! sing_36.htm#IDX101 != sing_36.htm#IDX95 != sing_95.htm#SEC135 " sing_36.htm#IDX104 # sing_36.htm#IDX118 $ sing_36.htm#IDX119 % sing_36.htm#IDX91 % sing_76.htm#SEC116 % sing_93.htm#SEC133 % sing_105.htm#SEC145 % sing_142.htm#SEC182 && sing_36.htm#IDX102 && sing_96.htm#SEC136 ( sing_36.htm#IDX80 () sing_126.htm#IDX130 ) sing_36.htm#IDX81 * bigintmat operations sing_36.htm#IDX89 * sing_76.htm#SEC116 * sing_82.htm#SEC122 * sing_88.htm#SEC128 * sing_93.htm#SEC133 * sing_101.htm#SEC141 * sing_105.htm#SEC145 * sing_132.htm#SEC172 * sing_137.htm#SEC177 * sing_142.htm#SEC182 * sing_150.htm#SEC190 ** sing_36.htm#IDX93 + bigintmat operations sing_36.htm#IDX85 + sing_76.htm#SEC116 + sing_82.htm#SEC122 + sing_88.htm#SEC128 + sing_93.htm#SEC133 + sing_101.htm#SEC141 + sing_105.htm#SEC145 + sing_121.htm#SEC161 + sing_132.htm#SEC172 + sing_137.htm#SEC177 + sing_142.htm#SEC182 + sing_150.htm#SEC190 + sing_164.htm#SEC204 + sing_170.htm#SEC210 + sing_175.htm#SEC215 ++ sing_36.htm#IDX86 - bigintmat operations sing_36.htm#IDX87 - sing_76.htm#SEC116 - sing_82.htm#SEC122 - sing_93.htm#SEC133 - sing_101.htm#SEC141 - sing_105.htm#SEC145 - sing_132.htm#SEC172 - sing_142.htm#SEC182 - sing_150.htm#SEC190 - sing_175.htm#SEC215 -- 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_154.htm#SEC194 -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_105.htm#SEC145 / sing_132.htm#SEC172 / sing_142.htm#SEC182 / sing_150.htm#SEC190 / sing_175.htm#SEC215 // sing_36.htm#IDX107 // sing_36.htm#IDX109 // sing_36.htm#IDX110 : sing_36.htm#IDX114 : sing_105.htm#SEC145 :: sing_36.htm#IDX115 :: sing_144.htm#SEC184 ; sing_36.htm#IDX111 < sing_36.htm#IDX100 < sing_150.htm#SEC190 < sing_175.htm#SEC215 < sing_241.htm#SEC281 <= sing_36.htm#IDX99 <= sing_95.htm#SEC135 <= sing_142.htm#SEC182 <= sing_150.htm#SEC190 <= sing_170.htm#SEC210 <= sing_175.htm#SEC215 <> sing_36.htm#IDX96 <> sing_95.htm#SEC135 <> sing_132.htm#SEC172 <> sing_142.htm#SEC182 <> sing_150.htm#SEC190 <> sing_164.htm#SEC204 <> sing_170.htm#SEC210 <> sing_175.htm#SEC215 = sing_36.htm#IDX77 == sing_36.htm#IDX94 == sing_95.htm#SEC135 == sing_132.htm#SEC172 == sing_142.htm#SEC182 == sing_150.htm#SEC190 == sing_164.htm#SEC204 == sing_170.htm#SEC210 == sing_175.htm#SEC215 > sing_36.htm#IDX98 > sing_150.htm#SEC190 > sing_175.htm#SEC215 >= sing_36.htm#IDX97 >= sing_95.htm#SEC135 >= sing_142.htm#SEC182 >= sing_150.htm#SEC190 >= sing_170.htm#SEC210 >= sing_175.htm#SEC215 ? sing_36.htm#IDX106 ? sing_251.htm#IDX148 AG codes sing_832.htm#SEC884 AGcode_L sing_1781.htm#SEC1857 60329 AGcode_Omega sing_1782.htm#SEC1858 56285 ASCII sing_881.htm#SEC957 26816 ASCII links sing_112.htm#SEC152 ASSUME sing_64.htm#SEC101 A_L sing_1480.htm#SEC1556 16721 A_Z sing_880.htm#SEC956 50866 Access to elements of a user defined type Access to elements of a user defined type sing_180.htm#SEC220 Adj_div sing_1776.htm#SEC1852 44919 Adjoint ideal sing_1357.htm#IDX592 Alexander polynomial sing_1451.htm#IDX616 Algebraic Geometry codes sing_1775.htm#IDX764 Algebraic dependence Algebraic dependence sing_813.htm#SEC865 Algebraic geometry sing_1332.htm#SEC1408 AltVarEnd sing_726.htm#SEC778 11020 AltVarStart sing_725.htm#SEC777 21592 Ann sing_1271.htm#SEC1347 61560 Appel function sing_555.htm#IDX349 Appel hypergeometric function sing_555.htm#IDX350 Applications sing_830.htm#SEC882 ArnoldAction sing_1573.htm#SEC1649 26958 Assignments for user defined types Assignments for user defined types sing_182.htm#SEC222 AssocTanToEnv sing_917.htm#SEC993 39826 Atkin sing_1864.htm#SEC1940 sprintf Authors sing_1.htm#IDX16 BINresol sing_1370.htm#SEC1446 52996 Background sing_3.htm#SEC5 Basic programming sing_788.htm#SEC840 Basic programming sing_788.htm#SEC840 BelongSemig sing_2295.htm#SEC2371 22405 BerlekampMassey sing_2345.htm#SEC2421 2172 Bern sing_2268.htm#SEC2344 64051 Bernstein operator sing_532.htm#IDX331 Bernstein-Sato polynomial sing_497.htm#IDX312 Bernstein-Sato polynomial sing_532.htm#IDX328 Bernstein-Sato polynomial sing_1514.htm#IDX647 Bernstein-Sato polynomial sing_1518.htm#IDX664 Bernstein-Sato polynomial for variety sing_588.htm#IDX353 Betti number Syzygies and resolutions sing_847.htm#SEC904 BettiNumsH sing_2375.htm#SEC2451 18661 BettiNumsS sing_2378.htm#SEC2454 14964 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_857.htm#SEC914 BlowingUp sing_1493.htm#SEC1569 43153 Blowupcenter sing_1373.htm#SEC1449 3423 BorelCheck sing_1448.htm#SEC1524 48787 Bott's formula sing_2508.htm#IDX977 Branches of space curve singularities Branches of space curve singularities sing_821.htm#SEC873 Briancon-Maisonobe algorithm sing_532.htm#IDX337 Brieskorn lattice sing_1514.htm#IDX643 Brieskorn lattice sing_1515.htm#IDX654 Brieskorn lattice sing_1516.htm#IDX657 Brieskorn lattice sing_1517.htm#IDX660 Brieskorn lattice sing_1518.htm#IDX663 Brieskorn lattice sing_1519.htm#IDX667 Brieskorn lattice sing_1520.htm#IDX671 Brieskorn lattice sing_1521.htm#IDX677 Brieskorn lattice sing_1522.htm#IDX685 Brieskorn lattice sing_1523.htm#IDX691 Brieskorn lattice sing_1524.htm#IDX699 Brieskorn lattice sing_1525.htm#IDX709 Brieskorn lattice sing_1536.htm#IDX715 Brieskorn lattice sing_1538.htm#IDX726 Brieskorn lattice sing_1566.htm#IDX753 Brill-Noether algorithm sing_1775.htm#IDX765 BrillNoether sing_1778.htm#SEC1854 39919 Buchberger algorithm for toric ideals Buchberger algorithm sing_858.htm#SEC915 Budur-Mustata-Saito approach sing_588.htm#IDX357 Building Singular sing_2562.htm#SEC2652 C programming language Major differences to the C programming language sing_401.htm#SEC441 C, module ordering sing_840.htm#IDX411 CGS sing_903.htm#IDX426 CM_regularity sing_1435.htm#SEC1511 33865 CMtype sing_1604.htm#SEC1680 24849 CRHT-ideal sing_864.htm#SEC928 CSMA sing_2291.htm#SEC2367 49080 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 Castelnuovo-Mumford regularity sing_1435.htm#IDX608 Category string sing_51.htm#SEC88 CenCharDec sing_682.htm#SEC734 44505 Center sing_1412.htm#SEC1488 25541 CenterBO sing_1419.htm#SEC1495 34701 CentralQuot sing_680.htm#SEC732 56490 CentralSaturation sing_681.htm#SEC733 31585 Change of rings sing_9.htm#SEC15 Characteristic sets sing_848.htm#SEC905 CharacteristicExponents CharacteristicExponents sing_1499.htm#SEC1575 21795 ChernClass sing_2521.htm#SEC2597 32965 ChernRootsDual sing_2247.htm#SEC2323 40100 ChernRootsHom sing_2256.htm#SEC2332 48446 ChernRootsProd sing_2249.htm#SEC2325 13967 ChernRootsSum sing_2245.htm#SEC2321 57286 ChernRootsSymm sing_2258.htm#SEC2334 59304 ChernRootsWedge sing_2259.htm#SEC2335 7239 Chevalley-Rosenlicht theorem sing_1351.htm#IDX577 Chevalley-Rosenlicht theorem sing_1352.htm#IDX580 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2512.htm#IDX982 ChowRing sing_2512.htm#SEC2588 57977 Classification of hypersurface singularities Classification of hypersurface singularities sing_822.htm#SEC874 Classification of singularities sing_2504.htm#IDX969 Code Codes and the decoding problem sing_863.htm#SEC921 Codes and the decoding problem Codes and the decoding problem sing_863.htm#SEC920 Coding theory sing_1774.htm#SEC1850 Coefficient rings Notes for Singular users sing_2560.htm#SEC2644 Command line options Command line options sing_19.htm#SEC26 Commands Functions and system variables sing_201.htm#SEC241 Commands for user defined types Commands for user defined types sing_181.htm#SEC221 Commutative Algebra sing_801.htm#SEC853 Commutative algebra sing_1089.htm#SEC1165 CompDecomp sing_494.htm#SEC546 9959 CompInt sing_2297.htm#SEC2373 7518 CompleteHomog sing_2235.htm#SEC2311 42123 ComplexValue sing_2367.htm#SEC2443 45546 Comprehensive Groebner System sing_903.htm#IDX429 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_797.htm#SEC849 ConsLevels sing_911.htm#SEC987 45986 ConsLevelsToLevels sing_912.htm#SEC988 56302 ContactMatrix sing_1501.htm#SEC1577 40767 Conti-Traverso algorithm sing_853.htm#SEC910 Contributors sing_1.htm#IDX15 Control structures sing_369.htm#SEC409 Control theory System and Control theory sing_1808.htm#SEC1884 Cooper philosophy sing_864.htm#SEC926 Cornacchia sing_1854.htm#SEC1930 63434 CornacchiaModified sing_1855.htm#SEC1931 59790 Crep sing_906.htm#SEC982 35724 Critical points sing_816.htm#SEC868 CurveParam sing_1495.htm#SEC1571 359 CurveRes sing_1494.htm#SEC1570 48848 Curves sing_1357.htm#IDX589 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 Cyclic code sing_1789.htm#IDX772 Cyclic roots sing_794.htm#SEC846 D-integration sing_555.htm#IDX346 D-localization sing_555.htm#IDX342 D-localization sing_760.htm#IDX380 D-module purityfiltration_lib sing_497.htm#IDX310 D-module sing_532.htm#IDX325 D-module sing_555.htm#IDX339 D-module sing_588.htm#IDX351 D-module sing_738.htm#IDX365 D-module sing_760.htm#IDX377 D-module structure sing_532.htm#IDX326 D-module structure sing_588.htm#IDX352 D-restriction sing_555.htm#IDX344 DBM links sing_117.htm#SEC157 DISPLAY environment variable The online help system sing_16.htm#IDX28 DLoc sing_558.htm#SEC610 5981 DLoc0 sing_560.htm#SEC612 14327 Data types sing_72.htm#SEC112 Data types (plural) sing_414.htm#IDX296 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_179.htm#SEC219 Decoding sing_1789.htm#IDX774 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_862.htm#SEC919 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_867.htm#SEC937 Definition of a user defined type Definition of a user defined type sing_178.htm#SEC218 Deformations sing_819.htm#SEC871 Deformations, T1 and T2 sing_818.htm#SEC870 Degree sing_1336.htm#SEC1412 47790 Delta sing_1420.htm#SEC1496 33497 DeltaList sing_1421.htm#SEC1497 65148 Demo mode sing_24.htm#SEC35 Depth sing_808.htm#SEC860 Determinacy sing_2507.htm#IDX973 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_856.htm#SEC913 Distributed computing sing_931.htm#IDX478 Dlocalization sing_761.htm#SEC813 22140 Documentation Tool sing_60.htm#SEC97 Dp, global ordering sing_838.htm#IDX394 Ds, local ordering sing_839.htm#IDX404 DsingularLocus sing_765.htm#SEC817 46495 Dynamic loading sing_71.htm#SEC111 Dynamic modules sing_796.htm#SEC848 ECPP sing_1898.htm#SEC1974 55777 ECoef sing_1379.htm#SEC1455 14154 EOrdlist sing_1377.htm#SEC1453 36329 ERROR sing_230.htm#SEC270 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 Edatalist sing_1376.htm#SEC1452 61593 Edelman-Reiner sing_2185.htm#IDX855 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 Editing input sing_18.htm#SEC25 Elimination sing_804.htm#SEC856 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_1381.htm#SEC1457 47312 Enumerative geometry sing_2508.htm#IDX975 Equal sing_1335.htm#SEC1411 19984 Eresol sing_1371.htm#SEC1447 12842 EulerAff sing_2292.htm#SEC2368 54325 EulerProj sing_2293.htm#SEC2369 13537 Evaluation of logical expressions Evaluation of logical expressions sing_403.htm#SEC443 Examples sing_786.htm#SEC838 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 Exp for matrices sing_1353.htm#IDX581 Experimental libraries Experimental libraries sing_2229.htm#SEC2305 Ext sing_1149.htm#SEC1225 21909 Ext, computation of sing_807.htm#SEC859 Ext_R sing_1148.htm#SEC1224 53310 Exterior sing_712.htm#SEC764 23593 Extra weight vector sing_843.htm#SEC895 Factorization sing_809.htm#SEC861 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_918.htm#SEC994 61191 Feynman graph sing_1125.htm#IDX514 Finite fields sing_803.htm#SEC855 First steps sing_6.htm#SEC12 Fitzgerald-Lax method Fitzgerald-Lax method sing_866.htm#SEC934 Flow control sing_40.htm#SEC70 Formal Checker sing_59.htm#SEC96 Formatting output sing_793.htm#SEC845 Free resolution sing_805.htm#SEC857 Free resolution, graded Handling graded modules sing_806.htm#SEC858 FultonA sing_2290.htm#SEC2366 33688 Functions sing_202.htm#SEC242 Future benefits of Singular 4 Notes for Singular users sing_2560.htm#SEC2650 G-algebra sing_478.htm#SEC518 G-algebra sing_478.htm#SEC520 G-algebra, setup sing_478.htm#SEC522 GBWeight sing_561.htm#SEC613 24641 GBsolve sing_1688.htm#SEC1764 16830 GIT sing_2386.htm#IDX949 GKZsystem sing_678.htm#SEC730 20528 GKdim sing_651.htm#SEC703 9814 GMP sing_1.htm#IDX3 GMP sing_2564.htm#SEC2654 GND.lib sing_2393.htm#SEC2469 GND_lib sing_2393.htm#SEC2469 GTZmod sing_1197.htm#SEC1273 30091 GTZopt sing_1204.htm#SEC1280 14642 G_a -Invariants sing_825.htm#SEC877 Gamma sing_1386.htm#SEC1462 3820 Gauss-Manin connection Gauss-Manin connection sing_849.htm#SEC906 Gauss-Manin connection sing_1566.htm#IDX752 Gauss-Manin connection sing_1613.htm#IDX755 Gauss-Manin system sing_1514.htm#IDX642 Gauss-Manin system sing_1515.htm#IDX653 Gauss-Manin system sing_1516.htm#IDX656 Gauss-Manin system sing_1517.htm#IDX659 Gauss-Manin system sing_1518.htm#IDX662 Gauss-Manin system sing_1519.htm#IDX666 Gauss-Manin system sing_1520.htm#IDX670 Gauss-Manin system sing_1521.htm#IDX676 Gauss-Manin system sing_1522.htm#IDX684 Gauss-Manin system sing_1523.htm#IDX690 Gauss-Manin system sing_1524.htm#IDX698 Gauss-Manin system sing_1525.htm#IDX708 Gauss-Manin system sing_1536.htm#IDX714 Gauss-Manin system sing_1538.htm#IDX725 General command syntax General command syntax sing_35.htm#SEC59 General concepts sing_12.htm#SEC18 General purpose sing_874.htm#SEC950 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_480.htm#SEC530 Generalized Newton identities Generalized Newton identities sing_865.htm#SEC931 Geometric genus sing_1357.htm#IDX593 German Umlaute sing_399.htm#IDX283 Getting started sing_5.htm#SEC11 Global orderings sing_838.htm#SEC890 GoettscheF sing_2373.htm#SEC2449 27881 Graded commutative algebras Graded commutative algebras (SCA) sing_482.htm#SEC534 Grassmannian sing_2513.htm#SEC2589 43898 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2513.htm#IDX983 Greuel, Gert-Martin sing_1.htm#IDX18 Groebner Bases Computing Groebner and Standard Bases sing_797.htm#SEC849 Groebner bases in G-algebras Groebner bases in G-algebras sing_479.htm#SEC523 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_485.htm#SEC537 Groebner bases, decodeGB sing_1789.htm#IDX776 Groebner bases, slim sing_800.htm#SEC852 Groebner basis conversion Groebner basis conversion sing_799.htm#SEC851 Groebner cover sing_902.htm#IDX422 Groebner cover sing_909.htm#IDX435 Groebner cover sing_910.htm#IDX441 Groebner fan sing_2052.htm#IDX793 Groebner walk sing_1140.htm#IDX535 Groebner walk sing_1142.htm#IDX537 Groebner walk sing_2497.htm#IDX964 Groebner walk sing_2498.htm#IDX965 Groebnerwalk sing_1136.htm#IDX531 Groebnerwalk sing_2432.htm#IDX958 Groebnerwalk sing_2496.htm#IDX963 Groebnerwalk sing_2500.htm#IDX968 Gromov-Witten invariants sing_1125.htm#IDX511 Gromov-Witten invariants sing_1131.htm#IDX520 Gromov-Witten invariants sing_1132.htm#IDX524 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2538.htm#IDX995 Gromov-Witten invariants, multiple covers sing_2537.htm#IDX994 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2539.htm#IDX996 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2540.htm#IDX997 Gromov-Witten invariants. sing_2508.htm#IDX978 Gweights sing_706.htm#SEC758 651 H2basis sing_1571.htm#SEC1647 3414 HHnormalForm sing_2305.htm#SEC2381 33972 Hamburger-Noether expansion sing_1451.htm#IDX612 Hamburger-Noether expansion sing_1539.htm#IDX734 Hamburger-Noether expansions sing_1776.htm#IDX766 Handling graded modules Handling graded modules sing_806.htm#SEC858 Hcode sing_1473.htm#SEC1549 26628 Help string sing_45.htm#SEC82 Hensel sing_235.htm#SEC275 Hilbert function sing_348.htm#IDX188 Hilbert function sing_846.htm#SEC900 Hilbert series sing_846.htm#SEC900 Hilbert-driven GB algorithm Groebner basis conversion sing_799.htm#SEC851 HilbertClassPoly sing_1861.htm#SEC1937 sprintf HilbertSeries sing_1666.htm#SEC1742 21249 HilbertWeights sing_1667.htm#SEC1743 sprintf Hom sing_1152.htm#SEC1228 61434 HomJJ sing_1227.htm#SEC1303 1525 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_855.htm#SEC912 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_1131.htm#IDX523 Hurwitz numbers sing_1132.htm#IDX527 Hypersurface singularities, classification of Classification of hypersurface singularities sing_822.htm#SEC874 IN sing_272.htm#IDX149 Ideal membership sing_845.htm#IDX416 Identifiers, syntax of sing_37.htm#SEC65 ImageGroup sing_1669.htm#SEC1745 28808 ImageVariety sing_1668.htm#SEC1744 15252 Imap, option sing_307.htm#IDX175 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 Incl sing_1334.htm#SEC1410 7621 Index sing_2569.htm#SEC2659 Info string sing_52.htm#SEC89 InterDiv sing_1402.htm#SEC1478 46142 Interactive use sing_13.htm#SEC19 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 IntersectWithSub sing_683.htm#SEC735 56289 Intersection theory sing_2508.htm#IDX974 IntersectionMatrix sing_1500.htm#SEC1576 29351 Introduction sing_2.htm#SEC4 Invariant Theory sing_824.htm#SEC876 Invariant theory sing_1618.htm#SEC1694 InvariantQ sing_1671.htm#SEC1747 53256 InvariantRing sing_1670.htm#SEC1746 22928 Invariants of a finite group Invariants of a finite group sing_826.htm#SEC878 Invariants of plane curve singularities Invariants of plane curve singularities sing_820.htm#SEC872 IsSCA sing_727.htm#SEC779 58445 J-marked schemes sing_1442.htm#IDX610 J-marked schemes, Borel ideals sing_1447.htm#IDX611 JMBTest.lib sing_1442.htm#SEC1518 JMBTest_lib sing_1442.htm#SEC1518 JMSConst.lib sing_1447.htm#SEC1523 JMSConst_lib sing_1447.htm#SEC1523 JMarkedScheme sing_1449.htm#SEC1525 60696 Jacobi sing_1871.htm#SEC1947 29843 Jacobson form sing_1826.htm#IDX777 Jacobson normal form sing_1826.htm#IDX778 JuReTopDim sing_1344.htm#SEC1420 sprintf JuReZeroDim sing_1345.htm#SEC1421 sprintf KScoef sing_1564.htm#SEC1640 sprintf KSconvert sing_1562.htm#SEC1638 3585 KSker sing_1561.htm#SEC1637 40166 KSlinear sing_1563.htm#SEC1639 19896 KSpencerKernel sing_1611.htm#SEC1687 12490 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2412.htm#SEC2488 20741 Kernel of module homomorphisms Kernel of module homomorphisms sing_812.htm#SEC864 KoszulHomology sing_1161.htm#SEC1237 sprintf LETTERPLACE sing_483.htm#SEC535 LIB sing_276.htm#SEC316 LIB commands sing_53.htm#SEC90 LIBs sing_870.htm#SEC946 LLL sing_350.htm#IDX220 LOT algorithm sing_532.htm#IDX338 LU-decomposition of a matrix of numbers sing_281.htm#SEC321 Laurent series sing_1129.htm#IDX519 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_828.htm#SEC880 Left ideal membership Groebner bases in G-algebras sing_479.htm#SEC526 Left normal form Groebner bases in G-algebras sing_479.htm#SEC525 LengthSym sing_737.htm#SEC789 16591 LengthSymElement sing_736.htm#SEC788 28292 Letterplace sing_483.htm#SEC535 Lexicographic Groebner bases, computation of Groebner basis conversion sing_799.htm#SEC851 Libraries Writing procedures and libraries sing_48.htm#SEC85 Libraries sing_789.htm#SEC841 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 Library versioning Notes for Singular users sing_2560.htm#SEC2648 Lie algebra sing_1352.htm#IDX578 Lie group sing_1355.htm#IDX583 Lie group sing_1356.htm#IDX586 Limitations sing_399.htm#SEC439 Linear algebra sing_1029.htm#SEC1105 Linear code sing_1789.htm#IDX773 LinearActionQ sing_1673.htm#SEC1749 62218 LinearCombinationQ sing_1674.htm#SEC1750 59373 LinearizeAction sing_1672.htm#SEC1748 60266 Loading a library sing_62.htm#SEC99 Local orderings sing_839.htm#SEC891 Log for matrices sing_1354.htm#IDX582 Long coefficients sing_791.htm#SEC843 M, ordering sing_841.htm#SEC893 MVComplex sing_2321.htm#SEC2397 62126 MacdonaldF sing_2376.htm#SEC2452 12751 Macintosh installation Macintosh installation instructions sing_2568.htm#SEC2658 Mathematical background Mathematical background sing_844.htm#SEC896 Mathematical background (plural) Mathematical background (plural) sing_477.htm#SEC517 Matrix orderings sing_841.htm#SEC893 Max sing_1580.htm#SEC1656 23 Maximus sing_1444.htm#SEC1520 10010 Maxord sing_1385.htm#SEC1461 14124 MillerRabin sing_1881.htm#SEC1957 15740 Milnor number Milnor and Tjurina number sing_815.htm#SEC867 Milnor number sing_2506.htm#IDX972 Min sing_1581.htm#SEC1657 29622 MinMult sing_2296.htm#SEC2372 39835 MinimalDecomposition MinimalDecomposition sing_1675.htm#SEC1751 24161 Minimum distance sing_1789.htm#IDX775 Minimus sing_1443.htm#SEC1519 61721 Miscellaneous libraries Miscellaneous libraries sing_2156.htm#SEC2232 ModEqn sing_1574.htm#SEC1650 59394 Modular techniques sing_931.htm#IDX475 Module orderings sing_840.htm#SEC892 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 Monodromy sing_1566.htm#IDX750 Monomial orderings sing_835.htm#SEC887 Monomial orderings, Term orderings sing_31.htm#SEC44 Morse lemma sing_2505.htm#IDX970 MultiplicitySequence MultiplicitySequence sing_1498.htm#SEC1574 1309 NF sing_326.htm#SEC366 NF sing_469.htm#SEC509 NFMora sing_1947.htm#SEC2023 40670 NPos sing_1217.htm#SEC1293 15702 NPos_test sing_1215.htm#SEC1291 48172 NSplaces sing_1777.htm#SEC1853 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 libraries depending on Singular 4 Notes for Singular users sing_2560.htm#SEC2646 New orderings for modules Notes for Singular users sing_2560.htm#SEC2649 Newton non-degenerate sing_1553.htm#IDX748 Newton polygon sing_1552.htm#IDX747 Newton polygon sing_1553.htm#IDX749 Newton polygons sing_2547.htm#IDX1000 Newton polytope sing_2052.htm#IDX792 NoetherPosition sing_1211.htm#SEC1287 18735 Non-commutative LIBs Non-commutative libraries sing_489.htm#SEC541 Non-commutative algebra Non-commutative algebra sing_827.htm#SEC879 Non-commutative algebra sing_861.htm#SEC918 Non-commutative libraries Non-commutative libraries sing_489.htm#SEC541 Non-commutative subsystem Non-commutative subsystem sing_412.htm#SEC452 Nonhyp sing_1374.htm#SEC1450 sprintf Normal form sing_845.htm#IDX415 Normalization sing_811.htm#SEC863 Notes for Singular users Notes for Singular users sing_2560.htm#SEC2643 Notes for developers Notes for developers sing_2561.htm#SEC2651 NullCone sing_1676.htm#SEC1752 64635 NumIrrDecom sing_1348.htm#SEC1424 sprintf NumLocalDim sing_1337.htm#SEC1413 1739 NumPrimDecom sing_1350.htm#SEC1426 34134 Oaku-Takayama algorithm sing_532.htm#IDX336 Objects sing_38.htm#SEC66 Orlik-Solomon sing_2186.htm#IDX856 Output, formatting of sing_793.htm#SEC845 PBW sing_511.htm#IDX324 PBW basis sing_478.htm#SEC519 PBW_eqDeg sing_529.htm#SEC581 23181 PBW_maxDeg sing_530.htm#SEC582 59566 PBW_maxMonom sing_531.htm#SEC583 1155 PEsolve sing_1686.htm#SEC1762 9229 PH_ais sing_2208.htm#SEC2284 49473 PH_nais sing_2209.htm#SEC2285 46271 PLURAL sing_413.htm#SEC453 PLURAL LIBs Non-commutative libraries sing_489.htm#SEC541 PPolyH sing_2374.htm#SEC2450 25241 PPolyS sing_2377.htm#SEC2453 13817 ParToVar sing_2369.htm#SEC2445 13991 Parallelization Parallelization with ssi links sing_795.htm#SEC847 Parallelization sing_931.htm#IDX476 Parameter list sing_44.htm#SEC81 Parameters sing_792.htm#SEC844 Parametrization sing_1357.htm#IDX590 Parametrization, image. sing_1367.htm#IDX602 PartC sing_2286.htm#SEC2362 54120 PartitionVar sing_2366.htm#SEC2442 41350 Path names Notes for Singular users sing_2560.htm#SEC2647 PerfectPowerTest sing_1844.htm#SEC1920 17450 Perturbation walk sing_1141.htm#IDX536 Pfister, Gerhard sing_1.htm#IDX19 Pipe links sing_116.htm#SEC156 PocklingtonLehmer sing_1883.htm#SEC1959 13634 Poincare polynomial sing_2198.htm#IDX880 Polar curves sing_817.htm#SEC869 PollardRho sing_1884.htm#SEC1960 49602 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2211.htm#IDX896 PolyBoRi, Boolean Groebner Basis sing_2213.htm#IDX897 PolyBoRi, Boolean Groebner Basis sing_2214.htm#IDX898 PolyBoRi, Boolean Groebner Basis sing_2215.htm#IDX899 PolyBoRi, Boolean Groebner Basis sing_2216.htm#IDX900 PolyBoRi, Boolean Groebner Basis sing_2217.htm#IDX901 PolyBoRi, Boolean Groebner Basis sing_2218.htm#IDX902 PolyBoRi, Boolean Groebner Basis sing_2219.htm#IDX903 PolyBoRi, Boolean Groebner Basis sing_2220.htm#IDX904 PolyBoRi, Boolean Groebner Basis sing_2221.htm#IDX905 PolyBoRi, Boolean Groebner Basis sing_2222.htm#IDX906 PolyBoRi, Boolean Groebner Basis sing_2223.htm#IDX907 PolyBoRi, Boolean Groebner Basis sing_2224.htm#IDX908 PolyBoRi, Boolean Groebner Basis sing_2225.htm#IDX909 PolyBoRi, Boolean Groebner Basis sing_2227.htm#IDX911 PolyBoRi, zero-supressed decision diagram sing_2226.htm#IDX910 Polybori, Boolean Groebner Basis sing_2228.htm#IDX912 Polynomial data sing_833.htm#SEC885 Pottier algorithm sing_854.htm#SEC911 Preface sing_1.htm#SEC1 Prep sing_907.htm#SEC983 49657 Primary decomposition Primary decomposition sing_810.htm#SEC862 PrimdecA sing_1193.htm#SEC1269 248 PrimdecB sing_1194.htm#SEC1270 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_789.htm#SEC841 Procedures in a library Procedures in a library sing_54.htm#SEC91 Product orderings sing_842.htm#SEC894 Programming sing_787.htm#SEC839 PtoCrep sing_908.htm#SEC984 30456 Puiseux expansion sing_1451.htm#IDX613 Puiseux expansion sing_1539.htm#IDX735 Puiseux pairs Invariants of plane curve singularities sing_820.htm#SEC872 Puiseux pairs sing_1545.htm#IDX740 QQ sing_28.htm#SEC39 Qso3Casimir sing_677.htm#SEC729 40212 Quotient sing_1728.htm#SEC1804 24888 QuotientEquations sing_1575.htm#SEC1651 18230 Rational curves sing_1357.htm#IDX591 ReJunkUseHomo sing_1343.htm#SEC1419 10186 ReesAlgebra sing_1310.htm#SEC1386 59951 References sing_869.htm#SEC943 References (plural) sing_481.htm#SEC531 Release Notes sing_2556.htm#SEC2632 ResTree sing_1403.htm#SEC1479 58727 Resolution sing_11.htm#SEC17 Resolution of singularities Resolution of singularities sing_823.htm#SEC875 Resolution, free sing_805.htm#SEC857 ReynoldsImage sing_1677.htm#SEC1753 35172 ReynoldsOperator sing_1678.htm#SEC1754 14986 RiemannRochBN sing_2231.htm#SEC2307 20085 RiemannRochHess sing_2431.htm#SEC2507 sprintf Right Groebner bases and syzygies Right Groebner bases and syzygies sing_829.htm#SEC881 Ring-dependent options Notes for Singular users sing_2560.htm#SEC2645 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_482.htm#SEC534 SDB breakpoint Source code debugger sing_66.htm#SEC106 SDB debugger Source code debugger sing_66.htm#SEC106 SDLoc sing_559.htm#SEC611 9512 SINGULAR libraries sing_870.htm#SEC946 SINGULARHIST sing_18.htm#SEC25 SScontinue sing_1013.htm#SEC1089 38390 SSres sing_1011.htm#SEC1087 4648 SSsyz sing_1012.htm#SEC1088 34610 SV-decoding algorithm sing_1784.htm#IDX769 SV-decoding algorithm, preprocessing sing_1783.htm#IDX768 Sannfs sing_535.htm#SEC587 42932 SannfsBFCT sing_544.htm#SEC596 59702 SannfsVar sing_591.htm#SEC643 37522 Sannfslog sing_536.htm#SEC588 49313 Saturation sing_802.htm#SEC854 Saturation sing_1122.htm#IDX505 Sch@"onemann, Hans sing_1.htm#IDX20 Schoof sing_1895.htm#SEC1971 49281 Schreyer ordering sing_1006.htm#IDX492 Schreyer resolution sing_1006.htm#IDX493 Schubert calculus sing_2508.htm#IDX976 SchubertClass sing_2545.htm#SEC2621 62336 SchurCh sing_2283.htm#SEC2359 58575 SchurS sing_2282.htm#SEC2358 46004 Scontinue sing_1010.htm#SEC1086 11534 SegreA sing_2289.htm#SEC2365 55776 Semigroup sing_1491.htm#SEC1567 22323 Setting up a G-algebra sing_478.htm#SEC522 ShanksMestre sing_1894.htm#SEC1970 12973 SimplifyIdeal sing_1679.htm#SEC1755 sprintf Singular sing_350.htm#IDX255 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2558.htm#SEC2641 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_1341.htm#SEC1417 7552 SingularLib sing_350.htm#IDX257 Singularities sing_1450.htm#SEC1526 Singularity Theory sing_814.htm#SEC866 Skeletons for parallelization sing_931.htm#IDX477 Smith form sing_1826.htm#IDX779 Smith normal form sing_1826.htm#IDX780 SolowayStrassen sing_1882.htm#SEC1958 22680 Solving systems of polynomial equations Solving systems of polynomial equations sing_831.htm#SEC883 Source code debugger, invocation Command line options sing_19.htm#IDX33 Space curve singularities, branches of Branches of space curve singularities sing_821.htm#SEC873 Special characters sing_36.htm#SEC64 Splitting lemma sing_2505.htm#IDX971 Sres sing_1008.htm#SEC1084 60186 Ssi file links sing_114.htm#SEC154 Ssi links sing_113.htm#SEC153 Ssi tcp links sing_115.htm#SEC155 Ssyz sing_1009.htm#SEC1085 56541 StabEqn sing_1576.htm#SEC1652 28539 StabEqnId sing_1577.htm#SEC1653 27955 StabOrder sing_1578.htm#SEC1654 55603 Standard Bases Computing Groebner and Standard Bases sing_797.htm#SEC849 Standard bases sing_845.htm#SEC897 StartOrderingV sing_1445.htm#SEC1521 58927 Startup sequence sing_20.htm#SEC27 StringF sing_1565.htm#SEC1641 11590 SymGroup sing_735.htm#SEC787 56676 Symbolic-numerical solving Symbolic-numerical solving sing_831.htm#SEC883 Symbolic-numerical solving sing_1683.htm#SEC1759 System and Control theory System and Control theory sing_1808.htm#SEC1884 System dependent limitations System dependent limitations sing_400.htm#SEC440 System variables sing_386.htm#SEC426 Syzygies and resolutions Syzygies and resolutions sing_847.htm#SEC901 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_480.htm#SEC527 T1 sing_818.htm#SEC870 T2 sing_818.htm#SEC870 TRACE Tracing of procedures sing_65.htm#SEC102 TRACE sing_395.htm#SEC435 T_1 sing_1598.htm#SEC1674 59277 T_12 sing_1600.htm#SEC1676 12923 T_2 sing_1599.htm#SEC1675 55781 Teaching sing_1840.htm#SEC1916 Template for writing a library sing_55.htm#SEC92 TestGRRes sing_2411.htm#SEC2487 8315 TestJMark sing_1446.htm#SEC1522 41314 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 The Tran algorithm sing_1138.htm#IDX533 The fractal walk algorithm sing_1137.htm#IDX532 The fractal walk algorithm sing_2499.htm#IDX966 The online help system The online help system sing_16.htm#SEC22 Tjurina sing_1596.htm#SEC1672 11249 Tjurina number Milnor and Tjurina number sing_815.htm#SEC867 Tjurina number sing_1232.htm#IDX560 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 Tor sing_1163.htm#SEC1239 sprintf Toric ideals and integer programming Toric ideals and integer programming sing_850.htm#SEC907 Tricks and pitfalls sing_398.htm#SEC438 Tropical Geometry sing_1992.htm#SEC2068 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_1078.htm#SEC1154 26192 Unix installation Unix installation instructions sing_2566.htm#SEC2656 UpOneMatrix sing_724.htm#SEC776 63020 UpperMonomials sing_1579.htm#SEC1655 20941 UseBertini sing_1340.htm#SEC1416 43362 User defined types sing_177.htm#SEC217 V-filtration sing_1514.htm#IDX645 V-filtration sing_1520.htm#IDX673 V-filtration sing_1521.htm#IDX679 V-filtration sing_1522.htm#IDX687 V-filtration sing_1523.htm#IDX693 V-filtration sing_1524.htm#IDX701 V-filtration sing_1525.htm#IDX711 V-filtration sing_1536.htm#IDX717 V-filtration sing_1538.htm#IDX728 VarToPar sing_2368.htm#SEC2444 10508 Variables, indexed sing_37.htm#SEC65 Version number Version schema for Singular sing_2559.htm#SEC2642 Version schema for Singular Version schema for Singular sing_2559.htm#SEC2642 Version string sing_50.htm#SEC87 Visualization sing_1746.htm#SEC1822 WLemma sing_920.htm#SEC996 3921 WP, global ordering sing_838.htm#IDX398 WSemigroup sing_1496.htm#SEC1572 57449 Weierstrass sing_1779.htm#SEC1855 58220 Weierstrass semigroup sing_1775.htm#IDX763 Weyl sing_709.htm#SEC761 29212 Weyl algebra sing_532.htm#IDX330 Weyl algebra sing_588.htm#IDX355 Weyl closure sing_760.htm#IDX383 WeylClosure sing_762.htm#SEC814 23845 WeylClosure1 sing_763.htm#SEC815 15759 Wibmer's Lemma sing_920.htm#IDX473 Windows installation Windows installation instructions sing_2567.htm#SEC2657 WitSet sing_1347.htm#SEC1423 39803 WitSupSet sing_1346.htm#SEC1422 47758 Ws, local ordering sing_839.htm#IDX410 XLsolve sing_1689.htm#SEC1765 34970 ZZ sing_28.htm#SEC39 ZZ/m sing_28.htm#SEC39 ZZ/p sing_28.htm#SEC39 ZZsolve sing_1690.htm#SEC1766 18657 [ sing_36.htm#IDX83 [] sing_137.htm#SEC177 [] sing_150.htm#SEC190 [] sing_170.htm#SEC210 [] sing_175.htm#SEC215 \ sing_36.htm#IDX112 ] sing_36.htm#IDX84 ^ sing_36.htm#IDX92 ^ sing_76.htm#SEC116 ^ sing_88.htm#SEC128 ^ sing_142.htm#SEC182 ^ sing_150.htm#SEC190 _ sing_36.htm#IDX116 ` sing_36.htm#IDX105 a, ordering sing_843.htm#SEC895 absFactorize sing_1091.htm#SEC1167 52546 absFactorizeBCG sing_1092.htm#SEC1168 55510 absPrimdecGTZ sing_1290.htm#SEC1366 46393 absPrimdecGTZE sing_1291.htm#SEC1367 48005 absValue sing_882.htm#SEC958 54595 absfact.lib sing_1090.htm#SEC1166 absfact_lib sing_1090.htm#SEC1166 absolute factorization. sing_1090.htm#IDX504 abstract variety, projective space, Grassmannian printVariety sing_2509.htm#IDX979 abstract variety, projective space, Grassmannian sing_2510.htm#IDX980 abstractR sing_1429.htm#SEC1505 22284 actionIsProper sing_1659.htm#SEC1735 52474 addNvarsTo sing_1005.htm#SEC1081 63123 addRat sing_781.htm#SEC833 4768 addSheaf sing_2528.htm#SEC2604 27062 addcol sing_1047.htm#SEC1123 52204 addcores sing_974.htm#SEC1050 41254 addrow sing_1048.htm#SEC1124 47055 addvarsTo sing_1004.htm#SEC1080 17717 ademRelations sing_641.htm#SEC693 30263 adjoint sing_1072.htm#SEC1148 56619 adjointIdeal sing_1358.htm#SEC1434 11455 adjunction divisor sing_1776.htm#IDX767 admissibleSub sing_700.htm#SEC752 6583 afaces sing_2387.htm#SEC2463 41634 affine code Fitzgerald-Lax method sing_866.htm#SEC935 ainvar.lib sing_1656.htm#SEC1732 ainvar_lib sing_1656.htm#SEC1732 aksaka.lib sing_1841.htm#SEC1917 aksaka_lib sing_1841.htm#SEC1917 alexanderpolynomial sing_1454.htm#SEC1530 36814 alexpoly.lib sing_1451.htm#SEC1527 alexpoly_lib sing_1451.htm#SEC1527 algDependent sing_1097.htm#SEC1173 20789 alg_kernel sing_1098.htm#SEC1174 307 algebra.lib sing_1093.htm#SEC1169 algebra_containment sing_1094.htm#SEC1170 47912 algebra_lib sing_1093.htm#SEC1169 algebraic dependence sing_730.htm#IDX361 algebraic field extension sing_1304.htm#IDX567 algebraicDependence sing_1317.htm#SEC1393 38500 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_857.htm#SEC914 algorithm of Conti and Traverso sing_853.htm#SEC910 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_856.htm#SEC913 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_855.htm#SEC912 algorithm of Pottier sing_854.htm#SEC911 align sing_203.htm#SEC243 all.lib sing_875.htm#SEC951 allDoubleExt sing_747.htm#SEC799 43457 allExtOfLeft sing_744.htm#SEC796 6405 allExtOfRight sing_745.htm#SEC797 56781 allPositive sing_508.htm#SEC560 1409 all_lib sing_875.htm#SEC951 allowing net access Command line options sing_19.htm#IDX41 allprint sing_922.htm#SEC998 5195 allreal sing_1984.htm#SEC2060 57232 allrealst sing_1982.htm#SEC2058 40962 allsquarefree sing_1558.htm#SEC1634 45545 ambientDimension sing_1997.htm#SEC2073 18907 and Evaluation of logical expressions sing_96.htm#SEC136 and sing_403.htm#SEC443 annPoly sing_556.htm#SEC608 18228 annRat sing_557.htm#SEC609 62662 annRatSyz sing_770.htm#SEC822 15672 annfs sing_533.htm#SEC585 38155 annfs0 sing_545.htm#SEC597 26476 annfs2 sing_546.htm#SEC598 47962 annfsBMI sing_542.htm#SEC594 2532 annfsParamBM sing_541.htm#SEC593 43587 annfsRB sing_547.htm#SEC599 31892 annfspecial sing_534.htm#SEC586 27566 annihilator of polynomial sing_555.htm#IDX340 annihilator of rational function sing_555.htm#IDX341 annihilator of rational function sing_760.htm#IDX386 annil sing_1199.htm#SEC1275 48744 appelF1 sing_574.htm#SEC626 63146 appelF2 sing_575.htm#SEC627 22460 appelF4 sing_576.htm#SEC628 6847 appendWeight2Ord sing_702.htm#SEC754 21488 apply sing_370.htm#SEC410 applyAdF sing_524.htm#SEC576 40329 arcpoint.lib sing_1464.htm#SEC1540 arcpoint_lib sing_1464.htm#SEC1540 areZeroElements sing_2473.htm#SEC2549 14728 argument, default sing_44.htm#SEC81 argument, optional sing_44.htm#SEC81 arr.lib sing_2157.htm#SEC2233 arr2multarr sing_2190.htm#SEC2266 15063 arrBoolean sing_2179.htm#SEC2255 63256 arrBoundedChambers sing_2200.htm#SEC2276 18347 arrBraid sing_2180.htm#SEC2256 34093 arrCenter sing_2167.htm#SEC2243 24565 arrCentered sing_2169.htm#SEC2245 15904 arrCentral sing_2168.htm#SEC2244 14086 arrCentralize sing_2170.htm#SEC2246 53235 arrChambers sing_2199.htm#SEC2275 44578 arrCharPoly sing_2197.htm#SEC2273 44129 arrCone sing_2173.htm#SEC2249 38068 arrCoordChange sing_2171.htm#SEC2247 61430 arrCoordNormalize sing_2172.htm#SEC2248 46273 arrDecone sing_2174.htm#SEC2250 54637 arrDer sing_2187.htm#SEC2263 48815 arrEdelmanReiner sing_2185.htm#SEC2261 59091 arrEssentialize sing_2178.htm#SEC2254 6667 arrExponents sing_2189.htm#SEC2265 1948 arrFlats sing_2194.htm#SEC2270 64792 arrIsEssential sing_2177.htm#SEC2253 34363 arrIsFree sing_2188.htm#SEC2264 3860 arrLastVar sing_2166.htm#SEC2242 25835 arrLattice sing_2195.htm#SEC2271 58951 arrLocalize sing_2175.htm#SEC2251 56070 arrOrlikSolomon sing_2186.htm#SEC2262 31686 arrPoincare sing_2198.htm#SEC2274 412 arrPrintMatrix sing_2162.htm#SEC2238 21204 arrRandom sing_2183.htm#SEC2259 59986 arrRandomCentral sing_2184.htm#SEC2260 43698 arrRestrict sing_2176.htm#SEC2252 sprintf arrSet sing_2158.htm#SEC2234 53769 arrSwapVar sing_2165.htm#SEC2241 44919 arrTypeB sing_2181.htm#SEC2257 22358 arrTypeD sing_2182.htm#SEC2258 26495 arr_lib sing_2157.htm#SEC2233 arrange sing_549.htm#SEC601 50350 arrangement sing_2158.htm#IDX798 arrangement sing_2159.htm#IDX803 arrangement sing_2190.htm#IDX865 arrangement sing_2191.htm#IDX868 ask sing_1849.htm#SEC1925 3862 assPrimes sing_1108.htm#SEC1184 sprintf assign sing_2158.htm#IDX800 assignment,custom Assignments for user defined types sing_182.htm#SEC222 associated tangent FamElemsAtEnvCompPoints sing_917.htm#IDX466 associated tangent sing_918.htm#IDX470 assprimeszerodim.lib assprimeszerodim_lib sing_1106.htm#SEC1182 assprimeszerodim_lib assprimeszerodim_lib sing_1106.htm#SEC1182 atkins.lib sing_1850.htm#SEC1926 atkins_lib sing_1850.htm#SEC1926 attrib sing_204.htm#SEC244 autonom sing_1813.htm#SEC1889 57044 autonomDim sing_1814.htm#SEC1890 30055 awalk1 sing_1139.htm#SEC1215 11044 awalk2 sing_1140.htm#SEC1216 8955 b-function sing_497.htm#IDX313 bFactor sing_579.htm#SEC631 15179 babyGiant sing_1879.htm#SEC1955 41113 backward sing_2355.htm#SEC2431 11225 bareiss sing_205.htm#SEC245 base2str sing_878.htm#SEC954 sprintf basering sing_28.htm#IDX76 basering sing_83.htm#SEC123 basicinvariants sing_1470.htm#SEC1546 32136 belongSemigroup sing_1111.htm#SEC1187 19983 bernstein sing_1518.htm#SEC1594 5605 bernsteinBM sing_537.htm#SEC589 57689 bernsteinLift sing_538.htm#SEC590 22885 bertini2Singular sing_1342.htm#SEC1418 58501 betti sing_206.htm#SEC246 betti (plural) sing_447.htm#SEC487 bfct sing_498.htm#SEC550 29858 bfctAnn sing_500.htm#SEC552 36658 bfctBound sing_769.htm#SEC821 5630 bfctIdeal sing_502.htm#SEC554 41018 bfctOneGB sing_501.htm#SEC553 9696 bfctSyz sing_499.htm#SEC551 26796 bfctVarAnn sing_590.htm#SEC642 51667 bfctVarIn sing_589.htm#SEC641 9274 bfun.lib sing_497.htm#SEC549 bfun_lib sing_497.htm#SEC549 bigint sing_73.htm#SEC113 bigint declarations sing_74.htm#SEC114 bigint expressions sing_75.htm#SEC115 bigint operations sing_76.htm#SEC116 bigint related functions bigint related functions sing_77.htm#SEC117 bigintmat sing_78.htm#SEC118 bigintmat declarations bigintmat declarations sing_79.htm#SEC119 bigintmat expressions bigintmat expressions sing_80.htm#SEC120 bigintmat operations bigintmat operations sing_82.htm#SEC122 bigintmat type cast sing_81.htm#SEC121 bimodules sing_490.htm#IDX301 bimodules.lib sing_490.htm#SEC542 bimodules_lib sing_490.htm#SEC542 binary_add sing_1902.htm#SEC1978 42817 binomial sing_883.htm#SEC959 23208 binomials2intmat sing_1265.htm#SEC1341 58804 birational map, image, inverse. sing_1359.htm#IDX596 bistd sing_491.htm#SEC543 45237 bisyzygies sing_490.htm#IDX302 bitrinity sing_492.htm#SEC544 3516 blackbox sing_186.htm#SEC226 blackbox sing_194.htm#SEC234 block sing_40.htm#SEC70 block sing_369.htm#SEC409 blowUp sing_1410.htm#SEC1486 34819 blowUp2 sing_1411.htm#SEC1487 65264 blowUpBO sing_1417.htm#SEC1493 58146 blowup0 sing_1116.htm#SEC1192 44451 boolean sing_2179.htm#IDX842 boolean expressions sing_95.htm#SEC135 boolean operations sing_96.htm#SEC136 boolean_constant sing_2213.htm#SEC2289 52873 boolean_ideal sing_2217.htm#SEC2293 53515 boolean_poly sing_2214.htm#SEC2290 41652 boolean_poly_ring sing_2212.htm#SEC2288 sprintf boolean_set sing_2218.htm#SEC2294 58235 boolean_std sing_2211.htm#SEC2287 5921 boundBuFou sing_1979.htm#SEC2055 26589 boundDes sing_1981.htm#SEC2057 35149 boundaryLatticePoints boundaryLatticePoints sing_2070.htm#SEC2146 6238 boundposDes sing_1980.htm#SEC2056 58854 bracket sing_350.htm#IDX197 bracket sing_406.htm#SEC446 bracket sing_448.htm#SEC488 braid sing_2180.htm#IDX844 branchTo procs with different argument types sing_155.htm#SEC195 break sing_371.htm#SEC411 break point sing_385.htm#SEC425 breakpoint sing_372.htm#SEC412 brillnoether.lib sing_2230.htm#SEC2306 brillnoether_lib sing_2230.htm#SEC2306 brnoeth.lib sing_1775.htm#SEC1851 brnoeth_lib sing_1775.htm#SEC1851 browser, command line option Command line options sing_19.htm#IDX44 browser, setting the sing_350.htm#IDX193 browsers The online help system sing_16.htm#IDX21 browsers, setting the sing_350.htm#IDX192 bubblesort sing_1852.htm#SEC1928 63278 busadj sing_1070.htm#SEC1146 36301 bvar sing_2225.htm#SEC2301 52773 c, module ordering sing_840.htm#IDX413 cProj sing_2272.htm#SEC2348 24037 calculateI sing_1384.htm#SEC1460 31107 calculate_max_sum sing_1921.htm#SEC1997 4706 calculate_ordering sing_1899.htm#SEC1975 42616 cancelunit, option sing_307.htm#IDX171 canonMap sing_1144.htm#SEC1220 47599 canonical sing_902.htm#IDX424 canonical form sing_911.htm#IDX447 canonical form sing_912.htm#IDX449 canonical, discussion of parametric ideal sing_910.htm#IDX443 canonicalizeCone sing_1998.htm#SEC2074 6251 canonize sing_1821.htm#SEC1897 54090 cantoradd sing_1935.htm#SEC2011 55304 cantormult sing_1938.htm#SEC2014 57569 cantorred sing_1936.htm#SEC2012 46502 cardGroup sing_1113.htm#SEC1189 5553 case No case or switch statement sing_404.htm#SEC444 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2551.htm#SEC2627 55393 cdd sing_1.htm#IDX10 cddlib sing_1.htm#IDX11 center sing_511.htm#IDX320 65108 center sing_517.htm#SEC569 center sing_2167.htm#IDX824 center sing_2168.htm#IDX825 center sing_2169.htm#IDX827 center sing_2170.htm#IDX829 centerRed sing_516.htm#SEC568 59910 centerVS sing_515.htm#SEC567 27548 central sing_2161.htm#IDX810 central sing_2168.htm#IDX826 central sing_2170.htm#IDX828 central sing_2184.htm#IDX853 central.lib sing_511.htm#SEC563 central1st sing_2356.htm#SEC2432 29090 central2nd sing_2357.htm#SEC2433 37545 central_lib sing_511.htm#SEC563 centralize sing_511.htm#IDX323 centralizeSet sing_512.htm#SEC564 55737 centralizer sing_511.htm#IDX321 65261 centralizer sing_518.htm#SEC570 centralizerRed sing_514.htm#SEC566 8209 centralizerVS sing_513.htm#SEC565 22925 cf_class sing_204.htm#IDX132 cgs sing_877.htm#SEC953 57776 cgsdr sing_903.htm#SEC979 11367 chAll sing_2242.htm#SEC2318 2690 chAllInv sing_2243.htm#SEC2319 57760 chDual sing_2248.htm#SEC2324 17745 chHE sing_2244.htm#SEC2320 63916 chHom sing_2257.htm#SEC2333 54776 chNum sing_2238.htm#SEC2314 54415 chNumbers sing_2239.htm#SEC2315 42134 chNumbersProj sing_2276.htm#SEC2352 28837 chProd sing_2250.htm#SEC2326 40209 chProdE sing_2251.htm#SEC2327 33460 chProdL sing_2252.htm#SEC2328 44795 chProdLP sing_2253.htm#SEC2329 8881 chProdM sing_2254.htm#SEC2330 64514 chProdMP sing_2255.htm#SEC2331 17103 chProj sing_2273.htm#SEC2349 32311 chSum sing_2246.htm#SEC2322 21088 chSymm sing_2260.htm#SEC2336 24066 chSymm2L sing_2261.htm#SEC2337 51625 chSymm2LP sing_2262.htm#SEC2338 26099 chWedge sing_2263.htm#SEC2339 57678 chWedge2L sing_2264.htm#SEC2340 46597 chWedge2LP sing_2265.htm#SEC2341 8876 chaincrit sing_1949.htm#SEC2025 9502 chambers sing_2199.htm#IDX881 chambers sing_2200.htm#IDX882 changeDenominator sing_1237.htm#SEC1313 21094 changechar sing_979.htm#SEC1055 65454 changeord sing_980.htm#SEC1056 55156 changeordTo sing_1003.htm#SEC1079 41903 changes sing_2557.htm#SEC2633 changevar sing_981.htm#SEC1057 32829 char sing_207.htm#SEC247 charInfo sing_572.htm#SEC624 11034 charVariety sing_571.htm#SEC623 18306 char_series sing_208.htm#SEC248 characteristic exponents sing_1458.htm#IDX620 characteristic exponents sing_1459.htm#IDX625 characteristic exponents sing_1460.htm#IDX628 characteristic exponents sing_1461.htm#IDX632 characteristic exponents sing_1545.htm#IDX738 characteristic polynomial sing_2197.htm#IDX879 characteristic variety sing_555.htm#IDX348 characteristic variety sing_760.htm#IDX382 charexp2conductor sing_1461.htm#SEC1537 sprintf charexp2generators sing_1459.htm#SEC1535 16838 charexp2inter sing_1460.htm#SEC1536 39881 charexp2multseq sing_1458.htm#SEC1534 334 charexp2poly sing_1462.htm#SEC1538 sprintf charpoly sing_1071.htm#SEC1147 29561 charstr sing_209.htm#SEC249 checkFactor sing_548.htm#SEC600 55900 checkRoot sing_543.htm#SEC595 37045 chern sing_2237.htm#SEC2313 4916 chern.lib sing_2232.htm#SEC2308 chernCharPoly sing_2279.htm#SEC2355 31610 chernPoly sing_2278.htm#SEC2354 31316 chern_lib sing_2232.htm#SEC2308 chineseRem sing_1870.htm#SEC1946 38560 chinrem sing_210.htm#SEC250 chinrempoly sing_2492.htm#SEC2568 42312 chinrestp sing_1929.htm#SEC2005 24779 cimonom.lib sing_2294.htm#SEC2370 cimonom_lib sing_2294.htm#SEC2370 cisimplicial.lib sing_1109.htm#SEC1185 cisimplicial_lib sing_1109.htm#SEC1185 classify sing_1471.htm#SEC1547 4953 classify.lib sing_1469.htm#SEC1545 classifyCeq sing_1488.htm#SEC1564 42719 classifyMapGerms.lib classifyMapGerms_lib sing_2306.htm#SEC2382 classifyMapGerms_lib classifyMapGerms_lib sing_2306.htm#SEC2382 classifySimpleMaps sing_2312.htm#SEC2388 62176 classifySimpleMaps1 sing_2313.htm#SEC2389 24789 classify_aeq.lib sing_2298.htm#SEC2374 classify_aeq_lib sing_2298.htm#SEC2374 classify_lib sing_1469.htm#SEC1545 classifyceq.lib sing_1487.htm#IDX635 classifyceq_lib sing_1487.htm#IDX636 classifyci.lib sing_1489.htm#IDX637 classifyci_lib sing_1489.htm#IDX638 classifyicis sing_1490.htm#SEC1566 37651 classpoly sing_2277.htm#SEC2353 45724 cleanTmp sing_2148.htm#SEC2224 14108 cleanunit sing_1382.htm#SEC1458 sprintf cleardenom sing_211.htm#SEC251 close sing_212.htm#SEC252 closed_points sing_1785.htm#SEC1861 47269 closetex sing_1752.htm#SEC1828 42334 closureFrac sing_1230.htm#SEC1306 9252 coDim sing_2308.htm#SEC2384 60680 coDimMap sing_2307.htm#SEC2383 2002 coHom sing_753.htm#SEC805 51043 codim sing_1583.htm#SEC1659 14253 codimension sing_1999.htm#SEC2075 32207 coding theory sing_832.htm#SEC884 coef sing_213.htm#SEC253 coefficient sing_2160.htm#IDX806 coefficient sing_2161.htm#IDX809 coefficient sing_2162.htm#IDX813 coefficient field sing_139.htm#SEC179 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 coefficients, long sing_791.htm#SEC843 coeffmod sing_1847.htm#SEC1923 23531 coeffs sing_214.htm#SEC254 colength of derivations curveColengthDerivations sing_2318.htm#IDX925 collectDiv sing_1427.htm#SEC1503 50348 colrank sing_1819.htm#SEC1895 52290 colred sing_1054.htm#SEC1130 1693 commRing sing_784.htm#SEC836 30892 comma sing_405.htm#SEC445 command,custom Commands for user defined types sing_181.htm#SEC221 command-line option, setting value of sing_350.htm#IDX279 command-line option, value of sing_350.htm#IDX277 command-line options, print all values of sing_350.htm#IDX276 command-line options, short help Command line options sing_19.htm#IDX38 commands (plural) sing_446.htm#IDX300 comment sing_36.htm#IDX108 compareTasks sing_1018.htm#SEC1094 45157 completeReduction sing_1661.htm#SEC1737 57157 complex sing_28.htm#IDX75 complexSingType sing_1485.htm#SEC1561 34483 compregb.lib sing_876.htm#SEC952 compregb_lib sing_876.htm#SEC952 comprehensive Groebner system sing_876.htm#IDX419 compress sing_1031.htm#SEC1107 61998 computeConstant sing_1129.htm#SEC1205 55024 computeGromovWitten sing_1132.htm#SEC1208 18834 computeN sing_1431.htm#SEC1507 61628 computeV sing_1430.htm#SEC1506 40316 computemcm sing_1389.htm#SEC1465 36956 concat sing_1032.htm#SEC1108 16653 conductor sing_1238.htm#IDX561 conductor sing_1461.htm#IDX631 conductor sing_2316.htm#IDX919 conductor, degree sing_1545.htm#IDX741 cone sing_183.htm#SEC223 cone sing_2173.htm#IDX833 cone sing_2174.htm#IDX835 coneLink sing_2002.htm#SEC2078 13635 coneViaInequalities sing_2001.htm#SEC2077 25661 coneViaPoints sing_2000.htm#SEC2076 3386 conic, parametrization, rational point. sing_1366.htm#IDX601 conicWithTangents sing_2124.htm#SEC2200 60752 constructH sing_1390.htm#SEC1466 59577 constructblwup sing_1391.htm#SEC1467 19326 constructible set sing_911.htm#IDX445 constructible sets sing_912.htm#IDX448 constructlastblwup sing_1392.htm#SEC1468 7639 constructor sing_2190.htm#IDX866 constructor sing_2191.htm#IDX869 contact matrix sing_1460.htm#IDX627 containedQ sing_1740.htm#SEC1816 46718 containsAsFace sing_2003.htm#SEC2079 25159 containsInCollection containsInCollection sing_2036.htm#SEC2112 14368 containsInSupport sing_2004.htm#SEC2080 32493 containsPositiveVector containsPositiveVector sing_2005.htm#SEC2081 27042 containsRelatively sing_2006.htm#SEC2082 17126 content sing_953.htm#SEC1029 9095 contentSB, option sing_307.htm#IDX172 continue Behavior of continue sing_373.htm#SEC413 continue sing_407.htm#SEC447 contraHom sing_754.htm#SEC806 24706 contract sing_215.htm#SEC255 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2535.htm#IDX992 contributionBundle sing_2535.htm#SEC2611 32874 contributors sing_350.htm#IDX200 control sing_1811.htm#SEC1887 44498 control.lib sing_1810.htm#SEC1886 controlDim sing_1812.htm#SEC1888 2417 controlExample sing_1824.htm#SEC1900 2678 control_Matrix sing_1513.htm#SEC1589 sprintf control_lib sing_1810.htm#SEC1886 convertdata sing_1387.htm#SEC1463 54629 convexHull sing_2007.htm#SEC2083 56690 convexIntersection sing_2008.htm#SEC2084 63587 convloc sing_552.htm#SEC604 19122 coordinate change sing_2170.htm#IDX830 coordinate change sing_2171.htm#IDX831 coordinate change sing_2172.htm#IDX832 coordinates sing_1967.htm#IDX783 coords sing_1967.htm#SEC2043 29362 copyTask sing_1017.htm#SEC1093 65331 copyright sing_1.htm#IDX1 corank sing_1472.htm#SEC1548 33709 cornerMonomials sing_1268.htm#SEC1344 33995 countPoints sing_1892.htm#SEC1968 58566 coverings sing_1131.htm#IDX522 coverings sing_1132.htm#IDX526 cpu sing_350.htm#IDX202 cpu sing_350.htm#IDX273 createBO sing_1418.htm#SEC1494 32669 createGradedRingHomomorphism createGradedRingHomomorphism sing_2449.htm#SEC2525 62177 createGroup sing_2442.htm#SEC2518 28500 createQuotientGroup sing_2443.htm#SEC2519 26374 createTask sing_1015.htm#SEC1091 48404 createTorsionFreeGroup createTorsionFreeGroup sing_2444.htm#SEC2520 51944 createlist sing_1400.htm#SEC1476 61781 crypto.lib sing_1865.htm#SEC1941 crypto_lib sing_1865.htm#SEC1941 cup sing_1145.htm#SEC1221 57972 cupproduct sing_1146.htm#SEC1222 43349 curve singularities sing_1451.htm#IDX614 curve singularities sing_1539.htm#IDX736 curve singularity sing_2314.htm#IDX914 curveColengthDerivations curveColengthDerivations sing_2318.htm#SEC2394 2078 curveConductorMult sing_2316.htm#SEC2392 15897 curveDeligneNumber sing_2317.htm#SEC2393 12294 curveDeltaInv sing_2315.htm#SEC2391 16375 curveInv.lib sing_2314.htm#SEC2390 curveInv_lib sing_2314.htm#SEC2390 curvepar.lib sing_1492.htm#SEC1568 curvepar_lib sing_1492.htm#SEC1568 custom assignment Assignments for user defined types sing_182.htm#SEC222 custom command Commands for user defined types sing_181.htm#SEC221 custom type Definition of a user defined type sing_178.htm#SEC218 customstd.lib sing_2202.htm#SEC2278 customstd_lib sing_2202.htm#SEC2278 cycleLength sing_2061.htm#SEC2137 16898 cyclePoints sing_2065.htm#SEC2141 54460 cyclic sing_940.htm#SEC1016 21375 cyclic code Codes and the decoding problem sing_863.htm#SEC922 cyclotomic sing_1626.htm#SEC1702 33749 datetime sing_216.htm#SEC256 50127 dbprint sing_217.htm#SEC257 deRham.lib sing_2319.htm#SEC2395 deRhamCohom sing_569.htm#SEC621 58222 deRhamCohomIdeal sing_570.htm#SEC622 42169 deRhamCohomology sing_2320.htm#SEC2396 41947 deRham_lib sing_2319.htm#SEC2395 debugLib, option sing_307.htm#IDX176 debug_log sing_1482.htm#SEC1558 62043 debugger Source code debugger sing_66.htm#SEC103 debugging library code Source code debugger sing_66.htm#SEC103 dec1var sing_1198.htm#SEC1274 36098 decimal sing_1866.htm#SEC1942 56066 decode sing_1802.htm#SEC1878 64330 decodeCode sing_1804.htm#SEC1880 28262 decodeRandom sing_1803.htm#SEC1879 40118 decodeRandomFL sing_1807.htm#SEC1883 35423 decodeSV sing_1784.htm#SEC1860 37975 decodegb.lib sing_1789.htm#SEC1865 decodegb_lib sing_1789.htm#SEC1865 decoding, decoding problem Codes and the decoding problem sing_863.htm#SEC923 decoef sing_1832.htm#SEC1908 60284 decone sing_2173.htm#IDX834 decone sing_2174.htm#IDX836 def sing_83.htm#SEC123 def declarations sing_84.htm#SEC124 defRes, option sing_307.htm#IDX177 default argument sing_44.htm#SEC81 defineHomogeneous sing_2482.htm#SEC2558 55072 defined sing_218.htm#SEC258 defl sing_1349.htm#SEC1425 11825 deform sing_1584.htm#SEC1660 5250 deform.lib sing_1503.htm#SEC1579 deform_lib sing_1503.htm#SEC1579 defring sing_982.htm#SEC1058 1814 defringp sing_984.htm#SEC1060 42905 defrings sing_983.htm#SEC1059 1034 deg sing_219.htm#SEC259 degBound sing_387.htm#SEC427 degree Miscellaneous oddities sing_220.htm#SEC260 degree sing_410.htm#IDX290 degree lexicographical ordering sing_838.htm#IDX393 degree of a polynomial Miscellaneous oddities sing_410.htm#IDX294 degree reverse lexicographical ordering sing_838.htm#IDX391 degreeDivisor sing_2330.htm#SEC2406 31751 degreeFormalDivisor sing_2338.htm#SEC2414 42503 degreepart sing_1692.htm#SEC1768 53036 delete sing_121.htm#SEC161 delete sing_221.htm#SEC261 delete sing_268.htm#SEC308 deleteGenerator sing_584.htm#SEC636 24917 deleteSublist sing_884.htm#SEC960 20406 deligne number curveColengthDerivations sing_2314.htm#IDX916 deligne number sing_2317.htm#IDX921 deligne number sing_2318.htm#IDX923 delta sing_1551.htm#SEC1627 56952 delta invariant sing_1232.htm#IDX559 delta invariant sing_1551.htm#IDX746 delta invariant sing_2315.htm#IDX917 delta invariant. sing_1224.htm#IDX552 delta invariant. sing_1225.htm#IDX555 delta invariant. sing_1226.htm#IDX558 deltaLoc sing_1232.htm#SEC1308 35192 denom_list sing_350.htm#IDX204 denominator sing_222.htm#SEC262 depth sing_1147.htm#SEC1223 17777 depthIdeal sing_1208.htm#SEC1284 54782 derivate sing_1658.htm#SEC1734 15409 derivation sing_2187.htm#IDX857 desingularization sing_2393.htm#IDX952 59041 desingularization sing_2394.htm#SEC2470 det sing_223.htm#SEC263 det_B sing_1073.htm#SEC1149 60143 detadj sing_1567.htm#SEC1643 5914 determinacy sing_2507.htm#SEC2583 44818 determinecenter sing_1372.htm#SEC1448 44496 detropicalise sing_2142.htm#SEC2218 38025 develop sing_1541.htm#SEC1617 48457 diag sing_1033.htm#SEC1109 56759 diagInvariants sing_1247.htm#SEC1323 62096 diag_test sing_1069.htm#SEC1145 31469 diff sing_224.htm#SEC264 diffRat sing_783.htm#SEC835 36134 difpoly2tex sing_1833.htm#SEC1909 6451 dim sing_225.htm#SEC265 dim (plural) sing_449.htm#SEC489 dimGradedPart sing_1440.htm#SEC1516 11262 dimH sing_1439.htm#SEC1515 38534 dimMon sing_1188.htm#SEC1264 39971 dimStack sing_2533.htm#SEC2609 47772 dim_slocus sing_1585.htm#SEC1661 47218 dimension sing_2009.htm#SEC2085 35262 dimension, moduli space of stable maps, rational curves dimStack sing_2533.htm#IDX990 dimensionOfLocalization dimensionOfLocalization sing_2381.htm#SEC2457 25632 direct_boolean_poly sing_2215.htm#SEC2291 49893 direct_from_boolean_poly direct_from_boolean_poly sing_2221.htm#SEC2297 36941 disc sing_1853.htm#SEC1929 45279 discr sing_1607.htm#SEC1683 9642 discrepancy sing_1425.htm#SEC1501 5597 discrim sing_919.htm#SEC995 21370 discussion of parametric ideal sing_902.htm#IDX425 disjoint sing_903.htm#IDX427 disp_zdd sing_2228.htm#SEC2304 41439 displayCohom sing_1441.htm#SEC1517 22633 displayHNE sing_1544.htm#SEC1620 29845 displayInvariants sing_1546.htm#SEC1622 13678 displayMultsequence sing_1548.htm#SEC1624 16668 displayPuiseuxExpansion displayPuiseuxExpansion sing_2117.htm#SEC2193 560 displayTropicalLifting displayTropicalLifting sing_2115.htm#SEC2191 28144 distributed computing sing_933.htm#IDX481 distributed computing sing_973.htm#IDX483 distributed computing sing_1014.htm#IDX496 div Miscellaneous oddities sing_76.htm#SEC116 div sing_93.htm#SEC133 div sing_410.htm#IDX287 divideUnits sing_1829.htm#SEC1905 26711 dividelist sing_1399.htm#SEC1475 34210 division sing_226.htm#SEC266 division sing_904.htm#IDX430 division sing_905.htm#IDX432 division (plural) sing_450.htm#SEC490 divisor sing_1932.htm#SEC2008 47231 divisorplus sing_2324.htm#SEC2400 34248 divisors negativeformaldivisor sing_2323.htm#IDX926 divisors sing_2324.htm#IDX927 divisors sing_2325.htm#IDX928 divisors sing_2326.htm#IDX929 divisors sing_2327.htm#IDX930 divisors sing_2328.htm#IDX931 divisors sing_2329.htm#IDX932 divisors sing_2330.htm#IDX933 divisors sing_2331.htm#IDX934 divisors sing_2332.htm#IDX935 divisors sing_2333.htm#IDX936 divisors sing_2334.htm#IDX937 divisors sing_2335.htm#IDX938 divisors sing_2336.htm#IDX939 divisors sing_2337.htm#IDX940 divisors sing_2338.htm#IDX941 divisors, polyhedra sing_2339.htm#IDX942 divisors, polyhedra sing_2340.htm#IDX943 divisors, polyhedra sing_2341.htm#IDX944 divisors.lib sing_2322.htm#SEC2398 divisors_lib sing_2322.htm#SEC2398 dmod.lib sing_532.htm#SEC584 dmodAction sing_778.htm#SEC830 9763 dmodActionRat sing_779.htm#SEC831 6277 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_771.htm#SEC823 44337 dmod_lib sing_532.htm#SEC584 dmodapp.lib sing_555.htm#SEC607 dmodapp_lib sing_555.htm#SEC607 dmodloc.lib sing_760.htm#IDX375 dmodloc_lib sing_760.htm#IDX376 dmodoublext sing_755.htm#SEC807 60637 dmodvar.lib sing_588.htm#SEC640 dmodvar_lib sing_588.htm#SEC640 double sing_1937.htm#SEC2013 34697 doubleExt sing_746.htm#SEC798 56896 downloading Download instructions sing_2565.htm#SEC2655 dp, global ordering sing_838.htm#IDX392 drawNewtonSubdivision drawNewtonSubdivision sing_2120.htm#SEC2196 61060 drawTropicalCurve sing_2119.htm#SEC2195 27590 ds, local ordering sing_839.htm#IDX402 dsum sing_1034.htm#SEC1110 1303 dualCone sing_2010.htm#SEC2086 61460 dualConic sing_2144.htm#SEC2220 31080 dualPart sing_2285.htm#SEC2361 13279 dualPartition sing_2546.htm#SEC2622 24739 dualPolytope sing_2049.htm#SEC2125 32081 dualSheaf sing_2524.htm#SEC2600 633 dual_code sing_1786.htm#SEC1862 57229 dump sing_227.htm#SEC267 dynamic geometry sing_913.htm#IDX452 dynamic geometry sing_914.htm#IDX455 ecart sing_1940.htm#SEC2016 32475 echo sing_388.htm#SEC428 eexgcdN sing_1867.htm#SEC1943 53237 effective sing_2332.htm#SEC2408 53028 egcdMain sing_1733.htm#SEC1809 25359 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2071.htm#SEC2147 38271 ehrhartRing sing_1243.htm#SEC1319 16966 eigenvals sing_1081.htm#SEC1157 11228 eigenvalue sing_320.htm#SEC360 eigenvalue sing_1081.htm#IDX502 eigenvalues sing_1326.htm#SEC1402 2182 elemSymmId sing_941.htm#SEC1017 sprintf elim sing_1118.htm#SEC1194 62585 elim.lib sing_1115.htm#SEC1191 elim1 sing_1119.htm#SEC1195 15653 elim2 sing_1120.htm#SEC1196 44749 elimRing sing_1117.htm#SEC1193 12194 elimWeight sing_703.htm#SEC755 54297 elim_lib sing_1115.htm#SEC1191 eliminate sing_228.htm#SEC268 eliminate (plural) sing_451.htm#SEC491 eliminateNC sing_698.htm#SEC750 3777 elimination sing_697.htm#IDX360 elimlinearpart sing_1693.htm#SEC1769 14251 elimpart sing_1694.htm#SEC1770 10258 elimpartanyr sing_1695.htm#SEC1771 39751 elimrep sing_1380.htm#SEC1456 23641 elliptic curve sing_1128.htm#IDX518 elliptic curves sing_1125.htm#IDX512 elliptic curves sing_1131.htm#IDX521 elliptic curves sing_1132.htm#IDX525 ellipticAdd sing_1888.htm#SEC1964 13279 ellipticAllPoints sing_1893.htm#SEC1969 60770 ellipticMult sing_1889.htm#SEC1965 1558 ellipticNF sing_2068.htm#SEC2144 5045 ellipticNFDB sing_2069.htm#SEC2145 27917 ellipticRandomCurve sing_1890.htm#SEC1966 36980 ellipticRandomPoint sing_1891.htm#SEC1967 6866 ellipticcovers.lib sing_1125.htm#IDX506 ellipticcovers_lib sing_1125.htm#IDX507 else sing_378.htm#SEC418 embedMat sing_729.htm#SEC781 17119 emptyFan sing_2037.htm#SEC2113 7396 encode sing_1794.htm#SEC1870 56687 endomorphism filtration sing_1525.htm#IDX712 endvfilt sing_1525.htm#SEC1601 26670 engine sing_585.htm#SEC637 30876 envelop FamElemsAtEnvCompPoints sing_915.htm#SEC991 9501 envelop sing_915.htm#IDX458 envelop sing_916.htm#IDX461 envelop sing_917.htm#IDX465 envelop sing_918.htm#IDX469 envelope sing_452.htm#SEC492 enveloping algebra sing_350.htm#IDX208 enveloping algebra sing_490.htm#IDX304 environment variable, DISPLAY The online help system sing_16.htm#IDX29 equalJinI sing_1468.htm#SEC1544 18502 equalMultiDeg sing_2475.htm#SEC2551 37090 equations sing_2011.htm#SEC2087 7896 equiRadical sing_1284.htm#SEC1360 8884 equidim sing_1286.htm#SEC1362 38541 equidimMax sing_1287.htm#SEC1363 49289 equidimMaxEHV sing_1288.htm#SEC1364 42650 equidimZ sing_1299.htm#SEC1375 49610 equising.lib sing_1508.htm#SEC1584 equising_lib sing_1508.htm#SEC1584 equisingular Tjurina number sing_1451.htm#IDX619 equisingularity ideal sing_1510.htm#IDX639 equisingularity stratum sing_1511.htm#IDX640 error recovery sing_15.htm#SEC21 errorInsert sing_1797.htm#SEC1873 59470 errorRand sing_1798.htm#SEC1874 5727 errormap sing_2362.htm#SEC2438 7782 esIdeal sing_1510.htm#SEC1586 60477 esStratum sing_1511.htm#SEC1587 50094 essential sing_2177.htm#IDX839 essential sing_2178.htm#IDX840 eta sing_2063.htm#SEC2139 60729 euler sing_1846.htm#SEC1922 10519 eulerChProj sing_2275.htm#SEC2351 28549 eval sing_229.htm#SEC269 evaluateFormalDivisor evaluateFormalDivisor sing_2334.htm#SEC2410 3535 evaluatePDivisor sing_2340.htm#SEC2416 18855 evaluate_reynolds sing_1631.htm#SEC1707 46353 evalutateIntegral sing_1130.htm#SEC1206 sprintf example sing_231.htm#SEC271 example sing_2179.htm#IDX841 example sing_2180.htm#IDX843 example sing_2181.htm#IDX845 example sing_2182.htm#IDX847 example sing_2183.htm#IDX849 example sing_2184.htm#IDX851 example sing_2185.htm#IDX854 execute sing_232.htm#SEC272 exit sing_382.htm#SEC422 exp2pt sing_1834.htm#SEC1910 19621 expo sing_1858.htm#SEC1934 8833 exponents sing_2189.htm#IDX862 export sing_375.htm#SEC415 exportNuminvs sing_1251.htm#SEC1327 10423 exportto sing_376.htm#SEC416 expp sing_2544.htm#SEC2620 15751 expression list sing_72.htm#IDX128 expression list sing_414.htm#IDX297 ext-module purityfiltration_lib sing_738.htm#IDX366 extcurve sing_1780.htm#SEC1856 6730 extdevelop sing_1542.htm#SEC1618 51044 extendGC sing_910.htm#SEC986 19135 extendWeyl sing_772.htm#SEC824 49954 extendedTensor sing_704.htm#SEC756 4975 extendpoly sing_909.htm#SEC985 29113 extendring sing_985.htm#SEC1061 64781 extension of rings sing_1304.htm#IDX568 exterior basis sing_1060.htm#IDX499 exterior power sing_1062.htm#IDX501 exteriorBasis sing_1060.htm#SEC1136 sprintf exteriorPower sing_1062.htm#SEC1138 20173 extgcd sing_233.htm#SEC273 fVector sing_2040.htm#SEC2116 3715 fVectorP sing_2072.htm#SEC2148 31843 facFirstShift sing_691.htm#SEC743 6469 facFirstWeyl sing_687.htm#SEC739 42412 facGBIdeal sing_1269.htm#SEC1345 9924 facShift sing_690.htm#SEC742 21253 facSubWeyl sing_689.htm#SEC741 9630 facWeyl sing_686.htm#SEC738 32331 faceContaining sing_2012.htm#SEC2088 64804 facetVertexLatticeDistances facetVertexLatticeDistances sing_2073.htm#SEC2149 60714 facetWidth sing_2074.htm#SEC2150 62810 facetWidths sing_2075.htm#SEC2151 5503 facets sing_2013.htm#SEC2089 8112 facstd sing_234.htm#SEC274 factmodd sing_235.htm#SEC275 factor sing_314.htm#SEC354 factorH sing_899.htm#SEC975 24814 factorLenstraECM sing_1897.htm#SEC1973 54951 factorMain sing_1734.htm#SEC1810 65152 factorgroup sing_2465.htm#SEC2541 59914 factorial sing_885.htm#SEC961 32871 factorization sing_315.htm#SEC355 factorization sing_1090.htm#IDX503 factorize sing_236.htm#SEC276 factorize sing_314.htm#SEC354 factory sing_1.htm#IDX2 fan sing_184.htm#SEC224 fan sing_2052.htm#IDX788 fanViaCones sing_2038.htm#SEC2114 16418 farey sing_237.htm#SEC277 fareypoly sing_2343.htm#SEC2419 12389 fastExpt sing_1842.htm#SEC1918 43912 fastHC, option sing_307.htm#IDX153 fastelim sing_1696.htm#SEC1772 7409 fetch sing_238.htm#SEC278 fetch (plural) sing_453.htm#SEC493 fetchall sing_986.htm#SEC1062 7537 ffmodStd sing_2347.htm#SEC2423 50680 ffmodstd.lib sing_2342.htm#SEC2418 ffmodstd_lib sing_2342.htm#SEC2418 ffsolve sing_1685.htm#SEC1761 20432 ffsolve.lib sing_1684.htm#SEC1760 ffsolve_lib sing_1684.htm#SEC1760 fglm sing_239.htm#SEC279 fglm sing_347.htm#IDX187 fglm_solve sing_1712.htm#SEC1788 51398 fglmquot sing_240.htm#SEC280 fibonacci sing_886.htm#SEC962 24750 field sing_139.htm#SEC179 file, .singularrc sing_20.htm#IDX71 filecmd sing_241.htm#SEC281 filtration purityfiltration_lib sing_738.htm#IDX367 finalCharts sing_1404.htm#SEC1480 37296 find sing_242.htm#SEC282 findAuto sing_645.htm#SEC697 51205 findInvo sing_643.htm#SEC695 18177 findInvoDiag sing_644.htm#SEC696 7365 findOrientedBoundary findOrientedBoundary sing_2064.htm#SEC2140 24110 findTorsion sing_1823.htm#SEC1899 29572 find_first_primitive_root find_first_primitive_root sing_1901.htm#SEC1977 33327 find_index sing_1905.htm#SEC1981 62564 findifs.lib sing_1830.htm#SEC1906 findifs_example sing_1831.htm#SEC1907 33849 findifs_lib sing_1830.htm#SEC1906 findimAlgebra sing_713.htm#SEC765 64612 finduni sing_243.htm#SEC283 findvars sing_1697.htm#SEC1773 54503 finite field sing_139.htm#SEC179 finite field sing_1684.htm#IDX761 finiteDiagInvariants finiteDiagInvariants sing_1246.htm#SEC1322 3508 finitediff.lib sing_2348.htm#IDX945 finitediff_lib sing_2348.htm#IDX946 finitenessTest sing_1104.htm#SEC1180 40633 finvar.lib sing_1619.htm#SEC1695 finvar_lib sing_1619.htm#SEC1695 first index is 1 sing_409.htm#SEC449 firstoct sing_1745.htm#SEC1821 11498 fitting sing_1150.htm#SEC1226 20661 fixed points, moduli space of stable maps, graph fixedPoints sing_2534.htm#IDX991 fixedPoints sing_2534.htm#SEC2610 25366 fl2poly sing_582.htm#SEC634 51682 flatten sing_1035.htm#SEC1111 55617 flatteningStrat sing_1151.htm#SEC1227 15622 floating point sing_995.htm#IDX486 for sing_377.htm#SEC417 formaldivisorplus sing_2335.htm#SEC2411 31959 forward sing_2354.htm#SEC2430 15383 fourier sing_577.htm#SEC629 5326 fouriersystem sing_2365.htm#SEC2441 43681 fpadim.lib sing_593.htm#SEC645 fpadim_lib sing_593.htm#SEC645 fprintf sing_244.htm#SEC284 13662 frandwalk sing_2499.htm#SEC2575 25555 free sing_2188.htm#IDX859 free sing_2189.htm#IDX861 free associative algebra, tensor algebra Free associative algebras sing_484.htm#SEC536 freeGBasis sing_628.htm#SEC680 43055 freegb.lib sing_624.htm#SEC676 freegb_lib sing_624.htm#SEC676 freemodule sing_245.htm#SEC285 freerank sing_943.htm#SEC1019 52218 from_boolean_constant from_boolean_constant sing_2219.htm#SEC2295 44881 from_boolean_ideal sing_2223.htm#SEC2299 62698 from_boolean_poly sing_2220.htm#SEC2296 27864 from_boolean_set sing_2224.htm#SEC2300 60615 frwalk sing_246.htm#SEC286 full representation sing_909.htm#IDX440 full representation sing_910.htm#IDX444 fullFan sing_2039.htm#SEC2115 7534 fullSerreRelations sing_639.htm#SEC691 27691 fullSpace sing_1994.htm#SEC2070 19485 furtherInvar sing_1663.htm#SEC1739 19209 further_hn_proc sing_1559.htm#SEC1635 63500 fwalk sing_1137.htm#SEC1213 15070 galois field sing_139.htm#SEC179 gauss_col sing_1045.htm#SEC1121 36252 gauss_nf sing_1076.htm#SEC1152 51060 gauss_row sing_1046.htm#SEC1122 58877 gaussred sing_1074.htm#SEC1150 29001 gaussred_pivot sing_1075.htm#SEC1151 25477 gcd sing_247.htm#SEC287 gcdMon sing_1177.htm#SEC1253 42448 gcddivisor sing_1933.htm#SEC2009 1276 gen sing_248.htm#SEC288 genMDSMat sing_1800.htm#SEC1876 3347 genSymId sing_1323.htm#SEC1399 17521 general error-locator polynomial sing_864.htm#SEC929 general neron. sing_2393.htm#IDX953 general weighted lexicographical ordering sing_839.htm#IDX408 general weighted reverse lexicographical ordering Local orderings sing_839.htm#IDX405 general.lib sing_879.htm#SEC955 generalOrder sing_1958.htm#SEC2034 42536 general_lib sing_879.htm#SEC955 generateG sing_1896.htm#SEC1972 51697 generators sing_1459.htm#IDX623 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2014.htm#SEC2090 4454 generatorsOfSpan sing_2015.htm#SEC2091 40297 generic representation sing_909.htm#IDX439 genericid sing_961.htm#SEC1037 29731 genericity sing_1820.htm#SEC1896 16822 genericmat sing_1036.htm#SEC1112 35016 genoutput sing_1393.htm#SEC1469 18973 genus sing_1228.htm#SEC1304 sprintf geometric invariant theory sing_2386.htm#IDX950 geometrical locus FamElemsAtEnvCompPoints sing_913.htm#IDX450 geometrical locus sing_914.htm#IDX453 geometrical locus sing_915.htm#IDX456 geometrical locus sing_916.htm#IDX459 geometrical locus sing_917.htm#IDX463 geometrical locus sing_918.htm#IDX467 getArguments sing_1026.htm#SEC1102 14254 getCommand sing_1025.htm#SEC1101 32181 getCone sing_2041.htm#SEC2117 41394 getGradingGroup sing_2440.htm#SEC2516 18137 getLattice sing_2441.htm#SEC2517 7775 getLinearForms sing_2016.htm#SEC2092 47590 getModuleGrading sing_2451.htm#SEC2527 43451 getMultiplicity sing_2017.htm#SEC2093 639 getOneVar sing_1236.htm#SEC1312 55402 getResult sing_1027.htm#SEC1103 51722 getSmallest sing_1235.htm#SEC1311 1623 getState sing_1028.htm#SEC1104 36453 getVariableWeights sing_2439.htm#SEC2515 9591 getcores sing_976.htm#SEC1052 30785 getdump sing_249.htm#SEC289 getenv sing_350.htm#IDX211 gfan.lib sing_1993.htm#SEC2069 gfan_lib sing_1993.htm#SEC2069 gfanlib sing_1.htm#IDX9 gitCone sing_2388.htm#SEC2464 23853 gitFan sing_2389.htm#SEC2465 sprintf gitfan sing_2386.htm#IDX948 gitfan.lib sing_2386.htm#SEC2462 gitfan_lib sing_2386.htm#SEC2462 gkdim.lib sing_650.htm#SEC702 gkdim_lib sing_650.htm#SEC702 gkzFan sing_2390.htm#SEC2466 35496 global sing_204.htm#IDX133 global Bernstein-Sato polynomial sing_497.htm#IDX311 global Bernstein-Sato polynomial sing_532.htm#IDX329 global Bernstein-Sato polynomial for variety sing_588.htm#IDX354 globalSections sing_2329.htm#SEC2405 55191 gmscoeffs sing_1517.htm#SEC1593 13182 gmsnf sing_1516.htm#SEC1592 44676 gmspoly.lib sing_1536.htm#SEC1612 gmspoly_lib sing_1536.htm#SEC1612 gmsring sing_1515.htm#SEC1591 59438 gmssing.lib sing_1514.htm#SEC1590 gmssing_lib sing_1514.htm#SEC1590 goettsche.lib sing_2372.htm#SEC2448 goettsche_lib sing_2372.htm#SEC2448 good basis sing_1514.htm#IDX651 good basis sing_1524.htm#IDX706 good basis sing_1536.htm#IDX722 good basis sing_1538.htm#IDX733 goodBasis sing_1538.htm#SEC1614 41606 gorensteinIndex sing_2076.htm#SEC2152 52919 gorensteinVector sing_2077.htm#SEC2153 50407 graal.lib sing_2379.htm#SEC2455 graalMixed sing_2380.htm#SEC2456 6401 graal_lib sing_2379.htm#SEC2455 gradeNumber sing_742.htm#SEC794 29956 graded Weyl algebra sing_497.htm#IDX314 graded module, graded piece sing_1440.htm#IDX609 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2395.htm#IDX954 graded modules, handling of Handling graded modules sing_806.htm#SEC858 gradedModules.lib sing_2395.htm#SEC2471 gradedModules_lib sing_2395.htm#SEC2471 gradiator sing_2484.htm#SEC2560 53802 graph sing_1126.htm#IDX516 graph sing_1127.htm#IDX517 graph sing_2529.htm#IDX986 graph sing_2530.htm#IDX987 graphics.lib sing_1747.htm#SEC1823 graphics_lib sing_1747.htm#SEC1823 graphviz sing_1.htm#IDX13 graver4ti2 sing_1321.htm#SEC1397 39635 grconcat sing_2418.htm#SEC2494 16754 grdeg sing_2398.htm#SEC2474 22879 grgens sing_2407.htm#SEC2483 12823 grgroebner sing_2417.htm#SEC2493 29288 grlift sing_2415.htm#SEC2491 21656 grlifting sing_2422.htm#SEC2498 51177 grlifting2 sing_2423.htm#SEC2499 59011 grlifting3 sing_2425.htm#SEC2501 6369 grneg sing_2428.htm#SEC2504 64584 grobcov sing_902.htm#SEC978 27432 grobcov.lib sing_900.htm#SEC976 grobcov_lib sing_900.htm#SEC976 grobj sing_2396.htm#SEC2472 18115 groebner sing_250.htm#SEC290 5130 groebner sing_798.htm#SEC850 groebner basis computations sing_250.htm#IDX147 groebnerComplex sing_2155.htm#SEC2231 2421 groebnerCone sing_2149.htm#SEC2225 58776 groebnerFan sing_2154.htm#SEC2230 48157 groebnerFanP sing_2057.htm#SEC2133 5802 gromovWitten sing_1131.htm#SEC1207 28559 grorder sing_2409.htm#SEC2485 20857 ground field sing_139.htm#SEC179 group_reynolds sing_1627.htm#SEC1703 35079 grpower sing_2405.htm#SEC2481 3960 grpres sing_2408.htm#SEC2484 18145 grprod sing_2416.htm#SEC2492 41525 grrange sing_2427.htm#SEC2503 41835 grres sing_2414.htm#SEC2490 35795 grrndmap sing_2420.htm#SEC2496 4054 grrndmap2 sing_2421.htm#SEC2497 50536 grrndmat sing_2419.htm#SEC2495 42634 grshift sing_2400.htm#SEC2476 1415 grsum sing_2404.htm#SEC2480 60602 grsyz sing_2413.htm#SEC2489 61843 grtest sing_2397.htm#SEC2473 62577 grtranspose sing_2406.htm#SEC2482 13865 grtranspose1 sing_2410.htm#SEC2486 3637 grtwist sing_2402.htm#SEC2478 10498 grtwists sing_2403.htm#SEC2479 56638 grview sing_2399.htm#SEC2475 6878 grwalk.lib sing_1136.htm#SEC1212 grwalk_lib sing_1136.htm#SEC1212 grzero sing_2401.htm#SEC2477 4212 gwalk sing_1142.htm#SEC1218 38238 hStarVector sing_2078.htm#SEC2154 60821 hVector sing_2079.htm#SEC2155 46486 h_increasing_knapsack h_increasing_knapsack sing_1919.htm#SEC1995 62968 hardware platform sing_350.htm#IDX269 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_999.htm#SEC1075 54609 hasCommutativeVars sing_996.htm#SEC1072 3152 hasGlobalOrdering sing_997.htm#SEC1073 34053 hasMixedOrdering sing_998.htm#SEC1074 29738 hasNumericCoeffs sing_995.htm#SEC1071 14522 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1000.htm#SEC1076 56211 headStand sing_1058.htm#SEC1134 14413 heightZ sing_1298.htm#SEC1374 16800 help sing_251.htm#SEC291 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_350.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_2485.htm#SEC2561 37225 hess.lib sing_2430.htm#SEC2506 hess_lib sing_2430.htm#SEC2506 hessenberg sing_350.htm#IDX217 24168 hessenberg sing_1080.htm#SEC1156 highcorner sing_252.htm#SEC292 hilb sing_253.htm#SEC293 hilbPoly sing_959.htm#SEC1035 36118 hilbert4ti2 sing_1320.htm#SEC1396 13993 hilbertBasis sing_2080.htm#SEC2156 35423 hilbertSeries sing_2487.htm#SEC2563 60148 hilbvec sing_1698.htm#SEC1774 9204 hnexpansion sing_1540.htm#SEC1616 46990 hnoether.lib sing_1539.htm#SEC1615 hnoether_lib sing_1539.htm#SEC1615 holonomic rank sing_760.htm#IDX378 holonomicRank sing_764.htm#SEC816 41306 hom_kernel sing_1158.htm#SEC1234 32604 homog sing_254.htm#SEC294 homog_part sing_2541.htm#SEC2617 20875 homog_parts sing_2542.htm#SEC2618 12854 homogeneitySpace sing_2151.htm#SEC2227 48243 homogfacFirstQWeyl sing_693.htm#SEC745 32751 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_695.htm#SEC747 9014 homogfacNthQWeyl sing_692.htm#SEC744 55267 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_694.htm#SEC746 62161 homolog.lib sing_1143.htm#SEC1219 homolog_lib sing_1143.htm#SEC1219 homology sing_1153.htm#SEC1229 15040 howto, download Download instructions sing_2565.htm#SEC2655 howto, install on Macintosh Macintosh installation instructions sing_2568.htm#SEC2658 howto, install on Unix Unix installation instructions sing_2566.htm#SEC2656 howto, install on Windows Windows installation instructions sing_2567.htm#SEC2657 hres sing_255.htm#SEC295 html, default help The online help system sing_16.htm#IDX24 hyperel.lib sing_1926.htm#SEC2002 hyperel_lib sing_1926.htm#SEC2002 hyperplane sing_2158.htm#IDX799 hyperplane arrangement sing_532.htm#IDX335 hypersurface singularity sing_1566.htm#IDX751 iMult sing_1231.htm#SEC1307 22059 id2mod sing_955.htm#SEC1031 32918 ideal sing_85.htm#SEC125 ideal declarations sing_86.htm#SEC126 ideal declarations (plural) ideal declarations (plural) sing_416.htm#SEC456 ideal expressions sing_87.htm#SEC127 ideal expressions (plural) ideal expressions (plural) sing_417.htm#SEC457 ideal operations sing_88.htm#SEC128 ideal operations (plural) ideal operations (plural) sing_418.htm#SEC458 ideal related functions ideal related functions sing_89.htm#SEC129 ideal related functions (plural) ideal related functions (plural) sing_419.htm#SEC459 ideal, toric sing_851.htm#SEC908 idealSplit sing_1705.htm#SEC1781 4673 ideals Miscellaneous oddities sing_410.htm#IDX291 idealsimplify sing_1467.htm#SEC1543 38569 identifier Identifier resolution sing_411.htm#SEC451 identifyvar sing_1375.htm#SEC1451 59662 if sing_378.htm#SEC418 imageLattice sing_2453.htm#SEC2529 15740 image_of_variety sing_1655.htm#SEC1731 43711 imap sing_256.htm#SEC296 imap (plural) sing_454.htm#SEC494 imapall sing_987.htm#SEC1063 16023 impart sing_257.htm#SEC297 importfrom sing_379.htm#SEC419 inCenter sing_521.htm#SEC573 22152 inCentralizer sing_522.htm#SEC574 49000 inForm sing_564.htm#SEC616 5283 inSubring sing_1096.htm#SEC1172 24817 indSet sing_1203.htm#SEC1279 32828 indepSet sing_258.htm#SEC298 indexed names sing_36.htm#IDX82 indexed names sing_37.htm#SEC65 indices, multi sing_37.htm#SEC65 inequalities sing_2018.htm#SEC2094 10122 infRedTail, option sing_307.htm#IDX154 info The online help system sing_16.htm#SEC23 iniD sing_1395.htm#SEC1471 35084 init_debug sing_1474.htm#SEC1550 29863 initial sing_2152.htm#SEC2228 8678 initial form sing_497.htm#IDX316 initial ideal sing_497.htm#IDX315 initial ideal approach sing_497.htm#IDX319 initial ideal approach sing_588.htm#IDX358 initialForm sing_2129.htm#SEC2205 57793 initialIdeal sing_2130.htm#SEC2206 22205 initialIdealW sing_563.htm#SEC615 36086 initialMalgrange sing_562.htm#SEC614 26846 injective_knapsack sing_1920.htm#SEC1996 7619 inout.lib sing_921.htm#SEC997 inout_lib sing_921.htm#SEC997 input sing_41.htm#SEC71 insert sing_121.htm#SEC161 insert sing_259.htm#SEC299 insertCone sing_2042.htm#SEC2118 13858 insertGenerator sing_583.htm#SEC635 13951 instructions, Macintosh installation Macintosh installation instructions sing_2568.htm#SEC2658 instructions, Unix installation Unix installation instructions sing_2566.htm#SEC2656 instructions, Windows installation Windows installation instructions sing_2567.htm#SEC2657 instructions, downloading Download instructions sing_2565.htm#SEC2655 int sing_90.htm#SEC130 int declarations sing_91.htm#SEC131 int expressions sing_92.htm#SEC132 int operations sing_93.htm#SEC133 int related functions int related functions sing_94.htm#SEC134 intInverse sing_2462.htm#SEC2538 sprintf intPart sing_1874.htm#SEC1950 48360 intRank sing_2454.htm#SEC2530 1830 intRoot sing_1875.htm#SEC1951 54582 intRoots sing_580.htm#SEC632 24538 intStrategy, option sing_307.htm#IDX155 intclMonIdeal sing_1244.htm#SEC1320 22338 intclToricRing sing_1240.htm#SEC1316 62143 integer division Miscellaneous oddities sing_410.htm#IDX286 integer programming sing_859.htm#SEC916 integral sing_2516.htm#SEC2592 62683 integral basis sing_1165.htm#IDX538 integral basis sing_1358.htm#IDX594 integral closure sing_1224.htm#IDX551 integral closure sing_1225.htm#IDX554 integral closure sing_1226.htm#IDX557 integral closure sing_1239.htm#IDX563 integralBasis sing_1165.htm#SEC1241 38114 integralIdeal sing_567.htm#SEC619 29194 integralModule sing_568.htm#SEC620 58078 integralSection sing_2463.htm#SEC2539 sprintf integralbasis.lib sing_1164.htm#SEC1240 integralbasis_lib sing_1164.htm#SEC1240 integration of D-module sing_555.htm#IDX347 interface, Emacs Emacs user interface sing_21.htm#SEC28 interiorLatticePoints interiorLatticePoints sing_2081.htm#SEC2157 49868 internalfunctions sing_1475.htm#SEC1551 61230 interpolate sing_1711.htm#SEC1787 51502 interpolation sing_260.htm#SEC300 interred sing_261.htm#SEC301 intersect sing_262.htm#SEC302 intersect (plural) sing_455.htm#SEC495 intersectElim, option sing_307.htm#IDX173 intersectLattices sing_2459.htm#SEC2535 41354 intersectMon sing_1180.htm#SEC1256 44572 intersectSyz, option sing_307.htm#IDX174 intersectZ sing_1300.htm#SEC1376 sprintf intersection sing_1549.htm#SEC1625 46938 intersection lattice sing_2194.htm#IDX874 intersection lattice sing_2195.htm#IDX875 intersection multiplicity sing_1460.htm#IDX629 intersection multiplicity sing_1549.htm#IDX744 intersectionDiv sing_1423.htm#SEC1499 29017 intersectionValRingIdeals intersectionValRingIdeals sing_1249.htm#SEC1325 38773 intersectionValRings intersectionValRings sing_1248.htm#SEC1324 35761 intmat sing_97.htm#SEC137 intmat declarations sing_98.htm#SEC138 intmat expressions sing_99.htm#SEC139 intmat operations sing_101.htm#SEC141 intmat related functions intmat related functions sing_102.htm#SEC142 intmat type cast sing_100.htm#SEC140 intmat2mons sing_1264.htm#SEC1340 21150 intprog.lib sing_1166.htm#SEC1242 intprog_lib sing_1166.htm#SEC1242 intvec sing_103.htm#SEC143 intvec declarations sing_104.htm#SEC144 intvec expressions sing_105.htm#SEC145 intvec operations sing_106.htm#SEC146 intvec related functions intvec related functions sing_107.htm#SEC147 invariant sing_2317.htm#IDX922 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1624.htm#IDX757 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1625.htm#IDX758 invariantRing sing_1657.htm#SEC1733 18582 invariant_algebra_perm invariant_algebra_perm sing_1625.htm#SEC1701 63525 invariant_algebra_reynolds invariant_algebra_reynolds sing_1624.htm#SEC1700 35705 invariant_basis sing_1632.htm#SEC1708 18343 invariant_basis_reynolds invariant_basis_reynolds sing_1633.htm#SEC1709 54788 invariant_ring sing_1620.htm#SEC1696 8059 invariant_ring_random invariant_ring_random sing_1621.htm#SEC1697 6986 invariants curveColengthDerivations sing_1545.htm#SEC1621 57499 invariants sing_2314.htm#IDX915 invariants sing_2318.htm#IDX924 inverse sing_1064.htm#SEC1140 27411 inverse of a matrix via its LU-decomposition sing_282.htm#SEC322 inverseFourier sing_578.htm#SEC630 65140 inverse_B sing_1065.htm#SEC1141 17616 inverse_L sing_1066.htm#SEC1142 49271 inverse_modulus sing_1903.htm#SEC1979 60822 invertBirMap sing_1359.htm#SEC1435 16086 invertNumberMain sing_1735.htm#SEC1811 62615 involut.lib sing_642.htm#SEC694 involut_lib sing_642.htm#SEC694 involution sing_647.htm#SEC699 34280 invunit sing_1568.htm#SEC1644 62398 iostruct sing_1822.htm#SEC1898 60444 irrRealizationDim sing_2111.htm#SEC2187 7814 irred_secondary_char0 irred_secondary_char0 sing_1646.htm#SEC1722 2943 irred_secondary_no_molien irred_secondary_no_molien sing_1649.htm#SEC1725 55905 irreddecMon sing_1189.htm#SEC1265 20160 irreducible power series sing_1550.htm#IDX745 irreducible secondary invariant irred_secondary_char0 sing_1646.htm#IDX759 isAface sing_2391.htm#SEC2467 47756 isAntiEndo sing_649.htm#SEC701 19156 isBounded sing_2082.htm#SEC2158 28183 isCI sing_204.htm#IDX139 58425 isCI sing_1114.htm#SEC1190 isCM sing_204.htm#IDX140 50469 isCM sing_1154.htm#SEC1230 isCMcod2 sing_1603.htm#SEC1679 2563 isCanonical sing_2083.htm#SEC2159 51109 isCartan sing_523.htm#SEC575 39541 isCentral sing_720.htm#SEC772 54650 isCommutative sing_722.htm#SEC774 60728 isCompatible sing_2043.htm#SEC2119 57323 isCompressed sing_2084.htm#SEC2160 2849 isEqualDivisor sing_2328.htm#SEC2404 17569 isEquising sing_1512.htm#SEC1588 1424 isFlat sing_1155.htm#SEC1231 14706 isFsat sing_573.htm#SEC625 28225 isFullSpace sing_2019.htm#SEC2095 27433 isGorenstein sing_2085.htm#SEC2161 24010 isGradedRingHomomorphism isGradedRingHomomorphism sing_2448.htm#SEC2524 39551 isGroup sing_2446.htm#SEC2522 55744 isGroupHomomorphism sing_2447.htm#SEC2523 65475 isHolonomic sing_551.htm#SEC603 30274 isHomg sing_204.htm#IDX135 isHomogeneous sing_2474.htm#SEC2550 3034 isInt sing_586.htm#SEC638 9879 isIntegralSurjective isIntegralSurjective sing_2460.htm#SEC2536 sprintf isInvolution sing_648.htm#SEC700 13601 isLatticeEmpty sing_2086.htm#SEC2162 48517 isLocalizationRegular isLocalizationRegular sing_2383.htm#SEC2459 11221 isLocallyFree sing_1156.htm#SEC1232 46389 isMonomial sing_1175.htm#SEC1251 57615 isNC sing_721.htm#SEC773 57151 isNormal sing_2087.htm#SEC2163 64236 isOnCurve sing_1887.htm#SEC1963 36324 isOrigin sing_2020.htm#SEC2096 13977 isPositive sing_2471.htm#SEC2547 50852 isPrimitiveSublattice isPrimitiveSublattice sing_2461.htm#SEC2537 sprintf isPure sing_2044.htm#SEC2120 44002 isPureTensor sing_495.htm#SEC547 21323 isQuotientRing sing_1001.htm#SEC1077 sprintf isRational sing_554.htm#SEC606 57398 isReflexive sing_2088.htm#SEC2164 3991 isReg sing_1157.htm#SEC1233 40920 isSB sing_204.htm#IDX134 isSimplicial sing_2021.htm#SEC2097 57789 isSmooth sing_2089.htm#SEC2165 37647 isSubModule sing_1002.htm#SEC1078 sprintf isSublattice sing_2452.htm#SEC2528 10501 isSymmetric sing_1324.htm#SEC1400 61363 isTame sing_1537.htm#SEC1613 31925 isTerminal sing_2090.htm#SEC2166 29416 isTorsionFree sing_2470.htm#SEC2546 52228 isTwoSidedGB sing_496.htm#SEC548 36558 isUpperTriangular sing_701.htm#SEC753 40655 isVar sing_640.htm#SEC692 43851 isVeryAmple sing_2091.htm#SEC2167 64652 isWeyl sing_723.htm#SEC775 28994 isZeroElement sing_2472.htm#SEC2548 514 is_NND sing_1553.htm#SEC1629 26564 is_NP sing_1212.htm#SEC1288 43891 is_active sing_1586.htm#SEC1662 6867 is_bijective sing_1101.htm#SEC1177 49512 is_cenBimodule sing_756.htm#SEC808 35450 is_cenSubbimodule sing_757.htm#SEC809 26181 is_ci sing_1587.htm#SEC1663 35370 is_complex sing_1037.htm#SEC1113 1234 is_fix_injective sing_1924.htm#SEC2000 11663 is_h_injective sing_1923.htm#SEC1999 36696 is_injective sing_1099.htm#SEC1175 15776 is_irred sing_1550.htm#SEC1626 51150 is_is sing_1588.htm#SEC1664 64105 is_nested sing_1213.htm#SEC1289 9200 is_prime sing_1904.htm#SEC1980 29018 is_primitive_root sing_1900.htm#SEC1976 42838 is_pure sing_748.htm#SEC800 59105 is_reg sing_1589.htm#SEC1665 18146 is_regs sing_1590.htm#SEC1666 50242 is_surjective sing_1100.htm#SEC1176 57044 is_zero sing_944.htm#SEC1020 24341 isartinianMon sing_1186.htm#SEC1262 1103 isgenericMon sing_1187.htm#SEC1263 14444 ishyper sing_1927.htm#SEC2003 65518 isirreducibleMon sing_1185.htm#SEC1261 22428 isoncurve sing_1928.htm#SEC2004 16384 isparam sing_1991.htm#SEC2067 56395 isprimaryMon sing_1184.htm#SEC1260 57367 isprimeMon sing_1183.htm#SEC1259 9124 isuni sing_1976.htm#SEC2052 39427 iv2lp sing_618.htm#SEC670 53390 iv2lpList sing_619.htm#SEC671 38626 iv2lpMat sing_620.htm#SEC672 41720 ivDHilbert sing_594.htm#SEC646 18825 ivDHilbertSickle sing_595.htm#SEC647 16102 ivDimCheck sing_596.htm#SEC648 42112 ivHilbert sing_597.htm#SEC649 34233 ivKDim sing_598.htm#SEC650 40986 ivL2lpI sing_617.htm#SEC669 45855 ivMis2Base sing_599.htm#SEC651 57812 ivMis2Dim sing_600.htm#SEC652 15557 ivOrdMisLex sing_601.htm#SEC653 40656 ivSickle sing_602.htm#SEC654 48016 ivSickleDim sing_604.htm#SEC656 57209 ivSickleHil sing_603.htm#SEC655 1967 jInvariant sing_2123.htm#SEC2199 2369 jOft sing_1859.htm#SEC1935 25716 jacob sing_263.htm#SEC303 jacoblift sing_1569.htm#SEC1645 40125 jacobson sing_1828.htm#SEC1904 59267 jacobson.lib sing_1826.htm#SEC1902 jacobson_lib sing_1826.htm#SEC1902 janet sing_264.htm#SEC304 jet sing_265.htm#SEC305 jordan sing_1085.htm#SEC1161 16602 jordanbasis sing_1086.htm#SEC1162 12736 jordanmatrix sing_1087.htm#SEC1163 2886 jordannf sing_1088.htm#SEC1164 20535 jungfib sing_1408.htm#SEC1484 5432 jungnormal sing_1407.htm#SEC1483 43561 jungresolve sing_1406.htm#SEC1482 45004 katsura sing_942.htm#SEC1018 45913 kbase sing_266.htm#SEC306 kbase (plural) sing_456.htm#SEC496 keepring sing_380.htm#SEC420 kernel sing_267.htm#SEC307 kernelLattice sing_2455.htm#SEC2531 36320 kill sing_268.htm#SEC308 killTask sing_1016.htm#SEC1092 39317 killall sing_888.htm#SEC964 34661 killattrib sing_269.htm#SEC309 kmemory sing_887.htm#SEC963 52193 kohom sing_1159.htm#SEC1235 50086 kontrahom sing_1160.htm#SEC1236 58549 koszul sing_270.htm#SEC310 kskernel.lib sing_1560.htm#SEC1636 kskernel_lib sing_1560.htm#SEC1636 l-adic numbers sing_32.htm#SEC46 laguerre sing_271.htm#SEC311 laguerre_solve sing_1707.htm#SEC1783 10155 lastvarGeneral sing_1957.htm#SEC2033 28645 latex.lib sing_1751.htm#SEC1827 latex_lib sing_1751.htm#SEC1827 lattice sing_2195.htm#IDX877 latticeArea sing_2066.htm#SEC2142 53771 latticeBasis sing_2456.htm#SEC2532 43162 latticeCodegree sing_2092.htm#SEC2168 25482 latticeDegree sing_2093.htm#SEC2169 52881 latticePoints sing_2094.htm#SEC2170 41965 latticeVolume sing_2095.htm#SEC2171 42234 laxfrT sing_2352.htm#SEC2428 60899 laxfrX sing_2353.htm#SEC2429 57254 lazy, option sing_307.htm#IDX156 lcm sing_945.htm#SEC1021 44755 lcmMon sing_1178.htm#SEC1254 52749 lcmN sing_1868.htm#SEC1944 52355 lcmofall sing_1388.htm#SEC1464 56889 lead sing_272.htm#SEC312 leadcoef sing_273.htm#SEC313 leadexp sing_274.htm#SEC314 leadmonom sing_275.htm#SEC315 leadmonomial sing_1943.htm#SEC2019 8195 left annihilator ideal sing_532.htm#IDX327 leftInverse sing_1817.htm#SEC1893 41469 leftKernel sing_1815.htm#SEC1891 9292 length, option sing_307.htm#IDX157 letplaceGBasis sing_626.htm#SEC678 33757 letterplace correspondence Letterplace correspondence sing_486.htm#SEC538 lex_solve sing_1713.htm#SEC1789 48692 lexicographical ordering sing_838.htm#IDX388 lib2doc sing_60.htm#SEC97 libSingular sing_2564.htm#SEC2654 libcdd sing_1.htm#IDX12 libfac sing_1.htm#IDX6 libparse sing_69.htm#SEC109 library sing_2210.htm#IDX892 library sing_2386.htm#IDX947 library, info string sing_55.htm#IDX124 library, polybori.lib sing_2210.htm#IDX889 library, template sing_55.htm#SEC92 library, template.lib sing_55.htm#IDX122 lieBracket sing_637.htm#SEC689 50745 lift sing_277.htm#SEC317 lift sing_490.htm#IDX303 lift (plural) sing_457.htm#SEC497 lift_kbase sing_1506.htm#SEC1582 10906 lift_rel_kb sing_1507.htm#SEC1583 13673 liftenvelope sing_493.htm#SEC545 58802 liftstd sing_278.htm#SEC318 liftstd (plural) sing_458.htm#SEC498 linReduce sing_505.htm#SEC557 57527 linReduceIdeal sing_506.htm#SEC558 19076 linSyzSolve sing_507.htm#SEC559 26185 linalg.lib sing_1063.htm#SEC1139 linalg_lib sing_1063.htm#SEC1139 linealityDimension sing_2022.htm#SEC2098 30751 linealitySpace sing_2023.htm#SEC2099 14489 linear algebra sing_205.htm#SEC245 linear algebra sing_281.htm#SEC321 linear algebra sing_282.htm#SEC322 linear algebra sing_283.htm#SEC323 linear code, dual sing_1786.htm#IDX770 linear code, systematic sing_1787.htm#IDX771 linear interreduction sing_497.htm#IDX318 linearCombinations sing_526.htm#SEC578 20514 linearMapKernel sing_525.htm#SEC577 43761 linear_relations sing_1055.htm#SEC1131 45983 linearlyEquivalent sing_2331.htm#SEC2407 28351 linearpart sing_1699.htm#SEC1775 2162 linesHypersurface sing_2538.htm#SEC2614 9129 link Parallelization with ssi links sing_108.htm#SEC148 link sing_795.htm#SEC847 link declarations sing_109.htm#SEC149 link expressions sing_110.htm#SEC150 link related functions link related functions sing_111.htm#SEC151 list sing_118.htm#SEC158 list declarations sing_119.htm#SEC159 list expressions sing_120.htm#SEC160 list operations sing_121.htm#SEC161 list related functions list related functions sing_122.htm#SEC162 listvar sing_279.htm#SEC319 lll sing_2488.htm#SEC2564 35827 load sing_381.htm#SEC421 loadLib, option sing_307.htm#IDX178 loadProc, option sing_307.htm#IDX179 locAtZero sing_1233.htm#SEC1309 5687 locNormal sing_1169.htm#SEC1245 52237 local methods sing_1168.htm#IDX541 local methods sing_1169.htm#IDX544 local names sing_46.htm#SEC83 local rings, computing in Rings associated to monomial orderings sing_790.htm#SEC842 local weighted lexicographical ordering sing_839.htm#IDX409 local weighted reverse lexicographical ordering Local orderings sing_839.htm#IDX406 localInvar sing_1662.htm#SEC1738 38478 localization Rings associated to monomial orderings sing_790.htm#SEC842 localization sing_2175.htm#IDX837 localization of D-module sing_555.htm#IDX343 localization of D-module sing_760.htm#IDX381 locally closed set sing_909.htm#IDX437 locally closed set sing_911.htm#IDX446 localstd sing_1953.htm#SEC2029 25562 locnormal.lib sing_1168.htm#SEC1244 locnormal_lib sing_1168.htm#SEC1244 locstd sing_1591.htm#SEC1667 25864 locus FamElemsAtEnvCompPoints sing_913.htm#SEC989 49563 locus sing_913.htm#IDX451 locus sing_914.htm#IDX454 locus sing_915.htm#IDX457 locus sing_916.htm#IDX460 locus sing_917.htm#IDX464 locus sing_918.htm#IDX468 locusdg sing_914.htm#SEC990 62891 locusto sing_916.htm#SEC992 17047 log2 sing_1843.htm#SEC1919 40703 logarithmic annihilator ideal sing_532.htm#IDX332 logg sing_2543.htm#SEC2619 38736 lp, global ordering sing_838.htm#IDX387 lp2iv sing_621.htm#SEC673 26909 lp2ivId sing_622.htm#SEC674 15628 lp2lstr sing_633.htm#SEC685 24713 lpDHilbert sing_605.htm#SEC657 11075 lpDHilbertSickle sing_606.htm#SEC658 46653 lpDimCheck sing_608.htm#SEC660 50239 lpHilbert sing_607.htm#SEC659 53685 lpId2ivLi sing_623.htm#SEC675 29846 lpKDim sing_609.htm#SEC661 53650 lpMis2Base sing_610.htm#SEC662 10826 lpMis2Dim sing_611.htm#SEC663 47442 lpMult sing_630.htm#SEC682 58898 lpNF sing_627.htm#SEC679 55144 lpOrdMisLex sing_612.htm#SEC664 21260 lpPower sing_632.htm#SEC684 7325 lpSickle sing_613.htm#SEC665 19646 lpSickleDim sing_615.htm#SEC667 50163 lpSickleHil sing_614.htm#SEC666 19038 lprint sing_923.htm#SEC999 5285 lres sing_280.htm#SEC320 ls, local ordering sing_839.htm#IDX400 lst2str sing_634.htm#SEC686 10088 lsum sing_1135.htm#SEC1211 50315 ludecomp sing_281.htm#SEC321 luinverse sing_282.htm#SEC322 lusolve sing_283.htm#SEC323 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1915.htm#SEC1991 57945 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1914.htm#SEC1990 33857 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1913.htm#SEC1989 7880 magnitude sing_1837.htm#SEC1913 37967 makeDivisor sing_2323.htm#SEC2399 3414 makeFormalDivisor sing_2333.htm#SEC2409 54579 makeGraph sing_1126.htm#SEC1202 21758 makeGraphVE sing_2529.htm#SEC2605 sprintf makeHeisenberg sing_711.htm#SEC763 2050 makeLetterplaceRing sing_625.htm#SEC677 41789 makeMalgrange sing_592.htm#SEC644 41377 makeModElimRing sing_728.htm#SEC780 56092 makePDivisor sing_2339.htm#SEC2415 45273 makeQsl2 sing_675.htm#SEC727 3997 makeQsl3 sing_676.htm#SEC728 41249 makeQso3 sing_674.htm#SEC726 58910 makeSheaf sing_2517.htm#SEC2593 10497 makeUe6 sing_671.htm#SEC723 58585 makeUe7 sing_672.htm#SEC724 61849 makeUe8 sing_673.htm#SEC725 64987 makeUf4 sing_670.htm#SEC722 8408 makeUg2 sing_669.htm#SEC721 34512 makeUgl sing_655.htm#SEC707 3543 makeUsl sing_654.htm#SEC706 24536 makeUsl2 sing_653.htm#SEC705 42637 makeUso10 sing_661.htm#SEC713 6936 makeUso11 sing_662.htm#SEC714 35873 makeUso12 sing_663.htm#SEC715 19319 makeUso5 sing_656.htm#SEC708 34378 makeUso6 sing_657.htm#SEC709 65009 makeUso7 sing_658.htm#SEC710 49142 makeUso8 sing_659.htm#SEC711 33275 makeUso9 sing_660.htm#SEC712 16896 makeUsp1 sing_664.htm#SEC716 44522 makeUsp2 sing_665.htm#SEC717 18017 makeUsp3 sing_666.htm#SEC718 57445 makeUsp4 sing_667.htm#SEC719 51690 makeUsp5 sing_668.htm#SEC720 35951 makeVariety sing_2509.htm#SEC2585 23915 makeWeyl sing_710.htm#SEC762 8554 map sing_123.htm#SEC163 map (plural) sing_420.htm#SEC460 map declarations sing_124.htm#SEC164 map declarations (plural) map declarations (plural) sing_421.htm#SEC461 map expressions sing_125.htm#SEC165 map expressions (plural) map expressions (plural) sing_422.htm#SEC462 map operations sing_126.htm#IDX129 map operations (plural) map operations (plural) sing_423.htm#IDX298 map related functions map related functions sing_127.htm#IDX131 map related functions (plural) map related functions (plural) sing_424.htm#IDX299 mapIsFinite sing_1103.htm#SEC1179 60897 mapToRatNormCurve sing_1363.htm#SEC1439 8877 mapall sing_988.htm#SEC1064 14907 mappingcone sing_2424.htm#SEC2500 48219 mappingcone3 sing_2426.htm#SEC2502 58973 markov4ti2 sing_1319.htm#SEC1395 9163 mat2arr sing_2160.htm#SEC2236 20840 mat2carr sing_2161.htm#SEC2237 13777 mat_rk sing_1077.htm#SEC1153 32196 matbil sing_1964.htm#SEC2040 1611 mathematical objects Representation of mathematical objects sing_834.htm#SEC886 mathinit sing_1749.htm#SEC1825 16793 matmult sing_1965.htm#SEC2041 60088 matrix sing_128.htm#SEC168 matrix sing_2160.htm#IDX805 matrix sing_2161.htm#IDX808 matrix sing_2162.htm#IDX812 matrix declarations sing_129.htm#SEC169 matrix diagonalization sing_1826.htm#IDX781 matrix expressions sing_130.htm#SEC170 matrix operations sing_132.htm#SEC172 matrix related functions matrix related functions sing_133.htm#SEC173 matrix type cast sing_131.htm#SEC171 matrix.lib sing_1030.htm#SEC1106 matrixExp sing_1353.htm#SEC1429 53063 matrixLog sing_1354.htm#SEC1430 26235 matrixT1 sing_1605.htm#SEC1681 15051 matrix_lib sing_1030.htm#SEC1106 matrixpres sing_2429.htm#SEC2505 60645 matrixsystem sing_2363.htm#SEC2439 62950 max sing_284.htm#SEC324 23624 maxEord sing_1378.htm#SEC1454 64032 maxExp sing_204.htm#IDX136 maxIntRoot sing_777.htm#SEC829 37127 maxZeros sing_1356.htm#SEC1432 35964 maxabs sing_1983.htm#SEC2059 64510 maxcoef sing_946.htm#SEC1022 50577 maxdeg sing_947.htm#SEC1023 39794 maxdeg1 sing_948.htm#SEC1024 21545 maxideal sing_285.htm#SEC325 maximalFace sing_2096.htm#SEC2172 35224 maximalGroebnerCone sing_2150.htm#SEC2226 62935 maximalValue sing_2097.htm#SEC2173 32783 maximum sing_1856.htm#SEC1932 2355 maximum number of zeroes sing_1356.htm#IDX588 mdouble sing_56.htm#SEC93 56685 mem, option sing_307.htm#IDX180 membershipMon sing_1179.htm#SEC1255 40876 memory sing_286.htm#SEC326 memory managment sing_286.htm#SEC326 merkle_hellman_decryption merkle_hellman_decryption sing_1917.htm#SEC1993 49106 merkle_hellman_encryption merkle_hellman_encryption sing_1916.htm#SEC1992 13645 midpoint sing_2359.htm#SEC2435 29391 milnor sing_1592.htm#SEC1668 23173 milnorcode sing_1476.htm#SEC1552 13849 milnornumber sing_2506.htm#SEC2582 21855 min sing_287.htm#SEC327 56342 minAssChar sing_1278.htm#SEC1354 18758 minAssCharE sing_1279.htm#SEC1355 31570 minAssGTZ sing_1276.htm#SEC1352 41315 minAssGTZE sing_1277.htm#SEC1353 50867 minAssZ sing_1296.htm#SEC1372 54152 minEcart sing_1946.htm#SEC2022 34890 minIntRoot sing_553.htm#SEC605 3288 minIntRoot2 sing_776.htm#SEC828 46494 minMult sing_1110.htm#SEC1186 31978 minbase sing_288.htm#SEC328 minbaseMon sing_1176.htm#SEC1252 1501 mindeg sing_949.htm#SEC1025 16307 mindeg1 sing_950.htm#SEC1026 39698 mindist sing_1801.htm#SEC1877 55281 minimal display time, setting the sing_350.htm#IDX282 minimalFace sing_2098.htm#SEC2174 40971 minimalValue sing_2099.htm#SEC2175 31262 minipoly sing_1082.htm#SEC1158 4927 minkowskiSum sing_2100.htm#SEC2176 3969 minor sing_289.htm#SEC329 minpoly sing_389.htm#SEC429 minres sing_290.htm#SEC330 minres (plural) sing_459.htm#SEC499 mirror symmetry sing_1125.htm#IDX509 mixed Hodge structure sing_1514.htm#IDX644 mixed Hodge structure sing_1520.htm#IDX672 mixed Hodge structure sing_1521.htm#IDX678 mixed Hodge structure sing_1522.htm#IDX686 mixed Hodge structure sing_1523.htm#IDX692 mixed Hodge structure sing_1524.htm#IDX700 mixed Hodge structure sing_1525.htm#IDX710 mixed Hodge structure sing_1536.htm#IDX716 mixed Hodge structure sing_1538.htm#IDX727 mod sing_76.htm#SEC116 mod sing_93.htm#SEC133 mod sing_142.htm#SEC182 mod2id sing_954.htm#SEC1030 27927 mod2str sing_635.htm#SEC687 35236 modDec sing_1195.htm#SEC1271 48578 modNPos sing_1218.htm#SEC1294 17130 modNormal sing_1171.htm#SEC1247 39654 modNpos_test sing_1216.htm#SEC1292 34326 modStd sing_1173.htm#SEC1249 4500 modVStd sing_2310.htm#SEC2386 38529 modVStd0 sing_2311.htm#SEC2387 46080 modWalk sing_2433.htm#SEC2509 sprintf mod_versal sing_1505.htm#SEC1581 63927 modality sing_1484.htm#SEC1560 49951 modfWalk sing_2435.htm#SEC2511 sprintf modfrWalk sing_2436.htm#SEC2512 sprintf modnormal.lib sing_1170.htm#SEC1246 modnormal_lib sing_1170.htm#SEC1246 modrWalk sing_2434.htm#SEC2510 sprintf modregCM sing_1222.htm#SEC1298 5049 modsatiety sing_1220.htm#SEC1296 44506 modstd.lib sing_1172.htm#SEC1248 modstd_lib sing_1172.htm#SEC1248 modular sing_932.htm#SEC1008 16950 modular methods sing_1168.htm#IDX542 modular methods sing_1170.htm#IDX547 modular methods. sing_1169.htm#IDX545 modular techniques. sing_1171.htm#IDX549 modular.lib sing_931.htm#SEC1007 modular_lib sing_931.htm#SEC1007 modular_lib sing_931.htm#IDX474 module sing_134.htm#SEC174 module (plural) sing_425.htm#SEC465 module declarations sing_135.htm#SEC175 module declarations (plural) module declarations (plural) sing_426.htm#SEC466 module expressions sing_136.htm#SEC176 module expressions (plural) module expressions (plural) sing_427.htm#SEC467 module operations sing_137.htm#SEC177 module operations (plural) module operations (plural) sing_428.htm#SEC468 module ordering C sing_840.htm#IDX412 module ordering c sing_840.htm#IDX414 module related functions module related functions sing_138.htm#SEC178 module related functions (plural) module related functions (plural) sing_429.htm#SEC469 module_containment sing_1095.htm#SEC1171 31620 moduliSpace sing_2531.htm#SEC2607 37013 modulo sing_291.htm#SEC331 modulo (plural) sing_460.htm#SEC500 moduloSlim sing_718.htm#SEC770 52636 modwalk.lib sing_2432.htm#IDX955 modwalk_lib sing_2432.htm#IDX956 moebius sing_2196.htm#SEC2272 61319 moebius function sing_2196.htm#IDX878 molien sing_1628.htm#SEC1704 63561 mondromy.lib sing_1566.htm#SEC1642 mondromy_lib sing_1566.htm#SEC1642 monitor sing_292.htm#SEC332 monodromy sing_1514.htm#IDX648 40112 monodromy sing_1519.htm#SEC1595 monodromy sing_1519.htm#IDX668 monodromy sing_1524.htm#IDX703 monodromy sing_1536.htm#IDX719 monodromy sing_1538.htm#IDX730 monodromyB sing_1570.htm#SEC1646 46517 monomial sing_293.htm#SEC333 monomial ordering sing_997.htm#IDX488 monomial orderings General definitions for orderings sing_790.htm#SEC842 monomial orderings sing_837.htm#SEC889 monomial orderings introduction Introduction to orderings sing_836.htm#SEC888 monomialInIdeal sing_774.htm#SEC826 4687 monomialLcm sing_1944.htm#SEC2020 36233 monomialabortstd sing_2203.htm#SEC2279 14901 monomialideal.lib sing_1174.htm#SEC1250 monomialideal_lib sing_1174.htm#SEC1250 monomials and precedence Miscellaneous oddities sing_410.htm#IDX288 mons2intmat sing_1263.htm#SEC1339 15555 morsesplit sing_1477.htm#SEC1553 3417 mp_res_mat sing_1710.htm#SEC1786 44453 mplot sing_1750.htm#SEC1826 21740 mpresmat sing_294.htm#SEC334 mprimdec.lib sing_1191.htm#SEC1267 mprimdec_lib sing_1191.htm#SEC1267 mregular.lib sing_1206.htm#SEC1282 mregular_lib sing_1206.htm#SEC1282 mres sing_295.htm#SEC335 mres (plural) sing_461.htm#SEC501 mstd sing_296.htm#SEC336 msum sing_58.htm#SEC95 53344 mtriple sing_57.htm#SEC94 55390 mult Miscellaneous oddities sing_297.htm#SEC337 mult sing_410.htm#IDX289 multBound sing_390.htm#SEC430 multRat sing_782.htm#SEC834 44047 multarr2arr sing_2191.htm#SEC2267 44731 multarrMultRestrict sing_2193.htm#SEC2269 41742 multarrRestrict sing_2192.htm#SEC2268 sprintf multcol sing_1049.htm#SEC1125 21899 multdivisor sing_2325.htm#SEC2401 65139 multformaldivisor sing_2337.htm#SEC2413 32238 multi sing_1931.htm#SEC2007 18473 multi indices sing_37.htm#SEC65 multiDeg sing_2467.htm#SEC2543 7049 multiDegBasis sing_2468.htm#SEC2544 3320 multiDegGroebner sing_2476.htm#SEC2552 1040 multiDegModulo sing_2478.htm#SEC2554 27244 multiDegPartition sing_2469.htm#SEC2545 9577 multiDegResolution sing_2479.htm#SEC2555 38535 multiDegSyzygy sing_2477.htm#SEC2553 54075 multiDegTensor sing_2480.htm#SEC2556 45108 multiDegTor sing_2481.htm#SEC2557 sprintf multiarrangement sing_2187.htm#IDX858 multiarrangement sing_2188.htm#IDX860 multiarrangement sing_2189.htm#IDX863 multiarrangement sing_2190.htm#IDX864 multiarrangement sing_2191.htm#IDX867 multiarrangement sing_2192.htm#IDX870 multiarrangement sing_2193.htm#IDX872 multidimensional_knapsack multidimensional_knapsack sing_1909.htm#SEC1985 15647 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2437.htm#IDX961 multigrading.lib sing_2437.htm#IDX959 multigrading_lib sing_2437.htm#IDX960 multipleCover sing_2537.htm#SEC2613 55988 multiplicities, sequence of sing_1545.htm#IDX742 multiplicity sing_2316.htm#IDX920 multiplicity sequence sing_1458.htm#IDX621 multiplicity sequence sing_1461.htm#IDX633 multiplicity sequence sing_1547.htm#IDX743 multiplylist sing_1398.htm#SEC1474 34999 multivariate equations sing_1684.htm#IDX760 multrow sing_1050.htm#SEC1126 871 multseq2charexp sing_1457.htm#SEC1533 sprintf multsequence sing_1547.htm#SEC1623 35117 nBoundaryLatticePoints nBoundaryLatticePoints sing_2101.htm#SEC2177 49670 nHilbertBasis sing_2102.htm#SEC2178 173 nInteriorLatticePoints nInteriorLatticePoints sing_2103.htm#SEC2179 42152 nLatticePoints sing_2104.htm#SEC2180 5977 naccache_stern_decryption naccache_stern_decryption sing_1912.htm#SEC1988 31429 naccache_stern_encryption naccache_stern_encryption sing_1911.htm#SEC1987 60034 naccache_stern_generation naccache_stern_generation sing_1910.htm#SEC1986 2559 nameof sing_298.htm#SEC338 names sing_299.htm#SEC339 nashmult sing_1465.htm#SEC1541 8491 nblocks sing_350.htm#IDX221 ncExt_R sing_751.htm#SEC803 14357 ncHilb.lib sing_2489.htm#SEC2565 ncHilb_lib sing_2489.htm#SEC2565 ncHom sing_752.htm#SEC804 45033 ncRelations sing_719.htm#SEC771 7225 nc_algebra sing_462.htm#SEC502 nc_hilb sing_350.htm#IDX223 ncalg.lib sing_652.htm#SEC704 ncalg_lib sing_652.htm#SEC704 ncalgebra sing_463.htm#SEC503 ncdecomp.lib sing_679.htm#SEC731 ncdecomp_lib sing_679.htm#SEC731 ncdetection sing_646.htm#SEC698 24994 ncfactor sing_685.htm#SEC737 53809 ncfactor.lib sing_684.htm#SEC736 ncfactor_lib sing_684.htm#SEC736 nchilb sing_2490.htm#SEC2566 36922 nchomolog.lib sing_750.htm#IDX371 nchomolog_lib sing_750.htm#IDX372 ncols sing_300.htm#SEC340 ncones sing_2046.htm#SEC2122 48316 ncpreim.lib sing_697.htm#SEC749 ncpreim_lib sing_697.htm#SEC749 nctools.lib sing_705.htm#SEC757 nctools_lib sing_705.htm#SEC757 ndcond sing_708.htm#SEC760 1006 negatedCone sing_2024.htm#SEC2100 38527 negative degree lexicographical ordering sing_839.htm#IDX403 negative degree reverse lexicographical ordering Local orderings sing_839.htm#IDX401 negative lexicographical ordering sing_839.htm#IDX399 negativedivisor sing_2326.htm#SEC2402 8274 negativeformaldivisor negativeformaldivisor sing_2336.htm#SEC2412 55026 net access Command line options sing_19.htm#IDX40 newTest sing_1851.htm#SEC1927 36655 newline sing_166.htm#SEC206 news sing_2557.htm#SEC2633 newstruct sing_177.htm#SEC217 newstruct sing_2210.htm#IDX894 newtonDiag sing_958.htm#SEC1034 56652 newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2550.htm#SEC2626 22052 newtonPolytope sing_2050.htm#SEC2126 56291 newtonPolytopeLP sing_2055.htm#SEC2131 36186 newtonPolytopeP sing_2054.htm#SEC2130 29927 newtonpoly sing_1552.htm#SEC1628 31930 nf_icis sing_1593.htm#SEC1669 49093 nfmodStd sing_2493.htm#SEC2569 46077 nfmodSyz sing_2495.htm#SEC2571 55942 nfmodstd.lib sing_2491.htm#SEC2567 nfmodstd_lib sing_2491.htm#SEC2567 nfmodsyz.lib sing_2494.htm#SEC2570 nfmodsyz_lib sing_2494.htm#SEC2570 nilpotent Lie algebras sing_1351.htm#IDX573 nmaxcones sing_2045.htm#SEC2121 660 noether sing_391.htm#SEC431 noether.lib sing_1214.htm#SEC1290 noetherNormal sing_1102.htm#SEC1178 44522 noether_lib sing_1214.htm#SEC1290 non-english special characters sing_399.htm#IDX284 nonMonomials sing_1267.htm#SEC1343 16309 nonZeroEntry sing_1105.htm#SEC1181 933 none, option sing_307.htm#IDX150 norTest sing_1234.htm#SEC1310 sprintf norm sing_1930.htm#SEC2006 31143 normal sing_1224.htm#SEC1300 61073 normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2536.htm#IDX993 normal.lib sing_1223.htm#SEC1299 normalBundle sing_2536.htm#SEC2612 sprintf normalC sing_1226.htm#SEC1302 34842 normalConductor sing_1238.htm#SEC1314 26085 normalFan sing_2105.htm#SEC2181 39216 normalFanL sing_2056.htm#SEC2132 55096 normalForm sing_2327.htm#SEC2403 34962 normalI sing_1311.htm#SEC1387 7516 normalP sing_1225.htm#SEC1301 36584 normalToricRing sing_1241.htm#SEC1317 29638 normalToricRingFromBinomials normalToricRingFromBinomials sing_1242.htm#SEC1318 2301 normal_lib sing_1223.htm#SEC1299 normalform sing_1481.htm#SEC1557 5550 normalform sing_2305.htm#IDX913 normaliz sing_1.htm#IDX14 18426 normaliz sing_1254.htm#SEC1330 normaliz.lib sing_1239.htm#SEC1315 normaliz_lib sing_1239.htm#SEC1315 normalization sing_1168.htm#IDX540 normalization sing_1169.htm#IDX543 normalization sing_1170.htm#IDX546 normalization sing_1171.htm#IDX548 normalization sing_1224.htm#IDX550 normalization sing_1225.htm#IDX553 normalization sing_1226.htm#IDX556 normalization sing_1238.htm#IDX562 normalization sing_1239.htm#IDX564 normalization sing_2315.htm#IDX918 normalization. sing_1165.htm#IDX539 normalization. sing_1358.htm#IDX595 normalize sing_951.htm#SEC1027 44788 not sing_96.htm#SEC136 notBuckets, option sing_307.htm#IDX160 notRegularity, option sing_307.htm#IDX158 notSugar, option sing_307.htm#IDX159 notWarnSB, option sing_307.htm#IDX181 npar sing_1836.htm#SEC1912 5753 npars sing_301.htm#SEC341 nrRootsDeterm sing_1961.htm#SEC2037 sprintf nrRootsProbab sing_1960.htm#SEC2036 sprintf nres sing_302.htm#SEC342 nres (plural) sing_464.htm#SEC504 nrows sing_303.htm#SEC343 nrroots sing_1990.htm#SEC2066 54867 nsatiety sing_1219.htm#SEC1295 53333 nselect sing_1121.htm#SEC1197 34057 nt_solve sing_1725.htm#SEC1801 33061 ntsolve.lib sing_1724.htm#SEC1800 ntsolve_lib sing_1724.htm#SEC1800 number sing_139.htm#SEC179 number sing_2164.htm#IDX818 number declarations sing_140.htm#SEC180 number expressions sing_141.htm#SEC181 number operations sing_142.htm#SEC182 number related functions number related functions sing_143.htm#SEC183 numberOfConesOfDimension numberOfConesOfDimension sing_2047.htm#SEC2123 5905 number_e sing_889.htm#SEC965 59152 number_pi sing_890.htm#SEC966 15492 numerAlg.lib sing_1333.htm#IDX569 numerAlg_lib sing_1333.htm#IDX570 numerDecom.lib sing_1338.htm#IDX571 numerDecom_lib sing_1338.htm#IDX572 numerator sing_304.htm#SEC344 nvars sing_305.htm#SEC345 oneDimBelongSemigroup oneDimBelongSemigroup sing_1112.htm#SEC1188 34399 online help The online help system sing_16.htm#SEC22 open sing_306.htm#SEC346 opentex sing_1753.htm#SEC1829 54236 operatorBM sing_539.htm#SEC591 54875 operatorModulo sing_540.htm#SEC592 26064 oppose sing_465.htm#SEC505 opposite sing_466.htm#SEC506 opposite polynomial sing_350.htm#IDX231 opposite ring sing_350.htm#IDX228 option sing_307.htm#SEC347 option(warn) sing_70.htm#SEC110 optionIsSet sing_994.htm#SEC1070 57325 or Evaluation of logical expressions sing_96.htm#SEC136 or sing_403.htm#SEC443 orbit sing_1351.htm#IDX575 orbit sing_1352.htm#IDX579 orbit sing_1355.htm#IDX584 orbit sing_1356.htm#IDX587 orbitCones sing_2392.htm#SEC2468 5522 orbit_variety sing_1652.htm#SEC1728 22665 orbitparam.lib sing_1351.htm#SEC1427 orbitparam_lib sing_1351.htm#SEC1427 ord sing_308.htm#SEC348 ord_test sing_989.htm#SEC1065 36532 orderings General definitions for orderings sing_837.htm#SEC889 orderings introduction Introduction to orderings sing_836.htm#SEC888 orderings, M sing_841.htm#SEC893 orderings, a sing_843.htm#SEC895 orderings, global sing_838.htm#SEC890 orderings, local sing_839.htm#SEC891 orderings, product sing_842.htm#SEC894 ordstr sing_309.htm#SEC349 origin sing_1995.htm#SEC2071 31408 orthogonalize sing_1068.htm#SEC1144 63711 outer sing_1038.htm#SEC1114 64048 output sing_41.htm#SEC71 p-adic numbers sing_32.htm#SEC46 pFactor sing_1885.htm#SEC1961 31504 pIntersect sing_503.htm#SEC555 44055 pIntersectSyz sing_504.htm#SEC556 45608 package sing_144.htm#SEC184 package declarations package declarations sing_145.htm#SEC185 package related functions package related functions sing_146.htm#SEC186 pairset sing_1950.htm#SEC2026 38258 par sing_310.htm#SEC350 par2varRing sing_873.htm#SEC949 44769 paraConic sing_1366.htm#SEC1442 9828 paraPlaneCurve sing_1360.htm#SEC1436 34094 parallel skeletons sing_933.htm#IDX480 parallel.lib sing_933.htm#SEC1009 parallelTestAND sing_937.htm#SEC1013 1415 parallelTestOR sing_938.htm#SEC1014 14920 parallelWaitAll sing_936.htm#SEC1012 2017 parallelWaitFirst sing_935.htm#SEC1011 32 parallelWaitN sing_934.htm#SEC1010 38878 parallel_lib sing_933.htm#SEC1009 parallelization sing_933.htm#IDX479 parallelization sing_973.htm#IDX482 parallelization sing_1014.htm#IDX495 param sing_1543.htm#SEC1619 57220 parameter, as numbers sing_139.htm#SEC179 parameterSubstitute sing_2145.htm#SEC2221 63147 parametric annihilator sing_532.htm#IDX333 parametric annihilator for variety sing_588.htm#IDX356 parametric ideal sing_902.htm#IDX423 parametric ideal sing_909.htm#IDX436 parametric ideal sing_909.htm#IDX438 parametric ideal sing_910.htm#IDX442 parametrization sing_1351.htm#IDX576 parametrization sing_1355.htm#IDX585 parametrization sing_1543.htm#IDX737 parametrizeOrbit sing_1355.htm#SEC1431 26969 paraplanecurves.lib sing_1357.htm#SEC1433 paraplanecurves_lib sing_1357.htm#SEC1433 pardeg sing_311.htm#SEC351 parstr sing_312.htm#SEC352 part sing_2284.htm#SEC2360 31485 partOver sing_2287.htm#SEC2363 25555 partUnder sing_2288.htm#SEC2364 13123 partial_molien sing_1630.htm#SEC1706 21772 partitions sing_1133.htm#SEC1209 48089 partitions sing_1133.htm#IDX528 path integral sing_1125.htm#IDX515 pause sing_930.htm#SEC1006 2273 pdivi sing_904.htm#SEC980 39081 pdivi sing_905.htm#IDX433 pdivisorplus sing_2341.htm#SEC2417 47486 permcol sing_1051.htm#SEC1127 12886 permrow sing_1052.htm#SEC1128 26561 permutations sing_1134.htm#IDX529 permute sing_1134.htm#SEC1210 40893 permute_L sing_1788.htm#SEC1864 10716 perron sing_731.htm#SEC783 3782 perron.lib sing_730.htm#SEC782 perron_lib sing_730.htm#SEC782 phindex.lib sing_2205.htm#IDX885 phindex_lib sing_2205.htm#IDX886 picksFormula sing_2067.htm#SEC2143 14656 pid sing_350.htm#IDX240 plainInvariants sing_1502.htm#SEC1578 40916 planeCur sing_2303.htm#SEC2379 sprintf plot sing_1766.htm#SEC1842 46610 plotRot sing_1770.htm#SEC1846 57150 plotRotated sing_1769.htm#SEC1845 33009 plotRotatedDirect sing_1772.htm#SEC1848 18202 plotRotatedList sing_1771.htm#SEC1847 41668 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1773.htm#SEC1849 38856 plural sing_996.htm#IDX487 pmat sing_924.htm#SEC1000 3857 pnormalf sing_905.htm#SEC981 34068 pointid.lib sing_1266.htm#SEC1342 pointid_lib sing_1266.htm#SEC1342 polSol sing_766.htm#SEC818 323 polSolFiniteRank sing_767.htm#SEC819 30875 pollTask sing_1024.htm#SEC1100 53950 poly sing_147.htm#SEC187 poly (plural) sing_430.htm#SEC470 poly declarations sing_148.htm#SEC188 poly declarations (plural) poly declarations (plural) sing_431.htm#SEC471 poly expressions sing_149.htm#SEC189 poly expressions (plural) poly expressions (plural) sing_432.htm#SEC472 poly operations sing_150.htm#SEC190 poly operations (plural) poly operations (plural) sing_433.htm#SEC473 poly related functions poly related functions sing_151.htm#SEC191 poly related functions (plural) poly related functions (plural) sing_434.htm#SEC474 poly.lib sing_939.htm#SEC1015 poly2list sing_581.htm#SEC633 4960 poly2zdd sing_2226.htm#SEC2302 61839 polyInterpolation sing_2344.htm#SEC2420 45866 polyVars sing_773.htm#SEC825 43882 poly_lib sing_939.htm#SEC1015 polybori sing_2210.htm#IDX890 polybori.lib sing_2210.htm#IDX887 polybori.lib sing_2210.htm#IDX891 polybori_lib sing_2210.htm#IDX888 polymake sing_2052.htm#IDX791 polymake.lib sing_2052.htm#SEC2128 polymakePolytope sing_2053.htm#SEC2129 47302 polymake_lib sing_2052.htm#SEC2128 polynomial solutions sing_760.htm#IDX384 polynomial, opposite sing_350.htm#IDX232 polytope sing_185.htm#SEC225 polytope sing_2052.htm#IDX787 polytopeViaInequalities polytopeViaInequalities sing_2025.htm#SEC2101 52084 polytopeViaPoints sing_2026.htm#SEC2102 281 pos_def sing_1079.htm#SEC1155 4994 poset sing_2195.htm#IDX876 positiveOrthant sing_1996.htm#SEC2072 42102 posweight sing_1610.htm#SEC1686 3364 powSumSym sing_2241.htm#SEC2317 2339 power sing_1039.htm#SEC1115 23365 powerN sing_1869.htm#SEC1945 20170 powerX sing_1878.htm#SEC1954 47971 power_products sing_1644.htm#SEC1720 54629 powerpolyX sing_1848.htm#SEC1924 37247 powersums sing_1971.htm#SEC2047 59049 preComp sing_1202.htm#SEC1278 16160 preimage sing_313.htm#SEC353 preimage sing_697.htm#IDX359 preimage (plural) sing_467.htm#SEC507 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_992.htm#IDX485 preimageLattice sing_2457.htm#SEC2533 37348 preimageLoc sing_992.htm#SEC1068 33315 preimageNC sing_699.htm#SEC751 16037 prepEmbDiv sing_1428.htm#SEC1504 36708 prepMat sing_1681.htm#SEC1757 39868 prepRealclassify sing_1486.htm#SEC1562 10994 prepSV sing_1783.htm#SEC1859 50095 prepareAss sing_1285.htm#SEC1361 21802 presentTree sing_1415.htm#SEC1491 10731 presolve.lib sing_1691.htm#SEC1767 presolve_lib sing_1691.htm#SEC1767 primL sing_1873.htm#SEC1949 14513 primList sing_1872.htm#SEC1948 6802 primRoot sing_1325.htm#SEC1401 14210 primTest sing_1201.htm#SEC1277 8105 primary_char0 sing_1634.htm#SEC1710 61413 primary_char0_no_molien primary_char0_no_molien sing_1636.htm#SEC1712 50477 primary_char0_no_molien_random primary_char0_no_molien_random sing_1641.htm#SEC1717 8422 primary_char0_random primary_char0_random sing_1639.htm#SEC1715 5996 primary_charp sing_1635.htm#SEC1711 37863 primary_charp_no_molien primary_charp_no_molien sing_1637.htm#SEC1713 32282 primary_charp_no_molien_random primary_charp_no_molien_random sing_1642.htm#SEC1718 11498 primary_charp_random primary_charp_random sing_1640.htm#SEC1716 24739 primary_charp_without primary_charp_without sing_1638.htm#SEC1714 49585 primary_charp_without_random primary_charp_without_random sing_1643.htm#SEC1719 36998 primary_invariants sing_1622.htm#SEC1698 5500 primary_invariants_random primary_invariants_random sing_1623.htm#SEC1699 28958 primdec.lib sing_1270.htm#SEC1346 primdecGTZ sing_1272.htm#SEC1348 6091 primdecGTZE sing_1273.htm#SEC1349 64882 primdecMon sing_1190.htm#SEC1266 3856 primdecSY sing_1274.htm#SEC1350 6547 primdecSYE sing_1275.htm#SEC1351 52788 primdecZ sing_1294.htm#SEC1370 48194 primdecZM sing_1295.htm#SEC1371 17214 primdec_lib sing_1270.htm#SEC1346 primdecint.lib sing_1293.htm#SEC1369 primdecint_lib sing_1293.htm#SEC1369 prime sing_314.htm#SEC354 primeClosure sing_1229.htm#SEC1305 43589 primecoeffs sing_896.htm#SEC972 46153 primefactors sing_315.htm#SEC355 primes sing_891.htm#SEC967 24408 primitiv.lib sing_1301.htm#SEC1377 primitiv_lib sing_1301.htm#SEC1377 primitive sing_1302.htm#SEC1378 36163 primitive element sing_1302.htm#IDX566 primitiveSpan sing_2464.htm#SEC2540 sprintf primitive_extra sing_1303.htm#SEC1379 49025 primparam sing_1497.htm#SEC1573 35357 principal intersection sing_497.htm#IDX317 print sing_316.htm#SEC356 print sing_2162.htm#IDX811 printGraph sing_1127.htm#SEC1203 45041 printGraphG sing_2530.htm#SEC2606 48742 printGroup sing_2445.htm#SEC2521 6791 printMoebius sing_2201.htm#SEC2277 45828 printSheaf sing_2518.htm#SEC2594 31762 printStack sing_2532.htm#SEC2608 3692 printTask sing_1019.htm#SEC1095 54549 printVariety sing_2510.htm#SEC2586 2846 printf sing_317.htm#SEC357 2294 printlevel sing_392.htm#SEC432 proc sing_152.htm#SEC192 proc declaration sing_153.htm#SEC193 proc expression sing_154.htm#SEC194 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_155.htm#SEC195 prodcrit sing_1948.htm#SEC2024 56231 product sing_892.htm#SEC968 54431 product variety, abstract variety sing_2511.htm#IDX981 productVariety sing_2511.htm#SEC2587 54191 productgroup sing_2466.htm#SEC2542 55937 progress watch sing_307.htm#IDX163 projectLattice sing_2458.htm#SEC2534 28463 projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2515.htm#IDX985 projective dimension purityfiltration_lib sing_738.htm#IDX368 projective limes sing_32.htm#SEC46 projective space, abstract variety sing_2514.htm#IDX984 projectiveBundle sing_2515.htm#SEC2591 13791 projectiveDimension sing_739.htm#SEC791 8165 projectiveSpace sing_2514.htm#SEC2590 21729 prompt sing_15.htm#SEC21 prompt, option sing_307.htm#IDX182 propagator sing_1125.htm#IDX513 42460 propagator sing_1128.htm#SEC1204 prot, option sing_307.htm#IDX161 protocol of computations sing_307.htm#IDX162 proximitymatrix sing_1456.htm#SEC1532 58403 prune sing_318.htm#SEC358 prwalk sing_2497.htm#SEC2573 46963 psigncnd sing_1744.htm#SEC1820 57734 puiseux2generators sing_1555.htm#SEC1631 64508 puiseuxExpansion sing_2116.htm#SEC2192 46277 pure tensor sing_490.htm#IDX305 purelist sing_749.htm#SEC801 15517 purity purityfiltration_lib sing_738.htm#IDX370 purityFiltration sing_740.htm#SEC792 5742 purityTriang sing_741.htm#SEC793 3665 purityfiltration.lib purityfiltration_lib sing_738.htm#IDX363 purityfiltration_lib purityfiltration_lib sing_738.htm#IDX364 pushForward sing_2483.htm#SEC2559 26697 pwalk sing_1141.htm#SEC1217 61187 pyobject sing_186.htm#SEC226 pyobject sing_2210.htm#IDX893 pyobject declarations pyobject declarations sing_187.htm#SEC227 pyobject expressions pyobject expressions sing_188.htm#SEC228 pyobject operations sing_189.htm#SEC229 pyobject related functions pyobject related functions sing_190.htm#SEC230 pyramid sing_2360.htm#SEC2436 7421 python_eval sing_191.htm#SEC231 python_import sing_192.htm#SEC232 python_run sing_193.htm#SEC233 qbase sing_1974.htm#SEC2050 8633 qepcad sing_2370.htm#SEC2446 39171 qepcadsystem sing_2371.htm#SEC2447 31977 qhmatrix sing_1608.htm#SEC1684 61813 qhmoduli.lib sing_1572.htm#SEC1648 qhmoduli_lib sing_1572.htm#SEC1648 qhspectrum sing_1595.htm#SEC1671 13732 qhweight sing_319.htm#SEC359 qmatrix.lib sing_732.htm#SEC784 qmatrix_lib sing_732.htm#SEC784 qminor sing_734.htm#SEC786 52670 qrds sing_320.htm#SEC360 qring Miscellaneous oddities sing_161.htm#SEC201 qring sing_410.htm#IDX293 qring (plural) sing_435.htm#SEC475 qring declaration sing_165.htm#SEC205 qring declaration (plural) qring declaration (plural) sing_436.htm#SEC476 qring related functions (plural) qring related functions (plural) sing_437.htm#SEC477 qring ring ideal 'factor ring' sing_1001.htm#IDX491 qringNF, option sing_307.htm#IDX164 qslimgb sing_872.htm#SEC948 51999 quadraticSieve sing_1886.htm#SEC1962 58557 quantMat sing_733.htm#SEC785 56227 quickclass sing_1478.htm#SEC1554 14018 quit sing_382.htm#SEC422 quotSheaf sing_2527.htm#SEC2603 49619 quote sing_321.htm#SEC361 quotient sing_322.htm#SEC362 quotient (plural) sing_468.htm#SEC508 quotientLatticeBasis quotientLatticeBasis sing_2027.htm#SEC2103 15613 quotientMain sing_1736.htm#SEC1812 39870 quotientMon sing_1181.htm#SEC1257 57149 quotients sing_2386.htm#IDX951 rHRR sing_2281.htm#SEC2357 20131 rMacaulay sing_925.htm#SEC1001 45499 rad_con sing_952.htm#SEC1028 21777 radical sing_1282.htm#SEC1358 1407 radicalEHV sing_1283.htm#SEC1359 33703 radicalMemberShip sing_2138.htm#SEC2214 28527 radicalMon sing_1182.htm#SEC1258 64912 radicalZ sing_1297.htm#SEC1373 5783 randcharpoly sing_1968.htm#SEC2044 37737 randlinpoly sing_1970.htm#SEC2046 22330 random sing_323.htm#SEC363 random sing_350.htm#IDX244 random sing_2183.htm#IDX850 random sing_2184.htm#IDX852 random number generator, seed sing_350.htm#IDX242 random.lib sing_960.htm#SEC1036 randomBinomial sing_972.htm#SEC1048 17913 randomCheck sing_1799.htm#SEC1875 20973 randomLast sing_971.htm#SEC1047 2046 randomPoint sing_2028.htm#SEC2104 22561 randomPolyInT sing_2147.htm#SEC2223 2264 random_lib sing_960.htm#SEC1036 randomid sing_962.htm#SEC1038 7815 randommat sing_963.htm#SEC1039 33569 rank sing_204.htm#IDX137 rank sing_324.htm#SEC364 rankSheaf sing_2519.htm#SEC2595 11850 ratSol sing_768.htm#SEC820 62488 ratgb.lib sing_758.htm#IDX373 ratgb_lib sing_758.htm#IDX374 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1360.htm#IDX597 rational normal curve, projection. sing_1361.htm#IDX598 rational normal curve, projection. sing_1364.htm#IDX599 rational normal curve, projection. sing_1365.htm#IDX600 rational solutions sing_760.htm#IDX385 rational univariate projection sing_1968.htm#IDX784 rationalCurve sing_2539.htm#SEC2615 61201 rationalPointConic sing_1362.htm#SEC1438 9761 ratstd sing_759.htm#SEC811 61346 rays sing_2029.htm#SEC2105 44445 re2squ sing_1339.htm#SEC1415 24350 read sing_325.htm#SEC365 readNmzData sing_1257.htm#SEC1333 18957 reading, option sing_307.htm#IDX183 readline sing_1.htm#IDX5 real sing_28.htm#IDX74 real roots, univariate polynomial sing_1975.htm#IDX786 real roots, univariate projection sing_1959.htm#IDX782 real roots,sign conditions sing_1742.htm#IDX762 realclassify sing_2504.htm#SEC2580 60279 realclassify.lib sing_2503.htm#SEC2579 realclassify_lib sing_2503.htm#SEC2579 realizationDim sing_2110.htm#SEC2186 37756 realizationDimPoly sing_2112.htm#SEC2188 3611 realizationMatroids.lib realizationMatroids_lib sing_2109.htm#SEC2185 realizationMatroids_lib realizationMatroids_lib sing_2109.htm#SEC2185 realmorsesplit sing_2505.htm#SEC2581 16318 realpoly sing_1306.htm#SEC1382 9453 realrad sing_1308.htm#SEC1384 43381 realrad.lib sing_1305.htm#SEC1381 realrad_lib sing_1305.htm#SEC1381 realzero sing_1307.htm#SEC1383 12712 recursive_boolean_poly recursive_boolean_poly sing_2216.htm#SEC2292 17045 recursive_from_boolean_poly recursive_from_boolean_poly sing_2222.htm#SEC2298 37794 redSB, option sing_307.htm#IDX165 redTail, option sing_307.htm#IDX167 redThrough, option sing_307.htm#IDX168 redefine, option sing_307.htm#IDX184 reduce sing_326.htm#SEC366 reduce sing_511.htm#IDX322 reduce sing_904.htm#IDX431 reduce sing_905.htm#IDX434 reduce (plural) sing_469.htm#SEC509 reduced sing_903.htm#IDX428 reduced standard basis sing_307.htm#IDX166 reduction sing_1660.htm#SEC1736 31048 reesclos.lib sing_1309.htm#SEC1385 reesclos_lib sing_1309.htm#SEC1385 reference sing_194.htm#SEC234 reference declarations reference declarations sing_195.htm#SEC235 reference expressions reference expressions sing_196.htm#SEC236 reference operations reference and shared operations sing_199.htm#SEC239 reference related functions reference and shared related functions sing_200.htm#SEC240 regCM sing_1221.htm#SEC1297 25488 regIdeal sing_1207.htm#SEC1283 3827 regMonCurve sing_1210.htm#SEC1286 41311 regularity Syzygies and resolutions sing_327.htm#SEC367 regularity sing_847.htm#SEC904 reiffen sing_550.htm#SEC602 32856 rel_orbit_variety sing_1653.htm#SEC1729 34278 relations sing_730.htm#IDX362 relativeInteriorPoint relativeInteriorPoint sing_2030.htm#SEC2106 30097 relative_orbit_variety relative_orbit_variety sing_1654.htm#SEC1730 32995 relweight sing_1609.htm#SEC1685 10658 remainder sing_1729.htm#SEC1805 1191 remainderMain sing_1737.htm#SEC1813 3532 removeCone sing_2048.htm#SEC2124 33877 removepower sing_1466.htm#SEC1542 47644 repart sing_328.htm#SEC368 replace sing_1838.htm#SEC1914 50075 representation, math objects Representation of mathematical objects sing_834.htm#SEC886 res sing_329.htm#SEC369 53499 resbinomial.lib sing_1369.htm#IDX603 resbinomial_lib sing_1369.htm#IDX604 reservedName sing_330.htm#SEC370 resfunction sing_1383.htm#SEC1459 59312 resgraph.lib sing_1401.htm#SEC1477 resgraph_lib sing_1401.htm#SEC1477 resjung.lib sing_1405.htm#SEC1481 resjung_lib sing_1405.htm#SEC1481 reslist sing_1397.htm#SEC1473 64950 resolution purityfiltration_lib sing_156.htm#SEC196 resolution sing_738.htm#IDX369 resolution (plural) sing_438.htm#SEC478 resolution declarations resolution declarations sing_157.htm#SEC197 resolution declarations (plural) resolution declarations (plural) sing_439.htm#SEC479 resolution expressions resolution expressions sing_158.htm#SEC198 resolution expressions (plural) resolution expressions (plural) sing_440.htm#SEC480 resolution graph sing_1451.htm#IDX617 resolution related functions resolution related functions sing_159.htm#SEC199 resolution related functions (plural) resolution related functions (plural) sing_441.htm#SEC481 resolution, La Scala's method sing_280.htm#SEC320 resolution, computation of sing_329.htm#IDX186 resolution, hilbert-driven sing_255.htm#SEC295 resolutionInLocalization resolutionInLocalization sing_2385.htm#SEC2461 31106 resolutiongraph sing_1452.htm#SEC1528 32697 resolve sing_1413.htm#SEC1489 27374 resolve.lib sing_1409.htm#SEC1485 resolve_lib sing_1409.htm#SEC1485 resources.lib sing_973.htm#SEC1049 resources_lib sing_973.htm#SEC1049 restriction sing_2176.htm#IDX838 restriction sing_2192.htm#IDX871 restriction sing_2193.htm#IDX873 restriction of sing_555.htm#IDX345 restrictionIdeal sing_565.htm#SEC617 49796 restrictionModule sing_566.htm#SEC618 62461 resultant sing_294.htm#SEC334 resultant sing_331.htm#SEC371 reszeta.lib sing_1422.htm#SEC1498 reszeta_lib sing_1422.htm#SEC1498 return sing_383.htm#SEC423 return type of procedures Return type of procedures sing_408.htm#SEC448 returnSB, option sing_307.htm#IDX152 reverse sing_1989.htm#SEC2065 35880 reverse lexicographical ordering sing_838.htm#IDX390 reynolds_molien sing_1629.htm#SEC1705 45316 rho sing_1880.htm#SEC1956 51414 rightInverse sing_1818.htm#SEC1894 6558 rightKernel sing_1816.htm#SEC1892 46603 rightModulo sing_717.htm#SEC769 12618 rightNF sing_716.htm#SEC768 42610 rightNFWeyl sing_785.htm#SEC837 35828 rightStd sing_715.htm#SEC767 5740 ring sing_160.htm#SEC200 ring sing_901.htm#IDX420 ring (plural) sing_442.htm#SEC482 ring coefficients hasTransExtensionCoefficient sing_999.htm#IDX489 ring coefficients sing_1000.htm#IDX490 ring declarations sing_162.htm#SEC202 ring declarations (plural) ring declarations (plural) sing_443.htm#SEC483 ring operations sing_164.htm#SEC204 ring operations (plural) ring operations (plural) sing_444.htm#SEC484 ring related functions ring related functions sing_163.htm#SEC203 ring related functions (plural) ring related functions (plural) sing_445.htm#SEC485 ring, opposite sing_350.htm#IDX229 ring.lib sing_978.htm#SEC1054 ring_cf sing_204.htm#IDX138 ring_lib sing_978.htm#SEC1054 ring_list sing_333.htm#SEC373 ring_variable sing_2163.htm#IDX815 ring_variable sing_2164.htm#IDX817 ring_variable sing_2165.htm#IDX821 ring_variable sing_2166.htm#IDX823 ringlist sing_332.htm#SEC372 ringlist (plural) sing_470.htm#SEC510 rings sing_901.htm#IDX421 ringtensor sing_990.htm#SEC1066 56648 ringweights sing_991.htm#SEC1067 33307 rinvar.lib sing_1665.htm#SEC1741 rinvar_lib sing_1665.htm#SEC1741 rmNmzFiles sing_1262.htm#SEC1338 32601 rm_unitcol sing_1057.htm#SEC1133 5591 rm_unitrow sing_1056.htm#SEC1132 35694 rmx sing_1763.htm#SEC1839 17675 rncAntiCanonicalMap sing_1361.htm#SEC1437 41965 rncItProjEven sing_1365.htm#SEC1441 18200 rncItProjOdd sing_1364.htm#SEC1440 61976 root of Bernstein-Sato polynomial sing_532.htm#IDX334 rootofUnity sing_993.htm#SEC1069 21365 roots sing_1730.htm#SEC1806 18436 rootsMain sing_1738.htm#SEC1814 54934 rootsModp sing_1862.htm#SEC1938 47315 rootsmr.lib sing_1959.htm#SEC2035 rootsmr_lib sing_1959.htm#SEC2035 rootsur.lib sing_1975.htm#SEC2051 rootsur_lib sing_1975.htm#SEC2051 round sing_1860.htm#SEC1936 9248 rowShift sing_204.htm#IDX141 rowShift sing_206.htm#SEC246 rowred sing_1053.htm#SEC1129 63416 rp, global ordering sing_838.htm#IDX389 rswalk sing_2502.htm#SEC2578 50903 rtimer sing_396.htm#SEC436 rvalue No rvalue of increments and assignments sing_402.htm#SEC442 rvar sing_334.htm#SEC374 rwalk sing_2498.htm#SEC2574 42525 rwalk.lib sing_2496.htm#SEC2572 rwalk_lib sing_2496.htm#SEC2572 s_res sing_1007.htm#SEC1083 47429 sa_poly_reduce sing_520.htm#SEC572 60856 sa_reduce sing_519.htm#SEC571 55799 sagbi sing_1315.htm#SEC1391 46653 sagbi.lib sing_1312.htm#SEC1388 sagbiAlg sing_2299.htm#SEC2375 sprintf sagbiMod sing_2300.htm#SEC2376 sprintf sagbiPart sing_1316.htm#SEC1392 56066 sagbiReduce sing_1314.htm#SEC1390 19036 sagbiSPoly sing_1313.htm#SEC1389 17365 sagbi_lib sing_1312.htm#SEC1388 salida sing_1394.htm#SEC1470 9839 sameComponent sing_1942.htm#SEC2018 13540 sameQ sing_1741.htm#SEC1817 45579 sat sing_1122.htm#SEC1198 6266 satiety sing_1209.htm#SEC1285 34323 satstd sing_2204.htm#SEC2280 63657 sba sing_335.htm#SEC375 scalarProd sing_509.htm#SEC561 54488 scheme sing_2351.htm#SEC2427 15722 schreyer.lib sing_1006.htm#SEC1082 schreyer_lib sing_1006.htm#SEC1082 schubert.lib sing_2508.htm#SEC2584 schubert_lib sing_2508.htm#SEC2584 sdb, source code debugger Source code debugger sing_66.htm#SEC103 second degree sing_919.htm#IDX471 secondary fan sing_2052.htm#IDX789 secondary polytope sing_2052.htm#IDX790 secondaryFan sing_2060.htm#SEC2136 43205 secondaryPolytope sing_2059.htm#SEC2135 48451 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1650.htm#SEC1726 37058 secondary_char0 sing_1645.htm#SEC1721 31029 secondary_charp sing_1647.htm#SEC1723 16364 secondary_no_molien sing_1648.htm#SEC1724 3616 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1651.htm#SEC1727 31675 segre sing_2236.htm#SEC2312 44035 select sing_1123.htm#SEC1199 17096 select1 sing_1124.htm#SEC1200 32617 semaphore sing_350.htm#IDX247 44342 semaphore sing_977.htm#SEC1053 semaphores sing_973.htm#IDX484 semiCMcod2 sing_1606.htm#SEC1682 15905 semiGroup sing_2301.htm#SEC2377 sprintf semiMod sing_2302.htm#SEC2378 sprintf semidiv sing_1934.htm#SEC2010 58107 semigroup sing_1455.htm#SEC1531 29045 semigroup sing_1459.htm#IDX624 semigroup of values sing_1545.htm#IDX739 semigroupGenerator sing_2031.htm#SEC2107 59446 sep sing_1292.htm#SEC1368 sprintf separateHNE sing_1556.htm#SEC1632 12052 separator sing_1192.htm#SEC1268 33000 serreRelations sing_638.htm#SEC690 33994 set sing_2158.htm#IDX801 setBaseMultigrading sing_2438.htm#SEC2514 6575 setLetterplaceAttributes setLetterplaceAttributes sing_629.htm#SEC681 5759 setLinearForms sing_2032.htm#SEC2108 62731 setModuleGrading sing_2450.htm#SEC2526 59018 setMultiplicity sing_2033.htm#SEC2109 27537 setNmzDataPath sing_1259.htm#SEC1335 18123 setNmzExecPath sing_1255.htm#SEC1331 38993 setNmzFilename sing_1258.htm#SEC1334 20206 setNmzOption sing_1252.htm#SEC1328 9012 setUniformizingParameter setUniformizingParameter sing_2548.htm#SEC2624 63635 set_is_injective sing_1922.htm#SEC1998 8429 setcores sing_975.htm#SEC1051 49704 setenv sing_350.htm#IDX250 setglobalrings sing_901.htm#SEC977 33379 setinitials sing_2361.htm#SEC2437 24792 setring sing_336.htm#SEC376 sh sing_350.htm#IDX252 shared sing_194.htm#SEC234 shared declarations sing_197.htm#SEC237 shared expressions sing_198.htm#SEC238 shared operations reference and shared operations sing_199.htm#SEC239 shared related functions reference and shared related functions sing_200.htm#SEC240 sheaf cohomology sing_1432.htm#IDX605 sheafCoh sing_1438.htm#SEC1514 64501 sheafCohBGG sing_1436.htm#SEC1512 13439 sheafCohBGG2 sing_1437.htm#SEC1513 3338 sheafcoh.lib sing_1432.htm#SEC1508 sheafcoh_lib sing_1432.htm#SEC1508 shiftPoly sing_631.htm#SEC683 65223 short sing_393.htm#SEC433 show sing_926.htm#SEC1002 15599 showBO sing_1414.htm#SEC1490 20089 showDataTypes sing_1416.htm#SEC1492 4270 showNmzOptions sing_1253.htm#SEC1329 64955 showNuminvs sing_1250.htm#SEC1326 18934 showgrades sing_743.htm#SEC795 48081 showrecursive sing_927.htm#SEC1003 6127 sickle sing_616.htm#SEC668 17166 signal handler sing_2564.htm#SEC2654 signatureBrieskorn sing_1615.htm#SEC1691 26283 signatureL sing_2206.htm#SEC2282 65493 signatureLqf sing_2207.htm#SEC2283 18811 signatureNemethi sing_1617.htm#SEC1693 21981 signaturePuiseux sing_1616.htm#SEC1692 23398 signcnd sing_1743.htm#SEC1819 40147 signcond.lib sing_1742.htm#SEC1818 signcond_lib sing_1742.htm#SEC1818 simplesolver sing_1687.htm#SEC1763 13418 simplex sing_337.htm#SEC377 simplexOut sing_1714.htm#SEC1790 56099 simplify sing_338.htm#SEC378 simplifyRat sing_780.htm#SEC832 52658 sing.lib sing_1582.htm#SEC1658 sing4ti2.lib sing_1318.htm#SEC1394 sing4ti2_lib sing_1318.htm#SEC1394 sing_lib sing_1582.htm#SEC1658 singular locus of D-module sing_760.htm#IDX379 singularities sing_1514.htm#IDX641 singularities sing_1515.htm#IDX652 singularities sing_1516.htm#IDX655 singularities sing_1517.htm#IDX658 singularities sing_1518.htm#IDX661 singularities sing_1519.htm#IDX665 singularities sing_1520.htm#IDX669 singularities sing_1521.htm#IDX675 singularities sing_1522.htm#IDX683 singularities sing_1523.htm#IDX689 singularities sing_1524.htm#IDX697 singularities sing_1525.htm#IDX707 singularities sing_1613.htm#IDX754 singularities, resolution of Resolution of singularities sing_823.htm#SEC875 singularity sing_1479.htm#SEC1555 23002 singularrc sing_20.htm#IDX73 size Miscellaneous oddities sing_339.htm#SEC379 size sing_410.htm#IDX292 skewmat sing_1040.htm#SEC1116 2167 sleep sing_345.htm#SEC385 slimgb sing_340.htm#SEC380 slimgb sing_800.htm#SEC852 slimgb (plural) sing_471.htm#SEC511 slocus sing_1594.htm#SEC1670 27853 smith sing_1827.htm#SEC1903 61915 smithNormalForm sing_2486.htm#SEC2562 7174 solutionsMod2 sing_1877.htm#SEC1953 53360 solve sing_919.htm#IDX472 3078 solve sing_1708.htm#SEC1784 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_283.htm#SEC323 solve.lib sing_1706.htm#SEC1782 solveTInitialFormPar solveTInitialFormPar sing_2141.htm#SEC2217 36670 solve_IP sing_1167.htm#SEC1243 59518 solve_lib sing_1706.htm#SEC1782 solvelinearpart sing_1701.htm#SEC1777 42872 sort sing_893.htm#SEC969 58207 sortIntvec sing_587.htm#SEC639 60798 sortandmap sing_1702.htm#SEC1778 10314 sortier sing_1664.htm#SEC1740 3555 sortvars sing_1703.htm#SEC1779 61778 sortvec sing_341.htm#SEC381 source code debugger, sdb Source code debugger sing_66.htm#SEC103 spaceCur sing_2304.htm#SEC2380 sprintf spadd sing_1528.htm#SEC1604 48739 span sing_2034.htm#SEC2110 64343 sparseHomogIdeal sing_969.htm#SEC1045 22631 sparseInterpolation sing_2346.htm#SEC2422 28771 sparseid sing_964.htm#SEC1040 20824 sparsemat sing_966.htm#SEC1042 17653 sparsematrix sing_965.htm#SEC1041 41031 sparsepoly sing_967.htm#SEC1043 21649 sparsetriag sing_968.htm#SEC1044 50657 spcurve.lib sing_1602.htm#SEC1678 spcurve_lib sing_1602.htm#SEC1678 special characters, non-english sing_399.htm#IDX285 spectral pairs sing_1514.htm#IDX650 spectral pairs sing_1521.htm#IDX682 spectral pairs sing_1523.htm#IDX696 spectral pairs sing_1524.htm#IDX705 spectral pairs sing_1536.htm#IDX721 spectral pairs sing_1538.htm#IDX732 spectralNeg sing_1424.htm#SEC1500 36691 spectrum sing_1514.htm#IDX649 47545 spectrum sing_1520.htm#SEC1596 spectrum sing_1520.htm#IDX674 spectrum sing_1521.htm#IDX681 spectrum sing_1522.htm#IDX688 spectrum sing_1523.htm#IDX695 spectrum sing_1524.htm#IDX704 spectrum sing_1536.htm#IDX720 spectrum sing_1538.htm#IDX731 spectrum sing_1613.htm#IDX756 spectrum.lib sing_1612.htm#SEC1688 spectrum_lib sing_1612.htm#SEC1688 spectrumnd sing_1613.htm#SEC1689 29943 spgamma sing_1535.htm#SEC1611 59653 spgeomgenus sing_1534.htm#SEC1610 57796 spissemicont sing_1531.htm#SEC1607 23679 split sing_928.htm#SEC1004 29794 splitPolygon sing_2062.htm#SEC2138 706 splitring sing_1304.htm#SEC1380 56404 splitting sing_1200.htm#SEC1276 34734 spmilnor sing_1533.htm#SEC1609 32933 spmul sing_1530.htm#SEC1606 43607 spnf sing_1083.htm#SEC1159 57309 spoly sing_1945.htm#SEC2021 35454 sppairs sing_1521.htm#SEC1597 49513 sppnf sing_1526.htm#SEC1602 16650 sppprint sing_1527.htm#SEC1603 43682 spprint sing_1084.htm#SEC1160 18671 sprintf sing_343.htm#SEC383 55889 spsemicont sing_1532.htm#SEC1608 61169 spsub sing_1529.htm#SEC1605 54296 sqfrNorm sing_1731.htm#SEC1807 20546 sqfrNormMain sing_1739.htm#SEC1815 9890 sqr sing_1857.htm#SEC1933 sprintf sqrfree sing_342.htm#SEC382 squareRoot sing_1876.htm#SEC1952 17446 squarefree sing_1557.htm#SEC1633 48485 sres sing_344.htm#SEC384 ssi Parallelization with ssi links sing_795.htm#SEC847 stack, moduli space of stable maps sing_2532.htm#IDX989 stack, moduli space of stable maps, rational curves moduliSpace sing_2531.htm#IDX988 staircase sing_1748.htm#SEC1824 49781 standard sing_1952.htm#SEC2028 14067 standard bases. sing_2203.htm#IDX883 standard bases. sing_2204.htm#IDX884 standard.lib sing_871.htm#IDX417 standard_lib sing_871.htm#IDX418 startNmz sing_1261.htm#SEC1337 21925 startTasks sing_1020.htm#SEC1096 16715 static procedures Procedure definition sing_43.htm#SEC78 status sing_345.htm#SEC385 std sing_346.htm#SEC386 std sing_798.htm#SEC850 std (plural) sing_472.htm#SEC512 stdfglm sing_347.htm#SEC387 256 stdhilb sing_348.htm#SEC388 63138 stopTask sing_1021.htm#SEC1097 6801 stratify sing_1682.htm#SEC1758 56744 stratify.lib sing_1680.htm#SEC1756 stratify_lib sing_1680.htm#SEC1756 string Miscellaneous oddities sing_166.htm#SEC206 string sing_410.htm#IDX295 string sing_916.htm#IDX462 string declarations sing_167.htm#SEC207 string expressions sing_168.htm#SEC208 string operations sing_170.htm#SEC210 string related functions string related functions sing_171.htm#SEC211 string type cast sing_169.htm#SEC209 stripHNE sing_1554.htm#SEC1630 19265 sturm sing_1985.htm#SEC2061 54353 sturmha sing_1987.htm#SEC2063 12467 sturmhaseq sing_1988.htm#SEC2064 59133 sturmquery sing_1963.htm#SEC2039 10805 sturmseq sing_1986.htm#SEC2062 23005 submat sing_1041.htm#SEC1117 37665 subrInterred sing_957.htm#SEC1033 10165 subset_sum01 sing_1906.htm#SEC1982 60620 subset_sum02 sing_1907.htm#SEC1983 37340 subst sing_349.htm#SEC389 subst (plural) sing_473.htm#SEC513 substitute sing_956.htm#SEC1032 28919 sugarCrit, option sing_307.htm#IDX169 sum sing_894.htm#SEC970 555 sum_of_powers sing_2240.htm#SEC2316 12170 sumlist sing_1396.htm#SEC1472 59918 sumofquotients sing_2540.htm#SEC2616 4569 super-commutative algebras Graded commutative algebras (SCA) sing_482.htm#SEC534 superCommutative sing_714.htm#SEC766 45528 super_increasing_knapsack super_increasing_knapsack sing_1918.htm#SEC1994 9177 surf.lib sing_1765.htm#SEC1841 surf_lib sing_1765.htm#SEC1841 surfacesignature.lib surfacesignature_lib sing_1614.htm#SEC1690 surfacesignature_lib surfacesignature_lib sing_1614.htm#SEC1690 surfer sing_1.htm#IDX8 14287 surfer sing_1767.htm#SEC1843 surfex sing_1.htm#IDX7 surfex.lib sing_1768.htm#SEC1844 surfex_lib sing_1768.htm#SEC1844 suspend sing_345.htm#SEC385 swalk sing_2501.htm#SEC2577 16794 swalk.lib sing_2500.htm#SEC2576 swalk_lib sing_2500.htm#SEC2576 swap sing_1483.htm#SEC1559 15408 swap sing_2165.htm#IDX819 switch No case or switch statement sing_404.htm#SEC444 switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2553.htm#SEC2629 1827 syModStd sing_1328.htm#SEC1404 50246 symNsym sing_2234.htm#SEC2310 55230 sym_gauss sing_1067.htm#SEC1143 5121 symm sing_2233.htm#SEC2309 64628 symmStd sing_1327.htm#SEC1403 39353 symmat sing_1042.htm#SEC1118 61294 symmetric basis sing_1059.htm#IDX498 symmetric power sing_1061.htm#IDX500 symmetricBasis sing_1059.htm#SEC1135 sprintf symmetricPower sing_1061.htm#SEC1137 6542 symmetricPowerSheaf sing_2526.htm#SEC2602 56922 symmfunc sing_1972.htm#SEC2048 45575 symodstd.lib sing_1322.htm#SEC1398 symodstd_lib sing_1322.htm#SEC1398 symsignature sing_1962.htm#SEC2038 10520 syndrome sing_1795.htm#SEC1871 14057 sysBin sing_1793.htm#SEC1869 41948 sysCRHT sing_1790.htm#SEC1866 58930 sysCRHTMindist sing_1791.htm#SEC1867 13692 sysFL sing_1806.htm#SEC1882 53040 sysNewton sing_1792.htm#SEC1868 19704 sysQE sing_1796.htm#SEC1872 61026 sys_code sing_1787.htm#SEC1863 20220 system sing_350.htm#SEC390 system, -- sing_350.htm#IDX275 system, --long_option_name sing_350.htm#IDX278 system, --long_option_name=value sing_350.htm#IDX280 system, HC sing_350.htm#IDX215 system, LLL sing_350.htm#IDX219 system, Singular sing_350.htm#IDX256 system, SingularLib sing_350.htm#IDX258 system, absFact sing_350.htm#IDX190 system, alarm sing_350.htm#IDX189 system, blackbox sing_350.htm#IDX191 system, bracket sing_350.htm#IDX196 system, browsers sing_350.htm#IDX195 system, btest sing_350.htm#IDX198 system, complexNearZero sing_350.htm#IDX199 system, contributors sing_350.htm#IDX201 system, cpu sing_350.htm#IDX203 system, cpu sing_350.htm#IDX274 system, denom_list sing_350.htm#IDX205 system, eigenvals sing_350.htm#IDX206 system, env sing_350.htm#IDX207 system, executable sing_350.htm#IDX209 system, freegb sing_350.htm#IDX210 system, getPrecDigits sing_350.htm#IDX213 system, getenv sing_350.htm#IDX212 system, gmsnf sing_350.htm#IDX214 system, hessenberg sing_350.htm#IDX216 system, install sing_350.htm#IDX218 system, nblocks sing_350.htm#IDX222 system, nc_hilb sing_350.htm#IDX224 system, neworder sing_350.htm#IDX225 system, newstruct sing_350.htm#IDX226 system, opp sing_350.htm#IDX227 system, oppose sing_350.htm#IDX230 system, pcvBasis sing_350.htm#IDX239 system, pcvCV2P sing_350.htm#IDX237 system, pcvDim sing_350.htm#IDX238 system, pcvLAddL sing_350.htm#IDX233 system, pcvMinDeg sing_350.htm#IDX235 system, pcvP2CV sing_350.htm#IDX236 system, pcvPMulL sing_350.htm#IDX234 system, pid sing_350.htm#IDX241 system, random sing_350.htm#IDX243 system, reserve sing_350.htm#IDX245 system, reservedLink sing_350.htm#IDX246 system, semaphore sing_350.htm#IDX248 system, semic sing_350.htm#IDX249 system, setenv sing_350.htm#IDX251 system, sh sing_350.htm#IDX253 system, shrinktest sing_350.htm#IDX254 system, spadd sing_350.htm#IDX259 system, spectrum sing_350.htm#IDX260 system, spmul sing_350.htm#IDX261 system, std_syz sing_350.htm#IDX262 system, stest sing_350.htm#IDX263 system, tensorModuleMult sing_350.htm#IDX264 system, twostd sing_350.htm#IDX265 system, uname sing_350.htm#IDX268 system, version sing_350.htm#IDX271 system, with sing_350.htm#IDX272 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2382.htm#SEC2458 63094 syz sing_351.htm#SEC391 syz (plural) sing_474.htm#SEC514 syzygy sing_1006.htm#IDX494 tDetropicalise sing_2143.htm#SEC2219 23532 tInitialForm sing_2127.htm#SEC2203 24484 tInitialFormPar sing_2139.htm#SEC2215 9584 tInitialFormParMax sing_2140.htm#SEC2216 7829 tInitialIdeal sing_2128.htm#SEC2204 17937 tab sing_929.htm#SEC1005 60407 tail sing_1941.htm#SEC2017 13066 tame polynomial sing_1536.htm#IDX713 tame polynomial sing_1537.htm#IDX723 tame polynomial sing_1538.htm#IDX724 tangentGens sing_1352.htm#SEC1428 37797 tangentcone sing_1601.htm#SEC1677 20056 task sing_1014.htm#IDX497 tasks.lib sing_1014.htm#SEC1090 tasks_lib sing_1014.htm#SEC1090 tau_es sing_1509.htm#SEC1585 17043 tau_es2 sing_1463.htm#SEC1539 38083 tdCf sing_2269.htm#SEC2345 21522 tdFactor sing_2271.htm#SEC2347 37910 tdProj sing_2274.htm#SEC2350 38406 tdTerms sing_2270.htm#SEC2346 30166 teachstd.lib sing_1939.htm#SEC2015 teachstd_lib sing_1939.htm#SEC2015 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_490.htm#IDX309 65451 tensor sing_1043.htm#SEC1119 tensorMod sing_1162.htm#SEC1238 21961 tensorSheaf sing_2525.htm#SEC2601 24072 term orderings General definitions for orderings sing_837.htm#SEC889 term orderings introduction Introduction to orderings sing_836.htm#SEC888 testNCfac sing_688.htm#SEC740 60394 testParametrization sing_1367.htm#SEC1443 18686 testPointConic sing_1368.htm#SEC1444 25315 testPrimary sing_1280.htm#SEC1356 34254 testPrimaryE sing_1281.htm#SEC1357 20693 tex sing_1754.htm#SEC1830 12226 texDrawBasic sing_2134.htm#SEC2210 3635 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2136.htm#SEC2212 42021 texDrawTriangulation texDrawTriangulation sing_2137.htm#SEC2213 18865 texDrawTropical sing_2135.htm#SEC2211 58447 texMatrix sing_2133.htm#SEC2209 1334 texNumber sing_2131.htm#SEC2207 12628 texPolynomial sing_2132.htm#SEC2208 41136 texcoef sing_1835.htm#SEC1911 28189 texdemo sing_1755.htm#SEC1831 13008 texfactorize sing_1756.htm#SEC1832 6682 texmap sing_1757.htm#SEC1833 35265 texname sing_1758.htm#SEC1834 1008 texobj sing_1759.htm#SEC1835 2107 texpoly sing_1760.htm#SEC1836 64109 texproc sing_1761.htm#SEC1837 23626 texring sing_1762.htm#SEC1838 38275 the first alternative algorithm sing_1139.htm#IDX534 three_elements sing_1925.htm#SEC2001 513 timeFactorize sing_898.htm#SEC974 49531 timeStd sing_897.htm#SEC973 31506 timer sing_394.htm#SEC434 timer resolution, setting the sing_350.htm#IDX281 timestep sing_2364.htm#SEC2440 38225 tjurina sing_1597.htm#SEC1673 9100 tmatrix sing_1524.htm#SEC1600 57332 todd sing_2266.htm#SEC2342 25618 toddE sing_2267.htm#SEC2343 17823 toddPoly sing_2280.htm#SEC2356 65066 tolessvars sing_1700.htm#SEC1776 56590 topChernClass sing_2522.htm#SEC2598 17374 topological invariants sing_1451.htm#IDX615 topological invariants sing_1458.htm#IDX622 topological invariants sing_1459.htm#IDX626 topological invariants sing_1460.htm#IDX630 topological invariants sing_1461.htm#IDX634 toric ideals sing_851.htm#SEC908 toric ring sing_1239.htm#IDX565 toric.lib sing_1329.htm#SEC1405 toric_ideal sing_1330.htm#SEC1406 2041 toric_lib sing_1329.htm#SEC1405 toric_std sing_1331.htm#SEC1407 26141 torusInvariants sing_1245.htm#SEC1321 911 total divisors sing_490.htm#IDX306 total multiplicities sing_1451.htm#IDX618 totalChernClass sing_2520.htm#SEC2596 6153 totalSegreClass sing_2523.htm#SEC2599 3291 totalmultiplicities sing_1453.htm#SEC1529 58264 trace sing_352.htm#SEC392 tracemult sing_1966.htm#SEC2042 58303 transpose sing_353.htm#SEC393 trapezoid sing_2358.htm#SEC2434 61525 triMNewton sing_1726.htm#SEC1802 62822 triagmatrix sing_970.htm#SEC1046 17944 triang.lib sing_1719.htm#SEC1795 triangL sing_1720.htm#SEC1796 51847 triangL_solve sing_1717.htm#SEC1793 10101 triangLf_solve sing_1715.htm#SEC1791 49796 triangLfak sing_1721.htm#SEC1797 50093 triangM sing_1722.htm#SEC1798 59334 triangMH sing_1723.htm#SEC1799 34277 triangM_solve sing_1716.htm#SEC1792 63652 triang_lib sing_1719.htm#SEC1795 triang_solve sing_1718.htm#SEC1794 64404 triangulations sing_2058.htm#SEC2134 61888 tropical curves sing_2113.htm#IDX796 tropical geometry sing_1125.htm#IDX508 tropical geometry sing_2547.htm#IDX998 tropical mirror symmetry sing_1125.htm#IDX510 tropical polynomials sing_2113.htm#IDX797 tropical varieties sing_2547.htm#IDX999 tropical.lib sing_2113.htm#IDX794 tropicalCurve sing_2118.htm#SEC2194 16865 tropicalJInvariant sing_2121.htm#SEC2197 40395 tropicalLifting sing_2114.htm#SEC2190 7052 tropicalLinkNewton sing_2555.htm#SEC2631 63886 tropicalNewton.lib sing_2547.htm#SEC2623 tropicalNewton_lib sing_2547.htm#SEC2623 tropicalPointNewton sing_2552.htm#SEC2628 18572 tropicalSubst sing_2146.htm#SEC2222 49846 tropicalVariety sing_2153.htm#SEC2229 39087 tropicalVarietyNewton tropicalVarietyNewton sing_2554.htm#SEC2630 28532 tropical_lib sing_2113.htm#IDX795 tropicalise sing_2125.htm#SEC2201 49739 tropicaliseSet sing_2126.htm#SEC2202 35136 truncate sing_1433.htm#SEC1509 13545 truncateFast sing_1434.htm#SEC1510 5124 truncated module sing_1433.htm#IDX606 truncated module sing_1434.htm#IDX607 tst_ncfactor sing_696.htm#SEC748 3339 twalk sing_1138.htm#SEC1214 35753 two-sided sing_490.htm#IDX307 two-sided Groebner basis sing_490.htm#IDX308 twostd sing_350.htm#IDX266 twostd sing_475.htm#SEC515 type sing_354.htm#SEC394 type B sing_2181.htm#IDX846 type D sing_2182.htm#IDX848 type,custom Definition of a user defined type sing_178.htm#SEC218 type2arr sing_2159.htm#SEC2235 62624 typecasting sing_2159.htm#IDX802 typecasting sing_2160.htm#IDX804 typecasting sing_2161.htm#IDX807 typeof sing_355.htm#SEC395 u sing_2350.htm#SEC2426 12154 uname sing_350.htm#IDX267 unbounded_knapsack sing_1908.htm#SEC1984 17226 unipotent groups sing_1351.htm#IDX574 uniquePoint sing_2035.htm#SEC2111 893 unitmat sing_1044.htm#SEC1120 12862 univariate sing_356.htm#SEC396 univarpoly sing_1973.htm#SEC2049 46288 unknown syndrome Decoding method based on quadratic equations sing_867.htm#SEC938 unset sing_268.htm#SEC308 untyped definitions sing_83.htm#SEC123 untyped definitions sing_415.htm#SEC455 updatePairs sing_1951.htm#SEC2027 51144 ures_solve sing_1709.htm#SEC1785 32449 uressolve sing_357.htm#SEC397 usage, option sing_307.htm#IDX185 user interface, Emacs Emacs user interface sing_21.htm#SEC28 vStd sing_2309.htm#SEC2385 12321 val sing_2549.htm#SEC2625 62171 valvars sing_1704.htm#SEC1780 15723 vandermonde sing_358.htm#SEC398 vanishId sing_1805.htm#SEC1881 49148 var sing_359.htm#SEC399 varMat sing_2163.htm#SEC2239 51772 varNum sing_2164.htm#SEC2240 18485 variables sing_360.htm#SEC400 variables sing_2163.htm#IDX814 variables sing_2164.htm#IDX816 variables sing_2165.htm#IDX820 variables sing_2166.htm#IDX822 variablesSorted sing_528.htm#SEC580 13533 variablesStandard sing_527.htm#SEC579 56500 vars2pars sing_775.htm#SEC827 47343 varsigns sing_1978.htm#SEC2054 3471 varstr sing_361.htm#SEC401 vct2str sing_636.htm#SEC688 51983 vdim sing_362.htm#SEC402 vdim (plural) sing_476.htm#SEC516 vec2poly sing_510.htm#SEC562 27377 vector sing_172.htm#SEC212 vector declarations sing_173.htm#SEC213 vector expressions sing_174.htm#SEC214 vector operations sing_175.htm#SEC215 vector related functions vector related functions sing_176.htm#SEC216 verify sing_1969.htm#SEC2045 32271 versal sing_1504.htm#SEC1580 46247 version sing_350.htm#IDX270 vertexAdjacencyGraph vertexAdjacencyGraph sing_2106.htm#SEC2182 60102 vertexEdgeGraph sing_2107.htm#SEC2183 32816 vertices sing_2051.htm#SEC2127 11398 vfilt sing_1522.htm#SEC1598 9283 view sing_1825.htm#SEC1901 29284 visual sing_2108.htm#SEC2184 51434 visualize sing_2349.htm#SEC2425 6750 voice sing_397.htm#SEC437 vwfilt sing_1523.htm#SEC1599 8281 wUnit sing_1863.htm#SEC1939 27198 waitAllTasks sing_1023.htm#SEC1099 7087 waitTasks sing_1022.htm#SEC1098 52857 waitall sing_363.htm#SEC403 waitfirst sing_364.htm#SEC404 walk, groebner sing_1136.htm#IDX530 walk, groebner sing_2432.htm#IDX957 walk, groebner sing_2496.htm#IDX962 walk, groebner sing_2500.htm#IDX967 warkedPreimageStd sing_2384.htm#SEC2460 14759 warn, option sing_70.htm#SEC110 warn, option sing_307.htm#IDX151 watchdog sing_895.htm#SEC971 sprintf wedge sing_365.htm#SEC405 weierstr.lib sing_1954.htm#SEC2030 weierstrDiv sing_1955.htm#SEC2031 260 weierstrPrep sing_1956.htm#SEC2032 5752 weierstr_lib sing_1954.htm#SEC2030 weierstrassForm sing_2122.htm#SEC2198 60874 weight sing_366.htm#SEC406 weight filtration sing_1514.htm#IDX646 weight filtration sing_1521.htm#IDX680 weight filtration sing_1523.htm#IDX694 weight filtration sing_1524.htm#IDX702 weight filtration sing_1536.htm#IDX718 weight filtration sing_1538.htm#IDX729 weightKB sing_367.htm#SEC407 21753 weightM, option sing_307.htm#IDX170 weighted lexicographical ordering sing_838.htm#IDX397 weighted reverse lexicographical ordering Global orderings sing_838.htm#IDX395 weightedRing sing_707.htm#SEC759 33786 whichvariable sing_1977.htm#SEC2053 27122 while sing_384.htm#SEC424 withDim sing_204.htm#IDX145 withHilb sing_204.htm#IDX143 withMult sing_204.htm#IDX146 withRes sing_204.htm#IDX144 withSB sing_204.htm#IDX142 wp, global ordering sing_838.htm#IDX396 write sing_368.htm#SEC408 writeNmzData sing_1256.htm#SEC1332 38467 writeNmzPaths sing_1260.htm#SEC1336 sprintf ws, local ordering sing_839.htm#IDX407 wurzel sing_1845.htm#SEC1921 12755 xchange sing_1839.htm#SEC1915 40741 xdvi sing_1764.htm#SEC1840 16898 zdd sing_2210.htm#IDX895 zdd2poly sing_2227.htm#SEC2303 55047 zero-dimensional sing_1974.htm#IDX785 zeroMod sing_1196.htm#SEC1272 60609 zeroOpt sing_1205.htm#SEC1281 19260 zeroRadical sing_1107.htm#SEC1183 35598 zeroSet sing_1732.htm#SEC1808 60030 zerodec sing_1289.htm#SEC1365 30765 zeroset.lib sing_1727.htm#SEC1803 zeroset_lib sing_1727.htm#SEC1803 zetaDL sing_1426.htm#SEC1502 sprintf { sing_36.htm#IDX78 || sing_36.htm#IDX103 || sing_96.htm#SEC136 } sing_36.htm#IDX79 ~ sing_36.htm#IDX117 ~ sing_385.htm#SEC425