC639 1372 dmodAction sing_833.htm#SEC884 1373 dmodActionRat sing_834.htm#SEC885 1374 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_826.htm#SEC877 1375 dmod_lib sing_588.htm#SEC639 1376 dmodapp.lib sing_611.htm#SEC662 1377 dmodapp_lib sing_611.htm#SEC662 1378 dmodloc.lib sing_815.htm#IDX366 1379 dmodloc_lib sing_815.htm#IDX367 1380 dmodoublext sing_810.htm#SEC861 1381 dmodvar.lib sing_644.htm#SEC695 1382 dmodvar_lib sing_644.htm#SEC695 1383 double sing_1982.htm#SEC2057 1384 doubleExt sing_801.htm#SEC852 1385 downloading Download instructions sing_2458.htm#SEC2545 1386 dp, global ordering sing_893.htm#IDX383 1387 drawNewtonSubdivision drawNewtonSubdivision sing_2067.htm#SEC2142 1388 drawTropicalCurve sing_2066.htm#SEC2141 1389 ds, local ordering sing_894.htm#IDX393 1390 dsum sing_1080.htm#SEC1155 1391 dualCone sing_198.htm#SEC237 1392 dualConic sing_2091.htm#SEC2166 1393 dualPart sing_2220.htm#SEC2295 1394 dualPolytope sing_240.htm#SEC279 1395 dual_code sing_1831.htm#SEC1906 1396 dump sing_284.htm#SEC323 1397 ecart sing_1985.htm#SEC2060 1398 echo sing_444.htm#SEC483 1399 eexgcdN sing_1912.htm#SEC1987 1400 effective sing_2238.htm#SEC2313 1401 egcdMain sing_1778.htm#SEC1853 1402 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2412.htm#SEC2487 1403 ehrhartRing sing_1288.htm#SEC1363 16966 1404 eigenvals sing_1127.htm#SEC1202 1405 eigenvalue sing_377.htm#SEC416 1406 eigenvalue sing_1127.htm#IDX450 1407 eigenvalues sing_1371.htm#SEC1446 1408 elemSymmId sing_990.htm#SEC1065 1409 elim sing_1164.htm#SEC1239 1410 elim.lib sing_1161.htm#SEC1236 1411 elim1 sing_1165.htm#SEC1240 1412 elim2 sing_1166.htm#SEC1241 1413 elimRing sing_1163.htm#SEC1238 1414 elimWeight sing_758.htm#SEC809 1415 elim_lib sing_1161.htm#SEC1236 1416 eliminate sing_285.htm#SEC324 1417 eliminate (plural) sing_507.htm#SEC546 1418 eliminateNC sing_753.htm#SEC804 1419 elimination sing_752.htm#IDX351 1420 elimlinearpart sing_1738.htm#SEC1813 1421 elimpart sing_1739.htm#SEC1814 1422 elimpartanyr sing_1740.htm#SEC1815 1423 elimrep sing_1425.htm#SEC1500 1424 elliptic curve sing_1174.htm#IDX465 1425 elliptic curves sing_1171.htm#IDX459 1426 elliptic curves sing_1177.htm#IDX468 1427 elliptic curves sing_1178.htm#IDX472 1428 ellipticAdd sing_1933.htm#SEC2008 1429 ellipticAllPoints sing_1938.htm#SEC2013 1430 ellipticMult sing_1934.htm#SEC2009 1431 ellipticNF sing_2054.htm#SEC2129 1432 ellipticNFDB sing_2055.htm#SEC2130 1433 ellipticRandomCurve sing_1935.htm#SEC2010 1434 ellipticRandomPoint sing_1936.htm#SEC2011 1435 ellipticcovers.lib sing_1171.htm#IDX453 1436 ellipticcovers_lib sing_1171.htm#IDX454 1437 else sing_434.htm#SEC473 1438 embedMat sing_784.htm#SEC835 1439 emptyFan sing_224.htm#SEC263 1440 encode sing_1839.htm#SEC1914 1441 endomorphism filtration sing_1570.htm#IDX655 1442 endvfilt sing_1570.htm#SEC1645 1443 engine sing_641.htm#SEC692 1444 envelop sing_967.htm#SEC1042 1445 envelopdg sing_968.htm#SEC1043 1446 envelope sing_508.htm#SEC547 1447 enveloping algebra sing_406.htm#IDX203 1448 enveloping algebra sing_546.htm#IDX295 1215 corank sing_1520.htm#SEC1596 1216 cornerMonomials sing_1316.htm#SEC1392 1217 countPoints sing_1940.htm#SEC2016 1218 coverings sing_1180.htm#IDX469 1219 coverings sing_1181.htm#IDX473 1220 cpu sing_406.htm#IDX196 1221 cpu sing_406.htm#IDX263 1222 createBO sing_1466.htm#SEC1542 1223 createGradedRingHomomorphism createGradedRingHomomorphism sing_2353.htm#SEC2429 1224 createGroup sing_2346.htm#SEC2422 1225 createQuotientGroup sing_2347.htm#SEC2423 1226 createTask sing_1064.htm#SEC1140 1227 createTorsionFreeGroup createTorsionFreeGroup sing_2348.htm#SEC2424 1228 createlist sing_1448.htm#SEC1524 1229 crypto.lib sing_1913.htm#SEC1989 1230 crypto_lib sing_1913.htm#SEC1989 1231 cup sing_1194.htm#SEC1270 1232 cupproduct sing_1195.htm#SEC1271 1233 curve singularities sing_1499.htm#IDX557 1234 curve singularities sing_1587.htm#IDX679 1235 curvepar.lib sing_1540.htm#SEC1616 1236 curvepar_lib sing_1540.htm#SEC1616 1237 custom assignment Assignments for user defined types sing_182.htm#SEC222 1238 custom command Commands for user defined types sing_181.htm#SEC221 1239 custom type Definition of a user defined type sing_178.htm#SEC218 1240 customstd.so sing_2462.htm#SEC2538 1241 cycleLength sing_2050.htm#SEC2126 1242 cyclePoints sing_2054.htm#SEC2130 1243 cyclic sing_989.htm#SEC1065 1244 cyclic code Codes and the decoding problem sing_918.htm#SEC977 1245 cyclotomic sing_1674.htm#SEC1750 1246 datetime sing_273.htm#SEC313 1247 dbprint sing_274.htm#SEC314 1248 deRham.lib sing_2408.htm#IDX896 1249 deRhamCohom sing_625.htm#SEC677 1250 deRhamCohomIdeal sing_626.htm#SEC678 1251 deRhamCohomology sing_2409.htm#SEC2485 1252 deRham_lib sing_2408.htm#IDX897 1253 debugLib, option sing_364.htm#IDX171 1254 debug_log sing_1530.htm#SEC1606 1255 debugger Source code debugger sing_66.htm#SEC103 1256 debugging library code Source code debugger sing_66.htm#SEC103 1257 dec1var sing_1247.htm#SEC1323 1258 decimal sing_1914.htm#SEC1990 1259 decode sing_1850.htm#SEC1926 1260 decodeCode sing_1852.htm#SEC1928 1261 decodeRandom sing_1851.htm#SEC1927 1262 decodeRandomFL sing_1855.htm#SEC1931 1263 decodeSV sing_1832.htm#SEC1908 1264 decodegb.lib sing_1837.htm#SEC1913 1265 decodegb_lib sing_1837.htm#SEC1913 1266 decoding, decoding problem Codes and the decoding problem sing_918.htm#SEC978 1267 decoef sing_1880.htm#SEC1956 1268 decone sing_2141.htm#IDX805 1269 decone sing_2142.htm#IDX807 1270 def sing_83.htm#SEC123 1271 def declarations sing_84.htm#SEC124 1272 defRes, option sing_364.htm#IDX172 1273 default argument sing_44.htm#SEC81 1274 defineHomogeneous sing_2386.htm#SEC2462 1275 defined sing_275.htm#SEC315 1276 defl sing_1397.htm#SEC1473 1277 deform sing_1632.htm#SEC1708 1278 deform.lib sing_1551.htm#SEC1627 1279 deform_lib sing_1551.htm#SEC1627 1280 defring sing_1031.htm#SEC1107 1281 defringp sing_1033.htm#SEC1109 1282 defrings sing_1032.htm#SEC1108 1283 deg sing_276.htm#SEC316 1284 degBound sing_443.htm#SEC483 1285 degree Miscellaneous oddities sing_277.htm#SEC317 1286 degree sing_466.htm#IDX280 1287 degree lexicographical ordering sing_893.htm#IDX383 1288 degree of a polynomial Miscellaneous oddities sing_466.htm#IDX284 1289 degree reverse lexicographical ordering sing_893.htm#IDX381 1290 degreeDivisor sing_2241.htm#SEC2317 1291 degreeFormalDivisor sing_2249.htm#SEC2325 1292 degreepart sing_1740.htm#SEC1816 1293 delete sing_278.htm#SEC318 1294 delete sing_325.htm#SEC365 1295 deleteGenerator sing_640.htm#SEC692 1296 deleteSublist sing_939.htm#SEC1015 1297 delta sing_1599.htm#SEC1675 1298 delta invariant sing_1281.htm#IDX504 1299 delta invariant sing_1599.htm#IDX689 1300 delta invariant. sing_1273.htm#IDX497 1301 delta invariant. sing_1274.htm#IDX500 1302 delta invariant. sing_1275.htm#IDX503 1303 deltaLoc sing_1281.htm#SEC1357 1304 denom_list sing_406.htm#IDX198 1305 denominator sing_279.htm#SEC319 1306 depth sing_1196.htm#SEC1272 1307 depthIdeal sing_1257.htm#SEC1333 1308 derivate sing_1706.htm#SEC1782 1309 derivation sing_2155.htm#IDX828 1310 desingularization sing_2297.htm#IDX880 1311 desingularization sing_2298.htm#SEC2374 1312 det sing_280.htm#SEC320 1313 det_B sing_1122.htm#SEC1198 1314 detadj sing_1615.htm#SEC1691 1315 determinacy sing_2407.htm#SEC2483 1316 determinecenter sing_1420.htm#SEC1496 1317 detropicalise sing_2092.htm#SEC2168 1318 develop sing_1589.htm#SEC1665 1319 diag sing_1082.htm#SEC1158 1320 diagInvariants sing_1295.htm#SEC1371 62096 1321 diag_test sing_1118.htm#SEC1194 1322 diff sing_281.htm#SEC321 1323 diffRat sing_838.htm#SEC890 1324 difpoly2tex sing_1881.htm#SEC1957 1325 dim sing_282.htm#SEC322 1326 dim (plural) sing_505.htm#SEC545 1327 dimGradedPart sing_1488.htm#SEC1564 11262 1328 dimH sing_1487.htm#SEC1563 38534 1329 dimMon sing_1237.htm#SEC1313 1330 dim_slocus sing_1633.htm#SEC1709 1331 dimension sing_197.htm#SEC237 1332 dimensionOfLocalization dimensionOfLocalization sing_2285.htm#SEC2361 1333 direct_boolean_poly sing_2110.htm#SEC2186 49893 1334 direct_from_boolean_poly direct_from_boolean_poly sing_2116.htm#SEC2192 36941 1335 disc sing_1901.htm#SEC1977 1336 discr sing_1655.htm#SEC1731 1337 discrepancy sing_1473.htm#SEC1549 1338 disp_zdd sing_2123.htm#SEC2199 41439 1339 displayCohom sing_1489.htm#SEC1565 22633 1340 displayHNE sing_1592.htm#SEC1668 1341 displayInvariants sing_1594.htm#SEC1670 1342 displayMultsequence sing_1596.htm#SEC1672 1343 displayPuiseuxExpansion displayPuiseuxExpansion sing_2067.htm#SEC2143 1344 displayTropicalLifting displayTropicalLifting sing_2065.htm#SEC2141 1345 distributed computing sing_982.htm#IDX428 1346 distributed computing sing_1022.htm#IDX430 1347 distributed computing sing_1063.htm#IDX443 1348 div Miscellaneous oddities sing_76.htm#SEC116 1349 div sing_93.htm#SEC133 1350 div sing_466.htm#IDX277 1351 divideUnits sing_1877.htm#SEC1953 1352 dividelist sing_1447.htm#SEC1523 1353 division sing_283.htm#SEC323 1354 division (plural) sing_506.htm#SEC546 1355 division, pdivi, reduce sing_959.htm#IDX413 1356 division, reduce sing_958.htm#IDX412 1357 divisor sing_1980.htm#SEC2056 1358 divisorplus sing_2235.htm#SEC2311 1359 divisors negativeformaldivisor sing_2234.htm#IDX854 1360 divisors sing_2235.htm#IDX855 1361 divisors sing_2236.htm#IDX856 1362 divisors sing_2237.htm#IDX857 1363 divisors sing_2238.htm#IDX858 1364 divisors sing_2239.htm#IDX859 1365 divisors sing_2240.htm#IDX860 1366 divisors sing_2241.htm#IDX861 1367 divisors sing_2242.htm#IDX862 1368 divisors sing_2243.htm#IDX863 1369 divisors sing_2244.htm#IDX864 1370 divisors sing_2245.htm#IDX865 1371 divisors sing_2246.htm#IDX866 1372 divisors sing_2247.htm#IDX867 1373 divisors sing_2248.htm#IDX868 1374 divisors sing_2249.htm#IDX869 1375 divisors, polyhedra sing_2250.htm#IDX870 1376 divisors, polyhedra sing_2251.htm#IDX871 1377 divisors, polyhedra sing_2252.htm#IDX872 1378 divisors.lib sing_2233.htm#SEC2309 1379 divisors_lib sing_2233.htm#SEC2309 1380 dmod.lib sing_588.htm#SEC640 1381 dmodAction sing_833.htm#SEC885 1382 dmodActionRat sing_834.htm#SEC886 1383 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_826.htm#SEC878 1384 dmod_lib sing_588.htm#SEC640 1385 dmodapp.lib sing_611.htm#SEC663 1386 dmodapp_lib sing_611.htm#SEC663 1387 dmodloc.lib sing_815.htm#IDX365 1388 dmodloc_lib sing_815.htm#IDX366 1389 dmodoublext sing_810.htm#SEC862 1390 dmodvar.lib sing_644.htm#SEC696 1391 dmodvar_lib sing_644.htm#SEC696 1392 double sing_1985.htm#SEC2061 1393 doubleExt sing_801.htm#SEC853 1394 downloading Download instructions sing_2472.htm#SEC2561 1395 dp, global ordering sing_893.htm#IDX382 1396 drawNewtonSubdivision drawNewtonSubdivision sing_2070.htm#SEC2146 1397 drawTropicalCurve sing_2069.htm#SEC2145 1398 ds, local ordering sing_894.htm#IDX392 1399 dsum sing_1083.htm#SEC1159 1400 dualCone sing_198.htm#SEC238 1401 dualConic sing_2094.htm#SEC2170 1402 dualPart sing_2225.htm#SEC2301 1403 dualPolytope sing_240.htm#SEC280 1404 dual_code sing_1834.htm#SEC1910 1405 dump sing_284.htm#SEC324 1406 ecart sing_1988.htm#SEC2064 1407 echo sing_444.htm#SEC484 1408 eexgcdN sing_1915.htm#SEC1991 1409 effective sing_2243.htm#SEC2319 1410 egcdMain sing_1781.htm#SEC1857 1411 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2423.htm#SEC2499 1412 ehrhartRing sing_1291.htm#SEC1367 16966 1413 eigenvals sing_1130.htm#SEC1206 1414 eigenvalue sing_377.htm#SEC417 1415 eigenvalue sing_1130.htm#IDX449 1416 eigenvalues sing_1374.htm#SEC1450 1417 elemSymmId sing_990.htm#SEC1066 1418 elim sing_1167.htm#SEC1243 1419 elim.lib sing_1164.htm#SEC1240 1420 elim1 sing_1168.htm#SEC1244 1421 elim2 sing_1169.htm#SEC1245 1422 elimRing sing_1166.htm#SEC1242 1423 elimWeight sing_758.htm#SEC810 1424 elim_lib sing_1164.htm#SEC1240 1425 eliminate sing_285.htm#SEC325 1426 eliminate (plural) sing_507.htm#SEC547 1427 eliminateNC sing_753.htm#SEC805 1428 elimination sing_752.htm#IDX350 1429 elimlinearpart sing_1741.htm#SEC1817 1430 elimpart sing_1742.htm#SEC1818 1431 elimpartanyr sing_1743.htm#SEC1819 1432 elimrep sing_1428.htm#SEC1504 1433 elliptic curve sing_1177.htm#IDX465 1434 elliptic curves sing_1174.htm#IDX459 1435 elliptic curves sing_1180.htm#IDX468 1436 elliptic curves sing_1181.htm#IDX472 1437 ellipticAdd sing_1936.htm#SEC2012 1438 ellipticAllPoints sing_1941.htm#SEC2017 1439 ellipticMult sing_1937.htm#SEC2013 1440 ellipticNF sing_2057.htm#SEC2133 1441 ellipticNFDB sing_2058.htm#SEC2134 1442 ellipticRandomCurve sing_1938.htm#SEC2014 1443 ellipticRandomPoint sing_1939.htm#SEC2015 1444 ellipticcovers.lib sing_1174.htm#IDX453 1445 ellipticcovers_lib sing_1174.htm#IDX454 1446 else sing_434.htm#SEC474 1447 embedMat sing_784.htm#SEC836 1448 emptyFan sing_224.htm#SEC264 1449 encode sing_1842.htm#SEC1918 1450 endomorphism filtration sing_1573.htm#IDX655 1451 endvfilt sing_1573.htm#SEC1649 1452 engine sing_641.htm#SEC693 1453 envelop sing_967.htm#SEC1043 1454 envelopdg sing_968.htm#SEC1044 1455 envelope sing_508.htm#SEC548 1456 enveloping algebra sing_406.htm#IDX202 1457 enveloping algebra sing_546.htm#IDX294 1449 1458 environment variable, DISPLAY The online help system sing_16.htm#IDX29 1450 equalJinI sing_151 3.htm#SEC15881451 equalMultiDeg sing_23 68.htm#SEC24431452 equations sing_199.htm#SEC23 81453 equiRadical sing_13 29.htm#SEC14041454 equidim sing_133 1.htm#SEC14061455 equidimMax sing_133 2.htm#SEC14071456 equidimMaxEHV sing_133 3.htm#SEC14081457 equidimZ sing_134 4.htm#SEC14191458 equising.lib sing_155 3.htm#SEC16281459 equising_lib sing_155 3.htm#SEC16281460 equisingular Tjurina number sing_149 6.htm#IDX5621461 equisingularity ideal sing_155 5.htm#IDX5821462 equisingularity stratum sing_155 6.htm#IDX5831459 equalJinI sing_1516.htm#SEC1592 1460 equalMultiDeg sing_2379.htm#SEC2455 1461 equations sing_199.htm#SEC239 1462 equiRadical sing_1332.htm#SEC1408 1463 equidim sing_1334.htm#SEC1410 1464 equidimMax sing_1335.htm#SEC1411 1465 equidimMaxEHV sing_1336.htm#SEC1412 1466 equidimZ sing_1347.htm#SEC1423 1467 equising.lib sing_1556.htm#SEC1632 1468 equising_lib sing_1556.htm#SEC1632 1469 equisingular Tjurina number sing_1499.htm#IDX562 1470 equisingularity ideal sing_1558.htm#IDX582 1471 equisingularity stratum sing_1559.htm#IDX583 1463 1472 error recovery sing_15.htm#SEC21 1464 errorInsert sing_184 2.htm#SEC19171465 errorRand sing_184 3.htm#SEC19181466 errormap sing_22 62.htm#SEC23371467 esIdeal sing_155 5.htm#SEC16301468 esStratum sing_155 6.htm#SEC16311469 essential sing_214 2.htm#IDX8101470 essential sing_214 3.htm#IDX8111471 eta sing_20 49.htm#SEC21241472 euler sing_189 1.htm#SEC19661473 eulerChProj sing_221 0.htm#SEC22851474 eval sing_286.htm#SEC32 51475 evaluateFormalDivisor evaluateFormalDivisor sing_224 0.htm#SEC23151476 evaluatePDivisor sing_22 46.htm#SEC23211477 evaluate_reynolds sing_167 6.htm#SEC17511478 evalutateIntegral sing_117 6.htm#SEC12511479 example sing_288.htm#SEC32 71480 example sing_214 4.htm#IDX8121481 example sing_214 5.htm#IDX8141482 example sing_214 6.htm#IDX8161483 example sing_21 47.htm#IDX8181484 example sing_21 48.htm#IDX8201485 example sing_21 49.htm#IDX8221486 example sing_215 0.htm#IDX8251487 execute sing_289.htm#SEC32 81488 exit sing_438.htm#SEC47 71489 exp2pt sing_18 79.htm#SEC19541490 expo sing_190 3.htm#SEC19781491 exponents sing_215 4.htm#IDX8331492 export sing_431.htm#SEC47 01493 exportNuminvs sing_129 6.htm#SEC1371104231494 exportto sing_432.htm#SEC47 11495 expression list sing_72.htm#IDX12 91496 expression list sing_470.htm#IDX28 81497 ext-module purityfiltration_lib sing_793.htm#IDX35 71498 extcurve sing_182 5.htm#SEC19001499 extdevelop sing_15 87.htm#SEC16621500 extend sing_963.htm#SEC103 81501 extendWeyl sing_827.htm#SEC87 81502 extendedTensor sing_759.htm#SEC81 01503 extendring sing_1034.htm#SEC11 091504 extension of rings sing_13 49.htm#IDX5111505 exterior basis sing_110 6.htm#IDX4471506 exterior power sing_11 08.htm#IDX4491507 exteriorBasis sing_110 6.htm#SEC11811508 exteriorPower sing_11 08.htm#SEC11831509 extgcd sing_290.htm#SEC3 291510 fVector sing_227.htm#SEC26 61511 fVector sing_24 16.htm#SEC24911512 fVectorP(polymake) sing_24 16.htm#SEC24911513 facFirstShift sing_746.htm#SEC79 71514 facFirstWeyl sing_742.htm#SEC79 31515 facGBIdeal sing_131 4.htm#SEC13891516 facShift sing_745.htm#SEC79 61517 facSubWeyl sing_744.htm#SEC79 51518 facWeyl sing_741.htm#SEC79 21519 facetVertexLatticeDistances facetVertexLatticeDistances sing_24 13.htm#SEC24881520 facetWidth sing_24 14.htm#SEC24891521 facetWidths sing_24 15.htm#SEC24901522 facets sing_200.htm#SEC2 391523 facstd sing_291.htm#SEC33 01524 factmodd sing_292.htm#SEC33 11525 factorH sing_954.htm#SEC10 291526 factorLenstraECM sing_194 2.htm#SEC20171527 factorMain sing_17 79.htm#SEC18541528 factorgroup sing_23 58.htm#SEC24331529 factorial sing_940.htm#SEC101 51530 factorization sing_113 6.htm#IDX4511531 factorize sing_293.htm#SEC33 21473 errorInsert sing_1845.htm#SEC1921 1474 errorRand sing_1846.htm#SEC1922 1475 errormap sing_2273.htm#SEC2349 1476 esIdeal sing_1558.htm#SEC1634 1477 esStratum sing_1559.htm#SEC1635 1478 essential sing_2145.htm#IDX810 1479 essential sing_2146.htm#IDX811 1480 eta sing_2052.htm#SEC2128 1481 euler sing_1894.htm#SEC1970 1482 eulerChProj sing_2215.htm#SEC2291 1483 eval sing_286.htm#SEC326 1484 evaluateFormalDivisor evaluateFormalDivisor sing_2245.htm#SEC2321 1485 evaluatePDivisor sing_2251.htm#SEC2327 1486 evaluate_reynolds sing_1679.htm#SEC1755 1487 evalutateIntegral sing_1179.htm#SEC1255 1488 example sing_288.htm#SEC328 1489 example sing_2147.htm#IDX812 1490 example sing_2148.htm#IDX814 1491 example sing_2149.htm#IDX816 1492 example sing_2150.htm#IDX818 1493 example sing_2151.htm#IDX820 1494 example sing_2152.htm#IDX822 1495 example sing_2153.htm#IDX825 1496 execute sing_289.htm#SEC329 1497 exit sing_438.htm#SEC478 1498 exp2pt sing_1882.htm#SEC1958 1499 expo sing_1906.htm#SEC1982 1500 exponents sing_2157.htm#IDX833 1501 export sing_431.htm#SEC471 1502 exportNuminvs sing_1299.htm#SEC1375 10423 1503 exportto sing_432.htm#SEC472 1504 expression list sing_72.htm#IDX128 1505 expression list sing_470.htm#IDX287 1506 ext-module purityfiltration_lib sing_793.htm#IDX356 1507 extcurve sing_1828.htm#SEC1904 1508 extdevelop sing_1590.htm#SEC1666 1509 extend sing_963.htm#SEC1039 1510 extendWeyl sing_827.htm#SEC879 1511 extendedTensor sing_759.htm#SEC811 1512 extendring sing_1034.htm#SEC1110 1513 extension of rings sing_1352.htm#IDX511 1514 exterior basis sing_1109.htm#IDX446 1515 exterior power sing_1111.htm#IDX448 1516 exteriorBasis sing_1109.htm#SEC1185 1517 exteriorPower sing_1111.htm#SEC1187 1518 extgcd sing_290.htm#SEC330 1519 fVector sing_227.htm#SEC267 1520 fVector sing_2427.htm#SEC2503 1521 fVectorP(polymake) sing_2427.htm#SEC2503 1522 facFirstShift sing_746.htm#SEC798 1523 facFirstWeyl sing_742.htm#SEC794 1524 facGBIdeal sing_1317.htm#SEC1393 1525 facShift sing_745.htm#SEC797 1526 facSubWeyl sing_744.htm#SEC796 1527 facWeyl sing_741.htm#SEC793 1528 facetVertexLatticeDistances facetVertexLatticeDistances sing_2424.htm#SEC2500 1529 facetWidth sing_2425.htm#SEC2501 1530 facetWidths sing_2426.htm#SEC2502 1531 facets sing_200.htm#SEC240 1532 facstd sing_291.htm#SEC331 1533 factmodd sing_292.htm#SEC332 1534 factorH sing_954.htm#SEC1030 1535 factorLenstraECM sing_1945.htm#SEC2021 1536 factorMain sing_1782.htm#SEC1858 1537 factorgroup sing_2369.htm#SEC2445 1538 factorial sing_940.htm#SEC1016 1539 factorization sing_1139.htm#IDX450 1540 factorize sing_293.htm#SEC333 1532 1541 factory sing_1.htm#IDX2 1533 fan sing_221.htm#SEC260 1534 fan sing_2038.htm#IDX731 1535 fan related functions fan related functions sing_222.htm#SEC261 1536 fanViaCones sing_225.htm#SEC264 1537 farey sing_294.htm#SEC333 1538 fastExpt sing_1887.htm#SEC1962 1539 fastHC, option sing_364.htm#IDX149 1540 fastelim sing_1741.htm#SEC1816 1541 fetch sing_295.htm#SEC334 1542 fetch (plural) sing_509.htm#SEC548 1543 fetchall sing_1035.htm#SEC1110 1544 ffsolve sing_1730.htm#SEC1805 1545 ffsolve.lib sing_1729.htm#SEC1804 1546 ffsolve_lib sing_1729.htm#SEC1804 1547 fglm sing_296.htm#SEC335 1548 fglm sing_403.htm#IDX183 1549 fglm_solve sing_1757.htm#SEC1832 1550 fglmquot sing_297.htm#SEC336 1551 fibonacci sing_941.htm#SEC1016 1552 field sing_139.htm#SEC178 1553 file, .singularrc sing_20.htm#IDX72 1554 filecmd sing_298.htm#SEC337 1555 filtration purityfiltration_lib sing_793.htm#IDX358 1556 finalCharts sing_1449.htm#SEC1524 1557 find sing_299.htm#SEC338 1558 findAuto sing_701.htm#SEC752 1559 findInvo sing_699.htm#SEC750 1560 findInvoDiag sing_700.htm#SEC751 1561 findOrientedBoundary findOrientedBoundary sing_2050.htm#SEC2125 1562 findTorsion sing_1868.htm#SEC1943 1563 find_first_primitive_root find_first_primitive_root sing_1946.htm#SEC2021 1564 find_index sing_1950.htm#SEC2025 1565 findifs.lib sing_1875.htm#SEC1950 1566 findifs_example sing_1876.htm#SEC1951 1567 findifs_lib sing_1875.htm#SEC1950 1568 findimAlgebra sing_768.htm#SEC819 1569 finduni sing_300.htm#SEC339 1570 findvars sing_1742.htm#SEC1817 1571 finite field sing_139.htm#SEC178 1572 finite field sing_1729.htm#IDX704 1573 finiteDiagInvariants finiteDiagInvariants sing_1291.htm#SEC1366 3508 1574 finitediff.lib sing_2248.htm#IDX873 1575 finitediff_lib sing_2248.htm#IDX874 1576 finitenessTest sing_1150.htm#SEC1225 1577 finvar.lib sing_1664.htm#SEC1739 1578 finvar_lib sing_1664.htm#SEC1739 1579 first index is 1 sing_465.htm#SEC504 1580 firstoct sing_1790.htm#SEC1865 1581 fitting sing_1196.htm#SEC1271 1582 fl2poly sing_638.htm#SEC689 1583 flatten sing_1081.htm#SEC1156 1584 flatteningStrat sing_1197.htm#SEC1272 1585 floating point sing_1044.htm#IDX434 1586 for sing_433.htm#SEC472 1587 formaldivisorplus sing_2241.htm#SEC2316 1588 forward sing_2254.htm#SEC2329 1589 fourier sing_633.htm#SEC684 1590 fouriersystem sing_2265.htm#SEC2340 1591 fpadim.lib sing_649.htm#SEC700 1592 fpadim_lib sing_649.htm#SEC700 1593 fprintf sing_301.htm#SEC340 1594 frandwalk sing_2388.htm#SEC2463 1595 free sing_2153.htm#IDX830 1596 free sing_2154.htm#IDX832 1597 free associative algebra, tensor algebra Free associative algebras sing_540.htm#SEC591 1598 freeGBasis sing_684.htm#SEC735 1599 freegb.lib sing_680.htm#SEC731 1600 freegb_lib sing_680.htm#SEC731 1601 freemodule sing_302.htm#SEC341 1602 freerank sing_992.htm#SEC1067 1603 from_boolean_constant from_boolean_constant sing_2111.htm#SEC2186 44881 1604 from_boolean_ideal sing_2115.htm#SEC2190 62698 1605 from_boolean_poly sing_2112.htm#SEC2187 27864 1606 from_boolean_set sing_2116.htm#SEC2191 60615 1607 frwalk sing_303.htm#SEC342 1608 fullFan sing_226.htm#SEC265 1609 fullSerreRelations sing_695.htm#SEC746 1610 furtherInvar sing_1708.htm#SEC1783 1611 further_hn_proc sing_1604.htm#SEC1679 1612 fwalk sing_1183.htm#SEC1258 1613 galois field sing_139.htm#SEC178 1614 gauss_col sing_1091.htm#SEC1166 1615 gauss_nf sing_1122.htm#SEC1197 1616 gauss_row sing_1092.htm#SEC1167 1617 gaussred sing_1120.htm#SEC1195 1618 gaussred_pivot sing_1121.htm#SEC1196 1619 gcd sing_304.htm#SEC343 1620 gcdMon sing_1223.htm#SEC1298 1621 gcddivisor sing_1978.htm#SEC2053 1622 gen sing_305.htm#SEC344 1623 genMDSMat sing_1845.htm#SEC1920 1624 genSymId sing_1368.htm#SEC1443 1625 general error-locator polynomial sing_919.htm#SEC983 1626 general neron. sing_2286.htm#IDX881 1627 general weighted lexicographical ordering sing_894.htm#IDX399 1628 general weighted reverse lexicographical ordering Local orderings sing_894.htm#IDX396 1629 general.lib sing_934.htm#SEC1009 1630 generalOrder sing_2003.htm#SEC2078 1631 general_lib sing_934.htm#SEC1009 1632 generateG sing_1941.htm#SEC2016 1633 generators sing_1504.htm#IDX566 1634 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_201.htm#SEC240 1635 generatorsOfSpan sing_202.htm#SEC241 1636 genericid sing_1010.htm#SEC1085 1637 genericity sing_1865.htm#SEC1940 1638 genericmat sing_1082.htm#SEC1157 1639 genoutput sing_1438.htm#SEC1513 1640 genus sing_1274.htm#SEC1349 1641 geometric invariant theory sing_2279.htm#IDX878 1642 geometrical locus, locus, loci, dynamic geometry sing_966.htm#IDX418 1643 geometrical locus, locus, loci, envelop sing_967.htm#IDX419 1644 geometrical locus, locus, loci, envelop. sing_968.htm#IDX420 1645 geometrical locus, locus, loci. sing_965.htm#IDX417 1646 geometrical locus, locus, loci. sing_969.htm#IDX421 1647 getArguments sing_1072.htm#SEC1147 1648 getCommand sing_1071.htm#SEC1146 1649 getCone sing_228.htm#SEC267 1650 getGradingGroup sing_2333.htm#SEC2408 1651 getLattice sing_2334.htm#SEC2409 1652 getLinearForms sing_203.htm#SEC242 1653 getModuleGrading sing_2344.htm#SEC2419 1654 getMultiplicity sing_204.htm#SEC243 1655 getOneVar sing_1282.htm#SEC1357 1656 getResult sing_1073.htm#SEC1148 1657 getSmallest sing_1281.htm#SEC1356 1658 getState sing_1074.htm#SEC1149 1659 getVariableWeights sing_2332.htm#SEC2407 1660 getcores sing_1025.htm#SEC1100 1661 getdump sing_306.htm#SEC345 1662 getenv sing_406.htm#IDX205 1542 fan sing_221.htm#SEC261 1543 fan sing_2041.htm#IDX731 1544 fan related functions fan related functions sing_222.htm#SEC262 1545 fanViaCones sing_225.htm#SEC265 1546 farey sing_294.htm#SEC334 1547 fareypoly sing_2254.htm#SEC2330 1548 fastExpt sing_1890.htm#SEC1966 1549 fastHC, option sing_364.htm#IDX148 1550 fastelim sing_1744.htm#SEC1820 1551 fetch sing_295.htm#SEC335 1552 fetch (plural) sing_509.htm#SEC549 1553 fetchall sing_1035.htm#SEC1111 1554 ffmodStd sing_2258.htm#SEC2334 1555 ffmodstd.lib sing_2253.htm#SEC2329 1556 ffmodstd_lib sing_2253.htm#SEC2329 1557 ffsolve sing_1733.htm#SEC1809 1558 ffsolve.lib sing_1732.htm#SEC1808 1559 ffsolve_lib sing_1732.htm#SEC1808 1560 fglm sing_296.htm#SEC336 1561 fglm sing_403.htm#IDX182 1562 fglm_solve sing_1760.htm#SEC1836 1563 fglmquot sing_297.htm#SEC337 1564 fibonacci sing_941.htm#SEC1017 1565 field sing_139.htm#SEC179 1566 file, .singularrc sing_20.htm#IDX71 1567 filecmd sing_298.htm#SEC338 1568 filtration purityfiltration_lib sing_793.htm#IDX357 1569 finalCharts sing_1452.htm#SEC1528 1570 find sing_299.htm#SEC339 1571 findAuto sing_701.htm#SEC753 1572 findInvo sing_699.htm#SEC751 1573 findInvoDiag sing_700.htm#SEC752 1574 findOrientedBoundary findOrientedBoundary sing_2053.htm#SEC2129 1575 findTorsion sing_1871.htm#SEC1947 1576 find_first_primitive_root find_first_primitive_root sing_1949.htm#SEC2025 1577 find_index sing_1953.htm#SEC2029 1578 findifs.lib sing_1878.htm#SEC1954 1579 findifs_example sing_1879.htm#SEC1955 1580 findifs_lib sing_1878.htm#SEC1954 1581 findimAlgebra sing_768.htm#SEC820 1582 finduni sing_300.htm#SEC340 1583 findvars sing_1745.htm#SEC1821 1584 finite field sing_139.htm#SEC179 1585 finite field sing_1732.htm#IDX704 1586 finiteDiagInvariants finiteDiagInvariants sing_1294.htm#SEC1370 3508 1587 finitediff.lib sing_2259.htm#IDX873 1588 finitediff_lib sing_2259.htm#IDX874 1589 finitenessTest sing_1153.htm#SEC1229 1590 finvar.lib sing_1667.htm#SEC1743 1591 finvar_lib sing_1667.htm#SEC1743 1592 first index is 1 sing_465.htm#SEC505 1593 firstoct sing_1793.htm#SEC1869 1594 fitting sing_1199.htm#SEC1275 1595 fl2poly sing_638.htm#SEC690 1596 flatten sing_1084.htm#SEC1160 1597 flatteningStrat sing_1200.htm#SEC1276 1598 floating point sing_1044.htm#IDX433 1599 for sing_433.htm#SEC473 1600 formaldivisorplus sing_2246.htm#SEC2322 1601 forward sing_2265.htm#SEC2341 1602 fourier sing_633.htm#SEC685 1603 fouriersystem sing_2276.htm#SEC2352 1604 fpadim.lib sing_649.htm#SEC701 1605 fpadim_lib sing_649.htm#SEC701 1606 fprintf sing_301.htm#SEC341 1607 frandwalk sing_2399.htm#SEC2475 1608 free sing_2156.htm#IDX830 1609 free sing_2157.htm#IDX832 1610 free associative algebra, tensor algebra Free associative algebras sing_540.htm#SEC592 1611 freeGBasis sing_684.htm#SEC736 1612 freegb.lib sing_680.htm#SEC732 1613 freegb_lib sing_680.htm#SEC732 1614 freemodule sing_302.htm#SEC342 1615 freerank sing_992.htm#SEC1068 1616 from_boolean_constant from_boolean_constant sing_2114.htm#SEC2190 44881 1617 from_boolean_ideal sing_2118.htm#SEC2194 62698 1618 from_boolean_poly sing_2115.htm#SEC2191 27864 1619 from_boolean_set sing_2119.htm#SEC2195 60615 1620 frwalk sing_303.htm#SEC343 1621 fullFan sing_226.htm#SEC266 1622 fullSerreRelations sing_695.htm#SEC747 1623 furtherInvar sing_1711.htm#SEC1787 1624 further_hn_proc sing_1607.htm#SEC1683 1625 fwalk sing_1186.htm#SEC1262 1626 galois field sing_139.htm#SEC179 1627 gauss_col sing_1094.htm#SEC1170 1628 gauss_nf sing_1125.htm#SEC1201 1629 gauss_row sing_1095.htm#SEC1171 1630 gaussred sing_1123.htm#SEC1199 1631 gaussred_pivot sing_1124.htm#SEC1200 1632 gcd sing_304.htm#SEC344 1633 gcdMon sing_1226.htm#SEC1302 1634 gcddivisor sing_1981.htm#SEC2057 1635 gen sing_305.htm#SEC345 1636 genMDSMat sing_1848.htm#SEC1924 1637 genSymId sing_1371.htm#SEC1447 1638 general error-locator polynomial sing_919.htm#SEC984 1639 general neron. sing_2297.htm#IDX881 1640 general weighted lexicographical ordering sing_894.htm#IDX398 1641 general weighted reverse lexicographical ordering Local orderings sing_894.htm#IDX395 1642 general.lib sing_934.htm#SEC1010 1643 generalOrder sing_2006.htm#SEC2082 1644 general_lib sing_934.htm#SEC1010 1645 generateG sing_1944.htm#SEC2020 1646 generators sing_1507.htm#IDX566 1647 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_201.htm#SEC241 1648 generatorsOfSpan sing_202.htm#SEC242 1649 genericid sing_1010.htm#SEC1086 1650 genericity sing_1868.htm#SEC1944 1651 genericmat sing_1085.htm#SEC1161 1652 genoutput sing_1441.htm#SEC1517 1653 genus sing_1277.htm#SEC1353 1654 geometric invariant theory sing_2290.htm#IDX878 1655 geometrical locus, locus, loci, dynamic geometry sing_966.htm#IDX417 1656 geometrical locus, locus, loci, envelop sing_967.htm#IDX418 1657 geometrical locus, locus, loci, envelop. sing_968.htm#IDX419 1658 geometrical locus, locus, loci. sing_965.htm#IDX416 1659 geometrical locus, locus, loci. sing_969.htm#IDX420 1660 getArguments sing_1075.htm#SEC1151 1661 getCommand sing_1074.htm#SEC1150 1662 getCone sing_228.htm#SEC268 1663 getGradingGroup sing_2344.htm#SEC2420 1664 getLattice sing_2345.htm#SEC2421 1665 getLinearForms sing_203.htm#SEC243 1666 getModuleGrading sing_2355.htm#SEC2431 1667 getMultiplicity sing_204.htm#SEC244 1668 getOneVar sing_1285.htm#SEC1361 1669 getResult sing_1076.htm#SEC1152 1670 getSmallest sing_1284.htm#SEC1360 1671 getState sing_1077.htm#SEC1153 1672 getVariableWeights sing_2343.htm#SEC2419 1673 getcores sing_1025.htm#SEC1101 1674 getdump sing_306.htm#SEC346 1675 getenv sing_406.htm#IDX204 1663 1676 gfanlib sing_1.htm#IDX9 1664 gfanlib_so sing_24 01.htm#IDX8981665 gitCone sing_22 81.htm#SEC23561666 gitFan sing_22 82.htm#SEC23571667 gitfan sing_22 79.htm#IDX8761668 gitfan.lib sing_22 79.htm#SEC23541669 gitfan_lib sing_22 79.htm#SEC23541670 gkdim.lib sing_706.htm#SEC75 71671 gkdim_lib sing_706.htm#SEC75 71672 gkzFan sing_22 83.htm#SEC23581673 global Bernstein-Sato polynomial sing_553.htm#IDX30 21674 global Bernstein-Sato polynomial sing_588.htm#IDX3 201675 global Bernstein-Sato polynomial for variety sing_644.htm#IDX34 51676 globalSections sing_22 35.htm#SEC23101677 gmscoeffs sing_156 2.htm#SEC16371678 gmsnf sing_156 1.htm#SEC16361679 gmspoly.lib sing_158 1.htm#SEC16561680 gmspoly_lib sing_158 1.htm#SEC16561681 gmsring sing_156 0.htm#SEC16351682 gmssing.lib sing_15 59.htm#SEC16341683 gmssing_lib sing_15 59.htm#SEC16341684 good basis sing_15 59.htm#IDX5941685 good basis sing_15 69.htm#IDX6491686 good basis sing_158 1.htm#IDX6651687 good basis sing_158 3.htm#IDX6761688 goodBasis sing_158 3.htm#SEC16581689 gorensteinIndex sing_24 17.htm#SEC24921690 gorensteinVector sing_24 18.htm#SEC24931691 graal.lib sing_22 72.htm#SEC23471692 graalMixed sing_22 73.htm#SEC23481693 graal_lib sing_22 72.htm#SEC23471694 gradeNumber sing_797.htm#SEC84 81695 graded Weyl algebra sing_553.htm#IDX30 51696 graded module, graded piece sing_148 5.htm#IDX5521697 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_22 88.htm#IDX8821698 graded modules, handling of Handling graded modules sing_861.htm#SEC91 21699 gradedModules.lib sing_22 88.htm#SEC23631700 gradedModules_lib sing_22 88.htm#SEC23631701 gradiator sing_23 77.htm#SEC24521702 graph sing_117 2.htm#IDX4631703 graph sing_117 3.htm#IDX4641704 graphics.lib sing_179 2.htm#SEC18671705 graphics_lib sing_179 2.htm#SEC18671677 gfanlib_so sing_2412.htm#IDX898 1678 gitCone sing_2292.htm#SEC2368 1679 gitFan sing_2293.htm#SEC2369 1680 gitfan sing_2290.htm#IDX876 1681 gitfan.lib sing_2290.htm#SEC2366 1682 gitfan_lib sing_2290.htm#SEC2366 1683 gkdim.lib sing_706.htm#SEC758 1684 gkdim_lib sing_706.htm#SEC758 1685 gkzFan sing_2294.htm#SEC2370 1686 global Bernstein-Sato polynomial sing_553.htm#IDX301 1687 global Bernstein-Sato polynomial sing_588.htm#IDX319 1688 global Bernstein-Sato polynomial for variety sing_644.htm#IDX344 1689 globalSections sing_2240.htm#SEC2316 1690 gmscoeffs sing_1565.htm#SEC1641 1691 gmsnf sing_1564.htm#SEC1640 1692 gmspoly.lib sing_1584.htm#SEC1660 1693 gmspoly_lib sing_1584.htm#SEC1660 1694 gmsring sing_1563.htm#SEC1639 1695 gmssing.lib sing_1562.htm#SEC1638 1696 gmssing_lib sing_1562.htm#SEC1638 1697 good basis sing_1562.htm#IDX594 1698 good basis sing_1572.htm#IDX649 1699 good basis sing_1584.htm#IDX665 1700 good basis sing_1586.htm#IDX676 1701 goodBasis sing_1586.htm#SEC1662 1702 gorensteinIndex sing_2428.htm#SEC2504 1703 gorensteinVector sing_2429.htm#SEC2505 1704 graal.lib sing_2283.htm#SEC2359 1705 graalMixed sing_2284.htm#SEC2360 1706 graal_lib sing_2283.htm#SEC2359 1707 gradeNumber sing_797.htm#SEC849 1708 graded Weyl algebra sing_553.htm#IDX304 1709 graded module, graded piece sing_1488.htm#IDX552 1710 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2299.htm#IDX882 1711 graded modules, handling of Handling graded modules sing_861.htm#SEC913 1712 gradedModules.lib sing_2299.htm#SEC2375 1713 gradedModules_lib sing_2299.htm#SEC2375 1714 gradiator sing_2388.htm#SEC2464 1715 graph sing_1175.htm#IDX463 1716 graph sing_1176.htm#IDX464 1717 graphics.lib sing_1795.htm#SEC1871 1718 graphics_lib sing_1795.htm#SEC1871 1706 1719 graphviz sing_1.htm#IDX13 1707 graver4ti2 sing_136 6.htm#SEC1441396351708 grconcat sing_23 11.htm#SEC23861709 grdeg sing_2 291.htm#SEC23661710 grgens sing_23 00.htm#SEC23751711 grgroebner sing_23 10.htm#SEC23851712 grlift sing_23 08.htm#SEC23831713 grlifting sing_23 15.htm#SEC23901714 grlifting2 sing_23 16.htm#SEC23911715 grlifting3 sing_23 18.htm#SEC23931716 grneg sing_23 21.htm#SEC23961717 grobcov sing_956.htm#SEC103 11718 grobcov.lib sing_955.htm#SEC103 01719 grobcov_lib sing_955.htm#SEC103 01720 grobj sing_2 289.htm#SEC23641721 groebner sing_307.htm#SEC34 61722 groebner sing_853.htm#SEC90 41723 groebner basis computations sing_307.htm#IDX14 31724 groebnerComplex sing_24 08.htm#SEC24831725 groebnerCone sing_24 04.htm#SEC24791726 groebnerFan sing_24 06.htm#SEC24811727 groebnerFanP sing_204 3.htm#SEC21181728 gromovWitten sing_11 77.htm#SEC12521729 grorder sing_23 02.htm#SEC23771730 ground field sing_139.htm#SEC17 81731 group_reynolds sing_167 2.htm#SEC17471732 grpower sing_2 298.htm#SEC23731733 grpres sing_23 01.htm#SEC23761734 grprod sing_23 09.htm#SEC23841735 grrange sing_23 20.htm#SEC23951736 grres sing_23 07.htm#SEC23821737 grrndmap sing_23 13.htm#SEC23881738 grrndmap2 sing_23 14.htm#SEC23891739 grrndmat sing_23 12.htm#SEC23871740 grshift sing_2 293.htm#SEC23681741 grsum sing_2 297.htm#SEC23721742 grsyz sing_23 06.htm#SEC23811743 grtest sing_2 290.htm#SEC23651744 grtranspose sing_2 299.htm#SEC23741745 grtranspose1 sing_23 03.htm#SEC23781746 grtwist sing_2 295.htm#SEC23701747 grtwists sing_2 296.htm#SEC23711748 grview sing_2 292.htm#SEC23671749 grwalk.lib sing_118 2.htm#SEC12571750 grwalk_lib sing_118 2.htm#SEC12571751 grzero sing_2 294.htm#SEC23691752 gwalk sing_11 88.htm#SEC12631753 hStarVector sing_24 20.htm#SEC24951754 hVector sing_24 21.htm#SEC24961755 h_increasing_knapsack h_increasing_knapsack sing_196 4.htm#SEC20391756 hardware platform sing_406.htm#IDX2 601757 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1049.htm#SEC112 41758 hasCommutativeVars sing_1045.htm#SEC112 01759 hasFieldCoefficient sing_1048.htm#SEC112 31760 hasGlobalOrdering sing_1046.htm#SEC112 11761 hasMixedOrdering sing_1047.htm#SEC112 21762 hasNumericCoeffs sing_1044.htm#SEC11 191763 headStand sing_110 4.htm#SEC11791764 heightZ sing_134 3.htm#SEC14181765 help sing_308.htm#SEC34 71720 graver4ti2 sing_1369.htm#SEC1445 39635 1721 grconcat sing_2322.htm#SEC2398 1722 grdeg sing_2302.htm#SEC2378 1723 grgens sing_2311.htm#SEC2387 1724 grgroebner sing_2321.htm#SEC2397 1725 grlift sing_2319.htm#SEC2395 1726 grlifting sing_2326.htm#SEC2402 1727 grlifting2 sing_2327.htm#SEC2403 1728 grlifting3 sing_2329.htm#SEC2405 1729 grneg sing_2332.htm#SEC2408 1730 grobcov sing_956.htm#SEC1032 1731 grobcov.lib sing_955.htm#SEC1031 1732 grobcov_lib sing_955.htm#SEC1031 1733 grobj sing_2300.htm#SEC2376 1734 groebner sing_307.htm#SEC347 1735 groebner sing_853.htm#SEC905 1736 groebner basis computations sing_307.htm#IDX142 1737 groebnerComplex sing_2419.htm#SEC2495 1738 groebnerCone sing_2415.htm#SEC2491 1739 groebnerFan sing_2417.htm#SEC2493 1740 groebnerFanP sing_2046.htm#SEC2122 1741 gromovWitten sing_1180.htm#SEC1256 1742 grorder sing_2313.htm#SEC2389 1743 ground field sing_139.htm#SEC179 1744 group_reynolds sing_1675.htm#SEC1751 1745 grpower sing_2309.htm#SEC2385 1746 grpres sing_2312.htm#SEC2388 1747 grprod sing_2320.htm#SEC2396 1748 grrange sing_2331.htm#SEC2407 1749 grres sing_2318.htm#SEC2394 1750 grrndmap sing_2324.htm#SEC2400 1751 grrndmap2 sing_2325.htm#SEC2401 1752 grrndmat sing_2323.htm#SEC2399 1753 grshift sing_2304.htm#SEC2380 1754 grsum sing_2308.htm#SEC2384 1755 grsyz sing_2317.htm#SEC2393 1756 grtest sing_2301.htm#SEC2377 1757 grtranspose sing_2310.htm#SEC2386 1758 grtranspose1 sing_2314.htm#SEC2390 1759 grtwist sing_2306.htm#SEC2382 1760 grtwists sing_2307.htm#SEC2383 1761 grview sing_2303.htm#SEC2379 1762 grwalk.lib sing_1185.htm#SEC1261 1763 grwalk_lib sing_1185.htm#SEC1261 1764 grzero sing_2305.htm#SEC2381 1765 gwalk sing_1191.htm#SEC1267 1766 hStarVector sing_2431.htm#SEC2507 1767 hVector sing_2432.htm#SEC2508 1768 h_increasing_knapsack h_increasing_knapsack sing_1967.htm#SEC2043 1769 hardware platform sing_406.htm#IDX259 1770 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1049.htm#SEC1125 1771 hasCommutativeVars sing_1045.htm#SEC1121 1772 hasFieldCoefficient sing_1048.htm#SEC1124 1773 hasGlobalOrdering sing_1046.htm#SEC1122 1774 hasMixedOrdering sing_1047.htm#SEC1123 1775 hasNumericCoeffs sing_1044.htm#SEC1120 1776 headStand sing_1107.htm#SEC1183 1777 heightZ sing_1346.htm#SEC1422 1778 help sing_308.htm#SEC348 1766 1779 help browsers The online help system sing_16.htm#IDX22 1767 1780 help browsers, dummy The online help system sing_16.htm#IDX25 … … 1770 1783 help browsers, html The online help system sing_16.htm#IDX23 1771 1784 help browsers, setting command to use The online help system sing_16.htm#IDX30 1772 help browsers, setting the sing_406.htm#IDX18 91785 help browsers, setting the sing_406.htm#IDX188 1773 1786 help, accessing over the net Command line options sing_19.htm#IDX42 1774 1787 help, online help system The online help system sing_16.htm#SEC22 1775 hermiteNormalForm sing_23 78.htm#SEC24531776 hess.lib sing_23 23.htm#SEC23981777 hess_lib sing_23 23.htm#SEC23981778 hessenberg sing_406.htm#IDX21 11779 hessenberg sing_112 6.htm#SEC12011780 highcorner sing_309.htm#SEC34 81781 hilb sing_310.htm#SEC3 491782 hilbPoly sing_1008.htm#SEC108 31783 hilbert4ti2 sing_136 5.htm#SEC1440139931784 hilbertBasis sing_24 19.htm#SEC24941785 hilbertSeries sing_23 80.htm#SEC24551786 hilbvec sing_174 3.htm#SEC18181787 hnexpansion sing_158 5.htm#SEC16601788 hnoether.lib sing_158 4.htm#SEC16591789 hnoether_lib sing_158 4.htm#SEC16591790 holonomic rank sing_815.htm#IDX36 91791 holonomicRank sing_819.htm#SEC87 01792 hom_kernel sing_120 4.htm#SEC12791793 homog sing_311.htm#SEC35 01794 homogeneitySpace sing_24 03.htm#SEC24781795 homogfacFirstQWeyl sing_748.htm#SEC 7991796 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_750.htm#SEC80 11797 homogfacNthQWeyl sing_747.htm#SEC79 81798 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_749.htm#SEC80 01799 homolog.lib sing_11 89.htm#SEC12641800 homolog_lib sing_11 89.htm#SEC12641801 homology sing_1 199.htm#SEC12741802 howto, download Download instructions sing_24 58.htm#SEC25451803 howto, install on Macintosh Macintosh installation instructions sing_24 61.htm#SEC25481804 howto, install on Unix Unix installation instructions sing_24 59.htm#SEC25461805 howto, install on Windows Windows installation instructions sing_24 60.htm#SEC25471806 hres sing_312.htm#SEC35 11788 hermiteNormalForm sing_2389.htm#SEC2465 1789 hess.lib sing_2334.htm#SEC2410 1790 hess_lib sing_2334.htm#SEC2410 1791 hessenberg sing_406.htm#IDX210 1792 hessenberg sing_1129.htm#SEC1205 1793 highcorner sing_309.htm#SEC349 1794 hilb sing_310.htm#SEC350 1795 hilbPoly sing_1008.htm#SEC1084 1796 hilbert4ti2 sing_1368.htm#SEC1444 13993 1797 hilbertBasis sing_2430.htm#SEC2506 1798 hilbertSeries sing_2391.htm#SEC2467 1799 hilbvec sing_1746.htm#SEC1822 1800 hnexpansion sing_1588.htm#SEC1664 1801 hnoether.lib sing_1587.htm#SEC1663 1802 hnoether_lib sing_1587.htm#SEC1663 1803 holonomic rank sing_815.htm#IDX368 1804 holonomicRank sing_819.htm#SEC871 1805 hom_kernel sing_1207.htm#SEC1283 1806 homog sing_311.htm#SEC351 1807 homogeneitySpace sing_2414.htm#SEC2490 1808 homogfacFirstQWeyl sing_748.htm#SEC800 1809 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_750.htm#SEC802 1810 homogfacNthQWeyl sing_747.htm#SEC799 1811 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_749.htm#SEC801 1812 homolog.lib sing_1192.htm#SEC1268 1813 homolog_lib sing_1192.htm#SEC1268 1814 homology sing_1202.htm#SEC1278 1815 howto, download Download instructions sing_2472.htm#SEC2561 1816 howto, install on Macintosh Macintosh installation instructions sing_2475.htm#SEC2564 1817 howto, install on Unix Unix installation instructions sing_2473.htm#SEC2562 1818 howto, install on Windows Windows installation instructions sing_2474.htm#SEC2563 1819 hres sing_312.htm#SEC352 1807 1820 html, default help The online help system sing_16.htm#IDX24 1808 hyperel.lib sing_197 1.htm#SEC20461809 hyperel_lib sing_197 1.htm#SEC20461810 hyperplane sing_212 3.htm#IDX7701811 hyperplane arrangement sing_588.htm#IDX32 61812 hypersurface singularity sing_161 1.htm#IDX6941813 iMult sing_12 77.htm#SEC13521814 id2mod sing_1004.htm#SEC10 791815 ideal sing_85.htm#SEC12 41816 ideal declarations sing_86.htm#SEC12 51817 ideal declarations (plural) ideal declarations (plural) sing_472.htm#SEC51 11818 ideal expressions sing_87.htm#SEC12 61819 ideal expressions (plural) ideal expressions (plural) sing_473.htm#SEC51 21820 ideal operations sing_88.htm#SEC12 71821 ideal operations (plural) ideal operations (plural) sing_474.htm#SEC51 31822 ideal related functions ideal related functions sing_89.htm#SEC12 81823 ideal related functions (plural) ideal related functions (plural) sing_475.htm#SEC51 41824 ideal, toric sing_906.htm#SEC96 21825 idealSplit sing_175 0.htm#SEC18251826 ideals Miscellaneous oddities sing_466.htm#IDX28 21827 idealsimplify sing_151 2.htm#SEC15871828 identifier Identifier resolution sing_467.htm#SEC50 61829 identifyvar sing_142 0.htm#SEC14951830 if sing_434.htm#SEC47 31831 imageLattice sing_23 46.htm#SEC24211832 image_of_variety sing_170 0.htm#SEC17751833 imap sing_313.htm#SEC35 21834 imap (plural) sing_510.htm#SEC5 491835 imapall sing_1036.htm#SEC111 11836 impart sing_314.htm#SEC35 31837 importfrom sing_435.htm#SEC47 41838 inCenter sing_577.htm#SEC62 81839 inCentralizer sing_578.htm#SEC6 291840 inForm sing_620.htm#SEC67 11841 inSubring sing_114 2.htm#SEC12171842 indSet sing_12 49.htm#SEC13241843 indepSet sing_315.htm#SEC35 41844 indexed names sing_36.htm#IDX8 31845 indexed names sing_37.htm#SEC6 41846 inequalities sing_205.htm#SEC24 41847 infRedTail, option sing_364.htm#IDX1 501821 hyperel.lib sing_1974.htm#SEC2050 1822 hyperel_lib sing_1974.htm#SEC2050 1823 hyperplane sing_2126.htm#IDX770 1824 hyperplane arrangement sing_588.htm#IDX325 1825 hypersurface singularity sing_1614.htm#IDX694 1826 iMult sing_1280.htm#SEC1356 1827 id2mod sing_1004.htm#SEC1080 1828 ideal sing_85.htm#SEC125 1829 ideal declarations sing_86.htm#SEC126 1830 ideal declarations (plural) ideal declarations (plural) sing_472.htm#SEC512 1831 ideal expressions sing_87.htm#SEC127 1832 ideal expressions (plural) ideal expressions (plural) sing_473.htm#SEC513 1833 ideal operations sing_88.htm#SEC128 1834 ideal operations (plural) ideal operations (plural) sing_474.htm#SEC514 1835 ideal related functions ideal related functions sing_89.htm#SEC129 1836 ideal related functions (plural) ideal related functions (plural) sing_475.htm#SEC515 1837 ideal, toric sing_906.htm#SEC963 1838 idealSplit sing_1753.htm#SEC1829 1839 ideals Miscellaneous oddities sing_466.htm#IDX281 1840 idealsimplify sing_1515.htm#SEC1591 1841 identifier Identifier resolution sing_467.htm#SEC507 1842 identifyvar sing_1423.htm#SEC1499 1843 if sing_434.htm#SEC474 1844 imageLattice sing_2357.htm#SEC2433 1845 image_of_variety sing_1703.htm#SEC1779 1846 imap sing_313.htm#SEC353 1847 imap (plural) sing_510.htm#SEC550 1848 imapall sing_1036.htm#SEC1112 1849 impart sing_314.htm#SEC354 1850 importfrom sing_435.htm#SEC475 1851 inCenter sing_577.htm#SEC629 1852 inCentralizer sing_578.htm#SEC630 1853 inForm sing_620.htm#SEC672 1854 inSubring sing_1145.htm#SEC1221 1855 indSet sing_1252.htm#SEC1328 1856 indepSet sing_315.htm#SEC355 1857 indexed names sing_36.htm#IDX82 1858 indexed names sing_37.htm#SEC65 1859 inequalities sing_205.htm#SEC245 1860 infRedTail, option sing_364.htm#IDX149 1848 1861 info The online help system sing_16.htm#SEC23 1849 iniD sing_144 0.htm#SEC15151850 init_debug sing_15 19.htm#SEC15941851 initial sing_24 02.htm#SEC24771852 initial form sing_553.htm#IDX30 71853 initial ideal sing_553.htm#IDX30 61854 initial ideal approach sing_553.htm#IDX3 101855 initial ideal approach sing_644.htm#IDX34 91856 initialForm sing_207 6.htm#SEC21511857 initialIdeal sing_20 77.htm#SEC21521858 initialIdealW sing_619.htm#SEC67 01859 initialMalgrange sing_618.htm#SEC6 691860 injective_knapsack sing_196 5.htm#SEC20401861 inout.lib sing_970.htm#SEC104 51862 inout_lib sing_970.htm#SEC104 51863 input sing_41.htm#SEC7 01864 insert sing_316.htm#SEC35 51865 insertCone sing_229.htm#SEC26 81866 insertGenerator sing_639.htm#SEC69 01867 instructions, Macintosh installation Macintosh installation instructions sing_24 61.htm#SEC25481868 instructions, Unix installation Unix installation instructions sing_24 59.htm#SEC25461869 instructions, Windows installation Windows installation instructions sing_24 60.htm#SEC25471870 instructions, downloading Download instructions sing_24 58.htm#SEC25451871 int sing_90.htm#SEC1 291872 int declarations sing_91.htm#SEC13 01873 int expressions sing_92.htm#SEC13 11874 int operations sing_93.htm#SEC13 21875 int related functions int related functions sing_94.htm#SEC13 31876 intInverse sing_23 55.htm#SEC24301877 intPart sing_19 19.htm#SEC19941878 intRank sing_23 47.htm#SEC24221879 intRoot sing_192 0.htm#SEC19951880 intRoots sing_636.htm#SEC68 71881 intStrategy, option sing_364.htm#IDX15 11882 intclMonIdeal sing_12 89.htm#SEC1364223381883 intclToricRing sing_128 5.htm#SEC1360621431884 integer division Miscellaneous oddities sing_466.htm#IDX27 71885 integer programming sing_914.htm#SEC97 01886 integral basis sing_121 1.htm#IDX4831887 integral basis sing_140 3.htm#IDX5371888 integral closure sing_127 0.htm#IDX4961889 integral closure sing_127 1.htm#IDX4991890 integral closure sing_127 2.htm#IDX5021891 integral closure sing_128 4.htm#IDX5061892 integralBasis sing_121 1.htm#SEC12861893 integralIdeal sing_623.htm#SEC67 41894 integralModule sing_624.htm#SEC67 51895 integralSection sing_23 56.htm#SEC24311896 integralbasis.lib sing_121 0.htm#SEC12851897 integralbasis_lib sing_121 0.htm#SEC12851898 integration of D-module sing_611.htm#IDX33 81862 iniD sing_1443.htm#SEC1519 1863 init_debug sing_1522.htm#SEC1598 1864 initial sing_2413.htm#SEC2489 1865 initial form sing_553.htm#IDX306 1866 initial ideal sing_553.htm#IDX305 1867 initial ideal approach sing_553.htm#IDX309 1868 initial ideal approach sing_644.htm#IDX348 1869 initialForm sing_2079.htm#SEC2155 1870 initialIdeal sing_2080.htm#SEC2156 1871 initialIdealW sing_619.htm#SEC671 1872 initialMalgrange sing_618.htm#SEC670 1873 injective_knapsack sing_1968.htm#SEC2044 1874 inout.lib sing_970.htm#SEC1046 1875 inout_lib sing_970.htm#SEC1046 1876 input sing_41.htm#SEC71 1877 insert sing_316.htm#SEC356 1878 insertCone sing_229.htm#SEC269 1879 insertGenerator sing_639.htm#SEC691 1880 instructions, Macintosh installation Macintosh installation instructions sing_2475.htm#SEC2564 1881 instructions, Unix installation Unix installation instructions sing_2473.htm#SEC2562 1882 instructions, Windows installation Windows installation instructions sing_2474.htm#SEC2563 1883 instructions, downloading Download instructions sing_2472.htm#SEC2561 1884 int sing_90.htm#SEC130 1885 int declarations sing_91.htm#SEC131 1886 int expressions sing_92.htm#SEC132 1887 int operations sing_93.htm#SEC133 1888 int related functions int related functions sing_94.htm#SEC134 1889 intInverse sing_2366.htm#SEC2442 1890 intPart sing_1922.htm#SEC1998 1891 intRank sing_2358.htm#SEC2434 1892 intRoot sing_1923.htm#SEC1999 1893 intRoots sing_636.htm#SEC688 1894 intStrategy, option sing_364.htm#IDX150 1895 intclMonIdeal sing_1292.htm#SEC1368 22338 1896 intclToricRing sing_1288.htm#SEC1364 62143 1897 integer division Miscellaneous oddities sing_466.htm#IDX276 1898 integer programming sing_914.htm#SEC971 1899 integral basis sing_1214.htm#IDX483 1900 integral basis sing_1406.htm#IDX537 1901 integral closure sing_1273.htm#IDX496 1902 integral closure sing_1274.htm#IDX499 1903 integral closure sing_1275.htm#IDX502 1904 integral closure sing_1287.htm#IDX506 1905 integralBasis sing_1214.htm#SEC1290 1906 integralIdeal sing_623.htm#SEC675 1907 integralModule sing_624.htm#SEC676 1908 integralSection sing_2367.htm#SEC2443 1909 integralbasis.lib sing_1213.htm#SEC1289 1910 integralbasis_lib sing_1213.htm#SEC1289 1911 integration of D-module sing_611.htm#IDX337 1899 1912 interface, Emacs Emacs user interface sing_21.htm#SEC28 1900 interiorLatticePoints interiorLatticePoints sing_24 22.htm#SEC24971901 internalfunctions sing_152 0.htm#SEC15951902 interpolate sing_175 6.htm#SEC18311903 interpolation sing_317.htm#SEC35 61904 interred sing_318.htm#SEC35 71905 intersect sing_319.htm#SEC35 81906 intersect (plural) sing_511.htm#SEC55 01907 intersectElim, option sing_364.htm#IDX16 91908 intersectLattices sing_23 52.htm#SEC24271909 intersectMon sing_122 6.htm#SEC13011910 intersectSyz, option sing_364.htm#IDX1 701911 intersectZ sing_134 5.htm#SEC14201912 intersection sing_159 4.htm#SEC16691913 intersection lattice sing_21 59.htm#IDX8451914 intersection lattice sing_216 0.htm#IDX8461915 intersection multiplicity sing_150 5.htm#IDX5721916 intersection multiplicity sing_159 4.htm#IDX6871917 intersectionDiv sing_14 68.htm#SEC15431918 intersectionValRingIdeals intersectionValRingIdeals sing_129 4.htm#SEC1369387731919 intersectionValRings intersectionValRings sing_129 3.htm#SEC1368357611920 intmat sing_97.htm#SEC13 61921 intmat declarations sing_98.htm#SEC13 71922 intmat expressions sing_99.htm#SEC13 81923 intmat operations sing_101.htm#SEC14 01924 intmat related functions intmat related functions sing_102.htm#SEC14 11925 intmat type cast sing_100.htm#SEC1 391926 intmat2mons sing_13 09.htm#SEC1384211501927 intprog.lib sing_121 2.htm#SEC12871928 intprog_lib sing_121 2.htm#SEC12871929 intvec sing_103.htm#SEC14 21930 intvec declarations sing_104.htm#SEC14 31931 intvec expressions sing_105.htm#SEC14 41932 intvec operations sing_106.htm#SEC14 51933 intvec related functions intvec related functions sing_107.htm#SEC14 61934 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_16 69.htm#IDX7001935 invariant ring minimal generating set permutation group invariant_algebra_perm sing_167 0.htm#IDX7011936 invariantRing sing_170 2.htm#SEC17771937 invariant_algebra_perm invariant_algebra_perm sing_167 0.htm#SEC17451938 invariant_algebra_reynolds invariant_algebra_reynolds sing_16 69.htm#SEC17441939 invariant_basis sing_16 77.htm#SEC17521940 invariant_basis_reynolds invariant_basis_reynolds sing_16 78.htm#SEC17531941 invariant_ring sing_166 5.htm#SEC17401942 invariant_ring_random invariant_ring_random sing_166 6.htm#SEC17411943 invariants sing_159 0.htm#SEC16651944 inverse sing_111 0.htm#SEC11851945 inverse of a matrix via its LU-decomposition sing_339.htm#SEC37 81946 inverseFourier sing_634.htm#SEC68 51947 inverse_B sing_111 1.htm#SEC11861948 inverse_L sing_111 2.htm#SEC11871949 inverse_modulus sing_19 48.htm#SEC20231950 invertBirMap sing_140 4.htm#SEC14791951 invertNumberMain sing_178 0.htm#SEC18551952 involut.lib sing_698.htm#SEC7 491953 involut_lib sing_698.htm#SEC7 491954 involution sing_703.htm#SEC75 41955 invunit sing_161 3.htm#SEC16881956 iostruct sing_18 67.htm#SEC19421957 irrRealizationDim sing_20 58.htm#SEC21331958 irred_secondary_char0 irred_secondary_char0 sing_169 1.htm#SEC17661959 irred_secondary_no_molien irred_secondary_no_molien sing_169 4.htm#SEC17691960 irreddecMon sing_123 5.htm#SEC13101961 irreducible power series sing_159 5.htm#IDX6881962 irreducible secondary invariant irred_secondary_char0 sing_169 1.htm#IDX7021963 isAface sing_22 84.htm#SEC23591964 isAntiEndo sing_705.htm#SEC75 61965 isBounded sing_24 23.htm#SEC24981966 isCI sing_261.htm#IDX13 61967 isCI sing_116 0.htm#SEC12351968 isCM sing_261.htm#IDX13 71969 isCM sing_120 0.htm#SEC12751970 isCMcod2 sing_16 48.htm#SEC17231971 isCanonical sing_24 24.htm#SEC24991972 isCartan sing_579.htm#SEC63 01973 isCentral sing_775.htm#SEC82 61974 isCommutative sing_777.htm#SEC82 81975 isCompatible sing_230.htm#SEC2 691976 isCompressed sing_24 25.htm#SEC25001977 isEqualDivisor sing_223 4.htm#SEC23091978 isEquising sing_15 57.htm#SEC16321979 isFlat sing_120 1.htm#SEC12761980 isFsat sing_629.htm#SEC68 01981 isFullSpace sing_206.htm#SEC24 51982 isGorenstein sing_24 26.htm#SEC25011983 isGradedRingHomomorphism isGradedRingHomomorphism sing_23 41.htm#SEC24161984 isGroup sing_23 39.htm#SEC24141985 isGroupHomomorphism sing_23 40.htm#SEC24151986 isHolonomic sing_607.htm#SEC65 81987 isHomg sing_261.htm#IDX13 31988 isHomogeneous sing_23 67.htm#SEC24421989 isInt sing_642.htm#SEC69 31990 isIntegralSurjective isIntegralSurjective sing_23 53.htm#SEC24281991 isInvolution sing_704.htm#SEC75 51992 isLatticeEmpty sing_24 27.htm#SEC25021993 isLocalizationRegular isLocalizationRegular sing_22 76.htm#SEC23511994 isLocallyFree sing_120 2.htm#SEC12771995 isMonomial sing_122 1.htm#SEC12961996 isNC sing_776.htm#SEC82 71997 isNormal sing_24 28.htm#SEC25031998 isOnCurve sing_193 2.htm#SEC20071999 isOrigin sing_207.htm#SEC24 62000 isPositive sing_23 64.htm#SEC24392001 isPrimitiveSublattice isPrimitiveSublattice sing_23 54.htm#SEC24292002 isPure sing_231.htm#SEC27 02003 isPureTensor sing_551.htm#SEC60 22004 isQuotientRing sing_1050.htm#SEC112 52005 isRational sing_610.htm#SEC66 12006 isReflexive sing_24 29.htm#SEC25042007 isReg sing_120 3.htm#SEC12782008 isSB sing_261.htm#IDX13 22009 isSimplicial sing_208.htm#SEC24 72010 isSmooth sing_24 30.htm#SEC25052011 isSubModule sing_1051.htm#SEC112 62012 isSublattice sing_23 45.htm#SEC24202013 isSymmetric sing_13 69.htm#SEC14442014 isTame sing_158 2.htm#SEC16572015 isTerminal sing_24 31.htm#SEC25062016 isTorsionFree sing_23 63.htm#SEC24382017 isTwoSidedGB sing_552.htm#SEC60 32018 isUpperTriangular sing_756.htm#SEC80 72019 isVar sing_696.htm#SEC74 72020 isVeryAmple sing_24 32.htm#SEC25072021 isWeyl sing_778.htm#SEC8 292022 isZeroElement sing_23 65.htm#SEC24402023 is_NND sing_1 598.htm#SEC16732024 is_NP sing_12 58.htm#SEC13332025 is_active sing_163 1.htm#SEC17062026 is_bijective sing_11 47.htm#SEC12222027 is_cenBimodule sing_811.htm#SEC86 22028 is_cenSubbimodule sing_812.htm#SEC86 32029 is_ci sing_163 2.htm#SEC17072030 is_complex sing_108 3.htm#SEC11582031 is_fix_injective sing_19 69.htm#SEC20442032 is_h_injective sing_19 68.htm#SEC20432033 is_injective sing_114 5.htm#SEC12202034 is_irred sing_159 5.htm#SEC16702035 is_is sing_163 3.htm#SEC17082036 is_nested sing_12 59.htm#SEC13342037 is_prime sing_19 49.htm#SEC20242038 is_primitive_root sing_194 5.htm#SEC20202039 is_pure sing_803.htm#SEC85 42040 is_reg sing_163 4.htm#SEC17092041 is_regs sing_163 5.htm#SEC17102042 is_surjective sing_114 6.htm#SEC12212043 is_zero sing_993.htm#SEC106 82044 isartinianMon sing_123 2.htm#SEC13072045 isgenericMon sing_123 3.htm#SEC13082046 ishyper sing_197 2.htm#SEC20472047 isirreducibleMon sing_123 1.htm#SEC13062048 isoncurve sing_197 3.htm#SEC20482049 isparam sing_203 6.htm#SEC21112050 isprimaryMon sing_123 0.htm#SEC13052051 isprimeMon sing_12 29.htm#SEC13042052 isuni sing_202 1.htm#SEC20962053 iv2lp sing_674.htm#SEC72 52054 iv2lpList sing_675.htm#SEC72 62055 iv2lpMat sing_676.htm#SEC72 72056 ivDHilbert sing_650.htm#SEC70 12057 ivDHilbertSickle sing_651.htm#SEC70 22058 ivDimCheck sing_652.htm#SEC70 32059 ivHilbert sing_653.htm#SEC70 42060 ivKDim sing_654.htm#SEC70 52061 ivL2lpI sing_673.htm#SEC72 42062 ivMis2Base sing_655.htm#SEC70 62063 ivMis2Dim sing_656.htm#SEC70 72064 ivOrdMisLex sing_657.htm#SEC70 82065 ivSickle sing_658.htm#SEC7 092066 ivSickleDim sing_660.htm#SEC71 12067 ivSickleHil sing_659.htm#SEC71 02068 jInvariant sing_207 0.htm#SEC21452069 jOft sing_190 4.htm#SEC19792070 jacob sing_320.htm#SEC3 592071 jacoblift sing_161 4.htm#SEC16892072 jacobson sing_187 3.htm#SEC19482073 jacobson.lib sing_187 1.htm#SEC19462074 jacobson_lib sing_187 1.htm#SEC19462075 janet sing_321.htm#SEC36 02076 jet sing_322.htm#SEC36 12077 jordan sing_113 1.htm#SEC12062078 jordanbasis sing_113 2.htm#SEC12072079 jordanmatrix sing_113 3.htm#SEC12082080 jordannf sing_113 4.htm#SEC12092081 jungfib sing_145 3.htm#SEC15282082 jungnormal sing_145 2.htm#SEC15272083 jungresolve sing_145 1.htm#SEC15262084 katsura sing_991.htm#SEC106 62085 kbase sing_323.htm#SEC36 22086 kbase (plural) sing_512.htm#SEC55 12087 keepring sing_436.htm#SEC47 52088 kernel sing_324.htm#SEC36 32089 kernelLattice sing_23 48.htm#SEC24232090 kill sing_325.htm#SEC36 42091 killTask sing_106 2.htm#SEC11372092 killall sing_943.htm#SEC101 82093 killattrib sing_326.htm#SEC36 52094 kmemory sing_942.htm#SEC101 72095 kohom sing_120 5.htm#SEC12802096 kontrahom sing_120 6.htm#SEC12812097 koszul sing_327.htm#SEC36 62098 kskernel.lib sing_160 5.htm#SEC16802099 kskernel_lib sing_160 5.htm#SEC16802100 l-adic numbers sing_32.htm#SEC4 52101 laguerre sing_328.htm#SEC36 72102 laguerre_solve sing_175 2.htm#SEC18272103 lastvarGeneral sing_200 2.htm#SEC20772104 latex.lib sing_179 6.htm#SEC18712105 latex_lib sing_179 6.htm#SEC18712106 lattice sing_216 0.htm#IDX8482107 latticeArea sing_205 2.htm#SEC21272108 latticeBasis sing_23 49.htm#SEC24242109 latticeCodegree sing_24 33.htm#SEC25082110 latticeDegree sing_24 34.htm#SEC25092111 latticePoints sing_24 35.htm#SEC25102112 latticeVolume sing_24 36.htm#SEC25112113 laxfrT sing_22 52.htm#SEC23272114 laxfrX sing_22 53.htm#SEC23282115 lazy, option sing_364.htm#IDX15 22116 lcm sing_994.htm#SEC10 692117 lcmMon sing_122 4.htm#SEC12992118 lcmN sing_191 3.htm#SEC19882119 lcmofall sing_143 3.htm#SEC15082120 lead sing_329.htm#SEC36 82121 leadcoef sing_330.htm#SEC3 692122 leadexp sing_331.htm#SEC37 02123 leadmonom sing_332.htm#SEC37 12124 leadmonomial sing_19 88.htm#SEC20632125 left annihilator ideal sing_588.htm#IDX31 82126 leftInverse sing_186 2.htm#SEC19372127 leftKernel sing_186 0.htm#SEC19352128 length, option sing_364.htm#IDX15 32129 letplaceGBasis sing_682.htm#SEC73 32130 letterplace correspondence Letterplace correspondence sing_542.htm#SEC59 32131 lex_solve sing_17 58.htm#SEC18332132 lexicographical ordering sing_893.htm#IDX37 92133 lib2doc sing_60.htm#SEC9 61913 interiorLatticePoints interiorLatticePoints sing_2433.htm#SEC2509 1914 internalfunctions sing_1523.htm#SEC1599 1915 interpolate sing_1759.htm#SEC1835 1916 interpolation sing_317.htm#SEC357 1917 interred sing_318.htm#SEC358 1918 intersect sing_319.htm#SEC359 1919 intersect (plural) sing_511.htm#SEC551 1920 intersectElim, option sing_364.htm#IDX168 1921 intersectLattices sing_2363.htm#SEC2439 1922 intersectMon sing_1229.htm#SEC1305 1923 intersectSyz, option sing_364.htm#IDX169 1924 intersectZ sing_1348.htm#SEC1424 1925 intersection sing_1597.htm#SEC1673 1926 intersection lattice sing_2162.htm#IDX845 1927 intersection lattice sing_2163.htm#IDX846 1928 intersection multiplicity sing_1508.htm#IDX572 1929 intersection multiplicity sing_1597.htm#IDX687 1930 intersectionDiv sing_1471.htm#SEC1547 1931 intersectionValRingIdeals intersectionValRingIdeals sing_1297.htm#SEC1373 38773 1932 intersectionValRings intersectionValRings sing_1296.htm#SEC1372 35761 1933 intmat sing_97.htm#SEC137 1934 intmat declarations sing_98.htm#SEC138 1935 intmat expressions sing_99.htm#SEC139 1936 intmat operations sing_101.htm#SEC141 1937 intmat related functions intmat related functions sing_102.htm#SEC142 1938 intmat type cast sing_100.htm#SEC140 1939 intmat2mons sing_1312.htm#SEC1388 21150 1940 intprog.lib sing_1215.htm#SEC1291 1941 intprog_lib sing_1215.htm#SEC1291 1942 intvec sing_103.htm#SEC143 1943 intvec declarations sing_104.htm#SEC144 1944 intvec expressions sing_105.htm#SEC145 1945 intvec operations sing_106.htm#SEC146 1946 intvec related functions intvec related functions sing_107.htm#SEC147 1947 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1672.htm#IDX700 1948 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1673.htm#IDX701 1949 invariantRing sing_1705.htm#SEC1781 1950 invariant_algebra_perm invariant_algebra_perm sing_1673.htm#SEC1749 1951 invariant_algebra_reynolds invariant_algebra_reynolds sing_1672.htm#SEC1748 1952 invariant_basis sing_1680.htm#SEC1756 1953 invariant_basis_reynolds invariant_basis_reynolds sing_1681.htm#SEC1757 1954 invariant_ring sing_1668.htm#SEC1744 1955 invariant_ring_random invariant_ring_random sing_1669.htm#SEC1745 1956 invariants sing_1593.htm#SEC1669 1957 inverse sing_1113.htm#SEC1189 1958 inverse of a matrix via its LU-decomposition sing_339.htm#SEC379 1959 inverseFourier sing_634.htm#SEC686 1960 inverse_B sing_1114.htm#SEC1190 1961 inverse_L sing_1115.htm#SEC1191 1962 inverse_modulus sing_1951.htm#SEC2027 1963 invertBirMap sing_1407.htm#SEC1483 1964 invertNumberMain sing_1783.htm#SEC1859 1965 involut.lib sing_698.htm#SEC750 1966 involut_lib sing_698.htm#SEC750 1967 involution sing_703.htm#SEC755 1968 invunit sing_1616.htm#SEC1692 1969 iostruct sing_1870.htm#SEC1946 1970 irrRealizationDim sing_2061.htm#SEC2137 1971 irred_secondary_char0 irred_secondary_char0 sing_1694.htm#SEC1770 1972 irred_secondary_no_molien irred_secondary_no_molien sing_1697.htm#SEC1773 1973 irreddecMon sing_1238.htm#SEC1314 1974 irreducible power series sing_1598.htm#IDX688 1975 irreducible secondary invariant irred_secondary_char0 sing_1694.htm#IDX702 1976 isAface sing_2295.htm#SEC2371 1977 isAntiEndo sing_705.htm#SEC757 1978 isBounded sing_2434.htm#SEC2510 1979 isCI sing_261.htm#IDX135 1980 isCI sing_1163.htm#SEC1239 1981 isCM sing_261.htm#IDX136 1982 isCM sing_1203.htm#SEC1279 1983 isCMcod2 sing_1651.htm#SEC1727 1984 isCanonical sing_2435.htm#SEC2511 1985 isCartan sing_579.htm#SEC631 1986 isCentral sing_775.htm#SEC827 1987 isCommutative sing_777.htm#SEC829 1988 isCompatible sing_230.htm#SEC270 1989 isCompressed sing_2436.htm#SEC2512 1990 isEqualDivisor sing_2239.htm#SEC2315 1991 isEquising sing_1560.htm#SEC1636 1992 isFlat sing_1204.htm#SEC1280 1993 isFsat sing_629.htm#SEC681 1994 isFullSpace sing_206.htm#SEC246 1995 isGorenstein sing_2437.htm#SEC2513 1996 isGradedRingHomomorphism isGradedRingHomomorphism sing_2352.htm#SEC2428 1997 isGroup sing_2350.htm#SEC2426 1998 isGroupHomomorphism sing_2351.htm#SEC2427 1999 isHolonomic sing_607.htm#SEC659 2000 isHomg sing_261.htm#IDX132 2001 isHomogeneous sing_2378.htm#SEC2454 2002 isInt sing_642.htm#SEC694 2003 isIntegralSurjective isIntegralSurjective sing_2364.htm#SEC2440 2004 isInvolution sing_704.htm#SEC756 2005 isLatticeEmpty sing_2438.htm#SEC2514 2006 isLocalizationRegular isLocalizationRegular sing_2287.htm#SEC2363 2007 isLocallyFree sing_1205.htm#SEC1281 2008 isMonomial sing_1224.htm#SEC1300 2009 isNC sing_776.htm#SEC828 2010 isNormal sing_2439.htm#SEC2515 2011 isOnCurve sing_1935.htm#SEC2011 2012 isOrigin sing_207.htm#SEC247 2013 isPositive sing_2375.htm#SEC2451 2014 isPrimitiveSublattice isPrimitiveSublattice sing_2365.htm#SEC2441 2015 isPure sing_231.htm#SEC271 2016 isPureTensor sing_551.htm#SEC603 2017 isQuotientRing sing_1050.htm#SEC1126 2018 isRational sing_610.htm#SEC662 2019 isReflexive sing_2440.htm#SEC2516 2020 isReg sing_1206.htm#SEC1282 2021 isSB sing_261.htm#IDX131 2022 isSimplicial sing_208.htm#SEC248 2023 isSmooth sing_2441.htm#SEC2517 2024 isSubModule sing_1051.htm#SEC1127 2025 isSublattice sing_2356.htm#SEC2432 2026 isSymmetric sing_1372.htm#SEC1448 2027 isTame sing_1585.htm#SEC1661 2028 isTerminal sing_2442.htm#SEC2518 2029 isTorsionFree sing_2374.htm#SEC2450 2030 isTwoSidedGB sing_552.htm#SEC604 2031 isUpperTriangular sing_756.htm#SEC808 2032 isVar sing_696.htm#SEC748 2033 isVeryAmple sing_2443.htm#SEC2519 2034 isWeyl sing_778.htm#SEC830 2035 isZeroElement sing_2376.htm#SEC2452 2036 is_NND sing_1601.htm#SEC1677 2037 is_NP sing_1261.htm#SEC1337 2038 is_active sing_1634.htm#SEC1710 2039 is_bijective sing_1150.htm#SEC1226 2040 is_cenBimodule sing_811.htm#SEC863 2041 is_cenSubbimodule sing_812.htm#SEC864 2042 is_ci sing_1635.htm#SEC1711 2043 is_complex sing_1086.htm#SEC1162 2044 is_fix_injective sing_1972.htm#SEC2048 2045 is_h_injective sing_1971.htm#SEC2047 2046 is_injective sing_1148.htm#SEC1224 2047 is_irred sing_1598.htm#SEC1674 2048 is_is sing_1636.htm#SEC1712 2049 is_nested sing_1262.htm#SEC1338 2050 is_prime sing_1952.htm#SEC2028 2051 is_primitive_root sing_1948.htm#SEC2024 2052 is_pure sing_803.htm#SEC855 2053 is_reg sing_1637.htm#SEC1713 2054 is_regs sing_1638.htm#SEC1714 2055 is_surjective sing_1149.htm#SEC1225 2056 is_zero sing_993.htm#SEC1069 2057 isartinianMon sing_1235.htm#SEC1311 2058 isgenericMon sing_1236.htm#SEC1312 2059 ishyper sing_1975.htm#SEC2051 2060 isirreducibleMon sing_1234.htm#SEC1310 2061 isoncurve sing_1976.htm#SEC2052 2062 isparam sing_2039.htm#SEC2115 2063 isprimaryMon sing_1233.htm#SEC1309 2064 isprimeMon sing_1232.htm#SEC1308 2065 isuni sing_2024.htm#SEC2100 2066 iv2lp sing_674.htm#SEC726 2067 iv2lpList sing_675.htm#SEC727 2068 iv2lpMat sing_676.htm#SEC728 2069 ivDHilbert sing_650.htm#SEC702 2070 ivDHilbertSickle sing_651.htm#SEC703 2071 ivDimCheck sing_652.htm#SEC704 2072 ivHilbert sing_653.htm#SEC705 2073 ivKDim sing_654.htm#SEC706 2074 ivL2lpI sing_673.htm#SEC725 2075 ivMis2Base sing_655.htm#SEC707 2076 ivMis2Dim sing_656.htm#SEC708 2077 ivOrdMisLex sing_657.htm#SEC709 2078 ivSickle sing_658.htm#SEC710 2079 ivSickleDim sing_660.htm#SEC712 2080 ivSickleHil sing_659.htm#SEC711 2081 jInvariant sing_2073.htm#SEC2149 2082 jOft sing_1907.htm#SEC1983 2083 jacob sing_320.htm#SEC360 2084 jacoblift sing_1617.htm#SEC1693 2085 jacobson sing_1876.htm#SEC1952 2086 jacobson.lib sing_1874.htm#SEC1950 2087 jacobson_lib sing_1874.htm#SEC1950 2088 janet sing_321.htm#SEC361 2089 jet sing_322.htm#SEC362 2090 jordan sing_1134.htm#SEC1210 2091 jordanbasis sing_1135.htm#SEC1211 2092 jordanmatrix sing_1136.htm#SEC1212 2093 jordannf sing_1137.htm#SEC1213 2094 jungfib sing_1456.htm#SEC1532 2095 jungnormal sing_1455.htm#SEC1531 2096 jungresolve sing_1454.htm#SEC1530 2097 katsura sing_991.htm#SEC1067 2098 kbase sing_323.htm#SEC363 2099 kbase (plural) sing_512.htm#SEC552 2100 keepring sing_436.htm#SEC476 2101 kernel sing_324.htm#SEC364 2102 kernelLattice sing_2359.htm#SEC2435 2103 kill sing_325.htm#SEC365 2104 killTask sing_1065.htm#SEC1141 2105 killall sing_943.htm#SEC1019 2106 killattrib sing_326.htm#SEC366 2107 kmemory sing_942.htm#SEC1018 2108 kohom sing_1208.htm#SEC1284 2109 kontrahom sing_1209.htm#SEC1285 2110 koszul sing_327.htm#SEC367 2111 kskernel.lib sing_1608.htm#SEC1684 2112 kskernel_lib sing_1608.htm#SEC1684 2113 l-adic numbers sing_32.htm#SEC46 2114 laguerre sing_328.htm#SEC368 2115 laguerre_solve sing_1755.htm#SEC1831 2116 lastvarGeneral sing_2005.htm#SEC2081 2117 latex.lib sing_1799.htm#SEC1875 2118 latex_lib sing_1799.htm#SEC1875 2119 lattice sing_2163.htm#IDX848 2120 latticeArea sing_2055.htm#SEC2131 2121 latticeBasis sing_2360.htm#SEC2436 2122 latticeCodegree sing_2444.htm#SEC2520 2123 latticeDegree sing_2445.htm#SEC2521 2124 latticePoints sing_2446.htm#SEC2522 2125 latticeVolume sing_2447.htm#SEC2523 2126 laxfrT sing_2263.htm#SEC2339 2127 laxfrX sing_2264.htm#SEC2340 2128 lazy, option sing_364.htm#IDX151 2129 lcm sing_994.htm#SEC1070 2130 lcmMon sing_1227.htm#SEC1303 2131 lcmN sing_1916.htm#SEC1992 2132 lcmofall sing_1436.htm#SEC1512 2133 lead sing_329.htm#SEC369 2134 leadcoef sing_330.htm#SEC370 2135 leadexp sing_331.htm#SEC371 2136 leadmonom sing_332.htm#SEC372 2137 leadmonomial sing_1991.htm#SEC2067 2138 left annihilator ideal sing_588.htm#IDX317 2139 leftInverse sing_1865.htm#SEC1941 2140 leftKernel sing_1863.htm#SEC1939 2141 length, option sing_364.htm#IDX152 2142 letplaceGBasis sing_682.htm#SEC734 2143 letterplace correspondence Letterplace correspondence sing_542.htm#SEC594 2144 lex_solve sing_1761.htm#SEC1837 2145 lexicographical ordering sing_893.htm#IDX378 2146 lib2doc sing_60.htm#SEC97 2134 2147 libcdd sing_1.htm#IDX12 2135 2148 libfac sing_1.htm#IDX6 2136 libparse sing_69.htm#SEC10 82137 library sing_210 2.htm#IDX7482138 library sing_22 79.htm#IDX8752139 library, info string sing_55.htm#IDX12 52140 library, polybori.lib sing_210 2.htm#IDX7452141 library, template sing_55.htm#SEC9 12142 library, template.lib sing_55.htm#IDX12 32143 lieBracket sing_693.htm#SEC74 42144 lift sing_334.htm#SEC37 32145 lift sing_546.htm#IDX29 42146 lift (plural) sing_513.htm#SEC55 22147 lift_kbase sing_155 1.htm#SEC16262148 lift_rel_kb sing_155 2.htm#SEC16272149 liftenvelope sing_549.htm#SEC60 02150 liftstd sing_335.htm#SEC37 42151 liftstd (plural) sing_514.htm#SEC55 32152 linReduce sing_561.htm#SEC61 22153 linReduceIdeal sing_562.htm#SEC61 32154 linSyzSolve sing_563.htm#SEC61 42155 linalg.lib sing_11 09.htm#SEC11842156 linalg_lib sing_11 09.htm#SEC11842157 linealityDimension sing_209.htm#SEC24 82158 linealitySpace sing_210.htm#SEC2 492159 linear algebra sing_262.htm#SEC30 12160 linear algebra sing_338.htm#SEC37 72161 linear algebra sing_339.htm#SEC37 82162 linear algebra sing_340.htm#SEC3 792163 linear code, dual sing_183 1.htm#IDX7132164 linear code, systematic sing_183 2.htm#IDX7142165 linear interreduction sing_553.htm#IDX30 92166 linearCombinations sing_582.htm#SEC63 32167 linearMapKernel sing_581.htm#SEC63 22168 linear_relations sing_110 1.htm#SEC11762169 linearlyEquivalent sing_22 37.htm#SEC23122170 linearpart sing_174 4.htm#SEC18192171 link Parallelization with ssi links sing_108.htm#SEC14 72172 link sing_850.htm#SEC90 12173 link declarations sing_109.htm#SEC14 82174 link expressions sing_110.htm#SEC1 492175 link related functions link related functions sing_111.htm#SEC15 02176 list sing_118.htm#SEC15 72177 list declarations sing_119.htm#SEC15 82178 list expressions sing_120.htm#SEC1 592179 list operations sing_121.htm#SEC16 02180 list related functions list related functions sing_122.htm#SEC16 12181 listvar sing_336.htm#SEC37 52182 lll sing_23 81.htm#SEC24562183 load sing_437.htm#SEC47 62184 loadLib, option sing_364.htm#IDX17 42185 loadProc, option sing_364.htm#IDX17 52186 locAtZero sing_12 79.htm#SEC13542187 locNormal sing_121 5.htm#SEC12902188 local methods sing_121 4.htm#IDX4862189 local methods sing_121 5.htm#IDX4892190 local names sing_46.htm#SEC8 22191 local rings, computing in Rings associated to monomial orderings sing_845.htm#SEC89 62192 local weighted lexicographical ordering sing_894.htm#IDX 4002193 local weighted reverse lexicographical ordering Local orderings sing_894.htm#IDX39 72194 localInvar sing_17 07.htm#SEC17822195 localization Rings associated to monomial orderings sing_845.htm#SEC89 62196 localization sing_214 0.htm#IDX8082197 localization of D-module sing_611.htm#IDX33 42198 localization of D-module sing_815.htm#IDX37 22199 locally closed set, constructible set sing_964.htm#IDX41 62200 localstd sing_ 1998.htm#SEC20732201 locnormal.lib sing_121 4.htm#SEC12892202 locnormal_lib sing_121 4.htm#SEC12892203 locstd sing_163 6.htm#SEC17112204 locus sing_965.htm#SEC104 02205 locusdg sing_966.htm#SEC104 12206 locusto sing_969.htm#SEC104 42207 log2 sing_18 88.htm#SEC19632208 logarithmic annihilator ideal sing_588.htm#IDX32 32209 lowerHomogeneitySpace lowerHomogeneitySpace sing_24 07.htm#SEC24822210 lp, global ordering sing_893.htm#IDX37 82211 lp2iv sing_677.htm#SEC72 82212 lp2ivId sing_678.htm#SEC7 292213 lp2lstr sing_689.htm#SEC74 02214 lpDHilbert sing_661.htm#SEC71 22215 lpDHilbertSickle sing_662.htm#SEC71 32216 lpDimCheck sing_664.htm#SEC71 52217 lpHilbert sing_663.htm#SEC71 42218 lpId2ivLi sing_679.htm#SEC73 02219 lpKDim sing_665.htm#SEC71 62220 lpMis2Base sing_666.htm#SEC71 72221 lpMis2Dim sing_667.htm#SEC71 82222 lpMult sing_686.htm#SEC73 72223 lpNF sing_683.htm#SEC73 42224 lpOrdMisLex sing_668.htm#SEC7 192225 lpPower sing_688.htm#SEC7 392226 lpSickle sing_669.htm#SEC72 02227 lpSickleDim sing_671.htm#SEC72 22228 lpSickleHil sing_670.htm#SEC72 12229 lprint sing_972.htm#SEC104 72230 lres sing_337.htm#SEC37 62231 ls, local ordering sing_894.htm#IDX39 12232 lst2str sing_690.htm#SEC74 12233 lsum sing_118 1.htm#SEC12562234 ludecomp sing_338.htm#SEC37 72235 luinverse sing_339.htm#SEC37 82236 lusolve sing_340.htm#SEC3 792237 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_196 0.htm#SEC20352238 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_19 59.htm#SEC20342239 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_19 58.htm#SEC20332240 magnitude sing_188 2.htm#SEC19572241 makeDivisor sing_22 29.htm#SEC23042242 makeFormalDivisor sing_22 39.htm#SEC23142243 makeGraph sing_117 2.htm#SEC12472244 makeHeisenberg sing_766.htm#SEC81 72245 makeLetterplaceRing sing_681.htm#SEC73 22246 makeMalgrange sing_648.htm#SEC 6992247 makeModElimRing sing_783.htm#SEC83 42248 makePDivisor sing_22 45.htm#SEC23202249 makeQsl2 sing_731.htm#SEC78 22250 makeQsl3 sing_732.htm#SEC78 32251 makeQso3 sing_730.htm#SEC78 12252 makeUe6 sing_727.htm#SEC77 82253 makeUe7 sing_728.htm#SEC7 792254 makeUe8 sing_729.htm#SEC78 02255 makeUf4 sing_726.htm#SEC77 72256 makeUg2 sing_725.htm#SEC77 62257 makeUgl sing_711.htm#SEC76 22258 makeUsl sing_710.htm#SEC76 12259 makeUsl2 sing_709.htm#SEC76 02260 makeUso10 sing_717.htm#SEC76 82261 makeUso11 sing_718.htm#SEC7 692262 makeUso12 sing_719.htm#SEC77 02263 makeUso5 sing_712.htm#SEC76 32264 makeUso6 sing_713.htm#SEC76 42265 makeUso7 sing_714.htm#SEC76 52266 makeUso8 sing_715.htm#SEC76 62267 makeUso9 sing_716.htm#SEC76 72268 makeUsp1 sing_720.htm#SEC77 12269 makeUsp2 sing_721.htm#SEC77 22270 makeUsp3 sing_722.htm#SEC77 32271 makeUsp4 sing_723.htm#SEC77 42272 makeUsp5 sing_724.htm#SEC77 52273 makeWeyl sing_765.htm#SEC81 62274 map sing_123.htm#SEC16 22275 map (plural) sing_476.htm#SEC51 52276 map declarations sing_124.htm#SEC16 32277 map declarations (plural) map declarations (plural) sing_477.htm#SEC51 62278 map expressions sing_125.htm#SEC16 42279 map expressions (plural) map expressions (plural) sing_478.htm#SEC51 72280 map operations sing_126.htm#IDX1 302281 map operations (plural) map operations (plural) sing_479.htm#IDX28 92282 map related functions map related functions sing_127.htm#IDX13 12283 map related functions (plural) map related functions (plural) sing_480.htm#IDX2 902284 mapIsFinite sing_11 49.htm#SEC12242285 mapToRatNormCurve sing_14 08.htm#SEC14832286 mapall sing_1037.htm#SEC111 22287 mappingcone sing_23 17.htm#SEC23922288 mappingcone3 sing_23 19.htm#SEC23942289 markov4ti2 sing_136 4.htm#SEC143991632290 mat2arr sing_212 5.htm#SEC22002291 mat2carr sing_212 6.htm#SEC22012292 mat_rk sing_112 3.htm#SEC11982293 matbil sing_20 09.htm#SEC20842294 mathematical objects Representation of mathematical objects sing_889.htm#SEC94 02295 mathinit sing_179 4.htm#SEC18692296 matmult sing_201 0.htm#SEC20852297 matrix sing_128.htm#SEC16 72298 matrix sing_212 5.htm#IDX7762299 matrix sing_212 6.htm#IDX7792300 matrix sing_21 27.htm#IDX7832301 matrix declarations sing_129.htm#SEC16 82302 matrix diagonalization sing_187 1.htm#IDX7242303 matrix expressions sing_130.htm#SEC1 692304 matrix operations sing_132.htm#SEC17 12305 matrix related functions matrix related functions sing_133.htm#SEC17 22306 matrix type cast sing_131.htm#SEC17 02307 matrix.lib sing_107 6.htm#SEC11512308 matrixExp sing_1 398.htm#SEC14732309 matrixLog sing_1 399.htm#SEC14742310 matrixT1 sing_165 0.htm#SEC17252311 matrix_lib sing_107 6.htm#SEC11512312 matrixpres sing_23 22.htm#SEC23972313 matrixsystem sing_22 63.htm#SEC23382314 max sing_341.htm#SEC38 02315 maxEord sing_142 3.htm#SEC14982316 maxIntRoot sing_832.htm#SEC88 32317 maxZeros sing_140 1.htm#SEC14762318 maxabs sing_20 28.htm#SEC21032319 maxcoef sing_995.htm#SEC107 02320 maxdeg sing_996.htm#SEC107 12321 maxdeg1 sing_997.htm#SEC107 22322 maxideal sing_342.htm#SEC38 12323 maximalFace sing_24 37.htm#SEC25122324 maximalGroebnerCone sing_24 05.htm#SEC24802325 maximalValue sing_24 38.htm#SEC25132326 maximum sing_190 1.htm#SEC19762327 maximum number of zeroes sing_140 1.htm#IDX5312328 mdouble sing_56.htm#SEC9 22329 mem, option sing_364.htm#IDX17 62330 membershipMon sing_122 5.htm#SEC13002331 memory sing_343.htm#SEC38 22332 memory managment sing_343.htm#SEC38 22333 merkle_hellman_decryption merkle_hellman_decryption sing_196 2.htm#SEC20372334 merkle_hellman_encryption merkle_hellman_encryption sing_196 1.htm#SEC20362335 midpoint sing_22 59.htm#SEC23342336 milnor sing_16 37.htm#SEC17122337 milnorcode sing_152 1.htm#SEC15962338 milnornumber sing_2 395.htm#SEC24702339 min sing_344.htm#SEC38 32340 minAssChar sing_132 3.htm#SEC13982341 minAssCharE sing_132 4.htm#SEC13992342 minAssGTZ sing_132 1.htm#SEC13962343 minAssGTZE sing_132 2.htm#SEC13972344 minAssZ sing_134 1.htm#SEC14162345 minEcart sing_199 1.htm#SEC20662346 minIntRoot sing_609.htm#SEC66 02347 minIntRoot2 sing_831.htm#SEC88 22348 minMult sing_115 6.htm#SEC12312349 minbase sing_345.htm#SEC38 42350 minbaseMon sing_122 2.htm#SEC12972351 mindeg sing_998.htm#SEC107 32352 mindeg1 sing_999.htm#SEC107 42353 mindist sing_184 6.htm#SEC19212354 minimal display time, setting the sing_406.htm#IDX27 32355 minimalFace sing_24 39.htm#SEC25142356 minimalValue sing_24 40.htm#SEC25152357 minipoly sing_11 28.htm#SEC12032358 minkowskiSum sing_24 41.htm#SEC25162359 minor sing_346.htm#SEC38 52360 minpoly sing_445.htm#SEC48 42361 minres sing_347.htm#SEC38 62362 minres (plural) sing_515.htm#SEC55 42363 mirror symmetry sing_117 1.htm#IDX4562364 mixed Hodge structure sing_15 59.htm#IDX5872365 mixed Hodge structure sing_156 5.htm#IDX6152366 mixed Hodge structure sing_156 6.htm#IDX6212367 mixed Hodge structure sing_15 67.htm#IDX6292368 mixed Hodge structure sing_15 68.htm#IDX6352369 mixed Hodge structure sing_15 69.htm#IDX6432370 mixed Hodge structure sing_157 0.htm#IDX6532371 mixed Hodge structure sing_158 1.htm#IDX6592372 mixed Hodge structure sing_158 3.htm#IDX6702373 mod sing_76.htm#SEC11 52374 mod sing_93.htm#SEC13 22375 mod sing_142.htm#SEC18 12376 mod2id sing_1003.htm#SEC107 82377 mod2str sing_691.htm#SEC74 22378 modDec sing_124 1.htm#SEC13162379 modNPos sing_126 4.htm#SEC13392380 modNormal sing_12 17.htm#SEC12922381 modNpos_test sing_126 2.htm#SEC13372382 modStd sing_12 19.htm#SEC12942383 modWalk sing_23 26.htm#SEC24012384 mod_versal sing_155 0.htm#SEC16252385 modality sing_15 29.htm#SEC16042386 modfWalk sing_23 28.htm#SEC24032387 modfrWalk sing_23 29.htm#SEC24042388 modnormal.lib sing_121 6.htm#SEC12912389 modnormal_lib sing_121 6.htm#SEC12912390 modrWalk sing_23 27.htm#SEC24022391 modregCM sing_12 68.htm#SEC13432392 modsatiety sing_126 6.htm#SEC13412393 modstd.lib sing_12 18.htm#SEC12932394 modstd_lib sing_12 18.htm#SEC12932395 modular sing_981.htm#SEC105 62396 modular methods sing_121 4.htm#IDX4872397 modular methods sing_121 6.htm#IDX4922398 modular methods. sing_121 5.htm#IDX4902399 modular techniques. sing_12 17.htm#IDX4942400 modular.lib sing_980.htm#SEC105 52401 modular_lib sing_980.htm#SEC105 52402 modular_lib sing_980.htm#IDX42 22403 module sing_134.htm#SEC17 32404 module (plural) sing_481.htm#SEC52 02405 module declarations sing_135.htm#SEC17 42406 module declarations (plural) module declarations (plural) sing_482.htm#SEC52 12407 module expressions sing_136.htm#SEC17 52408 module expressions (plural) module expressions (plural) sing_483.htm#SEC52 22409 module operations sing_137.htm#SEC17 62410 module operations (plural) module operations (plural) sing_484.htm#SEC52 32411 module ordering C sing_895.htm#IDX40 32412 module ordering c sing_895.htm#IDX40 52413 module related functions module related functions sing_138.htm#SEC17 72414 module related functions (plural) module related functions (plural) sing_485.htm#SEC52 42415 module_containment sing_114 1.htm#SEC12162416 modulo sing_348.htm#SEC38 72417 modulo (plural) sing_516.htm#SEC55 52418 moduloSlim sing_773.htm#SEC82 42419 modwalk.lib sing_23 25.htm#IDX8832420 modwalk_lib sing_23 25.htm#IDX8842421 moebius sing_216 1.htm#SEC22362422 moebius function sing_216 1.htm#IDX8492423 molien sing_167 3.htm#SEC17482424 mondromy.lib sing_161 1.htm#SEC16862425 mondromy_lib sing_161 1.htm#SEC16862426 monitor sing_349.htm#SEC38 82427 monodromy sing_15 59.htm#IDX5912428 monodromy sing_156 4.htm#SEC16392429 monodromy sing_156 4.htm#IDX6112430 monodromy sing_15 69.htm#IDX6462431 monodromy sing_158 1.htm#IDX6622432 monodromy sing_158 3.htm#IDX6732433 monodromyB sing_161 5.htm#SEC16902434 monomial sing_350.htm#SEC3 892435 monomial ordering sing_1046.htm#IDX43 62436 monomial orderings General definitions for orderings sing_845.htm#SEC89 62437 monomial orderings sing_892.htm#SEC94 32438 monomial orderings introduction Introduction to orderings sing_891.htm#SEC94 22439 monomialInIdeal sing_829.htm#SEC88 02440 monomialLcm sing_19 89.htm#SEC20642441 monomialideal.lib sing_122 0.htm#SEC12952442 monomialideal_lib sing_122 0.htm#SEC12952443 monomials and precedence Miscellaneous oddities sing_466.htm#IDX27 92444 mons2intmat sing_13 08.htm#SEC1383155552445 morsesplit sing_152 2.htm#SEC15972446 mp_res_mat sing_175 5.htm#SEC18302447 mplot sing_179 5.htm#SEC18702448 mpresmat sing_351.htm#SEC39 02449 mprimdec.lib sing_12 37.htm#SEC13122450 mprimdec_lib sing_12 37.htm#SEC13122451 mregular.lib sing_125 2.htm#SEC13272452 mregular_lib sing_125 2.htm#SEC13272453 mres sing_352.htm#SEC39 12454 mres (plural) sing_517.htm#SEC55 62455 mstd sing_353.htm#SEC39 22456 msum sing_58.htm#SEC9 42457 mtriple sing_57.htm#SEC9 32458 mult Miscellaneous oddities sing_354.htm#SEC39 32459 mult sing_466.htm#IDX2 802460 multBound sing_446.htm#SEC48 52461 multRat sing_837.htm#SEC88 82462 multarr2arr sing_215 6.htm#SEC22312463 multarrMultRestrict sing_21 58.htm#SEC22332464 multarrRestrict sing_21 57.htm#SEC22322465 multcol sing_109 5.htm#SEC11702466 multdivisor sing_223 1.htm#SEC23062467 multformaldivisor sing_224 3.htm#SEC23182468 multi sing_197 6.htm#SEC20512469 multi indices sing_37.htm#SEC6 42470 multiDeg sing_23 60.htm#SEC24352471 multiDegBasis sing_23 61.htm#SEC24362472 multiDegGroebner sing_23 69.htm#SEC24442473 multiDegModulo sing_23 71.htm#SEC24462474 multiDegPartition sing_23 62.htm#SEC24372475 multiDegResolution sing_23 72.htm#SEC24472476 multiDegSyzygy sing_23 70.htm#SEC24452477 multiDegTensor sing_23 73.htm#SEC24482478 multiDegTor sing_23 74.htm#SEC24492479 multiarrangement sing_215 2.htm#IDX8292480 multiarrangement sing_215 3.htm#IDX8312481 multiarrangement sing_215 4.htm#IDX8342482 multiarrangement sing_215 5.htm#IDX8352483 multiarrangement sing_215 6.htm#IDX8382484 multiarrangement sing_21 57.htm#IDX8412485 multiarrangement sing_21 58.htm#IDX8432486 multidimensional_knapsack multidimensional_knapsack sing_195 4.htm#SEC20292487 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_23 30.htm#IDX8872488 multigrading.lib sing_23 30.htm#IDX8852489 multigrading_lib sing_23 30.htm#IDX8862490 multiplicities, sequence of sing_159 0.htm#IDX6852491 multiplicity sequence sing_150 3.htm#IDX5642492 multiplicity sequence sing_150 6.htm#IDX5762493 multiplicity sequence sing_159 2.htm#IDX6862494 multiplylist sing_144 3.htm#SEC15182495 multivariate equations sing_17 29.htm#IDX7032496 multrow sing_109 6.htm#SEC11712497 multseq2charexp sing_150 2.htm#SEC15772498 multsequence sing_159 2.htm#SEC16672499 nBoundaryLatticePoints nBoundaryLatticePoints sing_24 42.htm#SEC25172500 nHilbertBasis sing_24 43.htm#SEC25182501 nInteriorLatticePoints nInteriorLatticePoints sing_24 44.htm#SEC25192502 nLatticePoints sing_24 45.htm#SEC25202503 naccache_stern_decryption naccache_stern_decryption sing_19 57.htm#SEC20322504 naccache_stern_encryption naccache_stern_encryption sing_195 6.htm#SEC20312505 naccache_stern_generation naccache_stern_generation sing_195 5.htm#SEC20302506 nameof sing_355.htm#SEC39 42507 names sing_356.htm#SEC39 52508 nashmult sing_151 0.htm#SEC15852509 nblocks sing_406.htm#IDX21 52510 ncExt_R sing_806.htm#SEC85 72511 ncHom sing_807.htm#SEC85 82512 ncRelations sing_774.htm#SEC82 52513 nc_algebra sing_518.htm#SEC55 72514 ncalg.lib sing_708.htm#SEC7 592515 ncalg_lib sing_708.htm#SEC7 592516 ncalgebra sing_519.htm#SEC55 82517 ncdecomp.lib sing_735.htm#SEC78 62518 ncdecomp_lib sing_735.htm#SEC78 62519 ncdetection sing_702.htm#SEC75 32520 ncfactor.lib sing_740.htm#SEC79 12521 ncfactor_lib sing_740.htm#SEC79 12522 nchomolog.lib sing_805.htm#IDX36 22523 nchomolog_lib sing_805.htm#IDX36 32524 ncols sing_357.htm#SEC39 62525 ncones sing_233.htm#SEC27 22526 ncpreim.lib sing_752.htm#SEC80 32527 ncpreim_lib sing_752.htm#SEC80 32528 nctools.lib sing_760.htm#SEC81 12529 nctools_lib sing_760.htm#SEC81 12530 ndcond sing_763.htm#SEC81 42531 negatedCone sing_211.htm#SEC25 02532 negative degree lexicographical ordering sing_894.htm#IDX39 42533 negative degree reverse lexicographical ordering Local orderings sing_894.htm#IDX39 22534 negative lexicographical ordering sing_894.htm#IDX3 902535 negativedivisor sing_223 2.htm#SEC23072536 negativeformaldivisor negativeformaldivisor sing_224 2.htm#SEC23172149 libparse sing_69.htm#SEC109 2150 library sing_2105.htm#IDX748 2151 library sing_2290.htm#IDX875 2152 library, info string sing_55.htm#IDX124 2153 library, polybori.lib sing_2105.htm#IDX745 2154 library, template sing_55.htm#SEC92 2155 library, template.lib sing_55.htm#IDX122 2156 lieBracket sing_693.htm#SEC745 2157 lift sing_334.htm#SEC374 2158 lift sing_546.htm#IDX293 2159 lift (plural) sing_513.htm#SEC553 2160 lift_kbase sing_1554.htm#SEC1630 2161 lift_rel_kb sing_1555.htm#SEC1631 2162 liftenvelope sing_549.htm#SEC601 2163 liftstd sing_335.htm#SEC375 2164 liftstd (plural) sing_514.htm#SEC554 2165 linReduce sing_561.htm#SEC613 2166 linReduceIdeal sing_562.htm#SEC614 2167 linSyzSolve sing_563.htm#SEC615 2168 linalg.lib sing_1112.htm#SEC1188 2169 linalg_lib sing_1112.htm#SEC1188 2170 linealityDimension sing_209.htm#SEC249 2171 linealitySpace sing_210.htm#SEC250 2172 linear algebra sing_262.htm#SEC302 2173 linear algebra sing_338.htm#SEC378 2174 linear algebra sing_339.htm#SEC379 2175 linear algebra sing_340.htm#SEC380 2176 linear code, dual sing_1834.htm#IDX713 2177 linear code, systematic sing_1835.htm#IDX714 2178 linear interreduction sing_553.htm#IDX308 2179 linearCombinations sing_582.htm#SEC634 2180 linearMapKernel sing_581.htm#SEC633 2181 linear_relations sing_1104.htm#SEC1180 2182 linearlyEquivalent sing_2242.htm#SEC2318 2183 linearpart sing_1747.htm#SEC1823 2184 link Parallelization with ssi links sing_108.htm#SEC148 2185 link sing_850.htm#SEC902 2186 link declarations sing_109.htm#SEC149 2187 link expressions sing_110.htm#SEC150 2188 link related functions link related functions sing_111.htm#SEC151 2189 list sing_118.htm#SEC158 2190 list declarations sing_119.htm#SEC159 2191 list expressions sing_120.htm#SEC160 2192 list operations sing_121.htm#SEC161 2193 list related functions list related functions sing_122.htm#SEC162 2194 listvar sing_336.htm#SEC376 2195 lll sing_2392.htm#SEC2468 2196 load sing_437.htm#SEC477 2197 loadLib, option sing_364.htm#IDX173 2198 loadProc, option sing_364.htm#IDX174 2199 locAtZero sing_1282.htm#SEC1358 2200 locNormal sing_1218.htm#SEC1294 2201 local methods sing_1217.htm#IDX486 2202 local methods sing_1218.htm#IDX489 2203 local names sing_46.htm#SEC83 2204 local rings, computing in Rings associated to monomial orderings sing_845.htm#SEC897 2205 local weighted lexicographical ordering sing_894.htm#IDX399 2206 local weighted reverse lexicographical ordering Local orderings sing_894.htm#IDX396 2207 localInvar sing_1710.htm#SEC1786 2208 localization Rings associated to monomial orderings sing_845.htm#SEC897 2209 localization sing_2143.htm#IDX808 2210 localization of D-module sing_611.htm#IDX333 2211 localization of D-module sing_815.htm#IDX371 2212 locally closed set, constructible set sing_964.htm#IDX415 2213 localstd sing_2001.htm#SEC2077 2214 locnormal.lib sing_1217.htm#SEC1293 2215 locnormal_lib sing_1217.htm#SEC1293 2216 locstd sing_1639.htm#SEC1715 2217 locus sing_965.htm#SEC1041 2218 locusdg sing_966.htm#SEC1042 2219 locusto sing_969.htm#SEC1045 2220 log2 sing_1891.htm#SEC1967 2221 logarithmic annihilator ideal sing_588.htm#IDX322 2222 lowerHomogeneitySpace lowerHomogeneitySpace sing_2418.htm#SEC2494 2223 lp, global ordering sing_893.htm#IDX377 2224 lp2iv sing_677.htm#SEC729 2225 lp2ivId sing_678.htm#SEC730 2226 lp2lstr sing_689.htm#SEC741 2227 lpDHilbert sing_661.htm#SEC713 2228 lpDHilbertSickle sing_662.htm#SEC714 2229 lpDimCheck sing_664.htm#SEC716 2230 lpHilbert sing_663.htm#SEC715 2231 lpId2ivLi sing_679.htm#SEC731 2232 lpKDim sing_665.htm#SEC717 2233 lpMis2Base sing_666.htm#SEC718 2234 lpMis2Dim sing_667.htm#SEC719 2235 lpMult sing_686.htm#SEC738 2236 lpNF sing_683.htm#SEC735 2237 lpOrdMisLex sing_668.htm#SEC720 2238 lpPower sing_688.htm#SEC740 2239 lpSickle sing_669.htm#SEC721 2240 lpSickleDim sing_671.htm#SEC723 2241 lpSickleHil sing_670.htm#SEC722 2242 lprint sing_972.htm#SEC1048 2243 lres sing_337.htm#SEC377 2244 ls, local ordering sing_894.htm#IDX390 2245 lst2str sing_690.htm#SEC742 2246 lsum sing_1184.htm#SEC1260 2247 ludecomp sing_338.htm#SEC378 2248 luinverse sing_339.htm#SEC379 2249 lusolve sing_340.htm#SEC380 2250 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1963.htm#SEC2039 2251 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1962.htm#SEC2038 2252 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1961.htm#SEC2037 2253 magnitude sing_1885.htm#SEC1961 2254 makeDivisor sing_2234.htm#SEC2310 2255 makeFormalDivisor sing_2244.htm#SEC2320 2256 makeGraph sing_1175.htm#SEC1251 2257 makeHeisenberg sing_766.htm#SEC818 2258 makeLetterplaceRing sing_681.htm#SEC733 2259 makeMalgrange sing_648.htm#SEC700 2260 makeModElimRing sing_783.htm#SEC835 2261 makePDivisor sing_2250.htm#SEC2326 2262 makeQsl2 sing_731.htm#SEC783 2263 makeQsl3 sing_732.htm#SEC784 2264 makeQso3 sing_730.htm#SEC782 2265 makeUe6 sing_727.htm#SEC779 2266 makeUe7 sing_728.htm#SEC780 2267 makeUe8 sing_729.htm#SEC781 2268 makeUf4 sing_726.htm#SEC778 2269 makeUg2 sing_725.htm#SEC777 2270 makeUgl sing_711.htm#SEC763 2271 makeUsl sing_710.htm#SEC762 2272 makeUsl2 sing_709.htm#SEC761 2273 makeUso10 sing_717.htm#SEC769 2274 makeUso11 sing_718.htm#SEC770 2275 makeUso12 sing_719.htm#SEC771 2276 makeUso5 sing_712.htm#SEC764 2277 makeUso6 sing_713.htm#SEC765 2278 makeUso7 sing_714.htm#SEC766 2279 makeUso8 sing_715.htm#SEC767 2280 makeUso9 sing_716.htm#SEC768 2281 makeUsp1 sing_720.htm#SEC772 2282 makeUsp2 sing_721.htm#SEC773 2283 makeUsp3 sing_722.htm#SEC774 2284 makeUsp4 sing_723.htm#SEC775 2285 makeUsp5 sing_724.htm#SEC776 2286 makeWeyl sing_765.htm#SEC817 2287 map sing_123.htm#SEC163 2288 map (plural) sing_476.htm#SEC516 2289 map declarations sing_124.htm#SEC164 2290 map declarations (plural) map declarations (plural) sing_477.htm#SEC517 2291 map expressions sing_125.htm#SEC165 2292 map expressions (plural) map expressions (plural) sing_478.htm#SEC518 2293 map operations sing_126.htm#IDX129 2294 map operations (plural) map operations (plural) sing_479.htm#IDX288 2295 map related functions map related functions sing_127.htm#IDX130 2296 map related functions (plural) map related functions (plural) sing_480.htm#IDX289 2297 mapIsFinite sing_1152.htm#SEC1228 2298 mapToRatNormCurve sing_1411.htm#SEC1487 2299 mapall sing_1037.htm#SEC1113 2300 mappingcone sing_2328.htm#SEC2404 2301 mappingcone3 sing_2330.htm#SEC2406 2302 markov4ti2 sing_1367.htm#SEC1443 9163 2303 mat2arr sing_2128.htm#SEC2204 2304 mat2carr sing_2129.htm#SEC2205 2305 mat_rk sing_1126.htm#SEC1202 2306 matbil sing_2012.htm#SEC2088 2307 mathematical objects Representation of mathematical objects sing_889.htm#SEC941 2308 mathinit sing_1797.htm#SEC1873 2309 matmult sing_2013.htm#SEC2089 2310 matrix sing_128.htm#SEC168 2311 matrix sing_2128.htm#IDX776 2312 matrix sing_2129.htm#IDX779 2313 matrix sing_2130.htm#IDX783 2314 matrix declarations sing_129.htm#SEC169 2315 matrix diagonalization sing_1874.htm#IDX724 2316 matrix expressions sing_130.htm#SEC170 2317 matrix operations sing_132.htm#SEC172 2318 matrix related functions matrix related functions sing_133.htm#SEC173 2319 matrix type cast sing_131.htm#SEC171 2320 matrix.lib sing_1079.htm#SEC1155 2321 matrixExp sing_1401.htm#SEC1477 2322 matrixLog sing_1402.htm#SEC1478 2323 matrixT1 sing_1653.htm#SEC1729 2324 matrix_lib sing_1079.htm#SEC1155 2325 matrixpres sing_2333.htm#SEC2409 2326 matrixsystem sing_2274.htm#SEC2350 2327 max sing_341.htm#SEC381 2328 maxEord sing_1426.htm#SEC1502 2329 maxIntRoot sing_832.htm#SEC884 2330 maxZeros sing_1404.htm#SEC1480 2331 maxabs sing_2031.htm#SEC2107 2332 maxcoef sing_995.htm#SEC1071 2333 maxdeg sing_996.htm#SEC1072 2334 maxdeg1 sing_997.htm#SEC1073 2335 maxideal sing_342.htm#SEC382 2336 maximalFace sing_2448.htm#SEC2524 2337 maximalGroebnerCone sing_2416.htm#SEC2492 2338 maximalValue sing_2449.htm#SEC2525 2339 maximum sing_1904.htm#SEC1980 2340 maximum number of zeroes sing_1404.htm#IDX531 2341 mdouble sing_56.htm#SEC93 2342 mem, option sing_364.htm#IDX175 2343 membershipMon sing_1228.htm#SEC1304 2344 memory sing_343.htm#SEC383 2345 memory managment sing_343.htm#SEC383 2346 merkle_hellman_decryption merkle_hellman_decryption sing_1965.htm#SEC2041 2347 merkle_hellman_encryption merkle_hellman_encryption sing_1964.htm#SEC2040 2348 midpoint sing_2270.htm#SEC2346 2349 milnor sing_1640.htm#SEC1716 2350 milnorcode sing_1524.htm#SEC1600 2351 milnornumber sing_2406.htm#SEC2482 2352 min sing_344.htm#SEC384 2353 minAssChar sing_1326.htm#SEC1402 2354 minAssCharE sing_1327.htm#SEC1403 2355 minAssGTZ sing_1324.htm#SEC1400 2356 minAssGTZE sing_1325.htm#SEC1401 2357 minAssZ sing_1344.htm#SEC1420 2358 minEcart sing_1994.htm#SEC2070 2359 minIntRoot sing_609.htm#SEC661 2360 minIntRoot2 sing_831.htm#SEC883 2361 minMult sing_1159.htm#SEC1235 2362 minbase sing_345.htm#SEC385 2363 minbaseMon sing_1225.htm#SEC1301 2364 mindeg sing_998.htm#SEC1074 2365 mindeg1 sing_999.htm#SEC1075 2366 mindist sing_1849.htm#SEC1925 2367 minimal display time, setting the sing_406.htm#IDX272 2368 minimalFace sing_2450.htm#SEC2526 2369 minimalValue sing_2451.htm#SEC2527 2370 minipoly sing_1131.htm#SEC1207 2371 minkowskiSum sing_2452.htm#SEC2528 2372 minor sing_346.htm#SEC386 2373 minpoly sing_445.htm#SEC485 2374 minres sing_347.htm#SEC387 2375 minres (plural) sing_515.htm#SEC555 2376 mirror symmetry sing_1174.htm#IDX456 2377 mixed Hodge structure sing_1562.htm#IDX587 2378 mixed Hodge structure sing_1568.htm#IDX615 2379 mixed Hodge structure sing_1569.htm#IDX621 2380 mixed Hodge structure sing_1570.htm#IDX629 2381 mixed Hodge structure sing_1571.htm#IDX635 2382 mixed Hodge structure sing_1572.htm#IDX643 2383 mixed Hodge structure sing_1573.htm#IDX653 2384 mixed Hodge structure sing_1584.htm#IDX659 2385 mixed Hodge structure sing_1586.htm#IDX670 2386 mod sing_76.htm#SEC116 2387 mod sing_93.htm#SEC133 2388 mod sing_142.htm#SEC182 2389 mod2id sing_1003.htm#SEC1079 2390 mod2str sing_691.htm#SEC743 2391 modDec sing_1244.htm#SEC1320 2392 modNPos sing_1267.htm#SEC1343 2393 modNormal sing_1220.htm#SEC1296 2394 modNpos_test sing_1265.htm#SEC1341 2395 modStd sing_1222.htm#SEC1298 2396 modWalk sing_2337.htm#SEC2413 2397 mod_versal sing_1553.htm#SEC1629 2398 modality sing_1532.htm#SEC1608 2399 modfWalk sing_2339.htm#SEC2415 2400 modfrWalk sing_2340.htm#SEC2416 2401 modnormal.lib sing_1219.htm#SEC1295 2402 modnormal_lib sing_1219.htm#SEC1295 2403 modrWalk sing_2338.htm#SEC2414 2404 modregCM sing_1271.htm#SEC1347 2405 modsatiety sing_1269.htm#SEC1345 2406 modstd.lib sing_1221.htm#SEC1297 2407 modstd_lib sing_1221.htm#SEC1297 2408 modular sing_981.htm#SEC1057 2409 modular methods sing_1217.htm#IDX487 2410 modular methods sing_1219.htm#IDX492 2411 modular methods. sing_1218.htm#IDX490 2412 modular techniques. sing_1220.htm#IDX494 2413 modular.lib sing_980.htm#SEC1056 2414 modular_lib sing_980.htm#SEC1056 2415 modular_lib sing_980.htm#IDX421 2416 module sing_134.htm#SEC174 2417 module (plural) sing_481.htm#SEC521 2418 module declarations sing_135.htm#SEC175 2419 module declarations (plural) module declarations (plural) sing_482.htm#SEC522 2420 module expressions sing_136.htm#SEC176 2421 module expressions (plural) module expressions (plural) sing_483.htm#SEC523 2422 module operations sing_137.htm#SEC177 2423 module operations (plural) module operations (plural) sing_484.htm#SEC524 2424 module ordering C sing_895.htm#IDX402 2425 module ordering c sing_895.htm#IDX404 2426 module related functions module related functions sing_138.htm#SEC178 2427 module related functions (plural) module related functions (plural) sing_485.htm#SEC525 2428 module_containment sing_1144.htm#SEC1220 2429 modulo sing_348.htm#SEC388 2430 modulo (plural) sing_516.htm#SEC556 2431 moduloSlim sing_773.htm#SEC825 2432 modwalk.lib sing_2336.htm#IDX883 2433 modwalk_lib sing_2336.htm#IDX884 2434 moebius sing_2164.htm#SEC2240 2435 moebius function sing_2164.htm#IDX849 2436 molien sing_1676.htm#SEC1752 2437 mondromy.lib sing_1614.htm#SEC1690 2438 mondromy_lib sing_1614.htm#SEC1690 2439 monitor sing_349.htm#SEC389 2440 monodromy sing_1562.htm#IDX591 2441 monodromy sing_1567.htm#SEC1643 2442 monodromy sing_1567.htm#IDX611 2443 monodromy sing_1572.htm#IDX646 2444 monodromy sing_1584.htm#IDX662 2445 monodromy sing_1586.htm#IDX673 2446 monodromyB sing_1618.htm#SEC1694 2447 monomial sing_350.htm#SEC390 2448 monomial ordering sing_1046.htm#IDX435 2449 monomial orderings General definitions for orderings sing_845.htm#SEC897 2450 monomial orderings sing_892.htm#SEC944 2451 monomial orderings introduction Introduction to orderings sing_891.htm#SEC943 2452 monomialInIdeal sing_829.htm#SEC881 2453 monomialLcm sing_1992.htm#SEC2068 2454 monomialideal.lib sing_1223.htm#SEC1299 2455 monomialideal_lib sing_1223.htm#SEC1299 2456 monomials and precedence Miscellaneous oddities sing_466.htm#IDX278 2457 mons2intmat sing_1311.htm#SEC1387 15555 2458 morsesplit sing_1525.htm#SEC1601 2459 mp_res_mat sing_1758.htm#SEC1834 2460 mplot sing_1798.htm#SEC1874 2461 mpresmat sing_351.htm#SEC391 2462 mprimdec.lib sing_1240.htm#SEC1316 2463 mprimdec_lib sing_1240.htm#SEC1316 2464 mregular.lib sing_1255.htm#SEC1331 2465 mregular_lib sing_1255.htm#SEC1331 2466 mres sing_352.htm#SEC392 2467 mres (plural) sing_517.htm#SEC557 2468 mstd sing_353.htm#SEC393 2469 msum sing_58.htm#SEC95 2470 mtriple sing_57.htm#SEC94 2471 mult Miscellaneous oddities sing_354.htm#SEC394 2472 mult sing_466.htm#IDX279 2473 multBound sing_446.htm#SEC486 2474 multRat sing_837.htm#SEC889 2475 multarr2arr sing_2159.htm#SEC2235 2476 multarrMultRestrict sing_2161.htm#SEC2237 2477 multarrRestrict sing_2160.htm#SEC2236 2478 multcol sing_1098.htm#SEC1174 2479 multdivisor sing_2236.htm#SEC2312 2480 multformaldivisor sing_2248.htm#SEC2324 2481 multi sing_1979.htm#SEC2055 2482 multi indices sing_37.htm#SEC65 2483 multiDeg sing_2371.htm#SEC2447 2484 multiDegBasis sing_2372.htm#SEC2448 2485 multiDegGroebner sing_2380.htm#SEC2456 2486 multiDegModulo sing_2382.htm#SEC2458 2487 multiDegPartition sing_2373.htm#SEC2449 2488 multiDegResolution sing_2383.htm#SEC2459 2489 multiDegSyzygy sing_2381.htm#SEC2457 2490 multiDegTensor sing_2384.htm#SEC2460 2491 multiDegTor sing_2385.htm#SEC2461 2492 multiarrangement sing_2155.htm#IDX829 2493 multiarrangement sing_2156.htm#IDX831 2494 multiarrangement sing_2157.htm#IDX834 2495 multiarrangement sing_2158.htm#IDX835 2496 multiarrangement sing_2159.htm#IDX838 2497 multiarrangement sing_2160.htm#IDX841 2498 multiarrangement sing_2161.htm#IDX843 2499 multidimensional_knapsack multidimensional_knapsack sing_1957.htm#SEC2033 2500 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2341.htm#IDX887 2501 multigrading.lib sing_2341.htm#IDX885 2502 multigrading_lib sing_2341.htm#IDX886 2503 multiplicities, sequence of sing_1593.htm#IDX685 2504 multiplicity sequence sing_1506.htm#IDX564 2505 multiplicity sequence sing_1509.htm#IDX576 2506 multiplicity sequence sing_1595.htm#IDX686 2507 multiplylist sing_1446.htm#SEC1522 2508 multivariate equations sing_1732.htm#IDX703 2509 multrow sing_1099.htm#SEC1175 2510 multseq2charexp sing_1505.htm#SEC1581 2511 multsequence sing_1595.htm#SEC1671 2512 nBoundaryLatticePoints nBoundaryLatticePoints sing_2453.htm#SEC2529 2513 nHilbertBasis sing_2454.htm#SEC2530 2514 nInteriorLatticePoints nInteriorLatticePoints sing_2455.htm#SEC2531 2515 nLatticePoints sing_2456.htm#SEC2532 2516 naccache_stern_decryption naccache_stern_decryption sing_1960.htm#SEC2036 2517 naccache_stern_encryption naccache_stern_encryption sing_1959.htm#SEC2035 2518 naccache_stern_generation naccache_stern_generation sing_1958.htm#SEC2034 2519 nameof sing_355.htm#SEC395 2520 names sing_356.htm#SEC396 2521 nashmult sing_1513.htm#SEC1589 2522 nblocks sing_406.htm#IDX214 2523 ncExt_R sing_806.htm#SEC858 2524 ncHom sing_807.htm#SEC859 2525 ncRelations sing_774.htm#SEC826 2526 nc_algebra sing_518.htm#SEC558 2527 ncalg.lib sing_708.htm#SEC760 2528 ncalg_lib sing_708.htm#SEC760 2529 ncalgebra sing_519.htm#SEC559 2530 ncdecomp.lib sing_735.htm#SEC787 2531 ncdecomp_lib sing_735.htm#SEC787 2532 ncdetection sing_702.htm#SEC754 2533 ncfactor.lib sing_740.htm#SEC792 2534 ncfactor_lib sing_740.htm#SEC792 2535 nchomolog.lib sing_805.htm#IDX361 2536 nchomolog_lib sing_805.htm#IDX362 2537 ncols sing_357.htm#SEC397 2538 ncones sing_233.htm#SEC273 2539 ncpreim.lib sing_752.htm#SEC804 2540 ncpreim_lib sing_752.htm#SEC804 2541 nctools.lib sing_760.htm#SEC812 2542 nctools_lib sing_760.htm#SEC812 2543 ndcond sing_763.htm#SEC815 2544 negatedCone sing_211.htm#SEC251 2545 negative degree lexicographical ordering sing_894.htm#IDX393 2546 negative degree reverse lexicographical ordering Local orderings sing_894.htm#IDX391 2547 negative lexicographical ordering sing_894.htm#IDX389 2548 negativedivisor sing_2237.htm#SEC2313 2549 negativeformaldivisor negativeformaldivisor sing_2247.htm#SEC2323 2537 2550 net access Command line options sing_19.htm#IDX40 2538 newTest sing_189 6.htm#SEC19712539 newline sing_166.htm#SEC20 52540 news sing_24 51.htm#SEC25262541 newstruct sing_177.htm#SEC21 62542 newstruct sing_210 2.htm#IDX7502543 newtonDiag sing_1007.htm#SEC108 22544 newtonPolytope sing_241.htm#SEC28 02545 newtonPolytopeLP sing_204 1.htm#SEC21162546 newtonPolytopeP sing_204 0.htm#SEC21152547 newtonpoly sing_1 597.htm#SEC16722548 nf_icis sing_16 38.htm#SEC17132549 nfmodStd sing_23 84.htm#SEC24592550 nfmodstd.lib sing_23 82.htm#SEC24572551 nfmodstd_lib sing_23 82.htm#SEC24572552 nilpotent Lie algebras sing_139 6.htm#IDX5162553 nmaxcones sing_232.htm#SEC27 12554 noether sing_447.htm#SEC48 62555 noether.lib sing_126 0.htm#SEC13352556 noetherNormal sing_11 48.htm#SEC12232557 noether_lib sing_126 0.htm#SEC13352558 non-english special characters sing_455.htm#IDX27 52559 nonMonomials sing_131 2.htm#SEC13872560 nonZeroEntry sing_115 1.htm#SEC12262561 none, option sing_364.htm#IDX14 62562 norTest sing_128 0.htm#SEC13552563 norm sing_197 5.htm#SEC20502564 normal sing_127 0.htm#SEC13452565 normal.lib sing_12 69.htm#SEC13442566 normalC sing_127 2.htm#SEC13472567 normalFan sing_24 46.htm#SEC25212568 normalFanL sing_204 2.htm#SEC21172569 normalForm sing_223 3.htm#SEC23082570 normalI sing_135 6.htm#SEC14312571 normalP sing_127 1.htm#SEC13462572 normalToricRing sing_128 6.htm#SEC1361296382573 normalToricRingFromBinomials normalToricRingFromBinomials sing_12 87.htm#SEC136223012574 normal_lib sing_12 69.htm#SEC13442575 normalform sing_152 6.htm#SEC16012551 newTest sing_1899.htm#SEC1975 2552 newline sing_166.htm#SEC206 2553 news sing_2465.htm#SEC2541 2554 newstruct sing_177.htm#SEC217 2555 newstruct sing_2105.htm#IDX750 2556 newtonDiag sing_1007.htm#SEC1083 2557 newtonPolytope sing_241.htm#SEC281 2558 newtonPolytopeLP sing_2044.htm#SEC2120 2559 newtonPolytopeP sing_2043.htm#SEC2119 2560 newtonpoly sing_1600.htm#SEC1676 2561 nf_icis sing_1641.htm#SEC1717 2562 nfmodStd sing_2395.htm#SEC2471 2563 nfmodstd.lib sing_2393.htm#SEC2469 2564 nfmodstd_lib sing_2393.htm#SEC2469 2565 nilpotent Lie algebras sing_1399.htm#IDX516 2566 nmaxcones sing_232.htm#SEC272 2567 noether sing_447.htm#SEC487 2568 noether.lib sing_1263.htm#SEC1339 2569 noetherNormal sing_1151.htm#SEC1227 2570 noether_lib sing_1263.htm#SEC1339 2571 non-english special characters sing_455.htm#IDX274 2572 nonMonomials sing_1315.htm#SEC1391 2573 nonZeroEntry sing_1154.htm#SEC1230 2574 none, option sing_364.htm#IDX145 2575 norTest sing_1283.htm#SEC1359 2576 norm sing_1978.htm#SEC2054 2577 normal sing_1273.htm#SEC1349 2578 normal.lib sing_1272.htm#SEC1348 2579 normalC sing_1275.htm#SEC1351 2580 normalFan sing_2457.htm#SEC2533 2581 normalFanL sing_2045.htm#SEC2121 2582 normalForm sing_2238.htm#SEC2314 2583 normalI sing_1359.htm#SEC1435 2584 normalP sing_1274.htm#SEC1350 2585 normalToricRing sing_1289.htm#SEC1365 29638 2586 normalToricRingFromBinomials normalToricRingFromBinomials sing_1290.htm#SEC1366 2301 2587 normal_lib sing_1272.htm#SEC1348 2588 normalform sing_1529.htm#SEC1605 2576 2589 normaliz sing_1.htm#IDX14 18426 2577 normaliz sing_1 299.htm#SEC13742578 normaliz.lib sing_128 4.htm#SEC13592579 normaliz_lib sing_128 4.htm#SEC13592580 normalization sing_121 4.htm#IDX4852581 normalization sing_121 5.htm#IDX4882582 normalization sing_121 6.htm#IDX4912583 normalization sing_12 17.htm#IDX4932584 normalization sing_127 0.htm#IDX4952585 normalization sing_127 1.htm#IDX4982586 normalization sing_127 2.htm#IDX5012587 normalization sing_128 4.htm#IDX5072588 normalization. sing_121 1.htm#IDX4842589 normalization. sing_140 3.htm#IDX5382590 normalize sing_1000.htm#SEC107 52591 not sing_96.htm#SEC13 52592 notBuckets, option sing_364.htm#IDX15 62593 notRegularity, option sing_364.htm#IDX15 42594 notSugar, option sing_364.htm#IDX15 52595 notWarnSB, option sing_364.htm#IDX17 72596 npar sing_188 1.htm#SEC19562597 npars sing_358.htm#SEC39 72598 nrRootsDeterm sing_200 6.htm#SEC20812599 nrRootsProbab sing_200 5.htm#SEC20802600 nres sing_359.htm#SEC39 82601 nres (plural) sing_520.htm#SEC5 592602 nrows sing_360.htm#SEC 3992603 nrroots sing_203 5.htm#SEC21102604 nsatiety sing_126 5.htm#SEC13402605 nselect sing_11 67.htm#SEC12422606 nt_solve sing_177 0.htm#SEC18452607 ntsolve.lib sing_17 69.htm#SEC18442608 ntsolve_lib sing_17 69.htm#SEC18442609 number sing_139.htm#SEC17 82610 number sing_21 29.htm#IDX7892611 number declarations sing_140.htm#SEC1 792612 number expressions sing_141.htm#SEC18 02613 number operations sing_142.htm#SEC18 12614 number related functions number related functions sing_143.htm#SEC18 22615 numberOfConesOfDimension numberOfConesOfDimension sing_234.htm#SEC27 32616 number_e sing_944.htm#SEC10 192617 number_pi sing_945.htm#SEC102 02618 numerAlg.lib sing_13 78.htm#IDX5122619 numerAlg_lib sing_13 78.htm#IDX5132620 numerDecom.lib sing_138 3.htm#IDX5142621 numerDecom_lib sing_138 3.htm#IDX5152622 numerator sing_361.htm#SEC40 02623 nvars sing_362.htm#SEC40 12624 oneDimBelongSemigroup oneDimBelongSemigroup sing_11 58.htm#SEC12332590 normaliz sing_1302.htm#SEC1378 2591 normaliz.lib sing_1287.htm#SEC1363 2592 normaliz_lib sing_1287.htm#SEC1363 2593 normalization sing_1217.htm#IDX485 2594 normalization sing_1218.htm#IDX488 2595 normalization sing_1219.htm#IDX491 2596 normalization sing_1220.htm#IDX493 2597 normalization sing_1273.htm#IDX495 2598 normalization sing_1274.htm#IDX498 2599 normalization sing_1275.htm#IDX501 2600 normalization sing_1287.htm#IDX507 2601 normalization. sing_1214.htm#IDX484 2602 normalization. sing_1406.htm#IDX538 2603 normalize sing_1000.htm#SEC1076 2604 not sing_96.htm#SEC136 2605 notBuckets, option sing_364.htm#IDX155 2606 notRegularity, option sing_364.htm#IDX153 2607 notSugar, option sing_364.htm#IDX154 2608 notWarnSB, option sing_364.htm#IDX176 2609 npar sing_1884.htm#SEC1960 2610 npars sing_358.htm#SEC398 2611 nrRootsDeterm sing_2009.htm#SEC2085 2612 nrRootsProbab sing_2008.htm#SEC2084 2613 nres sing_359.htm#SEC399 2614 nres (plural) sing_520.htm#SEC560 2615 nrows sing_360.htm#SEC400 2616 nrroots sing_2038.htm#SEC2114 2617 nsatiety sing_1268.htm#SEC1344 2618 nselect sing_1170.htm#SEC1246 2619 nt_solve sing_1773.htm#SEC1849 2620 ntsolve.lib sing_1772.htm#SEC1848 2621 ntsolve_lib sing_1772.htm#SEC1848 2622 number sing_139.htm#SEC179 2623 number sing_2132.htm#IDX789 2624 number declarations sing_140.htm#SEC180 2625 number expressions sing_141.htm#SEC181 2626 number operations sing_142.htm#SEC182 2627 number related functions number related functions sing_143.htm#SEC183 2628 numberOfConesOfDimension numberOfConesOfDimension sing_234.htm#SEC274 2629 number_e sing_944.htm#SEC1020 2630 number_pi sing_945.htm#SEC1021 2631 numerAlg.lib sing_1381.htm#IDX512 2632 numerAlg_lib sing_1381.htm#IDX513 2633 numerDecom.lib sing_1386.htm#IDX514 2634 numerDecom_lib sing_1386.htm#IDX515 2635 numerator sing_361.htm#SEC401 2636 nvars sing_362.htm#SEC402 2637 oneDimBelongSemigroup oneDimBelongSemigroup sing_1161.htm#SEC1237 2625 2638 online help The online help system sing_16.htm#SEC22 2626 open sing_363.htm#SEC402 2627 opentex sing_1798.htm#SEC1873 2628 operatorBM sing_595.htm#SEC646 2629 operatorModulo sing_596.htm#SEC647 2630 oppose sing_521.htm#SEC560 2631 opposite sing_522.htm#SEC561 2632 opposite polynomial sing_406.htm#IDX222 2633 opposite ring sing_406.htm#IDX219 2634 option sing_364.htm#SEC403 2635 option(warn) sing_70.htm#SEC109 2636 optionIsSet sing_1043.htm#SEC1118 2637 or Evaluation of logical expressions sing_96.htm#SEC135 2638 or sing_459.htm#SEC498 2639 orbit sing_1396.htm#IDX518 2640 orbit sing_1397.htm#IDX522 2641 orbit sing_1400.htm#IDX527 2642 orbit sing_1401.htm#IDX530 2643 orbitCones sing_2285.htm#SEC2360 2644 orbit_variety sing_1697.htm#SEC1772 2645 orbitparam.lib sing_1396.htm#SEC1471 2646 orbitparam_lib sing_1396.htm#SEC1471 2647 ord sing_365.htm#SEC404 2648 ord_test sing_1038.htm#SEC1113 2649 orderings General definitions for orderings sing_892.htm#SEC943 2650 orderings introduction Introduction to orderings sing_891.htm#SEC942 2651 orderings, M sing_896.htm#SEC947 2652 orderings, a sing_898.htm#SEC949 2653 orderings, global sing_893.htm#SEC944 2654 orderings, local sing_894.htm#SEC945 2655 orderings, product sing_897.htm#SEC948 2656 ordstr sing_366.htm#SEC405 2657 orthogonalize sing_1114.htm#SEC1189 2658 outer sing_1084.htm#SEC1159 2659 output sing_41.htm#SEC70 2660 p-adic numbers sing_32.htm#SEC45 2661 pFactor sing_1930.htm#SEC2005 2662 pIntersect sing_559.htm#SEC610 2663 pIntersectSyz sing_560.htm#SEC611 2664 package sing_144.htm#SEC183 2665 package declarations package declarations sing_145.htm#SEC184 2666 package related functions package related functions sing_146.htm#SEC185 2667 pairset sing_1995.htm#SEC2070 2668 par sing_367.htm#SEC406 2669 par2varRing sing_928.htm#SEC1003 2670 paraConic sing_1411.htm#SEC1486 2671 paraPlaneCurve sing_1405.htm#SEC1480 2672 parallel skeletons sing_982.htm#IDX428 2673 parallel.lib sing_982.htm#SEC1057 2674 parallelTestAND sing_986.htm#SEC1061 2675 parallelTestOR sing_987.htm#SEC1062 2676 parallelWaitAll sing_985.htm#SEC1060 2677 parallelWaitFirst sing_984.htm#SEC1059 2678 parallelWaitN sing_983.htm#SEC1058 2679 parallel_lib sing_982.htm#SEC1057 2680 parallelization sing_982.htm#IDX427 2681 parallelization sing_1022.htm#IDX430 2682 parallelization sing_1060.htm#IDX443 2683 param sing_1588.htm#SEC1663 2684 parameter, as numbers sing_139.htm#SEC178 2685 parameterSubstitute sing_2092.htm#SEC2167 2686 parametric annihilator sing_588.htm#IDX324 2687 parametric annihilator for variety sing_644.htm#IDX347 2688 parametrization sing_1396.htm#IDX519 2689 parametrization sing_1400.htm#IDX528 2690 parametrization sing_1588.htm#IDX680 2691 parametrizeOrbit sing_1400.htm#SEC1475 2692 paraplanecurves.lib sing_1402.htm#SEC1477 2693 paraplanecurves_lib sing_1402.htm#SEC1477 2694 pardeg sing_368.htm#SEC407 2695 parstr sing_369.htm#SEC408 2696 part sing_2219.htm#SEC2294 2697 partOver sing_2222.htm#SEC2297 2698 partUnder sing_2223.htm#SEC2298 2699 partial_molien sing_1675.htm#SEC1750 2700 partitions sing_1179.htm#SEC1254 2701 partitions sing_1179.htm#IDX475 2702 path integral sing_1171.htm#IDX462 2703 pause sing_979.htm#SEC1054 2704 pdivi sing_958.htm#SEC1033 2705 pdivisorplus sing_2247.htm#SEC2322 2706 permcol sing_1097.htm#SEC1172 2707 permrow sing_1098.htm#SEC1173 2708 permutations sing_1180.htm#IDX476 2709 permute sing_1180.htm#SEC1255 2710 permute_L sing_1833.htm#SEC1908 2711 perron sing_786.htm#SEC837 2712 perron.lib sing_785.htm#SEC836 2713 perron_lib sing_785.htm#SEC836 2714 phindex.lib sing_2097.htm#IDX741 2715 phindex_lib sing_2097.htm#IDX742 2716 picksFormula sing_2053.htm#SEC2128 2717 pid sing_406.htm#IDX231 2718 plainInvariants sing_1547.htm#SEC1622 2719 plot sing_1811.htm#SEC1886 2720 plotRot sing_1815.htm#SEC1890 2721 plotRotated sing_1814.htm#SEC1889 2722 plotRotatedDirect sing_1817.htm#SEC1892 2723 plotRotatedList sing_1816.htm#SEC1891 2724 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1818.htm#SEC1893 2725 plural sing_1045.htm#IDX435 2726 pmat sing_973.htm#SEC1048 2727 pnormalf sing_959.htm#SEC1034 2728 pointid.lib sing_1311.htm#SEC1386 2729 pointid_lib sing_1311.htm#SEC1386 2730 polSol sing_821.htm#SEC872 2731 polSolFiniteRank sing_822.htm#SEC873 2732 pollTask sing_1070.htm#SEC1145 2733 poly sing_147.htm#SEC186 2734 poly (plural) sing_486.htm#SEC525 2735 poly declarations sing_148.htm#SEC187 2736 poly declarations (plural) poly declarations (plural) sing_487.htm#SEC526 2737 poly expressions sing_149.htm#SEC188 2738 poly expressions (plural) poly expressions (plural) sing_488.htm#SEC527 2739 poly operations sing_150.htm#SEC189 2740 poly operations (plural) poly operations (plural) sing_489.htm#SEC528 2741 poly related functions poly related functions sing_151.htm#SEC190 2742 poly related functions (plural) poly related functions (plural) sing_490.htm#SEC529 2743 poly.lib sing_988.htm#SEC1063 2744 poly2list sing_637.htm#SEC688 2745 poly2zdd sing_2118.htm#SEC2193 61839 2746 polyVars sing_828.htm#SEC879 2747 poly_lib sing_988.htm#SEC1063 2748 polybori sing_2102.htm#IDX746 2749 polybori.lib sing_2102.htm#IDX743 2750 polybori.lib sing_2102.htm#IDX747 2751 polybori_lib sing_2102.htm#IDX744 2752 polymake sing_2038.htm#IDX734 2753 polymake.lib sing_2038.htm#SEC2113 2754 polymakePolytope sing_2039.htm#SEC2114 2755 polymake_lib sing_2038.htm#SEC2113 2756 polymake_so sing_2410.htm#IDX899 2757 polynomial solutions sing_815.htm#IDX375 2758 polynomial, opposite sing_406.htm#IDX223 2759 polytope sing_236.htm#SEC275 2760 polytope sing_2038.htm#IDX730 2761 polytope related functions polytope related functions sing_239.htm#SEC278 2762 polytopeViaInequalities polytopeViaInequalities sing_238.htm#SEC277 2763 polytopeViaPoints sing_237.htm#SEC276 2764 pos_def sing_1125.htm#SEC1200 2765 poset sing_2160.htm#IDX847 2766 posweight sing_1655.htm#SEC1730 2767 powSumSym sing_2178.htm#SEC2253 2768 power sing_1085.htm#SEC1160 2769 powerN sing_1914.htm#SEC1989 2770 powerX sing_1923.htm#SEC1998 2771 power_products sing_1689.htm#SEC1764 2772 powerpolyX sing_1893.htm#SEC1968 2773 powersums sing_2016.htm#SEC2091 2774 preComp sing_1248.htm#SEC1323 2775 preimage sing_370.htm#SEC409 2776 preimage sing_752.htm#IDX350 2777 preimage (plural) sing_523.htm#SEC562 2778 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1041.htm#IDX433 2779 preimageLattice sing_2350.htm#SEC2425 2780 preimageLoc sing_1041.htm#SEC1116 2781 preimageNC sing_754.htm#SEC805 2782 prepEmbDiv sing_1473.htm#SEC1548 2783 prepMat sing_1726.htm#SEC1801 2784 prepRealclassify sing_1531.htm#SEC1606 2785 prepSV sing_1828.htm#SEC1903 2786 prepareAss sing_1330.htm#SEC1405 2787 presentTree sing_1460.htm#SEC1535 2788 presolve.lib sing_1736.htm#SEC1811 2789 presolve_lib sing_1736.htm#SEC1811 2790 primL sing_1918.htm#SEC1993 2791 primList sing_1917.htm#SEC1992 2792 primRoot sing_1370.htm#SEC1445 2793 primTest sing_1247.htm#SEC1322 2794 primary_char0 sing_1679.htm#SEC1754 2795 primary_char0_no_molien primary_char0_no_molien sing_1681.htm#SEC1756 2796 primary_char0_no_molien_random primary_char0_no_molien_random sing_1686.htm#SEC1761 2797 primary_char0_random primary_char0_random sing_1684.htm#SEC1759 2798 primary_charp sing_1680.htm#SEC1755 2799 primary_charp_no_molien primary_charp_no_molien sing_1682.htm#SEC1757 2800 primary_charp_no_molien_random primary_charp_no_molien_random sing_1687.htm#SEC1762 2801 primary_charp_random primary_charp_random sing_1685.htm#SEC1760 2802 primary_charp_without primary_charp_without sing_1683.htm#SEC1758 2803 primary_charp_without_random primary_charp_without_random sing_1688.htm#SEC1763 2804 primary_invariants sing_1667.htm#SEC1742 2805 primary_invariants_random primary_invariants_random sing_1668.htm#SEC1743 2806 primdec.lib sing_1315.htm#SEC1390 2807 primdecGTZ sing_1317.htm#SEC1392 2808 primdecGTZE sing_1318.htm#SEC1393 2809 primdecMon sing_1236.htm#SEC1311 2810 primdecSY sing_1319.htm#SEC1394 2811 primdecSYE sing_1320.htm#SEC1395 2812 primdecZ sing_1339.htm#SEC1414 2813 primdecZM sing_1340.htm#SEC1415 2814 primdec_lib sing_1315.htm#SEC1390 2815 primdecint.lib sing_1338.htm#SEC1413 2816 primdecint_lib sing_1338.htm#SEC1413 2817 prime sing_371.htm#SEC410 2818 primeClosure sing_1275.htm#SEC1350 2819 primecoeffs sing_951.htm#SEC1026 2820 primefactors sing_372.htm#SEC411 2821 primes sing_946.htm#SEC1021 2822 primitiv.lib sing_1346.htm#SEC1421 2823 primitiv_lib sing_1346.htm#SEC1421 2824 primitive sing_1347.htm#SEC1422 2825 primitive element sing_1347.htm#IDX509 2826 primitiveSpan sing_2357.htm#SEC2432 2827 primitive_extra sing_1348.htm#SEC1423 2828 primparam sing_1542.htm#SEC1617 2829 principal intersection sing_553.htm#IDX308 2830 print sing_373.htm#SEC412 2831 print sing_2127.htm#IDX782 2832 printGraph sing_1173.htm#SEC1248 2833 printGroup sing_2338.htm#SEC2413 2834 printMoebius sing_2166.htm#SEC2241 2835 printTask sing_1065.htm#SEC1140 2836 printf sing_374.htm#SEC413 2837 printlevel sing_448.htm#SEC487 2838 proc sing_152.htm#SEC191 2839 proc declaration sing_153.htm#SEC192 2840 proc expression sing_154.htm#SEC193 2841 procedure, ASCII help sing_56.htm#IDX126 2842 procedure, ASCII/Texinfo help sing_58.htm#IDX128 2843 procedure, texinfo help sing_57.htm#IDX127 2844 procedures, help string sing_45.htm#SEC81 2845 procedures, static Procedure definition sing_43.htm#SEC77 2846 procs with different argument types procs with different argument types sing_155.htm#SEC194 2847 prodcrit sing_1993.htm#SEC2068 2848 product sing_947.htm#SEC1022 2849 productgroup sing_2359.htm#SEC2434 2850 progress watch sing_364.htm#IDX159 2851 projectLattice sing_2351.htm#SEC2426 2852 projective dimension purityfiltration_lib sing_793.htm#IDX359 2853 projective limes sing_32.htm#SEC45 2854 projectiveDimension sing_794.htm#SEC845 2639 open sing_363.htm#SEC403 2640 opentex sing_1801.htm#SEC1877 2641 operatorBM sing_595.htm#SEC647 2642 operatorModulo sing_596.htm#SEC648 2643 oppose sing_521.htm#SEC561 2644 opposite sing_522.htm#SEC562 2645 opposite polynomial sing_406.htm#IDX221 2646 opposite ring sing_406.htm#IDX218 2647 option sing_364.htm#SEC404 2648 option(warn) sing_70.htm#SEC110 2649 optionIsSet sing_1043.htm#SEC1119 2650 or Evaluation of logical expressions sing_96.htm#SEC136 2651 or sing_459.htm#SEC499 2652 orbit sing_1399.htm#IDX518 2653 orbit sing_1400.htm#IDX522 2654 orbit sing_1403.htm#IDX527 2655 orbit sing_1404.htm#IDX530 2656 orbitCones sing_2296.htm#SEC2372 2657 orbit_variety sing_1700.htm#SEC1776 2658 orbitparam.lib sing_1399.htm#SEC1475 2659 orbitparam_lib sing_1399.htm#SEC1475 2660 ord sing_365.htm#SEC405 2661 ord_test sing_1038.htm#SEC1114 2662 orderings General definitions for orderings sing_892.htm#SEC944 2663 orderings introduction Introduction to orderings sing_891.htm#SEC943 2664 orderings, M sing_896.htm#SEC948 2665 orderings, a sing_898.htm#SEC950 2666 orderings, global sing_893.htm#SEC945 2667 orderings, local sing_894.htm#SEC946 2668 orderings, product sing_897.htm#SEC949 2669 ordstr sing_366.htm#SEC406 2670 orthogonalize sing_1117.htm#SEC1193 2671 outer sing_1087.htm#SEC1163 2672 output sing_41.htm#SEC71 2673 p-adic numbers sing_32.htm#SEC46 2674 pFactor sing_1933.htm#SEC2009 2675 pIntersect sing_559.htm#SEC611 2676 pIntersectSyz sing_560.htm#SEC612 2677 package sing_144.htm#SEC184 2678 package declarations package declarations sing_145.htm#SEC185 2679 package related functions package related functions sing_146.htm#SEC186 2680 pairset sing_1998.htm#SEC2074 2681 par sing_367.htm#SEC407 2682 par2varRing sing_928.htm#SEC1004 2683 paraConic sing_1414.htm#SEC1490 2684 paraPlaneCurve sing_1408.htm#SEC1484 2685 parallel skeletons sing_982.htm#IDX427 2686 parallel.lib sing_982.htm#SEC1058 2687 parallelTestAND sing_986.htm#SEC1062 2688 parallelTestOR sing_987.htm#SEC1063 2689 parallelWaitAll sing_985.htm#SEC1061 2690 parallelWaitFirst sing_984.htm#SEC1060 2691 parallelWaitN sing_983.htm#SEC1059 2692 parallel_lib sing_982.htm#SEC1058 2693 parallelization sing_982.htm#IDX426 2694 parallelization sing_1022.htm#IDX429 2695 parallelization sing_1063.htm#IDX442 2696 param sing_1591.htm#SEC1667 2697 parameter, as numbers sing_139.htm#SEC179 2698 parameterSubstitute sing_2095.htm#SEC2171 2699 parametric annihilator sing_588.htm#IDX323 2700 parametric annihilator for variety sing_644.htm#IDX346 2701 parametrization sing_1399.htm#IDX519 2702 parametrization sing_1403.htm#IDX528 2703 parametrization sing_1591.htm#IDX680 2704 parametrizeOrbit sing_1403.htm#SEC1479 2705 paraplanecurves.lib sing_1405.htm#SEC1481 2706 paraplanecurves_lib sing_1405.htm#SEC1481 2707 pardeg sing_368.htm#SEC408 2708 parstr sing_369.htm#SEC409 2709 part sing_2224.htm#SEC2300 2710 partOver sing_2227.htm#SEC2303 2711 partUnder sing_2228.htm#SEC2304 2712 partial_molien sing_1678.htm#SEC1754 2713 partitions sing_1182.htm#SEC1258 2714 partitions sing_1182.htm#IDX475 2715 path integral sing_1174.htm#IDX462 2716 pause sing_979.htm#SEC1055 2717 pdivi sing_958.htm#SEC1034 2718 pdivisorplus sing_2252.htm#SEC2328 2719 permcol sing_1100.htm#SEC1176 2720 permrow sing_1101.htm#SEC1177 2721 permutations sing_1183.htm#IDX476 2722 permute sing_1183.htm#SEC1259 2723 permute_L sing_1836.htm#SEC1912 2724 perron sing_786.htm#SEC838 2725 perron.lib sing_785.htm#SEC837 2726 perron_lib sing_785.htm#SEC837 2727 phindex.lib sing_2100.htm#IDX741 2728 phindex_lib sing_2100.htm#IDX742 2729 picksFormula sing_2056.htm#SEC2132 2730 pid sing_406.htm#IDX230 2731 plainInvariants sing_1550.htm#SEC1626 2732 plot sing_1814.htm#SEC1890 2733 plotRot sing_1818.htm#SEC1894 2734 plotRotated sing_1817.htm#SEC1893 2735 plotRotatedDirect sing_1820.htm#SEC1896 2736 plotRotatedList sing_1819.htm#SEC1895 2737 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1821.htm#SEC1897 2738 plural sing_1045.htm#IDX434 2739 pmat sing_973.htm#SEC1049 2740 pnormalf sing_959.htm#SEC1035 2741 pointid.lib sing_1314.htm#SEC1390 2742 pointid_lib sing_1314.htm#SEC1390 2743 polSol sing_821.htm#SEC873 2744 polSolFiniteRank sing_822.htm#SEC874 2745 pollTask sing_1073.htm#SEC1149 2746 poly sing_147.htm#SEC187 2747 poly (plural) sing_486.htm#SEC526 2748 poly declarations sing_148.htm#SEC188 2749 poly declarations (plural) poly declarations (plural) sing_487.htm#SEC527 2750 poly expressions sing_149.htm#SEC189 2751 poly expressions (plural) poly expressions (plural) sing_488.htm#SEC528 2752 poly operations sing_150.htm#SEC190 2753 poly operations (plural) poly operations (plural) sing_489.htm#SEC529 2754 poly related functions poly related functions sing_151.htm#SEC191 2755 poly related functions (plural) poly related functions (plural) sing_490.htm#SEC530 2756 poly.lib sing_988.htm#SEC1064 2757 poly2list sing_637.htm#SEC689 2758 poly2zdd sing_2121.htm#SEC2197 61839 2759 polyInterpolation sing_2255.htm#SEC2331 2760 polyVars sing_828.htm#SEC880 2761 poly_lib sing_988.htm#SEC1064 2762 polybori sing_2105.htm#IDX746 2763 polybori.lib sing_2105.htm#IDX743 2764 polybori.lib sing_2105.htm#IDX747 2765 polybori_lib sing_2105.htm#IDX744 2766 polymake sing_2041.htm#IDX734 2767 polymake.lib sing_2041.htm#SEC2117 2768 polymakePolytope sing_2042.htm#SEC2118 2769 polymake_lib sing_2041.htm#SEC2117 2770 polymake_so sing_2421.htm#IDX899 2771 polynomial solutions sing_815.htm#IDX374 2772 polynomial, opposite sing_406.htm#IDX222 2773 polytope sing_236.htm#SEC276 2774 polytope sing_2041.htm#IDX730 2775 polytope related functions polytope related functions sing_239.htm#SEC279 2776 polytopeViaInequalities polytopeViaInequalities sing_238.htm#SEC278 2777 polytopeViaPoints sing_237.htm#SEC277 2778 pos_def sing_1128.htm#SEC1204 2779 poset sing_2163.htm#IDX847 2780 posweight sing_1658.htm#SEC1734 2781 powSumSym sing_2181.htm#SEC2257 2782 power sing_1088.htm#SEC1164 2783 powerN sing_1917.htm#SEC1993 2784 powerX sing_1926.htm#SEC2002 2785 power_products sing_1692.htm#SEC1768 2786 powerpolyX sing_1896.htm#SEC1972 2787 powersums sing_2019.htm#SEC2095 2788 preComp sing_1251.htm#SEC1327 2789 preimage sing_370.htm#SEC410 2790 preimage sing_752.htm#IDX349 2791 preimage (plural) sing_523.htm#SEC563 2792 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1041.htm#IDX432 2793 preimageLattice sing_2361.htm#SEC2437 2794 preimageLoc sing_1041.htm#SEC1117 2795 preimageNC sing_754.htm#SEC806 2796 prepEmbDiv sing_1476.htm#SEC1552 2797 prepMat sing_1729.htm#SEC1805 2798 prepRealclassify sing_1534.htm#SEC1610 2799 prepSV sing_1831.htm#SEC1907 2800 prepareAss sing_1333.htm#SEC1409 2801 presentTree sing_1463.htm#SEC1539 2802 presolve.lib sing_1739.htm#SEC1815 2803 presolve_lib sing_1739.htm#SEC1815 2804 primL sing_1921.htm#SEC1997 2805 primList sing_1920.htm#SEC1996 2806 primRoot sing_1373.htm#SEC1449 2807 primTest sing_1250.htm#SEC1326 2808 primary_char0 sing_1682.htm#SEC1758 2809 primary_char0_no_molien primary_char0_no_molien sing_1684.htm#SEC1760 2810 primary_char0_no_molien_random primary_char0_no_molien_random sing_1689.htm#SEC1765 2811 primary_char0_random primary_char0_random sing_1687.htm#SEC1763 2812 primary_charp sing_1683.htm#SEC1759 2813 primary_charp_no_molien primary_charp_no_molien sing_1685.htm#SEC1761 2814 primary_charp_no_molien_random primary_charp_no_molien_random sing_1690.htm#SEC1766 2815 primary_charp_random primary_charp_random sing_1688.htm#SEC1764 2816 primary_charp_without primary_charp_without sing_1686.htm#SEC1762 2817 primary_charp_without_random primary_charp_without_random sing_1691.htm#SEC1767 2818 primary_invariants sing_1670.htm#SEC1746 2819 primary_invariants_random primary_invariants_random sing_1671.htm#SEC1747 2820 primdec.lib sing_1318.htm#SEC1394 2821 primdecGTZ sing_1320.htm#SEC1396 2822 primdecGTZE sing_1321.htm#SEC1397 2823 primdecMon sing_1239.htm#SEC1315 2824 primdecSY sing_1322.htm#SEC1398 2825 primdecSYE sing_1323.htm#SEC1399 2826 primdecZ sing_1342.htm#SEC1418 2827 primdecZM sing_1343.htm#SEC1419 2828 primdec_lib sing_1318.htm#SEC1394 2829 primdecint.lib sing_1341.htm#SEC1417 2830 primdecint_lib sing_1341.htm#SEC1417 2831 prime sing_371.htm#SEC411 2832 primeClosure sing_1278.htm#SEC1354 2833 primecoeffs sing_951.htm#SEC1027 2834 primefactors sing_372.htm#SEC412 2835 primes sing_946.htm#SEC1022 2836 primitiv.lib sing_1349.htm#SEC1425 2837 primitiv_lib sing_1349.htm#SEC1425 2838 primitive sing_1350.htm#SEC1426 2839 primitive element sing_1350.htm#IDX509 2840 primitiveSpan sing_2368.htm#SEC2444 2841 primitive_extra sing_1351.htm#SEC1427 2842 primparam sing_1545.htm#SEC1621 2843 principal intersection sing_553.htm#IDX307 2844 print sing_373.htm#SEC413 2845 print sing_2130.htm#IDX782 2846 printGraph sing_1176.htm#SEC1252 2847 printGroup sing_2349.htm#SEC2425 2848 printMoebius sing_2169.htm#SEC2245 2849 printTask sing_1068.htm#SEC1144 2850 printf sing_374.htm#SEC414 2851 printlevel sing_448.htm#SEC488 2852 proc sing_152.htm#SEC192 2853 proc declaration sing_153.htm#SEC193 2854 proc expression sing_154.htm#SEC194 2855 procedure, ASCII help sing_56.htm#IDX125 2856 procedure, ASCII/Texinfo help sing_58.htm#IDX127 2857 procedure, texinfo help sing_57.htm#IDX126 2858 procedures, help string sing_45.htm#SEC82 2859 procedures, static Procedure definition sing_43.htm#SEC78 2860 procs with different argument types procs with different argument types sing_155.htm#SEC195 2861 prodcrit sing_1996.htm#SEC2072 2862 product sing_947.htm#SEC1023 2863 productgroup sing_2370.htm#SEC2446 2864 progress watch sing_364.htm#IDX158 2865 projectLattice sing_2362.htm#SEC2438 2866 projective dimension purityfiltration_lib sing_793.htm#IDX358 2867 projective limes sing_32.htm#SEC46 2868 projectiveDimension sing_794.htm#SEC846 2855 2869 prompt sing_15.htm#SEC21 2856 prompt, option sing_364.htm#IDX17 82857 propagator sing_117 1.htm#IDX4602858 propagator sing_117 4.htm#SEC12492859 prot, option sing_364.htm#IDX15 72860 protocol of computations sing_364.htm#IDX15 82861 proximitymatrix sing_150 1.htm#SEC15762862 prune sing_375.htm#SEC41 42863 prwalk sing_23 86.htm#SEC24612864 psigncnd sing_17 89.htm#SEC18642865 puiseux2generators sing_160 0.htm#SEC16752866 puiseuxExpansion sing_206 3.htm#SEC21382867 pure tensor sing_546.htm#IDX29 62868 purelist sing_804.htm#SEC85 52869 purity purityfiltration_lib sing_793.htm#IDX36 12870 purityFiltration sing_795.htm#SEC84 62871 purityTriang sing_796.htm#SEC84 72872 purityfiltration.lib purityfiltration_lib sing_793.htm#IDX35 42873 purityfiltration_lib purityfiltration_lib sing_793.htm#IDX35 52874 pushForward sing_23 76.htm#SEC24512875 pwalk sing_11 87.htm#SEC12622876 pyobject sing_243.htm#SEC28 22877 pyobject sing_210 2.htm#IDX7492878 pyobject declarations pyobject declarations sing_244.htm#SEC28 32879 pyobject expressions pyobject expressions sing_245.htm#SEC28 42880 pyobject operations sing_246.htm#SEC28 52881 pyobject related functions pyobject related functions sing_247.htm#SEC28 62882 pyramid sing_22 60.htm#SEC23352883 python_eval sing_248.htm#SEC28 72884 python_import sing_249.htm#SEC28 82885 python_run sing_250.htm#SEC2 892886 qbase sing_20 19.htm#SEC20942887 qepcad sing_22 70.htm#SEC23452888 qepcadsystem sing_22 71.htm#SEC23462889 qhmatrix sing_165 3.htm#SEC17282890 qhmoduli.lib sing_16 17.htm#SEC16922891 qhmoduli_lib sing_16 17.htm#SEC16922892 qhspectrum sing_164 0.htm#SEC17152893 qhweight sing_376.htm#SEC41 52894 qmatrix.lib sing_787.htm#SEC83 82895 qmatrix_lib sing_787.htm#SEC83 82896 qminor sing_789.htm#SEC84 02897 qrds sing_377.htm#SEC41 62898 qring Miscellaneous oddities sing_161.htm#SEC20 02899 qring sing_466.htm#IDX28 42900 qring (plural) sing_491.htm#SEC53 02901 qring declaration sing_165.htm#SEC20 42902 qring declaration (plural) qring declaration (plural) sing_492.htm#SEC53 12903 qring related functions (plural) qring related functions (plural) sing_493.htm#SEC53 22904 qring ring ideal 'factor ring' sing_1050.htm#IDX43 92905 qringNF, option sing_364.htm#IDX1 602906 qslimgb sing_927.htm#SEC100 22907 quadraticSieve sing_193 1.htm#SEC20062908 quantMat sing_788.htm#SEC8 392909 quickclass sing_152 3.htm#SEC15982910 quit sing_438.htm#SEC47 72911 quote sing_378.htm#SEC41 72912 quotient sing_379.htm#SEC41 82913 quotient (plural) sing_524.htm#SEC56 32914 quotientLatticeBasis quotientLatticeBasis sing_212.htm#SEC25 12915 quotientMain sing_178 1.htm#SEC18562916 quotientMon sing_12 27.htm#SEC13022917 quotients sing_22 79.htm#IDX8792918 rHRR sing_22 16.htm#SEC22912919 rMacaulay sing_974.htm#SEC10 492920 rad_con sing_1001.htm#SEC107 62921 radical sing_13 27.htm#SEC14022922 radicalEHV sing_13 28.htm#SEC14032923 radicalMemberShip sing_208 5.htm#SEC21602924 radicalMon sing_12 28.htm#SEC13032925 radicalZ sing_134 2.htm#SEC14172926 randcharpoly sing_201 3.htm#SEC20882927 randlinpoly sing_201 5.htm#SEC20902928 random sing_380.htm#SEC4 192929 random sing_406.htm#IDX23 52930 random sing_21 48.htm#IDX8212931 random sing_21 49.htm#IDX8232932 random number generator, seed sing_406.htm#IDX23 32933 random.lib sing_1009.htm#SEC108 42934 randomBinomial sing_1021.htm#SEC109 62935 randomCheck sing_184 4.htm#SEC19192936 randomLast sing_1020.htm#SEC109 52937 randomPoint sing_213.htm#SEC25 22938 randomPolyInT sing_209 4.htm#SEC21692939 random_lib sing_1009.htm#SEC108 42940 randomid sing_1011.htm#SEC108 62941 randommat sing_1012.htm#SEC108 72942 rank sing_261.htm#IDX13 42943 rank sing_381.htm#SEC42 02944 ratSol sing_823.htm#SEC87 42945 ratgb.lib sing_813.htm#IDX36 42946 ratgb_lib sing_813.htm#IDX36 52947 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_140 5.htm#IDX5402948 rational normal curve, projection. sing_140 6.htm#IDX5412949 rational normal curve, projection. sing_14 09.htm#IDX5422950 rational normal curve, projection. sing_141 0.htm#IDX5432951 rational solutions sing_815.htm#IDX37 62952 rational univariate projection sing_201 3.htm#IDX7272953 rationalPointConic sing_14 07.htm#SEC14822954 ratstd sing_814.htm#SEC86 52955 rays sing_214.htm#SEC25 32956 re2squ sing_138 4.htm#SEC14592957 read sing_382.htm#SEC42 12958 readNmzData sing_130 2.htm#SEC1377189572959 reading, option sing_364.htm#IDX17 92870 prompt, option sing_364.htm#IDX177 2871 propagator sing_1174.htm#IDX460 2872 propagator sing_1177.htm#SEC1253 2873 prot, option sing_364.htm#IDX156 2874 protocol of computations sing_364.htm#IDX157 2875 proximitymatrix sing_1504.htm#SEC1580 2876 prune sing_375.htm#SEC415 2877 prwalk sing_2397.htm#SEC2473 2878 psigncnd sing_1792.htm#SEC1868 2879 puiseux2generators sing_1603.htm#SEC1679 2880 puiseuxExpansion sing_2066.htm#SEC2142 2881 pure tensor sing_546.htm#IDX295 2882 purelist sing_804.htm#SEC856 2883 purity purityfiltration_lib sing_793.htm#IDX360 2884 purityFiltration sing_795.htm#SEC847 2885 purityTriang sing_796.htm#SEC848 2886 purityfiltration.lib purityfiltration_lib sing_793.htm#IDX353 2887 purityfiltration_lib purityfiltration_lib sing_793.htm#IDX354 2888 pushForward sing_2387.htm#SEC2463 2889 pwalk sing_1190.htm#SEC1266 2890 pyobject sing_243.htm#SEC283 2891 pyobject sing_2105.htm#IDX749 2892 pyobject declarations pyobject declarations sing_244.htm#SEC284 2893 pyobject expressions pyobject expressions sing_245.htm#SEC285 2894 pyobject operations sing_246.htm#SEC286 2895 pyobject related functions pyobject related functions sing_247.htm#SEC287 2896 pyramid sing_2271.htm#SEC2347 2897 python_eval sing_248.htm#SEC288 2898 python_import sing_249.htm#SEC289 2899 python_run sing_250.htm#SEC290 2900 qbase sing_2022.htm#SEC2098 2901 qepcad sing_2281.htm#SEC2357 2902 qepcadsystem sing_2282.htm#SEC2358 2903 qhmatrix sing_1656.htm#SEC1732 2904 qhmoduli.lib sing_1620.htm#SEC1696 2905 qhmoduli_lib sing_1620.htm#SEC1696 2906 qhspectrum sing_1643.htm#SEC1719 2907 qhweight sing_376.htm#SEC416 2908 qmatrix.lib sing_787.htm#SEC839 2909 qmatrix_lib sing_787.htm#SEC839 2910 qminor sing_789.htm#SEC841 2911 qrds sing_377.htm#SEC417 2912 qring Miscellaneous oddities sing_161.htm#SEC201 2913 qring sing_466.htm#IDX283 2914 qring (plural) sing_491.htm#SEC531 2915 qring declaration sing_165.htm#SEC205 2916 qring declaration (plural) qring declaration (plural) sing_492.htm#SEC532 2917 qring related functions (plural) qring related functions (plural) sing_493.htm#SEC533 2918 qring ring ideal 'factor ring' sing_1050.htm#IDX438 2919 qringNF, option sing_364.htm#IDX159 2920 qslimgb sing_927.htm#SEC1003 2921 quadraticSieve sing_1934.htm#SEC2010 2922 quantMat sing_788.htm#SEC840 2923 quickclass sing_1526.htm#SEC1602 2924 quit sing_438.htm#SEC478 2925 quote sing_378.htm#SEC418 2926 quotient sing_379.htm#SEC419 2927 quotient (plural) sing_524.htm#SEC564 2928 quotientLatticeBasis quotientLatticeBasis sing_212.htm#SEC252 2929 quotientMain sing_1784.htm#SEC1860 2930 quotientMon sing_1230.htm#SEC1306 2931 quotients sing_2290.htm#IDX879 2932 rHRR sing_2221.htm#SEC2297 2933 rMacaulay sing_974.htm#SEC1050 2934 rad_con sing_1001.htm#SEC1077 2935 radical sing_1330.htm#SEC1406 2936 radicalEHV sing_1331.htm#SEC1407 2937 radicalMemberShip sing_2088.htm#SEC2164 2938 radicalMon sing_1231.htm#SEC1307 2939 radicalZ sing_1345.htm#SEC1421 2940 randcharpoly sing_2016.htm#SEC2092 2941 randlinpoly sing_2018.htm#SEC2094 2942 random sing_380.htm#SEC420 2943 random sing_406.htm#IDX234 2944 random sing_2151.htm#IDX821 2945 random sing_2152.htm#IDX823 2946 random number generator, seed sing_406.htm#IDX232 2947 random.lib sing_1009.htm#SEC1085 2948 randomBinomial sing_1021.htm#SEC1097 2949 randomCheck sing_1847.htm#SEC1923 2950 randomLast sing_1020.htm#SEC1096 2951 randomPoint sing_213.htm#SEC253 2952 randomPolyInT sing_2097.htm#SEC2173 2953 random_lib sing_1009.htm#SEC1085 2954 randomid sing_1011.htm#SEC1087 2955 randommat sing_1012.htm#SEC1088 2956 rank sing_261.htm#IDX133 2957 rank sing_381.htm#SEC421 2958 ratSol sing_823.htm#SEC875 2959 ratgb.lib sing_813.htm#IDX363 2960 ratgb_lib sing_813.htm#IDX364 2961 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1408.htm#IDX540 2962 rational normal curve, projection. sing_1409.htm#IDX541 2963 rational normal curve, projection. sing_1412.htm#IDX542 2964 rational normal curve, projection. sing_1413.htm#IDX543 2965 rational solutions sing_815.htm#IDX375 2966 rational univariate projection sing_2016.htm#IDX727 2967 rationalPointConic sing_1410.htm#SEC1486 2968 ratstd sing_814.htm#SEC866 2969 rays sing_214.htm#SEC254 2970 re2squ sing_1387.htm#SEC1463 2971 read sing_382.htm#SEC422 2972 readNmzData sing_1305.htm#SEC1381 18957 2973 reading, option sing_364.htm#IDX178 2960 2974 readline sing_1.htm#IDX5 2961 real sing_28.htm#IDX75 2962 real roots, univariate polynomial sing_2020.htm#IDX729 2963 real roots, univariate projection sing_2004.htm#IDX725 2964 real roots,sign conditions sing_1787.htm#IDX705 2965 realclassify sing_2393.htm#SEC2468 2966 realclassify.lib sing_2392.htm#SEC2467 2967 realclassify_lib sing_2392.htm#SEC2467 2968 realizationDim sing_2057.htm#SEC2132 2969 realizationDimPoly sing_2059.htm#SEC2134 2970 realizationMatroids.lib realizationMatroids_lib sing_2056.htm#SEC2131 2971 realizationMatroids_lib realizationMatroids_lib sing_2056.htm#SEC2131 2972 realmorsesplit sing_2394.htm#SEC2469 2973 realpoly sing_1351.htm#SEC1426 2974 realrad sing_1353.htm#SEC1428 2975 realrad.lib sing_1350.htm#SEC1425 2976 realrad_lib sing_1350.htm#SEC1425 2977 realzero sing_1352.htm#SEC1427 2978 recursive_boolean_poly recursive_boolean_poly sing_2108.htm#SEC2183 17045 2979 recursive_from_boolean_poly recursive_from_boolean_poly sing_2114.htm#SEC2189 37794 2980 redSB, option sing_364.htm#IDX161 2981 redTail, option sing_364.htm#IDX163 2982 redThrough, option sing_364.htm#IDX164 2983 redefine, option sing_364.htm#IDX180 2984 reduce sing_383.htm#SEC422 2985 reduce sing_567.htm#IDX313 2986 reduce (plural) sing_525.htm#SEC564 2987 reduced standard basis sing_364.htm#IDX162 2988 reduction sing_1705.htm#SEC1780 2989 reesclos.lib sing_1354.htm#SEC1429 2990 reesclos_lib sing_1354.htm#SEC1429 2991 reference sing_251.htm#SEC290 2992 reference declarations reference declarations sing_252.htm#SEC291 2993 reference expressions reference expressions sing_253.htm#SEC292 2994 reference operations reference and shared operations sing_256.htm#SEC295 2995 reference related functions reference and shared related functions sing_257.htm#SEC296 2996 regCM sing_1267.htm#SEC1342 2997 regIdeal sing_1253.htm#SEC1328 2998 regMonCurve sing_1256.htm#SEC1331 2999 regularity Syzygies and resolutions sing_384.htm#SEC423 3000 regularity sing_902.htm#SEC958 3001 reiffen sing_606.htm#SEC657 3002 rel_orbit_variety sing_1698.htm#SEC1773 3003 relations sing_785.htm#IDX353 3004 relativeInteriorPoint relativeInteriorPoint sing_215.htm#SEC254 3005 relative_orbit_variety relative_orbit_variety sing_1699.htm#SEC1774 3006 relweight sing_1654.htm#SEC1729 3007 remainder sing_1774.htm#SEC1849 3008 remainderMain sing_1782.htm#SEC1857 3009 removeCone sing_235.htm#SEC274 3010 removepower sing_1511.htm#SEC1586 3011 repart sing_385.htm#SEC424 3012 replace sing_1883.htm#SEC1958 3013 representation, math objects Representation of mathematical objects sing_889.htm#SEC940 3014 res sing_386.htm#SEC425 3015 resbinomial.lib sing_1414.htm#IDX546 3016 resbinomial_lib sing_1414.htm#IDX547 3017 reservedName sing_387.htm#SEC426 3018 resfunction sing_1428.htm#SEC1503 3019 resgraph.lib sing_1446.htm#SEC1521 3020 resgraph_lib sing_1446.htm#SEC1521 3021 resjung.lib sing_1450.htm#SEC1525 3022 resjung_lib sing_1450.htm#SEC1525 3023 reslist sing_1442.htm#SEC1517 3024 resolution purityfiltration_lib sing_156.htm#SEC195 3025 resolution sing_793.htm#IDX360 3026 resolution (plural) sing_494.htm#SEC533 3027 resolution declarations resolution declarations sing_157.htm#SEC196 3028 resolution declarations (plural) resolution declarations (plural) sing_495.htm#SEC534 3029 resolution expressions resolution expressions sing_158.htm#SEC197 3030 resolution expressions (plural) resolution expressions (plural) sing_496.htm#SEC535 3031 resolution graph sing_1496.htm#IDX560 3032 resolution related functions resolution related functions sing_159.htm#SEC198 3033 resolution related functions (plural) resolution related functions (plural) sing_497.htm#SEC536 3034 resolution, La Scala's method sing_337.htm#SEC376 3035 resolution, computation of sing_386.htm#IDX182 3036 resolution, hilbert-driven sing_312.htm#SEC351 3037 resolutionInLocalization resolutionInLocalization sing_2278.htm#SEC2353 3038 resolutiongraph sing_1497.htm#SEC1572 3039 resolve sing_1458.htm#SEC1533 3040 resolve.lib sing_1454.htm#SEC1529 3041 resolve_lib sing_1454.htm#SEC1529 3042 resources.lib sing_1022.htm#SEC1097 3043 resources_lib sing_1022.htm#SEC1097 3044 restriction sing_2141.htm#IDX809 3045 restriction sing_2157.htm#IDX842 3046 restriction sing_2158.htm#IDX844 3047 restriction of sing_611.htm#IDX336 3048 restrictionIdeal sing_621.htm#SEC672 3049 restrictionModule sing_622.htm#SEC673 3050 resultant sing_351.htm#SEC390 3051 resultant sing_388.htm#SEC427 3052 reszeta.lib sing_1467.htm#SEC1542 3053 reszeta_lib sing_1467.htm#SEC1542 3054 return sing_439.htm#SEC478 3055 return type of procedures Return type of procedures sing_464.htm#SEC503 3056 returnSB, option sing_364.htm#IDX148 3057 reverse sing_2034.htm#SEC2109 3058 reverse lexicographical ordering sing_893.htm#IDX381 3059 reynolds_molien sing_1674.htm#SEC1749 3060 rho sing_1925.htm#SEC2000 3061 rightInverse sing_1863.htm#SEC1938 3062 rightKernel sing_1861.htm#SEC1936 3063 rightModulo sing_772.htm#SEC823 3064 rightNF sing_771.htm#SEC822 3065 rightNFWeyl sing_840.htm#SEC891 3066 rightStd sing_770.htm#SEC821 3067 ring sing_160.htm#SEC199 3068 ring (plural) sing_498.htm#SEC537 3069 ring coefficients hasAlgExtensionCoefficient sing_1048.htm#IDX437 3070 ring coefficients sing_1049.htm#IDX438 3071 ring declarations sing_162.htm#SEC201 3072 ring declarations (plural) ring declarations (plural) sing_499.htm#SEC538 3073 ring operations sing_164.htm#SEC203 3074 ring operations (plural) ring operations (plural) sing_500.htm#SEC539 3075 ring related functions ring related functions sing_163.htm#SEC202 3076 ring related functions (plural) ring related functions (plural) sing_501.htm#SEC540 3077 ring, opposite sing_406.htm#IDX220 3078 ring.lib sing_1027.htm#SEC1102 3079 ring_cf sing_261.htm#IDX135 3080 ring_lib sing_1027.htm#SEC1102 3081 ring_variable sing_2128.htm#IDX786 3082 ring_variable sing_2129.htm#IDX788 3083 ring_variable sing_2130.htm#IDX792 3084 ring_variable sing_2131.htm#IDX794 3085 ringlist sing_389.htm#SEC428 3086 ringlist (plural) sing_526.htm#SEC565 3087 ringtensor sing_1039.htm#SEC1114 3088 ringweights sing_1040.htm#SEC1115 3089 rinvar.lib sing_1710.htm#SEC1785 3090 rinvar_lib sing_1710.htm#SEC1785 3091 rmNmzFiles sing_1307.htm#SEC1382 32601 3092 rm_unitcol sing_1103.htm#SEC1178 3093 rm_unitrow sing_1102.htm#SEC1177 3094 rmx sing_1808.htm#SEC1883 3095 rncAntiCanonicalMap sing_1406.htm#SEC1481 3096 rncItProjEven sing_1410.htm#SEC1485 3097 rncItProjOdd sing_1409.htm#SEC1484 3098 root of Bernstein-Sato polynomial sing_588.htm#IDX325 3099 rootofUnity sing_1042.htm#SEC1117 3100 roots sing_1775.htm#SEC1850 3101 rootsMain sing_1783.htm#SEC1858 3102 rootsModp sing_1907.htm#SEC1982 3103 rootsmr.lib sing_2004.htm#SEC2079 3104 rootsmr_lib sing_2004.htm#SEC2079 3105 rootsur.lib sing_2020.htm#SEC2095 3106 rootsur_lib sing_2020.htm#SEC2095 3107 round sing_1905.htm#SEC1980 3108 rowred sing_1099.htm#SEC1174 3109 rp, global ordering sing_893.htm#IDX380 3110 rswalk sing_2391.htm#SEC2466 3111 rtimer sing_452.htm#SEC491 3112 rvalue No rvalue of increments and assignments sing_458.htm#SEC497 3113 rvar sing_390.htm#SEC429 3114 rwalk sing_2387.htm#SEC2462 3115 rwalk.lib sing_2385.htm#SEC2460 3116 rwalk_lib sing_2385.htm#SEC2460 3117 s_res sing_1056.htm#SEC1131 3118 sa_poly_reduce sing_576.htm#SEC627 3119 sa_reduce sing_575.htm#SEC626 3120 sagbi sing_1360.htm#SEC1435 3121 sagbi.lib sing_1357.htm#SEC1432 3122 sagbiPart sing_1361.htm#SEC1436 3123 sagbiReduce sing_1359.htm#SEC1434 3124 sagbiSPoly sing_1358.htm#SEC1433 3125 sagbi_lib sing_1357.htm#SEC1432 3126 salida sing_1439.htm#SEC1514 3127 sameComponent sing_1987.htm#SEC2062 3128 sameQ sing_1786.htm#SEC1861 3129 sat sing_1168.htm#SEC1243 3130 satiety sing_1255.htm#SEC1330 3131 sba sing_391.htm#SEC430 3132 scalarProd sing_565.htm#SEC616 3133 scheme sing_2251.htm#SEC2326 3134 schreyer.lib sing_1055.htm#SEC1130 3135 schreyer_lib sing_1055.htm#SEC1130 3136 sdb, source code debugger Source code debugger sing_66.htm#SEC102 3137 secondary fan sing_2038.htm#IDX732 3138 secondary polytope sing_2038.htm#IDX733 3139 secondaryFan sing_2046.htm#SEC2121 3140 secondaryPolytope sing_2045.htm#SEC2120 3141 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1695.htm#SEC1770 3142 secondary_char0 sing_1690.htm#SEC1765 3143 secondary_charp sing_1692.htm#SEC1767 3144 secondary_no_molien sing_1693.htm#SEC1768 3145 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1696.htm#SEC1771 3146 segre sing_2173.htm#SEC2248 3147 select sing_1169.htm#SEC1244 3148 select1 sing_1170.htm#SEC1245 3149 semaphore sing_406.htm#IDX238 3150 semaphore sing_1026.htm#SEC1101 3151 semaphores sing_1022.htm#IDX432 3152 semiCMcod2 sing_1651.htm#SEC1726 3153 semidiv sing_1979.htm#SEC2054 3154 semigroup sing_1500.htm#SEC1575 3155 semigroup sing_1504.htm#IDX567 3156 semigroup of values sing_1590.htm#IDX682 3157 semigroupGenerator sing_216.htm#SEC255 3158 sep sing_1337.htm#SEC1412 3159 separateHNE sing_1601.htm#SEC1676 3160 separator sing_1238.htm#SEC1313 3161 serreRelations sing_694.htm#SEC745 3162 set sing_2123.htm#IDX772 3163 setBaseMultigrading sing_2331.htm#SEC2406 3164 setLetterplaceAttributes setLetterplaceAttributes sing_685.htm#SEC736 3165 setLinearForms sing_217.htm#SEC256 3166 setModuleGrading sing_2343.htm#SEC2418 3167 setMultiplicity sing_218.htm#SEC257 3168 setNmzDataPath sing_1304.htm#SEC1379 18123 3169 setNmzExecPath sing_1300.htm#SEC1375 38993 3170 setNmzFilename sing_1303.htm#SEC1378 20206 3171 setNmzOption sing_1297.htm#SEC1372 9012 3172 set_is_injective sing_1967.htm#SEC2042 3173 setcores sing_1024.htm#SEC1099 3174 setenv sing_406.htm#IDX241 3175 setinitials sing_2261.htm#SEC2336 3176 setring sing_392.htm#SEC431 3177 sh sing_406.htm#IDX243 3178 shared sing_251.htm#SEC290 3179 shared declarations sing_254.htm#SEC293 3180 shared expressions sing_255.htm#SEC294 3181 shared operations reference and shared operations sing_256.htm#SEC295 3182 shared related functions reference and shared related functions sing_257.htm#SEC296 3183 sheaf cohomology sing_1477.htm#IDX548 3184 sheafCoh sing_1483.htm#SEC1558 64501 3185 sheafCohBGG sing_1481.htm#SEC1556 13439 3186 sheafCohBGG2 sing_1482.htm#SEC1557 3338 3187 sheafcoh.lib sing_1477.htm#SEC1552 3188 sheafcoh_lib sing_1477.htm#SEC1552 3189 shiftPoly sing_687.htm#SEC738 3190 short sing_449.htm#SEC488 3191 show sing_975.htm#SEC1050 3192 showBO sing_1459.htm#SEC1534 3193 showDataTypes sing_1461.htm#SEC1536 3194 showNmzOptions sing_1298.htm#SEC1373 64955 3195 showNuminvs sing_1295.htm#SEC1370 18934 3196 showgrades sing_798.htm#SEC849 3197 showrecursive sing_976.htm#SEC1051 3198 sickle sing_672.htm#SEC723 3199 signatureBrieskorn sing_1660.htm#SEC1735 3200 signatureL sing_2098.htm#SEC2173 3201 signatureLqf sing_2099.htm#SEC2174 3202 signatureNemethi sing_1662.htm#SEC1737 3203 signaturePuiseux sing_1661.htm#SEC1736 3204 signcnd sing_1788.htm#SEC1863 3205 signcond.lib sing_1787.htm#SEC1862 3206 signcond_lib sing_1787.htm#SEC1862 3207 simplesolver sing_1732.htm#SEC1807 3208 simplex sing_393.htm#SEC432 3209 simplexOut sing_1759.htm#SEC1834 3210 simplify sing_394.htm#SEC433 3211 simplifyRat sing_835.htm#SEC886 3212 sing.lib sing_1627.htm#SEC1702 3213 sing4ti2.lib sing_1363.htm#SEC1438 3214 sing4ti2_lib sing_1363.htm#SEC1438 3215 sing_lib sing_1627.htm#SEC1702 3216 singular locus of D-module sing_815.htm#IDX370 3217 singularities sing_1559.htm#IDX584 3218 singularities sing_1560.htm#IDX595 3219 singularities sing_1561.htm#IDX598 3220 singularities sing_1562.htm#IDX601 3221 singularities sing_1563.htm#IDX604 3222 singularities sing_1564.htm#IDX608 3223 singularities sing_1565.htm#IDX612 3224 singularities sing_1566.htm#IDX618 3225 singularities sing_1567.htm#IDX626 3226 singularities sing_1568.htm#IDX632 3227 singularities sing_1569.htm#IDX640 3228 singularities sing_1570.htm#IDX650 3229 singularities sing_1658.htm#IDX697 3230 singularities, resolution of Resolution of singularities sing_878.htm#SEC929 3231 singularity sing_1524.htm#SEC1599 3232 singularrc sing_20.htm#IDX74 3233 size Miscellaneous oddities sing_395.htm#SEC434 3234 size sing_466.htm#IDX283 3235 skewmat sing_1086.htm#SEC1161 3236 sleep sing_401.htm#SEC440 3237 slimgb sing_396.htm#SEC435 3238 slimgb sing_855.htm#SEC906 3239 slimgb (plural) sing_527.htm#SEC566 3240 slocus sing_1639.htm#SEC1714 3241 smith sing_1872.htm#SEC1947 3242 smithNormalForm sing_2379.htm#SEC2454 3243 solutionsMod2 sing_1922.htm#SEC1997 3244 solve sing_1753.htm#SEC1828 3245 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_340.htm#SEC379 3246 solve.lib sing_1751.htm#SEC1826 3247 solveTInitialFormPar solveTInitialFormPar sing_2088.htm#SEC2163 3248 solve_IP sing_1213.htm#SEC1288 3249 solve_lib sing_1751.htm#SEC1826 3250 solvelinearpart sing_1746.htm#SEC1821 3251 sort sing_948.htm#SEC1023 3252 sortIntvec sing_643.htm#SEC694 3253 sortandmap sing_1747.htm#SEC1822 3254 sortier sing_1709.htm#SEC1784 3255 sortvars sing_1748.htm#SEC1823 3256 sortvec sing_397.htm#SEC436 3257 source code debugger, sdb Source code debugger sing_66.htm#SEC102 3258 spadd sing_1573.htm#SEC1648 3259 span sing_219.htm#SEC258 3260 sparseHomogIdeal sing_1018.htm#SEC1093 3261 sparseid sing_1013.htm#SEC1088 3262 sparsemat sing_1015.htm#SEC1090 3263 sparsematrix sing_1014.htm#SEC1089 3264 sparsepoly sing_1016.htm#SEC1091 3265 sparsetriag sing_1017.htm#SEC1092 3266 spcurve.lib sing_1647.htm#SEC1722 3267 spcurve_lib sing_1647.htm#SEC1722 3268 special characters, non-english sing_455.htm#IDX276 3269 spectral pairs sing_1559.htm#IDX593 3270 spectral pairs sing_1566.htm#IDX625 3271 spectral pairs sing_1568.htm#IDX639 3272 spectral pairs sing_1569.htm#IDX648 3273 spectral pairs sing_1581.htm#IDX664 3274 spectral pairs sing_1583.htm#IDX675 3275 spectralNeg sing_1469.htm#SEC1544 3276 spectrum sing_1559.htm#IDX592 3277 spectrum sing_1565.htm#SEC1640 3278 spectrum sing_1565.htm#IDX617 3279 spectrum sing_1566.htm#IDX624 3280 spectrum sing_1567.htm#IDX631 3281 spectrum sing_1568.htm#IDX638 3282 spectrum sing_1569.htm#IDX647 3283 spectrum sing_1581.htm#IDX663 3284 spectrum sing_1583.htm#IDX674 3285 spectrum sing_1658.htm#IDX699 3286 spectrum.lib sing_1657.htm#SEC1732 3287 spectrum_lib sing_1657.htm#SEC1732 3288 spectrumnd sing_1658.htm#SEC1733 3289 spgamma sing_1580.htm#SEC1655 3290 spgeomgenus sing_1579.htm#SEC1654 3291 spissemicont sing_1576.htm#SEC1651 3292 split sing_977.htm#SEC1052 3293 splitPolygon sing_2048.htm#SEC2123 3294 splitring sing_1349.htm#SEC1424 3295 splitting sing_1246.htm#SEC1321 3296 spmilnor sing_1578.htm#SEC1653 3297 spmul sing_1575.htm#SEC1650 3298 spnf sing_1129.htm#SEC1204 3299 spoly sing_1990.htm#SEC2065 3300 sppairs sing_1566.htm#SEC1641 3301 sppnf sing_1571.htm#SEC1646 3302 sppprint sing_1572.htm#SEC1647 3303 spprint sing_1130.htm#SEC1205 3304 sprintf sing_399.htm#SEC438 3305 spsemicont sing_1577.htm#SEC1652 3306 spsub sing_1574.htm#SEC1649 3307 sqfrNorm sing_1776.htm#SEC1851 3308 sqfrNormMain sing_1784.htm#SEC1859 3309 sqr sing_1902.htm#SEC1977 3310 sqrfree sing_398.htm#SEC437 3311 squareRoot sing_1921.htm#SEC1996 3312 squarefree sing_1602.htm#SEC1677 3313 sres sing_400.htm#SEC439 3314 ssi Parallelization with ssi links sing_850.htm#SEC901 3315 staircase sing_1793.htm#SEC1868 3316 standard sing_1997.htm#SEC2072 3317 standard.lib sing_926.htm#IDX408 3318 standard_lib sing_926.htm#IDX409 3319 startNmz sing_1306.htm#SEC1381 21925 3320 startTasks sing_1066.htm#SEC1141 3321 static procedures Procedure definition sing_43.htm#SEC77 3322 status sing_401.htm#SEC440 3323 std sing_402.htm#SEC441 3324 std sing_853.htm#SEC904 3325 std (plural) sing_528.htm#SEC567 3326 stdfglm sing_403.htm#SEC442 3327 stdhilb sing_404.htm#SEC443 3328 stopTask sing_1067.htm#SEC1142 3329 stratify sing_1727.htm#SEC1802 3330 stratify.lib sing_1725.htm#SEC1800 3331 stratify_lib sing_1725.htm#SEC1800 3332 string Miscellaneous oddities sing_166.htm#SEC205 3333 string sing_466.htm#IDX286 3334 string declarations sing_167.htm#SEC206 3335 string expressions sing_168.htm#SEC207 3336 string operations sing_170.htm#SEC209 3337 string related functions string related functions sing_171.htm#SEC210 3338 string type cast sing_169.htm#SEC208 3339 stripHNE sing_1599.htm#SEC1674 3340 sturm sing_2030.htm#SEC2105 3341 sturmha sing_2032.htm#SEC2107 3342 sturmhaseq sing_2033.htm#SEC2108 3343 sturmquery sing_2008.htm#SEC2083 3344 sturmseq sing_2031.htm#SEC2106 3345 submat sing_1087.htm#SEC1162 3346 subrInterred sing_1006.htm#SEC1081 3347 subset_sum01 sing_1951.htm#SEC2026 3348 subset_sum02 sing_1952.htm#SEC2027 3349 subst sing_405.htm#SEC444 3350 subst (plural) sing_529.htm#SEC568 3351 substitute sing_1005.htm#SEC1080 3352 sugarCrit, option sing_364.htm#IDX165 3353 sum sing_949.htm#SEC1024 3354 sum_of_powers sing_2177.htm#SEC2252 3355 sumlist sing_1441.htm#SEC1516 3356 super-commutative algebras Graded commutative algebras (SCA) sing_538.htm#SEC589 3357 superCommutative sing_769.htm#SEC820 3358 super_increasing_knapsack super_increasing_knapsack sing_1963.htm#SEC2038 3359 surf.lib sing_1810.htm#SEC1885 3360 surf_lib sing_1810.htm#SEC1885 3361 surfacesignature.lib surfacesignature_lib sing_1659.htm#SEC1734 3362 surfacesignature_lib surfacesignature_lib sing_1659.htm#SEC1734 2975 real sing_28.htm#IDX74 2976 real roots, univariate polynomial sing_2023.htm#IDX729 2977 real roots, univariate projection sing_2007.htm#IDX725 2978 real roots,sign conditions sing_1790.htm#IDX705 2979 realclassify sing_2404.htm#SEC2480 2980 realclassify.lib sing_2403.htm#SEC2479 2981 realclassify_lib sing_2403.htm#SEC2479 2982 realizationDim sing_2060.htm#SEC2136 2983 realizationDimPoly sing_2062.htm#SEC2138 2984 realizationMatroids.lib realizationMatroids_lib sing_2059.htm#SEC2135 2985 realizationMatroids_lib realizationMatroids_lib sing_2059.htm#SEC2135 2986 realmorsesplit sing_2405.htm#SEC2481 2987 realpoly sing_1354.htm#SEC1430 2988 realrad sing_1356.htm#SEC1432 2989 realrad.lib sing_1353.htm#SEC1429 2990 realrad_lib sing_1353.htm#SEC1429 2991 realzero sing_1355.htm#SEC1431 2992 recursive_boolean_poly recursive_boolean_poly sing_2111.htm#SEC2187 17045 2993 recursive_from_boolean_poly recursive_from_boolean_poly sing_2117.htm#SEC2193 37794 2994 redSB, option sing_364.htm#IDX160 2995 redTail, option sing_364.htm#IDX162 2996 redThrough, option sing_364.htm#IDX163 2997 redefine, option sing_364.htm#IDX179 2998 reduce sing_383.htm#SEC423 2999 reduce sing_567.htm#IDX312 3000 reduce (plural) sing_525.htm#SEC565 3001 reduced standard basis sing_364.htm#IDX161 3002 reduction sing_1708.htm#SEC1784 3003 reesclos.lib sing_1357.htm#SEC1433 3004 reesclos_lib sing_1357.htm#SEC1433 3005 reference sing_251.htm#SEC291 3006 reference declarations reference declarations sing_252.htm#SEC292 3007 reference expressions reference expressions sing_253.htm#SEC293 3008 reference operations reference and shared operations sing_256.htm#SEC296 3009 reference related functions reference and shared related functions sing_257.htm#SEC297 3010 regCM sing_1270.htm#SEC1346 3011 regIdeal sing_1256.htm#SEC1332 3012 regMonCurve sing_1259.htm#SEC1335 3013 regularity Syzygies and resolutions sing_384.htm#SEC424 3014 regularity sing_902.htm#SEC959 3015 reiffen sing_606.htm#SEC658 3016 rel_orbit_variety sing_1701.htm#SEC1777 3017 relations sing_785.htm#IDX352 3018 relativeInteriorPoint relativeInteriorPoint sing_215.htm#SEC255 3019 relative_orbit_variety relative_orbit_variety sing_1702.htm#SEC1778 3020 relweight sing_1657.htm#SEC1733 3021 remainder sing_1777.htm#SEC1853 3022 remainderMain sing_1785.htm#SEC1861 3023 removeCone sing_235.htm#SEC275 3024 removepower sing_1514.htm#SEC1590 3025 repart sing_385.htm#SEC425 3026 replace sing_1886.htm#SEC1962 3027 representation, math objects Representation of mathematical objects sing_889.htm#SEC941 3028 res sing_386.htm#SEC426 3029 resbinomial.lib sing_1417.htm#IDX546 3030 resbinomial_lib sing_1417.htm#IDX547 3031 reservedName sing_387.htm#SEC427 3032 resfunction sing_1431.htm#SEC1507 3033 resgraph.lib sing_1449.htm#SEC1525 3034 resgraph_lib sing_1449.htm#SEC1525 3035 resjung.lib sing_1453.htm#SEC1529 3036 resjung_lib sing_1453.htm#SEC1529 3037 reslist sing_1445.htm#SEC1521 3038 resolution purityfiltration_lib sing_156.htm#SEC196 3039 resolution sing_793.htm#IDX359 3040 resolution (plural) sing_494.htm#SEC534 3041 resolution declarations resolution declarations sing_157.htm#SEC197 3042 resolution declarations (plural) resolution declarations (plural) sing_495.htm#SEC535 3043 resolution expressions resolution expressions sing_158.htm#SEC198 3044 resolution expressions (plural) resolution expressions (plural) sing_496.htm#SEC536 3045 resolution graph sing_1499.htm#IDX560 3046 resolution related functions resolution related functions sing_159.htm#SEC199 3047 resolution related functions (plural) resolution related functions (plural) sing_497.htm#SEC537 3048 resolution, La Scala's method sing_337.htm#SEC377 3049 resolution, computation of sing_386.htm#IDX181 3050 resolution, hilbert-driven sing_312.htm#SEC352 3051 resolutionInLocalization resolutionInLocalization sing_2289.htm#SEC2365 3052 resolutiongraph sing_1500.htm#SEC1576 3053 resolve sing_1461.htm#SEC1537 3054 resolve.lib sing_1457.htm#SEC1533 3055 resolve_lib sing_1457.htm#SEC1533 3056 resources.lib sing_1022.htm#SEC1098 3057 resources_lib sing_1022.htm#SEC1098 3058 restriction sing_2144.htm#IDX809 3059 restriction sing_2160.htm#IDX842 3060 restriction sing_2161.htm#IDX844 3061 restriction of sing_611.htm#IDX335 3062 restrictionIdeal sing_621.htm#SEC673 3063 restrictionModule sing_622.htm#SEC674 3064 resultant sing_351.htm#SEC391 3065 resultant sing_388.htm#SEC428 3066 reszeta.lib sing_1470.htm#SEC1546 3067 reszeta_lib sing_1470.htm#SEC1546 3068 return sing_439.htm#SEC479 3069 return type of procedures Return type of procedures sing_464.htm#SEC504 3070 returnSB, option sing_364.htm#IDX147 3071 reverse sing_2037.htm#SEC2113 3072 reverse lexicographical ordering sing_893.htm#IDX380 3073 reynolds_molien sing_1677.htm#SEC1753 3074 rho sing_1928.htm#SEC2004 3075 rightInverse sing_1866.htm#SEC1942 3076 rightKernel sing_1864.htm#SEC1940 3077 rightModulo sing_772.htm#SEC824 3078 rightNF sing_771.htm#SEC823 3079 rightNFWeyl sing_840.htm#SEC892 3080 rightStd sing_770.htm#SEC822 3081 ring sing_160.htm#SEC200 3082 ring (plural) sing_498.htm#SEC538 3083 ring coefficients hasAlgExtensionCoefficient sing_1048.htm#IDX436 3084 ring coefficients sing_1049.htm#IDX437 3085 ring declarations sing_162.htm#SEC202 3086 ring declarations (plural) ring declarations (plural) sing_499.htm#SEC539 3087 ring operations sing_164.htm#SEC204 3088 ring operations (plural) ring operations (plural) sing_500.htm#SEC540 3089 ring related functions ring related functions sing_163.htm#SEC203 3090 ring related functions (plural) ring related functions (plural) sing_501.htm#SEC541 3091 ring, opposite sing_406.htm#IDX219 3092 ring.lib sing_1027.htm#SEC1103 3093 ring_cf sing_261.htm#IDX134 3094 ring_lib sing_1027.htm#SEC1103 3095 ring_variable sing_2131.htm#IDX786 3096 ring_variable sing_2132.htm#IDX788 3097 ring_variable sing_2133.htm#IDX792 3098 ring_variable sing_2134.htm#IDX794 3099 ringlist sing_389.htm#SEC429 3100 ringlist (plural) sing_526.htm#SEC566 3101 ringtensor sing_1039.htm#SEC1115 3102 ringweights sing_1040.htm#SEC1116 3103 rinvar.lib sing_1713.htm#SEC1789 3104 rinvar_lib sing_1713.htm#SEC1789 3105 rmNmzFiles sing_1310.htm#SEC1386 32601 3106 rm_unitcol sing_1106.htm#SEC1182 3107 rm_unitrow sing_1105.htm#SEC1181 3108 rmx sing_1811.htm#SEC1887 3109 rncAntiCanonicalMap sing_1409.htm#SEC1485 3110 rncItProjEven sing_1413.htm#SEC1489 3111 rncItProjOdd sing_1412.htm#SEC1488 3112 root of Bernstein-Sato polynomial sing_588.htm#IDX324 3113 rootofUnity sing_1042.htm#SEC1118 3114 roots sing_1778.htm#SEC1854 3115 rootsMain sing_1786.htm#SEC1862 3116 rootsModp sing_1910.htm#SEC1986 3117 rootsmr.lib sing_2007.htm#SEC2083 3118 rootsmr_lib sing_2007.htm#SEC2083 3119 rootsur.lib sing_2023.htm#SEC2099 3120 rootsur_lib sing_2023.htm#SEC2099 3121 round sing_1908.htm#SEC1984 3122 rowred sing_1102.htm#SEC1178 3123 rp, global ordering sing_893.htm#IDX379 3124 rswalk sing_2402.htm#SEC2478 3125 rtimer sing_452.htm#SEC492 3126 rvalue No rvalue of increments and assignments sing_458.htm#SEC498 3127 rvar sing_390.htm#SEC430 3128 rwalk sing_2398.htm#SEC2474 3129 rwalk.lib sing_2396.htm#SEC2472 3130 rwalk_lib sing_2396.htm#SEC2472 3131 s_res sing_1056.htm#SEC1132 3132 sa_poly_reduce sing_576.htm#SEC628 3133 sa_reduce sing_575.htm#SEC627 3134 sagbi sing_1363.htm#SEC1439 3135 sagbi.lib sing_1360.htm#SEC1436 3136 sagbiPart sing_1364.htm#SEC1440 3137 sagbiReduce sing_1362.htm#SEC1438 3138 sagbiSPoly sing_1361.htm#SEC1437 3139 sagbi_lib sing_1360.htm#SEC1436 3140 salida sing_1442.htm#SEC1518 3141 sameComponent sing_1990.htm#SEC2066 3142 sameQ sing_1789.htm#SEC1865 3143 sat sing_1171.htm#SEC1247 3144 satiety sing_1258.htm#SEC1334 3145 satstd sing_2463.htm#SEC2539 3146 sba sing_391.htm#SEC431 3147 scalarProd sing_565.htm#SEC617 3148 scheme sing_2262.htm#SEC2338 3149 schreyer.lib sing_1055.htm#SEC1131 3150 schreyer_lib sing_1055.htm#SEC1131 3151 sdb, source code debugger Source code debugger sing_66.htm#SEC103 3152 secondary fan sing_2041.htm#IDX732 3153 secondary polytope sing_2041.htm#IDX733 3154 secondaryFan sing_2049.htm#SEC2125 3155 secondaryPolytope sing_2048.htm#SEC2124 3156 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1698.htm#SEC1774 3157 secondary_char0 sing_1693.htm#SEC1769 3158 secondary_charp sing_1695.htm#SEC1771 3159 secondary_no_molien sing_1696.htm#SEC1772 3160 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1699.htm#SEC1775 3161 segre sing_2176.htm#SEC2252 3162 select sing_1172.htm#SEC1248 3163 select1 sing_1173.htm#SEC1249 3164 semaphore sing_406.htm#IDX237 3165 semaphore sing_1026.htm#SEC1102 3166 semaphores sing_1022.htm#IDX431 3167 semiCMcod2 sing_1654.htm#SEC1730 3168 semidiv sing_1982.htm#SEC2058 3169 semigroup sing_1503.htm#SEC1579 3170 semigroup sing_1507.htm#IDX567 3171 semigroup of values sing_1593.htm#IDX682 3172 semigroupGenerator sing_216.htm#SEC256 3173 sep sing_1340.htm#SEC1416 3174 separateHNE sing_1604.htm#SEC1680 3175 separator sing_1241.htm#SEC1317 3176 serreRelations sing_694.htm#SEC746 3177 set sing_2126.htm#IDX772 3178 setBaseMultigrading sing_2342.htm#SEC2418 3179 setLetterplaceAttributes setLetterplaceAttributes sing_685.htm#SEC737 3180 setLinearForms sing_217.htm#SEC257 3181 setModuleGrading sing_2354.htm#SEC2430 3182 setMultiplicity sing_218.htm#SEC258 3183 setNmzDataPath sing_1307.htm#SEC1383 18123 3184 setNmzExecPath sing_1303.htm#SEC1379 38993 3185 setNmzFilename sing_1306.htm#SEC1382 20206 3186 setNmzOption sing_1300.htm#SEC1376 9012 3187 set_is_injective sing_1970.htm#SEC2046 3188 setcores sing_1024.htm#SEC1100 3189 setenv sing_406.htm#IDX240 3190 setinitials sing_2272.htm#SEC2348 3191 setring sing_392.htm#SEC432 3192 sh sing_406.htm#IDX242 3193 shared sing_251.htm#SEC291 3194 shared declarations sing_254.htm#SEC294 3195 shared expressions sing_255.htm#SEC295 3196 shared operations reference and shared operations sing_256.htm#SEC296 3197 shared related functions reference and shared related functions sing_257.htm#SEC297 3198 sheaf cohomology sing_1480.htm#IDX548 3199 sheafCoh sing_1486.htm#SEC1562 64501 3200 sheafCohBGG sing_1484.htm#SEC1560 13439 3201 sheafCohBGG2 sing_1485.htm#SEC1561 3338 3202 sheafcoh.lib sing_1480.htm#SEC1556 3203 sheafcoh_lib sing_1480.htm#SEC1556 3204 shiftPoly sing_687.htm#SEC739 3205 short sing_449.htm#SEC489 3206 show sing_975.htm#SEC1051 3207 showBO sing_1462.htm#SEC1538 3208 showDataTypes sing_1464.htm#SEC1540 3209 showNmzOptions sing_1301.htm#SEC1377 64955 3210 showNuminvs sing_1298.htm#SEC1374 18934 3211 showgrades sing_798.htm#SEC850 3212 showrecursive sing_976.htm#SEC1052 3213 sickle sing_672.htm#SEC724 3214 signatureBrieskorn sing_1663.htm#SEC1739 3215 signatureL sing_2101.htm#SEC2177 3216 signatureLqf sing_2102.htm#SEC2178 3217 signatureNemethi sing_1665.htm#SEC1741 3218 signaturePuiseux sing_1664.htm#SEC1740 3219 signcnd sing_1791.htm#SEC1867 3220 signcond.lib sing_1790.htm#SEC1866 3221 signcond_lib sing_1790.htm#SEC1866 3222 simplesolver sing_1735.htm#SEC1811 3223 simplex sing_393.htm#SEC433 3224 simplexOut sing_1762.htm#SEC1838 3225 simplify sing_394.htm#SEC434 3226 simplifyRat sing_835.htm#SEC887 3227 sing.lib sing_1630.htm#SEC1706 3228 sing4ti2.lib sing_1366.htm#SEC1442 3229 sing4ti2_lib sing_1366.htm#SEC1442 3230 sing_lib sing_1630.htm#SEC1706 3231 singular locus of D-module sing_815.htm#IDX369 3232 singularities sing_1562.htm#IDX584 3233 singularities sing_1563.htm#IDX595 3234 singularities sing_1564.htm#IDX598 3235 singularities sing_1565.htm#IDX601 3236 singularities sing_1566.htm#IDX604 3237 singularities sing_1567.htm#IDX608 3238 singularities sing_1568.htm#IDX612 3239 singularities sing_1569.htm#IDX618 3240 singularities sing_1570.htm#IDX626 3241 singularities sing_1571.htm#IDX632 3242 singularities sing_1572.htm#IDX640 3243 singularities sing_1573.htm#IDX650 3244 singularities sing_1661.htm#IDX697 3245 singularities, resolution of Resolution of singularities sing_878.htm#SEC930 3246 singularity sing_1527.htm#SEC1603 3247 singularrc sing_20.htm#IDX73 3248 size Miscellaneous oddities sing_395.htm#SEC435 3249 size sing_466.htm#IDX282 3250 skewmat sing_1089.htm#SEC1165 3251 sleep sing_401.htm#SEC441 3252 slimgb sing_396.htm#SEC436 3253 slimgb sing_855.htm#SEC907 3254 slimgb (plural) sing_527.htm#SEC567 3255 slocus sing_1642.htm#SEC1718 3256 smith sing_1875.htm#SEC1951 3257 smithNormalForm sing_2390.htm#SEC2466 3258 solutionsMod2 sing_1925.htm#SEC2001 3259 solve sing_1756.htm#SEC1832 3260 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_340.htm#SEC380 3261 solve.lib sing_1754.htm#SEC1830 3262 solveTInitialFormPar solveTInitialFormPar sing_2091.htm#SEC2167 3263 solve_IP sing_1216.htm#SEC1292 3264 solve_lib sing_1754.htm#SEC1830 3265 solvelinearpart sing_1749.htm#SEC1825 3266 sort sing_948.htm#SEC1024 3267 sortIntvec sing_643.htm#SEC695 3268 sortandmap sing_1750.htm#SEC1826 3269 sortier sing_1712.htm#SEC1788 3270 sortvars sing_1751.htm#SEC1827 3271 sortvec sing_397.htm#SEC437 3272 source code debugger, sdb Source code debugger sing_66.htm#SEC103 3273 spadd sing_1576.htm#SEC1652 3274 span sing_219.htm#SEC259 3275 sparseHomogIdeal sing_1018.htm#SEC1094 3276 sparseInterpolation sing_2257.htm#SEC2333 3277 sparseid sing_1013.htm#SEC1089 3278 sparsemat sing_1015.htm#SEC1091 3279 sparsematrix sing_1014.htm#SEC1090 3280 sparsepoly sing_1016.htm#SEC1092 3281 sparsetriag sing_1017.htm#SEC1093 3282 spcurve.lib sing_1650.htm#SEC1726 3283 spcurve_lib sing_1650.htm#SEC1726 3284 special characters, non-english sing_455.htm#IDX275 3285 spectral pairs sing_1562.htm#IDX593 3286 spectral pairs sing_1569.htm#IDX625 3287 spectral pairs sing_1571.htm#IDX639 3288 spectral pairs sing_1572.htm#IDX648 3289 spectral pairs sing_1584.htm#IDX664 3290 spectral pairs sing_1586.htm#IDX675 3291 spectralNeg sing_1472.htm#SEC1548 3292 spectrum sing_1562.htm#IDX592 3293 spectrum sing_1568.htm#SEC1644 3294 spectrum sing_1568.htm#IDX617 3295 spectrum sing_1569.htm#IDX624 3296 spectrum sing_1570.htm#IDX631 3297 spectrum sing_1571.htm#IDX638 3298 spectrum sing_1572.htm#IDX647 3299 spectrum sing_1584.htm#IDX663 3300 spectrum sing_1586.htm#IDX674 3301 spectrum sing_1661.htm#IDX699 3302 spectrum.lib sing_1660.htm#SEC1736 3303 spectrum_lib sing_1660.htm#SEC1736 3304 spectrumnd sing_1661.htm#SEC1737 3305 spgamma sing_1583.htm#SEC1659 3306 spgeomgenus sing_1582.htm#SEC1658 3307 spissemicont sing_1579.htm#SEC1655 3308 split sing_977.htm#SEC1053 3309 splitPolygon sing_2051.htm#SEC2127 3310 splitring sing_1352.htm#SEC1428 3311 splitting sing_1249.htm#SEC1325 3312 spmilnor sing_1581.htm#SEC1657 3313 spmul sing_1578.htm#SEC1654 3314 spnf sing_1132.htm#SEC1208 3315 spoly sing_1993.htm#SEC2069 3316 sppairs sing_1569.htm#SEC1645 3317 sppnf sing_1574.htm#SEC1650 3318 sppprint sing_1575.htm#SEC1651 3319 spprint sing_1133.htm#SEC1209 3320 sprintf sing_399.htm#SEC439 3321 spsemicont sing_1580.htm#SEC1656 3322 spsub sing_1577.htm#SEC1653 3323 sqfrNorm sing_1779.htm#SEC1855 3324 sqfrNormMain sing_1787.htm#SEC1863 3325 sqr sing_1905.htm#SEC1981 3326 sqrfree sing_398.htm#SEC438 3327 squareRoot sing_1924.htm#SEC2000 3328 squarefree sing_1605.htm#SEC1681 3329 sres sing_400.htm#SEC440 3330 ssi Parallelization with ssi links sing_850.htm#SEC902 3331 staircase sing_1796.htm#SEC1872 3332 standard sing_2000.htm#SEC2076 3333 standard.lib sing_926.htm#IDX407 3334 standard_lib sing_926.htm#IDX408 3335 startNmz sing_1309.htm#SEC1385 21925 3336 startTasks sing_1069.htm#SEC1145 3337 static procedures Procedure definition sing_43.htm#SEC78 3338 status sing_401.htm#SEC441 3339 std sing_402.htm#SEC442 3340 std sing_853.htm#SEC905 3341 std (plural) sing_528.htm#SEC568 3342 stdfglm sing_403.htm#SEC443 3343 stdhilb sing_404.htm#SEC444 3344 stopTask sing_1070.htm#SEC1146 3345 stratify sing_1730.htm#SEC1806 3346 stratify.lib sing_1728.htm#SEC1804 3347 stratify_lib sing_1728.htm#SEC1804 3348 string Miscellaneous oddities sing_166.htm#SEC206 3349 string sing_466.htm#IDX285 3350 string declarations sing_167.htm#SEC207 3351 string expressions sing_168.htm#SEC208 3352 string operations sing_170.htm#SEC210 3353 string related functions string related functions sing_171.htm#SEC211 3354 string type cast sing_169.htm#SEC209 3355 stripHNE sing_1602.htm#SEC1678 3356 sturm sing_2033.htm#SEC2109 3357 sturmha sing_2035.htm#SEC2111 3358 sturmhaseq sing_2036.htm#SEC2112 3359 sturmquery sing_2011.htm#SEC2087 3360 sturmseq sing_2034.htm#SEC2110 3361 submat sing_1090.htm#SEC1166 3362 subrInterred sing_1006.htm#SEC1082 3363 subset_sum01 sing_1954.htm#SEC2030 3364 subset_sum02 sing_1955.htm#SEC2031 3365 subst sing_405.htm#SEC445 3366 subst (plural) sing_529.htm#SEC569 3367 substitute sing_1005.htm#SEC1081 3368 sugarCrit, option sing_364.htm#IDX164 3369 sum sing_949.htm#SEC1025 3370 sum_of_powers sing_2180.htm#SEC2256 3371 sumlist sing_1444.htm#SEC1520 3372 super-commutative algebras Graded commutative algebras (SCA) sing_538.htm#SEC590 3373 superCommutative sing_769.htm#SEC821 3374 super_increasing_knapsack super_increasing_knapsack sing_1966.htm#SEC2042 3375 surf.lib sing_1813.htm#SEC1889 3376 surf_lib sing_1813.htm#SEC1889 3377 surfacesignature.lib surfacesignature_lib sing_1662.htm#SEC1738 3378 surfacesignature_lib surfacesignature_lib sing_1662.htm#SEC1738 3363 3379 surfer sing_1.htm#IDX8 3364 surfer sing_181 2.htm#SEC18873380 surfer sing_1815.htm#SEC1891 3365 3381 surfex sing_1.htm#IDX7 3366 surfex.lib sing_1813.htm#SEC1888 3367 surfex_lib sing_1813.htm#SEC1888 3368 suspend sing_401.htm#SEC440 3369 swalk sing_2390.htm#SEC2465 3370 swalk.lib sing_2389.htm#SEC2464 3371 swalk_lib sing_2389.htm#SEC2464 3372 swap sing_1528.htm#SEC1603 3373 swap sing_2130.htm#IDX790 3374 switch No case or switch statement sing_460.htm#SEC499 3375 syModStd sing_1373.htm#SEC1448 3376 symNsym sing_2171.htm#SEC2246 3377 sym_gauss sing_1113.htm#SEC1188 3378 symm sing_2170.htm#SEC2245 3379 symmStd sing_1372.htm#SEC1447 3380 symmat sing_1088.htm#SEC1163 3381 symmetric basis sing_1105.htm#IDX446 3382 symmetric power sing_1107.htm#IDX448 3383 symmetricBasis sing_1105.htm#SEC1180 3384 symmetricPower sing_1107.htm#SEC1182 3385 symmfunc sing_2017.htm#SEC2092 3386 symodstd.lib sing_1367.htm#SEC1442 3387 symodstd_lib sing_1367.htm#SEC1442 3388 symsignature sing_2007.htm#SEC2082 3389 syndrome sing_1840.htm#SEC1915 3390 sysBin sing_1838.htm#SEC1913 3391 sysCRHT sing_1835.htm#SEC1910 3392 sysCRHTMindist sing_1836.htm#SEC1911 3393 sysFL sing_1851.htm#SEC1926 3394 sysNewton sing_1837.htm#SEC1912 3395 sysQE sing_1841.htm#SEC1916 3396 sys_code sing_1832.htm#SEC1907 3397 system sing_406.htm#SEC445 3398 system, -- sing_406.htm#IDX266 3399 system, --long_option_name sing_406.htm#IDX269 3400 system, --long_option_name=value sing_406.htm#IDX271 3401 system, HC sing_406.htm#IDX209 3402 system, LLL sing_406.htm#IDX213 3403 system, Singular sing_406.htm#IDX247 3404 system, SingularLib sing_406.htm#IDX249 3405 system, absFact sing_406.htm#IDX185 3406 system, blackbox sing_406.htm#IDX186 3407 system, bracket sing_406.htm#IDX191 3408 system, browsers sing_406.htm#IDX190 3409 system, btest sing_406.htm#IDX193 3410 system, complexNearZero sing_406.htm#IDX194 3411 system, contributors sing_406.htm#IDX196 3412 system, cpu sing_406.htm#IDX198 3413 system, cpu sing_406.htm#IDX265 3414 system, denom_list sing_406.htm#IDX200 3415 system, eigenvals sing_406.htm#IDX201 3416 system, env sing_406.htm#IDX202 3417 system, freegb sing_406.htm#IDX204 3418 system, getPrecDigits sing_406.htm#IDX207 3419 system, getenv sing_406.htm#IDX206 3420 system, gmsnf sing_406.htm#IDX208 3421 system, hessenberg sing_406.htm#IDX210 3422 system, install sing_406.htm#IDX212 3423 system, nblocks sing_406.htm#IDX216 3424 system, newstruct sing_406.htm#IDX217 3425 system, opp sing_406.htm#IDX218 3426 system, oppose sing_406.htm#IDX221 3427 system, pcvBasis sing_406.htm#IDX230 3428 system, pcvCV2P sing_406.htm#IDX228 3429 system, pcvDim sing_406.htm#IDX229 3430 system, pcvLAddL sing_406.htm#IDX224 3431 system, pcvMinDeg sing_406.htm#IDX226 3432 system, pcvP2CV sing_406.htm#IDX227 3433 system, pcvPMulL sing_406.htm#IDX225 3434 system, pid sing_406.htm#IDX232 3435 system, random sing_406.htm#IDX234 3436 system, reserve sing_406.htm#IDX236 3437 system, reservedLink sing_406.htm#IDX237 3438 system, semaphore sing_406.htm#IDX239 3439 system, semic sing_406.htm#IDX240 3440 system, setenv sing_406.htm#IDX242 3441 system, sh sing_406.htm#IDX244 3442 system, shrinktest sing_406.htm#IDX245 3443 system, spadd sing_406.htm#IDX250 3444 system, spectrum sing_406.htm#IDX251 3445 system, spmul sing_406.htm#IDX252 3446 system, std_syz sing_406.htm#IDX253 3447 system, stest sing_406.htm#IDX254 3448 system, tensorModuleMult sing_406.htm#IDX255 3449 system, twostd sing_406.htm#IDX256 3450 system, uname sing_406.htm#IDX259 3451 system, version sing_406.htm#IDX262 3452 system, with sing_406.htm#IDX263 3453 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2275.htm#SEC2350 3454 syz sing_407.htm#SEC446 3455 syz (plural) sing_530.htm#SEC569 3456 syzygy sing_1055.htm#IDX442 3457 tDetropicalise sing_2090.htm#SEC2165 3458 tInitialForm sing_2074.htm#SEC2149 3459 tInitialFormPar sing_2086.htm#SEC2161 3460 tInitialFormParMax sing_2087.htm#SEC2162 3461 tInitialIdeal sing_2075.htm#SEC2150 3462 tab sing_978.htm#SEC1053 3463 tail sing_1986.htm#SEC2061 3464 tame polynomial sing_1581.htm#IDX656 3465 tame polynomial sing_1582.htm#IDX666 3466 tame polynomial sing_1583.htm#IDX667 3467 tangentGens sing_1397.htm#SEC1472 3468 tangentcone sing_1646.htm#SEC1721 3469 task sing_1060.htm#IDX445 3470 tasks.lib sing_1060.htm#SEC1135 3471 tasks_lib sing_1060.htm#SEC1135 3472 tau_es sing_1554.htm#SEC1629 3473 tau_es2 sing_1508.htm#SEC1583 3474 tdCf sing_2204.htm#SEC2279 3475 tdFactor sing_2206.htm#SEC2281 3476 tdProj sing_2209.htm#SEC2284 3477 tdTerms sing_2205.htm#SEC2280 3478 teachstd.lib sing_1984.htm#SEC2059 3479 teachstd_lib sing_1984.htm#SEC2059 3480 template.lib sing_55.htm#IDX121 3481 template.lib sing_55.htm#IDX124 3482 template_lib sing_55.htm#SEC91 3483 template_lib sing_55.htm#IDX122 3484 tensor sing_546.htm#IDX300 3485 tensor sing_1089.htm#SEC1164 3486 tensorMod sing_1208.htm#SEC1283 3487 term orderings General definitions for orderings sing_892.htm#SEC943 3488 term orderings introduction Introduction to orderings sing_891.htm#SEC942 3489 testNCfac sing_743.htm#SEC794 3490 testParametrization sing_1412.htm#SEC1487 3491 testPointConic sing_1413.htm#SEC1488 3492 testPrimary sing_1325.htm#SEC1400 3493 testPrimaryE sing_1326.htm#SEC1401 3494 tex sing_1799.htm#SEC1874 3495 texDrawBasic sing_2081.htm#SEC2156 3496 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2083.htm#SEC2158 3497 texDrawTriangulation texDrawTriangulation sing_2084.htm#SEC2159 3498 texDrawTropical sing_2082.htm#SEC2157 3499 texMatrix sing_2080.htm#SEC2155 3500 texNumber sing_2078.htm#SEC2153 3501 texPolynomial sing_2079.htm#SEC2154 3502 texcoef sing_1880.htm#SEC1955 3503 texdemo sing_1800.htm#SEC1875 3504 texfactorize sing_1801.htm#SEC1876 3505 texmap sing_1802.htm#SEC1877 3506 texname sing_1803.htm#SEC1878 3507 texobj sing_1804.htm#SEC1879 3508 texpoly sing_1805.htm#SEC1880 3509 texproc sing_1806.htm#SEC1881 3510 texring sing_1807.htm#SEC1882 3511 the first alternative algorithm sing_1185.htm#IDX479 3512 three_elements sing_1970.htm#SEC2045 3513 timeFactorize sing_953.htm#SEC1028 3514 timeStd sing_952.htm#SEC1027 3515 timer sing_450.htm#SEC489 3516 timer resolution, setting the sing_406.htm#IDX272 3517 timestep sing_2264.htm#SEC2339 3518 tjurina sing_1642.htm#SEC1717 3519 tmatrix sing_1569.htm#SEC1644 3520 todd sing_2201.htm#SEC2276 3521 toddE sing_2202.htm#SEC2277 3522 toddPoly sing_2215.htm#SEC2290 3523 tolessvars sing_1745.htm#SEC1820 3524 topological invariants sing_1496.htm#IDX558 3525 topological invariants sing_1503.htm#IDX565 3526 topological invariants sing_1504.htm#IDX569 3527 topological invariants sing_1505.htm#IDX573 3528 topological invariants sing_1506.htm#IDX577 3529 toric ideals sing_906.htm#SEC962 3530 toric ring sing_1284.htm#IDX508 3531 toric.lib sing_1374.htm#SEC1449 3532 toric_ideal sing_1375.htm#SEC1450 3533 toric_lib sing_1374.htm#SEC1449 3534 toric_std sing_1376.htm#SEC1451 3535 torusInvariants sing_1290.htm#SEC1365 911 3536 total divisors sing_546.htm#IDX297 3537 total multiplicities sing_1496.htm#IDX561 3538 totalmultiplicities sing_1498.htm#SEC1573 3539 trace sing_408.htm#SEC447 3540 tracemult sing_2011.htm#SEC2086 3541 transpose sing_409.htm#SEC448 3542 trapezoid sing_2258.htm#SEC2333 3543 triMNewton sing_1771.htm#SEC1846 3544 triagmatrix sing_1019.htm#SEC1094 3545 triang.lib sing_1764.htm#SEC1839 3546 triangL sing_1765.htm#SEC1840 3547 triangL_solve sing_1762.htm#SEC1837 3548 triangLf_solve sing_1760.htm#SEC1835 3549 triangLfak sing_1766.htm#SEC1841 3550 triangM sing_1767.htm#SEC1842 3551 triangMH sing_1768.htm#SEC1843 3552 triangM_solve sing_1761.htm#SEC1836 3553 triang_lib sing_1764.htm#SEC1839 3554 triang_solve sing_1763.htm#SEC1838 3555 triangulations sing_2044.htm#SEC2119 3556 tropical curves sing_2060.htm#IDX739 3557 tropical geometry sing_1171.htm#IDX455 3558 tropical mirror symmetry sing_1171.htm#IDX457 3559 tropical polynomials sing_2060.htm#IDX740 3560 tropical.lib sing_2060.htm#IDX737 3561 tropicalCurve sing_2065.htm#SEC2140 3562 tropicalJInvariant sing_2068.htm#SEC2143 3563 tropicalLifting sing_2061.htm#SEC2136 3564 tropicalSubst sing_2093.htm#SEC2168 3565 tropicalVariety sing_2409.htm#SEC2484 3566 tropical_lib sing_2060.htm#IDX738 3567 tropicalise sing_2072.htm#SEC2147 3568 tropicaliseSet sing_2073.htm#SEC2148 3569 truncate sing_1478.htm#SEC1553 13545 3570 truncateFast sing_1479.htm#SEC1554 5124 3571 truncated module sing_1478.htm#IDX549 3572 truncated module sing_1479.htm#IDX550 3573 tst_ncfactor sing_751.htm#SEC802 3574 twalk sing_1184.htm#SEC1259 3575 two-sided sing_546.htm#IDX298 3576 two-sided Groebner basis sing_546.htm#IDX299 3577 twostd sing_406.htm#IDX257 3578 twostd sing_531.htm#SEC570 3579 type sing_410.htm#SEC449 3580 type B sing_2146.htm#IDX817 3581 type D sing_2147.htm#IDX819 3582 type,custom Definition of a user defined type sing_178.htm#SEC217 3583 type2arr sing_2124.htm#SEC2199 3584 typecasting sing_2124.htm#IDX773 3585 typecasting sing_2125.htm#IDX775 3586 typecasting sing_2126.htm#IDX778 3587 typeof sing_411.htm#SEC450 3588 u sing_2250.htm#SEC2325 3589 uname sing_406.htm#IDX258 3590 unbounded_knapsack sing_1953.htm#SEC2028 3591 unipotent groups sing_1396.htm#IDX517 3592 uniquePoint sing_220.htm#SEC259 3593 unitmat sing_1090.htm#SEC1165 3594 univariate sing_412.htm#SEC451 3595 univarpoly sing_2018.htm#SEC2093 3596 unknown syndrome Decoding method based on quadratic equations sing_922.htm#SEC992 3597 unset sing_325.htm#SEC364 3598 untyped definitions sing_83.htm#SEC122 3599 untyped definitions sing_471.htm#SEC510 3600 updatePairs sing_1996.htm#SEC2071 3601 ures_solve sing_1754.htm#SEC1829 3602 uressolve sing_413.htm#SEC452 3603 usage, option sing_364.htm#IDX181 3382 surfex.lib sing_1816.htm#SEC1892 3383 surfex_lib sing_1816.htm#SEC1892 3384 suspend sing_401.htm#SEC441 3385 swalk sing_2401.htm#SEC2477 3386 swalk.lib sing_2400.htm#SEC2476 3387 swalk_lib sing_2400.htm#SEC2476 3388 swap sing_1531.htm#SEC1607 3389 swap sing_2133.htm#IDX790 3390 switch No case or switch statement sing_460.htm#SEC500 3391 syModStd sing_1376.htm#SEC1452 3392 symNsym sing_2174.htm#SEC2250 3393 sym_gauss sing_1116.htm#SEC1192 3394 symm sing_2173.htm#SEC2249 3395 symmStd sing_1375.htm#SEC1451 3396 symmat sing_1091.htm#SEC1167 3397 symmetric basis sing_1108.htm#IDX445 3398 symmetric power sing_1110.htm#IDX447 3399 symmetricBasis sing_1108.htm#SEC1184 3400 symmetricPower sing_1110.htm#SEC1186 3401 symmfunc sing_2020.htm#SEC2096 3402 symodstd.lib sing_1370.htm#SEC1446 3403 symodstd_lib sing_1370.htm#SEC1446 3404 symsignature sing_2010.htm#SEC2086 3405 syndrome sing_1843.htm#SEC1919 3406 sysBin sing_1841.htm#SEC1917 3407 sysCRHT sing_1838.htm#SEC1914 3408 sysCRHTMindist sing_1839.htm#SEC1915 3409 sysFL sing_1854.htm#SEC1930 3410 sysNewton sing_1840.htm#SEC1916 3411 sysQE sing_1844.htm#SEC1920 3412 sys_code sing_1835.htm#SEC1911 3413 system sing_406.htm#SEC446 3414 system, -- sing_406.htm#IDX265 3415 system, --long_option_name sing_406.htm#IDX268 3416 system, --long_option_name=value sing_406.htm#IDX270 3417 system, HC sing_406.htm#IDX208 3418 system, LLL sing_406.htm#IDX212 3419 system, Singular sing_406.htm#IDX246 3420 system, SingularLib sing_406.htm#IDX248 3421 system, absFact sing_406.htm#IDX184 3422 system, blackbox sing_406.htm#IDX185 3423 system, bracket sing_406.htm#IDX190 3424 system, browsers sing_406.htm#IDX189 3425 system, btest sing_406.htm#IDX192 3426 system, complexNearZero sing_406.htm#IDX193 3427 system, contributors sing_406.htm#IDX195 3428 system, cpu sing_406.htm#IDX197 3429 system, cpu sing_406.htm#IDX264 3430 system, denom_list sing_406.htm#IDX199 3431 system, eigenvals sing_406.htm#IDX200 3432 system, env sing_406.htm#IDX201 3433 system, freegb sing_406.htm#IDX203 3434 system, getPrecDigits sing_406.htm#IDX206 3435 system, getenv sing_406.htm#IDX205 3436 system, gmsnf sing_406.htm#IDX207 3437 system, hessenberg sing_406.htm#IDX209 3438 system, install sing_406.htm#IDX211 3439 system, nblocks sing_406.htm#IDX215 3440 system, newstruct sing_406.htm#IDX216 3441 system, opp sing_406.htm#IDX217 3442 system, oppose sing_406.htm#IDX220 3443 system, pcvBasis sing_406.htm#IDX229 3444 system, pcvCV2P sing_406.htm#IDX227 3445 system, pcvDim sing_406.htm#IDX228 3446 system, pcvLAddL sing_406.htm#IDX223 3447 system, pcvMinDeg sing_406.htm#IDX225 3448 system, pcvP2CV sing_406.htm#IDX226 3449 system, pcvPMulL sing_406.htm#IDX224 3450 system, pid sing_406.htm#IDX231 3451 system, random sing_406.htm#IDX233 3452 system, reserve sing_406.htm#IDX235 3453 system, reservedLink sing_406.htm#IDX236 3454 system, semaphore sing_406.htm#IDX238 3455 system, semic sing_406.htm#IDX239 3456 system, setenv sing_406.htm#IDX241 3457 system, sh sing_406.htm#IDX243 3458 system, shrinktest sing_406.htm#IDX244 3459 system, spadd sing_406.htm#IDX249 3460 system, spectrum sing_406.htm#IDX250 3461 system, spmul sing_406.htm#IDX251 3462 system, std_syz sing_406.htm#IDX252 3463 system, stest sing_406.htm#IDX253 3464 system, tensorModuleMult sing_406.htm#IDX254 3465 system, twostd sing_406.htm#IDX255 3466 system, uname sing_406.htm#IDX258 3467 system, version sing_406.htm#IDX261 3468 system, with sing_406.htm#IDX262 3469 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2286.htm#SEC2362 3470 syz sing_407.htm#SEC447 3471 syz (plural) sing_530.htm#SEC570 3472 syzygy sing_1055.htm#IDX441 3473 tDetropicalise sing_2093.htm#SEC2169 3474 tInitialForm sing_2077.htm#SEC2153 3475 tInitialFormPar sing_2089.htm#SEC2165 3476 tInitialFormParMax sing_2090.htm#SEC2166 3477 tInitialIdeal sing_2078.htm#SEC2154 3478 tab sing_978.htm#SEC1054 3479 tail sing_1989.htm#SEC2065 3480 tame polynomial sing_1584.htm#IDX656 3481 tame polynomial sing_1585.htm#IDX666 3482 tame polynomial sing_1586.htm#IDX667 3483 tangentGens sing_1400.htm#SEC1476 3484 tangentcone sing_1649.htm#SEC1725 3485 task sing_1063.htm#IDX444 3486 tasks.lib sing_1063.htm#SEC1139 3487 tasks_lib sing_1063.htm#SEC1139 3488 tau_es sing_1557.htm#SEC1633 3489 tau_es2 sing_1511.htm#SEC1587 3490 tdCf sing_2209.htm#SEC2285 3491 tdFactor sing_2211.htm#SEC2287 3492 tdProj sing_2214.htm#SEC2290 3493 tdTerms sing_2210.htm#SEC2286 3494 teachstd.lib sing_1987.htm#SEC2063 3495 teachstd_lib sing_1987.htm#SEC2063 3496 template.lib sing_55.htm#IDX120 3497 template.lib sing_55.htm#IDX123 3498 template_lib sing_55.htm#SEC92 3499 template_lib sing_55.htm#IDX121 3500 tensor sing_546.htm#IDX299 3501 tensor sing_1092.htm#SEC1168 3502 tensorMod sing_1211.htm#SEC1287 3503 term orderings General definitions for orderings sing_892.htm#SEC944 3504 term orderings introduction Introduction to orderings sing_891.htm#SEC943 3505 testNCfac sing_743.htm#SEC795 3506 testParametrization sing_1415.htm#SEC1491 3507 testPointConic sing_1416.htm#SEC1492 3508 testPrimary sing_1328.htm#SEC1404 3509 testPrimaryE sing_1329.htm#SEC1405 3510 tex sing_1802.htm#SEC1878 3511 texDrawBasic sing_2084.htm#SEC2160 3512 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2086.htm#SEC2162 3513 texDrawTriangulation texDrawTriangulation sing_2087.htm#SEC2163 3514 texDrawTropical sing_2085.htm#SEC2161 3515 texMatrix sing_2083.htm#SEC2159 3516 texNumber sing_2081.htm#SEC2157 3517 texPolynomial sing_2082.htm#SEC2158 3518 texcoef sing_1883.htm#SEC1959 3519 texdemo sing_1803.htm#SEC1879 3520 texfactorize sing_1804.htm#SEC1880 3521 texmap sing_1805.htm#SEC1881 3522 texname sing_1806.htm#SEC1882 3523 texobj sing_1807.htm#SEC1883 3524 texpoly sing_1808.htm#SEC1884 3525 texproc sing_1809.htm#SEC1885 3526 texring sing_1810.htm#SEC1886 3527 the first alternative algorithm sing_1188.htm#IDX479 3528 three_elements sing_1973.htm#SEC2049 3529 timeFactorize sing_953.htm#SEC1029 3530 timeStd sing_952.htm#SEC1028 3531 timer sing_450.htm#SEC490 3532 timer resolution, setting the sing_406.htm#IDX271 3533 timestep sing_2275.htm#SEC2351 3534 tjurina sing_1645.htm#SEC1721 3535 tmatrix sing_1572.htm#SEC1648 3536 todd sing_2206.htm#SEC2282 3537 toddE sing_2207.htm#SEC2283 3538 toddPoly sing_2220.htm#SEC2296 3539 tolessvars sing_1748.htm#SEC1824 3540 topological invariants sing_1499.htm#IDX558 3541 topological invariants sing_1506.htm#IDX565 3542 topological invariants sing_1507.htm#IDX569 3543 topological invariants sing_1508.htm#IDX573 3544 topological invariants sing_1509.htm#IDX577 3545 toric geometry sing_2461.htm#SEC2537 3546 toric ideals sing_906.htm#SEC963 3547 toric ring sing_1287.htm#IDX508 3548 toric.lib sing_1377.htm#SEC1453 3549 toric_ideal sing_1378.htm#SEC1454 3550 toric_lib sing_1377.htm#SEC1453 3551 toric_std sing_1379.htm#SEC1455 3552 torusInvariants sing_1293.htm#SEC1369 911 3553 total divisors sing_546.htm#IDX296 3554 total multiplicities sing_1499.htm#IDX561 3555 totalmultiplicities sing_1501.htm#SEC1577 3556 trace sing_408.htm#SEC448 3557 tracemult sing_2014.htm#SEC2090 3558 transpose sing_409.htm#SEC449 3559 trapezoid sing_2269.htm#SEC2345 3560 triMNewton sing_1774.htm#SEC1850 3561 triagmatrix sing_1019.htm#SEC1095 3562 triang.lib sing_1767.htm#SEC1843 3563 triangL sing_1768.htm#SEC1844 3564 triangL_solve sing_1765.htm#SEC1841 3565 triangLf_solve sing_1763.htm#SEC1839 3566 triangLfak sing_1769.htm#SEC1845 3567 triangM sing_1770.htm#SEC1846 3568 triangMH sing_1771.htm#SEC1847 3569 triangM_solve sing_1764.htm#SEC1840 3570 triang_lib sing_1767.htm#SEC1843 3571 triang_solve sing_1766.htm#SEC1842 3572 triangulations sing_2047.htm#SEC2123 3573 tropical curves sing_2063.htm#IDX739 3574 tropical geometry sing_1174.htm#IDX455 3575 tropical mirror symmetry sing_1174.htm#IDX457 3576 tropical polynomials sing_2063.htm#IDX740 3577 tropical.lib sing_2063.htm#IDX737 3578 tropicalCurve sing_2068.htm#SEC2144 3579 tropicalJInvariant sing_2071.htm#SEC2147 3580 tropicalLifting sing_2064.htm#SEC2140 3581 tropicalSubst sing_2096.htm#SEC2172 3582 tropicalVariety sing_2420.htm#SEC2496 3583 tropical_lib sing_2063.htm#IDX738 3584 tropicalise sing_2075.htm#SEC2151 3585 tropicaliseSet sing_2076.htm#SEC2152 3586 truncate sing_1481.htm#SEC1557 13545 3587 truncateFast sing_1482.htm#SEC1558 5124 3588 truncated module sing_1481.htm#IDX549 3589 truncated module sing_1482.htm#IDX550 3590 tst_ncfactor sing_751.htm#SEC803 3591 twalk sing_1187.htm#SEC1263 3592 two-sided sing_546.htm#IDX297 3593 two-sided Groebner basis sing_546.htm#IDX298 3594 twostd sing_406.htm#IDX256 3595 twostd sing_531.htm#SEC571 3596 type sing_410.htm#SEC450 3597 type B sing_2149.htm#IDX817 3598 type D sing_2150.htm#IDX819 3599 type,custom Definition of a user defined type sing_178.htm#SEC218 3600 type2arr sing_2127.htm#SEC2203 3601 typecasting sing_2127.htm#IDX773 3602 typecasting sing_2128.htm#IDX775 3603 typecasting sing_2129.htm#IDX778 3604 typeof sing_411.htm#SEC451 3605 u sing_2261.htm#SEC2337 3606 uname sing_406.htm#IDX257 3607 unbounded_knapsack sing_1956.htm#SEC2032 3608 unipotent groups sing_1399.htm#IDX517 3609 uniquePoint sing_220.htm#SEC260 3610 unitmat sing_1093.htm#SEC1169 3611 univariate sing_412.htm#SEC452 3612 univarpoly sing_2021.htm#SEC2097 3613 unknown syndrome Decoding method based on quadratic equations sing_922.htm#SEC993 3614 unset sing_325.htm#SEC365 3615 untyped definitions sing_83.htm#SEC123 3616 untyped definitions sing_471.htm#SEC511 3617 updatePairs sing_1999.htm#SEC2075 3618 ures_solve sing_1757.htm#SEC1833 3619 uressolve sing_413.htm#SEC453 3620 usage, option sing_364.htm#IDX180 3604 3621 user interface, Emacs Emacs user interface sing_21.htm#SEC28 3605 valvars sing_17 49.htm#SEC18243606 vandermonde sing_414.htm#SEC45 33607 vanishId sing_185 0.htm#SEC19253608 var sing_415.htm#SEC45 43609 varMat sing_21 28.htm#SEC22033610 varNum sing_21 29.htm#SEC22043611 variables sing_416.htm#SEC45 53612 variables sing_21 28.htm#IDX7853613 variables sing_21 29.htm#IDX7873614 variables sing_213 0.htm#IDX7913615 variables sing_213 1.htm#IDX7933616 variablesSorted sing_584.htm#SEC63 53617 variablesStandard sing_583.htm#SEC63 43618 vars2pars sing_830.htm#SEC88 13619 varsigns sing_202 3.htm#SEC20983620 varstr sing_417.htm#SEC45 63621 vct2str sing_692.htm#SEC74 33622 vdim sing_418.htm#SEC45 73623 vdim (plural) sing_532.htm#SEC57 13624 vec2poly sing_566.htm#SEC61 73625 vector sing_172.htm#SEC21 13626 vector declarations sing_173.htm#SEC21 23627 vector expressions sing_174.htm#SEC21 33628 vector operations sing_175.htm#SEC21 43629 vector related functions vector related functions sing_176.htm#SEC21 53630 verify sing_201 4.htm#SEC20893631 versal sing_15 49.htm#SEC16243632 version sing_406.htm#IDX26 13633 vertexAdjacencyGraph vertexAdjacencyGraph sing_24 47.htm#SEC25223634 vertexEdgeGraph sing_24 48.htm#SEC25233635 vertices sing_242.htm#SEC28 13636 vfilt sing_15 67.htm#SEC16423637 view sing_187 0.htm#SEC19453638 visual sing_24 49.htm#SEC25243639 visualize sing_22 49.htm#SEC23243640 voice sing_453.htm#SEC49 23641 vwfilt sing_15 68.htm#SEC16433642 wUnit sing_19 08.htm#SEC19833643 waitAllTasks sing_10 69.htm#SEC11443644 waitTasks sing_10 68.htm#SEC11433645 waitall sing_419.htm#SEC45 83646 waitfirst sing_420.htm#SEC4 593647 warkedPreimageStd sing_22 77.htm#SEC23523648 warn, option sing_70.htm#SEC1 093649 warn, option sing_364.htm#IDX14 73650 watchdog sing_950.htm#SEC102 53651 wedge sing_421.htm#SEC46 03652 weierstr.lib sing_ 1999.htm#SEC20743653 weierstrDiv sing_200 0.htm#SEC20753654 weierstrPrep sing_200 1.htm#SEC20763655 weierstr_lib sing_ 1999.htm#SEC20743656 weierstrassForm sing_20 69.htm#SEC21443657 weight sing_422.htm#SEC46 13658 weight filtration sing_15 59.htm#IDX5893659 weight filtration sing_156 6.htm#IDX6233660 weight filtration sing_15 68.htm#IDX6373661 weight filtration sing_15 69.htm#IDX6453662 weight filtration sing_158 1.htm#IDX6613663 weight filtration sing_158 3.htm#IDX6723664 weightKB sing_423.htm#SEC46 23665 weightM, option sing_364.htm#IDX16 63666 weighted lexicographical ordering sing_893.htm#IDX38 83667 weighted reverse lexicographical ordering Global orderings sing_893.htm#IDX38 63668 weightedRing sing_762.htm#SEC81 33669 whichvariable sing_202 2.htm#SEC20973670 while sing_440.htm#SEC4 793671 withDim sing_261.htm#IDX14 13672 withHilb sing_261.htm#IDX13 93673 withMult sing_261.htm#IDX14 23674 withRes sing_261.htm#IDX1 403675 withSB sing_261.htm#IDX13 83676 wp, global ordering sing_893.htm#IDX38 73677 write sing_424.htm#SEC46 33678 writeNmzData sing_130 1.htm#SEC1376384673679 writeNmzPaths sing_130 5.htm#SEC1380sprintf3680 ws, local ordering sing_894.htm#IDX39 83681 wurzel sing_189 0.htm#SEC19653682 xchange sing_188 4.htm#SEC19593683 xdvi sing_18 09.htm#SEC18843684 zdd sing_210 2.htm#IDX7513685 zdd2poly sing_21 19.htm#SEC2194550473686 zero-dimensional sing_20 19.htm#IDX7283687 zeroMod sing_124 2.htm#SEC13173688 zeroOpt sing_125 1.htm#SEC13263689 zeroRadical sing_115 3.htm#SEC12283690 zeroSet sing_17 77.htm#SEC18523691 zerodec sing_133 4.htm#SEC14093692 zeroset.lib sing_177 2.htm#SEC18473693 zeroset_lib sing_177 2.htm#SEC18473694 zetaDL sing_147 1.htm#SEC15463695 { sing_36.htm#IDX7 93696 || sing_36.htm#IDX10 43697 || sing_96.htm#SEC13 53698 } sing_36.htm#IDX 803699 ~ sing_36.htm#IDX11 83700 ~ sing_441.htm#SEC48 03622 valvars sing_1752.htm#SEC1828 3623 vandermonde sing_414.htm#SEC454 3624 vanishId sing_1853.htm#SEC1929 3625 var sing_415.htm#SEC455 3626 varMat sing_2131.htm#SEC2207 3627 varNum sing_2132.htm#SEC2208 3628 variables sing_416.htm#SEC456 3629 variables sing_2131.htm#IDX785 3630 variables sing_2132.htm#IDX787 3631 variables sing_2133.htm#IDX791 3632 variables sing_2134.htm#IDX793 3633 variablesSorted sing_584.htm#SEC636 3634 variablesStandard sing_583.htm#SEC635 3635 vars2pars sing_830.htm#SEC882 3636 varsigns sing_2026.htm#SEC2102 3637 varstr sing_417.htm#SEC457 3638 vct2str sing_692.htm#SEC744 3639 vdim sing_418.htm#SEC458 3640 vdim (plural) sing_532.htm#SEC572 3641 vec2poly sing_566.htm#SEC618 3642 vector sing_172.htm#SEC212 3643 vector declarations sing_173.htm#SEC213 3644 vector expressions sing_174.htm#SEC214 3645 vector operations sing_175.htm#SEC215 3646 vector related functions vector related functions sing_176.htm#SEC216 3647 verify sing_2017.htm#SEC2093 3648 versal sing_1552.htm#SEC1628 3649 version sing_406.htm#IDX260 3650 vertexAdjacencyGraph vertexAdjacencyGraph sing_2458.htm#SEC2534 3651 vertexEdgeGraph sing_2459.htm#SEC2535 3652 vertices sing_242.htm#SEC282 3653 vfilt sing_1570.htm#SEC1646 3654 view sing_1873.htm#SEC1949 3655 visual sing_2460.htm#SEC2536 3656 visualize sing_2260.htm#SEC2336 3657 voice sing_453.htm#SEC493 3658 vwfilt sing_1571.htm#SEC1647 3659 wUnit sing_1911.htm#SEC1987 3660 waitAllTasks sing_1072.htm#SEC1148 3661 waitTasks sing_1071.htm#SEC1147 3662 waitall sing_419.htm#SEC459 3663 waitfirst sing_420.htm#SEC460 3664 warkedPreimageStd sing_2288.htm#SEC2364 3665 warn, option sing_70.htm#SEC110 3666 warn, option sing_364.htm#IDX146 3667 watchdog sing_950.htm#SEC1026 3668 wedge sing_421.htm#SEC461 3669 weierstr.lib sing_2002.htm#SEC2078 3670 weierstrDiv sing_2003.htm#SEC2079 3671 weierstrPrep sing_2004.htm#SEC2080 3672 weierstr_lib sing_2002.htm#SEC2078 3673 weierstrassForm sing_2072.htm#SEC2148 3674 weight sing_422.htm#SEC462 3675 weight filtration sing_1562.htm#IDX589 3676 weight filtration sing_1569.htm#IDX623 3677 weight filtration sing_1571.htm#IDX637 3678 weight filtration sing_1572.htm#IDX645 3679 weight filtration sing_1584.htm#IDX661 3680 weight filtration sing_1586.htm#IDX672 3681 weightKB sing_423.htm#SEC463 3682 weightM, option sing_364.htm#IDX165 3683 weighted lexicographical ordering sing_893.htm#IDX387 3684 weighted reverse lexicographical ordering Global orderings sing_893.htm#IDX385 3685 weightedRing sing_762.htm#SEC814 3686 whichvariable sing_2025.htm#SEC2101 3687 while sing_440.htm#SEC480 3688 withDim sing_261.htm#IDX140 3689 withHilb sing_261.htm#IDX138 3690 withMult sing_261.htm#IDX141 3691 withRes sing_261.htm#IDX139 3692 withSB sing_261.htm#IDX137 3693 wp, global ordering sing_893.htm#IDX386 3694 write sing_424.htm#SEC464 3695 writeNmzData sing_1304.htm#SEC1380 38467 3696 writeNmzPaths sing_1308.htm#SEC1384 sprintf 3697 ws, local ordering sing_894.htm#IDX397 3698 wurzel sing_1893.htm#SEC1969 3699 xchange sing_1887.htm#SEC1963 3700 xdvi sing_1812.htm#SEC1888 3701 zdd sing_2105.htm#IDX751 3702 zdd2poly sing_2122.htm#SEC2198 55047 3703 zero-dimensional sing_2022.htm#IDX728 3704 zeroMod sing_1245.htm#SEC1321 3705 zeroOpt sing_1254.htm#SEC1330 3706 zeroRadical sing_1156.htm#SEC1232 3707 zeroSet sing_1780.htm#SEC1856 3708 zerodec sing_1337.htm#SEC1413 3709 zeroset.lib sing_1775.htm#SEC1851 3710 zeroset_lib sing_1775.htm#SEC1851 3711 zetaDL sing_1474.htm#SEC1550 3712 { sing_36.htm#IDX78 3713 || sing_36.htm#IDX103 3714 || sing_96.htm#SEC136 3715 } sing_36.htm#IDX79 3716 ~ sing_36.htm#IDX117 3717 ~ sing_441.htm#SEC481 -
emacs/hlp-cmpl.el
r449825 ra719149 50 50 ("-user-option" . "Command line options") 51 51 ("-v" . "Command line options") 52 ("-verbose" . "Command line options")53 52 (".." . "Special characters. (line 104") 54 53 (".singularrc file" . "Startup sequence. (line 10") … … 242 241 ("BelongSemig" . "BelongSemig. (line 6") 243 242 ("belongSemigroup" . "belongSemigroup. (line 6") 243 ("BerlekampMassey" . "BerlekampMassey. (line 6") 244 244 ("Bern" . "Bern. (line 6") 245 245 ("bernstein" . "bernstein. (line 6") … … 429 429 ("chProdL" . "chProdL. (line 6") 430 430 ("chProdLP" . "chProdLP. (line 6") 431 ("chProdM" . "chProdM. (line 6") 432 ("chProdMP" . "chProdMP. (line 6") 431 433 ("chProj" . "chProj. (line 6") 432 434 ("chSum" . "chSum. (line 6") … … 594 596 ("custom type" . "Definition of a user defined type") 595 597 ("Customization of the Emacs interface" . "Customization of the Emacs interface") 598 ("customstd.so" . "customstd_so. (line 6") 596 599 ("cycleLength" . "cycleLength. (line 6") 597 600 ("cyclePoints" . "cyclePoints. (line 6") … … 601 604 ("Cyclic roots" . "Cyclic roots. (line 6") 602 605 ("cyclotomic" . "cyclotomic. (line 6") 606 ("CYGWIN and ESingular" . "Running SINGULAR under Emacs") 603 607 ("D-integration" . "dmodapp_lib. (line 104") 604 608 ("D-localization" . "dmodloc_lib. (line 93") … … 856 860 ("errorRand" . "errorRand. (line 6") 857 861 ("esIdeal" . "esIdeal. (line 6") 862 ("ESingular, CYGWIN" . "Running SINGULAR under Emacs") 858 863 ("essential" . "arrEssentialize. (line 17") 859 864 ("esStratum" . "esStratum. (line 6") … … 924 929 ("fanViaCones" . "fanViaCones. (line 6") 925 930 ("farey" . "farey. (line 6") 931 ("fareypoly" . "fareypoly. (line 6") 926 932 ("fastelim" . "fastelim. (line 6") 927 933 ("fastExpt" . "fastExpt. (line 6") … … 931 937 ("fetchall" . "fetchall. (line 6") 932 938 ("Feynman graph" . "ellipticcovers_lib. (line 49") 939 ("ffmodStd" . "ffmodStd. (line 6") 940 ("ffmodstd.lib" . "ffmodstd_lib. (line 6") 941 ("ffmodstd_lib" . "ffmodstd_lib. (line 6") 933 942 ("ffsolve" . "ffsolve. (line 6") 934 943 ("ffsolve.lib" . "ffsolve_lib. (line 6") … … 2290 2299 ("polybori.lib" . "polybori_lib. (line 6") 2291 2300 ("polybori_lib" . "polybori_lib. (line 6") 2301 ("polyInterpolation" . "polyInterpolation. (line 6") 2292 2302 ("polymake" . "polymake_lib. (line 83") 2293 2303 ("polymake.lib" . "polymake_lib. (line 6") … … 2691 2701 ("sat" . "sat. (line 6") 2692 2702 ("satiety" . "satiety. (line 6") 2693 ("Saturation" . "Saturation. (line 6") 2703 ("satstd" . "satstd. (line 6") 2704 ("Saturation" . "satstd. (line 6") 2694 2705 ("sba" . "sba. (line 6") 2695 2706 ("SCA" . "Graded commutative algebras (SCA)") … … 2842 2853 ("sparseHomogIdeal" . "sparseHomogIdeal. (line 6") 2843 2854 ("sparseid" . "sparseid. (line 6") 2855 ("sparseInterpolation" . "sparseInterpolation. (line 6") 2844 2856 ("sparsemat" . "sparsemat. (line 6") 2845 2857 ("sparsematrix" . "sparsematrix. (line 6") … … 2883 2895 ("Sres" . "Sres. (line 6") 2884 2896 ("sres" . "sres. (line 6") 2897 ("SScontinue" . "SScontinue. (line 6") 2885 2898 ("ssi" . "Parallelization with ssi links") 2886 2899 ("Ssi file links" . "Ssi file links. (line 6") 2887 2900 ("Ssi links" . "Ssi links. (line 6") 2888 2901 ("Ssi tcp links" . "Ssi tcp links. (line 6") 2902 ("SSres" . "SSres. (line 6") 2903 ("SSsyz" . "SSsyz. (line 6") 2889 2904 ("Ssyz" . "Ssyz. (line 6") 2890 2905 ("StabEqn" . "StabEqn. (line 6") … … 3122 3137 ("topological invariants" . "charexp2conductor. (line 18") 3123 3138 ("Tor" . "Tor. (line 6") 3139 ("toric geometry" . "toric geometry. (line 6") 3124 3140 ("toric ideals" . "Toric ideals. (line 6") 3125 3141 ("Toric ideals and integer programming" . "Toric ideals and integer programming")
Note: See TracChangeset
for help on using the changeset viewer.
