Changeset cd8a2b5 in git
- Timestamp:
- Oct 11, 2016, 4:41:29 PM (8 years ago)
- Branches:
- (u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')
- Children:
- 007710def9a33026054f24e63eaa28238c13d4bc
- Parents:
- 72404e00161a44bb7e5a435b3005d17219209366
- File:
-
- 1 edited
-
doc/singular.idx (modified) (16 diffs)
Legend:
- Unmodified
- Added
- Removed
-
doc/singular.idx
r72404e rcd8a2b5 1 sing_901.htm#IDX418 2 sing_902.htm#IDX423 3 sing_903.htm#IDX428 4 sing_904.htm#IDX431 5 sing_905.htm#IDX435 6 sing_909.htm#IDX442 7 sing_910.htm#IDX447 8 sing_911.htm#IDX451 9 sing_912.htm#IDX454 10 sing_913.htm#IDX458 11 sing_914.htm#IDX462 12 sing_915.htm#IDX466 13 sing_916.htm#IDX471 14 sing_917.htm#IDX476 15 sing_918.htm#IDX481 16 sing_919.htm#IDX484 17 sing_920.htm#IDX486 1 18 ! sing_36.htm#IDX101 2 19 != sing_36.htm#IDX95 … … 132 149 < sing_150.htm#SEC190 133 150 < sing_175.htm#SEC215 134 < sing_2 98.htm#SEC338151 < sing_241.htm#SEC281 135 152 <= sing_36.htm#IDX99 136 153 <= sing_95.htm#SEC135 … … 166 183 >= sing_175.htm#SEC215 167 184 ? sing_36.htm#IDX106 168 ? sing_ 308.htm#IDX148169 AG codes sing_8 89.htm#SEC941170 AGcode_L sing_1 832.htm#SEC1908171 AGcode_Omega sing_1 833.htm#SEC1909172 ASCII sing_ 938.htm#SEC1014185 ? sing_251.htm#IDX148 186 AG codes sing_832.htm#SEC884 187 AGcode_L sing_1782.htm#SEC1858 188 AGcode_Omega sing_1783.htm#SEC1859 189 ASCII sing_881.htm#SEC957 173 190 ASCII links sing_112.htm#SEC152 174 191 ASSUME sing_64.htm#SEC101 175 A_L sing_1 531.htm#SEC1607176 A_Z sing_ 937.htm#SEC1013192 A_L sing_1481.htm#SEC1557 193 A_Z sing_880.htm#SEC956 177 194 Access to elements of a user defined type Access to elements of a user defined type sing_180.htm#SEC220 178 Adj_div sing_1 827.htm#SEC1903179 Adjoint ideal sing_1 408.htm#IDX542180 Alexander polynomial sing_1 502.htm#IDX566181 Algebraic Geometry codes sing_1 826.htm#IDX714182 Algebraic dependence Algebraic dependence sing_8 70.htm#SEC922183 Algebraic geometry sing_13 83.htm#SEC1459184 AltVarEnd sing_7 83.htm#SEC835185 AltVarStart sing_7 82.htm#SEC834186 Ann sing_1 322.htm#SEC1398187 Appel function sing_ 612.htm#IDX345188 Appel hypergeometric function sing_ 612.htm#IDX346189 Applications sing_8 87.htm#SEC939190 ArnoldAction sing_1 624.htm#SEC1700195 Adj_div sing_1777.htm#SEC1853 196 Adjoint ideal sing_1358.htm#IDX606 197 Alexander polynomial sing_1452.htm#IDX630 198 Algebraic Geometry codes sing_1776.htm#IDX778 199 Algebraic dependence Algebraic dependence sing_813.htm#SEC865 200 Algebraic geometry sing_1333.htm#SEC1409 201 AltVarEnd sing_726.htm#SEC778 202 AltVarStart sing_725.htm#SEC777 203 Ann sing_1272.htm#SEC1348 204 Appel function sing_555.htm#IDX345 205 Appel hypergeometric function sing_555.htm#IDX346 206 Applications sing_830.htm#SEC882 207 ArnoldAction sing_1574.htm#SEC1650 191 208 Assignments for user defined types Assignments for user defined types sing_182.htm#SEC222 192 Atkin sing_1915.htm#SEC1991 209 AssocTanToEnv sing_917.htm#SEC993 210 Atkin sing_1865.htm#SEC1941 193 211 Authors sing_1.htm#IDX16 194 BINresol sing_1 421.htm#SEC1497212 BINresol sing_1371.htm#SEC1447 195 213 Background sing_3.htm#SEC5 196 Basic programming sing_ 845.htm#SEC897197 Basic programming sing_ 845.htm#SEC897198 BelongSemig sing_22 33.htm#SEC2309199 BerlekampMassey sing_2 259.htm#SEC2335200 Bern sing_22 11.htm#SEC2287201 Bernstein operator sing_5 89.htm#IDX327202 Bernstein-Sato polynomial sing_ 554.htm#IDX308203 Bernstein-Sato polynomial sing_5 89.htm#IDX324204 Bernstein-Sato polynomial sing_15 65.htm#IDX597205 Bernstein-Sato polynomial sing_15 69.htm#IDX614206 Bernstein-Sato polynomial for variety sing_ 645.htm#IDX349207 Betti number Syzygies and resolutions sing_ 904.htm#SEC961208 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_ 914.htm#SEC971209 BlowingUp sing_1 544.htm#SEC1620210 Blowupcenter sing_1 424.htm#SEC1500211 BorelCheck sing_14 99.htm#SEC1575212 Branches of space curve singularities Branches of space curve singularities sing_8 78.htm#SEC930213 Briancon-Maisonobe algorithm sing_5 89.htm#IDX333214 Brieskorn lattice sing_15 65.htm#IDX593215 Brieskorn lattice sing_15 66.htm#IDX604216 Brieskorn lattice sing_15 67.htm#IDX607217 Brieskorn lattice sing_15 68.htm#IDX610218 Brieskorn lattice sing_15 69.htm#IDX613219 Brieskorn lattice sing_15 70.htm#IDX617220 Brieskorn lattice sing_15 71.htm#IDX621221 Brieskorn lattice sing_15 72.htm#IDX627222 Brieskorn lattice sing_15 73.htm#IDX635223 Brieskorn lattice sing_15 74.htm#IDX641224 Brieskorn lattice sing_15 75.htm#IDX649225 Brieskorn lattice sing_15 76.htm#IDX659226 Brieskorn lattice sing_15 87.htm#IDX665227 Brieskorn lattice sing_15 89.htm#IDX676228 Brieskorn lattice sing_1 617.htm#IDX703229 Brill-Noether algorithm sing_1 826.htm#IDX715230 BrillNoether sing_1 829.htm#SEC1905231 Buchberger algorithm for toric ideals Buchberger algorithm sing_ 915.htm#SEC972232 Budur-Mustata-Saito approach sing_ 645.htm#IDX353233 Building Singular sing_2 475.htm#SEC2564234 C programming language Major differences to the C programming language sing_4 57.htm#SEC497235 C, module ordering sing_8 97.htm#IDX407236 CGS , disjoint, reduced, Comprehensive Groebner System cgsdr sing_959.htm#IDX417237 CM_regularity sing_14 86.htm#SEC1562 33865238 CMtype sing_16 55.htm#SEC1731239 CRHT-ideal sing_ 921.htm#SEC985214 Basic programming sing_788.htm#SEC840 215 Basic programming sing_788.htm#SEC840 216 BelongSemig sing_2291.htm#SEC2367 217 BerlekampMassey sing_2339.htm#SEC2415 218 Bern sing_2269.htm#SEC2345 219 Bernstein operator sing_532.htm#IDX327 220 Bernstein-Sato polynomial sing_497.htm#IDX308 221 Bernstein-Sato polynomial sing_532.htm#IDX324 222 Bernstein-Sato polynomial sing_1515.htm#IDX661 223 Bernstein-Sato polynomial sing_1519.htm#IDX678 224 Bernstein-Sato polynomial for variety sing_588.htm#IDX349 225 Betti number Syzygies and resolutions sing_847.htm#SEC904 226 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_857.htm#SEC914 227 BlowingUp sing_1494.htm#SEC1570 228 Blowupcenter sing_1374.htm#SEC1450 229 BorelCheck sing_1449.htm#SEC1525 230 Branches of space curve singularities Branches of space curve singularities sing_821.htm#SEC873 231 Briancon-Maisonobe algorithm sing_532.htm#IDX333 232 Brieskorn lattice sing_1515.htm#IDX657 233 Brieskorn lattice sing_1516.htm#IDX668 234 Brieskorn lattice sing_1517.htm#IDX671 235 Brieskorn lattice sing_1518.htm#IDX674 236 Brieskorn lattice sing_1519.htm#IDX677 237 Brieskorn lattice sing_1520.htm#IDX681 238 Brieskorn lattice sing_1521.htm#IDX685 239 Brieskorn lattice sing_1522.htm#IDX691 240 Brieskorn lattice sing_1523.htm#IDX699 241 Brieskorn lattice sing_1524.htm#IDX705 242 Brieskorn lattice sing_1525.htm#IDX713 243 Brieskorn lattice sing_1526.htm#IDX723 244 Brieskorn lattice sing_1537.htm#IDX729 245 Brieskorn lattice sing_1539.htm#IDX740 246 Brieskorn lattice sing_1567.htm#IDX767 247 Brill-Noether algorithm sing_1776.htm#IDX779 248 BrillNoether sing_1779.htm#SEC1855 249 Buchberger algorithm for toric ideals Buchberger algorithm sing_858.htm#SEC915 250 Budur-Mustata-Saito approach sing_588.htm#IDX353 251 Building Singular sing_2502.htm#SEC2591 252 C programming language Major differences to the C programming language sing_400.htm#SEC440 253 C, module ordering sing_840.htm#IDX407 254 CGS sing_903.htm#IDX424 255 CM_regularity sing_1436.htm#SEC1512 33865 256 CMtype sing_1605.htm#SEC1681 257 CRHT-ideal sing_864.htm#SEC928 240 258 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 241 Castelnuovo-Mumford regularity sing_14 86.htm#IDX558259 Castelnuovo-Mumford regularity sing_1436.htm#IDX622 242 260 Category string sing_51.htm#SEC88 243 CenCharDec sing_ 739.htm#SEC791244 Center sing_14 63.htm#SEC1539245 CenterBO sing_14 70.htm#SEC1546246 CentralQuot sing_ 737.htm#SEC789247 CentralSaturation sing_ 738.htm#SEC790261 CenCharDec sing_682.htm#SEC734 262 Center sing_1413.htm#SEC1489 263 CenterBO sing_1420.htm#SEC1496 264 CentralQuot sing_680.htm#SEC732 265 CentralSaturation sing_681.htm#SEC733 248 266 Change of rings sing_9.htm#SEC15 249 Characteristic sets sing_ 905.htm#SEC962250 CharacteristicExponents CharacteristicExponents sing_15 50.htm#SEC1626251 ChernRootsDual sing_2 190.htm#SEC2266252 ChernRootsHom sing_2 199.htm#SEC2275253 ChernRootsProd sing_2 192.htm#SEC2268254 ChernRootsSum sing_2 188.htm#SEC2264255 ChernRootsSymm sing_22 01.htm#SEC2277256 ChernRootsWedge sing_22 02.htm#SEC2278257 Chevalley-Rosenlicht theorem sing_1 402.htm#IDX527258 Chevalley-Rosenlicht theorem sing_1 403.htm#IDX530259 Classification of hypersurface singularities Classification of hypersurface singularities sing_8 79.htm#SEC931260 Classification of singularities sing_24 09.htm#IDX898261 Code Codes and the decoding problem sing_ 920.htm#SEC978262 Codes and the decoding problem Codes and the decoding problem sing_ 920.htm#SEC977263 Coding theory sing_1 825.htm#SEC1901264 Coefficient rings Notes for Singular users sing_2 473.htm#SEC2556267 Characteristic sets sing_848.htm#SEC905 268 CharacteristicExponents CharacteristicExponents sing_1500.htm#SEC1576 269 ChernRootsDual sing_2248.htm#SEC2324 270 ChernRootsHom sing_2257.htm#SEC2333 271 ChernRootsProd sing_2250.htm#SEC2326 272 ChernRootsSum sing_2246.htm#SEC2322 273 ChernRootsSymm sing_2259.htm#SEC2335 274 ChernRootsWedge sing_2260.htm#SEC2336 275 Chevalley-Rosenlicht theorem sing_1352.htm#IDX591 276 Chevalley-Rosenlicht theorem sing_1353.htm#IDX594 277 Classification of hypersurface singularities Classification of hypersurface singularities sing_822.htm#SEC874 278 Classification of singularities sing_2489.htm#IDX982 279 Code Codes and the decoding problem sing_863.htm#SEC921 280 Codes and the decoding problem Codes and the decoding problem sing_863.htm#SEC920 281 Coding theory sing_1775.htm#SEC1851 282 Coefficient rings Notes for Singular users sing_2500.htm#SEC2583 265 283 Command line options Command line options sing_19.htm#SEC26 266 Commands Functions and system variables sing_2 58.htm#SEC298284 Commands Functions and system variables sing_201.htm#SEC241 267 285 Commands for user defined types Commands for user defined types sing_181.htm#SEC221 268 Commutative Algebra sing_858.htm#SEC910 269 Commutative algebra sing_1141.htm#SEC1217 270 CompDecomp sing_551.htm#SEC603 271 CompInt sing_2235.htm#SEC2311 272 CompleteHomog sing_2178.htm#SEC2254 273 ComplexValue sing_2281.htm#SEC2357 274 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_854.htm#SEC906 275 ConsLevels sing_966.htm#SEC1042 276 ContactMatrix sing_1552.htm#SEC1628 277 Conti-Traverso algorithm sing_910.htm#SEC967 286 Commutative Algebra sing_801.htm#SEC853 287 Commutative algebra sing_1090.htm#SEC1166 288 CompDecomp sing_494.htm#SEC546 289 CompInt sing_2293.htm#SEC2369 290 CompleteHomog sing_2236.htm#SEC2312 291 ComplexValue sing_2361.htm#SEC2437 292 Comprehensive Groebner System sing_903.htm#IDX427 293 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_797.htm#SEC849 294 ConsLevels sing_911.htm#SEC987 295 ConsLevelsToLevels sing_912.htm#SEC988 296 ContactMatrix sing_1502.htm#SEC1578 297 Conti-Traverso algorithm sing_853.htm#SEC910 278 298 Contributors sing_1.htm#IDX15 279 Control structures sing_ 425.htm#SEC465280 Control theory System and Control theory sing_18 59.htm#SEC1935281 Cooper philosophy sing_ 921.htm#SEC983282 Cornacchia sing_1 905.htm#SEC1981283 CornacchiaModified sing_1 906.htm#SEC1982284 Crep sing_9 62.htm#SEC1038285 Critical points sing_8 73.htm#SEC925286 CurveParam sing_1 546.htm#SEC1622287 CurveRes sing_1 545.htm#SEC1621288 Curves sing_1 408.htm#IDX539299 Control structures sing_368.htm#SEC408 300 Control theory System and Control theory sing_1809.htm#SEC1885 301 Cooper philosophy sing_864.htm#SEC926 302 Cornacchia sing_1855.htm#SEC1931 303 CornacchiaModified sing_1856.htm#SEC1932 304 Crep sing_906.htm#SEC982 305 Critical points sing_816.htm#SEC868 306 CurveParam sing_1496.htm#SEC1572 307 CurveRes sing_1495.htm#SEC1571 308 Curves sing_1358.htm#IDX603 289 309 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 290 Cyclic code sing_1 840.htm#IDX722291 Cyclic roots sing_ 851.htm#SEC903292 D-integration sing_ 612.htm#IDX342293 D-localization sing_ 612.htm#IDX338294 D-localization sing_ 817.htm#IDX376295 D-module purityfiltration_lib sing_ 554.htm#IDX306296 D-module sing_5 89.htm#IDX321297 D-module sing_ 612.htm#IDX335298 D-module sing_ 645.htm#IDX347299 D-module sing_7 95.htm#IDX361300 D-module sing_ 817.htm#IDX373301 D-module structure sing_5 89.htm#IDX322302 D-module structure sing_ 645.htm#IDX348303 D-restriction sing_ 612.htm#IDX340310 Cyclic code sing_1790.htm#IDX786 311 Cyclic roots sing_794.htm#SEC846 312 D-integration sing_555.htm#IDX342 313 D-localization sing_555.htm#IDX338 314 D-localization sing_760.htm#IDX376 315 D-module purityfiltration_lib sing_497.htm#IDX306 316 D-module sing_532.htm#IDX321 317 D-module sing_555.htm#IDX335 318 D-module sing_588.htm#IDX347 319 D-module sing_738.htm#IDX361 320 D-module sing_760.htm#IDX373 321 D-module structure sing_532.htm#IDX322 322 D-module structure sing_588.htm#IDX348 323 D-restriction sing_555.htm#IDX340 304 324 DBM links sing_117.htm#SEC157 305 325 DISPLAY environment variable The online help system sing_16.htm#IDX28 306 DLoc sing_ 615.htm#SEC667307 DLoc0 sing_ 617.htm#SEC669326 DLoc sing_558.htm#SEC610 327 DLoc0 sing_560.htm#SEC612 308 328 Data types sing_72.htm#SEC112 309 Data types (plural) sing_4 71.htm#IDX292329 Data types (plural) sing_414.htm#IDX292 310 330 Debugging tools sing_63.htm#SEC100 311 331 Decker, Wolfram sing_1.htm#IDX17 312 332 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_179.htm#SEC219 313 Decoding sing_1 840.htm#IDX724314 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_ 919.htm#SEC976315 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_ 924.htm#SEC994333 Decoding sing_1790.htm#IDX788 334 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_862.htm#SEC919 335 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_867.htm#SEC937 316 336 Definition of a user defined type Definition of a user defined type sing_178.htm#SEC218 317 Deformations sing_8 76.htm#SEC928318 Deformations, T1 and T2 sing_8 75.htm#SEC927319 Degree sing_13 87.htm#SEC1463320 Delta sing_14 71.htm#SEC1547321 DeltaList sing_14 72.htm#SEC1548337 Deformations sing_819.htm#SEC871 338 Deformations, T1 and T2 sing_818.htm#SEC870 339 Degree sing_1337.htm#SEC1413 340 Delta sing_1421.htm#SEC1497 341 DeltaList sing_1422.htm#SEC1498 322 342 Demo mode sing_24.htm#SEC35 323 Depth sing_8 65.htm#SEC917324 Determinacy sing_24 12.htm#IDX902325 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_ 913.htm#SEC970326 Distributed computing sing_9 82.htm#IDX431327 Dlocalization sing_ 818.htm#SEC870343 Depth sing_808.htm#SEC860 344 Determinacy sing_2492.htm#IDX986 345 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_856.htm#SEC913 346 Distributed computing sing_931.htm#IDX491 347 Dlocalization sing_761.htm#SEC813 328 348 Documentation Tool sing_60.htm#SEC97 329 Dp, global ordering sing_8 95.htm#IDX390330 Ds, local ordering sing_8 96.htm#IDX400331 DsingularLocus sing_ 822.htm#SEC874349 Dp, global ordering sing_838.htm#IDX390 350 Ds, local ordering sing_839.htm#IDX400 351 DsingularLocus sing_765.htm#SEC817 332 352 Dynamic loading sing_71.htm#SEC111 333 Dynamic modules sing_ 853.htm#SEC905334 ECPP sing_1 949.htm#SEC2025335 ECoef sing_1 430.htm#SEC1506336 EOrdlist sing_1 428.htm#SEC1504337 ERROR sing_2 87.htm#SEC327353 Dynamic modules sing_796.htm#SEC848 354 ECPP sing_1899.htm#SEC1975 355 ECoef sing_1380.htm#SEC1456 356 EOrdlist sing_1378.htm#SEC1454 357 ERROR sing_230.htm#SEC270 338 358 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 339 Edatalist sing_1 427.htm#SEC1503340 Edelman-Reiner sing_21 56.htm#IDX833359 Edatalist sing_1377.htm#SEC1453 360 Edelman-Reiner sing_2186.htm#IDX869 341 361 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 342 362 Editing input sing_18.htm#SEC25 343 Elimination sing_8 61.htm#SEC913363 Elimination sing_804.htm#SEC856 344 364 Emacs Emacs user interface sing_21.htm#SEC28 345 365 Emacs, Singular demo mode sing_24.htm#SEC35 … … 351 371 Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30 352 372 Emacs, user interface Emacs user interface sing_21.htm#SEC28 353 Emaxcont sing_1 432.htm#SEC1508354 Equal sing_13 86.htm#SEC1462355 Eresol sing_1 422.htm#SEC1498356 Evaluation of logical expressions Evaluation of logical expressions sing_4 59.htm#SEC499357 Examples sing_ 843.htm#SEC895373 Emaxcont sing_1382.htm#SEC1458 374 Equal sing_1336.htm#SEC1412 375 Eresol sing_1372.htm#SEC1448 376 Evaluation of logical expressions Evaluation of logical expressions sing_402.htm#SEC442 377 Examples sing_786.htm#SEC838 358 378 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 359 Exp for matrices sing_1404.htm#IDX531 360 Experimental libraries Experimental libraries sing_2127.htm#SEC2203 361 Ext sing_1201.htm#SEC1277 362 Ext, computation of sing_864.htm#SEC916 363 Ext_R sing_1200.htm#SEC1276 364 Exterior sing_769.htm#SEC821 365 Extra weight vector sing_900.htm#SEC952 366 Factorization sing_866.htm#SEC918 367 Feynman graph sing_1177.htm#IDX468 368 Finite fields sing_860.htm#SEC912 379 Exp for matrices sing_1354.htm#IDX595 380 Experimental libraries Experimental libraries sing_2230.htm#SEC2306 381 Ext sing_1150.htm#SEC1226 382 Ext, computation of sing_807.htm#SEC859 383 Ext_R sing_1149.htm#SEC1225 384 Exterior sing_712.htm#SEC764 385 Extra weight vector sing_843.htm#SEC895 386 Factorization sing_809.htm#SEC861 387 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_918.htm#SEC994 388 Feynman graph sing_1126.htm#IDX528 389 Finite fields sing_803.htm#SEC855 369 390 First steps sing_6.htm#SEC12 370 Fitzgerald-Lax method Fitzgerald-Lax method sing_ 923.htm#SEC991391 Fitzgerald-Lax method Fitzgerald-Lax method sing_866.htm#SEC934 371 392 Flow control sing_40.htm#SEC70 372 393 Formal Checker sing_59.htm#SEC96 373 Formatting output sing_ 850.htm#SEC902374 Free resolution sing_8 62.htm#SEC914375 Free resolution, graded Handling graded modules sing_8 63.htm#SEC915376 Functions sing_2 59.htm#SEC299377 Future benefits of Singular 4 Notes for Singular users sing_2 473.htm#SEC2562378 G-algebra sing_ 535.htm#SEC575379 G-algebra sing_ 535.htm#SEC577380 G-algebra, setup sing_ 535.htm#SEC579381 GBWeight sing_ 618.htm#SEC670382 GBsolve sing_1 739.htm#SEC1815383 GIT sing_2 293.htm#IDX884384 GKZsystem sing_ 735.htm#SEC787385 GKdim sing_ 708.htm#SEC760394 Formatting output sing_793.htm#SEC845 395 Free resolution sing_805.htm#SEC857 396 Free resolution, graded Handling graded modules sing_806.htm#SEC858 397 Functions sing_202.htm#SEC242 398 Future benefits of Singular 4 Notes for Singular users sing_2500.htm#SEC2589 399 G-algebra sing_478.htm#SEC518 400 G-algebra sing_478.htm#SEC520 401 G-algebra, setup sing_478.htm#SEC522 402 GBWeight sing_561.htm#SEC613 403 GBsolve sing_1689.htm#SEC1765 404 GIT sing_2373.htm#IDX962 405 GKZsystem sing_678.htm#SEC730 406 GKdim sing_651.htm#SEC703 386 407 GMP sing_1.htm#IDX3 387 GND.lib sing_23 00.htm#SEC2376388 GND_lib sing_23 00.htm#SEC2376389 GTZmod sing_1 249.htm#SEC1325390 GTZopt sing_12 56.htm#SEC1332391 G_a -Invariants sing_8 82.htm#SEC934392 Gamma sing_1 437.htm#SEC1513393 Gauss-Manin connection Gauss-Manin connection sing_ 906.htm#SEC963394 Gauss-Manin connection sing_1 617.htm#IDX702395 Gauss-Manin connection sing_16 64.htm#IDX705396 Gauss-Manin system sing_15 65.htm#IDX592397 Gauss-Manin system sing_15 66.htm#IDX603398 Gauss-Manin system sing_15 67.htm#IDX606399 Gauss-Manin system sing_15 68.htm#IDX609400 Gauss-Manin system sing_15 69.htm#IDX612401 Gauss-Manin system sing_15 70.htm#IDX616402 Gauss-Manin system sing_15 71.htm#IDX620403 Gauss-Manin system sing_15 72.htm#IDX626404 Gauss-Manin system sing_15 73.htm#IDX634405 Gauss-Manin system sing_15 74.htm#IDX640406 Gauss-Manin system sing_15 75.htm#IDX648407 Gauss-Manin system sing_15 76.htm#IDX658408 Gauss-Manin system sing_15 87.htm#IDX664409 Gauss-Manin system sing_15 89.htm#IDX675408 GND.lib sing_2380.htm#SEC2456 409 GND_lib sing_2380.htm#SEC2456 410 GTZmod sing_1198.htm#SEC1274 411 GTZopt sing_1205.htm#SEC1281 412 G_a -Invariants sing_825.htm#SEC877 413 Gamma sing_1387.htm#SEC1463 414 Gauss-Manin connection Gauss-Manin connection sing_849.htm#SEC906 415 Gauss-Manin connection sing_1567.htm#IDX766 416 Gauss-Manin connection sing_1614.htm#IDX769 417 Gauss-Manin system sing_1515.htm#IDX656 418 Gauss-Manin system sing_1516.htm#IDX667 419 Gauss-Manin system sing_1517.htm#IDX670 420 Gauss-Manin system sing_1518.htm#IDX673 421 Gauss-Manin system sing_1519.htm#IDX676 422 Gauss-Manin system sing_1520.htm#IDX680 423 Gauss-Manin system sing_1521.htm#IDX684 424 Gauss-Manin system sing_1522.htm#IDX690 425 Gauss-Manin system sing_1523.htm#IDX698 426 Gauss-Manin system sing_1524.htm#IDX704 427 Gauss-Manin system sing_1525.htm#IDX712 428 Gauss-Manin system sing_1526.htm#IDX722 429 Gauss-Manin system sing_1537.htm#IDX728 430 Gauss-Manin system sing_1539.htm#IDX739 410 431 General command syntax General command syntax sing_35.htm#SEC59 411 432 General concepts sing_12.htm#SEC18 412 General purpose sing_ 931.htm#SEC1007433 General purpose sing_874.htm#SEC950 413 434 General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41 414 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_ 537.htm#SEC587415 Generalized Newton identities Generalized Newton identities sing_ 922.htm#SEC988416 Geometric genus sing_1 408.htm#IDX543417 German Umlaute sing_ 455.htm#IDX279435 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_480.htm#SEC530 436 Generalized Newton identities Generalized Newton identities sing_865.htm#SEC931 437 Geometric genus sing_1358.htm#IDX607 438 German Umlaute sing_398.htm#IDX279 418 439 Getting started sing_5.htm#SEC11 419 Global orderings sing_8 95.htm#SEC947420 Graded commutative algebras Graded commutative algebras (SCA) sing_ 539.htm#SEC591440 Global orderings sing_838.htm#SEC890 441 Graded commutative algebras Graded commutative algebras (SCA) sing_482.htm#SEC534 421 442 Greuel, Gert-Martin sing_1.htm#IDX18 422 Groebner Bases Computing Groebner and Standard Bases sing_854.htm#SEC906 423 Groebner bases in G-algebras Groebner bases in G-algebras sing_536.htm#SEC580 424 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_542.htm#SEC594 425 Groebner bases, decodeGB sing_1840.htm#IDX726 426 Groebner bases, slim sing_857.htm#SEC909 427 Groebner basis conversion Groebner basis conversion sing_856.htm#SEC908 428 Groebner cover, parametric ideal, canonical, discussion of extend sing_958.htm#IDX416 429 Groebner cover, parametric ideal, canonical, discussion of sing_965.htm#IDX420 430 Groebner fan sing_2044.htm#IDX743 431 Groebner walk sing_1192.htm#IDX487 432 Groebner walk sing_1194.htm#IDX489 433 Groebner walk sing_2402.htm#IDX895 434 Groebner walk sing_2403.htm#IDX896 435 Gromov-Witten invariants sing_1177.htm#IDX465 436 Gromov-Witten invariants sing_1183.htm#IDX474 437 Gromov-Witten invariants sing_1184.htm#IDX478 438 Gweights sing_763.htm#SEC815 439 H2basis sing_1622.htm#SEC1698 440 Hamburger-Noether expansion sing_1502.htm#IDX562 441 Hamburger-Noether expansion sing_1590.htm#IDX684 442 Hamburger-Noether expansions sing_1827.htm#IDX716 443 Handling graded modules Handling graded modules sing_863.htm#SEC915 444 Hcode sing_1524.htm#SEC1600 443 Groebner Bases Computing Groebner and Standard Bases sing_797.htm#SEC849 444 Groebner bases in G-algebras Groebner bases in G-algebras sing_479.htm#SEC523 445 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_485.htm#SEC537 446 Groebner bases, decodeGB sing_1790.htm#IDX790 447 Groebner bases, slim sing_800.htm#SEC852 448 Groebner basis conversion Groebner basis conversion sing_799.htm#SEC851 449 Groebner cover sing_902.htm#IDX419 450 Groebner cover sing_909.htm#IDX436 451 Groebner cover sing_910.htm#IDX443 452 Groebner fan sing_2053.htm#IDX807 453 Groebner walk sing_1141.htm#IDX549 454 Groebner walk sing_1143.htm#IDX551 455 Groebner walk sing_2482.htm#IDX977 456 Groebner walk sing_2483.htm#IDX978 457 Groebnerwalk sing_1137.htm#IDX545 458 Groebnerwalk sing_2419.htm#IDX971 459 Groebnerwalk sing_2481.htm#IDX976 460 Groebnerwalk sing_2485.htm#IDX981 461 Gromov-Witten invariants sing_1126.htm#IDX525 462 Gromov-Witten invariants sing_1132.htm#IDX534 463 Gromov-Witten invariants sing_1133.htm#IDX538 464 Gweights sing_706.htm#SEC758 465 H2basis sing_1572.htm#SEC1648 466 HHnormalForm sing_2302.htm#SEC2378 467 Hamburger-Noether expansion sing_1452.htm#IDX626 468 Hamburger-Noether expansion sing_1540.htm#IDX748 469 Hamburger-Noether expansions sing_1777.htm#IDX780 470 Handling graded modules Handling graded modules sing_806.htm#SEC858 471 Hcode sing_1474.htm#SEC1550 445 472 Help string sing_45.htm#SEC82 446 Hensel sing_2 92.htm#SEC332447 Hilbert function sing_ 404.htm#IDX188448 Hilbert function sing_ 903.htm#SEC957449 Hilbert series sing_ 903.htm#SEC957450 Hilbert-driven GB algorithm Groebner basis conversion sing_ 856.htm#SEC908451 HilbertClassPoly sing_1 912.htm#SEC1988452 HilbertSeries sing_1 717.htm#SEC1793453 HilbertWeights sing_1 718.htm#SEC1794454 Hom sing_1 204.htm#SEC1280455 HomJJ sing_12 79.htm#SEC1355456 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_ 912.htm#SEC969473 Hensel sing_235.htm#SEC275 474 Hilbert function sing_347.htm#IDX188 475 Hilbert function sing_846.htm#SEC900 476 Hilbert series sing_846.htm#SEC900 477 Hilbert-driven GB algorithm Groebner basis conversion sing_799.htm#SEC851 478 HilbertClassPoly sing_1862.htm#SEC1938 479 HilbertSeries sing_1667.htm#SEC1743 480 HilbertWeights sing_1668.htm#SEC1744 481 Hom sing_1153.htm#SEC1229 482 HomJJ sing_1228.htm#SEC1304 483 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_855.htm#SEC912 457 484 How to enter and exit How to enter and exit sing_14.htm#SEC20 458 485 How to use this manual How to use this manual sing_4.htm#SEC6 459 Hurwitz numbers sing_11 83.htm#IDX477460 Hurwitz numbers sing_11 84.htm#IDX481461 Hypersurface singularities, classification of Classification of hypersurface singularities sing_8 79.htm#SEC931462 IN sing_ 329.htm#IDX149463 Ideal membership sing_ 902.htm#IDX412486 Hurwitz numbers sing_1132.htm#IDX537 487 Hurwitz numbers sing_1133.htm#IDX541 488 Hypersurface singularities, classification of Classification of hypersurface singularities sing_822.htm#SEC874 489 IN sing_272.htm#IDX149 490 Ideal membership sing_845.htm#IDX412 464 491 Identifiers, syntax of sing_37.htm#SEC65 465 ImageGroup sing_1 720.htm#SEC1796466 ImageVariety sing_1 719.htm#SEC1795467 Imap, option sing_3 64.htm#IDX175492 ImageGroup sing_1670.htm#SEC1746 493 ImageVariety sing_1669.htm#SEC1745 494 Imap, option sing_307.htm#IDX175 468 495 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 469 Incl sing_13 85.htm#SEC1461470 Index sing_2 481.htm#SEC2570496 Incl sing_1335.htm#SEC1411 497 Index sing_2508.htm#SEC2597 471 498 Info string sing_52.htm#SEC89 472 InterDiv sing_14 53.htm#SEC1529499 InterDiv sing_1403.htm#SEC1479 473 500 Interactive use sing_13.htm#SEC19 474 501 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 475 IntersectWithSub sing_ 740.htm#SEC792476 IntersectionMatrix sing_15 51.htm#SEC1627502 IntersectWithSub sing_683.htm#SEC735 503 IntersectionMatrix sing_1501.htm#SEC1577 477 504 Introduction sing_2.htm#SEC4 478 Invariant Theory sing_8 81.htm#SEC933479 Invariant theory sing_16 69.htm#SEC1745480 InvariantQ sing_1 722.htm#SEC1798481 InvariantRing sing_1 721.htm#SEC1797482 Invariants of a finite group Invariants of a finite group sing_8 83.htm#SEC935483 Invariants of plane curve singularities Invariants of plane curve singularities sing_8 77.htm#SEC929484 IsSCA sing_7 84.htm#SEC836485 J-marked schemes sing_14 93.htm#IDX560486 J-marked schemes, Borel ideals sing_14 98.htm#IDX561487 JMBTest.lib sing_14 93.htm#SEC1569488 JMBTest_lib sing_14 93.htm#SEC1569489 JMSConst.lib sing_14 98.htm#SEC1574490 JMSConst_lib sing_14 98.htm#SEC1574491 JMarkedScheme sing_1 500.htm#SEC1576492 Jacobi sing_1 922.htm#SEC1998493 Jacobson form sing_18 77.htm#IDX727494 Jacobson normal form sing_18 77.htm#IDX728495 JuReTopDim sing_13 95.htm#SEC1471496 JuReZeroDim sing_13 96.htm#SEC1472497 KScoef sing_1 615.htm#SEC1691498 KSconvert sing_1 613.htm#SEC1689499 KSker sing_1 612.htm#SEC1688500 KSlinear sing_1 614.htm#SEC1690501 KSpencerKernel sing_16 62.htm#SEC1738502 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_23 19.htm#SEC2395503 Kernel of module homomorphisms Kernel of module homomorphisms sing_8 69.htm#SEC921504 KoszulHomology sing_1 213.htm#SEC1289505 LETTERPLACE sing_ 540.htm#SEC592506 LIB sing_ 333.htm#SEC373505 Invariant Theory sing_824.htm#SEC876 506 Invariant theory sing_1619.htm#SEC1695 507 InvariantQ sing_1672.htm#SEC1748 508 InvariantRing sing_1671.htm#SEC1747 509 Invariants of a finite group Invariants of a finite group sing_826.htm#SEC878 510 Invariants of plane curve singularities Invariants of plane curve singularities sing_820.htm#SEC872 511 IsSCA sing_727.htm#SEC779 512 J-marked schemes sing_1443.htm#IDX624 513 J-marked schemes, Borel ideals sing_1448.htm#IDX625 514 JMBTest.lib sing_1443.htm#SEC1519 515 JMBTest_lib sing_1443.htm#SEC1519 516 JMSConst.lib sing_1448.htm#SEC1524 517 JMSConst_lib sing_1448.htm#SEC1524 518 JMarkedScheme sing_1450.htm#SEC1526 519 Jacobi sing_1872.htm#SEC1948 520 Jacobson form sing_1827.htm#IDX791 521 Jacobson normal form sing_1827.htm#IDX792 522 JuReTopDim sing_1345.htm#SEC1421 523 JuReZeroDim sing_1346.htm#SEC1422 524 KScoef sing_1565.htm#SEC1641 525 KSconvert sing_1563.htm#SEC1639 526 KSker sing_1562.htm#SEC1638 527 KSlinear sing_1564.htm#SEC1640 528 KSpencerKernel sing_1612.htm#SEC1688 529 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2399.htm#SEC2475 530 Kernel of module homomorphisms Kernel of module homomorphisms sing_812.htm#SEC864 531 KoszulHomology sing_1162.htm#SEC1238 532 LETTERPLACE sing_483.htm#SEC535 533 LIB sing_276.htm#SEC316 507 534 LIB commands sing_53.htm#SEC90 508 LIBs sing_ 927.htm#SEC1003509 LLL sing_ 406.htm#IDX219510 LOT algorithm sing_5 89.htm#IDX334511 LU-decomposition of a matrix of numbers sing_ 338.htm#SEC378512 Laurent series sing_11 81.htm#IDX473513 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_8 85.htm#SEC937514 Left ideal membership Groebner bases in G-algebras sing_ 536.htm#SEC583515 Left normal form Groebner bases in G-algebras sing_ 536.htm#SEC582516 LengthSym sing_7 94.htm#SEC846517 LengthSymElement sing_7 93.htm#SEC845518 Letterplace sing_ 540.htm#SEC592519 Lexicographic Groebner bases, computation of Groebner basis conversion sing_ 856.htm#SEC908535 LIBs sing_870.htm#SEC946 536 LLL sing_349.htm#IDX219 537 LOT algorithm sing_532.htm#IDX334 538 LU-decomposition of a matrix of numbers sing_281.htm#SEC321 539 Laurent series sing_1130.htm#IDX533 540 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_828.htm#SEC880 541 Left ideal membership Groebner bases in G-algebras sing_479.htm#SEC526 542 Left normal form Groebner bases in G-algebras sing_479.htm#SEC525 543 LengthSym sing_737.htm#SEC789 544 LengthSymElement sing_736.htm#SEC788 545 Letterplace sing_483.htm#SEC535 546 Lexicographic Groebner bases, computation of Groebner basis conversion sing_799.htm#SEC851 520 547 Libraries Writing procedures and libraries sing_48.htm#SEC85 521 Libraries sing_ 846.htm#SEC898548 Libraries sing_789.htm#SEC841 522 549 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 523 Library versioning Notes for Singular users sing_2 473.htm#SEC2560524 Lie algebra sing_1 403.htm#IDX528525 Lie group sing_1 406.htm#IDX533526 Lie group sing_1 407.htm#IDX536527 Limitations sing_ 455.htm#SEC495528 Linear algebra sing_10 81.htm#SEC1157529 Linear code sing_1 840.htm#IDX723530 LinearActionQ sing_1 724.htm#SEC1800531 LinearCombinationQ sing_1 725.htm#SEC1801532 LinearizeAction sing_1 723.htm#SEC1799550 Library versioning Notes for Singular users sing_2500.htm#SEC2587 551 Lie algebra sing_1353.htm#IDX592 552 Lie group sing_1356.htm#IDX597 553 Lie group sing_1357.htm#IDX600 554 Limitations sing_398.htm#SEC438 555 Linear algebra sing_1030.htm#SEC1106 556 Linear code sing_1790.htm#IDX787 557 LinearActionQ sing_1674.htm#SEC1750 558 LinearCombinationQ sing_1675.htm#SEC1751 559 LinearizeAction sing_1673.htm#SEC1749 533 560 Loading a library sing_62.htm#SEC99 534 Local orderings sing_8 96.htm#SEC948535 Log for matrices sing_1 405.htm#IDX532536 Long coefficients sing_ 848.htm#SEC900537 M, ordering sing_8 98.htm#SEC950538 MVComplex sing_24 15.htm#SEC2491539 Macintosh installation Macintosh installation instructions sing_2 480.htm#SEC2569540 Mathematical background Mathematical background sing_ 901.htm#SEC953541 Mathematical background (plural) Mathematical background (plural) sing_ 534.htm#SEC574542 Matrix orderings sing_8 98.htm#SEC950543 Max sing_1 631.htm#SEC1707544 Maximus sing_14 95.htm#SEC1571545 Maxord sing_1 436.htm#SEC1512546 MillerRabin sing_1 932.htm#SEC2008547 Milnor number Milnor and Tjurina number sing_8 72.htm#SEC924548 Milnor number sing_24 11.htm#IDX901549 Min sing_1 632.htm#SEC1708550 MinMult sing_22 34.htm#SEC2310551 MinimalDecomposition MinimalDecomposition sing_1 726.htm#SEC1802552 Minimum distance sing_1 840.htm#IDX725553 Minimus sing_14 94.htm#SEC1570554 Miscellaneous libraries Miscellaneous libraries sing_21 02.htm#SEC2178555 ModEqn sing_1 625.htm#SEC1701556 Modular techniques sing_9 82.htm#IDX428557 Module orderings sing_8 97.htm#SEC949561 Local orderings sing_839.htm#SEC891 562 Log for matrices sing_1355.htm#IDX596 563 Long coefficients sing_791.htm#SEC843 564 M, ordering sing_841.htm#SEC893 565 MVComplex sing_2495.htm#SEC2571 566 Macintosh installation Macintosh installation instructions sing_2507.htm#SEC2596 567 Mathematical background Mathematical background sing_844.htm#SEC896 568 Mathematical background (plural) Mathematical background (plural) sing_477.htm#SEC517 569 Matrix orderings sing_841.htm#SEC893 570 Max sing_1581.htm#SEC1657 571 Maximus sing_1445.htm#SEC1521 572 Maxord sing_1386.htm#SEC1462 573 MillerRabin sing_1882.htm#SEC1958 574 Milnor number Milnor and Tjurina number sing_815.htm#SEC867 575 Milnor number sing_2491.htm#IDX985 576 Min sing_1582.htm#SEC1658 577 MinMult sing_2292.htm#SEC2368 578 MinimalDecomposition MinimalDecomposition sing_1676.htm#SEC1752 579 Minimum distance sing_1790.htm#IDX789 580 Minimus sing_1444.htm#SEC1520 581 Miscellaneous libraries Miscellaneous libraries sing_2157.htm#SEC2233 582 ModEqn sing_1575.htm#SEC1651 583 Modular techniques sing_931.htm#IDX488 584 Module orderings sing_840.htm#SEC892 558 585 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 559 Monodromy sing_1 617.htm#IDX700560 Monomial orderings sing_8 92.htm#SEC944586 Monodromy sing_1567.htm#IDX764 587 Monomial orderings sing_835.htm#SEC887 561 588 Monomial orderings, Term orderings sing_31.htm#SEC44 562 Morse lemma sing_24 10.htm#IDX899563 MultiplicitySequence MultiplicitySequence sing_1 549.htm#SEC1625564 NF sing_3 83.htm#SEC423565 NF sing_ 526.htm#SEC566566 NFMora sing_19 98.htm#SEC2074567 NPos sing_12 69.htm#SEC1345568 NPos_test sing_12 67.htm#SEC1343569 NSplaces sing_1 828.htm#SEC1904589 Morse lemma sing_2490.htm#IDX983 590 MultiplicitySequence MultiplicitySequence sing_1499.htm#SEC1575 591 NF sing_326.htm#SEC366 592 NF sing_469.htm#SEC509 593 NFMora sing_1948.htm#SEC2024 594 NPos sing_1218.htm#SEC1294 595 NPos_test sing_1216.htm#SEC1292 596 NSplaces sing_1778.htm#SEC1854 570 597 NTL sing_1.htm#IDX4 571 598 Names sing_37.htm#SEC65 572 599 Names in procedures sing_46.htm#SEC83 573 600 Names, indexed sing_37.htm#SEC65 574 New libraries depending on Singular 4 Notes for Singular users sing_2 473.htm#SEC2558575 New orderings for modules Notes for Singular users sing_2 473.htm#SEC2561576 Newton non-degenerate sing_1 604.htm#IDX698577 Newton polygon sing_1 603.htm#IDX697578 Newton polygon sing_1 604.htm#IDX699579 Newton polytope sing_20 44.htm#IDX742580 NoetherPosition sing_12 63.htm#SEC1339581 Non-commutative LIBs Non-commutative libraries sing_ 546.htm#SEC598582 Non-commutative algebra Non-commutative algebra sing_8 84.htm#SEC936583 Non-commutative algebra sing_ 918.htm#SEC975584 Non-commutative libraries Non-commutative libraries sing_ 546.htm#SEC598585 Non-commutative subsystem Non-commutative subsystem sing_4 69.htm#SEC509586 Nonhyp sing_1 425.htm#SEC1501587 Normal form sing_ 902.htm#IDX411588 Normalization sing_8 68.htm#SEC920589 Notes for Singular users Notes for Singular users sing_2 473.htm#SEC2555590 Notes for developers Notes for developers sing_2 474.htm#SEC2563591 NullCone sing_1 727.htm#SEC1803592 NumIrrDecom sing_13 99.htm#SEC1475593 NumLocalDim sing_13 88.htm#SEC1464594 NumPrimDecom sing_1 401.htm#SEC1477595 Oaku-Takayama algorithm sing_5 89.htm#IDX332601 New libraries depending on Singular 4 Notes for Singular users sing_2500.htm#SEC2585 602 New orderings for modules Notes for Singular users sing_2500.htm#SEC2588 603 Newton non-degenerate sing_1554.htm#IDX762 604 Newton polygon sing_1553.htm#IDX761 605 Newton polygon sing_1554.htm#IDX763 606 Newton polytope sing_2053.htm#IDX806 607 NoetherPosition sing_1212.htm#SEC1288 608 Non-commutative LIBs Non-commutative libraries sing_489.htm#SEC541 609 Non-commutative algebra Non-commutative algebra sing_827.htm#SEC879 610 Non-commutative algebra sing_861.htm#SEC918 611 Non-commutative libraries Non-commutative libraries sing_489.htm#SEC541 612 Non-commutative subsystem Non-commutative subsystem sing_412.htm#SEC452 613 Nonhyp sing_1375.htm#SEC1451 614 Normal form sing_845.htm#IDX411 615 Normalization sing_811.htm#SEC863 616 Notes for Singular users Notes for Singular users sing_2500.htm#SEC2582 617 Notes for developers Notes for developers sing_2501.htm#SEC2590 618 NullCone sing_1677.htm#SEC1753 619 NumIrrDecom sing_1349.htm#SEC1425 620 NumLocalDim sing_1338.htm#SEC1414 621 NumPrimDecom sing_1351.htm#SEC1427 622 Oaku-Takayama algorithm sing_532.htm#IDX332 596 623 Objects sing_38.htm#SEC66 597 Orlik-Solomon sing_21 57.htm#IDX834598 Output, formatting of sing_ 850.htm#SEC902599 PBW sing_5 68.htm#IDX320600 PBW basis sing_ 535.htm#SEC576601 PBW_eqDeg sing_5 86.htm#SEC638602 PBW_maxDeg sing_5 87.htm#SEC639603 PBW_maxMonom sing_5 88.htm#SEC640604 PEsolve sing_1 737.htm#SEC1813605 PH_ais sing_2 106.htm#SEC2182606 PH_nais sing_2 107.htm#SEC2183607 PLURAL sing_4 70.htm#SEC510608 PLURAL LIBs Non-commutative libraries sing_ 546.htm#SEC598609 ParToVar sing_2 283.htm#SEC2359610 Parallelization Parallelization with ssi links sing_ 852.htm#SEC904611 Parallelization sing_9 82.htm#IDX429624 Orlik-Solomon sing_2187.htm#IDX870 625 Output, formatting of sing_793.htm#SEC845 626 PBW sing_511.htm#IDX320 627 PBW basis sing_478.htm#SEC519 628 PBW_eqDeg sing_529.htm#SEC581 629 PBW_maxDeg sing_530.htm#SEC582 630 PBW_maxMonom sing_531.htm#SEC583 631 PEsolve sing_1687.htm#SEC1763 632 PH_ais sing_2209.htm#SEC2285 633 PH_nais sing_2210.htm#SEC2286 634 PLURAL sing_413.htm#SEC453 635 PLURAL LIBs Non-commutative libraries sing_489.htm#SEC541 636 ParToVar sing_2363.htm#SEC2439 637 Parallelization Parallelization with ssi links sing_795.htm#SEC847 638 Parallelization sing_931.htm#IDX489 612 639 Parameter list sing_44.htm#SEC81 613 Parameters sing_ 849.htm#SEC901614 Parametrization sing_1 408.htm#IDX540615 Parametrization, image. sing_1 418.htm#IDX552616 PartC sing_22 29.htm#SEC2305617 PartitionVar sing_2 280.htm#SEC2356618 Path names Notes for Singular users sing_2 473.htm#SEC2559619 PerfectPowerTest sing_18 95.htm#SEC1971620 Perturbation walk sing_11 93.htm#IDX488640 Parameters sing_792.htm#SEC844 641 Parametrization sing_1358.htm#IDX604 642 Parametrization, image. sing_1368.htm#IDX616 643 PartC sing_2287.htm#SEC2363 644 PartitionVar sing_2360.htm#SEC2436 645 Path names Notes for Singular users sing_2500.htm#SEC2586 646 PerfectPowerTest sing_1845.htm#SEC1921 647 Perturbation walk sing_1142.htm#IDX550 621 648 Pfister, Gerhard sing_1.htm#IDX19 622 649 Pipe links sing_116.htm#SEC156 623 PocklingtonLehmer sing_1 934.htm#SEC2010624 Poincare polynomial sing_21 69.htm#IDX858625 Polar curves sing_8 74.htm#SEC926626 PollardRho sing_1 935.htm#SEC2011627 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2 109.htm#IDX759628 PolyBoRi, Boolean Groebner Basis sing_2 111.htm#IDX760629 PolyBoRi, Boolean Groebner Basis sing_2 112.htm#IDX761630 PolyBoRi, Boolean Groebner Basis sing_2 113.htm#IDX762631 PolyBoRi, Boolean Groebner Basis sing_2 114.htm#IDX763632 PolyBoRi, Boolean Groebner Basis sing_2 115.htm#IDX764633 PolyBoRi, Boolean Groebner Basis sing_2 116.htm#IDX765634 PolyBoRi, Boolean Groebner Basis sing_2 117.htm#IDX766635 PolyBoRi, Boolean Groebner Basis sing_2 118.htm#IDX767636 PolyBoRi, Boolean Groebner Basis sing_2 119.htm#IDX768637 PolyBoRi, Boolean Groebner Basis sing_2 120.htm#IDX769638 PolyBoRi, Boolean Groebner Basis sing_2 121.htm#IDX770639 PolyBoRi, Boolean Groebner Basis sing_2 122.htm#IDX771640 PolyBoRi, Boolean Groebner Basis sing_2 123.htm#IDX772641 PolyBoRi, Boolean Groebner Basis sing_2 125.htm#IDX774642 PolyBoRi, zero-supressed decision diagram sing_2 124.htm#IDX773643 Polybori, Boolean Groebner Basis sing_2 126.htm#IDX775644 Polynomial data sing_8 90.htm#SEC942645 Pottier algorithm sing_ 911.htm#SEC968650 PocklingtonLehmer sing_1884.htm#SEC1960 651 Poincare polynomial sing_2199.htm#IDX894 652 Polar curves sing_817.htm#SEC869 653 PollardRho sing_1885.htm#SEC1961 654 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2212.htm#IDX910 655 PolyBoRi, Boolean Groebner Basis sing_2214.htm#IDX911 656 PolyBoRi, Boolean Groebner Basis sing_2215.htm#IDX912 657 PolyBoRi, Boolean Groebner Basis sing_2216.htm#IDX913 658 PolyBoRi, Boolean Groebner Basis sing_2217.htm#IDX914 659 PolyBoRi, Boolean Groebner Basis sing_2218.htm#IDX915 660 PolyBoRi, Boolean Groebner Basis sing_2219.htm#IDX916 661 PolyBoRi, Boolean Groebner Basis sing_2220.htm#IDX917 662 PolyBoRi, Boolean Groebner Basis sing_2221.htm#IDX918 663 PolyBoRi, Boolean Groebner Basis sing_2222.htm#IDX919 664 PolyBoRi, Boolean Groebner Basis sing_2223.htm#IDX920 665 PolyBoRi, Boolean Groebner Basis sing_2224.htm#IDX921 666 PolyBoRi, Boolean Groebner Basis sing_2225.htm#IDX922 667 PolyBoRi, Boolean Groebner Basis sing_2226.htm#IDX923 668 PolyBoRi, Boolean Groebner Basis sing_2228.htm#IDX925 669 PolyBoRi, zero-supressed decision diagram sing_2227.htm#IDX924 670 Polybori, Boolean Groebner Basis sing_2229.htm#IDX926 671 Polynomial data sing_833.htm#SEC885 672 Pottier algorithm sing_854.htm#SEC911 646 673 Preface sing_1.htm#SEC1 647 Prep sing_9 63.htm#SEC1039648 Primary decomposition Primary decomposition sing_8 67.htm#SEC919649 PrimdecA sing_1 245.htm#SEC1321650 PrimdecB sing_1 246.htm#SEC1322674 Prep sing_907.htm#SEC983 675 Primary decomposition Primary decomposition sing_810.htm#SEC862 676 PrimdecA sing_1194.htm#SEC1270 677 PrimdecB sing_1195.htm#SEC1271 651 678 Procedure definition Procedure definition sing_43.htm#SEC78 652 679 Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84 653 680 Procedures sing_42.htm#SEC77 654 681 Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14 655 Procedures and libraries sing_ 846.htm#SEC898682 Procedures and libraries sing_789.htm#SEC841 656 683 Procedures in a library Procedures in a library sing_54.htm#SEC91 657 Product orderings sing_8 99.htm#SEC951658 Programming sing_ 844.htm#SEC896659 PtoCrep sing_9 64.htm#SEC1040660 Puiseux expansion sing_1 502.htm#IDX563661 Puiseux expansion sing_15 90.htm#IDX685662 Puiseux pairs Invariants of plane curve singularities sing_8 77.htm#SEC929663 Puiseux pairs sing_15 96.htm#IDX690664 Qso3Casimir sing_ 734.htm#SEC786665 Quotient sing_17 79.htm#SEC1855666 QuotientEquations sing_1 626.htm#SEC1702667 Rational curves sing_1 408.htm#IDX541668 ReJunkUseHomo sing_13 94.htm#SEC1470669 ReesAlgebra sing_13 61.htm#SEC1437670 References sing_ 926.htm#SEC1000671 References (plural) sing_ 538.htm#SEC588672 Release Notes sing_24 69.htm#SEC2545673 ResTree sing_14 54.htm#SEC1530684 Product orderings sing_842.htm#SEC894 685 Programming sing_787.htm#SEC839 686 PtoCrep sing_908.htm#SEC984 687 Puiseux expansion sing_1452.htm#IDX627 688 Puiseux expansion sing_1540.htm#IDX749 689 Puiseux pairs Invariants of plane curve singularities sing_820.htm#SEC872 690 Puiseux pairs sing_1546.htm#IDX754 691 Qso3Casimir sing_677.htm#SEC729 692 Quotient sing_1729.htm#SEC1805 693 QuotientEquations sing_1576.htm#SEC1652 694 Rational curves sing_1358.htm#IDX605 695 ReJunkUseHomo sing_1344.htm#SEC1420 696 ReesAlgebra sing_1311.htm#SEC1387 697 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singularities, branches of Branches of space curve singularities sing_8 78.htm#SEC930758 Space curve singularities, branches of Branches of space curve singularities sing_821.htm#SEC873 733 759 Special characters sing_36.htm#SEC64 734 Splitting lemma sing_24 10.htm#IDX900735 Sres sing_10 60.htm#SEC1136760 Splitting lemma sing_2490.htm#IDX984 761 Sres sing_1009.htm#SEC1085 736 762 Ssi file links sing_114.htm#SEC154 737 763 Ssi links sing_113.htm#SEC153 738 764 Ssi tcp links sing_115.htm#SEC155 739 Ssyz sing_10 61.htm#SEC1137740 StabEqn sing_1 627.htm#SEC1703741 StabEqnId sing_1 628.htm#SEC1704742 StabOrder sing_1 629.htm#SEC1705743 Standard Bases Computing Groebner and Standard Bases sing_ 854.htm#SEC906744 Standard bases sing_ 902.htm#SEC954745 StartOrderingV sing_14 96.htm#SEC1572765 Ssyz sing_1010.htm#SEC1086 766 StabEqn sing_1577.htm#SEC1653 767 StabEqnId sing_1578.htm#SEC1654 768 StabOrder sing_1579.htm#SEC1655 769 Standard Bases Computing Groebner and Standard Bases 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chern.lib sing_2233.htm#SEC2309 1187 chernCharPoly sing_2280.htm#SEC2356 1188 chernPoly sing_2279.htm#SEC2355 1189 chern_lib sing_2233.htm#SEC2309 1190 chineseRem sing_1871.htm#SEC1947 1191 chinrem sing_210.htm#SEC250 1192 chinrempoly sing_2477.htm#SEC2553 1193 chinrestp sing_1930.htm#SEC2006 1194 cimonom.lib sing_2290.htm#SEC2366 1195 cimonom_lib sing_2290.htm#SEC2366 1196 cisimplicial.lib sing_1110.htm#SEC1186 1197 cisimplicial_lib sing_1110.htm#SEC1186 1198 classify sing_1472.htm#SEC1548 1199 classify.lib sing_1470.htm#SEC1546 1200 classifyCeq sing_1489.htm#SEC1565 1201 classifyMapGerms.lib classifyMapGerms_lib sing_2303.htm#SEC2379 1202 classifyMapGerms_lib classifyMapGerms_lib sing_2303.htm#SEC2379 1203 classifySimpleMaps sing_2309.htm#SEC2385 1204 classifySimpleMaps1 sing_2310.htm#SEC2386 1205 classify_aeq.lib sing_2294.htm#SEC2370 1206 classify_aeq_lib sing_2294.htm#SEC2370 1207 classify_lib sing_1470.htm#SEC1546 1208 classifyceq.lib sing_1488.htm#IDX649 1209 classifyceq_lib sing_1488.htm#IDX650 1210 classifyci.lib sing_1490.htm#IDX651 1211 classifyci_lib sing_1490.htm#IDX652 1212 classifyicis sing_1491.htm#SEC1567 1213 classpoly sing_2278.htm#SEC2354 1214 cleanTmp sing_2149.htm#SEC2225 1215 cleanunit sing_1383.htm#SEC1459 1216 cleardenom sing_211.htm#SEC251 1217 close sing_212.htm#SEC252 1218 closed_points sing_1786.htm#SEC1862 1219 closetex sing_1753.htm#SEC1829 1220 closureFrac sing_1231.htm#SEC1307 1221 coDim sing_2305.htm#SEC2381 1222 coDimMap sing_2304.htm#SEC2380 1223 coHom sing_753.htm#SEC805 1224 codim sing_1584.htm#SEC1660 1225 codimension sing_2000.htm#SEC2076 1226 coding theory sing_832.htm#SEC884 1227 coef sing_213.htm#SEC253 1228 coefficient sing_2161.htm#IDX820 1229 coefficient sing_2162.htm#IDX823 1230 coefficient sing_2163.htm#IDX827 1189 1231 coefficient field sing_139.htm#SEC179 1190 1232 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 1191 coefficients, long sing_848.htm#SEC900 1192 coeffmod sing_1898.htm#SEC1974 1193 coeffs sing_271.htm#SEC311 1194 collectDiv sing_1478.htm#SEC1554 1195 colrank sing_1870.htm#SEC1946 1196 colred sing_1106.htm#SEC1182 1197 commRing sing_841.htm#SEC893 1198 comma sing_461.htm#SEC501 1233 coefficients, long sing_791.htm#SEC843 1234 coeffmod sing_1848.htm#SEC1924 1235 coeffs sing_214.htm#SEC254 1236 colength of derivations curveColengthDerivations sing_2315.htm#IDX938 1237 collectDiv sing_1428.htm#SEC1504 1238 colrank sing_1820.htm#SEC1896 1239 colred sing_1055.htm#SEC1131 1240 commRing sing_784.htm#SEC836 1241 comma sing_404.htm#SEC444 1199 1242 command,custom Commands for user defined types sing_181.htm#SEC221 1200 command-line option, setting value of sing_ 406.htm#IDX2751201 command-line option, value of sing_ 406.htm#IDX2731202 command-line options, print all values of sing_ 406.htm#IDX2721243 command-line option, setting value of sing_349.htm#IDX275 1244 command-line option, value of sing_349.htm#IDX273 1245 command-line options, print all values of sing_349.htm#IDX272 1203 1246 command-line options, short help Command line options sing_19.htm#IDX38 1204 commands (plural) sing_ 503.htm#IDX2961247 commands (plural) sing_446.htm#IDX296 1205 1248 comment sing_36.htm#IDX108 1206 compareTasks sing_10 70.htm#SEC11461207 completeReduction sing_1 712.htm#SEC17881249 compareTasks sing_1019.htm#SEC1095 1250 completeReduction sing_1662.htm#SEC1738 1208 1251 complex sing_28.htm#IDX75 1209 complexSingType sing_1536.htm#SEC1612 1210 compregb.lib sing_933.htm#SEC1009 1211 compregb_lib sing_933.htm#SEC1009 1212 comprehensive Groebner system sing_933.htm#IDX415 1213 compress sing_1083.htm#SEC1159 1214 computeConstant sing_1181.htm#SEC1257 1215 computeGromovWitten sing_1184.htm#SEC1260 1216 computeN sing_1482.htm#SEC1558 1217 computeV sing_1481.htm#SEC1557 1218 computemcm sing_1440.htm#SEC1516 1219 concat sing_1084.htm#SEC1160 1220 conductor sing_1512.htm#IDX581 1221 conductor, degree sing_1596.htm#IDX691 1252 complexSingType sing_1486.htm#SEC1562 1253 compregb.lib sing_876.htm#SEC952 1254 compregb_lib sing_876.htm#SEC952 1255 comprehensive Groebner system sing_876.htm#IDX415 1256 compress sing_1032.htm#SEC1108 1257 computeConstant sing_1130.htm#SEC1206 1258 computeGromovWitten sing_1133.htm#SEC1209 1259 computeN sing_1432.htm#SEC1508 1260 computeV sing_1431.htm#SEC1507 1261 computemcm sing_1390.htm#SEC1466 1262 concat sing_1033.htm#SEC1109 1263 conductor sing_1239.htm#IDX575 1264 conductor sing_1462.htm#IDX645 1265 conductor sing_2313.htm#IDX932 1266 conductor, degree sing_1546.htm#IDX755 1222 1267 cone sing_183.htm#SEC223 1223 cone sing_21 44.htm#IDX8111224 cone sing_21 45.htm#IDX8131225 cone related functions cone related functions sing_186.htm#SEC2261226 cone Link sing_190.htm#SEC2301227 coneVia Inequalities sing_185.htm#SEC2251228 con eViaPoints sing_184.htm#SEC2241229 conic , parametrization, rational point. sing_1417.htm#IDX5511230 con icWithTangents sing_2077.htm#SEC21531231 construct H sing_1441.htm#SEC15171232 construct blwup sing_1442.htm#SEC15181233 construct lastblwup sing_1443.htm#SEC15191234 construct or sing_2161.htm#IDX8441235 constructor sing_2162.htm#IDX8471236 con tact matrix sing_1511.htm#IDX5771237 conta inedQ sing_1791.htm#SEC18671238 contain sAsFace sing_191.htm#SEC2311239 contains InCollection containsInCollection sing_223.htm#SEC2631240 containsIn Support sing_192.htm#SEC2321241 contains PositiveVector containsPositiveVector sing_193.htm#SEC2331242 contains Relatively sing_194.htm#SEC2341243 cont ent sing_1004.htm#SEC10801244 content SB, option sing_364.htm#IDX1721245 cont inue Behavior of continue sing_429.htm#SEC4691246 continue sing_463.htm#SEC5031247 cont raHom sing_811.htm#SEC8631248 contra ct sing_272.htm#SEC3121249 contr ibutors sing_406.htm#IDX1991250 contr ol sing_1862.htm#SEC19381251 control .lib sing_1861.htm#SEC19371252 control Dim sing_1863.htm#SEC19391253 control Example sing_1875.htm#SEC19511254 control _Matrix sing_1564.htm#SEC16401255 control_ lib sing_1861.htm#SEC19371256 con vertdata sing_1438.htm#SEC15141257 conve x geometry sing_2416.htm#SEC24921258 convexHull sing_ 195.htm#SEC2351259 convexIntersection sing_ 196.htm#SEC2361260 convloc sing_ 609.htm#SEC6611261 coordinate change sing_21 41.htm#IDX8081262 coordinate change sing_21 42.htm#IDX8091263 coordinate change sing_21 43.htm#IDX8101264 coordinates sing_ 2018.htm#IDX7331265 coords sing_ 2018.htm#SEC20941266 copyTask sing_10 69.htm#SEC11451268 cone sing_2174.htm#IDX847 1269 cone sing_2175.htm#IDX849 1270 coneLink sing_2003.htm#SEC2079 1271 coneViaInequalities sing_2002.htm#SEC2078 1272 coneViaPoints sing_2001.htm#SEC2077 1273 conic, parametrization, rational point. sing_1367.htm#IDX615 1274 conicWithTangents sing_2125.htm#SEC2201 1275 constructH sing_1391.htm#SEC1467 1276 constructblwup sing_1392.htm#SEC1468 1277 constructible set sing_911.htm#IDX448 1278 constructible sets sing_912.htm#IDX452 1279 constructlastblwup sing_1393.htm#SEC1469 1280 constructor sing_2191.htm#IDX880 1281 constructor sing_2192.htm#IDX883 1282 contact matrix sing_1461.htm#IDX641 1283 containedQ sing_1741.htm#SEC1817 1284 containsAsFace sing_2004.htm#SEC2080 1285 containsInCollection containsInCollection sing_2037.htm#SEC2113 1286 containsInSupport sing_2005.htm#SEC2081 1287 containsPositiveVector containsPositiveVector sing_2006.htm#SEC2082 1288 containsRelatively sing_2007.htm#SEC2083 1289 content sing_953.htm#SEC1029 1290 contentSB, option sing_307.htm#IDX172 1291 continue Behavior of continue sing_372.htm#SEC412 1292 continue sing_406.htm#SEC446 1293 contraHom sing_754.htm#SEC806 1294 contract sing_215.htm#SEC255 1295 contributors sing_349.htm#IDX199 1296 control sing_1812.htm#SEC1888 1297 control.lib sing_1811.htm#SEC1887 1298 controlDim sing_1813.htm#SEC1889 1299 controlExample sing_1825.htm#SEC1901 1300 control_Matrix sing_1514.htm#SEC1590 1301 control_lib sing_1811.htm#SEC1887 1302 convertdata sing_1388.htm#SEC1464 1303 convexHull sing_2008.htm#SEC2084 1304 convexIntersection sing_2009.htm#SEC2085 1305 convloc sing_552.htm#SEC604 1306 coordinate change sing_2171.htm#IDX844 1307 coordinate change sing_2172.htm#IDX845 1308 coordinate change sing_2173.htm#IDX846 1309 coordinates sing_1968.htm#IDX797 1310 coords sing_1968.htm#SEC2044 1311 copyTask sing_1018.htm#SEC1094 1267 1312 copyright sing_1.htm#IDX1 1268 corank sing_1523.htm#SEC1599 1269 cornerMonomials sing_1319.htm#SEC1395 1270 countPoints sing_1943.htm#SEC2019 1271 coverings sing_1183.htm#IDX476 1272 coverings sing_1184.htm#IDX480 1273 cpu sing_406.htm#IDX201 1274 cpu sing_406.htm#IDX269 1275 createBO sing_1469.htm#SEC1545 1276 createGradedRingHomomorphism createGradedRingHomomorphism sing_2356.htm#SEC2432 1277 createGroup sing_2349.htm#SEC2425 1278 createQuotientGroup sing_2350.htm#SEC2426 1279 createTask sing_1067.htm#SEC1143 1280 createTorsionFreeGroup createTorsionFreeGroup sing_2351.htm#SEC2427 1281 createlist sing_1451.htm#SEC1527 1282 crypto.lib sing_1916.htm#SEC1992 1283 crypto_lib sing_1916.htm#SEC1992 1284 cup sing_1197.htm#SEC1273 1285 cupproduct sing_1198.htm#SEC1274 1286 curve singularities sing_1502.htm#IDX564 1287 curve singularities sing_1590.htm#IDX686 1288 curvepar.lib sing_1543.htm#SEC1619 1289 curvepar_lib sing_1543.htm#SEC1619 1313 corank sing_1473.htm#SEC1549 1314 cornerMonomials sing_1269.htm#SEC1345 1315 countPoints sing_1893.htm#SEC1969 1316 coverings sing_1132.htm#IDX536 1317 coverings sing_1133.htm#IDX540 1318 cpu sing_349.htm#IDX201 1319 cpu sing_349.htm#IDX269 1320 createBO sing_1419.htm#SEC1495 1321 createGradedRingHomomorphism createGradedRingHomomorphism sing_2436.htm#SEC2512 1322 createGroup sing_2429.htm#SEC2505 1323 createQuotientGroup sing_2430.htm#SEC2506 1324 createTask sing_1016.htm#SEC1092 1325 createTorsionFreeGroup createTorsionFreeGroup sing_2431.htm#SEC2507 1326 createlist sing_1401.htm#SEC1477 1327 crypto.lib sing_1866.htm#SEC1942 1328 crypto_lib sing_1866.htm#SEC1942 1329 cup sing_1146.htm#SEC1222 1330 cupproduct sing_1147.htm#SEC1223 1331 curve singularities sing_1452.htm#IDX628 1332 curve singularities sing_1540.htm#IDX750 1333 curve singularity sing_2311.htm#IDX927 1334 curveColengthDerivations curveColengthDerivations sing_2315.htm#SEC2391 1335 curveConductorMult sing_2313.htm#SEC2389 1336 curveDeligneNumber sing_2314.htm#SEC2390 1337 curveDeltaInv sing_2312.htm#SEC2388 1338 curveInv.lib sing_2311.htm#SEC2387 1339 curveInv_lib sing_2311.htm#SEC2387 1340 curvepar.lib sing_1493.htm#SEC1569 1341 curvepar_lib sing_1493.htm#SEC1569 1290 1342 custom assignment Assignments for user defined types sing_182.htm#SEC222 1291 1343 custom command Commands for user defined types sing_181.htm#SEC221 1292 1344 custom type Definition of a user defined type sing_178.htm#SEC218 1293 customstd.so sing_2467.htm#SEC2543 1294 cycleLength sing_2053.htm#SEC2129 1295 cyclePoints sing_2057.htm#SEC2133 1296 cyclic sing_991.htm#SEC1067 1297 cyclic code Codes and the decoding problem sing_920.htm#SEC979 1298 cyclotomic sing_1677.htm#SEC1753 1299 datetime sing_273.htm#SEC313 1300 dbprint sing_274.htm#SEC314 1301 deRham.lib sing_2413.htm#SEC2489 1302 deRhamCohom sing_626.htm#SEC678 1303 deRhamCohomIdeal sing_627.htm#SEC679 1304 deRhamCohomology sing_2414.htm#SEC2490 1305 deRham_lib sing_2413.htm#SEC2489 1306 debugLib, option sing_364.htm#IDX176 1307 debug_log sing_1533.htm#SEC1609 1345 customstd.lib sing_2203.htm#SEC2279 1346 customstd_lib sing_2203.htm#SEC2279 1347 cycleLength sing_2062.htm#SEC2138 1348 cyclePoints sing_2066.htm#SEC2142 1349 cyclic sing_940.htm#SEC1016 1350 cyclic code Codes and the decoding problem sing_863.htm#SEC922 1351 cyclotomic sing_1627.htm#SEC1703 1352 datetime sing_216.htm#SEC256 1353 dbprint sing_217.htm#SEC257 1354 deRham.lib sing_2493.htm#SEC2569 1355 deRhamCohom sing_569.htm#SEC621 1356 deRhamCohomIdeal sing_570.htm#SEC622 1357 deRhamCohomology sing_2494.htm#SEC2570 1358 deRham_lib sing_2493.htm#SEC2569 1359 debugLib, option sing_307.htm#IDX176 1360 debug_log sing_1483.htm#SEC1559 1308 1361 debugger Source code debugger sing_66.htm#SEC103 1309 1362 debugging library code Source code debugger sing_66.htm#SEC103 1310 dec1var sing_1 250.htm#SEC13261311 decimal sing_1 917.htm#SEC19931312 decode sing_18 53.htm#SEC19291313 decodeCode sing_18 55.htm#SEC19311314 decodeRandom sing_18 54.htm#SEC19301315 decodeRandomFL sing_18 58.htm#SEC19341316 decodeSV sing_1 835.htm#SEC19111317 decodegb.lib sing_1 840.htm#SEC19161318 decodegb_lib sing_1 840.htm#SEC19161319 decoding, decoding problem Codes and the decoding problem sing_ 920.htm#SEC9801320 decoef sing_18 83.htm#SEC19591321 decone sing_21 44.htm#IDX8121322 decone sing_21 45.htm#IDX8141363 dec1var sing_1199.htm#SEC1275 1364 decimal sing_1867.htm#SEC1943 1365 decode sing_1803.htm#SEC1879 1366 decodeCode sing_1805.htm#SEC1881 1367 decodeRandom sing_1804.htm#SEC1880 1368 decodeRandomFL sing_1808.htm#SEC1884 1369 decodeSV sing_1785.htm#SEC1861 1370 decodegb.lib sing_1790.htm#SEC1866 1371 decodegb_lib sing_1790.htm#SEC1866 1372 decoding, decoding problem Codes and the decoding problem sing_863.htm#SEC923 1373 decoef sing_1833.htm#SEC1909 1374 decone sing_2174.htm#IDX848 1375 decone sing_2175.htm#IDX850 1323 1376 def sing_83.htm#SEC123 1324 1377 def declarations sing_84.htm#SEC124 1325 defRes, option sing_3 64.htm#IDX1771378 defRes, option sing_307.htm#IDX177 1326 1379 default argument sing_44.htm#SEC81 1327 defineHomogeneous sing_2 389.htm#SEC24651328 defined sing_2 75.htm#SEC3151329 defl sing_1 400.htm#SEC14761330 deform sing_1 635.htm#SEC17111331 deform.lib sing_15 54.htm#SEC16301332 deform_lib sing_15 54.htm#SEC16301333 defring sing_ 1033.htm#SEC11091334 defringp sing_ 1035.htm#SEC11111335 defrings sing_ 1034.htm#SEC11101336 deg sing_2 76.htm#SEC3161337 degBound sing_ 443.htm#SEC4831338 degree Miscellaneous oddities sing_2 77.htm#SEC3171339 degree sing_4 66.htm#IDX2861340 degree lexicographical ordering sing_8 95.htm#IDX3891341 degree of a polynomial Miscellaneous oddities sing_4 66.htm#IDX2901342 degree reverse lexicographical ordering sing_8 95.htm#IDX3871343 degreeDivisor sing_2 244.htm#SEC23201344 degreeFormalDivisor sing_2 252.htm#SEC23281345 degreepart sing_1 743.htm#SEC18191380 defineHomogeneous sing_2469.htm#SEC2545 1381 defined sing_218.htm#SEC258 1382 defl sing_1350.htm#SEC1426 1383 deform sing_1585.htm#SEC1661 1384 deform.lib sing_1504.htm#SEC1580 1385 deform_lib sing_1504.htm#SEC1580 1386 defring sing_982.htm#SEC1058 1387 defringp sing_984.htm#SEC1060 1388 defrings sing_983.htm#SEC1059 1389 deg sing_219.htm#SEC259 1390 degBound sing_386.htm#SEC426 1391 degree Miscellaneous oddities sing_220.htm#SEC260 1392 degree sing_409.htm#IDX286 1393 degree lexicographical ordering sing_838.htm#IDX389 1394 degree of a polynomial Miscellaneous oddities sing_409.htm#IDX290 1395 degree reverse lexicographical ordering sing_838.htm#IDX387 1396 degreeDivisor sing_2324.htm#SEC2400 1397 degreeFormalDivisor sing_2332.htm#SEC2408 1398 degreepart sing_1693.htm#SEC1769 1346 1399 delete sing_121.htm#SEC161 1347 delete sing_278.htm#SEC318 1348 delete sing_325.htm#SEC365 1349 deleteGenerator sing_641.htm#SEC693 1350 deleteSublist sing_941.htm#SEC1017 1351 delta sing_1602.htm#SEC1678 1352 delta invariant sing_1284.htm#IDX511 1353 delta invariant sing_1602.htm#IDX696 1354 delta invariant. sing_1276.htm#IDX504 1355 delta invariant. sing_1277.htm#IDX507 1356 delta invariant. sing_1278.htm#IDX510 1357 deltaLoc sing_1284.htm#SEC1360 1358 denom_list sing_406.htm#IDX203 1359 denominator sing_279.htm#SEC319 1360 depth sing_1199.htm#SEC1275 1361 depthIdeal sing_1260.htm#SEC1336 1362 derivate sing_1709.htm#SEC1785 1363 derivation sing_2158.htm#IDX835 1364 desingularization sing_2300.htm#IDX887 1365 desingularization sing_2301.htm#SEC2377 1366 det sing_280.htm#SEC320 1367 det_B sing_1125.htm#SEC1201 1368 detadj sing_1618.htm#SEC1694 1369 determinacy sing_2412.htm#SEC2488 1370 determinecenter sing_1423.htm#SEC1499 1371 detropicalise sing_2095.htm#SEC2171 1372 develop sing_1592.htm#SEC1668 1373 diag sing_1085.htm#SEC1161 1374 diagInvariants sing_1298.htm#SEC1374 62096 1375 diag_test sing_1121.htm#SEC1197 1376 diff sing_281.htm#SEC321 1377 diffRat sing_840.htm#SEC892 1378 difpoly2tex sing_1884.htm#SEC1960 1379 dim sing_282.htm#SEC322 1380 dim (plural) sing_506.htm#SEC546 1381 dimGradedPart sing_1491.htm#SEC1567 11262 1382 dimH sing_1490.htm#SEC1566 38534 1383 dimMon sing_1240.htm#SEC1316 1384 dim_slocus sing_1636.htm#SEC1712 1385 dimension sing_197.htm#SEC237 1386 dimensionOfLocalization dimensionOfLocalization sing_2288.htm#SEC2364 1387 direct_boolean_poly sing_2113.htm#SEC2189 49893 1388 direct_from_boolean_poly direct_from_boolean_poly sing_2119.htm#SEC2195 36941 1389 disc sing_1904.htm#SEC1980 1390 discr sing_1658.htm#SEC1734 1391 discrepancy sing_1476.htm#SEC1552 1392 disp_zdd sing_2126.htm#SEC2202 41439 1393 displayCohom sing_1492.htm#SEC1568 22633 1394 displayHNE sing_1595.htm#SEC1671 1395 displayInvariants sing_1597.htm#SEC1673 1396 displayMultsequence sing_1599.htm#SEC1675 1397 displayPuiseuxExpansion displayPuiseuxExpansion sing_2070.htm#SEC2146 1398 displayTropicalLifting displayTropicalLifting sing_2068.htm#SEC2144 1399 distributed computing sing_984.htm#IDX434 1400 distributed computing sing_1024.htm#IDX436 1401 distributed computing sing_1066.htm#IDX450 1400 delete sing_221.htm#SEC261 1401 delete sing_268.htm#SEC308 1402 deleteGenerator sing_584.htm#SEC636 1403 deleteSublist sing_884.htm#SEC960 1404 deligne number curveColengthDerivations sing_2311.htm#IDX929 1405 deligne number sing_2314.htm#IDX934 1406 deligne number sing_2315.htm#IDX936 1407 delta sing_1552.htm#SEC1628 1408 delta invariant sing_1233.htm#IDX573 1409 delta invariant sing_1552.htm#IDX760 1410 delta invariant sing_2312.htm#IDX930 1411 delta invariant. sing_1225.htm#IDX566 1412 delta invariant. sing_1226.htm#IDX569 1413 delta invariant. sing_1227.htm#IDX572 1414 deltaLoc sing_1233.htm#SEC1309 1415 denom_list sing_349.htm#IDX203 1416 denominator sing_222.htm#SEC262 1417 depth sing_1148.htm#SEC1224 1418 depthIdeal sing_1209.htm#SEC1285 1419 derivate sing_1659.htm#SEC1735 1420 derivation sing_2188.htm#IDX871 1421 desingularization sing_2380.htm#IDX965 1422 desingularization sing_2381.htm#SEC2457 1423 det sing_223.htm#SEC263 1424 det_B sing_1074.htm#SEC1150 1425 detadj sing_1568.htm#SEC1644 1426 determinacy sing_2492.htm#SEC2568 1427 determinecenter sing_1373.htm#SEC1449 1428 detropicalise sing_2143.htm#SEC2219 1429 develop sing_1542.htm#SEC1618 1430 diag sing_1034.htm#SEC1110 1431 diagInvariants sing_1248.htm#SEC1324 62096 1432 diag_test sing_1070.htm#SEC1146 1433 diff sing_224.htm#SEC264 1434 diffRat sing_783.htm#SEC835 1435 difpoly2tex sing_1834.htm#SEC1910 1436 dim sing_225.htm#SEC265 1437 dim (plural) sing_449.htm#SEC489 1438 dimGradedPart sing_1441.htm#SEC1517 11262 1439 dimH sing_1440.htm#SEC1516 38534 1440 dimMon sing_1189.htm#SEC1265 1441 dim_slocus sing_1586.htm#SEC1662 1442 dimension sing_2010.htm#SEC2086 1443 dimensionOfLocalization dimensionOfLocalization sing_2368.htm#SEC2444 1444 direct_boolean_poly sing_2216.htm#SEC2292 49893 1445 direct_from_boolean_poly direct_from_boolean_poly sing_2222.htm#SEC2298 36941 1446 disc sing_1854.htm#SEC1930 1447 discr sing_1608.htm#SEC1684 1448 discrepancy sing_1426.htm#SEC1502 1449 discrim sing_919.htm#SEC995 1450 discussion of parametric ideal sing_902.htm#IDX422 1451 disjoint sing_903.htm#IDX425 1452 disp_zdd sing_2229.htm#SEC2305 41439 1453 displayCohom sing_1442.htm#SEC1518 22633 1454 displayHNE sing_1545.htm#SEC1621 1455 displayInvariants sing_1547.htm#SEC1623 1456 displayMultsequence sing_1549.htm#SEC1625 1457 displayPuiseuxExpansion displayPuiseuxExpansion sing_2118.htm#SEC2194 1458 displayTropicalLifting displayTropicalLifting sing_2116.htm#SEC2192 1459 distributed computing sing_933.htm#IDX494 1460 distributed computing sing_973.htm#IDX496 1461 distributed computing sing_1015.htm#IDX510 1402 1462 div Miscellaneous oddities sing_76.htm#SEC116 1403 1463 div sing_93.htm#SEC133 1404 div sing_466.htm#IDX283 1405 divideUnits sing_1880.htm#SEC1956 1406 dividelist sing_1450.htm#SEC1526 1407 division sing_283.htm#SEC323 1408 division (plural) sing_507.htm#SEC547 1409 division, pdivi, reduce sing_961.htm#IDX419 1410 division, reduce sing_960.htm#IDX418 1411 divisor sing_1983.htm#SEC2059 1412 divisorplus sing_2238.htm#SEC2314 1413 divisors negativeformaldivisor sing_2237.htm#IDX861 1414 divisors sing_2238.htm#IDX862 1415 divisors sing_2239.htm#IDX863 1416 divisors sing_2240.htm#IDX864 1417 divisors sing_2241.htm#IDX865 1418 divisors sing_2242.htm#IDX866 1419 divisors sing_2243.htm#IDX867 1420 divisors sing_2244.htm#IDX868 1421 divisors sing_2245.htm#IDX869 1422 divisors sing_2246.htm#IDX870 1423 divisors sing_2247.htm#IDX871 1424 divisors sing_2248.htm#IDX872 1425 divisors sing_2249.htm#IDX873 1426 divisors sing_2250.htm#IDX874 1427 divisors sing_2251.htm#IDX875 1428 divisors sing_2252.htm#IDX876 1429 divisors, polyhedra sing_2253.htm#IDX877 1430 divisors, polyhedra sing_2254.htm#IDX878 1431 divisors, polyhedra sing_2255.htm#IDX879 1432 divisors.lib sing_2236.htm#SEC2312 1433 divisors_lib sing_2236.htm#SEC2312 1434 dmod.lib sing_589.htm#SEC641 1435 dmodAction sing_835.htm#SEC887 1436 dmodActionRat sing_836.htm#SEC888 1437 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_828.htm#SEC880 1438 dmod_lib sing_589.htm#SEC641 1439 dmodapp.lib sing_612.htm#SEC664 1440 dmodapp_lib sing_612.htm#SEC664 1441 dmodloc.lib sing_817.htm#IDX371 1442 dmodloc_lib sing_817.htm#IDX372 1443 dmodoublext sing_812.htm#SEC864 1444 dmodvar.lib sing_645.htm#SEC697 1445 dmodvar_lib sing_645.htm#SEC697 1446 double sing_1988.htm#SEC2064 1447 doubleExt sing_803.htm#SEC855 1448 downloading Download instructions sing_2477.htm#SEC2566 1449 dp, global ordering sing_895.htm#IDX388 1450 drawNewtonSubdivision drawNewtonSubdivision sing_2073.htm#SEC2149 1451 drawTropicalCurve sing_2072.htm#SEC2148 1452 ds, local ordering sing_896.htm#IDX398 1453 dsum sing_1086.htm#SEC1162 1454 dualCone sing_198.htm#SEC238 1455 dualConic sing_2097.htm#SEC2173 1456 dualPart sing_2228.htm#SEC2304 1457 dualPolytope sing_240.htm#SEC280 1458 dual_code sing_1837.htm#SEC1913 1459 dump sing_284.htm#SEC324 1460 ecart sing_1991.htm#SEC2067 1461 echo sing_444.htm#SEC484 1462 eexgcdN sing_1918.htm#SEC1994 1463 effective sing_2246.htm#SEC2322 1464 egcdMain sing_1784.htm#SEC1860 1465 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2428.htm#SEC2504 1466 ehrhartRing sing_1294.htm#SEC1370 16966 1467 eigenvals sing_1133.htm#SEC1209 1468 eigenvalue sing_377.htm#SEC417 1469 eigenvalue sing_1133.htm#IDX456 1470 eigenvalues sing_1377.htm#SEC1453 1471 elemSymmId sing_992.htm#SEC1068 1472 elim sing_1170.htm#SEC1246 1473 elim.lib sing_1167.htm#SEC1243 1474 elim1 sing_1171.htm#SEC1247 1475 elim2 sing_1172.htm#SEC1248 1476 elimRing sing_1169.htm#SEC1245 1477 elimWeight sing_760.htm#SEC812 1478 elim_lib sing_1167.htm#SEC1243 1479 eliminate sing_285.htm#SEC325 1480 eliminate (plural) sing_508.htm#SEC548 1481 eliminateNC sing_755.htm#SEC807 1482 elimination sing_754.htm#IDX356 1483 elimlinearpart sing_1744.htm#SEC1820 1484 elimpart sing_1745.htm#SEC1821 1485 elimpartanyr sing_1746.htm#SEC1822 1486 elimrep sing_1431.htm#SEC1507 1487 elliptic curve sing_1180.htm#IDX472 1488 elliptic curves sing_1177.htm#IDX466 1489 elliptic curves sing_1183.htm#IDX475 1490 elliptic curves sing_1184.htm#IDX479 1491 ellipticAdd sing_1939.htm#SEC2015 1492 ellipticAllPoints sing_1944.htm#SEC2020 1493 ellipticMult sing_1940.htm#SEC2016 1494 ellipticNF sing_2060.htm#SEC2136 1495 ellipticNFDB sing_2061.htm#SEC2137 1496 ellipticRandomCurve sing_1941.htm#SEC2017 1497 ellipticRandomPoint sing_1942.htm#SEC2018 1498 ellipticcovers.lib sing_1177.htm#IDX460 1499 ellipticcovers_lib sing_1177.htm#IDX461 1500 else sing_434.htm#SEC474 1501 embedMat sing_786.htm#SEC838 1502 emptyFan sing_224.htm#SEC264 1503 encode sing_1845.htm#SEC1921 1504 endomorphism filtration sing_1576.htm#IDX662 1505 endvfilt sing_1576.htm#SEC1652 1506 engine sing_642.htm#SEC694 1507 envelop sing_969.htm#SEC1045 1508 envelopdg sing_970.htm#SEC1046 1509 envelope sing_509.htm#SEC549 1510 enveloping algebra sing_406.htm#IDX207 1511 enveloping algebra sing_547.htm#IDX300 1464 div sing_409.htm#IDX283 1465 divideUnits sing_1830.htm#SEC1906 1466 dividelist sing_1400.htm#SEC1476 1467 division sing_226.htm#SEC266 1468 division sing_904.htm#IDX429 1469 division sing_905.htm#IDX432 1470 division (plural) sing_450.htm#SEC490 1471 divisor sing_1933.htm#SEC2009 1472 divisorplus sing_2318.htm#SEC2394 1473 divisors negativeformaldivisor sing_2317.htm#IDX939 1474 divisors sing_2318.htm#IDX940 1475 divisors sing_2319.htm#IDX941 1476 divisors sing_2320.htm#IDX942 1477 divisors sing_2321.htm#IDX943 1478 divisors sing_2322.htm#IDX944 1479 divisors sing_2323.htm#IDX945 1480 divisors sing_2324.htm#IDX946 1481 divisors sing_2325.htm#IDX947 1482 divisors sing_2326.htm#IDX948 1483 divisors sing_2327.htm#IDX949 1484 divisors sing_2328.htm#IDX950 1485 divisors sing_2329.htm#IDX951 1486 divisors sing_2330.htm#IDX952 1487 divisors sing_2331.htm#IDX953 1488 divisors sing_2332.htm#IDX954 1489 divisors, polyhedra sing_2333.htm#IDX955 1490 divisors, polyhedra sing_2334.htm#IDX956 1491 divisors, polyhedra sing_2335.htm#IDX957 1492 divisors.lib sing_2316.htm#SEC2392 1493 divisors_lib sing_2316.htm#SEC2392 1494 dmod.lib sing_532.htm#SEC584 1495 dmodAction sing_778.htm#SEC830 1496 dmodActionRat sing_779.htm#SEC831 1497 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_771.htm#SEC823 1498 dmod_lib sing_532.htm#SEC584 1499 dmodapp.lib sing_555.htm#SEC607 1500 dmodapp_lib sing_555.htm#SEC607 1501 dmodloc.lib sing_760.htm#IDX371 1502 dmodloc_lib sing_760.htm#IDX372 1503 dmodoublext sing_755.htm#SEC807 1504 dmodvar.lib sing_588.htm#SEC640 1505 dmodvar_lib sing_588.htm#SEC640 1506 double sing_1938.htm#SEC2014 1507 doubleExt sing_746.htm#SEC798 1508 downloading Download instructions sing_2504.htm#SEC2593 1509 dp, global ordering sing_838.htm#IDX388 1510 drawNewtonSubdivision drawNewtonSubdivision sing_2121.htm#SEC2197 1511 drawTropicalCurve sing_2120.htm#SEC2196 1512 ds, local ordering sing_839.htm#IDX398 1513 dsum sing_1035.htm#SEC1111 1514 dualCone sing_2011.htm#SEC2087 1515 dualConic sing_2145.htm#SEC2221 1516 dualPart sing_2286.htm#SEC2362 1517 dualPolytope sing_2050.htm#SEC2126 1518 dual_code sing_1787.htm#SEC1863 1519 dump sing_227.htm#SEC267 1520 dynamic geometry sing_913.htm#IDX457 1521 dynamic geometry sing_914.htm#IDX461 1522 ecart sing_1941.htm#SEC2017 1523 echo sing_387.htm#SEC427 1524 eexgcdN sing_1868.htm#SEC1944 1525 effective sing_2326.htm#SEC2402 1526 egcdMain sing_1734.htm#SEC1810 1527 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2072.htm#SEC2148 1528 ehrhartRing sing_1244.htm#SEC1320 16966 1529 eigenvals sing_1082.htm#SEC1158 1530 eigenvalue sing_320.htm#SEC360 1531 eigenvalue sing_1082.htm#IDX516 1532 eigenvalues sing_1327.htm#SEC1403 1533 elemSymmId sing_941.htm#SEC1017 1534 elim sing_1119.htm#SEC1195 1535 elim.lib sing_1116.htm#SEC1192 1536 elim1 sing_1120.htm#SEC1196 1537 elim2 sing_1121.htm#SEC1197 1538 elimRing sing_1118.htm#SEC1194 1539 elimWeight sing_703.htm#SEC755 1540 elim_lib sing_1116.htm#SEC1192 1541 eliminate sing_228.htm#SEC268 1542 eliminate (plural) sing_451.htm#SEC491 1543 eliminateNC sing_698.htm#SEC750 1544 elimination sing_697.htm#IDX356 1545 elimlinearpart sing_1694.htm#SEC1770 1546 elimpart sing_1695.htm#SEC1771 1547 elimpartanyr sing_1696.htm#SEC1772 1548 elimrep sing_1381.htm#SEC1457 1549 elliptic curve sing_1129.htm#IDX532 1550 elliptic curves sing_1126.htm#IDX526 1551 elliptic curves sing_1132.htm#IDX535 1552 elliptic curves sing_1133.htm#IDX539 1553 ellipticAdd sing_1889.htm#SEC1965 1554 ellipticAllPoints sing_1894.htm#SEC1970 1555 ellipticMult sing_1890.htm#SEC1966 1556 ellipticNF sing_2069.htm#SEC2145 1557 ellipticNFDB sing_2070.htm#SEC2146 1558 ellipticRandomCurve sing_1891.htm#SEC1967 1559 ellipticRandomPoint sing_1892.htm#SEC1968 1560 ellipticcovers.lib sing_1126.htm#IDX520 1561 ellipticcovers_lib sing_1126.htm#IDX521 1562 else sing_377.htm#SEC417 1563 embedMat sing_729.htm#SEC781 1564 emptyFan sing_2038.htm#SEC2114 1565 encode sing_1795.htm#SEC1871 1566 endomorphism filtration sing_1526.htm#IDX726 1567 endvfilt sing_1526.htm#SEC1602 1568 engine sing_585.htm#SEC637 1569 envelop FamElemsAtEnvCompPoints sing_915.htm#SEC991 1570 envelop sing_915.htm#IDX465 1571 envelop sing_916.htm#IDX469 1572 envelop sing_917.htm#IDX474 1573 envelop sing_918.htm#IDX479 1574 envelope sing_452.htm#SEC492 1575 enveloping algebra sing_349.htm#IDX207 1576 enveloping algebra sing_490.htm#IDX300 1512 1577 environment variable, DISPLAY The online help system sing_16.htm#IDX29 1513 equalJinI sing_1 519.htm#SEC15951514 equalMultiDeg sing_2 382.htm#SEC24581515 equations sing_ 199.htm#SEC2391516 equiRadical sing_1 335.htm#SEC14111517 equidim sing_1 337.htm#SEC14131518 equidimMax sing_1 338.htm#SEC14141519 equidimMaxEHV sing_1 339.htm#SEC14151520 equidimZ sing_13 50.htm#SEC14261521 equising.lib sing_15 59.htm#SEC16351522 equising_lib sing_15 59.htm#SEC16351523 equisingular Tjurina number sing_1 502.htm#IDX5691524 equisingularity ideal sing_15 61.htm#IDX5891525 equisingularity stratum sing_15 62.htm#IDX5901578 equalJinI sing_1469.htm#SEC1545 1579 equalMultiDeg sing_2462.htm#SEC2538 1580 equations sing_2012.htm#SEC2088 1581 equiRadical sing_1285.htm#SEC1361 1582 equidim sing_1287.htm#SEC1363 1583 equidimMax sing_1288.htm#SEC1364 1584 equidimMaxEHV sing_1289.htm#SEC1365 1585 equidimZ sing_1300.htm#SEC1376 1586 equising.lib sing_1509.htm#SEC1585 1587 equising_lib sing_1509.htm#SEC1585 1588 equisingular Tjurina number sing_1452.htm#IDX633 1589 equisingularity ideal sing_1511.htm#IDX653 1590 equisingularity stratum sing_1512.htm#IDX654 1526 1591 error recovery sing_15.htm#SEC21 1527 errorInsert sing_1 848.htm#SEC19241528 errorRand sing_1 849.htm#SEC19251529 errormap sing_2 276.htm#SEC23521530 esIdeal sing_15 61.htm#SEC16371531 esStratum sing_15 62.htm#SEC16381532 essential sing_21 48.htm#IDX8171533 essential sing_21 49.htm#IDX8181534 eta sing_20 55.htm#SEC21311535 euler sing_18 97.htm#SEC19731536 eulerChProj sing_22 18.htm#SEC22941537 eval sing_2 86.htm#SEC3261538 evaluateFormalDivisor evaluateFormalDivisor sing_2 248.htm#SEC23241539 evaluatePDivisor sing_2 254.htm#SEC23301540 evaluate_reynolds sing_16 82.htm#SEC17581541 evalutateIntegral sing_11 82.htm#SEC12581542 example sing_2 88.htm#SEC3281543 example sing_21 50.htm#IDX8191544 example sing_21 51.htm#IDX8211545 example sing_21 52.htm#IDX8231546 example sing_21 53.htm#IDX8251547 example sing_21 54.htm#IDX8271548 example sing_21 55.htm#IDX8291549 example sing_21 56.htm#IDX8321550 execute sing_2 89.htm#SEC3291551 exit sing_ 438.htm#SEC4781552 exp2pt sing_18 85.htm#SEC19611553 expo sing_1 909.htm#SEC19851554 exponents sing_21 60.htm#IDX8401555 export sing_ 431.htm#SEC4711556 exportNuminvs sing_1 302.htm#SEC1378 104231557 exportto sing_ 432.htm#SEC4721592 errorInsert sing_1798.htm#SEC1874 1593 errorRand sing_1799.htm#SEC1875 1594 errormap sing_2356.htm#SEC2432 1595 esIdeal sing_1511.htm#SEC1587 1596 esStratum sing_1512.htm#SEC1588 1597 essential sing_2178.htm#IDX853 1598 essential sing_2179.htm#IDX854 1599 eta sing_2064.htm#SEC2140 1600 euler sing_1847.htm#SEC1923 1601 eulerChProj sing_2276.htm#SEC2352 1602 eval sing_229.htm#SEC269 1603 evaluateFormalDivisor evaluateFormalDivisor sing_2328.htm#SEC2404 1604 evaluatePDivisor sing_2334.htm#SEC2410 1605 evaluate_reynolds sing_1632.htm#SEC1708 1606 evalutateIntegral sing_1131.htm#SEC1207 1607 example sing_231.htm#SEC271 1608 example sing_2180.htm#IDX855 1609 example sing_2181.htm#IDX857 1610 example sing_2182.htm#IDX859 1611 example sing_2183.htm#IDX861 1612 example sing_2184.htm#IDX863 1613 example sing_2185.htm#IDX865 1614 example sing_2186.htm#IDX868 1615 execute sing_232.htm#SEC272 1616 exit sing_381.htm#SEC421 1617 exp2pt sing_1835.htm#SEC1911 1618 expo sing_1859.htm#SEC1935 1619 exponents sing_2190.htm#IDX876 1620 export sing_374.htm#SEC414 1621 exportNuminvs sing_1252.htm#SEC1328 10423 1622 exportto sing_375.htm#SEC415 1558 1623 expression list sing_72.htm#IDX128 1559 expression list sing_471.htm#IDX293 1560 ext-module purityfiltration_lib sing_795.htm#IDX362 1561 extcurve sing_1831.htm#SEC1907 1562 extdevelop sing_1593.htm#SEC1669 1563 extend sing_965.htm#SEC1041 1564 extendWeyl sing_829.htm#SEC881 1565 extendedTensor sing_761.htm#SEC813 1566 extendring sing_1036.htm#SEC1112 1567 extension of rings sing_1355.htm#IDX518 1568 exterior basis sing_1112.htm#IDX453 1569 exterior power sing_1114.htm#IDX455 1570 exteriorBasis sing_1112.htm#SEC1188 1571 exteriorPower sing_1114.htm#SEC1190 1572 extgcd sing_290.htm#SEC330 1573 fVector sing_227.htm#SEC267 1574 fVector sing_2432.htm#SEC2508 1575 fVectorP(polymake) sing_2432.htm#SEC2508 1576 facFirstShift sing_748.htm#SEC800 1577 facFirstWeyl sing_744.htm#SEC796 1578 facGBIdeal sing_1320.htm#SEC1396 1579 facShift sing_747.htm#SEC799 1580 facSubWeyl sing_746.htm#SEC798 1581 facWeyl sing_743.htm#SEC795 1582 facetVertexLatticeDistances facetVertexLatticeDistances sing_2429.htm#SEC2505 1583 facetWidth sing_2430.htm#SEC2506 1584 facetWidths sing_2431.htm#SEC2507 1585 facets sing_200.htm#SEC240 1586 facstd sing_291.htm#SEC331 1587 factmodd sing_292.htm#SEC332 1588 factorH sing_956.htm#SEC1032 1589 factorLenstraECM sing_1948.htm#SEC2024 1590 factorMain sing_1785.htm#SEC1861 1591 factorgroup sing_2372.htm#SEC2448 1592 factorial sing_942.htm#SEC1018 1593 factorization sing_372.htm#SEC412 1594 factorization sing_1142.htm#IDX457 1595 factorize sing_293.htm#SEC333 1624 expression list sing_414.htm#IDX293 1625 ext-module purityfiltration_lib sing_738.htm#IDX362 1626 extcurve sing_1781.htm#SEC1857 1627 extdevelop sing_1543.htm#SEC1619 1628 extendGC sing_910.htm#SEC986 1629 extendWeyl sing_772.htm#SEC824 1630 extendedTensor sing_704.htm#SEC756 1631 extendpoly sing_909.htm#SEC985 1632 extendring sing_985.htm#SEC1061 1633 extension of rings sing_1305.htm#IDX582 1634 exterior basis sing_1061.htm#IDX513 1635 exterior power sing_1063.htm#IDX515 1636 exteriorBasis sing_1061.htm#SEC1137 1637 exteriorPower sing_1063.htm#SEC1139 1638 extgcd sing_233.htm#SEC273 1639 fVector sing_2041.htm#SEC2117 1640 fVectorP sing_2073.htm#SEC2149 1641 facFirstShift sing_691.htm#SEC743 1642 facFirstWeyl sing_687.htm#SEC739 1643 facGBIdeal sing_1270.htm#SEC1346 1644 facShift sing_690.htm#SEC742 1645 facSubWeyl sing_689.htm#SEC741 1646 facWeyl sing_686.htm#SEC738 1647 faceContaining sing_2013.htm#SEC2089 1648 facetVertexLatticeDistances facetVertexLatticeDistances sing_2074.htm#SEC2150 1649 facetWidth sing_2075.htm#SEC2151 1650 facetWidths sing_2076.htm#SEC2152 1651 facets sing_2014.htm#SEC2090 1652 facstd sing_234.htm#SEC274 1653 factmodd sing_235.htm#SEC275 1654 factorH sing_899.htm#SEC975 1655 factorLenstraECM sing_1898.htm#SEC1974 1656 factorMain sing_1735.htm#SEC1811 1657 factorgroup sing_2452.htm#SEC2528 1658 factorial sing_885.htm#SEC961 1659 factorization sing_315.htm#SEC355 1660 factorization sing_1091.htm#IDX517 1661 factorize sing_236.htm#SEC276 1596 1662 factory sing_1.htm#IDX2 1597 fan sing_221.htm#SEC261 1598 fan sing_2044.htm#IDX738 1599 fan related functions fan related functions sing_222.htm#SEC262 1600 fanViaCones sing_225.htm#SEC265 1601 farey sing_294.htm#SEC334 1602 fareypoly sing_2257.htm#SEC2333 1603 fastExpt sing_1893.htm#SEC1969 1604 fastHC, option sing_364.htm#IDX153 1605 fastelim sing_1747.htm#SEC1823 1606 fetch sing_295.htm#SEC335 1607 fetch (plural) sing_510.htm#SEC550 1608 fetchall sing_1037.htm#SEC1113 1609 ffmodStd sing_2261.htm#SEC2337 1610 ffmodstd.lib sing_2256.htm#SEC2332 1611 ffmodstd_lib sing_2256.htm#SEC2332 1612 ffsolve sing_1736.htm#SEC1812 1613 ffsolve.lib sing_1735.htm#SEC1811 1614 ffsolve_lib sing_1735.htm#SEC1811 1615 fglm sing_296.htm#SEC336 1616 fglm sing_403.htm#IDX187 1617 fglm_solve sing_1763.htm#SEC1839 1618 fglmquot sing_297.htm#SEC337 1619 fibonacci sing_943.htm#SEC1019 1663 fan sing_184.htm#SEC224 1664 fan sing_2053.htm#IDX802 1665 fanViaCones sing_2039.htm#SEC2115 1666 farey sing_237.htm#SEC277 1667 fareypoly sing_2337.htm#SEC2413 1668 fastExpt sing_1843.htm#SEC1919 1669 fastHC, option sing_307.htm#IDX153 1670 fastelim sing_1697.htm#SEC1773 1671 fetch sing_238.htm#SEC278 1672 fetch (plural) sing_453.htm#SEC493 1673 fetchall sing_986.htm#SEC1062 1674 ffmodStd sing_2341.htm#SEC2417 1675 ffmodstd.lib sing_2336.htm#SEC2412 1676 ffmodstd_lib sing_2336.htm#SEC2412 1677 ffsolve sing_1686.htm#SEC1762 1678 ffsolve.lib sing_1685.htm#SEC1761 1679 ffsolve_lib sing_1685.htm#SEC1761 1680 fglm sing_239.htm#SEC279 1681 fglm sing_346.htm#IDX187 1682 fglm_solve sing_1713.htm#SEC1789 1683 fglmquot sing_240.htm#SEC280 1684 fibonacci sing_886.htm#SEC962 1620 1685 field sing_139.htm#SEC179 1621 1686 file, .singularrc sing_20.htm#IDX71 1622 filecmd sing_2 98.htm#SEC3381623 filtration purityfiltration_lib sing_7 95.htm#IDX3631624 finalCharts sing_14 55.htm#SEC15311625 find sing_2 99.htm#SEC3391626 findAuto sing_ 702.htm#SEC7541627 findInvo sing_ 700.htm#SEC7521628 findInvoDiag sing_ 701.htm#SEC7531629 findOrientedBoundary findOrientedBoundary sing_20 56.htm#SEC21321630 findTorsion sing_18 74.htm#SEC19501631 find_first_primitive_root find_first_primitive_root sing_19 52.htm#SEC20281632 find_index sing_19 56.htm#SEC20321633 findifs.lib sing_18 81.htm#SEC19571634 findifs_example sing_18 82.htm#SEC19581635 findifs_lib sing_18 81.htm#SEC19571636 findimAlgebra sing_7 70.htm#SEC8221637 finduni sing_ 300.htm#SEC3401638 findvars sing_1 748.htm#SEC18241687 filecmd sing_241.htm#SEC281 1688 filtration purityfiltration_lib sing_738.htm#IDX363 1689 finalCharts sing_1405.htm#SEC1481 1690 find sing_242.htm#SEC282 1691 findAuto sing_645.htm#SEC697 1692 findInvo sing_643.htm#SEC695 1693 findInvoDiag sing_644.htm#SEC696 1694 findOrientedBoundary findOrientedBoundary sing_2065.htm#SEC2141 1695 findTorsion sing_1824.htm#SEC1900 1696 find_first_primitive_root find_first_primitive_root sing_1902.htm#SEC1978 1697 find_index sing_1906.htm#SEC1982 1698 findifs.lib sing_1831.htm#SEC1907 1699 findifs_example sing_1832.htm#SEC1908 1700 findifs_lib sing_1831.htm#SEC1907 1701 findimAlgebra sing_713.htm#SEC765 1702 finduni sing_243.htm#SEC283 1703 findvars sing_1698.htm#SEC1774 1639 1704 finite field sing_139.htm#SEC179 1640 finite field sing_1735.htm#IDX711 1641 finiteDiagInvariants finiteDiagInvariants sing_1297.htm#SEC1373 3508 1642 finitediff.lib sing_2262.htm#IDX880 1643 finitediff_lib sing_2262.htm#IDX881 1644 finitenessTest sing_1156.htm#SEC1232 1645 finvar.lib sing_1670.htm#SEC1746 1646 finvar_lib sing_1670.htm#SEC1746 1647 first index is 1 sing_465.htm#SEC505 1648 firstoct sing_1796.htm#SEC1872 1649 fitting sing_1202.htm#SEC1278 1650 fl2poly sing_639.htm#SEC691 1651 flatten sing_1087.htm#SEC1163 1652 flatteningStrat sing_1203.htm#SEC1279 1653 floating point sing_1046.htm#IDX439 1654 for sing_433.htm#SEC473 1655 formaldivisorplus sing_2249.htm#SEC2325 1656 forward sing_2268.htm#SEC2344 1657 fourier sing_634.htm#SEC686 1658 fouriersystem sing_2279.htm#SEC2355 1659 fpadim.lib sing_650.htm#SEC702 1660 fpadim_lib sing_650.htm#SEC702 1661 fprintf sing_301.htm#SEC341 1662 frandwalk sing_2404.htm#SEC2480 1663 free sing_2159.htm#IDX837 1664 free sing_2160.htm#IDX839 1665 free associative algebra, tensor algebra Free associative algebras sing_541.htm#SEC593 1666 freeGBasis sing_685.htm#SEC737 1667 freegb.lib sing_681.htm#SEC733 1668 freegb_lib sing_681.htm#SEC733 1669 freemodule sing_302.htm#SEC342 1670 freerank sing_994.htm#SEC1070 1671 from_boolean_constant from_boolean_constant sing_2117.htm#SEC2193 44881 1672 from_boolean_ideal sing_2121.htm#SEC2197 62698 1673 from_boolean_poly sing_2118.htm#SEC2194 27864 1674 from_boolean_set sing_2122.htm#SEC2198 60615 1675 frwalk sing_303.htm#SEC343 1676 fullFan sing_226.htm#SEC266 1677 fullSerreRelations sing_696.htm#SEC748 1678 furtherInvar sing_1714.htm#SEC1790 1679 further_hn_proc sing_1610.htm#SEC1686 1680 fwalk sing_1189.htm#SEC1265 1705 finite field sing_1685.htm#IDX775 1706 finiteDiagInvariants finiteDiagInvariants sing_1247.htm#SEC1323 3508 1707 finitediff.lib sing_2342.htm#IDX958 1708 finitediff_lib sing_2342.htm#IDX959 1709 finitenessTest sing_1105.htm#SEC1181 1710 finvar.lib sing_1620.htm#SEC1696 1711 finvar_lib sing_1620.htm#SEC1696 1712 first index is 1 sing_408.htm#SEC448 1713 firstoct sing_1746.htm#SEC1822 1714 fitting sing_1151.htm#SEC1227 1715 fl2poly sing_582.htm#SEC634 1716 flatten sing_1036.htm#SEC1112 1717 flatteningStrat sing_1152.htm#SEC1228 1718 floating point sing_995.htm#IDX499 1719 for sing_376.htm#SEC416 1720 formaldivisorplus sing_2329.htm#SEC2405 1721 forward sing_2348.htm#SEC2424 1722 fourier sing_577.htm#SEC629 1723 fouriersystem sing_2359.htm#SEC2435 1724 fpadim.lib sing_593.htm#SEC645 1725 fpadim_lib sing_593.htm#SEC645 1726 fprintf sing_244.htm#SEC284 1727 frandwalk sing_2484.htm#SEC2560 1728 free sing_2189.htm#IDX873 1729 free sing_2190.htm#IDX875 1730 free associative algebra, tensor algebra Free associative algebras sing_484.htm#SEC536 1731 freeGBasis sing_628.htm#SEC680 1732 freegb.lib sing_624.htm#SEC676 1733 freegb_lib sing_624.htm#SEC676 1734 freemodule sing_245.htm#SEC285 1735 freerank sing_943.htm#SEC1019 1736 from_boolean_constant from_boolean_constant sing_2220.htm#SEC2296 44881 1737 from_boolean_ideal sing_2224.htm#SEC2300 62698 1738 from_boolean_poly sing_2221.htm#SEC2297 27864 1739 from_boolean_set sing_2225.htm#SEC2301 60615 1740 frwalk sing_246.htm#SEC286 1741 full representation sing_909.htm#IDX441 1742 full representation sing_910.htm#IDX446 1743 fullFan sing_2040.htm#SEC2116 1744 fullSerreRelations sing_639.htm#SEC691 1745 fullSpace sing_1995.htm#SEC2071 1746 furtherInvar sing_1664.htm#SEC1740 1747 further_hn_proc sing_1560.htm#SEC1636 1748 fwalk sing_1138.htm#SEC1214 1681 1749 galois field sing_139.htm#SEC179 1682 gauss_col sing_1097.htm#SEC1173 1683 gauss_nf sing_1128.htm#SEC1204 1684 gauss_row sing_1098.htm#SEC1174 1685 gaussred sing_1126.htm#SEC1202 1686 gaussred_pivot sing_1127.htm#SEC1203 1687 gcd sing_304.htm#SEC344 1688 gcdMon sing_1229.htm#SEC1305 1689 gcddivisor sing_1984.htm#SEC2060 1690 gen sing_305.htm#SEC345 1691 genMDSMat sing_1851.htm#SEC1927 1692 genSymId sing_1374.htm#SEC1450 1693 general error-locator polynomial sing_921.htm#SEC986 1694 general neron. sing_2300.htm#IDX888 1695 general weighted lexicographical ordering sing_896.htm#IDX404 1696 general weighted reverse lexicographical ordering Local orderings sing_896.htm#IDX401 1697 general.lib sing_936.htm#SEC1012 1698 generalOrder sing_2009.htm#SEC2085 1699 general_lib sing_936.htm#SEC1012 1700 generateG sing_1947.htm#SEC2023 1701 generators sing_1510.htm#IDX573 1702 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_201.htm#SEC241 1703 generatorsOfSpan sing_202.htm#SEC242 1704 genericid sing_1012.htm#SEC1088 1705 genericity sing_1871.htm#SEC1947 1706 genericmat sing_1088.htm#SEC1164 1707 genoutput sing_1444.htm#SEC1520 1708 genus sing_1280.htm#SEC1356 1709 geometric invariant theory sing_2293.htm#IDX885 1710 geometrical locus, locus, loci, dynamic geometry sing_968.htm#IDX423 1711 geometrical locus, locus, loci, envelop sing_969.htm#IDX424 1712 geometrical locus, locus, loci, envelop. sing_970.htm#IDX425 1713 geometrical locus, locus, loci. sing_967.htm#IDX422 1714 geometrical locus, locus, loci. sing_971.htm#IDX426 1715 getArguments sing_1078.htm#SEC1154 1716 getCommand sing_1077.htm#SEC1153 1717 getCone sing_228.htm#SEC268 1718 getGradingGroup sing_2347.htm#SEC2423 1719 getLattice sing_2348.htm#SEC2424 1720 getLinearForms sing_203.htm#SEC243 1721 getModuleGrading sing_2358.htm#SEC2434 1722 getMultiplicity sing_204.htm#SEC244 1723 getOneVar sing_1288.htm#SEC1364 1724 getResult sing_1079.htm#SEC1155 1725 getSmallest sing_1287.htm#SEC1363 1726 getState sing_1080.htm#SEC1156 1727 getVariableWeights sing_2346.htm#SEC2422 1728 getcores sing_1027.htm#SEC1103 1729 getdump sing_306.htm#SEC346 1730 getenv sing_406.htm#IDX210 1750 gauss_col sing_1046.htm#SEC1122 1751 gauss_nf sing_1077.htm#SEC1153 1752 gauss_row sing_1047.htm#SEC1123 1753 gaussred sing_1075.htm#SEC1151 1754 gaussred_pivot sing_1076.htm#SEC1152 1755 gcd sing_247.htm#SEC287 1756 gcdMon sing_1178.htm#SEC1254 1757 gcddivisor sing_1934.htm#SEC2010 1758 gen sing_248.htm#SEC288 1759 genMDSMat sing_1801.htm#SEC1877 1760 genSymId sing_1324.htm#SEC1400 1761 general error-locator polynomial sing_864.htm#SEC929 1762 general neron. sing_2380.htm#IDX966 1763 general weighted lexicographical ordering sing_839.htm#IDX404 1764 general weighted reverse lexicographical ordering Local orderings sing_839.htm#IDX401 1765 general.lib sing_879.htm#SEC955 1766 generalOrder sing_1959.htm#SEC2035 1767 general_lib sing_879.htm#SEC955 1768 generateG sing_1897.htm#SEC1973 1769 generators sing_1460.htm#IDX637 1770 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2015.htm#SEC2091 1771 generatorsOfSpan sing_2016.htm#SEC2092 1772 generic representation sing_909.htm#IDX440 1773 genericid sing_961.htm#SEC1037 1774 genericity sing_1821.htm#SEC1897 1775 genericmat sing_1037.htm#SEC1113 1776 genoutput sing_1394.htm#SEC1470 1777 genus sing_1229.htm#SEC1305 1778 geometric invariant theory sing_2373.htm#IDX963 1779 geometrical locus FamElemsAtEnvCompPoints sing_913.htm#IDX455 1780 geometrical locus sing_914.htm#IDX459 1781 geometrical locus sing_915.htm#IDX463 1782 geometrical locus sing_916.htm#IDX467 1783 geometrical locus sing_917.htm#IDX472 1784 geometrical locus sing_918.htm#IDX477 1785 getArguments sing_1027.htm#SEC1103 1786 getCommand sing_1026.htm#SEC1102 1787 getCone sing_2042.htm#SEC2118 1788 getGradingGroup sing_2427.htm#SEC2503 1789 getLattice sing_2428.htm#SEC2504 1790 getLinearForms sing_2017.htm#SEC2093 1791 getModuleGrading sing_2438.htm#SEC2514 1792 getMultiplicity sing_2018.htm#SEC2094 1793 getOneVar sing_1237.htm#SEC1313 1794 getResult sing_1028.htm#SEC1104 1795 getSmallest sing_1236.htm#SEC1312 1796 getState sing_1029.htm#SEC1105 1797 getVariableWeights sing_2426.htm#SEC2502 1798 getcores sing_976.htm#SEC1052 1799 getdump sing_249.htm#SEC289 1800 getenv sing_349.htm#IDX210 1801 gfan.lib sing_1994.htm#SEC2070 1802 gfan_lib sing_1994.htm#SEC2070 1731 1803 gfanlib sing_1.htm#IDX9 1732 gfanlib_so sing_2417.htm#IDX903 1733 gitCone sing_2295.htm#SEC2371 1734 gitFan sing_2296.htm#SEC2372 1735 gitfan sing_2293.htm#IDX883 1736 gitfan.lib sing_2293.htm#SEC2369 1737 gitfan_lib sing_2293.htm#SEC2369 1738 gkdim.lib sing_707.htm#SEC759 1739 gkdim_lib sing_707.htm#SEC759 1740 gkzFan sing_2297.htm#SEC2373 1741 global sing_261.htm#IDX133 1742 global Bernstein-Sato polynomial sing_554.htm#IDX307 1743 global Bernstein-Sato polynomial sing_589.htm#IDX325 1744 global Bernstein-Sato polynomial for variety sing_645.htm#IDX350 1745 globalSections sing_2243.htm#SEC2319 1746 gmscoeffs sing_1568.htm#SEC1644 1747 gmsnf sing_1567.htm#SEC1643 1748 gmspoly.lib sing_1587.htm#SEC1663 1749 gmspoly_lib sing_1587.htm#SEC1663 1750 gmsring sing_1566.htm#SEC1642 1751 gmssing.lib sing_1565.htm#SEC1641 1752 gmssing_lib sing_1565.htm#SEC1641 1753 good basis sing_1565.htm#IDX601 1754 good basis sing_1575.htm#IDX656 1755 good basis sing_1587.htm#IDX672 1756 good basis sing_1589.htm#IDX683 1757 goodBasis sing_1589.htm#SEC1665 1758 gorensteinIndex sing_2433.htm#SEC2509 1759 gorensteinVector sing_2434.htm#SEC2510 1760 graal.lib sing_2286.htm#SEC2362 1761 graalMixed sing_2287.htm#SEC2363 1762 graal_lib sing_2286.htm#SEC2362 1763 gradeNumber sing_799.htm#SEC851 1764 graded Weyl algebra sing_554.htm#IDX310 1765 graded module, graded piece sing_1491.htm#IDX559 1766 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2302.htm#IDX889 1767 graded modules, handling of Handling graded modules sing_863.htm#SEC915 1768 gradedModules.lib sing_2302.htm#SEC2378 1769 gradedModules_lib sing_2302.htm#SEC2378 1770 gradiator sing_2391.htm#SEC2467 1771 graph sing_1178.htm#IDX470 1772 graph sing_1179.htm#IDX471 1773 graphics.lib sing_1798.htm#SEC1874 1774 graphics_lib sing_1798.htm#SEC1874 1804 gitCone sing_2375.htm#SEC2451 1805 gitFan sing_2376.htm#SEC2452 1806 gitfan sing_2373.htm#IDX961 1807 gitfan.lib sing_2373.htm#SEC2449 1808 gitfan_lib sing_2373.htm#SEC2449 1809 gkdim.lib sing_650.htm#SEC702 1810 gkdim_lib sing_650.htm#SEC702 1811 gkzFan sing_2377.htm#SEC2453 1812 global sing_204.htm#IDX133 1813 global Bernstein-Sato polynomial sing_497.htm#IDX307 1814 global Bernstein-Sato polynomial sing_532.htm#IDX325 1815 global Bernstein-Sato polynomial for variety sing_588.htm#IDX350 1816 globalSections sing_2323.htm#SEC2399 1817 gmscoeffs sing_1518.htm#SEC1594 1818 gmsnf sing_1517.htm#SEC1593 1819 gmspoly.lib sing_1537.htm#SEC1613 1820 gmspoly_lib sing_1537.htm#SEC1613 1821 gmsring sing_1516.htm#SEC1592 1822 gmssing.lib sing_1515.htm#SEC1591 1823 gmssing_lib sing_1515.htm#SEC1591 1824 good basis sing_1515.htm#IDX665 1825 good basis sing_1525.htm#IDX720 1826 good basis sing_1537.htm#IDX736 1827 good basis sing_1539.htm#IDX747 1828 goodBasis sing_1539.htm#SEC1615 1829 gorensteinIndex sing_2077.htm#SEC2153 1830 gorensteinVector sing_2078.htm#SEC2154 1831 graal.lib sing_2366.htm#SEC2442 1832 graalMixed sing_2367.htm#SEC2443 1833 graal_lib sing_2366.htm#SEC2442 1834 gradeNumber sing_742.htm#SEC794 1835 graded Weyl algebra sing_497.htm#IDX310 1836 graded module, graded piece sing_1441.htm#IDX623 1837 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2382.htm#IDX967 1838 graded modules, handling of Handling graded modules sing_806.htm#SEC858 1839 gradedModules.lib sing_2382.htm#SEC2458 1840 gradedModules_lib sing_2382.htm#SEC2458 1841 gradiator sing_2471.htm#SEC2547 1842 graph sing_1127.htm#IDX530 1843 graph sing_1128.htm#IDX531 1844 graphics.lib sing_1748.htm#SEC1824 1845 graphics_lib sing_1748.htm#SEC1824 1775 1846 graphviz sing_1.htm#IDX13 1776 graver4ti2 sing_13 72.htm#SEC1448 396351777 grconcat sing_2 325.htm#SEC24011778 grdeg sing_23 05.htm#SEC23811779 grgens sing_23 14.htm#SEC23901780 grgroebner sing_2 324.htm#SEC24001781 grlift sing_2 322.htm#SEC23981782 grlifting sing_2 329.htm#SEC24051783 grlifting2 sing_2 330.htm#SEC24061784 grlifting3 sing_2 332.htm#SEC24081785 grneg sing_2 335.htm#SEC24111786 grobcov sing_9 58.htm#SEC10341787 grobcov.lib sing_9 57.htm#SEC10331788 grobcov_lib sing_9 57.htm#SEC10331789 grobj sing_23 03.htm#SEC23791790 groebner sing_ 307.htm#SEC3471791 groebner sing_ 855.htm#SEC9071792 groebner basis computations sing_ 307.htm#IDX1471793 groebnerComplex sing_2 424.htm#SEC25001794 groebnerCone sing_2 420.htm#SEC24961795 groebnerFan sing_2 422.htm#SEC24981796 groebnerFanP sing_20 49.htm#SEC21251797 gromovWitten sing_11 83.htm#SEC12591798 grorder sing_23 16.htm#SEC23921847 graver4ti2 sing_1322.htm#SEC1398 39635 1848 grconcat sing_2405.htm#SEC2481 1849 grdeg sing_2385.htm#SEC2461 1850 grgens sing_2394.htm#SEC2470 1851 grgroebner sing_2404.htm#SEC2480 1852 grlift sing_2402.htm#SEC2478 1853 grlifting sing_2409.htm#SEC2485 1854 grlifting2 sing_2410.htm#SEC2486 1855 grlifting3 sing_2412.htm#SEC2488 1856 grneg sing_2415.htm#SEC2491 1857 grobcov sing_902.htm#SEC978 1858 grobcov.lib sing_900.htm#SEC976 1859 grobcov_lib sing_900.htm#SEC976 1860 grobj sing_2383.htm#SEC2459 1861 groebner sing_250.htm#SEC290 1862 groebner sing_798.htm#SEC850 1863 groebner basis computations sing_250.htm#IDX147 1864 groebnerComplex sing_2156.htm#SEC2232 1865 groebnerCone sing_2150.htm#SEC2226 1866 groebnerFan sing_2155.htm#SEC2231 1867 groebnerFanP sing_2058.htm#SEC2134 1868 gromovWitten sing_1132.htm#SEC1208 1869 grorder sing_2396.htm#SEC2472 1799 1870 ground field sing_139.htm#SEC179 1800 group_reynolds sing_16 78.htm#SEC17541801 grpower sing_23 12.htm#SEC23881802 grpres sing_23 15.htm#SEC23911803 grprod sing_2 323.htm#SEC23991804 grrange sing_2 334.htm#SEC24101805 grres sing_2 321.htm#SEC23971806 grrndmap sing_2 327.htm#SEC24031807 grrndmap2 sing_2 328.htm#SEC24041808 grrndmat sing_2 326.htm#SEC24021809 grshift sing_23 07.htm#SEC23831810 grsum sing_23 11.htm#SEC23871811 grsyz sing_2 320.htm#SEC23961812 grtest sing_23 04.htm#SEC23801813 grtranspose sing_23 13.htm#SEC23891814 grtranspose1 sing_23 17.htm#SEC23931815 grtwist sing_23 09.htm#SEC23851816 grtwists sing_23 10.htm#SEC23861817 grview sing_23 06.htm#SEC23821818 grwalk.lib sing_11 88.htm#SEC12641819 grwalk_lib sing_11 88.htm#SEC12641820 grzero sing_23 08.htm#SEC23841821 gwalk sing_11 94.htm#SEC12701822 hStarVector sing_2 436.htm#SEC25121823 hVector sing_2 437.htm#SEC25131824 h_increasing_knapsack h_increasing_knapsack sing_19 70.htm#SEC20461825 hardware platform sing_ 406.htm#IDX2651826 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_10 51.htm#SEC11271827 hasCommutativeVars sing_ 1047.htm#SEC11231828 hasFieldCoefficient sing_ 1050.htm#SEC11261829 hasGlobalOrdering sing_ 1048.htm#SEC11241830 hasMixedOrdering sing_ 1049.htm#SEC11251831 hasNumericCoeffs sing_ 1046.htm#SEC11221832 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_10 52.htm#SEC11281833 headStand sing_1 110.htm#SEC11861834 heightZ sing_1 349.htm#SEC14251835 help sing_ 308.htm#SEC3481871 group_reynolds sing_1628.htm#SEC1704 1872 grpower sing_2392.htm#SEC2468 1873 grpres sing_2395.htm#SEC2471 1874 grprod sing_2403.htm#SEC2479 1875 grrange sing_2414.htm#SEC2490 1876 grres sing_2401.htm#SEC2477 1877 grrndmap sing_2407.htm#SEC2483 1878 grrndmap2 sing_2408.htm#SEC2484 1879 grrndmat sing_2406.htm#SEC2482 1880 grshift sing_2387.htm#SEC2463 1881 grsum sing_2391.htm#SEC2467 1882 grsyz sing_2400.htm#SEC2476 1883 grtest sing_2384.htm#SEC2460 1884 grtranspose sing_2393.htm#SEC2469 1885 grtranspose1 sing_2397.htm#SEC2473 1886 grtwist sing_2389.htm#SEC2465 1887 grtwists sing_2390.htm#SEC2466 1888 grview sing_2386.htm#SEC2462 1889 grwalk.lib sing_1137.htm#SEC1213 1890 grwalk_lib sing_1137.htm#SEC1213 1891 grzero sing_2388.htm#SEC2464 1892 gwalk sing_1143.htm#SEC1219 1893 hStarVector sing_2079.htm#SEC2155 1894 hVector sing_2080.htm#SEC2156 1895 h_increasing_knapsack h_increasing_knapsack sing_1920.htm#SEC1996 1896 hardware platform sing_349.htm#IDX265 1897 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1000.htm#SEC1076 1898 hasCommutativeVars sing_996.htm#SEC1072 1899 hasFieldCoefficient sing_999.htm#SEC1075 1900 hasGlobalOrdering sing_997.htm#SEC1073 1901 hasMixedOrdering sing_998.htm#SEC1074 1902 hasNumericCoeffs sing_995.htm#SEC1071 1903 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1001.htm#SEC1077 1904 headStand sing_1059.htm#SEC1135 1905 heightZ sing_1299.htm#SEC1375 1906 help sing_251.htm#SEC291 1836 1907 help browsers The online help system sing_16.htm#IDX22 1837 1908 help browsers, dummy The online help system sing_16.htm#IDX25 … … 1840 1911 help browsers, html The online help system sing_16.htm#IDX23 1841 1912 help browsers, setting command to use The online help system sing_16.htm#IDX30 1842 help browsers, setting the sing_ 406.htm#IDX1931913 help browsers, setting the sing_349.htm#IDX193 1843 1914 help, accessing over the net Command line options sing_19.htm#IDX42 1844 1915 help, online help system The online help system sing_16.htm#SEC22 1845 hermiteNormalForm sing_2 392.htm#SEC24681846 hess.lib sing_2 337.htm#SEC24131847 hess_lib sing_2 337.htm#SEC24131848 hessenberg sing_ 406.htm#IDX2161849 hessenberg sing_1 132.htm#SEC12081850 highcorner sing_ 309.htm#SEC3491851 hilb sing_ 310.htm#SEC3501852 hilbPoly sing_ 1010.htm#SEC10861853 hilbert4ti2 sing_13 71.htm#SEC1447 139931854 hilbertBasis sing_2 435.htm#SEC25111855 hilbertSeries sing_2 394.htm#SEC24701856 hilbvec sing_1 749.htm#SEC18251857 hnexpansion sing_15 91.htm#SEC16671858 hnoether.lib sing_15 90.htm#SEC16661859 hnoether_lib sing_15 90.htm#SEC16661860 holonomic rank sing_ 817.htm#IDX3741861 holonomicRank sing_ 821.htm#SEC8731862 hom_kernel sing_1 210.htm#SEC12861863 homog sing_ 311.htm#SEC3511864 homogeneitySpace sing_2 419.htm#SEC24951865 homogfacFirstQWeyl sing_ 750.htm#SEC8021866 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_ 752.htm#SEC8041867 homogfacNthQWeyl sing_ 749.htm#SEC8011868 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_ 751.htm#SEC8031869 homolog.lib sing_11 95.htm#SEC12711870 homolog_lib sing_11 95.htm#SEC12711871 homology sing_1 205.htm#SEC12811872 howto, download Download instructions sing_2 477.htm#SEC25661873 howto, install on Macintosh Macintosh installation instructions sing_2 480.htm#SEC25691874 howto, install on Unix Unix installation instructions sing_2 478.htm#SEC25671875 howto, install on Windows Windows installation instructions sing_2 479.htm#SEC25681876 hres sing_ 312.htm#SEC3521916 hermiteNormalForm sing_2472.htm#SEC2548 1917 hess.lib sing_2417.htm#SEC2493 1918 hess_lib sing_2417.htm#SEC2493 1919 hessenberg sing_349.htm#IDX216 1920 hessenberg sing_1081.htm#SEC1157 1921 highcorner sing_252.htm#SEC292 1922 hilb sing_253.htm#SEC293 1923 hilbPoly sing_959.htm#SEC1035 1924 hilbert4ti2 sing_1321.htm#SEC1397 13993 1925 hilbertBasis sing_2081.htm#SEC2157 1926 hilbertSeries sing_2474.htm#SEC2550 1927 hilbvec sing_1699.htm#SEC1775 1928 hnexpansion sing_1541.htm#SEC1617 1929 hnoether.lib sing_1540.htm#SEC1616 1930 hnoether_lib sing_1540.htm#SEC1616 1931 holonomic rank sing_760.htm#IDX374 1932 holonomicRank sing_764.htm#SEC816 1933 hom_kernel sing_1159.htm#SEC1235 1934 homog sing_254.htm#SEC294 1935 homogeneitySpace sing_2152.htm#SEC2228 1936 homogfacFirstQWeyl sing_693.htm#SEC745 1937 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_695.htm#SEC747 1938 homogfacNthQWeyl sing_692.htm#SEC744 1939 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_694.htm#SEC746 1940 homolog.lib sing_1144.htm#SEC1220 1941 homolog_lib sing_1144.htm#SEC1220 1942 homology sing_1154.htm#SEC1230 1943 howto, download Download instructions sing_2504.htm#SEC2593 1944 howto, install on Macintosh Macintosh installation instructions sing_2507.htm#SEC2596 1945 howto, install on Unix Unix installation instructions sing_2505.htm#SEC2594 1946 howto, install on Windows Windows installation instructions sing_2506.htm#SEC2595 1947 hres sing_255.htm#SEC295 1877 1948 html, default help The online help system sing_16.htm#IDX24 1878 hyperel.lib sing_19 77.htm#SEC20531879 hyperel_lib sing_19 77.htm#SEC20531880 hyperplane sing_21 29.htm#IDX7771881 hyperplane arrangement sing_5 89.htm#IDX3311882 hypersurface singularity sing_1 617.htm#IDX7011883 iMult sing_12 83.htm#SEC13591884 id2mod sing_ 1006.htm#SEC10821949 hyperel.lib sing_1927.htm#SEC2003 1950 hyperel_lib sing_1927.htm#SEC2003 1951 hyperplane sing_2159.htm#IDX813 1952 hyperplane arrangement sing_532.htm#IDX331 1953 hypersurface singularity sing_1567.htm#IDX765 1954 iMult sing_1232.htm#SEC1308 1955 id2mod sing_955.htm#SEC1031 1885 1956 ideal sing_85.htm#SEC125 1886 1957 ideal declarations sing_86.htm#SEC126 1887 ideal declarations (plural) ideal declarations (plural) sing_4 73.htm#SEC5131958 ideal declarations (plural) ideal declarations (plural) sing_416.htm#SEC456 1888 1959 ideal expressions sing_87.htm#SEC127 1889 ideal expressions (plural) ideal expressions (plural) sing_4 74.htm#SEC5141960 ideal expressions (plural) ideal expressions (plural) sing_417.htm#SEC457 1890 1961 ideal operations sing_88.htm#SEC128 1891 ideal operations (plural) ideal operations (plural) sing_4 75.htm#SEC5151962 ideal operations (plural) ideal operations (plural) sing_418.htm#SEC458 1892 1963 ideal related functions ideal related functions sing_89.htm#SEC129 1893 ideal related functions (plural) ideal related functions (plural) sing_476.htm#SEC516 1894 ideal, toric sing_908.htm#SEC965 1895 idealSplit sing_1756.htm#SEC1832 1896 ideals Miscellaneous oddities sing_466.htm#IDX287 1897 idealsimplify sing_1518.htm#SEC1594 1898 identifier Identifier resolution sing_467.htm#SEC507 1899 identifyvar sing_1426.htm#SEC1502 1900 if sing_434.htm#SEC474 1901 imageLattice sing_2360.htm#SEC2436 1902 image_of_variety sing_1706.htm#SEC1782 1903 imap sing_313.htm#SEC353 1904 imap (plural) sing_511.htm#SEC551 1905 imapall sing_1038.htm#SEC1114 1906 impart sing_314.htm#SEC354 1907 importfrom sing_435.htm#SEC475 1908 inCenter sing_578.htm#SEC630 1909 inCentralizer sing_579.htm#SEC631 1910 inForm sing_621.htm#SEC673 1911 inSubring sing_1148.htm#SEC1224 1912 indSet sing_1255.htm#SEC1331 1913 indepSet sing_315.htm#SEC355 1964 ideal related functions (plural) ideal related functions (plural) sing_419.htm#SEC459 1965 ideal, toric sing_851.htm#SEC908 1966 idealSplit sing_1706.htm#SEC1782 1967 ideals Miscellaneous oddities sing_409.htm#IDX287 1968 idealsimplify sing_1468.htm#SEC1544 1969 identifier Identifier resolution sing_410.htm#SEC450 1970 identifyvar sing_1376.htm#SEC1452 1971 if sing_377.htm#SEC417 1972 imageLattice sing_2440.htm#SEC2516 1973 image_of_variety sing_1656.htm#SEC1732 1974 imap sing_256.htm#SEC296 1975 imap (plural) sing_454.htm#SEC494 1976 imapall sing_987.htm#SEC1063 1977 impart sing_257.htm#SEC297 1978 importfrom sing_378.htm#SEC418 1979 inCenter sing_521.htm#SEC573 1980 inCentralizer sing_522.htm#SEC574 1981 inForm sing_564.htm#SEC616 1982 inSubring sing_1097.htm#SEC1173 1983 inVar sing_2301.htm#SEC2377 1984 indSet sing_1204.htm#SEC1280 1985 indepSet sing_258.htm#SEC298 1914 1986 indexed names sing_36.htm#IDX82 1915 1987 indexed names sing_37.htm#SEC65 1916 inequalities sing_20 5.htm#SEC2451917 infRedTail, option sing_3 64.htm#IDX1541988 inequalities sing_2019.htm#SEC2095 1989 infRedTail, option sing_307.htm#IDX154 1918 1990 info The online help system sing_16.htm#SEC23 1919 iniD sing_1 446.htm#SEC15221920 init_debug sing_1 525.htm#SEC16011921 initial sing_2 418.htm#SEC24941922 initial form sing_ 554.htm#IDX3121923 initial ideal sing_ 554.htm#IDX3111924 initial ideal approach sing_ 554.htm#IDX3151925 initial ideal approach sing_ 645.htm#IDX3541926 initialForm sing_2 082.htm#SEC21581927 initialIdeal sing_2 083.htm#SEC21591928 initialIdealW sing_ 620.htm#SEC6721929 initialMalgrange sing_ 619.htm#SEC6711930 injective_knapsack sing_19 71.htm#SEC20471931 inout.lib sing_9 72.htm#SEC10481932 inout_lib sing_9 72.htm#SEC10481991 iniD sing_1396.htm#SEC1472 1992 init_debug sing_1475.htm#SEC1551 1993 initial sing_2153.htm#SEC2229 1994 initial form sing_497.htm#IDX312 1995 initial ideal sing_497.htm#IDX311 1996 initial ideal approach sing_497.htm#IDX315 1997 initial ideal approach sing_588.htm#IDX354 1998 initialForm sing_2130.htm#SEC2206 1999 initialIdeal sing_2131.htm#SEC2207 2000 initialIdealW sing_563.htm#SEC615 2001 initialMalgrange sing_562.htm#SEC614 2002 injective_knapsack sing_1921.htm#SEC1997 2003 inout.lib sing_921.htm#SEC997 2004 inout_lib sing_921.htm#SEC997 1933 2005 input sing_41.htm#SEC71 1934 2006 insert sing_121.htm#SEC161 1935 insert sing_ 316.htm#SEC3561936 insertCone sing_2 29.htm#SEC2691937 insertGenerator sing_ 640.htm#SEC6921938 instructions, Macintosh installation Macintosh installation instructions sing_2 480.htm#SEC25691939 instructions, Unix installation Unix installation instructions sing_2 478.htm#SEC25671940 instructions, Windows installation Windows installation instructions sing_2 479.htm#SEC25681941 instructions, downloading Download instructions sing_2 477.htm#SEC25662007 insert sing_259.htm#SEC299 2008 insertCone sing_2043.htm#SEC2119 2009 insertGenerator sing_583.htm#SEC635 2010 instructions, Macintosh installation Macintosh installation instructions sing_2507.htm#SEC2596 2011 instructions, Unix installation Unix installation instructions sing_2505.htm#SEC2594 2012 instructions, Windows installation Windows installation instructions sing_2506.htm#SEC2595 2013 instructions, downloading Download instructions sing_2504.htm#SEC2593 1942 2014 int sing_90.htm#SEC130 1943 2015 int declarations sing_91.htm#SEC131 … … 1945 2017 int operations sing_93.htm#SEC133 1946 2018 int related functions int related functions sing_94.htm#SEC134 1947 intInverse sing_2 369.htm#SEC24451948 intPart sing_1 925.htm#SEC20011949 intRank sing_2 361.htm#SEC24371950 intRoot sing_1 926.htm#SEC20021951 intRoots sing_ 637.htm#SEC6891952 intStrategy, option sing_3 64.htm#IDX1551953 intclMonIdeal sing_12 95.htm#SEC1371 223381954 intclToricRing sing_12 91.htm#SEC1367 621431955 integer division Miscellaneous oddities sing_4 66.htm#IDX2821956 integer programming sing_ 916.htm#SEC9731957 integral basis sing_1 217.htm#IDX4901958 integral basis sing_1 409.htm#IDX5441959 integral closure sing_12 76.htm#IDX5031960 integral closure sing_12 77.htm#IDX5061961 integral closure sing_12 78.htm#IDX5091962 integral closure sing_12 90.htm#IDX5131963 integralBasis sing_1 217.htm#SEC12931964 integralIdeal sing_ 624.htm#SEC6761965 integralModule sing_ 625.htm#SEC6771966 integralSection sing_2 370.htm#SEC24461967 integralbasis.lib sing_1 216.htm#SEC12921968 integralbasis_lib sing_1 216.htm#SEC12921969 integration of D-module sing_ 612.htm#IDX3432019 intInverse sing_2449.htm#SEC2525 2020 intPart sing_1875.htm#SEC1951 2021 intRank sing_2441.htm#SEC2517 2022 intRoot sing_1876.htm#SEC1952 2023 intRoots sing_580.htm#SEC632 2024 intStrategy, option sing_307.htm#IDX155 2025 intclMonIdeal sing_1245.htm#SEC1321 22338 2026 intclToricRing sing_1241.htm#SEC1317 62143 2027 integer division Miscellaneous oddities sing_409.htm#IDX282 2028 integer programming sing_859.htm#SEC916 2029 integral basis sing_1166.htm#IDX552 2030 integral basis sing_1359.htm#IDX608 2031 integral closure sing_1225.htm#IDX565 2032 integral closure sing_1226.htm#IDX568 2033 integral closure sing_1227.htm#IDX571 2034 integral closure sing_1240.htm#IDX577 2035 integralBasis sing_1166.htm#SEC1242 2036 integralIdeal sing_567.htm#SEC619 2037 integralModule sing_568.htm#SEC620 2038 integralSection sing_2450.htm#SEC2526 2039 integralbasis.lib sing_1165.htm#SEC1241 2040 integralbasis_lib sing_1165.htm#SEC1241 2041 integration of D-module sing_555.htm#IDX343 1970 2042 interface, Emacs Emacs user interface sing_21.htm#SEC28 1971 interiorLatticePoints interiorLatticePoints sing_2 438.htm#SEC25141972 internalfunctions sing_1 526.htm#SEC16021973 interpolate sing_17 62.htm#SEC18381974 interpolation sing_ 317.htm#SEC3571975 interred sing_ 318.htm#SEC3581976 intersect sing_ 319.htm#SEC3591977 intersect (plural) sing_ 512.htm#SEC5521978 intersectElim, option sing_3 64.htm#IDX1731979 intersectLattices sing_2 366.htm#SEC24421980 intersectMon sing_1 232.htm#SEC13081981 intersectSyz, option sing_3 64.htm#IDX1741982 intersectZ sing_13 51.htm#SEC14271983 intersection sing_1 600.htm#SEC16761984 intersection lattice sing_21 65.htm#IDX8521985 intersection lattice sing_21 66.htm#IDX8531986 intersection multiplicity sing_1 511.htm#IDX5791987 intersection multiplicity sing_1 600.htm#IDX6941988 intersectionDiv sing_14 74.htm#SEC15501989 intersectionValRingIdeals intersectionValRingIdeals sing_1 300.htm#SEC1376 387731990 intersectionValRings intersectionValRings sing_12 99.htm#SEC1375 357612043 interiorLatticePoints interiorLatticePoints sing_2082.htm#SEC2158 2044 internalfunctions sing_1476.htm#SEC1552 2045 interpolate sing_1712.htm#SEC1788 2046 interpolation sing_260.htm#SEC300 2047 interred sing_261.htm#SEC301 2048 intersect sing_262.htm#SEC302 2049 intersect (plural) sing_455.htm#SEC495 2050 intersectElim, option sing_307.htm#IDX173 2051 intersectLattices sing_2446.htm#SEC2522 2052 intersectMon sing_1181.htm#SEC1257 2053 intersectSyz, option sing_307.htm#IDX174 2054 intersectZ sing_1301.htm#SEC1377 2055 intersection sing_1550.htm#SEC1626 2056 intersection lattice sing_2195.htm#IDX888 2057 intersection lattice sing_2196.htm#IDX889 2058 intersection multiplicity sing_1461.htm#IDX643 2059 intersection multiplicity sing_1550.htm#IDX758 2060 intersectionDiv sing_1424.htm#SEC1500 2061 intersectionValRingIdeals intersectionValRingIdeals sing_1250.htm#SEC1326 38773 2062 intersectionValRings intersectionValRings sing_1249.htm#SEC1325 35761 1991 2063 intmat sing_97.htm#SEC137 1992 2064 intmat declarations sing_98.htm#SEC138 … … 1995 2067 intmat related functions intmat related functions sing_102.htm#SEC142 1996 2068 intmat type cast sing_100.htm#SEC140 1997 intmat2mons sing_1 315.htm#SEC1391 211501998 intprog.lib sing_1 218.htm#SEC12941999 intprog_lib sing_1 218.htm#SEC12942069 intmat2mons sing_1265.htm#SEC1341 21150 2070 intprog.lib sing_1167.htm#SEC1243 2071 intprog_lib sing_1167.htm#SEC1243 2000 2072 intvec sing_103.htm#SEC143 2001 2073 intvec declarations sing_104.htm#SEC144 … … 2003 2075 intvec operations sing_106.htm#SEC146 2004 2076 intvec related functions intvec related functions sing_107.htm#SEC147 2005 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1675.htm#IDX707 2006 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1676.htm#IDX708 2007 invariantRing sing_1708.htm#SEC1784 2008 invariant_algebra_perm invariant_algebra_perm sing_1676.htm#SEC1752 2009 invariant_algebra_reynolds invariant_algebra_reynolds sing_1675.htm#SEC1751 2010 invariant_basis sing_1683.htm#SEC1759 2011 invariant_basis_reynolds invariant_basis_reynolds sing_1684.htm#SEC1760 2012 invariant_ring sing_1671.htm#SEC1747 2013 invariant_ring_random invariant_ring_random sing_1672.htm#SEC1748 2014 invariants sing_1596.htm#SEC1672 2015 inverse sing_1116.htm#SEC1192 2016 inverse of a matrix via its LU-decomposition sing_339.htm#SEC379 2017 inverseFourier sing_635.htm#SEC687 2018 inverse_B sing_1117.htm#SEC1193 2019 inverse_L sing_1118.htm#SEC1194 2020 inverse_modulus sing_1954.htm#SEC2030 2021 invertBirMap sing_1410.htm#SEC1486 2022 invertNumberMain sing_1786.htm#SEC1862 2023 involut.lib sing_699.htm#SEC751 2024 involut_lib sing_699.htm#SEC751 2025 involution sing_704.htm#SEC756 2026 invunit sing_1619.htm#SEC1695 2027 iostruct sing_1873.htm#SEC1949 2028 irrRealizationDim sing_2064.htm#SEC2140 2029 irred_secondary_char0 irred_secondary_char0 sing_1697.htm#SEC1773 2030 irred_secondary_no_molien irred_secondary_no_molien sing_1700.htm#SEC1776 2031 irreddecMon sing_1241.htm#SEC1317 2032 irreducible power series sing_1601.htm#IDX695 2033 irreducible secondary invariant irred_secondary_char0 sing_1697.htm#IDX709 2034 isAface sing_2298.htm#SEC2374 2035 isAntiEndo sing_706.htm#SEC758 2036 isBounded sing_2439.htm#SEC2515 2037 isCI sing_261.htm#IDX139 2038 isCI sing_1166.htm#SEC1242 2039 isCM sing_261.htm#IDX140 2040 isCM sing_1206.htm#SEC1282 2041 isCMcod2 sing_1654.htm#SEC1730 2042 isCanonical sing_2440.htm#SEC2516 2043 isCartan sing_580.htm#SEC632 2044 isCentral sing_777.htm#SEC829 2045 isCommutative sing_779.htm#SEC831 2046 isCompatible sing_230.htm#SEC270 2047 isCompressed sing_2441.htm#SEC2517 2048 isEqualDivisor sing_2242.htm#SEC2318 2049 isEquising sing_1563.htm#SEC1639 2050 isFlat sing_1207.htm#SEC1283 2051 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is_complex sing_1089.htm#SEC1165 2102 is_fix_injective sing_1975.htm#SEC2051 2103 is_h_injective sing_1974.htm#SEC2050 2104 is_injective sing_1151.htm#SEC1227 2105 is_irred sing_1601.htm#SEC1677 2106 is_is sing_1639.htm#SEC1715 2107 is_nested sing_1265.htm#SEC1341 2108 is_prime sing_1955.htm#SEC2031 2109 is_primitive_root sing_1951.htm#SEC2027 2110 is_pure sing_805.htm#SEC857 2111 is_reg sing_1640.htm#SEC1716 2112 is_regs sing_1641.htm#SEC1717 2113 is_surjective sing_1152.htm#SEC1228 2114 is_zero sing_995.htm#SEC1071 2115 isartinianMon sing_1238.htm#SEC1314 2116 isgenericMon sing_1239.htm#SEC1315 2117 ishyper sing_1978.htm#SEC2054 2118 isirreducibleMon sing_1237.htm#SEC1313 2119 isoncurve sing_1979.htm#SEC2055 2120 isparam sing_2042.htm#SEC2118 2121 isprimaryMon sing_1236.htm#SEC1312 2122 isprimeMon sing_1235.htm#SEC1311 2123 isuni sing_2027.htm#SEC2103 2124 iv2lp sing_675.htm#SEC727 2125 iv2lpList sing_676.htm#SEC728 2126 iv2lpMat sing_677.htm#SEC729 2127 ivDHilbert sing_651.htm#SEC703 2128 ivDHilbertSickle sing_652.htm#SEC704 2129 ivDimCheck sing_653.htm#SEC705 2130 ivHilbert sing_654.htm#SEC706 2131 ivKDim sing_655.htm#SEC707 2132 ivL2lpI sing_674.htm#SEC726 2133 ivMis2Base sing_656.htm#SEC708 2134 ivMis2Dim sing_657.htm#SEC709 2135 ivOrdMisLex sing_658.htm#SEC710 2136 ivSickle sing_659.htm#SEC711 2137 ivSickleDim sing_661.htm#SEC713 2138 ivSickleHil sing_660.htm#SEC712 2139 jInvariant sing_2076.htm#SEC2152 2140 jOft sing_1910.htm#SEC1986 2141 jacob sing_320.htm#SEC360 2142 jacoblift sing_1620.htm#SEC1696 2143 jacobson sing_1879.htm#SEC1955 2144 jacobson.lib sing_1877.htm#SEC1953 2145 jacobson_lib sing_1877.htm#SEC1953 2146 janet sing_321.htm#SEC361 2147 jet sing_322.htm#SEC362 2148 jordan sing_1137.htm#SEC1213 2149 jordanbasis sing_1138.htm#SEC1214 2150 jordanmatrix sing_1139.htm#SEC1215 2151 jordannf sing_1140.htm#SEC1216 2152 jungfib sing_1459.htm#SEC1535 2153 jungnormal sing_1458.htm#SEC1534 2154 jungresolve sing_1457.htm#SEC1533 2155 katsura sing_993.htm#SEC1069 2156 kbase sing_323.htm#SEC363 2157 kbase (plural) sing_513.htm#SEC553 2158 keepring sing_436.htm#SEC476 2159 kernel sing_324.htm#SEC364 2160 kernelLattice sing_2362.htm#SEC2438 2161 kill sing_325.htm#SEC365 2162 killTask sing_1068.htm#SEC1144 2163 killall sing_945.htm#SEC1021 2164 killattrib sing_326.htm#SEC366 2165 kmemory sing_944.htm#SEC1020 2166 kohom sing_1211.htm#SEC1287 2167 kontrahom sing_1212.htm#SEC1288 2168 koszul sing_327.htm#SEC367 2169 kskernel.lib sing_1611.htm#SEC1687 2170 kskernel_lib sing_1611.htm#SEC1687 2077 invariant sing_2314.htm#IDX935 2078 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1625.htm#IDX771 2079 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1626.htm#IDX772 2080 invariantRing sing_1658.htm#SEC1734 2081 invariant_algebra_perm invariant_algebra_perm sing_1626.htm#SEC1702 2082 invariant_algebra_reynolds invariant_algebra_reynolds sing_1625.htm#SEC1701 2083 invariant_basis sing_1633.htm#SEC1709 2084 invariant_basis_reynolds invariant_basis_reynolds sing_1634.htm#SEC1710 2085 invariant_ring sing_1621.htm#SEC1697 2086 invariant_ring_random invariant_ring_random sing_1622.htm#SEC1698 2087 invariants curveColengthDerivations sing_1546.htm#SEC1622 2088 invariants sing_2311.htm#IDX928 2089 invariants sing_2315.htm#IDX937 2090 inverse sing_1065.htm#SEC1141 2091 inverse of a matrix via its LU-decomposition sing_282.htm#SEC322 2092 inverseFourier sing_578.htm#SEC630 2093 inverse_B sing_1066.htm#SEC1142 2094 inverse_L sing_1067.htm#SEC1143 2095 inverse_modulus sing_1904.htm#SEC1980 2096 invertBirMap sing_1360.htm#SEC1436 2097 invertNumberMain sing_1736.htm#SEC1812 2098 involut.lib sing_642.htm#SEC694 2099 involut_lib sing_642.htm#SEC694 2100 involution sing_647.htm#SEC699 2101 invunit sing_1569.htm#SEC1645 2102 iostruct sing_1823.htm#SEC1899 2103 irrRealizationDim sing_2112.htm#SEC2188 2104 irred_secondary_char0 irred_secondary_char0 sing_1647.htm#SEC1723 2105 irred_secondary_no_molien irred_secondary_no_molien sing_1650.htm#SEC1726 2106 irreddecMon sing_1190.htm#SEC1266 2107 irreducible power series sing_1551.htm#IDX759 2108 irreducible secondary invariant irred_secondary_char0 sing_1647.htm#IDX773 2109 isAface sing_2378.htm#SEC2454 2110 isAntiEndo sing_649.htm#SEC701 2111 isBounded sing_2083.htm#SEC2159 2112 isCI sing_204.htm#IDX139 2113 isCI sing_1115.htm#SEC1191 2114 isCM sing_204.htm#IDX140 2115 isCM sing_1155.htm#SEC1231 2116 isCMcod2 sing_1604.htm#SEC1680 2117 isCanonical sing_2084.htm#SEC2160 2118 isCartan sing_523.htm#SEC575 2119 isCentral sing_720.htm#SEC772 2120 isCommutative sing_722.htm#SEC774 2121 isCompatible sing_2044.htm#SEC2120 2122 isCompressed sing_2085.htm#SEC2161 2123 isEqualDivisor sing_2322.htm#SEC2398 2124 isEquising sing_1513.htm#SEC1589 2125 isFlat sing_1156.htm#SEC1232 2126 isFsat sing_573.htm#SEC625 2127 isFullSpace sing_2020.htm#SEC2096 2128 isGorenstein sing_2086.htm#SEC2162 2129 isGradedRingHomomorphism isGradedRingHomomorphism sing_2435.htm#SEC2511 2130 isGroup sing_2433.htm#SEC2509 2131 isGroupHomomorphism sing_2434.htm#SEC2510 2132 isHolonomic sing_551.htm#SEC603 2133 isHomg sing_204.htm#IDX135 2134 isHomogeneous sing_2461.htm#SEC2537 2135 isInt sing_586.htm#SEC638 2136 isIntegralSurjective isIntegralSurjective sing_2447.htm#SEC2523 2137 isInvolution sing_648.htm#SEC700 2138 isLatticeEmpty sing_2087.htm#SEC2163 2139 isLocalizationRegular isLocalizationRegular sing_2370.htm#SEC2446 2140 isLocallyFree sing_1157.htm#SEC1233 2141 isMonomial sing_1176.htm#SEC1252 2142 isNC sing_721.htm#SEC773 2143 isNormal sing_2088.htm#SEC2164 2144 isOnCurve sing_1888.htm#SEC1964 2145 isOrigin sing_2021.htm#SEC2097 2146 isPositive sing_2458.htm#SEC2534 2147 isPrimitiveSublattice isPrimitiveSublattice sing_2448.htm#SEC2524 2148 isPure sing_2045.htm#SEC2121 2149 isPureTensor sing_495.htm#SEC547 2150 isQuotientRing sing_1002.htm#SEC1078 2151 isRational sing_554.htm#SEC606 2152 isReflexive sing_2089.htm#SEC2165 2153 isReg sing_1158.htm#SEC1234 2154 isSB sing_204.htm#IDX134 2155 isSimplicial sing_2022.htm#SEC2098 2156 isSmooth sing_2090.htm#SEC2166 2157 isSubModule sing_1003.htm#SEC1079 2158 isSublattice sing_2439.htm#SEC2515 2159 isSymmetric sing_1325.htm#SEC1401 2160 isTame sing_1538.htm#SEC1614 2161 isTerminal sing_2091.htm#SEC2167 2162 isTorsionFree sing_2457.htm#SEC2533 2163 isTwoSidedGB sing_496.htm#SEC548 2164 isUpperTriangular sing_701.htm#SEC753 2165 isVar sing_640.htm#SEC692 2166 isVeryAmple sing_2092.htm#SEC2168 2167 isWeyl sing_723.htm#SEC775 2168 isZeroElement sing_2459.htm#SEC2535 2169 is_NND sing_1554.htm#SEC1630 2170 is_NP sing_1213.htm#SEC1289 2171 is_active sing_1587.htm#SEC1663 2172 is_bijective sing_1102.htm#SEC1178 2173 is_cenBimodule sing_756.htm#SEC808 2174 is_cenSubbimodule sing_757.htm#SEC809 2175 is_ci sing_1588.htm#SEC1664 2176 is_complex sing_1038.htm#SEC1114 2177 is_fix_injective sing_1925.htm#SEC2001 2178 is_h_injective sing_1924.htm#SEC2000 2179 is_injective sing_1100.htm#SEC1176 2180 is_irred sing_1551.htm#SEC1627 2181 is_is sing_1589.htm#SEC1665 2182 is_nested sing_1214.htm#SEC1290 2183 is_prime sing_1905.htm#SEC1981 2184 is_primitive_root sing_1901.htm#SEC1977 2185 is_pure sing_748.htm#SEC800 2186 is_reg sing_1590.htm#SEC1666 2187 is_regs sing_1591.htm#SEC1667 2188 is_surjective sing_1101.htm#SEC1177 2189 is_zero sing_944.htm#SEC1020 2190 isartinianMon sing_1187.htm#SEC1263 2191 isgenericMon sing_1188.htm#SEC1264 2192 ishyper sing_1928.htm#SEC2004 2193 isirreducibleMon sing_1186.htm#SEC1262 2194 isoncurve sing_1929.htm#SEC2005 2195 isparam sing_1992.htm#SEC2068 2196 isprimaryMon sing_1185.htm#SEC1261 2197 isprimeMon sing_1184.htm#SEC1260 2198 isuni sing_1977.htm#SEC2053 2199 iv2lp sing_618.htm#SEC670 2200 iv2lpList sing_619.htm#SEC671 2201 iv2lpMat sing_620.htm#SEC672 2202 ivDHilbert sing_594.htm#SEC646 2203 ivDHilbertSickle sing_595.htm#SEC647 2204 ivDimCheck sing_596.htm#SEC648 2205 ivHilbert sing_597.htm#SEC649 2206 ivKDim sing_598.htm#SEC650 2207 ivL2lpI sing_617.htm#SEC669 2208 ivMis2Base sing_599.htm#SEC651 2209 ivMis2Dim sing_600.htm#SEC652 2210 ivOrdMisLex sing_601.htm#SEC653 2211 ivSickle sing_602.htm#SEC654 2212 ivSickleDim sing_604.htm#SEC656 2213 ivSickleHil sing_603.htm#SEC655 2214 jInvariant sing_2124.htm#SEC2200 2215 jOft sing_1860.htm#SEC1936 2216 jacob sing_263.htm#SEC303 2217 jacoblift sing_1570.htm#SEC1646 2218 jacobson sing_1829.htm#SEC1905 2219 jacobson.lib sing_1827.htm#SEC1903 2220 jacobson_lib sing_1827.htm#SEC1903 2221 janet sing_264.htm#SEC304 2222 jet sing_265.htm#SEC305 2223 jordan sing_1086.htm#SEC1162 2224 jordanbasis sing_1087.htm#SEC1163 2225 jordanmatrix sing_1088.htm#SEC1164 2226 jordannf sing_1089.htm#SEC1165 2227 jungfib sing_1409.htm#SEC1485 2228 jungnormal sing_1408.htm#SEC1484 2229 jungresolve sing_1407.htm#SEC1483 2230 katsura sing_942.htm#SEC1018 2231 kbase sing_266.htm#SEC306 2232 kbase (plural) sing_456.htm#SEC496 2233 keepring sing_379.htm#SEC419 2234 kernel sing_267.htm#SEC307 2235 kernelLattice sing_2442.htm#SEC2518 2236 kill sing_268.htm#SEC308 2237 killTask sing_1017.htm#SEC1093 2238 killall sing_888.htm#SEC964 2239 killattrib sing_269.htm#SEC309 2240 kmemory sing_887.htm#SEC963 2241 kohom sing_1160.htm#SEC1236 2242 kontrahom sing_1161.htm#SEC1237 2243 koszul sing_270.htm#SEC310 2244 kskernel.lib sing_1561.htm#SEC1637 2245 kskernel_lib sing_1561.htm#SEC1637 2171 2246 l-adic numbers sing_32.htm#SEC46 2172 laguerre sing_ 328.htm#SEC3682173 laguerre_solve sing_17 58.htm#SEC18342174 lastvarGeneral sing_ 2008.htm#SEC20842175 latex.lib sing_1 802.htm#SEC18782176 latex_lib sing_1 802.htm#SEC18782177 lattice sing_21 66.htm#IDX8552178 latticeArea sing_20 58.htm#SEC21342179 latticeBasis sing_2 363.htm#SEC24392180 latticeCodegree sing_2 449.htm#SEC25252181 latticeDegree sing_2 450.htm#SEC25262182 latticePoints sing_2 451.htm#SEC25272183 latticeVolume sing_2 452.htm#SEC25282184 laxfrT sing_2 266.htm#SEC23422185 laxfrX sing_2 267.htm#SEC23432186 lazy, option sing_3 64.htm#IDX1562187 lcm sing_9 96.htm#SEC10722188 lcmMon sing_1 230.htm#SEC13062189 lcmN sing_1 919.htm#SEC19952190 lcmofall sing_1 439.htm#SEC15152191 lead sing_ 329.htm#SEC3692192 leadcoef sing_ 330.htm#SEC3702193 leadexp sing_ 331.htm#SEC3712194 leadmonom sing_ 332.htm#SEC3722195 leadmonomial sing_19 94.htm#SEC20702196 left annihilator ideal sing_5 89.htm#IDX3232197 leftInverse sing_18 68.htm#SEC19442198 leftKernel sing_18 66.htm#SEC19422199 length, option sing_3 64.htm#IDX1572200 letplaceGBasis sing_6 83.htm#SEC7352201 letterplace correspondence Letterplace correspondence sing_ 543.htm#SEC5952202 lex_solve sing_17 64.htm#SEC18402203 lexicographical ordering sing_8 95.htm#IDX3842247 laguerre sing_271.htm#SEC311 2248 laguerre_solve sing_1708.htm#SEC1784 2249 lastvarGeneral sing_1958.htm#SEC2034 2250 latex.lib sing_1752.htm#SEC1828 2251 latex_lib sing_1752.htm#SEC1828 2252 lattice sing_2196.htm#IDX891 2253 latticeArea sing_2067.htm#SEC2143 2254 latticeBasis sing_2443.htm#SEC2519 2255 latticeCodegree sing_2093.htm#SEC2169 2256 latticeDegree sing_2094.htm#SEC2170 2257 latticePoints sing_2095.htm#SEC2171 2258 latticeVolume sing_2096.htm#SEC2172 2259 laxfrT sing_2346.htm#SEC2422 2260 laxfrX sing_2347.htm#SEC2423 2261 lazy, option sing_307.htm#IDX156 2262 lcm sing_945.htm#SEC1021 2263 lcmMon sing_1179.htm#SEC1255 2264 lcmN sing_1869.htm#SEC1945 2265 lcmofall sing_1389.htm#SEC1465 2266 lead sing_272.htm#SEC312 2267 leadcoef sing_273.htm#SEC313 2268 leadexp sing_274.htm#SEC314 2269 leadmonom sing_275.htm#SEC315 2270 leadmonomial sing_1944.htm#SEC2020 2271 left annihilator ideal sing_532.htm#IDX323 2272 leftInverse sing_1818.htm#SEC1894 2273 leftKernel sing_1816.htm#SEC1892 2274 length, option sing_307.htm#IDX157 2275 letplaceGBasis sing_626.htm#SEC678 2276 letterplace correspondence Letterplace correspondence sing_486.htm#SEC538 2277 lex_solve sing_1714.htm#SEC1790 2278 lexicographical ordering sing_838.htm#IDX384 2204 2279 lib2doc sing_60.htm#SEC97 2205 libSingular sing_4 68.htm#SEC5082280 libSingular sing_411.htm#SEC451 2206 2281 libcdd sing_1.htm#IDX12 2207 2282 libfac sing_1.htm#IDX6 2208 2283 libparse sing_69.htm#SEC109 2209 library sing_2 108.htm#IDX7552210 library sing_2 293.htm#IDX8822284 library sing_2211.htm#IDX906 2285 library sing_2373.htm#IDX960 2211 2286 library, info string sing_55.htm#IDX124 2212 library, polybori.lib sing_2 108.htm#IDX7522287 library, polybori.lib sing_2211.htm#IDX903 2213 2288 library, template sing_55.htm#SEC92 2214 2289 library, template.lib sing_55.htm#IDX122 2215 lieBracket sing_6 94.htm#SEC7462216 lift sing_ 334.htm#SEC3742217 lift sing_ 547.htm#IDX2992218 lift (plural) sing_ 514.htm#SEC5542219 lift_kbase sing_15 57.htm#SEC16332220 lift_rel_kb sing_15 58.htm#SEC16342221 liftenvelope sing_ 550.htm#SEC6022222 liftstd sing_ 335.htm#SEC3752223 liftstd (plural) sing_ 515.htm#SEC5552224 linReduce sing_5 62.htm#SEC6142225 linReduceIdeal sing_5 63.htm#SEC6152226 linSyzSolve sing_5 64.htm#SEC6162227 linalg.lib sing_1 115.htm#SEC11912228 linalg_lib sing_1 115.htm#SEC11912229 linealityDimension sing_20 9.htm#SEC2492230 linealitySpace sing_2 10.htm#SEC2502231 linear algebra sing_2 62.htm#SEC3022232 linear algebra sing_ 338.htm#SEC3782233 linear algebra sing_ 339.htm#SEC3792234 linear algebra sing_ 340.htm#SEC3802235 linear code, dual sing_1 837.htm#IDX7202236 linear code, systematic sing_1 838.htm#IDX7212237 linear interreduction sing_ 554.htm#IDX3142238 linearCombinations sing_5 83.htm#SEC6352239 linearMapKernel sing_5 82.htm#SEC6342240 linear_relations sing_1 107.htm#SEC11832241 linearlyEquivalent sing_2 245.htm#SEC23212242 linearpart sing_17 50.htm#SEC18262290 lieBracket sing_637.htm#SEC689 2291 lift sing_277.htm#SEC317 2292 lift sing_490.htm#IDX299 2293 lift (plural) sing_457.htm#SEC497 2294 lift_kbase sing_1507.htm#SEC1583 2295 lift_rel_kb sing_1508.htm#SEC1584 2296 liftenvelope sing_493.htm#SEC545 2297 liftstd sing_278.htm#SEC318 2298 liftstd (plural) sing_458.htm#SEC498 2299 linReduce sing_505.htm#SEC557 2300 linReduceIdeal sing_506.htm#SEC558 2301 linSyzSolve sing_507.htm#SEC559 2302 linalg.lib sing_1064.htm#SEC1140 2303 linalg_lib sing_1064.htm#SEC1140 2304 linealityDimension sing_2023.htm#SEC2099 2305 linealitySpace sing_2024.htm#SEC2100 2306 linear algebra sing_205.htm#SEC245 2307 linear algebra sing_281.htm#SEC321 2308 linear algebra sing_282.htm#SEC322 2309 linear algebra sing_283.htm#SEC323 2310 linear code, dual sing_1787.htm#IDX784 2311 linear code, systematic sing_1788.htm#IDX785 2312 linear interreduction sing_497.htm#IDX314 2313 linearCombinations sing_526.htm#SEC578 2314 linearMapKernel sing_525.htm#SEC577 2315 linear_relations sing_1056.htm#SEC1132 2316 linearlyEquivalent sing_2325.htm#SEC2401 2317 linearpart sing_1700.htm#SEC1776 2243 2318 link Parallelization with ssi links sing_108.htm#SEC148 2244 link sing_ 852.htm#SEC9042319 link sing_795.htm#SEC847 2245 2320 link declarations sing_109.htm#SEC149 2246 2321 link expressions sing_110.htm#SEC150 … … 2251 2326 list operations sing_121.htm#SEC161 2252 2327 list related functions list related functions sing_122.htm#SEC162 2253 listvar sing_ 336.htm#SEC3762254 lll sing_2 395.htm#SEC24712255 load sing_ 437.htm#SEC4772256 loadLib, option sing_3 64.htm#IDX1782257 loadProc, option sing_3 64.htm#IDX1792258 locAtZero sing_12 85.htm#SEC13612259 locNormal sing_1 221.htm#SEC12972260 local methods sing_1 220.htm#IDX4932261 local methods sing_1 221.htm#IDX4962328 listvar sing_279.htm#SEC319 2329 lll sing_2475.htm#SEC2551 2330 load sing_380.htm#SEC420 2331 loadLib, option sing_307.htm#IDX178 2332 loadProc, option sing_307.htm#IDX179 2333 locAtZero sing_1234.htm#SEC1310 2334 locNormal sing_1170.htm#SEC1246 2335 local methods sing_1169.htm#IDX555 2336 local methods sing_1170.htm#IDX558 2262 2337 local names sing_46.htm#SEC83 2263 local rings, computing in Rings associated to monomial orderings sing_847.htm#SEC899 2264 local weighted lexicographical ordering sing_896.htm#IDX405 2265 local weighted reverse lexicographical ordering Local orderings sing_896.htm#IDX402 2266 localInvar sing_1713.htm#SEC1789 2267 localization Rings associated to monomial orderings sing_847.htm#SEC899 2268 localization sing_2146.htm#IDX815 2269 localization of D-module sing_612.htm#IDX339 2270 localization of D-module sing_817.htm#IDX377 2271 locally closed set, constructible set sing_966.htm#IDX421 2272 localstd sing_2004.htm#SEC2080 2273 locnormal.lib sing_1220.htm#SEC1296 2274 locnormal_lib sing_1220.htm#SEC1296 2275 locstd sing_1642.htm#SEC1718 2276 locus sing_967.htm#SEC1043 2277 locusdg sing_968.htm#SEC1044 2278 locusto sing_971.htm#SEC1047 2279 log2 sing_1894.htm#SEC1970 2280 logarithmic annihilator ideal sing_589.htm#IDX328 2281 lowerHomogeneitySpace lowerHomogeneitySpace sing_2423.htm#SEC2499 2282 lp, global ordering sing_895.htm#IDX383 2283 lp2iv sing_678.htm#SEC730 2284 lp2ivId sing_679.htm#SEC731 2285 lp2lstr sing_690.htm#SEC742 2286 lpDHilbert sing_662.htm#SEC714 2287 lpDHilbertSickle sing_663.htm#SEC715 2288 lpDimCheck sing_665.htm#SEC717 2289 lpHilbert sing_664.htm#SEC716 2290 lpId2ivLi sing_680.htm#SEC732 2291 lpKDim sing_666.htm#SEC718 2292 lpMis2Base sing_667.htm#SEC719 2293 lpMis2Dim sing_668.htm#SEC720 2294 lpMult sing_687.htm#SEC739 2295 lpNF sing_684.htm#SEC736 2296 lpOrdMisLex sing_669.htm#SEC721 2297 lpPower sing_689.htm#SEC741 2298 lpSickle sing_670.htm#SEC722 2299 lpSickleDim sing_672.htm#SEC724 2300 lpSickleHil sing_671.htm#SEC723 2301 lprint sing_974.htm#SEC1050 2302 lres sing_337.htm#SEC377 2303 ls, local ordering sing_896.htm#IDX396 2304 lst2str sing_691.htm#SEC743 2305 lsum sing_1187.htm#SEC1263 2306 ludecomp sing_338.htm#SEC378 2307 luinverse sing_339.htm#SEC379 2308 lusolve sing_340.htm#SEC380 2309 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1966.htm#SEC2042 2310 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1965.htm#SEC2041 2311 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1964.htm#SEC2040 2312 magnitude sing_1888.htm#SEC1964 2313 makeDivisor sing_2237.htm#SEC2313 2314 makeFormalDivisor sing_2247.htm#SEC2323 2315 makeGraph sing_1178.htm#SEC1254 2316 makeHeisenberg sing_768.htm#SEC820 2317 makeLetterplaceRing sing_682.htm#SEC734 2318 makeMalgrange sing_649.htm#SEC701 2319 makeModElimRing sing_785.htm#SEC837 2320 makePDivisor sing_2253.htm#SEC2329 2321 makeQsl2 sing_732.htm#SEC784 2322 makeQsl3 sing_733.htm#SEC785 2323 makeQso3 sing_731.htm#SEC783 2324 makeUe6 sing_728.htm#SEC780 2325 makeUe7 sing_729.htm#SEC781 2326 makeUe8 sing_730.htm#SEC782 2327 makeUf4 sing_727.htm#SEC779 2328 makeUg2 sing_726.htm#SEC778 2329 makeUgl sing_712.htm#SEC764 2330 makeUsl sing_711.htm#SEC763 2331 makeUsl2 sing_710.htm#SEC762 2332 makeUso10 sing_718.htm#SEC770 2333 makeUso11 sing_719.htm#SEC771 2334 makeUso12 sing_720.htm#SEC772 2335 makeUso5 sing_713.htm#SEC765 2336 makeUso6 sing_714.htm#SEC766 2337 makeUso7 sing_715.htm#SEC767 2338 makeUso8 sing_716.htm#SEC768 2339 makeUso9 sing_717.htm#SEC769 2340 makeUsp1 sing_721.htm#SEC773 2341 makeUsp2 sing_722.htm#SEC774 2342 makeUsp3 sing_723.htm#SEC775 2343 makeUsp4 sing_724.htm#SEC776 2344 makeUsp5 sing_725.htm#SEC777 2345 makeWeyl sing_767.htm#SEC819 2338 local rings, computing in Rings associated to monomial orderings sing_790.htm#SEC842 2339 local weighted lexicographical ordering sing_839.htm#IDX405 2340 local weighted reverse lexicographical ordering Local orderings sing_839.htm#IDX402 2341 localInvar sing_1663.htm#SEC1739 2342 localization Rings associated to monomial orderings sing_790.htm#SEC842 2343 localization sing_2176.htm#IDX851 2344 localization of D-module sing_555.htm#IDX339 2345 localization of D-module sing_760.htm#IDX377 2346 locally closed set sing_909.htm#IDX438 2347 locally closed set sing_911.htm#IDX449 2348 localstd sing_1954.htm#SEC2030 2349 locnormal.lib sing_1169.htm#SEC1245 2350 locnormal_lib sing_1169.htm#SEC1245 2351 locstd sing_1592.htm#SEC1668 2352 locus FamElemsAtEnvCompPoints sing_913.htm#SEC989 2353 locus sing_913.htm#IDX456 2354 locus sing_914.htm#IDX460 2355 locus sing_915.htm#IDX464 2356 locus sing_916.htm#IDX468 2357 locus sing_917.htm#IDX473 2358 locus sing_918.htm#IDX478 2359 locusdg sing_914.htm#SEC990 2360 locusto sing_916.htm#SEC992 2361 log2 sing_1844.htm#SEC1920 2362 logarithmic annihilator ideal sing_532.htm#IDX328 2363 lp, global ordering sing_838.htm#IDX383 2364 lp2iv sing_621.htm#SEC673 2365 lp2ivId sing_622.htm#SEC674 2366 lp2lstr sing_633.htm#SEC685 2367 lpDHilbert sing_605.htm#SEC657 2368 lpDHilbertSickle sing_606.htm#SEC658 2369 lpDimCheck sing_608.htm#SEC660 2370 lpHilbert sing_607.htm#SEC659 2371 lpId2ivLi sing_623.htm#SEC675 2372 lpKDim sing_609.htm#SEC661 2373 lpMis2Base sing_610.htm#SEC662 2374 lpMis2Dim sing_611.htm#SEC663 2375 lpMult sing_630.htm#SEC682 2376 lpNF sing_627.htm#SEC679 2377 lpOrdMisLex sing_612.htm#SEC664 2378 lpPower sing_632.htm#SEC684 2379 lpSickle sing_613.htm#SEC665 2380 lpSickleDim sing_615.htm#SEC667 2381 lpSickleHil sing_614.htm#SEC666 2382 lprint sing_923.htm#SEC999 2383 lres sing_280.htm#SEC320 2384 ls, local ordering sing_839.htm#IDX396 2385 lst2str sing_634.htm#SEC686 2386 lsum sing_1136.htm#SEC1212 2387 ludecomp sing_281.htm#SEC321 2388 luinverse sing_282.htm#SEC322 2389 lusolve sing_283.htm#SEC323 2390 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1916.htm#SEC1992 2391 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1915.htm#SEC1991 2392 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1914.htm#SEC1990 2393 magnitude sing_1838.htm#SEC1914 2394 makeDivisor sing_2317.htm#SEC2393 2395 makeFormalDivisor sing_2327.htm#SEC2403 2396 makeGraph sing_1127.htm#SEC1203 2397 makeHeisenberg sing_711.htm#SEC763 2398 makeLetterplaceRing sing_625.htm#SEC677 2399 makeMalgrange sing_592.htm#SEC644 2400 makeModElimRing sing_728.htm#SEC780 2401 makePDivisor sing_2333.htm#SEC2409 2402 makeQsl2 sing_675.htm#SEC727 2403 makeQsl3 sing_676.htm#SEC728 2404 makeQso3 sing_674.htm#SEC726 2405 makeUe6 sing_671.htm#SEC723 2406 makeUe7 sing_672.htm#SEC724 2407 makeUe8 sing_673.htm#SEC725 2408 makeUf4 sing_670.htm#SEC722 2409 makeUg2 sing_669.htm#SEC721 2410 makeUgl sing_655.htm#SEC707 2411 makeUsl sing_654.htm#SEC706 2412 makeUsl2 sing_653.htm#SEC705 2413 makeUso10 sing_661.htm#SEC713 2414 makeUso11 sing_662.htm#SEC714 2415 makeUso12 sing_663.htm#SEC715 2416 makeUso5 sing_656.htm#SEC708 2417 makeUso6 sing_657.htm#SEC709 2418 makeUso7 sing_658.htm#SEC710 2419 makeUso8 sing_659.htm#SEC711 2420 makeUso9 sing_660.htm#SEC712 2421 makeUsp1 sing_664.htm#SEC716 2422 makeUsp2 sing_665.htm#SEC717 2423 makeUsp3 sing_666.htm#SEC718 2424 makeUsp4 sing_667.htm#SEC719 2425 makeUsp5 sing_668.htm#SEC720 2426 makeWeyl sing_710.htm#SEC762 2346 2427 map sing_123.htm#SEC163 2347 map (plural) sing_4 77.htm#SEC5172428 map (plural) sing_420.htm#SEC460 2348 2429 map declarations sing_124.htm#SEC164 2349 map declarations (plural) map declarations (plural) sing_4 78.htm#SEC5182430 map declarations (plural) map declarations (plural) sing_421.htm#SEC461 2350 2431 map expressions sing_125.htm#SEC165 2351 map expressions (plural) map expressions (plural) sing_4 79.htm#SEC5192432 map expressions (plural) map expressions (plural) sing_422.htm#SEC462 2352 2433 map operations sing_126.htm#IDX129 2353 map operations (plural) map operations (plural) sing_4 80.htm#IDX2942434 map operations (plural) map operations (plural) sing_423.htm#IDX294 2354 2435 map related functions map related functions sing_127.htm#IDX131 2355 map related functions (plural) map related functions (plural) sing_4 81.htm#IDX2952356 mapIsFinite sing_11 55.htm#SEC12312357 mapToRatNormCurve sing_1 414.htm#SEC14902358 mapall sing_ 1039.htm#SEC11152359 mappingcone sing_2 331.htm#SEC24072360 mappingcone3 sing_2 333.htm#SEC24092361 markov4ti2 sing_13 70.htm#SEC1446 91632362 mat2arr sing_21 31.htm#SEC22072363 mat2carr sing_21 32.htm#SEC22082364 mat_rk sing_1 129.htm#SEC12052365 matbil sing_ 2015.htm#SEC20912366 mathematical objects Representation of mathematical objects sing_8 91.htm#SEC9432367 mathinit sing_1 800.htm#SEC18762368 matmult sing_ 2016.htm#SEC20922436 map related functions (plural) map related functions (plural) sing_424.htm#IDX295 2437 mapIsFinite sing_1104.htm#SEC1180 2438 mapToRatNormCurve sing_1364.htm#SEC1440 2439 mapall sing_988.htm#SEC1064 2440 mappingcone sing_2411.htm#SEC2487 2441 mappingcone3 sing_2413.htm#SEC2489 2442 markov4ti2 sing_1320.htm#SEC1396 9163 2443 mat2arr sing_2161.htm#SEC2237 2444 mat2carr sing_2162.htm#SEC2238 2445 mat_rk sing_1078.htm#SEC1154 2446 matbil sing_1965.htm#SEC2041 2447 mathematical objects Representation of mathematical objects sing_834.htm#SEC886 2448 mathinit sing_1750.htm#SEC1826 2449 matmult sing_1966.htm#SEC2042 2369 2450 matrix sing_128.htm#SEC168 2370 matrix sing_21 31.htm#IDX7832371 matrix sing_21 32.htm#IDX7862372 matrix sing_21 33.htm#IDX7902451 matrix sing_2161.htm#IDX819 2452 matrix sing_2162.htm#IDX822 2453 matrix sing_2163.htm#IDX826 2373 2454 matrix declarations sing_129.htm#SEC169 2374 matrix diagonalization sing_18 77.htm#IDX7312455 matrix diagonalization sing_1827.htm#IDX795 2375 2456 matrix expressions sing_130.htm#SEC170 2376 2457 matrix operations sing_132.htm#SEC172 2377 2458 matrix related functions matrix related functions sing_133.htm#SEC173 2378 2459 matrix type cast sing_131.htm#SEC171 2379 matrix.lib sing_10 82.htm#SEC11582380 matrixExp sing_1 404.htm#SEC14802381 matrixLog sing_1 405.htm#SEC14812382 matrixT1 sing_16 56.htm#SEC17322383 matrix_lib sing_10 82.htm#SEC11582384 matrixpres sing_2 336.htm#SEC24122385 matrixsystem sing_2 277.htm#SEC23532386 max sing_ 341.htm#SEC3812387 maxEord sing_1 429.htm#SEC15052388 maxExp sing_2 61.htm#IDX1362389 maxIntRoot sing_ 834.htm#SEC8862390 maxZeros sing_1 407.htm#SEC14832391 maxabs sing_ 2034.htm#SEC21102392 maxcoef sing_9 97.htm#SEC10732393 maxdeg sing_9 98.htm#SEC10742394 maxdeg1 sing_9 99.htm#SEC10752395 maxideal sing_ 342.htm#SEC3822396 maximalFace sing_2 453.htm#SEC25292397 maximalGroebnerCone sing_2 421.htm#SEC24972398 maximalValue sing_2 454.htm#SEC25302399 maximum sing_1 907.htm#SEC19832400 maximum number of zeroes sing_1 407.htm#IDX5382460 matrix.lib sing_1031.htm#SEC1107 2461 matrixExp sing_1354.htm#SEC1430 2462 matrixLog sing_1355.htm#SEC1431 2463 matrixT1 sing_1606.htm#SEC1682 2464 matrix_lib sing_1031.htm#SEC1107 2465 matrixpres sing_2416.htm#SEC2492 2466 matrixsystem sing_2357.htm#SEC2433 2467 max sing_284.htm#SEC324 2468 maxEord sing_1379.htm#SEC1455 2469 maxExp sing_204.htm#IDX136 2470 maxIntRoot sing_777.htm#SEC829 2471 maxZeros sing_1357.htm#SEC1433 2472 maxabs sing_1984.htm#SEC2060 2473 maxcoef sing_946.htm#SEC1022 2474 maxdeg sing_947.htm#SEC1023 2475 maxdeg1 sing_948.htm#SEC1024 2476 maxideal sing_285.htm#SEC325 2477 maximalFace sing_2097.htm#SEC2173 2478 maximalGroebnerCone sing_2151.htm#SEC2227 2479 maximalValue sing_2098.htm#SEC2174 2480 maximum sing_1857.htm#SEC1933 2481 maximum number of zeroes sing_1357.htm#IDX602 2401 2482 mdouble sing_56.htm#SEC93 2402 mem, option sing_3 64.htm#IDX1802403 membershipMon sing_1 231.htm#SEC13072404 memory sing_ 343.htm#SEC3832405 memory managment sing_ 343.htm#SEC3832406 merkle_hellman_decryption merkle_hellman_decryption sing_19 68.htm#SEC20442407 merkle_hellman_encryption merkle_hellman_encryption sing_19 67.htm#SEC20432408 midpoint sing_2 273.htm#SEC23492409 milnor sing_1 643.htm#SEC17192410 milnorcode sing_1 527.htm#SEC16032411 milnornumber sing_24 11.htm#SEC24872412 min sing_ 344.htm#SEC3842413 minAssChar sing_1 329.htm#SEC14052414 minAssCharE sing_1 330.htm#SEC14062415 minAssGTZ sing_1 327.htm#SEC14032416 minAssGTZE sing_1 328.htm#SEC14042417 minAssZ sing_1 347.htm#SEC14232418 minEcart sing_19 97.htm#SEC20732419 minIntRoot sing_ 610.htm#SEC6622420 minIntRoot2 sing_ 833.htm#SEC8852421 minMult sing_11 62.htm#SEC12382422 minbase sing_ 345.htm#SEC3852423 minbaseMon sing_1 228.htm#SEC13042424 mindeg sing_ 1000.htm#SEC10762425 mindeg1 sing_ 1001.htm#SEC10772426 mindist sing_18 52.htm#SEC19282427 minimal display time, setting the sing_ 406.htm#IDX2782428 minimalFace sing_2 455.htm#SEC25312429 minimalValue sing_2 456.htm#SEC25322430 minipoly sing_1 134.htm#SEC12102431 minkowskiSum sing_2 457.htm#SEC25332432 minor sing_ 346.htm#SEC3862433 minpoly sing_ 445.htm#SEC4852434 minres sing_ 347.htm#SEC3872435 minres (plural) sing_ 516.htm#SEC5562436 mirror symmetry sing_11 77.htm#IDX4632437 mixed Hodge structure sing_15 65.htm#IDX5942438 mixed Hodge structure sing_15 71.htm#IDX6222439 mixed Hodge structure sing_15 72.htm#IDX6282440 mixed Hodge structure sing_15 73.htm#IDX6362441 mixed Hodge structure sing_15 74.htm#IDX6422442 mixed Hodge structure sing_15 75.htm#IDX6502443 mixed Hodge structure sing_15 76.htm#IDX6602444 mixed Hodge structure sing_15 87.htm#IDX6662445 mixed Hodge structure sing_15 89.htm#IDX6772483 mem, option sing_307.htm#IDX180 2484 membershipMon sing_1180.htm#SEC1256 2485 memory sing_286.htm#SEC326 2486 memory managment sing_286.htm#SEC326 2487 merkle_hellman_decryption merkle_hellman_decryption sing_1918.htm#SEC1994 2488 merkle_hellman_encryption merkle_hellman_encryption sing_1917.htm#SEC1993 2489 midpoint sing_2353.htm#SEC2429 2490 milnor sing_1593.htm#SEC1669 2491 milnorcode sing_1477.htm#SEC1553 2492 milnornumber sing_2491.htm#SEC2567 2493 min sing_287.htm#SEC327 2494 minAssChar sing_1279.htm#SEC1355 2495 minAssCharE sing_1280.htm#SEC1356 2496 minAssGTZ sing_1277.htm#SEC1353 2497 minAssGTZE sing_1278.htm#SEC1354 2498 minAssZ sing_1297.htm#SEC1373 2499 minEcart sing_1947.htm#SEC2023 2500 minIntRoot sing_553.htm#SEC605 2501 minIntRoot2 sing_776.htm#SEC828 2502 minMult sing_1111.htm#SEC1187 2503 minbase sing_288.htm#SEC328 2504 minbaseMon sing_1177.htm#SEC1253 2505 mindeg sing_949.htm#SEC1025 2506 mindeg1 sing_950.htm#SEC1026 2507 mindist sing_1802.htm#SEC1878 2508 minimal display time, setting the sing_349.htm#IDX278 2509 minimalFace sing_2099.htm#SEC2175 2510 minimalValue sing_2100.htm#SEC2176 2511 minipoly sing_1083.htm#SEC1159 2512 minkowskiSum sing_2101.htm#SEC2177 2513 minor sing_289.htm#SEC329 2514 minpoly sing_388.htm#SEC428 2515 minres sing_290.htm#SEC330 2516 minres (plural) sing_459.htm#SEC499 2517 mirror symmetry sing_1126.htm#IDX523 2518 mixed Hodge structure sing_1515.htm#IDX658 2519 mixed Hodge structure sing_1521.htm#IDX686 2520 mixed Hodge structure sing_1522.htm#IDX692 2521 mixed Hodge structure sing_1523.htm#IDX700 2522 mixed Hodge structure sing_1524.htm#IDX706 2523 mixed Hodge structure sing_1525.htm#IDX714 2524 mixed Hodge structure sing_1526.htm#IDX724 2525 mixed Hodge structure sing_1537.htm#IDX730 2526 mixed Hodge structure sing_1539.htm#IDX741 2446 2527 mod sing_76.htm#SEC116 2447 2528 mod sing_93.htm#SEC133 2448 2529 mod sing_142.htm#SEC182 2449 mod2id sing_1005.htm#SEC1081 2450 mod2str sing_692.htm#SEC744 2451 modDec sing_1247.htm#SEC1323 2452 modNPos sing_1270.htm#SEC1346 2453 modNormal sing_1223.htm#SEC1299 2454 modNpos_test sing_1268.htm#SEC1344 2455 modStd sing_1225.htm#SEC1301 2456 modWalk sing_2340.htm#SEC2416 2457 mod_versal sing_1556.htm#SEC1632 2458 modality sing_1535.htm#SEC1611 2459 modfWalk sing_2342.htm#SEC2418 2460 modfrWalk sing_2343.htm#SEC2419 2461 modnormal.lib sing_1222.htm#SEC1298 2462 modnormal_lib sing_1222.htm#SEC1298 2463 modrWalk sing_2341.htm#SEC2417 2464 modregCM sing_1274.htm#SEC1350 2465 modsatiety sing_1272.htm#SEC1348 2466 modstd.lib sing_1224.htm#SEC1300 2467 modstd_lib sing_1224.htm#SEC1300 2468 modular sing_983.htm#SEC1059 2469 modular methods sing_1220.htm#IDX494 2470 modular methods sing_1222.htm#IDX499 2471 modular methods. sing_1221.htm#IDX497 2472 modular techniques. sing_1223.htm#IDX501 2473 modular.lib sing_982.htm#SEC1058 2474 modular_lib sing_982.htm#SEC1058 2475 modular_lib sing_982.htm#IDX427 2530 mod2id sing_954.htm#SEC1030 2531 mod2str sing_635.htm#SEC687 2532 modDec sing_1196.htm#SEC1272 2533 modNPos sing_1219.htm#SEC1295 2534 modNormal sing_1172.htm#SEC1248 2535 modNpos_test sing_1217.htm#SEC1293 2536 modStd sing_1174.htm#SEC1250 2537 modVStd sing_2307.htm#SEC2383 2538 modVStd0 sing_2308.htm#SEC2384 2539 modWalk sing_2420.htm#SEC2496 2540 mod_versal sing_1506.htm#SEC1582 2541 modality sing_1485.htm#SEC1561 2542 modfWalk sing_2422.htm#SEC2498 2543 modfrWalk sing_2423.htm#SEC2499 2544 modnormal.lib sing_1171.htm#SEC1247 2545 modnormal_lib sing_1171.htm#SEC1247 2546 modrWalk sing_2421.htm#SEC2497 2547 modregCM sing_1223.htm#SEC1299 2548 modsatiety sing_1221.htm#SEC1297 2549 modstd.lib sing_1173.htm#SEC1249 2550 modstd_lib sing_1173.htm#SEC1249 2551 modular sing_932.htm#SEC1008 2552 modular methods sing_1169.htm#IDX556 2553 modular methods sing_1171.htm#IDX561 2554 modular methods. sing_1170.htm#IDX559 2555 modular techniques. sing_1172.htm#IDX563 2556 modular.lib sing_931.htm#SEC1007 2557 modular_lib sing_931.htm#SEC1007 2558 modular_lib sing_931.htm#IDX487 2476 2559 module sing_134.htm#SEC174 2477 module (plural) sing_4 82.htm#SEC5222560 module (plural) sing_425.htm#SEC465 2478 2561 module declarations sing_135.htm#SEC175 2479 module declarations (plural) module declarations (plural) sing_4 83.htm#SEC5232562 module declarations (plural) module declarations (plural) sing_426.htm#SEC466 2480 2563 module expressions sing_136.htm#SEC176 2481 module expressions (plural) module expressions (plural) sing_4 84.htm#SEC5242564 module expressions (plural) module expressions (plural) sing_427.htm#SEC467 2482 2565 module operations sing_137.htm#SEC177 2483 module operations (plural) module operations (plural) sing_4 85.htm#SEC5252484 module ordering C sing_8 97.htm#IDX4082485 module ordering c sing_8 97.htm#IDX4102566 module operations (plural) module operations (plural) sing_428.htm#SEC468 2567 module ordering C sing_840.htm#IDX408 2568 module ordering c sing_840.htm#IDX410 2486 2569 module related functions module related functions sing_138.htm#SEC178 2487 module related functions (plural) module related functions (plural) sing_486.htm#SEC526 2488 module_containment sing_1147.htm#SEC1223 2489 modulo sing_348.htm#SEC388 2490 modulo (plural) sing_517.htm#SEC557 2491 moduloSlim sing_775.htm#SEC827 2492 modwalk.lib sing_2339.htm#IDX890 2493 modwalk_lib sing_2339.htm#IDX891 2494 moebius sing_2167.htm#SEC2243 2495 moebius function sing_2167.htm#IDX856 2496 molien sing_1679.htm#SEC1755 2497 mondromy.lib sing_1617.htm#SEC1693 2498 mondromy_lib sing_1617.htm#SEC1693 2499 monitor sing_349.htm#SEC389 2500 monodromy sing_1565.htm#IDX598 2501 monodromy sing_1570.htm#SEC1646 2502 monodromy sing_1570.htm#IDX618 2503 monodromy sing_1575.htm#IDX653 2504 monodromy sing_1587.htm#IDX669 2505 monodromy sing_1589.htm#IDX680 2506 monodromyB sing_1621.htm#SEC1697 2507 monomial sing_350.htm#SEC390 2508 monomial ordering sing_1048.htm#IDX441 2509 monomial orderings General definitions for orderings sing_847.htm#SEC899 2510 monomial orderings sing_894.htm#SEC946 2511 monomial orderings introduction Introduction to orderings sing_893.htm#SEC945 2512 monomialInIdeal sing_831.htm#SEC883 2513 monomialLcm sing_1995.htm#SEC2071 2514 monomialideal.lib sing_1226.htm#SEC1302 2515 monomialideal_lib sing_1226.htm#SEC1302 2516 monomials and precedence Miscellaneous oddities sing_466.htm#IDX284 2517 mons2intmat sing_1314.htm#SEC1390 15555 2518 morsesplit sing_1528.htm#SEC1604 2519 mp_res_mat sing_1761.htm#SEC1837 2520 mplot sing_1801.htm#SEC1877 2521 mpresmat sing_351.htm#SEC391 2522 mprimdec.lib sing_1243.htm#SEC1319 2523 mprimdec_lib sing_1243.htm#SEC1319 2524 mregular.lib sing_1258.htm#SEC1334 2525 mregular_lib sing_1258.htm#SEC1334 2526 mres sing_352.htm#SEC392 2527 mres (plural) sing_518.htm#SEC558 2528 mstd sing_353.htm#SEC393 2570 module related functions (plural) module related functions (plural) sing_429.htm#SEC469 2571 module_containment sing_1096.htm#SEC1172 2572 modulo sing_291.htm#SEC331 2573 modulo (plural) sing_460.htm#SEC500 2574 moduloSlim sing_718.htm#SEC770 2575 modwalk.lib sing_2419.htm#IDX968 2576 modwalk_lib sing_2419.htm#IDX969 2577 moebius sing_2197.htm#SEC2273 2578 moebius function sing_2197.htm#IDX892 2579 molien sing_1629.htm#SEC1705 2580 mondromy.lib sing_1567.htm#SEC1643 2581 mondromy_lib sing_1567.htm#SEC1643 2582 monitor sing_292.htm#SEC332 2583 monodromy sing_1515.htm#IDX662 2584 monodromy sing_1520.htm#SEC1596 2585 monodromy sing_1520.htm#IDX682 2586 monodromy sing_1525.htm#IDX717 2587 monodromy sing_1537.htm#IDX733 2588 monodromy sing_1539.htm#IDX744 2589 monodromyB sing_1571.htm#SEC1647 2590 monomial sing_293.htm#SEC333 2591 monomial ordering sing_997.htm#IDX501 2592 monomial orderings General definitions for orderings sing_790.htm#SEC842 2593 monomial orderings sing_837.htm#SEC889 2594 monomial orderings introduction Introduction to orderings sing_836.htm#SEC888 2595 monomialInIdeal sing_774.htm#SEC826 2596 monomialLcm sing_1945.htm#SEC2021 2597 monomialabortstd sing_2204.htm#SEC2280 2598 monomialideal.lib sing_1175.htm#SEC1251 2599 monomialideal_lib sing_1175.htm#SEC1251 2600 monomials and precedence Miscellaneous oddities sing_409.htm#IDX284 2601 mons2intmat sing_1264.htm#SEC1340 15555 2602 morsesplit sing_1478.htm#SEC1554 2603 mp_res_mat sing_1711.htm#SEC1787 2604 mplot sing_1751.htm#SEC1827 2605 mpresmat sing_294.htm#SEC334 2606 mprimdec.lib sing_1192.htm#SEC1268 2607 mprimdec_lib sing_1192.htm#SEC1268 2608 mregular.lib sing_1207.htm#SEC1283 2609 mregular_lib sing_1207.htm#SEC1283 2610 mres sing_295.htm#SEC335 2611 mres (plural) sing_461.htm#SEC501 2612 mstd sing_296.htm#SEC336 2529 2613 msum sing_58.htm#SEC95 2530 2614 mtriple sing_57.htm#SEC94 2531 mult Miscellaneous oddities sing_ 354.htm#SEC3942532 mult sing_4 66.htm#IDX2852533 multBound sing_ 446.htm#SEC4862534 multRat sing_ 839.htm#SEC8912535 multarr2arr sing_21 62.htm#SEC22382536 multarrMultRestrict sing_21 64.htm#SEC22402537 multarrRestrict sing_21 63.htm#SEC22392538 multcol sing_1 101.htm#SEC11772539 multdivisor sing_2 239.htm#SEC23152540 multformaldivisor sing_2 251.htm#SEC23272541 multi sing_19 82.htm#SEC20582615 mult Miscellaneous oddities sing_297.htm#SEC337 2616 mult sing_409.htm#IDX285 2617 multBound sing_389.htm#SEC429 2618 multRat sing_782.htm#SEC834 2619 multarr2arr sing_2192.htm#SEC2268 2620 multarrMultRestrict sing_2194.htm#SEC2270 2621 multarrRestrict sing_2193.htm#SEC2269 2622 multcol sing_1050.htm#SEC1126 2623 multdivisor sing_2319.htm#SEC2395 2624 multformaldivisor sing_2331.htm#SEC2407 2625 multi sing_1932.htm#SEC2008 2542 2626 multi indices sing_37.htm#SEC65 2543 multiDeg sing_2374.htm#SEC2450 2544 multiDegBasis sing_2375.htm#SEC2451 2545 multiDegGroebner sing_2383.htm#SEC2459 2546 multiDegModulo sing_2385.htm#SEC2461 2547 multiDegPartition sing_2376.htm#SEC2452 2548 multiDegResolution sing_2386.htm#SEC2462 2549 multiDegSyzygy sing_2384.htm#SEC2460 2550 multiDegTensor sing_2387.htm#SEC2463 2551 multiDegTor sing_2388.htm#SEC2464 2552 multiarrangement sing_2158.htm#IDX836 2553 multiarrangement sing_2159.htm#IDX838 2554 multiarrangement sing_2160.htm#IDX841 2555 multiarrangement sing_2161.htm#IDX842 2556 multiarrangement sing_2162.htm#IDX845 2557 multiarrangement sing_2163.htm#IDX848 2558 multiarrangement sing_2164.htm#IDX850 2559 multidimensional_knapsack multidimensional_knapsack sing_1960.htm#SEC2036 2560 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2344.htm#IDX894 2561 multigrading.lib sing_2344.htm#IDX892 2562 multigrading_lib sing_2344.htm#IDX893 2563 multiplicities, sequence of sing_1596.htm#IDX692 2564 multiplicity sequence sing_1509.htm#IDX571 2565 multiplicity sequence sing_1512.htm#IDX583 2566 multiplicity sequence sing_1598.htm#IDX693 2567 multiplylist sing_1449.htm#SEC1525 2568 multivariate equations sing_1735.htm#IDX710 2569 multrow sing_1102.htm#SEC1178 2570 multseq2charexp sing_1508.htm#SEC1584 2571 multsequence sing_1598.htm#SEC1674 2572 nBoundaryLatticePoints nBoundaryLatticePoints sing_2458.htm#SEC2534 2573 nHilbertBasis sing_2459.htm#SEC2535 2574 nInteriorLatticePoints nInteriorLatticePoints sing_2460.htm#SEC2536 2575 nLatticePoints sing_2461.htm#SEC2537 2576 naccache_stern_decryption naccache_stern_decryption sing_1963.htm#SEC2039 2577 naccache_stern_encryption naccache_stern_encryption sing_1962.htm#SEC2038 2578 naccache_stern_generation naccache_stern_generation sing_1961.htm#SEC2037 2579 nameof sing_355.htm#SEC395 2580 names sing_356.htm#SEC396 2581 nashmult sing_1516.htm#SEC1592 2582 nblocks sing_406.htm#IDX220 2583 ncExt_R sing_808.htm#SEC860 2584 ncHom sing_809.htm#SEC861 2585 ncRelations sing_776.htm#SEC828 2586 nc_algebra sing_519.htm#SEC559 2587 ncalg.lib sing_709.htm#SEC761 2588 ncalg_lib sing_709.htm#SEC761 2589 ncalgebra sing_520.htm#SEC560 2590 ncdecomp.lib sing_736.htm#SEC788 2591 ncdecomp_lib sing_736.htm#SEC788 2592 ncdetection sing_703.htm#SEC755 2593 ncfactor sing_742.htm#SEC794 2594 ncfactor.lib sing_741.htm#SEC793 2595 ncfactor_lib sing_741.htm#SEC793 2596 nchomolog.lib sing_807.htm#IDX367 2597 nchomolog_lib sing_807.htm#IDX368 2598 ncols sing_357.htm#SEC397 2599 ncones sing_233.htm#SEC273 2600 ncpreim.lib sing_754.htm#SEC806 2601 ncpreim_lib sing_754.htm#SEC806 2602 nctools.lib sing_762.htm#SEC814 2603 nctools_lib sing_762.htm#SEC814 2604 ndcond sing_765.htm#SEC817 2605 negatedCone sing_211.htm#SEC251 2606 negative degree lexicographical ordering sing_896.htm#IDX399 2607 negative degree reverse lexicographical ordering Local orderings sing_896.htm#IDX397 2608 negative lexicographical ordering sing_896.htm#IDX395 2609 negativedivisor sing_2240.htm#SEC2316 2610 negativeformaldivisor negativeformaldivisor sing_2250.htm#SEC2326 2627 multiDeg sing_2454.htm#SEC2530 2628 multiDegBasis sing_2455.htm#SEC2531 2629 multiDegGroebner sing_2463.htm#SEC2539 2630 multiDegModulo sing_2465.htm#SEC2541 2631 multiDegPartition sing_2456.htm#SEC2532 2632 multiDegResolution sing_2466.htm#SEC2542 2633 multiDegSyzygy sing_2464.htm#SEC2540 2634 multiDegTensor sing_2467.htm#SEC2543 2635 multiDegTor sing_2468.htm#SEC2544 2636 multiarrangement sing_2188.htm#IDX872 2637 multiarrangement sing_2189.htm#IDX874 2638 multiarrangement sing_2190.htm#IDX877 2639 multiarrangement sing_2191.htm#IDX878 2640 multiarrangement sing_2192.htm#IDX881 2641 multiarrangement sing_2193.htm#IDX884 2642 multiarrangement sing_2194.htm#IDX886 2643 multidimensional_knapsack multidimensional_knapsack sing_1910.htm#SEC1986 2644 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2424.htm#IDX974 2645 multigrading.lib sing_2424.htm#IDX972 2646 multigrading_lib sing_2424.htm#IDX973 2647 multiplicities, sequence of sing_1546.htm#IDX756 2648 multiplicity sing_2313.htm#IDX933 2649 multiplicity sequence sing_1459.htm#IDX635 2650 multiplicity sequence sing_1462.htm#IDX647 2651 multiplicity sequence sing_1548.htm#IDX757 2652 multiplylist sing_1399.htm#SEC1475 2653 multivariate equations sing_1685.htm#IDX774 2654 multrow sing_1051.htm#SEC1127 2655 multseq2charexp sing_1458.htm#SEC1534 2656 multsequence sing_1548.htm#SEC1624 2657 nBoundaryLatticePoints nBoundaryLatticePoints sing_2102.htm#SEC2178 2658 nHilbertBasis sing_2103.htm#SEC2179 2659 nInteriorLatticePoints nInteriorLatticePoints sing_2104.htm#SEC2180 2660 nLatticePoints sing_2105.htm#SEC2181 2661 naccache_stern_decryption naccache_stern_decryption sing_1913.htm#SEC1989 2662 naccache_stern_encryption naccache_stern_encryption sing_1912.htm#SEC1988 2663 naccache_stern_generation naccache_stern_generation sing_1911.htm#SEC1987 2664 nameof sing_298.htm#SEC338 2665 names sing_299.htm#SEC339 2666 nashmult sing_1466.htm#SEC1542 2667 nblocks sing_349.htm#IDX220 2668 ncExt_R sing_751.htm#SEC803 2669 ncHom sing_752.htm#SEC804 2670 ncRelations sing_719.htm#SEC771 2671 nc_algebra sing_462.htm#SEC502 2672 ncalg.lib sing_652.htm#SEC704 2673 ncalg_lib sing_652.htm#SEC704 2674 ncalgebra sing_463.htm#SEC503 2675 ncdecomp.lib sing_679.htm#SEC731 2676 ncdecomp_lib sing_679.htm#SEC731 2677 ncdetection sing_646.htm#SEC698 2678 ncfactor sing_685.htm#SEC737 2679 ncfactor.lib sing_684.htm#SEC736 2680 ncfactor_lib sing_684.htm#SEC736 2681 nchomolog.lib sing_750.htm#IDX367 2682 nchomolog_lib sing_750.htm#IDX368 2683 ncols sing_300.htm#SEC340 2684 ncones sing_2047.htm#SEC2123 2685 ncpreim.lib sing_697.htm#SEC749 2686 ncpreim_lib sing_697.htm#SEC749 2687 nctools.lib sing_705.htm#SEC757 2688 nctools_lib sing_705.htm#SEC757 2689 ndcond sing_708.htm#SEC760 2690 negatedCone sing_2025.htm#SEC2101 2691 negative degree lexicographical ordering sing_839.htm#IDX399 2692 negative degree reverse lexicographical ordering Local orderings sing_839.htm#IDX397 2693 negative lexicographical ordering sing_839.htm#IDX395 2694 negativedivisor sing_2320.htm#SEC2396 2695 negativeformaldivisor negativeformaldivisor sing_2330.htm#SEC2406 2611 2696 net access Command line options sing_19.htm#IDX40 2612 newTest sing_1 902.htm#SEC19782697 newTest sing_1852.htm#SEC1928 2613 2698 newline sing_166.htm#SEC206 2614 news sing_24 70.htm#SEC25462699 news sing_2497.htm#SEC2573 2615 2700 newstruct sing_177.htm#SEC217 2616 newstruct sing_2108.htm#IDX757 2617 newtonDiag sing_1009.htm#SEC1085 2618 newtonPolytope sing_241.htm#SEC281 2619 newtonPolytopeLP sing_2047.htm#SEC2123 2620 newtonPolytopeP sing_2046.htm#SEC2122 2621 newtonpoly sing_1603.htm#SEC1679 2622 nf_icis sing_1644.htm#SEC1720 2623 nfmodStd sing_2398.htm#SEC2474 2624 nfmodSyz sing_2400.htm#SEC2476 2625 nfmodstd.lib sing_2396.htm#SEC2472 2626 nfmodstd_lib sing_2396.htm#SEC2472 2627 nfmodsyz.lib sing_2399.htm#SEC2475 2628 nfmodsyz_lib sing_2399.htm#SEC2475 2629 nilpotent Lie algebras sing_1402.htm#IDX523 2630 nmaxcones sing_232.htm#SEC272 2631 noether sing_447.htm#SEC487 2632 noether.lib sing_1266.htm#SEC1342 2633 noetherNormal sing_1154.htm#SEC1230 2634 noether_lib sing_1266.htm#SEC1342 2635 non-english special characters sing_455.htm#IDX280 2636 nonMonomials sing_1318.htm#SEC1394 2637 nonZeroEntry sing_1157.htm#SEC1233 2638 none, option sing_364.htm#IDX150 2639 norTest sing_1286.htm#SEC1362 2640 norm sing_1981.htm#SEC2057 2641 normal sing_1276.htm#SEC1352 2642 normal.lib sing_1275.htm#SEC1351 2643 normalC sing_1278.htm#SEC1354 2644 normalFan sing_2462.htm#SEC2538 2645 normalFanL sing_2048.htm#SEC2124 2646 normalForm sing_2241.htm#SEC2317 2647 normalI sing_1362.htm#SEC1438 2648 normalP sing_1277.htm#SEC1353 2649 normalToricRing sing_1292.htm#SEC1368 29638 2650 normalToricRingFromBinomials normalToricRingFromBinomials sing_1293.htm#SEC1369 2301 2651 normal_lib sing_1275.htm#SEC1351 2652 normalform sing_1532.htm#SEC1608 2701 newstruct sing_2211.htm#IDX908 2702 newtonDiag sing_958.htm#SEC1034 2703 newtonPolytope sing_2051.htm#SEC2127 2704 newtonPolytopeLP sing_2056.htm#SEC2132 2705 newtonPolytopeP sing_2055.htm#SEC2131 2706 newtonpoly sing_1553.htm#SEC1629 2707 nf_icis sing_1594.htm#SEC1670 2708 nfmodStd sing_2478.htm#SEC2554 2709 nfmodSyz sing_2480.htm#SEC2556 2710 nfmodstd.lib sing_2476.htm#SEC2552 2711 nfmodstd_lib sing_2476.htm#SEC2552 2712 nfmodsyz.lib sing_2479.htm#SEC2555 2713 nfmodsyz_lib sing_2479.htm#SEC2555 2714 nilpotent Lie algebras sing_1352.htm#IDX587 2715 nmaxcones sing_2046.htm#SEC2122 2716 noether sing_390.htm#SEC430 2717 noether.lib sing_1215.htm#SEC1291 2718 noetherNormal sing_1103.htm#SEC1179 2719 noether_lib sing_1215.htm#SEC1291 2720 non-english special characters sing_398.htm#IDX280 2721 nonMonomials sing_1268.htm#SEC1344 2722 nonZeroEntry sing_1106.htm#SEC1182 2723 none, option sing_307.htm#IDX150 2724 norTest sing_1235.htm#SEC1311 2725 norm sing_1931.htm#SEC2007 2726 normal sing_1225.htm#SEC1301 2727 normal.lib sing_1224.htm#SEC1300 2728 normalC sing_1227.htm#SEC1303 2729 normalConductor sing_1239.htm#SEC1315 2730 normalFan sing_2106.htm#SEC2182 2731 normalFanL sing_2057.htm#SEC2133 2732 normalForm sing_2321.htm#SEC2397 2733 normalI sing_1312.htm#SEC1388 2734 normalP sing_1226.htm#SEC1302 2735 normalToricRing sing_1242.htm#SEC1318 29638 2736 normalToricRingFromBinomials normalToricRingFromBinomials sing_1243.htm#SEC1319 2301 2737 normal_lib sing_1224.htm#SEC1300 2738 normalform sing_1482.htm#SEC1558 2653 2739 normaliz sing_1.htm#IDX14 18426 2654 normaliz sing_1305.htm#SEC1381 2655 normaliz.lib sing_1290.htm#SEC1366 2656 normaliz_lib sing_1290.htm#SEC1366 2657 normalization sing_1220.htm#IDX492 2658 normalization sing_1221.htm#IDX495 2659 normalization sing_1222.htm#IDX498 2660 normalization sing_1223.htm#IDX500 2661 normalization sing_1276.htm#IDX502 2662 normalization sing_1277.htm#IDX505 2663 normalization sing_1278.htm#IDX508 2664 normalization sing_1290.htm#IDX514 2665 normalization. sing_1217.htm#IDX491 2666 normalization. sing_1409.htm#IDX545 2667 normalize sing_1002.htm#SEC1078 2740 normaliz sing_1255.htm#SEC1331 2741 normaliz.lib sing_1240.htm#SEC1316 2742 normaliz_lib sing_1240.htm#SEC1316 2743 normalization sing_1169.htm#IDX554 2744 normalization sing_1170.htm#IDX557 2745 normalization sing_1171.htm#IDX560 2746 normalization sing_1172.htm#IDX562 2747 normalization sing_1225.htm#IDX564 2748 normalization sing_1226.htm#IDX567 2749 normalization sing_1227.htm#IDX570 2750 normalization sing_1239.htm#IDX576 2751 normalization sing_1240.htm#IDX578 2752 normalization sing_2312.htm#IDX931 2753 normalization. sing_1166.htm#IDX553 2754 normalization. sing_1359.htm#IDX609 2755 normalize sing_951.htm#SEC1027 2668 2756 not sing_96.htm#SEC136 2669 notBuckets, option sing_3 64.htm#IDX1602670 notRegularity, option sing_3 64.htm#IDX1582671 notSugar, option sing_3 64.htm#IDX1592672 notWarnSB, option sing_3 64.htm#IDX1812673 npar sing_18 87.htm#SEC19632674 npars sing_3 58.htm#SEC3982675 nrRootsDeterm sing_ 2012.htm#SEC20882676 nrRootsProbab sing_ 2011.htm#SEC20872677 nres sing_3 59.htm#SEC3992678 nres (plural) sing_ 521.htm#SEC5612679 nrows sing_3 60.htm#SEC4002680 nrroots sing_ 2041.htm#SEC21172681 nsatiety sing_12 71.htm#SEC13472682 nselect sing_11 73.htm#SEC12492683 nt_solve sing_17 76.htm#SEC18522684 ntsolve.lib sing_17 75.htm#SEC18512685 ntsolve_lib sing_17 75.htm#SEC18512757 notBuckets, option sing_307.htm#IDX160 2758 notRegularity, option sing_307.htm#IDX158 2759 notSugar, option sing_307.htm#IDX159 2760 notWarnSB, option sing_307.htm#IDX181 2761 npar sing_1837.htm#SEC1913 2762 npars sing_301.htm#SEC341 2763 nrRootsDeterm sing_1962.htm#SEC2038 2764 nrRootsProbab sing_1961.htm#SEC2037 2765 nres sing_302.htm#SEC342 2766 nres (plural) sing_464.htm#SEC504 2767 nrows sing_303.htm#SEC343 2768 nrroots sing_1991.htm#SEC2067 2769 nsatiety sing_1220.htm#SEC1296 2770 nselect sing_1122.htm#SEC1198 2771 nt_solve sing_1726.htm#SEC1802 2772 ntsolve.lib sing_1725.htm#SEC1801 2773 ntsolve_lib sing_1725.htm#SEC1801 2686 2774 number sing_139.htm#SEC179 2687 number sing_21 35.htm#IDX7962775 number sing_2165.htm#IDX832 2688 2776 number declarations sing_140.htm#SEC180 2689 2777 number expressions sing_141.htm#SEC181 2690 2778 number operations sing_142.htm#SEC182 2691 2779 number related functions number related functions sing_143.htm#SEC183 2692 numberOfConesOfDimension numberOfConesOfDimension sing_2 34.htm#SEC2742693 number_e sing_ 946.htm#SEC10222694 number_pi sing_ 947.htm#SEC10232695 numerAlg.lib sing_13 84.htm#IDX5192696 numerAlg_lib sing_13 84.htm#IDX5202697 numerDecom.lib sing_13 89.htm#IDX5212698 numerDecom_lib sing_13 89.htm#IDX5222699 numerator sing_3 61.htm#SEC4012700 nvars sing_3 62.htm#SEC4022701 oneDimBelongSemigroup oneDimBelongSemigroup sing_11 64.htm#SEC12402780 numberOfConesOfDimension numberOfConesOfDimension sing_2048.htm#SEC2124 2781 number_e sing_889.htm#SEC965 2782 number_pi sing_890.htm#SEC966 2783 numerAlg.lib sing_1334.htm#IDX583 2784 numerAlg_lib sing_1334.htm#IDX584 2785 numerDecom.lib sing_1339.htm#IDX585 2786 numerDecom_lib sing_1339.htm#IDX586 2787 numerator sing_304.htm#SEC344 2788 nvars sing_305.htm#SEC345 2789 oneDimBelongSemigroup oneDimBelongSemigroup sing_1113.htm#SEC1189 2702 2790 online help The online help system sing_16.htm#SEC22 2703 open sing_3 63.htm#SEC4032704 opentex sing_1 804.htm#SEC18802705 operatorBM sing_5 96.htm#SEC6482706 operatorModulo sing_5 97.htm#SEC6492707 oppose sing_ 522.htm#SEC5622708 opposite sing_ 523.htm#SEC5632709 opposite polynomial sing_ 406.htm#IDX2272710 opposite ring sing_ 406.htm#IDX2242711 option sing_3 64.htm#SEC4042791 open sing_306.htm#SEC346 2792 opentex sing_1754.htm#SEC1830 2793 operatorBM sing_539.htm#SEC591 2794 operatorModulo sing_540.htm#SEC592 2795 oppose sing_465.htm#SEC505 2796 opposite sing_466.htm#SEC506 2797 opposite polynomial sing_349.htm#IDX227 2798 opposite ring sing_349.htm#IDX224 2799 option sing_307.htm#SEC347 2712 2800 option(warn) sing_70.htm#SEC110 2713 optionIsSet sing_ 1045.htm#SEC11212801 optionIsSet sing_994.htm#SEC1070 2714 2802 or Evaluation of logical expressions sing_96.htm#SEC136 2715 or sing_459.htm#SEC499 2716 orbit sing_1402.htm#IDX525 2717 orbit sing_1403.htm#IDX529 2718 orbit sing_1406.htm#IDX534 2719 orbit sing_1407.htm#IDX537 2720 orbitCones sing_2299.htm#SEC2375 2721 orbit_variety sing_1703.htm#SEC1779 2722 orbitparam.lib sing_1402.htm#SEC1478 2723 orbitparam_lib sing_1402.htm#SEC1478 2724 ord sing_365.htm#SEC405 2725 ord_test sing_1040.htm#SEC1116 2726 orderings General definitions for orderings sing_894.htm#SEC946 2727 orderings introduction Introduction to orderings sing_893.htm#SEC945 2728 orderings, M sing_898.htm#SEC950 2729 orderings, a sing_900.htm#SEC952 2730 orderings, global sing_895.htm#SEC947 2731 orderings, local sing_896.htm#SEC948 2732 orderings, product sing_899.htm#SEC951 2733 ordstr sing_366.htm#SEC406 2734 orthogonalize sing_1120.htm#SEC1196 2735 outer sing_1090.htm#SEC1166 2803 or sing_402.htm#SEC442 2804 orbit sing_1352.htm#IDX589 2805 orbit sing_1353.htm#IDX593 2806 orbit sing_1356.htm#IDX598 2807 orbit sing_1357.htm#IDX601 2808 orbitCones sing_2379.htm#SEC2455 2809 orbit_variety sing_1653.htm#SEC1729 2810 orbitparam.lib sing_1352.htm#SEC1428 2811 orbitparam_lib sing_1352.htm#SEC1428 2812 ord sing_308.htm#SEC348 2813 ord_test sing_989.htm#SEC1065 2814 orderings General definitions for orderings sing_837.htm#SEC889 2815 orderings introduction Introduction to orderings sing_836.htm#SEC888 2816 orderings, M sing_841.htm#SEC893 2817 orderings, a sing_843.htm#SEC895 2818 orderings, global sing_838.htm#SEC890 2819 orderings, local sing_839.htm#SEC891 2820 orderings, product sing_842.htm#SEC894 2821 ordstr sing_309.htm#SEC349 2822 origin sing_1996.htm#SEC2072 2823 orthogonalize sing_1069.htm#SEC1145 2824 outer sing_1039.htm#SEC1115 2736 2825 output sing_41.htm#SEC71 2737 2826 p-adic numbers sing_32.htm#SEC46 2738 pFactor sing_1 936.htm#SEC20122739 pIntersect sing_5 60.htm#SEC6122740 pIntersectSyz sing_5 61.htm#SEC6132827 pFactor sing_1886.htm#SEC1962 2828 pIntersect sing_503.htm#SEC555 2829 pIntersectSyz sing_504.htm#SEC556 2741 2830 package sing_144.htm#SEC184 2742 2831 package declarations package declarations sing_145.htm#SEC185 2743 2832 package related functions package related functions sing_146.htm#SEC186 2744 pairset sing_ 2001.htm#SEC20772745 par sing_3 67.htm#SEC4072746 par2varRing sing_ 930.htm#SEC10062747 paraConic sing_1 417.htm#SEC14932748 paraPlaneCurve sing_1 411.htm#SEC14872749 parallel skeletons sing_9 84.htm#IDX4332750 parallel.lib sing_9 84.htm#SEC10602751 parallelTestAND sing_9 88.htm#SEC10642752 parallelTestOR sing_9 89.htm#SEC10652753 parallelWaitAll sing_9 87.htm#SEC10632754 parallelWaitFirst sing_9 86.htm#SEC10622755 parallelWaitN sing_9 85.htm#SEC10612756 parallel_lib sing_9 84.htm#SEC10602757 parallelization sing_9 84.htm#IDX4322758 parallelization sing_ 1024.htm#IDX4352759 parallelization sing_10 66.htm#IDX4492760 param sing_15 94.htm#SEC16702833 pairset sing_1951.htm#SEC2027 2834 par sing_310.htm#SEC350 2835 par2varRing sing_873.htm#SEC949 2836 paraConic sing_1367.htm#SEC1443 2837 paraPlaneCurve sing_1361.htm#SEC1437 2838 parallel skeletons sing_933.htm#IDX493 2839 parallel.lib sing_933.htm#SEC1009 2840 parallelTestAND sing_937.htm#SEC1013 2841 parallelTestOR sing_938.htm#SEC1014 2842 parallelWaitAll sing_936.htm#SEC1012 2843 parallelWaitFirst sing_935.htm#SEC1011 2844 parallelWaitN sing_934.htm#SEC1010 2845 parallel_lib sing_933.htm#SEC1009 2846 parallelization sing_933.htm#IDX492 2847 parallelization sing_973.htm#IDX495 2848 parallelization sing_1015.htm#IDX509 2849 param sing_1544.htm#SEC1620 2761 2850 parameter, as numbers sing_139.htm#SEC179 2762 parameterSubstitute sing_2098.htm#SEC2174 2763 parametric annihilator sing_589.htm#IDX329 2764 parametric annihilator for variety sing_645.htm#IDX352 2765 parametrization sing_1402.htm#IDX526 2766 parametrization sing_1406.htm#IDX535 2767 parametrization sing_1594.htm#IDX687 2768 parametrizeOrbit sing_1406.htm#SEC1482 2769 paraplanecurves.lib sing_1408.htm#SEC1484 2770 paraplanecurves_lib sing_1408.htm#SEC1484 2771 pardeg sing_368.htm#SEC408 2772 parstr sing_369.htm#SEC409 2773 part sing_2227.htm#SEC2303 2774 partOver sing_2230.htm#SEC2306 2775 partUnder sing_2231.htm#SEC2307 2776 partial_molien sing_1681.htm#SEC1757 2777 partitions sing_1185.htm#SEC1261 2778 partitions sing_1185.htm#IDX482 2779 path integral sing_1177.htm#IDX469 2780 pause sing_981.htm#SEC1057 2781 pdivi sing_960.htm#SEC1036 2782 pdivisorplus sing_2255.htm#SEC2331 2783 permcol sing_1103.htm#SEC1179 2784 permrow sing_1104.htm#SEC1180 2785 permutations sing_1186.htm#IDX483 2786 permute sing_1186.htm#SEC1262 2787 permute_L sing_1839.htm#SEC1915 2788 perron sing_788.htm#SEC840 2789 perron.lib sing_787.htm#SEC839 2790 perron_lib sing_787.htm#SEC839 2791 phindex.lib sing_2103.htm#IDX748 2792 phindex_lib sing_2103.htm#IDX749 2793 picksFormula sing_2059.htm#SEC2135 2794 pid sing_406.htm#IDX236 2795 plainInvariants sing_1553.htm#SEC1629 2796 plot sing_1817.htm#SEC1893 2797 plotRot sing_1821.htm#SEC1897 2798 plotRotated sing_1820.htm#SEC1896 2799 plotRotatedDirect sing_1823.htm#SEC1899 2800 plotRotatedList sing_1822.htm#SEC1898 2801 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1824.htm#SEC1900 2802 plural sing_1047.htm#IDX440 2803 pmat sing_975.htm#SEC1051 2804 pnormalf sing_961.htm#SEC1037 2805 pointid.lib sing_1317.htm#SEC1393 2806 pointid_lib sing_1317.htm#SEC1393 2807 polSol sing_823.htm#SEC875 2808 polSolFiniteRank sing_824.htm#SEC876 2809 pollTask sing_1076.htm#SEC1152 2851 parameterSubstitute sing_2146.htm#SEC2222 2852 parametric annihilator sing_532.htm#IDX329 2853 parametric annihilator for variety sing_588.htm#IDX352 2854 parametric ideal sing_902.htm#IDX420 2855 parametric ideal sing_909.htm#IDX437 2856 parametric ideal sing_909.htm#IDX439 2857 parametric ideal sing_910.htm#IDX444 2858 parametrization sing_1352.htm#IDX590 2859 parametrization sing_1356.htm#IDX599 2860 parametrization sing_1544.htm#IDX751 2861 parametrizeOrbit sing_1356.htm#SEC1432 2862 paraplanecurves.lib sing_1358.htm#SEC1434 2863 paraplanecurves_lib sing_1358.htm#SEC1434 2864 pardeg sing_311.htm#SEC351 2865 parstr sing_312.htm#SEC352 2866 part sing_2285.htm#SEC2361 2867 partOver sing_2288.htm#SEC2364 2868 partUnder sing_2289.htm#SEC2365 2869 partial_molien sing_1631.htm#SEC1707 2870 partitions sing_1134.htm#SEC1210 2871 partitions sing_1134.htm#IDX542 2872 path integral sing_1126.htm#IDX529 2873 pause sing_930.htm#SEC1006 2874 pdivi sing_904.htm#SEC980 2875 pdivi sing_905.htm#IDX433 2876 pdivisorplus sing_2335.htm#SEC2411 2877 permcol sing_1052.htm#SEC1128 2878 permrow sing_1053.htm#SEC1129 2879 permutations sing_1135.htm#IDX543 2880 permute sing_1135.htm#SEC1211 2881 permute_L sing_1789.htm#SEC1865 2882 perron sing_731.htm#SEC783 2883 perron.lib sing_730.htm#SEC782 2884 perron_lib sing_730.htm#SEC782 2885 phindex.lib sing_2206.htm#IDX899 2886 phindex_lib sing_2206.htm#IDX900 2887 picksFormula sing_2068.htm#SEC2144 2888 pid sing_349.htm#IDX236 2889 plainInvariants sing_1503.htm#SEC1579 2890 planeCur sing_2299.htm#SEC2375 2891 plot sing_1767.htm#SEC1843 2892 plotRot sing_1771.htm#SEC1847 2893 plotRotated sing_1770.htm#SEC1846 2894 plotRotatedDirect sing_1773.htm#SEC1849 2895 plotRotatedList sing_1772.htm#SEC1848 2896 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1774.htm#SEC1850 2897 plural sing_996.htm#IDX500 2898 pmat sing_924.htm#SEC1000 2899 pnormalf sing_905.htm#SEC981 2900 pointid.lib sing_1267.htm#SEC1343 2901 pointid_lib sing_1267.htm#SEC1343 2902 polSol sing_766.htm#SEC818 2903 polSolFiniteRank sing_767.htm#SEC819 2904 pollTask sing_1025.htm#SEC1101 2810 2905 poly sing_147.htm#SEC187 2811 poly (plural) sing_4 87.htm#SEC5272906 poly (plural) sing_430.htm#SEC470 2812 2907 poly declarations sing_148.htm#SEC188 2813 poly declarations (plural) poly declarations (plural) sing_4 88.htm#SEC5282908 poly declarations (plural) poly declarations (plural) sing_431.htm#SEC471 2814 2909 poly expressions sing_149.htm#SEC189 2815 poly expressions (plural) poly expressions (plural) sing_4 89.htm#SEC5292910 poly expressions (plural) poly expressions (plural) sing_432.htm#SEC472 2816 2911 poly operations sing_150.htm#SEC190 2817 poly operations (plural) poly operations (plural) sing_4 90.htm#SEC5302912 poly operations (plural) poly operations (plural) sing_433.htm#SEC473 2818 2913 poly related functions poly related functions sing_151.htm#SEC191 2819 poly related functions (plural) poly related functions (plural) sing_491.htm#SEC531 2820 poly.lib sing_990.htm#SEC1066 2821 poly2list sing_638.htm#SEC690 2822 poly2zdd sing_2124.htm#SEC2200 61839 2823 polyInterpolation sing_2258.htm#SEC2334 2824 polyVars sing_830.htm#SEC882 2825 poly_lib sing_990.htm#SEC1066 2826 polybori sing_2108.htm#IDX753 2827 polybori.lib sing_2108.htm#IDX750 2828 polybori.lib sing_2108.htm#IDX754 2829 polybori_lib sing_2108.htm#IDX751 2830 polymake sing_2044.htm#IDX741 2831 polymake.lib sing_2044.htm#SEC2120 2832 polymakePolytope sing_2045.htm#SEC2121 2833 polymake_lib sing_2044.htm#SEC2120 2834 polymake_so sing_2426.htm#IDX904 2835 polynomial solutions sing_817.htm#IDX380 2836 polynomial, opposite sing_406.htm#IDX228 2837 polytope sing_236.htm#SEC276 2838 polytope sing_2044.htm#IDX737 2839 polytope related functions polytope related functions sing_239.htm#SEC279 2840 polytopeViaInequalities polytopeViaInequalities sing_238.htm#SEC278 2841 polytopeViaPoints sing_237.htm#SEC277 2842 pos_def sing_1131.htm#SEC1207 2843 poset sing_2166.htm#IDX854 2844 posweight sing_1661.htm#SEC1737 2845 powSumSym sing_2184.htm#SEC2260 2846 power sing_1091.htm#SEC1167 2847 powerN sing_1920.htm#SEC1996 2848 powerX sing_1929.htm#SEC2005 2849 power_products sing_1695.htm#SEC1771 2850 powerpolyX sing_1899.htm#SEC1975 2851 powersums sing_2022.htm#SEC2098 2852 preComp sing_1254.htm#SEC1330 2853 preimage sing_370.htm#SEC410 2854 preimage sing_754.htm#IDX355 2855 preimage (plural) sing_524.htm#SEC564 2856 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1043.htm#IDX438 2857 preimageLattice sing_2364.htm#SEC2440 2858 preimageLoc sing_1043.htm#SEC1119 2859 preimageNC sing_756.htm#SEC808 2860 prepEmbDiv sing_1479.htm#SEC1555 2861 prepMat sing_1732.htm#SEC1808 2862 prepRealclassify sing_1537.htm#SEC1613 2863 prepSV sing_1834.htm#SEC1910 2864 prepareAss sing_1336.htm#SEC1412 2865 presentTree sing_1466.htm#SEC1542 2866 presolve.lib sing_1742.htm#SEC1818 2867 presolve_lib sing_1742.htm#SEC1818 2868 primL sing_1924.htm#SEC2000 2869 primList sing_1923.htm#SEC1999 2870 primRoot sing_1376.htm#SEC1452 2871 primTest sing_1253.htm#SEC1329 2872 primary_char0 sing_1685.htm#SEC1761 2873 primary_char0_no_molien primary_char0_no_molien sing_1687.htm#SEC1763 2874 primary_char0_no_molien_random primary_char0_no_molien_random sing_1692.htm#SEC1768 2875 primary_char0_random primary_char0_random sing_1690.htm#SEC1766 2876 primary_charp sing_1686.htm#SEC1762 2877 primary_charp_no_molien primary_charp_no_molien sing_1688.htm#SEC1764 2878 primary_charp_no_molien_random primary_charp_no_molien_random sing_1693.htm#SEC1769 2879 primary_charp_random primary_charp_random sing_1691.htm#SEC1767 2880 primary_charp_without primary_charp_without sing_1689.htm#SEC1765 2881 primary_charp_without_random primary_charp_without_random sing_1694.htm#SEC1770 2882 primary_invariants sing_1673.htm#SEC1749 2883 primary_invariants_random primary_invariants_random sing_1674.htm#SEC1750 2884 primdec.lib sing_1321.htm#SEC1397 2885 primdecGTZ sing_1323.htm#SEC1399 2886 primdecGTZE sing_1324.htm#SEC1400 2887 primdecMon sing_1242.htm#SEC1318 2888 primdecSY sing_1325.htm#SEC1401 2889 primdecSYE sing_1326.htm#SEC1402 2890 primdecZ sing_1345.htm#SEC1421 2891 primdecZM sing_1346.htm#SEC1422 2892 primdec_lib sing_1321.htm#SEC1397 2893 primdecint.lib sing_1344.htm#SEC1420 2894 primdecint_lib sing_1344.htm#SEC1420 2895 prime sing_371.htm#SEC411 2896 primeClosure sing_1281.htm#SEC1357 2897 primecoeffs sing_953.htm#SEC1029 2898 primefactors sing_372.htm#SEC412 2899 primes sing_948.htm#SEC1024 2900 primitiv.lib sing_1352.htm#SEC1428 2901 primitiv_lib sing_1352.htm#SEC1428 2902 primitive sing_1353.htm#SEC1429 2903 primitive element sing_1353.htm#IDX516 2904 primitiveSpan sing_2371.htm#SEC2447 2905 primitive_extra sing_1354.htm#SEC1430 2906 primparam sing_1548.htm#SEC1624 2907 principal intersection sing_554.htm#IDX313 2908 print sing_373.htm#SEC413 2909 print sing_2133.htm#IDX789 2910 printGraph sing_1179.htm#SEC1255 2911 printGroup sing_2352.htm#SEC2428 2912 printMoebius sing_2172.htm#SEC2248 2913 printTask sing_1071.htm#SEC1147 2914 printf sing_374.htm#SEC414 2915 printlevel sing_448.htm#SEC488 2914 poly related functions (plural) poly related functions (plural) sing_434.htm#SEC474 2915 poly.lib sing_939.htm#SEC1015 2916 poly2list sing_581.htm#SEC633 2917 poly2zdd sing_2227.htm#SEC2303 61839 2918 polyInterpolation sing_2338.htm#SEC2414 2919 polyVars sing_773.htm#SEC825 2920 poly_lib sing_939.htm#SEC1015 2921 polybori sing_2211.htm#IDX904 2922 polybori.lib sing_2211.htm#IDX901 2923 polybori.lib sing_2211.htm#IDX905 2924 polybori_lib sing_2211.htm#IDX902 2925 polymake sing_2053.htm#IDX805 2926 polymake.lib sing_2053.htm#SEC2129 2927 polymakePolytope sing_2054.htm#SEC2130 2928 polymake_lib sing_2053.htm#SEC2129 2929 polynomial solutions sing_760.htm#IDX380 2930 polynomial, opposite sing_349.htm#IDX228 2931 polytope sing_185.htm#SEC225 2932 polytope sing_2053.htm#IDX801 2933 polytopeViaInequalities polytopeViaInequalities sing_2026.htm#SEC2102 2934 polytopeViaPoints sing_2027.htm#SEC2103 2935 pos_def sing_1080.htm#SEC1156 2936 poset sing_2196.htm#IDX890 2937 positiveOrthant sing_1997.htm#SEC2073 2938 posweight sing_1611.htm#SEC1687 2939 powSumSym sing_2242.htm#SEC2318 2940 power sing_1040.htm#SEC1116 2941 powerN sing_1870.htm#SEC1946 2942 powerX sing_1879.htm#SEC1955 2943 power_products sing_1645.htm#SEC1721 2944 powerpolyX sing_1849.htm#SEC1925 2945 powersums sing_1972.htm#SEC2048 2946 preComp sing_1203.htm#SEC1279 2947 preimage sing_313.htm#SEC353 2948 preimage sing_697.htm#IDX355 2949 preimage (plural) sing_467.htm#SEC507 2950 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_992.htm#IDX498 2951 preimageLattice sing_2444.htm#SEC2520 2952 preimageLoc sing_992.htm#SEC1068 2953 preimageNC sing_699.htm#SEC751 2954 prepEmbDiv sing_1429.htm#SEC1505 2955 prepMat sing_1682.htm#SEC1758 2956 prepRealclassify sing_1487.htm#SEC1563 2957 prepSV sing_1784.htm#SEC1860 2958 prepareAss sing_1286.htm#SEC1362 2959 presentTree sing_1416.htm#SEC1492 2960 presolve.lib sing_1692.htm#SEC1768 2961 presolve_lib sing_1692.htm#SEC1768 2962 primL sing_1874.htm#SEC1950 2963 primList sing_1873.htm#SEC1949 2964 primRoot sing_1326.htm#SEC1402 2965 primTest sing_1202.htm#SEC1278 2966 primary_char0 sing_1635.htm#SEC1711 2967 primary_char0_no_molien primary_char0_no_molien sing_1637.htm#SEC1713 2968 primary_char0_no_molien_random primary_char0_no_molien_random sing_1642.htm#SEC1718 2969 primary_char0_random primary_char0_random sing_1640.htm#SEC1716 2970 primary_charp sing_1636.htm#SEC1712 2971 primary_charp_no_molien primary_charp_no_molien sing_1638.htm#SEC1714 2972 primary_charp_no_molien_random primary_charp_no_molien_random sing_1643.htm#SEC1719 2973 primary_charp_random primary_charp_random sing_1641.htm#SEC1717 2974 primary_charp_without primary_charp_without sing_1639.htm#SEC1715 2975 primary_charp_without_random primary_charp_without_random sing_1644.htm#SEC1720 2976 primary_invariants sing_1623.htm#SEC1699 2977 primary_invariants_random primary_invariants_random sing_1624.htm#SEC1700 2978 primdec.lib sing_1271.htm#SEC1347 2979 primdecGTZ sing_1273.htm#SEC1349 2980 primdecGTZE sing_1274.htm#SEC1350 2981 primdecMon sing_1191.htm#SEC1267 2982 primdecSY sing_1275.htm#SEC1351 2983 primdecSYE sing_1276.htm#SEC1352 2984 primdecZ sing_1295.htm#SEC1371 2985 primdecZM sing_1296.htm#SEC1372 2986 primdec_lib sing_1271.htm#SEC1347 2987 primdecint.lib sing_1294.htm#SEC1370 2988 primdecint_lib sing_1294.htm#SEC1370 2989 prime sing_314.htm#SEC354 2990 primeClosure sing_1230.htm#SEC1306 2991 primecoeffs sing_896.htm#SEC972 2992 primefactors sing_315.htm#SEC355 2993 primes sing_891.htm#SEC967 2994 primitiv.lib sing_1302.htm#SEC1378 2995 primitiv_lib sing_1302.htm#SEC1378 2996 primitive sing_1303.htm#SEC1379 2997 primitive element sing_1303.htm#IDX580 2998 primitiveSpan sing_2451.htm#SEC2527 2999 primitive_extra sing_1304.htm#SEC1380 3000 primparam sing_1498.htm#SEC1574 3001 principal intersection sing_497.htm#IDX313 3002 print sing_316.htm#SEC356 3003 print sing_2163.htm#IDX825 3004 printGraph sing_1128.htm#SEC1204 3005 printGroup sing_2432.htm#SEC2508 3006 printMoebius sing_2202.htm#SEC2278 3007 printTask sing_1020.htm#SEC1096 3008 printf sing_317.htm#SEC357 3009 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python_import sing_192.htm#SEC232 3057 python_run sing_193.htm#SEC233 3058 qbase sing_1975.htm#SEC2051 3059 qepcad sing_2364.htm#SEC2440 3060 qepcadsystem sing_2365.htm#SEC2441 3061 qhmatrix sing_1609.htm#SEC1685 3062 qhmoduli.lib sing_1573.htm#SEC1649 3063 qhmoduli_lib sing_1573.htm#SEC1649 3064 qhspectrum sing_1596.htm#SEC1672 3065 qhweight sing_319.htm#SEC359 3066 qmatrix.lib sing_732.htm#SEC784 3067 qmatrix_lib sing_732.htm#SEC784 3068 qminor sing_734.htm#SEC786 3069 qrds sing_320.htm#SEC360 2976 3070 qring Miscellaneous oddities sing_161.htm#SEC201 2977 qring sing_4 66.htm#IDX2892978 qring (plural) sing_4 92.htm#SEC5323071 qring sing_409.htm#IDX289 3072 qring (plural) sing_435.htm#SEC475 2979 3073 qring declaration sing_165.htm#SEC205 2980 qring declaration (plural) qring declaration (plural) sing_4 93.htm#SEC5332981 qring related functions (plural) qring related functions (plural) sing_4 94.htm#SEC5342982 qring ring ideal 'factor ring' sing_10 53.htm#IDX4452983 qringNF, option sing_3 64.htm#IDX1642984 qslimgb sing_ 929.htm#SEC10052985 quadraticSieve sing_1 937.htm#SEC20132986 quantMat sing_7 90.htm#SEC8422987 quickclass sing_1 529.htm#SEC16052988 quit sing_ 438.htm#SEC4782989 quote sing_3 78.htm#SEC4182990 quotient sing_3 79.htm#SEC4192991 quotient (plural) sing_ 525.htm#SEC5652992 quotientLatticeBasis quotientLatticeBasis sing_2 12.htm#SEC2522993 quotientMain sing_17 87.htm#SEC18632994 quotientMon sing_1 233.htm#SEC13092995 quotients sing_2 293.htm#IDX8862996 rHRR sing_22 24.htm#SEC23002997 rMacaulay sing_9 76.htm#SEC10522998 rad_con sing_ 1003.htm#SEC10792999 radical sing_1 333.htm#SEC14093000 radicalEHV sing_1 334.htm#SEC14103001 radicalMemberShip sing_2 091.htm#SEC21673002 radicalMon sing_1 234.htm#SEC13103003 radicalZ sing_1 348.htm#SEC14243004 randcharpoly sing_ 2019.htm#SEC20953005 randlinpoly sing_ 2021.htm#SEC20973006 random sing_3 80.htm#SEC4203007 random sing_ 406.htm#IDX2403008 random sing_21 54.htm#IDX8283009 random sing_21 55.htm#IDX8303010 random number generator, seed sing_ 406.htm#IDX2383011 random.lib sing_ 1011.htm#SEC10873012 randomBinomial sing_ 1023.htm#SEC10993013 randomCheck sing_18 50.htm#SEC19263014 randomLast sing_ 1022.htm#SEC10983015 randomPoint sing_2 13.htm#SEC2533016 randomPolyInT sing_21 00.htm#SEC21763017 random_lib sing_ 1011.htm#SEC10873018 randomid sing_ 1013.htm#SEC10893019 randommat sing_ 1014.htm#SEC10903020 rank sing_2 61.htm#IDX1373021 rank sing_3 81.htm#SEC4213022 ratSol sing_ 825.htm#SEC8773023 ratgb.lib sing_ 815.htm#IDX3693024 ratgb_lib sing_ 815.htm#IDX3703025 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1 411.htm#IDX5473026 rational normal curve, projection. sing_1 412.htm#IDX5483027 rational normal curve, projection. sing_1 415.htm#IDX5493028 rational normal curve, projection. sing_1 416.htm#IDX5503029 rational solutions sing_ 817.htm#IDX3813030 rational univariate projection sing_ 2019.htm#IDX7343031 rationalPointConic sing_1 413.htm#SEC14893032 ratstd sing_ 816.htm#SEC8683033 rays sing_2 14.htm#SEC2543034 re2squ sing_13 90.htm#SEC14663035 read sing_3 82.htm#SEC4223036 readNmzData sing_1 308.htm#SEC1384 189573037 reading, option sing_3 64.htm#IDX1833074 qring declaration (plural) qring declaration (plural) sing_436.htm#SEC476 3075 qring related functions (plural) qring related functions (plural) sing_437.htm#SEC477 3076 qring ring ideal 'factor ring' sing_1002.htm#IDX505 3077 qringNF, option sing_307.htm#IDX164 3078 qslimgb sing_872.htm#SEC948 3079 quadraticSieve sing_1887.htm#SEC1963 3080 quantMat sing_733.htm#SEC785 3081 quickclass sing_1479.htm#SEC1555 3082 quit sing_381.htm#SEC421 3083 quote sing_321.htm#SEC361 3084 quotient sing_322.htm#SEC362 3085 quotient (plural) sing_468.htm#SEC508 3086 quotientLatticeBasis quotientLatticeBasis sing_2028.htm#SEC2104 3087 quotientMain sing_1737.htm#SEC1813 3088 quotientMon sing_1182.htm#SEC1258 3089 quotients sing_2373.htm#IDX964 3090 rHRR sing_2282.htm#SEC2358 3091 rMacaulay sing_925.htm#SEC1001 3092 rad_con sing_952.htm#SEC1028 3093 radical sing_1283.htm#SEC1359 3094 radicalEHV sing_1284.htm#SEC1360 3095 radicalMemberShip sing_2139.htm#SEC2215 3096 radicalMon sing_1183.htm#SEC1259 3097 radicalZ sing_1298.htm#SEC1374 3098 randcharpoly sing_1969.htm#SEC2045 3099 randlinpoly sing_1971.htm#SEC2047 3100 random sing_323.htm#SEC363 3101 random sing_349.htm#IDX240 3102 random sing_2184.htm#IDX864 3103 random sing_2185.htm#IDX866 3104 random number generator, seed sing_349.htm#IDX238 3105 random.lib sing_960.htm#SEC1036 3106 randomBinomial sing_972.htm#SEC1048 3107 randomCheck sing_1800.htm#SEC1876 3108 randomLast sing_971.htm#SEC1047 3109 randomPoint sing_2029.htm#SEC2105 3110 randomPolyInT sing_2148.htm#SEC2224 3111 random_lib sing_960.htm#SEC1036 3112 randomid sing_962.htm#SEC1038 3113 randommat sing_963.htm#SEC1039 3114 rank sing_204.htm#IDX137 3115 rank sing_324.htm#SEC364 3116 ratSol sing_768.htm#SEC820 3117 ratgb.lib sing_758.htm#IDX369 3118 ratgb_lib sing_758.htm#IDX370 3119 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1361.htm#IDX611 3120 rational normal curve, projection. sing_1362.htm#IDX612 3121 rational normal curve, projection. sing_1365.htm#IDX613 3122 rational normal curve, projection. sing_1366.htm#IDX614 3123 rational solutions sing_760.htm#IDX381 3124 rational univariate projection sing_1969.htm#IDX798 3125 rationalPointConic sing_1363.htm#SEC1439 3126 ratstd sing_759.htm#SEC811 3127 rays sing_2030.htm#SEC2106 3128 re2squ sing_1340.htm#SEC1416 3129 read sing_325.htm#SEC365 3130 readNmzData sing_1258.htm#SEC1334 18957 3131 reading, option sing_307.htm#IDX183 3038 3132 readline sing_1.htm#IDX5 3039 3133 real sing_28.htm#IDX74 3040 real roots, univariate polynomial sing_2026.htm#IDX736 3041 real roots, univariate projection sing_2010.htm#IDX732 3042 real roots,sign conditions sing_1793.htm#IDX712 3043 realclassify sing_2409.htm#SEC2485 3044 realclassify.lib sing_2408.htm#SEC2484 3045 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reduction sing_1711.htm#SEC1787 3067 reesclos.lib sing_1360.htm#SEC1436 3068 reesclos_lib sing_1360.htm#SEC1436 3069 reference sing_251.htm#SEC291 3070 reference declarations reference declarations sing_252.htm#SEC292 3071 reference expressions reference expressions sing_253.htm#SEC293 3072 reference operations reference and shared operations sing_256.htm#SEC296 3073 reference related functions reference and shared related functions sing_257.htm#SEC297 3074 regCM sing_1273.htm#SEC1349 3075 regIdeal sing_1259.htm#SEC1335 3076 regMonCurve sing_1262.htm#SEC1338 3077 regularity Syzygies and resolutions sing_384.htm#SEC424 3078 regularity sing_904.htm#SEC961 3079 reiffen sing_607.htm#SEC659 3080 rel_orbit_variety sing_1704.htm#SEC1780 3081 relations sing_787.htm#IDX358 3082 relativeInteriorPoint relativeInteriorPoint sing_215.htm#SEC255 3083 relative_orbit_variety relative_orbit_variety sing_1705.htm#SEC1781 3084 relweight sing_1660.htm#SEC1736 3085 remainder sing_1780.htm#SEC1856 3086 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3141 realizationDimPoly sing_2113.htm#SEC2189 3142 realizationMatroids.lib realizationMatroids_lib sing_2110.htm#SEC2186 3143 realizationMatroids_lib realizationMatroids_lib sing_2110.htm#SEC2186 3144 realmorsesplit sing_2490.htm#SEC2566 3145 realpoly sing_1307.htm#SEC1383 3146 realrad sing_1309.htm#SEC1385 3147 realrad.lib sing_1306.htm#SEC1382 3148 realrad_lib sing_1306.htm#SEC1382 3149 realzero sing_1308.htm#SEC1384 3150 recursive_boolean_poly recursive_boolean_poly sing_2217.htm#SEC2293 17045 3151 recursive_from_boolean_poly recursive_from_boolean_poly sing_2223.htm#SEC2299 37794 3152 redSB, option sing_307.htm#IDX165 3153 redTail, option sing_307.htm#IDX167 3154 redThrough, option sing_307.htm#IDX168 3155 redefine, option sing_307.htm#IDX184 3156 reduce sing_326.htm#SEC366 3157 reduce sing_511.htm#IDX318 3158 reduce sing_904.htm#IDX430 3159 reduce sing_905.htm#IDX434 3160 reduce (plural) sing_469.htm#SEC509 3161 reduced sing_903.htm#IDX426 3162 reduced standard basis sing_307.htm#IDX166 3163 reduction sing_1661.htm#SEC1737 3164 reesclos.lib sing_1310.htm#SEC1386 3165 reesclos_lib sing_1310.htm#SEC1386 3166 reference sing_194.htm#SEC234 3167 reference declarations reference declarations sing_195.htm#SEC235 3168 reference expressions reference expressions sing_196.htm#SEC236 3169 reference operations reference and shared operations sing_199.htm#SEC239 3170 reference related functions reference and shared related functions sing_200.htm#SEC240 3171 regCM sing_1222.htm#SEC1298 3172 regIdeal sing_1208.htm#SEC1284 3173 regMonCurve sing_1211.htm#SEC1287 3174 regularity Syzygies and resolutions sing_327.htm#SEC367 3175 regularity sing_847.htm#SEC904 3176 reiffen sing_550.htm#SEC602 3177 rel_orbit_variety sing_1654.htm#SEC1730 3178 relations sing_730.htm#IDX358 3179 relativeInteriorPoint relativeInteriorPoint sing_2031.htm#SEC2107 3180 relative_orbit_variety relative_orbit_variety sing_1655.htm#SEC1731 3181 relweight sing_1610.htm#SEC1686 3182 remainder sing_1730.htm#SEC1806 3183 remainderMain sing_1738.htm#SEC1814 3184 removeCone sing_2049.htm#SEC2125 3185 removepower sing_1467.htm#SEC1543 3186 repart sing_328.htm#SEC368 3187 replace sing_1839.htm#SEC1915 3188 representation, math objects Representation of mathematical objects sing_834.htm#SEC886 3189 res sing_329.htm#SEC369 3190 resbinomial.lib sing_1370.htm#IDX617 3191 resbinomial_lib sing_1370.htm#IDX618 3192 reservedName sing_330.htm#SEC370 3193 resfunction sing_1384.htm#SEC1460 3194 resgraph.lib sing_1402.htm#SEC1478 3195 resgraph_lib sing_1402.htm#SEC1478 3196 resjung.lib sing_1406.htm#SEC1482 3197 resjung_lib sing_1406.htm#SEC1482 3198 reslist sing_1398.htm#SEC1474 3102 3199 resolution purityfiltration_lib sing_156.htm#SEC196 3103 resolution sing_7 95.htm#IDX3653104 resolution (plural) sing_4 95.htm#SEC5353200 resolution sing_738.htm#IDX365 3201 resolution (plural) sing_438.htm#SEC478 3105 3202 resolution declarations resolution declarations sing_157.htm#SEC197 3106 resolution declarations (plural) resolution declarations (plural) sing_4 96.htm#SEC5363203 resolution declarations (plural) resolution declarations (plural) sing_439.htm#SEC479 3107 3204 resolution expressions resolution expressions sing_158.htm#SEC198 3108 resolution expressions (plural) resolution expressions (plural) sing_4 97.htm#SEC5373109 resolution graph sing_1 502.htm#IDX5673205 resolution expressions (plural) resolution expressions (plural) sing_440.htm#SEC480 3206 resolution graph sing_1452.htm#IDX631 3110 3207 resolution related functions resolution related functions sing_159.htm#SEC199 3111 resolution related functions (plural) resolution related functions (plural) sing_4 98.htm#SEC5383112 resolution, La Scala's method sing_ 337.htm#SEC3773113 resolution, computation of sing_3 86.htm#IDX1863114 resolution, hilbert-driven sing_ 312.htm#SEC3523115 resolutionInLocalization resolutionInLocalization sing_2 292.htm#SEC23683116 resolutiongraph sing_1 503.htm#SEC15793117 resolve sing_14 64.htm#SEC15403118 resolve.lib sing_14 60.htm#SEC15363119 resolve_lib sing_14 60.htm#SEC15363120 resources.lib sing_ 1024.htm#SEC11003121 resources_lib sing_ 1024.htm#SEC11003122 restriction sing_21 47.htm#IDX8163123 restriction sing_21 63.htm#IDX8493124 restriction sing_21 64.htm#IDX8513125 restriction of sing_ 612.htm#IDX3413126 restrictionIdeal sing_ 622.htm#SEC6743127 restrictionModule sing_ 623.htm#SEC6753128 resultant sing_ 351.htm#SEC3913129 resultant sing_3 88.htm#SEC4283130 reszeta.lib sing_14 73.htm#SEC15493131 reszeta_lib sing_14 73.htm#SEC15493132 return sing_ 439.htm#SEC4793133 return type of procedures Return type of procedures sing_4 64.htm#SEC5043134 returnSB, option sing_3 64.htm#IDX1523135 reverse sing_ 2040.htm#SEC21163136 reverse lexicographical ordering sing_8 95.htm#IDX3863137 reynolds_molien sing_16 80.htm#SEC17563138 rho sing_1 931.htm#SEC20073139 rightInverse sing_18 69.htm#SEC19453140 rightKernel sing_18 67.htm#SEC19433141 rightModulo sing_7 74.htm#SEC8263142 rightNF sing_7 73.htm#SEC8253143 rightNFWeyl sing_ 842.htm#SEC8943144 rightStd sing_7 72.htm#SEC8243208 resolution related functions (plural) resolution related functions (plural) sing_441.htm#SEC481 3209 resolution, La Scala's method sing_280.htm#SEC320 3210 resolution, computation of sing_329.htm#IDX186 3211 resolution, hilbert-driven sing_255.htm#SEC295 3212 resolutionInLocalization resolutionInLocalization sing_2372.htm#SEC2448 3213 resolutiongraph sing_1453.htm#SEC1529 3214 resolve sing_1414.htm#SEC1490 3215 resolve.lib sing_1410.htm#SEC1486 3216 resolve_lib sing_1410.htm#SEC1486 3217 resources.lib sing_973.htm#SEC1049 3218 resources_lib sing_973.htm#SEC1049 3219 restriction sing_2177.htm#IDX852 3220 restriction sing_2193.htm#IDX885 3221 restriction sing_2194.htm#IDX887 3222 restriction of sing_555.htm#IDX341 3223 restrictionIdeal sing_565.htm#SEC617 3224 restrictionModule sing_566.htm#SEC618 3225 resultant sing_294.htm#SEC334 3226 resultant sing_331.htm#SEC371 3227 reszeta.lib sing_1423.htm#SEC1499 3228 reszeta_lib sing_1423.htm#SEC1499 3229 return sing_382.htm#SEC422 3230 return type of procedures Return type of procedures sing_407.htm#SEC447 3231 returnSB, option sing_307.htm#IDX152 3232 reverse sing_1990.htm#SEC2066 3233 reverse lexicographical ordering sing_838.htm#IDX386 3234 reynolds_molien sing_1630.htm#SEC1706 3235 rho sing_1881.htm#SEC1957 3236 rightInverse sing_1819.htm#SEC1895 3237 rightKernel sing_1817.htm#SEC1893 3238 rightModulo sing_717.htm#SEC769 3239 rightNF sing_716.htm#SEC768 3240 rightNFWeyl sing_785.htm#SEC837 3241 rightStd sing_715.htm#SEC767 3145 3242 ring sing_160.htm#SEC200 3146 ring (plural) sing_499.htm#SEC539 3147 ring coefficients hasTransExtensionCoefficient sing_1050.htm#IDX442 3148 ring coefficients sing_1051.htm#IDX443 3149 ring coefficients sing_1052.htm#IDX444 3243 ring sing_901.htm#IDX416 3244 ring (plural) sing_442.htm#SEC482 3245 ring coefficients hasTransExtensionCoefficient sing_999.htm#IDX502 3246 ring coefficients sing_1000.htm#IDX503 3247 ring coefficients sing_1001.htm#IDX504 3150 3248 ring declarations sing_162.htm#SEC202 3151 ring declarations (plural) ring declarations (plural) sing_ 500.htm#SEC5403249 ring declarations (plural) ring declarations (plural) sing_443.htm#SEC483 3152 3250 ring operations sing_164.htm#SEC204 3153 ring operations (plural) ring operations (plural) sing_ 501.htm#SEC5413251 ring operations (plural) ring operations (plural) sing_444.htm#SEC484 3154 3252 ring related functions ring related functions sing_163.htm#SEC203 3155 ring related functions (plural) ring related functions (plural) sing_502.htm#SEC542 3156 ring, opposite sing_406.htm#IDX225 3157 ring.lib sing_1029.htm#SEC1105 3158 ring_cf sing_261.htm#IDX138 3159 ring_lib sing_1029.htm#SEC1105 3160 ring_variable sing_2134.htm#IDX793 3161 ring_variable sing_2135.htm#IDX795 3162 ring_variable sing_2136.htm#IDX799 3163 ring_variable sing_2137.htm#IDX801 3164 ringlist sing_389.htm#SEC429 3165 ringlist (plural) sing_527.htm#SEC567 3166 ringtensor sing_1041.htm#SEC1117 3167 ringweights sing_1042.htm#SEC1118 3168 rinvar.lib sing_1716.htm#SEC1792 3169 rinvar_lib sing_1716.htm#SEC1792 3170 rmNmzFiles sing_1313.htm#SEC1389 32601 3171 rm_unitcol sing_1109.htm#SEC1185 3172 rm_unitrow sing_1108.htm#SEC1184 3173 rmx sing_1814.htm#SEC1890 3174 rncAntiCanonicalMap sing_1412.htm#SEC1488 3175 rncItProjEven sing_1416.htm#SEC1492 3176 rncItProjOdd sing_1415.htm#SEC1491 3177 root of Bernstein-Sato polynomial sing_589.htm#IDX330 3178 rootofUnity sing_1044.htm#SEC1120 3179 roots sing_1781.htm#SEC1857 3180 rootsMain sing_1789.htm#SEC1865 3181 rootsModp sing_1913.htm#SEC1989 3182 rootsmr.lib sing_2010.htm#SEC2086 3183 rootsmr_lib sing_2010.htm#SEC2086 3184 rootsur.lib sing_2026.htm#SEC2102 3185 rootsur_lib sing_2026.htm#SEC2102 3186 round sing_1911.htm#SEC1987 3187 rowShift sing_261.htm#IDX141 3188 rowShift sing_263.htm#SEC303 3189 rowred sing_1105.htm#SEC1181 3190 rp, global ordering sing_895.htm#IDX385 3191 rswalk sing_2407.htm#SEC2483 3192 rtimer sing_452.htm#SEC492 3193 rvalue No rvalue of increments and assignments sing_458.htm#SEC498 3194 rvar sing_390.htm#SEC430 3195 rwalk sing_2403.htm#SEC2479 3196 rwalk.lib sing_2401.htm#SEC2477 3197 rwalk_lib sing_2401.htm#SEC2477 3198 s_res sing_1059.htm#SEC1135 3199 sa_poly_reduce sing_577.htm#SEC629 3200 sa_reduce sing_576.htm#SEC628 3201 sagbi sing_1366.htm#SEC1442 3202 sagbi.lib sing_1363.htm#SEC1439 3203 sagbiPart sing_1367.htm#SEC1443 3204 sagbiReduce sing_1365.htm#SEC1441 3205 sagbiSPoly sing_1364.htm#SEC1440 3206 sagbi_lib sing_1363.htm#SEC1439 3207 salida sing_1445.htm#SEC1521 3208 sameComponent sing_1993.htm#SEC2069 3209 sameQ sing_1792.htm#SEC1868 3210 sat sing_1174.htm#SEC1250 3211 satiety sing_1261.htm#SEC1337 3212 satstd sing_2468.htm#SEC2544 3213 sba sing_391.htm#SEC431 3214 scalarProd sing_566.htm#SEC618 3215 scheme sing_2265.htm#SEC2341 3216 schreyer.lib sing_1058.htm#SEC1134 3217 schreyer_lib sing_1058.htm#SEC1134 3253 ring related functions (plural) ring related functions (plural) sing_445.htm#SEC485 3254 ring, opposite sing_349.htm#IDX225 3255 ring.lib sing_978.htm#SEC1054 3256 ring_cf sing_204.htm#IDX138 3257 ring_lib sing_978.htm#SEC1054 3258 ring_variable sing_2164.htm#IDX829 3259 ring_variable sing_2165.htm#IDX831 3260 ring_variable sing_2166.htm#IDX835 3261 ring_variable sing_2167.htm#IDX837 3262 ringlist sing_332.htm#SEC372 3263 ringlist (plural) sing_470.htm#SEC510 3264 rings sing_901.htm#IDX417 3265 ringtensor sing_990.htm#SEC1066 3266 ringweights sing_991.htm#SEC1067 3267 rinvar.lib sing_1666.htm#SEC1742 3268 rinvar_lib sing_1666.htm#SEC1742 3269 rmNmzFiles sing_1263.htm#SEC1339 32601 3270 rm_unitcol sing_1058.htm#SEC1134 3271 rm_unitrow sing_1057.htm#SEC1133 3272 rmx sing_1764.htm#SEC1840 3273 rncAntiCanonicalMap sing_1362.htm#SEC1438 3274 rncItProjEven sing_1366.htm#SEC1442 3275 rncItProjOdd sing_1365.htm#SEC1441 3276 root of Bernstein-Sato polynomial sing_532.htm#IDX330 3277 rootofUnity sing_993.htm#SEC1069 3278 roots sing_1731.htm#SEC1807 3279 rootsMain sing_1739.htm#SEC1815 3280 rootsModp sing_1863.htm#SEC1939 3281 rootsmr.lib sing_1960.htm#SEC2036 3282 rootsmr_lib sing_1960.htm#SEC2036 3283 rootsur.lib sing_1976.htm#SEC2052 3284 rootsur_lib sing_1976.htm#SEC2052 3285 round sing_1861.htm#SEC1937 3286 rowShift sing_204.htm#IDX141 3287 rowShift sing_206.htm#SEC246 3288 rowred sing_1054.htm#SEC1130 3289 rp, global ordering sing_838.htm#IDX385 3290 rswalk sing_2487.htm#SEC2563 3291 rtimer sing_395.htm#SEC435 3292 rvalue No rvalue of increments and assignments sing_401.htm#SEC441 3293 rvar sing_333.htm#SEC373 3294 rwalk sing_2483.htm#SEC2559 3295 rwalk.lib sing_2481.htm#SEC2557 3296 rwalk_lib sing_2481.htm#SEC2557 3297 s_res sing_1008.htm#SEC1084 3298 sa_poly_reduce sing_520.htm#SEC572 3299 sa_reduce sing_519.htm#SEC571 3300 sagbi sing_1316.htm#SEC1392 3301 sagbi.lib sing_1313.htm#SEC1389 3302 sagbiAlg sing_2295.htm#SEC2371 3303 sagbiMod sing_2296.htm#SEC2372 3304 sagbiPart sing_1317.htm#SEC1393 3305 sagbiReduce sing_1315.htm#SEC1391 3306 sagbiSPoly sing_1314.htm#SEC1390 3307 sagbi_lib sing_1313.htm#SEC1389 3308 salida sing_1395.htm#SEC1471 3309 sameComponent sing_1943.htm#SEC2019 3310 sameQ sing_1742.htm#SEC1818 3311 sat sing_1123.htm#SEC1199 3312 satiety sing_1210.htm#SEC1286 3313 satstd sing_2205.htm#SEC2281 3314 sba sing_334.htm#SEC374 3315 scalarProd sing_509.htm#SEC561 3316 scheme sing_2345.htm#SEC2421 3317 schreyer.lib sing_1007.htm#SEC1083 3318 schreyer_lib sing_1007.htm#SEC1083 3218 3319 sdb, source code debugger Source code debugger sing_66.htm#SEC103 3219 secondary fan sing_2044.htm#IDX739 3220 secondary polytope sing_2044.htm#IDX740 3221 secondaryFan sing_2052.htm#SEC2128 3222 secondaryPolytope sing_2051.htm#SEC2127 3223 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1701.htm#SEC1777 3224 secondary_char0 sing_1696.htm#SEC1772 3225 secondary_charp sing_1698.htm#SEC1774 3226 secondary_no_molien sing_1699.htm#SEC1775 3227 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1702.htm#SEC1778 3228 segre sing_2179.htm#SEC2255 3229 select sing_1175.htm#SEC1251 3230 select1 sing_1176.htm#SEC1252 3231 semaphore sing_406.htm#IDX243 3232 semaphore sing_1028.htm#SEC1104 3233 semaphores sing_1024.htm#IDX437 3234 semiCMcod2 sing_1657.htm#SEC1733 3235 semidiv sing_1985.htm#SEC2061 3236 semigroup sing_1506.htm#SEC1582 3237 semigroup sing_1510.htm#IDX574 3238 semigroup of values sing_1596.htm#IDX689 3239 semigroupGenerator sing_216.htm#SEC256 3240 sep sing_1343.htm#SEC1419 3241 separateHNE sing_1607.htm#SEC1683 3242 separator sing_1244.htm#SEC1320 3243 serreRelations sing_695.htm#SEC747 3244 set sing_2129.htm#IDX779 3245 setBaseMultigrading sing_2345.htm#SEC2421 3246 setLetterplaceAttributes setLetterplaceAttributes sing_686.htm#SEC738 3247 setLinearForms sing_217.htm#SEC257 3248 setModuleGrading sing_2357.htm#SEC2433 3249 setMultiplicity sing_218.htm#SEC258 3250 setNmzDataPath sing_1310.htm#SEC1386 18123 3251 setNmzExecPath sing_1306.htm#SEC1382 38993 3252 setNmzFilename sing_1309.htm#SEC1385 20206 3253 setNmzOption sing_1303.htm#SEC1379 9012 3254 set_is_injective sing_1973.htm#SEC2049 3255 setcores sing_1026.htm#SEC1102 3256 setenv sing_406.htm#IDX246 3257 setinitials sing_2275.htm#SEC2351 3258 setring sing_392.htm#SEC432 3259 sh sing_406.htm#IDX248 3260 shared sing_251.htm#SEC291 3261 shared declarations sing_254.htm#SEC294 3262 shared expressions sing_255.htm#SEC295 3263 shared operations reference and shared operations sing_256.htm#SEC296 3264 shared related functions reference and shared related functions sing_257.htm#SEC297 3265 sheaf cohomology sing_1483.htm#IDX555 3266 sheafCoh sing_1489.htm#SEC1565 64501 3267 sheafCohBGG sing_1487.htm#SEC1563 13439 3268 sheafCohBGG2 sing_1488.htm#SEC1564 3338 3269 sheafcoh.lib sing_1483.htm#SEC1559 3270 sheafcoh_lib sing_1483.htm#SEC1559 3271 shiftPoly sing_688.htm#SEC740 3272 short sing_449.htm#SEC489 3273 show sing_977.htm#SEC1053 3274 showBO sing_1465.htm#SEC1541 3275 showDataTypes sing_1467.htm#SEC1543 3276 showNmzOptions sing_1304.htm#SEC1380 64955 3277 showNuminvs sing_1301.htm#SEC1377 18934 3278 showgrades sing_800.htm#SEC852 3279 showrecursive sing_978.htm#SEC1054 3280 sickle sing_673.htm#SEC725 3281 signatureBrieskorn sing_1666.htm#SEC1742 3282 signatureL sing_2104.htm#SEC2180 3283 signatureLqf sing_2105.htm#SEC2181 3284 signatureNemethi sing_1668.htm#SEC1744 3285 signaturePuiseux sing_1667.htm#SEC1743 3286 signcnd sing_1794.htm#SEC1870 3287 signcond.lib sing_1793.htm#SEC1869 3288 signcond_lib sing_1793.htm#SEC1869 3289 simplesolver sing_1738.htm#SEC1814 3290 simplex sing_393.htm#SEC433 3291 simplexOut sing_1765.htm#SEC1841 3292 simplify sing_394.htm#SEC434 3293 simplifyRat sing_837.htm#SEC889 3294 sing.lib sing_1633.htm#SEC1709 3295 sing4ti2.lib sing_1369.htm#SEC1445 3296 sing4ti2_lib sing_1369.htm#SEC1445 3297 sing_lib sing_1633.htm#SEC1709 3298 singular locus of D-module sing_817.htm#IDX375 3299 singularities sing_1565.htm#IDX591 3300 singularities sing_1566.htm#IDX602 3301 singularities sing_1567.htm#IDX605 3302 singularities sing_1568.htm#IDX608 3303 singularities sing_1569.htm#IDX611 3304 singularities sing_1570.htm#IDX615 3305 singularities sing_1571.htm#IDX619 3306 singularities sing_1572.htm#IDX625 3307 singularities sing_1573.htm#IDX633 3308 singularities sing_1574.htm#IDX639 3309 singularities sing_1575.htm#IDX647 3310 singularities sing_1576.htm#IDX657 3311 singularities sing_1664.htm#IDX704 3312 singularities, resolution of Resolution of singularities sing_880.htm#SEC932 3313 singularity sing_1530.htm#SEC1606 3320 second degree sing_919.htm#IDX482 3321 secondary fan sing_2053.htm#IDX803 3322 secondary polytope sing_2053.htm#IDX804 3323 secondaryFan sing_2061.htm#SEC2137 3324 secondaryPolytope sing_2060.htm#SEC2136 3325 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1651.htm#SEC1727 3326 secondary_char0 sing_1646.htm#SEC1722 3327 secondary_charp sing_1648.htm#SEC1724 3328 secondary_no_molien sing_1649.htm#SEC1725 3329 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1652.htm#SEC1728 3330 segre sing_2237.htm#SEC2313 3331 select sing_1124.htm#SEC1200 3332 select1 sing_1125.htm#SEC1201 3333 semaphore sing_349.htm#IDX243 3334 semaphore sing_977.htm#SEC1053 3335 semaphores sing_973.htm#IDX497 3336 semiCMcod2 sing_1607.htm#SEC1683 3337 semiGroup sing_2297.htm#SEC2373 3338 semiMod sing_2298.htm#SEC2374 3339 semidiv sing_1935.htm#SEC2011 3340 semigroup sing_1456.htm#SEC1532 3341 semigroup sing_1460.htm#IDX638 3342 semigroup of values sing_1546.htm#IDX753 3343 semigroupGenerator sing_2032.htm#SEC2108 3344 sep sing_1293.htm#SEC1369 3345 separateHNE sing_1557.htm#SEC1633 3346 separator sing_1193.htm#SEC1269 3347 serreRelations sing_638.htm#SEC690 3348 set sing_2159.htm#IDX815 3349 setBaseMultigrading sing_2425.htm#SEC2501 3350 setLetterplaceAttributes setLetterplaceAttributes sing_629.htm#SEC681 3351 setLinearForms sing_2033.htm#SEC2109 3352 setModuleGrading sing_2437.htm#SEC2513 3353 setMultiplicity sing_2034.htm#SEC2110 3354 setNmzDataPath sing_1260.htm#SEC1336 18123 3355 setNmzExecPath sing_1256.htm#SEC1332 38993 3356 setNmzFilename sing_1259.htm#SEC1335 20206 3357 setNmzOption sing_1253.htm#SEC1329 9012 3358 set_is_injective sing_1923.htm#SEC1999 3359 setcores sing_975.htm#SEC1051 3360 setenv sing_349.htm#IDX246 3361 setglobalrings sing_901.htm#SEC977 3362 setinitials sing_2355.htm#SEC2431 3363 setring sing_335.htm#SEC375 3364 sh sing_349.htm#IDX248 3365 shared sing_194.htm#SEC234 3366 shared declarations sing_197.htm#SEC237 3367 shared expressions sing_198.htm#SEC238 3368 shared operations reference and shared operations sing_199.htm#SEC239 3369 shared related functions reference and shared related functions sing_200.htm#SEC240 3370 sheaf cohomology sing_1433.htm#IDX619 3371 sheafCoh sing_1439.htm#SEC1515 64501 3372 sheafCohBGG sing_1437.htm#SEC1513 13439 3373 sheafCohBGG2 sing_1438.htm#SEC1514 3338 3374 sheafcoh.lib sing_1433.htm#SEC1509 3375 sheafcoh_lib sing_1433.htm#SEC1509 3376 shiftPoly sing_631.htm#SEC683 3377 short sing_392.htm#SEC432 3378 show sing_926.htm#SEC1002 3379 showBO sing_1415.htm#SEC1491 3380 showDataTypes sing_1417.htm#SEC1493 3381 showNmzOptions sing_1254.htm#SEC1330 64955 3382 showNuminvs sing_1251.htm#SEC1327 18934 3383 showgrades sing_743.htm#SEC795 3384 showrecursive sing_927.htm#SEC1003 3385 sickle sing_616.htm#SEC668 3386 signatureBrieskorn sing_1616.htm#SEC1692 3387 signatureL sing_2207.htm#SEC2283 3388 signatureLqf sing_2208.htm#SEC2284 3389 signatureNemethi sing_1618.htm#SEC1694 3390 signaturePuiseux sing_1617.htm#SEC1693 3391 signcnd sing_1744.htm#SEC1820 3392 signcond.lib sing_1743.htm#SEC1819 3393 signcond_lib sing_1743.htm#SEC1819 3394 simplesolver sing_1688.htm#SEC1764 3395 simplex sing_336.htm#SEC376 3396 simplexOut sing_1715.htm#SEC1791 3397 simplify sing_337.htm#SEC377 3398 simplifyRat sing_780.htm#SEC832 3399 sing.lib sing_1583.htm#SEC1659 3400 sing4ti2.lib sing_1319.htm#SEC1395 3401 sing4ti2_lib sing_1319.htm#SEC1395 3402 sing_lib sing_1583.htm#SEC1659 3403 singular locus of D-module sing_760.htm#IDX375 3404 singularities sing_1515.htm#IDX655 3405 singularities sing_1516.htm#IDX666 3406 singularities sing_1517.htm#IDX669 3407 singularities sing_1518.htm#IDX672 3408 singularities sing_1519.htm#IDX675 3409 singularities sing_1520.htm#IDX679 3410 singularities sing_1521.htm#IDX683 3411 singularities sing_1522.htm#IDX689 3412 singularities sing_1523.htm#IDX697 3413 singularities sing_1524.htm#IDX703 3414 singularities sing_1525.htm#IDX711 3415 singularities sing_1526.htm#IDX721 3416 singularities sing_1614.htm#IDX768 3417 singularities, resolution of Resolution of singularities sing_823.htm#SEC875 3418 singularity sing_1480.htm#SEC1556 3314 3419 singularrc sing_20.htm#IDX73 3315 size Miscellaneous oddities sing_395.htm#SEC435 3316 size sing_466.htm#IDX288 3317 skewmat sing_1092.htm#SEC1168 3318 sleep sing_401.htm#SEC441 3319 slimgb sing_396.htm#SEC436 3320 slimgb sing_857.htm#SEC909 3321 slimgb (plural) sing_528.htm#SEC568 3322 slocus sing_1645.htm#SEC1721 3323 smith sing_1878.htm#SEC1954 3324 smithNormalForm sing_2393.htm#SEC2469 3325 solutionsMod2 sing_1928.htm#SEC2004 3326 solve sing_1759.htm#SEC1835 3327 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_340.htm#SEC380 3328 solve.lib sing_1757.htm#SEC1833 3329 solveTInitialFormPar solveTInitialFormPar sing_2094.htm#SEC2170 3330 solve_IP sing_1219.htm#SEC1295 3331 solve_lib sing_1757.htm#SEC1833 3332 solvelinearpart sing_1752.htm#SEC1828 3333 sort sing_950.htm#SEC1026 3334 sortIntvec sing_644.htm#SEC696 3335 sortandmap sing_1753.htm#SEC1829 3336 sortier sing_1715.htm#SEC1791 3337 sortvars sing_1754.htm#SEC1830 3338 sortvec sing_397.htm#SEC437 3420 size Miscellaneous oddities sing_338.htm#SEC378 3421 size sing_409.htm#IDX288 3422 skewmat sing_1041.htm#SEC1117 3423 sleep sing_344.htm#SEC384 3424 slimgb sing_339.htm#SEC379 3425 slimgb sing_800.htm#SEC852 3426 slimgb (plural) sing_471.htm#SEC511 3427 slocus sing_1595.htm#SEC1671 3428 smith sing_1828.htm#SEC1904 3429 smithNormalForm sing_2473.htm#SEC2549 3430 solutionsMod2 sing_1878.htm#SEC1954 3431 solve sing_919.htm#IDX483 3432 solve sing_1709.htm#SEC1785 3433 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_283.htm#SEC323 3434 solve.lib sing_1707.htm#SEC1783 3435 solveTInitialFormPar solveTInitialFormPar sing_2142.htm#SEC2218 3436 solve_IP sing_1168.htm#SEC1244 3437 solve_lib sing_1707.htm#SEC1783 3438 solvelinearpart sing_1702.htm#SEC1778 3439 sort sing_893.htm#SEC969 3440 sortIntvec sing_587.htm#SEC639 3441 sortandmap sing_1703.htm#SEC1779 3442 sortier sing_1665.htm#SEC1741 3443 sortvars sing_1704.htm#SEC1780 3444 sortvec sing_340.htm#SEC380 3339 3445 source code debugger, sdb Source code debugger sing_66.htm#SEC103 3340 spadd sing_1579.htm#SEC1655 3341 span sing_219.htm#SEC259 3342 sparseHomogIdeal sing_1020.htm#SEC1096 3343 sparseInterpolation sing_2260.htm#SEC2336 3344 sparseid sing_1015.htm#SEC1091 3345 sparsemat sing_1017.htm#SEC1093 3346 sparsematrix sing_1016.htm#SEC1092 3347 sparsepoly sing_1018.htm#SEC1094 3348 sparsetriag sing_1019.htm#SEC1095 3349 spcurve.lib sing_1653.htm#SEC1729 3350 spcurve_lib sing_1653.htm#SEC1729 3351 special characters, non-english sing_455.htm#IDX281 3352 spectral pairs sing_1565.htm#IDX600 3353 spectral pairs sing_1572.htm#IDX632 3354 spectral pairs sing_1574.htm#IDX646 3355 spectral pairs sing_1575.htm#IDX655 3356 spectral pairs sing_1587.htm#IDX671 3357 spectral pairs sing_1589.htm#IDX682 3358 spectralNeg sing_1475.htm#SEC1551 3359 spectrum sing_1565.htm#IDX599 3360 spectrum sing_1571.htm#SEC1647 3361 spectrum sing_1571.htm#IDX624 3362 spectrum sing_1572.htm#IDX631 3363 spectrum sing_1573.htm#IDX638 3364 spectrum sing_1574.htm#IDX645 3365 spectrum sing_1575.htm#IDX654 3366 spectrum sing_1587.htm#IDX670 3367 spectrum sing_1589.htm#IDX681 3368 spectrum sing_1664.htm#IDX706 3369 spectrum.lib sing_1663.htm#SEC1739 3370 spectrum_lib sing_1663.htm#SEC1739 3371 spectrumnd sing_1664.htm#SEC1740 3372 spgamma sing_1586.htm#SEC1662 3373 spgeomgenus sing_1585.htm#SEC1661 3374 spissemicont sing_1582.htm#SEC1658 3375 split sing_979.htm#SEC1055 3376 splitPolygon sing_2054.htm#SEC2130 3377 splitring sing_1355.htm#SEC1431 3378 splitting sing_1252.htm#SEC1328 3379 spmilnor sing_1584.htm#SEC1660 3380 spmul sing_1581.htm#SEC1657 3381 spnf sing_1135.htm#SEC1211 3382 spoly sing_1996.htm#SEC2072 3383 sppairs sing_1572.htm#SEC1648 3384 sppnf sing_1577.htm#SEC1653 3385 sppprint sing_1578.htm#SEC1654 3386 spprint sing_1136.htm#SEC1212 3387 sprintf sing_399.htm#SEC439 3388 spsemicont sing_1583.htm#SEC1659 3389 spsub sing_1580.htm#SEC1656 3390 sqfrNorm sing_1782.htm#SEC1858 3391 sqfrNormMain sing_1790.htm#SEC1866 3392 sqr sing_1908.htm#SEC1984 3393 sqrfree sing_398.htm#SEC438 3394 squareRoot sing_1927.htm#SEC2003 3395 squarefree sing_1608.htm#SEC1684 3396 sres sing_400.htm#SEC440 3397 ssi Parallelization with ssi links sing_852.htm#SEC904 3398 staircase sing_1799.htm#SEC1875 3399 standard sing_2003.htm#SEC2079 3400 standard.lib sing_928.htm#IDX413 3401 standard_lib sing_928.htm#IDX414 3402 startNmz sing_1312.htm#SEC1388 21925 3403 startTasks sing_1072.htm#SEC1148 3446 spaceCur sing_2300.htm#SEC2376 3447 spadd sing_1529.htm#SEC1605 3448 span sing_2035.htm#SEC2111 3449 sparseHomogIdeal sing_969.htm#SEC1045 3450 sparseInterpolation sing_2340.htm#SEC2416 3451 sparseid sing_964.htm#SEC1040 3452 sparsemat sing_966.htm#SEC1042 3453 sparsematrix sing_965.htm#SEC1041 3454 sparsepoly sing_967.htm#SEC1043 3455 sparsetriag sing_968.htm#SEC1044 3456 spcurve.lib sing_1603.htm#SEC1679 3457 spcurve_lib sing_1603.htm#SEC1679 3458 special characters, non-english sing_398.htm#IDX281 3459 spectral pairs sing_1515.htm#IDX664 3460 spectral pairs sing_1522.htm#IDX696 3461 spectral pairs sing_1524.htm#IDX710 3462 spectral pairs sing_1525.htm#IDX719 3463 spectral pairs sing_1537.htm#IDX735 3464 spectral pairs sing_1539.htm#IDX746 3465 spectralNeg sing_1425.htm#SEC1501 3466 spectrum sing_1515.htm#IDX663 3467 spectrum sing_1521.htm#SEC1597 3468 spectrum sing_1521.htm#IDX688 3469 spectrum sing_1522.htm#IDX695 3470 spectrum sing_1523.htm#IDX702 3471 spectrum sing_1524.htm#IDX709 3472 spectrum sing_1525.htm#IDX718 3473 spectrum sing_1537.htm#IDX734 3474 spectrum sing_1539.htm#IDX745 3475 spectrum sing_1614.htm#IDX770 3476 spectrum.lib sing_1613.htm#SEC1689 3477 spectrum_lib sing_1613.htm#SEC1689 3478 spectrumnd sing_1614.htm#SEC1690 3479 spgamma sing_1536.htm#SEC1612 3480 spgeomgenus sing_1535.htm#SEC1611 3481 spissemicont sing_1532.htm#SEC1608 3482 split sing_928.htm#SEC1004 3483 splitPolygon sing_2063.htm#SEC2139 3484 splitring sing_1305.htm#SEC1381 3485 splitting sing_1201.htm#SEC1277 3486 spmilnor sing_1534.htm#SEC1610 3487 spmul sing_1531.htm#SEC1607 3488 spnf sing_1084.htm#SEC1160 3489 spoly sing_1946.htm#SEC2022 3490 sppairs sing_1522.htm#SEC1598 3491 sppnf sing_1527.htm#SEC1603 3492 sppprint sing_1528.htm#SEC1604 3493 spprint sing_1085.htm#SEC1161 3494 sprintf sing_342.htm#SEC382 3495 spsemicont sing_1533.htm#SEC1609 3496 spsub sing_1530.htm#SEC1606 3497 sqfrNorm sing_1732.htm#SEC1808 3498 sqfrNormMain sing_1740.htm#SEC1816 3499 sqr sing_1858.htm#SEC1934 3500 sqrfree sing_341.htm#SEC381 3501 squareRoot sing_1877.htm#SEC1953 3502 squarefree sing_1558.htm#SEC1634 3503 sres sing_343.htm#SEC383 3504 ssi Parallelization with ssi links sing_795.htm#SEC847 3505 staircase sing_1749.htm#SEC1825 3506 standard sing_1953.htm#SEC2029 3507 standard bases. sing_2204.htm#IDX897 3508 standard bases. sing_2205.htm#IDX898 3509 standard.lib sing_871.htm#IDX413 3510 standard_lib sing_871.htm#IDX414 3511 startNmz sing_1262.htm#SEC1338 21925 3512 startTasks sing_1021.htm#SEC1097 3404 3513 static procedures Procedure definition sing_43.htm#SEC78 3405 status sing_ 401.htm#SEC4413406 std sing_ 402.htm#SEC4423407 std sing_ 855.htm#SEC9073408 std (plural) sing_ 529.htm#SEC5693409 stdfglm sing_ 403.htm#SEC4433410 stdhilb sing_ 404.htm#SEC4443411 stopTask sing_10 73.htm#SEC11493412 stratify sing_1 733.htm#SEC18093413 stratify.lib sing_1 731.htm#SEC18073414 stratify_lib sing_1 731.htm#SEC18073514 status sing_344.htm#SEC384 3515 std sing_345.htm#SEC385 3516 std sing_798.htm#SEC850 3517 std (plural) sing_472.htm#SEC512 3518 stdfglm sing_346.htm#SEC386 3519 stdhilb sing_347.htm#SEC387 3520 stopTask sing_1022.htm#SEC1098 3521 stratify sing_1683.htm#SEC1759 3522 stratify.lib sing_1681.htm#SEC1757 3523 stratify_lib sing_1681.htm#SEC1757 3415 3524 string Miscellaneous oddities sing_166.htm#SEC206 3416 string sing_466.htm#IDX291 3525 string sing_409.htm#IDX291 3526 string sing_916.htm#IDX470 3417 3527 string declarations sing_167.htm#SEC207 3418 3528 string expressions sing_168.htm#SEC208 … … 3420 3530 string related functions string related functions sing_171.htm#SEC211 3421 3531 string type cast sing_169.htm#SEC209 3422 stripHNE sing_1 605.htm#SEC16813423 sturm sing_ 2036.htm#SEC21123424 sturmha sing_ 2038.htm#SEC21143425 sturmhaseq sing_ 2039.htm#SEC21153426 sturmquery sing_ 2014.htm#SEC20903427 sturmseq sing_ 2037.htm#SEC21133428 submat sing_10 93.htm#SEC11693429 subrInterred sing_ 1008.htm#SEC10843430 subset_sum01 sing_19 57.htm#SEC20333431 subset_sum02 sing_19 58.htm#SEC20343432 subst sing_ 405.htm#SEC4453433 subst (plural) sing_ 530.htm#SEC5703434 substitute sing_ 1007.htm#SEC10833435 sugarCrit, option sing_3 64.htm#IDX1693436 sum sing_ 951.htm#SEC10273437 sum_of_powers sing_2 183.htm#SEC22593438 sumlist sing_1 447.htm#SEC15233439 super-commutative algebras Graded commutative algebras (SCA) sing_ 539.htm#SEC5913440 superCommutative sing_7 71.htm#SEC8233441 super_increasing_knapsack super_increasing_knapsack sing_19 69.htm#SEC20453442 surf.lib sing_1 816.htm#SEC18923443 surf_lib sing_1 816.htm#SEC18923444 surfacesignature.lib surfacesignature_lib sing_16 65.htm#SEC17413445 surfacesignature_lib surfacesignature_lib sing_16 65.htm#SEC17413532 stripHNE sing_1555.htm#SEC1631 3533 sturm sing_1986.htm#SEC2062 3534 sturmha sing_1988.htm#SEC2064 3535 sturmhaseq sing_1989.htm#SEC2065 3536 sturmquery sing_1964.htm#SEC2040 3537 sturmseq sing_1987.htm#SEC2063 3538 submat sing_1042.htm#SEC1118 3539 subrInterred sing_957.htm#SEC1033 3540 subset_sum01 sing_1907.htm#SEC1983 3541 subset_sum02 sing_1908.htm#SEC1984 3542 subst sing_348.htm#SEC388 3543 subst (plural) sing_473.htm#SEC513 3544 substitute sing_956.htm#SEC1032 3545 sugarCrit, option sing_307.htm#IDX169 3546 sum sing_894.htm#SEC970 3547 sum_of_powers sing_2241.htm#SEC2317 3548 sumlist sing_1397.htm#SEC1473 3549 super-commutative algebras Graded commutative algebras (SCA) sing_482.htm#SEC534 3550 superCommutative sing_714.htm#SEC766 3551 super_increasing_knapsack super_increasing_knapsack sing_1919.htm#SEC1995 3552 surf.lib sing_1766.htm#SEC1842 3553 surf_lib sing_1766.htm#SEC1842 3554 surfacesignature.lib surfacesignature_lib sing_1615.htm#SEC1691 3555 surfacesignature_lib surfacesignature_lib sing_1615.htm#SEC1691 3446 3556 surfer sing_1.htm#IDX8 3447 surfer sing_1 818.htm#SEC18943557 surfer sing_1768.htm#SEC1844 3448 3558 surfex sing_1.htm#IDX7 3449 surfex.lib sing_1 819.htm#SEC18953450 surfex_lib sing_1 819.htm#SEC18953451 suspend sing_ 401.htm#SEC4413452 swalk sing_24 06.htm#SEC24823453 swalk.lib sing_24 05.htm#SEC24813454 swalk_lib sing_24 05.htm#SEC24813455 swap sing_1 534.htm#SEC16103456 swap sing_21 36.htm#IDX7973457 switch No case or switch statement sing_4 60.htm#SEC5003458 syModStd sing_13 79.htm#SEC14553459 symNsym sing_2 177.htm#SEC22533460 sym_gauss sing_1 119.htm#SEC11953461 symm sing_2 176.htm#SEC22523462 symmStd sing_13 78.htm#SEC14543463 symmat sing_10 94.htm#SEC11703464 symmetric basis sing_1 111.htm#IDX4523465 symmetric power sing_1 113.htm#IDX4543466 symmetricBasis sing_1 111.htm#SEC11873467 symmetricPower sing_1 113.htm#SEC11893468 symmfunc sing_ 2023.htm#SEC20993469 symodstd.lib sing_13 73.htm#SEC14493470 symodstd_lib sing_13 73.htm#SEC14493471 symsignature sing_ 2013.htm#SEC20893472 syndrome sing_1 846.htm#SEC19223473 sysBin sing_1 844.htm#SEC19203474 sysCRHT sing_1 841.htm#SEC19173475 sysCRHTMindist sing_1 842.htm#SEC19183476 sysFL sing_18 57.htm#SEC19333477 sysNewton sing_1 843.htm#SEC19193478 sysQE sing_1 847.htm#SEC19233479 sys_code sing_1 838.htm#SEC19143480 system sing_ 406.htm#SEC4463481 system, -- sing_ 406.htm#IDX2713482 system, --long_option_name sing_ 406.htm#IDX2743483 system, --long_option_name=value sing_ 406.htm#IDX2763484 system, HC sing_ 406.htm#IDX2143485 system, LLL sing_ 406.htm#IDX2183486 system, Singular sing_ 406.htm#IDX2523487 system, SingularLib sing_ 406.htm#IDX2543488 system, absFact sing_ 406.htm#IDX1893489 system, blackbox sing_ 406.htm#IDX1903490 system, bracket sing_ 406.htm#IDX1953491 system, browsers sing_ 406.htm#IDX1943492 system, btest sing_ 406.htm#IDX1973493 system, complexNearZero sing_ 406.htm#IDX1983494 system, contributors sing_ 406.htm#IDX2003495 system, cpu sing_ 406.htm#IDX2023496 system, cpu sing_ 406.htm#IDX2703497 system, denom_list sing_ 406.htm#IDX2043498 system, eigenvals sing_ 406.htm#IDX2053499 system, env sing_ 406.htm#IDX2063500 system, executable sing_ 406.htm#IDX2083501 system, freegb sing_ 406.htm#IDX2093502 system, getPrecDigits sing_ 406.htm#IDX2123503 system, getenv sing_ 406.htm#IDX2113504 system, gmsnf sing_ 406.htm#IDX2133505 system, hessenberg sing_ 406.htm#IDX2153506 system, install sing_ 406.htm#IDX2173507 system, nblocks sing_ 406.htm#IDX2213508 system, newstruct sing_ 406.htm#IDX2223509 system, opp sing_ 406.htm#IDX2233510 system, oppose sing_ 406.htm#IDX2263511 system, pcvBasis sing_ 406.htm#IDX2353512 system, pcvCV2P sing_ 406.htm#IDX2333513 system, pcvDim sing_ 406.htm#IDX2343514 system, pcvLAddL sing_ 406.htm#IDX2293515 system, pcvMinDeg sing_ 406.htm#IDX2313516 system, pcvP2CV sing_ 406.htm#IDX2323517 system, pcvPMulL sing_ 406.htm#IDX2303518 system, pid sing_ 406.htm#IDX2373519 system, random sing_ 406.htm#IDX2393520 system, reserve sing_ 406.htm#IDX2413521 system, reservedLink sing_ 406.htm#IDX2423522 system, semaphore sing_ 406.htm#IDX2443523 system, semic sing_ 406.htm#IDX2453524 system, setenv sing_ 406.htm#IDX2473525 system, sh sing_ 406.htm#IDX2493526 system, shrinktest sing_ 406.htm#IDX2503527 system, spadd sing_ 406.htm#IDX2553528 system, spectrum sing_ 406.htm#IDX2563529 system, spmul sing_ 406.htm#IDX2573530 system, std_syz sing_ 406.htm#IDX2583531 system, stest sing_ 406.htm#IDX2593532 system, tensorModuleMult sing_ 406.htm#IDX2603533 system, twostd sing_ 406.htm#IDX2613534 system, uname sing_ 406.htm#IDX2643535 system, version sing_ 406.htm#IDX2673536 system, with sing_ 406.htm#IDX2683537 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2 289.htm#SEC23653538 syz sing_ 407.htm#SEC4473539 syz (plural) sing_ 531.htm#SEC5713540 syzygy sing_10 58.htm#IDX4483541 tDetropicalise sing_2 096.htm#SEC21723542 tInitialForm sing_2 080.htm#SEC21563543 tInitialFormPar sing_2 092.htm#SEC21683544 tInitialFormParMax sing_2 093.htm#SEC21693545 tInitialIdeal sing_2 081.htm#SEC21573546 tab sing_9 80.htm#SEC10563547 tail sing_19 92.htm#SEC20683548 tame polynomial sing_15 87.htm#IDX6633549 tame polynomial sing_15 88.htm#IDX6733550 tame polynomial sing_15 89.htm#IDX6743551 tangentGens sing_1 403.htm#SEC14793552 tangentcone sing_16 52.htm#SEC17283553 task sing_10 66.htm#IDX4513554 tasks.lib sing_10 66.htm#SEC11423555 tasks_lib sing_10 66.htm#SEC11423556 tau_es sing_15 60.htm#SEC16363557 tau_es2 sing_1 514.htm#SEC15903558 tdCf sing_22 12.htm#SEC22883559 tdFactor sing_22 14.htm#SEC22903560 tdProj sing_22 17.htm#SEC22933561 tdTerms sing_22 13.htm#SEC22893562 teachstd.lib sing_19 90.htm#SEC20663563 teachstd_lib sing_19 90.htm#SEC20663559 surfex.lib sing_1769.htm#SEC1845 3560 surfex_lib sing_1769.htm#SEC1845 3561 suspend sing_344.htm#SEC384 3562 swalk sing_2486.htm#SEC2562 3563 swalk.lib sing_2485.htm#SEC2561 3564 swalk_lib sing_2485.htm#SEC2561 3565 swap sing_1484.htm#SEC1560 3566 swap sing_2166.htm#IDX833 3567 switch No case or switch statement sing_403.htm#SEC443 3568 syModStd sing_1329.htm#SEC1405 3569 symNsym sing_2235.htm#SEC2311 3570 sym_gauss sing_1068.htm#SEC1144 3571 symm sing_2234.htm#SEC2310 3572 symmStd sing_1328.htm#SEC1404 3573 symmat sing_1043.htm#SEC1119 3574 symmetric basis sing_1060.htm#IDX512 3575 symmetric power sing_1062.htm#IDX514 3576 symmetricBasis sing_1060.htm#SEC1136 3577 symmetricPower sing_1062.htm#SEC1138 3578 symmfunc sing_1973.htm#SEC2049 3579 symodstd.lib sing_1323.htm#SEC1399 3580 symodstd_lib sing_1323.htm#SEC1399 3581 symsignature sing_1963.htm#SEC2039 3582 syndrome sing_1796.htm#SEC1872 3583 sysBin sing_1794.htm#SEC1870 3584 sysCRHT sing_1791.htm#SEC1867 3585 sysCRHTMindist sing_1792.htm#SEC1868 3586 sysFL sing_1807.htm#SEC1883 3587 sysNewton sing_1793.htm#SEC1869 3588 sysQE sing_1797.htm#SEC1873 3589 sys_code sing_1788.htm#SEC1864 3590 system sing_349.htm#SEC389 3591 system, -- sing_349.htm#IDX271 3592 system, --long_option_name sing_349.htm#IDX274 3593 system, --long_option_name=value sing_349.htm#IDX276 3594 system, HC sing_349.htm#IDX214 3595 system, LLL sing_349.htm#IDX218 3596 system, Singular sing_349.htm#IDX252 3597 system, SingularLib sing_349.htm#IDX254 3598 system, absFact sing_349.htm#IDX189 3599 system, blackbox sing_349.htm#IDX190 3600 system, bracket sing_349.htm#IDX195 3601 system, browsers sing_349.htm#IDX194 3602 system, btest sing_349.htm#IDX197 3603 system, complexNearZero sing_349.htm#IDX198 3604 system, contributors sing_349.htm#IDX200 3605 system, cpu sing_349.htm#IDX202 3606 system, cpu sing_349.htm#IDX270 3607 system, denom_list sing_349.htm#IDX204 3608 system, eigenvals sing_349.htm#IDX205 3609 system, env sing_349.htm#IDX206 3610 system, executable sing_349.htm#IDX208 3611 system, freegb sing_349.htm#IDX209 3612 system, getPrecDigits sing_349.htm#IDX212 3613 system, getenv sing_349.htm#IDX211 3614 system, gmsnf sing_349.htm#IDX213 3615 system, hessenberg sing_349.htm#IDX215 3616 system, install sing_349.htm#IDX217 3617 system, nblocks sing_349.htm#IDX221 3618 system, newstruct sing_349.htm#IDX222 3619 system, opp sing_349.htm#IDX223 3620 system, oppose sing_349.htm#IDX226 3621 system, pcvBasis sing_349.htm#IDX235 3622 system, pcvCV2P sing_349.htm#IDX233 3623 system, pcvDim sing_349.htm#IDX234 3624 system, pcvLAddL sing_349.htm#IDX229 3625 system, pcvMinDeg sing_349.htm#IDX231 3626 system, pcvP2CV sing_349.htm#IDX232 3627 system, pcvPMulL sing_349.htm#IDX230 3628 system, pid sing_349.htm#IDX237 3629 system, random sing_349.htm#IDX239 3630 system, reserve sing_349.htm#IDX241 3631 system, reservedLink sing_349.htm#IDX242 3632 system, semaphore sing_349.htm#IDX244 3633 system, semic sing_349.htm#IDX245 3634 system, setenv sing_349.htm#IDX247 3635 system, sh sing_349.htm#IDX249 3636 system, shrinktest sing_349.htm#IDX250 3637 system, spadd sing_349.htm#IDX255 3638 system, spectrum sing_349.htm#IDX256 3639 system, spmul sing_349.htm#IDX257 3640 system, std_syz sing_349.htm#IDX258 3641 system, stest sing_349.htm#IDX259 3642 system, tensorModuleMult sing_349.htm#IDX260 3643 system, twostd sing_349.htm#IDX261 3644 system, uname sing_349.htm#IDX264 3645 system, version sing_349.htm#IDX267 3646 system, with sing_349.htm#IDX268 3647 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2369.htm#SEC2445 3648 syz sing_350.htm#SEC390 3649 syz (plural) sing_474.htm#SEC514 3650 syzygy sing_1007.htm#IDX508 3651 tDetropicalise sing_2144.htm#SEC2220 3652 tInitialForm sing_2128.htm#SEC2204 3653 tInitialFormPar sing_2140.htm#SEC2216 3654 tInitialFormParMax sing_2141.htm#SEC2217 3655 tInitialIdeal sing_2129.htm#SEC2205 3656 tab sing_929.htm#SEC1005 3657 tail sing_1942.htm#SEC2018 3658 tame polynomial sing_1537.htm#IDX727 3659 tame polynomial sing_1538.htm#IDX737 3660 tame polynomial sing_1539.htm#IDX738 3661 tangentGens sing_1353.htm#SEC1429 3662 tangentcone sing_1602.htm#SEC1678 3663 task sing_1015.htm#IDX511 3664 tasks.lib sing_1015.htm#SEC1091 3665 tasks_lib sing_1015.htm#SEC1091 3666 tau_es sing_1510.htm#SEC1586 3667 tau_es2 sing_1464.htm#SEC1540 3668 tdCf sing_2270.htm#SEC2346 3669 tdFactor sing_2272.htm#SEC2348 3670 tdProj sing_2275.htm#SEC2351 3671 tdTerms sing_2271.htm#SEC2347 3672 teachstd.lib sing_1940.htm#SEC2016 3673 teachstd_lib sing_1940.htm#SEC2016 3564 3674 template.lib sing_55.htm#IDX120 3565 3675 template.lib sing_55.htm#IDX123 3566 3676 template_lib sing_55.htm#SEC92 3567 3677 template_lib sing_55.htm#IDX121 3568 tensor sing_547.htm#IDX305 3569 tensor sing_1095.htm#SEC1171 3570 tensorMod sing_1214.htm#SEC1290 3571 term orderings General definitions for orderings sing_894.htm#SEC946 3572 term orderings introduction Introduction to orderings sing_893.htm#SEC945 3573 testNCfac sing_745.htm#SEC797 3574 testParametrization sing_1418.htm#SEC1494 3575 testPointConic sing_1419.htm#SEC1495 3576 testPrimary sing_1331.htm#SEC1407 3577 testPrimaryE sing_1332.htm#SEC1408 3578 tex sing_1805.htm#SEC1881 3579 texDrawBasic sing_2087.htm#SEC2163 3580 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2089.htm#SEC2165 3581 texDrawTriangulation texDrawTriangulation sing_2090.htm#SEC2166 3582 texDrawTropical sing_2088.htm#SEC2164 3583 texMatrix sing_2086.htm#SEC2162 3584 texNumber sing_2084.htm#SEC2160 3585 texPolynomial sing_2085.htm#SEC2161 3586 texcoef sing_1886.htm#SEC1962 3587 texdemo sing_1806.htm#SEC1882 3588 texfactorize sing_1807.htm#SEC1883 3589 texmap sing_1808.htm#SEC1884 3590 texname sing_1809.htm#SEC1885 3591 texobj sing_1810.htm#SEC1886 3592 texpoly sing_1811.htm#SEC1887 3593 texproc sing_1812.htm#SEC1888 3594 texring sing_1813.htm#SEC1889 3595 the first alternative algorithm sing_1191.htm#IDX486 3596 three_elements sing_1976.htm#SEC2052 3597 timeFactorize sing_955.htm#SEC1031 3598 timeStd sing_954.htm#SEC1030 3599 timer sing_450.htm#SEC490 3600 timer resolution, setting the sing_406.htm#IDX277 3601 timestep sing_2278.htm#SEC2354 3602 tjurina sing_1648.htm#SEC1724 3603 tmatrix sing_1575.htm#SEC1651 3604 todd sing_2209.htm#SEC2285 3605 toddE sing_2210.htm#SEC2286 3606 toddPoly sing_2223.htm#SEC2299 3607 tolessvars sing_1751.htm#SEC1827 3608 topological invariants sing_1502.htm#IDX565 3609 topological invariants sing_1509.htm#IDX572 3610 topological invariants sing_1510.htm#IDX576 3611 topological invariants sing_1511.htm#IDX580 3612 topological invariants sing_1512.htm#IDX584 3613 toric geometry sing_2466.htm#SEC2542 3614 toric ideals sing_908.htm#SEC965 3615 toric ring sing_1290.htm#IDX515 3616 toric.lib sing_1380.htm#SEC1456 3617 toric_ideal sing_1381.htm#SEC1457 3618 toric_lib sing_1380.htm#SEC1456 3619 toric_std sing_1382.htm#SEC1458 3620 torusInvariants sing_1296.htm#SEC1372 911 3621 total divisors sing_547.htm#IDX302 3622 total multiplicities sing_1502.htm#IDX568 3623 totalmultiplicities sing_1504.htm#SEC1580 3624 trace sing_408.htm#SEC448 3625 tracemult sing_2017.htm#SEC2093 3626 transpose sing_409.htm#SEC449 3627 trapezoid sing_2272.htm#SEC2348 3628 triMNewton sing_1777.htm#SEC1853 3629 triagmatrix sing_1021.htm#SEC1097 3630 triang.lib sing_1770.htm#SEC1846 3631 triangL sing_1771.htm#SEC1847 3632 triangL_solve sing_1768.htm#SEC1844 3633 triangLf_solve sing_1766.htm#SEC1842 3634 triangLfak sing_1772.htm#SEC1848 3635 triangM sing_1773.htm#SEC1849 3636 triangMH sing_1774.htm#SEC1850 3637 triangM_solve sing_1767.htm#SEC1843 3638 triang_lib sing_1770.htm#SEC1846 3639 triang_solve sing_1769.htm#SEC1845 3640 triangulations sing_2050.htm#SEC2126 3641 tropical curves sing_2066.htm#IDX746 3642 tropical geometry sing_1177.htm#IDX462 3643 tropical mirror symmetry sing_1177.htm#IDX464 3644 tropical polynomials sing_2066.htm#IDX747 3645 tropical.lib sing_2066.htm#IDX744 3646 tropicalCurve sing_2071.htm#SEC2147 3647 tropicalJInvariant sing_2074.htm#SEC2150 3648 tropicalLifting sing_2067.htm#SEC2143 3649 tropicalSubst sing_2099.htm#SEC2175 3650 tropicalVariety sing_2425.htm#SEC2501 3651 tropical_lib sing_2066.htm#IDX745 3652 tropicalise sing_2078.htm#SEC2154 3653 tropicaliseSet sing_2079.htm#SEC2155 3654 truncate sing_1484.htm#SEC1560 13545 3655 truncateFast sing_1485.htm#SEC1561 5124 3656 truncated module sing_1484.htm#IDX556 3657 truncated module sing_1485.htm#IDX557 3658 tst_ncfactor sing_753.htm#SEC805 3659 twalk sing_1190.htm#SEC1266 3660 two-sided sing_547.htm#IDX303 3661 two-sided Groebner basis sing_547.htm#IDX304 3662 twostd sing_406.htm#IDX262 3663 twostd sing_532.htm#SEC572 3664 type sing_410.htm#SEC450 3665 type B sing_2152.htm#IDX824 3666 type D sing_2153.htm#IDX826 3678 tensor sing_490.htm#IDX305 3679 tensor sing_1044.htm#SEC1120 3680 tensorMod sing_1163.htm#SEC1239 3681 term orderings General definitions for orderings sing_837.htm#SEC889 3682 term orderings introduction Introduction to orderings sing_836.htm#SEC888 3683 testNCfac sing_688.htm#SEC740 3684 testParametrization sing_1368.htm#SEC1444 3685 testPointConic sing_1369.htm#SEC1445 3686 testPrimary sing_1281.htm#SEC1357 3687 testPrimaryE sing_1282.htm#SEC1358 3688 tex sing_1755.htm#SEC1831 3689 texDrawBasic sing_2135.htm#SEC2211 3690 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2137.htm#SEC2213 3691 texDrawTriangulation texDrawTriangulation sing_2138.htm#SEC2214 3692 texDrawTropical sing_2136.htm#SEC2212 3693 texMatrix sing_2134.htm#SEC2210 3694 texNumber sing_2132.htm#SEC2208 3695 texPolynomial sing_2133.htm#SEC2209 3696 texcoef sing_1836.htm#SEC1912 3697 texdemo sing_1756.htm#SEC1832 3698 texfactorize sing_1757.htm#SEC1833 3699 texmap sing_1758.htm#SEC1834 3700 texname sing_1759.htm#SEC1835 3701 texobj sing_1760.htm#SEC1836 3702 texpoly sing_1761.htm#SEC1837 3703 texproc sing_1762.htm#SEC1838 3704 texring sing_1763.htm#SEC1839 3705 the first alternative algorithm sing_1140.htm#IDX548 3706 three_elements sing_1926.htm#SEC2002 3707 timeFactorize sing_898.htm#SEC974 3708 timeStd sing_897.htm#SEC973 3709 timer sing_393.htm#SEC433 3710 timer resolution, setting the sing_349.htm#IDX277 3711 timestep sing_2358.htm#SEC2434 3712 tjurina sing_1598.htm#SEC1674 3713 tmatrix sing_1525.htm#SEC1601 3714 todd sing_2267.htm#SEC2343 3715 toddE sing_2268.htm#SEC2344 3716 toddPoly sing_2281.htm#SEC2357 3717 tolessvars sing_1701.htm#SEC1777 3718 topological invariants sing_1452.htm#IDX629 3719 topological invariants sing_1459.htm#IDX636 3720 topological invariants sing_1460.htm#IDX640 3721 topological invariants sing_1461.htm#IDX644 3722 topological invariants sing_1462.htm#IDX648 3723 toric ideals sing_851.htm#SEC908 3724 toric ring sing_1240.htm#IDX579 3725 toric.lib sing_1330.htm#SEC1406 3726 toric_ideal sing_1331.htm#SEC1407 3727 toric_lib sing_1330.htm#SEC1406 3728 toric_std sing_1332.htm#SEC1408 3729 torusInvariants sing_1246.htm#SEC1322 911 3730 total divisors sing_490.htm#IDX302 3731 total multiplicities 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