! sing_36.htm#IDX101 != sing_36.htm#IDX95 != sing_100.htm#SEC140 " sing_36.htm#IDX104 # sing_36.htm#IDX118 $ sing_36.htm#IDX119 % sing_36.htm#IDX91 % sing_81.htm#SEC121 % sing_98.htm#SEC138 % sing_110.htm#SEC150 % sing_147.htm#SEC187 % sing_155.htm#SEC195 && sing_36.htm#IDX102 && sing_101.htm#SEC141 ( sing_36.htm#IDX80 () sing_131.htm#IDX130 ) sing_36.htm#IDX81 * bigintmat operations sing_36.htm#IDX89 * sing_81.htm#SEC121 * sing_87.htm#SEC127 * sing_93.htm#SEC133 * sing_98.htm#SEC138 * sing_106.htm#SEC146 * sing_110.htm#SEC150 * sing_137.htm#SEC177 * sing_142.htm#SEC182 * sing_147.htm#SEC187 * sing_155.htm#SEC195 ** sing_36.htm#IDX93 + bigintmat operations sing_36.htm#IDX85 + sing_81.htm#SEC121 + sing_87.htm#SEC127 + sing_93.htm#SEC133 + sing_98.htm#SEC138 + sing_106.htm#SEC146 + sing_110.htm#SEC150 + sing_126.htm#SEC166 + sing_137.htm#SEC177 + sing_142.htm#SEC182 + sing_147.htm#SEC187 + sing_155.htm#SEC195 + sing_169.htm#SEC209 + sing_175.htm#SEC215 + sing_180.htm#SEC220 ++ sing_36.htm#IDX86 - bigintmat operations sing_36.htm#IDX87 - sing_81.htm#SEC121 - sing_87.htm#SEC127 - sing_98.htm#SEC138 - sing_106.htm#SEC146 - sing_110.htm#SEC150 - sing_137.htm#SEC177 - sing_147.htm#SEC187 - sing_155.htm#SEC195 - sing_180.htm#SEC220 -- sing_36.htm#IDX88 --MPhost sing_19.htm#IDX66 --MPport sing_19.htm#IDX65 --allow-net sing_19.htm#IDX39 --batch sing_19.htm#IDX64 --browser sing_19.htm#IDX43 --echo sing_19.htm#IDX35 --emacs sing_19.htm#IDX67 --emacs-dir sing_19.htm#IDX68 --emacs-load sing_19.htm#IDX69 --execute sing_19.htm#IDX56 --help sing_19.htm#IDX37 --min-time sing_19.htm#IDX61 --no-out sing_19.htm#IDX49 --no-rc sing_19.htm#IDX45 --no-shell sing_19.htm#IDX50 --no-stdlib sing_19.htm#IDX47 --no-tty sing_19.htm#IDX51 --no-warn sing_19.htm#IDX48 --quiet sing_19.htm#IDX53 --random sing_19.htm#IDX60 --sdb sing_19.htm#IDX32 --singular sing_19.htm#IDX70 --ticks-per-sec sing_19.htm#IDX62 --user-option sing_19.htm#IDX58 -> sing_159.htm#SEC199 -MPhost Command line options -MPport Command line options -allow-net Command line options -b Command line options sing_19.htm#IDX63 -batch Command line options -browser Command line options -c Command line options sing_19.htm#IDX55 -d Command line options sing_19.htm#IDX31 -e Command line options sing_19.htm#IDX34 -echo Command line options -emacs Command line options -emacs-dir Command line options -emacs-load Command line options -execute Command line options -h Command line options sing_19.htm#IDX36 -help Command line options -min-time Command line options -no-out Command line options -no-rc Command line options -no-shell Command line options -no-stdlib Command line options -no-tty Command line options -no-warn Command line options -q Command line options sing_19.htm#IDX52 -quiet Command line options -r Command line options sing_19.htm#IDX59 -random Command line options -sdb Command line options -singular Command line options -ticks-per-sec Command line options -u Command line options sing_19.htm#IDX57 -user-option Command line options -v Command line options sing_19.htm#IDX54 .. sing_36.htm#IDX113 .singularrc file sing_20.htm#IDX72 .singularrc file, no loading Command line options sing_19.htm#IDX46 / sing_36.htm#IDX90 / sing_76.htm#SEC116 / sing_110.htm#SEC150 / sing_137.htm#SEC177 / sing_147.htm#SEC187 / sing_155.htm#SEC195 / sing_180.htm#SEC220 // sing_36.htm#IDX107 // sing_36.htm#IDX109 // sing_36.htm#IDX110 : sing_36.htm#IDX114 : sing_110.htm#SEC150 :: sing_36.htm#IDX115 :: sing_149.htm#SEC189 ; sing_36.htm#IDX111 < sing_36.htm#IDX100 < sing_155.htm#SEC195 < sing_180.htm#SEC220 < sing_247.htm#SEC287 <= sing_36.htm#IDX99 <= sing_100.htm#SEC140 <= sing_147.htm#SEC187 <= sing_155.htm#SEC195 <= sing_175.htm#SEC215 <= sing_180.htm#SEC220 <> sing_36.htm#IDX96 <> sing_100.htm#SEC140 <> sing_137.htm#SEC177 <> sing_147.htm#SEC187 <> sing_155.htm#SEC195 <> sing_169.htm#SEC209 <> sing_175.htm#SEC215 <> sing_180.htm#SEC220 = sing_36.htm#IDX77 == sing_36.htm#IDX94 == sing_100.htm#SEC140 == sing_137.htm#SEC177 == sing_147.htm#SEC187 == sing_155.htm#SEC195 == sing_169.htm#SEC209 == sing_175.htm#SEC215 == sing_180.htm#SEC220 > sing_36.htm#IDX98 > sing_155.htm#SEC195 > sing_180.htm#SEC220 >= sing_36.htm#IDX97 >= sing_100.htm#SEC140 >= sing_147.htm#SEC187 >= sing_155.htm#SEC195 >= sing_175.htm#SEC215 >= sing_180.htm#SEC220 ? sing_36.htm#IDX106 ? sing_259.htm#IDX148 ADGT sing_945.htm#SEC1021 65350 AG codes sing_854.htm#SEC906 AGcode_L sing_1800.htm#SEC1876 60329 AGcode_Omega sing_1801.htm#SEC1877 56285 ASCII sing_904.htm#SEC980 26816 ASCII links sing_117.htm#SEC157 ASSUME sing_64.htm#SEC101 A_L sing_1499.htm#SEC1575 16721 A_Z sing_903.htm#SEC979 50866 Access to elements of a user defined type Access to elements of a user defined type sing_185.htm#SEC225 Adj_div sing_1795.htm#SEC1871 44919 Adjoint ideal sing_1376.htm#IDX611 Alexander polynomial sing_1470.htm#IDX635 Algebraic Geometry codes sing_1794.htm#IDX783 Algebraic dependence Algebraic dependence sing_833.htm#SEC885 Algebraic geometry sing_1351.htm#SEC1427 AltVarEnd sing_746.htm#SEC798 11020 AltVarStart sing_745.htm#SEC797 21592 Ann sing_1290.htm#SEC1366 61560 Appel function sing_563.htm#IDX351 Appel hypergeometric function sing_563.htm#IDX352 Applications sing_852.htm#SEC904 Arnold, classification. sing_2322.htm#IDX939 Arnold, classification. sing_2323.htm#IDX940 ArnoldAction sing_1592.htm#SEC1668 26958 Assignments for user defined types Assignments for user defined types sing_187.htm#SEC227 AssocTanToEnv sing_940.htm#SEC1016 46214 Atkin sing_1883.htm#SEC1959 sprintf Authors sing_1.htm#IDX16 Automatic Deduction sing_945.htm#IDX482 Automatic Demonstration sing_945.htm#IDX483 BINresol sing_1389.htm#SEC1465 52996 Background sing_3.htm#SEC5 Basic programming sing_808.htm#SEC860 Basic programming sing_808.htm#SEC860 BelongSemig sing_2318.htm#SEC2394 22405 BerlekampMassey sing_2377.htm#SEC2453 2172 Bern sing_2291.htm#SEC2367 64051 Bernstein operator sing_540.htm#IDX333 Bernstein-Sato polynomial sing_505.htm#IDX314 Bernstein-Sato polynomial sing_540.htm#IDX330 Bernstein-Sato polynomial sing_1533.htm#IDX666 Bernstein-Sato polynomial sing_1537.htm#IDX683 Bernstein-Sato polynomial for variety sing_596.htm#IDX355 Betti sing_2507.htm#SEC2583 21134 Betti number Syzygies and resolutions sing_870.htm#SEC927 BettiNumsH sing_2407.htm#SEC2483 18661 BettiNumsN sing_2412.htm#SEC2488 44681 BettiNumsS sing_2410.htm#SEC2486 14964 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_880.htm#SEC937 BlowingUp sing_1512.htm#SEC1588 43153 Blowupcenter sing_1392.htm#SEC1468 3423 BorelCheck sing_1467.htm#SEC1543 48787 Bott's formula sing_2702.htm#IDX1045 Branches of space curve singularities Branches of space curve singularities sing_841.htm#SEC893 Briancon-Maisonobe algorithm sing_540.htm#IDX339 Brieskorn lattice sing_1533.htm#IDX662 Brieskorn lattice sing_1534.htm#IDX673 Brieskorn lattice sing_1535.htm#IDX676 Brieskorn lattice sing_1536.htm#IDX679 Brieskorn lattice sing_1537.htm#IDX682 Brieskorn lattice sing_1538.htm#IDX686 Brieskorn lattice sing_1539.htm#IDX690 Brieskorn lattice sing_1540.htm#IDX696 Brieskorn lattice sing_1541.htm#IDX704 Brieskorn lattice sing_1542.htm#IDX710 Brieskorn lattice sing_1543.htm#IDX718 Brieskorn lattice sing_1544.htm#IDX728 Brieskorn lattice sing_1555.htm#IDX734 Brieskorn lattice sing_1557.htm#IDX745 Brieskorn lattice sing_1585.htm#IDX772 Brill-Noether algorithm sing_1794.htm#IDX784 BrillNoether sing_1797.htm#SEC1873 39919 Buchberger algorithm for toric ideals Buchberger algorithm sing_881.htm#SEC938 Budur-Mustata-Saito approach sing_596.htm#IDX359 Building Singular sing_2759.htm#SEC2848 C programming language Major differences to the C programming language sing_409.htm#SEC449 C, module ordering sing_862.htm#IDX413 CGS sing_925.htm#IDX426 CM_regularity sing_1454.htm#SEC1530 33865 CMtype sing_1623.htm#SEC1699 24849 CRHT-ideal sing_887.htm#SEC951 CSMA sing_2314.htm#SEC2390 49080 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 Castelnuovo-Mumford regularity sing_1454.htm#IDX627 Category string sing_51.htm#SEC88 CenCharDec sing_702.htm#SEC754 44505 Center sing_1431.htm#SEC1507 25541 CenterBO sing_1438.htm#SEC1514 34701 CentralQuot sing_700.htm#SEC752 56490 CentralSaturation sing_701.htm#SEC753 31585 Change of rings sing_9.htm#SEC15 Characteristic sets sing_871.htm#SEC928 CharacteristicExponents CharacteristicExponents sing_1518.htm#SEC1594 21795 ChernClass sing_2715.htm#SEC2791 32965 ChernRootsDual sing_2270.htm#SEC2346 40100 ChernRootsHom sing_2279.htm#SEC2355 48446 ChernRootsProd sing_2272.htm#SEC2348 13967 ChernRootsSum sing_2268.htm#SEC2344 57286 ChernRootsSymm sing_2281.htm#SEC2357 59304 ChernRootsWedge sing_2282.htm#SEC2358 7239 Chevalley-Rosenlicht theorem sing_1370.htm#IDX596 Chevalley-Rosenlicht theorem sing_1371.htm#IDX599 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2706.htm#IDX1050 ChowRing sing_2706.htm#SEC2782 57977 Classification of hypersurface singularities Classification of hypersurface singularities sing_842.htm#SEC894 Classification of singularities sing_2675.htm#IDX1021 Code Codes and the decoding problem sing_886.htm#SEC944 Codes and the decoding problem Codes and the decoding problem sing_886.htm#SEC943 Coding theory sing_1793.htm#SEC1869 Coefficient rings Notes for Singular users sing_2757.htm#SEC2841 Command line options Command line options sing_19.htm#SEC26 Commands Functions and system variables sing_206.htm#SEC246 Commands for user defined types Commands for user defined types sing_186.htm#SEC226 Commutative Algebra sing_821.htm#SEC873 Commutative algebra sing_1106.htm#SEC1182 CompDecomp sing_502.htm#SEC554 9959 CompInt sing_2320.htm#SEC2396 7518 CompleteHomog sing_2258.htm#SEC2334 42123 ComplexValue sing_2399.htm#SEC2475 45546 Comprehensive Groebner System sing_925.htm#IDX429 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_817.htm#SEC869 ConsLevels sing_933.htm#SEC1009 14282 ContactMatrix sing_1520.htm#SEC1596 40767 Conti-Traverso algorithm sing_876.htm#SEC933 Contributors sing_1.htm#IDX15 Control structures sing_377.htm#SEC417 Control theory System and Control theory sing_1827.htm#SEC1903 Cooper philosophy sing_887.htm#SEC949 Cornacchia sing_1873.htm#SEC1949 63434 CornacchiaModified sing_1874.htm#SEC1950 59790 Crep sing_928.htm#SEC1004 17485 Critical points sing_836.htm#SEC888 CurveParam sing_1514.htm#SEC1590 53605 CurveRes sing_1513.htm#SEC1589 48848 Curves sing_1376.htm#IDX608 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 Cyclic code sing_1808.htm#IDX791 Cyclic roots sing_814.htm#SEC866 D-integration sing_563.htm#IDX348 D-localization sing_563.htm#IDX344 D-localization sing_780.htm#IDX382 D-module purityfiltration_lib sing_505.htm#IDX312 D-module sing_540.htm#IDX327 D-module sing_563.htm#IDX341 D-module sing_596.htm#IDX353 D-module sing_758.htm#IDX367 D-module sing_780.htm#IDX379 D-module structure sing_540.htm#IDX328 D-module structure sing_596.htm#IDX354 D-restriction sing_563.htm#IDX346 DBM links sing_122.htm#SEC162 DISPLAY environment variable The online help system sing_16.htm#IDX28 DLoc sing_566.htm#SEC618 5981 DLoc0 sing_568.htm#SEC620 14327 Data types sing_72.htm#SEC112 Data types (plural) sing_422.htm#IDX298 Debugging tools sing_63.htm#SEC100 Decker, Wolfram sing_1.htm#IDX17 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_184.htm#SEC224 Decoding sing_1808.htm#IDX793 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_885.htm#SEC942 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_890.htm#SEC960 Definition of a user defined type Definition of a user defined type sing_183.htm#SEC223 Deformations sing_839.htm#SEC891 Deformations, T1 and T2 sing_838.htm#SEC890 Deg sing_2510.htm#SEC2586 35419 Degree sing_2511.htm#SEC2587 48523 DegreePure sing_1355.htm#SEC1431 33003 Degrees sing_2512.htm#SEC2588 50349 Delta sing_1439.htm#SEC1515 33497 DeltaList sing_1440.htm#SEC1516 65148 Demo mode sing_24.htm#SEC35 Depth sing_828.htm#SEC880 Determinacy sing_2678.htm#IDX1025 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_879.htm#SEC936 Distributed computing sing_956.htm#IDX489 Dlocalization sing_781.htm#SEC833 22140 Documentation Tool sing_60.htm#SEC97 Dp, global ordering sing_860.htm#IDX396 Ds, local ordering sing_861.htm#IDX406 DsingularLocus sing_785.htm#SEC837 46495 Dynamic loading sing_71.htm#SEC111 Dynamic modules sing_816.htm#SEC868 ECPP sing_1917.htm#SEC1993 55777 ECoef sing_1398.htm#SEC1474 14154 EOrdlist sing_1396.htm#SEC1472 36329 ERROR sing_236.htm#SEC276 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 Edatalist sing_1395.htm#SEC1471 61593 Edelman-Reiner sing_2201.htm#IDX874 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 Editing input sing_18.htm#SEC25 Elimination sing_824.htm#SEC876 Emacs Emacs user interface sing_21.htm#SEC28 Emacs, Singular demo mode sing_24.htm#SEC35 Emacs, a quick guide A quick guide to Emacs sing_22.htm#SEC29 Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC36 Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC37 Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC38 Emacs, overview A quick guide to Emacs sing_22.htm#SEC29 Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30 Emacs, user interface Emacs user interface sing_21.htm#SEC28 Emaxcont sing_1400.htm#SEC1476 47312 Enumerative geometry sing_2702.htm#IDX1043 Equal sing_1354.htm#SEC1430 19984 Eresol sing_1390.htm#SEC1466 12842 EulerAff sing_2315.htm#SEC2391 54325 EulerProj sing_2316.htm#SEC2392 13537 Evaluation of logical expressions Evaluation of logical expressions sing_411.htm#SEC451 Examples sing_806.htm#SEC858 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 Exp for matrices sing_1372.htm#IDX600 Experimental libraries Experimental libraries sing_2245.htm#SEC2321 Ext sing_1166.htm#SEC1242 21909 Ext, computation of sing_827.htm#SEC879 Ext_R sing_1165.htm#SEC1241 53310 Exterior sing_732.htm#SEC784 23593 Extra weight vector sing_865.htm#SEC917 Factorization sing_829.htm#SEC881 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_941.htm#SEC1017 18153 Feynman graph sing_1142.htm#IDX522 Finite fields sing_823.htm#SEC875 First steps sing_6.htm#SEC12 Fitzgerald-Lax method Fitzgerald-Lax method sing_889.htm#SEC957 Float sing_250.htm#SEC290 Flow control sing_40.htm#SEC70 Formal Checker sing_59.htm#SEC96 Formatting output sing_813.htm#SEC865 Free resolution sing_825.htm#SEC877 Free resolution, graded Handling graded modules sing_826.htm#SEC878 FultonA sing_2313.htm#SEC2389 33688 Functions sing_207.htm#SEC247 Future benefits of Singular 4 Notes for Singular users sing_2757.htm#SEC2846 G-algebra sing_486.htm#SEC526 G-algebra sing_486.htm#SEC528 G-algebra, setup sing_486.htm#SEC530 GBWeight sing_569.htm#SEC621 24641 GBsolve sing_1707.htm#SEC1783 16830 GIT-Fans sing_848.htm#SEC900 GITcone sing_2426.htm#SEC2502 64643 GITfan sing_2427.htm#SEC2503 32549 GITfanFromOrbitCones GITfanFromOrbitCones sing_2428.htm#SEC2504 63104 GITfanParallel sing_2429.htm#SEC2505 53071 GITfanParallelSymmetric GITfanParallelSymmetric sing_2444.htm#SEC2520 30232 GITfanSymmetric sing_2443.htm#SEC2519 25831 GKZfan sing_2430.htm#SEC2506 sprintf GKZsystem sing_698.htm#SEC750 20528 GKdim sing_671.htm#SEC723 9814 GMP sing_1.htm#IDX3 GMP sing_2761.htm#SEC2850 GND.lib sing_2451.htm#SEC2527 GND_lib sing_2451.htm#SEC2527 GTZmod sing_1216.htm#SEC1292 30091 GTZopt sing_1223.htm#SEC1299 14642 G_a -Invariants sing_845.htm#SEC897 Gamma sing_1405.htm#SEC1481 3820 Gauss-Manin connection Gauss-Manin connection sing_872.htm#SEC929 Gauss-Manin connection sing_1585.htm#IDX771 Gauss-Manin connection sing_1632.htm#IDX774 Gauss-Manin system sing_1533.htm#IDX661 Gauss-Manin system sing_1534.htm#IDX672 Gauss-Manin system sing_1535.htm#IDX675 Gauss-Manin system sing_1536.htm#IDX678 Gauss-Manin system sing_1537.htm#IDX681 Gauss-Manin system sing_1538.htm#IDX685 Gauss-Manin system sing_1539.htm#IDX689 Gauss-Manin system sing_1540.htm#IDX695 Gauss-Manin system sing_1541.htm#IDX703 Gauss-Manin system sing_1542.htm#IDX709 Gauss-Manin system sing_1543.htm#IDX717 Gauss-Manin system sing_1544.htm#IDX727 Gauss-Manin system sing_1555.htm#IDX733 Gauss-Manin system sing_1557.htm#IDX744 General command syntax General command syntax sing_35.htm#SEC59 General concepts sing_12.htm#SEC18 General purpose sing_897.htm#SEC973 General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_488.htm#SEC538 Generalized Newton identities Generalized Newton identities sing_888.htm#SEC954 Geometric Invariant Theory Geometric Invariant Theory sing_847.htm#SEC899 Geometric Theorems sing_945.htm#IDX484 Geometric genus sing_1376.htm#IDX612 German Umlaute sing_407.htm#IDX285 Getting started sing_5.htm#SEC11 Global orderings sing_860.htm#SEC912 Goettsche's formula sing_2404.htm#IDX981 GoettscheF sing_2405.htm#SEC2481 27881 Graded commutative algebras Graded commutative algebras (SCA) sing_490.htm#SEC542 Grassmannian sing_2707.htm#SEC2783 43898 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2707.htm#IDX1051 Greuel, Gert-Martin sing_1.htm#IDX18 Groebner Bases Computing Groebner and Standard Bases sing_817.htm#SEC869 Groebner bases in G-algebras Groebner bases in G-algebras sing_487.htm#SEC531 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_493.htm#SEC545 Groebner bases, decodeGB sing_1808.htm#IDX795 Groebner bases, slim sing_820.htm#SEC872 Groebner basis conversion Groebner basis conversion sing_819.htm#SEC871 Groebner cover sing_924.htm#IDX422 Groebner cover sing_931.htm#IDX441 Groebner cover sing_932.htm#IDX448 Groebner fan sing_2071.htm#IDX812 Groebner walk sing_1157.htm#IDX543 Groebner walk sing_1159.htm#IDX545 Groebner walk sing_2699.htm#IDX1039 Groebner walk sing_2700.htm#IDX1040 Groebnerwalk sing_1153.htm#IDX539 Groebnerwalk sing_2544.htm#IDX992 Groebnerwalk sing_2698.htm#IDX1038 Groebnerwalk sing_2741.htm#IDX1067 Gromov-Witten invariants sing_1142.htm#IDX519 Gromov-Witten invariants sing_1148.htm#IDX528 Gromov-Witten invariants sing_1149.htm#IDX532 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2732.htm#IDX1063 Gromov-Witten invariants, multiple covers sing_2731.htm#IDX1062 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2733.htm#IDX1064 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2734.htm#IDX1065 Gromov-Witten invariants. sing_2702.htm#IDX1046 Gweights sing_726.htm#SEC778 651 H2basis sing_1590.htm#SEC1666 3414 HHnormalForm sing_2331.htm#SEC2407 33972 Hamburger-Noether expansion sing_1470.htm#IDX631 Hamburger-Noether expansion sing_1558.htm#IDX753 Hamburger-Noether expansions sing_1795.htm#IDX785 Handling graded modules Handling graded modules sing_826.htm#SEC878 Hcode sing_1492.htm#SEC1568 26628 Help string sing_45.htm#SEC82 Hensel sing_241.htm#SEC281 Hilbert function sing_356.htm#IDX188 Hilbert function sing_869.htm#SEC923 Hilbert series sing_869.htm#SEC923 Hilbert-driven GB algorithm Groebner basis conversion sing_819.htm#SEC871 HilbertClassPoly sing_1880.htm#SEC1956 sprintf HilbertSeries sing_1685.htm#SEC1761 21249 HilbertWeights sing_1686.htm#SEC1762 sprintf Hom sing_1169.htm#SEC1245 61434 HomJJ sing_1246.htm#SEC1322 1525 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_878.htm#SEC935 How to enter and exit How to enter and exit sing_14.htm#SEC20 How to use this manual How to use this manual sing_4.htm#SEC6 Hurwitz numbers sing_1148.htm#IDX531 Hurwitz numbers sing_1149.htm#IDX535 Hypersurface singularities, classification of Classification of hypersurface singularities sing_842.htm#SEC894 I-regular function sing_931.htm#IDX447 IN sing_280.htm#IDX149 Ideal membership sing_868.htm#IDX418 Identifiers, syntax of sing_37.htm#SEC65 ImageGroup sing_1688.htm#SEC1764 28808 ImageVariety sing_1687.htm#SEC1763 15252 Imap, option sing_315.htm#IDX175 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 Incl sing_1353.htm#SEC1429 7621 Index sing_2766.htm#SEC2855 Info string sing_52.htm#SEC89 InterDiv sing_1421.htm#SEC1497 46142 Interactive use sing_13.htm#SEC19 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 IntersectWithSub sing_703.htm#SEC755 56289 Intersection theory sing_2702.htm#IDX1042 IntersectionMatrix sing_1519.htm#SEC1595 29351 Introduction sing_2.htm#SEC4 Invariant Theory sing_844.htm#SEC896 Invariant theory sing_1637.htm#SEC1713 InvariantQ sing_1690.htm#SEC1766 53256 InvariantRing sing_1689.htm#SEC1765 22928 Invariants of a finite group Invariants of a finite group sing_846.htm#SEC898 Invariants of plane curve singularities Invariants of plane curve singularities sing_840.htm#SEC892 IsSCA sing_747.htm#SEC799 58445 J-marked schemes sing_1461.htm#IDX629 J-marked schemes, Borel ideals sing_1466.htm#IDX630 JMBTest.lib sing_1461.htm#SEC1537 JMBTest_lib sing_1461.htm#SEC1537 JMSConst.lib sing_1466.htm#SEC1542 JMSConst_lib sing_1466.htm#SEC1542 JMarkedScheme sing_1468.htm#SEC1544 60696 Jacobi sing_1890.htm#SEC1966 29843 Jacobson form sing_1845.htm#IDX796 Jacobson normal form sing_1845.htm#IDX797 Janet basis sing_2697.htm#IDX1036 Janet division, Janet basis sing_2696.htm#IDX1035 JuReTopDim sing_1363.htm#SEC1439 sprintf JuReZeroDim sing_1364.htm#SEC1440 sprintf KScoef sing_1583.htm#SEC1659 sprintf KSconvert sing_1581.htm#SEC1657 3585 KSker sing_1580.htm#SEC1656 40166 KSlinear sing_1582.htm#SEC1658 19896 KSpencerKernel sing_1630.htm#SEC1706 12490 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2470.htm#SEC2546 20741 Ker sing_2516.htm#SEC2592 58279 Kernel of module homomorphisms Kernel of module homomorphisms sing_832.htm#SEC884 KoszulHomology sing_1178.htm#SEC1254 sprintf Kronecker modules sing_2404.htm#IDX983 L, ordering sing_866.htm#SEC918 LETTERPLACE sing_491.htm#SEC543 LIB sing_284.htm#SEC324 LIB commands sing_53.htm#SEC90 LIBs sing_893.htm#SEC969 LLL sing_358.htm#IDX220 LOT algorithm sing_540.htm#IDX340 LU-decomposition of a matrix of numbers sing_289.htm#SEC329 Laurent series sing_1146.htm#IDX527 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_850.htm#SEC902 Left ideal membership Groebner bases in G-algebras sing_487.htm#SEC534 Left normal form Groebner bases in G-algebras sing_487.htm#SEC533 LengthSym sing_757.htm#SEC809 16591 LengthSymElement sing_756.htm#SEC808 28292 Letterplace sing_491.htm#SEC543 Levels sing_934.htm#SEC1010 16031 Lexicographic Groebner bases, computation of Groebner basis conversion sing_819.htm#SEC871 Libraries Writing procedures and libraries sing_48.htm#SEC85 Libraries sing_809.htm#SEC861 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 Library versioning Notes for Singular users sing_2757.htm#SEC2844 Lie algebra sing_1371.htm#IDX597 Lie group sing_1374.htm#IDX602 Lie group sing_1375.htm#IDX605 Limitations sing_407.htm#SEC447 Linear algebra sing_1046.htm#SEC1122 Linear code sing_1808.htm#IDX792 LinearActionQ sing_1692.htm#SEC1768 62218 LinearCombinationQ sing_1693.htm#SEC1769 59373 LinearizeAction sing_1691.htm#SEC1767 60266 Loading a library sing_62.htm#SEC99 Local orderings sing_861.htm#SEC913 Log for matrices sing_1373.htm#IDX601 Long coefficients sing_811.htm#SEC863 M, ordering sing_863.htm#SEC915 MVComplex sing_2353.htm#SEC2429 62126 Macdonald's formula sing_2404.htm#IDX982 MacdonaldF sing_2408.htm#SEC2484 12751 Macintosh installation Macintosh installation instructions sing_2765.htm#SEC2854 Mathematical background Mathematical background sing_867.htm#SEC919 Mathematical background (plural) Mathematical background (plural) sing_485.htm#SEC525 Matrix orderings sing_863.htm#SEC915 Max sing_1599.htm#SEC1675 23 Maximus sing_1463.htm#SEC1539 10010 Maxord sing_1404.htm#SEC1480 14124 MillerRabin sing_1900.htm#SEC1976 15740 Milnor number Milnor and Tjurina number sing_835.htm#SEC887 Milnor number sing_2677.htm#IDX1024 Min sing_1600.htm#SEC1676 29622 MinMult sing_2319.htm#SEC2395 39835 MinimalDecomposition MinimalDecomposition sing_1694.htm#SEC1770 24161 Minimum distance sing_1808.htm#IDX794 Minimus sing_1462.htm#SEC1538 61721 Miscellaneous libraries Miscellaneous libraries sing_2172.htm#SEC2248 ModEqn sing_1593.htm#SEC1669 59394 Modular techniques sing_956.htm#IDX486 Module orderings sing_862.htm#SEC914 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 Monodromy sing_1585.htm#IDX769 Monomial orderings sing_857.htm#SEC909 Monomial orderings, Term orderings sing_31.htm#SEC44 Mori dream spaces sing_2246.htm#IDX934 Morse lemma addnondegeneratevariables sing_2676.htm#IDX1022 Morse lemma sing_2679.htm#IDX1026 MultiplicitySequence MultiplicitySequence sing_1517.htm#SEC1593 1309 NF sing_334.htm#SEC374 NF sing_477.htm#SEC517 NFMora sing_1966.htm#SEC2042 40670 NPos sing_1236.htm#SEC1312 15702 NPos_test sing_1234.htm#SEC1310 48172 NSplaces sing_1796.htm#SEC1872 48675 NTL sing_1.htm#IDX4 Names sing_37.htm#SEC65 Names in procedures sing_46.htm#SEC83 Names, indexed sing_37.htm#SEC65 New orderings for modules Notes for Singular users sing_2757.htm#SEC2845 Newton non-degenerate sing_1572.htm#IDX767 Newton polygon sing_1571.htm#IDX766 Newton polygon sing_1572.htm#IDX768 Newton polygons sing_2744.htm#IDX1070 Newton polytope sing_2071.htm#IDX811 Newton step sing_2680.htm#IDX1030 NoetherPosition sing_1230.htm#SEC1306 18735 Non-commutative LIBs Non-commutative libraries sing_497.htm#SEC549 Non-commutative algebra Non-commutative algebra sing_849.htm#SEC901 Non-commutative algebra sing_884.htm#SEC941 Non-commutative libraries Non-commutative libraries sing_497.htm#SEC549 Non-commutative subsystem Non-commutative subsystem sing_420.htm#SEC460 Nonhyp sing_1393.htm#SEC1469 sprintf Normalization sing_831.htm#SEC883 Notes for Singular users Notes for Singular users sing_2757.htm#SEC2840 Notes for developers Notes for developers sing_2758.htm#SEC2847 NullCone sing_1695.htm#SEC1771 64635 NumIrrDecom sing_1367.htm#SEC1443 sprintf NumLocalDim sing_1356.htm#SEC1432 1739 NumPrimDecom sing_1369.htm#SEC1445 34134 Oaku-Takayama algorithm sing_540.htm#IDX338 Objects sing_38.htm#SEC66 Orlik-Solomon sing_2202.htm#IDX875 Output sing_2526.htm#IDX990 Output sing_2623.htm#IDX997 Output sing_2625.htm#IDX998 Output sing_2626.htm#IDX999 Output sing_2627.htm#IDX1000 Output sing_2628.htm#IDX1001 Output sing_2629.htm#IDX1002 Output sing_2630.htm#IDX1003 Output sing_2631.htm#IDX1004 Output sing_2632.htm#IDX1005 Output sing_2633.htm#IDX1006 Output sing_2634.htm#IDX1007 Output sing_2635.htm#IDX1008 Output sing_2636.htm#IDX1009 Output sing_2637.htm#IDX1010 Output sing_2638.htm#IDX1011 Output sing_2639.htm#IDX1012 Output sing_2640.htm#IDX1013 Output sing_2641.htm#IDX1014 Output sing_2642.htm#IDX1015 Output sing_2643.htm#IDX1016 Output sing_2644.htm#IDX1017 Output sing_2645.htm#IDX1018 Output sing_2646.htm#IDX1019 Output sing_2647.htm#IDX1020 Output, formatting of sing_813.htm#SEC865 PBW sing_519.htm#IDX326 PBW basis sing_486.htm#SEC527 PBW_eqDeg sing_537.htm#SEC589 23181 PBW_maxDeg sing_538.htm#SEC590 59566 PBW_maxMonom sing_539.htm#SEC591 1155 PEsolve sing_1705.htm#SEC1781 9229 PH_ais sing_2224.htm#SEC2300 49473 PH_nais sing_2225.htm#SEC2301 46271 PLURAL sing_421.htm#SEC461 PLURAL LIBs Non-commutative libraries sing_497.htm#SEC549 PPolyH sing_2406.htm#SEC2482 25241 PPolyN sing_2411.htm#SEC2487 39067 PPolyS sing_2409.htm#SEC2485 13817 ParToVar sing_2401.htm#SEC2477 13991 Parallelization Parallelization with ssi links sing_815.htm#SEC867 Parallelization sing_956.htm#IDX487 Parameter list sing_44.htm#SEC81 Parameters sing_812.htm#SEC864 Parametrization sing_1376.htm#IDX609 Parametrization, image. sing_1386.htm#IDX621 PartC sing_2309.htm#SEC2385 54120 PartitionVar sing_2398.htm#SEC2474 41350 Path names Notes for Singular users sing_2757.htm#SEC2843 PerfectPowerTest sing_1863.htm#SEC1939 17450 Perturbation walk sing_1158.htm#IDX544 Pfister, Gerhard sing_1.htm#IDX19 Pipe links sing_121.htm#SEC161 PocklingtonLehmer sing_1902.htm#SEC1978 13634 Poincare polynomial sing_2214.htm#IDX899 Polar curves sing_837.htm#SEC889 PollardRho sing_1903.htm#SEC1979 49602 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2227.htm#IDX915 PolyBoRi, Boolean Groebner Basis sing_2229.htm#IDX916 PolyBoRi, Boolean Groebner Basis sing_2230.htm#IDX917 PolyBoRi, Boolean Groebner Basis sing_2231.htm#IDX918 PolyBoRi, Boolean Groebner Basis sing_2232.htm#IDX919 PolyBoRi, Boolean Groebner Basis sing_2233.htm#IDX920 PolyBoRi, Boolean Groebner Basis sing_2234.htm#IDX921 PolyBoRi, Boolean Groebner Basis sing_2235.htm#IDX922 PolyBoRi, Boolean Groebner Basis sing_2236.htm#IDX923 PolyBoRi, Boolean Groebner Basis sing_2237.htm#IDX924 PolyBoRi, Boolean Groebner Basis sing_2238.htm#IDX925 PolyBoRi, Boolean Groebner Basis sing_2239.htm#IDX926 PolyBoRi, Boolean Groebner Basis sing_2240.htm#IDX927 PolyBoRi, Boolean Groebner Basis sing_2241.htm#IDX928 PolyBoRi, Boolean Groebner Basis sing_2243.htm#IDX930 PolyBoRi, zero-supressed decision diagram sing_2242.htm#IDX929 Polybori, Boolean Groebner Basis sing_2244.htm#IDX931 Polynomial data sing_855.htm#SEC907 Pottier algorithm sing_877.htm#SEC934 Preface sing_1.htm#SEC1 Prep sing_929.htm#SEC1005 55342 Primary decomposition Primary decomposition sing_830.htm#SEC882 PrimdecA sing_1212.htm#SEC1288 248 PrimdecB sing_1213.htm#SEC1289 9653 Procedure definition Procedure definition sing_43.htm#SEC78 Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84 Procedures sing_42.htm#SEC77 Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14 Procedures and libraries sing_809.htm#SEC861 Procedures in a library Procedures in a library sing_54.htm#SEC91 Product orderings sing_864.htm#SEC916 Programming sing_807.htm#SEC859 Pseudo ordering L sing_866.htm#SEC918 PtoCrep sing_930.htm#SEC1006 52961 Puiseux expansion sing_1470.htm#IDX632 Puiseux expansion sing_1558.htm#IDX754 Puiseux pairs Invariants of plane curve singularities sing_840.htm#SEC892 Puiseux pairs sing_1564.htm#IDX759 QQ sing_28.htm#SEC39 Qso3Casimir sing_697.htm#SEC749 40212 Quotient sing_1747.htm#SEC1823 24888 QuotientEquations sing_1594.htm#SEC1670 18230 Rational curves sing_1376.htm#IDX610 ReJunkUseHomo sing_1362.htm#SEC1438 10186 ReesAlgebra sing_1329.htm#SEC1405 59951 References sing_892.htm#SEC966 References (plural) sing_489.htm#SEC539 Release Notes sing_2753.htm#SEC2829 Res sing_2506.htm#SEC2582 92 ResTree sing_1422.htm#SEC1498 58727 Resolution sing_11.htm#SEC17 Resolution of singularities Resolution of singularities sing_843.htm#SEC895 Resolution, free sing_825.htm#SEC877 ReynoldsImage sing_1696.htm#SEC1772 35172 ReynoldsOperator sing_1697.htm#SEC1773 14986 RiemannRochBN sing_2254.htm#SEC2330 20085 RiemannRochHess sing_2489.htm#SEC2565 sprintf Right Groebner bases and syzygies Right Groebner bases and syzygies sing_851.htm#SEC903 Ring-dependent options Notes for Singular users sing_2757.htm#SEC2842 Rings and orderings sing_28.htm#SEC39 Rings and standard bases Rings and standard bases sing_7.htm#SEC13 Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 SCA Graded commutative algebras (SCA) sing_490.htm#SEC542 SDB breakpoint Source code debugger sing_66.htm#SEC106 SDB debugger Source code debugger sing_66.htm#SEC106 SDLoc sing_567.htm#SEC619 9512 SINGULAR libraries sing_893.htm#SEC969 SINGULARHIST sing_18.htm#SEC25 SV-decoding algorithm sing_1803.htm#IDX788 SV-decoding algorithm, preprocessing sing_1802.htm#IDX787 Sannfs sing_543.htm#SEC595 42932 SannfsBFCT sing_552.htm#SEC604 59702 SannfsVar sing_599.htm#SEC651 37522 Sannfslog sing_544.htm#SEC596 49313 Saturation sing_822.htm#SEC874 Saturation sing_1139.htm#IDX513 Sch@"onemann, Hans sing_1.htm#IDX20 Schoof sing_1914.htm#SEC1990 49281 Schubert calculus sing_2702.htm#IDX1044 SchubertClass sing_2739.htm#SEC2815 62336 SchurCh sing_2306.htm#SEC2382 58575 SchurS sing_2305.htm#SEC2381 46004 SegreA sing_2312.htm#SEC2388 55776 Semigroup sing_1510.htm#SEC1586 22323 SetDeg sing_2509.htm#SEC2585 40547 Setting up a G-algebra sing_486.htm#SEC530 ShanksMestre sing_1913.htm#SEC1989 12973 SimplifyIdeal sing_1698.htm#SEC1774 sprintf Singular sing_358.htm#IDX257 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2755.htm#SEC2838 Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36 Singular, demo mode sing_24.htm#SEC35 Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38 Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 Singular2bertini sing_1360.htm#SEC1436 7552 SingularLib sing_358.htm#IDX259 Singularities sing_1469.htm#SEC1545 Singularity Theory sing_834.htm#SEC886 Skeletons for parallelization sing_956.htm#IDX488 Smith form sing_1845.htm#IDX798 Smith normal form sing_1845.htm#IDX799 SolowayStrassen sing_1901.htm#SEC1977 22680 Solving systems of polynomial equations Solving systems of polynomial equations sing_853.htm#SEC905 Source sing_2498.htm#SEC2574 10351 Source code debugger, invocation Command line options sing_19.htm#IDX33 Space curve singularities, branches of Branches of space curve singularities sing_841.htm#SEC893 Special characters sing_36.htm#SEC64 Splitting lemma addnondegeneratevariables sing_2676.htm#IDX1023 Splitting lemma sing_2679.htm#IDX1027 Ssi file links sing_119.htm#SEC159 Ssi links sing_118.htm#SEC158 Ssi tcp links sing_120.htm#SEC160 StabEqn sing_1595.htm#SEC1671 28539 StabEqnId sing_1596.htm#SEC1672 27955 StabOrder sing_1597.htm#SEC1673 55603 Standard Bases Computing Groebner and Standard Bases sing_817.htm#SEC869 Standard bases sing_868.htm#SEC920 StartOrderingV sing_1464.htm#SEC1540 58927 Startup sequence sing_20.htm#SEC27 StringF sing_1584.htm#SEC1660 11590 SymGroup sing_755.htm#SEC807 56676 Symbolic-numerical solving Symbolic-numerical solving sing_853.htm#SEC905 Symbolic-numerical solving sing_1702.htm#SEC1778 System and Control theory System and Control theory sing_1827.htm#SEC1903 System dependent limitations System dependent limitations sing_408.htm#SEC448 System variables sing_394.htm#SEC434 Syzygies and resolutions Syzygies and resolutions sing_870.htm#SEC924 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_488.htm#SEC535 T1 sing_838.htm#SEC890 T2 sing_838.htm#SEC890 TRACE Tracing of procedures sing_65.htm#SEC102 TRACE sing_403.htm#SEC443 T_1 sing_1617.htm#SEC1693 59277 T_12 sing_1619.htm#SEC1695 12923 T_2 sing_1618.htm#SEC1694 55781 Target sing_2497.htm#SEC2573 16006 Teaching sing_1859.htm#SEC1935 Template for writing a library sing_55.htm#SEC92 TestGRRes sing_2469.htm#SEC2545 8315 TestJMark sing_1465.htm#SEC1541 41314 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 The Tran algorithm sing_1155.htm#IDX541 The fractal walk algorithm sing_1154.htm#IDX540 The fractal walk algorithm sing_2701.htm#IDX1041 The online help system The online help system sing_16.htm#SEC22 Tjurina sing_1615.htm#SEC1691 11249 Tjurina number Milnor and Tjurina number sing_835.htm#SEC887 Tjurina number sing_1251.htm#IDX570 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 Tor sing_1180.htm#SEC1256 sprintf Toric ideals and integer programming Toric ideals and integer programming sing_873.htm#SEC930 Tricks and pitfalls sing_406.htm#SEC446 Tropical Geometry sing_2011.htm#SEC2087 Type casting Type conversion and casting sing_39.htm#SEC69 Type conversion Type conversion and casting sing_39.htm#SEC68 Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98 U_D_O sing_1095.htm#SEC1171 26192 Unix installation Unix installation instructions sing_2763.htm#SEC2852 UpOneMatrix sing_744.htm#SEC796 63020 UpperMonomials sing_1598.htm#SEC1674 20941 UseBertini sing_1359.htm#SEC1435 43362 User defined types sing_182.htm#SEC222 V-filtration sing_1533.htm#IDX664 V-filtration sing_1539.htm#IDX692 V-filtration sing_1540.htm#IDX698 V-filtration sing_1541.htm#IDX706 V-filtration sing_1542.htm#IDX712 V-filtration sing_1543.htm#IDX720 V-filtration sing_1544.htm#IDX730 V-filtration sing_1555.htm#IDX736 V-filtration sing_1557.htm#IDX747 VarToPar sing_2400.htm#SEC2476 10508 Variables, indexed sing_37.htm#SEC65 Version number Version schema for Singular sing_2756.htm#SEC2839 Version schema for Singular Version schema for Singular sing_2756.htm#SEC2839 Version string sing_50.htm#SEC87 Visualization sing_1765.htm#SEC1841 WLemma sing_943.htm#SEC1019 7302 WP, global ordering sing_860.htm#IDX400 WSemigroup sing_1515.htm#SEC1591 57449 Weierstrass sing_1798.htm#SEC1874 58220 Weierstrass semigroup sing_1794.htm#IDX782 Weyl sing_729.htm#SEC781 29212 Weyl algebra sing_540.htm#IDX332 Weyl algebra sing_596.htm#IDX357 Weyl closure sing_780.htm#IDX385 WeylClosure sing_782.htm#SEC834 23845 WeylClosure1 sing_783.htm#SEC835 15759 Wibmer's Lemma sing_943.htm#IDX481 Windows installation Windows installation instructions sing_2764.htm#SEC2853 WitSet sing_1366.htm#SEC1442 39803 WitSupSet sing_1365.htm#SEC1441 47758 Ws, local ordering sing_861.htm#IDX412 XLsolve sing_1708.htm#SEC1784 34970 ZZ sing_28.htm#SEC39 ZZ/m sing_28.htm#SEC39 ZZ/p sing_28.htm#SEC39 ZZsolve sing_1709.htm#SEC1785 18657 [ sing_36.htm#IDX83 [] sing_142.htm#SEC182 [] sing_155.htm#SEC195 [] sing_175.htm#SEC215 [] sing_180.htm#SEC220 \ sing_36.htm#IDX112 ] sing_36.htm#IDX84 ^ sing_36.htm#IDX92 ^ sing_81.htm#SEC121 ^ sing_93.htm#SEC133 ^ sing_147.htm#SEC187 ^ sing_155.htm#SEC195 _ sing_36.htm#IDX116 ` sing_36.htm#IDX105 a, ordering sing_865.htm#SEC917 absFactorize sing_1108.htm#SEC1184 52546 absFactorizeBCG sing_1109.htm#SEC1185 55510 absPrimdecGTZ sing_1309.htm#SEC1385 46393 absPrimdecGTZE sing_1310.htm#SEC1386 48005 absValue sing_905.htm#SEC981 54595 absfact.lib sing_1107.htm#SEC1183 absfact_lib sing_1107.htm#SEC1183 absolute factorization. sing_1107.htm#IDX512 abstract variety, projective space, Grassmannian printVariety sing_2703.htm#IDX1047 abstract variety, projective space, Grassmannian sing_2704.htm#IDX1048 abstractR sing_1448.htm#SEC1524 22284 actionIsProper sing_1678.htm#SEC1754 52474 addLeftFractions sing_2663.htm#SEC2739 38826 addModules sing_2518.htm#SEC2594 51193 addNvarsTo sing_1030.htm#SEC1106 63123 addRat sing_801.htm#SEC853 4768 addSheaf sing_2722.htm#SEC2798 27062 addcol sing_1064.htm#SEC1140 52204 addcores sing_999.htm#SEC1075 41254 addnondegeneratevariables addnondegeneratevariables sing_2679.htm#SEC2755 40483 addrow sing_1065.htm#SEC1141 47055 addvarsTo sing_1029.htm#SEC1105 17717 ademRelations sing_661.htm#SEC713 30263 adjoint sing_1089.htm#SEC1165 56619 adjointIdeal sing_1377.htm#SEC1453 11455 adjunction divisor sing_1795.htm#IDX786 admissibleSub sing_720.htm#SEC772 6583 afaces sing_2422.htm#SEC2498 28045 affine code Fitzgerald-Lax method sing_889.htm#SEC958 ainvar.lib sing_1675.htm#SEC1751 ainvar_lib sing_1675.htm#SEC1751 aksaka.lib sing_1860.htm#SEC1936 aksaka_lib sing_1860.htm#SEC1936 alexanderpolynomial sing_1473.htm#SEC1549 36814 alexpoly.lib sing_1470.htm#SEC1546 alexpoly_lib sing_1470.htm#SEC1546 algDependent sing_1114.htm#SEC1190 20789 alg_kernel sing_1115.htm#SEC1191 307 algebra.lib sing_1110.htm#SEC1186 algebra_containment sing_1111.htm#SEC1187 47912 algebra_lib sing_1110.htm#SEC1186 algebraic dependence sing_750.htm#IDX363 algebraic field extension sing_1323.htm#IDX579 algebraicDependence sing_1336.htm#SEC1412 38500 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_880.htm#SEC937 algorithm of Conti and Traverso sing_876.htm#SEC933 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_879.htm#SEC936 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_878.htm#SEC935 algorithm of Pottier sing_877.htm#SEC934 alias General command syntax sing_35.htm#SEC59 align sing_208.htm#SEC248 all.lib sing_898.htm#SEC974 allDoubleExt sing_767.htm#SEC819 43457 allExtOfLeft sing_764.htm#SEC816 6405 allExtOfRight sing_765.htm#SEC817 56781 allPositive sing_516.htm#SEC568 1409 all_lib sing_898.htm#SEC974 allowing net access Command line options sing_19.htm#IDX41 allprint sing_947.htm#SEC1023 5195 allreal sing_2003.htm#SEC2079 57232 allrealst sing_2001.htm#SEC2077 40962 allsquarefree sing_1577.htm#SEC1653 45545 ambientDimension sing_2016.htm#SEC2092 18907 and Evaluation of logical expressions sing_101.htm#SEC141 and sing_411.htm#SEC451 annPoly sing_564.htm#SEC616 18228 annRat sing_565.htm#SEC617 62662 annRatSyz sing_790.htm#SEC842 15672 annfs sing_541.htm#SEC593 38155 annfs0 sing_553.htm#SEC605 26476 annfs2 sing_554.htm#SEC606 47962 annfsBMI sing_550.htm#SEC602 2532 annfsParamBM sing_549.htm#SEC601 43587 annfsRB sing_555.htm#SEC607 31892 annfspecial sing_542.htm#SEC594 27566 annihilator of polynomial sing_563.htm#IDX342 annihilator of rational function sing_563.htm#IDX343 annihilator of rational function sing_780.htm#IDX388 annil sing_1218.htm#SEC1294 48744 appelF1 sing_582.htm#SEC634 63146 appelF2 sing_583.htm#SEC635 22460 appelF4 sing_584.htm#SEC636 6847 appendWeight2Ord sing_722.htm#SEC774 21488 apply sing_378.htm#SEC418 applyAdF sing_532.htm#SEC584 40329 applyPermutationToIntvec applyPermutationToIntvec sing_2447.htm#SEC2523 28900 arcpoint.lib sing_1483.htm#SEC1559 arcpoint_lib sing_1483.htm#SEC1559 areEqualLeftFractions areEqualLeftFractions sing_2665.htm#SEC2741 29498 areZeroElements sing_2585.htm#SEC2661 14728 argument, default sing_44.htm#SEC81 argument, optional sing_44.htm#SEC81 arr.lib sing_2173.htm#SEC2249 arr2multarr sing_2206.htm#SEC2282 15063 arrBoolean sing_2195.htm#SEC2271 63256 arrBoundedChambers sing_2216.htm#SEC2292 18347 arrBraid sing_2196.htm#SEC2272 34093 arrCenter sing_2183.htm#SEC2259 24565 arrCentered sing_2185.htm#SEC2261 15904 arrCentral sing_2184.htm#SEC2260 14086 arrCentralize sing_2186.htm#SEC2262 53235 arrChambers sing_2215.htm#SEC2291 44578 arrCharPoly sing_2213.htm#SEC2289 44129 arrCone sing_2189.htm#SEC2265 38068 arrCoordChange sing_2187.htm#SEC2263 61430 arrCoordNormalize sing_2188.htm#SEC2264 46273 arrDecone sing_2190.htm#SEC2266 54637 arrDer sing_2203.htm#SEC2279 48815 arrEdelmanReiner sing_2201.htm#SEC2277 59091 arrEssentialize sing_2194.htm#SEC2270 6667 arrExponents sing_2205.htm#SEC2281 1948 arrFlats sing_2210.htm#SEC2286 64792 arrIsEssential sing_2193.htm#SEC2269 34363 arrIsFree sing_2204.htm#SEC2280 3860 arrLastVar sing_2182.htm#SEC2258 25835 arrLattice sing_2211.htm#SEC2287 58951 arrLocalize sing_2191.htm#SEC2267 56070 arrOrlikSolomon sing_2202.htm#SEC2278 31686 arrPoincare sing_2214.htm#SEC2290 412 arrPrintMatrix sing_2178.htm#SEC2254 21204 arrRandom sing_2199.htm#SEC2275 59986 arrRandomCentral sing_2200.htm#SEC2276 43698 arrRestrict sing_2192.htm#SEC2268 sprintf arrSet sing_2174.htm#SEC2250 53769 arrSwapVar sing_2181.htm#SEC2257 44919 arrTypeB sing_2197.htm#SEC2273 22358 arrTypeD sing_2198.htm#SEC2274 26495 arr_lib sing_2173.htm#SEC2249 arrange sing_557.htm#SEC609 50350 arrangement sing_2174.htm#IDX817 arrangement sing_2175.htm#IDX822 arrangement sing_2206.htm#IDX884 arrangement sing_2207.htm#IDX887 ask sing_1868.htm#SEC1944 3862 assPrimes sing_1125.htm#SEC1201 sprintf assign sing_2174.htm#IDX819 assignment,custom Assignments for user defined types sing_187.htm#SEC227 associated tangent FamElemsAtEnvCompPoints sing_940.htm#IDX474 associated tangent sing_941.htm#IDX478 assprimeszerodim.lib assprimeszerodim_lib sing_1123.htm#SEC1199 assprimeszerodim_lib assprimeszerodim_lib sing_1123.htm#SEC1199 atkins.lib sing_1869.htm#SEC1945 atkins_lib sing_1869.htm#SEC1945 attrib sing_209.htm#SEC249 autGenWeights sing_2249.htm#SEC2325 32642 autGradAlg sing_2248.htm#SEC2324 21136 autKS sing_2247.htm#SEC2323 51607 autX sing_2252.htm#SEC2328 43261 autXhat sing_2251.htm#SEC2327 35932 autgradalg.lib sing_2246.htm#SEC2322 autgradalg_lib sing_2246.htm#SEC2322 automorphism group sing_2246.htm#IDX935 automorphisms sing_2246.htm#IDX932 autonom sing_1832.htm#SEC1908 57044 autonomDim sing_1833.htm#SEC1909 30055 awalk1 sing_1156.htm#SEC1232 11044 awalk2 sing_1157.htm#SEC1233 8955 b-function sing_505.htm#IDX315 bFactor sing_587.htm#SEC639 15179 babyGiant sing_1898.htm#SEC1974 41113 backward sing_2387.htm#SEC2463 11225 bareiss sing_210.htm#SEC250 base2str sing_901.htm#SEC977 sprintf basering sing_28.htm#IDX76 basering sing_88.htm#SEC128 basicinvariants sing_1489.htm#SEC1565 32136 belongSemigroup sing_1128.htm#SEC1204 19983 bernstein sing_1537.htm#SEC1613 5605 bernsteinBM sing_545.htm#SEC597 57689 bernsteinLift sing_546.htm#SEC598 22885 bertini sing_1352.htm#IDX583 bertini sing_1357.htm#IDX590 bertini2Singular sing_1361.htm#SEC1437 58501 betti sing_211.htm#SEC251 betti (plural) sing_455.htm#SEC495 betti number sing_2404.htm#IDX980 bfct sing_506.htm#SEC558 29858 bfctAnn sing_508.htm#SEC560 36658 bfctBound sing_789.htm#SEC841 5630 bfctIdeal sing_510.htm#SEC562 41018 bfctOneGB sing_509.htm#SEC561 9696 bfctSyz sing_507.htm#SEC559 26796 bfctVarAnn sing_598.htm#SEC650 51667 bfctVarIn sing_597.htm#SEC649 9274 bfun.lib sing_505.htm#SEC557 bfun_lib sing_505.htm#SEC557 bigint sing_78.htm#SEC118 bigint declarations sing_79.htm#SEC119 bigint expressions sing_80.htm#SEC120 bigint operations sing_81.htm#SEC121 bigint related functions bigint related functions sing_82.htm#SEC122 bigintToBinary sing_2445.htm#SEC2521 59742 bigintmat sing_83.htm#SEC123 bigintmat declarations bigintmat declarations sing_84.htm#SEC124 bigintmat expressions bigintmat expressions sing_85.htm#SEC125 bigintmat operations bigintmat operations sing_87.htm#SEC127 bigintmat type cast sing_86.htm#SEC126 bimodules sing_498.htm#IDX303 bimodules.lib sing_498.htm#SEC550 bimodules_lib sing_498.htm#SEC550 binaryToBigint sing_2446.htm#SEC2522 sprintf binary_add sing_1921.htm#SEC1997 42817 binomial sing_906.htm#SEC982 23208 binomials2intmat sing_1284.htm#SEC1360 58804 birational map, image, inverse. sing_1378.htm#IDX615 bistd sing_499.htm#SEC551 45237 bisyzygies sing_498.htm#IDX304 bitrinity sing_500.htm#SEC552 3516 blackbox sing_191.htm#SEC231 blackbox sing_199.htm#SEC239 block sing_40.htm#SEC70 block sing_377.htm#SEC417 blowUp sing_1429.htm#SEC1505 34819 blowUp2 sing_1430.htm#SEC1506 65264 blowUpBO sing_1436.htm#SEC1512 58146 blowup0 sing_1133.htm#SEC1209 44451 boolean sing_2195.htm#IDX861 boolean expressions sing_100.htm#SEC140 boolean operations sing_101.htm#SEC141 boolean_constant sing_2229.htm#SEC2305 52873 boolean_ideal sing_2233.htm#SEC2309 53515 boolean_poly sing_2230.htm#SEC2306 41652 boolean_poly_ring sing_2228.htm#SEC2304 sprintf boolean_set sing_2234.htm#SEC2310 58235 boolean_std sing_2227.htm#SEC2303 5921 border basis sing_2693.htm#IDX1031 borderBasis sing_2694.htm#SEC2770 33172 boundBuFou sing_1998.htm#SEC2074 26589 boundDes sing_2000.htm#SEC2076 35149 boundaryLatticePoints boundaryLatticePoints sing_2086.htm#SEC2162 6238 boundposDes sing_1999.htm#SEC2075 58854 bounds sing_2681.htm#SEC2757 50218 boxSet sing_2683.htm#SEC2759 8552 bracket sing_358.htm#IDX197 bracket sing_414.htm#SEC454 bracket sing_456.htm#SEC496 braid sing_2196.htm#IDX863 branchTo procs with different argument types sing_160.htm#SEC200 break sing_379.htm#SEC419 break point sing_393.htm#SEC433 breakpoint sing_380.htm#SEC420 brillnoether.lib sing_2253.htm#SEC2329 brillnoether_lib sing_2253.htm#SEC2329 brnoeth.lib sing_1794.htm#SEC1870 brnoeth_lib sing_1794.htm#SEC1870 browser, command line option Command line options sing_19.htm#IDX44 browser, setting the sing_358.htm#IDX193 browsers The online help system sing_16.htm#IDX21 browsers, setting the sing_358.htm#IDX192 bubblesort sing_1871.htm#SEC1947 63278 busadj sing_1087.htm#SEC1163 36301 bvar sing_2241.htm#SEC2317 52773 c, module ordering sing_862.htm#IDX415 cProj sing_2295.htm#SEC2371 24037 calculateI sing_1403.htm#SEC1479 31107 calculate_max_sum sing_1940.htm#SEC2016 4706 calculate_ordering sing_1918.htm#SEC1994 42616 cancelunit, option sing_315.htm#IDX171 canonMap sing_1161.htm#SEC1237 47599 canoncial form sing_928.htm#IDX436 canoncial form sing_929.htm#IDX438 canoncial form sing_930.htm#IDX440 canonical sing_924.htm#IDX424 canonical form sing_933.htm#IDX454 canonical form sing_934.htm#IDX456 canonical, sing_932.htm#IDX450 canonicalizeCone sing_2017.htm#SEC2093 6251 canonize sing_1840.htm#SEC1916 54090 cantoradd sing_1954.htm#SEC2030 55304 cantormult sing_1957.htm#SEC2033 57569 cantorred sing_1955.htm#SEC2031 46502 cardGroup sing_1130.htm#SEC1206 5553 case No case or switch statement sing_412.htm#SEC452 catNets sing_2623.htm#SEC2699 24760 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2748.htm#SEC2824 55393 cdd sing_1.htm#IDX10 cddlib sing_1.htm#IDX11 center sing_519.htm#IDX322 65108 center sing_525.htm#SEC577 center sing_2183.htm#IDX843 center sing_2184.htm#IDX844 center sing_2185.htm#IDX846 center sing_2186.htm#IDX848 centerRed sing_524.htm#SEC576 59910 centerVS sing_523.htm#SEC575 27548 central sing_2177.htm#IDX829 central sing_2184.htm#IDX845 central sing_2186.htm#IDX847 central sing_2200.htm#IDX872 central.lib sing_519.htm#SEC571 central1st sing_2388.htm#SEC2464 29090 central2nd sing_2389.htm#SEC2465 37545 central_lib sing_519.htm#SEC571 centralize sing_519.htm#IDX325 centralizeSet sing_520.htm#SEC572 55737 centralizer sing_519.htm#IDX323 65261 centralizer sing_526.htm#SEC578 centralizerRed sing_522.htm#SEC574 8209 centralizerVS sing_521.htm#SEC573 22925 cf_class sing_209.htm#IDX132 cgs sing_900.htm#SEC976 57776 cgsdr sing_925.htm#SEC1001 44460 chAll sing_2265.htm#SEC2341 2690 chAllInv sing_2266.htm#SEC2342 57760 chDual sing_2271.htm#SEC2347 17745 chHE sing_2267.htm#SEC2343 63916 chHom sing_2280.htm#SEC2356 54776 chNum sing_2261.htm#SEC2337 54415 chNumbers sing_2262.htm#SEC2338 42134 chNumbersProj sing_2299.htm#SEC2375 28837 chProd sing_2273.htm#SEC2349 40209 chProdE sing_2274.htm#SEC2350 33460 chProdL sing_2275.htm#SEC2351 44795 chProdLP sing_2276.htm#SEC2352 8881 chProdM sing_2277.htm#SEC2353 64514 chProdMP sing_2278.htm#SEC2354 17103 chProj sing_2296.htm#SEC2372 32311 chSum sing_2269.htm#SEC2345 21088 chSymm sing_2283.htm#SEC2359 24066 chSymm2L sing_2284.htm#SEC2360 51625 chSymm2LP sing_2285.htm#SEC2361 26099 chWedge sing_2286.htm#SEC2362 57678 chWedge2L sing_2287.htm#SEC2363 46597 chWedge2LP sing_2288.htm#SEC2364 8876 chaincrit sing_1968.htm#SEC2044 9502 chambers sing_2215.htm#IDX900 chambers sing_2216.htm#IDX901 changeDenominator sing_1256.htm#SEC1332 21094 changechar sing_1004.htm#SEC1080 65454 changeord sing_1005.htm#SEC1081 55156 changeordTo sing_1028.htm#SEC1104 41903 changes sing_2754.htm#SEC2830 changevar sing_1006.htm#SEC1082 32829 char sing_212.htm#SEC252 charInfo sing_580.htm#SEC632 11034 charVariety sing_579.htm#SEC631 18306 char_series sing_213.htm#SEC253 characteristic exponents sing_1477.htm#IDX639 characteristic exponents sing_1478.htm#IDX644 characteristic exponents sing_1479.htm#IDX647 characteristic exponents sing_1480.htm#IDX651 characteristic exponents sing_1564.htm#IDX757 characteristic polynomial sing_2213.htm#IDX898 characteristic variety sing_563.htm#IDX350 characteristic variety sing_780.htm#IDX384 charexp2conductor sing_1480.htm#SEC1556 sprintf charexp2generators sing_1478.htm#SEC1554 16838 charexp2inter sing_1479.htm#SEC1555 39881 charexp2multseq sing_1477.htm#SEC1553 334 charexp2poly sing_1481.htm#SEC1557 sprintf charpoly sing_1088.htm#SEC1164 29561 charstr sing_214.htm#SEC254 checkFactor sing_556.htm#SEC608 55900 checkRoot sing_551.htm#SEC603 37045 chern sing_2260.htm#SEC2336 4916 chern.lib sing_2255.htm#SEC2331 chernCharPoly sing_2302.htm#SEC2378 31610 chernPoly sing_2301.htm#SEC2377 31316 chern_lib sing_2255.htm#SEC2331 chineseRem sing_1889.htm#SEC1965 38560 chinrem sing_215.htm#SEC255 chinrempoly sing_2649.htm#SEC2725 42312 chinrestp sing_1948.htm#SEC2024 24779 cimonom.lib sing_2317.htm#SEC2393 cimonom_lib sing_2317.htm#SEC2393 cisimplicial.lib sing_1126.htm#SEC1202 cisimplicial_lib sing_1126.htm#SEC1202 classification sing_2321.htm#IDX938 classify sing_1490.htm#SEC1566 4953 classify.lib sing_1488.htm#SEC1564 classify2.lib sing_2321.htm#SEC2397 classify2_lib sing_2321.htm#SEC2397 classifyCeq sing_1507.htm#SEC1583 42719 classifyMapGerms.lib classifyMapGerms_lib sing_2333.htm#SEC2409 classifyMapGerms_lib classifyMapGerms_lib sing_2333.htm#SEC2409 classifySimpleMaps sing_2339.htm#SEC2415 62176 classifySimpleMaps1 sing_2340.htm#SEC2416 24789 classifyUnimodalMaps classifyUnimodalMaps sing_2341.htm#SEC2417 63464 classify_aeq.lib sing_2324.htm#SEC2400 classify_aeq_lib sing_2324.htm#SEC2400 classify_lib sing_1488.htm#SEC1564 classifyceq.lib sing_1506.htm#IDX654 classifyceq_lib sing_1506.htm#IDX655 classifyci.lib sing_1508.htm#IDX656 classifyci_lib sing_1508.htm#IDX657 classifyicis sing_1509.htm#SEC1585 37651 classpoly sing_2300.htm#SEC2376 45724 cleanTmp sing_2164.htm#SEC2240 14108 cleanunit sing_1401.htm#SEC1477 sprintf cleardenom sing_216.htm#SEC256 close sing_217.htm#SEC257 closed_points sing_1804.htm#SEC1880 47269 closetex sing_1771.htm#SEC1847 42334 closureFrac sing_1249.htm#SEC1325 9252 coDim sing_2335.htm#SEC2411 60680 coDimMap sing_2334.htm#SEC2410 2002 coHom sing_773.htm#SEC825 51043 codim sing_1602.htm#SEC1678 14253 codimension sing_2018.htm#SEC2094 32207 coding theory sing_854.htm#SEC906 coef sing_218.htm#SEC258 coefficient sing_2176.htm#IDX825 coefficient sing_2177.htm#IDX828 coefficient sing_2178.htm#IDX832 coefficient field sing_144.htm#SEC184 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 coefficients, long sing_811.htm#SEC863 coeffmod sing_1866.htm#SEC1942 23531 coeffs sing_219.htm#SEC259 coker sing_2514.htm#SEC2590 35639 colength of derivations curveColengthDerivations sing_2350.htm#IDX958 collectDiv sing_1446.htm#SEC1522 50348 colrank sing_1838.htm#SEC1914 52290 colred sing_1071.htm#SEC1147 1693 combinat.lib sing_2342.htm#SEC2418 combinat_lib sing_2342.htm#SEC2418 commRing sing_804.htm#SEC856 30892 comma sing_413.htm#SEC453 command,custom Commands for user defined types sing_186.htm#SEC226 command-line option, setting value of sing_358.htm#IDX281 command-line option, value of sing_358.htm#IDX279 command-line options, print all values of sing_358.htm#IDX278 command-line options, short help Command line options sing_19.htm#IDX38 commands (plural) sing_454.htm#IDX302 comment sing_36.htm#IDX108 compareMatrix sing_2522.htm#SEC2598 49930 compareModules sing_2517.htm#SEC2593 3692 compareTasks sing_1035.htm#SEC1111 45157 compareVectors sing_2542.htm#SEC2618 12881 completeReduction sing_1680.htm#SEC1756 57157 complex sing_28.htm#IDX75 complexClassify sing_2322.htm#SEC2398 22796 complexSingType sing_1504.htm#SEC1580 34483 complexType sing_2323.htm#SEC2399 55772 compregb.lib sing_899.htm#SEC975 compregb_lib sing_899.htm#SEC975 comprehensive Groebner system sing_899.htm#IDX421 compress sing_1048.htm#SEC1124 61998 computeAfaceOrbits sing_2432.htm#SEC2508 28683 computeConstant sing_1146.htm#SEC1222 55024 computeGromovWitten sing_1149.htm#SEC1225 18834 computeN sing_1450.htm#SEC1526 61628 computeV sing_1449.htm#SEC1525 40316 computemcm sing_1408.htm#SEC1484 36956 concat sing_1049.htm#SEC1125 16653 conductor sing_1257.htm#IDX571 conductor sing_1480.htm#IDX650 conductor sing_2348.htm#IDX952 conductor, degree sing_1564.htm#IDX760 cone sing_188.htm#SEC228 cone sing_2189.htm#IDX852 cone sing_2190.htm#IDX854 coneLink sing_2021.htm#SEC2097 13635 coneViaInequalities sing_2020.htm#SEC2096 25661 coneViaPoints sing_2019.htm#SEC2095 3386 conic, parametrization, rational point. sing_1385.htm#IDX620 conicWithTangents sing_2140.htm#SEC2216 60752 constructH sing_1409.htm#SEC1485 59577 constructblwup sing_1410.htm#SEC1486 19326 constructible set sing_933.htm#IDX452 constructible sets sing_934.htm#IDX455 constructlastblwup sing_1411.htm#SEC1487 7639 constructor sing_2206.htm#IDX885 constructor sing_2207.htm#IDX888 contact matrix sing_1479.htm#IDX646 containedQ sing_1759.htm#SEC1835 46718 containsAsFace sing_2022.htm#SEC2098 25159 containsInCollection containsInCollection sing_2055.htm#SEC2131 14368 containsInSupport sing_2023.htm#SEC2099 32493 containsPositiveVector containsPositiveVector sing_2024.htm#SEC2100 27042 containsRelatively sing_2025.htm#SEC2101 17126 content sing_978.htm#SEC1054 9095 contentSB, option sing_315.htm#IDX172 continue Behavior of continue sing_381.htm#SEC421 continue sing_415.htm#SEC455 contraHom sing_774.htm#SEC826 54270 contract sing_220.htm#SEC260 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2729.htm#IDX1060 contributionBundle sing_2729.htm#SEC2805 32874 contributors sing_358.htm#IDX200 control sing_1830.htm#SEC1906 44498 control.lib sing_1829.htm#SEC1905 controlDim sing_1831.htm#SEC1907 2417 controlExample sing_1843.htm#SEC1919 2678 control_Matrix sing_1532.htm#SEC1608 sprintf control_lib sing_1829.htm#SEC1905 convertLeftToRightFraction convertLeftToRightFraction sing_2662.htm#SEC2738 4318 convertRightToLeftFraction convertRightToLeftFraction sing_2661.htm#SEC2737 19389 convertdata sing_1406.htm#SEC1482 54629 convexHull sing_2026.htm#SEC2102 56690 convexIntersection sing_2027.htm#SEC2103 63587 convloc sing_560.htm#SEC612 19122 coordinate change sing_2186.htm#IDX849 coordinate change sing_2187.htm#IDX850 coordinate change sing_2188.htm#IDX851 coordinates sing_1986.htm#IDX802 coords sing_1986.htm#SEC2062 29362 copyTask sing_1034.htm#SEC1110 65331 copyright sing_1.htm#IDX1 corank sing_1491.htm#SEC1567 33709 cornerMonomials sing_1287.htm#SEC1363 33995 countPoints sing_1911.htm#SEC1987 58566 coverings sing_1148.htm#IDX530 coverings sing_1149.htm#IDX534 cpu sing_358.htm#IDX202 cpu sing_358.htm#IDX275 createBO sing_1437.htm#SEC1513 32669 createGradedRingHomomorphism createGradedRingHomomorphism sing_2561.htm#SEC2637 62177 createGroup sing_2554.htm#SEC2630 28500 createQuotientGroup sing_2555.htm#SEC2631 26374 createTask sing_1032.htm#SEC1108 48404 createTorsionFreeGroup createTorsionFreeGroup sing_2556.htm#SEC2632 51944 createlist sing_1419.htm#SEC1495 61781 cring sing_73.htm#SEC113 cring declarations sing_74.htm#SEC114 cring expressions sing_75.htm#SEC115 cring operations sing_76.htm#SEC116 cring related functions cring related functions sing_77.htm#SEC117 crossprod sing_221.htm#SEC261 crypto.lib sing_1884.htm#SEC1960 crypto_lib sing_1884.htm#SEC1960 cup sing_1162.htm#SEC1238 57972 cupproduct sing_1163.htm#SEC1239 43349 curve singularities sing_1470.htm#IDX633 curve singularities sing_1558.htm#IDX755 curve singularity sing_2346.htm#IDX947 curveColengthDerivations curveColengthDerivations sing_2350.htm#SEC2426 2078 curveConductorMult sing_2348.htm#SEC2424 15897 curveDeligneNumber sing_2349.htm#SEC2425 12294 curveDeltaInv sing_2347.htm#SEC2423 16375 curveInv.lib sing_2346.htm#SEC2422 curveInv_lib sing_2346.htm#SEC2422 curvepar.lib sing_1511.htm#SEC1587 curvepar_lib sing_1511.htm#SEC1587 custom assignment Assignments for user defined types sing_187.htm#SEC227 custom command Commands for user defined types sing_186.htm#SEC226 custom type Definition of a user defined type sing_183.htm#SEC223 customstd.lib sing_2218.htm#SEC2294 customstd_lib sing_2218.htm#SEC2294 cycleLength sing_2077.htm#SEC2153 16898 cyclePoints sing_2081.htm#SEC2157 54460 cyclic sing_965.htm#SEC1041 21375 cyclic code Codes and the decoding problem sing_886.htm#SEC945 cyclotomic sing_1645.htm#SEC1721 33749 datetime sing_222.htm#SEC262 50127 dbprint sing_223.htm#SEC263 deRham.lib sing_2351.htm#SEC2427 deRhamCohom sing_577.htm#SEC629 58222 deRhamCohomIdeal sing_578.htm#SEC630 42169 deRhamCohomology sing_2352.htm#SEC2428 41947 deRham_lib sing_2351.htm#SEC2427 debugLib, option sing_315.htm#IDX176 debug_log sing_1501.htm#SEC1577 62043 debugger Source code debugger sing_66.htm#SEC103 debugging library code Source code debugger sing_66.htm#SEC103 dec1var sing_1217.htm#SEC1293 36098 decimal sing_1885.htm#SEC1961 56066 decode sing_1821.htm#SEC1897 64330 decodeCode sing_1823.htm#SEC1899 28262 decodeRandom sing_1822.htm#SEC1898 40118 decodeRandomFL sing_1826.htm#SEC1902 35423 decodeSV sing_1803.htm#SEC1879 37975 decodegb.lib sing_1808.htm#SEC1884 decodegb_lib sing_1808.htm#SEC1884 decoding, decoding problem Codes and the decoding problem sing_886.htm#SEC946 decoef sing_1851.htm#SEC1927 60284 decomposition of modules sing_1210.htm#IDX559 decomposition, numerical sing_1357.htm#IDX588 decone sing_2189.htm#IDX853 decone sing_2190.htm#IDX855 def sing_88.htm#SEC128 def declarations sing_89.htm#SEC129 defRes, option sing_315.htm#IDX177 default argument sing_44.htm#SEC81 defineHomogeneous sing_2594.htm#SEC2670 55072 defined sing_224.htm#SEC264 defl sing_1368.htm#SEC1444 11825 deform sing_1603.htm#SEC1679 5250 deform.lib sing_1522.htm#SEC1598 deform_lib sing_1522.htm#SEC1598 defring sing_1007.htm#SEC1083 1814 defringp sing_1009.htm#SEC1085 42905 defrings sing_1008.htm#SEC1084 1034 deg sing_225.htm#SEC265 degBound sing_395.htm#SEC435 degree Miscellaneous oddities sing_226.htm#SEC266 degree sing_418.htm#IDX292 degree lexicographical ordering sing_860.htm#IDX395 degree of a polynomial Miscellaneous oddities sing_418.htm#IDX296 degree reverse lexicographical ordering sing_860.htm#IDX393 degreeDivisor sing_2362.htm#SEC2438 31751 degreeFormalDivisor sing_2370.htm#SEC2446 42503 degreepart sing_1711.htm#SEC1787 53036 delete sing_126.htm#SEC166 delete sing_227.htm#SEC267 delete sing_276.htm#SEC316 deleteGenerator sing_592.htm#SEC644 24917 deleteSublist sing_907.htm#SEC983 20406 deligne number curveColengthDerivations sing_2346.htm#IDX949 deligne number sing_2349.htm#IDX954 deligne number sing_2350.htm#IDX956 delta sing_1570.htm#SEC1646 56952 delta invariant sing_1251.htm#IDX569 delta invariant sing_1570.htm#IDX765 delta invariant sing_2347.htm#IDX950 delta invariant. sing_1243.htm#IDX562 delta invariant. sing_1244.htm#IDX565 delta invariant. sing_1245.htm#IDX568 deltaLoc sing_1251.htm#SEC1327 35192 denom_list sing_358.htm#IDX204 denominator sing_228.htm#SEC268 depth sing_1164.htm#SEC1240 17777 depthIdeal sing_1227.htm#SEC1303 54782 derivate sing_1677.htm#SEC1753 15409 derivation sing_2203.htm#IDX876 desingularization sing_2451.htm#IDX985 59041 desingularization sing_2452.htm#SEC2528 det sing_229.htm#SEC269 det_B sing_1090.htm#SEC1166 60143 detadj sing_1586.htm#SEC1662 5914 determinacy sing_2678.htm#SEC2754 44818 determinecenter sing_1391.htm#SEC1467 44496 detropicalise sing_2158.htm#SEC2234 38025 develop sing_1560.htm#SEC1636 48457 diag sing_1050.htm#SEC1126 56759 diagInvariants sing_1266.htm#SEC1342 62096 diag_test sing_1086.htm#SEC1162 31469 diff sing_230.htm#SEC270 diffRat sing_803.htm#SEC855 36134 difpoly2tex sing_1852.htm#SEC1928 6451 dim sing_231.htm#SEC271 dim (plural) sing_457.htm#SEC497 dimGradedPart sing_1459.htm#SEC1535 11262 dimH sing_1458.htm#SEC1534 38534 dimMon sing_1207.htm#SEC1283 39971 dimStack sing_2727.htm#SEC2803 47772 dim_slocus sing_1604.htm#SEC1680 47218 dimension sing_2028.htm#SEC2104 35262 dimension, moduli space of stable maps, rational curves dimStack sing_2727.htm#IDX1058 dimensionOfLocalization dimensionOfLocalization sing_2415.htm#SEC2491 25632 direct_boolean_poly sing_2231.htm#SEC2307 49893 direct_from_boolean_poly direct_from_boolean_poly sing_2237.htm#SEC2313 36941 disc sing_1872.htm#SEC1948 45279 discr sing_1626.htm#SEC1702 9642 discrepancy sing_1444.htm#SEC1520 5597 discrim sing_942.htm#SEC1018 44091 discussion of parametric ideal sing_924.htm#IDX425 disjoint sing_925.htm#IDX427 disp_zdd sing_2244.htm#SEC2320 41439 displayCohom sing_1460.htm#SEC1536 22633 displayHNE sing_1563.htm#SEC1639 29845 displayInvariants sing_1565.htm#SEC1641 13678 displayMultsequence sing_1567.htm#SEC1643 16668 displayPuiseuxExpansion displayPuiseuxExpansion sing_2133.htm#SEC2209 560 displayTropicalLifting displayTropicalLifting sing_2131.htm#SEC2207 28144 distributed computing sing_958.htm#IDX492 distributed computing sing_998.htm#IDX494 distributed computing sing_1031.htm#IDX504 div Miscellaneous oddities sing_81.htm#SEC121 div sing_98.htm#SEC138 div sing_155.htm#SEC195 div sing_418.htm#IDX289 divideUnits sing_1848.htm#SEC1924 26711 dividelist sing_1418.htm#SEC1494 34210 division sing_232.htm#SEC272 division sing_926.htm#IDX430 division sing_927.htm#IDX432 division (plural) sing_458.htm#SEC498 divisor sing_1951.htm#SEC2027 47231 divisorplus sing_2356.htm#SEC2432 34248 divisors negativeformaldivisor sing_2355.htm#IDX959 divisors sing_2356.htm#IDX960 divisors sing_2357.htm#IDX961 divisors sing_2358.htm#IDX962 divisors sing_2359.htm#IDX963 divisors sing_2360.htm#IDX964 divisors sing_2361.htm#IDX965 divisors sing_2362.htm#IDX966 divisors sing_2363.htm#IDX967 divisors sing_2364.htm#IDX968 divisors sing_2365.htm#IDX969 divisors sing_2366.htm#IDX970 divisors sing_2367.htm#IDX971 divisors sing_2368.htm#IDX972 divisors sing_2369.htm#IDX973 divisors sing_2370.htm#IDX974 divisors, polyhedra sing_2371.htm#IDX975 divisors, polyhedra sing_2372.htm#IDX976 divisors, polyhedra sing_2373.htm#IDX977 divisors.lib sing_2354.htm#SEC2430 divisors_lib sing_2354.htm#SEC2430 dmod.lib sing_540.htm#SEC592 dmodAction sing_798.htm#SEC850 9763 dmodActionRat sing_799.htm#SEC851 6277 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_791.htm#SEC843 44337 dmod_lib sing_540.htm#SEC592 dmodapp.lib sing_563.htm#SEC615 dmodapp_lib sing_563.htm#SEC615 dmodloc.lib sing_780.htm#IDX377 dmodloc_lib sing_780.htm#IDX378 dmodoublext sing_775.htm#SEC827 60637 dmodvar.lib sing_596.htm#SEC648 dmodvar_lib sing_596.htm#SEC648 double sing_1956.htm#SEC2032 34697 doubleExt sing_766.htm#SEC818 56896 downloading Download instructions sing_2762.htm#SEC2851 dp, global ordering sing_860.htm#IDX394 drawNewtonSubdivision drawNewtonSubdivision sing_2136.htm#SEC2212 50904 drawTropicalCurve sing_2135.htm#SEC2211 10441 ds, local ordering sing_861.htm#IDX404 dsum sing_1051.htm#SEC1127 1303 dualCone sing_2029.htm#SEC2105 61460 dualConic sing_2160.htm#SEC2236 31080 dualPart sing_2308.htm#SEC2384 13279 dualPartition sing_2740.htm#SEC2816 24739 dualPolytope sing_2068.htm#SEC2144 32081 dualSheaf sing_2718.htm#SEC2794 633 dual_code sing_1805.htm#SEC1881 57229 dump sing_233.htm#SEC273 dynamic geometry sing_935.htm#IDX459 dynamic geometry sing_936.htm#IDX462 ecart sing_1959.htm#SEC2035 32475 echo sing_396.htm#SEC436 eexgcdN sing_1886.htm#SEC1962 53237 effective sing_2364.htm#SEC2440 53028 egcdMain sing_1752.htm#SEC1828 25359 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2087.htm#SEC2163 38271 ehrhartRing sing_1262.htm#SEC1338 16966 eigenvals sing_1098.htm#SEC1174 11228 eigenvalue sing_328.htm#SEC368 eigenvalue sing_1098.htm#IDX510 eigenvalues sing_1345.htm#SEC1421 2182 elemSymmId sing_966.htm#SEC1042 sprintf elim sing_1135.htm#SEC1211 62585 elim.lib sing_1132.htm#SEC1208 elim1 sing_1136.htm#SEC1212 15653 elim2 sing_1137.htm#SEC1213 44749 elimRing sing_1134.htm#SEC1210 12194 elimWeight sing_723.htm#SEC775 54297 elim_lib sing_1132.htm#SEC1208 eliminate sing_234.htm#SEC274 eliminate (plural) sing_459.htm#SEC499 eliminateNC sing_718.htm#SEC770 3777 elimination sing_717.htm#IDX362 elimlinearpart sing_1712.htm#SEC1788 14251 elimpart sing_1713.htm#SEC1789 10258 elimpartanyr sing_1714.htm#SEC1790 39751 elimrep sing_1399.htm#SEC1475 23641 elliptic curve sing_1145.htm#IDX526 elliptic curves sing_1142.htm#IDX520 elliptic curves sing_1148.htm#IDX529 elliptic curves sing_1149.htm#IDX533 ellipticAdd sing_1907.htm#SEC1983 13279 ellipticAllPoints sing_1912.htm#SEC1988 60770 ellipticMult sing_1908.htm#SEC1984 1558 ellipticNF sing_2084.htm#SEC2160 5045 ellipticNFDB sing_2085.htm#SEC2161 27917 ellipticRandomCurve sing_1909.htm#SEC1985 36980 ellipticRandomPoint sing_1910.htm#SEC1986 6866 ellipticcovers.lib sing_1142.htm#IDX514 ellipticcovers_lib sing_1142.htm#IDX515 else sing_386.htm#SEC426 embedMat sing_749.htm#SEC801 17119 emptyFan sing_2056.htm#SEC2132 7396 encode sing_1813.htm#SEC1889 56687 endomorphism filtration sing_1544.htm#IDX731 endvfilt sing_1544.htm#SEC1620 26670 engine sing_593.htm#SEC645 30876 ensureLeftNcfrac sing_2611.htm#SEC2687 64571 ensureRightNcfrac sing_2612.htm#SEC2688 14107 envelop FamElemsAtEnvCompPoints sing_937.htm#SEC1013 27362 envelop sing_937.htm#IDX465 envelop sing_938.htm#IDX468 envelop sing_940.htm#IDX473 envelop sing_941.htm#IDX477 envelope sing_460.htm#SEC500 enveloping algebra sing_358.htm#IDX208 enveloping algebra sing_498.htm#IDX306 environment variable, DISPLAY The online help system sing_16.htm#IDX29 equalJinI sing_1487.htm#SEC1563 18502 equalMultiDeg sing_2587.htm#SEC2663 37090 equations sing_2030.htm#SEC2106 7896 equiRadical sing_1303.htm#SEC1379 8884 equidim sing_1305.htm#SEC1381 38541 equidimMax sing_1306.htm#SEC1382 49289 equidimMaxEHV sing_1307.htm#SEC1383 42650 equidimZ sing_1318.htm#SEC1394 49610 equising.lib sing_1527.htm#SEC1603 equising_lib sing_1527.htm#SEC1603 equisingular Tjurina number sing_1470.htm#IDX638 equisingularity ideal sing_1529.htm#IDX658 equisingularity stratum sing_1530.htm#IDX659 error recovery sing_15.htm#SEC21 errorInsert sing_1816.htm#SEC1892 59470 errorRand sing_1817.htm#SEC1893 5727 errormap sing_2394.htm#SEC2470 7782 esIdeal sing_1529.htm#SEC1605 60477 esStratum sing_1530.htm#SEC1606 50094 essential sing_2193.htm#IDX858 essential sing_2194.htm#IDX859 eta sing_2079.htm#SEC2155 60729 euler sing_1865.htm#SEC1941 10519 eulerChProj sing_2298.htm#SEC2374 28549 eval sing_235.htm#SEC275 evalJacobianAtBox sing_2689.htm#SEC2765 42716 evalPolyAtBox sing_2688.htm#SEC2764 43040 evaluateFormalDivisor evaluateFormalDivisor sing_2366.htm#SEC2442 3535 evaluatePDivisor sing_2372.htm#SEC2448 18855 evaluateProduct sing_2442.htm#SEC2518 54515 evaluate_reynolds sing_1650.htm#SEC1726 46353 evalutateIntegral sing_1147.htm#SEC1223 sprintf example sing_237.htm#SEC277 example sing_2195.htm#IDX860 example sing_2196.htm#IDX862 example sing_2197.htm#IDX864 example sing_2198.htm#IDX866 example sing_2199.htm#IDX868 example sing_2200.htm#IDX870 example sing_2201.htm#IDX873 execute sing_238.htm#SEC278 exit sing_390.htm#SEC430 exp2pt sing_1853.htm#SEC1929 19621 expo sing_1877.htm#SEC1953 8833 exponents sing_2205.htm#IDX881 export sing_383.htm#SEC423 exportNuminvs sing_1270.htm#SEC1346 10423 exportto sing_384.htm#SEC424 expp sing_2738.htm#SEC2814 15751 expression list sing_72.htm#IDX128 expression list sing_422.htm#IDX299 ext-module purityfiltration_lib sing_758.htm#IDX368 extcurve sing_1799.htm#SEC1875 6730 extdevelop sing_1561.htm#SEC1637 51044 extendGC sing_932.htm#SEC1008 40951 extendWeyl sing_792.htm#SEC844 49954 extendedTensor sing_724.htm#SEC776 4975 extendpoly sing_931.htm#SEC1007 29201 extendring sing_1010.htm#SEC1086 64781 extension of rings sing_1323.htm#IDX580 exterior basis sing_1077.htm#IDX507 exterior power sing_1079.htm#IDX509 exteriorBasis sing_1077.htm#SEC1153 sprintf exteriorPower sing_1079.htm#SEC1155 20173 extgcd sing_239.htm#SEC279 fVector sing_2059.htm#SEC2135 3715 fVectorP sing_2088.htm#SEC2164 31843 facFirstShift sing_711.htm#SEC763 6469 facFirstWeyl sing_707.htm#SEC759 42412 facGBIdeal sing_1288.htm#SEC1364 9924 facShift sing_710.htm#SEC762 48551 facSubWeyl sing_709.htm#SEC761 9630 facWeyl sing_706.htm#SEC758 32331 faceContaining sing_2031.htm#SEC2107 64804 facetVertexLatticeDistances facetVertexLatticeDistances sing_2089.htm#SEC2165 60714 facetWidth sing_2090.htm#SEC2166 62810 facetWidths sing_2091.htm#SEC2167 5503 facets sing_2032.htm#SEC2108 8112 facstd sing_240.htm#SEC280 factmodd sing_241.htm#SEC281 factor sing_322.htm#SEC362 factorH sing_922.htm#SEC998 24814 factorLenstraECM sing_1916.htm#SEC1992 54951 factorMain sing_1753.htm#SEC1829 65152 factorgroup sing_2577.htm#SEC2653 59914 factorial sing_908.htm#SEC984 32871 factorization sing_323.htm#SEC363 factorization sing_1107.htm#IDX511 factorize sing_242.htm#SEC282 factorize sing_322.htm#SEC362 factory sing_1.htm#IDX2 fan sing_189.htm#SEC229 fan sing_2071.htm#IDX807 fanViaCones sing_2057.htm#SEC2133 16418 farey sing_243.htm#SEC283 fareypoly sing_2375.htm#SEC2451 12389 fastExpt sing_1861.htm#SEC1937 43912 fastHC, option sing_315.htm#IDX153 fastelim sing_1715.htm#SEC1791 7409 fetch sing_244.htm#SEC284 fetch (plural) sing_461.htm#SEC501 fetchall sing_1011.htm#SEC1087 7537 ffmodStd sing_2379.htm#SEC2455 50680 ffmodstd.lib sing_2374.htm#SEC2450 ffmodstd_lib sing_2374.htm#SEC2450 ffsolve sing_1704.htm#SEC1780 20432 ffsolve.lib sing_1703.htm#SEC1779 ffsolve_lib sing_1703.htm#SEC1779 fglm sing_245.htm#SEC285 fglm sing_355.htm#IDX187 fglm_solve sing_1731.htm#SEC1807 51398 fglmquot sing_246.htm#SEC286 fibonacci sing_909.htm#SEC985 24750 field sing_144.htm#SEC184 file, .singularrc sing_20.htm#IDX71 filecmd sing_247.htm#SEC287 filtration purityfiltration_lib sing_758.htm#IDX369 finalCharts sing_1423.htm#SEC1499 37296 find sing_248.htm#SEC288 findAuto sing_665.htm#SEC717 51205 findInvo sing_663.htm#SEC715 18177 findInvoDiag sing_664.htm#SEC716 7365 findOrientedBoundary findOrientedBoundary sing_2080.htm#SEC2156 24110 findTorsion sing_1842.htm#SEC1918 29572 find_first_primitive_root find_first_primitive_root sing_1920.htm#SEC1996 33327 find_index sing_1924.htm#SEC2000 62564 findifs.lib sing_1849.htm#SEC1925 findifs_example sing_1850.htm#SEC1926 33849 findifs_lib sing_1849.htm#SEC1925 findimAlgebra sing_733.htm#SEC785 64612 finduni sing_249.htm#SEC289 findvars sing_1716.htm#SEC1792 54503 finite field sing_144.htm#SEC184 finite field sing_1703.htm#IDX780 finiteDiagInvariants finiteDiagInvariants sing_1265.htm#SEC1341 3508 finitediff.lib sing_2380.htm#IDX978 finitediff_lib sing_2380.htm#IDX979 finitenessTest sing_1121.htm#SEC1197 40633 finvar.lib sing_1638.htm#SEC1714 finvar_lib sing_1638.htm#SEC1714 first index is 1 sing_417.htm#SEC457 firstoct sing_1764.htm#SEC1840 11498 fitting sing_1167.htm#SEC1243 20661 fixed points, moduli space of stable maps, graph fixedPoints sing_2728.htm#IDX1059 fixedPoints sing_2728.htm#SEC2804 25366 fl2poly sing_590.htm#SEC642 51682 flatten sing_1052.htm#SEC1128 55617 flatteningStrat sing_1168.htm#SEC1244 15622 floating point sing_1020.htm#IDX497 for sing_385.htm#SEC425 formaldivisorplus sing_2367.htm#SEC2443 31959 forward sing_2386.htm#SEC2462 15383 fourier sing_585.htm#SEC637 5326 fouriersystem sing_2397.htm#SEC2473 43681 fpadim.lib sing_601.htm#SEC653 fpadim_lib sing_601.htm#SEC653 fpaprops.lib sing_635.htm#SEC687 fpaprops_lib sing_635.htm#SEC687 fprintf sing_251.htm#SEC291 13662 fracStatus sing_2657.htm#SEC2733 14582 frandwalk sing_2701.htm#SEC2777 25555 free sing_2204.htm#IDX878 free sing_2205.htm#IDX880 free associative algebra, tensor algebra Free associative algebras sing_492.htm#SEC544 freeGBasis sing_649.htm#SEC701 43055 freeModule sing_2494.htm#SEC2570 34173 freeModule2Module sing_2523.htm#SEC2599 15296 freegb.lib sing_644.htm#SEC696 freegb_lib sing_644.htm#SEC696 freemodule sing_252.htm#SEC292 freerank sing_968.htm#SEC1044 52218 fres sing_253.htm#SEC293 from_boolean_constant from_boolean_constant sing_2235.htm#SEC2311 44881 from_boolean_ideal sing_2239.htm#SEC2315 62698 from_boolean_poly sing_2236.htm#SEC2312 27864 from_boolean_set sing_2240.htm#SEC2316 60615 frwalk sing_254.htm#SEC294 full representation sing_931.htm#IDX446 full representation sing_932.htm#IDX451 fullDimImages sing_2423.htm#SEC2499 20094 fullFan sing_2058.htm#SEC2134 7534 fullSerreRelations sing_659.htm#SEC711 27691 fullSpace sing_2013.htm#SEC2089 19485 furtherInvar sing_1682.htm#SEC1758 19209 further_hn_proc sing_1578.htm#SEC1654 63500 fwalk sing_1154.htm#SEC1230 15070 galois field sing_144.htm#SEC184 gauss_col sing_1062.htm#SEC1138 36252 gauss_nf sing_1093.htm#SEC1169 51060 gauss_row sing_1063.htm#SEC1139 58877 gaussred sing_1091.htm#SEC1167 29001 gaussred_pivot sing_1092.htm#SEC1168 25477 gcd sing_255.htm#SEC295 gcdMon sing_1196.htm#SEC1272 42448 gcddivisor sing_1952.htm#SEC2028 1276 gen sing_256.htm#SEC296 genMDSMat sing_1819.htm#SEC1895 3347 genSymId sing_1342.htm#SEC1418 17521 general error-locator polynomial sing_887.htm#SEC952 general neron. sing_2451.htm#IDX986 general weighted lexicographical ordering sing_861.htm#IDX410 general weighted reverse lexicographical ordering Local orderings sing_861.htm#IDX407 general.lib sing_902.htm#SEC978 generalOrder sing_1977.htm#SEC2053 42536 general_lib sing_902.htm#SEC978 generateG sing_1915.htm#SEC1991 51697 generators sing_1478.htm#IDX642 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2033.htm#SEC2109 4454 generatorsOfSpan sing_2034.htm#SEC2110 40297 generic representation sing_931.htm#IDX445 genericid sing_986.htm#SEC1062 29731 genericity sing_1839.htm#SEC1915 16822 genericmat sing_1053.htm#SEC1129 35016 genoutput sing_1412.htm#SEC1488 18973 genus sing_1247.htm#SEC1323 sprintf geometrical locus FamElemsAtEnvCompPoints sing_935.htm#IDX457 geometrical locus sing_936.htm#IDX460 geometrical locus sing_937.htm#IDX463 geometrical locus sing_938.htm#IDX466 geometrical locus sing_939.htm#IDX469 geometrical locus sing_940.htm#IDX471 geometrical locus sing_941.htm#IDX475 getArguments sing_1043.htm#SEC1119 14254 getCommand sing_1042.htm#SEC1118 32181 getCone sing_2060.htm#SEC2136 41394 getGradingGroup sing_2552.htm#SEC2628 18137 getLattice sing_2553.htm#SEC2629 7775 getLinearForms sing_2035.htm#SEC2111 47590 getModuleGrading sing_2563.htm#SEC2639 43451 getMultiplicity sing_2036.htm#SEC2112 639 getOneVar sing_1255.htm#SEC1331 55402 getResult sing_1044.htm#SEC1120 51722 getSmallest sing_1254.htm#SEC1330 1623 getState sing_1045.htm#SEC1121 36453 getVariableWeights sing_2551.htm#SEC2627 9591 getcores sing_1001.htm#SEC1077 30785 getdump sing_257.htm#SEC297 getenv sing_358.htm#IDX211 gfan.lib sing_2012.htm#SEC2088 gfan_lib sing_2012.htm#SEC2088 gfanlib sing_1.htm#IDX9 gitCone sing_2450.htm#SEC2526 23853 gitfan.lib sing_2420.htm#SEC2496 gitfan_lib sing_2420.htm#SEC2496 gkdim.lib sing_670.htm#SEC722 gkdim_lib sing_670.htm#SEC722 global sing_209.htm#IDX133 global Bernstein-Sato polynomial sing_505.htm#IDX313 global Bernstein-Sato polynomial sing_540.htm#IDX331 global Bernstein-Sato polynomial for variety sing_596.htm#IDX356 globalSections sing_2361.htm#SEC2437 55191 gmscoeffs sing_1536.htm#SEC1612 13182 gmsnf sing_1535.htm#SEC1611 44676 gmspoly.lib sing_1555.htm#SEC1631 gmspoly_lib sing_1555.htm#SEC1631 gmsring sing_1534.htm#SEC1610 59438 gmssing.lib sing_1533.htm#SEC1609 gmssing_lib sing_1533.htm#SEC1609 goettsche.lib sing_2404.htm#SEC2480 goettsche_lib sing_2404.htm#SEC2480 good basis sing_1533.htm#IDX670 good basis sing_1543.htm#IDX725 good basis sing_1555.htm#IDX741 good basis sing_1557.htm#IDX752 goodBasis sing_1557.htm#SEC1633 41606 gorensteinIndex sing_2092.htm#SEC2168 52919 gorensteinVector sing_2093.htm#SEC2169 50407 graal.lib sing_2413.htm#SEC2489 graalMixed sing_2414.htm#SEC2490 6401 graal_lib sing_2413.htm#SEC2489 gradeNumber sing_762.htm#SEC814 29956 graded Weyl algebra sing_505.htm#IDX316 graded algebra sing_2246.htm#IDX933 graded module, graded piece sing_1459.htm#IDX628 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2453.htm#IDX987 graded modules, handling of Handling graded modules sing_826.htm#SEC878 graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2491.htm#IDX989 gradedModules.lib sing_2453.htm#SEC2529 gradedModules_lib sing_2453.htm#SEC2529 gradiator sing_2596.htm#SEC2672 53802 graph sing_1143.htm#IDX524 graph sing_1144.htm#IDX525 graph sing_2723.htm#IDX1054 graph sing_2724.htm#IDX1055 graphics.lib sing_1766.htm#SEC1842 graphics_lib sing_1766.htm#SEC1842 graphviz sing_1.htm#IDX13 graver4ti2 sing_1340.htm#SEC1416 39635 grconcat sing_2476.htm#SEC2552 16754 grdeg sing_2456.htm#SEC2532 22879 grgens sing_2465.htm#SEC2541 12823 grgroebner sing_2475.htm#SEC2551 29288 grlift sing_2473.htm#SEC2549 21656 grlifting sing_2480.htm#SEC2556 51177 grlifting2 sing_2481.htm#SEC2557 59011 grlifting3 sing_2483.htm#SEC2559 6369 grneg sing_2486.htm#SEC2562 64584 grobcov sing_924.htm#SEC1000 44826 grobcov.lib sing_923.htm#SEC999 grobcov_lib sing_923.htm#SEC999 grobj sing_2454.htm#SEC2530 18115 groebner sing_258.htm#SEC298 53038 groebner sing_818.htm#SEC870 groebner basis computations sing_258.htm#IDX147 groebnerComplex sing_2171.htm#SEC2247 2421 groebnerCone sing_2165.htm#SEC2241 58776 groebnerFan sing_2170.htm#SEC2246 48157 gromovWitten sing_1148.htm#SEC1224 28559 grorder sing_2467.htm#SEC2543 20857 ground field sing_144.htm#SEC184 groupActionOnHashes sing_2438.htm#SEC2514 406 groupActionOnQImage sing_2437.htm#SEC2513 53270 group_reynolds sing_1646.htm#SEC1722 35079 grpower sing_2463.htm#SEC2539 3960 grpres sing_2466.htm#SEC2542 18145 grprod sing_2474.htm#SEC2550 41525 grrange sing_2485.htm#SEC2561 41835 grres sing_2472.htm#SEC2548 35795 grrndmap sing_2478.htm#SEC2554 4054 grrndmap2 sing_2479.htm#SEC2555 50536 grrndmat sing_2477.htm#SEC2553 42634 grshift sing_2458.htm#SEC2534 1415 grsum sing_2462.htm#SEC2538 60602 grsyz sing_2471.htm#SEC2547 61843 grtest sing_2455.htm#SEC2531 62577 grtranspose sing_2464.htm#SEC2540 13865 grtranspose1 sing_2468.htm#SEC2544 3637 grtwist sing_2460.htm#SEC2536 10498 grtwists sing_2461.htm#SEC2537 56638 grview sing_2457.htm#SEC2533 6878 grwalk.lib sing_1153.htm#SEC1229 grwalk_lib sing_1153.htm#SEC1229 grzero sing_2459.htm#SEC2535 4212 gwalk sing_1159.htm#SEC1235 38238 hStarVector sing_2094.htm#SEC2170 60821 hVector sing_2095.htm#SEC2171 46486 h_increasing_knapsack h_increasing_knapsack sing_1938.htm#SEC2014 62968 hardware platform sing_358.htm#IDX271 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1024.htm#SEC1100 54609 hasCommutativeVars sing_1021.htm#SEC1097 3152 hasGlobalOrdering sing_1022.htm#SEC1098 34053 hasLeftDenom sing_2605.htm#SEC2681 47260 hasMixedOrdering sing_1023.htm#SEC1099 29738 hasNumericCoeffs sing_1020.htm#SEC1096 14522 hasRightDenom sing_2606.htm#SEC2682 34279 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1025.htm#SEC1101 56211 hashToCone sing_2448.htm#SEC2524 6929 hashesToFan sing_2449.htm#SEC2525 26774 headStand sing_1075.htm#SEC1151 14413 heightZ sing_1317.htm#SEC1393 16800 help sing_259.htm#SEC299 help browsers The online help system sing_16.htm#IDX22 help browsers, dummy The online help system sing_16.htm#IDX25 help browsers, dummy sing_16.htm#IDX27 help browsers, emacs The online help system sing_16.htm#IDX26 help browsers, html The online help system sing_16.htm#IDX23 help browsers, setting command to use The online help system sing_16.htm#IDX30 help browsers, setting the sing_358.htm#IDX194 help, accessing over the net Command line options sing_19.htm#IDX42 help, online help system The online help system sing_16.htm#SEC22 hermiteNormalForm sing_2597.htm#SEC2673 37225 hess.lib sing_2488.htm#SEC2564 hess_lib sing_2488.htm#SEC2564 hessenberg sing_358.htm#IDX217 24168 hessenberg sing_1097.htm#SEC1173 highcorner sing_260.htm#SEC300 hilb sing_261.htm#SEC301 hilbPoly sing_984.htm#SEC1060 36118 hilbert4ti2 sing_1339.htm#SEC1415 13993 hilbertBasis sing_2096.htm#SEC2172 35423 hilbertSeries sing_2599.htm#SEC2675 60148 hilbvec sing_1717.htm#SEC1793 9204 hnexpansion sing_1559.htm#SEC1635 46990 hnoether.lib sing_1558.htm#SEC1634 hnoether_lib sing_1558.htm#SEC1634 holonomic rank sing_780.htm#IDX380 holonomicRank sing_784.htm#SEC836 41306 hom sing_2535.htm#SEC2611 40032 hom_kernel sing_1175.htm#SEC1251 32604 homog sing_262.htm#SEC302 homog_part sing_2735.htm#SEC2811 20875 homog_parts sing_2736.htm#SEC2812 12854 homogeneitySpace sing_2167.htm#SEC2243 48243 homogfacFirstQWeyl sing_713.htm#SEC765 32751 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_715.htm#SEC767 9014 homogfacNthQWeyl sing_712.htm#SEC764 19238 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_714.htm#SEC766 56179 homolog.lib sing_1160.htm#SEC1236 homolog_lib sing_1160.htm#SEC1236 homology sing_1170.htm#SEC1246 15040 homomorphism sing_2519.htm#SEC2595 27115 howto, download Download instructions sing_2762.htm#SEC2851 howto, install on Macintosh Macintosh installation instructions sing_2765.htm#SEC2854 howto, install on Unix Unix installation instructions sing_2763.htm#SEC2852 howto, install on Windows Windows installation instructions sing_2764.htm#SEC2853 hres sing_263.htm#SEC303 html, default help The online help system sing_16.htm#IDX24 hyperel.lib sing_1945.htm#SEC2021 hyperel_lib sing_1945.htm#SEC2021 hyperplane sing_2174.htm#IDX818 hyperplane arrangement sing_540.htm#IDX337 hypersurface singularity sing_1585.htm#IDX770 iMult sing_1250.htm#SEC1326 22059 id sing_2492.htm#SEC2568 47592 id2mod sing_980.htm#SEC1056 32918 ideal sing_90.htm#SEC130 ideal declarations sing_91.htm#SEC131 ideal declarations (plural) ideal declarations (plural) sing_424.htm#SEC464 ideal expressions sing_92.htm#SEC132 ideal expressions (plural) ideal expressions (plural) sing_425.htm#SEC465 ideal operations sing_93.htm#SEC133 ideal operations (plural) ideal operations (plural) sing_426.htm#SEC466 ideal related functions ideal related functions sing_94.htm#SEC134 ideal related functions (plural) ideal related functions (plural) sing_427.htm#SEC467 ideal, toric sing_874.htm#SEC931 idealSplit sing_1724.htm#SEC1800 4673 ideals Miscellaneous oddities sing_418.htm#IDX293 idealsimplify sing_1486.htm#SEC1562 38569 identifier Identifier resolution sing_419.htm#SEC459 identifyvar sing_1394.htm#SEC1470 59662 if sing_386.htm#SEC426 image sing_2515.htm#SEC2591 43481 imageLattice sing_2565.htm#SEC2641 15740 image_of_variety sing_1674.htm#SEC1750 43711 imap sing_264.htm#SEC304 imap (plural) sing_462.htm#SEC502 imapall sing_1012.htm#SEC1088 16023 impart sing_265.htm#SEC305 importfrom sing_387.htm#SEC427 inCenter sing_529.htm#SEC581 22152 inCentralizer sing_530.htm#SEC582 49000 inForm sing_572.htm#SEC624 5283 inSubring sing_1113.htm#SEC1189 24817 indSet sing_1222.htm#SEC1298 32828 indepSet sing_266.htm#SEC306 indexed names sing_36.htm#IDX82 indexed names sing_37.htm#SEC65 indices, multi sing_37.htm#SEC65 inequalities sing_2037.htm#SEC2113 10122 infRedTail, option sing_315.htm#IDX154 info The online help system sing_16.htm#SEC23 iniD sing_1414.htm#SEC1490 35084 init_debug sing_1493.htm#SEC1569 29863 initial sing_2168.htm#SEC2244 8678 initial form sing_505.htm#IDX318 initial ideal sing_505.htm#IDX317 initial ideal approach sing_505.htm#IDX321 initial ideal approach sing_596.htm#IDX360 initialForm sing_2145.htm#SEC2221 57793 initialIdeal sing_2146.htm#SEC2222 22205 initialIdealW sing_571.htm#SEC623 36086 initialMalgrange sing_570.htm#SEC622 26846 injective_knapsack sing_1939.htm#SEC2015 7619 inout.lib sing_946.htm#SEC1022 inout_lib sing_946.htm#SEC1022 input sing_41.htm#SEC71 insert sing_126.htm#SEC166 insert sing_267.htm#SEC307 insertCone sing_2061.htm#SEC2137 13858 insertGenerator sing_591.htm#SEC643 13951 instructions, Macintosh installation Macintosh installation instructions sing_2765.htm#SEC2854 instructions, Unix installation Unix installation instructions sing_2763.htm#SEC2852 instructions, Windows installation Windows installation instructions sing_2764.htm#SEC2853 instructions, downloading Download instructions sing_2762.htm#SEC2851 int sing_95.htm#SEC135 int declarations sing_96.htm#SEC136 int expressions sing_97.htm#SEC137 int operations sing_98.htm#SEC138 int related functions int related functions sing_99.htm#SEC139 intInverse sing_2574.htm#SEC2650 sprintf intPart sing_1893.htm#SEC1969 48360 intRank sing_2566.htm#SEC2642 1830 intRoot sing_1894.htm#SEC1970 54582 intRoots sing_588.htm#SEC640 24538 intStrategy, option sing_315.htm#IDX155 intclMonIdeal sing_1263.htm#SEC1339 22338 intclToricRing sing_1259.htm#SEC1335 62143 integer division Miscellaneous oddities sing_418.htm#IDX288 integer programming sing_882.htm#SEC939 integral sing_2710.htm#SEC2786 62683 integral basis sing_1182.htm#IDX546 integral basis sing_1377.htm#IDX613 integral closure sing_1243.htm#IDX561 integral closure sing_1244.htm#IDX564 integral closure sing_1245.htm#IDX567 integral closure sing_1258.htm#IDX573 integralBasis sing_1182.htm#SEC1258 38114 integralIdeal sing_575.htm#SEC627 29194 integralModule sing_576.htm#SEC628 58078 integralSection sing_2575.htm#SEC2651 sprintf integralbasis.lib sing_1181.htm#SEC1257 integralbasis_lib sing_1181.htm#SEC1257 integration of D-module sing_563.htm#IDX349 interface, Emacs Emacs user interface sing_21.htm#SEC28 interiorLatticePoints interiorLatticePoints sing_2097.htm#SEC2173 49868 internalfunctions sing_1494.htm#SEC1570 61230 interpolate sing_1730.htm#SEC1806 51502 interpolation sing_268.htm#SEC308 interpret sing_2537.htm#SEC2613 48499 interpretElem sing_2540.htm#SEC2616 51740 interpretInv sing_2538.htm#SEC2614 6149 interpretList sing_2541.htm#SEC2617 64061 interred sing_269.htm#SEC309 intersect sing_270.htm#SEC310 intersect (plural) sing_463.htm#SEC503 intersectElim, option sing_315.htm#IDX173 intersectLattices sing_2571.htm#SEC2647 41354 intersectLists sing_2343.htm#SEC2419 4153 intersectMon sing_1199.htm#SEC1275 44572 intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2436.htm#SEC2512 19444 intersectSyz, option sing_315.htm#IDX174 intersectZ sing_1319.htm#SEC1395 sprintf intersection sing_1568.htm#SEC1644 46938 intersection lattice sing_2210.htm#IDX893 intersection lattice sing_2211.htm#IDX894 intersection multiplicity sing_1479.htm#IDX648 intersection multiplicity sing_1568.htm#IDX763 intersectionDiv sing_1442.htm#SEC1518 29017 intersectionValRingIdeals intersectionValRingIdeals sing_1268.htm#SEC1344 38773 intersectionValRings intersectionValRings sing_1267.htm#SEC1343 35761 intersectpar sing_944.htm#SEC1020 2975 interval arithmetic sing_2680.htm#IDX1029 intmat sing_102.htm#SEC142 intmat declarations sing_103.htm#SEC143 intmat expressions sing_104.htm#SEC144 intmat operations sing_106.htm#SEC146 intmat related functions intmat related functions sing_107.htm#SEC147 intmat type cast sing_105.htm#SEC145 intmat2mons sing_1283.htm#SEC1359 21150 intprog.lib sing_1183.htm#SEC1259 intprog_lib sing_1183.htm#SEC1259 intvec sing_108.htm#SEC148 intvec declarations sing_109.htm#SEC149 intvec expressions sing_110.htm#SEC150 intvec operations sing_111.htm#SEC151 intvec related functions intvec related functions sing_112.htm#SEC152 invariant sing_2349.htm#IDX955 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1643.htm#IDX776 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1644.htm#IDX777 invariantRing sing_1676.htm#SEC1752 18582 invariant_algebra_perm invariant_algebra_perm sing_1644.htm#SEC1720 63525 invariant_algebra_reynolds invariant_algebra_reynolds sing_1643.htm#SEC1719 35705 invariant_basis sing_1651.htm#SEC1727 18343 invariant_basis_reynolds invariant_basis_reynolds sing_1652.htm#SEC1728 54788 invariant_ring sing_1639.htm#SEC1715 8059 invariant_ring_random invariant_ring_random sing_1640.htm#SEC1716 6986 invariants curveColengthDerivations sing_1564.htm#SEC1640 57499 invariants sing_2346.htm#IDX948 invariants sing_2350.htm#IDX957 inverse sing_1081.htm#SEC1157 27411 inverse of a matrix via its LU-decomposition sing_290.htm#SEC330 inverseFourier sing_586.htm#SEC638 65140 inverse_B sing_1082.htm#SEC1158 17616 inverse_L sing_1083.htm#SEC1159 49271 inverse_modulus sing_1922.htm#SEC1998 60822 invertBirMap sing_1378.htm#SEC1454 16086 invertLeftFraction sing_2667.htm#SEC2743 51903 invertNcfrac sing_2615.htm#SEC2691 50842 invertNumberMain sing_1754.htm#SEC1830 62615 involut.lib sing_662.htm#SEC714 involut_lib sing_662.htm#SEC714 involution sing_667.htm#SEC719 34280 invunit sing_1587.htm#SEC1663 62398 iostruct sing_1841.htm#SEC1917 60444 irrRealizationDim sing_2127.htm#SEC2203 7814 irred_secondary_char0 irred_secondary_char0 sing_1665.htm#SEC1741 2943 irred_secondary_no_molien irred_secondary_no_molien sing_1668.htm#SEC1744 55905 irreddecMon sing_1208.htm#SEC1284 20160 irreducible power series sing_1569.htm#IDX764 irreducible secondary invariant irred_secondary_char0 sing_1665.htm#IDX778 isAface sing_2421.htm#SEC2497 25344 isAntiEndo sing_669.htm#SEC721 19156 isBounded sing_2098.htm#SEC2174 28183 isCI sing_209.htm#IDX139 58425 isCI sing_1131.htm#SEC1207 isCM sing_209.htm#IDX140 50469 isCM sing_1171.htm#SEC1247 isCMcod2 sing_1622.htm#SEC1698 2563 isCanonical sing_2099.htm#SEC2175 51109 isCartan sing_531.htm#SEC583 39541 isCentral sing_740.htm#SEC792 54650 isCommutative sing_742.htm#SEC794 60728 isCompatible sing_2062.htm#SEC2138 57323 isCompressed sing_2100.htm#SEC2176 2849 isDenom sing_2619.htm#SEC2695 55537 isEqualDivisor sing_2360.htm#SEC2436 17569 isEquising sing_1531.htm#SEC1607 1424 isFlat sing_1172.htm#SEC1248 14706 isFsat sing_581.htm#SEC633 28225 isFullSpace sing_2038.htm#SEC2114 27433 isGorenstein sing_2101.htm#SEC2177 24010 isGradedRingHomomorphism isGradedRingHomomorphism sing_2560.htm#SEC2636 39551 isGroup sing_2558.htm#SEC2634 55744 isGroupHomomorphism sing_2559.htm#SEC2635 65475 isHolonomic sing_559.htm#SEC611 30274 isHomg sing_209.htm#IDX135 isHomogeneous sing_2586.htm#SEC2662 3034 isInS sing_2656.htm#SEC2732 30907 isInt sing_594.htm#SEC646 9879 isIntegralSurjective isIntegralSurjective sing_2572.htm#SEC2648 sprintf isInvertibleLeftFraction isInvertibleLeftFraction sing_2666.htm#SEC2742 623 isInvertibleNcfrac sing_2614.htm#SEC2690 48367 isInvolution sing_668.htm#SEC720 13601 isLatticeEmpty sing_2102.htm#SEC2178 48517 isLocalizationRegular isLocalizationRegular sing_2417.htm#SEC2493 11221 isLocallyFree sing_1173.htm#SEC1249 46389 isMonomial sing_1194.htm#SEC1270 57615 isNC sing_741.htm#SEC793 57151 isNormal sing_2103.htm#SEC2179 64236 isOnCurve sing_1906.htm#SEC1982 36324 isOneFraction sing_2669.htm#SEC2745 55015 isOneNcfrac sing_2608.htm#SEC2684 12754 isOrigin sing_2039.htm#SEC2115 13977 isPositive sing_2583.htm#SEC2659 50852 isPrimitiveSublattice isPrimitiveSublattice sing_2573.htm#SEC2649 sprintf isPure sing_2063.htm#SEC2139 44002 isPureTensor sing_503.htm#SEC555 21323 isQuotientRing sing_1026.htm#SEC1102 sprintf isRational sing_562.htm#SEC614 57398 isReflexive sing_2104.htm#SEC2180 3991 isReg sing_1174.htm#SEC1250 40920 isSB sing_209.htm#IDX134 isSimplicial sing_2040.htm#SEC2116 57789 isSmooth sing_2105.htm#SEC2181 37647 isSubModule sing_1027.htm#SEC1103 sprintf isSublattice sing_2564.htm#SEC2640 10501 isSymmetric sing_1343.htm#SEC1419 61363 isTame sing_1556.htm#SEC1632 31925 isTerminal sing_2106.htm#SEC2182 29416 isTorsionFree sing_2582.htm#SEC2658 52228 isTwoSidedGB sing_504.htm#SEC556 36558 isUpperTriangular sing_721.htm#SEC773 40655 isVar sing_660.htm#SEC712 43851 isVeryAmple sing_2107.htm#SEC2183 64652 isWeyl sing_743.htm#SEC795 28994 isZeroElement sing_2584.htm#SEC2660 514 isZeroFraction sing_2668.htm#SEC2744 1926 isZeroNcfrac sing_2607.htm#SEC2683 6841 is_NND sing_1572.htm#SEC1648 26564 is_NP sing_1231.htm#SEC1307 43891 is_active sing_1605.htm#SEC1681 6867 is_bijective sing_1118.htm#SEC1194 49512 is_cenBimodule sing_776.htm#SEC828 35450 is_cenSubbimodule sing_777.htm#SEC829 26181 is_ci sing_1606.htm#SEC1682 35370 is_complex sing_1054.htm#SEC1130 1234 is_fix_injective sing_1943.htm#SEC2019 11663 is_h_injective sing_1942.htm#SEC2018 36696 is_injective sing_1116.htm#SEC1192 15776 is_irred sing_1569.htm#SEC1645 51150 is_is sing_1607.htm#SEC1683 64105 is_nested sing_1232.htm#SEC1308 9200 is_prime sing_1923.htm#SEC1999 29018 is_primitive_root sing_1919.htm#SEC1995 42838 is_pure sing_768.htm#SEC820 59105 is_reg sing_1608.htm#SEC1684 18146 is_regs sing_1609.htm#SEC1685 50242 is_surjective sing_1117.htm#SEC1193 57044 is_zero sing_969.htm#SEC1045 24341 isartinianMon sing_1205.htm#SEC1281 1103 isgenericMon sing_1206.htm#SEC1282 14444 ishyper sing_1946.htm#SEC2022 65518 isirreducibleMon sing_1204.htm#SEC1280 22428 isoncurve sing_1947.htm#SEC2023 16384 isparam sing_2010.htm#SEC2086 56395 isprimaryMon sing_1203.htm#SEC1279 57367 isprimeMon sing_1202.htm#SEC1278 9124 isuni sing_1995.htm#SEC2071 39427 iv2lp sing_629.htm#SEC681 59849 iv2lpList sing_630.htm#SEC682 18518 iv2lpMat sing_631.htm#SEC683 21612 ivDHilbert sing_609.htm#SEC661 56709 ivDHilbertSickle sing_610.htm#SEC662 43194 ivDimCheck sing_611.htm#SEC663 258 ivHilbert sing_612.htm#SEC664 37184 ivKDim sing_613.htm#SEC665 26109 ivL2lpI sing_628.htm#SEC680 2454 ivMaxIdeal sing_625.htm#SEC677 48114 ivMis2Base sing_614.htm#SEC666 57812 ivMis2Dim sing_615.htm#SEC667 42072 ivOrdMisLex sing_616.htm#SEC668 27789 ivSickle sing_617.htm#SEC669 42888 ivSickleDim sing_619.htm#SEC671 64347 ivSickleHil sing_618.htm#SEC670 41396 ivmatGaussian sing_2687.htm#SEC2763 37718 ivmatInit sing_2684.htm#SEC2760 22774 ivmatSet sing_2685.htm#SEC2761 53480 jInvariant sing_2139.htm#SEC2215 2369 jOft sing_1878.htm#SEC1954 25716 jacob sing_271.htm#SEC311 jacoblift sing_1588.htm#SEC1664 40125 jacobson sing_1847.htm#SEC1923 59267 jacobson.lib sing_1845.htm#SEC1921 jacobson_lib sing_1845.htm#SEC1921 janet sing_272.htm#SEC312 janet basis sing_2693.htm#IDX1032 jet sing_273.htm#SEC313 jordan sing_1102.htm#SEC1178 16602 jordanbasis sing_1103.htm#SEC1179 12736 jordanmatrix sing_1104.htm#SEC1180 2886 jordannf sing_1105.htm#SEC1181 20535 jungfib sing_1427.htm#SEC1503 5432 jungnormal sing_1426.htm#SEC1502 43561 jungresolve sing_1425.htm#SEC1501 45004 katsura sing_967.htm#SEC1043 45913 kbase sing_274.htm#SEC314 kbase (plural) sing_464.htm#SEC504 keepring sing_388.htm#SEC428 kerHom sing_2536.htm#SEC2612 53906 kernel sing_275.htm#SEC315 kernelLattice sing_2567.htm#SEC2643 36320 kill sing_276.htm#SEC316 killTask sing_1033.htm#SEC1109 39317 killall sing_911.htm#SEC987 34661 killattrib sing_277.htm#SEC317 kmemory sing_910.htm#SEC986 52193 kohom sing_1176.htm#SEC1252 50086 kontrahom sing_1177.htm#SEC1253 58549 koszul sing_278.htm#SEC318 kskernel.lib sing_1579.htm#SEC1655 kskernel_lib sing_1579.htm#SEC1655 l-adic numbers sing_32.htm#SEC46 laguerre sing_279.htm#SEC319 laguerre_solve sing_1726.htm#SEC1802 10155 lastvarGeneral sing_1976.htm#SEC2052 28645 latex.lib sing_1770.htm#SEC1846 latex_lib sing_1770.htm#SEC1846 lattice sing_2211.htm#IDX896 latticeArea sing_2082.htm#SEC2158 53771 latticeBasis sing_2568.htm#SEC2644 43162 latticeCodegree sing_2108.htm#SEC2184 25482 latticeDegree sing_2109.htm#SEC2185 52881 latticePoints sing_2110.htm#SEC2186 41965 latticeVolume sing_2111.htm#SEC2187 42234 laxfrT sing_2384.htm#SEC2460 60899 laxfrX sing_2385.htm#SEC2461 57254 lazy, option sing_315.htm#IDX156 lcm sing_970.htm#SEC1046 44755 lcmMon sing_1197.htm#SEC1273 52749 lcmN sing_1887.htm#SEC1963 52355 lcmofall sing_1407.htm#SEC1483 56889 lead sing_280.htm#SEC320 leadcoef sing_281.htm#SEC321 leadexp sing_282.htm#SEC322 leadmonom sing_283.htm#SEC323 leadmonomial sing_1962.htm#SEC2038 8195 left annihilator ideal sing_540.htm#IDX329 leftInverse sing_1836.htm#SEC1912 41469 leftKernel sing_1834.htm#SEC1910 9292 leftOre sing_2659.htm#SEC2735 44669 length sing_2682.htm#SEC2758 9547 length, option sing_315.htm#IDX157 letplaceGBasis sing_646.htm#SEC698 33757 letterplace correspondence Letterplace correspondence sing_494.htm#SEC546 lex_solve sing_1732.htm#SEC1808 48692 lexicographical ordering sing_860.htm#IDX390 lib2doc sing_60.htm#SEC97 libSingular sing_2761.htm#SEC2850 libcdd sing_1.htm#IDX12 libfac sing_1.htm#IDX6 libparse sing_69.htm#SEC109 library sing_2226.htm#IDX911 library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2420.htm#IDX984 library, info string sing_55.htm#IDX124 library, polybori.lib sing_2226.htm#IDX908 library, template sing_55.htm#SEC92 library, template.lib sing_55.htm#IDX122 lieBracket sing_653.htm#SEC705 50745 lift sing_285.htm#SEC325 lift sing_498.htm#IDX305 lift (plural) sing_465.htm#SEC505 lift_kbase sing_1525.htm#SEC1601 10906 lift_rel_kb sing_1526.htm#SEC1602 13673 liftenvelope sing_501.htm#SEC553 58802 liftstd sing_286.htm#SEC326 liftstd (plural) sing_466.htm#SEC506 linReduce sing_513.htm#SEC565 57527 linReduceIdeal sing_514.htm#SEC566 19076 linSyzSolve sing_515.htm#SEC567 26185 linalg.lib sing_1080.htm#SEC1156 linalg_lib sing_1080.htm#SEC1156 linealityDimension sing_2041.htm#SEC2117 30751 linealitySpace sing_2042.htm#SEC2118 14489 linear algebra sing_210.htm#SEC250 linear algebra sing_289.htm#SEC329 linear algebra sing_290.htm#SEC330 linear algebra sing_291.htm#SEC331 linear code, dual sing_1805.htm#IDX789 linear code, systematic sing_1806.htm#IDX790 linear interreduction sing_505.htm#IDX320 linearCombinations sing_534.htm#SEC586 20514 linearMapKernel sing_533.htm#SEC585 43761 linear_relations sing_1072.htm#SEC1148 45983 linearlyEquivalent sing_2363.htm#SEC2439 28351 linearpart sing_1718.htm#SEC1794 2162 linesHypersurface sing_2732.htm#SEC2808 9129 link Parallelization with ssi links sing_113.htm#SEC153 link sing_815.htm#SEC867 link declarations sing_114.htm#SEC154 link expressions sing_115.htm#SEC155 link related functions link related functions sing_116.htm#SEC156 list sing_123.htm#SEC163 list declarations sing_124.htm#SEC164 list expressions sing_125.htm#SEC165 list operations sing_126.htm#SEC166 list related functions list related functions sing_127.htm#SEC167 lists sing_2343.htm#IDX944 lists, elements sing_2345.htm#IDX946 listvar sing_287.htm#SEC327 lll sing_2600.htm#SEC2676 35827 load sing_389.htm#SEC429 loadLib, option sing_315.htm#IDX178 loadProc, option sing_315.htm#IDX179 locAtZero sing_1252.htm#SEC1328 5687 locNormal sing_1186.htm#SEC1262 52237 locStatus sing_2654.htm#SEC2730 54575 local methods sing_1185.htm#IDX549 local methods sing_1186.htm#IDX552 local names sing_46.htm#SEC83 local rings, computing in Rings associated to monomial orderings sing_810.htm#SEC862 local weighted lexicographical ordering sing_861.htm#IDX411 local weighted reverse lexicographical ordering Local orderings sing_861.htm#IDX408 localInvar sing_1681.htm#SEC1757 38478 localization Rings associated to monomial orderings sing_810.htm#SEC862 localization sing_2191.htm#IDX856 localization of D-module sing_563.htm#IDX345 localization of D-module sing_780.htm#IDX383 locally closed set sing_928.htm#IDX435 locally closed set sing_929.htm#IDX437 locally closed set sing_930.htm#IDX439 locally closed set sing_931.htm#IDX443 locally closed set sing_933.htm#IDX453 localstd sing_1972.htm#SEC2048 25562 locnormal.lib sing_1185.htm#SEC1261 locnormal_lib sing_1185.htm#SEC1261 locstd sing_1610.htm#SEC1686 25864 locus FamElemsAtEnvCompPoints sing_935.htm#SEC1011 22530 locus sing_935.htm#IDX458 locus sing_936.htm#IDX461 locus sing_937.htm#IDX464 locus sing_938.htm#IDX467 locus sing_939.htm#IDX470 locus sing_940.htm#IDX472 locus sing_941.htm#IDX476 locusdg sing_936.htm#SEC1012 6077 locusto sing_938.htm#SEC1014 730 log2 sing_1862.htm#SEC1938 40703 logarithmic annihilator ideal sing_540.htm#IDX334 logg sing_2737.htm#SEC2813 38736 lp, global ordering sing_860.htm#IDX389 lp2iv sing_632.htm#SEC684 17398 lp2ivId sing_633.htm#SEC685 16290 lp2lstr sing_654.htm#SEC706 24713 lpCalcSubstDegBound sing_642.htm#SEC694 46179 lpCalcSubstDegBounds lpCalcSubstDegBounds sing_643.htm#SEC695 56500 lpDHilbert sing_607.htm#SEC659 10461 lpDHilbertSickle sing_608.htm#SEC660 41445 lpDimCheck sing_604.htm#SEC656 9807 lpGkDim sing_639.htm#SEC691 10351 lpGlDimBound sing_640.htm#SEC692 53074 lpHilbert sing_606.htm#SEC658 44093 lpId2ivLi sing_634.htm#SEC686 13273 lpIsPrime sing_638.htm#SEC690 27562 lpIsSemiPrime sing_637.htm#SEC689 27642 lpKDim sing_603.htm#SEC655 18278 lpMaxIdeal sing_626.htm#SEC678 37571 lpMis2Base sing_605.htm#SEC657 10826 lpMis2Dim sing_602.htm#SEC654 39947 lpMult sing_650.htm#SEC702 58898 lpNF sing_647.htm#SEC699 2851 lpNoetherian sing_636.htm#SEC688 43125 lpOrdMisLex sing_620.htm#SEC672 30943 lpPower sing_652.htm#SEC704 7325 lpSickle sing_621.htm#SEC673 288 lpSickleDim sing_623.htm#SEC675 61018 lpSickleHil sing_622.htm#SEC674 55268 lpSubstitute sing_641.htm#SEC693 54386 lprint sing_948.htm#SEC1024 5285 lres sing_288.htm#SEC328 ls, local ordering sing_861.htm#IDX402 lst2str sing_655.htm#SEC707 10088 lsum sing_1152.htm#SEC1228 50315 ludecomp sing_289.htm#SEC329 luinverse sing_290.htm#SEC330 lusolve sing_291.htm#SEC331 mRes sing_2504.htm#SEC2580 58702 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1934.htm#SEC2010 57945 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1933.htm#SEC2009 33857 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1932.htm#SEC2008 7880 magnitude sing_1856.htm#SEC1932 37967 makeDivisor sing_2355.htm#SEC2431 3414 makeFormalDivisor sing_2365.htm#SEC2441 54579 makeGraph sing_1143.htm#SEC1219 21758 makeGraphVE sing_2723.htm#SEC2799 sprintf makeHeisenberg sing_731.htm#SEC783 2050 makeIdeal sing_2496.htm#SEC2572 57829 makeLetterplaceRing sing_645.htm#SEC697 1592 makeMalgrange sing_600.htm#SEC652 41377 makeMatrix sing_2495.htm#SEC2571 64348 makeModElimRing sing_748.htm#SEC800 56092 makePDivisor sing_2371.htm#SEC2447 45273 makeQsl2 sing_695.htm#SEC747 3997 makeQsl3 sing_696.htm#SEC748 41249 makeQso3 sing_694.htm#SEC746 58910 makeSheaf sing_2711.htm#SEC2787 10497 makeUe6 sing_691.htm#SEC743 58585 makeUe7 sing_692.htm#SEC744 61849 makeUe8 sing_693.htm#SEC745 64987 makeUf4 sing_690.htm#SEC742 8408 makeUg2 sing_689.htm#SEC741 34512 makeUgl sing_675.htm#SEC727 3543 makeUsl sing_674.htm#SEC726 24536 makeUsl2 sing_673.htm#SEC725 42637 makeUso10 sing_681.htm#SEC733 6936 makeUso11 sing_682.htm#SEC734 35873 makeUso12 sing_683.htm#SEC735 19319 makeUso5 sing_676.htm#SEC728 34378 makeUso6 sing_677.htm#SEC729 65009 makeUso7 sing_678.htm#SEC730 49142 makeUso8 sing_679.htm#SEC731 33275 makeUso9 sing_680.htm#SEC732 16896 makeUsp1 sing_684.htm#SEC736 44522 makeUsp2 sing_685.htm#SEC737 18017 makeUsp3 sing_686.htm#SEC738 57445 makeUsp4 sing_687.htm#SEC739 51690 makeUsp5 sing_688.htm#SEC740 35951 makeVariety sing_2703.htm#SEC2779 23915 makeVector sing_2524.htm#SEC2600 9049 makeWeyl sing_730.htm#SEC782 8554 map sing_128.htm#SEC168 map (plural) sing_428.htm#SEC468 map declarations sing_129.htm#SEC169 map declarations (plural) map declarations (plural) sing_429.htm#SEC469 map expressions sing_130.htm#SEC170 map expressions (plural) map expressions (plural) sing_430.htm#SEC470 map operations sing_131.htm#IDX129 map operations (plural) map operations (plural) sing_431.htm#IDX300 map related functions map related functions sing_132.htm#IDX131 map related functions (plural) map related functions (plural) sing_432.htm#IDX301 mapIsFinite sing_1120.htm#SEC1196 60897 mapToRatNormCurve sing_1382.htm#SEC1458 8877 mapall sing_1013.htm#SEC1089 14907 mappingcone sing_2482.htm#SEC2558 48219 mappingcone3 sing_2484.htm#SEC2560 58973 markov4ti2 sing_1338.htm#SEC1414 9163 mat2arr sing_2176.htm#SEC2252 20840 mat2carr sing_2177.htm#SEC2253 13777 mat_rk sing_1094.htm#SEC1170 32196 matbil sing_1983.htm#SEC2059 1611 mathematical objects Representation of mathematical objects sing_856.htm#SEC908 mathinit sing_1768.htm#SEC1844 16793 matmult sing_1984.htm#SEC2060 60088 matrix sing_133.htm#SEC173 matrix sing_2176.htm#IDX824 matrix sing_2177.htm#IDX827 matrix sing_2178.htm#IDX831 matrix declarations sing_134.htm#SEC174 matrix diagonalization sing_1845.htm#IDX800 matrix expressions sing_135.htm#SEC175 matrix operations sing_137.htm#SEC177 matrix related functions matrix related functions sing_138.htm#SEC178 matrix type cast sing_136.htm#SEC176 matrix.lib sing_1047.htm#SEC1123 matrixExp sing_1372.htm#SEC1448 53063 matrixLog sing_1373.htm#SEC1449 26235 matrixT1 sing_1624.htm#SEC1700 15051 matrix_lib sing_1047.htm#SEC1123 matrixpres sing_2487.htm#SEC2563 60645 matrixsystem sing_2395.htm#SEC2471 62950 max sing_292.htm#SEC332 23624 maxEord sing_1397.htm#SEC1473 64032 maxExp sing_209.htm#IDX136 maxIntRoot sing_797.htm#SEC849 37127 maxZeros sing_1375.htm#SEC1451 35964 maxabs sing_2002.htm#SEC2078 64510 maxcoef sing_971.htm#SEC1047 50577 maxdeg sing_972.htm#SEC1048 39794 maxdeg1 sing_973.htm#SEC1049 21545 maxideal sing_293.htm#SEC333 maximalFace sing_2112.htm#SEC2188 35224 maximalGroebnerCone sing_2166.htm#SEC2242 62935 maximalValue sing_2113.htm#SEC2189 32783 maximum sing_1875.htm#SEC1951 2355 maximum number of zeroes sing_1375.htm#IDX607 mdouble sing_56.htm#SEC93 56685 mem, option sing_315.htm#IDX180 member sing_2345.htm#SEC2421 1765 membershipMon sing_1198.htm#SEC1274 40876 memory sing_294.htm#SEC334 memory managment sing_294.htm#SEC334 merkle_hellman_decryption merkle_hellman_decryption sing_1936.htm#SEC2012 49106 merkle_hellman_encryption merkle_hellman_encryption sing_1935.htm#SEC2011 13645 methods, hashtables sing_2490.htm#IDX988 methods.lib sing_2490.htm#SEC2566 methods_lib sing_2490.htm#SEC2566 midpoint sing_2391.htm#SEC2467 29391 milnor sing_1611.htm#SEC1687 23173 milnorcode sing_1495.htm#SEC1571 13849 milnornumber sing_2677.htm#SEC2753 21855 min sing_295.htm#SEC335 56342 minAssChar sing_1297.htm#SEC1373 18758 minAssCharE sing_1298.htm#SEC1374 31570 minAssGTZ sing_1295.htm#SEC1371 41315 minAssGTZE sing_1296.htm#SEC1372 50867 minAssZ sing_1315.htm#SEC1391 54152 minEcart sing_1965.htm#SEC2041 34890 minIntRoot sing_561.htm#SEC613 3288 minIntRoot2 sing_796.htm#SEC848 46494 minMult sing_1127.htm#SEC1203 31978 minbase sing_296.htm#SEC336 minbaseMon sing_1195.htm#SEC1271 1501 mindeg sing_974.htm#SEC1050 16307 mindeg1 sing_975.htm#SEC1051 39698 mindist sing_1820.htm#SEC1896 55281 minimal display time, setting the sing_358.htm#IDX284 minimalAfaceOrbits sing_2433.htm#SEC2509 2467 minimalAfaces sing_2424.htm#SEC2500 47736 minimalFace sing_2114.htm#SEC2190 40971 minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2435.htm#SEC2511 11756 minimalValue sing_2115.htm#SEC2191 31262 minipoly sing_1099.htm#SEC1175 4927 minkowskiSum sing_2116.htm#SEC2192 3969 minor sing_297.htm#SEC337 minpoly sing_397.htm#SEC437 minres sing_298.htm#SEC338 minres (plural) sing_467.htm#SEC507 mirror symmetry sing_1142.htm#IDX517 mixed Hodge structure sing_1533.htm#IDX663 mixed Hodge structure sing_1539.htm#IDX691 mixed Hodge structure sing_1540.htm#IDX697 mixed Hodge structure sing_1541.htm#IDX705 mixed Hodge structure sing_1542.htm#IDX711 mixed Hodge structure sing_1543.htm#IDX719 mixed Hodge structure sing_1544.htm#IDX729 mixed Hodge structure sing_1555.htm#IDX735 mixed Hodge structure sing_1557.htm#IDX746 mod sing_81.htm#SEC121 mod sing_98.htm#SEC138 mod sing_147.htm#SEC187 mod sing_155.htm#SEC195 mod2id sing_979.htm#SEC1055 27927 mod2str sing_656.htm#SEC708 35236 modBorder sing_2695.htm#SEC2771 19224 modDec sing_1214.htm#SEC1290 48578 modIntersect sing_1192.htm#SEC1268 43699 modJanet sing_2697.htm#SEC2773 8550 modNPos sing_1237.htm#SEC1313 17130 modNormal sing_1188.htm#SEC1264 39654 modNpos_test sing_1235.htm#SEC1311 34326 modSagbiAlg sing_2332.htm#SEC2408 25025 modStd sing_1190.htm#SEC1266 7824 modSyz sing_1191.htm#SEC1267 37065 modVStd sing_2337.htm#SEC2413 38529 modVStd0 sing_2338.htm#SEC2414 46080 modWalk sing_2545.htm#SEC2621 sprintf mod_versal sing_1524.htm#SEC1600 63927 modality sing_1503.htm#SEC1579 49951 modfWalk sing_2547.htm#SEC2623 sprintf modfrWalk sing_2548.htm#SEC2624 sprintf modnormal.lib sing_1187.htm#SEC1263 modnormal_lib sing_1187.htm#SEC1263 modrWalk sing_2546.htm#SEC2622 sprintf modregCM sing_1241.htm#SEC1317 5049 modsatiety sing_1239.htm#SEC1315 44506 modstd.lib sing_1189.htm#SEC1265 modstd_lib sing_1189.htm#SEC1265 modular sing_957.htm#SEC1033 16950 modular methods sing_1185.htm#IDX550 modular methods sing_1187.htm#IDX555 modular methods. sing_1186.htm#IDX553 modular techniques. sing_1188.htm#IDX557 modular.lib sing_956.htm#SEC1032 modular_lib sing_956.htm#SEC1032 modular_lib sing_956.htm#IDX485 module sing_139.htm#SEC179 module (plural) sing_433.htm#SEC473 module declarations sing_140.htm#SEC180 module declarations (plural) module declarations (plural) sing_434.htm#SEC474 module expressions sing_141.htm#SEC181 module expressions (plural) module expressions (plural) sing_435.htm#SEC475 module operations sing_142.htm#SEC182 module operations (plural) module operations (plural) sing_436.htm#SEC476 module ordering C sing_862.htm#IDX414 module ordering c sing_862.htm#IDX416 module related functions module related functions sing_143.htm#SEC183 module related functions (plural) module related functions (plural) sing_437.htm#SEC477 module_containment sing_1112.htm#SEC1188 31620 modules.lib sing_2491.htm#SEC2567 modules_lib sing_2491.htm#SEC2567 moduliSpace sing_2725.htm#SEC2801 37013 modulo sing_299.htm#SEC339 modulo (plural) sing_468.htm#SEC508 moduloSlim sing_738.htm#SEC790 52636 modwalk.lib sing_2544.htm#SEC2620 modwalk_lib sing_2544.htm#SEC2620 moebius sing_2212.htm#SEC2288 61319 moebius function sing_2212.htm#IDX897 molien sing_1647.htm#SEC1723 63561 mondromy.lib sing_1585.htm#SEC1661 mondromy_lib sing_1585.htm#SEC1661 monitor sing_300.htm#SEC340 monodromy sing_1533.htm#IDX667 40112 monodromy sing_1538.htm#SEC1614 monodromy sing_1538.htm#IDX687 monodromy sing_1543.htm#IDX722 monodromy sing_1555.htm#IDX738 monodromy sing_1557.htm#IDX749 monodromyB sing_1589.htm#SEC1665 46517 monomial sing_301.htm#SEC341 monomial ordering sing_1022.htm#IDX499 monomial orderings General definitions for orderings sing_810.htm#SEC862 monomial orderings sing_859.htm#SEC911 monomial orderings introduction Introduction to orderings sing_858.htm#SEC910 monomialBasis sing_627.htm#SEC679 14185 monomialInIdeal sing_794.htm#SEC846 4687 monomialLcm sing_1963.htm#SEC2039 36233 monomialabortstd sing_2219.htm#SEC2295 14901 monomialideal.lib sing_1193.htm#SEC1269 monomialideal_lib sing_1193.htm#SEC1269 monomials and precedence Miscellaneous oddities sing_418.htm#IDX290 mons2intmat sing_1282.htm#SEC1358 15555 morsesplit sing_1496.htm#SEC1572 3417 movingCone sing_2431.htm#SEC2507 39892 mp_res_mat sing_1729.htm#SEC1805 44453 mplot sing_1769.htm#SEC1845 21740 mpresmat sing_302.htm#SEC342 mprimdec.lib sing_1210.htm#SEC1286 mprimdec_lib sing_1210.htm#SEC1286 mregular.lib sing_1225.htm#SEC1301 mregular_lib sing_1225.htm#SEC1301 mres sing_303.htm#SEC343 mres (plural) sing_469.htm#SEC509 mstd sing_304.htm#SEC344 msum sing_58.htm#SEC95 53344 mtriple sing_57.htm#SEC94 55390 mult Miscellaneous oddities sing_305.htm#SEC345 mult sing_418.htm#IDX291 multBound sing_398.htm#SEC438 multRat sing_802.htm#SEC854 44047 multarr2arr sing_2207.htm#SEC2283 44731 multarrMultRestrict sing_2209.htm#SEC2285 41742 multarrRestrict sing_2208.htm#SEC2284 sprintf multcol sing_1066.htm#SEC1142 21899 multdivisor sing_2357.htm#SEC2433 65139 multformaldivisor sing_2369.htm#SEC2445 32238 multi sing_1950.htm#SEC2026 18473 multi indices sing_37.htm#SEC65 multiDeg sing_2579.htm#SEC2655 7049 multiDegBasis sing_2580.htm#SEC2656 3320 multiDegGroebner sing_2588.htm#SEC2664 1040 multiDegModulo sing_2590.htm#SEC2666 27244 multiDegPartition sing_2581.htm#SEC2657 9577 multiDegResolution sing_2591.htm#SEC2667 38535 multiDegSyzygy sing_2589.htm#SEC2665 54075 multiDegTensor sing_2592.htm#SEC2668 45108 multiDegTor sing_2593.htm#SEC2669 sprintf multiarrangement sing_2203.htm#IDX877 multiarrangement sing_2204.htm#IDX879 multiarrangement sing_2205.htm#IDX882 multiarrangement sing_2206.htm#IDX883 multiarrangement sing_2207.htm#IDX886 multiarrangement sing_2208.htm#IDX889 multiarrangement sing_2209.htm#IDX891 multidimensional_knapsack multidimensional_knapsack sing_1928.htm#SEC2004 15647 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2549.htm#IDX995 multigrading.lib sing_2549.htm#IDX993 multigrading_lib sing_2549.htm#IDX994 multipleCover sing_2731.htm#SEC2807 55988 multiplicities, sequence of sing_1564.htm#IDX761 multiplicity sing_2348.htm#IDX953 multiplicity sequence sing_1477.htm#IDX640 multiplicity sequence sing_1480.htm#IDX652 multiplicity sequence sing_1566.htm#IDX762 multiplyLeftFractions multiplyLeftFractions sing_2664.htm#SEC2740 57489 multiplylist sing_1417.htm#SEC1493 34999 multivariate equations sing_1703.htm#IDX779 multrow sing_1067.htm#SEC1143 871 multseq2charexp sing_1476.htm#SEC1552 sprintf multsequence sing_1566.htm#SEC1642 35117 nBoundaryLatticePoints nBoundaryLatticePoints sing_2117.htm#SEC2193 49670 nHilbertBasis sing_2118.htm#SEC2194 173 nInteriorLatticePoints nInteriorLatticePoints sing_2119.htm#SEC2195 42152 nLatticePoints sing_2120.htm#SEC2196 5977 naccache_stern_decryption naccache_stern_decryption sing_1931.htm#SEC2007 31429 naccache_stern_encryption naccache_stern_encryption sing_1930.htm#SEC2006 60034 naccache_stern_generation naccache_stern_generation sing_1929.htm#SEC2005 2559 nameof sing_306.htm#SEC346 names sing_307.htm#SEC347 nashmult sing_1484.htm#SEC1560 8491 nblocks sing_358.htm#IDX221 ncExt_R sing_771.htm#SEC823 14357 ncHilb.lib sing_2601.htm#SEC2677 ncHilb_lib sing_2601.htm#SEC2677 ncHom sing_772.htm#SEC824 45033 ncRelations sing_739.htm#SEC791 7225 nc_algebra sing_470.htm#SEC510 nc_hilb sing_358.htm#IDX223 ncalg.lib sing_672.htm#SEC724 ncalg_lib sing_672.htm#SEC724 ncalgebra sing_471.htm#SEC511 ncdecomp.lib sing_699.htm#SEC751 ncdecomp_lib sing_699.htm#SEC751 ncdetection sing_666.htm#SEC718 24994 ncfactor sing_705.htm#SEC757 53809 ncfactor.lib sing_704.htm#SEC756 ncfactor_lib sing_704.htm#SEC756 ncfrac.lib sing_2604.htm#SEC2680 ncfrac_lib sing_2604.htm#SEC2680 nchilb sing_2602.htm#SEC2678 40517 nchomolog.lib sing_770.htm#IDX373 nchomolog_lib sing_770.htm#IDX374 ncloc.lib sing_2618.htm#SEC2694 ncloc_lib sing_2618.htm#SEC2694 ncols sing_308.htm#SEC348 ncones sing_2065.htm#SEC2141 48316 ncpreim.lib sing_717.htm#SEC769 ncpreim_lib sing_717.htm#SEC769 nctools.lib sing_725.htm#SEC777 nctools_lib sing_725.htm#SEC777 ndcond sing_728.htm#SEC780 1006 negateNcfrac sing_2613.htm#SEC2689 23626 negatedCone sing_2043.htm#SEC2119 38527 negative degree lexicographical ordering sing_861.htm#IDX405 negative degree reverse lexicographical ordering Local orderings sing_861.htm#IDX403 negative lexicographical ordering sing_861.htm#IDX401 negativedivisor sing_2358.htm#SEC2434 8274 negativeformaldivisor negativeformaldivisor sing_2368.htm#SEC2444 55026 net sing_2622.htm#IDX996 sprintf net sing_2624.htm#SEC2700 net access Command line options sing_19.htm#IDX40 netBigInt sing_2630.htm#SEC2706 63523 netBigIntMat sing_2625.htm#SEC2701 36296 netBigIntMatShort sing_2626.htm#SEC2702 30702 netCoefficientRing sing_2627.htm#SEC2703 6081 netIdeal sing_2628.htm#SEC2704 64434 netInt sing_2629.htm#SEC2705 19545 netIntMat sing_2631.htm#SEC2707 34242 netIntMatShort sing_2632.htm#SEC2708 21160 netIntVector sing_2633.htm#SEC2709 17568 netIntVectorShort sing_2634.htm#SEC2710 16105 netList sing_2636.htm#SEC2712 29178 netMap sing_2637.htm#SEC2713 19115 netMap2 sing_2638.htm#SEC2714 44053 netMatrix sing_2526.htm#SEC2602 29311 netNumber sing_2635.htm#SEC2711 24930 netPoly sing_2641.htm#SEC2717 7938 netPrimePower sing_2642.htm#SEC2718 54219 netRing sing_2643.htm#SEC2719 42246 netString sing_2644.htm#SEC2720 43247 netVector sing_2525.htm#SEC2601 32453 netmatrix sing_2639.htm#SEC2715 4023 netmatrixShort sing_2640.htm#SEC2716 24709 nets.lib sing_2622.htm#SEC2698 nets_lib sing_2622.htm#SEC2698 netvector sing_2645.htm#SEC2721 39957 netvectorShort sing_2646.htm#SEC2722 22053 newTest sing_1870.htm#SEC1946 36655 newline sing_171.htm#SEC211 news sing_2754.htm#SEC2830 newstruct sing_182.htm#SEC222 newstruct sing_2226.htm#IDX913 newtonDiag sing_983.htm#SEC1059 56652 newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2747.htm#SEC2823 22052 newtonPolytope sing_2069.htm#SEC2145 56291 newtonPolytopeLP sing_2074.htm#SEC2150 36186 newtonPolytopeP sing_2073.htm#SEC2149 29927 newtonpoly sing_1571.htm#SEC1647 31930 nf_icis sing_1612.htm#SEC1688 49093 nfmodStd sing_2650.htm#SEC2726 46077 nfmodSyz sing_2652.htm#SEC2728 55942 nfmodstd.lib sing_2648.htm#SEC2724 nfmodstd_lib sing_2648.htm#SEC2724 nfmodsyz.lib sing_2651.htm#SEC2727 nfmodsyz_lib sing_2651.htm#SEC2727 nilpotent Lie algebras sing_1370.htm#IDX592 nmaxcones sing_2064.htm#SEC2140 660 noether sing_399.htm#SEC439 noether.lib sing_1233.htm#SEC1309 noetherNormal sing_1119.htm#SEC1195 44522 noether_lib sing_1233.htm#SEC1309 non-english special characters sing_407.htm#IDX286 nonMonomials sing_1286.htm#SEC1362 16309 nonZeroEntry sing_1122.htm#SEC1198 933 none, option sing_315.htm#IDX150 norTest sing_1253.htm#SEC1329 sprintf norm sing_1949.htm#SEC2025 31143 normaform (up to a bound) sing_358.htm#IDX246 normal sing_1243.htm#SEC1319 61073 normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2730.htm#IDX1061 normal form sing_868.htm#IDX417 normal.lib sing_1242.htm#SEC1318 normalBundle sing_2730.htm#SEC2806 sprintf normalC sing_1245.htm#SEC1321 34842 normalConductor sing_1257.htm#SEC1333 26085 normalFan sing_2121.htm#SEC2197 39216 normalForm sing_2359.htm#SEC2435 34962 normalI sing_1330.htm#SEC1406 7516 normalP sing_1244.htm#SEC1320 36584 normalToricRing sing_1260.htm#SEC1336 29638 normalToricRingFromBinomials normalToricRingFromBinomials sing_1261.htm#SEC1337 2301 normal_lib sing_1242.htm#SEC1318 normalform sing_1500.htm#SEC1576 5550 normalform sing_2331.htm#IDX941 normaliz sing_1.htm#IDX14 18426 normaliz sing_1273.htm#SEC1349 normaliz.lib sing_1258.htm#SEC1334 normaliz_lib sing_1258.htm#SEC1334 normalization sing_1185.htm#IDX548 normalization sing_1186.htm#IDX551 normalization sing_1187.htm#IDX554 normalization sing_1188.htm#IDX556 normalization sing_1243.htm#IDX560 normalization sing_1244.htm#IDX563 normalization sing_1245.htm#IDX566 normalization sing_1257.htm#IDX572 normalization sing_1258.htm#IDX574 normalization sing_2347.htm#IDX951 normalization. sing_1182.htm#IDX547 normalization. sing_1377.htm#IDX614 normalize sing_976.htm#SEC1052 44788 normalizeMonoidal sing_2670.htm#SEC2746 33071 normalizeRational sing_2671.htm#SEC2747 55177 not sing_101.htm#SEC141 notBuckets, option sing_315.htm#IDX160 notRegularity, option sing_315.htm#IDX158 notSugar, option sing_315.htm#IDX159 notWarnSB, option sing_315.htm#IDX181 npar sing_1855.htm#SEC1931 5753 npars sing_309.htm#SEC349 nrRootsDeterm sing_1980.htm#SEC2056 sprintf nrRootsProbab sing_1979.htm#SEC2055 sprintf nres sing_310.htm#SEC350 nres (plural) sing_472.htm#SEC512 nrows sing_311.htm#SEC351 nrroots sing_2009.htm#SEC2085 54867 nsatiety sing_1238.htm#SEC1314 53333 nselect sing_1138.htm#SEC1214 34057 nt_solve sing_1744.htm#SEC1820 33061 ntsolve.lib sing_1743.htm#SEC1819 ntsolve_lib sing_1743.htm#SEC1819 number sing_144.htm#SEC184 number sing_2180.htm#IDX837 number declarations sing_145.htm#SEC185 number expressions sing_146.htm#SEC186 number operations sing_147.htm#SEC187 number related functions number related functions sing_148.htm#SEC188 numberOfConesOfDimension numberOfConesOfDimension sing_2066.htm#SEC2142 5905 number_e sing_912.htm#SEC988 59152 number_pi sing_913.htm#SEC989 15492 numerAlg.lib sing_1352.htm#IDX581 numerAlg_lib sing_1352.htm#IDX582 numerAlg_lib sing_1357.htm#IDX591 numerDecom.lib sing_1357.htm#IDX585 numerDecom_lib sing_1352.htm#IDX584 numerDecom_lib sing_1357.htm#IDX586 numerator sing_312.htm#SEC352 numerical irreducible decomposition sing_1357.htm#IDX587 nvars sing_313.htm#SEC353 olga.lib sing_2653.htm#SEC2729 olga_lib sing_2653.htm#SEC2729 oneDimBelongSemigroup oneDimBelongSemigroup sing_1129.htm#SEC1205 34399 oneNcfrac sing_2610.htm#SEC2686 35654 online help The online help system sing_16.htm#SEC22 open sing_314.htm#SEC354 opentex sing_1772.htm#SEC1848 54236 operatorBM sing_547.htm#SEC599 54875 operatorModulo sing_548.htm#SEC600 26064 oppose sing_473.htm#SEC513 opposite sing_474.htm#SEC514 opposite polynomial sing_358.htm#IDX231 opposite ring sing_358.htm#IDX228 option sing_315.htm#SEC355 option(warn) sing_70.htm#SEC110 optionIsSet sing_1019.htm#SEC1095 57325 or Evaluation of logical expressions sing_101.htm#SEC141 or sing_411.htm#SEC451 orbit sing_1370.htm#IDX594 orbit sing_1371.htm#IDX598 orbit sing_1374.htm#IDX603 orbit sing_1375.htm#IDX606 orbitConeOrbits sing_2434.htm#SEC2510 60979 orbitCones sing_2425.htm#SEC2501 60528 orbit_variety sing_1671.htm#SEC1747 22665 orbitparam.lib sing_1370.htm#SEC1446 orbitparam_lib sing_1370.htm#SEC1446 ord sing_316.htm#SEC356 ord_test sing_1014.htm#SEC1090 36532 order ideal, border basis sing_2694.htm#IDX1033 order ideal, border basis sing_2695.htm#IDX1034 orderings General definitions for orderings sing_859.htm#SEC911 orderings introduction Introduction to orderings sing_858.htm#SEC910 orderings, L sing_866.htm#SEC918 orderings, M sing_863.htm#SEC915 orderings, a sing_865.htm#SEC917 orderings, global sing_860.htm#SEC912 orderings, local sing_861.htm#SEC913 orderings, product sing_864.htm#SEC916 ordstr sing_317.htm#SEC357 origin sing_2014.htm#SEC2090 31408 orthogonalize sing_1085.htm#SEC1161 63711 outer sing_1055.htm#SEC1131 64048 output sing_41.htm#SEC71 p-adic numbers sing_32.htm#SEC46 pFactor sing_1904.htm#SEC1980 31504 pIntersect sing_511.htm#SEC563 44055 pIntersectSyz sing_512.htm#SEC564 45608 package sing_149.htm#SEC189 package declarations package declarations sing_150.htm#SEC190 package related functions package related functions sing_151.htm#SEC191 pairset sing_1969.htm#SEC2045 38258 par sing_318.htm#SEC358 par2varRing sing_896.htm#SEC972 44769 paraConic sing_1385.htm#SEC1461 9828 paraPlaneCurve sing_1379.htm#SEC1455 34094 parallel skeletons sing_958.htm#IDX491 parallel.lib sing_958.htm#SEC1034 parallelTestAND sing_962.htm#SEC1038 1415 parallelTestOR sing_963.htm#SEC1039 14920 parallelWaitAll sing_961.htm#SEC1037 2017 parallelWaitFirst sing_960.htm#SEC1036 32 parallelWaitN sing_959.htm#SEC1035 38878 parallel_lib sing_958.htm#SEC1034 parallelization sing_958.htm#IDX490 parallelization sing_998.htm#IDX493 parallelization sing_1031.htm#IDX503 param sing_1562.htm#SEC1638 57220 parameter, as numbers sing_144.htm#SEC184 parameterSubstitute sing_2161.htm#SEC2237 63147 parametric annihilator sing_540.htm#IDX335 parametric annihilator for variety sing_596.htm#IDX358 parametric ideal sing_924.htm#IDX423 parametric ideal sing_931.htm#IDX442 parametric ideal sing_931.htm#IDX444 parametric ideal sing_932.htm#IDX449 parametrization sing_1370.htm#IDX595 parametrization sing_1374.htm#IDX604 parametrization sing_1562.htm#IDX756 parametrizeOrbit sing_1374.htm#SEC1450 26969 paraplanecurves.lib sing_1376.htm#SEC1452 paraplanecurves_lib sing_1376.htm#SEC1452 pardeg sing_319.htm#SEC359 parstr sing_320.htm#SEC360 part sing_2307.htm#SEC2383 31485 partOver sing_2310.htm#SEC2386 25555 partUnder sing_2311.htm#SEC2387 13123 partial_molien sing_1649.htm#SEC1725 21772 partitions sing_1150.htm#SEC1226 48089 partitions sing_1150.htm#IDX536 path integral sing_1142.htm#IDX523 pause sing_955.htm#SEC1031 2273 pdivi sing_926.htm#SEC1002 21786 pdivi sing_927.htm#IDX433 pdivisorplus sing_2373.htm#SEC2449 47486 permcol sing_1068.htm#SEC1144 12886 permrow sing_1069.htm#SEC1145 26561 permutationFromIntvec permutationFromIntvec sing_2440.htm#SEC2516 6533 permutationToIntvec sing_2441.htm#SEC2517 1989 permutations sing_1151.htm#IDX537 permutations, sum, max, min sing_2342.htm#IDX943 permute sing_1151.htm#SEC1227 40893 permute_L sing_1807.htm#SEC1883 10716 perron sing_751.htm#SEC803 3782 perron.lib sing_750.htm#SEC802 perron_lib sing_750.htm#SEC802 phindex.lib sing_2221.htm#IDX904 phindex_lib sing_2221.htm#IDX905 picksFormula sing_2083.htm#SEC2159 14656 pid sing_358.htm#IDX240 plainInvariants sing_1521.htm#SEC1597 40916 planeCur sing_2329.htm#SEC2405 sprintf plot sing_1785.htm#SEC1861 46610 plotRot sing_1789.htm#SEC1865 57150 plotRotated sing_1788.htm#SEC1864 33009 plotRotatedDirect sing_1791.htm#SEC1867 18202 plotRotatedList sing_1790.htm#SEC1866 41668 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1792.htm#SEC1868 38856 plural sing_1021.htm#IDX498 pmat sing_949.htm#SEC1025 3857 pnormalf sing_927.htm#SEC1003 26174 pointid.lib sing_1285.htm#SEC1361 pointid_lib sing_1285.htm#SEC1361 polSol sing_786.htm#SEC838 323 polSolFiniteRank sing_787.htm#SEC839 30875 pollTask sing_1041.htm#SEC1117 53950 poly sing_152.htm#SEC192 poly (plural) sing_438.htm#SEC478 poly declarations sing_153.htm#SEC193 poly declarations (plural) poly declarations (plural) sing_439.htm#SEC479 poly expressions sing_154.htm#SEC194 poly expressions (plural) poly expressions (plural) sing_440.htm#SEC480 poly operations sing_155.htm#SEC195 poly operations (plural) poly operations (plural) sing_441.htm#SEC481 poly related functions poly related functions sing_156.htm#SEC196 poly related functions (plural) poly related functions (plural) sing_442.htm#SEC482 poly.lib sing_964.htm#SEC1040 poly2list sing_589.htm#SEC641 4960 poly2zdd sing_2242.htm#SEC2318 61839 polyInterpolation sing_2376.htm#SEC2452 45866 polyVars sing_793.htm#SEC845 43882 poly_lib sing_964.htm#SEC1040 polybori sing_2226.htm#IDX909 polybori.lib sing_2226.htm#IDX906 polybori.lib sing_2226.htm#IDX910 polybori_lib sing_2226.htm#IDX907 polymake sing_2071.htm#IDX810 polymake.lib sing_2071.htm#SEC2147 polymakePolytope sing_2072.htm#SEC2148 47302 polymake_lib sing_2071.htm#SEC2147 polynomial solutions sing_780.htm#IDX386 polynomial, opposite sing_358.htm#IDX232 polytope sing_190.htm#SEC230 polytope sing_2071.htm#IDX806 polytopeViaInequalities polytopeViaInequalities sing_2044.htm#SEC2120 52084 polytopeViaPoints sing_2045.htm#SEC2121 281 pos_def sing_1096.htm#SEC1172 4994 poset sing_2211.htm#IDX895 positiveOrthant sing_2015.htm#SEC2091 42102 posweight sing_1629.htm#SEC1705 3364 powSumSym sing_2264.htm#SEC2340 2339 power sing_1056.htm#SEC1132 23365 power set sing_2344.htm#IDX945 powerN sing_1888.htm#SEC1964 20170 powerX sing_1897.htm#SEC1973 47971 power_products sing_1663.htm#SEC1739 54629 powerpolyX sing_1867.htm#SEC1943 37247 powersums sing_1990.htm#SEC2066 59049 preComp sing_1221.htm#SEC1297 16160 preimage sing_321.htm#SEC361 preimage sing_717.htm#IDX361 preimage (plural) sing_475.htm#SEC515 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1017.htm#IDX496 preimageLattice sing_2569.htm#SEC2645 37348 preimageLoc sing_1017.htm#SEC1093 33315 preimageNC sing_719.htm#SEC771 16037 prepEmbDiv sing_1447.htm#SEC1523 36708 prepMat sing_1700.htm#SEC1776 39868 prepRealclassify sing_1505.htm#SEC1581 10994 prepSV sing_1802.htm#SEC1878 50095 prepareAss sing_1304.htm#SEC1380 21802 presentTree sing_1434.htm#SEC1510 10731 presentation sing_2527.htm#SEC2603 40323 presolve.lib sing_1710.htm#SEC1786 presolve_lib sing_1710.htm#SEC1786 primL sing_1892.htm#SEC1968 14513 primList sing_1891.htm#SEC1967 6802 primRoot sing_1344.htm#SEC1420 14210 primTest sing_1220.htm#SEC1296 8105 primary decomposition sing_1289.htm#IDX576 primary decomposition sing_1312.htm#IDX577 primary decomposition of modules sing_1210.htm#IDX558 primary decomposition, numerical sing_1357.htm#IDX589 primary_char0 sing_1653.htm#SEC1729 61413 primary_char0_no_molien primary_char0_no_molien sing_1655.htm#SEC1731 50477 primary_char0_no_molien_random primary_char0_no_molien_random sing_1660.htm#SEC1736 8422 primary_char0_random primary_char0_random sing_1658.htm#SEC1734 5996 primary_charp sing_1654.htm#SEC1730 37863 primary_charp_no_molien primary_charp_no_molien sing_1656.htm#SEC1732 32282 primary_charp_no_molien_random primary_charp_no_molien_random sing_1661.htm#SEC1737 11498 primary_charp_random primary_charp_random sing_1659.htm#SEC1735 24739 primary_charp_without primary_charp_without sing_1657.htm#SEC1733 49585 primary_charp_without_random primary_charp_without_random sing_1662.htm#SEC1738 36998 primary_invariants sing_1641.htm#SEC1717 5500 primary_invariants_random primary_invariants_random sing_1642.htm#SEC1718 28958 primdec.lib sing_1289.htm#SEC1365 primdecGTZ sing_1291.htm#SEC1367 6091 primdecGTZE sing_1292.htm#SEC1368 64882 primdecMon sing_1209.htm#SEC1285 3856 primdecSY sing_1293.htm#SEC1369 6547 primdecSYE sing_1294.htm#SEC1370 52788 primdecZ sing_1313.htm#SEC1389 48194 primdecZM sing_1314.htm#SEC1390 17214 primdec_lib sing_1289.htm#SEC1365 primdecint.lib sing_1312.htm#SEC1388 primdecint_lib sing_1312.htm#SEC1388 prime sing_322.htm#SEC362 primeClosure sing_1248.htm#SEC1324 43589 primecoeffs sing_919.htm#SEC995 46153 primefactors sing_323.htm#SEC363 primes sing_914.htm#SEC990 24408 primitiv.lib sing_1320.htm#SEC1396 primitiv_lib sing_1320.htm#SEC1396 primitive sing_1321.htm#SEC1397 36163 primitive element sing_1321.htm#IDX578 primitiveSpan sing_2576.htm#SEC2652 sprintf primitive_extra sing_1322.htm#SEC1398 49025 primparam sing_1516.htm#SEC1592 35357 principal intersection sing_505.htm#IDX319 print sing_324.htm#SEC364 print sing_2178.htm#IDX830 printBetti sing_2508.htm#SEC2584 28941 printFreeModule sing_2500.htm#SEC2576 13316 printGraph sing_1144.htm#SEC1220 45041 printGraphG sing_2724.htm#SEC2800 48742 printGroup sing_2557.htm#SEC2633 6791 printHom sing_2503.htm#SEC2579 7070 printMatrix sing_2499.htm#SEC2575 15522 printModule sing_2502.htm#SEC2578 sprintf printMoebius sing_2217.htm#SEC2293 45828 printResolution sing_2501.htm#SEC2577 29278 printSheaf sing_2712.htm#SEC2788 31762 printStack sing_2726.htm#SEC2802 3692 printTask sing_1036.htm#SEC1112 54549 printVariety sing_2704.htm#SEC2780 2846 printf sing_325.htm#SEC365 2294 printlevel sing_400.htm#SEC440 proc sing_157.htm#SEC197 proc declaration sing_158.htm#SEC198 proc expression sing_159.htm#SEC199 procedure, ASCII help sing_56.htm#IDX125 procedure, ASCII/Texinfo help sing_58.htm#IDX127 procedure, texinfo help sing_57.htm#IDX126 procedures, help string sing_45.htm#SEC82 procedures, static Procedure definition sing_43.htm#SEC78 procs with different argument types procs with different argument types sing_160.htm#SEC200 prodcrit sing_1967.htm#SEC2043 56231 product sing_915.htm#SEC991 54431 product variety, abstract variety sing_2705.htm#IDX1049 productVariety sing_2705.htm#SEC2781 54191 productgroup sing_2578.htm#SEC2654 55937 progress watch sing_315.htm#IDX163 projectLattice sing_2570.htm#SEC2646 28463 projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2709.htm#IDX1053 projective dimension purityfiltration_lib sing_758.htm#IDX370 projective limes sing_32.htm#SEC46 projective space, abstract variety sing_2708.htm#IDX1052 projectiveBundle sing_2709.htm#SEC2785 13791 projectiveDimension sing_759.htm#SEC811 8165 projectiveSpace sing_2708.htm#SEC2784 21729 prompt sing_15.htm#SEC21 prompt, option sing_315.htm#IDX182 propagator sing_1142.htm#IDX521 42460 propagator sing_1145.htm#SEC1221 prot, option sing_315.htm#IDX161 protocol of computations sing_315.htm#IDX162 proximitymatrix sing_1475.htm#SEC1551 58403 prune sing_326.htm#SEC366 pruneModule sing_2534.htm#SEC2610 51453 prwalk sing_2699.htm#SEC2775 46963 psigncnd sing_1763.htm#SEC1839 57734 puiseux2generators sing_1574.htm#SEC1650 64508 puiseuxExpansion sing_2132.htm#SEC2208 46277 pure tensor sing_498.htm#IDX307 purelist sing_769.htm#SEC821 15517 purity purityfiltration_lib sing_758.htm#IDX372 purityFiltration sing_760.htm#SEC812 5742 purityTriang sing_761.htm#SEC813 3665 purityfiltration.lib purityfiltration_lib sing_758.htm#IDX365 purityfiltration_lib purityfiltration_lib sing_758.htm#IDX366 pushForward sing_2595.htm#SEC2671 26697 pwalk sing_1158.htm#SEC1234 61187 pyobject sing_191.htm#SEC231 pyobject sing_2226.htm#IDX912 pyobject declarations pyobject declarations sing_192.htm#SEC232 pyobject expressions pyobject expressions sing_193.htm#SEC233 pyobject operations sing_194.htm#SEC234 pyobject related functions pyobject related functions sing_195.htm#SEC235 pyramid sing_2392.htm#SEC2468 7421 python_eval sing_196.htm#SEC236 python_import sing_197.htm#SEC237 python_run sing_198.htm#SEC238 qbase sing_1993.htm#SEC2069 8633 qepcad sing_2402.htm#SEC2478 39171 qepcadsystem sing_2403.htm#SEC2479 31977 qhmatrix sing_1627.htm#SEC1703 61813 qhmoduli.lib sing_1591.htm#SEC1667 qhmoduli_lib sing_1591.htm#SEC1667 qhspectrum sing_1614.htm#SEC1690 13732 qhweight sing_327.htm#SEC367 qmatrix.lib sing_752.htm#SEC804 qmatrix_lib sing_752.htm#SEC804 qminor sing_754.htm#SEC806 52670 qrds sing_328.htm#SEC368 qring Miscellaneous oddities sing_166.htm#SEC206 qring sing_418.htm#IDX295 qring (plural) sing_443.htm#SEC483 qring declaration sing_170.htm#SEC210 qring declaration (plural) qring declaration (plural) sing_444.htm#SEC484 qring related functions (plural) qring related functions (plural) sing_445.htm#SEC485 qring ring ideal 'factor ring' sing_1026.htm#IDX502 qringNF, option sing_315.htm#IDX164 qslimgb sing_895.htm#SEC971 51999 quadraticSieve sing_1905.htm#SEC1981 58557 quantMat sing_753.htm#SEC805 56227 quickclass sing_1497.htm#SEC1573 14018 quit sing_390.htm#SEC430 quotSheaf sing_2721.htm#SEC2797 49619 quote sing_329.htm#SEC369 quotient sing_330.htm#SEC370 quotient (plural) sing_476.htm#SEC516 quotientLatticeBasis quotientLatticeBasis sing_2046.htm#SEC2122 15613 quotientMain sing_1755.htm#SEC1831 39870 quotientMon sing_1200.htm#SEC1276 57149 rHRR sing_2304.htm#SEC2380 20131 rJanet sing_2696.htm#SEC2772 30716 rMacaulay sing_950.htm#SEC1026 45499 rad_con sing_977.htm#SEC1053 21777 radical sing_1301.htm#SEC1377 1407 radicalEHV sing_1302.htm#SEC1378 33703 radicalMemberShip sing_2154.htm#SEC2230 28527 radicalMon sing_1201.htm#SEC1277 64912 radicalZ sing_1316.htm#SEC1392 5783 randcharpoly sing_1987.htm#SEC2063 37737 randlinpoly sing_1989.htm#SEC2065 22330 random sing_331.htm#SEC371 random sing_358.htm#IDX244 random sing_2199.htm#IDX869 random sing_2200.htm#IDX871 random number generator, seed sing_358.htm#IDX242 random.lib sing_985.htm#SEC1061 randomBinomial sing_997.htm#SEC1073 17913 randomCheck sing_1818.htm#SEC1894 20973 randomLast sing_996.htm#SEC1072 2046 randomPoint sing_2047.htm#SEC2123 22561 randomPolyInT sing_2163.htm#SEC2239 2264 random_lib sing_985.htm#SEC1061 randomid sing_987.htm#SEC1063 7815 randommat sing_988.htm#SEC1064 33569 rank sing_209.htm#IDX137 rank sing_332.htm#SEC372 rankSheaf sing_2713.htm#SEC2789 11850 ratSol sing_788.htm#SEC840 62488 ratgb.lib sing_778.htm#IDX375 ratgb_lib sing_778.htm#IDX376 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1379.htm#IDX616 rational normal curve, projection. sing_1380.htm#IDX617 rational normal curve, projection. sing_1383.htm#IDX618 rational normal curve, projection. sing_1384.htm#IDX619 rational solutions sing_780.htm#IDX387 rational univariate projection sing_1987.htm#IDX803 rationalCurve sing_2733.htm#SEC2809 61201 rationalPointConic sing_1381.htm#SEC1457 9761 ratstd sing_779.htm#SEC831 61346 rays sing_2048.htm#SEC2124 44445 rcolon sing_2603.htm#SEC2679 1208 re2squ sing_1358.htm#SEC1434 24350 read sing_333.htm#SEC373 readNmzData sing_1276.htm#SEC1352 18957 reading, option sing_315.htm#IDX183 readline sing_1.htm#IDX5 real sing_28.htm#IDX74 real root isolation sing_2680.htm#IDX1028 real roots, univariate polynomial sing_1994.htm#IDX805 real roots, univariate projection sing_1978.htm#IDX801 real roots,sign conditions sing_1761.htm#IDX781 realclassify sing_2675.htm#SEC2751 51416 realclassify.lib sing_2674.htm#SEC2750 realclassify_lib sing_2674.htm#SEC2750 realizationDim sing_2126.htm#SEC2202 37756 realizationDimPoly sing_2128.htm#SEC2204 3611 realizationMatroids.lib realizationMatroids_lib sing_2125.htm#SEC2201 realizationMatroids_lib realizationMatroids_lib sing_2125.htm#SEC2201 realmorsesplit sing_2676.htm#SEC2752 16318 realpoly sing_1325.htm#SEC1401 9453 realrad sing_1327.htm#SEC1403 43381 realrad.lib sing_1324.htm#SEC1400 realrad_lib sing_1324.htm#SEC1400 realzero sing_1326.htm#SEC1402 12712 recursive_boolean_poly recursive_boolean_poly sing_2232.htm#SEC2308 17045 recursive_from_boolean_poly recursive_from_boolean_poly sing_2238.htm#SEC2314 37794 redSB, option sing_315.htm#IDX165 redTail, option sing_315.htm#IDX167 redThrough, option sing_315.htm#IDX168 redefine, option sing_315.htm#IDX184 reduce sing_334.htm#SEC374 reduce sing_519.htm#IDX324 reduce sing_926.htm#IDX431 reduce sing_927.htm#IDX434 reduce (plural) sing_477.htm#SEC517 reduce (up to a bound) sing_358.htm#IDX245 reduceIntChain sing_2539.htm#SEC2615 17776 reduced sing_925.htm#IDX428 reduced standard basis sing_315.htm#IDX166 reduction sing_1679.htm#SEC1755 31048 reesclos.lib sing_1328.htm#SEC1404 reesclos_lib sing_1328.htm#SEC1404 reference sing_199.htm#SEC239 reference declarations reference declarations sing_200.htm#SEC240 reference expressions reference expressions sing_201.htm#SEC241 reference operations reference and shared operations sing_204.htm#SEC244 reference related functions reference and shared related functions sing_205.htm#SEC245 regCM sing_1240.htm#SEC1316 25488 regIdeal sing_1226.htm#SEC1302 3827 regMonCurve sing_1229.htm#SEC1305 41311 regularity Syzygies and resolutions sing_335.htm#SEC375 regularity sing_870.htm#SEC927 reiffen sing_558.htm#SEC610 32856 rel_orbit_variety sing_1672.htm#SEC1748 34278 relations sing_750.htm#IDX364 relativeInteriorPoint relativeInteriorPoint sing_2049.htm#SEC2125 30097 relative_orbit_variety relative_orbit_variety sing_1673.htm#SEC1749 32995 relweight sing_1628.htm#SEC1704 10658 remainder sing_1748.htm#SEC1824 1191 remainderMain sing_1756.htm#SEC1832 3532 removeCone sing_2067.htm#SEC2143 33877 removepower sing_1485.htm#SEC1561 47644 repart sing_336.htm#SEC376 replace sing_1857.htm#SEC1933 50075 representation, math objects Representation of mathematical objects sing_856.htm#SEC908 res sing_337.htm#SEC377 10393 resbinomial.lib sing_1388.htm#IDX622 resbinomial_lib sing_1388.htm#IDX623 reservedName sing_338.htm#SEC378 resfunction sing_1402.htm#SEC1478 59312 resgraph.lib sing_1420.htm#SEC1496 resgraph_lib sing_1420.htm#SEC1496 resjung.lib sing_1424.htm#SEC1500 resjung_lib sing_1424.htm#SEC1500 reslist sing_1416.htm#SEC1492 64950 resolution purityfiltration_lib sing_161.htm#SEC201 resolution sing_758.htm#IDX371 resolution (plural) sing_446.htm#SEC486 resolution declarations resolution declarations sing_162.htm#SEC202 resolution declarations (plural) resolution declarations (plural) sing_447.htm#SEC487 resolution expressions resolution expressions sing_163.htm#SEC203 resolution expressions (plural) resolution expressions (plural) sing_448.htm#SEC488 resolution graph sing_1470.htm#IDX636 resolution related functions resolution related functions sing_164.htm#SEC204 resolution related functions (plural) resolution related functions (plural) sing_449.htm#SEC489 resolution, La Scala's method sing_288.htm#SEC328 resolution, computation of sing_337.htm#IDX186 resolution, hilbert-driven sing_263.htm#SEC303 resolutionInLocalization resolutionInLocalization sing_2419.htm#SEC2495 31106 resolutiongraph sing_1471.htm#SEC1547 32697 resolve sing_1432.htm#SEC1508 27374 resolve.lib sing_1428.htm#SEC1504 resolve_lib sing_1428.htm#SEC1504 resources.lib sing_998.htm#SEC1074 resources_lib sing_998.htm#SEC1074 restriction sing_2192.htm#IDX857 restriction sing_2208.htm#IDX890 restriction sing_2209.htm#IDX892 restriction of sing_563.htm#IDX347 restrictionIdeal sing_573.htm#SEC625 49796 restrictionModule sing_574.htm#SEC626 62461 resultant sing_302.htm#SEC342 resultant sing_339.htm#SEC379 reszeta.lib sing_1441.htm#SEC1517 reszeta_lib sing_1441.htm#SEC1517 return sing_391.htm#SEC431 return type of procedures Return type of procedures sing_416.htm#SEC456 returnSB, option sing_315.htm#IDX152 reverse sing_2008.htm#SEC2084 35880 reverse lexicographical ordering sing_860.htm#IDX392 reynolds_molien sing_1648.htm#SEC1724 45316 rho sing_1899.htm#SEC1975 51414 rightInverse sing_1837.htm#SEC1913 6558 rightKernel sing_1835.htm#SEC1911 46603 rightModulo sing_737.htm#SEC789 12618 rightNF sing_736.htm#SEC788 42610 rightNFWeyl sing_805.htm#SEC857 35828 rightOre sing_2660.htm#SEC2736 56918 rightStd sing_735.htm#SEC787 5740 ring sing_165.htm#SEC205 ring (plural) sing_450.htm#SEC490 ring coefficients hasTransExtensionCoefficient sing_1024.htm#IDX500 ring coefficients sing_1025.htm#IDX501 ring declarations sing_167.htm#SEC207 ring declarations (plural) ring declarations (plural) sing_451.htm#SEC491 ring operations sing_169.htm#SEC209 ring operations (plural) ring operations (plural) sing_452.htm#SEC492 ring related functions ring related functions sing_168.htm#SEC208 ring related functions (plural) ring related functions (plural) sing_453.htm#SEC493 ring, opposite sing_358.htm#IDX229 ring.lib sing_1003.htm#SEC1079 ring_cf sing_209.htm#IDX138 ring_lib sing_1003.htm#SEC1079 ring_list sing_341.htm#SEC381 ring_variable sing_2179.htm#IDX834 ring_variable sing_2180.htm#IDX836 ring_variable sing_2181.htm#IDX840 ring_variable sing_2182.htm#IDX842 ringlist sing_340.htm#SEC380 ringlist (plural) sing_478.htm#SEC518 ringtensor sing_1015.htm#SEC1091 56648 ringweights sing_1016.htm#SEC1092 33307 rinvar.lib sing_1684.htm#SEC1760 rinvar_lib sing_1684.htm#SEC1760 rmNmzFiles sing_1281.htm#SEC1357 32601 rm_unitcol sing_1074.htm#SEC1150 5591 rm_unitrow sing_1073.htm#SEC1149 35694 rmx sing_1782.htm#SEC1858 17675 rncAntiCanonicalMap sing_1380.htm#SEC1456 41965 rncItProjEven sing_1384.htm#SEC1460 18200 rncItProjOdd sing_1383.htm#SEC1459 61976 root of Bernstein-Sato polynomial sing_540.htm#IDX336 rootIsolation sing_2691.htm#SEC2767 34513 rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2690.htm#SEC2766 42387 rootIsolationPrimdec rootIsolationPrimdec sing_2692.htm#SEC2768 35485 rootisolation.lib sing_2680.htm#SEC2756 rootisolation_lib sing_2680.htm#SEC2756 rootofUnity sing_1018.htm#SEC1094 21365 roots sing_1749.htm#SEC1825 18436 rootsMain sing_1757.htm#SEC1833 54934 rootsModp sing_1881.htm#SEC1957 47315 rootsmr.lib sing_1978.htm#SEC2054 rootsmr_lib sing_1978.htm#SEC2054 rootsur.lib sing_1994.htm#SEC2070 rootsur_lib sing_1994.htm#SEC2070 round sing_1879.htm#SEC1955 9248 rowShift sing_209.htm#IDX141 rowShift sing_211.htm#SEC251 rowred sing_1070.htm#SEC1146 63416 rp, global ordering sing_860.htm#IDX391 rstandard.lib sing_2693.htm#SEC2769 rstandard_lib sing_2693.htm#SEC2769 rswalk sing_2743.htm#SEC2819 50903 rtimer sing_404.htm#SEC444 rvalue No rvalue of increments and assignments sing_410.htm#SEC450 rvar sing_342.htm#SEC382 rwalk sing_2700.htm#SEC2776 42525 rwalk.lib sing_2698.htm#SEC2774 rwalk_lib sing_2698.htm#SEC2774 sRes sing_2505.htm#SEC2581 23381 sa_poly_reduce sing_528.htm#SEC580 60856 sa_reduce sing_527.htm#SEC579 55799 sagbi sing_1334.htm#SEC1410 46653 sagbi basis sing_2332.htm#IDX942 sagbi.lib sing_1331.htm#SEC1407 sagbiAlg sing_2325.htm#SEC2401 sprintf sagbiMod sing_2326.htm#SEC2402 sprintf sagbiPart sing_1335.htm#SEC1411 56066 sagbiReduce sing_1333.htm#SEC1409 19036 sagbiSPoly sing_1332.htm#SEC1408 17365 sagbi_lib sing_1331.htm#SEC1407 salida sing_1413.htm#SEC1489 9839 sameComponent sing_1961.htm#SEC2037 13540 sameQ sing_1760.htm#SEC1836 45579 sat sing_1139.htm#SEC1215 6266 satiety sing_1228.htm#SEC1304 34323 satstd sing_2220.htm#SEC2296 16128 sba sing_343.htm#SEC383 scalarProd sing_517.htm#SEC569 54488 scheme sing_2383.htm#SEC2459 15722 schubert.lib sing_2702.htm#SEC2778 schubert_lib sing_2702.htm#SEC2778 sdb, source code debugger Source code debugger sing_66.htm#SEC103 second degree sing_942.htm#IDX479 secondary fan sing_2071.htm#IDX808 secondary polytope sing_2071.htm#IDX809 secondaryPolytope sing_2076.htm#SEC2152 48451 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1669.htm#SEC1745 37058 secondary_char0 sing_1664.htm#SEC1740 31029 secondary_charp sing_1666.htm#SEC1742 16364 secondary_no_molien sing_1667.htm#SEC1743 3616 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1670.htm#SEC1746 31675 segre sing_2259.htm#SEC2335 44035 select sing_1140.htm#SEC1216 17096 select1 sing_1141.htm#SEC1217 32617 semaphore sing_358.htm#IDX249 44342 semaphore sing_1002.htm#SEC1078 semaphores sing_998.htm#IDX495 semiCMcod2 sing_1625.htm#SEC1701 15905 semiGroup sing_2327.htm#SEC2403 sprintf semiMod sing_2328.htm#SEC2404 sprintf semidiv sing_1953.htm#SEC2029 58107 semigroup sing_1474.htm#SEC1550 29045 semigroup sing_1478.htm#IDX643 semigroup of values sing_1564.htm#IDX758 semigroupGenerator sing_2050.htm#SEC2126 59446 sep sing_1311.htm#SEC1387 sprintf separateHNE sing_1575.htm#SEC1651 12052 separator sing_1211.htm#SEC1287 33000 serreRelations sing_658.htm#SEC710 33994 set sing_2174.htm#IDX820 setBaseMultigrading sing_2550.htm#SEC2626 6575 setLetterplaceAttributes setLetterplaceAttributes sing_648.htm#SEC700 5759 setLinearForms sing_2051.htm#SEC2127 62731 setModuleGrading sing_2562.htm#SEC2638 59018 setMultiplicity sing_2052.htm#SEC2128 27537 setNmzDataPath sing_1278.htm#SEC1354 18123 setNmzExecPath sing_1274.htm#SEC1350 38993 setNmzFilename sing_1277.htm#SEC1353 20206 setNmzOption sing_1271.htm#SEC1347 9012 setUniformizingParameter setUniformizingParameter sing_2745.htm#SEC2821 63635 set_is_injective sing_1941.htm#SEC2017 8429 setcores sing_1000.htm#SEC1076 49704 setenv sing_358.htm#IDX252 setinitials sing_2393.htm#SEC2469 24792 setring sing_344.htm#SEC384 sh sing_358.htm#IDX254 shared sing_199.htm#SEC239 shared declarations sing_202.htm#SEC242 shared expressions sing_203.htm#SEC243 shared operations reference and shared operations sing_204.htm#SEC244 shared related functions reference and shared related functions sing_205.htm#SEC245 sheaf cohomology sing_1451.htm#IDX624 sheafCoh sing_1457.htm#SEC1533 64501 sheafCohBGG sing_1455.htm#SEC1531 13439 sheafCohBGG2 sing_1456.htm#SEC1532 3338 sheafcoh.lib sing_1451.htm#SEC1527 sheafcoh_lib sing_1451.htm#SEC1527 shiftPoly sing_651.htm#SEC703 65223 short sing_401.htm#SEC441 show sing_951.htm#SEC1027 15599 showBO sing_1433.htm#SEC1509 20089 showDataTypes sing_1435.htm#SEC1511 4270 showNmzOptions sing_1272.htm#SEC1348 64955 showNuminvs sing_1269.htm#SEC1345 18934 showgrades sing_763.htm#SEC815 48081 showrecursive sing_952.htm#SEC1028 6127 sickle sing_624.htm#SEC676 54811 signal handler sing_2761.htm#SEC2850 signatureBrieskorn sing_1634.htm#SEC1710 26283 signatureL sing_2222.htm#SEC2298 65493 signatureLqf sing_2223.htm#SEC2299 18811 signatureNemethi sing_1636.htm#SEC1712 21981 signaturePuiseux sing_1635.htm#SEC1711 23398 signcnd sing_1762.htm#SEC1838 40147 signcond.lib sing_1761.htm#SEC1837 signcond_lib sing_1761.htm#SEC1837 simplePrune sing_2543.htm#SEC2619 sprintf simplesolver sing_1706.htm#SEC1782 13418 simplex sing_345.htm#SEC385 simplexOut sing_1733.htm#SEC1809 56099 simplify sing_346.htm#SEC386 simplifyRat sing_800.htm#SEC852 52658 sing.lib sing_1601.htm#SEC1677 sing4ti2.lib sing_1337.htm#SEC1413 sing4ti2_lib sing_1337.htm#SEC1413 sing_lib sing_1601.htm#SEC1677 singular locus of D-module sing_780.htm#IDX381 singularities sing_1533.htm#IDX660 singularities sing_1534.htm#IDX671 singularities sing_1535.htm#IDX674 singularities sing_1536.htm#IDX677 singularities sing_1537.htm#IDX680 singularities sing_1538.htm#IDX684 singularities sing_1539.htm#IDX688 singularities sing_1540.htm#IDX694 singularities sing_1541.htm#IDX702 singularities sing_1542.htm#IDX708 singularities sing_1543.htm#IDX716 singularities sing_1544.htm#IDX726 singularities sing_1632.htm#IDX773 singularities sing_2321.htm#IDX937 singularities, resolution of Resolution of singularities sing_843.htm#SEC895 singularity sing_1498.htm#SEC1574 23002 singularrc sing_20.htm#IDX73 size Miscellaneous oddities sing_347.htm#SEC387 size sing_418.htm#IDX294 skewmat sing_1057.htm#SEC1133 2167 sleep sing_353.htm#SEC393 slimgb sing_348.htm#SEC388 slimgb sing_820.htm#SEC872 slimgb (plural) sing_479.htm#SEC519 slocus sing_1613.htm#SEC1689 27853 smith sing_1846.htm#SEC1922 61915 smithNormalForm sing_2598.htm#SEC2674 7174 solutionsMod2 sing_1896.htm#SEC1972 53360 solve sing_942.htm#IDX480 3078 solve sing_1727.htm#SEC1803 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_291.htm#SEC331 solve.lib sing_1725.htm#SEC1801 solveTInitialFormPar solveTInitialFormPar sing_2157.htm#SEC2233 36670 solve_IP sing_1184.htm#SEC1260 59518 solve_lib sing_1725.htm#SEC1801 solvelinearpart sing_1720.htm#SEC1796 42872 sort sing_916.htm#SEC992 58207 sortIntvec sing_595.htm#SEC647 60798 sortandmap sing_1721.htm#SEC1797 10314 sortier sing_1683.htm#SEC1759 3555 sortvars sing_1722.htm#SEC1798 61778 sortvec sing_349.htm#SEC389 source sing_2521.htm#SEC2597 63163 source code debugger, sdb Source code debugger sing_66.htm#SEC103 spaceCur sing_2330.htm#SEC2406 sprintf spadd sing_1547.htm#SEC1623 48739 span sing_2053.htm#SEC2129 64343 sparseHomogIdeal sing_994.htm#SEC1070 22631 sparseInterpolation sing_2378.htm#SEC2454 28771 sparseid sing_989.htm#SEC1065 20824 sparsemat sing_991.htm#SEC1067 17653 sparsematrix sing_990.htm#SEC1066 41031 sparsepoly sing_992.htm#SEC1068 21649 sparsetriag sing_993.htm#SEC1069 50657 spcurve.lib sing_1621.htm#SEC1697 spcurve_lib sing_1621.htm#SEC1697 special characters, non-english sing_407.htm#IDX287 spectral pairs sing_1533.htm#IDX669 spectral pairs sing_1540.htm#IDX701 spectral pairs sing_1542.htm#IDX715 spectral pairs sing_1543.htm#IDX724 spectral pairs sing_1555.htm#IDX740 spectral pairs sing_1557.htm#IDX751 spectralNeg sing_1443.htm#SEC1519 36691 spectrum sing_1533.htm#IDX668 47545 spectrum sing_1539.htm#SEC1615 spectrum sing_1539.htm#IDX693 spectrum sing_1540.htm#IDX700 spectrum sing_1541.htm#IDX707 spectrum sing_1542.htm#IDX714 spectrum sing_1543.htm#IDX723 spectrum sing_1555.htm#IDX739 spectrum sing_1557.htm#IDX750 spectrum sing_1632.htm#IDX775 spectrum.lib sing_1631.htm#SEC1707 spectrum_lib sing_1631.htm#SEC1707 spectrumnd sing_1632.htm#SEC1708 29943 spgamma sing_1554.htm#SEC1630 59653 spgeomgenus sing_1553.htm#SEC1629 57796 spissemicont sing_1550.htm#SEC1626 23679 split sing_953.htm#SEC1029 29794 splitPolygon sing_2078.htm#SEC2154 706 splitring sing_1323.htm#SEC1399 56404 splitting sing_1219.htm#SEC1295 34734 spmilnor sing_1552.htm#SEC1628 32933 spmul sing_1549.htm#SEC1625 43607 spnf sing_1100.htm#SEC1176 57309 spoly sing_1964.htm#SEC2040 35454 sppairs sing_1540.htm#SEC1616 49513 sppnf sing_1545.htm#SEC1621 16650 sppprint sing_1546.htm#SEC1622 43682 spprint sing_1101.htm#SEC1177 18671 sprintf sing_351.htm#SEC391 55889 spsemicont sing_1551.htm#SEC1627 61169 spsub sing_1548.htm#SEC1624 54296 sqfrNorm sing_1750.htm#SEC1826 20546 sqfrNormMain sing_1758.htm#SEC1834 9890 sqr sing_1876.htm#SEC1952 sprintf sqrfree sing_350.htm#SEC390 squareRoot sing_1895.htm#SEC1971 17446 squarefree sing_1576.htm#SEC1652 48485 sres sing_352.htm#SEC392 ssi Parallelization with ssi links sing_815.htm#SEC867 stabilizer sing_2250.htm#SEC2326 36692 stack, moduli space of stable maps sing_2726.htm#IDX1057 stack, moduli space of stable maps, rational curves moduliSpace sing_2725.htm#IDX1056 stackNets sing_2647.htm#SEC2723 30974 staircase sing_1767.htm#SEC1843 49781 standard sing_1971.htm#SEC2047 14067 standard bases, saturation sing_2220.htm#IDX903 standard bases. sing_2219.htm#IDX902 standard.lib sing_894.htm#IDX419 standard_lib sing_894.htm#IDX420 startNmz sing_1280.htm#SEC1356 21925 startTasks sing_1037.htm#SEC1113 16715 static procedures Procedure definition sing_43.htm#SEC78 status sing_353.htm#SEC393 std sing_354.htm#SEC394 std sing_818.htm#SEC870 std (plural) sing_480.htm#SEC520 stdfglm sing_355.htm#SEC395 256 stdhilb sing_356.htm#SEC396 63138 stdlocus sing_939.htm#SEC1015 25619 stopTask sing_1038.htm#SEC1114 6801 storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2439.htm#SEC2515 64428 stratify sing_1701.htm#SEC1777 56744 stratify.lib sing_1699.htm#SEC1775 stratify_lib sing_1699.htm#SEC1775 string Miscellaneous oddities sing_171.htm#SEC211 string sing_418.htm#IDX297 string declarations sing_172.htm#SEC212 string expressions sing_173.htm#SEC213 string operations sing_175.htm#SEC215 string related functions string related functions sing_176.htm#SEC216 string type cast sing_174.htm#SEC214 stripHNE sing_1573.htm#SEC1649 19265 sturm sing_2004.htm#SEC2080 54353 sturmha sing_2006.htm#SEC2082 12467 sturmhaseq sing_2007.htm#SEC2083 59133 sturmquery sing_1982.htm#SEC2058 10805 sturmseq sing_2005.htm#SEC2081 23005 sublists sing_2344.htm#SEC2420 2979 submat sing_1058.htm#SEC1134 37665 subquotient sing_2513.htm#SEC2589 40364 subrInterred sing_982.htm#SEC1058 10165 subset_sum01 sing_1925.htm#SEC2001 60620 subset_sum02 sing_1926.htm#SEC2002 37340 subst sing_357.htm#SEC397 subst (plural) sing_481.htm#SEC521 substitute sing_981.htm#SEC1057 28919 sugarCrit, option sing_315.htm#IDX169 sum sing_917.htm#SEC993 555 sum_of_powers sing_2263.htm#SEC2339 12170 sumlist sing_1415.htm#SEC1491 59918 sumofquotients sing_2734.htm#SEC2810 4569 super-commutative algebras Graded commutative algebras (SCA) sing_490.htm#SEC542 superCommutative sing_734.htm#SEC786 45528 super_increasing_knapsack super_increasing_knapsack sing_1937.htm#SEC2013 9177 surf.lib sing_1784.htm#SEC1860 surf_lib sing_1784.htm#SEC1860 surfacesignature.lib surfacesignature_lib sing_1633.htm#SEC1709 surfacesignature_lib surfacesignature_lib sing_1633.htm#SEC1709 surfer sing_1.htm#IDX8 14287 surfer sing_1786.htm#SEC1862 surfex sing_1.htm#IDX7 surfex.lib sing_1787.htm#SEC1863 surfex_lib sing_1787.htm#SEC1863 suspend sing_353.htm#SEC393 swalk sing_2742.htm#SEC2818 16794 swalk.lib sing_2741.htm#SEC2817 swalk_lib sing_2741.htm#SEC2817 swap sing_1502.htm#SEC1578 15408 swap sing_2181.htm#IDX838 switch No case or switch statement sing_412.htm#SEC452 switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2750.htm#SEC2826 1827 syModStd sing_1347.htm#SEC1423 50246 symNsym sing_2257.htm#SEC2333 55230 sym_gauss sing_1084.htm#SEC1160 5121 symm sing_2256.htm#SEC2332 64628 symmStd sing_1346.htm#SEC1422 39353 symmat sing_1059.htm#SEC1135 61294 symmetric basis sing_1076.htm#IDX506 symmetric power sing_1078.htm#IDX508 symmetricBasis sing_1076.htm#SEC1152 sprintf symmetricPower sing_1078.htm#SEC1154 6542 symmetricPowerSheaf sing_2720.htm#SEC2796 56922 symmetries sing_2246.htm#IDX936 symmfunc sing_1991.htm#SEC2067 45575 symodstd.lib sing_1341.htm#SEC1417 symodstd_lib sing_1341.htm#SEC1417 symsignature sing_1981.htm#SEC2057 10520 syndrome sing_1814.htm#SEC1890 14057 sysBin sing_1812.htm#SEC1888 41948 sysCRHT sing_1809.htm#SEC1885 58930 sysCRHTMindist sing_1810.htm#SEC1886 13692 sysFL sing_1825.htm#SEC1901 53040 sysNewton sing_1811.htm#SEC1887 19704 sysQE sing_1815.htm#SEC1891 61026 sys_code sing_1806.htm#SEC1882 20220 system sing_358.htm#SEC398 system, -- sing_358.htm#IDX277 system, --long_option_name sing_358.htm#IDX280 system, --long_option_name=value sing_358.htm#IDX282 system, HC sing_358.htm#IDX215 system, LLL sing_358.htm#IDX219 system, Singular sing_358.htm#IDX258 system, SingularLib sing_358.htm#IDX260 system, absFact sing_358.htm#IDX190 system, alarm sing_358.htm#IDX189 system, blackbox sing_358.htm#IDX191 system, bracket sing_358.htm#IDX196 system, browsers sing_358.htm#IDX195 system, btest sing_358.htm#IDX198 system, complexNearZero sing_358.htm#IDX199 system, contributors sing_358.htm#IDX201 system, cpu sing_358.htm#IDX203 system, cpu sing_358.htm#IDX276 system, denom_list sing_358.htm#IDX205 system, eigenvals sing_358.htm#IDX206 system, env sing_358.htm#IDX207 system, executable sing_358.htm#IDX209 system, freegb sing_358.htm#IDX210 system, getPrecDigits sing_358.htm#IDX213 system, getenv sing_358.htm#IDX212 system, gmsnf sing_358.htm#IDX214 system, hessenberg sing_358.htm#IDX216 system, install sing_358.htm#IDX218 system, nblocks sing_358.htm#IDX222 system, nc_hilb sing_358.htm#IDX224 system, neworder sing_358.htm#IDX225 system, newstruct sing_358.htm#IDX226 system, opp sing_358.htm#IDX227 system, oppose sing_358.htm#IDX230 system, pcvBasis sing_358.htm#IDX239 system, pcvCV2P sing_358.htm#IDX237 system, pcvDim sing_358.htm#IDX238 system, pcvLAddL sing_358.htm#IDX233 system, pcvMinDeg sing_358.htm#IDX235 system, pcvP2CV sing_358.htm#IDX236 system, pcvPMulL sing_358.htm#IDX234 system, pid sing_358.htm#IDX241 system, random sing_358.htm#IDX243 system, reserve sing_358.htm#IDX247 system, reservedLink sing_358.htm#IDX248 system, semaphore sing_358.htm#IDX250 system, semic sing_358.htm#IDX251 system, setenv sing_358.htm#IDX253 system, sh sing_358.htm#IDX255 system, shrinktest sing_358.htm#IDX256 system, spadd sing_358.htm#IDX261 system, spectrum sing_358.htm#IDX262 system, spmul sing_358.htm#IDX263 system, std_syz sing_358.htm#IDX264 system, stest sing_358.htm#IDX265 system, tensorModuleMult sing_358.htm#IDX266 system, twostd sing_358.htm#IDX267 system, uname sing_358.htm#IDX270 system, version sing_358.htm#IDX273 system, with sing_358.htm#IDX274 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2416.htm#SEC2492 63094 syz sing_359.htm#SEC399 syz (plural) sing_482.htm#SEC522 tDetropicalise sing_2159.htm#SEC2235 23532 tInitialForm sing_2143.htm#SEC2219 24484 tInitialFormPar sing_2155.htm#SEC2231 9584 tInitialFormParMax sing_2156.htm#SEC2232 7829 tInitialIdeal sing_2144.htm#SEC2220 17937 tab sing_954.htm#SEC1030 60407 tail sing_1960.htm#SEC2036 13066 tame polynomial sing_1555.htm#IDX732 tame polynomial sing_1556.htm#IDX742 tame polynomial sing_1557.htm#IDX743 tangentGens sing_1371.htm#SEC1447 37797 tangentcone sing_1620.htm#SEC1696 20056 target sing_2520.htm#SEC2596 18743 task sing_1031.htm#IDX505 tasks.lib sing_1031.htm#SEC1107 tasks_lib sing_1031.htm#SEC1107 tau_es sing_1528.htm#SEC1604 17043 tau_es2 sing_1482.htm#SEC1558 38083 tdCf sing_2292.htm#SEC2368 21522 tdFactor sing_2294.htm#SEC2370 37910 tdProj sing_2297.htm#SEC2373 38406 tdTerms sing_2293.htm#SEC2369 30166 teachstd.lib sing_1958.htm#SEC2034 teachstd_lib sing_1958.htm#SEC2034 template.lib sing_55.htm#IDX120 template.lib sing_55.htm#IDX123 template_lib sing_55.htm#SEC92 template_lib sing_55.htm#IDX121 tensor sing_498.htm#IDX311 65451 tensor sing_1060.htm#SEC1136 tensorFreeModule sing_2532.htm#SEC2608 59314 tensorFreemodMod sing_2531.htm#SEC2607 sprintf tensorMatrix sing_2528.htm#SEC2604 31437 tensorMod sing_1179.htm#SEC1255 21961 tensorModFreemod sing_2530.htm#SEC2606 11852 tensorModule sing_2529.htm#SEC2605 58772 tensorProduct sing_2533.htm#SEC2609 sprintf tensorSheaf sing_2719.htm#SEC2795 24072 term orderings General definitions for orderings sing_859.htm#SEC911 term orderings introduction Introduction to orderings sing_858.htm#SEC910 testFraction sing_2658.htm#SEC2734 28466 testLocData sing_2655.htm#SEC2731 50986 testNCfac sing_708.htm#SEC760 60394 testNcfrac sing_2616.htm#SEC2692 34186 testNcfracExamples sing_2617.htm#SEC2693 15399 testNcloc sing_2620.htm#SEC2696 62706 testNclocExamples sing_2621.htm#SEC2697 14584 testOlga sing_2672.htm#SEC2748 53953 testOlgaExamples sing_2673.htm#SEC2749 62869 testParametrization sing_1386.htm#SEC1462 18686 testPointConic sing_1387.htm#SEC1463 25315 testPrimary sing_1299.htm#SEC1375 34254 testPrimaryE sing_1300.htm#SEC1376 20693 tex sing_1773.htm#SEC1849 12226 texDrawBasic sing_2150.htm#SEC2226 3635 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2152.htm#SEC2228 42021 texDrawTriangulation texDrawTriangulation sing_2153.htm#SEC2229 18865 texDrawTropical sing_2151.htm#SEC2227 58447 texMatrix sing_2149.htm#SEC2225 1334 texNumber sing_2147.htm#SEC2223 12628 texPolynomial sing_2148.htm#SEC2224 41136 texcoef sing_1854.htm#SEC1930 28189 texdemo sing_1774.htm#SEC1850 13008 texfactorize sing_1775.htm#SEC1851 6682 texmap sing_1776.htm#SEC1852 35265 texname sing_1777.htm#SEC1853 1008 texobj sing_1778.htm#SEC1854 2107 texpoly sing_1779.htm#SEC1855 64109 texproc sing_1780.htm#SEC1856 23626 texring sing_1781.htm#SEC1857 38275 the first alternative algorithm sing_1156.htm#IDX542 three_elements sing_1944.htm#SEC2020 513 timeFactorize sing_921.htm#SEC997 49531 timeStd sing_920.htm#SEC996 31506 timer sing_402.htm#SEC442 timer resolution, setting the sing_358.htm#IDX283 timestep sing_2396.htm#SEC2472 38225 tjurina sing_1616.htm#SEC1692 9100 tmatrix sing_1543.htm#SEC1619 57332 todd sing_2289.htm#SEC2365 25618 toddE sing_2290.htm#SEC2366 17823 toddPoly sing_2303.htm#SEC2379 65066 tolessvars sing_1719.htm#SEC1795 56590 topChernClass sing_2716.htm#SEC2792 17374 topological invariants sing_1470.htm#IDX634 topological invariants sing_1477.htm#IDX641 topological invariants sing_1478.htm#IDX645 topological invariants sing_1479.htm#IDX649 topological invariants sing_1480.htm#IDX653 toric ideals sing_874.htm#SEC931 toric ring sing_1258.htm#IDX575 toric.lib sing_1348.htm#SEC1424 toric_ideal sing_1349.htm#SEC1425 5760 toric_lib sing_1348.htm#SEC1424 toric_std sing_1350.htm#SEC1426 26141 torusInvariants sing_1264.htm#SEC1340 911 total divisors sing_498.htm#IDX308 total multiplicities sing_1470.htm#IDX637 totalChernClass sing_2714.htm#SEC2790 6153 totalSegreClass sing_2717.htm#SEC2793 3291 totalmultiplicities sing_1472.htm#SEC1548 58264 trace sing_360.htm#SEC400 tracemult sing_1985.htm#SEC2061 58303 transpose sing_361.htm#SEC401 trapezoid sing_2390.htm#SEC2466 61525 triMNewton sing_1745.htm#SEC1821 62822 triagmatrix sing_995.htm#SEC1071 17944 triang.lib sing_1738.htm#SEC1814 triangL sing_1739.htm#SEC1815 51847 triangL_solve sing_1736.htm#SEC1812 10101 triangLf_solve sing_1734.htm#SEC1810 49796 triangLfak sing_1740.htm#SEC1816 50093 triangM sing_1741.htm#SEC1817 59334 triangMH sing_1742.htm#SEC1818 34277 triangM_solve sing_1735.htm#SEC1811 63652 triang_lib sing_1738.htm#SEC1814 triang_solve sing_1737.htm#SEC1813 64404 triangulations sing_2075.htm#SEC2151 61888 tropical curves sing_2129.htm#IDX815 tropical geometry sing_1142.htm#IDX516 tropical geometry sing_2744.htm#IDX1068 tropical mirror symmetry sing_1142.htm#IDX518 tropical polynomials sing_2129.htm#IDX816 tropical varieties sing_2744.htm#IDX1069 tropical.lib sing_2129.htm#IDX813 tropicalCurve sing_2134.htm#SEC2210 16865 tropicalJInvariant sing_2137.htm#SEC2213 40395 tropicalLifting sing_2130.htm#SEC2206 7052 tropicalLinkNewton sing_2752.htm#SEC2828 63886 tropicalNewton.lib sing_2744.htm#SEC2820 tropicalNewton_lib sing_2744.htm#SEC2820 tropicalPointNewton sing_2749.htm#SEC2825 18572 tropicalSubst sing_2162.htm#SEC2238 49846 tropicalVariety sing_2169.htm#SEC2245 39087 tropicalVarietyNewton tropicalVarietyNewton sing_2751.htm#SEC2827 28532 tropical_lib sing_2129.htm#IDX814 tropicalise sing_2141.htm#SEC2217 49739 tropicaliseSet sing_2142.htm#SEC2218 35136 truncate sing_1452.htm#SEC1528 13545 truncateFast sing_1453.htm#SEC1529 5124 truncated module sing_1452.htm#IDX625 truncated module sing_1453.htm#IDX626 tst_ncfactor sing_716.htm#SEC768 3339 twalk sing_1155.htm#SEC1231 35753 two-sided sing_498.htm#IDX309 two-sided Groebner basis sing_498.htm#IDX310 twostd sing_358.htm#IDX268 twostd sing_483.htm#SEC523 type 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interface sing_21.htm#SEC28 vStd sing_2336.htm#SEC2412 12321 val sing_2746.htm#SEC2822 62171 valvars sing_1723.htm#SEC1799 15723 vandermonde sing_366.htm#SEC406 vanishId sing_1824.htm#SEC1900 49148 var sing_367.htm#SEC407 varMat sing_2179.htm#SEC2255 51772 varNum sing_2180.htm#SEC2256 18485 variables sing_368.htm#SEC408 variables sing_2179.htm#IDX833 variables sing_2180.htm#IDX835 variables sing_2181.htm#IDX839 variables sing_2182.htm#IDX841 variablesSorted sing_536.htm#SEC588 13533 variablesStandard sing_535.htm#SEC587 56500 vars2pars sing_795.htm#SEC847 47343 varsigns sing_1997.htm#SEC2073 3471 varstr sing_369.htm#SEC409 vct2str sing_657.htm#SEC709 51983 vdim sing_370.htm#SEC410 vdim (plural) sing_484.htm#SEC524 vec2poly sing_518.htm#SEC570 27377 vector sing_177.htm#SEC217 vector declarations sing_178.htm#SEC218 vector expressions sing_179.htm#SEC219 vector operations sing_180.htm#SEC220 vector related functions vector related functions sing_181.htm#SEC221 verify 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ordering sing_861.htm#IDX409 wurzel sing_1864.htm#SEC1940 12755 xchange sing_1858.htm#SEC1934 40741 xdvi sing_1783.htm#SEC1859 16898 zdd sing_2226.htm#IDX914 zdd2poly sing_2243.htm#SEC2319 55047 zero sing_2493.htm#SEC2569 12060 zero-dimensional sing_1993.htm#IDX804 zeroMod sing_1215.htm#SEC1291 60609 zeroNcfrac sing_2609.htm#SEC2685 50840 zeroOpt sing_1224.htm#SEC1300 19260 zeroRadical sing_1124.htm#SEC1200 35598 zeroSet sing_1751.htm#SEC1827 60030 zerodec sing_1308.htm#SEC1384 30765 zeroset.lib sing_1746.htm#SEC1822 zeroset_lib sing_1746.htm#SEC1822 zetaDL sing_1445.htm#SEC1521 sprintf { sing_36.htm#IDX78 || sing_36.htm#IDX103 || sing_101.htm#SEC141 } sing_36.htm#IDX79 ~ sing_36.htm#IDX117 ~ sing_393.htm#SEC433