Changeset 2542b2 in git
- Timestamp:
- Jul 31, 2018, 3:02:30 PM (5 years ago)
- Branches:
- (u'spielwiese', '8e0ad00ce244dfd0756200662572aef8402f13d5')
- Children:
- c4532ad56fe482b30e500057ca76121dac774af2
- Parents:
- c58025e5c3afe702c2dc7521575f785489149330
- Files:
-
- 2 edited
-
doc/singular.idx (modified) (19 diffs)
-
emacs/hlp-cmpl.el (modified) (30 diffs)
Legend:
- Unmodified
- Added
- Removed
-
doc/singular.idx
rc58025 r2542b2 41 41 + sing_155.htm#SEC195 42 42 + sing_169.htm#SEC209 43 + sing_17 5.htm#SEC21544 + sing_18 0.htm#SEC22043 + sing_176.htm#SEC216 44 + sing_181.htm#SEC221 45 45 ++ sing_36.htm#IDX86 46 46 - bigintmat operations sing_36.htm#IDX87 … … 53 53 - sing_147.htm#SEC187 54 54 - sing_155.htm#SEC195 55 - sing_18 0.htm#SEC22055 - sing_181.htm#SEC221 56 56 -- sing_36.htm#IDX88 57 57 --MPhost sing_19.htm#IDX66 … … 122 122 / sing_147.htm#SEC187 123 123 / sing_155.htm#SEC195 124 / sing_18 0.htm#SEC220124 / sing_181.htm#SEC221 125 125 // sing_36.htm#IDX107 126 126 // sing_36.htm#IDX109 … … 133 133 < sing_36.htm#IDX100 134 134 < sing_155.htm#SEC195 135 < sing_18 0.htm#SEC220136 < sing_24 7.htm#SEC287135 < sing_181.htm#SEC221 136 < sing_248.htm#SEC288 137 137 <= sing_36.htm#IDX99 138 138 <= sing_100.htm#SEC140 139 139 <= sing_147.htm#SEC187 140 140 <= sing_155.htm#SEC195 141 <= sing_17 5.htm#SEC215142 <= sing_18 0.htm#SEC220141 <= sing_176.htm#SEC216 142 <= sing_181.htm#SEC221 143 143 <> sing_36.htm#IDX96 144 144 <> sing_100.htm#SEC140 … … 147 147 <> sing_155.htm#SEC195 148 148 <> sing_169.htm#SEC209 149 <> sing_17 5.htm#SEC215150 <> sing_18 0.htm#SEC220149 <> sing_176.htm#SEC216 150 <> sing_181.htm#SEC221 151 151 = sing_36.htm#IDX77 152 152 == sing_36.htm#IDX94 … … 156 156 == sing_155.htm#SEC195 157 157 == sing_169.htm#SEC209 158 == sing_17 5.htm#SEC215159 == sing_18 0.htm#SEC220158 == sing_176.htm#SEC216 159 == sing_181.htm#SEC221 160 160 > sing_36.htm#IDX98 161 161 > sing_155.htm#SEC195 162 > sing_18 0.htm#SEC220162 > sing_181.htm#SEC221 163 163 >= sing_36.htm#IDX97 164 164 >= sing_100.htm#SEC140 165 165 >= sing_147.htm#SEC187 166 166 >= sing_155.htm#SEC195 167 >= sing_17 5.htm#SEC215168 >= sing_18 0.htm#SEC220167 >= sing_176.htm#SEC216 168 >= sing_181.htm#SEC221 169 169 ? sing_36.htm#IDX106 170 ? sing_2 59.htm#IDX148171 ADGT sing_ 945.htm#SEC1021 65350172 AG codes sing_ 854.htm#SEC906173 AGcode_L sing_18 00.htm#SEC187660329174 AGcode_Omega sing_18 01.htm#SEC187756285175 ASCII sing_9 04.htm#SEC98026816170 ? sing_260.htm#IDX148 171 ADGT sing_1008.htm#SEC1084 1598 172 AG codes sing_917.htm#SEC969 173 AGcode_L sing_1862.htm#SEC1938 60329 174 AGcode_Omega sing_1863.htm#SEC1939 56285 175 ASCII sing_967.htm#SEC1043 26816 176 176 ASCII links sing_117.htm#SEC157 177 177 ASSUME sing_64.htm#SEC101 178 A_L sing_1 499.htm#SEC157516721179 A_Z sing_9 03.htm#SEC97950866180 Access to elements of a user defined type Access to elements of a user defined type sing_18 5.htm#SEC225181 Adj_div sing_1 795.htm#SEC187144919182 Adjoint ideal sing_1 376.htm#IDX611183 Alexander polynomial sing_1 470.htm#IDX635184 Algebraic Geometry codes sing_1 794.htm#IDX783185 Algebraic dependence Algebraic dependence sing_8 33.htm#SEC885186 Algebraic geometry sing_1 351.htm#SEC1427187 AltVarEnd sing_7 46.htm#SEC79811020188 AltVarStart sing_7 45.htm#SEC79721592189 Ann sing_1 290.htm#SEC136661560190 Appel function sing_56 3.htm#IDX351191 Appel hypergeometric function sing_56 3.htm#IDX352192 Applications sing_ 852.htm#SEC904193 Arnold, classification. sing_23 22.htm#IDX939194 Arnold, classification. sing_23 23.htm#IDX940195 ArnoldAction sing_1 592.htm#SEC166826958196 Assignments for user defined types Assignments for user defined types sing_18 7.htm#SEC227197 AssocTanToEnv sing_ 940.htm#SEC101646214198 Atkin sing_1 883.htm#SEC1959sprintf178 A_L sing_1561.htm#SEC1637 16721 179 A_Z sing_966.htm#SEC1042 50866 180 Access to elements of a user defined type Access to elements of a user defined type sing_186.htm#SEC226 181 Adj_div sing_1857.htm#SEC1933 44919 182 Adjoint ideal sing_1438.htm#IDX617 183 Alexander polynomial sing_1532.htm#IDX641 184 Algebraic Geometry codes sing_1856.htm#IDX789 185 Algebraic dependence Algebraic dependence sing_896.htm#SEC948 186 Algebraic geometry sing_1413.htm#SEC1489 187 AltVarEnd sing_775.htm#SEC827 11020 188 AltVarStart sing_774.htm#SEC826 21592 189 Ann sing_1352.htm#SEC1428 61560 190 Appel function sing_565.htm#IDX351 191 Appel hypergeometric function sing_565.htm#IDX352 192 Applications sing_915.htm#SEC967 193 Arnold, classification. sing_2384.htm#IDX945 194 Arnold, classification. sing_2385.htm#IDX946 195 ArnoldAction sing_1654.htm#SEC1730 26958 196 Assignments for user defined types Assignments for user defined types sing_188.htm#SEC228 197 AssocTanToEnv sing_1003.htm#SEC1079 46214 198 Atkin sing_1945.htm#SEC2021 sprintf 199 199 Authors sing_1.htm#IDX16 200 Automatic Deduction sing_ 945.htm#IDX482201 Automatic Demonstration sing_ 945.htm#IDX483202 BINresol sing_1 389.htm#SEC146552996200 Automatic Deduction sing_1008.htm#IDX488 201 Automatic Demonstration sing_1008.htm#IDX489 202 BINresol sing_1451.htm#SEC1527 52996 203 203 Background sing_3.htm#SEC5 204 Basic programming sing_808.htm#SEC860 205 Basic programming sing_808.htm#SEC860 206 BelongSemig sing_2318.htm#SEC2394 22405 207 BerlekampMassey sing_2377.htm#SEC2453 2172 208 Bern sing_2291.htm#SEC2367 64051 209 Bernstein operator sing_540.htm#IDX333 210 Bernstein-Sato polynomial sing_505.htm#IDX314 211 Bernstein-Sato polynomial sing_540.htm#IDX330 212 Bernstein-Sato polynomial sing_1533.htm#IDX666 213 Bernstein-Sato polynomial sing_1537.htm#IDX683 214 Bernstein-Sato polynomial for variety sing_596.htm#IDX355 215 Betti sing_2507.htm#SEC2583 21134 216 Betti number Syzygies and resolutions sing_870.htm#SEC927 217 BettiNumsH sing_2407.htm#SEC2483 18661 218 BettiNumsN sing_2412.htm#SEC2488 44681 219 BettiNumsS sing_2410.htm#SEC2486 14964 220 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_880.htm#SEC937 221 BlowingUp sing_1512.htm#SEC1588 43153 222 Blowupcenter sing_1392.htm#SEC1468 3423 223 BorelCheck sing_1467.htm#SEC1543 48787 224 Bott's formula sing_2702.htm#IDX1045 225 Branches of space curve singularities Branches of space curve singularities sing_841.htm#SEC893 226 Briancon-Maisonobe algorithm sing_540.htm#IDX339 227 Brieskorn lattice sing_1533.htm#IDX662 228 Brieskorn lattice sing_1534.htm#IDX673 229 Brieskorn lattice sing_1535.htm#IDX676 230 Brieskorn lattice sing_1536.htm#IDX679 231 Brieskorn lattice sing_1537.htm#IDX682 232 Brieskorn lattice sing_1538.htm#IDX686 233 Brieskorn lattice sing_1539.htm#IDX690 234 Brieskorn lattice sing_1540.htm#IDX696 235 Brieskorn lattice sing_1541.htm#IDX704 236 Brieskorn lattice sing_1542.htm#IDX710 237 Brieskorn lattice sing_1543.htm#IDX718 238 Brieskorn lattice sing_1544.htm#IDX728 239 Brieskorn lattice sing_1555.htm#IDX734 240 Brieskorn lattice sing_1557.htm#IDX745 241 Brieskorn lattice sing_1585.htm#IDX772 242 Brill-Noether algorithm sing_1794.htm#IDX784 243 BrillNoether sing_1797.htm#SEC1873 39919 244 Buchberger algorithm for toric ideals Buchberger algorithm sing_881.htm#SEC938 245 Budur-Mustata-Saito approach sing_596.htm#IDX359 246 Building Singular sing_2759.htm#SEC2848 247 C programming language Major differences to the C programming language sing_409.htm#SEC449 248 C, module ordering sing_862.htm#IDX413 249 CGS sing_925.htm#IDX426 250 CM_regularity sing_1454.htm#SEC1530 33865 251 CMtype sing_1623.htm#SEC1699 24849 252 CRHT-ideal sing_887.htm#SEC951 253 CSMA sing_2314.htm#SEC2390 49080 204 Basic programming sing_871.htm#SEC923 205 Basic programming sing_871.htm#SEC923 206 BelongSemig sing_2380.htm#SEC2456 22405 207 BerlekampMassey sing_2439.htm#SEC2515 2172 208 Bern sing_2353.htm#SEC2429 64051 209 Bernstein operator sing_542.htm#IDX333 210 Bernstein-Sato polynomial sing_507.htm#IDX314 211 Bernstein-Sato polynomial sing_542.htm#IDX330 212 Bernstein-Sato polynomial sing_1595.htm#IDX672 213 Bernstein-Sato polynomial sing_1599.htm#IDX689 214 Bernstein-Sato polynomial for variety sing_598.htm#IDX355 215 Betti sing_2572.htm#SEC2648 21134 216 Betti number Syzygies and resolutions sing_933.htm#SEC990 217 BettiNumsH sing_2469.htm#SEC2545 18661 218 BettiNumsN sing_2477.htm#SEC2553 44681 219 BettiNumsQp sing_2472.htm#SEC2548 16693 220 BettiNumsS sing_2475.htm#SEC2551 14964 221 Betty number sing_2466.htm#IDX986 222 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_943.htm#SEC1000 223 BlowingUp sing_1574.htm#SEC1650 43153 224 Blowupcenter sing_1454.htm#SEC1530 3423 225 BorelCheck sing_1529.htm#SEC1605 48787 226 Bott's formula sing_2767.htm#IDX1055 227 Branches of space curve singularities Branches of space curve singularities sing_904.htm#SEC956 228 Briancon-Maisonobe algorithm sing_542.htm#IDX339 229 Brieskorn lattice sing_1595.htm#IDX668 230 Brieskorn lattice sing_1596.htm#IDX679 231 Brieskorn lattice sing_1597.htm#IDX682 232 Brieskorn lattice sing_1598.htm#IDX685 233 Brieskorn lattice sing_1599.htm#IDX688 234 Brieskorn lattice sing_1600.htm#IDX692 235 Brieskorn lattice sing_1601.htm#IDX696 236 Brieskorn lattice sing_1602.htm#IDX702 237 Brieskorn lattice sing_1603.htm#IDX710 238 Brieskorn lattice sing_1604.htm#IDX716 239 Brieskorn lattice sing_1605.htm#IDX724 240 Brieskorn lattice sing_1606.htm#IDX734 241 Brieskorn lattice sing_1617.htm#IDX740 242 Brieskorn lattice sing_1619.htm#IDX751 243 Brieskorn lattice sing_1647.htm#IDX778 244 Brill-Noether algorithm sing_1856.htm#IDX790 245 BrillNoether sing_1859.htm#SEC1935 39919 246 Buchberger algorithm for toric ideals Buchberger algorithm sing_944.htm#SEC1001 247 Budur-Mustata-Saito approach sing_598.htm#IDX359 248 Building Singular sing_2824.htm#SEC2914 249 C programming language Major differences to the C programming language sing_411.htm#SEC451 250 C, module ordering sing_925.htm#IDX419 251 CGS sing_988.htm#IDX432 252 CM_regularity sing_1516.htm#SEC1592 33865 253 CMtype sing_1685.htm#SEC1761 24849 254 CRHT-ideal sing_950.htm#SEC1014 255 CSMA sing_2376.htm#SEC2452 49080 254 256 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 255 Castelnuovo-Mumford regularity sing_1 454.htm#IDX627257 Castelnuovo-Mumford regularity sing_1516.htm#IDX633 256 258 Category string sing_51.htm#SEC88 257 CenCharDec sing_7 02.htm#SEC75444505258 Center sing_14 31.htm#SEC150725541259 CenterBO sing_1 438.htm#SEC151434701260 CentralQuot sing_7 00.htm#SEC75256490261 CentralSaturation sing_7 01.htm#SEC75331585259 CenCharDec sing_731.htm#SEC783 44505 260 Center sing_1493.htm#SEC1569 25541 261 CenterBO sing_1500.htm#SEC1576 34701 262 CentralQuot sing_729.htm#SEC781 56490 263 CentralSaturation sing_730.htm#SEC782 31585 262 264 Change of rings sing_9.htm#SEC15 263 Characteristic sets sing_ 871.htm#SEC928264 CharacteristicExponents CharacteristicExponents sing_15 18.htm#SEC159421795265 ChernClass sing_27 15.htm#SEC279132965266 ChernRootsDual sing_2 270.htm#SEC234640100267 ChernRootsHom sing_2 279.htm#SEC235548446268 ChernRootsProd sing_2 272.htm#SEC234813967269 ChernRootsSum sing_2 268.htm#SEC234457286270 ChernRootsSymm sing_2 281.htm#SEC235759304271 ChernRootsWedge sing_2 282.htm#SEC23587239272 Chevalley-Rosenlicht theorem sing_1 370.htm#IDX596273 Chevalley-Rosenlicht theorem sing_1 371.htm#IDX599274 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_27 06.htm#IDX1050275 ChowRing sing_27 06.htm#SEC278257977276 Classification of hypersurface singularities Classification of hypersurface singularities sing_ 842.htm#SEC894277 Classification of singularities sing_2 675.htm#IDX1021278 Code Codes and the decoding problem sing_ 886.htm#SEC944279 Codes and the decoding problem Codes and the decoding problem sing_ 886.htm#SEC943280 Coding theory sing_1 793.htm#SEC1869281 Coefficient rings Notes for Singular users sing_2 757.htm#SEC2841265 Characteristic sets sing_934.htm#SEC991 266 CharacteristicExponents CharacteristicExponents sing_1580.htm#SEC1656 21795 267 ChernClass sing_2780.htm#SEC2856 32965 268 ChernRootsDual sing_2332.htm#SEC2408 40100 269 ChernRootsHom sing_2341.htm#SEC2417 48446 270 ChernRootsProd sing_2334.htm#SEC2410 13967 271 ChernRootsSum sing_2330.htm#SEC2406 57286 272 ChernRootsSymm sing_2343.htm#SEC2419 59304 273 ChernRootsWedge sing_2344.htm#SEC2420 7239 274 Chevalley-Rosenlicht theorem sing_1432.htm#IDX602 275 Chevalley-Rosenlicht theorem sing_1433.htm#IDX605 276 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2771.htm#IDX1060 277 ChowRing sing_2771.htm#SEC2847 57977 278 Classification of hypersurface singularities Classification of hypersurface singularities sing_905.htm#SEC957 279 Classification of singularities sing_2740.htm#IDX1031 280 Code Codes and the decoding problem sing_949.htm#SEC1007 281 Codes and the decoding problem Codes and the decoding problem sing_949.htm#SEC1006 282 Coding theory sing_1855.htm#SEC1931 283 Coefficient rings Notes for Singular users sing_2822.htm#SEC2907 282 284 Command line options Command line options sing_19.htm#SEC26 283 Commands Functions and system variables sing_20 6.htm#SEC246284 Commands for user defined types Commands for user defined types sing_18 6.htm#SEC226285 Commutative Algebra sing_8 21.htm#SEC873286 Commutative algebra sing_11 06.htm#SEC1182287 CompDecomp sing_50 2.htm#SEC5549959288 CompInt sing_23 20.htm#SEC23967518289 CompleteHomog sing_2 258.htm#SEC233442123290 ComplexValue sing_2 399.htm#SEC247545546291 Comprehensive Groebner System sing_9 25.htm#IDX429292 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_8 17.htm#SEC869293 ConsLevels sing_9 33.htm#SEC100914282294 ContactMatrix sing_15 20.htm#SEC159640767295 Conti-Traverso algorithm sing_ 876.htm#SEC933285 Commands Functions and system variables sing_207.htm#SEC247 286 Commands for user defined types Commands for user defined types sing_187.htm#SEC227 287 Commutative Algebra sing_884.htm#SEC936 288 Commutative algebra sing_1168.htm#SEC1244 289 CompDecomp sing_504.htm#SEC556 9959 290 CompInt sing_2382.htm#SEC2458 7518 291 CompleteHomog sing_2320.htm#SEC2396 42123 292 ComplexValue sing_2461.htm#SEC2537 45546 293 Comprehensive Groebner System sing_988.htm#IDX435 294 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_880.htm#SEC932 295 ConsLevels sing_996.htm#SEC1072 14282 296 ContactMatrix sing_1582.htm#SEC1658 40767 297 Conti-Traverso algorithm sing_939.htm#SEC996 296 298 Contributors sing_1.htm#IDX15 297 Control structures sing_37 7.htm#SEC417298 Control theory System and Control theory sing_18 27.htm#SEC1903299 Cooper philosophy sing_ 887.htm#SEC949300 Cornacchia sing_1 873.htm#SEC194963434301 CornacchiaModified sing_1 874.htm#SEC195059790302 Crep sing_9 28.htm#SEC100417485303 Critical points sing_8 36.htm#SEC888304 CurveParam sing_15 14.htm#SEC159053605305 CurveRes sing_15 13.htm#SEC158948848306 Curves sing_1 376.htm#IDX608299 Control structures sing_379.htm#SEC419 300 Control theory System and Control theory sing_1889.htm#SEC1965 301 Cooper philosophy sing_950.htm#SEC1012 302 Cornacchia sing_1935.htm#SEC2011 63434 303 CornacchiaModified sing_1936.htm#SEC2012 59790 304 Crep sing_991.htm#SEC1067 17485 305 Critical points sing_899.htm#SEC951 306 CurveParam sing_1576.htm#SEC1652 53605 307 CurveRes sing_1575.htm#SEC1651 48848 308 Curves sing_1438.htm#IDX614 307 309 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 308 Cyclic code sing_18 08.htm#IDX791309 Cyclic roots sing_8 14.htm#SEC866310 D-integration sing_56 3.htm#IDX348311 D-localization sing_56 3.htm#IDX344312 D-localization sing_ 780.htm#IDX382313 D-module purityfiltration_lib sing_50 5.htm#IDX312314 D-module sing_54 0.htm#IDX327315 D-module sing_56 3.htm#IDX341316 D-module sing_59 6.htm#IDX353317 D-module sing_7 58.htm#IDX367318 D-module sing_ 780.htm#IDX379319 D-module structure sing_54 0.htm#IDX328320 D-module structure sing_59 6.htm#IDX354321 D-restriction sing_56 3.htm#IDX346310 Cyclic code sing_1870.htm#IDX797 311 Cyclic roots sing_877.htm#SEC929 312 D-integration sing_565.htm#IDX348 313 D-localization sing_565.htm#IDX344 314 D-localization sing_843.htm#IDX388 315 D-module purityfiltration_lib sing_507.htm#IDX312 316 D-module sing_542.htm#IDX327 317 D-module sing_565.htm#IDX341 318 D-module sing_598.htm#IDX353 319 D-module sing_787.htm#IDX367 320 D-module sing_843.htm#IDX385 321 D-module structure sing_542.htm#IDX328 322 D-module structure sing_598.htm#IDX354 323 D-restriction sing_565.htm#IDX346 322 324 DBM links sing_122.htm#SEC162 323 325 DISPLAY environment variable The online help system sing_16.htm#IDX28 324 DLoc sing_56 6.htm#SEC6185981325 DLoc0 sing_5 68.htm#SEC62014327326 DLoc sing_568.htm#SEC620 5981 327 DLoc0 sing_570.htm#SEC622 14327 326 328 Data types sing_72.htm#SEC112 327 Data types (plural) sing_42 2.htm#IDX298329 Data types (plural) sing_424.htm#IDX298 328 330 Debugging tools sing_63.htm#SEC100 329 331 Decker, Wolfram sing_1.htm#IDX17 330 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_18 4.htm#SEC224331 Decoding sing_18 08.htm#IDX793332 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_ 885.htm#SEC942333 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_ 890.htm#SEC960334 Definition of a user defined type Definition of a user defined type sing_18 3.htm#SEC223335 Deformations sing_ 839.htm#SEC891336 Deformations, T1 and T2 sing_ 838.htm#SEC890337 Deg sing_25 10.htm#SEC258635419338 Degree sing_25 11.htm#SEC258748523339 DegreePure sing_1 355.htm#SEC143133003340 Degrees sing_25 12.htm#SEC258850349341 Delta sing_1 439.htm#SEC151533497342 DeltaList sing_1 440.htm#SEC151665148332 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_185.htm#SEC225 333 Decoding sing_1870.htm#IDX799 334 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_948.htm#SEC1005 335 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_953.htm#SEC1023 336 Definition of a user defined type Definition of a user defined type sing_184.htm#SEC224 337 Deformations sing_902.htm#SEC954 338 Deformations, T1 and T2 sing_901.htm#SEC953 339 Deg sing_2575.htm#SEC2651 35419 340 Degree sing_2576.htm#SEC2652 48523 341 DegreePure sing_1417.htm#SEC1493 33003 342 Degrees sing_2577.htm#SEC2653 50349 343 Delta sing_1501.htm#SEC1577 33497 344 DeltaList sing_1502.htm#SEC1578 65148 343 345 Demo mode sing_24.htm#SEC35 344 Depth sing_8 28.htm#SEC880345 Determinacy sing_2 678.htm#IDX1025346 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_ 879.htm#SEC936347 Distributed computing sing_ 956.htm#IDX489348 Dlocalization sing_ 781.htm#SEC83322140346 Depth sing_891.htm#SEC943 347 Determinacy sing_2743.htm#IDX1035 348 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_942.htm#SEC999 349 Distributed computing sing_1019.htm#IDX495 350 Dlocalization sing_844.htm#SEC896 22140 349 351 Documentation Tool sing_60.htm#SEC97 350 Dp, global ordering sing_ 860.htm#IDX396351 Ds, local ordering sing_ 861.htm#IDX406352 DsingularLocus sing_ 785.htm#SEC83746495352 Dp, global ordering sing_923.htm#IDX402 353 Ds, local ordering sing_924.htm#IDX412 354 DsingularLocus sing_848.htm#SEC900 46495 353 355 Dynamic loading sing_71.htm#SEC111 354 Dynamic modules sing_8 16.htm#SEC868355 ECPP sing_19 17.htm#SEC199355777356 ECoef sing_1 398.htm#SEC147414154357 EOrdlist sing_1 396.htm#SEC147236329358 ERROR sing_23 6.htm#SEC276356 Dynamic modules sing_879.htm#SEC931 357 ECPP sing_1979.htm#SEC2055 55777 358 ECoef sing_1460.htm#SEC1536 14154 359 EOrdlist sing_1458.htm#SEC1534 36329 360 ERROR sing_237.htm#SEC277 359 361 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 360 Edatalist sing_1 395.htm#SEC147161593361 Edelman-Reiner sing_22 01.htm#IDX874362 Edatalist sing_1457.htm#SEC1533 61593 363 Edelman-Reiner sing_2263.htm#IDX880 362 364 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 363 365 Editing input sing_18.htm#SEC25 364 Elimination sing_8 24.htm#SEC876366 Elimination sing_887.htm#SEC939 365 367 Emacs Emacs user interface sing_21.htm#SEC28 366 368 Emacs, Singular demo mode sing_24.htm#SEC35 … … 372 374 Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30 373 375 Emacs, user interface Emacs user interface sing_21.htm#SEC28 374 Emaxcont sing_14 00.htm#SEC147647312375 Enumerative geometry sing_27 02.htm#IDX1043376 Equal sing_1 354.htm#SEC143019984377 Eresol sing_1 390.htm#SEC146612842378 EulerAff sing_23 15.htm#SEC239154325379 EulerProj sing_23 16.htm#SEC239213537380 Evaluation of logical expressions Evaluation of logical expressions sing_41 1.htm#SEC451381 Examples sing_8 06.htm#SEC858376 Emaxcont sing_1462.htm#SEC1538 47312 377 Enumerative geometry sing_2767.htm#IDX1053 378 Equal sing_1416.htm#SEC1492 19984 379 Eresol sing_1452.htm#SEC1528 12842 380 EulerAff sing_2377.htm#SEC2453 54325 381 EulerProj sing_2378.htm#SEC2454 13537 382 Evaluation of logical expressions Evaluation of logical expressions sing_413.htm#SEC453 383 Examples sing_869.htm#SEC921 382 384 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 383 Exp for matrices sing_1 372.htm#IDX600384 Experimental libraries Experimental libraries sing_2 245.htm#SEC2321385 Ext sing_1 166.htm#SEC124221909386 Ext, computation of sing_8 27.htm#SEC879387 Ext_R sing_1 165.htm#SEC124153310388 Exterior sing_7 32.htm#SEC78423593389 Extra weight vector sing_ 865.htm#SEC917390 Factorization sing_8 29.htm#SEC881391 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_ 941.htm#SEC101718153392 Feynman graph sing_1 142.htm#IDX522393 Finite fields sing_8 23.htm#SEC875385 Exp for matrices sing_1434.htm#IDX606 386 Experimental libraries Experimental libraries sing_2307.htm#SEC2383 387 Ext sing_1228.htm#SEC1304 21909 388 Ext, computation of sing_890.htm#SEC942 389 Ext_R sing_1227.htm#SEC1303 53310 390 Exterior sing_761.htm#SEC813 23593 391 Extra weight vector sing_928.htm#SEC980 392 Factorization sing_892.htm#SEC944 393 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_1004.htm#SEC1080 18153 394 Feynman graph sing_1204.htm#IDX528 395 Finite fields sing_886.htm#SEC938 394 396 First steps sing_6.htm#SEC12 395 Fitzgerald-Lax method Fitzgerald-Lax method sing_ 889.htm#SEC957396 Float sing_25 0.htm#SEC290397 Fitzgerald-Lax method Fitzgerald-Lax method sing_952.htm#SEC1020 398 Float sing_251.htm#SEC291 397 399 Flow control sing_40.htm#SEC70 398 400 Formal Checker sing_59.htm#SEC96 399 Formatting output sing_8 13.htm#SEC865400 Free resolution sing_8 25.htm#SEC877401 Free resolution, graded Handling graded modules sing_8 26.htm#SEC878402 FultonA sing_23 13.htm#SEC238933688403 Functions sing_20 7.htm#SEC247404 Future benefits of Singular 4 Notes for Singular users sing_2 757.htm#SEC2846405 G-algebra sing_48 6.htm#SEC526406 G-algebra sing_48 6.htm#SEC528407 G-algebra, setup sing_48 6.htm#SEC530408 GBWeight sing_5 69.htm#SEC62124641409 GBsolve sing_17 07.htm#SEC178316830410 GIT-Fans sing_ 848.htm#SEC900411 GITcone sing_24 26.htm#SEC250264643412 GITfan sing_24 27.htm#SEC250332549413 GITfanFromOrbitCones GITfanFromOrbitCones sing_24 28.htm#SEC250463104414 GITfanParallel sing_24 29.htm#SEC250553071415 GITfanParallelSymmetric GITfanParallelSymmetric sing_2 444.htm#SEC252030232416 GITfanSymmetric sing_2 443.htm#SEC251925831417 GKZfan sing_24 30.htm#SEC2506sprintf418 GKZsystem sing_ 698.htm#SEC75020528419 GKdim sing_ 671.htm#SEC7239814401 Formatting output sing_876.htm#SEC928 402 Free resolution sing_888.htm#SEC940 403 Free resolution, graded Handling graded modules sing_889.htm#SEC941 404 FultonA sing_2375.htm#SEC2451 33688 405 Functions sing_208.htm#SEC248 406 Future benefits of Singular 4 Notes for Singular users sing_2822.htm#SEC2912 407 G-algebra sing_488.htm#SEC528 408 G-algebra sing_488.htm#SEC530 409 G-algebra, setup sing_488.htm#SEC532 410 GBWeight sing_571.htm#SEC623 24641 411 GBsolve sing_1769.htm#SEC1845 16830 412 GIT-Fans sing_911.htm#SEC963 413 GITcone sing_2491.htm#SEC2567 64643 414 GITfan sing_2492.htm#SEC2568 32549 415 GITfanFromOrbitCones GITfanFromOrbitCones sing_2493.htm#SEC2569 63104 416 GITfanParallel sing_2494.htm#SEC2570 53071 417 GITfanParallelSymmetric GITfanParallelSymmetric sing_2509.htm#SEC2585 30232 418 GITfanSymmetric sing_2508.htm#SEC2584 25831 419 GKZfan sing_2495.htm#SEC2571 sprintf 420 GKZsystem sing_727.htm#SEC779 20528 421 GKdim sing_700.htm#SEC752 9814 420 422 GMP sing_1.htm#IDX3 421 GMP sing_2 761.htm#SEC2850422 GND.lib sing_2 451.htm#SEC2527423 GND_lib sing_2 451.htm#SEC2527424 GTZmod sing_12 16.htm#SEC129230091425 GTZopt sing_12 23.htm#SEC129914642426 G_a -Invariants sing_ 845.htm#SEC897427 Gamma sing_14 05.htm#SEC14813820428 Gauss-Manin connection Gauss-Manin connection sing_ 872.htm#SEC929429 Gauss-Manin connection sing_1 585.htm#IDX771430 Gauss-Manin connection sing_16 32.htm#IDX774431 Gauss-Manin system sing_15 33.htm#IDX661432 Gauss-Manin system sing_15 34.htm#IDX672433 Gauss-Manin system sing_15 35.htm#IDX675434 Gauss-Manin system sing_15 36.htm#IDX678435 Gauss-Manin system sing_15 37.htm#IDX681436 Gauss-Manin system sing_1 538.htm#IDX685437 Gauss-Manin system sing_1 539.htm#IDX689438 Gauss-Manin system sing_1 540.htm#IDX695439 Gauss-Manin system sing_1 541.htm#IDX703440 Gauss-Manin system sing_1 542.htm#IDX709441 Gauss-Manin system sing_1 543.htm#IDX717442 Gauss-Manin system sing_1 544.htm#IDX727443 Gauss-Manin system sing_1 555.htm#IDX733444 Gauss-Manin system sing_1 557.htm#IDX744423 GMP sing_2826.htm#SEC2916 424 GND.lib sing_2516.htm#SEC2592 425 GND_lib sing_2516.htm#SEC2592 426 GTZmod sing_1278.htm#SEC1354 30091 427 GTZopt sing_1285.htm#SEC1361 14642 428 G_a -Invariants sing_908.htm#SEC960 429 Gamma sing_1467.htm#SEC1543 3820 430 Gauss-Manin connection Gauss-Manin connection sing_935.htm#SEC992 431 Gauss-Manin connection sing_1647.htm#IDX777 432 Gauss-Manin connection sing_1694.htm#IDX780 433 Gauss-Manin system sing_1595.htm#IDX667 434 Gauss-Manin system sing_1596.htm#IDX678 435 Gauss-Manin system sing_1597.htm#IDX681 436 Gauss-Manin system sing_1598.htm#IDX684 437 Gauss-Manin system sing_1599.htm#IDX687 438 Gauss-Manin system sing_1600.htm#IDX691 439 Gauss-Manin system sing_1601.htm#IDX695 440 Gauss-Manin system sing_1602.htm#IDX701 441 Gauss-Manin system sing_1603.htm#IDX709 442 Gauss-Manin system sing_1604.htm#IDX715 443 Gauss-Manin system sing_1605.htm#IDX723 444 Gauss-Manin system sing_1606.htm#IDX733 445 Gauss-Manin system sing_1617.htm#IDX739 446 Gauss-Manin system sing_1619.htm#IDX750 445 447 General command syntax General command syntax sing_35.htm#SEC59 446 448 General concepts sing_12.htm#SEC18 447 General purpose sing_ 897.htm#SEC973449 General purpose sing_960.htm#SEC1036 448 450 General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41 449 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_4 88.htm#SEC538450 Generalized Newton identities Generalized Newton identities sing_ 888.htm#SEC954451 Geometric Invariant Theory Geometric Invariant Theory sing_ 847.htm#SEC899452 Geometric Theorems sing_ 945.htm#IDX484453 Geometric genus sing_1 376.htm#IDX612454 German Umlaute sing_40 7.htm#IDX285451 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_490.htm#SEC540 452 Generalized Newton identities Generalized Newton identities sing_951.htm#SEC1017 453 Geometric Invariant Theory Geometric Invariant Theory sing_910.htm#SEC962 454 Geometric Theorems sing_1008.htm#IDX490 455 Geometric genus sing_1438.htm#IDX618 456 German Umlaute sing_409.htm#IDX285 455 457 Getting started sing_5.htm#SEC11 456 Global orderings sing_ 860.htm#SEC912457 Goettsche's formula sing_24 04.htm#IDX981458 GoettscheF sing_24 05.htm#SEC248127881459 Graded commutative algebras Graded commutative algebras (SCA) sing_49 0.htm#SEC542460 Grassmannian sing_27 07.htm#SEC278343898461 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_27 07.htm#IDX1051458 Global orderings sing_923.htm#SEC975 459 Goettsche's formula sing_2466.htm#IDX987 460 GoettscheF sing_2467.htm#SEC2543 27881 461 Graded commutative algebras Graded commutative algebras (SCA) sing_492.htm#SEC544 462 Grassmannian sing_2772.htm#SEC2848 43898 463 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2772.htm#IDX1061 462 464 Greuel, Gert-Martin sing_1.htm#IDX18 463 Groebner Bases Computing Groebner and Standard Bases sing_8 17.htm#SEC869464 Groebner bases in G-algebras Groebner bases in G-algebras sing_48 7.htm#SEC531465 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_49 3.htm#SEC545466 Groebner bases, decodeGB sing_18 08.htm#IDX795467 Groebner bases, slim sing_8 20.htm#SEC872468 Groebner basis conversion Groebner basis conversion sing_8 19.htm#SEC871469 Groebner cover sing_9 24.htm#IDX422470 Groebner cover sing_9 31.htm#IDX441471 Groebner cover sing_9 32.htm#IDX448472 Groebner fan sing_2 071.htm#IDX812473 Groebner walk sing_1 157.htm#IDX543474 Groebner walk sing_1 159.htm#IDX545475 Groebner walk sing_2 699.htm#IDX1039476 Groebner walk sing_27 00.htm#IDX1040477 Groebnerwalk sing_1 153.htm#IDX539478 Groebnerwalk sing_2 544.htm#IDX992479 Groebnerwalk sing_2 698.htm#IDX1038480 Groebnerwalk sing_2 741.htm#IDX1067481 Gromov-Witten invariants sing_1 142.htm#IDX519482 Gromov-Witten invariants sing_1 148.htm#IDX528483 Gromov-Witten invariants sing_1 149.htm#IDX532484 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_27 32.htm#IDX1063485 Gromov-Witten invariants, multiple covers sing_27 31.htm#IDX1062486 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_27 33.htm#IDX1064487 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_27 34.htm#IDX1065488 Gromov-Witten invariants. sing_27 02.htm#IDX1046489 Gweights sing_7 26.htm#SEC778651490 H2basis sing_1 590.htm#SEC16663414491 HHnormalForm sing_23 31.htm#SEC240733972492 Hamburger-Noether expansion sing_1 470.htm#IDX631493 Hamburger-Noether expansion sing_1 558.htm#IDX753494 Hamburger-Noether expansions sing_1 795.htm#IDX785495 Handling graded modules Handling graded modules sing_8 26.htm#SEC878496 Hcode sing_1 492.htm#SEC156826628465 Groebner Bases Computing Groebner and Standard Bases sing_880.htm#SEC932 466 Groebner bases in G-algebras Groebner bases in G-algebras sing_489.htm#SEC533 467 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_495.htm#SEC547 468 Groebner bases, decodeGB sing_1870.htm#IDX801 469 Groebner bases, slim sing_883.htm#SEC935 470 Groebner basis conversion Groebner basis conversion sing_882.htm#SEC934 471 Groebner cover sing_987.htm#IDX428 472 Groebner cover sing_994.htm#IDX447 473 Groebner cover sing_995.htm#IDX454 474 Groebner fan sing_2133.htm#IDX818 475 Groebner walk sing_1219.htm#IDX549 476 Groebner walk sing_1221.htm#IDX551 477 Groebner walk sing_2764.htm#IDX1049 478 Groebner walk sing_2765.htm#IDX1050 479 Groebnerwalk sing_1215.htm#IDX545 480 Groebnerwalk sing_2609.htm#IDX1002 481 Groebnerwalk sing_2763.htm#IDX1048 482 Groebnerwalk sing_2806.htm#IDX1077 483 Gromov-Witten invariants sing_1204.htm#IDX525 484 Gromov-Witten invariants sing_1210.htm#IDX534 485 Gromov-Witten invariants sing_1211.htm#IDX538 486 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2797.htm#IDX1073 487 Gromov-Witten invariants, multiple covers sing_2796.htm#IDX1072 488 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2798.htm#IDX1074 489 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2799.htm#IDX1075 490 Gromov-Witten invariants. sing_2767.htm#IDX1056 491 Gweights sing_755.htm#SEC807 651 492 H2basis sing_1652.htm#SEC1728 3414 493 HHnormalForm sing_2393.htm#SEC2469 33972 494 Hamburger-Noether expansion sing_1532.htm#IDX637 495 Hamburger-Noether expansion sing_1620.htm#IDX759 496 Hamburger-Noether expansions sing_1857.htm#IDX791 497 Handling graded modules Handling graded modules sing_889.htm#SEC941 498 Hcode sing_1554.htm#SEC1630 26628 497 499 Help string sing_45.htm#SEC82 498 Hensel sing_241.htm#SEC281 499 Hilbert function sing_356.htm#IDX188 500 Hilbert function sing_869.htm#SEC923 501 Hilbert series sing_869.htm#SEC923 502 Hilbert-driven GB algorithm Groebner basis conversion sing_819.htm#SEC871 503 HilbertClassPoly sing_1880.htm#SEC1956 sprintf 504 HilbertSeries sing_1685.htm#SEC1761 21249 505 HilbertWeights sing_1686.htm#SEC1762 sprintf 506 Hom sing_1169.htm#SEC1245 61434 507 HomJJ sing_1246.htm#SEC1322 1525 508 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_878.htm#SEC935 500 Hensel sing_242.htm#SEC282 501 Hilbert function sing_357.htm#IDX188 502 Hilbert function sing_932.htm#SEC986 503 Hilbert scheme sing_2466.htm#IDX990 504 Hilbert series sing_932.htm#SEC986 505 Hilbert-driven GB algorithm Groebner basis conversion sing_882.htm#SEC934 506 HilbertClassPoly sing_1942.htm#SEC2018 sprintf 507 HilbertSeries sing_1747.htm#SEC1823 21249 508 HilbertWeights sing_1748.htm#SEC1824 sprintf 509 Hom sing_1231.htm#SEC1307 61434 510 HomJJ sing_1308.htm#SEC1384 1525 511 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_941.htm#SEC998 509 512 How to enter and exit How to enter and exit sing_14.htm#SEC20 510 513 How to use this manual How to use this manual sing_4.htm#SEC6 511 Hurwitz numbers sing_1 148.htm#IDX531512 Hurwitz numbers sing_1 149.htm#IDX535513 Hypersurface singularities, classification of Classification of hypersurface singularities sing_ 842.htm#SEC894514 I-regular function sing_9 31.htm#IDX447515 IN sing_28 0.htm#IDX149516 Ideal membership sing_ 868.htm#IDX418514 Hurwitz numbers sing_1210.htm#IDX537 515 Hurwitz numbers sing_1211.htm#IDX541 516 Hypersurface singularities, classification of Classification of hypersurface singularities sing_905.htm#SEC957 517 I-regular function sing_994.htm#IDX453 518 IN sing_281.htm#IDX149 519 Ideal membership sing_931.htm#IDX424 517 520 Identifiers, syntax of sing_37.htm#SEC65 518 ImageGroup sing_1 688.htm#SEC176428808519 ImageVariety sing_1 687.htm#SEC176315252520 Imap, option sing_31 5.htm#IDX175521 ImageGroup sing_1750.htm#SEC1826 28808 522 ImageVariety sing_1749.htm#SEC1825 15252 523 Imap, option sing_316.htm#IDX175 521 524 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 522 Incl sing_1 353.htm#SEC14297621523 Index sing_2 766.htm#SEC2855525 Incl sing_1415.htm#SEC1491 7621 526 Index sing_2831.htm#SEC2921 524 527 Info string sing_52.htm#SEC89 525 InterDiv sing_14 21.htm#SEC149746142528 InterDiv sing_1483.htm#SEC1559 46142 526 529 Interactive use sing_13.htm#SEC19 527 530 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 528 IntersectWithSub sing_7 03.htm#SEC75556289529 Intersection theory sing_27 02.htm#IDX1042530 IntersectionMatrix sing_15 19.htm#SEC159529351531 IntersectWithSub sing_732.htm#SEC784 56289 532 Intersection theory sing_2767.htm#IDX1052 533 IntersectionMatrix sing_1581.htm#SEC1657 29351 531 534 Introduction sing_2.htm#SEC4 532 Invariant Theory sing_844.htm#SEC896 533 Invariant theory sing_1637.htm#SEC1713 534 InvariantQ sing_1690.htm#SEC1766 53256 535 InvariantRing sing_1689.htm#SEC1765 22928 536 Invariants of a finite group Invariants of a finite group sing_846.htm#SEC898 537 Invariants of plane curve singularities Invariants of plane curve singularities sing_840.htm#SEC892 538 IsSCA sing_747.htm#SEC799 58445 539 J-marked schemes sing_1461.htm#IDX629 540 J-marked schemes, Borel ideals sing_1466.htm#IDX630 541 JMBTest.lib sing_1461.htm#SEC1537 542 JMBTest_lib sing_1461.htm#SEC1537 543 JMSConst.lib sing_1466.htm#SEC1542 544 JMSConst_lib sing_1466.htm#SEC1542 545 JMarkedScheme sing_1468.htm#SEC1544 60696 546 Jacobi sing_1890.htm#SEC1966 29843 547 Jacobson form sing_1845.htm#IDX796 548 Jacobson normal form sing_1845.htm#IDX797 549 Janet basis sing_2697.htm#IDX1036 550 Janet division, Janet basis sing_2696.htm#IDX1035 551 JuReTopDim sing_1363.htm#SEC1439 sprintf 552 JuReZeroDim sing_1364.htm#SEC1440 sprintf 553 KScoef sing_1583.htm#SEC1659 sprintf 554 KSconvert sing_1581.htm#SEC1657 3585 555 KSker sing_1580.htm#SEC1656 40166 556 KSlinear sing_1582.htm#SEC1658 19896 557 KSpencerKernel sing_1630.htm#SEC1706 12490 558 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2470.htm#SEC2546 20741 559 Ker sing_2516.htm#SEC2592 58279 560 Kernel of module homomorphisms Kernel of module homomorphisms sing_832.htm#SEC884 561 KoszulHomology sing_1178.htm#SEC1254 sprintf 562 Kronecker modules sing_2404.htm#IDX983 563 L, ordering sing_866.htm#SEC918 564 LETTERPLACE sing_491.htm#SEC543 565 LIB sing_284.htm#SEC324 535 Invariant Theory sing_907.htm#SEC959 536 Invariant theory sing_1699.htm#SEC1775 537 InvariantQ sing_1752.htm#SEC1828 53256 538 InvariantRing sing_1751.htm#SEC1827 22928 539 Invariants of a finite group Invariants of a finite group sing_909.htm#SEC961 540 Invariants of plane curve singularities Invariants of plane curve singularities sing_903.htm#SEC955 541 IsSCA sing_776.htm#SEC828 58445 542 J-marked schemes sing_1523.htm#IDX635 543 J-marked schemes, Borel ideals sing_1528.htm#IDX636 544 JMBTest.lib sing_1523.htm#SEC1599 545 JMBTest_lib sing_1523.htm#SEC1599 546 JMSConst.lib sing_1528.htm#SEC1604 547 JMSConst_lib sing_1528.htm#SEC1604 548 JMarkedScheme sing_1530.htm#SEC1606 60696 549 Jacobi sing_1952.htm#SEC2028 29843 550 Jacobson form sing_1907.htm#IDX802 551 Jacobson normal form sing_1907.htm#IDX803 552 Janet basis sing_2762.htm#IDX1046 553 Janet division, Janet basis sing_2761.htm#IDX1045 554 JuReTopDim sing_1425.htm#SEC1501 sprintf 555 JuReZeroDim sing_1426.htm#SEC1502 sprintf 556 KScoef sing_1645.htm#SEC1721 sprintf 557 KSconvert sing_1643.htm#SEC1719 3585 558 KSker sing_1642.htm#SEC1718 40166 559 KSlinear sing_1644.htm#SEC1720 19896 560 KSpencerKernel sing_1692.htm#SEC1768 12490 561 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2535.htm#SEC2611 20741 562 Ker sing_2581.htm#SEC2657 58279 563 Kernel of module homomorphisms Kernel of module homomorphisms sing_895.htm#SEC947 564 KoszulHomology sing_1240.htm#SEC1316 sprintf 565 Kronecker module sing_2466.htm#IDX989 566 Kronecker product sing_361.htm#SEC401 567 L, ordering sing_929.htm#SEC981 568 LETTERPLACE sing_493.htm#SEC545 569 LIB sing_285.htm#SEC325 566 570 LIB commands sing_53.htm#SEC90 567 LIBs sing_ 893.htm#SEC969568 LLL sing_35 8.htm#IDX220569 LOT algorithm sing_54 0.htm#IDX340570 LU-decomposition of a matrix of numbers sing_2 89.htm#SEC329571 Laurent series sing_1 146.htm#IDX527572 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_ 850.htm#SEC902573 Left ideal membership Groebner bases in G-algebras sing_48 7.htm#SEC534574 Left normal form Groebner bases in G-algebras sing_48 7.htm#SEC533575 LengthSym sing_7 57.htm#SEC80916591576 LengthSymElement sing_7 56.htm#SEC80828292577 Letterplace sing_49 1.htm#SEC543578 Levels sing_9 34.htm#SEC101016031579 Lexicographic Groebner bases, computation of Groebner basis conversion sing_8 19.htm#SEC871571 LIBs sing_956.htm#SEC1032 572 LLL sing_359.htm#IDX220 573 LOT algorithm sing_542.htm#IDX340 574 LU-decomposition of a matrix of numbers sing_290.htm#SEC330 575 Laurent series sing_1208.htm#IDX533 576 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_913.htm#SEC965 577 Left ideal membership Groebner bases in G-algebras sing_489.htm#SEC536 578 Left normal form Groebner bases in G-algebras sing_489.htm#SEC535 579 LengthSym sing_786.htm#SEC838 16591 580 LengthSymElement sing_785.htm#SEC837 28292 581 Letterplace sing_493.htm#SEC545 582 Levels sing_997.htm#SEC1073 16031 583 Lexicographic Groebner bases, computation of Groebner basis conversion sing_882.htm#SEC934 580 584 Libraries Writing procedures and libraries sing_48.htm#SEC85 581 Libraries sing_8 09.htm#SEC861585 Libraries sing_872.htm#SEC924 582 586 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 583 Library versioning Notes for Singular users sing_2 757.htm#SEC2844584 Lie algebra sing_1 371.htm#IDX597585 Lie group sing_1 374.htm#IDX602586 Lie group sing_1 375.htm#IDX605587 Limitations sing_40 7.htm#SEC447588 Linear algebra sing_1 046.htm#SEC1122589 Linear code sing_18 08.htm#IDX792590 LinearActionQ sing_1 692.htm#SEC176862218591 LinearCombinationQ sing_1 693.htm#SEC176959373592 LinearizeAction sing_1 691.htm#SEC176760266587 Library versioning Notes for Singular users sing_2822.htm#SEC2910 588 Lie algebra sing_1433.htm#IDX603 589 Lie group sing_1436.htm#IDX608 590 Lie group sing_1437.htm#IDX611 591 Limitations sing_409.htm#SEC449 592 Linear algebra sing_1109.htm#SEC1185 593 Linear code sing_1870.htm#IDX798 594 LinearActionQ sing_1754.htm#SEC1830 62218 595 LinearCombinationQ sing_1755.htm#SEC1831 59373 596 LinearizeAction sing_1753.htm#SEC1829 60266 593 597 Loading a library sing_62.htm#SEC99 594 Local orderings sing_ 861.htm#SEC913595 Log for matrices sing_1 373.htm#IDX601596 Long coefficients sing_8 11.htm#SEC863597 M, ordering sing_ 863.htm#SEC915598 MVComplex sing_2 353.htm#SEC242962126599 Macdonald's formula sing_24 04.htm#IDX982600 MacdonaldF sing_24 08.htm#SEC248412751601 Macintosh installation Macintosh installation instructions sing_2 765.htm#SEC2854602 Mathematical background Mathematical background sing_ 867.htm#SEC919603 Mathematical background (plural) Mathematical background (plural) sing_48 5.htm#SEC525604 Matrix orderings sing_ 863.htm#SEC915605 Max sing_1 599.htm#SEC167523606 Maximus sing_1 463.htm#SEC153910010607 Maxord sing_14 04.htm#SEC148014124608 MillerRabin sing_19 00.htm#SEC197615740609 Milnor number Milnor and Tjurina number sing_8 35.htm#SEC887610 Milnor number sing_2 677.htm#IDX1024611 Min sing_16 00.htm#SEC167629622612 MinMult sing_23 19.htm#SEC239539835613 MinimalDecomposition MinimalDecomposition sing_1 694.htm#SEC177024161614 Minimum distance sing_18 08.htm#IDX794615 Minimus sing_1 462.htm#SEC153861721616 Miscellaneous libraries Miscellaneous libraries sing_2 172.htm#SEC2248617 ModEqn sing_1 593.htm#SEC166959394618 Modular techniques sing_ 956.htm#IDX486619 Module orderings sing_ 862.htm#SEC914598 Local orderings sing_924.htm#SEC976 599 Log for matrices sing_1435.htm#IDX607 600 Long coefficients sing_874.htm#SEC926 601 M, ordering sing_926.htm#SEC978 602 MVComplex sing_2415.htm#SEC2491 62126 603 Macdonald's formula sing_2466.htm#IDX988 604 MacdonaldF sing_2473.htm#SEC2549 12751 605 Macintosh installation Macintosh installation instructions sing_2830.htm#SEC2920 606 Mathematical background Mathematical background sing_930.htm#SEC982 607 Mathematical background (plural) Mathematical background (plural) sing_487.htm#SEC527 608 Matrix orderings sing_926.htm#SEC978 609 Max sing_1661.htm#SEC1737 23 610 Maximus sing_1525.htm#SEC1601 10010 611 Maxord sing_1466.htm#SEC1542 14124 612 MillerRabin sing_1962.htm#SEC2038 15740 613 Milnor number Milnor and Tjurina number sing_898.htm#SEC950 614 Milnor number sing_2742.htm#IDX1034 615 Min sing_1662.htm#SEC1738 29622 616 MinMult sing_2381.htm#SEC2457 39835 617 MinimalDecomposition MinimalDecomposition sing_1756.htm#SEC1832 24161 618 Minimum distance sing_1870.htm#IDX800 619 Minimus sing_1524.htm#SEC1600 61721 620 Miscellaneous libraries Miscellaneous libraries sing_2234.htm#SEC2310 621 ModEqn sing_1655.htm#SEC1731 59394 622 Modular techniques sing_1019.htm#IDX492 623 Module orderings sing_925.htm#SEC977 620 624 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 621 Monodromy sing_1 585.htm#IDX769622 Monomial orderings sing_ 857.htm#SEC909625 Monodromy sing_1647.htm#IDX775 626 Monomial orderings sing_920.htm#SEC972 623 627 Monomial orderings, Term orderings sing_31.htm#SEC44 624 Mori dream spaces sing_2 246.htm#IDX934625 Morse lemma addnondegeneratevariables sing_2 676.htm#IDX1022626 Morse lemma sing_2 679.htm#IDX1026627 MultiplicitySequence MultiplicitySequence sing_15 17.htm#SEC15931309628 NF sing_33 4.htm#SEC374629 NF sing_47 7.htm#SEC517630 NFMora sing_ 1966.htm#SEC204240670631 NPos sing_12 36.htm#SEC131215702632 NPos_test sing_12 34.htm#SEC131048172633 NSplaces sing_1 796.htm#SEC187248675628 Mori dream spaces sing_2308.htm#IDX940 629 Morse lemma addnondegeneratevariables sing_2741.htm#IDX1032 630 Morse lemma sing_2744.htm#IDX1036 631 MultiplicitySequence MultiplicitySequence sing_1579.htm#SEC1655 1309 632 NF sing_335.htm#SEC375 633 NF sing_479.htm#SEC519 634 NFMora sing_2028.htm#SEC2104 40670 635 NPos sing_1298.htm#SEC1374 15702 636 NPos_test sing_1296.htm#SEC1372 48172 637 NSplaces sing_1858.htm#SEC1934 48675 634 638 NTL sing_1.htm#IDX4 639 NakYoshF sing_2470.htm#SEC2546 58602 635 640 Names sing_37.htm#SEC65 636 641 Names in procedures sing_46.htm#SEC83 637 642 Names, indexed sing_37.htm#SEC65 638 New orderings for modules Notes for Singular users sing_2 757.htm#SEC2845639 Newton non-degenerate sing_1 572.htm#IDX767640 Newton polygon sing_1 571.htm#IDX766641 Newton polygon sing_1 572.htm#IDX768642 Newton polygons sing_2 744.htm#IDX1070643 Newton polytope sing_2 071.htm#IDX811644 Newton step sing_2 680.htm#IDX1030645 NoetherPosition sing_12 30.htm#SEC130618735646 Non-commutative LIBs Non-commutative libraries sing_49 7.htm#SEC549647 Non-commutative algebra Non-commutative algebra sing_ 849.htm#SEC901648 Non-commutative algebra sing_ 884.htm#SEC941649 Non-commutative libraries Non-commutative libraries sing_49 7.htm#SEC549650 Non-commutative subsystem Non-commutative subsystem sing_42 0.htm#SEC460651 Nonhyp sing_1 393.htm#SEC1469sprintf652 Normalization sing_8 31.htm#SEC883653 Notes for Singular users Notes for Singular users sing_2 757.htm#SEC2840654 Notes for developers Notes for developers sing_2 758.htm#SEC2847655 NullCone sing_1 695.htm#SEC177164635656 NumIrrDecom sing_1 367.htm#SEC1443sprintf657 NumLocalDim sing_1 356.htm#SEC14321739658 NumPrimDecom sing_1 369.htm#SEC144534134659 Oaku-Takayama algorithm sing_54 0.htm#IDX338643 New orderings for modules Notes for Singular users sing_2822.htm#SEC2911 644 Newton non-degenerate sing_1634.htm#IDX773 645 Newton polygon sing_1633.htm#IDX772 646 Newton polygon sing_1634.htm#IDX774 647 Newton polygons sing_2809.htm#IDX1080 648 Newton polytope sing_2133.htm#IDX817 649 Newton step sing_2745.htm#IDX1040 650 NoetherPosition sing_1292.htm#SEC1368 18735 651 Non-commutative LIBs Non-commutative libraries sing_499.htm#SEC551 652 Non-commutative algebra Non-commutative algebra sing_912.htm#SEC964 653 Non-commutative algebra sing_947.htm#SEC1004 654 Non-commutative libraries Non-commutative libraries sing_499.htm#SEC551 655 Non-commutative subsystem Non-commutative subsystem sing_422.htm#SEC462 656 Nonhyp sing_1455.htm#SEC1531 sprintf 657 Normalization sing_894.htm#SEC946 658 Notes for Singular users Notes for Singular users sing_2822.htm#SEC2906 659 Notes for developers Notes for developers sing_2823.htm#SEC2913 660 NullCone sing_1757.htm#SEC1833 64635 661 NumIrrDecom sing_1429.htm#SEC1505 sprintf 662 NumLocalDim sing_1418.htm#SEC1494 1739 663 NumPrimDecom sing_1431.htm#SEC1507 34134 664 Oaku-Takayama algorithm sing_542.htm#IDX338 660 665 Objects sing_38.htm#SEC66 661 Orlik-Solomon sing_2202.htm#IDX875 662 Output sing_2526.htm#IDX990 663 Output sing_2623.htm#IDX997 664 Output sing_2625.htm#IDX998 665 Output sing_2626.htm#IDX999 666 Output sing_2627.htm#IDX1000 667 Output sing_2628.htm#IDX1001 668 Output sing_2629.htm#IDX1002 669 Output sing_2630.htm#IDX1003 670 Output sing_2631.htm#IDX1004 671 Output sing_2632.htm#IDX1005 672 Output sing_2633.htm#IDX1006 673 Output sing_2634.htm#IDX1007 674 Output sing_2635.htm#IDX1008 675 Output sing_2636.htm#IDX1009 676 Output sing_2637.htm#IDX1010 677 Output sing_2638.htm#IDX1011 678 Output sing_2639.htm#IDX1012 679 Output sing_2640.htm#IDX1013 680 Output sing_2641.htm#IDX1014 681 Output sing_2642.htm#IDX1015 682 Output sing_2643.htm#IDX1016 683 Output sing_2644.htm#IDX1017 684 Output sing_2645.htm#IDX1018 685 Output sing_2646.htm#IDX1019 686 Output sing_2647.htm#IDX1020 687 Output, formatting of sing_813.htm#SEC865 688 PBW sing_519.htm#IDX326 689 PBW basis sing_486.htm#SEC527 690 PBW_eqDeg sing_537.htm#SEC589 23181 691 PBW_maxDeg sing_538.htm#SEC590 59566 692 PBW_maxMonom sing_539.htm#SEC591 1155 693 PEsolve sing_1705.htm#SEC1781 9229 694 PH_ais sing_2224.htm#SEC2300 49473 695 PH_nais sing_2225.htm#SEC2301 46271 696 PLURAL sing_421.htm#SEC461 697 PLURAL LIBs Non-commutative libraries sing_497.htm#SEC549 698 PPolyH sing_2406.htm#SEC2482 25241 699 PPolyN sing_2411.htm#SEC2487 39067 700 PPolyS sing_2409.htm#SEC2485 13817 701 ParToVar sing_2401.htm#SEC2477 13991 702 Parallelization Parallelization with ssi links sing_815.htm#SEC867 703 Parallelization sing_956.htm#IDX487 666 Orlik-Solomon sing_2264.htm#IDX881 667 Output sing_2591.htm#IDX1000 668 Output sing_2688.htm#IDX1007 669 Output sing_2690.htm#IDX1008 670 Output sing_2691.htm#IDX1009 671 Output sing_2692.htm#IDX1010 672 Output sing_2693.htm#IDX1011 673 Output sing_2694.htm#IDX1012 674 Output sing_2695.htm#IDX1013 675 Output sing_2696.htm#IDX1014 676 Output sing_2697.htm#IDX1015 677 Output sing_2698.htm#IDX1016 678 Output sing_2699.htm#IDX1017 679 Output sing_2700.htm#IDX1018 680 Output sing_2701.htm#IDX1019 681 Output sing_2702.htm#IDX1020 682 Output sing_2703.htm#IDX1021 683 Output sing_2704.htm#IDX1022 684 Output sing_2705.htm#IDX1023 685 Output sing_2706.htm#IDX1024 686 Output sing_2707.htm#IDX1025 687 Output sing_2708.htm#IDX1026 688 Output sing_2709.htm#IDX1027 689 Output sing_2710.htm#IDX1028 690 Output sing_2711.htm#IDX1029 691 Output sing_2712.htm#IDX1030 692 Output, formatting of sing_876.htm#SEC928 693 PBW sing_521.htm#IDX326 694 PBW basis sing_488.htm#SEC529 695 PBW_eqDeg sing_539.htm#SEC591 23181 696 PBW_maxDeg sing_540.htm#SEC592 59566 697 PBW_maxMonom sing_541.htm#SEC593 1155 698 PEsolve sing_1767.htm#SEC1843 9229 699 PH_ais sing_2286.htm#SEC2362 49473 700 PH_nais sing_2287.htm#SEC2363 46271 701 PLURAL sing_423.htm#SEC463 702 PLURAL LIBs Non-commutative libraries sing_499.htm#SEC551 703 PPolyH sing_2468.htm#SEC2544 25241 704 PPolyN sing_2476.htm#SEC2552 39067 705 PPolyQp sing_2471.htm#SEC2547 35707 706 PPolyS sing_2474.htm#SEC2550 13817 707 ParToVar sing_2463.htm#SEC2539 13991 708 Parallelization Parallelization with ssi links sing_878.htm#SEC930 709 Parallelization sing_1019.htm#IDX493 704 710 Parameter list sing_44.htm#SEC81 705 Parameters sing_8 12.htm#SEC864706 Parametrization sing_1 376.htm#IDX609707 Parametrization, image. sing_1 386.htm#IDX621708 PartC sing_23 09.htm#SEC238554120709 PartitionVar sing_2 398.htm#SEC247441350710 Path names Notes for Singular users sing_2 757.htm#SEC2843711 PerfectPowerTest sing_1 863.htm#SEC193917450712 Perturbation walk sing_1 158.htm#IDX544711 Parameters sing_875.htm#SEC927 712 Parametrization sing_1438.htm#IDX615 713 Parametrization, image. sing_1448.htm#IDX627 714 PartC sing_2371.htm#SEC2447 54120 715 PartitionVar sing_2460.htm#SEC2536 41350 716 Path names Notes for Singular users sing_2822.htm#SEC2909 717 PerfectPowerTest sing_1925.htm#SEC2001 17450 718 Perturbation walk sing_1220.htm#IDX550 713 719 Pfister, Gerhard sing_1.htm#IDX19 714 720 Pipe links sing_121.htm#SEC161 715 PocklingtonLehmer sing_19 02.htm#SEC197813634716 Poincare polynomial sing_22 14.htm#IDX899717 Polar curves sing_ 837.htm#SEC889718 PollardRho sing_19 03.htm#SEC197949602719 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_22 27.htm#IDX915720 PolyBoRi, Boolean Groebner Basis sing_22 29.htm#IDX916721 PolyBoRi, Boolean Groebner Basis sing_22 30.htm#IDX917722 PolyBoRi, Boolean Groebner Basis sing_22 31.htm#IDX918723 PolyBoRi, Boolean Groebner Basis sing_22 32.htm#IDX919724 PolyBoRi, Boolean Groebner Basis sing_22 33.htm#IDX920725 PolyBoRi, Boolean Groebner Basis sing_22 34.htm#IDX921726 PolyBoRi, Boolean Groebner Basis sing_22 35.htm#IDX922727 PolyBoRi, Boolean Groebner Basis sing_22 36.htm#IDX923728 PolyBoRi, Boolean Groebner Basis sing_22 37.htm#IDX924729 PolyBoRi, Boolean Groebner Basis sing_2 238.htm#IDX925730 PolyBoRi, Boolean Groebner Basis sing_2 239.htm#IDX926731 PolyBoRi, Boolean Groebner Basis sing_2 240.htm#IDX927732 PolyBoRi, Boolean Groebner Basis sing_2 241.htm#IDX928733 PolyBoRi, Boolean Groebner Basis sing_2 243.htm#IDX930734 PolyBoRi, zero-supressed decision diagram sing_2 242.htm#IDX929735 Polybori, Boolean Groebner Basis sing_2 244.htm#IDX931736 Polynomial data sing_ 855.htm#SEC907737 Pottier algorithm sing_ 877.htm#SEC934721 PocklingtonLehmer sing_1964.htm#SEC2040 13634 722 Poincare polynomial sing_2276.htm#IDX905 723 Polar curves sing_900.htm#SEC952 724 PollardRho sing_1965.htm#SEC2041 49602 725 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2289.htm#IDX921 726 PolyBoRi, Boolean Groebner Basis sing_2291.htm#IDX922 727 PolyBoRi, Boolean Groebner Basis sing_2292.htm#IDX923 728 PolyBoRi, Boolean Groebner Basis sing_2293.htm#IDX924 729 PolyBoRi, Boolean Groebner Basis sing_2294.htm#IDX925 730 PolyBoRi, Boolean Groebner Basis sing_2295.htm#IDX926 731 PolyBoRi, Boolean Groebner Basis sing_2296.htm#IDX927 732 PolyBoRi, Boolean Groebner Basis sing_2297.htm#IDX928 733 PolyBoRi, Boolean Groebner Basis sing_2298.htm#IDX929 734 PolyBoRi, Boolean Groebner Basis sing_2299.htm#IDX930 735 PolyBoRi, Boolean Groebner Basis sing_2300.htm#IDX931 736 PolyBoRi, Boolean Groebner Basis sing_2301.htm#IDX932 737 PolyBoRi, Boolean Groebner Basis sing_2302.htm#IDX933 738 PolyBoRi, Boolean Groebner Basis sing_2303.htm#IDX934 739 PolyBoRi, Boolean Groebner Basis sing_2305.htm#IDX936 740 PolyBoRi, zero-supressed decision diagram sing_2304.htm#IDX935 741 Polybori, Boolean Groebner Basis sing_2306.htm#IDX937 742 Polynomial data sing_918.htm#SEC970 743 Pottier algorithm sing_940.htm#SEC997 738 744 Preface sing_1.htm#SEC1 739 Prep sing_9 29.htm#SEC100555342740 Primary decomposition Primary decomposition sing_8 30.htm#SEC882741 PrimdecA sing_12 12.htm#SEC1288248742 PrimdecB sing_12 13.htm#SEC12899653745 Prep sing_992.htm#SEC1068 55342 746 Primary decomposition Primary decomposition sing_893.htm#SEC945 747 PrimdecA sing_1274.htm#SEC1350 248 748 PrimdecB sing_1275.htm#SEC1351 9653 743 749 Procedure definition Procedure definition sing_43.htm#SEC78 744 750 Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84 745 751 Procedures sing_42.htm#SEC77 746 752 Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14 747 Procedures and libraries sing_8 09.htm#SEC861753 Procedures and libraries sing_872.htm#SEC924 748 754 Procedures in a library Procedures in a library sing_54.htm#SEC91 749 Product orderings sing_ 864.htm#SEC916750 Programming sing_8 07.htm#SEC859751 Pseudo ordering L sing_ 866.htm#SEC918752 PtoCrep sing_9 30.htm#SEC100652961753 Puiseux expansion sing_1 470.htm#IDX632754 Puiseux expansion sing_1 558.htm#IDX754755 Puiseux pairs Invariants of plane curve singularities sing_ 840.htm#SEC892756 Puiseux pairs sing_1 564.htm#IDX759755 Product orderings sing_927.htm#SEC979 756 Programming sing_870.htm#SEC922 757 Pseudo ordering L sing_929.htm#SEC981 758 PtoCrep sing_993.htm#SEC1069 52961 759 Puiseux expansion sing_1532.htm#IDX638 760 Puiseux expansion sing_1620.htm#IDX760 761 Puiseux pairs Invariants of plane curve singularities sing_903.htm#SEC955 762 Puiseux pairs sing_1626.htm#IDX765 757 763 QQ sing_28.htm#SEC39 758 Qso3Casimir sing_697.htm#SEC749 40212 759 Quotient sing_1747.htm#SEC1823 24888 760 QuotientEquations sing_1594.htm#SEC1670 18230 761 Rational curves sing_1376.htm#IDX610 762 ReJunkUseHomo sing_1362.htm#SEC1438 10186 763 ReesAlgebra sing_1329.htm#SEC1405 59951 764 References sing_892.htm#SEC966 765 References (plural) sing_489.htm#SEC539 766 Release Notes sing_2753.htm#SEC2829 767 Res sing_2506.htm#SEC2582 92 768 ResTree sing_1422.htm#SEC1498 58727 764 Qso3Casimir sing_726.htm#SEC778 40212 765 Quot-scheme sing_2466.htm#IDX991 766 Quotient sing_1809.htm#SEC1885 24888 767 QuotientEquations sing_1656.htm#SEC1732 18230 768 Rational curves sing_1438.htm#IDX616 769 ReJunkUseHomo sing_1424.htm#SEC1500 10186 770 ReesAlgebra sing_1391.htm#SEC1467 59951 771 References sing_955.htm#SEC1029 772 References (plural) sing_491.htm#SEC541 773 Release Notes sing_2818.htm#SEC2894 774 Res sing_2571.htm#SEC2647 92 775 ResTree sing_1484.htm#SEC1560 58727 769 776 Resolution sing_11.htm#SEC17 770 Resolution of singularities Resolution of singularities sing_ 843.htm#SEC895771 Resolution, free sing_8 25.htm#SEC877772 ReynoldsImage sing_1 696.htm#SEC177235172773 ReynoldsOperator sing_1 697.htm#SEC177314986774 RiemannRochBN sing_2 254.htm#SEC233020085775 RiemannRochHess sing_2 489.htm#SEC2565sprintf776 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_ 851.htm#SEC903777 Ring-dependent options Notes for Singular users sing_2 757.htm#SEC2842777 Resolution of singularities Resolution of singularities sing_906.htm#SEC958 778 Resolution, free sing_888.htm#SEC940 779 ReynoldsImage sing_1758.htm#SEC1834 35172 780 ReynoldsOperator sing_1759.htm#SEC1835 14986 781 RiemannRochBN sing_2316.htm#SEC2392 20085 782 RiemannRochHess sing_2554.htm#SEC2630 sprintf 783 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_914.htm#SEC966 784 Ring-dependent options Notes for Singular users sing_2822.htm#SEC2908 778 785 Rings and orderings sing_28.htm#SEC39 779 786 Rings and standard bases Rings and standard bases sing_7.htm#SEC13 780 787 Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 781 SCA Graded commutative algebras (SCA) sing_49 0.htm#SEC542788 SCA Graded commutative algebras (SCA) sing_492.htm#SEC544 782 789 SDB breakpoint Source code debugger sing_66.htm#SEC106 783 790 SDB debugger Source code debugger sing_66.htm#SEC106 784 SDLoc sing_56 7.htm#SEC6199512785 SINGULAR libraries sing_ 893.htm#SEC969791 SDLoc sing_569.htm#SEC621 9512 792 SINGULAR libraries sing_956.htm#SEC1032 786 793 SINGULARHIST sing_18.htm#SEC25 787 SV-decoding algorithm sing_18 03.htm#IDX788788 SV-decoding algorithm, preprocessing sing_18 02.htm#IDX787789 Sannfs sing_54 3.htm#SEC59542932790 SannfsBFCT sing_55 2.htm#SEC60459702791 SannfsVar sing_ 599.htm#SEC65137522792 Sannfslog sing_54 4.htm#SEC59649313793 Saturation sing_8 22.htm#SEC874794 Saturation sing_1 139.htm#IDX513794 SV-decoding algorithm sing_1865.htm#IDX794 795 SV-decoding algorithm, preprocessing sing_1864.htm#IDX793 796 Sannfs sing_545.htm#SEC597 42932 797 SannfsBFCT sing_554.htm#SEC606 59702 798 SannfsVar sing_601.htm#SEC653 37522 799 Sannfslog sing_546.htm#SEC598 49313 800 Saturation sing_885.htm#SEC937 801 Saturation sing_1201.htm#IDX519 795 802 Sch@"onemann, Hans sing_1.htm#IDX20 796 Schoof sing_19 14.htm#SEC199049281797 Schubert calculus sing_27 02.htm#IDX1044798 SchubertClass sing_2 739.htm#SEC281562336799 SchurCh sing_23 06.htm#SEC238258575800 SchurS sing_23 05.htm#SEC238146004801 SegreA sing_23 12.htm#SEC238855776802 Semigroup sing_15 10.htm#SEC158622323803 SetDeg sing_25 09.htm#SEC258540547804 Setting up a G-algebra sing_48 6.htm#SEC530805 ShanksMestre sing_19 13.htm#SEC198912973806 SimplifyIdeal sing_1 698.htm#SEC1774sprintf807 Singular sing_35 8.htm#IDX257808 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2 755.htm#SEC2838803 Schoof sing_1976.htm#SEC2052 49281 804 Schubert calculus sing_2767.htm#IDX1054 805 SchubertClass sing_2804.htm#SEC2880 62336 806 SchurCh sing_2368.htm#SEC2444 58575 807 SchurS sing_2367.htm#SEC2443 46004 808 SegreA sing_2374.htm#SEC2450 55776 809 Semigroup sing_1572.htm#SEC1648 22323 810 SetDeg sing_2574.htm#SEC2650 40547 811 Setting up a G-algebra sing_488.htm#SEC532 812 ShanksMestre sing_1975.htm#SEC2051 12973 813 SimplifyIdeal sing_1760.htm#SEC1836 sprintf 814 Singular sing_359.htm#IDX257 815 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2820.htm#SEC2904 809 816 Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36 810 817 Singular, demo mode sing_24.htm#SEC35 … … 812 819 Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38 813 820 Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 814 Singular2bertini sing_1 360.htm#SEC14367552815 SingularLib sing_35 8.htm#IDX259816 Singularities sing_1 469.htm#SEC1545817 Singularity Theory sing_8 34.htm#SEC886818 Skeletons for parallelization sing_ 956.htm#IDX488819 Smith form sing_1 845.htm#IDX798820 Smith normal form sing_1 845.htm#IDX799821 SolowayStrassen sing_19 01.htm#SEC197722680822 Solving systems of polynomial equations Solving systems of polynomial equations sing_ 853.htm#SEC905823 Source sing_2 498.htm#SEC257410351821 Singular2bertini sing_1422.htm#SEC1498 7552 822 SingularLib sing_359.htm#IDX259 823 Singularities sing_1531.htm#SEC1607 824 Singularity Theory sing_897.htm#SEC949 825 Skeletons for parallelization sing_1019.htm#IDX494 826 Smith form sing_1907.htm#IDX804 827 Smith normal form sing_1907.htm#IDX805 828 SolowayStrassen sing_1963.htm#SEC2039 22680 829 Solving systems of polynomial equations Solving systems of polynomial equations sing_916.htm#SEC968 830 Source sing_2563.htm#SEC2639 10351 824 831 Source code debugger, invocation Command line options sing_19.htm#IDX33 825 Space curve singularities, branches of Branches of space curve singularities sing_ 841.htm#SEC893832 Space curve singularities, branches of Branches of space curve singularities sing_904.htm#SEC956 826 833 Special characters sing_36.htm#SEC64 827 Splitting lemma addnondegeneratevariables sing_2 676.htm#IDX1023828 Splitting lemma sing_2 679.htm#IDX1027834 Splitting lemma addnondegeneratevariables sing_2741.htm#IDX1033 835 Splitting lemma sing_2744.htm#IDX1037 829 836 Ssi file links sing_119.htm#SEC159 830 837 Ssi links sing_118.htm#SEC158 831 838 Ssi tcp links sing_120.htm#SEC160 832 StabEqn sing_1 595.htm#SEC167128539833 StabEqnId sing_1 596.htm#SEC167227955834 StabOrder sing_1 597.htm#SEC167355603835 Standard Bases Computing Groebner and Standard Bases sing_8 17.htm#SEC869836 Standard bases sing_ 868.htm#SEC920837 StartOrderingV sing_1 464.htm#SEC154058927839 StabEqn sing_1657.htm#SEC1733 28539 840 StabEqnId sing_1658.htm#SEC1734 27955 841 StabOrder sing_1659.htm#SEC1735 55603 842 Standard Bases Computing Groebner and Standard Bases sing_880.htm#SEC932 843 Standard bases sing_931.htm#SEC983 844 StartOrderingV sing_1526.htm#SEC1602 58927 838 845 Startup sequence sing_20.htm#SEC27 839 StringF sing_1 584.htm#SEC166011590840 SymGroup sing_7 55.htm#SEC80756676841 Symbolic-numerical solving Symbolic-numerical solving sing_ 853.htm#SEC905842 Symbolic-numerical solving sing_17 02.htm#SEC1778843 System and Control theory System and Control theory sing_18 27.htm#SEC1903844 System dependent limitations System dependent limitations sing_4 08.htm#SEC448845 System variables sing_39 4.htm#SEC434846 Syzygies and resolutions Syzygies and resolutions sing_ 870.htm#SEC924847 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_4 88.htm#SEC535848 T1 sing_ 838.htm#SEC890849 T2 sing_ 838.htm#SEC890846 StringF sing_1646.htm#SEC1722 11590 847 SymGroup sing_784.htm#SEC836 56676 848 Symbolic-numerical solving Symbolic-numerical solving sing_916.htm#SEC968 849 Symbolic-numerical solving sing_1764.htm#SEC1840 850 System and Control theory System and Control theory sing_1889.htm#SEC1965 851 System dependent limitations System dependent limitations sing_410.htm#SEC450 852 System variables sing_396.htm#SEC436 853 Syzygies and resolutions Syzygies and resolutions sing_933.htm#SEC987 854 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_490.htm#SEC537 855 T1 sing_901.htm#SEC953 856 T2 sing_901.htm#SEC953 850 857 TRACE Tracing of procedures sing_65.htm#SEC102 851 TRACE sing_40 3.htm#SEC443852 T_1 sing_16 17.htm#SEC169359277853 T_12 sing_16 19.htm#SEC169512923854 T_2 sing_16 18.htm#SEC169455781855 Target sing_2 497.htm#SEC257316006856 Teaching sing_1 859.htm#SEC1935858 TRACE sing_405.htm#SEC445 859 T_1 sing_1679.htm#SEC1755 59277 860 T_12 sing_1681.htm#SEC1757 12923 861 T_2 sing_1680.htm#SEC1756 55781 862 Target sing_2562.htm#SEC2638 16006 863 Teaching sing_1921.htm#SEC1997 857 864 Template for writing a library sing_55.htm#SEC92 858 TestGRRes sing_2 469.htm#SEC25458315859 TestJMark sing_1 465.htm#SEC154141314865 TestGRRes sing_2534.htm#SEC2610 8315 866 TestJMark sing_1527.htm#SEC1603 41314 860 867 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 861 The Tran algorithm sing_1 155.htm#IDX541862 The fractal walk algorithm sing_1 154.htm#IDX540863 The fractal walk algorithm sing_27 01.htm#IDX1041868 The Tran algorithm sing_1217.htm#IDX547 869 The fractal walk algorithm sing_1216.htm#IDX546 870 The fractal walk algorithm sing_2766.htm#IDX1051 864 871 The online help system The online help system sing_16.htm#SEC22 865 Tjurina sing_16 15.htm#SEC169111249866 Tjurina number Milnor and Tjurina number sing_8 35.htm#SEC887867 Tjurina number sing_1 251.htm#IDX570872 Tjurina sing_1677.htm#SEC1753 11249 873 Tjurina number Milnor and Tjurina number sing_898.htm#SEC950 874 Tjurina number sing_1313.htm#IDX576 868 875 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 869 Tor sing_1 180.htm#SEC1256sprintf870 Toric ideals and integer programming Toric ideals and integer programming sing_ 873.htm#SEC930871 Tricks and pitfalls sing_40 6.htm#SEC446872 Tropical Geometry sing_20 11.htm#SEC2087876 Tor sing_1242.htm#SEC1318 sprintf 877 Toric ideals and integer programming Toric ideals and integer programming sing_936.htm#SEC993 878 Tricks and pitfalls sing_408.htm#SEC448 879 Tropical Geometry sing_2073.htm#SEC2149 873 880 Type casting Type conversion and casting sing_39.htm#SEC69 874 881 Type conversion Type conversion and casting sing_39.htm#SEC68 875 882 Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98 876 U_D_O sing_1 095.htm#SEC117126192877 Unix installation Unix installation instructions sing_2 763.htm#SEC2852878 UpOneMatrix sing_7 44.htm#SEC79663020879 UpperMonomials sing_1 598.htm#SEC167420941880 UseBertini sing_1 359.htm#SEC143543362881 User defined types sing_18 2.htm#SEC222882 V-filtration sing_15 33.htm#IDX664883 V-filtration sing_1 539.htm#IDX692884 V-filtration sing_1 540.htm#IDX698885 V-filtration sing_1 541.htm#IDX706886 V-filtration sing_1 542.htm#IDX712887 V-filtration sing_1 543.htm#IDX720888 V-filtration sing_1 544.htm#IDX730889 V-filtration sing_1 555.htm#IDX736890 V-filtration sing_1 557.htm#IDX747891 VarToPar sing_24 00.htm#SEC247610508883 U_D_O sing_1157.htm#SEC1233 26192 884 Unix installation Unix installation instructions sing_2828.htm#SEC2918 885 UpOneMatrix sing_773.htm#SEC825 63020 886 UpperMonomials sing_1660.htm#SEC1736 20941 887 UseBertini sing_1421.htm#SEC1497 43362 888 User defined types sing_183.htm#SEC223 889 V-filtration sing_1595.htm#IDX670 890 V-filtration sing_1601.htm#IDX698 891 V-filtration sing_1602.htm#IDX704 892 V-filtration sing_1603.htm#IDX712 893 V-filtration sing_1604.htm#IDX718 894 V-filtration sing_1605.htm#IDX726 895 V-filtration sing_1606.htm#IDX736 896 V-filtration sing_1617.htm#IDX742 897 V-filtration sing_1619.htm#IDX753 898 VarToPar sing_2462.htm#SEC2538 10508 892 899 Variables, indexed sing_37.htm#SEC65 893 Version number Version schema for Singular sing_2 756.htm#SEC2839894 Version schema for Singular Version schema for Singular sing_2 756.htm#SEC2839900 Version number Version schema for Singular sing_2821.htm#SEC2905 901 Version schema for Singular Version schema for Singular sing_2821.htm#SEC2905 895 902 Version string sing_50.htm#SEC87 896 Visualization sing_1 765.htm#SEC1841897 WLemma sing_ 943.htm#SEC10197302898 WP, global ordering sing_ 860.htm#IDX400899 WSemigroup sing_15 15.htm#SEC159157449900 Weierstrass sing_1 798.htm#SEC187458220901 Weierstrass semigroup sing_1 794.htm#IDX782902 Weyl sing_7 29.htm#SEC78129212903 Weyl algebra sing_54 0.htm#IDX332904 Weyl algebra sing_59 6.htm#IDX357905 Weyl closure sing_ 780.htm#IDX385906 WeylClosure sing_ 782.htm#SEC83423845907 WeylClosure1 sing_ 783.htm#SEC83515759908 Wibmer's Lemma sing_ 943.htm#IDX481909 Windows installation Windows installation instructions sing_2 764.htm#SEC2853910 WitSet sing_1 366.htm#SEC144239803911 WitSupSet sing_1 365.htm#SEC144147758912 Ws, local ordering sing_ 861.htm#IDX412913 XLsolve sing_17 08.htm#SEC178434970903 Visualization sing_1827.htm#SEC1903 904 WLemma sing_1006.htm#SEC1082 7302 905 WP, global ordering sing_923.htm#IDX406 906 WSemigroup sing_1577.htm#SEC1653 57449 907 Weierstrass sing_1860.htm#SEC1936 58220 908 Weierstrass semigroup sing_1856.htm#IDX788 909 Weyl sing_758.htm#SEC810 29212 910 Weyl algebra sing_542.htm#IDX332 911 Weyl algebra sing_598.htm#IDX357 912 Weyl closure sing_843.htm#IDX391 913 WeylClosure sing_845.htm#SEC897 23845 914 WeylClosure1 sing_846.htm#SEC898 15759 915 Wibmer's Lemma sing_1006.htm#IDX487 916 Windows installation Windows installation instructions sing_2829.htm#SEC2919 917 WitSet sing_1428.htm#SEC1504 39803 918 WitSupSet sing_1427.htm#SEC1503 47758 919 Ws, local ordering sing_924.htm#IDX418 920 XLsolve sing_1770.htm#SEC1846 34970 914 921 ZZ sing_28.htm#SEC39 915 922 ZZ/m sing_28.htm#SEC39 916 923 ZZ/p sing_28.htm#SEC39 917 ZZsolve sing_17 09.htm#SEC178518657924 ZZsolve sing_1771.htm#SEC1847 18657 918 925 [ sing_36.htm#IDX83 919 926 [] sing_142.htm#SEC182 920 927 [] sing_155.htm#SEC195 921 [] sing_17 5.htm#SEC215922 [] sing_18 0.htm#SEC220928 [] sing_176.htm#SEC216 929 [] sing_181.htm#SEC221 923 930 \ sing_36.htm#IDX112 924 931 ] sing_36.htm#IDX84 … … 930 937 _ sing_36.htm#IDX116 931 938 ` sing_36.htm#IDX105 932 a, ordering sing_ 865.htm#SEC917933 absFactorize sing_11 08.htm#SEC118452546934 absFactorizeBCG sing_11 09.htm#SEC118555510935 absPrimdecGTZ sing_13 09.htm#SEC138546393936 absPrimdecGTZE sing_13 10.htm#SEC138648005937 absValue sing_9 05.htm#SEC98154595938 absfact.lib sing_11 07.htm#SEC1183939 absfact_lib sing_11 07.htm#SEC1183940 absolute factorization. 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method sing_ 889.htm#SEC958962 ainvar.lib sing_1 675.htm#SEC1751963 ainvar_lib sing_1 675.htm#SEC1751964 aksaka.lib sing_1 860.htm#SEC1936965 aksaka_lib sing_1 860.htm#SEC1936966 alexanderpolynomial sing_1 473.htm#SEC154936814967 alexpoly.lib sing_1 470.htm#SEC1546968 alexpoly_lib sing_1 470.htm#SEC1546969 algDependent sing_11 14.htm#SEC119020789970 alg_kernel sing_11 15.htm#SEC1191307971 algebra.lib sing_11 10.htm#SEC1186972 algebra_containment sing_11 11.htm#SEC118747912973 algebra_lib sing_11 10.htm#SEC1186974 algebraic dependence sing_7 50.htm#IDX363975 algebraic field extension sing_13 23.htm#IDX579976 algebraicDependence sing_13 36.htm#SEC141238500977 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_ 880.htm#SEC937978 algorithm of Conti and Traverso sing_ 876.htm#SEC933979 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_ 879.htm#SEC936980 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_ 878.htm#SEC935981 algorithm of 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1011 annfsBMI sing_552.htm#SEC604 2532 1012 annfsParamBM sing_551.htm#SEC603 43587 1013 annfsRB sing_557.htm#SEC609 31892 1014 annfspecial sing_544.htm#SEC596 27566 1015 annihilator of polynomial sing_565.htm#IDX342 1016 annihilator of rational function sing_565.htm#IDX343 1017 annihilator of rational function sing_843.htm#IDX394 1018 annil sing_1280.htm#SEC1356 48744 1019 appelF1 sing_584.htm#SEC636 63146 1020 appelF2 sing_585.htm#SEC637 22460 1021 appelF4 sing_586.htm#SEC638 6847 1022 appendWeight2Ord sing_751.htm#SEC803 21488 1023 apply sing_380.htm#SEC420 1024 applyAdF sing_534.htm#SEC586 40329 1025 applyPermutationToIntvec applyPermutationToIntvec sing_2512.htm#SEC2588 28900 1026 arcpoint.lib sing_1545.htm#SEC1621 1027 arcpoint_lib sing_1545.htm#SEC1621 1028 areEqualLeftFractions areEqualLeftFractions sing_2730.htm#SEC2806 29498 1029 areZeroElements sing_2650.htm#SEC2726 14728 1023 1030 argument, default sing_44.htm#SEC81 1024 1031 argument, optional sing_44.htm#SEC81 1025 arr.lib 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sing_507.htm#SEC559 1126 bfun_lib sing_507.htm#SEC559 1119 1127 bigint sing_78.htm#SEC118 1120 1128 bigint declarations sing_79.htm#SEC119 … … 1122 1130 bigint operations sing_81.htm#SEC121 1123 1131 bigint related functions bigint related functions sing_82.htm#SEC122 1124 bigintToBinary sing_2 445.htm#SEC2521597421132 bigintToBinary sing_2510.htm#SEC2586 59742 1125 1133 bigintmat sing_83.htm#SEC123 1126 1134 bigintmat declarations bigintmat declarations sing_84.htm#SEC124 … … 1128 1136 bigintmat operations bigintmat operations sing_87.htm#SEC127 1129 1137 bigintmat type cast sing_86.htm#SEC126 1130 bimodules sing_ 498.htm#IDX3031131 bimodules.lib sing_ 498.htm#SEC5501132 bimodules_lib sing_ 498.htm#SEC5501133 binaryToBigint sing_2 446.htm#SEC2522sprintf1134 binary_add sing_19 21.htm#SEC1997428171135 binomial sing_9 06.htm#SEC982232081136 binomials2intmat sing_1 284.htm#SEC1360588041137 birational map, image, inverse. sing_1 378.htm#IDX6151138 bistd sing_ 499.htm#SEC551452371139 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6.htm#SEC4961169 braid sing_2 196.htm#IDX8631160 boolean_constant sing_2291.htm#SEC2367 52873 1161 boolean_ideal sing_2295.htm#SEC2371 53515 1162 boolean_poly sing_2292.htm#SEC2368 41652 1163 boolean_poly_ring sing_2290.htm#SEC2366 sprintf 1164 boolean_set sing_2296.htm#SEC2372 58235 1165 boolean_std sing_2289.htm#SEC2365 5921 1166 border basis sing_2758.htm#IDX1041 1167 borderBasis sing_2759.htm#SEC2835 33172 1168 boundBuFou sing_2060.htm#SEC2136 26589 1169 boundDes sing_2062.htm#SEC2138 35149 1170 boundaryLatticePoints boundaryLatticePoints sing_2148.htm#SEC2224 6238 1171 boundposDes sing_2061.htm#SEC2137 58854 1172 bounds sing_2746.htm#SEC2822 50218 1173 boxSet sing_2748.htm#SEC2824 8552 1174 bracket sing_359.htm#IDX197 1175 bracket sing_416.htm#SEC456 1176 bracket sing_458.htm#SEC498 1177 braid sing_2258.htm#IDX869 1170 1178 branchTo procs with different argument types sing_160.htm#SEC200 1171 break sing_3 79.htm#SEC4191172 break point sing_39 3.htm#SEC4331173 breakpoint sing_38 0.htm#SEC4201174 brillnoether.lib sing_2 253.htm#SEC23291175 brillnoether_lib sing_2 253.htm#SEC23291176 brnoeth.lib sing_1 794.htm#SEC18701177 brnoeth_lib sing_1 794.htm#SEC18701179 break sing_381.htm#SEC421 1180 break point sing_395.htm#SEC435 1181 breakpoint sing_382.htm#SEC422 1182 brillnoether.lib sing_2315.htm#SEC2391 1183 brillnoether_lib sing_2315.htm#SEC2391 1184 brnoeth.lib sing_1856.htm#SEC1932 1185 brnoeth_lib sing_1856.htm#SEC1932 1178 1186 browser, command line option Command line options sing_19.htm#IDX44 1179 browser, setting the sing_35 8.htm#IDX1931187 browser, setting the sing_359.htm#IDX193 1180 1188 browsers The online help system sing_16.htm#IDX21 1181 browsers, setting the sing_35 8.htm#IDX1921182 bubblesort sing_1 871.htm#SEC1947632781183 busadj sing_1 087.htm#SEC1163363011184 bvar sing_2 241.htm#SEC2317527731185 c, module ordering sing_ 862.htm#IDX4151186 cProj sing_2 295.htm#SEC2371240371187 calculateI sing_14 03.htm#SEC1479311071188 calculate_max_sum sing_ 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1192 bvar sing_2303.htm#SEC2379 52773 1193 c, module ordering sing_925.htm#IDX421 1194 cProj sing_2357.htm#SEC2433 24037 1195 calculateI sing_1465.htm#SEC1541 31107 1196 calculate_max_sum sing_2002.htm#SEC2078 4706 1197 calculate_ordering sing_1980.htm#SEC2056 42616 1198 cancelunit, option sing_316.htm#IDX171 1199 canonMap sing_1223.htm#SEC1299 47599 1200 canoncial form sing_991.htm#IDX442 1201 canoncial form sing_992.htm#IDX444 1202 canoncial form sing_993.htm#IDX446 1203 canonical sing_987.htm#IDX430 1204 canonical form sing_996.htm#IDX460 1205 canonical form sing_997.htm#IDX462 1206 canonical, sing_995.htm#IDX456 1207 canonicalizeCone sing_2079.htm#SEC2155 6251 1208 canonize sing_1902.htm#SEC1978 54090 1209 cantoradd sing_2016.htm#SEC2092 55304 1210 cantormult sing_2019.htm#SEC2095 57569 1211 cantorred sing_2017.htm#SEC2093 46502 1212 cardGroup sing_1192.htm#SEC1268 5553 1213 case No case or switch statement sing_414.htm#SEC454 1214 catNets sing_2688.htm#SEC2764 24760 1215 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2813.htm#SEC2889 55393 1208 1216 cdd sing_1.htm#IDX10 1209 1217 cddlib sing_1.htm#IDX11 1210 center sing_5 19.htm#IDX322 651081211 center sing_52 5.htm#SEC5771212 center sing_2 183.htm#IDX8431213 center sing_2 184.htm#IDX8441214 center sing_2 185.htm#IDX8461215 center sing_2 186.htm#IDX8481216 centerRed sing_52 4.htm#SEC576599101217 centerVS sing_52 3.htm#SEC575275481218 central sing_2 177.htm#IDX8291219 central sing_2 184.htm#IDX8451220 central sing_2 186.htm#IDX8471221 central sing_22 00.htm#IDX8721222 central.lib sing_5 19.htm#SEC5711223 central1st sing_2 388.htm#SEC2464290901224 central2nd sing_2 389.htm#SEC2465375451225 central_lib sing_5 19.htm#SEC5711226 centralize sing_5 19.htm#IDX3251227 centralizeSet sing_52 0.htm#SEC572557371228 centralizer sing_5 19.htm#IDX323 652611229 centralizer sing_52 6.htm#SEC5781230 centralizerRed sing_52 2.htm#SEC57482091231 centralizerVS sing_52 1.htm#SEC573229251232 cf_class sing_2 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478.htm#SEC1554168381280 charexp2inter sing_1 479.htm#SEC1555398811281 charexp2multseq sing_1 477.htm#SEC15533341282 charexp2poly sing_1 481.htm#SEC1557sprintf1283 charpoly sing_1 088.htm#SEC1164295611284 charstr sing_21 4.htm#SEC2541285 checkFactor sing_55 6.htm#SEC608559001286 checkRoot sing_55 1.htm#SEC603370451287 chern sing_2 260.htm#SEC233649161288 chern.lib sing_2 255.htm#SEC23311289 chernCharPoly sing_23 02.htm#SEC2378316101290 chernPoly sing_23 01.htm#SEC2377313161291 chern_lib sing_2 255.htm#SEC23311292 chineseRem sing_1 889.htm#SEC1965385601293 chinrem sing_21 5.htm#SEC2551294 chinrempoly sing_2 649.htm#SEC2725423121295 chinrestp sing_ 1948.htm#SEC2024247791296 cimonom.lib sing_23 17.htm#SEC23931297 cimonom_lib sing_23 17.htm#SEC23931298 cisimplicial.lib sing_11 26.htm#SEC12021299 cisimplicial_lib sing_11 26.htm#SEC12021300 classification sing_23 21.htm#IDX9381301 classify sing_1 490.htm#SEC156649531302 classify.lib sing_1 488.htm#SEC15641303 classify2.lib sing_23 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closetex sing_1 771.htm#SEC1847423341326 closureFrac sing_1 249.htm#SEC132592521327 coDim sing_23 35.htm#SEC2411606801328 coDimMap sing_23 34.htm#SEC241020021329 coHom sing_ 773.htm#SEC825510431330 codim sing_16 02.htm#SEC1678142531331 codimension sing_20 18.htm#SEC2094322071332 coding theory sing_ 854.htm#SEC9061333 coef sing_21 8.htm#SEC2581334 coefficient sing_2 176.htm#IDX8251335 coefficient sing_2 177.htm#IDX8281336 coefficient sing_2 178.htm#IDX8321218 center sing_521.htm#IDX322 65108 1219 center sing_527.htm#SEC579 1220 center sing_2245.htm#IDX849 1221 center sing_2246.htm#IDX850 1222 center sing_2247.htm#IDX852 1223 center sing_2248.htm#IDX854 1224 centerRed sing_526.htm#SEC578 59910 1225 centerVS sing_525.htm#SEC577 27548 1226 central sing_2239.htm#IDX835 1227 central sing_2246.htm#IDX851 1228 central sing_2248.htm#IDX853 1229 central sing_2262.htm#IDX878 1230 central.lib sing_521.htm#SEC573 1231 central1st sing_2450.htm#SEC2526 29090 1232 central2nd sing_2451.htm#SEC2527 37545 1233 central_lib sing_521.htm#SEC573 1234 centralize sing_521.htm#IDX325 1235 centralizeSet sing_522.htm#SEC574 55737 1236 centralizer sing_521.htm#IDX323 65261 1237 centralizer sing_528.htm#SEC580 1238 centralizerRed sing_524.htm#SEC576 8209 1239 centralizerVS sing_523.htm#SEC575 22925 1240 cf_class sing_210.htm#IDX132 1241 cgs sing_963.htm#SEC1039 57776 1242 cgsdr sing_988.htm#SEC1064 44460 1243 chAll sing_2327.htm#SEC2403 2690 1244 chAllInv sing_2328.htm#SEC2404 57760 1245 chDual sing_2333.htm#SEC2409 17745 1246 chHE sing_2329.htm#SEC2405 63916 1247 chHom sing_2342.htm#SEC2418 54776 1248 chNum sing_2323.htm#SEC2399 54415 1249 chNumbers sing_2324.htm#SEC2400 42134 1250 chNumbersProj sing_2361.htm#SEC2437 28837 1251 chProd sing_2335.htm#SEC2411 40209 1252 chProdE sing_2336.htm#SEC2412 33460 1253 chProdL sing_2337.htm#SEC2413 44795 1254 chProdLP sing_2338.htm#SEC2414 8881 1255 chProdM sing_2339.htm#SEC2415 64514 1256 chProdMP sing_2340.htm#SEC2416 17103 1257 chProj sing_2358.htm#SEC2434 32311 1258 chSum sing_2331.htm#SEC2407 21088 1259 chSymm sing_2345.htm#SEC2421 24066 1260 chSymm2L sing_2346.htm#SEC2422 51625 1261 chSymm2LP sing_2347.htm#SEC2423 26099 1262 chWedge sing_2348.htm#SEC2424 57678 1263 chWedge2L sing_2349.htm#SEC2425 46597 1264 chWedge2LP sing_2350.htm#SEC2426 8876 1265 chaincrit sing_2030.htm#SEC2106 9502 1266 chambers sing_2277.htm#IDX906 1267 chambers sing_2278.htm#IDX907 1268 changeDenominator sing_1318.htm#SEC1394 21094 1269 changechar sing_1067.htm#SEC1143 65454 1270 changeord sing_1068.htm#SEC1144 55156 1271 changeordTo sing_1091.htm#SEC1167 41903 1272 changes sing_2819.htm#SEC2895 1273 changevar sing_1069.htm#SEC1145 32829 1274 char sing_213.htm#SEC253 1275 charInfo sing_582.htm#SEC634 11034 1276 charVariety sing_581.htm#SEC633 18306 1277 char_series sing_214.htm#SEC254 1278 characteristic exponents sing_1539.htm#IDX645 1279 characteristic exponents sing_1540.htm#IDX650 1280 characteristic exponents sing_1541.htm#IDX653 1281 characteristic exponents sing_1542.htm#IDX657 1282 characteristic exponents sing_1626.htm#IDX763 1283 characteristic polynomial sing_2275.htm#IDX904 1284 characteristic variety sing_565.htm#IDX350 1285 characteristic variety sing_843.htm#IDX390 1286 charexp2conductor sing_1542.htm#SEC1618 sprintf 1287 charexp2generators sing_1540.htm#SEC1616 16838 1288 charexp2inter sing_1541.htm#SEC1617 39881 1289 charexp2multseq sing_1539.htm#SEC1615 334 1290 charexp2poly sing_1543.htm#SEC1619 sprintf 1291 charpoly sing_1150.htm#SEC1226 29561 1292 charstr sing_215.htm#SEC255 1293 checkFactor sing_558.htm#SEC610 55900 1294 checkRoot sing_553.htm#SEC605 37045 1295 chern sing_2322.htm#SEC2398 4916 1296 chern.lib sing_2317.htm#SEC2393 1297 chernCharPoly sing_2364.htm#SEC2440 31610 1298 chernPoly sing_2363.htm#SEC2439 31316 1299 chern_lib sing_2317.htm#SEC2393 1300 chineseRem sing_1951.htm#SEC2027 38560 1301 chinrem sing_216.htm#SEC256 1302 chinrempoly sing_2714.htm#SEC2790 42312 1303 chinrestp sing_2010.htm#SEC2086 24779 1304 cimonom.lib sing_2379.htm#SEC2455 1305 cimonom_lib sing_2379.htm#SEC2455 1306 cisimplicial.lib sing_1188.htm#SEC1264 1307 cisimplicial_lib sing_1188.htm#SEC1264 1308 classification sing_2383.htm#IDX944 1309 classify sing_1552.htm#SEC1628 4953 1310 classify.lib sing_1550.htm#SEC1626 1311 classify2.lib sing_2383.htm#SEC2459 1312 classify2_lib sing_2383.htm#SEC2459 1313 classifyCeq sing_1569.htm#SEC1645 42719 1314 classifyMapGerms.lib classifyMapGerms_lib sing_2395.htm#SEC2471 1315 classifyMapGerms_lib classifyMapGerms_lib sing_2395.htm#SEC2471 1316 classifySimpleMaps sing_2401.htm#SEC2477 62176 1317 classifySimpleMaps1 sing_2402.htm#SEC2478 24789 1318 classifyUnimodalMaps classifyUnimodalMaps sing_2403.htm#SEC2479 63464 1319 classify_aeq.lib sing_2386.htm#SEC2462 1320 classify_aeq_lib sing_2386.htm#SEC2462 1321 classify_lib sing_1550.htm#SEC1626 1322 classifyceq.lib sing_1568.htm#IDX660 1323 classifyceq_lib sing_1568.htm#IDX661 1324 classifyci.lib sing_1570.htm#IDX662 1325 classifyci_lib sing_1570.htm#IDX663 1326 classifyicis sing_1571.htm#SEC1647 37651 1327 classpoly sing_2362.htm#SEC2438 45724 1328 cleanTmp sing_2226.htm#SEC2302 14108 1329 cleanunit sing_1463.htm#SEC1539 sprintf 1330 cleardenom sing_217.htm#SEC257 1331 close sing_218.htm#SEC258 1332 closed_points sing_1866.htm#SEC1942 47269 1333 closetex sing_1833.htm#SEC1909 42334 1334 closureFrac sing_1311.htm#SEC1387 9252 1335 coDim sing_2397.htm#SEC2473 60680 1336 coDimMap sing_2396.htm#SEC2472 2002 1337 coHom sing_802.htm#SEC854 51043 1338 codim sing_1664.htm#SEC1740 14253 1339 codimension sing_2080.htm#SEC2156 32207 1340 coding theory sing_917.htm#SEC969 1341 coef sing_219.htm#SEC259 1342 coefficient sing_2238.htm#IDX831 1343 coefficient sing_2239.htm#IDX834 1344 coefficient sing_2240.htm#IDX838 1337 1345 coefficient field sing_144.htm#SEC184 1338 1346 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 1339 coefficients, long sing_8 11.htm#SEC8631340 coeffmod sing_1 866.htm#SEC1942235311341 coeffs sing_2 19.htm#SEC2591342 coker sing_25 14.htm#SEC2590356391343 colength of derivations curveColengthDerivations sing_2 350.htm#IDX9581344 collectDiv sing_1 446.htm#SEC1522503481345 colrank sing_1 838.htm#SEC1914522901346 colred sing_1 071.htm#SEC114716931347 combinat.lib sing_2 342.htm#SEC24181348 combinat_lib sing_2 342.htm#SEC24181349 commRing sing_8 04.htm#SEC856308921350 comma sing_41 3.htm#SEC4531351 command,custom Commands for user defined types sing_18 6.htm#SEC2261352 command-line option, setting value of sing_35 8.htm#IDX2811353 command-line option, value of sing_35 8.htm#IDX2791354 command-line options, print all values of sing_35 8.htm#IDX2781347 coefficients, long sing_874.htm#SEC926 1348 coeffmod sing_1928.htm#SEC2004 23531 1349 coeffs sing_220.htm#SEC260 1350 coker sing_2579.htm#SEC2655 35639 1351 colength of derivations curveColengthDerivations sing_2412.htm#IDX964 1352 collectDiv sing_1508.htm#SEC1584 50348 1353 colrank sing_1900.htm#SEC1976 52290 1354 colred sing_1133.htm#SEC1209 1693 1355 combinat.lib sing_2404.htm#SEC2480 1356 combinat_lib sing_2404.htm#SEC2480 1357 commRing sing_867.htm#SEC919 30892 1358 comma sing_415.htm#SEC455 1359 command,custom Commands for user defined types sing_187.htm#SEC227 1360 command-line option, setting value of sing_359.htm#IDX281 1361 command-line option, value of sing_359.htm#IDX279 1362 command-line options, print all values of sing_359.htm#IDX278 1355 1363 command-line options, short help Command line options sing_19.htm#IDX38 1356 commands (plural) sing_45 4.htm#IDX3021364 commands (plural) sing_456.htm#IDX302 1357 1365 comment sing_36.htm#IDX108 1358 compareMatrix sing_25 22.htm#SEC2598499301359 compareModules sing_25 17.htm#SEC259336921360 compareTasks sing_10 35.htm#SEC1111451571361 compareVectors sing_2 542.htm#SEC2618128811362 completeReduction sing_1 680.htm#SEC1756571571366 compareMatrix sing_2587.htm#SEC2663 49930 1367 compareModules sing_2582.htm#SEC2658 3692 1368 compareTasks sing_1098.htm#SEC1174 45157 1369 compareVectors sing_2607.htm#SEC2683 12881 1370 completeReduction sing_1742.htm#SEC1818 57157 1363 1371 complex sing_28.htm#IDX75 1364 complexClassify sing_23 22.htm#SEC2398227961365 complexSingType sing_15 04.htm#SEC1580344831366 complexType sing_23 23.htm#SEC2399557721367 compregb.lib sing_ 899.htm#SEC9751368 compregb_lib sing_ 899.htm#SEC9751369 comprehensive Groebner system sing_ 899.htm#IDX4211370 compress sing_1 048.htm#SEC1124619981371 computeAfaceOrbits sing_24 32.htm#SEC2508286831372 computeConstant sing_1 146.htm#SEC1222550241373 computeGromovWitten sing_1 149.htm#SEC1225188341374 computeN sing_1 450.htm#SEC1526616281375 computeV sing_1 449.htm#SEC1525403161376 computemcm sing_14 08.htm#SEC1484369561377 concat sing_1 049.htm#SEC1125166531378 conductor sing_1 257.htm#IDX5711379 conductor sing_1 480.htm#IDX6501380 conductor sing_2 348.htm#IDX9521381 conductor, degree sing_1 564.htm#IDX7601382 cone sing_18 8.htm#SEC2281383 cone sing_2 189.htm#IDX8521384 cone sing_2 190.htm#IDX8541385 coneLink sing_20 21.htm#SEC2097136351386 coneViaInequalities sing_20 20.htm#SEC2096256611387 coneViaPoints sing_20 19.htm#SEC209533861388 conic, parametrization, rational point. sing_1 385.htm#IDX6201389 conicWithTangents sing_2 140.htm#SEC2216607521390 constructH sing_14 09.htm#SEC1485595771391 constructblwup sing_14 10.htm#SEC1486193261392 constructible set sing_9 33.htm#IDX4521393 constructible sets sing_9 34.htm#IDX4551394 constructlastblwup sing_14 11.htm#SEC148776391395 constructor sing_22 06.htm#IDX8851396 constructor sing_22 07.htm#IDX8881397 contact matrix sing_1 479.htm#IDX6461398 containedQ sing_1 759.htm#SEC1835467181399 containsAsFace sing_20 22.htm#SEC2098251591400 containsInCollection containsInCollection sing_2 055.htm#SEC2131143681401 containsInSupport sing_20 23.htm#SEC2099324931402 containsPositiveVector containsPositiveVector sing_20 24.htm#SEC2100270421403 containsRelatively sing_20 25.htm#SEC2101171261404 content sing_ 978.htm#SEC105490951405 contentSB, option sing_31 5.htm#IDX1721406 continue Behavior of continue sing_38 1.htm#SEC4211407 continue sing_41 5.htm#SEC4551408 contraHom sing_ 774.htm#SEC826542701409 contract sing_22 0.htm#SEC2601410 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_27 29.htm#IDX10601411 contributionBundle sing_27 29.htm#SEC2805328741412 contributors sing_35 8.htm#IDX2001413 control sing_18 30.htm#SEC1906444981414 control.lib sing_18 29.htm#SEC19051415 controlDim sing_18 31.htm#SEC190724171416 controlExample sing_1 843.htm#SEC191926781417 control_Matrix sing_15 32.htm#SEC1608sprintf1418 control_lib sing_18 29.htm#SEC19051419 convertLeftToRightFraction convertLeftToRightFraction sing_2 662.htm#SEC273843181420 convertRightToLeftFraction convertRightToLeftFraction sing_2 661.htm#SEC2737193891421 convertdata sing_14 06.htm#SEC1482546291422 convexHull sing_20 26.htm#SEC2102566901423 convexIntersection sing_20 27.htm#SEC2103635871424 convloc sing_56 0.htm#SEC612191221425 coordinate change sing_2 186.htm#IDX8491426 coordinate change sing_2 187.htm#IDX8501427 coordinate change sing_2 188.htm#IDX8511428 coordinates sing_ 1986.htm#IDX8021429 coords sing_ 1986.htm#SEC2062293621430 copyTask sing_10 34.htm#SEC1110653311372 complexClassify sing_2384.htm#SEC2460 22796 1373 complexSingType sing_1566.htm#SEC1642 34483 1374 complexType sing_2385.htm#SEC2461 55772 1375 compregb.lib sing_962.htm#SEC1038 1376 compregb_lib sing_962.htm#SEC1038 1377 comprehensive Groebner system sing_962.htm#IDX427 1378 compress sing_1111.htm#SEC1187 61998 1379 computeAfaceOrbits sing_2497.htm#SEC2573 28683 1380 computeConstant sing_1208.htm#SEC1284 55024 1381 computeGromovWitten sing_1211.htm#SEC1287 18834 1382 computeN sing_1512.htm#SEC1588 61628 1383 computeV sing_1511.htm#SEC1587 40316 1384 computemcm sing_1470.htm#SEC1546 36956 1385 concat sing_1112.htm#SEC1188 16653 1386 conductor sing_1319.htm#IDX577 1387 conductor sing_1542.htm#IDX656 1388 conductor sing_2410.htm#IDX958 1389 conductor, degree sing_1626.htm#IDX766 1390 cone sing_189.htm#SEC229 1391 cone sing_2251.htm#IDX858 1392 cone sing_2252.htm#IDX860 1393 coneLink sing_2083.htm#SEC2159 13635 1394 coneViaInequalities sing_2082.htm#SEC2158 25661 1395 coneViaPoints sing_2081.htm#SEC2157 3386 1396 conic, parametrization, rational point. sing_1447.htm#IDX626 1397 conicWithTangents sing_2202.htm#SEC2278 60752 1398 constructH sing_1471.htm#SEC1547 59577 1399 constructblwup sing_1472.htm#SEC1548 19326 1400 constructible set sing_996.htm#IDX458 1401 constructible sets sing_997.htm#IDX461 1402 constructlastblwup sing_1473.htm#SEC1549 7639 1403 constructor sing_2268.htm#IDX891 1404 constructor sing_2269.htm#IDX894 1405 contact matrix sing_1541.htm#IDX652 1406 containedQ sing_1821.htm#SEC1897 46718 1407 containsAsFace sing_2084.htm#SEC2160 25159 1408 containsInCollection containsInCollection sing_2117.htm#SEC2193 14368 1409 containsInSupport sing_2085.htm#SEC2161 32493 1410 containsPositiveVector containsPositiveVector sing_2086.htm#SEC2162 27042 1411 containsRelatively sing_2087.htm#SEC2163 17126 1412 content sing_1041.htm#SEC1117 9095 1413 contentSB, option sing_316.htm#IDX172 1414 continue Behavior of continue sing_383.htm#SEC423 1415 continue sing_417.htm#SEC457 1416 contraHom sing_803.htm#SEC855 54270 1417 contract sing_221.htm#SEC261 1418 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2794.htm#IDX1070 1419 contributionBundle sing_2794.htm#SEC2870 32874 1420 contributors sing_359.htm#IDX200 1421 control sing_1892.htm#SEC1968 44498 1422 control.lib sing_1891.htm#SEC1967 1423 controlDim sing_1893.htm#SEC1969 2417 1424 controlExample sing_1905.htm#SEC1981 2678 1425 control_Matrix sing_1594.htm#SEC1670 sprintf 1426 control_lib sing_1891.htm#SEC1967 1427 convertLeftToRightFraction convertLeftToRightFraction sing_2727.htm#SEC2803 4318 1428 convertRightToLeftFraction convertRightToLeftFraction sing_2726.htm#SEC2802 19389 1429 convertdata sing_1468.htm#SEC1544 54629 1430 convexHull sing_2088.htm#SEC2164 56690 1431 convexIntersection sing_2089.htm#SEC2165 63587 1432 convloc sing_562.htm#SEC614 19122 1433 coordinate change sing_2248.htm#IDX855 1434 coordinate change sing_2249.htm#IDX856 1435 coordinate change sing_2250.htm#IDX857 1436 coordinates sing_2048.htm#IDX808 1437 coords sing_2048.htm#SEC2124 29362 1438 copyTask sing_1097.htm#SEC1173 65331 1431 1439 copyright sing_1.htm#IDX1 1432 corank sing_1 491.htm#SEC1567337091433 cornerMonomials sing_1 287.htm#SEC1363339951434 countPoints sing_19 11.htm#SEC1987585661435 coverings sing_1 148.htm#IDX5301436 coverings sing_1 149.htm#IDX5341437 cpu sing_35 8.htm#IDX2021438 cpu sing_35 8.htm#IDX2751439 createBO sing_14 37.htm#SEC1513326691440 createGradedRingHomomorphism createGradedRingHomomorphism sing_2 561.htm#SEC2637621771441 createGroup sing_2 554.htm#SEC2630285001442 createQuotientGroup sing_2 555.htm#SEC2631263741443 createTask sing_10 32.htm#SEC1108484041444 createTorsionFreeGroup createTorsionFreeGroup sing_2 556.htm#SEC2632519441445 createlist sing_14 19.htm#SEC1495617811440 corank sing_1553.htm#SEC1629 33709 1441 cornerMonomials sing_1349.htm#SEC1425 33995 1442 countPoints sing_1973.htm#SEC2049 58566 1443 coverings sing_1210.htm#IDX536 1444 coverings sing_1211.htm#IDX540 1445 cpu sing_359.htm#IDX202 1446 cpu sing_359.htm#IDX275 1447 createBO sing_1499.htm#SEC1575 32669 1448 createGradedRingHomomorphism createGradedRingHomomorphism sing_2626.htm#SEC2702 62177 1449 createGroup sing_2619.htm#SEC2695 28500 1450 createQuotientGroup sing_2620.htm#SEC2696 26374 1451 createTask sing_1095.htm#SEC1171 48404 1452 createTorsionFreeGroup createTorsionFreeGroup sing_2621.htm#SEC2697 51944 1453 createlist sing_1481.htm#SEC1557 61781 1446 1454 cring sing_73.htm#SEC113 1447 1455 cring declarations sing_74.htm#SEC114 … … 1449 1457 cring operations sing_76.htm#SEC116 1450 1458 cring related functions cring related functions sing_77.htm#SEC117 1451 crossprod sing_221.htm#SEC261 1452 crypto.lib sing_1884.htm#SEC1960 1453 crypto_lib sing_1884.htm#SEC1960 1454 cup sing_1162.htm#SEC1238 57972 1455 cupproduct sing_1163.htm#SEC1239 43349 1456 curve singularities sing_1470.htm#IDX633 1457 curve singularities sing_1558.htm#IDX755 1458 curve singularity sing_2346.htm#IDX947 1459 curveColengthDerivations curveColengthDerivations sing_2350.htm#SEC2426 2078 1460 curveConductorMult sing_2348.htm#SEC2424 15897 1461 curveDeligneNumber sing_2349.htm#SEC2425 12294 1462 curveDeltaInv sing_2347.htm#SEC2423 16375 1463 curveInv.lib sing_2346.htm#SEC2422 1464 curveInv_lib sing_2346.htm#SEC2422 1465 curvepar.lib sing_1511.htm#SEC1587 1466 curvepar_lib sing_1511.htm#SEC1587 1467 custom assignment Assignments for user defined types sing_187.htm#SEC227 1468 custom command Commands for user defined types sing_186.htm#SEC226 1469 custom type Definition of a user defined type sing_183.htm#SEC223 1470 customstd.lib sing_2218.htm#SEC2294 1471 customstd_lib sing_2218.htm#SEC2294 1472 cycleLength sing_2077.htm#SEC2153 16898 1473 cyclePoints sing_2081.htm#SEC2157 54460 1474 cyclic sing_965.htm#SEC1041 21375 1475 cyclic code Codes and the decoding problem sing_886.htm#SEC945 1476 cyclotomic sing_1645.htm#SEC1721 33749 1477 datetime sing_222.htm#SEC262 50127 1478 dbprint sing_223.htm#SEC263 1479 deRham.lib sing_2351.htm#SEC2427 1480 deRhamCohom sing_577.htm#SEC629 58222 1481 deRhamCohomIdeal sing_578.htm#SEC630 42169 1482 deRhamCohomology sing_2352.htm#SEC2428 41947 1483 deRham_lib sing_2351.htm#SEC2427 1484 debugLib, option sing_315.htm#IDX176 1485 debug_log sing_1501.htm#SEC1577 62043 1459 crossprod sing_222.htm#SEC262 1460 crypto.lib sing_1946.htm#SEC2022 1461 crypto_lib sing_1946.htm#SEC2022 1462 crystallographicGroupC2MM crystallographicGroupC2MM sing_648.htm#SEC700 41262 1463 crystallographicGroupCM crystallographicGroupCM sing_647.htm#SEC699 24754 1464 crystallographicGroupP1 crystallographicGroupP1 sing_641.htm#SEC693 48853 1465 crystallographicGroupP2 crystallographicGroupP2 sing_645.htm#SEC697 35903 1466 crystallographicGroupP2GG crystallographicGroupP2GG sing_646.htm#SEC698 27952 1467 crystallographicGroupP2MM crystallographicGroupP2MM sing_644.htm#SEC696 13909 1468 crystallographicGroupP3 crystallographicGroupP3 sing_652.htm#SEC704 10088 1469 crystallographicGroupP31M crystallographicGroupP31M sing_653.htm#SEC705 31189 1470 crystallographicGroupP3M1 crystallographicGroupP3M1 sing_654.htm#SEC706 1687 1471 crystallographicGroupP4 crystallographicGroupP4 sing_649.htm#SEC701 39932 1472 crystallographicGroupP4GM crystallographicGroupP4GM sing_651.htm#SEC703 52244 1473 crystallographicGroupP4MM crystallographicGroupP4MM sing_650.htm#SEC702 3914 1474 crystallographicGroupP6 crystallographicGroupP6 sing_655.htm#SEC707 38438 1475 crystallographicGroupP6MM crystallographicGroupP6MM sing_656.htm#SEC708 30180 1476 crystallographicGroupPG crystallographicGroupPG sing_643.htm#SEC695 39728 1477 crystallographicGroupPM crystallographicGroupPM sing_642.htm#SEC694 10105 1478 cup sing_1224.htm#SEC1300 57972 1479 cupproduct sing_1225.htm#SEC1301 43349 1480 curve singularities sing_1532.htm#IDX639 1481 curve singularities sing_1620.htm#IDX761 1482 curve singularity sing_2408.htm#IDX953 1483 curveColengthDerivations curveColengthDerivations sing_2412.htm#SEC2488 2078 1484 curveConductorMult sing_2410.htm#SEC2486 15897 1485 curveDeligneNumber sing_2411.htm#SEC2487 12294 1486 curveDeltaInv sing_2409.htm#SEC2485 16375 1487 curveInv.lib sing_2408.htm#SEC2484 1488 curveInv_lib sing_2408.htm#SEC2484 1489 curvepar.lib sing_1573.htm#SEC1649 1490 curvepar_lib sing_1573.htm#SEC1649 1491 custom assignment Assignments for user defined types sing_188.htm#SEC228 1492 custom command Commands for user defined types sing_187.htm#SEC227 1493 custom type Definition of a user defined type sing_184.htm#SEC224 1494 customstd.lib sing_2280.htm#SEC2356 1495 customstd_lib sing_2280.htm#SEC2356 1496 cycleLength sing_2139.htm#SEC2215 16898 1497 cyclePoints sing_2143.htm#SEC2219 54460 1498 cyclic sing_1028.htm#SEC1104 21375 1499 cyclic code Codes and the decoding problem sing_949.htm#SEC1008 1500 cyclotomic sing_1707.htm#SEC1783 33749 1501 datetime sing_223.htm#SEC263 50127 1502 dbprint sing_224.htm#SEC264 1503 deRham.lib sing_2413.htm#SEC2489 1504 deRhamCohom sing_579.htm#SEC631 58222 1505 deRhamCohomIdeal sing_580.htm#SEC632 42169 1506 deRhamCohomology sing_2414.htm#SEC2490 41947 1507 deRham_lib sing_2413.htm#SEC2489 1508 debugLib, option sing_316.htm#IDX176 1509 debug_log sing_1563.htm#SEC1639 62043 1486 1510 debugger Source code debugger sing_66.htm#SEC103 1487 1511 debugging library code Source code debugger sing_66.htm#SEC103 1488 dec1var sing_12 17.htm#SEC1293360981489 decimal sing_1 885.htm#SEC1961560661490 decode sing_18 21.htm#SEC1897643301491 decodeCode sing_18 23.htm#SEC1899282621492 decodeRandom sing_18 22.htm#SEC1898401181493 decodeRandomFL sing_18 26.htm#SEC1902354231494 decodeSV sing_18 03.htm#SEC1879379751495 decodegb.lib sing_18 08.htm#SEC18841496 decodegb_lib sing_18 08.htm#SEC18841497 decoding, decoding problem Codes and the decoding problem sing_ 886.htm#SEC9461498 decoef sing_1 851.htm#SEC1927602841499 decomposition of modules sing_12 10.htm#IDX5591500 decomposition, numerical sing_1 357.htm#IDX5881501 decone sing_2 189.htm#IDX8531502 decone sing_2 190.htm#IDX8551512 dec1var sing_1279.htm#SEC1355 36098 1513 decimal sing_1947.htm#SEC2023 56066 1514 decode sing_1883.htm#SEC1959 64330 1515 decodeCode sing_1885.htm#SEC1961 28262 1516 decodeRandom sing_1884.htm#SEC1960 40118 1517 decodeRandomFL sing_1888.htm#SEC1964 35423 1518 decodeSV sing_1865.htm#SEC1941 37975 1519 decodegb.lib sing_1870.htm#SEC1946 1520 decodegb_lib sing_1870.htm#SEC1946 1521 decoding, decoding problem Codes and the decoding problem sing_949.htm#SEC1009 1522 decoef sing_1913.htm#SEC1989 60284 1523 decomposition of modules sing_1272.htm#IDX565 1524 decomposition, numerical sing_1419.htm#IDX594 1525 decone sing_2251.htm#IDX859 1526 decone sing_2252.htm#IDX861 1503 1527 def sing_88.htm#SEC128 1504 1528 def declarations sing_89.htm#SEC129 1505 defRes, option sing_31 5.htm#IDX1771529 defRes, option sing_316.htm#IDX177 1506 1530 default argument sing_44.htm#SEC81 1507 defineHomogeneous sing_2 594.htm#SEC2670550721508 defined sing_22 4.htm#SEC2641509 defl sing_1 368.htm#SEC1444118251510 deform sing_16 03.htm#SEC167952501511 deform.lib sing_15 22.htm#SEC15981512 deform_lib sing_15 22.htm#SEC15981513 defring sing_10 07.htm#SEC108318141514 defringp sing_10 09.htm#SEC1085429051515 defrings sing_10 08.htm#SEC108410341516 deg sing_22 5.htm#SEC2651517 degBound sing_39 5.htm#SEC4351518 degree Miscellaneous oddities sing_22 6.htm#SEC2661519 degree sing_4 18.htm#IDX2921520 degree lexicographical ordering sing_ 860.htm#IDX3951521 degree of a polynomial Miscellaneous oddities sing_4 18.htm#IDX2961522 degree reverse lexicographical ordering sing_ 860.htm#IDX3931523 degreeDivisor sing_2 362.htm#SEC2438317511524 degreeFormalDivisor sing_2 370.htm#SEC2446425031525 degreepart sing_17 11.htm#SEC1787530361531 defineHomogeneous sing_2659.htm#SEC2735 55072 1532 defined sing_225.htm#SEC265 1533 defl sing_1430.htm#SEC1506 11825 1534 deform sing_1665.htm#SEC1741 5250 1535 deform.lib sing_1584.htm#SEC1660 1536 deform_lib sing_1584.htm#SEC1660 1537 defring sing_1070.htm#SEC1146 1814 1538 defringp sing_1072.htm#SEC1148 42905 1539 defrings sing_1071.htm#SEC1147 1034 1540 deg sing_226.htm#SEC266 1541 degBound sing_397.htm#SEC437 1542 degree Miscellaneous oddities sing_227.htm#SEC267 1543 degree sing_420.htm#IDX292 1544 degree lexicographical ordering sing_923.htm#IDX401 1545 degree of a polynomial Miscellaneous oddities sing_420.htm#IDX296 1546 degree reverse lexicographical ordering sing_923.htm#IDX399 1547 degreeDivisor sing_2424.htm#SEC2500 31751 1548 degreeFormalDivisor sing_2432.htm#SEC2508 42503 1549 degreepart sing_1773.htm#SEC1849 53036 1526 1550 delete sing_126.htm#SEC166 1527 delete sing_22 7.htm#SEC2671528 delete sing_27 6.htm#SEC3161529 deleteGenerator sing_59 2.htm#SEC644249171530 deleteSublist sing_9 07.htm#SEC983204061531 deligne number curveColengthDerivations sing_2 346.htm#IDX9491532 deligne number sing_2 349.htm#IDX9541533 deligne number sing_2 350.htm#IDX9561534 delta sing_1 570.htm#SEC1646569521535 delta invariant sing_1 251.htm#IDX5691536 delta invariant sing_1 570.htm#IDX7651537 delta invariant sing_2 347.htm#IDX9501538 delta invariant. sing_1 243.htm#IDX5621539 delta invariant. sing_1 244.htm#IDX5651540 delta invariant. sing_1 245.htm#IDX5681541 deltaLoc sing_1 251.htm#SEC1327351921542 denom_list sing_35 8.htm#IDX2041543 denominator sing_22 8.htm#SEC2681544 depth sing_1 164.htm#SEC1240177771545 depthIdeal sing_12 27.htm#SEC1303547821546 derivate sing_1 677.htm#SEC1753154091547 derivation sing_22 03.htm#IDX8761548 desingularization sing_2 451.htm#IDX985 590411549 desingularization sing_2 452.htm#SEC25281550 det sing_2 29.htm#SEC2691551 det_B sing_1 090.htm#SEC1166601431552 detadj sing_1 586.htm#SEC166259141553 determinacy sing_2 678.htm#SEC2754448181554 determinecenter sing_1 391.htm#SEC1467444961555 detropicalise sing_2 158.htm#SEC2234380251556 develop sing_1 560.htm#SEC1636484571557 diag sing_1 050.htm#SEC1126567591558 diagInvariants sing_1 266.htm#SEC1342620961559 diag_test sing_1 086.htm#SEC1162314691560 diff sing_23 0.htm#SEC2701561 diffRat sing_8 03.htm#SEC855361341562 difpoly2tex sing_1 852.htm#SEC192864511563 dim sing_23 1.htm#SEC2711564 dim (plural) sing_45 7.htm#SEC4971565 dimGradedPart sing_1 459.htm#SEC1535112621566 dimH sing_1 458.htm#SEC1534385341567 dimMon sing_12 07.htm#SEC1283399711568 dimStack sing_27 27.htm#SEC2803477721569 dim_slocus sing_16 04.htm#SEC1680472181570 dimension sing_20 28.htm#SEC2104352621571 dimension, moduli space of stable maps, rational curves dimStack sing_27 27.htm#IDX10581572 dimensionOfLocalization dimensionOfLocalization sing_24 15.htm#SEC2491256321573 direct_boolean_poly sing_22 31.htm#SEC2307498931574 direct_from_boolean_poly direct_from_boolean_poly sing_22 37.htm#SEC2313369411575 disc sing_1 872.htm#SEC1948452791576 discr sing_16 26.htm#SEC170296421577 discrepancy sing_1 444.htm#SEC152055971578 discrim sing_ 942.htm#SEC1018440911579 discussion of parametric ideal sing_9 24.htm#IDX4251580 disjoint sing_9 25.htm#IDX4271581 disp_zdd sing_2 244.htm#SEC2320414391582 displayCohom sing_1 460.htm#SEC1536226331583 displayHNE sing_1 563.htm#SEC1639298451584 displayInvariants sing_1 565.htm#SEC1641136781585 displayMultsequence sing_1 567.htm#SEC1643166681586 displayPuiseuxExpansion displayPuiseuxExpansion sing_21 33.htm#SEC22095601587 displayTropicalLifting displayTropicalLifting sing_21 31.htm#SEC2207281441588 distributed computing sing_ 958.htm#IDX4921589 distributed computing sing_ 998.htm#IDX4941590 distributed computing sing_10 31.htm#IDX5041551 delete sing_228.htm#SEC268 1552 delete sing_277.htm#SEC317 1553 deleteGenerator sing_594.htm#SEC646 24917 1554 deleteSublist sing_970.htm#SEC1046 20406 1555 deligne number curveColengthDerivations sing_2408.htm#IDX955 1556 deligne number sing_2411.htm#IDX960 1557 deligne number sing_2412.htm#IDX962 1558 delta sing_1632.htm#SEC1708 56952 1559 delta invariant sing_1313.htm#IDX575 1560 delta invariant sing_1632.htm#IDX771 1561 delta invariant sing_2409.htm#IDX956 1562 delta invariant. sing_1305.htm#IDX568 1563 delta invariant. sing_1306.htm#IDX571 1564 delta invariant. sing_1307.htm#IDX574 1565 deltaLoc sing_1313.htm#SEC1389 35192 1566 denom_list sing_359.htm#IDX204 1567 denominator sing_229.htm#SEC269 1568 depth sing_1226.htm#SEC1302 17777 1569 depthIdeal sing_1289.htm#SEC1365 54782 1570 derivate sing_1739.htm#SEC1815 15409 1571 derivation sing_2265.htm#IDX882 1572 desingularization sing_2516.htm#IDX995 59041 1573 desingularization sing_2517.htm#SEC2593 1574 det sing_230.htm#SEC270 1575 det_B sing_1152.htm#SEC1228 60143 1576 detadj sing_1648.htm#SEC1724 5914 1577 determinacy sing_2743.htm#SEC2819 44818 1578 determinecenter sing_1453.htm#SEC1529 44496 1579 detropicalise sing_2220.htm#SEC2296 38025 1580 develop sing_1622.htm#SEC1698 48457 1581 diag sing_1113.htm#SEC1189 56759 1582 diagInvariants sing_1328.htm#SEC1404 62096 1583 diag_test sing_1148.htm#SEC1224 31469 1584 diff sing_231.htm#SEC271 1585 diffRat sing_866.htm#SEC918 36134 1586 difpoly2tex sing_1914.htm#SEC1990 6451 1587 dim sing_232.htm#SEC272 1588 dim (plural) sing_459.htm#SEC499 1589 dimGradedPart sing_1521.htm#SEC1597 11262 1590 dimH sing_1520.htm#SEC1596 38534 1591 dimMon sing_1269.htm#SEC1345 39971 1592 dimStack sing_2792.htm#SEC2868 47772 1593 dim_slocus sing_1666.htm#SEC1742 47218 1594 dimension sing_2090.htm#SEC2166 35262 1595 dimension, moduli space of stable maps, rational curves dimStack sing_2792.htm#IDX1068 1596 dimensionOfLocalization dimensionOfLocalization sing_2480.htm#SEC2556 25632 1597 direct_boolean_poly sing_2293.htm#SEC2369 49893 1598 direct_from_boolean_poly direct_from_boolean_poly sing_2299.htm#SEC2375 36941 1599 disc sing_1934.htm#SEC2010 45279 1600 discr sing_1688.htm#SEC1764 9642 1601 discrepancy sing_1506.htm#SEC1582 5597 1602 discrim sing_1005.htm#SEC1081 44091 1603 discussion of parametric ideal sing_987.htm#IDX431 1604 disjoint sing_988.htm#IDX433 1605 disp_zdd sing_2306.htm#SEC2382 41439 1606 displayCohom sing_1522.htm#SEC1598 22633 1607 displayHNE sing_1625.htm#SEC1701 29845 1608 displayInvariants sing_1627.htm#SEC1703 13678 1609 displayMultsequence sing_1629.htm#SEC1705 16668 1610 displayPuiseuxExpansion displayPuiseuxExpansion sing_2195.htm#SEC2271 560 1611 displayTropicalLifting displayTropicalLifting sing_2193.htm#SEC2269 28144 1612 distributed computing sing_1021.htm#IDX498 1613 distributed computing sing_1061.htm#IDX500 1614 distributed computing sing_1094.htm#IDX510 1591 1615 div Miscellaneous oddities sing_81.htm#SEC121 1592 1616 div sing_98.htm#SEC138 1593 1617 div sing_155.htm#SEC195 1594 div sing_418.htm#IDX289 1595 divideUnits sing_1848.htm#SEC1924 26711 1596 dividelist sing_1418.htm#SEC1494 34210 1597 division sing_232.htm#SEC272 1598 division sing_926.htm#IDX430 1599 division sing_927.htm#IDX432 1600 division (plural) sing_458.htm#SEC498 1601 divisor sing_1951.htm#SEC2027 47231 1602 divisorplus sing_2356.htm#SEC2432 34248 1603 divisors negativeformaldivisor sing_2355.htm#IDX959 1604 divisors sing_2356.htm#IDX960 1605 divisors sing_2357.htm#IDX961 1606 divisors sing_2358.htm#IDX962 1607 divisors sing_2359.htm#IDX963 1608 divisors sing_2360.htm#IDX964 1609 divisors sing_2361.htm#IDX965 1610 divisors sing_2362.htm#IDX966 1611 divisors sing_2363.htm#IDX967 1612 divisors sing_2364.htm#IDX968 1613 divisors sing_2365.htm#IDX969 1614 divisors sing_2366.htm#IDX970 1615 divisors sing_2367.htm#IDX971 1616 divisors sing_2368.htm#IDX972 1617 divisors sing_2369.htm#IDX973 1618 divisors sing_2370.htm#IDX974 1619 divisors, polyhedra sing_2371.htm#IDX975 1620 divisors, polyhedra sing_2372.htm#IDX976 1621 divisors, polyhedra sing_2373.htm#IDX977 1622 divisors.lib sing_2354.htm#SEC2430 1623 divisors_lib sing_2354.htm#SEC2430 1624 dmod.lib sing_540.htm#SEC592 1625 dmodAction sing_798.htm#SEC850 9763 1626 dmodActionRat sing_799.htm#SEC851 6277 1627 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_791.htm#SEC843 44337 1628 dmod_lib sing_540.htm#SEC592 1629 dmodapp.lib sing_563.htm#SEC615 1630 dmodapp_lib sing_563.htm#SEC615 1631 dmodloc.lib sing_780.htm#IDX377 1632 dmodloc_lib sing_780.htm#IDX378 1633 dmodoublext sing_775.htm#SEC827 60637 1634 dmodvar.lib sing_596.htm#SEC648 1635 dmodvar_lib sing_596.htm#SEC648 1636 double sing_1956.htm#SEC2032 34697 1637 doubleExt sing_766.htm#SEC818 56896 1638 downloading Download instructions sing_2762.htm#SEC2851 1639 dp, global ordering sing_860.htm#IDX394 1640 drawNewtonSubdivision drawNewtonSubdivision sing_2136.htm#SEC2212 50904 1641 drawTropicalCurve sing_2135.htm#SEC2211 10441 1642 ds, local ordering sing_861.htm#IDX404 1643 dsum sing_1051.htm#SEC1127 1303 1644 dualCone sing_2029.htm#SEC2105 61460 1645 dualConic sing_2160.htm#SEC2236 31080 1646 dualPart sing_2308.htm#SEC2384 13279 1647 dualPartition sing_2740.htm#SEC2816 24739 1648 dualPolytope sing_2068.htm#SEC2144 32081 1649 dualSheaf sing_2718.htm#SEC2794 633 1650 dual_code sing_1805.htm#SEC1881 57229 1651 dump sing_233.htm#SEC273 1652 dynamic geometry sing_935.htm#IDX459 1653 dynamic geometry sing_936.htm#IDX462 1654 ecart sing_1959.htm#SEC2035 32475 1655 echo sing_396.htm#SEC436 1656 eexgcdN sing_1886.htm#SEC1962 53237 1657 effective sing_2364.htm#SEC2440 53028 1658 egcdMain sing_1752.htm#SEC1828 25359 1659 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2087.htm#SEC2163 38271 1660 ehrhartRing sing_1262.htm#SEC1338 16966 1661 eigenvals sing_1098.htm#SEC1174 11228 1662 eigenvalue sing_328.htm#SEC368 1663 eigenvalue sing_1098.htm#IDX510 1664 eigenvalues sing_1345.htm#SEC1421 2182 1665 elemSymmId sing_966.htm#SEC1042 sprintf 1666 elim sing_1135.htm#SEC1211 62585 1667 elim.lib sing_1132.htm#SEC1208 1668 elim1 sing_1136.htm#SEC1212 15653 1669 elim2 sing_1137.htm#SEC1213 44749 1670 elimRing sing_1134.htm#SEC1210 12194 1671 elimWeight sing_723.htm#SEC775 54297 1672 elim_lib sing_1132.htm#SEC1208 1673 eliminate sing_234.htm#SEC274 1674 eliminate (plural) sing_459.htm#SEC499 1675 eliminateNC sing_718.htm#SEC770 3777 1676 elimination sing_717.htm#IDX362 1677 elimlinearpart sing_1712.htm#SEC1788 14251 1678 elimpart sing_1713.htm#SEC1789 10258 1679 elimpartanyr sing_1714.htm#SEC1790 39751 1680 elimrep sing_1399.htm#SEC1475 23641 1681 elliptic curve sing_1145.htm#IDX526 1682 elliptic curves sing_1142.htm#IDX520 1683 elliptic curves sing_1148.htm#IDX529 1684 elliptic curves sing_1149.htm#IDX533 1685 ellipticAdd sing_1907.htm#SEC1983 13279 1686 ellipticAllPoints sing_1912.htm#SEC1988 60770 1687 ellipticMult sing_1908.htm#SEC1984 1558 1688 ellipticNF sing_2084.htm#SEC2160 5045 1689 ellipticNFDB sing_2085.htm#SEC2161 27917 1690 ellipticRandomCurve sing_1909.htm#SEC1985 36980 1691 ellipticRandomPoint sing_1910.htm#SEC1986 6866 1692 ellipticcovers.lib sing_1142.htm#IDX514 1693 ellipticcovers_lib sing_1142.htm#IDX515 1694 else sing_386.htm#SEC426 1695 embedMat sing_749.htm#SEC801 17119 1696 emptyFan sing_2056.htm#SEC2132 7396 1697 encode sing_1813.htm#SEC1889 56687 1698 endomorphism filtration sing_1544.htm#IDX731 1699 endvfilt sing_1544.htm#SEC1620 26670 1700 engine sing_593.htm#SEC645 30876 1701 ensureLeftNcfrac sing_2611.htm#SEC2687 64571 1702 ensureRightNcfrac sing_2612.htm#SEC2688 14107 1703 envelop FamElemsAtEnvCompPoints sing_937.htm#SEC1013 27362 1704 envelop sing_937.htm#IDX465 1705 envelop sing_938.htm#IDX468 1706 envelop sing_940.htm#IDX473 1707 envelop sing_941.htm#IDX477 1708 envelope sing_460.htm#SEC500 1709 enveloping algebra sing_358.htm#IDX208 1710 enveloping algebra sing_498.htm#IDX306 1618 div sing_420.htm#IDX289 1619 divideUnits sing_1910.htm#SEC1986 26711 1620 dividelist sing_1480.htm#SEC1556 34210 1621 division sing_233.htm#SEC273 1622 division sing_989.htm#IDX436 1623 division sing_990.htm#IDX438 1624 division (plural) sing_460.htm#SEC500 1625 divisor sing_2013.htm#SEC2089 47231 1626 divisorplus sing_2418.htm#SEC2494 34248 1627 divisors negativeformaldivisor sing_2417.htm#IDX965 1628 divisors sing_2418.htm#IDX966 1629 divisors sing_2419.htm#IDX967 1630 divisors sing_2420.htm#IDX968 1631 divisors sing_2421.htm#IDX969 1632 divisors sing_2422.htm#IDX970 1633 divisors sing_2423.htm#IDX971 1634 divisors sing_2424.htm#IDX972 1635 divisors sing_2425.htm#IDX973 1636 divisors sing_2426.htm#IDX974 1637 divisors sing_2427.htm#IDX975 1638 divisors sing_2428.htm#IDX976 1639 divisors sing_2429.htm#IDX977 1640 divisors sing_2430.htm#IDX978 1641 divisors sing_2431.htm#IDX979 1642 divisors sing_2432.htm#IDX980 1643 divisors, polyhedra sing_2433.htm#IDX981 1644 divisors, polyhedra sing_2434.htm#IDX982 1645 divisors, polyhedra sing_2435.htm#IDX983 1646 divisors.lib sing_2416.htm#SEC2492 1647 divisors_lib sing_2416.htm#SEC2492 1648 dmod.lib sing_542.htm#SEC594 1649 dmodAction sing_861.htm#SEC913 9763 1650 dmodActionRat sing_862.htm#SEC914 6277 1651 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_854.htm#SEC906 44337 1652 dmod_lib sing_542.htm#SEC594 1653 dmodapp.lib sing_565.htm#SEC617 1654 dmodapp_lib sing_565.htm#SEC617 1655 dmodloc.lib sing_843.htm#IDX383 1656 dmodloc_lib sing_843.htm#IDX384 1657 dmodoublext sing_804.htm#SEC856 60637 1658 dmodvar.lib sing_598.htm#SEC650 1659 dmodvar_lib sing_598.htm#SEC650 1660 double sing_2018.htm#SEC2094 34697 1661 doubleExt sing_795.htm#SEC847 56896 1662 downloading Download instructions sing_2827.htm#SEC2917 1663 dp, global ordering sing_923.htm#IDX400 1664 drawNewtonSubdivision drawNewtonSubdivision sing_2198.htm#SEC2274 50904 1665 drawTropicalCurve sing_2197.htm#SEC2273 10441 1666 ds, local ordering sing_924.htm#IDX410 1667 dsum sing_1114.htm#SEC1190 1303 1668 dualCone sing_2091.htm#SEC2167 61460 1669 dualConic sing_2222.htm#SEC2298 31080 1670 dualPart sing_2370.htm#SEC2446 13279 1671 dualPartition sing_2805.htm#SEC2881 24739 1672 dualPolytope sing_2130.htm#SEC2206 32081 1673 dualSheaf sing_2783.htm#SEC2859 633 1674 dual_code sing_1867.htm#SEC1943 57229 1675 dump sing_234.htm#SEC274 1676 dyckGroup1 sing_657.htm#SEC709 62819 1677 dyckGroup2 sing_658.htm#SEC710 13793 1678 dyckGroup3 sing_659.htm#SEC711 42596 1679 dynamic geometry sing_998.htm#IDX465 1680 dynamic geometry sing_999.htm#IDX468 1681 ecart sing_2021.htm#SEC2097 32475 1682 echo sing_398.htm#SEC438 1683 eexgcdN sing_1948.htm#SEC2024 53237 1684 effective sing_2426.htm#SEC2502 53028 1685 egcdMain sing_1814.htm#SEC1890 25359 1686 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2149.htm#SEC2225 38271 1687 ehrhartRing sing_1324.htm#SEC1400 16966 1688 eigenvals sing_1160.htm#SEC1236 11228 1689 eigenvalue sing_329.htm#SEC369 1690 eigenvalue sing_1160.htm#IDX516 1691 eigenvalues sing_1407.htm#SEC1483 2182 1692 elemSymmId sing_1029.htm#SEC1105 sprintf 1693 elim sing_1197.htm#SEC1273 62585 1694 elim.lib sing_1194.htm#SEC1270 1695 elim1 sing_1198.htm#SEC1274 15653 1696 elim2 sing_1199.htm#SEC1275 44749 1697 elimRing sing_1196.htm#SEC1272 12194 1698 elimWeight sing_752.htm#SEC804 54297 1699 elim_lib sing_1194.htm#SEC1270 1700 eliminate sing_235.htm#SEC275 1701 eliminate (plural) sing_461.htm#SEC501 1702 eliminateNC sing_747.htm#SEC799 3777 1703 elimination sing_746.htm#IDX362 1704 elimlinearpart sing_1774.htm#SEC1850 14251 1705 elimpart sing_1775.htm#SEC1851 10258 1706 elimpartanyr sing_1776.htm#SEC1852 39751 1707 elimrep sing_1461.htm#SEC1537 23641 1708 elliptic curve sing_1207.htm#IDX532 1709 elliptic curves sing_1204.htm#IDX526 1710 elliptic curves sing_1210.htm#IDX535 1711 elliptic curves sing_1211.htm#IDX539 1712 ellipticAdd sing_1969.htm#SEC2045 13279 1713 ellipticAllPoints sing_1974.htm#SEC2050 60770 1714 ellipticMult sing_1970.htm#SEC2046 1558 1715 ellipticNF sing_2146.htm#SEC2222 5045 1716 ellipticNFDB sing_2147.htm#SEC2223 27917 1717 ellipticRandomCurve sing_1971.htm#SEC2047 36980 1718 ellipticRandomPoint sing_1972.htm#SEC2048 6866 1719 ellipticcovers.lib sing_1204.htm#IDX520 1720 ellipticcovers_lib sing_1204.htm#IDX521 1721 else sing_388.htm#SEC428 1722 embedMat sing_778.htm#SEC830 17119 1723 emptyFan sing_2118.htm#SEC2194 7396 1724 encode sing_1875.htm#SEC1951 56687 1725 endomorphism filtration sing_1606.htm#IDX737 1726 endvfilt sing_1606.htm#SEC1682 26670 1727 engine sing_595.htm#SEC647 30876 1728 ensureLeftNcfrac sing_2676.htm#SEC2752 64571 1729 ensureRightNcfrac sing_2677.htm#SEC2753 14107 1730 envelop FamElemsAtEnvCompPoints sing_1000.htm#SEC1076 27362 1731 envelop sing_1000.htm#IDX471 1732 envelop sing_1001.htm#IDX474 1733 envelop sing_1003.htm#IDX479 1734 envelop sing_1004.htm#IDX483 1735 envelope sing_462.htm#SEC502 1736 enveloping algebra sing_359.htm#IDX208 1737 enveloping algebra sing_500.htm#IDX306 1711 1738 environment variable, DISPLAY The online help system sing_16.htm#IDX29 1712 equalJinI sing_1 487.htm#SEC1563185021713 equalMultiDeg sing_2 587.htm#SEC2663370901714 equations sing_20 30.htm#SEC210678961715 equiRadical sing_13 03.htm#SEC137988841716 equidim sing_13 05.htm#SEC1381385411717 equidimMax sing_13 06.htm#SEC1382492891718 equidimMaxEHV sing_13 07.htm#SEC1383426501719 equidimZ sing_13 18.htm#SEC1394496101720 equising.lib sing_15 27.htm#SEC16031721 equising_lib sing_15 27.htm#SEC16031722 equisingular Tjurina number sing_1 470.htm#IDX6381723 equisingularity ideal sing_15 29.htm#IDX6581724 equisingularity stratum sing_15 30.htm#IDX6591739 equalJinI sing_1549.htm#SEC1625 18502 1740 equalMultiDeg sing_2652.htm#SEC2728 37090 1741 equations sing_2092.htm#SEC2168 7896 1742 equiRadical sing_1365.htm#SEC1441 8884 1743 equidim sing_1367.htm#SEC1443 38541 1744 equidimMax sing_1368.htm#SEC1444 49289 1745 equidimMaxEHV sing_1369.htm#SEC1445 42650 1746 equidimZ sing_1380.htm#SEC1456 49610 1747 equising.lib sing_1589.htm#SEC1665 1748 equising_lib sing_1589.htm#SEC1665 1749 equisingular Tjurina number sing_1532.htm#IDX644 1750 equisingularity ideal sing_1591.htm#IDX664 1751 equisingularity stratum sing_1592.htm#IDX665 1725 1752 error recovery sing_15.htm#SEC21 1726 errorInsert sing_18 16.htm#SEC1892594701727 errorRand sing_18 17.htm#SEC189357271728 errormap sing_2 394.htm#SEC247077821729 esIdeal sing_15 29.htm#SEC1605604771730 esStratum sing_15 30.htm#SEC1606500941731 essential sing_2 193.htm#IDX8581732 essential sing_2 194.htm#IDX8591733 eta sing_2 079.htm#SEC2155607291734 euler sing_1 865.htm#SEC1941105191735 eulerChProj sing_2 298.htm#SEC2374285491736 eval sing_23 5.htm#SEC2751737 evalJacobianAtBox sing_2 689.htm#SEC2765427161738 evalPolyAtBox sing_2 688.htm#SEC2764430401739 evaluateFormalDivisor evaluateFormalDivisor sing_2 366.htm#SEC244235351740 evaluatePDivisor sing_2 372.htm#SEC2448188551741 evaluateProduct sing_2 442.htm#SEC2518545151742 evaluate_reynolds sing_1 650.htm#SEC1726463531743 evalutateIntegral sing_1 147.htm#SEC1223sprintf1744 example sing_23 7.htm#SEC2771745 example sing_2 195.htm#IDX8601746 example sing_2 196.htm#IDX8621747 example sing_2 197.htm#IDX8641748 example sing_2 198.htm#IDX8661749 example sing_2 199.htm#IDX8681750 example sing_22 00.htm#IDX8701751 example sing_22 01.htm#IDX8731752 execute sing_23 8.htm#SEC2781753 exit sing_39 0.htm#SEC4301754 exp2pt sing_1 853.htm#SEC1929196211755 expo sing_1 877.htm#SEC195388331756 exponents sing_22 05.htm#IDX8811757 export sing_38 3.htm#SEC4231758 exportNuminvs sing_1 270.htm#SEC1346104231759 exportto sing_38 4.htm#SEC4241760 expp sing_2 738.htm#SEC2814157511753 errorInsert sing_1878.htm#SEC1954 59470 1754 errorRand sing_1879.htm#SEC1955 5727 1755 errormap sing_2456.htm#SEC2532 7782 1756 esIdeal sing_1591.htm#SEC1667 60477 1757 esStratum sing_1592.htm#SEC1668 50094 1758 essential sing_2255.htm#IDX864 1759 essential sing_2256.htm#IDX865 1760 eta sing_2141.htm#SEC2217 60729 1761 euler sing_1927.htm#SEC2003 10519 1762 eulerChProj sing_2360.htm#SEC2436 28549 1763 eval sing_236.htm#SEC276 1764 evalJacobianAtBox sing_2754.htm#SEC2830 42716 1765 evalPolyAtBox sing_2753.htm#SEC2829 43040 1766 evaluateFormalDivisor evaluateFormalDivisor sing_2428.htm#SEC2504 3535 1767 evaluatePDivisor sing_2434.htm#SEC2510 18855 1768 evaluateProduct sing_2507.htm#SEC2583 54515 1769 evaluate_reynolds sing_1712.htm#SEC1788 46353 1770 evalutateIntegral sing_1209.htm#SEC1285 sprintf 1771 example sing_238.htm#SEC278 1772 example sing_2257.htm#IDX866 1773 example sing_2258.htm#IDX868 1774 example sing_2259.htm#IDX870 1775 example sing_2260.htm#IDX872 1776 example sing_2261.htm#IDX874 1777 example sing_2262.htm#IDX876 1778 example sing_2263.htm#IDX879 1779 execute sing_239.htm#SEC279 1780 exit sing_392.htm#SEC432 1781 exp2pt sing_1915.htm#SEC1991 19621 1782 expo sing_1939.htm#SEC2015 8833 1783 exponents sing_2267.htm#IDX887 1784 export sing_385.htm#SEC425 1785 exportNuminvs sing_1332.htm#SEC1408 10423 1786 exportto sing_386.htm#SEC426 1787 expp sing_2803.htm#SEC2879 15751 1761 1788 expression list sing_72.htm#IDX128 1762 expression list sing_42 2.htm#IDX2991763 ext-module purityfiltration_lib sing_7 58.htm#IDX3681764 extcurve sing_1 799.htm#SEC187567301765 extdevelop sing_1 561.htm#SEC1637510441766 extendGC sing_9 32.htm#SEC1008409511767 extendWeyl sing_ 792.htm#SEC844499541768 extendedTensor sing_7 24.htm#SEC77649751769 extendpoly sing_9 31.htm#SEC1007292011770 extendring sing_10 10.htm#SEC1086647811771 extension of rings sing_13 23.htm#IDX5801772 exterior basis sing_1 077.htm#IDX5071773 exterior power sing_1 079.htm#IDX5091774 exteriorBasis sing_1 077.htm#SEC1153sprintf1775 exteriorPower sing_1 079.htm#SEC1155201731776 extgcd sing_2 39.htm#SEC2791777 fVector sing_2 059.htm#SEC213537151778 fVectorP sing_2 088.htm#SEC2164318431779 facFirstShift sing_7 11.htm#SEC76364691780 facFirstWeyl sing_7 07.htm#SEC759424121781 facGBIdeal sing_1 288.htm#SEC136499241782 facShift sing_7 10.htm#SEC762485511783 facSubWeyl sing_7 09.htm#SEC76196301784 facWeyl sing_7 06.htm#SEC758323311785 faceContaining sing_20 31.htm#SEC2107648041786 facetVertexLatticeDistances facetVertexLatticeDistances sing_2 089.htm#SEC2165607141787 facetWidth sing_2 090.htm#SEC2166628101788 facetWidths sing_2 091.htm#SEC216755031789 facets sing_20 32.htm#SEC210881121790 facstd sing_24 0.htm#SEC2801791 factmodd sing_24 1.htm#SEC2811792 factor sing_32 2.htm#SEC3621793 factorH sing_9 22.htm#SEC998248141794 factorLenstraECM sing_19 16.htm#SEC1992549511795 factorMain sing_1 753.htm#SEC1829651521796 factorgroup sing_2 577.htm#SEC2653599141797 factorial sing_9 08.htm#SEC984328711798 factorization sing_32 3.htm#SEC3631799 factorization sing_11 07.htm#IDX5111800 factorize sing_24 2.htm#SEC2821801 factorize sing_32 2.htm#SEC3621789 expression list sing_424.htm#IDX299 1790 ext-module purityfiltration_lib sing_787.htm#IDX368 1791 extcurve sing_1861.htm#SEC1937 6730 1792 extdevelop sing_1623.htm#SEC1699 51044 1793 extendGC sing_995.htm#SEC1071 40951 1794 extendWeyl sing_855.htm#SEC907 49954 1795 extendedTensor sing_753.htm#SEC805 4975 1796 extendpoly sing_994.htm#SEC1070 29201 1797 extendring sing_1073.htm#SEC1149 64781 1798 extension of rings sing_1385.htm#IDX586 1799 exterior basis sing_1139.htm#IDX513 1800 exterior power sing_1141.htm#IDX515 1801 exteriorBasis sing_1139.htm#SEC1215 sprintf 1802 exteriorPower sing_1141.htm#SEC1217 20173 1803 extgcd sing_240.htm#SEC280 1804 fVector sing_2121.htm#SEC2197 3715 1805 fVectorP sing_2150.htm#SEC2226 31843 1806 facFirstShift sing_740.htm#SEC792 6469 1807 facFirstWeyl sing_736.htm#SEC788 42412 1808 facGBIdeal sing_1350.htm#SEC1426 9924 1809 facShift sing_739.htm#SEC791 48551 1810 facSubWeyl sing_738.htm#SEC790 9630 1811 facWeyl sing_735.htm#SEC787 32331 1812 faceContaining sing_2093.htm#SEC2169 64804 1813 facetVertexLatticeDistances facetVertexLatticeDistances sing_2151.htm#SEC2227 60714 1814 facetWidth sing_2152.htm#SEC2228 62810 1815 facetWidths sing_2153.htm#SEC2229 5503 1816 facets sing_2094.htm#SEC2170 8112 1817 facstd sing_241.htm#SEC281 1818 factmodd sing_242.htm#SEC282 1819 factor sing_323.htm#SEC363 1820 factorH sing_985.htm#SEC1061 24814 1821 factorLenstraECM sing_1978.htm#SEC2054 54951 1822 factorMain sing_1815.htm#SEC1891 65152 1823 factorgroup sing_2642.htm#SEC2718 59914 1824 factorial sing_971.htm#SEC1047 32871 1825 factorization sing_324.htm#SEC364 1826 factorization sing_1169.htm#IDX517 1827 factorize sing_243.htm#SEC283 1828 factorize sing_323.htm#SEC363 1802 1829 factory sing_1.htm#IDX2 1803 fan sing_189.htm#SEC229 1804 fan sing_2071.htm#IDX807 1805 fanViaCones sing_2057.htm#SEC2133 16418 1806 farey sing_243.htm#SEC283 1807 fareypoly sing_2375.htm#SEC2451 12389 1808 fastExpt sing_1861.htm#SEC1937 43912 1809 fastHC, option sing_315.htm#IDX153 1810 fastelim sing_1715.htm#SEC1791 7409 1811 fetch sing_244.htm#SEC284 1812 fetch (plural) sing_461.htm#SEC501 1813 fetchall sing_1011.htm#SEC1087 7537 1814 ffmodStd sing_2379.htm#SEC2455 50680 1815 ffmodstd.lib sing_2374.htm#SEC2450 1816 ffmodstd_lib sing_2374.htm#SEC2450 1817 ffsolve sing_1704.htm#SEC1780 20432 1818 ffsolve.lib sing_1703.htm#SEC1779 1819 ffsolve_lib sing_1703.htm#SEC1779 1820 fglm sing_245.htm#SEC285 1821 fglm sing_355.htm#IDX187 1822 fglm_solve sing_1731.htm#SEC1807 51398 1823 fglmquot sing_246.htm#SEC286 1824 fibonacci sing_909.htm#SEC985 24750 1830 fan sing_190.htm#SEC230 1831 fan sing_2133.htm#IDX813 1832 fanViaCones sing_2119.htm#SEC2195 16418 1833 farey sing_244.htm#SEC284 1834 fareypoly sing_2437.htm#SEC2513 12389 1835 fastExpt sing_1923.htm#SEC1999 43912 1836 fastHC, option sing_316.htm#IDX153 1837 fastelim sing_1777.htm#SEC1853 7409 1838 fetch sing_245.htm#SEC285 1839 fetch (plural) sing_463.htm#SEC503 1840 fetchall sing_1074.htm#SEC1150 7537 1841 ffmodStd sing_2441.htm#SEC2517 50680 1842 ffmodstd.lib sing_2436.htm#SEC2512 1843 ffmodstd_lib sing_2436.htm#SEC2512 1844 ffsolve sing_1766.htm#SEC1842 20432 1845 ffsolve.lib sing_1765.htm#SEC1841 1846 ffsolve_lib sing_1765.htm#SEC1841 1847 fglm sing_246.htm#SEC286 1848 fglm sing_356.htm#IDX187 1849 fglm_solve sing_1793.htm#SEC1869 51398 1850 fglmquot sing_247.htm#SEC287 1851 fibonacci sing_972.htm#SEC1048 24750 1852 fibonacciGroup sing_660.htm#SEC712 25145 1825 1853 field sing_144.htm#SEC184 1826 1854 file, .singularrc sing_20.htm#IDX71 1827 filecmd sing_24 7.htm#SEC2871828 filtration purityfiltration_lib sing_7 58.htm#IDX3691829 finalCharts sing_14 23.htm#SEC1499372961830 find sing_24 8.htm#SEC2881831 findAuto sing_6 65.htm#SEC717512051832 findInvo sing_6 63.htm#SEC715181771833 findInvoDiag sing_6 64.htm#SEC71673651834 findOrientedBoundary findOrientedBoundary sing_2 080.htm#SEC2156241101835 findTorsion sing_1 842.htm#SEC1918295721836 find_first_primitive_root find_first_primitive_root sing_19 20.htm#SEC1996333271837 find_index sing_19 24.htm#SEC2000625641838 findifs.lib sing_1 849.htm#SEC19251839 findifs_example sing_1 850.htm#SEC1926338491840 findifs_lib sing_1 849.htm#SEC19251841 findimAlgebra sing_7 33.htm#SEC785646121842 finduni sing_2 49.htm#SEC2891843 findvars sing_17 16.htm#SEC1792545031855 filecmd sing_248.htm#SEC288 1856 filtration purityfiltration_lib sing_787.htm#IDX369 1857 finalCharts sing_1485.htm#SEC1561 37296 1858 find sing_249.htm#SEC289 1859 findAuto sing_694.htm#SEC746 51205 1860 findInvo sing_692.htm#SEC744 18177 1861 findInvoDiag sing_693.htm#SEC745 7365 1862 findOrientedBoundary findOrientedBoundary sing_2142.htm#SEC2218 24110 1863 findTorsion sing_1904.htm#SEC1980 29572 1864 find_first_primitive_root find_first_primitive_root sing_1982.htm#SEC2058 33327 1865 find_index sing_1986.htm#SEC2062 62564 1866 findifs.lib sing_1911.htm#SEC1987 1867 findifs_example sing_1912.htm#SEC1988 33849 1868 findifs_lib sing_1911.htm#SEC1987 1869 findimAlgebra sing_762.htm#SEC814 64612 1870 finduni sing_250.htm#SEC290 1871 findvars sing_1778.htm#SEC1854 54503 1844 1872 finite field sing_144.htm#SEC184 1845 finite field sing_1703.htm#IDX780 1846 finiteDiagInvariants finiteDiagInvariants sing_1265.htm#SEC1341 3508 1847 finitediff.lib sing_2380.htm#IDX978 1848 finitediff_lib sing_2380.htm#IDX979 1849 finitenessTest sing_1121.htm#SEC1197 40633 1850 finvar.lib sing_1638.htm#SEC1714 1851 finvar_lib sing_1638.htm#SEC1714 1852 first index is 1 sing_417.htm#SEC457 1853 firstoct sing_1764.htm#SEC1840 11498 1854 fitting sing_1167.htm#SEC1243 20661 1855 fixed points, moduli space of stable maps, graph fixedPoints sing_2728.htm#IDX1059 1856 fixedPoints sing_2728.htm#SEC2804 25366 1857 fl2poly sing_590.htm#SEC642 51682 1858 flatten sing_1052.htm#SEC1128 55617 1859 flatteningStrat sing_1168.htm#SEC1244 15622 1860 floating point sing_1020.htm#IDX497 1861 for sing_385.htm#SEC425 1862 formaldivisorplus sing_2367.htm#SEC2443 31959 1863 forward sing_2386.htm#SEC2462 15383 1864 fourier sing_585.htm#SEC637 5326 1865 fouriersystem sing_2397.htm#SEC2473 43681 1866 fpadim.lib sing_601.htm#SEC653 1867 fpadim_lib sing_601.htm#SEC653 1868 fpaprops.lib sing_635.htm#SEC687 1869 fpaprops_lib sing_635.htm#SEC687 1870 fprintf sing_251.htm#SEC291 13662 1871 fracStatus sing_2657.htm#SEC2733 14582 1872 frandwalk sing_2701.htm#SEC2777 25555 1873 free sing_2204.htm#IDX878 1874 free sing_2205.htm#IDX880 1875 free associative algebra, tensor algebra Free associative algebras sing_492.htm#SEC544 1876 freeGBasis sing_649.htm#SEC701 43055 1877 freeModule sing_2494.htm#SEC2570 34173 1878 freeModule2Module sing_2523.htm#SEC2599 15296 1879 freegb.lib sing_644.htm#SEC696 1880 freegb_lib sing_644.htm#SEC696 1881 freemodule sing_252.htm#SEC292 1882 freerank sing_968.htm#SEC1044 52218 1883 fres sing_253.htm#SEC293 1884 from_boolean_constant from_boolean_constant sing_2235.htm#SEC2311 44881 1885 from_boolean_ideal sing_2239.htm#SEC2315 62698 1886 from_boolean_poly sing_2236.htm#SEC2312 27864 1887 from_boolean_set sing_2240.htm#SEC2316 60615 1888 frwalk sing_254.htm#SEC294 1889 full representation sing_931.htm#IDX446 1890 full representation sing_932.htm#IDX451 1891 fullDimImages sing_2423.htm#SEC2499 20094 1892 fullFan sing_2058.htm#SEC2134 7534 1893 fullSerreRelations sing_659.htm#SEC711 27691 1894 fullSpace sing_2013.htm#SEC2089 19485 1895 furtherInvar sing_1682.htm#SEC1758 19209 1896 further_hn_proc sing_1578.htm#SEC1654 63500 1897 fwalk sing_1154.htm#SEC1230 15070 1873 finite field sing_1765.htm#IDX786 1874 finiteDiagInvariants finiteDiagInvariants sing_1327.htm#SEC1403 3508 1875 finitediff.lib sing_2442.htm#IDX984 1876 finitediff_lib sing_2442.htm#IDX985 1877 finitenessTest sing_1183.htm#SEC1259 40633 1878 finvar.lib sing_1700.htm#SEC1776 1879 finvar_lib sing_1700.htm#SEC1776 1880 first index is 1 sing_419.htm#SEC459 1881 firstoct sing_1826.htm#SEC1902 11498 1882 fitting sing_1229.htm#SEC1305 20661 1883 fixed points, moduli space of stable maps, graph fixedPoints sing_2793.htm#IDX1069 1884 fixedPoints sing_2793.htm#SEC2869 25366 1885 fl2poly sing_592.htm#SEC644 51682 1886 flatten sing_1115.htm#SEC1191 58972 1887 flatteningStrat sing_1230.htm#SEC1306 15622 1888 floating point sing_1083.htm#IDX503 1889 for sing_387.htm#SEC427 1890 formal linear representations sing_807.htm#IDX379 1891 formaldivisorplus sing_2429.htm#SEC2505 31959 1892 forward sing_2448.htm#SEC2524 15383 1893 fourier sing_587.htm#SEC639 5326 1894 fouriersystem sing_2459.htm#SEC2535 43681 1895 fpadim.lib sing_603.htm#SEC655 1896 fpadim_lib sing_603.htm#SEC655 1897 fpalgebras.lib sing_637.htm#SEC689 1898 fpalgebras_lib sing_637.htm#SEC689 1899 fpaprops.lib sing_663.htm#SEC715 1900 fpaprops_lib sing_663.htm#SEC715 1901 fprintf sing_252.htm#SEC292 13662 1902 fracStatus sing_2722.htm#SEC2798 14582 1903 framed sheaves sing_2466.htm#IDX992 1904 frandwalk sing_2766.htm#SEC2842 25555 1905 free sing_2266.htm#IDX884 1906 free sing_2267.htm#IDX886 1907 free associative algebra, tensor algebra Free associative algebras sing_494.htm#SEC546 1908 freeGBasis sing_677.htm#SEC729 43055 1909 freeModule sing_2559.htm#SEC2635 34173 1910 freeModule2Module sing_2588.htm#SEC2664 15296 1911 freegb.lib sing_672.htm#SEC724 1912 freegb_lib sing_672.htm#SEC724 1913 freemodule sing_253.htm#SEC293 1914 freerank sing_1031.htm#SEC1107 52218 1915 fres sing_254.htm#SEC294 1916 from_boolean_constant from_boolean_constant sing_2297.htm#SEC2373 44881 1917 from_boolean_ideal sing_2301.htm#SEC2377 62698 1918 from_boolean_poly sing_2298.htm#SEC2374 27864 1919 from_boolean_set sing_2302.htm#SEC2378 60615 1920 frwalk sing_255.htm#SEC295 1921 full representation sing_994.htm#IDX452 1922 full representation sing_995.htm#IDX457 1923 fullDimImages sing_2488.htm#SEC2564 20094 1924 fullFan sing_2120.htm#SEC2196 7534 1925 fullSerreRelations sing_687.htm#SEC739 27691 1926 fullSpace sing_2075.htm#SEC2151 19485 1927 furtherInvar sing_1744.htm#SEC1820 19209 1928 further_hn_proc sing_1640.htm#SEC1716 63500 1929 fwalk sing_1216.htm#SEC1292 15070 1898 1930 galois field sing_144.htm#SEC184 1899 gauss_col sing_1 062.htm#SEC1138362521900 gauss_nf sing_1 093.htm#SEC1169510601901 gauss_row sing_1 063.htm#SEC1139588771902 gaussred sing_1 091.htm#SEC1167290011903 gaussred_pivot sing_1 092.htm#SEC1168254771904 gcd sing_25 5.htm#SEC2951905 gcdMon sing_1 196.htm#SEC1272424481906 gcddivisor sing_ 1952.htm#SEC202812761907 gen sing_25 6.htm#SEC2961908 genMDSMat sing_18 19.htm#SEC189533471909 genSymId sing_1 342.htm#SEC1418175211910 general error-locator polynomial sing_ 887.htm#SEC9521911 general neron. sing_2 451.htm#IDX9861912 general weighted lexicographical ordering sing_ 861.htm#IDX4101913 general weighted reverse lexicographical ordering Local orderings sing_ 861.htm#IDX4071914 general.lib sing_9 02.htm#SEC9781915 generalOrder sing_ 1977.htm#SEC2053425361916 general_lib sing_9 02.htm#SEC9781917 generateG sing_19 15.htm#SEC1991516971918 generators sing_1 478.htm#IDX6421919 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_20 33.htm#SEC210944541920 generatorsOfSpan sing_20 34.htm#SEC2110402971921 generic representation sing_9 31.htm#IDX4451922 genericid sing_ 986.htm#SEC1062297311923 genericity sing_1 839.htm#SEC1915168221924 genericmat sing_1 053.htm#SEC1129350161925 genoutput sing_14 12.htm#SEC1488189731926 genus sing_1 247.htm#SEC1323sprintf1927 geometrical locus FamElemsAtEnvCompPoints sing_9 35.htm#IDX4571928 geometrical locus sing_9 36.htm#IDX4601929 geometrical locus sing_ 937.htm#IDX4631930 geometrical locus sing_ 938.htm#IDX4661931 geometrical locus sing_ 939.htm#IDX4691932 geometrical locus sing_ 940.htm#IDX4711933 geometrical locus sing_ 941.htm#IDX4751934 getArguments sing_1 043.htm#SEC1119142541935 getCommand sing_1 042.htm#SEC1118321811936 getCone sing_2 060.htm#SEC2136413941937 getGradingGroup sing_2 552.htm#SEC2628181371938 getLattice sing_2 553.htm#SEC262977751939 getLinearForms sing_20 35.htm#SEC2111475901940 getModuleGrading sing_2 563.htm#SEC2639434511941 getMultiplicity sing_20 36.htm#SEC21126391942 getOneVar sing_1 255.htm#SEC1331554021943 getResult sing_1 044.htm#SEC1120517221944 getSmallest sing_1 254.htm#SEC133016231945 getState sing_1 045.htm#SEC1121364531946 getVariableWeights sing_2 551.htm#SEC262795911947 getcores sing_10 01.htm#SEC1077307851948 getdump sing_25 7.htm#SEC2971949 getenv sing_35 8.htm#IDX2111950 gfan.lib sing_20 12.htm#SEC20881951 gfan_lib sing_20 12.htm#SEC20881931 gauss_col sing_1124.htm#SEC1200 36252 1932 gauss_nf sing_1155.htm#SEC1231 51060 1933 gauss_row sing_1125.htm#SEC1201 58877 1934 gaussred sing_1153.htm#SEC1229 29001 1935 gaussred_pivot sing_1154.htm#SEC1230 25477 1936 gcd sing_256.htm#SEC296 1937 gcdMon sing_1258.htm#SEC1334 42448 1938 gcddivisor sing_2014.htm#SEC2090 1276 1939 gen sing_257.htm#SEC297 1940 genMDSMat sing_1881.htm#SEC1957 3347 1941 genSymId sing_1404.htm#SEC1480 17521 1942 general error-locator polynomial sing_950.htm#SEC1015 1943 general neron. sing_2516.htm#IDX996 1944 general weighted lexicographical ordering sing_924.htm#IDX416 1945 general weighted reverse lexicographical ordering Local orderings sing_924.htm#IDX413 1946 general.lib sing_965.htm#SEC1041 1947 generalOrder sing_2039.htm#SEC2115 42536 1948 general_lib sing_965.htm#SEC1041 1949 generateG sing_1977.htm#SEC2053 51697 1950 generators sing_1540.htm#IDX648 1951 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2095.htm#SEC2171 4454 1952 generatorsOfSpan sing_2096.htm#SEC2172 40297 1953 generic representation sing_994.htm#IDX451 1954 genericid sing_1049.htm#SEC1125 29731 1955 genericity sing_1901.htm#SEC1977 16822 1956 genericmat sing_1116.htm#SEC1192 35016 1957 genoutput sing_1474.htm#SEC1550 18973 1958 genus sing_1309.htm#SEC1385 sprintf 1959 geometrical locus FamElemsAtEnvCompPoints sing_998.htm#IDX463 1960 geometrical locus sing_999.htm#IDX466 1961 geometrical locus sing_1000.htm#IDX469 1962 geometrical locus sing_1001.htm#IDX472 1963 geometrical locus sing_1002.htm#IDX475 1964 geometrical locus sing_1003.htm#IDX477 1965 geometrical locus sing_1004.htm#IDX481 1966 getArguments sing_1106.htm#SEC1182 14254 1967 getCommand sing_1105.htm#SEC1181 32181 1968 getCone sing_2122.htm#SEC2198 41394 1969 getGradingGroup sing_2617.htm#SEC2693 18137 1970 getLattice sing_2618.htm#SEC2694 7775 1971 getLinearForms sing_2097.htm#SEC2173 47590 1972 getModuleGrading sing_2628.htm#SEC2704 43451 1973 getMultiplicity sing_2098.htm#SEC2174 639 1974 getOneVar sing_1317.htm#SEC1393 55402 1975 getResult sing_1107.htm#SEC1183 51722 1976 getSmallest sing_1316.htm#SEC1392 1623 1977 getState sing_1108.htm#SEC1184 36453 1978 getVariableWeights sing_2616.htm#SEC2692 9591 1979 getcores sing_1064.htm#SEC1140 30785 1980 getdump sing_258.htm#SEC298 1981 getenv sing_359.htm#IDX211 1982 gfan.lib sing_2074.htm#SEC2150 1983 gfan_lib sing_2074.htm#SEC2150 1952 1984 gfanlib sing_1.htm#IDX9 1953 gitCone sing_2 450.htm#SEC2526238531954 gitfan.lib sing_24 20.htm#SEC24961955 gitfan_lib sing_24 20.htm#SEC24961956 gkdim.lib sing_6 70.htm#SEC7221957 gkdim_lib sing_6 70.htm#SEC7221958 global sing_2 09.htm#IDX1331959 global Bernstein-Sato polynomial sing_50 5.htm#IDX3131960 global Bernstein-Sato polynomial sing_54 0.htm#IDX3311961 global Bernstein-Sato polynomial for variety sing_59 6.htm#IDX3561962 globalSections sing_2 361.htm#SEC2437551911963 gmscoeffs sing_15 36.htm#SEC1612131821964 gmsnf sing_15 35.htm#SEC1611446761965 gmspoly.lib sing_1 555.htm#SEC16311966 gmspoly_lib sing_1 555.htm#SEC16311967 gmsring sing_15 34.htm#SEC1610594381968 gmssing.lib sing_15 33.htm#SEC16091969 gmssing_lib sing_15 33.htm#SEC16091970 goettsche.lib sing_24 04.htm#SEC24801971 goettsche_lib sing_24 04.htm#SEC24801972 good basis sing_15 33.htm#IDX6701973 good basis sing_1 543.htm#IDX7251974 good basis sing_1 555.htm#IDX7411975 good basis sing_1 557.htm#IDX7521976 goodBasis sing_1 557.htm#SEC1633416061977 gorensteinIndex sing_2 092.htm#SEC2168529191978 gorensteinVector sing_2 093.htm#SEC2169504071979 graal.lib sing_24 13.htm#SEC24891980 graalMixed sing_24 14.htm#SEC249064011981 graal_lib sing_24 13.htm#SEC24891982 gradeNumber sing_7 62.htm#SEC814299561983 graded Weyl algebra sing_50 5.htm#IDX3161984 graded algebra sing_2 246.htm#IDX9331985 graded module, graded piece sing_1 459.htm#IDX6281986 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2 453.htm#IDX9871987 graded modules, handling of Handling graded modules sing_8 26.htm#SEC8781988 graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2 491.htm#IDX9891989 gradedModules.lib sing_2 453.htm#SEC25291990 gradedModules_lib sing_2 453.htm#SEC25291991 gradiator sing_2 596.htm#SEC2672538021992 graph sing_1 143.htm#IDX5241993 graph sing_1 144.htm#IDX5251994 graph sing_27 23.htm#IDX10541995 graph sing_27 24.htm#IDX10551996 graphics.lib sing_1 766.htm#SEC18421997 graphics_lib sing_1 766.htm#SEC18421985 gitCone sing_2515.htm#SEC2591 23853 1986 gitfan.lib sing_2485.htm#SEC2561 1987 gitfan_lib sing_2485.htm#SEC2561 1988 gkdim.lib sing_699.htm#SEC751 1989 gkdim_lib sing_699.htm#SEC751 1990 global sing_210.htm#IDX133 1991 global Bernstein-Sato polynomial sing_507.htm#IDX313 1992 global Bernstein-Sato polynomial sing_542.htm#IDX331 1993 global Bernstein-Sato polynomial for variety sing_598.htm#IDX356 1994 globalSections sing_2423.htm#SEC2499 55191 1995 gmscoeffs sing_1598.htm#SEC1674 13182 1996 gmsnf sing_1597.htm#SEC1673 44676 1997 gmspoly.lib sing_1617.htm#SEC1693 1998 gmspoly_lib sing_1617.htm#SEC1693 1999 gmsring sing_1596.htm#SEC1672 59438 2000 gmssing.lib sing_1595.htm#SEC1671 2001 gmssing_lib sing_1595.htm#SEC1671 2002 goettsche.lib sing_2466.htm#SEC2542 2003 goettsche_lib sing_2466.htm#SEC2542 2004 good basis sing_1595.htm#IDX676 2005 good basis sing_1605.htm#IDX731 2006 good basis sing_1617.htm#IDX747 2007 good basis sing_1619.htm#IDX758 2008 goodBasis sing_1619.htm#SEC1695 41606 2009 gorensteinIndex sing_2154.htm#SEC2230 52919 2010 gorensteinVector sing_2155.htm#SEC2231 50407 2011 graal.lib sing_2478.htm#SEC2554 2012 graalMixed sing_2479.htm#SEC2555 6401 2013 graal_lib sing_2478.htm#SEC2554 2014 gradeNumber sing_791.htm#SEC843 29956 2015 graded Weyl algebra sing_507.htm#IDX316 2016 graded algebra sing_2308.htm#IDX939 2017 graded module, graded piece sing_1521.htm#IDX634 2018 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2518.htm#IDX997 2019 graded modules, handling of Handling graded modules sing_889.htm#SEC941 2020 graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2556.htm#IDX999 2021 gradedModules.lib sing_2518.htm#SEC2594 2022 gradedModules_lib sing_2518.htm#SEC2594 2023 gradiator sing_2661.htm#SEC2737 53802 2024 graph sing_1205.htm#IDX530 2025 graph sing_1206.htm#IDX531 2026 graph sing_2788.htm#IDX1064 2027 graph sing_2789.htm#IDX1065 2028 graphics.lib sing_1828.htm#SEC1904 2029 graphics_lib sing_1828.htm#SEC1904 1998 2030 graphviz sing_1.htm#IDX13 1999 graver4ti2 sing_1 340.htm#SEC1416396352000 grconcat sing_2 476.htm#SEC2552167542001 grdeg sing_2 456.htm#SEC2532228792002 grgens sing_2 465.htm#SEC2541128232003 grgroebner sing_2 475.htm#SEC2551292882004 grlift sing_2 473.htm#SEC2549216562005 grlifting sing_2 480.htm#SEC2556511772006 grlifting2 sing_2 481.htm#SEC2557590112007 grlifting3 sing_2 483.htm#SEC255963692008 grneg sing_2 486.htm#SEC2562645842009 grobcov sing_9 24.htm#SEC1000 448262010 grobcov.lib sing_9 23.htm#SEC9992011 grobcov_lib sing_9 23.htm#SEC9992012 grobj sing_2 454.htm#SEC2530181152013 groebner sing_25 8.htm#SEC298530382014 groebner sing_8 18.htm#SEC8702015 groebner basis computations sing_25 8.htm#IDX1472016 groebnerComplex sing_2 171.htm#SEC224724212017 groebnerCone sing_2 165.htm#SEC2241587762018 groebnerFan sing_2 170.htm#SEC2246481572019 gromovWitten sing_1 148.htm#SEC1224285592020 grorder sing_2 467.htm#SEC2543208572031 graver4ti2 sing_1402.htm#SEC1478 39635 2032 grconcat sing_2541.htm#SEC2617 16754 2033 grdeg sing_2521.htm#SEC2597 22879 2034 grgens sing_2530.htm#SEC2606 12823 2035 grgroebner sing_2540.htm#SEC2616 29288 2036 grlift sing_2538.htm#SEC2614 21656 2037 grlifting sing_2545.htm#SEC2621 51177 2038 grlifting2 sing_2546.htm#SEC2622 59011 2039 grlifting3 sing_2548.htm#SEC2624 6369 2040 grneg sing_2551.htm#SEC2627 64584 2041 grobcov sing_987.htm#SEC1063 40493 2042 grobcov.lib sing_986.htm#SEC1062 2043 grobcov_lib sing_986.htm#SEC1062 2044 grobj sing_2519.htm#SEC2595 18115 2045 groebner sing_259.htm#SEC299 53038 2046 groebner sing_881.htm#SEC933 2047 groebner basis computations sing_259.htm#IDX147 2048 groebnerComplex sing_2233.htm#SEC2309 2421 2049 groebnerCone sing_2227.htm#SEC2303 58776 2050 groebnerFan sing_2232.htm#SEC2308 48157 2051 gromovWitten sing_1210.htm#SEC1286 28559 2052 grorder sing_2532.htm#SEC2608 20857 2021 2053 ground field sing_144.htm#SEC184 2022 groupActionOnHashes sing_2 438.htm#SEC25144062023 groupActionOnQImage sing_2 437.htm#SEC2513532702024 group_reynolds sing_1 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1938.htm#SEC2014629682049 hardware platform sing_35 8.htm#IDX2712050 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_10 24.htm#SEC1100546092051 hasCommutativeVars sing_10 21.htm#SEC109731522052 hasGlobalOrdering sing_10 22.htm#SEC1098340532053 hasLeftDenom sing_26 05.htm#SEC2681472602054 hasMixedOrdering sing_10 23.htm#SEC1099297382055 hasNumericCoeffs sing_10 20.htm#SEC1096145222056 hasRightDenom sing_26 06.htm#SEC2682342792057 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_10 25.htm#SEC1101562112058 hashToCone sing_2 448.htm#SEC252469292059 hashesToFan sing_2 449.htm#SEC2525267742060 headStand sing_1 075.htm#SEC1151144132061 heightZ sing_13 17.htm#SEC1393168002062 help sing_2 59.htm#SEC2992054 groupActionOnHashes sing_2503.htm#SEC2579 406 2055 groupActionOnQImage sing_2502.htm#SEC2578 53270 2056 group_reynolds sing_1708.htm#SEC1784 35079 2057 grpower sing_2528.htm#SEC2604 3960 2058 grpres sing_2531.htm#SEC2607 18145 2059 grprod sing_2539.htm#SEC2615 41525 2060 grrange sing_2550.htm#SEC2626 41835 2061 grres sing_2537.htm#SEC2613 35795 2062 grrndmap sing_2543.htm#SEC2619 4054 2063 grrndmap2 sing_2544.htm#SEC2620 50536 2064 grrndmat sing_2542.htm#SEC2618 42634 2065 grshift sing_2523.htm#SEC2599 1415 2066 grsum sing_2527.htm#SEC2603 60602 2067 grsyz sing_2536.htm#SEC2612 61843 2068 grtest sing_2520.htm#SEC2596 62577 2069 grtranspose sing_2529.htm#SEC2605 13865 2070 grtranspose1 sing_2533.htm#SEC2609 3637 2071 grtwist sing_2525.htm#SEC2601 10498 2072 grtwists sing_2526.htm#SEC2602 56638 2073 grview sing_2522.htm#SEC2598 6878 2074 grwalk.lib sing_1215.htm#SEC1291 2075 grwalk_lib sing_1215.htm#SEC1291 2076 grzero sing_2524.htm#SEC2600 4212 2077 gwalk sing_1221.htm#SEC1297 38238 2078 hStarVector sing_2156.htm#SEC2232 60821 2079 hVector sing_2157.htm#SEC2233 46486 2080 h_increasing_knapsack h_increasing_knapsack sing_2000.htm#SEC2076 62968 2081 hardware platform sing_359.htm#IDX271 2082 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1087.htm#SEC1163 54609 2083 hasCommutativeVars sing_1084.htm#SEC1160 3152 2084 hasGlobalOrdering sing_1085.htm#SEC1161 34053 2085 hasLeftDenom sing_2670.htm#SEC2746 47260 2086 hasMixedOrdering sing_1086.htm#SEC1162 29738 2087 hasNumericCoeffs sing_1083.htm#SEC1159 14522 2088 hasRightDenom sing_2671.htm#SEC2747 34279 2089 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1088.htm#SEC1164 56211 2090 hashToCone sing_2513.htm#SEC2589 6929 2091 hashesToFan sing_2514.htm#SEC2590 26774 2092 headStand sing_1137.htm#SEC1213 14413 2093 heightZ sing_1379.htm#SEC1455 16800 2094 help sing_260.htm#SEC300 2063 2095 help browsers The online help system sing_16.htm#IDX22 2064 2096 help browsers, dummy The online help system sing_16.htm#IDX25 … … 2067 2099 help browsers, html The online help system sing_16.htm#IDX23 2068 2100 help browsers, setting command to use The online help system sing_16.htm#IDX30 2069 help browsers, setting the sing_35 8.htm#IDX1942101 help browsers, setting the sing_359.htm#IDX194 2070 2102 help, accessing over the net Command line options sing_19.htm#IDX42 2071 2103 help, online help system The online help system sing_16.htm#SEC22 2072 hermiteNormalForm sing_2 597.htm#SEC2673372252073 hess.lib sing_2 488.htm#SEC25642074 hess_lib sing_2 488.htm#SEC25642075 hessenberg sing_35 8.htm#IDX217 241682076 hessenberg sing_1 097.htm#SEC11732077 highcorner sing_26 0.htm#SEC3002078 hilb sing_26 1.htm#SEC3012079 hilbPoly sing_ 984.htm#SEC1060361182080 hilbert4ti2 sing_1 339.htm#SEC1415139932081 hilbertBasis sing_2 096.htm#SEC2172354232082 hilbertSeries sing_2 599.htm#SEC2675601482083 hilbvec sing_17 17.htm#SEC179392042084 hnexpansion sing_1 559.htm#SEC1635469902085 hnoether.lib sing_1 558.htm#SEC16342086 hnoether_lib sing_1 558.htm#SEC16342087 holonomic rank sing_ 780.htm#IDX3802088 holonomicRank sing_ 784.htm#SEC836413062089 hom sing_2 535.htm#SEC2611400322090 hom_kernel sing_1 175.htm#SEC1251326042091 homog sing_26 2.htm#SEC3022092 homog_part sing_2 735.htm#SEC2811208752093 homog_parts sing_2 736.htm#SEC2812128542094 homogeneitySpace sing_2 167.htm#SEC2243482432095 homogfacFirstQWeyl sing_7 13.htm#SEC765327512096 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_7 15.htm#SEC76790142097 homogfacNthQWeyl sing_7 12.htm#SEC764192382098 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_7 14.htm#SEC766561792099 homolog.lib sing_1 160.htm#SEC12362100 homolog_lib sing_1 160.htm#SEC12362101 homology sing_1 170.htm#SEC1246150402102 homomorphism sing_25 19.htm#SEC2595271152103 howto, download Download instructions sing_2 762.htm#SEC28512104 howto, install on Macintosh Macintosh installation instructions sing_2 765.htm#SEC28542105 howto, install on Unix Unix installation instructions sing_2 763.htm#SEC28522106 howto, install on Windows Windows installation instructions sing_2 764.htm#SEC28532107 hres sing_26 3.htm#SEC3032104 hermiteNormalForm sing_2662.htm#SEC2738 37225 2105 hess.lib sing_2553.htm#SEC2629 2106 hess_lib sing_2553.htm#SEC2629 2107 hessenberg sing_359.htm#IDX217 24168 2108 hessenberg sing_1159.htm#SEC1235 2109 highcorner sing_261.htm#SEC301 2110 hilb sing_262.htm#SEC302 2111 hilbPoly sing_1047.htm#SEC1123 36118 2112 hilbert4ti2 sing_1401.htm#SEC1477 13993 2113 hilbertBasis sing_2158.htm#SEC2234 35423 2114 hilbertSeries sing_2664.htm#SEC2740 60148 2115 hilbvec sing_1779.htm#SEC1855 9204 2116 hnexpansion sing_1621.htm#SEC1697 46990 2117 hnoether.lib sing_1620.htm#SEC1696 2118 hnoether_lib sing_1620.htm#SEC1696 2119 holonomic rank sing_843.htm#IDX386 2120 holonomicRank sing_847.htm#SEC899 41306 2121 hom sing_2600.htm#SEC2676 40032 2122 hom_kernel sing_1237.htm#SEC1313 32604 2123 homog sing_263.htm#SEC303 2124 homog_part sing_2800.htm#SEC2876 20875 2125 homog_parts sing_2801.htm#SEC2877 12854 2126 homogeneitySpace sing_2229.htm#SEC2305 48243 2127 homogfacFirstQWeyl sing_742.htm#SEC794 32751 2128 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_744.htm#SEC796 9014 2129 homogfacNthQWeyl sing_741.htm#SEC793 19238 2130 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_743.htm#SEC795 56179 2131 homolog.lib sing_1222.htm#SEC1298 2132 homolog_lib sing_1222.htm#SEC1298 2133 homology sing_1232.htm#SEC1308 15040 2134 homomorphism sing_2584.htm#SEC2660 27115 2135 howto, download Download instructions sing_2827.htm#SEC2917 2136 howto, install on Macintosh Macintosh installation instructions sing_2830.htm#SEC2920 2137 howto, install on Unix Unix installation instructions sing_2828.htm#SEC2918 2138 howto, install on Windows Windows installation instructions sing_2829.htm#SEC2919 2139 hres sing_264.htm#SEC304 2108 2140 html, default help The online help system sing_16.htm#IDX24 2109 hyperel.lib sing_ 1945.htm#SEC20212110 hyperel_lib sing_ 1945.htm#SEC20212111 hyperplane sing_2 174.htm#IDX8182112 hyperplane arrangement sing_54 0.htm#IDX3372113 hypersurface singularity sing_1 585.htm#IDX7702114 iMult sing_1 250.htm#SEC1326220592115 id sing_2 492.htm#SEC2568475922116 id2mod sing_ 980.htm#SEC1056329182141 hyperel.lib sing_2007.htm#SEC2083 2142 hyperel_lib sing_2007.htm#SEC2083 2143 hyperplane sing_2236.htm#IDX824 2144 hyperplane arrangement sing_542.htm#IDX337 2145 hypersurface singularity sing_1647.htm#IDX776 2146 iMult sing_1312.htm#SEC1388 22059 2147 id sing_2557.htm#SEC2633 47592 2148 id2mod sing_1043.htm#SEC1119 32918 2117 2149 ideal sing_90.htm#SEC130 2118 2150 ideal declarations sing_91.htm#SEC131 2119 ideal declarations (plural) ideal declarations (plural) sing_42 4.htm#SEC4642151 ideal declarations (plural) ideal declarations (plural) sing_426.htm#SEC466 2120 2152 ideal expressions sing_92.htm#SEC132 2121 ideal expressions (plural) ideal expressions (plural) sing_42 5.htm#SEC4652153 ideal expressions (plural) ideal expressions (plural) sing_427.htm#SEC467 2122 2154 ideal operations sing_93.htm#SEC133 2123 ideal operations (plural) ideal operations (plural) sing_42 6.htm#SEC4662155 ideal operations (plural) ideal operations (plural) sing_428.htm#SEC468 2124 2156 ideal related functions ideal related functions sing_94.htm#SEC134 2125 ideal related functions (plural) ideal related functions (plural) sing_42 7.htm#SEC4672126 ideal, toric sing_ 874.htm#SEC9312127 idealSplit sing_17 24.htm#SEC180046732128 ideals Miscellaneous oddities sing_4 18.htm#IDX2932129 idealsimplify sing_1 486.htm#SEC1562385692130 identifier Identifier resolution sing_4 19.htm#SEC4592131 identifyvar sing_1 394.htm#SEC1470596622132 if sing_38 6.htm#SEC4262133 image sing_25 15.htm#SEC2591434812134 imageLattice sing_2 565.htm#SEC2641157402135 image_of_variety sing_1 674.htm#SEC1750437112136 imap sing_26 4.htm#SEC3042137 imap (plural) sing_46 2.htm#SEC5022138 imapall sing_10 12.htm#SEC1088160232139 impart sing_26 5.htm#SEC3052140 importfrom sing_38 7.htm#SEC4272141 inCenter sing_5 29.htm#SEC581221522142 inCentralizer sing_53 0.htm#SEC582490002143 inForm sing_57 2.htm#SEC62452832144 inSubring sing_11 13.htm#SEC1189248172145 indSet sing_12 22.htm#SEC1298328282146 indepSet sing_26 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sing_36.htm#IDX82 2148 2180 indexed names sing_37.htm#SEC65 2149 2181 indices, multi sing_37.htm#SEC65 2150 inequalities sing_20 37.htm#SEC2113101222151 infRedTail, option sing_31 5.htm#IDX1542182 inequalities sing_2099.htm#SEC2175 10122 2183 infRedTail, option sing_316.htm#IDX154 2152 2184 info The online help system sing_16.htm#SEC23 2153 iniD sing_14 14.htm#SEC1490350842154 init_debug sing_1 493.htm#SEC1569298632155 initial sing_2 168.htm#SEC224486782156 initial form sing_50 5.htm#IDX3182157 initial ideal sing_50 5.htm#IDX3172158 initial ideal approach sing_50 5.htm#IDX3212159 initial ideal approach sing_59 6.htm#IDX3602160 initialForm sing_2 145.htm#SEC2221577932161 initialIdeal sing_2 146.htm#SEC2222222052162 initialIdealW sing_57 1.htm#SEC623360862163 initialMalgrange sing_57 0.htm#SEC622268462164 injective_knapsack sing_ 1939.htm#SEC201576192165 inout.lib sing_ 946.htm#SEC10222166 inout_lib sing_ 946.htm#SEC10222185 iniD sing_1476.htm#SEC1552 35084 2186 init_debug sing_1555.htm#SEC1631 29863 2187 initial sing_2230.htm#SEC2306 8678 2188 initial form sing_507.htm#IDX318 2189 initial ideal sing_507.htm#IDX317 2190 initial ideal approach sing_507.htm#IDX321 2191 initial ideal approach sing_598.htm#IDX360 2192 initialForm sing_2207.htm#SEC2283 57793 2193 initialIdeal sing_2208.htm#SEC2284 22205 2194 initialIdealW sing_573.htm#SEC625 36086 2195 initialMalgrange sing_572.htm#SEC624 26846 2196 injective_knapsack sing_2001.htm#SEC2077 7619 2197 inout.lib sing_1009.htm#SEC1085 2198 inout_lib sing_1009.htm#SEC1085 2167 2199 input sing_41.htm#SEC71 2168 2200 insert sing_126.htm#SEC166 2169 insert sing_26 7.htm#SEC3072170 insertCone sing_2 061.htm#SEC2137138582171 insertGenerator sing_59 1.htm#SEC643139512172 instructions, Macintosh installation Macintosh installation instructions sing_2 765.htm#SEC28542173 instructions, Unix installation Unix installation instructions sing_2 763.htm#SEC28522174 instructions, Windows installation Windows installation instructions sing_2 764.htm#SEC28532175 instructions, downloading Download instructions sing_2 762.htm#SEC28512201 insert sing_268.htm#SEC308 2202 insertCone sing_2123.htm#SEC2199 13858 2203 insertGenerator sing_593.htm#SEC645 13951 2204 instructions, Macintosh installation Macintosh installation instructions sing_2830.htm#SEC2920 2205 instructions, Unix installation Unix installation instructions sing_2828.htm#SEC2918 2206 instructions, Windows installation Windows installation instructions sing_2829.htm#SEC2919 2207 instructions, downloading Download instructions sing_2827.htm#SEC2917 2176 2208 int sing_95.htm#SEC135 2177 2209 int declarations sing_96.htm#SEC136 … … 2179 2211 int operations sing_98.htm#SEC138 2180 2212 int related functions int related functions sing_99.htm#SEC139 2181 intInverse sing_2 574.htm#SEC2650sprintf2182 intPart sing_1 893.htm#SEC1969483602183 intRank sing_2 566.htm#SEC264218302184 intRoot sing_1 894.htm#SEC1970545822185 intRoots sing_5 88.htm#SEC640245382186 intStrategy, option sing_31 5.htm#IDX1552187 intclMonIdeal sing_1 263.htm#SEC1339223382188 intclToricRing sing_1 259.htm#SEC1335621432189 integer division Miscellaneous oddities sing_4 18.htm#IDX2882190 integer programming sing_ 882.htm#SEC9392191 integral sing_27 10.htm#SEC2786626832192 integral basis sing_1 182.htm#IDX5462193 integral basis sing_1 377.htm#IDX6132194 integral closure sing_1 243.htm#IDX5612195 integral closure sing_1 244.htm#IDX5642196 integral closure sing_1 245.htm#IDX5672197 integral closure sing_1 258.htm#IDX5732198 integralBasis sing_1 182.htm#SEC1258381142199 integralIdeal sing_57 5.htm#SEC627291942200 integralModule sing_57 6.htm#SEC628580782201 integralSection sing_2 575.htm#SEC2651sprintf2202 integralbasis.lib sing_1 181.htm#SEC12572203 integralbasis_lib sing_1 181.htm#SEC12572204 integration of D-module sing_56 3.htm#IDX3492213 intInverse sing_2639.htm#SEC2715 sprintf 2214 intPart sing_1955.htm#SEC2031 48360 2215 intRank sing_2631.htm#SEC2707 1830 2216 intRoot sing_1956.htm#SEC2032 54582 2217 intRoots sing_590.htm#SEC642 24538 2218 intStrategy, option sing_316.htm#IDX155 2219 intclMonIdeal sing_1325.htm#SEC1401 22338 2220 intclToricRing sing_1321.htm#SEC1397 62143 2221 integer division Miscellaneous oddities sing_420.htm#IDX288 2222 integer programming sing_945.htm#SEC1002 2223 integral sing_2775.htm#SEC2851 62683 2224 integral basis sing_1244.htm#IDX552 2225 integral basis sing_1439.htm#IDX619 2226 integral closure sing_1305.htm#IDX567 2227 integral closure sing_1306.htm#IDX570 2228 integral closure sing_1307.htm#IDX573 2229 integral closure sing_1320.htm#IDX579 2230 integralBasis sing_1244.htm#SEC1320 38114 2231 integralIdeal sing_577.htm#SEC629 29194 2232 integralModule sing_578.htm#SEC630 58078 2233 integralSection sing_2640.htm#SEC2716 sprintf 2234 integralbasis.lib sing_1243.htm#SEC1319 2235 integralbasis_lib sing_1243.htm#SEC1319 2236 integration of D-module sing_565.htm#IDX349 2205 2237 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