Changeset 7d21990 in git
- Timestamp:
- Nov 14, 2016, 3:12:47 PM (6 years ago)
- Branches:
- (u'jengelh-datetime', 'ceac47cbc86fe4a15902392bdbb9bd2ae0ea02c6')(u'spielwiese', 'a800fe4b3e9d37a38c5a10cc0ae9dfa0c15a4ee6')
- Children:
- 3fec5d04607bb2dbc78498417a5ca31c056e2b82
- Parents:
- 62686ae5a9b7978787335e4943e395b8d8238688
- Files:
-
- 7 edited
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doc/NEWS.texi (modified) (2 diffs)
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doc/general.doc (modified) (previous)
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doc/reference.doc (modified) (previous)
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doc/singular.idx (modified) (136 diffs)
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doc/types.doc (modified) (previous)
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dox/Doxyfile.in (modified) (1 diff)
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emacs/hlp-cmpl.el (modified) (91 diffs)
Legend:
- Unmodified
- Added
- Removed
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doc/NEWS.texi
r62686a r7d21990 21 21 22 22 @heading News for version @value{VERSION} 23 24 Syntax changes: 25 @itemize 26 @item new (additional) form of ring definitions: (for example @code{ring R=QQ[x,y,z];}) 27 (@nref{General syntax of a ring declaration}) 28 @item new (additional) form of multi-indicies: (for example @code{i(1,2,3,4,5)}) 29 (@nref{Names}) 30 @item changed behaviour of @code{charstr} (@nref{charstr}) 31 @item new data type @code{cring} to describe the coeffient rings, to be used 32 for the new definitions for (polynomial) rings (@nref{General syntax of a ring declaration}) 33 @item new command @code{ring_list} to decompose polynomial rings (@nref{ring_list}) 34 @item extended polynomial ring construction: also from lists produce by @code{ring_list} 35 @item new attribute @code{ring_cf} for @code{ring} (@nref{attrib}) 36 @item printing of rings changed to match @code{cring} names (@nref{charstr}) 37 @end itemize 23 38 24 39 New libraries: … … 123 138 Version 4-0-1 is a bug fix release. 124 139 125 New feature: attribute @code{ring_cf} for @code{ring} .140 New feature: attribute @code{ring_cf} for @code{ring} (@nref{attrib}) 126 141 127 142 @heading News for version 4-0-0 -
doc/singular.idx
r62686a r7d21990 1 sing_901.htm#IDX4182 sing_902.htm#IDX4233 sing_903.htm#IDX4284 sing_904.htm#IDX4315 sing_905.htm#IDX4356 sing_909.htm#IDX4427 sing_910.htm#IDX4478 sing_911.htm#IDX4519 sing_912.htm#IDX45410 sing_913.htm#IDX45811 sing_914.htm#IDX46212 sing_915.htm#IDX46613 sing_916.htm#IDX47114 sing_917.htm#IDX47615 sing_918.htm#IDX48116 sing_919.htm#IDX48417 sing_920.htm#IDX48618 1 ! sing_36.htm#IDX101 19 2 != sing_36.htm#IDX95 … … 184 167 ? sing_36.htm#IDX106 185 168 ? sing_251.htm#IDX148 186 AG codes sing_83 2.htm#SEC884169 AG codes sing_833.htm#SEC885 187 170 AGcode_L sing_1782.htm#SEC1858 188 171 AGcode_Omega sing_1783.htm#SEC1859 189 ASCII sing_88 1.htm#SEC957172 ASCII sing_882.htm#SEC958 190 173 ASCII links sing_112.htm#SEC152 191 174 ASSUME sing_64.htm#SEC101 192 175 A_L sing_1481.htm#SEC1557 193 A_Z sing_88 0.htm#SEC956176 A_Z sing_881.htm#SEC957 194 177 Access to elements of a user defined type Access to elements of a user defined type sing_180.htm#SEC220 195 178 Adj_div sing_1777.htm#SEC1853 196 Adjoint ideal sing_1358.htm#IDX 606197 Alexander polynomial sing_1452.htm#IDX6 30198 Algebraic Geometry codes sing_1776.htm#IDX7 78199 Algebraic dependence Algebraic dependence sing_81 3.htm#SEC865179 Adjoint ideal sing_1358.htm#IDX590 180 Alexander polynomial sing_1452.htm#IDX614 181 Algebraic Geometry codes sing_1776.htm#IDX762 182 Algebraic dependence Algebraic dependence sing_814.htm#SEC866 200 183 Algebraic geometry sing_1333.htm#SEC1409 201 AltVarEnd sing_72 6.htm#SEC778202 AltVarStart sing_72 5.htm#SEC777184 AltVarEnd sing_727.htm#SEC779 185 AltVarStart sing_726.htm#SEC778 203 186 Ann sing_1272.htm#SEC1348 204 Appel function sing_55 5.htm#IDX345205 Appel hypergeometric function sing_55 5.htm#IDX346206 Applications sing_83 0.htm#SEC882187 Appel function sing_556.htm#IDX347 188 Appel hypergeometric function sing_556.htm#IDX348 189 Applications sing_831.htm#SEC883 207 190 ArnoldAction sing_1574.htm#SEC1650 208 191 Assignments for user defined types Assignments for user defined types sing_182.htm#SEC222 209 AssocTanToEnv sing_91 7.htm#SEC993192 AssocTanToEnv sing_918.htm#SEC994 210 193 Atkin sing_1865.htm#SEC1941 211 194 Authors sing_1.htm#IDX16 212 195 BINresol sing_1371.htm#SEC1447 213 196 Background sing_3.htm#SEC5 214 Basic programming sing_78 8.htm#SEC840215 Basic programming sing_78 8.htm#SEC840197 Basic programming sing_789.htm#SEC841 198 Basic programming sing_789.htm#SEC841 216 199 BelongSemig sing_2291.htm#SEC2367 217 BerlekampMassey sing_233 9.htm#SEC2415200 BerlekampMassey sing_2338.htm#SEC2414 218 201 Bern sing_2269.htm#SEC2345 219 Bernstein operator sing_53 2.htm#IDX327220 Bernstein-Sato polynomial sing_49 7.htm#IDX308221 Bernstein-Sato polynomial sing_53 2.htm#IDX324222 Bernstein-Sato polynomial sing_1515.htm#IDX6 61223 Bernstein-Sato polynomial sing_1519.htm#IDX6 78224 Bernstein-Sato polynomial for variety sing_58 8.htm#IDX349225 Betti number Syzygies and resolutions sing_84 7.htm#SEC904226 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_85 7.htm#SEC914202 Bernstein operator sing_533.htm#IDX329 203 Bernstein-Sato polynomial sing_498.htm#IDX310 204 Bernstein-Sato polynomial sing_533.htm#IDX326 205 Bernstein-Sato polynomial sing_1515.htm#IDX645 206 Bernstein-Sato polynomial sing_1519.htm#IDX662 207 Bernstein-Sato polynomial for variety sing_589.htm#IDX351 208 Betti number Syzygies and resolutions sing_848.htm#SEC905 209 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_858.htm#SEC915 227 210 BlowingUp sing_1494.htm#SEC1570 228 211 Blowupcenter sing_1374.htm#SEC1450 229 212 BorelCheck sing_1449.htm#SEC1525 230 Branches of space curve singularities Branches of space curve singularities sing_82 1.htm#SEC873231 Briancon-Maisonobe algorithm sing_53 2.htm#IDX333232 Brieskorn lattice sing_1515.htm#IDX6 57233 Brieskorn lattice sing_1516.htm#IDX6 68234 Brieskorn lattice sing_1517.htm#IDX6 71235 Brieskorn lattice sing_1518.htm#IDX6 74236 Brieskorn lattice sing_1519.htm#IDX6 77237 Brieskorn lattice sing_1520.htm#IDX6 81238 Brieskorn lattice sing_1521.htm#IDX6 85239 Brieskorn lattice sing_1522.htm#IDX6 91240 Brieskorn lattice sing_1523.htm#IDX6 99241 Brieskorn lattice sing_1524.htm#IDX 705242 Brieskorn lattice sing_1525.htm#IDX 713243 Brieskorn lattice sing_1526.htm#IDX7 23244 Brieskorn lattice sing_1537.htm#IDX7 29245 Brieskorn lattice sing_1539.htm#IDX7 40246 Brieskorn lattice sing_1567.htm#IDX7 67247 Brill-Noether algorithm sing_1776.htm#IDX7 79213 Branches of space curve singularities Branches of space curve singularities sing_822.htm#SEC874 214 Briancon-Maisonobe algorithm sing_533.htm#IDX335 215 Brieskorn lattice sing_1515.htm#IDX641 216 Brieskorn lattice sing_1516.htm#IDX652 217 Brieskorn lattice sing_1517.htm#IDX655 218 Brieskorn lattice sing_1518.htm#IDX658 219 Brieskorn lattice sing_1519.htm#IDX661 220 Brieskorn lattice sing_1520.htm#IDX665 221 Brieskorn lattice sing_1521.htm#IDX669 222 Brieskorn lattice sing_1522.htm#IDX675 223 Brieskorn lattice sing_1523.htm#IDX683 224 Brieskorn lattice sing_1524.htm#IDX689 225 Brieskorn lattice sing_1525.htm#IDX697 226 Brieskorn lattice sing_1526.htm#IDX707 227 Brieskorn lattice sing_1537.htm#IDX713 228 Brieskorn lattice sing_1539.htm#IDX724 229 Brieskorn lattice sing_1567.htm#IDX751 230 Brill-Noether algorithm sing_1776.htm#IDX763 248 231 BrillNoether sing_1779.htm#SEC1855 249 Buchberger algorithm for toric ideals Buchberger algorithm sing_85 8.htm#SEC915250 Budur-Mustata-Saito approach sing_58 8.htm#IDX353251 Building Singular sing_250 2.htm#SEC2591252 C programming language Major differences to the C programming language sing_40 0.htm#SEC440253 C, module ordering sing_84 0.htm#IDX407254 CGS sing_90 3.htm#IDX424232 Buchberger algorithm for toric ideals Buchberger algorithm sing_859.htm#SEC916 233 Budur-Mustata-Saito approach sing_589.htm#IDX355 234 Building Singular sing_2503.htm#SEC2592 235 C programming language Major differences to the C programming language sing_401.htm#SEC441 236 C, module ordering sing_841.htm#IDX409 237 CGS sing_904.htm#IDX424 255 238 CM_regularity sing_1436.htm#SEC1512 33865 256 239 CMtype sing_1605.htm#SEC1681 257 CRHT-ideal sing_86 4.htm#SEC928240 CRHT-ideal sing_865.htm#SEC929 258 241 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 259 Castelnuovo-Mumford regularity sing_1436.htm#IDX6 22242 Castelnuovo-Mumford regularity sing_1436.htm#IDX606 260 243 Category string sing_51.htm#SEC88 261 CenCharDec sing_68 2.htm#SEC734244 CenCharDec sing_683.htm#SEC735 262 245 Center sing_1413.htm#SEC1489 263 246 CenterBO sing_1420.htm#SEC1496 264 CentralQuot sing_68 0.htm#SEC732265 CentralSaturation sing_68 1.htm#SEC733247 CentralQuot sing_681.htm#SEC733 248 CentralSaturation sing_682.htm#SEC734 266 249 Change of rings sing_9.htm#SEC15 267 Characteristic sets sing_84 8.htm#SEC905250 Characteristic sets sing_849.htm#SEC906 268 251 CharacteristicExponents CharacteristicExponents sing_1500.htm#SEC1576 269 252 ChernRootsDual sing_2248.htm#SEC2324 … … 273 256 ChernRootsSymm sing_2259.htm#SEC2335 274 257 ChernRootsWedge sing_2260.htm#SEC2336 275 Chevalley-Rosenlicht theorem sing_1352.htm#IDX5 91276 Chevalley-Rosenlicht theorem sing_1353.htm#IDX5 94277 Classification of hypersurface singularities Classification of hypersurface singularities sing_82 2.htm#SEC874278 Classification of singularities sing_24 89.htm#IDX982279 Code Codes and the decoding problem sing_86 3.htm#SEC921280 Codes and the decoding problem Codes and the decoding problem sing_86 3.htm#SEC920258 Chevalley-Rosenlicht theorem sing_1352.htm#IDX575 259 Chevalley-Rosenlicht theorem sing_1353.htm#IDX578 260 Classification of hypersurface singularities Classification of hypersurface singularities sing_823.htm#SEC875 261 Classification of singularities sing_2490.htm#IDX967 262 Code Codes and the decoding problem sing_864.htm#SEC922 263 Codes and the decoding problem Codes and the decoding problem sing_864.htm#SEC921 281 264 Coding theory sing_1775.htm#SEC1851 282 Coefficient rings Notes for Singular users sing_250 0.htm#SEC2583265 Coefficient rings Notes for Singular users sing_2501.htm#SEC2584 283 266 Command line options Command line options sing_19.htm#SEC26 284 267 Commands Functions and system variables sing_201.htm#SEC241 285 268 Commands for user defined types Commands for user defined types sing_181.htm#SEC221 286 Commutative Algebra sing_80 1.htm#SEC853269 Commutative Algebra sing_802.htm#SEC854 287 270 Commutative algebra sing_1090.htm#SEC1166 288 CompDecomp sing_49 4.htm#SEC546271 CompDecomp sing_495.htm#SEC547 289 272 CompInt sing_2293.htm#SEC2369 290 273 CompleteHomog sing_2236.htm#SEC2312 291 ComplexValue sing_236 1.htm#SEC2437292 Comprehensive Groebner System sing_90 3.htm#IDX427293 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_79 7.htm#SEC849294 ConsLevels sing_91 1.htm#SEC987295 ConsLevelsToLevels sing_91 2.htm#SEC988274 ComplexValue sing_2360.htm#SEC2436 275 Comprehensive Groebner System sing_904.htm#IDX427 276 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_798.htm#SEC850 277 ConsLevels sing_912.htm#SEC988 278 ConsLevelsToLevels sing_913.htm#SEC989 296 279 ContactMatrix sing_1502.htm#SEC1578 297 Conti-Traverso algorithm sing_85 3.htm#SEC910280 Conti-Traverso algorithm sing_854.htm#SEC911 298 281 Contributors sing_1.htm#IDX15 299 Control structures sing_36 8.htm#SEC408282 Control structures sing_369.htm#SEC409 300 283 Control theory System and Control theory sing_1809.htm#SEC1885 301 Cooper philosophy sing_86 4.htm#SEC926284 Cooper philosophy sing_865.htm#SEC927 302 285 Cornacchia sing_1855.htm#SEC1931 303 286 CornacchiaModified sing_1856.htm#SEC1932 304 Crep sing_90 6.htm#SEC982305 Critical points sing_81 6.htm#SEC868287 Crep sing_907.htm#SEC983 288 Critical points sing_817.htm#SEC869 306 289 CurveParam sing_1496.htm#SEC1572 307 290 CurveRes sing_1495.htm#SEC1571 308 Curves sing_1358.htm#IDX 603291 Curves sing_1358.htm#IDX587 309 292 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 310 Cyclic code sing_1790.htm#IDX7 86311 Cyclic roots sing_79 4.htm#SEC846312 D-integration sing_55 5.htm#IDX342313 D-localization sing_55 5.htm#IDX338314 D-localization sing_76 0.htm#IDX376315 D-module purityfiltration_lib sing_49 7.htm#IDX306316 D-module sing_53 2.htm#IDX321317 D-module sing_55 5.htm#IDX335318 D-module sing_58 8.htm#IDX347319 D-module sing_73 8.htm#IDX361320 D-module sing_76 0.htm#IDX373321 D-module structure sing_53 2.htm#IDX322322 D-module structure sing_58 8.htm#IDX348323 D-restriction sing_55 5.htm#IDX340293 Cyclic code sing_1790.htm#IDX770 294 Cyclic roots sing_795.htm#SEC847 295 D-integration sing_556.htm#IDX344 296 D-localization sing_556.htm#IDX340 297 D-localization sing_761.htm#IDX378 298 D-module purityfiltration_lib sing_498.htm#IDX308 299 D-module sing_533.htm#IDX323 300 D-module sing_556.htm#IDX337 301 D-module sing_589.htm#IDX349 302 D-module sing_739.htm#IDX363 303 D-module sing_761.htm#IDX375 304 D-module structure sing_533.htm#IDX324 305 D-module structure sing_589.htm#IDX350 306 D-restriction sing_556.htm#IDX342 324 307 DBM links sing_117.htm#SEC157 325 308 DISPLAY environment variable The online help system sing_16.htm#IDX28 326 DLoc sing_55 8.htm#SEC610327 DLoc0 sing_56 0.htm#SEC612309 DLoc sing_559.htm#SEC611 310 DLoc0 sing_561.htm#SEC613 328 311 Data types sing_72.htm#SEC112 329 Data types (plural) sing_41 4.htm#IDX292312 Data types (plural) sing_415.htm#IDX294 330 313 Debugging tools sing_63.htm#SEC100 331 314 Decker, Wolfram sing_1.htm#IDX17 332 315 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_179.htm#SEC219 333 Decoding sing_1790.htm#IDX7 88334 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_86 2.htm#SEC919335 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_86 7.htm#SEC937316 Decoding sing_1790.htm#IDX772 317 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_863.htm#SEC920 318 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_868.htm#SEC938 336 319 Definition of a user defined type Definition of a user defined type sing_178.htm#SEC218 337 Deformations sing_8 19.htm#SEC871338 Deformations, T1 and T2 sing_81 8.htm#SEC870320 Deformations sing_820.htm#SEC872 321 Deformations, T1 and T2 sing_819.htm#SEC871 339 322 Degree sing_1337.htm#SEC1413 340 323 Delta sing_1421.htm#SEC1497 341 324 DeltaList sing_1422.htm#SEC1498 342 325 Demo mode sing_24.htm#SEC35 343 Depth sing_80 8.htm#SEC860344 Determinacy sing_249 2.htm#IDX986345 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_85 6.htm#SEC913346 Distributed computing sing_93 1.htm#IDX491347 Dlocalization sing_76 1.htm#SEC813326 Depth sing_809.htm#SEC861 327 Determinacy sing_2493.htm#IDX971 328 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_857.htm#SEC914 329 Distributed computing sing_932.htm#IDX476 330 Dlocalization sing_762.htm#SEC814 348 331 Documentation Tool sing_60.htm#SEC97 349 Dp, global ordering sing_83 8.htm#IDX390350 Ds, local ordering sing_8 39.htm#IDX400351 DsingularLocus sing_76 5.htm#SEC817332 Dp, global ordering sing_839.htm#IDX392 333 Ds, local ordering sing_840.htm#IDX402 334 DsingularLocus sing_766.htm#SEC818 352 335 Dynamic loading sing_71.htm#SEC111 353 Dynamic modules sing_79 6.htm#SEC848336 Dynamic modules sing_797.htm#SEC849 354 337 ECPP sing_1899.htm#SEC1975 355 338 ECoef sing_1380.htm#SEC1456 … … 358 341 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 359 342 Edatalist sing_1377.htm#SEC1453 360 Edelman-Reiner sing_2186.htm#IDX8 69343 Edelman-Reiner sing_2186.htm#IDX853 361 344 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 362 345 Editing input sing_18.htm#SEC25 363 Elimination sing_80 4.htm#SEC856346 Elimination sing_805.htm#SEC857 364 347 Emacs Emacs user interface sing_21.htm#SEC28 365 348 Emacs, Singular demo mode sing_24.htm#SEC35 … … 374 357 Equal sing_1336.htm#SEC1412 375 358 Eresol sing_1372.htm#SEC1448 376 Evaluation of logical expressions Evaluation of logical expressions sing_40 2.htm#SEC442377 Examples sing_78 6.htm#SEC838359 Evaluation of logical expressions Evaluation of logical expressions sing_403.htm#SEC443 360 Examples sing_787.htm#SEC839 378 361 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 379 Exp for matrices sing_1354.htm#IDX5 95362 Exp for matrices sing_1354.htm#IDX579 380 363 Experimental libraries Experimental libraries sing_2230.htm#SEC2306 381 364 Ext sing_1150.htm#SEC1226 382 Ext, computation of sing_80 7.htm#SEC859365 Ext, computation of sing_808.htm#SEC860 383 366 Ext_R sing_1149.htm#SEC1225 384 Exterior sing_71 2.htm#SEC764385 Extra weight vector sing_84 3.htm#SEC895386 Factorization sing_8 09.htm#SEC861387 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_91 8.htm#SEC994388 Feynman graph sing_1126.htm#IDX5 28389 Finite fields sing_80 3.htm#SEC855367 Exterior sing_713.htm#SEC765 368 Extra weight vector sing_844.htm#SEC896 369 Factorization sing_810.htm#SEC862 370 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_919.htm#SEC995 371 Feynman graph sing_1126.htm#IDX512 372 Finite fields sing_804.htm#SEC856 390 373 First steps sing_6.htm#SEC12 391 Fitzgerald-Lax method Fitzgerald-Lax method sing_86 6.htm#SEC934374 Fitzgerald-Lax method Fitzgerald-Lax method sing_867.htm#SEC935 392 375 Flow control sing_40.htm#SEC70 393 376 Formal Checker sing_59.htm#SEC96 394 Formatting output sing_79 3.htm#SEC845395 Free resolution sing_80 5.htm#SEC857396 Free resolution, graded Handling graded modules sing_80 6.htm#SEC858377 Formatting output sing_794.htm#SEC846 378 Free resolution sing_806.htm#SEC858 379 Free resolution, graded Handling graded modules sing_807.htm#SEC859 397 380 Functions sing_202.htm#SEC242 398 Future benefits of Singular 4 Notes for Singular users sing_250 0.htm#SEC2589399 G-algebra sing_47 8.htm#SEC518400 G-algebra sing_47 8.htm#SEC520401 G-algebra, setup sing_47 8.htm#SEC522402 GBWeight sing_56 1.htm#SEC613381 Future benefits of Singular 4 Notes for Singular users sing_2501.htm#SEC2590 382 G-algebra sing_479.htm#SEC519 383 G-algebra sing_479.htm#SEC521 384 G-algebra, setup sing_479.htm#SEC523 385 GBWeight sing_562.htm#SEC614 403 386 GBsolve sing_1689.htm#SEC1765 404 GIT sing_237 3.htm#IDX962405 GKZsystem sing_67 8.htm#SEC730406 GKdim sing_65 1.htm#SEC703387 GIT sing_2372.htm#IDX947 388 GKZsystem sing_679.htm#SEC731 389 GKdim sing_652.htm#SEC704 407 390 GMP sing_1.htm#IDX3 408 GND.lib sing_23 80.htm#SEC2456409 GND_lib sing_23 80.htm#SEC2456391 GND.lib sing_2379.htm#SEC2455 392 GND_lib sing_2379.htm#SEC2455 410 393 GTZmod sing_1198.htm#SEC1274 411 394 GTZopt sing_1205.htm#SEC1281 412 G_a -Invariants sing_82 5.htm#SEC877395 G_a -Invariants sing_826.htm#SEC878 413 396 Gamma sing_1387.htm#SEC1463 414 Gauss-Manin connection Gauss-Manin connection sing_8 49.htm#SEC906415 Gauss-Manin connection sing_1567.htm#IDX7 66416 Gauss-Manin connection sing_1614.htm#IDX7 69417 Gauss-Manin system sing_1515.htm#IDX6 56418 Gauss-Manin system sing_1516.htm#IDX6 67419 Gauss-Manin system sing_1517.htm#IDX6 70420 Gauss-Manin system sing_1518.htm#IDX6 73421 Gauss-Manin system sing_1519.htm#IDX6 76422 Gauss-Manin system sing_1520.htm#IDX6 80423 Gauss-Manin system sing_1521.htm#IDX6 84424 Gauss-Manin system sing_1522.htm#IDX6 90425 Gauss-Manin system sing_1523.htm#IDX6 98426 Gauss-Manin system sing_1524.htm#IDX 704427 Gauss-Manin system sing_1525.htm#IDX 712428 Gauss-Manin system sing_1526.htm#IDX7 22429 Gauss-Manin system sing_1537.htm#IDX7 28430 Gauss-Manin system sing_1539.htm#IDX7 39397 Gauss-Manin connection Gauss-Manin connection sing_850.htm#SEC907 398 Gauss-Manin connection sing_1567.htm#IDX750 399 Gauss-Manin connection sing_1614.htm#IDX753 400 Gauss-Manin system sing_1515.htm#IDX640 401 Gauss-Manin system sing_1516.htm#IDX651 402 Gauss-Manin system sing_1517.htm#IDX654 403 Gauss-Manin system sing_1518.htm#IDX657 404 Gauss-Manin system sing_1519.htm#IDX660 405 Gauss-Manin system sing_1520.htm#IDX664 406 Gauss-Manin system sing_1521.htm#IDX668 407 Gauss-Manin system sing_1522.htm#IDX674 408 Gauss-Manin system sing_1523.htm#IDX682 409 Gauss-Manin system sing_1524.htm#IDX688 410 Gauss-Manin system sing_1525.htm#IDX696 411 Gauss-Manin system sing_1526.htm#IDX706 412 Gauss-Manin system sing_1537.htm#IDX712 413 Gauss-Manin system sing_1539.htm#IDX723 431 414 General command syntax General command syntax sing_35.htm#SEC59 432 415 General concepts sing_12.htm#SEC18 433 General purpose sing_87 4.htm#SEC950416 General purpose sing_875.htm#SEC951 434 417 General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41 435 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_48 0.htm#SEC530436 Generalized Newton identities Generalized Newton identities sing_86 5.htm#SEC931437 Geometric genus sing_1358.htm#IDX 607438 German Umlaute sing_39 8.htm#IDX279418 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_481.htm#SEC531 419 Generalized Newton identities Generalized Newton identities sing_866.htm#SEC932 420 Geometric genus sing_1358.htm#IDX591 421 German Umlaute sing_399.htm#IDX281 439 422 Getting started sing_5.htm#SEC11 440 Global orderings sing_83 8.htm#SEC890441 Graded commutative algebras Graded commutative algebras (SCA) sing_48 2.htm#SEC534423 Global orderings sing_839.htm#SEC891 424 Graded commutative algebras Graded commutative algebras (SCA) sing_483.htm#SEC535 442 425 Greuel, Gert-Martin sing_1.htm#IDX18 443 Groebner Bases Computing Groebner and Standard Bases sing_79 7.htm#SEC849444 Groebner bases in G-algebras Groebner bases in G-algebras sing_4 79.htm#SEC523445 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_48 5.htm#SEC537446 Groebner bases, decodeGB sing_1790.htm#IDX7 90447 Groebner bases, slim sing_80 0.htm#SEC852448 Groebner basis conversion Groebner basis conversion sing_ 799.htm#SEC851449 Groebner cover sing_90 2.htm#IDX419450 Groebner cover sing_9 09.htm#IDX436451 Groebner cover sing_91 0.htm#IDX443452 Groebner fan sing_2053.htm#IDX 807453 Groebner walk sing_1141.htm#IDX5 49454 Groebner walk sing_1143.htm#IDX5 51455 Groebner walk sing_248 2.htm#IDX977456 Groebner walk sing_248 3.htm#IDX978457 Groebnerwalk sing_1137.htm#IDX5 45458 Groebnerwalk sing_241 9.htm#IDX971459 Groebnerwalk sing_248 1.htm#IDX976460 Groebnerwalk sing_248 5.htm#IDX981461 Gromov-Witten invariants sing_1126.htm#IDX5 25462 Gromov-Witten invariants sing_1132.htm#IDX5 34463 Gromov-Witten invariants sing_1133.htm#IDX5 38464 Gweights sing_70 6.htm#SEC758426 Groebner Bases Computing Groebner and Standard Bases sing_798.htm#SEC850 427 Groebner bases in G-algebras Groebner bases in G-algebras sing_480.htm#SEC524 428 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_486.htm#SEC538 429 Groebner bases, decodeGB sing_1790.htm#IDX774 430 Groebner bases, slim sing_801.htm#SEC853 431 Groebner basis conversion Groebner basis conversion sing_800.htm#SEC852 432 Groebner cover sing_903.htm#IDX420 433 Groebner cover sing_910.htm#IDX433 434 Groebner cover sing_911.htm#IDX439 435 Groebner fan sing_2053.htm#IDX791 436 Groebner walk sing_1141.htm#IDX533 437 Groebner walk sing_1143.htm#IDX535 438 Groebner walk sing_2483.htm#IDX962 439 Groebner walk sing_2484.htm#IDX963 440 Groebnerwalk sing_1137.htm#IDX529 441 Groebnerwalk sing_2418.htm#IDX956 442 Groebnerwalk sing_2482.htm#IDX961 443 Groebnerwalk sing_2486.htm#IDX966 444 Gromov-Witten invariants sing_1126.htm#IDX509 445 Gromov-Witten invariants sing_1132.htm#IDX518 446 Gromov-Witten invariants sing_1133.htm#IDX522 447 Gweights sing_707.htm#SEC759 465 448 H2basis sing_1572.htm#SEC1648 466 HHnormalForm sing_230 2.htm#SEC2378467 Hamburger-Noether expansion sing_1452.htm#IDX6 26468 Hamburger-Noether expansion sing_1540.htm#IDX7 48469 Hamburger-Noether expansions sing_1777.htm#IDX7 80470 Handling graded modules Handling graded modules sing_80 6.htm#SEC858449 HHnormalForm sing_2301.htm#SEC2377 450 Hamburger-Noether expansion sing_1452.htm#IDX610 451 Hamburger-Noether expansion sing_1540.htm#IDX732 452 Hamburger-Noether expansions sing_1777.htm#IDX764 453 Handling graded modules Handling graded modules sing_807.htm#SEC859 471 454 Hcode sing_1474.htm#SEC1550 472 455 Help string sing_45.htm#SEC82 473 456 Hensel sing_235.htm#SEC275 474 Hilbert function sing_34 7.htm#IDX188475 Hilbert function sing_84 6.htm#SEC900476 Hilbert series sing_84 6.htm#SEC900477 Hilbert-driven GB algorithm Groebner basis conversion sing_ 799.htm#SEC851457 Hilbert function sing_348.htm#IDX188 458 Hilbert function sing_847.htm#SEC901 459 Hilbert series sing_847.htm#SEC901 460 Hilbert-driven GB algorithm Groebner basis conversion sing_800.htm#SEC852 478 461 HilbertClassPoly sing_1862.htm#SEC1938 479 462 HilbertSeries sing_1667.htm#SEC1743 … … 481 464 Hom sing_1153.htm#SEC1229 482 465 HomJJ sing_1228.htm#SEC1304 483 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_85 5.htm#SEC912466 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_856.htm#SEC913 484 467 How to enter and exit How to enter and exit sing_14.htm#SEC20 485 468 How to use this manual How to use this manual sing_4.htm#SEC6 486 Hurwitz numbers sing_1132.htm#IDX5 37487 Hurwitz numbers sing_1133.htm#IDX5 41488 Hypersurface singularities, classification of Classification of hypersurface singularities sing_82 2.htm#SEC874469 Hurwitz numbers sing_1132.htm#IDX521 470 Hurwitz numbers sing_1133.htm#IDX525 471 Hypersurface singularities, classification of Classification of hypersurface singularities sing_823.htm#SEC875 489 472 IN sing_272.htm#IDX149 490 Ideal membership sing_84 5.htm#IDX412473 Ideal membership sing_846.htm#IDX414 491 474 Identifiers, syntax of sing_37.htm#SEC65 492 475 ImageGroup sing_1670.htm#SEC1746 … … 495 478 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 496 479 Incl sing_1335.htm#SEC1411 497 Index sing_250 8.htm#SEC2597480 Index sing_2509.htm#SEC2598 498 481 Info string sing_52.htm#SEC89 499 482 InterDiv sing_1403.htm#SEC1479 500 483 Interactive use sing_13.htm#SEC19 501 484 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 502 IntersectWithSub sing_68 3.htm#SEC735485 IntersectWithSub sing_684.htm#SEC736 503 486 IntersectionMatrix sing_1501.htm#SEC1577 504 487 Introduction sing_2.htm#SEC4 505 Invariant Theory sing_82 4.htm#SEC876488 Invariant Theory sing_825.htm#SEC877 506 489 Invariant theory sing_1619.htm#SEC1695 507 490 InvariantQ sing_1672.htm#SEC1748 508 491 InvariantRing sing_1671.htm#SEC1747 509 Invariants of a finite group Invariants of a finite group sing_82 6.htm#SEC878510 Invariants of plane curve singularities Invariants of plane curve singularities sing_82 0.htm#SEC872511 IsSCA sing_72 7.htm#SEC779512 J-marked schemes sing_1443.htm#IDX6 24513 J-marked schemes, Borel ideals sing_1448.htm#IDX6 25492 Invariants of a finite group Invariants of a finite group sing_827.htm#SEC879 493 Invariants of plane curve singularities Invariants of plane curve singularities sing_821.htm#SEC873 494 IsSCA sing_728.htm#SEC780 495 J-marked schemes sing_1443.htm#IDX608 496 J-marked schemes, Borel ideals sing_1448.htm#IDX609 514 497 JMBTest.lib sing_1443.htm#SEC1519 515 498 JMBTest_lib sing_1443.htm#SEC1519 … … 518 501 JMarkedScheme sing_1450.htm#SEC1526 519 502 Jacobi sing_1872.htm#SEC1948 520 Jacobson form sing_1827.htm#IDX7 91521 Jacobson normal form sing_1827.htm#IDX7 92503 Jacobson form sing_1827.htm#IDX775 504 Jacobson normal form sing_1827.htm#IDX776 522 505 JuReTopDim sing_1345.htm#SEC1421 523 506 JuReZeroDim sing_1346.htm#SEC1422 … … 527 510 KSlinear sing_1564.htm#SEC1640 528 511 KSpencerKernel sing_1612.htm#SEC1688 529 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_239 9.htm#SEC2475530 Kernel of module homomorphisms Kernel of module homomorphisms sing_81 2.htm#SEC864512 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2398.htm#SEC2474 513 Kernel of module homomorphisms Kernel of module homomorphisms sing_813.htm#SEC865 531 514 KoszulHomology sing_1162.htm#SEC1238 532 LETTERPLACE sing_48 3.htm#SEC535515 LETTERPLACE sing_484.htm#SEC536 533 516 LIB sing_276.htm#SEC316 534 517 LIB commands sing_53.htm#SEC90 535 LIBs sing_87 0.htm#SEC946536 LLL sing_3 49.htm#IDX219537 LOT algorithm sing_53 2.htm#IDX334518 LIBs sing_871.htm#SEC947 519 LLL sing_350.htm#IDX219 520 LOT algorithm sing_533.htm#IDX336 538 521 LU-decomposition of a matrix of numbers sing_281.htm#SEC321 539 Laurent series sing_1130.htm#IDX5 33540 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_82 8.htm#SEC880541 Left ideal membership Groebner bases in G-algebras sing_4 79.htm#SEC526542 Left normal form Groebner bases in G-algebras sing_4 79.htm#SEC525543 LengthSym sing_73 7.htm#SEC789544 LengthSymElement sing_73 6.htm#SEC788545 Letterplace sing_48 3.htm#SEC535546 Lexicographic Groebner bases, computation of Groebner basis conversion sing_ 799.htm#SEC851522 Laurent series sing_1130.htm#IDX517 523 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_829.htm#SEC881 524 Left ideal membership Groebner bases in G-algebras sing_480.htm#SEC527 525 Left normal form Groebner bases in G-algebras sing_480.htm#SEC526 526 LengthSym sing_738.htm#SEC790 527 LengthSymElement sing_737.htm#SEC789 528 Letterplace sing_484.htm#SEC536 529 Lexicographic Groebner bases, computation of Groebner basis conversion sing_800.htm#SEC852 547 530 Libraries Writing procedures and libraries sing_48.htm#SEC85 548 Libraries sing_7 89.htm#SEC841531 Libraries sing_790.htm#SEC842 549 532 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 550 Library versioning Notes for Singular users sing_250 0.htm#SEC2587551 Lie algebra sing_1353.htm#IDX5 92552 Lie group sing_1356.htm#IDX5 97553 Lie group sing_1357.htm#IDX 600554 Limitations sing_39 8.htm#SEC438533 Library versioning Notes for Singular users sing_2501.htm#SEC2588 534 Lie algebra sing_1353.htm#IDX576 535 Lie group sing_1356.htm#IDX581 536 Lie group sing_1357.htm#IDX584 537 Limitations sing_399.htm#SEC439 555 538 Linear algebra sing_1030.htm#SEC1106 556 Linear code sing_1790.htm#IDX7 87539 Linear code sing_1790.htm#IDX771 557 540 LinearActionQ sing_1674.htm#SEC1750 558 541 LinearCombinationQ sing_1675.htm#SEC1751 559 542 LinearizeAction sing_1673.htm#SEC1749 560 543 Loading a library sing_62.htm#SEC99 561 Local orderings sing_8 39.htm#SEC891562 Log for matrices sing_1355.htm#IDX5 96563 Long coefficients sing_79 1.htm#SEC843564 M, ordering sing_84 1.htm#SEC893565 MVComplex sing_249 5.htm#SEC2571566 Macintosh installation Macintosh installation instructions sing_250 7.htm#SEC2596567 Mathematical background Mathematical background sing_84 4.htm#SEC896568 Mathematical background (plural) Mathematical background (plural) sing_47 7.htm#SEC517569 Matrix orderings sing_84 1.htm#SEC893544 Local orderings sing_840.htm#SEC892 545 Log for matrices sing_1355.htm#IDX580 546 Long coefficients sing_792.htm#SEC844 547 M, ordering sing_842.htm#SEC894 548 MVComplex sing_2496.htm#SEC2572 549 Macintosh installation Macintosh installation instructions sing_2508.htm#SEC2597 550 Mathematical background Mathematical background sing_845.htm#SEC897 551 Mathematical background (plural) Mathematical background (plural) sing_478.htm#SEC518 552 Matrix orderings sing_842.htm#SEC894 570 553 Max sing_1581.htm#SEC1657 571 554 Maximus sing_1445.htm#SEC1521 572 555 Maxord sing_1386.htm#SEC1462 573 556 MillerRabin sing_1882.htm#SEC1958 574 Milnor number Milnor and Tjurina number sing_81 5.htm#SEC867575 Milnor number sing_249 1.htm#IDX985557 Milnor number Milnor and Tjurina number sing_816.htm#SEC868 558 Milnor number sing_2492.htm#IDX970 576 559 Min sing_1582.htm#SEC1658 577 560 MinMult sing_2292.htm#SEC2368 578 561 MinimalDecomposition MinimalDecomposition sing_1676.htm#SEC1752 579 Minimum distance sing_1790.htm#IDX7 89562 Minimum distance sing_1790.htm#IDX773 580 563 Minimus sing_1444.htm#SEC1520 581 564 Miscellaneous libraries Miscellaneous libraries sing_2157.htm#SEC2233 582 565 ModEqn sing_1575.htm#SEC1651 583 Modular techniques sing_93 1.htm#IDX488584 Module orderings sing_84 0.htm#SEC892566 Modular techniques sing_932.htm#IDX473 567 Module orderings sing_841.htm#SEC893 585 568 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 586 Monodromy sing_1567.htm#IDX7 64587 Monomial orderings sing_83 5.htm#SEC887569 Monodromy sing_1567.htm#IDX748 570 Monomial orderings sing_836.htm#SEC888 588 571 Monomial orderings, Term orderings sing_31.htm#SEC44 589 Morse lemma sing_249 0.htm#IDX983572 Morse lemma sing_2491.htm#IDX968 590 573 MultiplicitySequence MultiplicitySequence sing_1499.htm#SEC1575 591 574 NF sing_326.htm#SEC366 592 NF sing_4 69.htm#SEC509575 NF sing_470.htm#SEC510 593 576 NFMora sing_1948.htm#SEC2024 594 577 NPos sing_1218.htm#SEC1294 … … 599 582 Names in procedures sing_46.htm#SEC83 600 583 Names, indexed sing_37.htm#SEC65 601 New libraries depending on Singular 4 Notes for Singular users sing_250 0.htm#SEC2585602 New orderings for modules Notes for Singular users sing_250 0.htm#SEC2588603 Newton non-degenerate sing_1554.htm#IDX7 62604 Newton polygon sing_1553.htm#IDX7 61605 Newton polygon sing_1554.htm#IDX7 63606 Newton polytope sing_2053.htm#IDX 806584 New libraries depending on Singular 4 Notes for Singular users sing_2501.htm#SEC2586 585 New orderings for modules Notes for Singular users sing_2501.htm#SEC2589 586 Newton non-degenerate sing_1554.htm#IDX746 587 Newton polygon sing_1553.htm#IDX745 588 Newton polygon sing_1554.htm#IDX747 589 Newton polytope sing_2053.htm#IDX790 607 590 NoetherPosition sing_1212.htm#SEC1288 608 Non-commutative LIBs Non-commutative libraries sing_4 89.htm#SEC541609 Non-commutative algebra Non-commutative algebra sing_82 7.htm#SEC879610 Non-commutative algebra sing_86 1.htm#SEC918611 Non-commutative libraries Non-commutative libraries sing_4 89.htm#SEC541612 Non-commutative subsystem Non-commutative subsystem sing_41 2.htm#SEC452591 Non-commutative LIBs Non-commutative libraries sing_490.htm#SEC542 592 Non-commutative algebra Non-commutative algebra sing_828.htm#SEC880 593 Non-commutative algebra sing_862.htm#SEC919 594 Non-commutative libraries Non-commutative libraries sing_490.htm#SEC542 595 Non-commutative subsystem Non-commutative subsystem sing_413.htm#SEC453 613 596 Nonhyp sing_1375.htm#SEC1451 614 Normal form sing_84 5.htm#IDX411615 Normalization sing_81 1.htm#SEC863616 Notes for Singular users Notes for Singular users sing_250 0.htm#SEC2582617 Notes for developers Notes for developers sing_250 1.htm#SEC2590597 Normal form sing_846.htm#IDX413 598 Normalization sing_812.htm#SEC864 599 Notes for Singular users Notes for Singular users sing_2501.htm#SEC2583 600 Notes for developers Notes for developers sing_2502.htm#SEC2591 618 601 NullCone sing_1677.htm#SEC1753 619 602 NumIrrDecom sing_1349.htm#SEC1425 620 603 NumLocalDim sing_1338.htm#SEC1414 621 604 NumPrimDecom sing_1351.htm#SEC1427 622 Oaku-Takayama algorithm sing_53 2.htm#IDX332605 Oaku-Takayama algorithm sing_533.htm#IDX334 623 606 Objects sing_38.htm#SEC66 624 Orlik-Solomon sing_2187.htm#IDX8 70625 Output, formatting of sing_79 3.htm#SEC845626 PBW sing_51 1.htm#IDX320627 PBW basis sing_47 8.htm#SEC519628 PBW_eqDeg sing_5 29.htm#SEC581629 PBW_maxDeg sing_53 0.htm#SEC582630 PBW_maxMonom sing_53 1.htm#SEC583607 Orlik-Solomon sing_2187.htm#IDX854 608 Output, formatting of sing_794.htm#SEC846 609 PBW sing_512.htm#IDX322 610 PBW basis sing_479.htm#SEC520 611 PBW_eqDeg sing_530.htm#SEC582 612 PBW_maxDeg sing_531.htm#SEC583 613 PBW_maxMonom sing_532.htm#SEC584 631 614 PEsolve sing_1687.htm#SEC1763 632 615 PH_ais sing_2209.htm#SEC2285 633 616 PH_nais sing_2210.htm#SEC2286 634 PLURAL sing_41 3.htm#SEC453635 PLURAL LIBs Non-commutative libraries sing_4 89.htm#SEC541636 ParToVar sing_236 3.htm#SEC2439637 Parallelization Parallelization with ssi links sing_79 5.htm#SEC847638 Parallelization sing_93 1.htm#IDX489617 PLURAL sing_414.htm#SEC454 618 PLURAL LIBs Non-commutative libraries sing_490.htm#SEC542 619 ParToVar sing_2362.htm#SEC2438 620 Parallelization Parallelization with ssi links sing_796.htm#SEC848 621 Parallelization sing_932.htm#IDX474 639 622 Parameter list sing_44.htm#SEC81 640 Parameters sing_79 2.htm#SEC844641 Parametrization sing_1358.htm#IDX 604642 Parametrization, image. sing_1368.htm#IDX6 16623 Parameters sing_793.htm#SEC845 624 Parametrization sing_1358.htm#IDX588 625 Parametrization, image. sing_1368.htm#IDX600 643 626 PartC sing_2287.htm#SEC2363 644 PartitionVar sing_23 60.htm#SEC2436645 Path names Notes for Singular users sing_250 0.htm#SEC2586627 PartitionVar sing_2359.htm#SEC2435 628 Path names Notes for Singular users sing_2501.htm#SEC2587 646 629 PerfectPowerTest sing_1845.htm#SEC1921 647 Perturbation walk sing_1142.htm#IDX5 50630 Perturbation walk sing_1142.htm#IDX534 648 631 Pfister, Gerhard sing_1.htm#IDX19 649 632 Pipe links sing_116.htm#SEC156 650 633 PocklingtonLehmer sing_1884.htm#SEC1960 651 Poincare polynomial sing_2199.htm#IDX8 94652 Polar curves sing_81 7.htm#SEC869634 Poincare polynomial sing_2199.htm#IDX878 635 Polar curves sing_818.htm#SEC870 653 636 PollardRho sing_1885.htm#SEC1961 654 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2212.htm#IDX 910655 PolyBoRi, Boolean Groebner Basis sing_2214.htm#IDX 911656 PolyBoRi, Boolean Groebner Basis sing_2215.htm#IDX 912657 PolyBoRi, Boolean Groebner Basis sing_2216.htm#IDX 913658 PolyBoRi, Boolean Groebner Basis sing_2217.htm#IDX 914659 PolyBoRi, Boolean Groebner Basis sing_2218.htm#IDX 915660 PolyBoRi, Boolean Groebner Basis sing_2219.htm#IDX9 16661 PolyBoRi, Boolean Groebner Basis sing_2220.htm#IDX9 17662 PolyBoRi, Boolean Groebner Basis sing_2221.htm#IDX9 18663 PolyBoRi, Boolean Groebner Basis sing_2222.htm#IDX9 19664 PolyBoRi, Boolean Groebner Basis sing_2223.htm#IDX9 20665 PolyBoRi, Boolean Groebner Basis sing_2224.htm#IDX9 21666 PolyBoRi, Boolean Groebner Basis sing_2225.htm#IDX9 22667 PolyBoRi, Boolean Groebner Basis sing_2226.htm#IDX9 23668 PolyBoRi, Boolean Groebner Basis sing_2228.htm#IDX9 25669 PolyBoRi, zero-supressed decision diagram sing_2227.htm#IDX9 24670 Polybori, Boolean Groebner Basis sing_2229.htm#IDX9 26671 Polynomial data sing_83 3.htm#SEC885672 Pottier algorithm sing_85 4.htm#SEC911637 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2212.htm#IDX894 638 PolyBoRi, Boolean Groebner Basis sing_2214.htm#IDX895 639 PolyBoRi, Boolean Groebner Basis sing_2215.htm#IDX896 640 PolyBoRi, Boolean Groebner Basis sing_2216.htm#IDX897 641 PolyBoRi, Boolean Groebner Basis sing_2217.htm#IDX898 642 PolyBoRi, Boolean Groebner Basis sing_2218.htm#IDX899 643 PolyBoRi, Boolean Groebner Basis sing_2219.htm#IDX900 644 PolyBoRi, Boolean Groebner Basis sing_2220.htm#IDX901 645 PolyBoRi, Boolean Groebner Basis sing_2221.htm#IDX902 646 PolyBoRi, Boolean Groebner Basis sing_2222.htm#IDX903 647 PolyBoRi, Boolean Groebner Basis sing_2223.htm#IDX904 648 PolyBoRi, Boolean Groebner Basis sing_2224.htm#IDX905 649 PolyBoRi, Boolean Groebner Basis sing_2225.htm#IDX906 650 PolyBoRi, Boolean Groebner Basis sing_2226.htm#IDX907 651 PolyBoRi, Boolean Groebner Basis sing_2228.htm#IDX909 652 PolyBoRi, zero-supressed decision diagram sing_2227.htm#IDX908 653 Polybori, Boolean Groebner Basis sing_2229.htm#IDX910 654 Polynomial data sing_834.htm#SEC886 655 Pottier algorithm sing_855.htm#SEC912 673 656 Preface sing_1.htm#SEC1 674 Prep sing_90 7.htm#SEC983675 Primary decomposition Primary decomposition sing_81 0.htm#SEC862657 Prep sing_908.htm#SEC984 658 Primary decomposition Primary decomposition sing_811.htm#SEC863 676 659 PrimdecA sing_1194.htm#SEC1270 677 660 PrimdecB sing_1195.htm#SEC1271 … … 680 663 Procedures sing_42.htm#SEC77 681 664 Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14 682 Procedures and libraries sing_7 89.htm#SEC841665 Procedures and libraries sing_790.htm#SEC842 683 666 Procedures in a library Procedures in a library sing_54.htm#SEC91 684 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 667 Product orderings sing_843.htm#SEC895 668 Programming sing_788.htm#SEC840 669 PtoCrep sing_909.htm#SEC985 670 Puiseux expansion sing_1452.htm#IDX611 671 Puiseux expansion sing_1540.htm#IDX733 672 Puiseux pairs Invariants of plane curve singularities sing_821.htm#SEC873 673 Puiseux pairs sing_1546.htm#IDX738 674 QQ sing_28.htm#SEC39 675 Qso3Casimir sing_678.htm#SEC730 692 676 Quotient sing_1729.htm#SEC1805 693 677 QuotientEquations sing_1576.htm#SEC1652 694 Rational curves sing_1358.htm#IDX 605678 Rational curves sing_1358.htm#IDX589 695 679 ReJunkUseHomo sing_1344.htm#SEC1420 696 680 ReesAlgebra sing_1311.htm#SEC1387 697 References sing_8 69.htm#SEC943698 References (plural) sing_48 1.htm#SEC531699 Release Notes sing_249 6.htm#SEC2572681 References sing_870.htm#SEC944 682 References (plural) sing_482.htm#SEC532 683 Release Notes sing_2497.htm#SEC2573 700 684 ResTree sing_1404.htm#SEC1480 701 685 Resolution sing_11.htm#SEC17 702 Resolution of singularities Resolution of singularities sing_82 3.htm#SEC875703 Resolution, free sing_80 5.htm#SEC857686 Resolution of singularities Resolution of singularities sing_824.htm#SEC876 687 Resolution, free sing_806.htm#SEC858 704 688 ReynoldsImage sing_1678.htm#SEC1754 705 689 ReynoldsOperator sing_1679.htm#SEC1755 706 690 RiemannRochBN sing_2232.htm#SEC2308 707 RiemannRochHess sing_241 8.htm#SEC2494708 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_8 29.htm#SEC881709 Ring-dependent options Notes for Singular users sing_250 0.htm#SEC2584691 RiemannRochHess sing_2417.htm#SEC2493 692 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_830.htm#SEC882 693 Ring-dependent options Notes for Singular users sing_2501.htm#SEC2585 710 694 Rings and orderings sing_28.htm#SEC39 711 695 Rings and standard bases Rings and standard bases sing_7.htm#SEC13 712 696 Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 713 SCA Graded commutative algebras (SCA) sing_48 2.htm#SEC534697 SCA Graded commutative algebras (SCA) sing_483.htm#SEC535 714 698 SDB breakpoint Source code debugger sing_66.htm#SEC106 715 699 SDB debugger Source code debugger sing_66.htm#SEC106 716 SDLoc sing_5 59.htm#SEC611717 SINGULAR libraries sing_87 0.htm#SEC946700 SDLoc sing_560.htm#SEC612 701 SINGULAR libraries sing_871.htm#SEC947 718 702 SINGULARHIST sing_18.htm#SEC25 719 703 SScontinue sing_1014.htm#SEC1090 720 704 SSres sing_1012.htm#SEC1088 721 705 SSsyz sing_1013.htm#SEC1089 722 SV-decoding algorithm sing_1785.htm#IDX7 83723 SV-decoding algorithm, preprocessing sing_1784.htm#IDX7 82724 Sannfs sing_53 5.htm#SEC587725 SannfsBFCT sing_54 4.htm#SEC596726 SannfsVar sing_59 1.htm#SEC643727 Sannfslog sing_53 6.htm#SEC588728 Saturation sing_80 2.htm#SEC854729 Saturation sing_1123.htm#IDX5 19706 SV-decoding algorithm sing_1785.htm#IDX767 707 SV-decoding algorithm, preprocessing sing_1784.htm#IDX766 708 Sannfs sing_536.htm#SEC588 709 SannfsBFCT sing_545.htm#SEC597 710 SannfsVar sing_592.htm#SEC644 711 Sannfslog sing_537.htm#SEC589 712 Saturation sing_803.htm#SEC855 713 Saturation sing_1123.htm#IDX503 730 714 Sch@"onemann, Hans sing_1.htm#IDX20 731 715 Schoof sing_1896.htm#SEC1972 732 Schreyer ordering sing_1007.htm#IDX 506733 Schreyer resolution sing_1007.htm#IDX 507716 Schreyer ordering sing_1007.htm#IDX490 717 Schreyer resolution sing_1007.htm#IDX491 734 718 SchurCh sing_2284.htm#SEC2360 735 719 SchurS sing_2283.htm#SEC2359 736 720 Scontinue sing_1011.htm#SEC1087 737 721 Semigroup sing_1492.htm#SEC1568 738 Setting up a G-algebra sing_47 8.htm#SEC522722 Setting up a G-algebra sing_479.htm#SEC523 739 723 ShanksMestre sing_1895.htm#SEC1971 740 724 SimplifyIdeal sing_1680.htm#SEC1756 741 Singular sing_3 49.htm#IDX251742 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_249 8.htm#SEC2580725 Singular sing_350.htm#IDX253 726 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2499.htm#SEC2581 743 727 Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36 744 728 Singular, demo mode sing_24.htm#SEC35 … … 747 731 Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 748 732 Singular2bertini sing_1342.htm#SEC1418 749 SingularLib sing_3 49.htm#IDX253733 SingularLib sing_350.htm#IDX255 750 734 Singularities sing_1451.htm#SEC1527 751 Singularity Theory sing_81 4.htm#SEC866752 Skeletons for parallelization sing_93 1.htm#IDX490753 Smith form sing_1827.htm#IDX7 93754 Smith normal form sing_1827.htm#IDX7 94735 Singularity Theory sing_815.htm#SEC867 736 Skeletons for parallelization sing_932.htm#IDX475 737 Smith form sing_1827.htm#IDX777 738 Smith normal form sing_1827.htm#IDX778 755 739 SolowayStrassen sing_1883.htm#SEC1959 756 Solving systems of polynomial equations Solving systems of polynomial equations sing_83 1.htm#SEC883740 Solving systems of polynomial equations Solving systems of polynomial equations sing_832.htm#SEC884 757 741 Source code debugger, invocation Command line options sing_19.htm#IDX33 758 Space curve singularities, branches of Branches of space curve singularities sing_82 1.htm#SEC873742 Space curve singularities, branches of Branches of space curve singularities sing_822.htm#SEC874 759 743 Special characters sing_36.htm#SEC64 760 Splitting lemma sing_249 0.htm#IDX984744 Splitting lemma sing_2491.htm#IDX969 761 745 Sres sing_1009.htm#SEC1085 762 746 Ssi file links sing_114.htm#SEC154 … … 767 751 StabEqnId sing_1578.htm#SEC1654 768 752 StabOrder sing_1579.htm#SEC1655 769 Standard Bases Computing Groebner and Standard Bases sing_79 7.htm#SEC849770 Standard bases sing_84 5.htm#SEC897753 Standard Bases Computing Groebner and Standard Bases sing_798.htm#SEC850 754 Standard bases sing_846.htm#SEC898 771 755 StartOrderingV sing_1446.htm#SEC1522 772 756 Startup sequence sing_20.htm#SEC27 773 757 StringF sing_1566.htm#SEC1642 774 SymGroup sing_73 5.htm#SEC787775 Symbolic-numerical solving Symbolic-numerical solving sing_83 1.htm#SEC883758 SymGroup sing_736.htm#SEC788 759 Symbolic-numerical solving Symbolic-numerical solving sing_832.htm#SEC884 776 760 Symbolic-numerical solving sing_1684.htm#SEC1760 777 761 System and Control theory System and Control theory sing_1809.htm#SEC1885 778 System dependent limitations System dependent limitations sing_ 399.htm#SEC439779 System variables sing_38 5.htm#SEC425780 Syzygies and resolutions Syzygies and resolutions sing_84 7.htm#SEC901781 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_48 0.htm#SEC527782 T1 sing_81 8.htm#SEC870783 T2 sing_81 8.htm#SEC870762 System dependent limitations System dependent limitations sing_400.htm#SEC440 763 System variables sing_386.htm#SEC426 764 Syzygies and resolutions Syzygies and resolutions sing_848.htm#SEC902 765 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_481.htm#SEC528 766 T1 sing_819.htm#SEC871 767 T2 sing_819.htm#SEC871 784 768 TRACE Tracing of procedures sing_65.htm#SEC102 785 TRACE sing_39 4.htm#SEC434769 TRACE sing_395.htm#SEC435 786 770 T_1 sing_1599.htm#SEC1675 787 771 T_12 sing_1601.htm#SEC1677 … … 789 773 Teaching sing_1841.htm#SEC1917 790 774 Template for writing a library sing_55.htm#SEC92 791 TestGRRes sing_239 8.htm#SEC2474775 TestGRRes sing_2397.htm#SEC2473 792 776 TestJMark sing_1447.htm#SEC1523 793 777 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 794 The Tran algorithm sing_1139.htm#IDX5 47795 The fractal walk algorithm sing_1138.htm#IDX5 46796 The fractal walk algorithm sing_248 4.htm#IDX979778 The Tran algorithm sing_1139.htm#IDX531 779 The fractal walk algorithm sing_1138.htm#IDX530 780 The fractal walk algorithm sing_2485.htm#IDX964 797 781 The online help system The online help system sing_16.htm#SEC22 798 782 Tjurina sing_1597.htm#SEC1673 799 Tjurina number Milnor and Tjurina number sing_81 5.htm#SEC867800 Tjurina number sing_1233.htm#IDX5 74783 Tjurina number Milnor and Tjurina number sing_816.htm#SEC868 784 Tjurina number sing_1233.htm#IDX558 801 785 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 802 786 Tor sing_1164.htm#SEC1240 803 Toric ideals and integer programming Toric ideals and integer programming sing_85 0.htm#SEC907804 Tricks and pitfalls sing_39 7.htm#SEC437787 Toric ideals and integer programming Toric ideals and integer programming sing_851.htm#SEC908 788 Tricks and pitfalls sing_398.htm#SEC438 805 789 Tropical Geometry sing_1993.htm#SEC2069 806 790 Type casting Type conversion and casting sing_39.htm#SEC69 … … 808 792 Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98 809 793 U_D_O sing_1079.htm#SEC1155 810 Unix installation Unix installation instructions sing_250 5.htm#SEC2594811 UpOneMatrix sing_72 4.htm#SEC776794 Unix installation Unix installation instructions sing_2506.htm#SEC2595 795 UpOneMatrix sing_725.htm#SEC777 812 796 UpperMonomials sing_1580.htm#SEC1656 813 797 UseBertini sing_1341.htm#SEC1417 814 798 User defined types sing_177.htm#SEC217 815 V-filtration sing_1515.htm#IDX6 59816 V-filtration 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Version schema for Singular sing_2500.htm#SEC2582 828 812 Version string sing_50.htm#SEC87 829 813 Visualization sing_1747.htm#SEC1823 830 WLemma sing_92 0.htm#SEC996831 WP, global ordering sing_83 8.htm#IDX394814 WLemma sing_921.htm#SEC997 815 WP, global ordering sing_839.htm#IDX396 832 816 WSemigroup sing_1497.htm#SEC1573 833 817 Weierstrass sing_1780.htm#SEC1856 834 Weierstrass semigroup sing_1776.htm#IDX7 77835 Weyl sing_7 09.htm#SEC761836 Weyl algebra sing_53 2.htm#IDX326837 Weyl algebra sing_58 8.htm#IDX351838 Weyl closure sing_76 0.htm#IDX379839 WeylClosure sing_76 2.htm#SEC814840 WeylClosure1 sing_76 3.htm#SEC815841 Wibmer's Lemma sing_92 0.htm#IDX485842 Windows installation Windows installation instructions sing_250 6.htm#SEC2595818 Weierstrass semigroup sing_1776.htm#IDX761 819 Weyl sing_710.htm#SEC762 820 Weyl algebra sing_533.htm#IDX328 821 Weyl algebra sing_589.htm#IDX353 822 Weyl closure sing_761.htm#IDX381 823 WeylClosure sing_763.htm#SEC815 824 WeylClosure1 sing_764.htm#SEC816 825 Wibmer's Lemma sing_921.htm#IDX471 826 Windows installation Windows installation instructions sing_2507.htm#SEC2596 843 827 WitSet sing_1348.htm#SEC1424 844 828 WitSupSet sing_1347.htm#SEC1423 845 Ws, local ordering sing_8 39.htm#IDX406829 Ws, local ordering sing_840.htm#IDX408 846 830 XLsolve sing_1690.htm#SEC1766 831 ZZ sing_28.htm#SEC39 832 ZZ/m sing_28.htm#SEC39 833 ZZ/p sing_28.htm#SEC39 847 834 ZZsolve sing_1691.htm#SEC1767 848 835 [ sing_36.htm#IDX83 … … 860 847 _ sing_36.htm#IDX116 861 848 ` sing_36.htm#IDX105 862 a, ordering sing_84 3.htm#SEC895849 a, ordering sing_844.htm#SEC896 863 850 absFactorize sing_1092.htm#SEC1168 864 851 absFactorizeBCG sing_1093.htm#SEC1169 865 852 absPrimdecGTZ sing_1291.htm#SEC1367 866 853 absPrimdecGTZE sing_1292.htm#SEC1368 867 absValue sing_88 2.htm#SEC958854 absValue sing_883.htm#SEC959 868 855 absfact.lib sing_1091.htm#SEC1167 869 856 absfact_lib sing_1091.htm#SEC1167 870 absolute factorization. sing_1091.htm#IDX5 18857 absolute factorization. sing_1091.htm#IDX502 871 858 abstractR sing_1430.htm#SEC1506 872 859 actionIsProper sing_1660.htm#SEC1736 873 860 addNvarsTo sing_1006.htm#SEC1082 874 addRat sing_78 1.htm#SEC833861 addRat sing_782.htm#SEC834 875 862 addcol sing_1048.htm#SEC1124 876 addcores sing_97 4.htm#SEC1050863 addcores sing_975.htm#SEC1051 877 864 addrow sing_1049.htm#SEC1125 878 865 addvarsTo sing_1005.htm#SEC1081 879 ademRelations sing_64 1.htm#SEC693866 ademRelations sing_642.htm#SEC694 880 867 adjoint sing_1073.htm#SEC1149 881 868 adjointIdeal sing_1359.htm#SEC1435 882 adjunction divisor sing_1777.htm#IDX7 81883 admissibleSub sing_70 0.htm#SEC752884 afaces sing_237 4.htm#SEC2450885 affine code Fitzgerald-Lax method sing_86 6.htm#SEC935869 adjunction divisor sing_1777.htm#IDX765 870 admissibleSub sing_701.htm#SEC753 871 afaces sing_2373.htm#SEC2449 872 affine code Fitzgerald-Lax method sing_867.htm#SEC936 886 873 ainvar.lib sing_1657.htm#SEC1733 887 874 ainvar_lib sing_1657.htm#SEC1733 … … 896 883 algebra_containment sing_1095.htm#SEC1171 897 884 algebra_lib sing_1094.htm#SEC1170 898 algebraic dependence sing_73 0.htm#IDX357899 algebraic field extension sing_1305.htm#IDX5 81885 algebraic dependence sing_731.htm#IDX359 886 algebraic field extension sing_1305.htm#IDX565 900 887 algebraicDependence sing_1318.htm#SEC1394 901 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_85 7.htm#SEC914902 algorithm of Conti and Traverso sing_85 3.htm#SEC910903 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_85 6.htm#SEC913904 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_85 5.htm#SEC912905 algorithm of Pottier sing_85 4.htm#SEC911888 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_858.htm#SEC915 889 algorithm of Conti and Traverso sing_854.htm#SEC911 890 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_857.htm#SEC914 891 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_856.htm#SEC913 892 algorithm of Pottier sing_855.htm#SEC912 906 893 align sing_203.htm#SEC243 907 all.lib sing_87 5.htm#SEC951908 allDoubleExt sing_74 7.htm#SEC799909 allExtOfLeft sing_74 4.htm#SEC796910 allExtOfRight sing_74 5.htm#SEC797911 allPositive sing_50 8.htm#SEC560912 all_lib sing_87 5.htm#SEC951894 all.lib sing_876.htm#SEC952 895 allDoubleExt sing_748.htm#SEC800 896 allExtOfLeft sing_745.htm#SEC797 897 allExtOfRight sing_746.htm#SEC798 898 allPositive sing_509.htm#SEC561 899 all_lib sing_876.htm#SEC952 913 900 allowing net access Command line options sing_19.htm#IDX41 914 allprint sing_92 2.htm#SEC998901 allprint sing_923.htm#SEC999 915 902 allreal sing_1985.htm#SEC2061 916 903 allrealst sing_1983.htm#SEC2059 … … 918 905 ambientDimension sing_1998.htm#SEC2074 919 906 and Evaluation of logical expressions sing_96.htm#SEC136 920 and sing_40 2.htm#SEC442921 annPoly sing_55 6.htm#SEC608922 annRat sing_55 7.htm#SEC609923 annRatSyz sing_77 0.htm#SEC822924 annfs sing_53 3.htm#SEC585925 annfs0 sing_54 5.htm#SEC597926 annfs2 sing_54 6.htm#SEC598927 annfsBMI sing_54 2.htm#SEC594928 annfsParamBM sing_54 1.htm#SEC593929 annfsRB sing_54 7.htm#SEC599930 annfspecial sing_53 4.htm#SEC586931 annihilator of polynomial sing_55 5.htm#IDX336932 annihilator of rational function sing_55 5.htm#IDX337933 annihilator of rational function sing_76 0.htm#IDX382907 and sing_403.htm#SEC443 908 annPoly sing_557.htm#SEC609 909 annRat sing_558.htm#SEC610 910 annRatSyz sing_771.htm#SEC823 911 annfs sing_534.htm#SEC586 912 annfs0 sing_546.htm#SEC598 913 annfs2 sing_547.htm#SEC599 914 annfsBMI sing_543.htm#SEC595 915 annfsParamBM sing_542.htm#SEC594 916 annfsRB sing_548.htm#SEC600 917 annfspecial sing_535.htm#SEC587 918 annihilator of polynomial sing_556.htm#IDX338 919 annihilator of rational function sing_556.htm#IDX339 920 annihilator of rational function sing_761.htm#IDX384 934 921 annil sing_1200.htm#SEC1276 935 appelF1 sing_57 4.htm#SEC626936 appelF2 sing_57 5.htm#SEC627937 appelF4 sing_57 6.htm#SEC628938 appendWeight2Ord sing_70 2.htm#SEC754939 apply sing_3 69.htm#SEC409940 applyAdF sing_52 4.htm#SEC576922 appelF1 sing_575.htm#SEC627 923 appelF2 sing_576.htm#SEC628 924 appelF4 sing_577.htm#SEC629 925 appendWeight2Ord sing_703.htm#SEC755 926 apply sing_370.htm#SEC410 927 applyAdF sing_525.htm#SEC577 941 928 arcpoint.lib sing_1465.htm#SEC1541 942 929 arcpoint_lib sing_1465.htm#SEC1541 943 areZeroElements sing_24 60.htm#SEC2536930 areZeroElements sing_2459.htm#SEC2535 944 931 argument, default sing_44.htm#SEC81 945 932 argument, optional sing_44.htm#SEC81 … … 980 967 arrTypeD sing_2183.htm#SEC2259 981 968 arr_lib sing_2158.htm#SEC2234 982 arrange sing_5 49.htm#SEC601983 arrangement sing_2159.htm#IDX 812984 arrangement sing_2160.htm#IDX8 17985 arrangement sing_2191.htm#IDX8 79986 arrangement sing_2192.htm#IDX8 82969 arrange sing_550.htm#SEC602 970 arrangement sing_2159.htm#IDX796 971 arrangement sing_2160.htm#IDX801 972 arrangement sing_2191.htm#IDX863 973 arrangement sing_2192.htm#IDX866 987 974 ask sing_1850.htm#SEC1926 988 975 assPrimes sing_1109.htm#SEC1185 989 assign sing_2159.htm#IDX 814976 assign sing_2159.htm#IDX798 990 977 assignment,custom Assignments for user defined types sing_182.htm#SEC222 991 associated tangent FamElemsAtEnvCompPoints sing_91 7.htm#IDX475992 associated tangent sing_91 8.htm#IDX480978 associated tangent FamElemsAtEnvCompPoints sing_918.htm#IDX464 979 associated tangent sing_919.htm#IDX468 993 980 assprimeszerodim.lib assprimeszerodim_lib sing_1107.htm#SEC1183 994 981 assprimeszerodim_lib assprimeszerodim_lib sing_1107.htm#SEC1183 … … 1000 987 awalk1 sing_1140.htm#SEC1216 1001 988 awalk2 sing_1141.htm#SEC1217 1002 b-function sing_49 7.htm#IDX3091003 bFactor sing_5 79.htm#SEC631989 b-function sing_498.htm#IDX311 990 bFactor sing_580.htm#SEC632 1004 991 babyGiant sing_1880.htm#SEC1956 1005 backward sing_234 9.htm#SEC2425992 backward sing_2348.htm#SEC2424 1006 993 bareiss sing_205.htm#SEC245 1007 base2str sing_87 8.htm#SEC954994 base2str sing_879.htm#SEC955 1008 995 basering sing_28.htm#IDX76 1009 996 basering sing_83.htm#SEC123 … … 1011 998 belongSemigroup sing_1112.htm#SEC1188 1012 999 bernstein sing_1519.htm#SEC1595 1013 bernsteinBM sing_53 7.htm#SEC5891014 bernsteinLift sing_53 8.htm#SEC5901000 bernsteinBM sing_538.htm#SEC590 1001 bernsteinLift sing_539.htm#SEC591 1015 1002 bertini2Singular sing_1343.htm#SEC1419 1016 1003 betti sing_206.htm#SEC246 1017 betti (plural) sing_44 7.htm#SEC4871018 bfct sing_49 8.htm#SEC5501019 bfctAnn sing_50 0.htm#SEC5521020 bfctBound sing_7 69.htm#SEC8211021 bfctIdeal sing_50 2.htm#SEC5541022 bfctOneGB sing_50 1.htm#SEC5531023 bfctSyz sing_ 499.htm#SEC5511024 bfctVarAnn sing_59 0.htm#SEC6421025 bfctVarIn sing_5 89.htm#SEC6411026 bfun.lib sing_49 7.htm#SEC5491027 bfun_lib sing_49 7.htm#SEC5491004 betti (plural) sing_448.htm#SEC488 1005 bfct sing_499.htm#SEC551 1006 bfctAnn sing_501.htm#SEC553 1007 bfctBound sing_770.htm#SEC822 1008 bfctIdeal sing_503.htm#SEC555 1009 bfctOneGB sing_502.htm#SEC554 1010 bfctSyz sing_500.htm#SEC552 1011 bfctVarAnn sing_591.htm#SEC643 1012 bfctVarIn sing_590.htm#SEC642 1013 bfun.lib sing_498.htm#SEC550 1014 bfun_lib sing_498.htm#SEC550 1028 1015 bigint sing_73.htm#SEC113 1029 1016 bigint declarations sing_74.htm#SEC114 … … 1036 1023 bigintmat operations bigintmat operations sing_82.htm#SEC122 1037 1024 bigintmat type cast sing_81.htm#SEC121 1038 bimodules sing_49 0.htm#IDX2971039 bimodules.lib sing_49 0.htm#SEC5421040 bimodules_lib sing_49 0.htm#SEC5421025 bimodules sing_491.htm#IDX299 1026 bimodules.lib sing_491.htm#SEC543 1027 bimodules_lib sing_491.htm#SEC543 1041 1028 binary_add sing_1903.htm#SEC1979 1042 binomial sing_88 3.htm#SEC9591029 binomial sing_884.htm#SEC960 1043 1030 binomials2intmat sing_1266.htm#SEC1342 58804 1044 birational map, image, inverse. sing_1360.htm#IDX 6101045 bistd sing_49 1.htm#SEC5431046 bisyzygies sing_49 0.htm#IDX2981047 bitrinity sing_49 2.htm#SEC5441031 birational map, image, inverse. sing_1360.htm#IDX594 1032 bistd sing_492.htm#SEC544 1033 bisyzygies sing_491.htm#IDX300 1034 bitrinity sing_493.htm#SEC545 1048 1035 blackbox sing_186.htm#SEC226 1049 1036 blackbox sing_194.htm#SEC234 1050 1037 block sing_40.htm#SEC70 1051 block sing_36 8.htm#SEC4081038 block sing_369.htm#SEC409 1052 1039 blowUp sing_1411.htm#SEC1487 1053 1040 blowUp2 sing_1412.htm#SEC1488 1054 1041 blowUpBO sing_1418.htm#SEC1494 1055 1042 blowup0 sing_1117.htm#SEC1193 1056 boolean sing_2180.htm#IDX8 561043 boolean sing_2180.htm#IDX840 1057 1044 boolean expressions sing_95.htm#SEC135 1058 1045 boolean operations sing_96.htm#SEC136 … … 1067 1054 boundaryLatticePoints boundaryLatticePoints sing_2071.htm#SEC2147 1068 1055 boundposDes sing_1981.htm#SEC2057 1069 bracket sing_3 49.htm#IDX1961070 bracket sing_40 5.htm#SEC4451071 bracket sing_44 8.htm#SEC4881072 braid sing_2181.htm#IDX8 581056 bracket sing_350.htm#IDX196 1057 bracket sing_406.htm#SEC446 1058 bracket sing_449.htm#SEC489 1059 braid sing_2181.htm#IDX842 1073 1060 branchTo procs with different argument types sing_155.htm#SEC195 1074 break sing_37 0.htm#SEC4101075 break point sing_38 4.htm#SEC4241076 breakpoint sing_37 1.htm#SEC4111061 break sing_371.htm#SEC411 1062 break point sing_385.htm#SEC425 1063 breakpoint sing_372.htm#SEC412 1077 1064 brillnoether.lib sing_2231.htm#SEC2307 1078 1065 brillnoether_lib sing_2231.htm#SEC2307 … … 1080 1067 brnoeth_lib sing_1776.htm#SEC1852 1081 1068 browser, command line option Command line options sing_19.htm#IDX44 1082 browser, setting the sing_3 49.htm#IDX1921069 browser, setting the sing_350.htm#IDX192 1083 1070 browsers The online help system sing_16.htm#IDX21 1084 browsers, setting the sing_3 49.htm#IDX1911071 browsers, setting the sing_350.htm#IDX191 1085 1072 bubblesort sing_1853.htm#SEC1929 1086 1073 busadj sing_1071.htm#SEC1147 1087 1074 bvar sing_2226.htm#SEC2302 52773 1088 c, module ordering sing_84 0.htm#IDX4091075 c, module ordering sing_841.htm#IDX411 1089 1076 cProj sing_2273.htm#SEC2349 1090 1077 calculateI sing_1385.htm#SEC1461 … … 1093 1080 cancelunit, option sing_307.htm#IDX171 1094 1081 canonMap sing_1145.htm#SEC1221 1095 canonical sing_90 2.htm#IDX4211096 canonical form sing_91 1.htm#IDX4501097 canonical form sing_91 2.htm#IDX4531098 canonical, discussion of parametric ideal sing_91 0.htm#IDX4451082 canonical sing_903.htm#IDX422 1083 canonical form sing_912.htm#IDX445 1084 canonical form sing_913.htm#IDX447 1085 canonical, discussion of parametric ideal sing_911.htm#IDX441 1099 1086 canonicalizeCone sing_1999.htm#SEC2075 1100 1087 canonize sing_1822.htm#SEC1898 … … 1103 1090 cantorred sing_1937.htm#SEC2013 1104 1091 cardGroup sing_1114.htm#SEC1190 1105 case No case or switch statement sing_40 3.htm#SEC4431092 case No case or switch statement sing_404.htm#SEC444 1106 1093 cdd sing_1.htm#IDX10 1107 1094 cddlib sing_1.htm#IDX11 1108 center sing_51 1.htm#IDX3161109 center sing_51 7.htm#SEC5691110 center sing_2168.htm#IDX8 381111 center sing_2169.htm#IDX8 391112 center sing_2170.htm#IDX8 411113 center sing_2171.htm#IDX8 431114 centerRed sing_51 6.htm#SEC5681115 centerVS sing_51 5.htm#SEC5671116 central sing_2162.htm#IDX8 241117 central sing_2169.htm#IDX8 401118 central sing_2171.htm#IDX8 421119 central sing_2185.htm#IDX8 671120 central.lib sing_51 1.htm#SEC5631121 central1st sing_23 50.htm#SEC24261122 central2nd sing_235 1.htm#SEC24271123 central_lib sing_51 1.htm#SEC5631124 centralize sing_51 1.htm#IDX3191125 centralizeSet sing_51 2.htm#SEC5641126 centralizer sing_51 1.htm#IDX3171127 centralizer sing_51 8.htm#SEC5701128 centralizerRed sing_51 4.htm#SEC5661129 centralizerVS sing_51 3.htm#SEC5651095 center sing_512.htm#IDX318 1096 center sing_518.htm#SEC570 1097 center sing_2168.htm#IDX822 1098 center sing_2169.htm#IDX823 1099 center sing_2170.htm#IDX825 1100 center sing_2171.htm#IDX827 1101 centerRed sing_517.htm#SEC569 1102 centerVS sing_516.htm#SEC568 1103 central sing_2162.htm#IDX808 1104 central sing_2169.htm#IDX824 1105 central sing_2171.htm#IDX826 1106 central sing_2185.htm#IDX851 1107 central.lib sing_512.htm#SEC564 1108 central1st sing_2349.htm#SEC2425 1109 central2nd sing_2350.htm#SEC2426 1110 central_lib sing_512.htm#SEC564 1111 centralize sing_512.htm#IDX321 1112 centralizeSet sing_513.htm#SEC565 1113 centralizer sing_512.htm#IDX319 1114 centralizer sing_519.htm#SEC571 1115 centralizerRed sing_515.htm#SEC567 1116 centralizerVS sing_514.htm#SEC566 1130 1117 cf_class sing_204.htm#IDX132 1131 cgs sing_87 7.htm#SEC9531132 cgsdr sing_90 3.htm#SEC9791118 cgs sing_878.htm#SEC954 1119 cgsdr sing_904.htm#SEC980 1133 1120 chAll sing_2243.htm#SEC2319 1134 1121 chAllInv sing_2244.htm#SEC2320 … … 1154 1141 chWedge2LP sing_2266.htm#SEC2342 1155 1142 chaincrit sing_1950.htm#SEC2026 1156 chambers sing_2200.htm#IDX8 951157 chambers sing_2201.htm#IDX8 961143 chambers sing_2200.htm#IDX879 1144 chambers sing_2201.htm#IDX880 1158 1145 changeDenominator sing_1238.htm#SEC1314 1159 changechar sing_9 79.htm#SEC10551160 changeord sing_98 0.htm#SEC10561146 changechar sing_980.htm#SEC1056 1147 changeord sing_981.htm#SEC1057 1161 1148 changeordTo sing_1004.htm#SEC1080 1162 changes sing_249 7.htm#SEC25731163 changevar sing_98 1.htm#SEC10571149 changes sing_2498.htm#SEC2574 1150 changevar sing_982.htm#SEC1058 1164 1151 char sing_207.htm#SEC247 1165 charInfo sing_57 2.htm#SEC6241166 charVariety sing_57 1.htm#SEC6231152 charInfo sing_573.htm#SEC625 1153 charVariety sing_572.htm#SEC624 1167 1154 char_series sing_208.htm#SEC248 1168 characteristic exponents sing_1459.htm#IDX6 341169 characteristic exponents sing_1460.htm#IDX6 391170 characteristic exponents sing_1461.htm#IDX6 421171 characteristic exponents sing_1462.htm#IDX6 461172 characteristic exponents sing_1546.htm#IDX7 521173 characteristic polynomial sing_2198.htm#IDX8 931174 characteristic variety sing_55 5.htm#IDX3441175 characteristic variety sing_76 0.htm#IDX3781155 characteristic exponents sing_1459.htm#IDX618 1156 characteristic exponents sing_1460.htm#IDX623 1157 characteristic exponents sing_1461.htm#IDX626 1158 characteristic exponents sing_1462.htm#IDX630 1159 characteristic exponents sing_1546.htm#IDX736 1160 characteristic polynomial sing_2198.htm#IDX877 1161 characteristic variety sing_556.htm#IDX346 1162 characteristic variety sing_761.htm#IDX380 1176 1163 charexp2conductor sing_1462.htm#SEC1538 1177 1164 charexp2generators sing_1460.htm#SEC1536 … … 1181 1168 charpoly sing_1072.htm#SEC1148 1182 1169 charstr sing_209.htm#SEC249 1183 checkFactor sing_54 8.htm#SEC6001184 checkRoot sing_54 3.htm#SEC5951170 checkFactor sing_549.htm#SEC601 1171 checkRoot sing_544.htm#SEC596 1185 1172 chern sing_2238.htm#SEC2314 1186 1173 chern.lib sing_2233.htm#SEC2309 … … 1190 1177 chineseRem sing_1871.htm#SEC1947 1191 1178 chinrem sing_210.htm#SEC250 1192 chinrempoly sing_247 7.htm#SEC25531179 chinrempoly sing_2478.htm#SEC2554 1193 1180 chinrestp sing_1930.htm#SEC2006 1194 1181 cimonom.lib sing_2290.htm#SEC2366 … … 1199 1186 classify.lib sing_1470.htm#SEC1546 1200 1187 classifyCeq sing_1489.htm#SEC1565 1201 classifyMapGerms.lib classifyMapGerms_lib sing_230 3.htm#SEC23791202 classifyMapGerms_lib classifyMapGerms_lib sing_230 3.htm#SEC23791203 classifySimpleMaps sing_230 9.htm#SEC23851204 classifySimpleMaps1 sing_23 10.htm#SEC23861188 classifyMapGerms.lib classifyMapGerms_lib sing_2302.htm#SEC2378 1189 classifyMapGerms_lib classifyMapGerms_lib sing_2302.htm#SEC2378 1190 classifySimpleMaps sing_2308.htm#SEC2384 1191 classifySimpleMaps1 sing_2309.htm#SEC2385 1205 1192 classify_aeq.lib sing_2294.htm#SEC2370 1206 1193 classify_aeq_lib sing_2294.htm#SEC2370 1207 1194 classify_lib sing_1470.htm#SEC1546 1208 classifyceq.lib sing_1488.htm#IDX6 491209 classifyceq_lib sing_1488.htm#IDX6 501210 classifyci.lib sing_1490.htm#IDX6 511211 classifyci_lib sing_1490.htm#IDX6 521195 classifyceq.lib sing_1488.htm#IDX633 1196 classifyceq_lib sing_1488.htm#IDX634 1197 classifyci.lib sing_1490.htm#IDX635 1198 classifyci_lib sing_1490.htm#IDX636 1212 1199 classifyicis sing_1491.htm#SEC1567 1213 1200 classpoly sing_2278.htm#SEC2354 … … 1219 1206 closetex sing_1753.htm#SEC1829 1220 1207 closureFrac sing_1231.htm#SEC1307 1221 coDim sing_230 5.htm#SEC23811222 coDimMap sing_230 4.htm#SEC23801223 coHom sing_75 3.htm#SEC8051208 coDim sing_2304.htm#SEC2380 1209 coDimMap sing_2303.htm#SEC2379 1210 coHom sing_754.htm#SEC806 1224 1211 codim sing_1584.htm#SEC1660 1225 1212 codimension sing_2000.htm#SEC2076 1226 coding theory sing_83 2.htm#SEC8841213 coding theory sing_833.htm#SEC885 1227 1214 coef sing_213.htm#SEC253 1228 coefficient sing_2161.htm#IDX8 201229 coefficient sing_2162.htm#IDX8 231230 coefficient sing_2163.htm#IDX8 271215 coefficient sing_2161.htm#IDX804 1216 coefficient sing_2162.htm#IDX807 1217 coefficient sing_2163.htm#IDX811 1231 1218 coefficient field sing_139.htm#SEC179 1232 1219 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 1233 coefficients, long sing_79 1.htm#SEC8431220 coefficients, long sing_792.htm#SEC844 1234 1221 coeffmod sing_1848.htm#SEC1924 1235 1222 coeffs sing_214.htm#SEC254 1236 colength of derivations curveColengthDerivations sing_231 5.htm#IDX9381223 colength of derivations curveColengthDerivations sing_2314.htm#IDX923 1237 1224 collectDiv sing_1428.htm#SEC1504 1238 1225 colrank sing_1820.htm#SEC1896 1239 1226 colred sing_1055.htm#SEC1131 1240 commRing sing_78 4.htm#SEC8361241 comma sing_40 4.htm#SEC4441227 commRing sing_785.htm#SEC837 1228 comma sing_405.htm#SEC445 1242 1229 command,custom Commands for user defined types sing_181.htm#SEC221 1243 command-line option, setting value of sing_3 49.htm#IDX2751244 command-line option, value of sing_3 49.htm#IDX2731245 command-line options, print all values of sing_3 49.htm#IDX2721230 command-line option, setting value of sing_350.htm#IDX277 1231 command-line option, value of sing_350.htm#IDX275 1232 command-line options, print all values of sing_350.htm#IDX274 1246 1233 command-line options, short help Command line options sing_19.htm#IDX38 1247 commands (plural) sing_44 6.htm#IDX2961234 commands (plural) sing_447.htm#IDX298 1248 1235 comment sing_36.htm#IDX108 1249 1236 compareTasks sing_1019.htm#SEC1095 … … 1251 1238 complex sing_28.htm#IDX75 1252 1239 complexSingType sing_1486.htm#SEC1562 1253 compregb.lib sing_87 6.htm#SEC9521254 compregb_lib sing_87 6.htm#SEC9521255 comprehensive Groebner system sing_87 6.htm#IDX4151240 compregb.lib sing_877.htm#SEC953 1241 compregb_lib sing_877.htm#SEC953 1242 comprehensive Groebner system sing_877.htm#IDX417 1256 1243 compress sing_1032.htm#SEC1108 1257 1244 computeConstant sing_1130.htm#SEC1206 … … 1261 1248 computemcm sing_1390.htm#SEC1466 1262 1249 concat sing_1033.htm#SEC1109 1263 conductor sing_1239.htm#IDX5 751264 conductor sing_1462.htm#IDX6 451265 conductor sing_231 3.htm#IDX9321266 conductor, degree sing_1546.htm#IDX7 551250 conductor sing_1239.htm#IDX559 1251 conductor sing_1462.htm#IDX629 1252 conductor sing_2312.htm#IDX917 1253 conductor, degree sing_1546.htm#IDX739 1267 1254 cone sing_183.htm#SEC223 1268 cone sing_2174.htm#IDX8 471269 cone sing_2175.htm#IDX8 491255 cone sing_2174.htm#IDX831 1256 cone sing_2175.htm#IDX833 1270 1257 coneLink sing_2003.htm#SEC2079 1271 1258 coneViaInequalities sing_2002.htm#SEC2078 1272 1259 coneViaPoints sing_2001.htm#SEC2077 1273 conic, parametrization, rational point. sing_1367.htm#IDX 6151260 conic, parametrization, rational point. sing_1367.htm#IDX599 1274 1261 conicWithTangents sing_2125.htm#SEC2201 1275 1262 constructH sing_1391.htm#SEC1467 1276 1263 constructblwup sing_1392.htm#SEC1468 1277 constructible set sing_91 1.htm#IDX4481278 constructible sets sing_91 2.htm#IDX4521264 constructible set sing_912.htm#IDX443 1265 constructible sets sing_913.htm#IDX446 1279 1266 constructlastblwup sing_1393.htm#SEC1469 1280 constructor sing_2191.htm#IDX8 801281 constructor sing_2192.htm#IDX8 831282 contact matrix sing_1461.htm#IDX6 411267 constructor sing_2191.htm#IDX864 1268 constructor sing_2192.htm#IDX867 1269 contact matrix sing_1461.htm#IDX625 1283 1270 containedQ sing_1741.htm#SEC1817 1284 1271 containsAsFace sing_2004.htm#SEC2080 … … 1287 1274 containsPositiveVector containsPositiveVector sing_2006.htm#SEC2082 1288 1275 containsRelatively sing_2007.htm#SEC2083 1289 content sing_95 3.htm#SEC10291276 content sing_954.htm#SEC1030 1290 1277 contentSB, option sing_307.htm#IDX172 1291 continue Behavior of continue sing_37 2.htm#SEC4121292 continue sing_40 6.htm#SEC4461293 contraHom sing_75 4.htm#SEC8061278 continue Behavior of continue sing_373.htm#SEC413 1279 continue sing_407.htm#SEC447 1280 contraHom sing_755.htm#SEC807 1294 1281 contract sing_215.htm#SEC255 1295 contributors sing_3 49.htm#IDX1991282 contributors sing_350.htm#IDX199 1296 1283 control sing_1812.htm#SEC1888 1297 1284 control.lib sing_1811.htm#SEC1887 … … 1303 1290 convexHull sing_2008.htm#SEC2084 1304 1291 convexIntersection sing_2009.htm#SEC2085 1305 convloc sing_55 2.htm#SEC6041306 coordinate change sing_2171.htm#IDX8 441307 coordinate change sing_2172.htm#IDX8 451308 coordinate change sing_2173.htm#IDX8 461309 coordinates sing_1968.htm#IDX7 971292 convloc sing_553.htm#SEC605 1293 coordinate change sing_2171.htm#IDX828 1294 coordinate change sing_2172.htm#IDX829 1295 coordinate change sing_2173.htm#IDX830 1296 coordinates sing_1968.htm#IDX781 1310 1297 coords sing_1968.htm#SEC2044 1311 1298 copyTask sing_1018.htm#SEC1094 … … 1314 1301 cornerMonomials sing_1269.htm#SEC1345 1315 1302 countPoints sing_1893.htm#SEC1969 1316 coverings sing_1132.htm#IDX5 361317 coverings sing_1133.htm#IDX5 401318 cpu sing_3 49.htm#IDX2011319 cpu sing_3 49.htm#IDX2691303 coverings sing_1132.htm#IDX520 1304 coverings sing_1133.htm#IDX524 1305 cpu sing_350.htm#IDX201 1306 cpu sing_350.htm#IDX271 1320 1307 createBO sing_1419.htm#SEC1495 1321 createGradedRingHomomorphism createGradedRingHomomorphism sing_243 6.htm#SEC25121322 createGroup sing_242 9.htm#SEC25051323 createQuotientGroup sing_24 30.htm#SEC25061308 createGradedRingHomomorphism createGradedRingHomomorphism sing_2435.htm#SEC2511 1309 createGroup sing_2428.htm#SEC2504 1310 createQuotientGroup sing_2429.htm#SEC2505 1324 1311 createTask sing_1016.htm#SEC1092 1325 createTorsionFreeGroup createTorsionFreeGroup sing_243 1.htm#SEC25071312 createTorsionFreeGroup createTorsionFreeGroup sing_2430.htm#SEC2506 1326 1313 createlist sing_1401.htm#SEC1477 1327 1314 crypto.lib sing_1866.htm#SEC1942 … … 1329 1316 cup sing_1146.htm#SEC1222 1330 1317 cupproduct sing_1147.htm#SEC1223 1331 curve singularities sing_1452.htm#IDX6 281332 curve singularities sing_1540.htm#IDX7 501333 curve singularity sing_231 1.htm#IDX9271334 curveColengthDerivations curveColengthDerivations sing_231 5.htm#SEC23911335 curveConductorMult sing_231 3.htm#SEC23891336 curveDeligneNumber sing_231 4.htm#SEC23901337 curveDeltaInv sing_231 2.htm#SEC23881338 curveInv.lib sing_231 1.htm#SEC23871339 curveInv_lib sing_231 1.htm#SEC23871318 curve singularities sing_1452.htm#IDX612 1319 curve singularities sing_1540.htm#IDX734 1320 curve singularity sing_2310.htm#IDX912 1321 curveColengthDerivations curveColengthDerivations sing_2314.htm#SEC2390 1322 curveConductorMult sing_2312.htm#SEC2388 1323 curveDeligneNumber sing_2313.htm#SEC2389 1324 curveDeltaInv sing_2311.htm#SEC2387 1325 curveInv.lib sing_2310.htm#SEC2386 1326 curveInv_lib sing_2310.htm#SEC2386 1340 1327 curvepar.lib sing_1493.htm#SEC1569 1341 1328 curvepar_lib sing_1493.htm#SEC1569 … … 1347 1334 cycleLength sing_2062.htm#SEC2138 1348 1335 cyclePoints sing_2066.htm#SEC2142 1349 cyclic sing_94 0.htm#SEC10161350 cyclic code Codes and the decoding problem sing_86 3.htm#SEC9221336 cyclic sing_941.htm#SEC1017 1337 cyclic code Codes and the decoding problem sing_864.htm#SEC923 1351 1338 cyclotomic sing_1627.htm#SEC1703 1352 1339 datetime sing_216.htm#SEC256 1353 1340 dbprint sing_217.htm#SEC257 1354 deRham.lib sing_249 3.htm#SEC25691355 deRhamCohom sing_5 69.htm#SEC6211356 deRhamCohomIdeal sing_57 0.htm#SEC6221357 deRhamCohomology sing_249 4.htm#SEC25701358 deRham_lib sing_249 3.htm#SEC25691341 deRham.lib sing_2494.htm#SEC2570 1342 deRhamCohom sing_570.htm#SEC622 1343 deRhamCohomIdeal sing_571.htm#SEC623 1344 deRhamCohomology sing_2495.htm#SEC2571 1345 deRham_lib sing_2494.htm#SEC2570 1359 1346 debugLib, option sing_307.htm#IDX176 1360 1347 debug_log sing_1483.htm#SEC1559 … … 1370 1357 decodegb.lib sing_1790.htm#SEC1866 1371 1358 decodegb_lib sing_1790.htm#SEC1866 1372 decoding, decoding problem Codes and the decoding problem sing_86 3.htm#SEC9231359 decoding, decoding problem Codes and the decoding problem sing_864.htm#SEC924 1373 1360 decoef sing_1833.htm#SEC1909 1374 decone sing_2174.htm#IDX8 481375 decone sing_2175.htm#IDX8 501361 decone sing_2174.htm#IDX832 1362 decone sing_2175.htm#IDX834 1376 1363 def sing_83.htm#SEC123 1377 1364 def declarations sing_84.htm#SEC124 1378 1365 defRes, option sing_307.htm#IDX177 1379 1366 default argument sing_44.htm#SEC81 1380 defineHomogeneous sing_246 9.htm#SEC25451367 defineHomogeneous sing_2468.htm#SEC2544 1381 1368 defined sing_218.htm#SEC258 1382 1369 defl sing_1350.htm#SEC1426 … … 1384 1371 deform.lib sing_1504.htm#SEC1580 1385 1372 deform_lib sing_1504.htm#SEC1580 1386 defring sing_98 2.htm#SEC10581387 defringp sing_98 4.htm#SEC10601388 defrings sing_98 3.htm#SEC10591373 defring sing_983.htm#SEC1059 1374 defringp sing_985.htm#SEC1061 1375 defrings sing_984.htm#SEC1060 1389 1376 deg sing_219.htm#SEC259 1390 degBound sing_38 6.htm#SEC4261377 degBound sing_387.htm#SEC427 1391 1378 degree Miscellaneous oddities sing_220.htm#SEC260 1392 degree sing_4 09.htm#IDX2861393 degree lexicographical ordering sing_83 8.htm#IDX3891394 degree of a polynomial Miscellaneous oddities sing_4 09.htm#IDX2901395 degree reverse lexicographical ordering sing_83 8.htm#IDX3871396 degreeDivisor sing_232 4.htm#SEC24001397 degreeFormalDivisor sing_233 2.htm#SEC24081379 degree sing_410.htm#IDX288 1380 degree lexicographical ordering sing_839.htm#IDX391 1381 degree of a polynomial Miscellaneous oddities sing_410.htm#IDX292 1382 degree reverse lexicographical ordering sing_839.htm#IDX389 1383 degreeDivisor sing_2323.htm#SEC2399 1384 degreeFormalDivisor sing_2331.htm#SEC2407 1398 1385 degreepart sing_1693.htm#SEC1769 1399 1386 delete sing_121.htm#SEC161 1400 1387 delete sing_221.htm#SEC261 1401 1388 delete sing_268.htm#SEC308 1402 deleteGenerator sing_58 4.htm#SEC6361403 deleteSublist sing_88 4.htm#SEC9601404 deligne number curveColengthDerivations sing_231 1.htm#IDX9291405 deligne number sing_231 4.htm#IDX9341406 deligne number sing_231 5.htm#IDX9361389 deleteGenerator sing_585.htm#SEC637 1390 deleteSublist sing_885.htm#SEC961 1391 deligne number curveColengthDerivations sing_2310.htm#IDX914 1392 deligne number sing_2313.htm#IDX919 1393 deligne number sing_2314.htm#IDX921 1407 1394 delta sing_1552.htm#SEC1628 1408 delta invariant sing_1233.htm#IDX5 731409 delta invariant sing_1552.htm#IDX7 601410 delta invariant sing_231 2.htm#IDX9301411 delta invariant. sing_1225.htm#IDX5 661412 delta invariant. sing_1226.htm#IDX5 691413 delta invariant. sing_1227.htm#IDX5 721395 delta invariant sing_1233.htm#IDX557 1396 delta invariant sing_1552.htm#IDX744 1397 delta invariant sing_2311.htm#IDX915 1398 delta invariant. sing_1225.htm#IDX550 1399 delta invariant. sing_1226.htm#IDX553 1400 delta invariant. sing_1227.htm#IDX556 1414 1401 deltaLoc sing_1233.htm#SEC1309 1415 denom_list sing_3 49.htm#IDX2031402 denom_list sing_350.htm#IDX203 1416 1403 denominator sing_222.htm#SEC262 1417 1404 depth sing_1148.htm#SEC1224 1418 1405 depthIdeal sing_1209.htm#SEC1285 1419 1406 derivate sing_1659.htm#SEC1735 1420 derivation sing_2188.htm#IDX8 711421 desingularization sing_23 80.htm#IDX9651422 desingularization sing_238 1.htm#SEC24571407 derivation sing_2188.htm#IDX855 1408 desingularization sing_2379.htm#IDX950 1409 desingularization sing_2380.htm#SEC2456 1423 1410 det sing_223.htm#SEC263 1424 1411 det_B sing_1074.htm#SEC1150 1425 1412 detadj sing_1568.htm#SEC1644 1426 determinacy sing_249 2.htm#SEC25681413 determinacy sing_2493.htm#SEC2569 1427 1414 determinecenter sing_1373.htm#SEC1449 1428 1415 detropicalise sing_2143.htm#SEC2219 … … 1432 1419 diag_test sing_1070.htm#SEC1146 1433 1420 diff sing_224.htm#SEC264 1434 diffRat sing_78 3.htm#SEC8351421 diffRat sing_784.htm#SEC836 1435 1422 difpoly2tex sing_1834.htm#SEC1910 1436 1423 dim sing_225.htm#SEC265 1437 dim (plural) sing_4 49.htm#SEC4891424 dim (plural) sing_450.htm#SEC490 1438 1425 dimGradedPart sing_1441.htm#SEC1517 11262 1439 1426 dimH sing_1440.htm#SEC1516 38534 … … 1441 1428 dim_slocus sing_1586.htm#SEC1662 1442 1429 dimension sing_2010.htm#SEC2086 1443 dimensionOfLocalization dimensionOfLocalization sing_236 8.htm#SEC24441430 dimensionOfLocalization dimensionOfLocalization sing_2367.htm#SEC2443 1444 1431 direct_boolean_poly sing_2216.htm#SEC2292 49893 1445 1432 direct_from_boolean_poly direct_from_boolean_poly sing_2222.htm#SEC2298 36941 … … 1447 1434 discr sing_1608.htm#SEC1684 1448 1435 discrepancy sing_1426.htm#SEC1502 1449 discrim sing_9 19.htm#SEC9951450 discussion of parametric ideal sing_90 2.htm#IDX4221451 disjoint sing_90 3.htm#IDX4251436 discrim sing_920.htm#SEC996 1437 discussion of parametric ideal sing_903.htm#IDX423 1438 disjoint sing_904.htm#IDX425 1452 1439 disp_zdd sing_2229.htm#SEC2305 41439 1453 1440 displayCohom sing_1442.htm#SEC1518 22633 … … 1457 1444 displayPuiseuxExpansion displayPuiseuxExpansion sing_2118.htm#SEC2194 1458 1445 displayTropicalLifting displayTropicalLifting sing_2116.htm#SEC2192 1459 distributed computing sing_93 3.htm#IDX4941460 distributed computing sing_97 3.htm#IDX4961461 distributed computing sing_1015.htm#IDX 5101446 distributed computing sing_934.htm#IDX479 1447 distributed computing sing_974.htm#IDX481 1448 distributed computing sing_1015.htm#IDX494 1462 1449 div Miscellaneous oddities sing_76.htm#SEC116 1463 1450 div sing_93.htm#SEC133 1464 div sing_4 09.htm#IDX2831451 div sing_410.htm#IDX285 1465 1452 divideUnits sing_1830.htm#SEC1906 1466 1453 dividelist sing_1400.htm#SEC1476 1467 1454 division sing_226.htm#SEC266 1468 division sing_90 4.htm#IDX4291469 division sing_90 5.htm#IDX4321470 division (plural) sing_45 0.htm#SEC4901455 division sing_905.htm#IDX428 1456 division sing_906.htm#IDX430 1457 division (plural) sing_451.htm#SEC491 1471 1458 divisor sing_1933.htm#SEC2009 1472 divisorplus sing_231 8.htm#SEC23941473 divisors negativeformaldivisor sing_231 7.htm#IDX9391474 divisors sing_231 8.htm#IDX9401475 divisors sing_231 9.htm#IDX9411476 divisors sing_23 20.htm#IDX9421477 divisors sing_232 1.htm#IDX9431478 divisors sing_232 2.htm#IDX9441479 divisors sing_232 3.htm#IDX9451480 divisors sing_232 4.htm#IDX9461481 divisors sing_232 5.htm#IDX9471482 divisors sing_232 6.htm#IDX9481483 divisors sing_232 7.htm#IDX9491484 divisors sing_232 8.htm#IDX9501485 divisors sing_232 9.htm#IDX9511486 divisors sing_23 30.htm#IDX9521487 divisors sing_233 1.htm#IDX9531488 divisors sing_233 2.htm#IDX9541489 divisors, polyhedra sing_233 3.htm#IDX9551490 divisors, polyhedra sing_233 4.htm#IDX9561491 divisors, polyhedra sing_233 5.htm#IDX9571492 divisors.lib sing_231 6.htm#SEC23921493 divisors_lib sing_231 6.htm#SEC23921494 dmod.lib sing_53 2.htm#SEC5841495 dmodAction sing_77 8.htm#SEC8301496 dmodActionRat sing_7 79.htm#SEC8311497 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_77 1.htm#SEC8231498 dmod_lib sing_53 2.htm#SEC5841499 dmodapp.lib sing_55 5.htm#SEC6071500 dmodapp_lib sing_55 5.htm#SEC6071501 dmodloc.lib sing_76 0.htm#IDX3711502 dmodloc_lib sing_76 0.htm#IDX3721503 dmodoublext sing_75 5.htm#SEC8071504 dmodvar.lib sing_58 8.htm#SEC6401505 dmodvar_lib sing_58 8.htm#SEC6401459 divisorplus sing_2317.htm#SEC2393 1460 divisors negativeformaldivisor sing_2316.htm#IDX924 1461 divisors sing_2317.htm#IDX925 1462 divisors sing_2318.htm#IDX926 1463 divisors sing_2319.htm#IDX927 1464 divisors sing_2320.htm#IDX928 1465 divisors sing_2321.htm#IDX929 1466 divisors sing_2322.htm#IDX930 1467 divisors sing_2323.htm#IDX931 1468 divisors sing_2324.htm#IDX932 1469 divisors sing_2325.htm#IDX933 1470 divisors sing_2326.htm#IDX934 1471 divisors sing_2327.htm#IDX935 1472 divisors sing_2328.htm#IDX936 1473 divisors sing_2329.htm#IDX937 1474 divisors sing_2330.htm#IDX938 1475 divisors sing_2331.htm#IDX939 1476 divisors, polyhedra sing_2332.htm#IDX940 1477 divisors, polyhedra sing_2333.htm#IDX941 1478 divisors, polyhedra sing_2334.htm#IDX942 1479 divisors.lib sing_2315.htm#SEC2391 1480 divisors_lib sing_2315.htm#SEC2391 1481 dmod.lib sing_533.htm#SEC585 1482 dmodAction sing_779.htm#SEC831 1483 dmodActionRat sing_780.htm#SEC832 1484 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_772.htm#SEC824 1485 dmod_lib sing_533.htm#SEC585 1486 dmodapp.lib sing_556.htm#SEC608 1487 dmodapp_lib sing_556.htm#SEC608 1488 dmodloc.lib sing_761.htm#IDX373 1489 dmodloc_lib sing_761.htm#IDX374 1490 dmodoublext sing_756.htm#SEC808 1491 dmodvar.lib sing_589.htm#SEC641 1492 dmodvar_lib sing_589.htm#SEC641 1506 1493 double sing_1938.htm#SEC2014 1507 doubleExt sing_74 6.htm#SEC7981508 downloading Download instructions sing_250 4.htm#SEC25931509 dp, global ordering sing_83 8.htm#IDX3881494 doubleExt sing_747.htm#SEC799 1495 downloading Download instructions sing_2505.htm#SEC2594 1496 dp, global ordering sing_839.htm#IDX390 1510 1497 drawNewtonSubdivision drawNewtonSubdivision sing_2121.htm#SEC2197 1511 1498 drawTropicalCurve sing_2120.htm#SEC2196 1512 ds, local ordering sing_8 39.htm#IDX3981499 ds, local ordering sing_840.htm#IDX400 1513 1500 dsum sing_1035.htm#SEC1111 1514 1501 dualCone sing_2011.htm#SEC2087 … … 1518 1505 dual_code sing_1787.htm#SEC1863 1519 1506 dump sing_227.htm#SEC267 1520 dynamic geometry sing_91 3.htm#IDX4571521 dynamic geometry sing_91 4.htm#IDX4611507 dynamic geometry sing_914.htm#IDX450 1508 dynamic geometry sing_915.htm#IDX453 1522 1509 ecart sing_1941.htm#SEC2017 1523 echo sing_38 7.htm#SEC4271510 echo sing_388.htm#SEC428 1524 1511 eexgcdN sing_1868.htm#SEC1944 1525 effective sing_232 6.htm#SEC24021512 effective sing_2325.htm#SEC2401 1526 1513 egcdMain sing_1734.htm#SEC1810 1527 1514 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2072.htm#SEC2148 … … 1529 1516 eigenvals sing_1082.htm#SEC1158 1530 1517 eigenvalue sing_320.htm#SEC360 1531 eigenvalue sing_1082.htm#IDX5 161518 eigenvalue sing_1082.htm#IDX500 1532 1519 eigenvalues sing_1327.htm#SEC1403 1533 elemSymmId sing_94 1.htm#SEC10171520 elemSymmId sing_942.htm#SEC1018 1534 1521 elim sing_1119.htm#SEC1195 1535 1522 elim.lib sing_1116.htm#SEC1192 … … 1537 1524 elim2 sing_1121.htm#SEC1197 1538 1525 elimRing sing_1118.htm#SEC1194 1539 elimWeight sing_70 3.htm#SEC7551526 elimWeight sing_704.htm#SEC756 1540 1527 elim_lib sing_1116.htm#SEC1192 1541 1528 eliminate sing_228.htm#SEC268 1542 eliminate (plural) sing_45 1.htm#SEC4911543 eliminateNC sing_69 8.htm#SEC7501544 elimination sing_69 7.htm#IDX3561529 eliminate (plural) sing_452.htm#SEC492 1530 eliminateNC sing_699.htm#SEC751 1531 elimination sing_698.htm#IDX358 1545 1532 elimlinearpart sing_1694.htm#SEC1770 1546 1533 elimpart sing_1695.htm#SEC1771 1547 1534 elimpartanyr sing_1696.htm#SEC1772 1548 1535 elimrep sing_1381.htm#SEC1457 1549 elliptic curve sing_1129.htm#IDX5 321550 elliptic curves sing_1126.htm#IDX5 261551 elliptic curves sing_1132.htm#IDX5 351552 elliptic curves sing_1133.htm#IDX5 391536 elliptic curve sing_1129.htm#IDX516 1537 elliptic curves sing_1126.htm#IDX510 1538 elliptic curves sing_1132.htm#IDX519 1539 elliptic curves sing_1133.htm#IDX523 1553 1540 ellipticAdd sing_1889.htm#SEC1965 1554 1541 ellipticAllPoints sing_1894.htm#SEC1970 … … 1558 1545 ellipticRandomCurve sing_1891.htm#SEC1967 1559 1546 ellipticRandomPoint sing_1892.htm#SEC1968 1560 ellipticcovers.lib sing_1126.htm#IDX5 201561 ellipticcovers_lib sing_1126.htm#IDX5 211562 else sing_37 7.htm#SEC4171563 embedMat sing_7 29.htm#SEC7811547 ellipticcovers.lib sing_1126.htm#IDX504 1548 ellipticcovers_lib sing_1126.htm#IDX505 1549 else sing_378.htm#SEC418 1550 embedMat sing_730.htm#SEC782 1564 1551 emptyFan sing_2038.htm#SEC2114 1565 1552 encode sing_1795.htm#SEC1871 1566 endomorphism filtration sing_1526.htm#IDX7 261553 endomorphism filtration sing_1526.htm#IDX710 1567 1554 endvfilt sing_1526.htm#SEC1602 1568 engine sing_58 5.htm#SEC6371569 envelop FamElemsAtEnvCompPoints sing_91 5.htm#SEC9911570 envelop sing_91 5.htm#IDX4651571 envelop sing_91 6.htm#IDX4691572 envelop sing_91 7.htm#IDX4741573 envelop sing_91 8.htm#IDX4791574 envelope sing_45 2.htm#SEC4921575 enveloping algebra sing_3 49.htm#IDX2071576 enveloping algebra sing_49 0.htm#IDX3001555 engine sing_586.htm#SEC638 1556 envelop FamElemsAtEnvCompPoints sing_916.htm#SEC992 1557 envelop sing_916.htm#IDX456 1558 envelop sing_917.htm#IDX459 1559 envelop sing_918.htm#IDX463 1560 envelop sing_919.htm#IDX467 1561 envelope sing_453.htm#SEC493 1562 enveloping algebra sing_350.htm#IDX207 1563 enveloping algebra sing_491.htm#IDX302 1577 1564 environment variable, DISPLAY The online help system sing_16.htm#IDX29 1578 1565 equalJinI sing_1469.htm#SEC1545 1579 equalMultiDeg sing_246 2.htm#SEC25381566 equalMultiDeg sing_2461.htm#SEC2537 1580 1567 equations sing_2012.htm#SEC2088 1581 1568 equiRadical sing_1285.htm#SEC1361 … … 1586 1573 equising.lib sing_1509.htm#SEC1585 1587 1574 equising_lib sing_1509.htm#SEC1585 1588 equisingular Tjurina number sing_1452.htm#IDX6 331589 equisingularity ideal sing_1511.htm#IDX6 531590 equisingularity stratum sing_1512.htm#IDX6 541575 equisingular Tjurina number sing_1452.htm#IDX617 1576 equisingularity ideal sing_1511.htm#IDX637 1577 equisingularity stratum sing_1512.htm#IDX638 1591 1578 error recovery sing_15.htm#SEC21 1592 1579 errorInsert sing_1798.htm#SEC1874 1593 1580 errorRand sing_1799.htm#SEC1875 1594 errormap sing_235 6.htm#SEC24321581 errormap sing_2355.htm#SEC2431 1595 1582 esIdeal sing_1511.htm#SEC1587 1596 1583 esStratum sing_1512.htm#SEC1588 1597 essential sing_2178.htm#IDX8 531598 essential sing_2179.htm#IDX8 541584 essential sing_2178.htm#IDX837 1585 essential sing_2179.htm#IDX838 1599 1586 eta sing_2064.htm#SEC2140 1600 1587 euler sing_1847.htm#SEC1923 1601 1588 eulerChProj sing_2276.htm#SEC2352 1602 1589 eval sing_229.htm#SEC269 1603 evaluateFormalDivisor evaluateFormalDivisor sing_232 8.htm#SEC24041604 evaluatePDivisor sing_233 4.htm#SEC24101590 evaluateFormalDivisor evaluateFormalDivisor sing_2327.htm#SEC2403 1591 evaluatePDivisor sing_2333.htm#SEC2409 1605 1592 evaluate_reynolds sing_1632.htm#SEC1708 1606 1593 evalutateIntegral sing_1131.htm#SEC1207 1607 1594 example sing_231.htm#SEC271 1608 example sing_2180.htm#IDX8 551609 example sing_2181.htm#IDX8 571610 example sing_2182.htm#IDX8 591611 example sing_2183.htm#IDX8 611612 example sing_2184.htm#IDX8 631613 example sing_2185.htm#IDX8 651614 example sing_2186.htm#IDX8 681595 example sing_2180.htm#IDX839 1596 example sing_2181.htm#IDX841 1597 example sing_2182.htm#IDX843 1598 example sing_2183.htm#IDX845 1599 example sing_2184.htm#IDX847 1600 example sing_2185.htm#IDX849 1601 example sing_2186.htm#IDX852 1615 1602 execute sing_232.htm#SEC272 1616 exit sing_38 1.htm#SEC4211603 exit sing_382.htm#SEC422 1617 1604 exp2pt sing_1835.htm#SEC1911 1618 1605 expo sing_1859.htm#SEC1935 1619 exponents sing_2190.htm#IDX8 761620 export sing_37 4.htm#SEC4141606 exponents sing_2190.htm#IDX860 1607 export sing_375.htm#SEC415 1621 1608 exportNuminvs sing_1252.htm#SEC1328 10423 1622 exportto sing_37 5.htm#SEC4151609 exportto sing_376.htm#SEC416 1623 1610 expression list sing_72.htm#IDX128 1624 expression list sing_41 4.htm#IDX2931625 ext-module purityfiltration_lib sing_73 8.htm#IDX3621611 expression list sing_415.htm#IDX295 1612 ext-module purityfiltration_lib sing_739.htm#IDX364 1626 1613 extcurve sing_1781.htm#SEC1857 1627 1614 extdevelop sing_1543.htm#SEC1619 1628 extendGC sing_91 0.htm#SEC9861629 extendWeyl sing_77 2.htm#SEC8241630 extendedTensor sing_70 4.htm#SEC7561631 extendpoly sing_9 09.htm#SEC9851632 extendring sing_98 5.htm#SEC10611633 extension of rings sing_1305.htm#IDX5 821634 exterior basis sing_1061.htm#IDX 5131635 exterior power sing_1063.htm#IDX 5151615 extendGC sing_911.htm#SEC987 1616 extendWeyl sing_773.htm#SEC825 1617 extendedTensor sing_705.htm#SEC757 1618 extendpoly sing_910.htm#SEC986 1619 extendring sing_986.htm#SEC1062 1620 extension of rings sing_1305.htm#IDX566 1621 exterior basis sing_1061.htm#IDX497 1622 exterior power sing_1063.htm#IDX499 1636 1623 exteriorBasis sing_1061.htm#SEC1137 1637 1624 exteriorPower sing_1063.htm#SEC1139 … … 1639 1626 fVector sing_2041.htm#SEC2117 1640 1627 fVectorP sing_2073.htm#SEC2149 1641 facFirstShift sing_69 1.htm#SEC7431642 facFirstWeyl sing_68 7.htm#SEC7391628 facFirstShift sing_692.htm#SEC744 1629 facFirstWeyl sing_688.htm#SEC740 1643 1630 facGBIdeal sing_1270.htm#SEC1346 1644 facShift sing_69 0.htm#SEC7421645 facSubWeyl sing_6 89.htm#SEC7411646 facWeyl sing_68 6.htm#SEC7381631 facShift sing_691.htm#SEC743 1632 facSubWeyl sing_690.htm#SEC742 1633 facWeyl sing_687.htm#SEC739 1647 1634 faceContaining sing_2013.htm#SEC2089 1648 1635 facetVertexLatticeDistances facetVertexLatticeDistances sing_2074.htm#SEC2150 … … 1652 1639 facstd sing_234.htm#SEC274 1653 1640 factmodd sing_235.htm#SEC275 1654 factorH sing_899.htm#SEC975 1641 factor sing_314.htm#SEC354 1642 factorH sing_900.htm#SEC976 1655 1643 factorLenstraECM sing_1898.htm#SEC1974 1656 1644 factorMain sing_1735.htm#SEC1811 1657 factorgroup sing_245 2.htm#SEC25281658 factorial sing_88 5.htm#SEC9611645 factorgroup sing_2451.htm#SEC2527 1646 factorial sing_886.htm#SEC962 1659 1647 factorization sing_315.htm#SEC355 1660 factorization sing_1091.htm#IDX5 171648 factorization sing_1091.htm#IDX501 1661 1649 factorize sing_236.htm#SEC276 1650 factorize sing_314.htm#SEC354 1662 1651 factory sing_1.htm#IDX2 1663 1652 fan sing_184.htm#SEC224 1664 fan sing_2053.htm#IDX 8021653 fan sing_2053.htm#IDX786 1665 1654 fanViaCones sing_2039.htm#SEC2115 1666 1655 farey sing_237.htm#SEC277 1667 fareypoly sing_233 7.htm#SEC24131656 fareypoly sing_2336.htm#SEC2412 1668 1657 fastExpt sing_1843.htm#SEC1919 1669 1658 fastHC, option sing_307.htm#IDX153 1670 1659 fastelim sing_1697.htm#SEC1773 1671 1660 fetch sing_238.htm#SEC278 1672 fetch (plural) sing_45 3.htm#SEC4931673 fetchall sing_98 6.htm#SEC10621674 ffmodStd sing_234 1.htm#SEC24171675 ffmodstd.lib sing_233 6.htm#SEC24121676 ffmodstd_lib sing_233 6.htm#SEC24121661 fetch (plural) sing_454.htm#SEC494 1662 fetchall sing_987.htm#SEC1063 1663 ffmodStd sing_2340.htm#SEC2416 1664 ffmodstd.lib sing_2335.htm#SEC2411 1665 ffmodstd_lib sing_2335.htm#SEC2411 1677 1666 ffsolve sing_1686.htm#SEC1762 1678 1667 ffsolve.lib sing_1685.htm#SEC1761 1679 1668 ffsolve_lib sing_1685.htm#SEC1761 1680 1669 fglm sing_239.htm#SEC279 1681 fglm sing_34 6.htm#IDX1871670 fglm sing_347.htm#IDX187 1682 1671 fglm_solve sing_1713.htm#SEC1789 1683 1672 fglmquot sing_240.htm#SEC280 1684 fibonacci sing_88 6.htm#SEC9621673 fibonacci sing_887.htm#SEC963 1685 1674 field sing_139.htm#SEC179 1686 1675 file, .singularrc sing_20.htm#IDX71 1687 1676 filecmd sing_241.htm#SEC281 1688 filtration purityfiltration_lib sing_73 8.htm#IDX3631677 filtration purityfiltration_lib sing_739.htm#IDX365 1689 1678 finalCharts sing_1405.htm#SEC1481 1690 1679 find sing_242.htm#SEC282 1691 findAuto sing_64 5.htm#SEC6971692 findInvo sing_64 3.htm#SEC6951693 findInvoDiag sing_64 4.htm#SEC6961680 findAuto sing_646.htm#SEC698 1681 findInvo sing_644.htm#SEC696 1682 findInvoDiag sing_645.htm#SEC697 1694 1683 findOrientedBoundary findOrientedBoundary sing_2065.htm#SEC2141 1695 1684 findTorsion sing_1824.htm#SEC1900 … … 1699 1688 findifs_example sing_1832.htm#SEC1908 1700 1689 findifs_lib sing_1831.htm#SEC1907 1701 findimAlgebra sing_71 3.htm#SEC7651690 findimAlgebra sing_714.htm#SEC766 1702 1691 finduni sing_243.htm#SEC283 1703 1692 findvars sing_1698.htm#SEC1774 1704 1693 finite field sing_139.htm#SEC179 1705 finite field sing_1685.htm#IDX7 751694 finite field sing_1685.htm#IDX759 1706 1695 finiteDiagInvariants finiteDiagInvariants sing_1247.htm#SEC1323 3508 1707 finitediff.lib sing_234 2.htm#IDX9581708 finitediff_lib sing_234 2.htm#IDX9591696 finitediff.lib sing_2341.htm#IDX943 1697 finitediff_lib sing_2341.htm#IDX944 1709 1698 finitenessTest sing_1105.htm#SEC1181 1710 1699 finvar.lib sing_1620.htm#SEC1696 1711 1700 finvar_lib sing_1620.htm#SEC1696 1712 first index is 1 sing_40 8.htm#SEC4481701 first index is 1 sing_409.htm#SEC449 1713 1702 firstoct sing_1746.htm#SEC1822 1714 1703 fitting sing_1151.htm#SEC1227 1715 fl2poly sing_58 2.htm#SEC6341704 fl2poly sing_583.htm#SEC635 1716 1705 flatten sing_1036.htm#SEC1112 1717 1706 flatteningStrat sing_1152.htm#SEC1228 1718 floating point sing_99 5.htm#IDX4991719 for sing_37 6.htm#SEC4161720 formaldivisorplus sing_232 9.htm#SEC24051721 forward sing_234 8.htm#SEC24241722 fourier sing_57 7.htm#SEC6291723 fouriersystem sing_235 9.htm#SEC24351724 fpadim.lib sing_59 3.htm#SEC6451725 fpadim_lib sing_59 3.htm#SEC6451707 floating point sing_996.htm#IDX484 1708 for sing_377.htm#SEC417 1709 formaldivisorplus sing_2328.htm#SEC2404 1710 forward sing_2347.htm#SEC2423 1711 fourier sing_578.htm#SEC630 1712 fouriersystem sing_2358.htm#SEC2434 1713 fpadim.lib sing_594.htm#SEC646 1714 fpadim_lib sing_594.htm#SEC646 1726 1715 fprintf sing_244.htm#SEC284 1727 frandwalk sing_248 4.htm#SEC25601728 free sing_2189.htm#IDX8 731729 free sing_2190.htm#IDX8 751730 free associative algebra, tensor algebra Free associative algebras sing_48 4.htm#SEC5361731 freeGBasis sing_62 8.htm#SEC6801732 freegb.lib sing_62 4.htm#SEC6761733 freegb_lib sing_62 4.htm#SEC6761716 frandwalk sing_2485.htm#SEC2561 1717 free sing_2189.htm#IDX857 1718 free sing_2190.htm#IDX859 1719 free associative algebra, tensor algebra Free associative algebras sing_485.htm#SEC537 1720 freeGBasis sing_629.htm#SEC681 1721 freegb.lib sing_625.htm#SEC677 1722 freegb_lib sing_625.htm#SEC677 1734 1723 freemodule sing_245.htm#SEC285 1735 freerank sing_94 3.htm#SEC10191724 freerank sing_944.htm#SEC1020 1736 1725 from_boolean_constant from_boolean_constant sing_2220.htm#SEC2296 44881 1737 1726 from_boolean_ideal sing_2224.htm#SEC2300 62698 … … 1739 1728 from_boolean_set sing_2225.htm#SEC2301 60615 1740 1729 frwalk sing_246.htm#SEC286 1741 full representation sing_9 09.htm#IDX4411742 full representation sing_91 0.htm#IDX4461730 full representation sing_910.htm#IDX438 1731 full representation sing_911.htm#IDX442 1743 1732 fullFan sing_2040.htm#SEC2116 1744 fullSerreRelations sing_6 39.htm#SEC6911733 fullSerreRelations sing_640.htm#SEC692 1745 1734 fullSpace sing_1995.htm#SEC2071 1746 1735 furtherInvar sing_1664.htm#SEC1740 … … 1759 1748 genMDSMat sing_1801.htm#SEC1877 1760 1749 genSymId sing_1324.htm#SEC1400 1761 general error-locator polynomial sing_86 4.htm#SEC9291762 general neron. sing_23 80.htm#IDX9661763 general weighted lexicographical ordering sing_8 39.htm#IDX4041764 general weighted reverse lexicographical ordering Local orderings sing_8 39.htm#IDX4011765 general.lib sing_8 79.htm#SEC9551750 general error-locator polynomial sing_865.htm#SEC930 1751 general neron. sing_2379.htm#IDX951 1752 general weighted lexicographical ordering sing_840.htm#IDX406 1753 general weighted reverse lexicographical ordering Local orderings sing_840.htm#IDX403 1754 general.lib sing_880.htm#SEC956 1766 1755 generalOrder sing_1959.htm#SEC2035 1767 general_lib sing_8 79.htm#SEC9551756 general_lib sing_880.htm#SEC956 1768 1757 generateG sing_1897.htm#SEC1973 1769 generators sing_1460.htm#IDX6 371758 generators sing_1460.htm#IDX621 1770 1759 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2015.htm#SEC2091 1771 1760 generatorsOfSpan sing_2016.htm#SEC2092 1772 generic representation sing_9 09.htm#IDX4401773 genericid sing_96 1.htm#SEC10371761 generic representation sing_910.htm#IDX437 1762 genericid sing_962.htm#SEC1038 1774 1763 genericity sing_1821.htm#SEC1897 1775 1764 genericmat sing_1037.htm#SEC1113 1776 1765 genoutput sing_1394.htm#SEC1470 1777 1766 genus sing_1229.htm#SEC1305 1778 geometric invariant theory sing_237 3.htm#IDX9631779 geometrical locus FamElemsAtEnvCompPoints sing_91 3.htm#IDX4551780 geometrical locus sing_91 4.htm#IDX4591781 geometrical locus sing_91 5.htm#IDX4631782 geometrical locus sing_91 6.htm#IDX4671783 geometrical locus sing_91 7.htm#IDX4721784 geometrical locus sing_91 8.htm#IDX4771767 geometric invariant theory sing_2372.htm#IDX948 1768 geometrical locus FamElemsAtEnvCompPoints sing_914.htm#IDX448 1769 geometrical locus sing_915.htm#IDX451 1770 geometrical locus sing_916.htm#IDX454 1771 geometrical locus sing_917.htm#IDX457 1772 geometrical locus sing_918.htm#IDX461 1773 geometrical locus sing_919.htm#IDX465 1785 1774 getArguments sing_1027.htm#SEC1103 1786 1775 getCommand sing_1026.htm#SEC1102 1787 1776 getCone sing_2042.htm#SEC2118 1788 getGradingGroup sing_242 7.htm#SEC25031789 getLattice sing_242 8.htm#SEC25041777 getGradingGroup sing_2426.htm#SEC2502 1778 getLattice sing_2427.htm#SEC2503 1790 1779 getLinearForms sing_2017.htm#SEC2093 1791 getModuleGrading sing_243 8.htm#SEC25141780 getModuleGrading sing_2437.htm#SEC2513 1792 1781 getMultiplicity sing_2018.htm#SEC2094 1793 1782 getOneVar sing_1237.htm#SEC1313 … … 1795 1784 getSmallest sing_1236.htm#SEC1312 1796 1785 getState sing_1029.htm#SEC1105 1797 getVariableWeights sing_242 6.htm#SEC25021798 getcores sing_97 6.htm#SEC10521786 getVariableWeights sing_2425.htm#SEC2501 1787 getcores sing_977.htm#SEC1053 1799 1788 getdump sing_249.htm#SEC289 1800 getenv sing_3 49.htm#IDX2101789 getenv sing_350.htm#IDX210 1801 1790 gfan.lib sing_1994.htm#SEC2070 1802 1791 gfan_lib sing_1994.htm#SEC2070 1803 1792 gfanlib sing_1.htm#IDX9 1804 gitCone sing_237 5.htm#SEC24511805 gitFan sing_237 6.htm#SEC24521806 gitfan sing_237 3.htm#IDX9611807 gitfan.lib sing_237 3.htm#SEC24491808 gitfan_lib sing_237 3.htm#SEC24491809 gkdim.lib sing_65 0.htm#SEC7021810 gkdim_lib sing_65 0.htm#SEC7021811 gkzFan sing_237 7.htm#SEC24531793 gitCone sing_2374.htm#SEC2450 1794 gitFan sing_2375.htm#SEC2451 1795 gitfan sing_2372.htm#IDX946 1796 gitfan.lib sing_2372.htm#SEC2448 1797 gitfan_lib sing_2372.htm#SEC2448 1798 gkdim.lib sing_651.htm#SEC703 1799 gkdim_lib sing_651.htm#SEC703 1800 gkzFan sing_2376.htm#SEC2452 1812 1801 global sing_204.htm#IDX133 1813 global Bernstein-Sato polynomial sing_49 7.htm#IDX3071814 global Bernstein-Sato polynomial sing_53 2.htm#IDX3251815 global Bernstein-Sato polynomial for variety sing_58 8.htm#IDX3501816 globalSections sing_232 3.htm#SEC23991802 global Bernstein-Sato polynomial sing_498.htm#IDX309 1803 global Bernstein-Sato polynomial sing_533.htm#IDX327 1804 global Bernstein-Sato polynomial for variety sing_589.htm#IDX352 1805 globalSections sing_2322.htm#SEC2398 1817 1806 gmscoeffs sing_1518.htm#SEC1594 1818 1807 gmsnf sing_1517.htm#SEC1593 … … 1822 1811 gmssing.lib sing_1515.htm#SEC1591 1823 1812 gmssing_lib sing_1515.htm#SEC1591 1824 good basis sing_1515.htm#IDX6 651825 good basis sing_1525.htm#IDX7 201826 good basis sing_1537.htm#IDX7 361827 good basis sing_1539.htm#IDX7 471813 good basis sing_1515.htm#IDX649 1814 good basis sing_1525.htm#IDX704 1815 good basis sing_1537.htm#IDX720 1816 good basis sing_1539.htm#IDX731 1828 1817 goodBasis sing_1539.htm#SEC1615 1829 1818 gorensteinIndex sing_2077.htm#SEC2153 1830 1819 gorensteinVector sing_2078.htm#SEC2154 1831 graal.lib sing_236 6.htm#SEC24421832 graalMixed sing_236 7.htm#SEC24431833 graal_lib sing_236 6.htm#SEC24421834 gradeNumber sing_74 2.htm#SEC7941835 graded Weyl algebra sing_49 7.htm#IDX3101836 graded module, graded piece sing_1441.htm#IDX6 231837 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_238 2.htm#IDX9671838 graded modules, handling of Handling graded modules sing_80 6.htm#SEC8581839 gradedModules.lib sing_238 2.htm#SEC24581840 gradedModules_lib sing_238 2.htm#SEC24581841 gradiator sing_247 1.htm#SEC25471842 graph sing_1127.htm#IDX5 301843 graph sing_1128.htm#IDX5 311820 graal.lib sing_2365.htm#SEC2441 1821 graalMixed sing_2366.htm#SEC2442 1822 graal_lib sing_2365.htm#SEC2441 1823 gradeNumber sing_743.htm#SEC795 1824 graded Weyl algebra sing_498.htm#IDX312 1825 graded module, graded piece sing_1441.htm#IDX607 1826 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2381.htm#IDX952 1827 graded modules, handling of Handling graded modules sing_807.htm#SEC859 1828 gradedModules.lib sing_2381.htm#SEC2457 1829 gradedModules_lib sing_2381.htm#SEC2457 1830 gradiator sing_2470.htm#SEC2546 1831 graph sing_1127.htm#IDX514 1832 graph sing_1128.htm#IDX515 1844 1833 graphics.lib sing_1748.htm#SEC1824 1845 1834 graphics_lib sing_1748.htm#SEC1824 1846 1835 graphviz sing_1.htm#IDX13 1847 1836 graver4ti2 sing_1322.htm#SEC1398 39635 1848 grconcat sing_240 5.htm#SEC24811849 grdeg sing_238 5.htm#SEC24611850 grgens sing_239 4.htm#SEC24701851 grgroebner sing_240 4.htm#SEC24801852 grlift sing_240 2.htm#SEC24781853 grlifting sing_240 9.htm#SEC24851854 grlifting2 sing_24 10.htm#SEC24861855 grlifting3 sing_241 2.htm#SEC24881856 grneg sing_241 5.htm#SEC24911857 grobcov sing_90 2.htm#SEC9781858 grobcov.lib sing_90 0.htm#SEC9761859 grobcov_lib sing_90 0.htm#SEC9761860 grobj sing_238 3.htm#SEC24591837 grconcat sing_2404.htm#SEC2480 1838 grdeg sing_2384.htm#SEC2460 1839 grgens sing_2393.htm#SEC2469 1840 grgroebner sing_2403.htm#SEC2479 1841 grlift sing_2401.htm#SEC2477 1842 grlifting sing_2408.htm#SEC2484 1843 grlifting2 sing_2409.htm#SEC2485 1844 grlifting3 sing_2411.htm#SEC2487 1845 grneg sing_2414.htm#SEC2490 1846 grobcov sing_903.htm#SEC979 1847 grobcov.lib sing_901.htm#SEC977 1848 grobcov_lib sing_901.htm#SEC977 1849 grobj sing_2382.htm#SEC2458 1861 1850 groebner sing_250.htm#SEC290 1862 groebner sing_79 8.htm#SEC8501851 groebner sing_799.htm#SEC851 1863 1852 groebner basis computations sing_250.htm#IDX147 1864 1853 groebnerComplex sing_2156.htm#SEC2232 … … 1867 1856 groebnerFanP sing_2058.htm#SEC2134 1868 1857 gromovWitten sing_1132.htm#SEC1208 1869 grorder sing_239 6.htm#SEC24721858 grorder sing_2395.htm#SEC2471 1870 1859 ground field sing_139.htm#SEC179 1871 1860 group_reynolds sing_1628.htm#SEC1704 1872 grpower sing_239 2.htm#SEC24681873 grpres sing_239 5.htm#SEC24711874 grprod sing_240 3.htm#SEC24791875 grrange sing_241 4.htm#SEC24901876 grres sing_240 1.htm#SEC24771877 grrndmap sing_240 7.htm#SEC24831878 grrndmap2 sing_240 8.htm#SEC24841879 grrndmat sing_240 6.htm#SEC24821880 grshift sing_238 7.htm#SEC24631881 grsum sing_239 1.htm#SEC24671882 grsyz sing_2 400.htm#SEC24761883 grtest sing_238 4.htm#SEC24601884 grtranspose sing_239 3.htm#SEC24691885 grtranspose1 sing_239 7.htm#SEC24731886 grtwist sing_238 9.htm#SEC24651887 grtwists sing_23 90.htm#SEC24661888 grview sing_238 6.htm#SEC24621861 grpower sing_2391.htm#SEC2467 1862 grpres sing_2394.htm#SEC2470 1863 grprod sing_2402.htm#SEC2478 1864 grrange sing_2413.htm#SEC2489 1865 grres sing_2400.htm#SEC2476 1866 grrndmap sing_2406.htm#SEC2482 1867 grrndmap2 sing_2407.htm#SEC2483 1868 grrndmat sing_2405.htm#SEC2481 1869 grshift sing_2386.htm#SEC2462 1870 grsum sing_2390.htm#SEC2466 1871 grsyz sing_2399.htm#SEC2475 1872 grtest sing_2383.htm#SEC2459 1873 grtranspose sing_2392.htm#SEC2468 1874 grtranspose1 sing_2396.htm#SEC2472 1875 grtwist sing_2388.htm#SEC2464 1876 grtwists sing_2389.htm#SEC2465 1877 grview sing_2385.htm#SEC2461 1889 1878 grwalk.lib sing_1137.htm#SEC1213 1890 1879 grwalk_lib sing_1137.htm#SEC1213 1891 grzero sing_238 8.htm#SEC24641880 grzero sing_2387.htm#SEC2463 1892 1881 gwalk sing_1143.htm#SEC1219 1893 1882 hStarVector sing_2079.htm#SEC2155 1894 1883 hVector sing_2080.htm#SEC2156 1895 1884 h_increasing_knapsack h_increasing_knapsack sing_1920.htm#SEC1996 1896 hardware platform sing_3 49.htm#IDX2651885 hardware platform sing_350.htm#IDX267 1897 1886 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 1887 hasCommutativeVars sing_997.htm#SEC1073 1888 hasGlobalOrdering sing_998.htm#SEC1074 1889 hasMixedOrdering sing_999.htm#SEC1075 1890 hasNumericCoeffs sing_996.htm#SEC1072 1903 1891 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1001.htm#SEC1077 1904 1892 headStand sing_1059.htm#SEC1135 … … 1911 1899 help browsers, html The online help system sing_16.htm#IDX23 1912 1900 help browsers, setting command to use The online help system sing_16.htm#IDX30 1913 help browsers, setting the sing_3 49.htm#IDX1931901 help browsers, setting the sing_350.htm#IDX193 1914 1902 help, accessing over the net Command line options sing_19.htm#IDX42 1915 1903 help, online help system The online help system sing_16.htm#SEC22 1916 hermiteNormalForm sing_247 2.htm#SEC25481917 hess.lib sing_241 7.htm#SEC24931918 hess_lib sing_241 7.htm#SEC24931919 hessenberg sing_3 49.htm#IDX2161904 hermiteNormalForm sing_2471.htm#SEC2547 1905 hess.lib sing_2416.htm#SEC2492 1906 hess_lib sing_2416.htm#SEC2492 1907 hessenberg sing_350.htm#IDX216 1920 1908 hessenberg sing_1081.htm#SEC1157 1921 1909 highcorner sing_252.htm#SEC292 1922 1910 hilb sing_253.htm#SEC293 1923 hilbPoly sing_9 59.htm#SEC10351911 hilbPoly sing_960.htm#SEC1036 1924 1912 hilbert4ti2 sing_1321.htm#SEC1397 13993 1925 1913 hilbertBasis sing_2081.htm#SEC2157 1926 hilbertSeries sing_247 4.htm#SEC25501914 hilbertSeries sing_2473.htm#SEC2549 1927 1915 hilbvec sing_1699.htm#SEC1775 1928 1916 hnexpansion sing_1541.htm#SEC1617 1929 1917 hnoether.lib sing_1540.htm#SEC1616 1930 1918 hnoether_lib sing_1540.htm#SEC1616 1931 holonomic rank sing_76 0.htm#IDX3741932 holonomicRank sing_76 4.htm#SEC8161919 holonomic rank sing_761.htm#IDX376 1920 holonomicRank sing_765.htm#SEC817 1933 1921 hom_kernel sing_1159.htm#SEC1235 1934 1922 homog sing_254.htm#SEC294 1935 1923 homogeneitySpace sing_2152.htm#SEC2228 1936 homogfacFirstQWeyl sing_69 3.htm#SEC7451937 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_69 5.htm#SEC7471938 homogfacNthQWeyl sing_69 2.htm#SEC7441939 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_69 4.htm#SEC7461924 homogfacFirstQWeyl sing_694.htm#SEC746 1925 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_696.htm#SEC748 1926 homogfacNthQWeyl sing_693.htm#SEC745 1927 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_695.htm#SEC747 1940 1928 homolog.lib sing_1144.htm#SEC1220 1941 1929 homolog_lib sing_1144.htm#SEC1220 1942 1930 homology sing_1154.htm#SEC1230 1943 howto, download Download instructions sing_250 4.htm#SEC25931944 howto, install on Macintosh Macintosh installation instructions sing_250 7.htm#SEC25961945 howto, install on Unix Unix installation instructions sing_250 5.htm#SEC25941946 howto, install on Windows Windows installation instructions sing_250 6.htm#SEC25951931 howto, download Download instructions sing_2505.htm#SEC2594 1932 howto, install on Macintosh Macintosh installation instructions sing_2508.htm#SEC2597 1933 howto, install on Unix Unix installation instructions sing_2506.htm#SEC2595 1934 howto, install on Windows Windows installation instructions sing_2507.htm#SEC2596 1947 1935 hres sing_255.htm#SEC295 1948 1936 html, default help The online help system sing_16.htm#IDX24 1949 1937 hyperel.lib sing_1927.htm#SEC2003 1950 1938 hyperel_lib sing_1927.htm#SEC2003 1951 hyperplane sing_2159.htm#IDX 8131952 hyperplane arrangement sing_53 2.htm#IDX3311953 hypersurface singularity sing_1567.htm#IDX7 651939 hyperplane sing_2159.htm#IDX797 1940 hyperplane arrangement sing_533.htm#IDX333 1941 hypersurface singularity sing_1567.htm#IDX749 1954 1942 iMult sing_1232.htm#SEC1308 1955 id2mod sing_95 5.htm#SEC10311943 id2mod sing_956.htm#SEC1032 1956 1944 ideal sing_85.htm#SEC125 1957 1945 ideal declarations sing_86.htm#SEC126 1958 ideal declarations (plural) ideal declarations (plural) sing_41 6.htm#SEC4561946 ideal declarations (plural) ideal declarations (plural) sing_417.htm#SEC457 1959 1947 ideal expressions sing_87.htm#SEC127 1960 ideal expressions (plural) ideal expressions (plural) sing_41 7.htm#SEC4571948 ideal expressions (plural) ideal expressions (plural) sing_418.htm#SEC458 1961 1949 ideal operations sing_88.htm#SEC128 1962 ideal operations (plural) ideal operations (plural) sing_41 8.htm#SEC4581950 ideal operations (plural) ideal operations (plural) sing_419.htm#SEC459 1963 1951 ideal related functions ideal related functions sing_89.htm#SEC129 1964 ideal related functions (plural) ideal related functions (plural) sing_4 19.htm#SEC4591965 ideal, toric sing_85 1.htm#SEC9081952 ideal related functions (plural) ideal related functions (plural) sing_420.htm#SEC460 1953 ideal, toric sing_852.htm#SEC909 1966 1954 idealSplit sing_1706.htm#SEC1782 1967 ideals Miscellaneous oddities sing_4 09.htm#IDX2871955 ideals Miscellaneous oddities sing_410.htm#IDX289 1968 1956 idealsimplify sing_1468.htm#SEC1544 1969 identifier Identifier resolution sing_41 0.htm#SEC4501957 identifier Identifier resolution sing_411.htm#SEC451 1970 1958 identifyvar sing_1376.htm#SEC1452 1971 if sing_37 7.htm#SEC4171972 imageLattice sing_24 40.htm#SEC25161959 if sing_378.htm#SEC418 1960 imageLattice sing_2439.htm#SEC2515 1973 1961 image_of_variety sing_1656.htm#SEC1732 1974 1962 imap sing_256.htm#SEC296 1975 imap (plural) sing_45 4.htm#SEC4941976 imapall sing_98 7.htm#SEC10631963 imap (plural) sing_455.htm#SEC495 1964 imapall sing_988.htm#SEC1064 1977 1965 impart sing_257.htm#SEC297 1978 importfrom sing_37 8.htm#SEC4181979 inCenter sing_52 1.htm#SEC5731980 inCentralizer sing_52 2.htm#SEC5741981 inForm sing_56 4.htm#SEC6161966 importfrom sing_379.htm#SEC419 1967 inCenter sing_522.htm#SEC574 1968 inCentralizer sing_523.htm#SEC575 1969 inForm sing_565.htm#SEC617 1982 1970 inSubring sing_1097.htm#SEC1173 1983 inVar sing_2301.htm#SEC23771984 1971 indSet sing_1204.htm#SEC1280 1985 1972 indepSet sing_258.htm#SEC298 1986 1973 indexed names sing_36.htm#IDX82 1987 1974 indexed names sing_37.htm#SEC65 1975 indices, multi sing_37.htm#SEC65 1988 1976 inequalities sing_2019.htm#SEC2095 1989 1977 infRedTail, option sing_307.htm#IDX154 … … 1992 1980 init_debug sing_1475.htm#SEC1551 1993 1981 initial sing_2153.htm#SEC2229 1994 initial form sing_49 7.htm#IDX3121995 initial ideal sing_49 7.htm#IDX3111996 initial ideal approach sing_49 7.htm#IDX3151997 initial ideal approach sing_58 8.htm#IDX3541982 initial form sing_498.htm#IDX314 1983 initial ideal sing_498.htm#IDX313 1984 initial ideal approach sing_498.htm#IDX317 1985 initial ideal approach sing_589.htm#IDX356 1998 1986 initialForm sing_2130.htm#SEC2206 1999 1987 initialIdeal sing_2131.htm#SEC2207 2000 initialIdealW sing_56 3.htm#SEC6152001 initialMalgrange sing_56 2.htm#SEC6141988 initialIdealW sing_564.htm#SEC616 1989 initialMalgrange sing_563.htm#SEC615 2002 1990 injective_knapsack sing_1921.htm#SEC1997 2003 inout.lib sing_92 1.htm#SEC9972004 inout_lib sing_92 1.htm#SEC9971991 inout.lib sing_922.htm#SEC998 1992 inout_lib sing_922.htm#SEC998 2005 1993 input sing_41.htm#SEC71 2006 1994 insert sing_121.htm#SEC161 2007 1995 insert sing_259.htm#SEC299 2008 1996 insertCone sing_2043.htm#SEC2119 2009 insertGenerator sing_58 3.htm#SEC6352010 instructions, Macintosh installation Macintosh installation instructions sing_250 7.htm#SEC25962011 instructions, Unix installation Unix installation instructions sing_250 5.htm#SEC25942012 instructions, Windows installation Windows installation instructions sing_250 6.htm#SEC25952013 instructions, downloading Download instructions sing_250 4.htm#SEC25931997 insertGenerator sing_584.htm#SEC636 1998 instructions, Macintosh installation Macintosh installation instructions sing_2508.htm#SEC2597 1999 instructions, Unix installation Unix installation instructions sing_2506.htm#SEC2595 2000 instructions, Windows installation Windows installation instructions sing_2507.htm#SEC2596 2001 instructions, downloading Download instructions sing_2505.htm#SEC2594 2014 2002 int sing_90.htm#SEC130 2015 2003 int declarations sing_91.htm#SEC131 … … 2017 2005 int operations sing_93.htm#SEC133 2018 2006 int related functions int related functions sing_94.htm#SEC134 2019 intInverse sing_244 9.htm#SEC25252007 intInverse sing_2448.htm#SEC2524 2020 2008 intPart sing_1875.htm#SEC1951 2021 intRank sing_244 1.htm#SEC25172009 intRank sing_2440.htm#SEC2516 2022 2010 intRoot sing_1876.htm#SEC1952 2023 intRoots sing_58 0.htm#SEC6322011 intRoots sing_581.htm#SEC633 2024 2012 intStrategy, option sing_307.htm#IDX155 2025 2013 intclMonIdeal sing_1245.htm#SEC1321 22338 2026 2014 intclToricRing sing_1241.htm#SEC1317 62143 2027 integer division Miscellaneous oddities sing_4 09.htm#IDX2822028 integer programming sing_8 59.htm#SEC9162029 integral basis sing_1166.htm#IDX5 522030 integral basis sing_1359.htm#IDX 6082031 integral closure sing_1225.htm#IDX5 652032 integral closure sing_1226.htm#IDX5 682033 integral closure sing_1227.htm#IDX5 712034 integral closure sing_1240.htm#IDX5 772015 integer division Miscellaneous oddities sing_410.htm#IDX284 2016 integer programming sing_860.htm#SEC917 2017 integral basis sing_1166.htm#IDX536 2018 integral basis sing_1359.htm#IDX592 2019 integral closure sing_1225.htm#IDX549 2020 integral closure sing_1226.htm#IDX552 2021 integral closure sing_1227.htm#IDX555 2022 integral closure sing_1240.htm#IDX561 2035 2023 integralBasis sing_1166.htm#SEC1242 2036 integralIdeal sing_56 7.htm#SEC6192037 integralModule sing_56 8.htm#SEC6202038 integralSection sing_24 50.htm#SEC25262024 integralIdeal sing_568.htm#SEC620 2025 integralModule sing_569.htm#SEC621 2026 integralSection sing_2449.htm#SEC2525 2039 2027 integralbasis.lib sing_1165.htm#SEC1241 2040 2028 integralbasis_lib sing_1165.htm#SEC1241 2041 integration of D-module sing_55 5.htm#IDX3432029 integration of D-module sing_556.htm#IDX345 2042 2030 interface, Emacs Emacs user interface sing_21.htm#SEC28 2043 2031 interiorLatticePoints interiorLatticePoints sing_2082.htm#SEC2158 … … 2047 2035 interred sing_261.htm#SEC301 2048 2036 intersect sing_262.htm#SEC302 2049 intersect (plural) sing_45 5.htm#SEC4952037 intersect (plural) sing_456.htm#SEC496 2050 2038 intersectElim, option sing_307.htm#IDX173 2051 intersectLattices sing_244 6.htm#SEC25222039 intersectLattices sing_2445.htm#SEC2521 2052 2040 intersectMon sing_1181.htm#SEC1257 2053 2041 intersectSyz, option sing_307.htm#IDX174 2054 2042 intersectZ sing_1301.htm#SEC1377 2055 2043 intersection sing_1550.htm#SEC1626 2056 intersection lattice sing_2195.htm#IDX8 882057 intersection lattice sing_2196.htm#IDX8 892058 intersection multiplicity 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invariant_algebra_perm sing_1626.htm#IDX756 2080 2068 invariantRing sing_1658.htm#SEC1734 2081 2069 invariant_algebra_perm invariant_algebra_perm sing_1626.htm#SEC1702 … … 2086 2074 invariant_ring_random invariant_ring_random sing_1622.htm#SEC1698 2087 2075 invariants curveColengthDerivations sing_1546.htm#SEC1622 2088 invariants sing_231 1.htm#IDX9282089 invariants sing_231 5.htm#IDX9372076 invariants sing_2310.htm#IDX913 2077 invariants sing_2314.htm#IDX922 2090 2078 inverse sing_1065.htm#SEC1141 2091 2079 inverse of a matrix via its LU-decomposition sing_282.htm#SEC322 2092 inverseFourier sing_57 8.htm#SEC6302080 inverseFourier sing_579.htm#SEC631 2093 2081 inverse_B sing_1066.htm#SEC1142 2094 2082 inverse_L sing_1067.htm#SEC1143 … … 2096 2084 invertBirMap sing_1360.htm#SEC1436 2097 2085 invertNumberMain sing_1736.htm#SEC1812 2098 involut.lib sing_64 2.htm#SEC6942099 involut_lib sing_64 2.htm#SEC6942100 involution sing_64 7.htm#SEC6992086 involut.lib sing_643.htm#SEC695 2087 involut_lib sing_643.htm#SEC695 2088 involution sing_648.htm#SEC700 2101 2089 invunit sing_1569.htm#SEC1645 2102 2090 iostruct sing_1823.htm#SEC1899 … … 2105 2093 irred_secondary_no_molien irred_secondary_no_molien sing_1650.htm#SEC1726 2106 2094 irreddecMon sing_1190.htm#SEC1266 2107 irreducible power series sing_1551.htm#IDX7 592108 irreducible secondary invariant irred_secondary_char0 sing_1647.htm#IDX7 732109 isAface sing_237 8.htm#SEC24542110 isAntiEndo sing_6 49.htm#SEC7012095 irreducible power series sing_1551.htm#IDX743 2096 irreducible secondary invariant irred_secondary_char0 sing_1647.htm#IDX757 2097 isAface sing_2377.htm#SEC2453 2098 isAntiEndo sing_650.htm#SEC702 2111 2099 isBounded sing_2083.htm#SEC2159 2112 2100 isCI sing_204.htm#IDX139 … … 2116 2104 isCMcod2 sing_1604.htm#SEC1680 2117 2105 isCanonical sing_2084.htm#SEC2160 2118 isCartan sing_52 3.htm#SEC5752119 isCentral sing_72 0.htm#SEC7722120 isCommutative sing_72 2.htm#SEC7742106 isCartan sing_524.htm#SEC576 2107 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2149 isPureTensor sing_49 5.htm#SEC5472137 isPureTensor sing_496.htm#SEC548 2150 2138 isQuotientRing sing_1002.htm#SEC1078 2151 isRational sing_55 4.htm#SEC6062139 isRational sing_555.htm#SEC607 2152 2140 isReflexive sing_2089.htm#SEC2165 2153 2141 isReg sing_1158.htm#SEC1234 … … 2156 2144 isSmooth sing_2090.htm#SEC2166 2157 2145 isSubModule sing_1003.htm#SEC1079 2158 isSublattice sing_243 9.htm#SEC25152146 isSublattice sing_2438.htm#SEC2514 2159 2147 isSymmetric sing_1325.htm#SEC1401 2160 2148 isTame sing_1538.htm#SEC1614 2161 2149 isTerminal sing_2091.htm#SEC2167 2162 isTorsionFree sing_245 7.htm#SEC25332163 isTwoSidedGB sing_49 6.htm#SEC5482164 isUpperTriangular sing_70 1.htm#SEC7532165 isVar sing_64 0.htm#SEC6922150 isTorsionFree sing_2456.htm#SEC2532 2151 isTwoSidedGB sing_497.htm#SEC549 2152 isUpperTriangular sing_702.htm#SEC754 2153 isVar sing_641.htm#SEC693 2166 2154 isVeryAmple sing_2092.htm#SEC2168 2167 isWeyl sing_72 3.htm#SEC7752168 isZeroElement sing_245 9.htm#SEC25352155 isWeyl sing_724.htm#SEC776 2156 isZeroElement sing_2458.htm#SEC2534 2169 2157 is_NND sing_1554.htm#SEC1630 2170 2158 is_NP sing_1213.htm#SEC1289 2171 2159 is_active sing_1587.htm#SEC1663 2172 2160 is_bijective sing_1102.htm#SEC1178 2173 is_cenBimodule sing_75 6.htm#SEC8082174 is_cenSubbimodule sing_75 7.htm#SEC8092161 is_cenBimodule sing_757.htm#SEC809 2162 is_cenSubbimodule sing_758.htm#SEC810 2175 2163 is_ci sing_1588.htm#SEC1664 2176 2164 is_complex sing_1038.htm#SEC1114 … … 2183 2171 is_prime sing_1905.htm#SEC1981 2184 2172 is_primitive_root sing_1901.htm#SEC1977 2185 is_pure sing_74 8.htm#SEC8002173 is_pure sing_749.htm#SEC801 2186 2174 is_reg sing_1590.htm#SEC1666 2187 2175 is_regs sing_1591.htm#SEC1667 2188 2176 is_surjective sing_1101.htm#SEC1177 2189 is_zero sing_94 4.htm#SEC10202177 is_zero sing_945.htm#SEC1021 2190 2178 isartinianMon sing_1187.htm#SEC1263 2191 2179 isgenericMon sing_1188.htm#SEC1264 … … 2197 2185 isprimeMon sing_1184.htm#SEC1260 2198 2186 isuni sing_1977.htm#SEC2053 2199 iv2lp sing_61 8.htm#SEC6702200 iv2lpList sing_6 19.htm#SEC6712201 iv2lpMat sing_62 0.htm#SEC6722202 ivDHilbert sing_59 4.htm#SEC6462203 ivDHilbertSickle sing_59 5.htm#SEC6472204 ivDimCheck sing_59 6.htm#SEC6482205 ivHilbert sing_59 7.htm#SEC6492206 ivKDim sing_59 8.htm#SEC6502207 ivL2lpI sing_61 7.htm#SEC6692208 ivMis2Base sing_ 599.htm#SEC6512209 ivMis2Dim sing_60 0.htm#SEC6522210 ivOrdMisLex sing_60 1.htm#SEC6532211 ivSickle sing_60 2.htm#SEC6542212 ivSickleDim sing_60 4.htm#SEC6562213 ivSickleHil sing_60 3.htm#SEC6552187 iv2lp sing_619.htm#SEC671 2188 iv2lpList sing_620.htm#SEC672 2189 iv2lpMat sing_621.htm#SEC673 2190 ivDHilbert sing_595.htm#SEC647 2191 ivDHilbertSickle sing_596.htm#SEC648 2192 ivDimCheck sing_597.htm#SEC649 2193 ivHilbert sing_598.htm#SEC650 2194 ivKDim sing_599.htm#SEC651 2195 ivL2lpI sing_618.htm#SEC670 2196 ivMis2Base sing_600.htm#SEC652 2197 ivMis2Dim sing_601.htm#SEC653 2198 ivOrdMisLex sing_602.htm#SEC654 2199 ivSickle sing_603.htm#SEC655 2200 ivSickleDim sing_605.htm#SEC657 2201 ivSickleHil sing_604.htm#SEC656 2214 2202 jInvariant sing_2124.htm#SEC2200 2215 2203 jOft sing_1860.htm#SEC1936 … … 2228 2216 jungnormal sing_1408.htm#SEC1484 2229 2217 jungresolve sing_1407.htm#SEC1483 2230 katsura sing_94 2.htm#SEC10182218 katsura sing_943.htm#SEC1019 2231 2219 kbase sing_266.htm#SEC306 2232 kbase (plural) sing_45 6.htm#SEC4962233 keepring sing_3 79.htm#SEC4192220 kbase (plural) sing_457.htm#SEC497 2221 keepring sing_380.htm#SEC420 2234 2222 kernel sing_267.htm#SEC307 2235 kernelLattice sing_244 2.htm#SEC25182223 kernelLattice sing_2441.htm#SEC2517 2236 2224 kill sing_268.htm#SEC308 2237 2225 killTask sing_1017.htm#SEC1093 2238 killall sing_88 8.htm#SEC9642226 killall sing_889.htm#SEC965 2239 2227 killattrib sing_269.htm#SEC309 2240 kmemory sing_88 7.htm#SEC9632228 kmemory sing_888.htm#SEC964 2241 2229 kohom sing_1160.htm#SEC1236 2242 2230 kontrahom sing_1161.htm#SEC1237 … … 2250 2238 latex.lib sing_1752.htm#SEC1828 2251 2239 latex_lib sing_1752.htm#SEC1828 2252 lattice sing_2196.htm#IDX8 912240 lattice sing_2196.htm#IDX875 2253 2241 latticeArea sing_2067.htm#SEC2143 2254 latticeBasis sing_244 3.htm#SEC25192242 latticeBasis sing_2442.htm#SEC2518 2255 2243 latticeCodegree sing_2093.htm#SEC2169 2256 2244 latticeDegree sing_2094.htm#SEC2170 2257 2245 latticePoints sing_2095.htm#SEC2171 2258 2246 latticeVolume sing_2096.htm#SEC2172 2259 laxfrT sing_234 6.htm#SEC24222260 laxfrX sing_234 7.htm#SEC24232247 laxfrT sing_2345.htm#SEC2421 2248 laxfrX sing_2346.htm#SEC2422 2261 2249 lazy, option sing_307.htm#IDX156 2262 lcm sing_94 5.htm#SEC10212250 lcm sing_946.htm#SEC1022 2263 2251 lcmMon sing_1179.htm#SEC1255 2264 2252 lcmN sing_1869.htm#SEC1945 … … 2269 2257 leadmonom sing_275.htm#SEC315 2270 2258 leadmonomial sing_1944.htm#SEC2020 2271 left annihilator ideal sing_53 2.htm#IDX3232259 left annihilator ideal sing_533.htm#IDX325 2272 2260 leftInverse sing_1818.htm#SEC1894 2273 2261 leftKernel sing_1816.htm#SEC1892 2274 2262 length, option sing_307.htm#IDX157 2275 letplaceGBasis sing_62 6.htm#SEC6782276 letterplace correspondence Letterplace correspondence sing_48 6.htm#SEC5382263 letplaceGBasis sing_627.htm#SEC679 2264 letterplace correspondence Letterplace correspondence sing_487.htm#SEC539 2277 2265 lex_solve sing_1714.htm#SEC1790 2278 lexicographical ordering sing_83 8.htm#IDX3842266 lexicographical ordering sing_839.htm#IDX386 2279 2267 lib2doc sing_60.htm#SEC97 2280 libSingular sing_41 1.htm#SEC4512268 libSingular sing_412.htm#SEC452 2281 2269 libcdd sing_1.htm#IDX12 2282 2270 libfac sing_1.htm#IDX6 2283 2271 libparse sing_69.htm#SEC109 2284 library sing_2211.htm#IDX 9062285 library sing_237 3.htm#IDX9602272 library sing_2211.htm#IDX890 2273 library sing_2372.htm#IDX945 2286 2274 library, info string sing_55.htm#IDX124 2287 library, polybori.lib sing_2211.htm#IDX 9032275 library, polybori.lib sing_2211.htm#IDX887 2288 2276 library, template sing_55.htm#SEC92 2289 2277 library, template.lib sing_55.htm#IDX122 2290 lieBracket sing_63 7.htm#SEC6892278 lieBracket sing_638.htm#SEC690 2291 2279 lift sing_277.htm#SEC317 2292 lift sing_49 0.htm#IDX2992293 lift (plural) sing_45 7.htm#SEC4972280 lift sing_491.htm#IDX301 2281 lift (plural) sing_458.htm#SEC498 2294 2282 lift_kbase sing_1507.htm#SEC1583 2295 2283 lift_rel_kb sing_1508.htm#SEC1584 2296 liftenvelope sing_49 3.htm#SEC5452284 liftenvelope sing_494.htm#SEC546 2297 2285 liftstd sing_278.htm#SEC318 2298 liftstd (plural) sing_45 8.htm#SEC4982299 linReduce sing_50 5.htm#SEC5572300 linReduceIdeal sing_50 6.htm#SEC5582301 linSyzSolve sing_50 7.htm#SEC5592286 liftstd (plural) sing_459.htm#SEC499 2287 linReduce sing_506.htm#SEC558 2288 linReduceIdeal sing_507.htm#SEC559 2289 linSyzSolve sing_508.htm#SEC560 2302 2290 linalg.lib sing_1064.htm#SEC1140 2303 2291 linalg_lib sing_1064.htm#SEC1140 … … 2308 2296 linear algebra sing_282.htm#SEC322 2309 2297 linear algebra sing_283.htm#SEC323 2310 linear code, dual sing_1787.htm#IDX7 842311 linear code, systematic sing_1788.htm#IDX7 852312 linear interreduction sing_49 7.htm#IDX3142313 linearCombinations sing_52 6.htm#SEC5782314 linearMapKernel sing_52 5.htm#SEC5772298 linear code, dual sing_1787.htm#IDX768 2299 linear code, systematic sing_1788.htm#IDX769 2300 linear interreduction sing_498.htm#IDX316 2301 linearCombinations sing_527.htm#SEC579 2302 linearMapKernel sing_526.htm#SEC578 2315 2303 linear_relations sing_1056.htm#SEC1132 2316 linearlyEquivalent sing_232 5.htm#SEC24012304 linearlyEquivalent sing_2324.htm#SEC2400 2317 2305 linearpart sing_1700.htm#SEC1776 2318 2306 link Parallelization with ssi links sing_108.htm#SEC148 2319 link sing_79 5.htm#SEC8472307 link sing_796.htm#SEC848 2320 2308 link declarations sing_109.htm#SEC149 2321 2309 link expressions sing_110.htm#SEC150 … … 2327 2315 list related functions list related functions sing_122.htm#SEC162 2328 2316 listvar sing_279.htm#SEC319 2329 lll sing_247 5.htm#SEC25512330 load sing_38 0.htm#SEC4202317 lll sing_2474.htm#SEC2550 2318 load sing_381.htm#SEC421 2331 2319 loadLib, option sing_307.htm#IDX178 2332 2320 loadProc, option sing_307.htm#IDX179 2333 2321 locAtZero sing_1234.htm#SEC1310 2334 2322 locNormal sing_1170.htm#SEC1246 2335 local methods sing_1169.htm#IDX5 552336 local methods sing_1170.htm#IDX5 582323 local methods sing_1169.htm#IDX539 2324 local methods sing_1170.htm#IDX542 2337 2325 local names sing_46.htm#SEC83 2338 local rings, computing in Rings associated to monomial orderings sing_79 0.htm#SEC8422339 local weighted lexicographical ordering sing_8 39.htm#IDX4052340 local weighted reverse lexicographical ordering Local orderings sing_8 39.htm#IDX4022326 local rings, computing in Rings associated to monomial orderings sing_791.htm#SEC843 2327 local weighted lexicographical ordering sing_840.htm#IDX407 2328 local weighted reverse lexicographical ordering Local orderings sing_840.htm#IDX404 2341 2329 localInvar sing_1663.htm#SEC1739 2342 localization Rings associated to monomial orderings sing_79 0.htm#SEC8422343 localization sing_2176.htm#IDX8 512344 localization of D-module sing_55 5.htm#IDX3392345 localization of D-module sing_76 0.htm#IDX3772346 locally closed set sing_9 09.htm#IDX4382347 locally closed set sing_91 1.htm#IDX4492330 localization Rings associated to monomial orderings sing_791.htm#SEC843 2331 localization sing_2176.htm#IDX835 2332 localization of D-module sing_556.htm#IDX341 2333 localization of D-module sing_761.htm#IDX379 2334 locally closed set sing_910.htm#IDX435 2335 locally closed set sing_912.htm#IDX444 2348 2336 localstd sing_1954.htm#SEC2030 2349 2337 locnormal.lib sing_1169.htm#SEC1245 2350 2338 locnormal_lib sing_1169.htm#SEC1245 2351 2339 locstd sing_1592.htm#SEC1668 2352 locus FamElemsAtEnvCompPoints sing_91 3.htm#SEC9892353 locus sing_91 3.htm#IDX4562354 locus sing_91 4.htm#IDX4602355 locus sing_91 5.htm#IDX4642356 locus sing_91 6.htm#IDX4682357 locus sing_91 7.htm#IDX4732358 locus sing_91 8.htm#IDX4782359 locusdg sing_91 4.htm#SEC9902360 locusto sing_91 6.htm#SEC9922340 locus FamElemsAtEnvCompPoints sing_914.htm#SEC990 2341 locus sing_914.htm#IDX449 2342 locus sing_915.htm#IDX452 2343 locus sing_916.htm#IDX455 2344 locus sing_917.htm#IDX458 2345 locus sing_918.htm#IDX462 2346 locus sing_919.htm#IDX466 2347 locusdg sing_915.htm#SEC991 2348 locusto sing_917.htm#SEC993 2361 2349 log2 sing_1844.htm#SEC1920 2362 logarithmic annihilator ideal sing_53 2.htm#IDX3282363 lp, global ordering sing_83 8.htm#IDX3832364 lp2iv sing_62 1.htm#SEC6732365 lp2ivId sing_62 2.htm#SEC6742366 lp2lstr sing_63 3.htm#SEC6852367 lpDHilbert sing_60 5.htm#SEC6572368 lpDHilbertSickle sing_60 6.htm#SEC6582369 lpDimCheck sing_60 8.htm#SEC6602370 lpHilbert sing_60 7.htm#SEC6592371 lpId2ivLi sing_62 3.htm#SEC6752372 lpKDim sing_6 09.htm#SEC6612373 lpMis2Base sing_61 0.htm#SEC6622374 lpMis2Dim sing_61 1.htm#SEC6632375 lpMult sing_63 0.htm#SEC6822376 lpNF sing_62 7.htm#SEC6792377 lpOrdMisLex sing_61 2.htm#SEC6642378 lpPower sing_63 2.htm#SEC6842379 lpSickle sing_61 3.htm#SEC6652380 lpSickleDim sing_61 5.htm#SEC6672381 lpSickleHil sing_61 4.htm#SEC6662382 lprint sing_92 3.htm#SEC9992350 logarithmic annihilator ideal sing_533.htm#IDX330 2351 lp, global ordering sing_839.htm#IDX385 2352 lp2iv sing_622.htm#SEC674 2353 lp2ivId sing_623.htm#SEC675 2354 lp2lstr sing_634.htm#SEC686 2355 lpDHilbert sing_606.htm#SEC658 2356 lpDHilbertSickle sing_607.htm#SEC659 2357 lpDimCheck sing_609.htm#SEC661 2358 lpHilbert sing_608.htm#SEC660 2359 lpId2ivLi sing_624.htm#SEC676 2360 lpKDim sing_610.htm#SEC662 2361 lpMis2Base sing_611.htm#SEC663 2362 lpMis2Dim sing_612.htm#SEC664 2363 lpMult sing_631.htm#SEC683 2364 lpNF sing_628.htm#SEC680 2365 lpOrdMisLex sing_613.htm#SEC665 2366 lpPower sing_633.htm#SEC685 2367 lpSickle sing_614.htm#SEC666 2368 lpSickleDim sing_616.htm#SEC668 2369 lpSickleHil sing_615.htm#SEC667 2370 lprint sing_924.htm#SEC1000 2383 2371 lres sing_280.htm#SEC320 2384 ls, local ordering sing_8 39.htm#IDX3962385 lst2str sing_63 4.htm#SEC6862372 ls, local ordering sing_840.htm#IDX398 2373 lst2str sing_635.htm#SEC687 2386 2374 lsum sing_1136.htm#SEC1212 2387 2375 ludecomp sing_281.htm#SEC321 … … 2392 2380 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1914.htm#SEC1990 2393 2381 magnitude sing_1838.htm#SEC1914 2394 makeDivisor sing_231 7.htm#SEC23932395 makeFormalDivisor sing_232 7.htm#SEC24032382 makeDivisor sing_2316.htm#SEC2392 2383 makeFormalDivisor sing_2326.htm#SEC2402 2396 2384 makeGraph sing_1127.htm#SEC1203 2397 makeHeisenberg sing_71 1.htm#SEC7632398 makeLetterplaceRing sing_62 5.htm#SEC6772399 makeMalgrange sing_59 2.htm#SEC6442400 makeModElimRing sing_72 8.htm#SEC7802401 makePDivisor sing_233 3.htm#SEC24092402 makeQsl2 sing_67 5.htm#SEC7272403 makeQsl3 sing_67 6.htm#SEC7282404 makeQso3 sing_67 4.htm#SEC7262405 makeUe6 sing_67 1.htm#SEC7232406 makeUe7 sing_67 2.htm#SEC7242407 makeUe8 sing_67 3.htm#SEC7252408 makeUf4 sing_67 0.htm#SEC7222409 makeUg2 sing_6 69.htm#SEC7212410 makeUgl sing_65 5.htm#SEC7072411 makeUsl sing_65 4.htm#SEC7062412 makeUsl2 sing_65 3.htm#SEC7052413 makeUso10 sing_66 1.htm#SEC7132414 makeUso11 sing_66 2.htm#SEC7142415 makeUso12 sing_66 3.htm#SEC7152416 makeUso5 sing_65 6.htm#SEC7082417 makeUso6 sing_65 7.htm#SEC7092418 makeUso7 sing_65 8.htm#SEC7102419 makeUso8 sing_6 59.htm#SEC7112420 makeUso9 sing_66 0.htm#SEC7122421 makeUsp1 sing_66 4.htm#SEC7162422 makeUsp2 sing_66 5.htm#SEC7172423 makeUsp3 sing_66 6.htm#SEC7182424 makeUsp4 sing_66 7.htm#SEC7192425 makeUsp5 sing_66 8.htm#SEC7202426 makeWeyl sing_71 0.htm#SEC7622385 makeHeisenberg sing_712.htm#SEC764 2386 makeLetterplaceRing sing_626.htm#SEC678 2387 makeMalgrange sing_593.htm#SEC645 2388 makeModElimRing sing_729.htm#SEC781 2389 makePDivisor sing_2332.htm#SEC2408 2390 makeQsl2 sing_676.htm#SEC728 2391 makeQsl3 sing_677.htm#SEC729 2392 makeQso3 sing_675.htm#SEC727 2393 makeUe6 sing_672.htm#SEC724 2394 makeUe7 sing_673.htm#SEC725 2395 makeUe8 sing_674.htm#SEC726 2396 makeUf4 sing_671.htm#SEC723 2397 makeUg2 sing_670.htm#SEC722 2398 makeUgl sing_656.htm#SEC708 2399 makeUsl sing_655.htm#SEC707 2400 makeUsl2 sing_654.htm#SEC706 2401 makeUso10 sing_662.htm#SEC714 2402 makeUso11 sing_663.htm#SEC715 2403 makeUso12 sing_664.htm#SEC716 2404 makeUso5 sing_657.htm#SEC709 2405 makeUso6 sing_658.htm#SEC710 2406 makeUso7 sing_659.htm#SEC711 2407 makeUso8 sing_660.htm#SEC712 2408 makeUso9 sing_661.htm#SEC713 2409 makeUsp1 sing_665.htm#SEC717 2410 makeUsp2 sing_666.htm#SEC718 2411 makeUsp3 sing_667.htm#SEC719 2412 makeUsp4 sing_668.htm#SEC720 2413 makeUsp5 sing_669.htm#SEC721 2414 makeWeyl sing_711.htm#SEC763 2427 2415 map sing_123.htm#SEC163 2428 map (plural) sing_42 0.htm#SEC4602416 map (plural) sing_421.htm#SEC461 2429 2417 map declarations sing_124.htm#SEC164 2430 map declarations (plural) map declarations (plural) sing_42 1.htm#SEC4612418 map declarations (plural) map declarations (plural) sing_422.htm#SEC462 2431 2419 map expressions sing_125.htm#SEC165 2432 map expressions (plural) map expressions (plural) sing_42 2.htm#SEC4622420 map expressions (plural) map expressions (plural) sing_423.htm#SEC463 2433 2421 map operations sing_126.htm#IDX129 2434 map operations (plural) map operations (plural) sing_42 3.htm#IDX2942422 map operations (plural) map operations (plural) sing_424.htm#IDX296 2435 2423 map related functions map related functions sing_127.htm#IDX131 2436 map related functions (plural) map related functions (plural) sing_42 4.htm#IDX2952424 map related functions (plural) map related functions (plural) sing_425.htm#IDX297 2437 2425 mapIsFinite sing_1104.htm#SEC1180 2438 2426 mapToRatNormCurve sing_1364.htm#SEC1440 2439 mapall sing_98 8.htm#SEC10642440 mappingcone sing_241 1.htm#SEC24872441 mappingcone3 sing_241 3.htm#SEC24892427 mapall sing_989.htm#SEC1065 2428 mappingcone sing_2410.htm#SEC2486 2429 mappingcone3 sing_2412.htm#SEC2488 2442 2430 markov4ti2 sing_1320.htm#SEC1396 9163 2443 2431 mat2arr sing_2161.htm#SEC2237 … … 2445 2433 mat_rk sing_1078.htm#SEC1154 2446 2434 matbil sing_1965.htm#SEC2041 2447 mathematical objects Representation of mathematical objects sing_83 4.htm#SEC8862435 mathematical objects Representation of mathematical objects sing_835.htm#SEC887 2448 2436 mathinit sing_1750.htm#SEC1826 2449 2437 matmult sing_1966.htm#SEC2042 2450 2438 matrix sing_128.htm#SEC168 2451 matrix sing_2161.htm#IDX8 192452 matrix sing_2162.htm#IDX8 222453 matrix sing_2163.htm#IDX8 262439 matrix sing_2161.htm#IDX803 2440 matrix sing_2162.htm#IDX806 2441 matrix sing_2163.htm#IDX810 2454 2442 matrix declarations sing_129.htm#SEC169 2455 matrix diagonalization sing_1827.htm#IDX7 952443 matrix diagonalization sing_1827.htm#IDX779 2456 2444 matrix expressions sing_130.htm#SEC170 2457 2445 matrix operations sing_132.htm#SEC172 … … 2463 2451 matrixT1 sing_1606.htm#SEC1682 2464 2452 matrix_lib sing_1031.htm#SEC1107 2465 matrixpres sing_241 6.htm#SEC24922466 matrixsystem sing_235 7.htm#SEC24332453 matrixpres sing_2415.htm#SEC2491 2454 matrixsystem sing_2356.htm#SEC2432 2467 2455 max sing_284.htm#SEC324 2468 2456 maxEord sing_1379.htm#SEC1455 2469 2457 maxExp sing_204.htm#IDX136 2470 maxIntRoot sing_77 7.htm#SEC8292458 maxIntRoot sing_778.htm#SEC830 2471 2459 maxZeros sing_1357.htm#SEC1433 2472 2460 maxabs sing_1984.htm#SEC2060 2473 maxcoef sing_94 6.htm#SEC10222474 maxdeg sing_94 7.htm#SEC10232475 maxdeg1 sing_94 8.htm#SEC10242461 maxcoef sing_947.htm#SEC1023 2462 maxdeg sing_948.htm#SEC1024 2463 maxdeg1 sing_949.htm#SEC1025 2476 2464 maxideal sing_285.htm#SEC325 2477 2465 maximalFace sing_2097.htm#SEC2173 … … 2479 2467 maximalValue sing_2098.htm#SEC2174 2480 2468 maximum sing_1857.htm#SEC1933 2481 maximum number of zeroes sing_1357.htm#IDX 6022469 maximum number of zeroes sing_1357.htm#IDX586 2482 2470 mdouble sing_56.htm#SEC93 2483 2471 mem, option sing_307.htm#IDX180 … … 2487 2475 merkle_hellman_decryption merkle_hellman_decryption sing_1918.htm#SEC1994 2488 2476 merkle_hellman_encryption merkle_hellman_encryption sing_1917.htm#SEC1993 2489 midpoint sing_235 3.htm#SEC24292477 midpoint sing_2352.htm#SEC2428 2490 2478 milnor sing_1593.htm#SEC1669 2491 2479 milnorcode sing_1477.htm#SEC1553 2492 milnornumber sing_249 1.htm#SEC25672480 milnornumber sing_2492.htm#SEC2568 2493 2481 min sing_287.htm#SEC327 2494 2482 minAssChar sing_1279.htm#SEC1355 … … 2498 2486 minAssZ sing_1297.htm#SEC1373 2499 2487 minEcart sing_1947.htm#SEC2023 2500 minIntRoot sing_55 3.htm#SEC6052501 minIntRoot2 sing_77 6.htm#SEC8282488 minIntRoot sing_554.htm#SEC606 2489 minIntRoot2 sing_777.htm#SEC829 2502 2490 minMult sing_1111.htm#SEC1187 2503 2491 minbase sing_288.htm#SEC328 2504 2492 minbaseMon sing_1177.htm#SEC1253 2505 mindeg sing_9 49.htm#SEC10252506 mindeg1 sing_95 0.htm#SEC10262493 mindeg sing_950.htm#SEC1026 2494 mindeg1 sing_951.htm#SEC1027 2507 2495 mindist sing_1802.htm#SEC1878 2508 minimal display time, setting the sing_3 49.htm#IDX2782496 minimal display time, setting the sing_350.htm#IDX280 2509 2497 minimalFace sing_2099.htm#SEC2175 2510 2498 minimalValue sing_2100.htm#SEC2176 … … 2512 2500 minkowskiSum sing_2101.htm#SEC2177 2513 2501 minor sing_289.htm#SEC329 2514 minpoly sing_38 8.htm#SEC4282502 minpoly sing_389.htm#SEC429 2515 2503 minres sing_290.htm#SEC330 2516 minres (plural) sing_4 59.htm#SEC4992517 mirror symmetry sing_1126.htm#IDX5 232518 mixed Hodge structure sing_1515.htm#IDX6 582519 mixed Hodge structure sing_1521.htm#IDX6 862520 mixed Hodge structure sing_1522.htm#IDX6 922521 mixed Hodge structure sing_1523.htm#IDX 7002522 mixed Hodge structure sing_1524.htm#IDX 7062523 mixed Hodge structure sing_1525.htm#IDX 7142524 mixed Hodge structure sing_1526.htm#IDX7 242525 mixed Hodge structure sing_1537.htm#IDX7 302526 mixed Hodge structure sing_1539.htm#IDX7 412504 minres (plural) sing_460.htm#SEC500 2505 mirror symmetry sing_1126.htm#IDX507 2506 mixed Hodge structure sing_1515.htm#IDX642 2507 mixed Hodge structure sing_1521.htm#IDX670 2508 mixed Hodge structure sing_1522.htm#IDX676 2509 mixed Hodge structure sing_1523.htm#IDX684 2510 mixed Hodge structure sing_1524.htm#IDX690 2511 mixed Hodge structure sing_1525.htm#IDX698 2512 mixed Hodge structure sing_1526.htm#IDX708 2513 mixed Hodge structure sing_1537.htm#IDX714 2514 mixed Hodge structure sing_1539.htm#IDX725 2527 2515 mod sing_76.htm#SEC116 2528 2516 mod sing_93.htm#SEC133 2529 2517 mod sing_142.htm#SEC182 2530 mod2id sing_95 4.htm#SEC10302531 mod2str sing_63 5.htm#SEC6872518 mod2id sing_955.htm#SEC1031 2519 mod2str sing_636.htm#SEC688 2532 2520 modDec sing_1196.htm#SEC1272 2533 2521 modNPos sing_1219.htm#SEC1295 … … 2535 2523 modNpos_test sing_1217.htm#SEC1293 2536 2524 modStd sing_1174.htm#SEC1250 2537 modVStd sing_230 7.htm#SEC23832538 modVStd0 sing_230 8.htm#SEC23842539 modWalk sing_24 20.htm#SEC24962525 modVStd sing_2306.htm#SEC2382 2526 modVStd0 sing_2307.htm#SEC2383 2527 modWalk sing_2419.htm#SEC2495 2540 2528 mod_versal sing_1506.htm#SEC1582 2541 2529 modality sing_1485.htm#SEC1561 2542 modfWalk sing_242 2.htm#SEC24982543 modfrWalk sing_242 3.htm#SEC24992530 modfWalk sing_2421.htm#SEC2497 2531 modfrWalk sing_2422.htm#SEC2498 2544 2532 modnormal.lib sing_1171.htm#SEC1247 2545 2533 modnormal_lib sing_1171.htm#SEC1247 2546 modrWalk sing_242 1.htm#SEC24972534 modrWalk sing_2420.htm#SEC2496 2547 2535 modregCM sing_1223.htm#SEC1299 2548 2536 modsatiety sing_1221.htm#SEC1297 2549 2537 modstd.lib sing_1173.htm#SEC1249 2550 2538 modstd_lib sing_1173.htm#SEC1249 2551 modular sing_93 2.htm#SEC10082552 modular methods sing_1169.htm#IDX5 562553 modular methods sing_1171.htm#IDX5 612554 modular methods. sing_1170.htm#IDX5 592555 modular techniques. sing_1172.htm#IDX5 632556 modular.lib sing_93 1.htm#SEC10072557 modular_lib sing_93 1.htm#SEC10072558 modular_lib sing_93 1.htm#IDX4872539 modular sing_933.htm#SEC1009 2540 modular methods sing_1169.htm#IDX540 2541 modular methods sing_1171.htm#IDX545 2542 modular methods. sing_1170.htm#IDX543 2543 modular techniques. sing_1172.htm#IDX547 2544 modular.lib sing_932.htm#SEC1008 2545 modular_lib sing_932.htm#SEC1008 2546 modular_lib sing_932.htm#IDX472 2559 2547 module sing_134.htm#SEC174 2560 module (plural) sing_42 5.htm#SEC4652548 module (plural) sing_426.htm#SEC466 2561 2549 module declarations sing_135.htm#SEC175 2562 module declarations (plural) module declarations (plural) sing_42 6.htm#SEC4662550 module declarations (plural) module declarations (plural) sing_427.htm#SEC467 2563 2551 module expressions sing_136.htm#SEC176 2564 module expressions (plural) module expressions (plural) sing_42 7.htm#SEC4672552 module expressions (plural) module expressions (plural) sing_428.htm#SEC468 2565 2553 module operations sing_137.htm#SEC177 2566 module operations (plural) module operations (plural) sing_42 8.htm#SEC4682567 module ordering C sing_84 0.htm#IDX4082568 module ordering c sing_84 0.htm#IDX4102554 module operations (plural) module operations (plural) sing_429.htm#SEC469 2555 module ordering C sing_841.htm#IDX410 2556 module ordering c sing_841.htm#IDX412 2569 2557 module related functions module related functions sing_138.htm#SEC178 2570 module related functions (plural) module related functions (plural) sing_4 29.htm#SEC4692558 module related functions (plural) module related functions (plural) sing_430.htm#SEC470 2571 2559 module_containment sing_1096.htm#SEC1172 2572 2560 modulo sing_291.htm#SEC331 2573 modulo (plural) sing_46 0.htm#SEC5002574 moduloSlim sing_71 8.htm#SEC7702575 modwalk.lib sing_241 9.htm#IDX9682576 modwalk_lib sing_241 9.htm#IDX9692561 modulo (plural) sing_461.htm#SEC501 2562 moduloSlim sing_719.htm#SEC771 2563 modwalk.lib sing_2418.htm#IDX953 2564 modwalk_lib sing_2418.htm#IDX954 2577 2565 moebius sing_2197.htm#SEC2273 2578 moebius function sing_2197.htm#IDX8 922566 moebius function sing_2197.htm#IDX876 2579 2567 molien sing_1629.htm#SEC1705 2580 2568 mondromy.lib sing_1567.htm#SEC1643 2581 2569 mondromy_lib sing_1567.htm#SEC1643 2582 2570 monitor sing_292.htm#SEC332 2583 monodromy sing_1515.htm#IDX6 622571 monodromy sing_1515.htm#IDX646 2584 2572 monodromy sing_1520.htm#SEC1596 2585 monodromy sing_1520.htm#IDX6 822586 monodromy sing_1525.htm#IDX7 172587 monodromy sing_1537.htm#IDX7 332588 monodromy sing_1539.htm#IDX7 442573 monodromy sing_1520.htm#IDX666 2574 monodromy sing_1525.htm#IDX701 2575 monodromy sing_1537.htm#IDX717 2576 monodromy sing_1539.htm#IDX728 2589 2577 monodromyB sing_1571.htm#SEC1647 2590 2578 monomial sing_293.htm#SEC333 2591 monomial ordering sing_99 7.htm#IDX5012592 monomial orderings General definitions for orderings sing_79 0.htm#SEC8422593 monomial orderings sing_83 7.htm#SEC8892594 monomial orderings introduction Introduction to orderings sing_83 6.htm#SEC8882595 monomialInIdeal sing_77 4.htm#SEC8262579 monomial ordering sing_998.htm#IDX486 2580 monomial orderings General definitions for orderings sing_791.htm#SEC843 2581 monomial orderings sing_838.htm#SEC890 2582 monomial orderings introduction Introduction to orderings sing_837.htm#SEC889 2583 monomialInIdeal sing_775.htm#SEC827 2596 2584 monomialLcm sing_1945.htm#SEC2021 2597 2585 monomialabortstd sing_2204.htm#SEC2280 2598 2586 monomialideal.lib sing_1175.htm#SEC1251 2599 2587 monomialideal_lib sing_1175.htm#SEC1251 2600 monomials and precedence Miscellaneous oddities sing_4 09.htm#IDX2842588 monomials and precedence Miscellaneous oddities sing_410.htm#IDX286 2601 2589 mons2intmat sing_1264.htm#SEC1340 15555 2602 2590 morsesplit sing_1478.htm#SEC1554 … … 2609 2597 mregular_lib sing_1207.htm#SEC1283 2610 2598 mres sing_295.htm#SEC335 2611 mres (plural) sing_46 1.htm#SEC5012599 mres (plural) sing_462.htm#SEC502 2612 2600 mstd sing_296.htm#SEC336 2613 2601 msum sing_58.htm#SEC95 2614 2602 mtriple sing_57.htm#SEC94 2615 2603 mult Miscellaneous oddities sing_297.htm#SEC337 2616 mult sing_4 09.htm#IDX2852617 multBound sing_3 89.htm#SEC4292618 multRat sing_78 2.htm#SEC8342604 mult sing_410.htm#IDX287 2605 multBound sing_390.htm#SEC430 2606 multRat sing_783.htm#SEC835 2619 2607 multarr2arr sing_2192.htm#SEC2268 2620 2608 multarrMultRestrict sing_2194.htm#SEC2270 2621 2609 multarrRestrict sing_2193.htm#SEC2269 2622 2610 multcol sing_1050.htm#SEC1126 2623 multdivisor sing_231 9.htm#SEC23952624 multformaldivisor sing_233 1.htm#SEC24072611 multdivisor sing_2318.htm#SEC2394 2612 multformaldivisor sing_2330.htm#SEC2406 2625 2613 multi sing_1932.htm#SEC2008 2626 2614 multi indices sing_37.htm#SEC65 2627 multiDeg sing_245 4.htm#SEC25302628 multiDegBasis sing_245 5.htm#SEC25312629 multiDegGroebner sing_246 3.htm#SEC25392630 multiDegModulo sing_246 5.htm#SEC25412631 multiDegPartition sing_245 6.htm#SEC25322632 multiDegResolution sing_246 6.htm#SEC25422633 multiDegSyzygy sing_246 4.htm#SEC25402634 multiDegTensor sing_246 7.htm#SEC25432635 multiDegTor sing_246 8.htm#SEC25442636 multiarrangement sing_2188.htm#IDX8 722637 multiarrangement sing_2189.htm#IDX8 742638 multiarrangement sing_2190.htm#IDX8 772639 multiarrangement sing_2191.htm#IDX8 782640 multiarrangement sing_2192.htm#IDX8 812641 multiarrangement sing_2193.htm#IDX8 842642 multiarrangement sing_2194.htm#IDX8 862615 multiDeg sing_2453.htm#SEC2529 2616 multiDegBasis sing_2454.htm#SEC2530 2617 multiDegGroebner sing_2462.htm#SEC2538 2618 multiDegModulo sing_2464.htm#SEC2540 2619 multiDegPartition sing_2455.htm#SEC2531 2620 multiDegResolution sing_2465.htm#SEC2541 2621 multiDegSyzygy sing_2463.htm#SEC2539 2622 multiDegTensor sing_2466.htm#SEC2542 2623 multiDegTor sing_2467.htm#SEC2543 2624 multiarrangement sing_2188.htm#IDX856 2625 multiarrangement sing_2189.htm#IDX858 2626 multiarrangement sing_2190.htm#IDX861 2627 multiarrangement sing_2191.htm#IDX862 2628 multiarrangement sing_2192.htm#IDX865 2629 multiarrangement sing_2193.htm#IDX868 2630 multiarrangement sing_2194.htm#IDX870 2643 2631 multidimensional_knapsack multidimensional_knapsack sing_1910.htm#SEC1986 2644 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_242 4.htm#IDX9742645 multigrading.lib sing_242 4.htm#IDX9722646 multigrading_lib sing_242 4.htm#IDX9732647 multiplicities, sequence of sing_1546.htm#IDX7 562648 multiplicity sing_231 3.htm#IDX9332649 multiplicity sequence sing_1459.htm#IDX6 352650 multiplicity sequence sing_1462.htm#IDX6 472651 multiplicity sequence sing_1548.htm#IDX7 572632 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2423.htm#IDX959 2633 multigrading.lib sing_2423.htm#IDX957 2634 multigrading_lib sing_2423.htm#IDX958 2635 multiplicities, sequence of sing_1546.htm#IDX740 2636 multiplicity sing_2312.htm#IDX918 2637 multiplicity sequence sing_1459.htm#IDX619 2638 multiplicity sequence sing_1462.htm#IDX631 2639 multiplicity sequence sing_1548.htm#IDX741 2652 2640 multiplylist sing_1399.htm#SEC1475 2653 multivariate equations sing_1685.htm#IDX7 742641 multivariate equations sing_1685.htm#IDX758 2654 2642 multrow sing_1051.htm#SEC1127 2655 2643 multseq2charexp sing_1458.htm#SEC1534 … … 2665 2653 names sing_299.htm#SEC339 2666 2654 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 2655 nblocks sing_350.htm#IDX220 2656 ncExt_R sing_752.htm#SEC804 2657 ncHilb.lib sing_2475.htm#SEC2551 2658 ncHilb_lib sing_2475.htm#SEC2551 2659 ncHom sing_753.htm#SEC805 2660 ncRelations sing_720.htm#SEC772 2661 nc_algebra sing_463.htm#SEC503 2662 nc_hilb sing_350.htm#IDX222 2663 ncalg.lib sing_653.htm#SEC705 2664 ncalg_lib sing_653.htm#SEC705 2665 ncalgebra sing_464.htm#SEC504 2666 ncdecomp.lib sing_680.htm#SEC732 2667 ncdecomp_lib sing_680.htm#SEC732 2668 ncdetection sing_647.htm#SEC699 2669 ncfactor sing_686.htm#SEC738 2670 ncfactor.lib sing_685.htm#SEC737 2671 ncfactor_lib sing_685.htm#SEC737 2672 nchilb sing_2476.htm#SEC2552 2673 nchomolog.lib sing_751.htm#IDX369 2674 nchomolog_lib sing_751.htm#IDX370 2683 2675 ncols sing_300.htm#SEC340 2684 2676 ncones sing_2047.htm#SEC2123 2685 ncpreim.lib sing_69 7.htm#SEC7492686 ncpreim_lib sing_69 7.htm#SEC7492687 nctools.lib sing_70 5.htm#SEC7572688 nctools_lib sing_70 5.htm#SEC7572689 ndcond sing_70 8.htm#SEC7602677 ncpreim.lib sing_698.htm#SEC750 2678 ncpreim_lib sing_698.htm#SEC750 2679 nctools.lib sing_706.htm#SEC758 2680 nctools_lib sing_706.htm#SEC758 2681 ndcond sing_709.htm#SEC761 2690 2682 negatedCone sing_2025.htm#SEC2101 2691 negative degree lexicographical ordering sing_8 39.htm#IDX3992692 negative degree reverse lexicographical ordering Local orderings sing_8 39.htm#IDX3972693 negative lexicographical ordering sing_8 39.htm#IDX3952694 negativedivisor sing_23 20.htm#SEC23962695 negativeformaldivisor negativeformaldivisor sing_23 30.htm#SEC24062683 negative degree lexicographical ordering sing_840.htm#IDX401 2684 negative degree reverse lexicographical ordering Local orderings sing_840.htm#IDX399 2685 negative lexicographical ordering sing_840.htm#IDX397 2686 negativedivisor sing_2319.htm#SEC2395 2687 negativeformaldivisor negativeformaldivisor sing_2329.htm#SEC2405 2696 2688 net access Command line options sing_19.htm#IDX40 2697 2689 newTest sing_1852.htm#SEC1928 2698 2690 newline sing_166.htm#SEC206 2699 news sing_249 7.htm#SEC25732691 news sing_2498.htm#SEC2574 2700 2692 newstruct sing_177.htm#SEC217 2701 newstruct sing_2211.htm#IDX 9082702 newtonDiag sing_95 8.htm#SEC10342693 newstruct sing_2211.htm#IDX892 2694 newtonDiag sing_959.htm#SEC1035 2703 2695 newtonPolytope sing_2051.htm#SEC2127 2704 2696 newtonPolytopeLP sing_2056.htm#SEC2132 … … 2706 2698 newtonpoly sing_1553.htm#SEC1629 2707 2699 nf_icis sing_1594.htm#SEC1670 2708 nfmodStd sing_247 8.htm#SEC25542709 nfmodSyz sing_248 0.htm#SEC25562710 nfmodstd.lib sing_247 6.htm#SEC25522711 nfmodstd_lib sing_247 6.htm#SEC25522712 nfmodsyz.lib sing_24 79.htm#SEC25552713 nfmodsyz_lib sing_24 79.htm#SEC25552714 nilpotent Lie algebras sing_1352.htm#IDX5 872700 nfmodStd sing_2479.htm#SEC2555 2701 nfmodSyz sing_2481.htm#SEC2557 2702 nfmodstd.lib sing_2477.htm#SEC2553 2703 nfmodstd_lib sing_2477.htm#SEC2553 2704 nfmodsyz.lib sing_2480.htm#SEC2556 2705 nfmodsyz_lib sing_2480.htm#SEC2556 2706 nilpotent Lie algebras sing_1352.htm#IDX571 2715 2707 nmaxcones sing_2046.htm#SEC2122 2716 noether sing_39 0.htm#SEC4302708 noether sing_391.htm#SEC431 2717 2709 noether.lib sing_1215.htm#SEC1291 2718 2710 noetherNormal sing_1103.htm#SEC1179 2719 2711 noether_lib sing_1215.htm#SEC1291 2720 non-english special characters sing_39 8.htm#IDX2802712 non-english special characters sing_399.htm#IDX282 2721 2713 nonMonomials sing_1268.htm#SEC1344 2722 2714 nonZeroEntry sing_1106.htm#SEC1182 … … 2730 2722 normalFan sing_2106.htm#SEC2182 2731 2723 normalFanL sing_2057.htm#SEC2133 2732 normalForm sing_232 1.htm#SEC23972724 normalForm sing_2320.htm#SEC2396 2733 2725 normalI sing_1312.htm#SEC1388 2734 2726 normalP sing_1226.htm#SEC1302 … … 2737 2729 normal_lib sing_1224.htm#SEC1300 2738 2730 normalform sing_1482.htm#SEC1558 2731 normalform sing_2301.htm#IDX911 2739 2732 normaliz sing_1.htm#IDX14 18426 2740 2733 normaliz sing_1255.htm#SEC1331 2741 2734 normaliz.lib sing_1240.htm#SEC1316 2742 2735 normaliz_lib sing_1240.htm#SEC1316 2743 normalization sing_1169.htm#IDX5 542744 normalization sing_1170.htm#IDX5 572745 normalization sing_1171.htm#IDX5 602746 normalization sing_1172.htm#IDX5 622747 normalization sing_1225.htm#IDX5 642748 normalization sing_1226.htm#IDX5 672749 normalization sing_1227.htm#IDX5 702750 normalization sing_1239.htm#IDX5 762751 normalization sing_1240.htm#IDX5 782752 normalization sing_231 2.htm#IDX9312753 normalization. sing_1166.htm#IDX5 532754 normalization. sing_1359.htm#IDX 6092755 normalize sing_95 1.htm#SEC10272736 normalization sing_1169.htm#IDX538 2737 normalization sing_1170.htm#IDX541 2738 normalization sing_1171.htm#IDX544 2739 normalization sing_1172.htm#IDX546 2740 normalization sing_1225.htm#IDX548 2741 normalization sing_1226.htm#IDX551 2742 normalization sing_1227.htm#IDX554 2743 normalization sing_1239.htm#IDX560 2744 normalization sing_1240.htm#IDX562 2745 normalization sing_2311.htm#IDX916 2746 normalization. sing_1166.htm#IDX537 2747 normalization. sing_1359.htm#IDX593 2748 normalize sing_952.htm#SEC1028 2756 2749 not sing_96.htm#SEC136 2757 2750 notBuckets, option sing_307.htm#IDX160 … … 2764 2757 nrRootsProbab sing_1961.htm#SEC2037 2765 2758 nres sing_302.htm#SEC342 2766 nres (plural) sing_46 4.htm#SEC5042759 nres (plural) sing_465.htm#SEC505 2767 2760 nrows sing_303.htm#SEC343 2768 2761 nrroots sing_1991.htm#SEC2067 … … 2773 2766 ntsolve_lib sing_1725.htm#SEC1801 2774 2767 number sing_139.htm#SEC179 2775 number sing_2165.htm#IDX8 322768 number sing_2165.htm#IDX816 2776 2769 number declarations sing_140.htm#SEC180 2777 2770 number expressions sing_141.htm#SEC181 … … 2779 2772 number related functions number related functions sing_143.htm#SEC183 2780 2773 numberOfConesOfDimension numberOfConesOfDimension sing_2048.htm#SEC2124 2781 number_e sing_8 89.htm#SEC9652782 number_pi sing_89 0.htm#SEC9662783 numerAlg.lib sing_1334.htm#IDX5 832784 numerAlg_lib sing_1334.htm#IDX5 842785 numerDecom.lib sing_1339.htm#IDX5 852786 numerDecom_lib sing_1339.htm#IDX5 862774 number_e sing_890.htm#SEC966 2775 number_pi sing_891.htm#SEC967 2776 numerAlg.lib sing_1334.htm#IDX567 2777 numerAlg_lib sing_1334.htm#IDX568 2778 numerDecom.lib sing_1339.htm#IDX569 2779 numerDecom_lib sing_1339.htm#IDX570 2787 2780 numerator sing_304.htm#SEC344 2788 2781 nvars sing_305.htm#SEC345 … … 2791 2784 open sing_306.htm#SEC346 2792 2785 opentex sing_1754.htm#SEC1830 2793 operatorBM sing_5 39.htm#SEC5912794 operatorModulo sing_54 0.htm#SEC5922795 oppose sing_46 5.htm#SEC5052796 opposite sing_46 6.htm#SEC5062797 opposite polynomial sing_3 49.htm#IDX2272798 opposite ring sing_3 49.htm#IDX2242786 operatorBM sing_540.htm#SEC592 2787 operatorModulo sing_541.htm#SEC593 2788 oppose sing_466.htm#SEC506 2789 opposite sing_467.htm#SEC507 2790 opposite polynomial sing_350.htm#IDX229 2791 opposite ring sing_350.htm#IDX226 2799 2792 option sing_307.htm#SEC347 2800 2793 option(warn) sing_70.htm#SEC110 2801 optionIsSet sing_99 4.htm#SEC10702794 optionIsSet sing_995.htm#SEC1071 2802 2795 or Evaluation of logical expressions sing_96.htm#SEC136 2803 or sing_40 2.htm#SEC4422804 orbit sing_1352.htm#IDX5 892805 orbit sing_1353.htm#IDX5 932806 orbit sing_1356.htm#IDX5 982807 orbit sing_1357.htm#IDX 6012808 orbitCones sing_237 9.htm#SEC24552796 or sing_403.htm#SEC443 2797 orbit sing_1352.htm#IDX573 2798 orbit sing_1353.htm#IDX577 2799 orbit sing_1356.htm#IDX582 2800 orbit sing_1357.htm#IDX585 2801 orbitCones sing_2378.htm#SEC2454 2809 2802 orbit_variety sing_1653.htm#SEC1729 2810 2803 orbitparam.lib sing_1352.htm#SEC1428 2811 2804 orbitparam_lib sing_1352.htm#SEC1428 2812 2805 ord sing_308.htm#SEC348 2813 ord_test sing_9 89.htm#SEC10652814 orderings General definitions for orderings sing_83 7.htm#SEC8892815 orderings introduction Introduction to orderings sing_83 6.htm#SEC8882816 orderings, M sing_84 1.htm#SEC8932817 orderings, a sing_84 3.htm#SEC8952818 orderings, global sing_83 8.htm#SEC8902819 orderings, local sing_8 39.htm#SEC8912820 orderings, product sing_84 2.htm#SEC8942806 ord_test sing_990.htm#SEC1066 2807 orderings General definitions for orderings sing_838.htm#SEC890 2808 orderings introduction Introduction to orderings sing_837.htm#SEC889 2809 orderings, M sing_842.htm#SEC894 2810 orderings, a sing_844.htm#SEC896 2811 orderings, global sing_839.htm#SEC891 2812 orderings, local sing_840.htm#SEC892 2813 orderings, product sing_843.htm#SEC895 2821 2814 ordstr sing_309.htm#SEC349 2822 2815 origin sing_1996.htm#SEC2072 … … 2826 2819 p-adic numbers sing_32.htm#SEC46 2827 2820 pFactor sing_1886.htm#SEC1962 2828 pIntersect sing_50 3.htm#SEC5552829 pIntersectSyz sing_50 4.htm#SEC5562821 pIntersect sing_504.htm#SEC556 2822 pIntersectSyz sing_505.htm#SEC557 2830 2823 package sing_144.htm#SEC184 2831 2824 package declarations package declarations sing_145.htm#SEC185 … … 2833 2826 pairset sing_1951.htm#SEC2027 2834 2827 par sing_310.htm#SEC350 2835 par2varRing sing_87 3.htm#SEC9492828 par2varRing sing_874.htm#SEC950 2836 2829 paraConic sing_1367.htm#SEC1443 2837 2830 paraPlaneCurve sing_1361.htm#SEC1437 2838 parallel skeletons sing_93 3.htm#IDX4932839 parallel.lib sing_93 3.htm#SEC10092840 parallelTestAND sing_93 7.htm#SEC10132841 parallelTestOR sing_93 8.htm#SEC10142842 parallelWaitAll sing_93 6.htm#SEC10122843 parallelWaitFirst sing_93 5.htm#SEC10112844 parallelWaitN sing_93 4.htm#SEC10102845 parallel_lib sing_93 3.htm#SEC10092846 parallelization sing_93 3.htm#IDX4922847 parallelization sing_97 3.htm#IDX4952848 parallelization sing_1015.htm#IDX 5092831 parallel skeletons sing_934.htm#IDX478 2832 parallel.lib sing_934.htm#SEC1010 2833 parallelTestAND sing_938.htm#SEC1014 2834 parallelTestOR sing_939.htm#SEC1015 2835 parallelWaitAll sing_937.htm#SEC1013 2836 parallelWaitFirst sing_936.htm#SEC1012 2837 parallelWaitN sing_935.htm#SEC1011 2838 parallel_lib sing_934.htm#SEC1010 2839 parallelization sing_934.htm#IDX477 2840 parallelization sing_974.htm#IDX480 2841 parallelization sing_1015.htm#IDX493 2849 2842 param sing_1544.htm#SEC1620 2850 2843 parameter, as numbers sing_139.htm#SEC179 2851 2844 parameterSubstitute sing_2146.htm#SEC2222 2852 parametric annihilator sing_53 2.htm#IDX3292853 parametric annihilator for variety sing_58 8.htm#IDX3522854 parametric ideal sing_90 2.htm#IDX4202855 parametric ideal sing_9 09.htm#IDX4372856 parametric ideal sing_9 09.htm#IDX4392857 parametric ideal sing_91 0.htm#IDX4442858 parametrization sing_1352.htm#IDX5 902859 parametrization sing_1356.htm#IDX5 992860 parametrization sing_1544.htm#IDX7 512845 parametric annihilator sing_533.htm#IDX331 2846 parametric annihilator for variety sing_589.htm#IDX354 2847 parametric ideal sing_903.htm#IDX421 2848 parametric ideal sing_910.htm#IDX434 2849 parametric ideal sing_910.htm#IDX436 2850 parametric ideal sing_911.htm#IDX440 2851 parametrization sing_1352.htm#IDX574 2852 parametrization sing_1356.htm#IDX583 2853 parametrization sing_1544.htm#IDX735 2861 2854 parametrizeOrbit sing_1356.htm#SEC1432 2862 2855 paraplanecurves.lib sing_1358.htm#SEC1434 … … 2869 2862 partial_molien sing_1631.htm#SEC1707 2870 2863 partitions sing_1134.htm#SEC1210 2871 partitions sing_1134.htm#IDX5 422872 path integral sing_1126.htm#IDX5 292873 pause sing_93 0.htm#SEC10062874 pdivi sing_90 4.htm#SEC9802875 pdivi sing_90 5.htm#IDX4332876 pdivisorplus sing_233 5.htm#SEC24112864 partitions sing_1134.htm#IDX526 2865 path integral sing_1126.htm#IDX513 2866 pause sing_931.htm#SEC1007 2867 pdivi sing_905.htm#SEC981 2868 pdivi sing_906.htm#IDX431 2869 pdivisorplus sing_2334.htm#SEC2410 2877 2870 permcol sing_1052.htm#SEC1128 2878 2871 permrow sing_1053.htm#SEC1129 2879 permutations sing_1135.htm#IDX5 432872 permutations sing_1135.htm#IDX527 2880 2873 permute sing_1135.htm#SEC1211 2881 2874 permute_L sing_1789.htm#SEC1865 2882 perron sing_73 1.htm#SEC7832883 perron.lib sing_73 0.htm#SEC7822884 perron_lib sing_73 0.htm#SEC7822885 phindex.lib sing_2206.htm#IDX8 992886 phindex_lib sing_2206.htm#IDX 9002875 perron sing_732.htm#SEC784 2876 perron.lib sing_731.htm#SEC783 2877 perron_lib sing_731.htm#SEC783 2878 phindex.lib sing_2206.htm#IDX883 2879 phindex_lib sing_2206.htm#IDX884 2887 2880 picksFormula sing_2068.htm#SEC2144 2888 pid sing_3 49.htm#IDX2362881 pid sing_350.htm#IDX238 2889 2882 plainInvariants sing_1503.htm#SEC1579 2890 2883 planeCur sing_2299.htm#SEC2375 … … 2895 2888 plotRotatedList sing_1772.htm#SEC1848 2896 2889 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1774.htm#SEC1850 2897 plural sing_99 6.htm#IDX5002898 pmat sing_92 4.htm#SEC10002899 pnormalf sing_90 5.htm#SEC9812890 plural sing_997.htm#IDX485 2891 pmat sing_925.htm#SEC1001 2892 pnormalf sing_906.htm#SEC982 2900 2893 pointid.lib sing_1267.htm#SEC1343 2901 2894 pointid_lib sing_1267.htm#SEC1343 2902 polSol sing_76 6.htm#SEC8182903 polSolFiniteRank sing_76 7.htm#SEC8192895 polSol sing_767.htm#SEC819 2896 polSolFiniteRank sing_768.htm#SEC820 2904 2897 pollTask sing_1025.htm#SEC1101 2905 2898 poly sing_147.htm#SEC187 2906 poly (plural) sing_43 0.htm#SEC4702899 poly (plural) sing_431.htm#SEC471 2907 2900 poly declarations sing_148.htm#SEC188 2908 poly declarations (plural) poly declarations (plural) sing_43 1.htm#SEC4712901 poly declarations (plural) poly declarations (plural) sing_432.htm#SEC472 2909 2902 poly expressions sing_149.htm#SEC189 2910 poly expressions (plural) poly expressions (plural) sing_43 2.htm#SEC4722903 poly expressions (plural) poly expressions (plural) sing_433.htm#SEC473 2911 2904 poly operations sing_150.htm#SEC190 2912 poly operations (plural) poly operations (plural) sing_43 3.htm#SEC4732905 poly operations (plural) poly operations (plural) sing_434.htm#SEC474 2913 2906 poly related functions poly related functions sing_151.htm#SEC191 2914 poly related functions (plural) poly related functions (plural) sing_43 4.htm#SEC4742915 poly.lib sing_9 39.htm#SEC10152916 poly2list sing_58 1.htm#SEC6332907 poly related functions (plural) poly related functions (plural) sing_435.htm#SEC475 2908 poly.lib sing_940.htm#SEC1016 2909 poly2list sing_582.htm#SEC634 2917 2910 poly2zdd sing_2227.htm#SEC2303 61839 2918 polyInterpolation sing_233 8.htm#SEC24142919 polyVars sing_77 3.htm#SEC8252920 poly_lib sing_9 39.htm#SEC10152921 polybori sing_2211.htm#IDX 9042922 polybori.lib sing_2211.htm#IDX 9012923 polybori.lib sing_2211.htm#IDX 9052924 polybori_lib sing_2211.htm#IDX 9022925 polymake sing_2053.htm#IDX 8052911 polyInterpolation sing_2337.htm#SEC2413 2912 polyVars sing_774.htm#SEC826 2913 poly_lib sing_940.htm#SEC1016 2914 polybori sing_2211.htm#IDX888 2915 polybori.lib sing_2211.htm#IDX885 2916 polybori.lib sing_2211.htm#IDX889 2917 polybori_lib sing_2211.htm#IDX886 2918 polymake sing_2053.htm#IDX789 2926 2919 polymake.lib sing_2053.htm#SEC2129 2927 2920 polymakePolytope sing_2054.htm#SEC2130 2928 2921 polymake_lib sing_2053.htm#SEC2129 2929 polynomial solutions sing_76 0.htm#IDX3802930 polynomial, opposite sing_3 49.htm#IDX2282922 polynomial solutions sing_761.htm#IDX382 2923 polynomial, opposite sing_350.htm#IDX230 2931 2924 polytope sing_185.htm#SEC225 2932 polytope sing_2053.htm#IDX 8012925 polytope sing_2053.htm#IDX785 2933 2926 polytopeViaInequalities polytopeViaInequalities sing_2026.htm#SEC2102 2934 2927 polytopeViaPoints sing_2027.htm#SEC2103 2935 2928 pos_def sing_1080.htm#SEC1156 2936 poset sing_2196.htm#IDX8 902929 poset sing_2196.htm#IDX874 2937 2930 positiveOrthant sing_1997.htm#SEC2073 2938 2931 posweight sing_1611.htm#SEC1687 … … 2946 2939 preComp sing_1203.htm#SEC1279 2947 2940 preimage sing_313.htm#SEC353 2948 preimage sing_69 7.htm#IDX3552949 preimage (plural) sing_46 7.htm#SEC5072950 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_99 2.htm#IDX4982951 preimageLattice sing_244 4.htm#SEC25202952 preimageLoc sing_99 2.htm#SEC10682953 preimageNC sing_ 699.htm#SEC7512941 preimage sing_698.htm#IDX357 2942 preimage (plural) sing_468.htm#SEC508 2943 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_993.htm#IDX483 2944 preimageLattice sing_2443.htm#SEC2519 2945 preimageLoc sing_993.htm#SEC1069 2946 preimageNC sing_700.htm#SEC752 2954 2947 prepEmbDiv sing_1429.htm#SEC1505 2955 2948 prepMat sing_1682.htm#SEC1758 … … 2989 2982 prime sing_314.htm#SEC354 2990 2983 primeClosure sing_1230.htm#SEC1306 2991 primecoeffs sing_89 6.htm#SEC9722984 primecoeffs sing_897.htm#SEC973 2992 2985 primefactors sing_315.htm#SEC355 2993 primes sing_89 1.htm#SEC9672986 primes sing_892.htm#SEC968 2994 2987 primitiv.lib sing_1302.htm#SEC1378 2995 2988 primitiv_lib sing_1302.htm#SEC1378 2996 2989 primitive sing_1303.htm#SEC1379 2997 primitive element sing_1303.htm#IDX5 802998 primitiveSpan sing_245 1.htm#SEC25272990 primitive element sing_1303.htm#IDX564 2991 primitiveSpan sing_2450.htm#SEC2526 2999 2992 primitive_extra sing_1304.htm#SEC1380 3000 2993 primparam sing_1498.htm#SEC1574 3001 principal intersection sing_49 7.htm#IDX3132994 principal intersection sing_498.htm#IDX315 3002 2995 print sing_316.htm#SEC356 3003 print sing_2163.htm#IDX8 252996 print sing_2163.htm#IDX809 3004 2997 printGraph sing_1128.htm#SEC1204 3005 printGroup sing_243 2.htm#SEC25082998 printGroup sing_2431.htm#SEC2507 3006 2999 printMoebius sing_2202.htm#SEC2278 3007 3000 printTask sing_1020.htm#SEC1096 3008 3001 printf sing_317.htm#SEC357 3009 printlevel sing_39 1.htm#SEC4313002 printlevel sing_392.htm#SEC432 3010 3003 proc sing_152.htm#SEC192 3011 3004 proc declaration sing_153.htm#SEC193 … … 3018 3011 procs with different argument types procs with different argument types sing_155.htm#SEC195 3019 3012 prodcrit sing_1949.htm#SEC2025 3020 product sing_89 2.htm#SEC9683021 productgroup sing_245 3.htm#SEC25293013 product sing_893.htm#SEC969 3014 productgroup sing_2452.htm#SEC2528 3022 3015 progress watch sing_307.htm#IDX163 3023 projectLattice sing_244 5.htm#SEC25213024 projective dimension purityfiltration_lib sing_73 8.htm#IDX3643016 projectLattice sing_2444.htm#SEC2520 3017 projective dimension purityfiltration_lib sing_739.htm#IDX366 3025 3018 projective limes sing_32.htm#SEC46 3026 projectiveDimension sing_7 39.htm#SEC7913019 projectiveDimension sing_740.htm#SEC792 3027 3020 prompt sing_15.htm#SEC21 3028 3021 prompt, option sing_307.htm#IDX182 3029 propagator sing_1126.htm#IDX5 273022 propagator sing_1126.htm#IDX511 3030 3023 propagator sing_1129.htm#SEC1205 3031 3024 prot, option sing_307.htm#IDX161 … … 3033 3026 proximitymatrix sing_1457.htm#SEC1533 3034 3027 prune sing_318.htm#SEC358 3035 prwalk sing_248 2.htm#SEC25583028 prwalk sing_2483.htm#SEC2559 3036 3029 psigncnd sing_1745.htm#SEC1821 3037 3030 puiseux2generators sing_1556.htm#SEC1632 3038 3031 puiseuxExpansion sing_2117.htm#SEC2193 3039 pure tensor sing_49 0.htm#IDX3013040 purelist sing_7 49.htm#SEC8013041 purity purityfiltration_lib sing_73 8.htm#IDX3663042 purityFiltration sing_74 0.htm#SEC7923043 purityTriang sing_74 1.htm#SEC7933044 purityfiltration.lib purityfiltration_lib sing_73 8.htm#IDX3593045 purityfiltration_lib purityfiltration_lib sing_73 8.htm#IDX3603046 pushForward sing_24 70.htm#SEC25463032 pure tensor sing_491.htm#IDX303 3033 purelist sing_750.htm#SEC802 3034 purity purityfiltration_lib sing_739.htm#IDX368 3035 purityFiltration sing_741.htm#SEC793 3036 purityTriang sing_742.htm#SEC794 3037 purityfiltration.lib purityfiltration_lib sing_739.htm#IDX361 3038 purityfiltration_lib purityfiltration_lib sing_739.htm#IDX362 3039 pushForward sing_2469.htm#SEC2545 3047 3040 pwalk sing_1142.htm#SEC1218 3048 3041 pyobject sing_186.htm#SEC226 3049 pyobject sing_2211.htm#IDX 9073042 pyobject sing_2211.htm#IDX891 3050 3043 pyobject declarations pyobject declarations sing_187.htm#SEC227 3051 3044 pyobject expressions pyobject expressions sing_188.htm#SEC228 3052 3045 pyobject operations sing_189.htm#SEC229 3053 3046 pyobject related functions pyobject related functions sing_190.htm#SEC230 3054 pyramid sing_235 4.htm#SEC24303047 pyramid sing_2353.htm#SEC2429 3055 3048 python_eval sing_191.htm#SEC231 3056 3049 python_import sing_192.htm#SEC232 3057 3050 python_run sing_193.htm#SEC233 3058 3051 qbase sing_1975.htm#SEC2051 3059 qepcad sing_236 4.htm#SEC24403060 qepcadsystem sing_236 5.htm#SEC24413052 qepcad sing_2363.htm#SEC2439 3053 qepcadsystem sing_2364.htm#SEC2440 3061 3054 qhmatrix sing_1609.htm#SEC1685 3062 3055 qhmoduli.lib sing_1573.htm#SEC1649 … … 3064 3057 qhspectrum sing_1596.htm#SEC1672 3065 3058 qhweight sing_319.htm#SEC359 3066 qmatrix.lib sing_73 2.htm#SEC7843067 qmatrix_lib sing_73 2.htm#SEC7843068 qminor sing_73 4.htm#SEC7863059 qmatrix.lib sing_733.htm#SEC785 3060 qmatrix_lib sing_733.htm#SEC785 3061 qminor sing_735.htm#SEC787 3069 3062 qrds sing_320.htm#SEC360 3070 3063 qring Miscellaneous oddities sing_161.htm#SEC201 3071 qring sing_4 09.htm#IDX2893072 qring (plural) sing_43 5.htm#SEC4753064 qring sing_410.htm#IDX291 3065 qring (plural) sing_436.htm#SEC476 3073 3066 qring declaration sing_165.htm#SEC205 3074 qring declaration (plural) qring declaration (plural) sing_43 6.htm#SEC4763075 qring related functions (plural) qring related functions (plural) sing_43 7.htm#SEC4773076 qring ring ideal 'factor ring' sing_1002.htm#IDX 5053067 qring declaration (plural) qring declaration (plural) sing_437.htm#SEC477 3068 qring related functions (plural) qring related functions (plural) sing_438.htm#SEC478 3069 qring ring ideal 'factor ring' sing_1002.htm#IDX489 3077 3070 qringNF, option sing_307.htm#IDX164 3078 qslimgb sing_87 2.htm#SEC9483071 qslimgb sing_873.htm#SEC949 3079 3072 quadraticSieve sing_1887.htm#SEC1963 3080 quantMat sing_73 3.htm#SEC7853073 quantMat sing_734.htm#SEC786 3081 3074 quickclass sing_1479.htm#SEC1555 3082 quit sing_38 1.htm#SEC4213075 quit sing_382.htm#SEC422 3083 3076 quote sing_321.htm#SEC361 3084 3077 quotient sing_322.htm#SEC362 3085 quotient (plural) sing_46 8.htm#SEC5083078 quotient (plural) sing_469.htm#SEC509 3086 3079 quotientLatticeBasis quotientLatticeBasis sing_2028.htm#SEC2104 3087 3080 quotientMain sing_1737.htm#SEC1813 3088 3081 quotientMon sing_1182.htm#SEC1258 3089 quotients sing_237 3.htm#IDX9643082 quotients sing_2372.htm#IDX949 3090 3083 rHRR sing_2282.htm#SEC2358 3091 rMacaulay sing_92 5.htm#SEC10013092 rad_con sing_95 2.htm#SEC10283084 rMacaulay sing_926.htm#SEC1002 3085 rad_con sing_953.htm#SEC1029 3093 3086 radical sing_1283.htm#SEC1359 3094 3087 radicalEHV sing_1284.htm#SEC1360 … … 3099 3092 randlinpoly sing_1971.htm#SEC2047 3100 3093 random sing_323.htm#SEC363 3101 random sing_3 49.htm#IDX2403102 random sing_2184.htm#IDX8 643103 random sing_2185.htm#IDX8 663104 random number generator, seed sing_3 49.htm#IDX2383105 random.lib sing_96 0.htm#SEC10363106 randomBinomial sing_97 2.htm#SEC10483094 random sing_350.htm#IDX242 3095 random sing_2184.htm#IDX848 3096 random sing_2185.htm#IDX850 3097 random number generator, seed sing_350.htm#IDX240 3098 random.lib sing_961.htm#SEC1037 3099 randomBinomial sing_973.htm#SEC1049 3107 3100 randomCheck sing_1800.htm#SEC1876 3108 randomLast sing_97 1.htm#SEC10473101 randomLast sing_972.htm#SEC1048 3109 3102 randomPoint sing_2029.htm#SEC2105 3110 3103 randomPolyInT sing_2148.htm#SEC2224 3111 random_lib sing_96 0.htm#SEC10363112 randomid sing_96 2.htm#SEC10383113 randommat sing_96 3.htm#SEC10393104 random_lib sing_961.htm#SEC1037 3105 randomid sing_963.htm#SEC1039 3106 randommat sing_964.htm#SEC1040 3114 3107 rank sing_204.htm#IDX137 3115 3108 rank sing_324.htm#SEC364 3116 ratSol sing_76 8.htm#SEC8203117 ratgb.lib sing_75 8.htm#IDX3693118 ratgb_lib sing_75 8.htm#IDX3703119 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1361.htm#IDX 6113120 rational normal curve, projection. sing_1362.htm#IDX 6123121 rational normal curve, projection. sing_1365.htm#IDX 6133122 rational normal curve, projection. sing_1366.htm#IDX 6143123 rational solutions sing_76 0.htm#IDX3813124 rational univariate projection sing_1969.htm#IDX7 983109 ratSol sing_769.htm#SEC821 3110 ratgb.lib sing_759.htm#IDX371 3111 ratgb_lib sing_759.htm#IDX372 3112 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1361.htm#IDX595 3113 rational normal curve, projection. sing_1362.htm#IDX596 3114 rational normal curve, projection. sing_1365.htm#IDX597 3115 rational normal curve, projection. sing_1366.htm#IDX598 3116 rational solutions sing_761.htm#IDX383 3117 rational univariate projection sing_1969.htm#IDX782 3125 3118 rationalPointConic sing_1363.htm#SEC1439 3126 ratstd sing_7 59.htm#SEC8113119 ratstd sing_760.htm#SEC812 3127 3120 rays sing_2030.htm#SEC2106 3128 3121 re2squ sing_1340.htm#SEC1416 … … 3132 3125 readline sing_1.htm#IDX5 3133 3126 real sing_28.htm#IDX74 3134 real roots, univariate polynomial sing_1976.htm#IDX 8003135 real roots, univariate projection sing_1960.htm#IDX7 963136 real roots,sign conditions sing_1743.htm#IDX7 763137 realclassify sing_24 89.htm#SEC25653138 realclassify.lib sing_248 8.htm#SEC25643139 realclassify_lib sing_248 8.htm#SEC25643127 real roots, univariate polynomial sing_1976.htm#IDX784 3128 real roots, univariate projection sing_1960.htm#IDX780 3129 real roots,sign conditions sing_1743.htm#IDX760 3130 realclassify sing_2490.htm#SEC2566 3131 realclassify.lib sing_2489.htm#SEC2565 3132 realclassify_lib sing_2489.htm#SEC2565 3140 3133 realizationDim sing_2111.htm#SEC2187 3141 3134 realizationDimPoly sing_2113.htm#SEC2189 3142 3135 realizationMatroids.lib realizationMatroids_lib sing_2110.htm#SEC2186 3143 3136 realizationMatroids_lib realizationMatroids_lib sing_2110.htm#SEC2186 3144 realmorsesplit sing_249 0.htm#SEC25663137 realmorsesplit sing_2491.htm#SEC2567 3145 3138 realpoly sing_1307.htm#SEC1383 3146 3139 realrad sing_1309.htm#SEC1385 … … 3155 3148 redefine, option sing_307.htm#IDX184 3156 3149 reduce sing_326.htm#SEC366 3157 reduce sing_51 1.htm#IDX3183158 reduce sing_90 4.htm#IDX4303159 reduce sing_90 5.htm#IDX4343160 reduce (plural) sing_4 69.htm#SEC5093161 reduced sing_90 3.htm#IDX4263150 reduce sing_512.htm#IDX320 3151 reduce sing_905.htm#IDX429 3152 reduce sing_906.htm#IDX432 3153 reduce (plural) sing_470.htm#SEC510 3154 reduced sing_904.htm#IDX426 3162 3155 reduced standard basis sing_307.htm#IDX166 3163 3156 reduction sing_1661.htm#SEC1737 … … 3173 3166 regMonCurve sing_1211.htm#SEC1287 3174 3167 regularity Syzygies and resolutions sing_327.htm#SEC367 3175 regularity sing_84 7.htm#SEC9043176 reiffen sing_55 0.htm#SEC6023168 regularity sing_848.htm#SEC905 3169 reiffen sing_551.htm#SEC603 3177 3170 rel_orbit_variety sing_1654.htm#SEC1730 3178 relations sing_73 0.htm#IDX3583171 relations sing_731.htm#IDX360 3179 3172 relativeInteriorPoint relativeInteriorPoint sing_2031.htm#SEC2107 3180 3173 relative_orbit_variety relative_orbit_variety sing_1655.htm#SEC1731 … … 3186 3179 repart sing_328.htm#SEC368 3187 3180 replace sing_1839.htm#SEC1915 3188 representation, math objects Representation of mathematical objects sing_83 4.htm#SEC8863181 representation, math objects Representation of mathematical objects sing_835.htm#SEC887 3189 3182 res sing_329.htm#SEC369 3190 resbinomial.lib sing_1370.htm#IDX6 173191 resbinomial_lib sing_1370.htm#IDX6 183183 resbinomial.lib sing_1370.htm#IDX601 3184 resbinomial_lib sing_1370.htm#IDX602 3192 3185 reservedName sing_330.htm#SEC370 3193 3186 resfunction sing_1384.htm#SEC1460 … … 3198 3191 reslist sing_1398.htm#SEC1474 3199 3192 resolution purityfiltration_lib sing_156.htm#SEC196 3200 resolution sing_73 8.htm#IDX3653201 resolution (plural) sing_43 8.htm#SEC4783193 resolution sing_739.htm#IDX367 3194 resolution (plural) sing_439.htm#SEC479 3202 3195 resolution declarations resolution declarations sing_157.htm#SEC197 3203 resolution declarations (plural) resolution declarations (plural) sing_4 39.htm#SEC4793196 resolution declarations (plural) resolution declarations (plural) sing_440.htm#SEC480 3204 3197 resolution expressions resolution expressions sing_158.htm#SEC198 3205 resolution expressions (plural) resolution expressions (plural) sing_44 0.htm#SEC4803206 resolution graph sing_1452.htm#IDX6 313198 resolution expressions (plural) resolution expressions (plural) sing_441.htm#SEC481 3199 resolution graph sing_1452.htm#IDX615 3207 3200 resolution related functions resolution related functions sing_159.htm#SEC199 3208 resolution related functions (plural) resolution related functions (plural) sing_44 1.htm#SEC4813201 resolution related functions (plural) resolution related functions (plural) sing_442.htm#SEC482 3209 3202 resolution, La Scala's method sing_280.htm#SEC320 3210 3203 resolution, computation of sing_329.htm#IDX186 3211 3204 resolution, hilbert-driven sing_255.htm#SEC295 3212 resolutionInLocalization resolutionInLocalization sing_237 2.htm#SEC24483205 resolutionInLocalization resolutionInLocalization sing_2371.htm#SEC2447 3213 3206 resolutiongraph sing_1453.htm#SEC1529 3214 3207 resolve sing_1414.htm#SEC1490 3215 3208 resolve.lib sing_1410.htm#SEC1486 3216 3209 resolve_lib sing_1410.htm#SEC1486 3217 resources.lib sing_97 3.htm#SEC10493218 resources_lib sing_97 3.htm#SEC10493219 restriction sing_2177.htm#IDX8 523220 restriction sing_2193.htm#IDX8 853221 restriction sing_2194.htm#IDX8 873222 restriction of sing_55 5.htm#IDX3413223 restrictionIdeal sing_56 5.htm#SEC6173224 restrictionModule sing_56 6.htm#SEC6183210 resources.lib sing_974.htm#SEC1050 3211 resources_lib sing_974.htm#SEC1050 3212 restriction sing_2177.htm#IDX836 3213 restriction sing_2193.htm#IDX869 3214 restriction sing_2194.htm#IDX871 3215 restriction of sing_556.htm#IDX343 3216 restrictionIdeal sing_566.htm#SEC618 3217 restrictionModule sing_567.htm#SEC619 3225 3218 resultant sing_294.htm#SEC334 3226 3219 resultant sing_331.htm#SEC371 3227 3220 reszeta.lib sing_1423.htm#SEC1499 3228 3221 reszeta_lib sing_1423.htm#SEC1499 3229 return sing_38 2.htm#SEC4223230 return type of procedures Return type of procedures sing_40 7.htm#SEC4473222 return sing_383.htm#SEC423 3223 return type of procedures Return type of procedures sing_408.htm#SEC448 3231 3224 returnSB, option sing_307.htm#IDX152 3232 3225 reverse sing_1990.htm#SEC2066 3233 reverse lexicographical ordering sing_83 8.htm#IDX3863226 reverse lexicographical ordering sing_839.htm#IDX388 3234 3227 reynolds_molien sing_1630.htm#SEC1706 3235 3228 rho sing_1881.htm#SEC1957 3236 3229 rightInverse sing_1819.htm#SEC1895 3237 3230 rightKernel sing_1817.htm#SEC1893 3238 rightModulo sing_71 7.htm#SEC7693239 rightNF sing_71 6.htm#SEC7683240 rightNFWeyl sing_78 5.htm#SEC837&nbs