! sing_36.htm#IDX101 != sing_36.htm#IDX95 != sing_100.htm#SEC140 " sing_36.htm#IDX104 # sing_36.htm#IDX118 $ sing_36.htm#IDX119 % sing_36.htm#IDX91 % sing_81.htm#SEC121 % sing_98.htm#SEC138 % sing_110.htm#SEC150 % sing_147.htm#SEC187 % sing_155.htm#SEC195 && sing_36.htm#IDX102 && sing_101.htm#SEC141 ( sing_36.htm#IDX80 () sing_131.htm#IDX130 ) sing_36.htm#IDX81 * bigintmat operations sing_36.htm#IDX89 * sing_81.htm#SEC121 * sing_87.htm#SEC127 * sing_93.htm#SEC133 * sing_98.htm#SEC138 * sing_106.htm#SEC146 * sing_110.htm#SEC150 * sing_137.htm#SEC177 * sing_142.htm#SEC182 * sing_147.htm#SEC187 * sing_155.htm#SEC195 ** sing_36.htm#IDX93 + bigintmat operations sing_36.htm#IDX85 + sing_81.htm#SEC121 + sing_87.htm#SEC127 + sing_93.htm#SEC133 + sing_98.htm#SEC138 + sing_106.htm#SEC146 + sing_110.htm#SEC150 + sing_126.htm#SEC166 + sing_137.htm#SEC177 + sing_142.htm#SEC182 + sing_147.htm#SEC187 + sing_155.htm#SEC195 + sing_169.htm#SEC209 + sing_176.htm#SEC216 + sing_181.htm#SEC221 ++ sing_36.htm#IDX86 - bigintmat operations sing_36.htm#IDX87 - sing_81.htm#SEC121 - sing_87.htm#SEC127 - sing_98.htm#SEC138 - sing_106.htm#SEC146 - sing_110.htm#SEC150 - sing_137.htm#SEC177 - sing_147.htm#SEC187 - sing_155.htm#SEC195 - sing_181.htm#SEC221 -- sing_36.htm#IDX88 --MPhost sing_19.htm#IDX66 --MPport sing_19.htm#IDX65 --allow-net sing_19.htm#IDX39 --batch sing_19.htm#IDX64 --browser sing_19.htm#IDX43 --echo sing_19.htm#IDX35 --emacs sing_19.htm#IDX67 --emacs-dir sing_19.htm#IDX68 --emacs-load sing_19.htm#IDX69 --execute sing_19.htm#IDX56 --help sing_19.htm#IDX37 --min-time sing_19.htm#IDX61 --no-out sing_19.htm#IDX49 --no-rc sing_19.htm#IDX45 --no-shell sing_19.htm#IDX50 --no-stdlib sing_19.htm#IDX47 --no-tty sing_19.htm#IDX51 --no-warn sing_19.htm#IDX48 --quiet sing_19.htm#IDX53 --random sing_19.htm#IDX60 --sdb sing_19.htm#IDX32 --singular sing_19.htm#IDX70 --ticks-per-sec sing_19.htm#IDX62 --user-option sing_19.htm#IDX58 -> sing_159.htm#SEC199 -MPhost Command line options -MPport Command line options -allow-net Command line options -b Command line options sing_19.htm#IDX63 -batch Command line options -browser Command line options -c Command line options sing_19.htm#IDX55 -d Command line options sing_19.htm#IDX31 -e Command line options sing_19.htm#IDX34 -echo Command line options -emacs Command line options -emacs-dir Command line options -emacs-load Command line options -execute Command line options -h Command line options sing_19.htm#IDX36 -help Command line options -min-time Command line options -no-out Command line options -no-rc Command line options -no-shell Command line options -no-stdlib Command line options -no-tty Command line options -no-warn Command line options -q Command line options sing_19.htm#IDX52 -quiet Command line options -r Command line options sing_19.htm#IDX59 -random Command line options -sdb Command line options -singular Command line options -ticks-per-sec Command line options -u Command line options sing_19.htm#IDX57 -user-option Command line options -v Command line options sing_19.htm#IDX54 .. sing_36.htm#IDX113 .singularrc file sing_20.htm#IDX72 .singularrc file, no loading Command line options sing_19.htm#IDX46 / sing_36.htm#IDX90 / sing_76.htm#SEC116 / sing_110.htm#SEC150 / sing_137.htm#SEC177 / sing_147.htm#SEC187 / sing_155.htm#SEC195 / sing_181.htm#SEC221 // sing_36.htm#IDX107 // sing_36.htm#IDX109 // sing_36.htm#IDX110 : sing_36.htm#IDX114 : sing_110.htm#SEC150 :: sing_36.htm#IDX115 :: sing_149.htm#SEC189 ; sing_36.htm#IDX111 < sing_36.htm#IDX100 < sing_155.htm#SEC195 < sing_181.htm#SEC221 < sing_249.htm#SEC289 <= sing_36.htm#IDX99 <= sing_100.htm#SEC140 <= sing_147.htm#SEC187 <= sing_155.htm#SEC195 <= sing_176.htm#SEC216 <= sing_181.htm#SEC221 <> sing_36.htm#IDX96 <> sing_100.htm#SEC140 <> sing_137.htm#SEC177 <> sing_147.htm#SEC187 <> sing_155.htm#SEC195 <> sing_169.htm#SEC209 <> sing_176.htm#SEC216 <> sing_181.htm#SEC221 = sing_36.htm#IDX77 == sing_36.htm#IDX94 == sing_100.htm#SEC140 == sing_137.htm#SEC177 == sing_147.htm#SEC187 == sing_155.htm#SEC195 == sing_169.htm#SEC209 == sing_176.htm#SEC216 == sing_181.htm#SEC221 > sing_36.htm#IDX98 > sing_155.htm#SEC195 > sing_181.htm#SEC221 >= sing_36.htm#IDX97 >= sing_100.htm#SEC140 >= sing_147.htm#SEC187 >= sing_155.htm#SEC195 >= sing_176.htm#SEC216 >= sing_181.htm#SEC221 ? sing_36.htm#IDX106 ? sing_262.htm#IDX148 ADGT sing_1054.htm#SEC1135 AG codes sing_963.htm#SEC1020 AGcode_L sing_2159.htm#SEC2240 AGcode_Omega sing_2160.htm#SEC2241 ASCII sing_1014.htm#SEC1095 ASCII links sing_117.htm#SEC157 ASSUME sing_64.htm#SEC101 A_L sing_1789.htm#SEC1870 A_Z sing_1012.htm#SEC1093 A_Z_L sing_1013.htm#SEC1094 Access to elements of a user defined type Access to elements of a user defined type sing_186.htm#SEC226 Adj_div sing_2154.htm#SEC2235 Adjoint ideal sing_1618.htm#IDX719 Alexander polynomial sing_1751.htm#IDX767 Algebraic Geometry codes sing_2153.htm#IDX936 Algebraic dependence Algebraic dependence sing_942.htm#SEC999 Algebraic geometry sing_1504.htm#SEC1585 AltVarEnd sing_751.htm#SEC805 AltVarStart sing_750.htm#SEC804 Ann sing_1438.htm#SEC1519 Appel function sing_560.htm#IDX351 Appel hypergeometric function sing_560.htm#IDX352 Applications sing_961.htm#SEC1018 Arnol'd sing_1769.htm#IDX787 Arnold, classification. sing_1797.htm#IDX792 Arnold, classification. sing_1798.htm#IDX793 ArnoldAction sing_1904.htm#SEC1985 Assignments for user defined types Assignments for user defined types sing_188.htm#SEC228 AssocTanToEnv sing_1048.htm#SEC1129 Atkin sing_2242.htm#SEC2323 Authors sing_1.htm#IDX16 Automatic Deduction sing_1054.htm#IDX527 Automatic Demonstration sing_1054.htm#IDX528 BFBoundsBudur sing_597.htm#SEC651 BINresol sing_1631.htm#SEC1712 BSidealFromAnn sing_595.htm#SEC649 Background sing_3.htm#SEC5 Basic programming sing_917.htm#SEC974 Basic programming sing_917.htm#SEC974 BelongSemig sing_2372.htm#SEC2453 BerlekampMassey sing_1289.htm#SEC1370 Bern sing_1543.htm#SEC1624 Bernstein operator sing_537.htm#IDX333 Bernstein-Sato ideal sing_592.htm#IDX354 Bernstein-Sato polynomial sing_502.htm#IDX314 Bernstein-Sato polynomial sing_537.htm#IDX330 Bernstein-Sato polynomial sing_1845.htm#IDX804 Bernstein-Sato polynomial sing_1849.htm#IDX821 Bernstein-Sato polynomial for variety sing_600.htm#IDX362 BernsteinSatoIdeal sing_596.htm#SEC650 Betti sing_2810.htm#SEC2891 Betti number Syzygies and resolutions sing_979.htm#SEC1041 BettiNumsH sing_2734.htm#SEC2815 BettiNumsN sing_2742.htm#SEC2823 BettiNumsQp sing_2737.htm#SEC2818 BettiNumsS sing_2740.htm#SEC2821 Betty number sing_2731.htm#IDX1196 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_989.htm#SEC1051 Bimodules Bimodules and syzygies and lifts sing_818.htm#SEC872 Bisyzygy Bimodules and syzygies and lifts sing_818.htm#SEC872 BlowingUp sing_1824.htm#SEC1905 Blowupcenter sing_1634.htm#SEC1715 BorelCheck sing_1748.htm#SEC1829 Bott's formula sing_1693.htm#IDX735 Branches of space curve singularities Branches of space curve singularities sing_950.htm#SEC1007 Briancon-Maisonobe algorithm sing_537.htm#IDX339 Brieskorn lattice sing_1845.htm#IDX800 Brieskorn lattice sing_1846.htm#IDX811 Brieskorn lattice sing_1847.htm#IDX814 Brieskorn lattice sing_1848.htm#IDX817 Brieskorn lattice sing_1849.htm#IDX820 Brieskorn lattice sing_1850.htm#IDX824 Brieskorn lattice sing_1851.htm#IDX828 Brieskorn lattice sing_1852.htm#IDX834 Brieskorn lattice sing_1853.htm#IDX842 Brieskorn lattice sing_1854.htm#IDX848 Brieskorn lattice sing_1855.htm#IDX856 Brieskorn lattice sing_1856.htm#IDX866 Brieskorn lattice sing_1867.htm#IDX872 Brieskorn lattice sing_1869.htm#IDX883 Brieskorn lattice sing_1897.htm#IDX910 Brill-Noether algorithm sing_2153.htm#IDX937 BrillNoether sing_2156.htm#SEC2237 Buchberger algorithm for toric ideals Buchberger algorithm sing_990.htm#SEC1052 Budur-Mustata-Saito approach sing_600.htm#IDX366 Building Singular sing_2991.htm#SEC3088 C programming language Major differences to the C programming language sing_413.htm#SEC453 C, module ordering sing_971.htm#IDX463 CGS sing_1035.htm#IDX476 CGS, disjoint, reduced, comprehensive Groebner system buildtree sing_1106.htm#IDX553 CM_regularity sing_1735.htm#SEC1816 33865 CMtype sing_1941.htm#SEC2022 CRHT-ideal sing_996.htm#SEC1065 CSMA sing_1566.htm#SEC1647 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 Castelnuovo-Mumford regularity sing_1735.htm#IDX759 Category string sing_51.htm#SEC88 CenCharDec sing_645.htm#SEC699 Center sing_1673.htm#SEC1754 CenterBO sing_1680.htm#SEC1761 CentralQuot sing_643.htm#SEC697 CentralSaturation sing_644.htm#SEC698 Change of rings sing_9.htm#SEC15 Characteristic sets sing_980.htm#SEC1042 CharacteristicExponents CharacteristicExponents sing_1830.htm#SEC1911 ChernClass sing_1706.htm#SEC1787 ChernRootsDual sing_1522.htm#SEC1603 ChernRootsHom sing_1531.htm#SEC1612 ChernRootsProd sing_1524.htm#SEC1605 ChernRootsSum sing_1520.htm#SEC1601 ChernRootsSymm sing_1533.htm#SEC1614 ChernRootsWedge sing_1534.htm#SEC1615 Chevalley-Rosenlicht theorem sing_1612.htm#IDX704 Chevalley-Rosenlicht theorem sing_1613.htm#IDX707 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_1697.htm#IDX740 ChowRing sing_1697.htm#SEC1778 Classification of hypersurface singularities Classification of hypersurface singularities sing_951.htm#SEC1008 Classification of singularities sing_1914.htm#IDX911 Code Codes and the decoding problem sing_995.htm#SEC1058 Codes and the decoding problem Codes and the decoding problem sing_995.htm#SEC1057 Coding theory sing_2152.htm#SEC2233 Coefficient rings Notes for Singular users sing_2989.htm#SEC3081 Command line options Command line options sing_19.htm#SEC26 Commands Functions and system variables sing_207.htm#SEC247 Commands for user defined types Commands for user defined types sing_187.htm#SEC227 Commutative Algebra sing_930.htm#SEC987 Commutative algebra sing_1233.htm#SEC1314 CompDecomp sing_499.htm#SEC553 CompInt sing_2374.htm#SEC2455 CompleteHomog sing_1510.htm#SEC1591 ComplexValue sing_2726.htm#SEC2807 Comprehensive Groebner System sing_1035.htm#IDX479 Comprehensive Groebner Systems sing_1033.htm#SEC1114 Comprehensive Groebner Systems sing_1098.htm#SEC1179 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_926.htm#SEC983 ConsLevels sing_1055.htm#SEC1136 ContactMatrix sing_1832.htm#SEC1913 Conti-Traverso algorithm sing_985.htm#SEC1047 Contributors sing_1.htm#IDX15 Control structures sing_381.htm#SEC421 Control theory System and Control theory sing_2186.htm#SEC2267 Cooper philosophy sing_996.htm#SEC1063 Cornacchia sing_2232.htm#SEC2313 CornacchiaModified sing_2233.htm#SEC2314 Crep sing_1038.htm#SEC1119 Critical points sing_945.htm#SEC1002 CurveParam sing_1826.htm#SEC1907 CurveRes sing_1825.htm#SEC1906 Curves sing_1618.htm#IDX716 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 Cyclic code sing_2167.htm#IDX944 Cyclic roots sing_923.htm#SEC980 D-integration sing_560.htm#IDX348 D-localization sing_560.htm#IDX344 D-localization sing_668.htm#IDX383 D-module purityfiltration_lib sing_502.htm#IDX312 D-module sing_537.htm#IDX327 D-module sing_560.htm#IDX341 D-module sing_592.htm#IDX353 D-module sing_600.htm#IDX360 D-module sing_668.htm#IDX380 D-module sing_778.htm#IDX398 D-module structure sing_537.htm#IDX328 D-module structure sing_592.htm#IDX356 D-module structure sing_600.htm#IDX361 D-restriction sing_560.htm#IDX346 DBM links sing_122.htm#SEC162 DISPLAY environment variable The online help system sing_16.htm#IDX28 DLoc sing_563.htm#SEC617 DLoc0 sing_565.htm#SEC619 Data types sing_72.htm#SEC112 Data types (plural) sing_426.htm#IDX298 Debugging tools sing_63.htm#SEC100 Decker, Wolfram sing_1.htm#IDX17 Declaration of objects of a user defined type Declaration of objects of a user defined type sing_185.htm#SEC225 Decoding sing_2167.htm#IDX946 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_994.htm#SEC1056 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_999.htm#SEC1074 Definition of a user defined type Definition of a user defined type sing_184.htm#SEC224 Deformations sing_948.htm#SEC1005 Deformations, T1 and T2 sing_947.htm#SEC1004 Deg sing_2813.htm#SEC2894 Degree sing_2814.htm#SEC2895 DegreePure sing_1597.htm#SEC1678 Degrees sing_2815.htm#SEC2896 Delta sing_1681.htm#SEC1762 DeltaList sing_1682.htm#SEC1763 Demo mode sing_24.htm#SEC35 Depth sing_937.htm#SEC994 Determinacy sing_1917.htm#IDX915 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_988.htm#SEC1050 DifConsLCSets sing_1058.htm#SEC1139 Distributed computing sing_1069.htm#IDX544 Dlocalization sing_669.htm#SEC723 Documentation Tool sing_60.htm#SEC97 Dp, global ordering sing_969.htm#IDX446 Ds, local ordering sing_970.htm#IDX456 DsingularLocus sing_673.htm#SEC727 Dynamic loading sing_71.htm#SEC111 Dynamic modules sing_925.htm#SEC982 ECPP sing_2276.htm#SEC2357 ECoef sing_1640.htm#SEC1721 EOrdlist sing_1638.htm#SEC1719 ERROR sing_238.htm#SEC278 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 Edatalist sing_1637.htm#SEC1718 Edelman-Reiner sing_2605.htm#IDX1029 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 Editing input sing_18.htm#SEC25 Elimination sing_933.htm#SEC990 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_1642.htm#SEC1723 Enumerative geometry sing_1693.htm#IDX733 Equal sing_1596.htm#SEC1677 Eresol sing_1632.htm#SEC1713 EulerAff sing_1567.htm#SEC1648 EulerProj sing_1568.htm#SEC1649 Evaluation of logical expressions Evaluation of logical expressions sing_415.htm#SEC455 Examples sing_915.htm#SEC972 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 Examples of use of Letterplace Examples of use of Letterplace sing_800.htm#SEC854 Examples of use of Letterplace over Z Examples of use of Letterplace over Z sing_801.htm#SEC855 Exp for matrices sing_1614.htm#IDX708 Experimental libraries Experimental libraries sing_2649.htm#SEC2730 Ext sing_1306.htm#SEC1387 Ext, computation of sing_936.htm#SEC993 Ext_R sing_1305.htm#SEC1386 Exterior sing_737.htm#SEC791 Extra weight vector sing_974.htm#SEC1031 Factorization sing_938.htm#SEC995 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_1049.htm#SEC1130 Feynman graph sing_1274.htm#IDX599 Finite fields sing_932.htm#SEC989 First steps sing_6.htm#SEC12 Fitzgerald-Lax method Fitzgerald-Lax method sing_998.htm#SEC1071 Float sing_253.htm#SEC293 Flow control sing_40.htm#SEC70 Formal Checker sing_59.htm#SEC96 Formatting output sing_922.htm#SEC979 Free associative algebras Free associative algebras sing_815.htm#SEC869 Free resolution sing_934.htm#SEC991 Free resolution, graded Handling graded modules sing_935.htm#SEC992 FultonA sing_1565.htm#SEC1646 Functionality and release notes of Letterplace Functionality and release notes of Letterplace sing_802.htm#SEC856 Functions sing_208.htm#SEC248 Functions (letterplace) Functions (letterplace) sing_804.htm#SEC858 Future benefits of Singular 4 Notes for Singular users sing_2989.htm#SEC3086 G-algebra sing_490.htm#SEC530 G-algebra sing_490.htm#SEC532 G-algebra sing_661.htm#IDX368 G-algebra sing_662.htm#IDX375 G-algebra, setup sing_490.htm#SEC534 GBWeight sing_566.htm#SEC620 GBsolve sing_2034.htm#SEC2115 GIT-Fans sing_957.htm#SEC1014 GITcone sing_2441.htm#SEC2522 GITfan sing_2442.htm#SEC2523 GITfanFromOrbitCones GITfanFromOrbitCones sing_2443.htm#SEC2524 GITfanParallel sing_2444.htm#SEC2525 GITfanParallelSymmetric GITfanParallelSymmetric sing_2459.htm#SEC2540 GITfanSymmetric sing_2458.htm#SEC2539 GKExp sing_666.htm#SEC720 GKZfan sing_2445.htm#SEC2526 GKZsystem sing_641.htm#SEC695 GKdim sing_614.htm#SEC668 GMP sing_1.htm#IDX3 GMP sing_2993.htm#SEC3090 GND.lib sing_2750.htm#SEC2831 GND_lib sing_2750.htm#SEC2831 GTZmod sing_1359.htm#SEC1440 GTZopt sing_1366.htm#SEC1447 G_a -Invariants sing_954.htm#SEC1011 Gamma sing_1647.htm#SEC1728 Gauss-Manin connection Gauss-Manin connection sing_981.htm#SEC1043 Gauss-Manin connection sing_1897.htm#IDX909 Gauss-Manin connection sing_1950.htm#IDX919 Gauss-Manin system sing_1845.htm#IDX799 Gauss-Manin system sing_1846.htm#IDX810 Gauss-Manin system sing_1847.htm#IDX813 Gauss-Manin system sing_1848.htm#IDX816 Gauss-Manin system sing_1849.htm#IDX819 Gauss-Manin system sing_1850.htm#IDX823 Gauss-Manin system sing_1851.htm#IDX827 Gauss-Manin system sing_1852.htm#IDX833 Gauss-Manin system sing_1853.htm#IDX841 Gauss-Manin system sing_1854.htm#IDX847 Gauss-Manin system sing_1855.htm#IDX855 Gauss-Manin system sing_1856.htm#IDX865 Gauss-Manin system sing_1867.htm#IDX871 Gauss-Manin system sing_1869.htm#IDX882 Gelfand-Kirillov dimension sing_856.htm#IDX420 Gelfand-Kirillov dimension, G-Algebra sing_666.htm#IDX376 General command syntax General command syntax sing_35.htm#SEC59 General concepts sing_12.htm#SEC18 General purpose sing_1006.htm#SEC1087 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_492.htm#SEC544 Generalized Newton identities Generalized Newton identities sing_997.htm#SEC1068 Geometric Invariant Theory Geometric Invariant Theory sing_956.htm#SEC1013 Geometric Theorems sing_1054.htm#IDX529 Geometric genus sing_1618.htm#IDX720 German Umlaute sing_411.htm#IDX285 Getting started sing_5.htm#SEC11 Global orderings sing_969.htm#SEC1026 Goettsche's formula sing_2731.htm#IDX1197 GoettscheF sing_2732.htm#SEC2813 Graded commutative algebras Graded commutative algebras (SCA) sing_798.htm#SEC852 Grassmannian sing_1698.htm#SEC1779 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_1698.htm#IDX741 Greuel, Gert-Martin sing_1.htm#IDX18 Grob1Levels sing_1057.htm#SEC1138 Groebner Bases Computing Groebner and Standard Bases sing_926.htm#SEC983 Groebner bases for two-sided ideals in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_817.htm#SEC871 Groebner bases in G-algebras Groebner bases in G-algebras sing_491.htm#SEC535 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_817.htm#SEC871 Groebner bases, decodeGB sing_2167.htm#IDX948 Groebner bases, slim sing_929.htm#SEC986 Groebner basis conversion Groebner basis conversion sing_928.htm#SEC985 Groebner cover sing_1034.htm#IDX472 Groebner cover sing_1041.htm#IDX491 Groebner cover sing_1042.htm#IDX498 Groebner fan sing_2466.htm#IDX966 Groebner walk sing_1297.htm#IDX620 Groebner walk sing_1299.htm#IDX622 Groebner walk sing_2951.htm#IDX1254 Groebner walk sing_2952.htm#IDX1255 Groebner-Shirshov bases Groebner bases for two-sided ideals in free associative algebras sing_817.htm#SEC871 Groebner-Shirshov bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_817.htm#SEC871 Groebnerwalk sing_1293.htm#IDX616 Groebnerwalk sing_2847.htm#IDX1214 Groebnerwalk sing_2950.htm#IDX1253 Groebnerwalk sing_2970.htm#IDX1267 Gromov-Witten invariants sing_1274.htm#IDX596 Gromov-Witten invariants sing_1280.htm#IDX605 Gromov-Witten invariants sing_1281.htm#IDX609 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_1723.htm#IDX753 Gromov-Witten invariants, multiple covers sing_1722.htm#IDX752 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_1724.htm#IDX754 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_1725.htm#IDX755 Gromov-Witten invariants. sing_1693.htm#IDX736 Gweights sing_731.htm#SEC785 H2basis sing_1902.htm#SEC1983 HHnormalForm sing_1806.htm#SEC1887 Hamburger-Noether expansion sing_1751.htm#IDX763 Hamburger-Noether expansion sing_1870.htm#IDX891 Hamburger-Noether expansions sing_2154.htm#IDX938 Handling graded modules Handling graded modules sing_935.htm#SEC992 Hcode sing_1782.htm#SEC1863 Help string sing_45.htm#SEC82 Hensel sing_243.htm#SEC283 Hilbert function sing_359.htm#IDX188 Hilbert function sing_661.htm#IDX369 Hilbert function sing_662.htm#IDX373 Hilbert function sing_978.htm#SEC1037 Hilbert polynomial sing_661.htm#IDX371 Hilbert scheme sing_2731.htm#IDX1200 Hilbert series sing_661.htm#IDX370 Hilbert series sing_662.htm#IDX374 Hilbert series sing_821.htm#IDX411 Hilbert series sing_978.htm#SEC1037 Hilbert-driven GB algorithm Groebner basis conversion sing_928.htm#SEC985 HilbertClassPoly sing_2239.htm#SEC2320 HilbertSeries sing_2003.htm#SEC2084 HilbertWeights sing_2004.htm#SEC2085 Hom sing_1309.htm#SEC1390 HomJJ sing_1394.htm#SEC1475 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_987.htm#SEC1049 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_1280.htm#IDX608 Hurwitz numbers sing_1281.htm#IDX612 Hypersurface singularities, classification of Classification of hypersurface singularities sing_951.htm#SEC1008 I-regular function sing_1041.htm#IDX497 IN sing_283.htm#IDX149 Ideal membership sing_977.htm#IDX468 Identifiers, syntax of sing_37.htm#SEC65 ImageGroup sing_2006.htm#SEC2087 ImageVariety sing_2005.htm#SEC2086 Imap, option sing_318.htm#IDX175 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 Incl sing_1595.htm#SEC1676 Index sing_2999.htm#SEC3096 Info string sing_52.htm#SEC89 InterDiv sing_1663.htm#SEC1744 Interactive use sing_13.htm#SEC19 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 IntersectWithSub sing_646.htm#SEC700 Intersection theory sing_1693.htm#IDX732 IntersectionMatrix sing_1831.htm#SEC1912 Introduction sing_2.htm#SEC4 Invariant Theory sing_953.htm#SEC1010 Invariant theory sing_1955.htm#SEC2036 InvariantQ sing_2008.htm#SEC2089 InvariantRing sing_2007.htm#SEC2088 Invariants of a finite group Invariants of a finite group sing_955.htm#SEC1012 Invariants of plane curve singularities Invariants of plane curve singularities sing_949.htm#SEC1006 IsSCA sing_752.htm#SEC806 J-marked schemes sing_1742.htm#IDX761 J-marked schemes, Borel ideals sing_1747.htm#IDX762 JMBTest.lib sing_1742.htm#SEC1823 JMBTest_lib sing_1742.htm#SEC1823 JMSConst.lib sing_1747.htm#SEC1828 JMSConst_lib sing_1747.htm#SEC1828 JMarkedScheme sing_1749.htm#SEC1830 Jacobi sing_2249.htm#SEC2330 Jacobson form sing_2204.htm#IDX949 Jacobson normal form sing_2204.htm#IDX950 Janet basis sing_1483.htm#IDX669 Janet division, Janet basis sing_1482.htm#IDX668 JuReTopDim sing_1605.htm#SEC1686 JuReZeroDim sing_1606.htm#SEC1687 K-basis sing_821.htm#IDX409 K-dimension sing_821.htm#IDX410 KScoef sing_1895.htm#SEC1976 KSconvert sing_1893.htm#SEC1974 KSker sing_1892.htm#SEC1973 KSlinear sing_1894.htm#SEC1975 KSpencerKernel sing_1948.htm#SEC2029 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2769.htm#SEC2850 Ker sing_2819.htm#SEC2900 Kernel of module homomorphisms Kernel of module homomorphisms sing_941.htm#SEC998 KoszulHomology sing_1318.htm#SEC1399 Kronecker module sing_2731.htm#IDX1199 Kronecker product sing_363.htm#SEC403 L, ordering sing_975.htm#SEC1032 LETTERPLACE sing_799.htm#SEC853 LETTERPLACE libraries LETTERPLACE libraries sing_820.htm#SEC874 LIB sing_287.htm#SEC327 LIB commands sing_53.htm#SEC90 LIBs sing_1002.htm#SEC1083 LLL sing_361.htm#IDX218 LOT algorithm sing_537.htm#IDX340 LU-decomposition of a matrix of numbers sing_292.htm#SEC332 Laurent series sing_1278.htm#IDX604 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_959.htm#SEC1016 Left ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC538 Left normal form Groebner bases in G-algebras sing_491.htm#SEC537 Leinartas sing_2930.htm#IDX1245 LengthSym sing_795.htm#SEC849 LengthSymElement sing_794.htm#SEC848 Letterplace sing_799.htm#SEC853 Letterplace Groebner basis sing_821.htm#IDX408 Letterplace Groebner basis sing_856.htm#IDX418 Letterplace Groebner basis sing_863.htm#IDX427 Letterplace correspondence Letterplace correspondence sing_819.htm#SEC873 Letterplace libraries LETTERPLACE libraries sing_820.htm#SEC874 Letterplace ring sing_357.htm#SEC397 Levels sing_1056.htm#SEC1137 Lexicographic Groebner bases, computation of Groebner basis conversion sing_928.htm#SEC985 Libraries Writing procedures and libraries sing_48.htm#SEC85 Libraries sing_918.htm#SEC975 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 Library versioning Notes for Singular users sing_2989.htm#SEC3084 Lie sing_2706.htm#IDX1192 Lie algebra sing_1613.htm#IDX705 Lie bracket sing_460.htm#SEC500 Lie group sing_1616.htm#IDX710 Lie group sing_1617.htm#IDX713 Limitations sing_411.htm#SEC451 Linear algebra sing_1174.htm#SEC1255 Linear code sing_2167.htm#IDX945 LinearActionQ sing_2010.htm#SEC2091 LinearCombinationQ sing_2011.htm#SEC2092 LinearizeAction sing_2009.htm#SEC2090 Loading a library sing_62.htm#SEC99 Local orderings sing_970.htm#SEC1027 Log for matrices sing_1615.htm#IDX709 Long coefficients sing_920.htm#SEC977 M, ordering sing_972.htm#SEC1029 MVComplex sing_1571.htm#SEC1652 Macdonald's formula sing_2731.htm#IDX1198 MacdonaldF sing_2738.htm#SEC2819 Macintosh installation Macintosh installation instructions sing_2998.htm#SEC3095 Mathematical background Mathematical background sing_976.htm#SEC1033 Mathematical background (letterplace) Mathematical background (letterplace) sing_814.htm#SEC868 Mathematical background (plural) Mathematical background (plural) sing_489.htm#SEC529 Matrix orderings sing_972.htm#SEC1029 Max sing_1911.htm#SEC1992 Maximus sing_1744.htm#SEC1825 Maxord sing_1646.htm#SEC1727 MillerRabin sing_2259.htm#SEC2340 Milnor code sing_1769.htm#IDX789 Milnor number Milnor and Tjurina number sing_944.htm#SEC1001 Milnor number sing_1916.htm#IDX914 Min sing_1912.htm#SEC1993 MinMult sing_2373.htm#SEC2454 MinimalDecomposition MinimalDecomposition sing_2012.htm#SEC2093 Minimum distance sing_2167.htm#IDX947 Minimus sing_1743.htm#SEC1824 Miscellaneous libraries Miscellaneous libraries sing_2576.htm#SEC2657 ModEqn sing_1905.htm#SEC1986 Modular techniques sing_1069.htm#IDX541 Module orderings sing_971.htm#SEC1028 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 Monodromy sing_1897.htm#IDX907 Monomial orderings sing_966.htm#SEC1023 Monomial orderings on free algebras Monomial orderings on free algebras sing_816.htm#SEC870 Monomial orderings, Term orderings sing_31.htm#SEC44 Mori dream spaces sing_2650.htm#IDX1089 Morse lemma addnondegeneratevariables sing_1915.htm#IDX912 Morse lemma sing_1918.htm#IDX916 MultiplicitySequence MultiplicitySequence sing_1829.htm#SEC1910 NF sing_337.htm#SEC377 NF (letterplace) reduce (letterplace) sing_809.htm#SEC863 NF (plural) sing_481.htm#SEC521 NFMora sing_2325.htm#SEC2406 NPos sing_1384.htm#SEC1465 NPos_test sing_1382.htm#SEC1463 NSplaces sing_2155.htm#SEC2236 NTL sing_1.htm#IDX4 NakYoshF sing_2735.htm#SEC2816 Names sing_37.htm#SEC65 Names in procedures sing_46.htm#SEC83 Names, indexed sing_37.htm#SEC65 New orderings for modules Notes for Singular users sing_2989.htm#SEC3085 Newton non-degenerate sing_1884.htm#IDX905 Newton polygon sing_1883.htm#IDX904 Newton polygon sing_1884.htm#IDX906 Newton polygons sing_2567.htm#IDX971 Newton polytope sing_2466.htm#IDX965 Newton step sing_2092.htm#IDX933 Noether position sing_1384.htm#IDX638 NoetherPosition sing_1373.htm#SEC1454 Non-commutative algebra Non-commutative algebra sing_958.htm#SEC1015 Non-commutative algebra sing_993.htm#SEC1055 Non-commutative subsystem Non-commutative subsystem sing_424.htm#SEC464 Nonhyp sing_1635.htm#SEC1716 Normalization sing_940.htm#SEC997 Notes for Singular users Notes for Singular users sing_2989.htm#SEC3080 Notes for developers Notes for developers sing_2990.htm#SEC3087 NullCone sing_2013.htm#SEC2094 NumIrrDecom sing_1609.htm#SEC1690 NumLocalDim sing_1598.htm#SEC1679 NumPrimDecom sing_1611.htm#SEC1692 Oaku-Takayama algorithm sing_537.htm#IDX338 Objects sing_38.htm#SEC66 Orlik-Solomon sing_2606.htm#IDX1030 Output sing_2829.htm#IDX1212 Output sing_2905.htm#IDX1219 Output sing_2907.htm#IDX1220 Output sing_2908.htm#IDX1221 Output sing_2909.htm#IDX1222 Output sing_2910.htm#IDX1223 Output sing_2911.htm#IDX1224 Output sing_2912.htm#IDX1225 Output sing_2913.htm#IDX1226 Output sing_2914.htm#IDX1227 Output sing_2915.htm#IDX1228 Output sing_2916.htm#IDX1229 Output sing_2917.htm#IDX1230 Output sing_2918.htm#IDX1231 Output sing_2919.htm#IDX1232 Output sing_2920.htm#IDX1233 Output sing_2921.htm#IDX1234 Output sing_2922.htm#IDX1235 Output sing_2923.htm#IDX1236 Output sing_2924.htm#IDX1237 Output sing_2925.htm#IDX1238 Output sing_2926.htm#IDX1239 Output sing_2927.htm#IDX1240 Output sing_2928.htm#IDX1241 Output sing_2929.htm#IDX1242 Output, formatting of sing_922.htm#SEC979 PBW sing_516.htm#IDX326 PBW basis sing_490.htm#SEC531 PBW_eqDeg sing_534.htm#SEC588 PBW_maxDeg sing_535.htm#SEC589 PBW_maxMonom sing_536.htm#SEC590 PEsolve sing_2032.htm#SEC2113 PH_ais sing_2628.htm#SEC2709 PH_nais sing_2629.htm#SEC2710 PLURAL sing_425.htm#SEC465 PLURAL LIBs sing_494.htm#SEC548 PLURAL libraries sing_494.htm#SEC548 PPolyH sing_2733.htm#SEC2814 PPolyN sing_2741.htm#SEC2822 PPolyQp sing_2736.htm#SEC2817 PPolyS sing_2739.htm#SEC2820 ParToVar sing_2728.htm#SEC2809 Parallelization Parallelization with ssi links sing_924.htm#SEC981 Parallelization sing_1069.htm#IDX542 Parameter list sing_44.htm#SEC81 Parameters sing_921.htm#SEC978 Parametrization sing_1618.htm#IDX717 Parametrization, image. sing_1628.htm#IDX729 PartC sing_1561.htm#SEC1642 PartitionVar sing_2725.htm#SEC2806 Path names Notes for Singular users sing_2989.htm#SEC3083 PerfectPowerTest sing_2222.htm#SEC2303 Perturbation walk sing_1298.htm#IDX621 Pfister, Gerhard sing_1.htm#IDX19 Pipe links sing_121.htm#SEC161 PocklingtonLehmer sing_2261.htm#SEC2342 Poincare polynomial sing_2618.htm#IDX1054 Polar curves sing_946.htm#SEC1003 PollardRho sing_2262.htm#SEC2343 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2631.htm#IDX1070 PolyBoRi, Boolean Groebner Basis sing_2633.htm#IDX1071 PolyBoRi, Boolean Groebner Basis sing_2634.htm#IDX1072 PolyBoRi, Boolean Groebner Basis sing_2635.htm#IDX1073 PolyBoRi, Boolean Groebner Basis sing_2636.htm#IDX1074 PolyBoRi, Boolean Groebner Basis sing_2637.htm#IDX1075 PolyBoRi, Boolean Groebner Basis sing_2638.htm#IDX1076 PolyBoRi, Boolean Groebner Basis sing_2639.htm#IDX1077 PolyBoRi, Boolean Groebner Basis sing_2640.htm#IDX1078 PolyBoRi, Boolean Groebner Basis sing_2641.htm#IDX1079 PolyBoRi, Boolean Groebner Basis sing_2642.htm#IDX1080 PolyBoRi, Boolean Groebner Basis sing_2643.htm#IDX1081 PolyBoRi, Boolean Groebner Basis sing_2644.htm#IDX1082 PolyBoRi, Boolean Groebner Basis sing_2645.htm#IDX1083 PolyBoRi, Boolean Groebner Basis sing_2647.htm#IDX1085 PolyBoRi, zero-supressed decision diagram sing_2646.htm#IDX1084 Polybori, Boolean Groebner Basis sing_2648.htm#IDX1086 Polynomial data sing_964.htm#SEC1021 Pottier algorithm sing_986.htm#SEC1048 Preface sing_1.htm#SEC1 Prep sing_1039.htm#SEC1120 Primary decomposition Primary decomposition sing_939.htm#SEC996 PrimdecA sing_1355.htm#SEC1436 PrimdecB sing_1356.htm#SEC1437 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_918.htm#SEC975 Procedures in a library Procedures in a library sing_54.htm#SEC91 Product orderings sing_973.htm#SEC1030 Programming sing_916.htm#SEC973 Pseudo ordering L sing_975.htm#SEC1032 PtoCrep sing_1040.htm#SEC1121 Puiseux expansion sing_1751.htm#IDX764 Puiseux expansion sing_1870.htm#IDX892 Puiseux pairs Invariants of plane curve singularities sing_949.htm#SEC1006 Puiseux pairs sing_1876.htm#IDX897 QPoly, quotient ring. sing_2966.htm#IDX1262 QQ sing_28.htm#SEC39 QQ sing_75.htm#SEC115 Qso3Casimir sing_640.htm#SEC694 Quot-scheme sing_2731.htm#IDX1201 Quotient sing_2110.htm#SEC2191 QuotientEquations sing_1906.htm#SEC1987 Rational curves sing_1618.htm#IDX718 ReJunkUseHomo sing_1604.htm#SEC1685 Reduced Comprehensive Groebner Systems sing_1098.htm#SEC1179 ReesAlgebra sing_1477.htm#SEC1558 References sing_1001.htm#SEC1080 References (plural) sing_493.htm#SEC545 References and history of Letterplace References and history of Letterplace sing_803.htm#SEC857 Release Notes sing_2985.htm#SEC3066 Release Notes (letterplace) Release Notes (letterplace) sing_914.htm#SEC968 Res sing_2809.htm#SEC2890 ResTree sing_1664.htm#SEC1745 Resolution sing_11.htm#SEC17 Resolution of singularities Resolution of singularities sing_952.htm#SEC1009 Resolution, free sing_934.htm#SEC991 ReynoldsImage sing_2014.htm#SEC2095 ReynoldsOperator sing_2015.htm#SEC2096 RiemannRochBN sing_1506.htm#SEC1587 RiemannRochHess sing_1593.htm#SEC1674 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_960.htm#SEC1017 Right ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC539 Ring-dependent options Notes for Singular users sing_2989.htm#SEC3082 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_798.htm#SEC852 SDB breakpoint Source code debugger sing_66.htm#SEC106 SDB debugger Source code debugger sing_66.htm#SEC106 SDLoc sing_564.htm#SEC618 SINGULAR libraries sing_1002.htm#SEC1083 SINGULARHIST sing_18.htm#SEC25 SL sing_2018.htm#SEC2099 SLreynolds sing_2024.htm#SEC2105 SV-decoding algorithm sing_2162.htm#IDX941 SV-decoding algorithm, preprocessing sing_2161.htm#IDX940 SaitoBase sing_2979.htm#SEC3060 Sannfs sing_540.htm#SEC594 SannfsBFCT sing_549.htm#SEC603 SannfsVar sing_603.htm#SEC657 Sannfslog sing_541.htm#SEC595 Saturation sing_931.htm#SEC988 Sch@"onemann, Hans sing_1.htm#IDX20 Schoof sing_2273.htm#SEC2354 Schubert calculus sing_1693.htm#IDX734 SchubertClass sing_1730.htm#SEC1811 SchurCh sing_1558.htm#SEC1639 SchurS sing_1557.htm#SEC1638 SegreA sing_1564.htm#SEC1645 Semigroup sing_1813.htm#SEC1894 Serre relations sing_827.htm#IDX415 SetDeg sing_2812.htm#SEC2893 Setting up a G-algebra sing_490.htm#SEC534 ShanksMestre sing_2272.htm#SEC2353 SimplifyIdeal sing_2016.htm#SEC2097 Singular sing_361.htm#IDX255 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2987.htm#SEC3078 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_1602.htm#SEC1683 SingularLib sing_361.htm#IDX257 Singularities sing_1750.htm#SEC1831 Singularity Theory sing_943.htm#SEC1000 SingularityDBM.lib sing_1769.htm#SEC1850 SingularityDBM_lib sing_1769.htm#SEC1850 Skeletons for parallelization sing_1069.htm#IDX543 Smith form sing_2204.htm#IDX951 Smith normal form sing_2204.htm#IDX952 SolowayStrassen sing_2260.htm#SEC2341 Solving systems of polynomial equations Solving systems of polynomial equations sing_962.htm#SEC1019 Source sing_2801.htm#SEC2882 Source code debugger, invocation Command line options sing_19.htm#IDX33 Space curve singularities, branches of Branches of space curve singularities sing_950.htm#SEC1007 Special characters sing_36.htm#SEC64 Splitting lemma addnondegeneratevariables sing_1915.htm#IDX913 Splitting lemma sing_1918.htm#IDX917 Ssi file links sing_119.htm#SEC159 Ssi links sing_118.htm#SEC158 Ssi tcp links sing_120.htm#SEC160 StabEqn sing_1907.htm#SEC1988 StabEqnId sing_1908.htm#SEC1989 StabOrder sing_1909.htm#SEC1990 Standard Bases Computing Groebner and Standard Bases sing_926.htm#SEC983 Standard bases sing_977.htm#SEC1034 Stanely-Reisner ideals, Stanley-Reisner rings, deformations stanleyreisner_lib sing_2963.htm#IDX1259 StartOrderingV sing_1745.htm#SEC1826 Startup sequence sing_20.htm#SEC27 StringF sing_1896.htm#SEC1977 SymGroup sing_793.htm#SEC847 Symbolic-numerical solving Symbolic-numerical solving sing_962.htm#SEC1019 Symbolic-numerical solving sing_2029.htm#SEC2110 System and Control theory System and Control theory sing_2186.htm#SEC2267 System dependent limitations System dependent limitations sing_412.htm#SEC452 System variables sing_398.htm#SEC438 Syzygies and resolutions Syzygies and resolutions sing_979.htm#SEC1038 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_492.htm#SEC541 Syzygy bimodule Bimodules and syzygies and lifts sing_818.htm#SEC872 T1 sing_947.htm#SEC1004 T1 sing_2964.htm#SEC3045 T2 sing_947.htm#SEC1004 T2 sing_2965.htm#SEC3046 TRACE Tracing of procedures sing_65.htm#SEC102 TRACE sing_407.htm#SEC447 T_1 sing_1935.htm#SEC2016 T_12 sing_1937.htm#SEC2018 T_2 sing_1936.htm#SEC2017 Target sing_2800.htm#SEC2881 Teaching sing_2218.htm#SEC2299 Template for writing a library sing_55.htm#SEC92 TestGRRes sing_2768.htm#SEC2849 TestJMark sing_1746.htm#SEC1827 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 The Tran algorithm sing_1295.htm#IDX618 The fractal walk algorithm sing_1294.htm#IDX617 The fractal walk algorithm sing_2953.htm#IDX1256 The online help system The online help system sing_16.htm#SEC22 Tjurina sing_1933.htm#SEC2014 Tjurina number Milnor and Tjurina number sing_944.htm#SEC1001 Tjurina number sing_1399.htm#IDX653 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 Tor sing_1320.htm#SEC1401 Toric ideals and integer programming Toric ideals and integer programming sing_982.htm#SEC1044 Tricks and pitfalls sing_410.htm#SEC450 Tropical Geometry sing_2370.htm#SEC2451 Two-sided ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC540 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_1222.htm#SEC1303 Ufnarovski graph sing_856.htm#IDX423 Unix installation Unix installation instructions sing_2996.htm#SEC3093 UpOneMatrix sing_749.htm#SEC803 UpperMonomials sing_1910.htm#SEC1991 UseBertini sing_1601.htm#SEC1682 User defined types sing_183.htm#SEC223 V-filtration sing_1845.htm#IDX802 V-filtration sing_1851.htm#IDX830 V-filtration sing_1852.htm#IDX836 V-filtration sing_1853.htm#IDX844 V-filtration sing_1854.htm#IDX850 V-filtration sing_1855.htm#IDX858 V-filtration sing_1856.htm#IDX868 V-filtration sing_1867.htm#IDX874 V-filtration sing_1869.htm#IDX885 VarToPar sing_2727.htm#SEC2808 Variables, indexed sing_37.htm#SEC65 VecField.lib sing_2974.htm#SEC3055 VecField_lib sing_2974.htm#SEC3055 Version number Version schema for Singular sing_2988.htm#SEC3079 Version schema for Singular Version schema for Singular sing_2988.htm#SEC3079 Version string sing_50.htm#SEC87 Visualization sing_2124.htm#SEC2205 WLCGS sing_1052.htm#SEC1133 WLemma sing_1051.htm#SEC1132 WP, global ordering sing_969.htm#IDX450 WSemigroup sing_1827.htm#SEC1908 Weierstrass sing_2157.htm#SEC2238 Weierstrass semigroup sing_2153.htm#IDX935 Weyl sing_734.htm#SEC788 Weyl algebra sing_537.htm#IDX332 Weyl algebra sing_592.htm#IDX358 Weyl algebra sing_600.htm#IDX364 Weyl closure sing_668.htm#IDX386 WeylClosure sing_670.htm#SEC724 WeylClosure1 sing_671.htm#SEC725 Wibmer's Lemma sing_1051.htm#IDX526 Windows installation Windows installation instructions sing_2997.htm#SEC3094 WitSet sing_1608.htm#SEC1689 WitSupSet sing_1607.htm#SEC1688 Ws, local ordering sing_970.htm#IDX462 XLsolve sing_2035.htm#SEC2116 ZZ sing_28.htm#SEC39 ZZ sing_75.htm#SEC115 ZZ/m sing_28.htm#SEC39 ZZ/p sing_28.htm#SEC39 ZZsolve sing_2036.htm#SEC2117 [ sing_36.htm#IDX83 [] sing_142.htm#SEC182 [] sing_155.htm#SEC195 [] sing_176.htm#SEC216 [] sing_181.htm#SEC221 \ sing_36.htm#IDX112 ] sing_36.htm#IDX84 ^ sing_36.htm#IDX92 ^ sing_81.htm#SEC121 ^ sing_93.htm#SEC133 ^ sing_147.htm#SEC187 ^ sing_155.htm#SEC195 _ sing_36.htm#IDX116 ` sing_36.htm#IDX105 a, ordering sing_974.htm#SEC1031 absFactorize sing_1235.htm#SEC1316 absFactorizeBCG sing_1236.htm#SEC1317 absPrimdecGTZ sing_1457.htm#SEC1538 absPrimdecGTZE sing_1458.htm#SEC1539 absValue sing_1015.htm#SEC1096 absfact.lib sing_1234.htm#SEC1315 absfact_lib sing_1234.htm#SEC1315 absolute factorization. sing_1234.htm#IDX579 abstract variety, projective space, Grassmannian printVariety sing_1694.htm#IDX737 abstract variety, projective space, Grassmannian sing_1695.htm#IDX738 abstractR sing_1690.htm#SEC1771 actionIsProper sing_1996.htm#SEC2077 add sing_2675.htm#IDX1125 add sing_2697.htm#IDX1173 addElement sing_2962.htm#SEC3043 addLeftFractions sing_765.htm#SEC819 addModules sing_2821.htm#SEC2902 addNvarsTo sing_1158.htm#SEC1239 addRat sing_689.htm#SEC743 addSheaf sing_1713.htm#SEC1794 addcol sing_1191.htm#SEC1272 addcores sing_1127.htm#SEC1208 addnondegeneratevariables addnondegeneratevariables sing_1918.htm#SEC1999 addrow sing_1192.htm#SEC1273 addvarsTo sing_1157.htm#SEC1238 ademRelations sing_831.htm#SEC885 adjoint sing_1216.htm#SEC1297 adjointIdeal sing_1619.htm#SEC1700 adjunction divisor sing_2154.htm#IDX939 admissibleSub sing_725.htm#SEC779 afaces sing_2437.htm#SEC2518 affine code Fitzgerald-Lax method sing_998.htm#SEC1072 ainvar.lib sing_1993.htm#SEC2074 ainvar_lib sing_1993.htm#SEC2074 aksaka.lib sing_2219.htm#SEC2300 aksaka_lib sing_2219.htm#SEC2300 alexanderpolynomial sing_1754.htm#SEC1835 alexpoly.lib sing_1751.htm#SEC1832 alexpoly_lib sing_1751.htm#SEC1832 algDependent sing_1241.htm#SEC1322 alg_kernel sing_1242.htm#SEC1323 algebra.lib sing_1237.htm#SEC1318 algebra_containment sing_1238.htm#SEC1319 algebra_lib sing_1237.htm#SEC1318 algebraic dependence sing_776.htm#IDX394 algebraic field extension sing_1471.htm#IDX662 algebraic statistics sing_2787.htm#IDX1207 algebraicDependence sing_1489.htm#SEC1570 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_989.htm#SEC1051 algorithm of Conti and Traverso sing_985.htm#SEC1047 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_988.htm#SEC1050 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_987.htm#SEC1049 algorithm of Pottier sing_986.htm#SEC1048 alias General command syntax sing_35.htm#SEC59 align sing_209.htm#SEC249 all.lib sing_1007.htm#SEC1088 allDoubleExt sing_787.htm#SEC841 allExtOfLeft sing_784.htm#SEC838 allExtOfRight sing_785.htm#SEC839 allPositive sing_513.htm#SEC567 all_lib sing_1007.htm#SEC1088 allowing net access Command line options sing_19.htm#IDX41 allprint sing_1060.htm#SEC1141 allreal sing_2362.htm#SEC2443 allrealst sing_2360.htm#SEC2441 allsquarefree sing_1889.htm#SEC1970 ambientDimension sing_2379.htm#SEC2460 and Evaluation of logical expressions sing_101.htm#SEC141 and sing_415.htm#SEC455 annPoly sing_561.htm#SEC615 annRat sing_562.htm#SEC616 annRatSyz sing_678.htm#SEC732 annfalphaI sing_598.htm#SEC652 annfs sing_538.htm#SEC592 annfs0 sing_550.htm#SEC604 annfs2 sing_551.htm#SEC605 annfsBMI sing_547.htm#SEC601 annfsLogIdeal sing_593.htm#SEC647 annfsParamBM sing_546.htm#SEC600 annfsRB sing_552.htm#SEC606 annfspecial sing_539.htm#SEC593 annihilator of polynomial sing_560.htm#IDX342 annihilator of rational function sing_560.htm#IDX343 annihilator of rational function sing_668.htm#IDX389 annihilatorMultiFs sing_594.htm#SEC648 annil sing_1361.htm#SEC1442 appelF1 sing_579.htm#SEC633 appelF2 sing_580.htm#SEC634 appelF4 sing_581.htm#SEC635 appendWeight2Ord sing_727.htm#SEC781 application sing_2703.htm#IDX1188 apply sing_382.htm#SEC422 applyAdF sing_529.htm#SEC583 applyPermutationToIntvec applyPermutationToIntvec sing_2462.htm#SEC2543 applyVecField sing_2975.htm#SEC3056 arcpoint.lib sing_1764.htm#SEC1845 arcpoint_lib sing_1764.htm#SEC1845 areEqualLeftFractions areEqualLeftFractions sing_767.htm#SEC821 areZeroElements sing_2888.htm#SEC2969 argument, default sing_44.htm#SEC81 argument, optional sing_44.htm#SEC81 arnoldClassify sing_1773.htm#SEC1854 arnoldCorank sing_1774.htm#SEC1855 arnoldDeterminacy sing_1775.htm#SEC1856 arnoldListAllSeries sing_1770.htm#SEC1851 arnoldMilnorCode sing_1776.htm#SEC1857 arnoldMorseSplit sing_1777.htm#SEC1858 arnoldNormalForm sing_1772.htm#SEC1853 arnoldShowSeries sing_1771.htm#SEC1852 arnoldclassify.lib sing_1769.htm#SEC1850 arnoldclassify_lib sing_1769.htm#SEC1850 arr.lib sing_2577.htm#SEC2658 arr2multarr sing_2610.htm#SEC2691 arrBoolean sing_2599.htm#SEC2680 arrBoundedChambers sing_2620.htm#SEC2701 arrBraid sing_2600.htm#SEC2681 arrCenter sing_2587.htm#SEC2668 arrCentered sing_2589.htm#SEC2670 arrCentral sing_2588.htm#SEC2669 arrCentralize sing_2590.htm#SEC2671 arrChambers sing_2619.htm#SEC2700 arrCharPoly sing_2617.htm#SEC2698 arrCone sing_2593.htm#SEC2674 arrCoordChange sing_2591.htm#SEC2672 arrCoordNormalize sing_2592.htm#SEC2673 arrDecone sing_2594.htm#SEC2675 arrDer sing_2607.htm#SEC2688 arrEdelmanReiner sing_2605.htm#SEC2686 arrEssentialize sing_2598.htm#SEC2679 arrExponents sing_2609.htm#SEC2690 arrFlats sing_2614.htm#SEC2695 arrIsEssential sing_2597.htm#SEC2678 arrIsFree sing_2608.htm#SEC2689 arrLastVar sing_2586.htm#SEC2667 arrLattice sing_2615.htm#SEC2696 arrLocalize sing_2595.htm#SEC2676 arrOrlikSolomon sing_2606.htm#SEC2687 arrPoincare sing_2618.htm#SEC2699 arrPrintMatrix sing_2582.htm#SEC2663 arrRandom sing_2603.htm#SEC2684 arrRandomCentral sing_2604.htm#SEC2685 arrRestrict sing_2596.htm#SEC2677 arrSet sing_2578.htm#SEC2659 arrSwapVar sing_2585.htm#SEC2666 arrTypeB sing_2601.htm#SEC2682 arrTypeD sing_2602.htm#SEC2683 arr_lib sing_2577.htm#SEC2658 arrange sing_554.htm#SEC608 arrangement sing_2578.htm#IDX972 arrangement sing_2579.htm#IDX977 arrangement sing_2610.htm#IDX1039 arrangement sing_2611.htm#IDX1042 ask sing_2227.htm#SEC2308 assPrimes sing_1252.htm#SEC1333 assign sing_2578.htm#IDX974 assignment,custom Assignments for user defined types sing_188.htm#SEC228 associated tangent FamElemsAtEnvCompPoints sing_1048.htm#IDX519 associated tangent sing_1049.htm#IDX523 assprimeszerodim.lib assprimeszerodim_lib sing_1250.htm#SEC1331 assprimeszerodim_lib assprimeszerodim_lib sing_1250.htm#SEC1331 atkins.lib sing_2228.htm#SEC2309 atkins_lib sing_2228.htm#SEC2309 attrib sing_210.htm#SEC250 autGenWeights sing_2653.htm#SEC2734 autGradAlg sing_2652.htm#SEC2733 autKS sing_2651.htm#SEC2732 autX sing_2656.htm#SEC2737 autXhat sing_2655.htm#SEC2736 autgradalg.lib sing_2650.htm#SEC2731 autgradalg_lib sing_2650.htm#SEC2731 automorphism group sing_2650.htm#IDX1090 automorphisms sing_2650.htm#IDX1087 autonom sing_2191.htm#SEC2272 autonomDim sing_2192.htm#SEC2273 awalk1 sing_1296.htm#SEC1377 awalk2 sing_1297.htm#SEC1378 b-function sing_502.htm#IDX315 bFactor sing_584.htm#SEC638 babyGiant sing_2257.htm#SEC2338 backward sing_2714.htm#SEC2795 bareiss sing_211.htm#SEC251 base2str sing_1010.htm#SEC1091 basering sing_28.htm#IDX76 basering sing_88.htm#SEC128 basicinvariants sing_1779.htm#SEC1860 baumslagGroup sing_833.htm#SEC887 baumslagSolitar sing_832.htm#SEC886 belongSemigroup sing_1255.htm#SEC1336 bernstein sing_1849.htm#SEC1930 bernsteinBM sing_542.htm#SEC596 bernsteinLift sing_543.htm#SEC597 bertini sing_1594.htm#IDX691 bertini sing_1599.htm#IDX698 bertini sing_2074.htm#IDX930 bertini2Singular sing_1603.htm#SEC1684 betti sing_212.htm#SEC252 betti (plural) sing_459.htm#SEC499 bfct sing_503.htm#SEC557 bfctAnn sing_505.htm#SEC559 bfctBound sing_677.htm#SEC731 bfctIdeal sing_507.htm#SEC561 bfctOneGB sing_506.htm#SEC560 bfctSyz sing_504.htm#SEC558 bfctVarAnn sing_602.htm#SEC656 bfctVarIn sing_601.htm#SEC655 bfun.lib sing_502.htm#SEC556 bfun_lib sing_502.htm#SEC556 bigger sing_2682.htm#IDX1139 bigint sing_78.htm#SEC118 bigint declarations sing_79.htm#SEC119 bigint expressions sing_80.htm#SEC120 bigint operations sing_81.htm#SEC121 bigint related functions bigint related functions sing_82.htm#SEC122 bigintToBinary sing_2460.htm#SEC2541 bigintmat sing_83.htm#SEC123 bigintmat declarations bigintmat declarations sing_84.htm#SEC124 bigintmat expressions bigintmat expressions sing_85.htm#SEC125 bigintmat operations bigintmat operations sing_87.htm#SEC127 bigintmat type cast sing_86.htm#SEC126 bimodules sing_495.htm#IDX303 bimodules.lib sing_495.htm#SEC549 bimodules_lib sing_495.htm#SEC549 binaryToBigint sing_2461.htm#SEC2542 binary_add sing_2280.htm#SEC2361 binomial sing_1016.htm#SEC1097 binomials2intmat sing_1432.htm#SEC1513 58804 birational map, image, inverse. sing_1620.htm#IDX723 bistd sing_496.htm#SEC550 bisyzygies sing_495.htm#IDX304 bitrinity sing_497.htm#SEC551 blackbox sing_192.htm#SEC232 blackbox sing_200.htm#SEC240 block sing_40.htm#SEC70 block sing_381.htm#SEC421 blowUp sing_1671.htm#SEC1752 blowUp2 sing_1672.htm#SEC1753 blowUpBO sing_1678.htm#SEC1759 blowup0 sing_1265.htm#SEC1346 boolean sing_2599.htm#IDX1016 boolean expressions sing_100.htm#SEC140 boolean operations sing_101.htm#SEC141 boolean_constant sing_2633.htm#SEC2714 52873 boolean_ideal sing_2637.htm#SEC2718 53515 boolean_poly sing_2634.htm#SEC2715 41652 boolean_poly_ring sing_2632.htm#SEC2713 sprintf boolean_set sing_2638.htm#SEC2719 58235 boolean_std sing_2631.htm#SEC2712 5921 border basis sing_1479.htm#IDX664 borderBasis sing_1480.htm#SEC1561 boundBuFou sing_2357.htm#SEC2438 boundDes sing_2359.htm#SEC2440 boundaryLatticePoints boundaryLatticePoints sing_2481.htm#SEC2562 boundposDes sing_2358.htm#SEC2439 bounds sing_2093.htm#SEC2174 boxSet sing_2095.htm#SEC2176 bracket sing_361.htm#IDX197 bracket sing_418.htm#SEC458 bracket sing_460.htm#SEC500 braid sing_2600.htm#IDX1018 branchTo procs with different argument types sing_160.htm#SEC200 break sing_383.htm#SEC423 break point sing_397.htm#SEC437 breakpoint sing_384.htm#SEC424 brillnoether.lib sing_1505.htm#SEC1586 brillnoether_lib sing_1505.htm#SEC1586 brnoeth.lib sing_2153.htm#SEC2234 brnoeth_lib sing_2153.htm#SEC2234 browser, command line option Command line options sing_19.htm#IDX44 browser, setting the sing_361.htm#IDX193 browsers The online help system sing_16.htm#IDX21 browsers, setting the sing_361.htm#IDX192 bubblesort sing_2230.htm#SEC2311 buildtree sing_1106.htm#SEC1187 buildtree, Maple sing_1107.htm#IDX554 buildtree, buildtreetoMaple, CGS sing_1108.htm#IDX555 buildtreetoMaple sing_1107.htm#SEC1188 busadj sing_1214.htm#SEC1295 bvar sing_2645.htm#SEC2726 52773 c, module ordering sing_971.htm#IDX465 cProj sing_1547.htm#SEC1628 calculateI sing_1645.htm#SEC1726 calculate_max_sum sing_2299.htm#SEC2380 calculate_ordering sing_2277.htm#SEC2358 cancelunit, option sing_318.htm#IDX171 canonMap sing_1301.htm#SEC1382 canonical sing_1034.htm#IDX474 canonical form sing_1038.htm#IDX486 canonical form sing_1039.htm#IDX488 canonical form sing_1040.htm#IDX490 canonical form sing_1055.htm#IDX532 canonical form sing_1056.htm#IDX534 canonical form sing_1057.htm#IDX537 canonical form sing_1058.htm#IDX539 canonical, sing_1042.htm#IDX500 canonicalizeCone sing_2380.htm#SEC2461 canonize sing_2199.htm#SEC2280 cantodiffcgs sing_1112.htm#SEC1193 cantoradd sing_2313.htm#SEC2394 cantormult sing_2316.htm#SEC2397 cantorred sing_2314.htm#SEC2395 cardGroup sing_1257.htm#SEC1338 case No case or switch statement sing_416.htm#SEC456 catNets sing_2905.htm#SEC2986 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2571.htm#SEC2652 cdd sing_1.htm#IDX10 cddlib sing_1.htm#IDX11 center sing_516.htm#IDX322 center sing_522.htm#SEC576 center sing_2587.htm#IDX998 center sing_2588.htm#IDX999 center sing_2589.htm#IDX1001 center sing_2590.htm#IDX1003 centerRed sing_521.htm#SEC575 centerVS sing_520.htm#SEC574 central sing_2581.htm#IDX984 central sing_2588.htm#IDX1000 central sing_2590.htm#IDX1002 central sing_2604.htm#IDX1027 central.lib sing_516.htm#SEC570 central1st sing_2715.htm#SEC2796 central2nd sing_2716.htm#SEC2797 central_lib sing_516.htm#SEC570 centralize sing_516.htm#IDX325 centralizeSet sing_517.htm#SEC571 centralizer sing_516.htm#IDX323 centralizer sing_523.htm#SEC577 centralizerRed sing_519.htm#SEC573 centralizerVS sing_518.htm#SEC572 cf_class sing_210.htm#IDX132 cgs sing_1009.htm#SEC1090 cgsdr sing_1035.htm#SEC1116 chAll sing_1517.htm#SEC1598 chAllInv sing_1518.htm#SEC1599 chDual sing_1523.htm#SEC1604 chHE sing_1519.htm#SEC1600 chHom sing_1532.htm#SEC1613 chNum sing_1513.htm#SEC1594 chNumbers sing_1514.htm#SEC1595 chNumbersProj sing_1551.htm#SEC1632 chProd sing_1525.htm#SEC1606 chProdE sing_1526.htm#SEC1607 chProdL sing_1527.htm#SEC1608 chProdLP sing_1528.htm#SEC1609 chProdM sing_1529.htm#SEC1610 chProdMP sing_1530.htm#SEC1611 chProj sing_1548.htm#SEC1629 chSum sing_1521.htm#SEC1602 chSymm sing_1535.htm#SEC1616 chSymm2L sing_1536.htm#SEC1617 chSymm2LP sing_1537.htm#SEC1618 chWedge sing_1538.htm#SEC1619 chWedge2L sing_1539.htm#SEC1620 chWedge2LP sing_1540.htm#SEC1621 chaincrit sing_2327.htm#SEC2408 chambers sing_2619.htm#IDX1055 chambers sing_2620.htm#IDX1056 changeCoordinates sing_2976.htm#SEC3057 changeDenominator sing_1404.htm#SEC1485 changechar sing_1132.htm#SEC1213 changeord sing_1133.htm#SEC1214 changeordTo sing_1156.htm#SEC1237 changes sing_2986.htm#SEC3067 changevar sing_1134.htm#SEC1215 char sing_213.htm#SEC253 charInfo sing_577.htm#SEC631 charVariety sing_576.htm#SEC630 char_series sing_214.htm#SEC254 characteristic exponents sing_1758.htm#IDX771 characteristic exponents sing_1759.htm#IDX776 characteristic exponents sing_1760.htm#IDX779 characteristic exponents sing_1761.htm#IDX783 characteristic exponents sing_1876.htm#IDX895 characteristic polynomial sing_2617.htm#IDX1053 characteristic variety sing_560.htm#IDX350 characteristic variety sing_668.htm#IDX385 charexp2conductor sing_1761.htm#SEC1842 charexp2generators sing_1759.htm#SEC1840 charexp2inter sing_1760.htm#SEC1841 charexp2multseq sing_1758.htm#SEC1839 charexp2poly sing_1762.htm#SEC1843 charpoly sing_1215.htm#SEC1296 charstr sing_215.htm#SEC255 checkFactor sing_553.htm#SEC607 checkRoot sing_548.htm#SEC602 checkpfd sing_2932.htm#SEC3013 checkpfdMat sing_2940.htm#SEC3021 chern sing_1512.htm#SEC1593 chern.lib sing_1507.htm#SEC1588 chernCharPoly sing_1554.htm#SEC1635 chernPoly sing_1553.htm#SEC1634 chern_lib sing_1507.htm#SEC1588 chineseRem sing_2248.htm#SEC2329 chinrem sing_216.htm#SEC256 chinrempoly sing_1377.htm#SEC1458 chinrestp sing_2307.htm#SEC2388 cimonom.lib sing_2371.htm#SEC2452 cimonom_lib sing_2371.htm#SEC2452 cisimplicial.lib sing_1253.htm#SEC1334 cisimplicial_lib sing_1253.htm#SEC1334 classSpaceCurve sing_1808.htm#SEC1889 classification sing_1769.htm#IDX788 classification sing_1796.htm#IDX791 classify sing_1780.htm#SEC1861 classify.lib sing_1778.htm#SEC1859 classify2.lib sing_1796.htm#SEC1877 classify2_lib sing_1796.htm#SEC1877 classifyCeq sing_1810.htm#SEC1891 classifyMapGerms.lib classifyMapGerms_lib sing_1814.htm#SEC1895 classifyMapGerms_lib classifyMapGerms_lib sing_1814.htm#SEC1895 classifySimpleMaps sing_1820.htm#SEC1901 classifySimpleMaps1 sing_1821.htm#SEC1902 classifyUnimodalMaps classifyUnimodalMaps sing_1822.htm#SEC1903 classify_aeq.lib sing_1799.htm#SEC1880 classify_aeq_lib sing_1799.htm#SEC1880 classify_lib sing_1778.htm#SEC1859 classifyceq.lib sing_1809.htm#SEC1890 classifyceq_lib sing_1809.htm#SEC1890 classifyci.lib sing_1811.htm#SEC1892 classifyci_lib sing_1811.htm#SEC1892 classifyicis sing_1812.htm#SEC1893 classpoly sing_1552.htm#SEC1633 cleanTmp sing_2559.htm#SEC2640 cleanunit sing_1643.htm#SEC1724 cleardenom sing_217.htm#SEC257 close sing_218.htm#SEC258 closed_points sing_2163.htm#SEC2244 closetex sing_2130.htm#SEC2211 closureFrac sing_1397.htm#SEC1478 coDim sing_1816.htm#SEC1897 coDimMap sing_1815.htm#SEC1896 coHom sing_711.htm#SEC765 codim sing_1920.htm#SEC2001 codimension sing_2381.htm#SEC2462 coding theory sing_963.htm#SEC1020 coef sing_219.htm#SEC259 coefficient sing_2580.htm#IDX980 coefficient sing_2581.htm#IDX983 coefficient sing_2582.htm#IDX987 coefficient field sing_144.htm#SEC184 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 coefficients sing_2669.htm#IDX1114 coefficients, long sing_920.htm#SEC977 coeffmod sing_2225.htm#SEC2306 coeffs sing_220.htm#SEC260 coker sing_2817.htm#SEC2898 colength of derivations curveColengthDerivations sing_1263.htm#IDX591 collectDiv sing_1688.htm#SEC1769 colrank sing_2197.htm#SEC2278 colred sing_1198.htm#SEC1279 combinat.lib sing_2657.htm#SEC2738 combinat_lib sing_2657.htm#SEC2738 commRing sing_692.htm#SEC746 comma sing_417.htm#SEC457 command,custom Commands for user defined types sing_187.htm#SEC227 command-line option, setting value of sing_361.htm#IDX281 command-line option, value of sing_361.htm#IDX279 command-line options, print all values of sing_361.htm#IDX278 command-line options, short help Command line options sing_19.htm#IDX38 commands (letterplace) Functions (letterplace) sing_804.htm#SEC858 commands (plural) sing_458.htm#IDX302 comment sing_36.htm#IDX108 compare sing_2680.htm#IDX1134 compare sing_2681.htm#IDX1136 compare sing_2682.htm#IDX1140 compare sing_2683.htm#IDX1143 compare sing_2701.htm#IDX1181 compare sing_2702.htm#IDX1183 compareMatrix sing_2825.htm#SEC2906 compareModules sing_2820.htm#SEC2901 compareTasks sing_1163.htm#SEC1244 compareVectors sing_2845.htm#SEC2926 complement sing_2958.htm#SEC3039 completeReduction sing_1998.htm#SEC2079 complex sing_28.htm#IDX75 complexClassify sing_1797.htm#SEC1878 complexSingType sing_1794.htm#SEC1875 complexType sing_1798.htm#SEC1879 compregb.lib sing_1008.htm#SEC1089 compregb_lib sing_1008.htm#SEC1089 comprehensive Groebner system sing_1008.htm#IDX471 compress sing_1176.htm#SEC1257 computeAfaceOrbits sing_2447.htm#SEC2528 computeConstant sing_1278.htm#SEC1359 computeGromovWitten sing_1281.htm#SEC1362 computeN sing_1692.htm#SEC1773 computeV sing_1691.htm#SEC1772 computemcm sing_1650.htm#SEC1731 concat sing_1177.htm#SEC1258 conductor sing_1261.htm#IDX585 conductor sing_1405.htm#IDX654 conductor sing_1761.htm#IDX782 conductor, degree sing_1876.htm#IDX898 cone sing_189.htm#SEC229 cone sing_2593.htm#IDX1007 cone sing_2594.htm#IDX1009 coneLink sing_2384.htm#SEC2465 coneViaInequalities sing_2383.htm#SEC2464 coneViaPoints sing_2382.htm#SEC2463 conic, parametrization, rational point. sing_1627.htm#IDX728 conicWithTangents sing_2535.htm#SEC2616 constructH sing_1651.htm#SEC1732 constructblwup sing_1652.htm#SEC1733 constructible set sing_1055.htm#IDX530 constructible set sing_1057.htm#IDX535 constructible sets sing_1056.htm#IDX533 constructible sets sing_1058.htm#IDX538 constructlastblwup sing_1653.htm#SEC1734 constructor derivationConstructor sing_2610.htm#IDX1040 constructor sing_2611.htm#IDX1043 constructor sing_2668.htm#IDX1110 constructor sing_2691.htm#IDX1159 constructor sing_2692.htm#IDX1161 constructor sing_2693.htm#IDX1164 constructor sing_2694.htm#IDX1167 contact matrix sing_1760.htm#IDX778 containedQ sing_2122.htm#SEC2203 containment sing_2687.htm#IDX1150 containsAsFace sing_2385.htm#SEC2466 containsInCollection containsInCollection sing_2418.htm#SEC2499 containsInSupport sing_2386.htm#SEC2467 containsPositiveVector containsPositiveVector sing_2387.htm#SEC2468 containsRelatively sing_2388.htm#SEC2469 content sing_1091.htm#SEC1172 contentSB, option sing_318.htm#IDX172 continue Behavior of continue sing_385.htm#SEC425 continue sing_419.htm#SEC459 contraHom sing_712.htm#SEC766 contract sing_221.htm#SEC261 contraction derivationContraction sing_2704.htm#IDX1189 contraction sing_2705.htm#IDX1191 contraction sing_2706.htm#IDX1193 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_1720.htm#IDX750 contributionBundle sing_1720.htm#SEC1801 contributors sing_361.htm#IDX199 control sing_2189.htm#SEC2270 control.lib sing_2188.htm#SEC2269 controlDim sing_2190.htm#SEC2271 controlExample sing_2202.htm#SEC2283 control_Matrix sing_1844.htm#SEC1925 control_lib sing_2188.htm#SEC2269 convertLeftToRightFraction convertLeftToRightFraction sing_764.htm#SEC818 convertRightToLeftFraction convertRightToLeftFraction sing_763.htm#SEC817 convertdata sing_1648.htm#SEC1729 convexHull sing_2389.htm#SEC2470 convexIntersection sing_2390.htm#SEC2471 convloc sing_557.htm#SEC611 coordinate change sing_2590.htm#IDX1004 coordinate change sing_2591.htm#IDX1005 coordinate change sing_2592.htm#IDX1006 coordinates sing_2345.htm#IDX955 coords sing_2345.htm#SEC2426 copyTask sing_1162.htm#SEC1243 copyright sing_1.htm#IDX1 corank sing_1781.htm#SEC1862 cornerMonomials sing_1435.htm#SEC1516 countPoints sing_2270.htm#SEC2351 coverings sing_1280.htm#IDX607 coverings sing_1281.htm#IDX611 cpu sing_361.htm#IDX201 cpu sing_361.htm#IDX275 crcgs sing_1111.htm#SEC1192 createBO sing_1679.htm#SEC1760 createGradedRingHomomorphism createGradedRingHomomorphism sing_2864.htm#SEC2945 createGroup sing_2857.htm#SEC2938 createQuotientGroup sing_2858.htm#SEC2939 createTask sing_1160.htm#SEC1241 createTorsionFreeGroup createTorsionFreeGroup sing_2859.htm#SEC2940 create_ring sing_222.htm#SEC262 createlist sing_1661.htm#SEC1742 cring sing_73.htm#SEC113 cring declarations sing_74.htm#SEC114 cring expressions sing_75.htm#SEC115 cring operations sing_76.htm#SEC116 cring related functions cring related functions sing_77.htm#SEC117 crossprod sing_223.htm#SEC263 crypto.lib sing_2243.htm#SEC2324 crypto_lib sing_2243.htm#SEC2324 crystallographicGroupC2MM crystallographicGroupC2MM sing_841.htm#SEC895 crystallographicGroupCM crystallographicGroupCM sing_840.htm#SEC894 crystallographicGroupP1 crystallographicGroupP1 sing_834.htm#SEC888 crystallographicGroupP2 crystallographicGroupP2 sing_838.htm#SEC892 crystallographicGroupP2GG crystallographicGroupP2GG sing_839.htm#SEC893 crystallographicGroupP2MM crystallographicGroupP2MM sing_837.htm#SEC891 crystallographicGroupP3 crystallographicGroupP3 sing_845.htm#SEC899 crystallographicGroupP31M crystallographicGroupP31M sing_846.htm#SEC900 crystallographicGroupP3M1 crystallographicGroupP3M1 sing_847.htm#SEC901 crystallographicGroupP4 crystallographicGroupP4 sing_842.htm#SEC896 crystallographicGroupP4GM crystallographicGroupP4GM sing_844.htm#SEC898 crystallographicGroupP4MM crystallographicGroupP4MM sing_843.htm#SEC897 crystallographicGroupP6 crystallographicGroupP6 sing_848.htm#SEC902 crystallographicGroupP6MM crystallographicGroupP6MM sing_849.htm#SEC903 crystallographicGroupPG crystallographicGroupPG sing_836.htm#SEC890 crystallographicGroupPM crystallographicGroupPM sing_835.htm#SEC889 cup sing_1302.htm#SEC1383 cupproduct sing_1303.htm#SEC1384 curve singularities sing_1751.htm#IDX765 curve singularities sing_1870.htm#IDX893 curve singularity sing_1259.htm#IDX580 curveColengthDerivations curveColengthDerivations sing_1263.htm#SEC1344 curveConductorMult sing_1261.htm#SEC1342 curveDeligneNumber sing_1262.htm#SEC1343 curveDeltaInv sing_1260.htm#SEC1341 curveInv.lib sing_1259.htm#SEC1340 curveInv_lib sing_1259.htm#SEC1340 curvepar.lib sing_1823.htm#SEC1904 curvepar_lib sing_1823.htm#SEC1904 custom assignment Assignments for user defined types sing_188.htm#SEC228 custom command Commands for user defined types sing_187.htm#SEC227 custom type Definition of a user defined type sing_184.htm#SEC224 customstd.lib sing_2622.htm#SEC2703 customstd_lib sing_2622.htm#SEC2703 cycleLength sing_2472.htm#SEC2553 cyclePoints sing_2476.htm#SEC2557 cyclic sing_1078.htm#SEC1159 cyclic code Codes and the decoding problem sing_995.htm#SEC1059 cyclotomic sing_1963.htm#SEC2044 datetime sing_224.htm#SEC264 dbprint sing_225.htm#SEC265 deRham.lib sing_1569.htm#SEC1650 deRhamCohom sing_574.htm#SEC628 deRhamCohomIdeal sing_575.htm#SEC629 deRhamCohomology sing_1570.htm#SEC1651 deRham_lib sing_1569.htm#SEC1650 debugLib, option sing_318.htm#IDX176 debug_log sing_1791.htm#SEC1872 debugger Source code debugger sing_66.htm#SEC103 debugging library code Source code debugger sing_66.htm#SEC103 dec1var sing_1360.htm#SEC1441 decimal sing_2244.htm#SEC2325 decode sing_2180.htm#SEC2261 decodeCode sing_2182.htm#SEC2263 decodeRandom sing_2181.htm#SEC2262 decodeRandomFL sing_2185.htm#SEC2266 decodeSV sing_2162.htm#SEC2243 decodegb.lib sing_2167.htm#SEC2248 decodegb_lib sing_2167.htm#SEC2248 decoding, decoding problem Codes and the decoding problem sing_995.htm#SEC1060 decoef sing_2210.htm#SEC2291 decomposeVecField sing_2982.htm#SEC3063 decomposition sing_2669.htm#IDX1112 decomposition sing_2930.htm#IDX1244 decomposition of modules sing_1353.htm#IDX637 decomposition, numerical sing_1599.htm#IDX696 decone sing_2593.htm#IDX1008 decone sing_2594.htm#IDX1010 def sing_88.htm#SEC128 def declarations sing_89.htm#SEC129 defRes, option sing_318.htm#IDX177 default argument sing_44.htm#SEC81 defineHomogeneous sing_2897.htm#SEC2978 defined sing_226.htm#SEC266 defl sing_1610.htm#SEC1691 deform sing_1921.htm#SEC2002 deform.lib sing_1834.htm#SEC1915 deform_lib sing_1834.htm#SEC1915 defring sing_1135.htm#SEC1216 defringp sing_1137.htm#SEC1218 defrings sing_1136.htm#SEC1217 deg sing_227.htm#SEC267 degBound sing_399.htm#SEC439 degree Miscellaneous oddities sing_228.htm#SEC268 degree sing_422.htm#IDX292 degree sing_2684.htm#IDX1145 degree sing_2686.htm#IDX1149 degree lexicographical ordering sing_969.htm#IDX445 degree of a polynomial Miscellaneous oddities sing_422.htm#IDX296 degree reverse lexicographical ordering sing_969.htm#IDX443 degreeDivisor sing_1580.htm#SEC1661 degreeFormalDivisor sing_1588.htm#SEC1669 degreepart sing_2039.htm#SEC2120 delete sing_126.htm#SEC166 delete sing_229.htm#SEC269 delete sing_279.htm#SEC319 deleteGenerator sing_589.htm#SEC643 deleteSublist sing_1017.htm#SEC1098 deligne number curveColengthDerivations sing_1259.htm#IDX582 deligne number sing_1262.htm#IDX587 deligne number sing_1263.htm#IDX589 delta sing_1882.htm#SEC1963 delta invariant sing_1260.htm#IDX583 delta invariant sing_1399.htm#IDX652 delta invariant sing_1882.htm#IDX903 delta invariant. sing_1391.htm#IDX645 delta invariant. sing_1392.htm#IDX648 delta invariant. sing_1393.htm#IDX651 deltaLoc sing_1399.htm#SEC1480 denom_list sing_361.htm#IDX203 denominator sing_230.htm#SEC270 depth sing_1304.htm#SEC1385 depthIdeal sing_1370.htm#SEC1451 derivate sing_1995.htm#SEC2076 derivation derivationConstructor sing_2607.htm#IDX1031 derivation sing_2689.htm#IDX1154 derivation sing_2690.htm#IDX1158 derivation sing_2691.htm#IDX1160 derivation sing_2692.htm#IDX1162 derivation sing_2693.htm#IDX1165 derivation sing_2694.htm#IDX1168 derivation sing_2703.htm#IDX1187 derivationAdd sing_2697.htm#SEC2778 derivationCheckList sing_2692.htm#SEC2773 derivationConstructor derivationConstructor sing_2694.htm#SEC2775 derivationContraction derivationContraction sing_2705.htm#SEC2786 derivationContractionGen derivationContractionGen sing_2704.htm#SEC2785 derivationEqu sing_2701.htm#SEC2782 derivationEval sing_2703.htm#SEC2784 derivationFromList sing_2691.htm#SEC2772 derivationFromPoly sing_2693.htm#SEC2774 derivationLie sing_2706.htm#SEC2787 derivationMul sing_2700.htm#SEC2781 derivationNeg sing_2699.htm#SEC2780 derivationNeq sing_2702.htm#SEC2783 derivationPrint sing_2696.htm#SEC2777 derivationSub sing_2698.htm#SEC2779 derivationToString sing_2695.htm#SEC2776 desingularization sing_2750.htm#IDX1204 desingularization sing_2751.htm#SEC2832 det sing_231.htm#SEC271 det_B sing_1217.htm#SEC1298 detadj sing_1898.htm#SEC1979 determinacy sing_1917.htm#SEC1998 determinecenter sing_1633.htm#SEC1714 detropicalise sing_2553.htm#SEC2634 develop sing_1872.htm#SEC1953 diag sing_1178.htm#SEC1259 diagInvariants sing_1414.htm#SEC1495 62096 diag_test sing_1213.htm#SEC1294 diagonalizeMatrixSimul diagonalizeMatrixSimul sing_2983.htm#SEC3064 diagonalizeVecField sing_2980.htm#SEC3061 diagonalizeVecFieldLin diagonalizeVecFieldLin sing_2978.htm#SEC3059 diff sing_232.htm#SEC272 diffAlgebra sing_2662.htm#SEC2743 diffAlgebraChangeOrd diffAlgebraChangeOrd sing_2666.htm#SEC2747 diffAlgebraGens sing_2664.htm#SEC2745 diffAlgebraListGen sing_2667.htm#SEC2748 diffAlgebraStructure diffAlgebraStructure sing_2663.htm#SEC2744 diffAlgebraUnivDerIdeal diffAlgebraUnivDerIdeal sing_2665.htm#SEC2746 diffRat sing_691.htm#SEC745 difference sing_2676.htm#IDX1128 difference sing_2698.htm#IDX1176 difference sing_2699.htm#IDX1178 differential sing_2668.htm#IDX1111 differential sing_2690.htm#IDX1156 differential algebra diffAlgebraUnivDerIdeal sing_2661.htm#IDX1098 differential algebra sing_2662.htm#IDX1099 differential algebra sing_2663.htm#IDX1102 differential algebra sing_2664.htm#IDX1103 differential algebra sing_2665.htm#IDX1105 differential forms sing_2661.htm#IDX1096 differential forms sing_2662.htm#IDX1100 differentials sing_2661.htm#IDX1097 differentials sing_2662.htm#IDX1101 difform.lib sing_2661.htm#SEC2742 difformAdd sing_2675.htm#SEC2756 difformCoef sing_2669.htm#SEC2750 difformDeg sing_2684.htm#SEC2765 difformDiff sing_2690.htm#SEC2771 difformDiv sing_2679.htm#SEC2760 difformEqu sing_2680.htm#SEC2761 difformFromPoly sing_2668.htm#SEC2749 difformGenToString sing_2670.htm#SEC2751 difformHomogDecomp sing_2671.htm#SEC2752 difformIsBigger sing_2682.htm#SEC2763 difformIsGen sing_2674.htm#SEC2755 difformIsHomog sing_2685.htm#SEC2766 difformIsHomogDeg sing_2686.htm#SEC2767 difformIsSmaller sing_2683.htm#SEC2764 difformListCont sing_2687.htm#SEC2768 difformListSort sing_2688.htm#SEC2769 difformMul sing_2678.htm#SEC2759 difformNeg sing_2677.htm#SEC2758 difformNeq sing_2681.htm#SEC2762 difformPrint sing_2673.htm#SEC2754 difformSub sing_2676.htm#SEC2757 difformToString sing_2672.htm#SEC2753 difformUnivDer sing_2689.htm#SEC2770 difform_lib sing_2661.htm#SEC2742 difpoly2tex sing_2211.htm#SEC2292 dim sing_233.htm#SEC273 dim (plural) sing_461.htm#SEC501 dimGradedPart sing_1740.htm#SEC1821 11262 dimH sing_1739.htm#SEC1820 38534 dimMon sing_1350.htm#SEC1431 dimStack sing_1718.htm#SEC1799 dim_slocus sing_1922.htm#SEC2003 dimension sing_2391.htm#SEC2472 dimension, moduli space of stable maps, rational curves dimStack sing_1718.htm#IDX748 dimensionOfLocalization dimensionOfLocalization sing_2745.htm#SEC2826 direct_boolean_poly sing_2635.htm#SEC2716 49893 direct_from_boolean_poly direct_from_boolean_poly sing_2641.htm#SEC2722 36941 disc sing_2231.htm#SEC2312 discr sing_1944.htm#SEC2025 discrepancy sing_1686.htm#SEC1767 discrim sing_1050.htm#SEC1131 discussion of parametric ideal sing_1034.htm#IDX475 disjoint sing_1035.htm#IDX477 disp_zdd sing_2648.htm#SEC2729 41439 displayCohom sing_1741.htm#SEC1822 22633 displayHNE sing_1875.htm#SEC1956 displayInvariants sing_1877.htm#SEC1958 displayMultsequence sing_1879.htm#SEC1960 displayPuiseuxExpansion displayPuiseuxExpansion sing_2528.htm#SEC2609 displayTropicalLifting displayTropicalLifting sing_2526.htm#SEC2607 displaypfd sing_2934.htm#SEC3015 displaypfd_long sing_2935.htm#SEC3016 distributed computing sing_1071.htm#IDX547 distributed computing sing_1126.htm#IDX561 distributed computing sing_1159.htm#IDX571 div Miscellaneous oddities sing_81.htm#SEC121 div sing_98.htm#SEC138 div sing_155.htm#SEC195 div sing_422.htm#IDX289 divideUnits sing_2207.htm#SEC2288 dividelist sing_1660.htm#SEC1741 division sing_234.htm#SEC274 division sing_1036.htm#IDX480 division sing_1037.htm#IDX482 division sing_2679.htm#IDX1133 division (plural) sing_462.htm#SEC502 division, pdivi2, reduce sing_1105.htm#IDX552 division, reduce sing_1102.htm#IDX549 divisor sing_2310.htm#SEC2391 divisorplus sing_1574.htm#SEC1655 divisors negativeformaldivisor sing_1573.htm#IDX670 divisors sing_1574.htm#IDX671 divisors sing_1575.htm#IDX672 divisors sing_1576.htm#IDX673 divisors sing_1577.htm#IDX674 divisors sing_1578.htm#IDX675 divisors sing_1579.htm#IDX676 divisors sing_1580.htm#IDX677 divisors sing_1581.htm#IDX678 divisors sing_1582.htm#IDX679 divisors sing_1583.htm#IDX680 divisors sing_1584.htm#IDX681 divisors sing_1585.htm#IDX682 divisors sing_1586.htm#IDX683 divisors sing_1587.htm#IDX684 divisors sing_1588.htm#IDX685 divisors, polyhedra sing_1589.htm#IDX686 divisors, polyhedra sing_1590.htm#IDX687 divisors, polyhedra sing_1591.htm#IDX688 divisors.lib sing_1572.htm#SEC1653 divisors_lib sing_1572.htm#SEC1653 dmod.lib sing_537.htm#SEC591 dmodAction sing_686.htm#SEC740 dmodActionRat sing_687.htm#SEC741 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_679.htm#SEC733 dmod_lib sing_537.htm#SEC591 dmodapp.lib sing_560.htm#SEC614 dmodapp_lib sing_560.htm#SEC614 dmodideal.lib sing_592.htm#SEC646 dmodideal_lib sing_592.htm#SEC646 dmodloc.lib sing_668.htm#IDX378 dmodloc_lib sing_668.htm#IDX379 dmodoublext sing_713.htm#SEC767 dmodvar.lib sing_600.htm#SEC654 dmodvar_lib sing_600.htm#SEC654 double sing_2315.htm#SEC2396 doubleExt sing_786.htm#SEC840 downloading Download instructions sing_2994.htm#SEC3091 dp, global ordering sing_969.htm#IDX444 drawNewtonSubdivision drawNewtonSubdivision sing_2531.htm#SEC2612 drawTropicalCurve sing_2530.htm#SEC2611 ds, local ordering sing_970.htm#IDX454 dsum sing_1179.htm#SEC1260 dualCone sing_2392.htm#SEC2473 dualConic sing_2555.htm#SEC2636 dualPart sing_1560.htm#SEC1641 dualPartition sing_1731.htm#SEC1812 dualPolytope sing_2431.htm#SEC2512 dualSheaf sing_1709.htm#SEC1790 dual_code sing_2164.htm#SEC2245 dump sing_235.htm#SEC275 dyckGroup1 sing_850.htm#SEC904 dyckGroup2 sing_851.htm#SEC905 dyckGroup3 sing_852.htm#SEC906 dynamic geometry sing_1043.htm#IDX504 dynamic geometry sing_1044.htm#IDX507 ecart sing_2318.htm#SEC2399 echo sing_400.htm#SEC440 eexgcdN sing_2245.htm#SEC2326 effective sing_1582.htm#SEC1663 egcdMain sing_2115.htm#SEC2196 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2482.htm#SEC2563 ehrhartRing sing_1410.htm#SEC1491 16966 eigenvals sing_1225.htm#SEC1306 eigenvalue sing_331.htm#SEC371 eigenvalue sing_1225.htm#IDX577 eigenvalues sing_1498.htm#SEC1579 elemSymmId sing_1079.htm#SEC1160 elim sing_1267.htm#SEC1348 elim.lib sing_1264.htm#SEC1345 elim1 sing_1268.htm#SEC1349 elim2 sing_1269.htm#SEC1350 elimRing sing_1266.htm#SEC1347 elimWeight sing_728.htm#SEC782 elim_lib sing_1264.htm#SEC1345 eliminate sing_236.htm#SEC276 eliminate (plural) sing_463.htm#SEC503 eliminateNC sing_723.htm#SEC777 elimination sing_722.htm#IDX393 elimlinearpart sing_2040.htm#SEC2121 elimpart sing_2041.htm#SEC2122 elimpartanyr sing_2042.htm#SEC2123 elimrep sing_1641.htm#SEC1722 elliptic curve sing_1277.htm#IDX603 elliptic curves sing_1274.htm#IDX597 elliptic curves sing_1280.htm#IDX606 elliptic curves sing_1281.htm#IDX610 ellipticAdd sing_2266.htm#SEC2347 ellipticAllPoints sing_2271.htm#SEC2352 ellipticMult sing_2267.htm#SEC2348 ellipticNF sing_2479.htm#SEC2560 ellipticNFDB sing_2480.htm#SEC2561 ellipticRandomCurve sing_2268.htm#SEC2349 ellipticRandomPoint sing_2269.htm#SEC2350 ellipticcovers.lib sing_1274.htm#SEC1355 ellipticcovers_lib sing_1274.htm#SEC1355 else sing_390.htm#SEC430 embedMat sing_754.htm#SEC808 emptyFan sing_2419.htm#SEC2500 encode sing_2172.htm#SEC2253 endomorphism filtration sing_1856.htm#IDX869 endvfilt sing_1856.htm#SEC1937 ensureLeftNcfrac sing_701.htm#SEC755 ensureRightNcfrac sing_702.htm#SEC756 envelop FamElemsAtEnvCompPoints sing_1045.htm#SEC1126 envelop sing_1045.htm#IDX510 envelop sing_1046.htm#IDX513 envelop sing_1048.htm#IDX518 envelop sing_1049.htm#IDX522 envelope sing_464.htm#SEC504 enveloping algebra sing_361.htm#IDX207 enveloping algebra sing_495.htm#IDX306 environment variable, DISPLAY The online help system sing_16.htm#IDX29 environment variables Used environment variables sing_2995.htm#SEC3092 equal sing_2680.htm#IDX1135 equal sing_2681.htm#IDX1137 equal sing_2701.htm#IDX1182 equal sing_2702.htm#IDX1184 equalJinI sing_1768.htm#SEC1849 equalMultiDeg sing_2890.htm#SEC2971 equations sing_2393.htm#SEC2474 equiRadical sing_1451.htm#SEC1532 equidim sing_1453.htm#SEC1534 equidimMax sing_1454.htm#SEC1535 equidimMaxEHV sing_1455.htm#SEC1536 equidimZ sing_1466.htm#SEC1547 equising.lib sing_1839.htm#SEC1920 equising_lib sing_1839.htm#SEC1920 equisingular Tjurina number sing_1751.htm#IDX770 equisingularity ideal sing_1841.htm#IDX796 equisingularity stratum sing_1842.htm#IDX797 error recovery sing_15.htm#SEC21 errorInsert sing_2175.htm#SEC2256 errorRand sing_2176.htm#SEC2257 errormap sing_2721.htm#SEC2802 esIdeal sing_1841.htm#SEC1922 esStratum sing_1842.htm#SEC1923 essential sing_2597.htm#IDX1013 essential sing_2598.htm#IDX1014 eta sing_2474.htm#SEC2555 euler sing_2224.htm#SEC2305 eulerChProj sing_1550.htm#SEC1631 eval sing_237.htm#SEC277 evalJacobianAtBox sing_2101.htm#SEC2182 evalPolyAtBox sing_2100.htm#SEC2181 evaluateFormalDivisor evaluateFormalDivisor sing_1584.htm#SEC1665 evaluatePDivisor sing_1590.htm#SEC1671 evaluateProduct sing_2457.htm#SEC2538 evaluate_reynolds sing_1968.htm#SEC2049 evaluatepfd sing_2933.htm#SEC3014 evaluation sing_2703.htm#IDX1186 evalutateIntegral sing_1279.htm#SEC1360 exactness recovery sing_2074.htm#IDX928 example sing_239.htm#SEC279 example sing_2599.htm#IDX1015 example sing_2600.htm#IDX1017 example sing_2601.htm#IDX1019 example sing_2602.htm#IDX1021 example sing_2603.htm#IDX1023 example sing_2604.htm#IDX1025 example sing_2605.htm#IDX1028 execute sing_240.htm#SEC280 exit sing_394.htm#SEC434 exp2pt sing_2212.htm#SEC2293 expo sing_2236.htm#SEC2317 exponents sing_2609.htm#IDX1036 export sing_387.htm#SEC427 exportNuminvs sing_1418.htm#SEC1499 10423 exportto sing_388.htm#SEC428 expp sing_1729.htm#SEC1810 expression list sing_72.htm#IDX128 expression list sing_426.htm#IDX299 ext-module purityfiltration_lib sing_778.htm#IDX399 extcurve sing_2158.htm#SEC2239 extdevelop sing_1873.htm#SEC1954 extendGC sing_1042.htm#SEC1123 extendWeyl sing_680.htm#SEC734 extendedTensor sing_729.htm#SEC783 extendpoly sing_1041.htm#SEC1122 extendring sing_1138.htm#SEC1219 extension of rings sing_1471.htm#IDX663 exterior basis sing_1204.htm#IDX574 exterior power sing_1206.htm#IDX576 exteriorBasis sing_1204.htm#SEC1285 exteriorPower sing_1206.htm#SEC1287 extgcd sing_241.htm#SEC281 extractS sing_599.htm#SEC653 fPiece sing_2967.htm#SEC3048 fVector sing_2422.htm#SEC2503 fVectorP sing_2483.htm#SEC2564 facFirstShift sing_654.htm#SEC708 facFirstWeyl sing_650.htm#SEC704 facGBIdeal sing_1436.htm#SEC1517 facShift sing_653.htm#SEC707 facSubWeyl sing_652.htm#SEC706 facWeyl sing_649.htm#SEC703 faceContaining sing_2394.htm#SEC2475 facetVertexLatticeDistances facetVertexLatticeDistances sing_2484.htm#SEC2565 facetWidth sing_2485.htm#SEC2566 facetWidths sing_2486.htm#SEC2567 facets sing_2395.htm#SEC2476 facstd sing_242.htm#SEC282 factmodd sing_243.htm#SEC283 factor sing_325.htm#SEC365 factor sing_1103.htm#IDX550 factorH sing_1032.htm#SEC1113 factorLenstraECM sing_2275.htm#SEC2356 factorMain sing_2116.htm#SEC2197 factorgroup sing_2880.htm#SEC2961 factorial sing_1018.htm#SEC1099 factorization sing_326.htm#SEC366 factorization sing_1234.htm#IDX578 factorize sing_244.htm#SEC284 factorize sing_325.htm#SEC365 factory sing_1.htm#IDX2 facvar sing_1103.htm#SEC1184 fan sing_190.htm#SEC230 fan sing_2466.htm#IDX961 fanViaCones sing_2420.htm#SEC2501 farey sing_245.htm#SEC285 fareypoly sing_1286.htm#SEC1367 fastExpt sing_2220.htm#SEC2301 fastHC, option sing_318.htm#IDX153 fastelim sing_2043.htm#SEC2124 fetch sing_246.htm#SEC286 fetch (plural) sing_465.htm#SEC505 fetchall sing_1139.htm#SEC1220 ffmodStd sing_1292.htm#SEC1373 ffmodstd.lib sing_1285.htm#SEC1366 ffmodstd_lib sing_1285.htm#SEC1366 ffsolve sing_2031.htm#SEC2112 ffsolve.lib sing_2030.htm#SEC2111 ffsolve_lib sing_2030.htm#SEC2111 fglm sing_247.htm#SEC287 fglm sing_358.htm#IDX187 fglm_solve sing_2059.htm#SEC2140 fglmquot sing_248.htm#SEC288 fibonacci sing_1019.htm#SEC1100 fibonacciGroup sing_853.htm#SEC907 field sing_144.htm#SEC184 file, .singularrc sing_20.htm#IDX71 filecmd sing_249.htm#SEC289 filtration purityfiltration_lib sing_778.htm#IDX400 finalCharts sing_1665.htm#SEC1746 finalcases sing_1108.htm#SEC1189 find sing_250.htm#SEC290 findAuto sing_608.htm#SEC662 findInvo sing_606.htm#SEC660 findInvoDiag sing_607.htm#SEC661 findOrientedBoundary findOrientedBoundary sing_2475.htm#SEC2556 findTorsion sing_2201.htm#SEC2282 findZeroPoly sing_2946.htm#SEC3027 find_first_primitive_root find_first_primitive_root sing_2279.htm#SEC2360 find_index sing_2283.htm#SEC2364 findifs.lib sing_2208.htm#SEC2289 findifs_example sing_2209.htm#SEC2290 findifs_lib sing_2208.htm#SEC2289 findimAlgebra sing_738.htm#SEC792 finduni sing_251.htm#SEC291 findvars sing_2044.htm#SEC2125 finite field sing_144.htm#SEC184 finite field sing_2030.htm#IDX925 finiteDiagInvariants finiteDiagInvariants sing_1413.htm#SEC1494 3508 finitediff.lib sing_2707.htm#IDX1194 finitediff_lib sing_2707.htm#IDX1195 finitely presented algebra sing_821.htm#IDX407 finitely presented algebra sing_827.htm#IDX413 finitely presented algebra sing_856.htm#IDX416 finitely presented algebra sing_863.htm#IDX428 finitely presented algebra sing_877.htm#IDX429 finitely presented algebra, standard finitely presented algebra Free associative algebras sing_815.htm#IDX406 finitely presented group sing_827.htm#IDX414 finitenessTest sing_1248.htm#SEC1329 finiterep sing_2021.htm#SEC2102 finvar.lib sing_1956.htm#SEC2037 finvar_lib sing_1956.htm#SEC2037 first index is 1 sing_421.htm#SEC461 first order deformation sing_2964.htm#IDX1260 first order deformation sing_2967.htm#IDX1263 firstoct sing_2108.htm#SEC2189 fitting sing_1307.htm#SEC1388 fixed points, moduli space of stable maps, graph fixedPoints sing_1719.htm#IDX749 fixedPoints sing_1719.htm#SEC1800 fl2poly sing_587.htm#SEC641 flatten sing_1180.htm#SEC1261 flatteningStrat sing_1308.htm#SEC1389 flintQ sing_252.htm#SEC292 floating point sing_1148.htm#IDX564 for sing_389.htm#SEC429 formal linear representations sing_880.htm#IDX437 formaldivisorplus sing_1585.htm#SEC1666 forward sing_2713.htm#SEC2794 fourier sing_582.htm#SEC636 fouriersystem sing_2724.htm#SEC2805 fpadim.lib sing_821.htm#SEC875 fpadim_lib sing_821.htm#SEC875 fpalgebras.lib sing_827.htm#SEC881 fpalgebras_lib sing_827.htm#SEC881 fpaprops.lib sing_856.htm#SEC910 fpaprops_lib sing_856.htm#SEC910 fprintf sing_254.htm#SEC294 fracStatus sing_759.htm#SEC813 framed sheaves sing_2731.htm#IDX1202 frandwalk sing_2953.htm#SEC3034 free sing_2608.htm#IDX1033 free sing_2609.htm#IDX1035 free associative algebra sing_827.htm#IDX412 free associative algebra sing_863.htm#IDX424 free associative algebra, tensor algebra Free associative algebras sing_815.htm#SEC869 free noncommutative Groebner basis sing_863.htm#IDX426 freeAlgebra (letterplace) freeAlgebra (letterplace) sing_805.htm#SEC859 freeModule sing_2797.htm#SEC2878 freeModule2Module sing_2826.htm#SEC2907 freegb.lib sing_863.htm#SEC917 freegb_lib sing_863.htm#SEC917 freemodule sing_255.htm#SEC295 freerank sing_1081.htm#SEC1162 fres sing_256.htm#SEC296 from_boolean_constant from_boolean_constant sing_2639.htm#SEC2720 44881 from_boolean_ideal sing_2643.htm#SEC2724 62698 from_boolean_poly sing_2640.htm#SEC2721 27864 from_boolean_set sing_2644.htm#SEC2725 60615 frwalk sing_257.htm#SEC297 full representation sing_1041.htm#IDX496 full representation sing_1042.htm#IDX501 fullDimImages sing_2438.htm#SEC2519 fullFan sing_2421.htm#SEC2502 fullSerreRelations sing_830.htm#SEC884 fullSpace sing_2376.htm#SEC2457 furtherInvar sing_2000.htm#SEC2081 further_hn_proc sing_1890.htm#SEC1971 fwalk sing_1294.htm#SEC1375 galois field sing_144.htm#SEC184 gaussColWithoutPerm sing_2080.htm#SEC2161 gaussRowWithoutPerm sing_2079.htm#SEC2160 gauss_col sing_1189.htm#SEC1270 gauss_nf sing_1220.htm#SEC1301 gauss_row sing_1190.htm#SEC1271 gaussred sing_1218.htm#SEC1299 gaussred_pivot sing_1219.htm#SEC1300 gcd sing_258.htm#SEC298 gcdMon sing_1339.htm#SEC1420 gcddivisor sing_2311.htm#SEC2392 gen sing_259.htm#SEC299 genMDSMat sing_2178.htm#SEC2259 genSymId sing_1495.htm#SEC1576 general error-locator polynomial sing_996.htm#SEC1066 general neron. sing_2750.htm#IDX1205 general weighted lexicographical ordering sing_970.htm#IDX460 general weighted reverse lexicographical ordering Local orderings sing_970.htm#IDX457 general.lib sing_1011.htm#SEC1092 generalOrder sing_2336.htm#SEC2417 general_lib sing_1011.htm#SEC1092 generateG sing_2274.htm#SEC2355 generator derivationContractionGen sing_2664.htm#IDX1104 generator sing_2674.htm#IDX1124 generator sing_2704.htm#IDX1190 generators sing_1759.htm#IDX774 generators sing_2667.htm#IDX1108 generators sing_2669.htm#IDX1113 generators sing_2670.htm#IDX1117 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2396.htm#SEC2477 generatorsOfSpan sing_2397.htm#SEC2478 generic representation sing_1041.htm#IDX495 genericid sing_1114.htm#SEC1195 genericity sing_2198.htm#SEC2279 genericmat sing_1181.htm#SEC1262 genoutput sing_1654.htm#SEC1735 genus sing_1395.htm#SEC1476 geometrical locus FamElemsAtEnvCompPoints sing_1043.htm#IDX502 geometrical locus sing_1044.htm#IDX505 geometrical locus sing_1045.htm#IDX508 geometrical locus sing_1046.htm#IDX511 geometrical locus sing_1047.htm#IDX514 geometrical locus sing_1048.htm#IDX516 geometrical locus sing_1049.htm#IDX520 getArguments sing_1171.htm#SEC1252 getCommand sing_1170.htm#SEC1251 getCone sing_2423.htm#SEC2504 getGradingGroup sing_2855.htm#SEC2936 getLattice sing_2856.htm#SEC2937 getLinearForms sing_2398.htm#SEC2479 getMaxPoints sing_2790.htm#SEC2871 getModuleGrading sing_2866.htm#SEC2947 getMultiplicity sing_2399.htm#SEC2480 getOneVar sing_1403.htm#SEC1484 getRelations sing_2077.htm#SEC2158 getRelationsRadical sing_2078.htm#SEC2159 getResult sing_1172.htm#SEC1253 getSmallest sing_1402.htm#SEC1483 getState sing_1173.htm#SEC1254 getStringpfd sing_2936.htm#SEC3017 getStringpfd_indexed getStringpfd_indexed sing_2937.htm#SEC3018 getVariableWeights sing_2854.htm#SEC2935 getWitnessSet sing_2081.htm#SEC2162 getcores sing_1129.htm#SEC1210 getdump sing_260.htm#SEC300 getenv sing_361.htm#IDX209 gfan.lib sing_2375.htm#SEC2456 gfan_lib sing_2375.htm#SEC2456 gfanlib sing_1.htm#IDX9 gitCone sing_2465.htm#SEC2546 gitfan.lib sing_2435.htm#SEC2516 gitfan_lib sing_2435.htm#SEC2516 gkdim.lib sing_613.htm#SEC667 gkdim_lib sing_613.htm#SEC667 global sing_210.htm#IDX133 global Bernstein-Sato ideal sing_592.htm#IDX355 global Bernstein-Sato polynomial sing_502.htm#IDX313 global Bernstein-Sato polynomial sing_537.htm#IDX331 global Bernstein-Sato polynomial for variety sing_600.htm#IDX363 global homological dimension sing_856.htm#IDX421 globalSections sing_1579.htm#SEC1660 gmscoeffs sing_1848.htm#SEC1929 gmsnf sing_1847.htm#SEC1928 gmspoly.lib sing_1867.htm#SEC1948 gmspoly_lib sing_1867.htm#SEC1948 gmsring sing_1846.htm#SEC1927 gmssing.lib sing_1845.htm#SEC1926 gmssing_lib sing_1845.htm#SEC1926 goettsche.lib sing_2731.htm#SEC2812 goettsche_lib sing_2731.htm#SEC2812 good basis sing_1845.htm#IDX808 good basis sing_1855.htm#IDX863 good basis sing_1867.htm#IDX879 good basis sing_1869.htm#IDX890 goodBasis sing_1869.htm#SEC1950 gorensteinIndex sing_2487.htm#SEC2568 gorensteinVector sing_2488.htm#SEC2569 graal.lib sing_2743.htm#SEC2824 graalMixed sing_2744.htm#SEC2825 graal_lib sing_2743.htm#SEC2824 gradeNumber sing_782.htm#SEC836 graded sing_2667.htm#IDX1109 graded Hilbert series sing_877.htm#IDX431 graded Weyl algebra sing_502.htm#IDX316 graded algebra sing_2650.htm#IDX1088 graded module, graded piece sing_1740.htm#IDX760 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2752.htm#IDX1206 graded modules, handling of Handling graded modules sing_935.htm#SEC992 graded piece, second order piece sing_2968.htm#IDX1264 graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2794.htm#IDX1211 gradedModules.lib sing_2752.htm#SEC2833 gradedModules_lib sing_2752.htm#SEC2833 gradiator sing_2899.htm#SEC2980 graph sing_1275.htm#IDX601 graph sing_1276.htm#IDX602 graph sing_1714.htm#IDX744 graph sing_1715.htm#IDX745 graphics.lib sing_2125.htm#SEC2206 graphics_lib sing_2125.htm#SEC2206 graphviz sing_1.htm#IDX13 graver4ti2 sing_1493.htm#SEC1574 39635 grconcat sing_2775.htm#SEC2856 grdeg sing_2755.htm#SEC2836 grgens sing_2764.htm#SEC2845 grgroebner sing_2774.htm#SEC2855 grlift sing_2772.htm#SEC2853 grlifting sing_2779.htm#SEC2860 grlifting2 sing_2780.htm#SEC2861 grlifting3 sing_2782.htm#SEC2863 grneg sing_2785.htm#SEC2866 grobcov sing_1034.htm#SEC1115 grobcov.lib sing_1033.htm#SEC1114 grobcov_lib sing_1033.htm#SEC1114 grobj sing_2753.htm#SEC2834 groebner sing_261.htm#SEC301 groebner sing_927.htm#SEC984 groebner basis computations sing_261.htm#IDX147 groebnerComplex sing_2566.htm#SEC2647 groebnerCone sing_2560.htm#SEC2641 groebnerFan sing_2565.htm#SEC2646 gromovWitten sing_1280.htm#SEC1361 grorder sing_2766.htm#SEC2847 ground field sing_144.htm#SEC184 groupActionOnHashes sing_2453.htm#SEC2534 groupActionOnQImage sing_2452.htm#SEC2533 group_reynolds sing_1964.htm#SEC2045 growth of algebra sing_856.htm#IDX419 grpower sing_2762.htm#SEC2843 grpres sing_2765.htm#SEC2846 grprod sing_2773.htm#SEC2854 grrange sing_2784.htm#SEC2865 grres sing_2771.htm#SEC2852 grrndmap sing_2777.htm#SEC2858 grrndmap2 sing_2778.htm#SEC2859 grrndmat sing_2776.htm#SEC2857 grshift sing_2757.htm#SEC2838 grsum sing_2761.htm#SEC2842 grsyz sing_2770.htm#SEC2851 grtest sing_2754.htm#SEC2835 grtranspose sing_2763.htm#SEC2844 grtranspose1 sing_2767.htm#SEC2848 grtwist sing_2759.htm#SEC2840 grtwists sing_2760.htm#SEC2841 grview sing_2756.htm#SEC2837 grwalk.lib sing_1293.htm#SEC1374 grwalk_lib sing_1293.htm#SEC1374 grzero sing_2758.htm#SEC2839 gwalk sing_1299.htm#SEC1380 hStarVector sing_2489.htm#SEC2570 hVector sing_2490.htm#SEC2571 h_increasing_knapsack h_increasing_knapsack sing_2297.htm#SEC2378 hardware platform sing_361.htm#IDX268 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1152.htm#SEC1233 hasCommutativeVars sing_1149.htm#SEC1230 hasGlobalOrdering sing_1150.htm#SEC1231 hasLeftDenom sing_695.htm#SEC749 hasMixedOrdering sing_1151.htm#SEC1232 hasNumericCoeffs sing_1148.htm#SEC1229 hasRightDenom sing_696.htm#SEC750 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1153.htm#SEC1234 hashToCone sing_2463.htm#SEC2544 hashesToFan sing_2464.htm#SEC2545 headStand sing_1202.htm#SEC1283 heightZ sing_1465.htm#SEC1546 help sing_262.htm#SEC302 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_361.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_2900.htm#SEC2981 hess.lib sing_1592.htm#SEC1673 hess_lib sing_1592.htm#SEC1673 hessenberg sing_361.htm#IDX215 hessenberg sing_1224.htm#SEC1305 highcorner sing_263.htm#SEC303 hilb sing_264.htm#SEC304 hilbPoly sing_1097.htm#SEC1178 hilbert4ti2 sing_1492.htm#SEC1573 13993 hilbertBasis sing_2491.htm#SEC2572 hilbertSeries sing_2902.htm#SEC2983 hilbvec sing_2045.htm#SEC2126 hnexpansion sing_1871.htm#SEC1952 hnoether.lib sing_1870.htm#SEC1951 hnoether_lib sing_1870.htm#SEC1951 holonomic rank sing_668.htm#IDX381 holonomicRank sing_672.htm#SEC726 hom sing_2838.htm#SEC2919 hom_kernel sing_1315.htm#SEC1396 homog sing_265.htm#SEC305 homog sing_2685.htm#IDX1147 homog_part sing_1726.htm#SEC1807 homog_parts sing_1727.htm#SEC1808 homogeneitySpace sing_2562.htm#SEC2643 homogeneous sing_2671.htm#IDX1118 homogeneous sing_2685.htm#IDX1146 homogeneous sing_2686.htm#IDX1148 homogeneous decomposition sing_2671.htm#IDX1119 homogfacFirstQWeyl sing_657.htm#SEC711 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_659.htm#SEC713 homogfacNthQWeyl sing_656.htm#SEC710 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_658.htm#SEC712 homogfacNthWeyl sing_655.htm#SEC709 homolog.lib sing_1300.htm#SEC1381 homolog_lib sing_1300.htm#SEC1381 homology sing_1310.htm#SEC1391 homomorphism sing_2822.htm#SEC2903 howto, download Download instructions sing_2994.htm#SEC3091 howto, install on Macintosh Macintosh installation instructions sing_2998.htm#SEC3095 howto, install on Unix Unix installation instructions sing_2996.htm#SEC3093 howto, install on Windows Windows installation instructions sing_2997.htm#SEC3094 hres sing_266.htm#SEC306 html, default help The online help system sing_16.htm#IDX24 hybrid algorithms sing_2074.htm#IDX927 hyperel.lib sing_2304.htm#SEC2385 hyperel_lib sing_2304.htm#SEC2385 hyperplane sing_2578.htm#IDX973 hyperplane arrangement sing_537.htm#IDX337 hypersurface singularity sing_1897.htm#IDX908 iMult sing_1398.htm#SEC1479 id sing_2795.htm#SEC2876 id2mod sing_1093.htm#SEC1174 ideal sing_90.htm#SEC130 ideal (plural) sing_427.htm#SEC467 ideal declarations sing_91.htm#SEC131 ideal declarations (plural) ideal declarations (plural) sing_428.htm#SEC468 ideal expressions sing_92.htm#SEC132 ideal expressions (plural) ideal expressions (plural) sing_429.htm#SEC469 ideal operations sing_93.htm#SEC133 ideal operations (plural) ideal operations (plural) sing_430.htm#SEC470 ideal related functions ideal related functions sing_94.htm#SEC134 ideal related functions (plural) ideal related functions (plural) sing_431.htm#SEC471 ideal, toric sing_983.htm#SEC1045 idealSplit sing_2052.htm#SEC2133 ideals Miscellaneous oddities sing_422.htm#IDX293 idealsimplify sing_1767.htm#SEC1848 identifier Identifier resolution sing_423.htm#SEC463 identifyvar sing_1636.htm#SEC1717 if sing_390.htm#SEC430 image sing_2818.htm#SEC2899 imageLattice sing_2868.htm#SEC2949 image_of_variety sing_1992.htm#SEC2073 imap sing_267.htm#SEC307 imap (plural) sing_466.htm#SEC506 imapall sing_1140.htm#SEC1221 impart sing_268.htm#SEC308 importfrom sing_391.htm#SEC431 inCenter sing_526.htm#SEC580 inCentralizer sing_527.htm#SEC581 inForm sing_569.htm#SEC623 inSubring sing_1240.htm#SEC1321 indSet sing_1365.htm#SEC1446 indepSet sing_269.htm#SEC309 indexed names sing_36.htm#IDX82 indexed names sing_37.htm#SEC65 indices, multi sing_37.htm#SEC65 inequalities sing_2400.htm#SEC2481 infRedTail, option sing_318.htm#IDX154 infinitely presented algebra sing_877.htm#IDX430 info The online help system sing_16.htm#SEC23 iniD sing_1656.htm#SEC1737 init_debug sing_1783.htm#SEC1864 initial sing_2563.htm#SEC2644 initial form sing_502.htm#IDX318 initial ideal sing_502.htm#IDX317 initial ideal approach sing_502.htm#IDX321 initial ideal approach sing_600.htm#IDX367 initialForm sing_2540.htm#SEC2621 initialIdeal sing_2541.htm#SEC2622 initialIdealW sing_568.htm#SEC622 initialMalgrange sing_567.htm#SEC621 injective_knapsack sing_2298.htm#SEC2379 inout.lib sing_1059.htm#SEC1140 inout_lib sing_1059.htm#SEC1140 input sing_41.htm#SEC71 insert sing_126.htm#SEC166 insert sing_270.htm#SEC310 insertCone sing_2424.htm#SEC2505 insertGenerator sing_588.htm#SEC642 instructions, Macintosh installation Macintosh installation instructions sing_2998.htm#SEC3095 instructions, Unix installation Unix installation instructions sing_2996.htm#SEC3093 instructions, Windows installation Windows installation instructions sing_2997.htm#SEC3094 instructions, downloading Download instructions sing_2994.htm#SEC3091 int sing_95.htm#SEC135 int declarations sing_96.htm#SEC136 int expressions sing_97.htm#SEC137 int operations sing_98.htm#SEC138 int related functions int related functions sing_99.htm#SEC139 intInverse sing_2877.htm#SEC2958 intPart sing_2252.htm#SEC2333 intRank sing_2869.htm#SEC2950 intRoot sing_2253.htm#SEC2334 intRoots sing_585.htm#SEC639 intStrategy, option sing_318.htm#IDX155 intclMonIdeal sing_1411.htm#SEC1492 62182 intclToricRing sing_1407.htm#SEC1488 62143 integer division Miscellaneous oddities sing_422.htm#IDX288 integer programming sing_991.htm#SEC1053 integral sing_1701.htm#SEC1782 integral basis sing_1322.htm#IDX623 integral basis sing_1619.htm#IDX721 integral closure sing_1391.htm#IDX644 integral closure sing_1392.htm#IDX647 integral closure sing_1393.htm#IDX650 integral closure sing_1406.htm#IDX656 integralBasis sing_1322.htm#SEC1403 integralIdeal sing_572.htm#SEC626 integralModule sing_573.htm#SEC627 integralSection sing_2878.htm#SEC2959 integralbasis.lib sing_1321.htm#SEC1402 integralbasis_lib sing_1321.htm#SEC1402 integration of D-module sing_560.htm#IDX349 interface, Emacs Emacs user interface sing_21.htm#SEC28 interiorLatticePoints interiorLatticePoints sing_2492.htm#SEC2573 internalfunctions sing_1784.htm#SEC1865 interpolate sing_2058.htm#SEC2139 interpolation sing_271.htm#SEC311 interpret sing_2840.htm#SEC2921 interpretElem sing_2843.htm#SEC2924 interpretInv sing_2841.htm#SEC2922 interpretList sing_2844.htm#SEC2925 interred sing_272.htm#SEC312 intersect sing_273.htm#SEC313 intersect (plural) sing_467.htm#SEC507 intersectElim, option sing_318.htm#IDX173 intersectLattices sing_2874.htm#SEC2955 intersectLists sing_2658.htm#SEC2739 intersectMon sing_1342.htm#SEC1423 intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2451.htm#SEC2532 intersectSyz, option sing_318.htm#IDX174 intersectZ sing_1467.htm#SEC1548 intersection sing_1880.htm#SEC1961 intersection sing_2957.htm#IDX1258 intersection lattice sing_2614.htm#IDX1048 intersection lattice sing_2615.htm#IDX1049 intersection multiplicity sing_1760.htm#IDX780 intersection multiplicity sing_1880.htm#IDX901 intersectionDiv sing_1684.htm#SEC1765 intersectionSet sing_2957.htm#SEC3038 intersectionValRingIdeals intersectionValRingIdeals 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isCompressed sing_2495.htm#SEC2576 isDenom sing_717.htm#SEC771 isElement sing_2959.htm#SEC3040 isEqualDivisor sing_1578.htm#SEC1659 isEquising sing_1843.htm#SEC1924 isFlat sing_1312.htm#SEC1393 isFreeAlgebra sing_864.htm#SEC918 isFsat sing_578.htm#SEC632 isFullSpace sing_2401.htm#SEC2482 isGorenstein sing_2496.htm#SEC2577 isGradedRingHomomorphism isGradedRingHomomorphism sing_2863.htm#SEC2944 isGroup sing_2861.htm#SEC2942 isGroupHomomorphism sing_2862.htm#SEC2943 isHolonomic sing_556.htm#SEC610 isHomog sing_210.htm#IDX135 isHomogeneous sing_2889.htm#SEC2970 isInS sing_758.htm#SEC812 isInt sing_590.htm#SEC644 isIntegralSurjective isIntegralSurjective sing_2875.htm#SEC2956 isInvertibleLeftFraction isInvertibleLeftFraction sing_768.htm#SEC822 isInvertibleNcfrac sing_704.htm#SEC758 isInvolution sing_611.htm#SEC665 isLatticeEmpty sing_2497.htm#SEC2578 isLocalizationRegular isLocalizationRegular sing_2747.htm#SEC2828 isLocallyFree sing_1313.htm#SEC1394 isMonomial sing_1337.htm#SEC1418 isNC sing_746.htm#SEC800 isNormal sing_2498.htm#SEC2579 isOnCurve sing_2265.htm#SEC2346 isOneFraction sing_771.htm#SEC825 isOneNcfrac sing_698.htm#SEC752 isOrderingShiftInvariant isOrderingShiftInvariant sing_870.htm#SEC924 isOrigin sing_2402.htm#SEC2483 isPositive sing_2886.htm#SEC2967 isPrimitiveSublattice isPrimitiveSublattice sing_2876.htm#SEC2957 isPure sing_2426.htm#SEC2507 isPureTensor sing_500.htm#SEC554 isQuotientRing sing_1154.htm#SEC1235 isRational sing_559.htm#SEC613 isReflexive sing_2499.htm#SEC2580 isReg sing_1314.htm#SEC1395 isSB sing_210.htm#IDX134 isSimplicial sing_2403.htm#SEC2484 isSmooth sing_2500.htm#SEC2581 isSubModule sing_1155.htm#SEC1236 isSublattice sing_2867.htm#SEC2948 isSubset sing_2960.htm#SEC3041 isSuperset sing_2961.htm#SEC3042 isSymmetric sing_1496.htm#SEC1577 isTame sing_1868.htm#SEC1949 isTerminal sing_2501.htm#SEC2582 isTorsionFree sing_2885.htm#SEC2966 isTwoSidedGB sing_501.htm#SEC555 isUpperTriangular sing_726.htm#SEC780 isVeryAmple sing_2502.htm#SEC2583 isWeyl sing_748.htm#SEC802 isZeroElement sing_2887.htm#SEC2968 isZeroFraction sing_770.htm#SEC824 isZeroNcfrac sing_697.htm#SEC751 is_NND sing_1884.htm#SEC1965 is_NP sing_1374.htm#SEC1455 is_active sing_1923.htm#SEC2004 is_bijective sing_1245.htm#SEC1326 is_cenBimodule sing_714.htm#SEC768 is_cenSubbimodule sing_715.htm#SEC769 is_ci sing_1924.htm#SEC2005 is_complex sing_1182.htm#SEC1263 is_fix_injective sing_2302.htm#SEC2383 is_h_injective sing_2301.htm#SEC2382 is_injective sing_1243.htm#SEC1324 is_irred sing_1881.htm#SEC1962 is_is sing_1925.htm#SEC2006 is_nested sing_1375.htm#SEC1456 is_prime sing_2282.htm#SEC2363 is_primitive_root sing_2278.htm#SEC2359 is_pure sing_788.htm#SEC842 is_reg sing_1926.htm#SEC2007 is_regs sing_1927.htm#SEC2008 is_surjective sing_1244.htm#SEC1325 is_zero sing_1082.htm#SEC1163 isartinianMon sing_1348.htm#SEC1429 isgenericMon sing_1349.htm#SEC1430 ishyper sing_2305.htm#SEC2386 isirreducibleMon sing_1347.htm#SEC1428 isoncurve sing_2306.htm#SEC2387 isparam sing_2369.htm#SEC2450 isprimaryMon sing_1346.htm#SEC1427 isprimeMon sing_1345.htm#SEC1426 isuni sing_2354.htm#SEC2435 ivmatGaussian sing_2099.htm#SEC2180 ivmatInit sing_2096.htm#SEC2177 ivmatSet sing_2097.htm#SEC2178 jInvariant sing_2534.htm#SEC2615 jOft sing_2237.htm#SEC2318 jacob sing_274.htm#SEC314 jacoblift sing_1900.htm#SEC1981 jacobson sing_2206.htm#SEC2287 jacobson.lib sing_2204.htm#SEC2285 jacobson_lib sing_2204.htm#SEC2285 janet sing_275.htm#SEC315 janet basis sing_1479.htm#IDX665 jet sing_276.htm#SEC316 jordan sing_1229.htm#SEC1310 jordanVecField sing_2977.htm#SEC3058 jordanbasis sing_1230.htm#SEC1311 jordanmatrix sing_1231.htm#SEC1312 jordannf sing_1232.htm#SEC1313 jungfib sing_1669.htm#SEC1750 jungnormal sing_1668.htm#SEC1749 jungresolve sing_1667.htm#SEC1748 katsura sing_1080.htm#SEC1161 kbase sing_277.htm#SEC317 kbase (plural) sing_468.htm#SEC508 keepring sing_392.htm#SEC432 kerHom sing_2839.htm#SEC2920 kernel sing_278.htm#SEC318 kernelLattice sing_2870.htm#SEC2951 kill sing_279.htm#SEC319 killTask sing_1161.htm#SEC1242 killall sing_1021.htm#SEC1102 killattrib sing_280.htm#SEC320 kmemory sing_1020.htm#SEC1101 kohom sing_1316.htm#SEC1397 kontrahom sing_1317.htm#SEC1398 koszul sing_281.htm#SEC321 kskernel.lib sing_1891.htm#SEC1972 kskernel_lib sing_1891.htm#SEC1972 l-adic numbers sing_32.htm#SEC46 laguerre sing_282.htm#SEC322 laguerre_solve sing_2054.htm#SEC2135 lastvarGeneral sing_2335.htm#SEC2416 latex.lib sing_2129.htm#SEC2210 latex_lib sing_2129.htm#SEC2210 lattice sing_2615.htm#IDX1051 latticeArea sing_2477.htm#SEC2558 latticeBasis sing_2871.htm#SEC2952 latticeCodegree sing_2503.htm#SEC2584 latticeDegree sing_2504.htm#SEC2585 latticePoints sing_2505.htm#SEC2586 latticeVolume sing_2506.htm#SEC2587 laxfrT sing_2711.htm#SEC2792 laxfrX sing_2712.htm#SEC2793 lazy, option sing_318.htm#IDX156 lcm sing_1083.htm#SEC1164 lcmMon sing_1340.htm#SEC1421 lcmN sing_2246.htm#SEC2327 lcmofall sing_1649.htm#SEC1730 lead sing_283.htm#SEC323 leadcoef sing_284.htm#SEC324 leadexp sing_285.htm#SEC325 leadmonom sing_286.htm#SEC326 leadmonomial sing_2321.htm#SEC2402 left annihilator ideal sing_537.htm#IDX329 left annihilator ideal sing_592.htm#IDX357 leftInverse sing_2195.htm#SEC2276 leftKernel sing_2193.htm#SEC2274 leftOre sing_761.htm#SEC815 length sing_2094.htm#SEC2175 length, option sing_318.htm#IDX157 letplaceGBasis sing_872.htm#SEC926 letterplace sing_296.htm#SEC336 letterplace sing_337.htm#SEC377 lex_solve sing_2060.htm#SEC2141 lexicographical ordering sing_969.htm#IDX440 lib2doc sing_60.htm#SEC97 libSingular sing_2993.htm#SEC3090 libcdd sing_1.htm#IDX12 libfac sing_1.htm#IDX6 libparse sing_69.htm#SEC109 library sing_2630.htm#IDX1066 library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2435.htm#IDX959 library, info string sing_55.htm#IDX124 library, polybori.lib sing_2630.htm#IDX1063 library, ringgb.lib sing_2945.htm#IDX1250 library, template sing_55.htm#SEC92 library, template.lib sing_55.htm#IDX122 lieBracket sing_873.htm#SEC927 lift sing_288.htm#SEC328 lift sing_495.htm#IDX305 lift (letterplace) sing_806.htm#SEC860 lift (plural) sing_469.htm#SEC509 lift_kbase sing_1837.htm#SEC1918 lift_rel_kb sing_1838.htm#SEC1919 liftenvelope sing_498.htm#SEC552 liftstd sing_289.htm#SEC329 liftstd (letterplace) liftstd (letterplace) sing_807.htm#SEC861 liftstd (plural) sing_470.htm#SEC510 likeIdeal sing_2788.htm#SEC2869 likelihood ideal sing_2787.htm#IDX1208 linReduce sing_510.htm#SEC564 linReduceIdeal sing_511.htm#SEC565 linSyzSolve sing_512.htm#SEC566 linalg.lib sing_1207.htm#SEC1288 linalg_lib sing_1207.htm#SEC1288 linealityDimension sing_2404.htm#SEC2485 linealitySpace sing_2405.htm#SEC2486 linear algebra sing_211.htm#SEC251 linear algebra sing_292.htm#SEC332 linear algebra sing_293.htm#SEC333 linear algebra sing_294.htm#SEC334 linear code, dual sing_2164.htm#IDX942 linear code, systematic sing_2165.htm#IDX943 linear interreduction sing_502.htm#IDX320 linearCombinations sing_531.htm#SEC585 linearMapKernel sing_530.htm#SEC584 linear_relations sing_1199.htm#SEC1280 linearlyEquivalent sing_1581.htm#SEC1662 linearpart sing_2046.htm#SEC2127 linesHypersurface sing_1723.htm#SEC1804 link Parallelization with ssi links sing_113.htm#SEC153 link sing_924.htm#SEC981 link declarations sing_114.htm#SEC154 link expressions sing_115.htm#SEC155 link related functions link related functions sing_116.htm#SEC156 links sing_2969.htm#IDX1265 list sing_123.htm#SEC163 list sing_2687.htm#IDX1151 list sing_2688.htm#IDX1153 list declarations sing_124.htm#SEC164 list expressions sing_125.htm#SEC165 list operations sing_126.htm#SEC166 list related functions list related functions sing_127.htm#SEC167 lists sing_2658.htm#IDX1093 lists, elements sing_2660.htm#IDX1095 listvar sing_290.htm#SEC330 lll sing_2903.htm#SEC2984 load sing_393.htm#SEC433 loadLib, option sing_318.htm#IDX178 loadProc, option sing_318.htm#IDX179 locAtZero sing_1400.htm#SEC1481 locNormal sing_1326.htm#SEC1407 locStatus sing_756.htm#SEC810 local methods sing_1325.htm#IDX626 local methods sing_1326.htm#IDX629 local names sing_46.htm#SEC83 local rings, computing in Rings associated to monomial orderings sing_919.htm#SEC976 local weighted lexicographical ordering sing_970.htm#IDX461 local weighted reverse lexicographical ordering Local orderings sing_970.htm#IDX458 localInvar sing_1999.htm#SEC2080 localization Rings associated to monomial orderings sing_919.htm#SEC976 localization sing_2595.htm#IDX1011 localization of D-module sing_560.htm#IDX345 localization of D-module sing_668.htm#IDX384 locally closed set sing_1038.htm#IDX485 locally closed set sing_1039.htm#IDX487 locally closed set sing_1040.htm#IDX489 locally closed set sing_1041.htm#IDX493 locally closed set sing_1055.htm#IDX531 locally closed set sing_1057.htm#IDX536 localstd sing_2331.htm#SEC2412 locnormal.lib sing_1325.htm#SEC1406 locnormal_lib sing_1325.htm#SEC1406 locstd sing_1928.htm#SEC2009 locus FamElemsAtEnvCompPoints sing_1043.htm#SEC1124 locus sing_1043.htm#IDX503 locus sing_1044.htm#IDX506 locus sing_1045.htm#IDX509 locus sing_1046.htm#IDX512 locus sing_1047.htm#IDX515 locus sing_1048.htm#IDX517 locus sing_1049.htm#IDX521 locusdg sing_1044.htm#SEC1125 locusto sing_1046.htm#SEC1127 log2 sing_2221.htm#SEC2302 logHessian sing_2789.htm#SEC2870 logarithmic annihilator ideal sing_537.htm#IDX334 logarithmic annihilator ideal sing_592.htm#IDX359 logg sing_1728.htm#SEC1809 lp, global ordering sing_969.htm#IDX439 lpCalcSubstDegBound sing_862.htm#SEC916 lpDegBound sing_865.htm#SEC919 lpDivision sing_868.htm#SEC922 lpGBPres2Poly sing_869.htm#SEC923 lpGlDimBound sing_860.htm#SEC914 lpHilbert sing_825.htm#SEC879 lpIsPrime sing_859.htm#SEC913 lpIsSemiPrime sing_858.htm#SEC912 lpKDim sing_823.htm#SEC877 lpKDimCheck sing_822.htm#SEC876 lpMonomialBasis sing_824.htm#SEC878 lpNcgenCount sing_867.htm#SEC921 lpNoetherian sing_857.htm#SEC911 lpSickleDim sing_826.htm#SEC880 lpSubstitute sing_861.htm#SEC915 lpVarBlockSize sing_866.htm#SEC920 lprint sing_1061.htm#SEC1142 lres sing_291.htm#SEC331 ls, local ordering sing_970.htm#IDX452 lsum sing_1284.htm#SEC1365 ludecomp sing_292.htm#SEC332 luinverse sing_293.htm#SEC333 lusolve sing_294.htm#SEC334 mRes sing_2807.htm#SEC2888 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_2293.htm#SEC2374 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_2292.htm#SEC2373 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_2291.htm#SEC2372 magnitude sing_2215.htm#SEC2296 makeDivisor sing_1573.htm#SEC1654 makeFormalDivisor sing_1583.htm#SEC1664 makeGraph sing_1275.htm#SEC1356 makeGraphVE sing_1714.htm#SEC1795 makeHeisenberg sing_736.htm#SEC790 makeIdeal sing_2799.htm#SEC2880 makeLetterplaceRing sing_871.htm#SEC925 makeLinks sing_2969.htm#SEC3050 makeMalgrange sing_604.htm#SEC658 makeMatrix sing_2798.htm#SEC2879 makeModElimRing sing_753.htm#SEC807 makePDivisor sing_1589.htm#SEC1670 makePoly sing_2942.htm#SEC3023 makeQPoly sing_2966.htm#SEC3047 makeQsl2 sing_638.htm#SEC692 makeQsl3 sing_639.htm#SEC693 makeQso3 sing_637.htm#SEC691 makeSheaf sing_1702.htm#SEC1783 makeUe6 sing_634.htm#SEC688 makeUe7 sing_635.htm#SEC689 makeUe8 sing_636.htm#SEC690 makeUf4 sing_633.htm#SEC687 makeUg2 sing_632.htm#SEC686 makeUgl sing_618.htm#SEC672 makeUsl sing_617.htm#SEC671 makeUsl2 sing_616.htm#SEC670 makeUso10 sing_624.htm#SEC678 makeUso11 sing_625.htm#SEC679 makeUso12 sing_626.htm#SEC680 makeUso5 sing_619.htm#SEC673 makeUso6 sing_620.htm#SEC674 makeUso7 sing_621.htm#SEC675 makeUso8 sing_622.htm#SEC676 makeUso9 sing_623.htm#SEC677 makeUsp1 sing_627.htm#SEC681 makeUsp2 sing_628.htm#SEC682 makeUsp3 sing_629.htm#SEC683 makeUsp4 sing_630.htm#SEC684 makeUsp5 sing_631.htm#SEC685 makeVariety sing_1694.htm#SEC1775 makeVector sing_2827.htm#SEC2908 makeWeyl sing_735.htm#SEC789 map sing_128.htm#SEC168 map (plural) sing_432.htm#SEC472 map declarations sing_129.htm#SEC169 map declarations (plural) map declarations (plural) sing_433.htm#SEC473 map expressions sing_130.htm#SEC170 map expressions (plural) map expressions (plural) sing_434.htm#SEC474 map operations sing_131.htm#IDX129 map operations (plural) map operations (plural) sing_435.htm#IDX300 map related functions map related functions sing_132.htm#IDX131 map related functions (plural) map related functions (plural) sing_436.htm#IDX301 mapIsFinite sing_1247.htm#SEC1328 mapToRatNormCurve sing_1624.htm#SEC1705 mapall sing_1141.htm#SEC1222 mappingcone sing_2781.htm#SEC2862 mappingcone3 sing_2783.htm#SEC2864 markov4ti2 sing_1491.htm#SEC1572 9163 mat2arr sing_2580.htm#SEC2661 mat2carr sing_2581.htm#SEC2662 mat_rk sing_1221.htm#SEC1302 matbil sing_2342.htm#SEC2423 mathematical objects Representation of mathematical objects sing_965.htm#SEC1022 mathinit sing_2127.htm#SEC2208 matmult sing_2343.htm#SEC2424 matrix sing_133.htm#SEC173 matrix sing_2580.htm#IDX979 matrix sing_2581.htm#IDX982 matrix sing_2582.htm#IDX986 matrix declarations sing_134.htm#SEC174 matrix diagonalization sing_2204.htm#IDX953 matrix expressions sing_135.htm#SEC175 matrix operations sing_137.htm#SEC177 matrix related functions matrix related functions sing_138.htm#SEC178 matrix type cast sing_136.htm#SEC176 matrix.lib sing_1175.htm#SEC1256 matrixExp sing_1614.htm#SEC1695 matrixLog sing_1615.htm#SEC1696 matrixT1 sing_1942.htm#SEC2023 matrix_lib sing_1175.htm#SEC1256 matrixpres sing_2786.htm#SEC2867 matrixsystem sing_2722.htm#SEC2803 max sing_295.htm#SEC335 maxEord sing_1639.htm#SEC1720 maxExp sing_210.htm#IDX136 maxIntRoot sing_685.htm#SEC739 maxPoints sing_2791.htm#SEC2872 maxPointsProb sing_2792.htm#SEC2873 maxZeros sing_1617.htm#SEC1698 maxabs sing_2361.htm#SEC2442 maxcoef sing_1084.htm#SEC1165 maxdeg sing_1085.htm#SEC1166 maxdeg1 sing_1086.htm#SEC1167 maxideal sing_296.htm#SEC336 maximalFace sing_2507.htm#SEC2588 maximalGroebnerCone sing_2561.htm#SEC2642 maximalValue sing_2508.htm#SEC2589 maximum sing_2234.htm#SEC2315 maximum likelihood estimate sing_2787.htm#IDX1209 maximum number of zeroes sing_1617.htm#IDX715 maxlike.lib sing_2787.htm#SEC2868 maxlike_lib sing_2787.htm#SEC2868 mdouble sing_56.htm#SEC93 mem, option sing_318.htm#IDX180 member sing_2660.htm#SEC2741 memberpos sing_1100.htm#SEC1181 membershipMon sing_1341.htm#SEC1422 memory sing_297.htm#SEC337 memory management sing_297.htm#SEC337 merkle_hellman_decryption merkle_hellman_decryption sing_2295.htm#SEC2376 merkle_hellman_encryption merkle_hellman_encryption sing_2294.htm#SEC2375 methods, hashtables sing_2793.htm#IDX1210 methods.lib sing_2793.htm#SEC2874 methods_lib sing_2793.htm#SEC2874 midpoint sing_2718.htm#SEC2799 milnor sing_1929.htm#SEC2010 milnorcode sing_1785.htm#SEC1866 milnornumber sing_1916.htm#SEC1997 min sing_298.htm#SEC338 minAssChar sing_1445.htm#SEC1526 minAssCharE sing_1446.htm#SEC1527 minAssGTZ sing_1443.htm#SEC1524 minAssGTZE sing_1444.htm#SEC1525 minAssZ sing_1463.htm#SEC1544 minEcart sing_2324.htm#SEC2405 minIntRoot sing_558.htm#SEC612 minIntRoot2 sing_684.htm#SEC738 minMult sing_1254.htm#SEC1335 minbase sing_299.htm#SEC339 minbaseMon sing_1338.htm#SEC1419 mindeg sing_1087.htm#SEC1168 mindeg1 sing_1088.htm#SEC1169 mindist sing_2179.htm#SEC2260 minimal display time, setting the sing_361.htm#IDX284 minimal representations sing_880.htm#IDX438 minimalAfaceOrbits sing_2448.htm#SEC2529 minimalAfaces sing_2439.htm#SEC2520 minimalFace sing_2509.htm#SEC2590 minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2450.htm#SEC2531 minimalValue sing_2510.htm#SEC2591 minipoly sing_1226.htm#SEC1307 minkowskiSum sing_2511.htm#SEC2592 minor sing_300.htm#SEC340 minpoly sing_401.htm#SEC441 minres sing_301.htm#SEC341 minres (plural) sing_471.htm#SEC511 minus sing_2676.htm#IDX1127 minus sing_2677.htm#IDX1129 minus sing_2698.htm#IDX1175 minus sing_2699.htm#IDX1177 mirror symmetry sing_1274.htm#IDX594 mixed Hodge structure sing_1845.htm#IDX801 mixed Hodge structure sing_1851.htm#IDX829 mixed Hodge structure sing_1852.htm#IDX835 mixed Hodge structure sing_1853.htm#IDX843 mixed Hodge structure sing_1854.htm#IDX849 mixed Hodge structure sing_1855.htm#IDX857 mixed Hodge structure sing_1856.htm#IDX867 mixed Hodge structure sing_1867.htm#IDX873 mixed Hodge structure sing_1869.htm#IDX884 mod sing_81.htm#SEC121 mod sing_98.htm#SEC138 mod sing_147.htm#SEC187 mod sing_155.htm#SEC195 mod2id sing_1092.htm#SEC1173 modBorder sing_1481.htm#SEC1562 modDec sing_1357.htm#SEC1438 modIntersect sing_1335.htm#SEC1416 modJanet sing_1483.htm#SEC1564 modNPos sing_1385.htm#SEC1466 modNormal sing_1331.htm#SEC1412 modNpos_test sing_1383.htm#SEC1464 modQuotient sing_1328.htm#SEC1409 modSagbiAlg sing_1807.htm#SEC1888 modSat sing_1329.htm#SEC1410 modStd sing_1333.htm#SEC1414 modSyz sing_1334.htm#SEC1415 modVStd sing_1818.htm#SEC1899 modVStd0 sing_1819.htm#SEC1900 modWalk sing_2848.htm#SEC2929 mod_versal sing_1836.htm#SEC1917 modality sing_1793.htm#SEC1874 modberlekampMassey sing_1290.htm#SEC1371 moddiq.lib sing_1327.htm#SEC1408 moddiq_lib sing_1327.htm#SEC1408 modfWalk sing_2850.htm#SEC2931 modfrWalk sing_2851.htm#SEC2932 modnormal.lib sing_1330.htm#SEC1411 modnormal_lib sing_1330.htm#SEC1411 modrWalk sing_2849.htm#SEC2930 modrationalInterpolation modrationalInterpolation sing_1288.htm#SEC1369 modregCM sing_1389.htm#SEC1470 modsatiety sing_1387.htm#SEC1468 modstd.lib sing_1332.htm#SEC1413 modstd_lib sing_1332.htm#SEC1413 modular sing_1070.htm#SEC1151 modular methods sing_1325.htm#IDX627 modular methods sing_1330.htm#IDX633 modular methods. sing_1326.htm#IDX630 modular techniques. sing_1331.htm#IDX635 modular.lib sing_1069.htm#SEC1150 modular_lib sing_1069.htm#SEC1150 modular_lib sing_1069.htm#IDX540 module sing_139.htm#SEC179 module (plural) sing_437.htm#SEC477 module declarations sing_140.htm#SEC180 module declarations (plural) module declarations (plural) sing_438.htm#SEC478 module expressions sing_141.htm#SEC181 module expressions (plural) module expressions (plural) sing_439.htm#SEC479 module operations sing_142.htm#SEC182 module operations (plural) module operations (plural) sing_440.htm#SEC480 module ordering C sing_971.htm#IDX464 module ordering c sing_971.htm#IDX466 module related functions module related functions sing_143.htm#SEC183 module related functions (plural) module related functions (plural) sing_441.htm#SEC481 module_containment sing_1239.htm#SEC1320 modules.lib sing_2794.htm#SEC2875 modules_lib sing_2794.htm#SEC2875 moduliSpace sing_1716.htm#SEC1797 modulo sing_302.htm#SEC342 modulo (plural) sing_472.htm#SEC512 moduloSlim sing_743.htm#SEC797 modwalk.lib sing_2847.htm#SEC2928 modwalk_lib sing_2847.htm#SEC2928 moebius sing_2616.htm#SEC2697 moebius function sing_2616.htm#IDX1052 molien sing_1965.htm#SEC2046 mondim sing_667.htm#SEC721 mondromy.lib sing_1897.htm#SEC1978 mondromy_lib sing_1897.htm#SEC1978 monitor sing_303.htm#SEC343 monodromy sing_1845.htm#IDX805 monodromy sing_1850.htm#SEC1931 monodromy sing_1850.htm#IDX825 monodromy sing_1855.htm#IDX860 monodromy sing_1867.htm#IDX876 monodromy sing_1869.htm#IDX887 monodromyB sing_1901.htm#SEC1982 monoideal, dimension sing_667.htm#IDX377 monomial sing_304.htm#SEC344 monomial ordering sing_1150.htm#IDX566 monomial orderings General definitions for orderings sing_919.htm#SEC976 monomial orderings sing_968.htm#SEC1025 monomial orderings introduction Introduction to orderings sing_967.htm#SEC1024 monomial output sing_405.htm#SEC445 monomial, write sing_405.htm#SEC445 monomialInIdeal sing_682.htm#SEC736 monomialLcm sing_2322.htm#SEC2403 monomialabortstd sing_2623.htm#SEC2704 monomialideal.lib sing_1336.htm#SEC1417 monomialideal_lib sing_1336.htm#SEC1417 monomials and precedence Miscellaneous oddities sing_422.htm#IDX290 mons2intmat sing_1430.htm#SEC1511 15555 morsesplit sing_1786.htm#SEC1867 movingCone sing_2446.htm#SEC2527 mp_res_mat sing_2057.htm#SEC2138 mplot sing_2128.htm#SEC2209 mpresmat sing_305.htm#SEC345 mprimdec.lib sing_1353.htm#SEC1434 mprimdec_lib sing_1353.htm#SEC1434 mrcgs sing_1109.htm#SEC1190 mrcgs, rcgs, buildtree, cantreetoMaple, cantodiffcgs crcgs sing_1111.htm#IDX558 mrcgs, rcgs, crcgs, Maple sing_1112.htm#IDX559 mregular.lib sing_1368.htm#SEC1449 mregular_lib sing_1368.htm#SEC1449 mres sing_306.htm#SEC346 mres (plural) sing_473.htm#SEC513 mstd sing_307.htm#SEC347 msum sing_58.htm#SEC95 mtriple sing_57.htm#SEC94 mult Miscellaneous oddities sing_308.htm#SEC348 mult sing_422.htm#IDX291 multBound sing_402.htm#SEC442 multRat sing_690.htm#SEC744 multarr2arr sing_2611.htm#SEC2692 multarrMultRestrict sing_2613.htm#SEC2694 multarrRestrict sing_2612.htm#SEC2693 multcol sing_1193.htm#SEC1274 multdivisor sing_1575.htm#SEC1656 multformaldivisor sing_1587.htm#SEC1668 multi sing_2309.htm#SEC2390 multi indices sing_37.htm#SEC65 multi-graded Hilbert series sing_877.htm#IDX432 multiDeg sing_2882.htm#SEC2963 multiDegBasis sing_2883.htm#SEC2964 multiDegGroebner sing_2891.htm#SEC2972 multiDegModulo sing_2893.htm#SEC2974 multiDegPartition sing_2884.htm#SEC2965 multiDegResolution sing_2894.htm#SEC2975 multiDegSyzygy sing_2892.htm#SEC2973 multiDegTensor sing_2895.htm#SEC2976 multiDegTor sing_2896.htm#SEC2977 multiarrangement sing_2607.htm#IDX1032 multiarrangement sing_2608.htm#IDX1034 multiarrangement sing_2609.htm#IDX1037 multiarrangement sing_2610.htm#IDX1038 multiarrangement sing_2611.htm#IDX1041 multiarrangement sing_2612.htm#IDX1044 multiarrangement sing_2613.htm#IDX1046 multidimensional_knapsack multidimensional_knapsack sing_2287.htm#SEC2368 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2852.htm#IDX1217 multigrading.lib sing_2852.htm#IDX1215 multigrading_lib sing_2852.htm#IDX1216 multipleCover sing_1722.htm#SEC1803 multiplication sing_2678.htm#IDX1131 multiplication sing_2700.htm#IDX1179 multiplicities, sequence of sing_1876.htm#IDX899 multiplicity sing_661.htm#IDX372 multiplicity sing_1261.htm#IDX586 multiplicity sequence sing_1758.htm#IDX772 multiplicity sequence sing_1761.htm#IDX784 multiplicity sequence sing_1878.htm#IDX900 multiplyLeftFractions multiplyLeftFractions sing_766.htm#SEC820 multiplylist sing_1659.htm#SEC1740 multivariate equations sing_2030.htm#IDX924 multrow sing_1194.htm#SEC1275 multseq2charexp sing_1757.htm#SEC1838 multsequence sing_1878.htm#SEC1959 nBoundaryLatticePoints nBoundaryLatticePoints sing_2512.htm#SEC2593 nHilbertBasis sing_2513.htm#SEC2594 nInteriorLatticePoints nInteriorLatticePoints sing_2514.htm#SEC2595 nLatticePoints sing_2515.htm#SEC2596 naccache_stern_decryption naccache_stern_decryption sing_2290.htm#SEC2371 naccache_stern_encryption naccache_stern_encryption sing_2289.htm#SEC2370 naccache_stern_generation naccache_stern_generation sing_2288.htm#SEC2369 nameof sing_309.htm#SEC349 names sing_310.htm#SEC350 nashmult sing_1765.htm#SEC1846 nblocks sing_361.htm#IDX219 ncExt_R sing_709.htm#SEC763 ncHilb sing_662.htm#SEC716 ncHilb.lib sing_877.htm#SEC931 ncHilb_lib sing_877.htm#SEC931 ncHilbertMultiplicity ncHilbertMultiplicity sing_665.htm#SEC719 ncHilbertPolynomial sing_664.htm#SEC718 ncHilbertSeries sing_663.htm#SEC717 ncHom sing_710.htm#SEC764 ncInit sing_881.htm#SEC935 ncModslimgb.lib sing_720.htm#SEC774 ncModslimgb_lib sing_720.htm#SEC774 ncRelations sing_744.htm#SEC798 ncVarsAdd sing_883.htm#SEC937 ncVarsGet sing_882.htm#SEC936 nc_algebra sing_474.htm#SEC514 nc_hilb sing_361.htm#IDX221 ncalg.lib sing_615.htm#SEC669 ncalg_lib sing_615.htm#SEC669 ncalgebra sing_475.htm#SEC515 ncdecomp.lib sing_642.htm#SEC696 ncdecomp_lib sing_642.htm#SEC696 ncdetection sing_609.htm#SEC663 ncfactor sing_648.htm#SEC702 ncfactor.lib sing_647.htm#SEC701 ncfactor_lib sing_647.htm#SEC701 ncfrac.lib sing_694.htm#SEC748 ncfrac_lib sing_694.htm#SEC748 ncgen sing_808.htm#SEC862 nchilb sing_878.htm#SEC932 nchilbert.lib sing_661.htm#SEC715 nchilbert_lib sing_661.htm#SEC715 nchomolog.lib sing_708.htm#IDX390 nchomolog_lib sing_708.htm#IDX391 ncloc.lib sing_716.htm#SEC770 ncloc_lib sing_716.htm#SEC770 ncmodslimgb sing_721.htm#SEC775 ncols sing_311.htm#SEC351 ncones sing_2428.htm#SEC2509 ncpreim.lib sing_722.htm#SEC776 ncpreim_lib sing_722.htm#SEC776 ncrat.lib sing_880.htm#IDX433 ncratAdd sing_885.htm#SEC939 ncratDefine sing_884.htm#SEC938 ncratEvaluateAt sing_894.htm#SEC948 ncratFromPoly sing_892.htm#SEC946 ncratFromString sing_891.htm#SEC945 ncratInvert sing_888.htm#SEC942 ncratMultiply sing_887.htm#SEC941 ncratPower sing_893.htm#SEC947 ncratPrint sing_890.htm#SEC944 ncratSPrint sing_889.htm#SEC943 ncratSubstract sing_886.htm#SEC940 ncrat_lib sing_880.htm#IDX434 ncrepAdd sing_896.htm#SEC950 ncrepDim sing_901.htm#SEC955 ncrepEvaluate sing_903.htm#SEC957 ncrepEvaluateAt sing_904.htm#SEC958 ncrepGet sing_895.htm#SEC949 ncrepGetRegularMinimal ncrepGetRegularMinimal sing_911.htm#SEC965 ncrepGetRegularZeroMinimal ncrepGetRegularZeroMinimal sing_910.htm#SEC964 ncrepInvert sing_899.htm#SEC953 ncrepIsDefined sing_906.htm#SEC960 ncrepIsDefinedDim sing_905.htm#SEC959 ncrepIsRegular sing_907.htm#SEC961 ncrepMultiply sing_898.htm#SEC952 ncrepPencilCombine sing_913.htm#SEC967 ncrepPencilGet sing_912.htm#SEC966 ncrepPrint sing_900.htm#SEC954 ncrepRegularMinimize ncrepRegularMinimize sing_909.htm#SEC963 ncrepRegularZeroMinimize ncrepRegularZeroMinimize sing_908.htm#SEC962 ncrepSubstitute sing_902.htm#SEC956 ncrepSubstract sing_897.htm#SEC951 nctools.lib sing_730.htm#SEC784 nctools_lib sing_730.htm#SEC784 ndcond sing_733.htm#SEC787 negateNcfrac sing_703.htm#SEC757 negatedCone sing_2406.htm#SEC2487 negation sing_2677.htm#IDX1130 negative degree lexicographical ordering sing_970.htm#IDX455 negative degree reverse lexicographical ordering Local orderings sing_970.htm#IDX453 negative lexicographical ordering sing_970.htm#IDX451 negativedivisor sing_1576.htm#SEC1657 negativeformaldivisor negativeformaldivisor sing_1586.htm#SEC1667 net sing_2904.htm#IDX1218 net sing_2906.htm#SEC2987 net access Command line options sing_19.htm#IDX40 netBigInt sing_2912.htm#SEC2993 netBigIntMat sing_2907.htm#SEC2988 netBigIntMatShort sing_2908.htm#SEC2989 netCoefficientRing sing_2909.htm#SEC2990 netIdeal sing_2910.htm#SEC2991 netInt sing_2911.htm#SEC2992 netIntMat sing_2913.htm#SEC2994 netIntMatShort sing_2914.htm#SEC2995 netIntVector sing_2915.htm#SEC2996 netIntVectorShort sing_2916.htm#SEC2997 netList sing_2918.htm#SEC2999 netMap sing_2919.htm#SEC3000 netMap2 sing_2920.htm#SEC3001 netMatrix sing_2829.htm#SEC2910 netNumber sing_2917.htm#SEC2998 netPoly sing_2923.htm#SEC3004 netPrimePower sing_2924.htm#SEC3005 netRing sing_2925.htm#SEC3006 netString sing_2926.htm#SEC3007 netVector sing_2828.htm#SEC2909 netmatrix sing_2921.htm#SEC3002 netmatrixShort sing_2922.htm#SEC3003 nets.lib sing_2904.htm#SEC2985 nets_lib sing_2904.htm#SEC2985 netvector sing_2927.htm#SEC3008 netvectorShort sing_2928.htm#SEC3009 newTest sing_2229.htm#SEC2310 newline sing_172.htm#SEC212 news sing_2986.htm#SEC3067 newstruct sing_183.htm#SEC223 newstruct sing_2630.htm#IDX1068 newtonDiag sing_1096.htm#SEC1177 newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2570.htm#SEC2651 newtonPolytope sing_2432.htm#SEC2513 newtonPolytopeLP sing_2469.htm#SEC2550 newtonPolytopeP sing_2468.htm#SEC2549 newtonpoly sing_1883.htm#SEC1964 nf_icis sing_1930.htm#SEC2011 nfmodStd sing_1378.htm#SEC1459 nfmodSyz sing_1380.htm#SEC1461 nfmodstd.lib sing_1376.htm#SEC1457 nfmodstd_lib sing_1376.htm#SEC1457 nfmodsyz.lib sing_1379.htm#SEC1460 nfmodsyz_lib sing_1379.htm#SEC1460 nilpotent Lie algebras sing_1612.htm#IDX700 nmaxcones sing_2427.htm#SEC2508 noElements sing_2949.htm#SEC3030 noether sing_403.htm#SEC443 noether.lib sing_1381.htm#SEC1462 noetherNormal sing_1246.htm#SEC1327 noether_lib sing_1381.htm#SEC1462 non-english special characters sing_411.htm#IDX286 nonMonomials sing_1434.htm#SEC1515 nonZeroEntry sing_1249.htm#SEC1330 noncommutative, rational expressions sing_880.htm#IDX435 none, option sing_318.htm#IDX150 norTest sing_1401.htm#SEC1482 norm sing_2308.htm#SEC2389 normaform (up to a bound) sing_361.htm#IDX244 normal sing_1391.htm#SEC1472 normal bundle, graph, rational curves, multiple covers, lines on normalBundle sing_1721.htm#IDX751 normal form sing_977.htm#IDX467 normal.lib sing_1390.htm#SEC1471 normalBundle sing_1721.htm#SEC1802 normalC sing_1393.htm#SEC1474 normalConductor sing_1405.htm#SEC1486 normalFan sing_2516.htm#SEC2597 normalForm sing_1577.htm#SEC1658 normalI sing_1478.htm#SEC1559 normalP sing_1392.htm#SEC1473 normalToricRing sing_1408.htm#SEC1489 29638 normalToricRingFromBinomials normalToricRingFromBinomials sing_1409.htm#SEC1490 2301 normal_lib sing_1390.htm#SEC1471 normalform sing_1790.htm#SEC1871 normalform sing_1806.htm#IDX794 normaliz sing_1.htm#IDX14 18426 normaliz sing_1421.htm#SEC1502 normaliz.lib sing_1406.htm#SEC1487 normaliz_lib sing_1406.htm#SEC1487 normalization sing_1260.htm#IDX584 normalization sing_1325.htm#IDX625 normalization sing_1326.htm#IDX628 normalization sing_1330.htm#IDX632 normalization sing_1331.htm#IDX634 normalization sing_1391.htm#IDX643 normalization sing_1392.htm#IDX646 normalization sing_1393.htm#IDX649 normalization sing_1405.htm#IDX655 normalization sing_1406.htm#IDX657 normalization. sing_1322.htm#IDX624 normalization. sing_1619.htm#IDX722 normalize sing_1089.htm#SEC1170 normalizeMonoidal sing_772.htm#SEC826 normalizeRational sing_773.htm#SEC827 not sing_101.htm#SEC141 not equal sing_2681.htm#IDX1138 not equal sing_2702.htm#IDX1185 notBuckets, option sing_318.htm#IDX160 notRegularity, option sing_318.htm#IDX158 notSugar, option sing_318.htm#IDX159 notWarnSB, option sing_318.htm#IDX181 npar sing_2214.htm#SEC2295 npars sing_312.htm#SEC352 nrRootsDeterm sing_2339.htm#SEC2420 nrRootsProbab sing_2338.htm#SEC2419 nres sing_313.htm#SEC353 nres (plural) sing_476.htm#SEC516 nrows sing_314.htm#SEC354 nrroots sing_2368.htm#SEC2449 nsatiety sing_1386.htm#SEC1467 nselect sing_1270.htm#SEC1351 nt_solve sing_2072.htm#SEC2153 ntsolve.lib sing_2071.htm#SEC2152 ntsolve_lib sing_2071.htm#SEC2152 num_elim sing_2089.htm#SEC2170 num_elim1 sing_2090.htm#SEC2171 num_prime_decom sing_2083.htm#SEC2164 num_prime_decom1 sing_2084.htm#SEC2165 num_radical1 sing_2087.htm#SEC2168 num_radical2 sing_2088.htm#SEC2169 num_radical_via_decom num_radical_via_decom sing_2085.htm#SEC2166 num_radical_via_randlincom num_radical_via_randlincom sing_2086.htm#SEC2167 number sing_144.htm#SEC184 number sing_2584.htm#IDX992 number declarations sing_145.htm#SEC185 number expressions sing_146.htm#SEC186 number operations sing_147.htm#SEC187 number related functions number related functions sing_148.htm#SEC188 numberOfConesOfDimension numberOfConesOfDimension sing_2429.htm#SEC2510 number_e sing_1022.htm#SEC1103 number_pi sing_1023.htm#SEC1104 numerAlg.lib sing_1594.htm#IDX689 numerAlg_lib sing_1594.htm#IDX690 numerAlg_lib sing_1599.htm#IDX699 numerDecom.lib sing_1599.htm#IDX693 numerDecom_lib sing_1594.htm#IDX692 numerDecom_lib sing_1599.htm#IDX694 numerator sing_315.htm#SEC355 numerical algebraic geometry sing_2074.htm#IDX926 numerical irreducible decomposition sing_1599.htm#IDX695 nvars sing_316.htm#SEC356 olga.lib sing_755.htm#SEC809 olga_lib sing_755.htm#SEC809 oneDimBelongSemigroup oneDimBelongSemigroup sing_1256.htm#SEC1337 oneNcfrac sing_700.htm#SEC754 onesVector sing_2434.htm#SEC2515 online help The online help system sing_16.htm#SEC22 open sing_317.htm#SEC357 opentex sing_2131.htm#SEC2212 operatorAlgebra sing_828.htm#SEC882 operatorBM sing_544.htm#SEC598 operatorModulo sing_545.htm#SEC599 oppose sing_477.htm#SEC517 opposite sing_478.htm#SEC518 opposite polynomial sing_361.htm#IDX229 opposite ring sing_361.htm#IDX226 option sing_318.htm#SEC358 option(warn) sing_70.htm#SEC110 optionIsSet sing_1147.htm#SEC1228 or Evaluation of logical expressions sing_101.htm#SEC141 or sing_415.htm#SEC455 orbit sing_1612.htm#IDX702 orbit sing_1613.htm#IDX706 orbit sing_1616.htm#IDX711 orbit sing_1617.htm#IDX714 orbitConeOrbits sing_2449.htm#SEC2530 orbitCones sing_2440.htm#SEC2521 orbit_variety sing_1989.htm#SEC2070 orbitparam.lib sing_1612.htm#SEC1693 orbitparam_lib sing_1612.htm#SEC1693 ord sing_319.htm#SEC359 ord_test sing_1142.htm#SEC1223 order ideal, border basis sing_1480.htm#IDX666 order ideal, border basis sing_1481.htm#IDX667 ordering diffAlgebraChangeOrd sing_2666.htm#IDX1107 ordering sing_2682.htm#IDX1141 ordering sing_2683.htm#IDX1144 orderings General definitions for orderings sing_968.htm#SEC1025 orderings introduction Introduction to orderings sing_967.htm#SEC1024 orderings, L sing_975.htm#SEC1032 orderings, M sing_972.htm#SEC1029 orderings, a sing_974.htm#SEC1031 orderings, global sing_969.htm#SEC1026 orderings, local sing_970.htm#SEC1027 orderings, product sing_973.htm#SEC1030 ordstr sing_320.htm#SEC360 origin sing_2377.htm#SEC2458 orthogonalize sing_1212.htm#SEC1293 outer sing_1183.htm#SEC1264 output sing_41.htm#SEC71 outputting monomials sing_405.htm#SEC445 p-adic numbers sing_32.htm#SEC46 pFactor sing_2263.htm#SEC2344 pIntersect sing_508.htm#SEC562 pIntersectSyz sing_509.htm#SEC563 package sing_149.htm#SEC189 package declarations package declarations sing_150.htm#SEC190 package related functions package related functions sing_151.htm#SEC191 pairset sing_2328.htm#SEC2409 par sing_321.htm#SEC361 par2varRing sing_1005.htm#SEC1086 paraConic sing_1627.htm#SEC1708 paraPlaneCurve sing_1621.htm#SEC1702 parallel computing sing_2973.htm#IDX1268 parallel skeletons sing_1071.htm#IDX546 parallel.lib sing_1071.htm#SEC1152 parallelTestAND sing_1075.htm#SEC1156 parallelTestOR sing_1076.htm#SEC1157 parallelWaitAll sing_1074.htm#SEC1155 parallelWaitFirst sing_1073.htm#SEC1154 parallelWaitN sing_1072.htm#SEC1153 parallel_lib sing_1071.htm#SEC1152 parallelization sing_1071.htm#IDX545 parallelization sing_1126.htm#IDX560 parallelization sing_1159.htm#IDX570 param sing_1874.htm#SEC1955 parameter, as numbers sing_144.htm#SEC184 parameterSubstitute sing_2556.htm#SEC2637 parametric annihilator sing_537.htm#IDX335 parametric annihilator for variety sing_600.htm#IDX365 parametric ideal sing_1034.htm#IDX473 parametric ideal sing_1041.htm#IDX492 parametric ideal sing_1041.htm#IDX494 parametric ideal sing_1042.htm#IDX499 parametrization sing_1612.htm#IDX703 parametrization sing_1616.htm#IDX712 parametrization sing_1874.htm#IDX894 parametrizeOrbit sing_1616.htm#SEC1697 paraplanecurves.lib sing_1618.htm#SEC1699 paraplanecurves_lib sing_1618.htm#SEC1699 pardeg sing_322.htm#SEC362 parstr sing_323.htm#SEC363 part sing_1559.htm#SEC1640 partOver sing_1562.htm#SEC1643 partUnder sing_1563.htm#SEC1644 partial fraction sing_2930.htm#IDX1243 partial_molien sing_1967.htm#SEC2048 partitions sing_1282.htm#SEC1363 partitions sing_1282.htm#IDX613 path Used environment variables sing_2995.htm#SEC3092 path integral sing_1274.htm#IDX600 paths Used environment variables sing_2995.htm#SEC3092 pause sing_1068.htm#SEC1149 pdivi sing_1036.htm#SEC1117 pdivi sing_1037.htm#IDX483 pdivi2 sing_1102.htm#SEC1183 pdivisorplus sing_1591.htm#SEC1672 permcol sing_1195.htm#SEC1276 permrow sing_1196.htm#SEC1277 permutationFromIntvec permutationFromIntvec sing_2455.htm#SEC2536 permutationToIntvec sing_2456.htm#SEC2537 permutations sing_1283.htm#IDX614 permutations, sum, max, min sing_2657.htm#IDX1092 permute sing_1283.htm#SEC1364 permute_L sing_2166.htm#SEC2247 perron sing_777.htm#SEC831 perron.lib sing_776.htm#SEC830 perron_lib sing_776.htm#SEC830 pfd sing_2931.htm#SEC3012 pfd.lib sing_2930.htm#SEC3011 pfdMat sing_2939.htm#SEC3020 pfd_lib sing_2930.htm#SEC3011 phindex.lib sing_2625.htm#IDX1059 phindex_lib sing_2625.htm#IDX1060 picksFormula sing_2478.htm#SEC2559 pid sing_361.htm#IDX238 plainInvariants sing_1833.htm#SEC1914 planeCur sing_1804.htm#SEC1885 plot sing_2144.htm#SEC2225 plotRot sing_2148.htm#SEC2229 plotRotated sing_2147.htm#SEC2228 plotRotatedDirect sing_2150.htm#SEC2231 plotRotatedList sing_2149.htm#SEC2230 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_2151.htm#SEC2232 plural sing_1149.htm#IDX565 pmat sing_1062.htm#SEC1143 pnormalf sing_1037.htm#SEC1118 pnormalform sing_1105.htm#SEC1186 pointid.lib sing_1433.htm#SEC1514 pointid_lib sing_1433.htm#SEC1514 polSol sing_674.htm#SEC728 polSolFiniteRank sing_675.htm#SEC729 pollTask sing_1169.htm#SEC1250 poly sing_152.htm#SEC192 poly (plural) sing_442.htm#SEC482 poly declarations sing_153.htm#SEC193 poly declarations (plural) poly declarations (plural) sing_443.htm#SEC483 poly expressions sing_154.htm#SEC194 poly expressions (plural) poly expressions (plural) sing_444.htm#SEC484 poly operations sing_155.htm#SEC195 poly operations (plural) poly operations (plural) sing_445.htm#SEC485 poly related functions poly related functions sing_156.htm#SEC196 poly related functions (plural) poly related functions (plural) sing_446.htm#SEC486 poly2list sing_586.htm#SEC640 poly2zdd sing_2646.htm#SEC2727 61839 polyInterpolation sing_1287.htm#SEC1368 polyVars sing_681.htm#SEC735 polybori sing_2630.htm#IDX1064 polybori.lib sing_2630.htm#IDX1061 polybori.lib sing_2630.htm#IDX1065 polybori_lib sing_2630.htm#IDX1062 polyclass.lib sing_2941.htm#SEC3022 polyclass_lib sing_2941.htm#SEC3022 polylib.lib sing_1077.htm#SEC1158 polylib_lib sing_1077.htm#SEC1158 polymake sing_2466.htm#IDX964 polymake.lib sing_2466.htm#SEC2547 polymakePolytope sing_2467.htm#SEC2548 polymake_lib sing_2466.htm#SEC2547 polynomial sing_2693.htm#IDX1166 polynomial functions sing_2945.htm#IDX1249 polynomial solutions sing_668.htm#IDX387 polynomial, opposite sing_361.htm#IDX230 polynomials sing_2941.htm#IDX1246 polytope sing_191.htm#SEC231 polytope sing_2466.htm#IDX960 polytopeViaInequalities polytopeViaInequalities sing_2407.htm#SEC2488 polytopeViaPoints sing_2408.htm#SEC2489 pos_def sing_1223.htm#SEC1304 poset sing_2615.htm#IDX1050 positiveOrthant sing_2378.htm#SEC2459 posweight sing_1947.htm#SEC2028 powSumSym sing_1516.htm#SEC1597 power sing_1184.htm#SEC1265 power set sing_2659.htm#IDX1094 powerN sing_2247.htm#SEC2328 powerX sing_2256.htm#SEC2337 power_products sing_1981.htm#SEC2062 powerpolyX sing_2226.htm#SEC2307 powersums sing_2349.htm#SEC2430 preComp sing_1364.htm#SEC1445 preimage sing_324.htm#SEC364 preimage sing_722.htm#IDX392 preimage (plural) sing_479.htm#SEC519 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1145.htm#IDX563 preimageLattice sing_2872.htm#SEC2953 preimageLoc sing_1145.htm#SEC1226 preimageNC sing_724.htm#SEC778 prepEmbDiv sing_1689.htm#SEC1770 prepMat sing_2027.htm#SEC2108 prepRealclassify sing_1795.htm#SEC1876 prepSV sing_2161.htm#SEC2242 prepareAss sing_1452.htm#SEC1533 presentTree sing_1676.htm#SEC1757 presentation sing_2830.htm#SEC2911 presolve.lib sing_2038.htm#SEC2119 presolve_lib sing_2038.htm#SEC2119 primL sing_2251.htm#SEC2332 primList sing_2250.htm#SEC2331 primRoot sing_1497.htm#SEC1578 primTest sing_1363.htm#SEC1444 primary decomposition sing_1437.htm#IDX659 primary decomposition sing_1460.htm#IDX660 primary decomposition of modules sing_1353.htm#IDX636 primary decomposition, numerical sing_1599.htm#IDX697 primary_char0 sing_1971.htm#SEC2052 primary_char0_no_molien primary_char0_no_molien sing_1973.htm#SEC2054 primary_char0_no_molien_random primary_char0_no_molien_random sing_1978.htm#SEC2059 primary_char0_random primary_char0_random sing_1976.htm#SEC2057 primary_charp sing_1972.htm#SEC2053 primary_charp_no_molien primary_charp_no_molien sing_1974.htm#SEC2055 primary_charp_no_molien_random primary_charp_no_molien_random sing_1979.htm#SEC2060 primary_charp_random primary_charp_random sing_1977.htm#SEC2058 primary_charp_without primary_charp_without sing_1975.htm#SEC2056 primary_charp_without_random primary_charp_without_random sing_1980.htm#SEC2061 primary_invariants sing_1959.htm#SEC2040 primary_invariants_random primary_invariants_random sing_1960.htm#SEC2041 primdec.lib sing_1437.htm#SEC1518 primdecGTZ sing_1439.htm#SEC1520 primdecGTZE sing_1440.htm#SEC1521 primdecMon sing_1352.htm#SEC1433 primdecSY sing_1441.htm#SEC1522 primdecSYE sing_1442.htm#SEC1523 primdecZ sing_1461.htm#SEC1542 primdecZM sing_1462.htm#SEC1543 primdec_lib sing_1437.htm#SEC1518 primdecint.lib sing_1460.htm#SEC1541 primdecint_lib sing_1460.htm#SEC1541 prime sing_325.htm#SEC365 primeClosure sing_1396.htm#SEC1477 primecoeffs sing_1029.htm#SEC1110 primefactors sing_326.htm#SEC366 primes sing_1024.htm#SEC1105 primitiv.lib sing_1468.htm#SEC1549 primitiv_lib sing_1468.htm#SEC1549 primitive sing_1469.htm#SEC1550 primitive element sing_1469.htm#IDX661 primitiveSpan sing_2879.htm#SEC2960 primitive_extra sing_1470.htm#SEC1551 primparam sing_1828.htm#SEC1909 principal intersection sing_502.htm#IDX319 print sing_327.htm#SEC367 print sing_2582.htm#IDX985 print sing_2670.htm#IDX1116 print sing_2672.htm#IDX1121 print sing_2673.htm#IDX1122 print sing_2695.htm#IDX1170 print sing_2696.htm#IDX1171 printBetti sing_2811.htm#SEC2892 printFreeModule sing_2803.htm#SEC2884 printGraph sing_1276.htm#SEC1357 printGraphG sing_1715.htm#SEC1796 printGroup sing_2860.htm#SEC2941 printHom sing_2806.htm#SEC2887 printMatrix sing_2802.htm#SEC2883 printModule sing_2805.htm#SEC2886 printMoebius sing_2621.htm#SEC2702 printNormalFormEquation printNormalFormEquation sing_2944.htm#SEC3025 printPoly sing_2943.htm#SEC3024 printResolution sing_2804.htm#SEC2885 printSheaf sing_1703.htm#SEC1784 printStack sing_1717.htm#SEC1798 printTask sing_1164.htm#SEC1245 printVariety sing_1695.htm#SEC1776 printf sing_328.htm#SEC368 printlevel sing_404.htm#SEC444 proc sing_157.htm#SEC197 proc declaration sing_158.htm#SEC198 proc expression sing_159.htm#SEC199 procedure, ASCII help sing_56.htm#IDX125 procedure, ASCII/Texinfo help sing_58.htm#IDX127 procedure, texinfo help sing_57.htm#IDX126 procedures, help string sing_45.htm#SEC82 procedures, static Procedure definition sing_43.htm#SEC78 procs with different argument types procs with different argument types sing_160.htm#SEC200 prodcrit sing_2326.htm#SEC2407 product sing_1025.htm#SEC1106 product sing_2678.htm#IDX1132 product sing_2700.htm#IDX1180 product variety, abstract variety sing_1696.htm#IDX739 productVariety sing_1696.htm#SEC1777 productgroup sing_2881.htm#SEC2962 progress watch sing_318.htm#IDX163 projectLattice sing_2873.htm#SEC2954 projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_1700.htm#IDX743 projective dimension purityfiltration_lib sing_778.htm#IDX401 projective limes sing_32.htm#SEC46 projective space, abstract variety sing_1699.htm#IDX742 projectiveBundle sing_1700.htm#SEC1781 projectiveDimension sing_779.htm#SEC833 projectiveSpace sing_1699.htm#SEC1780 prompt sing_15.htm#SEC21 prompt, option sing_318.htm#IDX182 propagator sing_1274.htm#IDX598 propagator sing_1277.htm#SEC1358 prot, option sing_318.htm#IDX161 protocol of computations sing_318.htm#IDX162 proximitymatrix sing_1756.htm#SEC1837 prune sing_329.htm#SEC369 pruneModule sing_2837.htm#SEC2918 prwalk sing_2951.htm#SEC3032 psigncnd sing_2107.htm#SEC2188 puiseux2generators sing_1886.htm#SEC1967 puiseuxExpansion sing_2527.htm#SEC2608 pure tensor sing_495.htm#IDX307 purelist sing_789.htm#SEC843 purity purityfiltration_lib sing_778.htm#IDX403 purityFiltration sing_780.htm#SEC834 purityTriang sing_781.htm#SEC835 purityfiltration.lib purityfiltration_lib sing_778.htm#IDX396 purityfiltration_lib purityfiltration_lib sing_778.htm#IDX397 pushForward sing_2898.htm#SEC2979 pwalk sing_1298.htm#SEC1379 pyobject sing_192.htm#SEC232 pyobject sing_2630.htm#IDX1067 pyobject declarations pyobject declarations sing_193.htm#SEC233 pyobject expressions pyobject expressions sing_194.htm#SEC234 pyobject operations sing_195.htm#SEC235 pyobject related functions pyobject related functions sing_196.htm#SEC236 pyramid sing_2719.htm#SEC2800 python_eval sing_197.htm#SEC237 python_import sing_198.htm#SEC238 python_run sing_199.htm#SEC239 qbase sing_2352.htm#SEC2433 qepcad sing_2729.htm#SEC2810 qepcadsystem sing_2730.htm#SEC2811 qhmatrix sing_1945.htm#SEC2026 qhmoduli.lib sing_1903.htm#SEC1984 qhmoduli_lib sing_1903.htm#SEC1984 qhspectrum sing_1932.htm#SEC2013 qhweight sing_330.htm#SEC370 qmatrix.lib sing_790.htm#SEC844 qmatrix_lib sing_790.htm#SEC844 qminor sing_792.htm#SEC846 qrds sing_331.htm#SEC371 qring Miscellaneous oddities sing_166.htm#SEC206 qring sing_422.htm#IDX295 qring (plural) sing_447.htm#SEC487 qring declaration sing_170.htm#SEC210 qring declaration (plural) qring declaration (plural) sing_448.htm#SEC488 qring related functions (plural) qring related functions (plural) sing_449.htm#SEC489 qring ring ideal 'factor ring' sing_1154.htm#IDX569 qringNF, option sing_318.htm#IDX164 qslimgb sing_1004.htm#SEC1085 quadraticSieve sing_2264.htm#SEC2345 quantMat sing_791.htm#SEC845 quickclass sing_1787.htm#SEC1868 quit sing_394.htm#SEC434 quotSheaf sing_1712.htm#SEC1793 quote sing_332.htm#SEC372 quotient sing_333.htm#SEC373 quotient (plural) sing_480.htm#SEC520 quotientLatticeBasis quotientLatticeBasis sing_2409.htm#SEC2490 quotientMain sing_2118.htm#SEC2199 quotientMon sing_1343.htm#SEC1424 rHRR sing_1556.htm#SEC1637 rJanet sing_1482.htm#SEC1563 rMacaulay sing_1063.htm#SEC1144 rad_con sing_1090.htm#SEC1171 radical sing_1449.htm#SEC1530 radicalEHV sing_1450.htm#SEC1531 radicalMemberShip sing_2549.htm#SEC2630 radicalMon sing_1344.htm#SEC1425 radicalZ sing_1464.htm#SEC1545 randcharpoly sing_2346.htm#SEC2427 randlinpoly sing_2348.htm#SEC2429 random sing_334.htm#SEC374 random sing_361.htm#IDX242 random sing_2603.htm#IDX1024 random sing_2604.htm#IDX1026 random number generator, seed sing_361.htm#IDX240 random.lib sing_1113.htm#SEC1194 randomBinomial sing_1125.htm#SEC1206 randomCheck sing_2177.htm#SEC2258 randomLast sing_1124.htm#SEC1205 randomPoint sing_2410.htm#SEC2491 randomPolyInT sing_2558.htm#SEC2639 random_lib sing_1113.htm#SEC1194 randomid sing_1115.htm#SEC1196 randommat sing_1116.htm#SEC1197 rank sing_210.htm#IDX137 rank sing_335.htm#SEC375 rankSheaf sing_1704.htm#SEC1785 ratSol sing_676.htm#SEC730 ratgb.lib sing_796.htm#IDX404 ratgb_lib sing_796.htm#IDX405 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1621.htm#IDX724 rational functions sing_880.htm#IDX436 rational normal curve, projection. sing_1622.htm#IDX725 rational normal curve, projection. sing_1625.htm#IDX726 rational normal curve, projection. sing_1626.htm#IDX727 rational solutions sing_668.htm#IDX388 rational univariate projection sing_2346.htm#IDX956 rationalCurve sing_1724.htm#SEC1805 rationalPointConic sing_1623.htm#SEC1704 ratstd sing_797.htm#SEC851 rays sing_2411.htm#SEC2492 rcgs sing_1110.htm#SEC1191 rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs rcgs sing_1109.htm#IDX556 rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs sing_1110.htm#IDX557 rcolon sing_879.htm#SEC933 re2squ sing_1600.htm#SEC1681 read sing_336.htm#SEC376 readInputTXT sing_2938.htm#SEC3019 readNmzData sing_1424.htm#SEC1505 18957 reading, option sing_318.htm#IDX183 readline sing_1.htm#IDX5 real sing_28.htm#IDX74 real root isolation sing_2092.htm#IDX931 real roots, univariate polynomial sing_2353.htm#IDX958 real roots, univariate projection sing_2337.htm#IDX954 real roots,sign conditions sing_2105.htm#IDX934 realLLL sing_2091.htm#SEC2172 realclassify sing_1914.htm#SEC1995 realclassify.lib sing_1913.htm#SEC1994 realclassify_lib sing_1913.htm#SEC1994 realizationDim sing_2521.htm#SEC2602 realizationDimPoly sing_2523.htm#SEC2604 realizationMatroids.lib realizationMatroids_lib sing_2520.htm#SEC2601 realizationMatroids_lib realizationMatroids_lib sing_2520.htm#SEC2601 realmorsesplit sing_1915.htm#SEC1996 realpoly sing_1473.htm#SEC1554 realrad sing_1475.htm#SEC1556 realrad.lib sing_1472.htm#SEC1553 realrad_lib sing_1472.htm#SEC1553 realzero sing_1474.htm#SEC1555 recover.lib sing_2074.htm#SEC2155 recover_lib sing_2074.htm#SEC2155 recursive_boolean_poly recursive_boolean_poly sing_2636.htm#SEC2717 17045 recursive_from_boolean_poly recursive_from_boolean_poly sing_2642.htm#SEC2723 37794 redSB, option sing_318.htm#IDX165 redTail, option sing_318.htm#IDX167 redThrough, option sing_318.htm#IDX168 redcgs.lib sing_1098.htm#SEC1179 redcgs_lib sing_1098.htm#SEC1179 redefine, option sing_318.htm#IDX184 redspec sing_1104.htm#SEC1185 reduce sing_337.htm#SEC377 reduce sing_516.htm#IDX324 reduce sing_1036.htm#IDX481 reduce sing_1037.htm#IDX484 reduce (letterplace) reduce (letterplace) sing_809.htm#SEC863 reduce (plural) sing_481.htm#SEC521 reduce (up to a bound) sing_361.htm#IDX243 reduceIntChain sing_2842.htm#SEC2923 reduced sing_1035.htm#IDX478 reduced standard basis sing_318.htm#IDX166 reduction sing_1997.htm#SEC2078 reesclos.lib sing_1476.htm#SEC1557 reesclos_lib sing_1476.htm#SEC1557 reference sing_200.htm#SEC240 reference declarations reference declarations sing_201.htm#SEC241 reference expressions reference expressions sing_202.htm#SEC242 reference operations reference and shared operations sing_205.htm#SEC245 reference related functions reference and shared related functions sing_206.htm#SEC246 regCM sing_1388.htm#SEC1469 regIdeal sing_1369.htm#SEC1450 regMonCurve sing_1372.htm#SEC1453 regularity Syzygies and resolutions sing_338.htm#SEC378 regularity sing_979.htm#SEC1041 regularity sing_1388.htm#IDX641 regularity sing_1389.htm#IDX642 reiffen sing_555.htm#SEC609 rel_orbit_variety sing_1990.htm#SEC2071 relations sing_776.htm#IDX395 relativeInteriorPoint relativeInteriorPoint sing_2412.htm#SEC2493 relative_orbit_variety relative_orbit_variety sing_1991.htm#SEC2072 relweight sing_1946.htm#SEC2027 remainder sing_2111.htm#SEC2192 remainderMain sing_2119.htm#SEC2200 removeCone sing_2430.htm#SEC2511 removepower sing_1766.htm#SEC1847 repart sing_339.htm#SEC379 replace sing_2216.htm#SEC2297 representation, math objects Representation of mathematical objects sing_965.htm#SEC1022 res sing_340.htm#SEC380 resbinomial.lib sing_1630.htm#IDX730 resbinomial_lib sing_1630.htm#IDX731 reservedName sing_341.htm#SEC381 resfunction sing_1644.htm#SEC1725 resgraph.lib sing_1662.htm#SEC1743 resgraph_lib sing_1662.htm#SEC1743 resjung.lib sing_1666.htm#SEC1747 resjung_lib sing_1666.htm#SEC1747 reslist sing_1658.htm#SEC1739 resolution purityfiltration_lib sing_161.htm#SEC201 resolution sing_778.htm#IDX402 resolution (plural) sing_450.htm#SEC490 resolution declarations resolution declarations sing_162.htm#SEC202 resolution declarations (plural) resolution declarations (plural) sing_451.htm#SEC491 resolution expressions resolution expressions sing_163.htm#SEC203 resolution expressions (plural) resolution expressions (plural) sing_452.htm#SEC492 resolution graph sing_1751.htm#IDX768 resolution related functions resolution related functions sing_164.htm#SEC204 resolution related functions (plural) resolution related functions (plural) sing_453.htm#SEC493 resolution, La Scala's method sing_291.htm#SEC331 resolution, computation of sing_340.htm#IDX186 resolution, hilbert-driven sing_266.htm#SEC306 resolutionInLocalization resolutionInLocalization sing_2749.htm#SEC2830 resolutiongraph sing_1752.htm#SEC1833 resolve sing_1674.htm#SEC1755 resolve.lib sing_1670.htm#SEC1751 resolve_lib sing_1670.htm#SEC1751 resources.lib sing_1126.htm#SEC1207 resources_lib sing_1126.htm#SEC1207 restriction sing_2596.htm#IDX1012 restriction sing_2612.htm#IDX1045 restriction sing_2613.htm#IDX1047 restriction of sing_560.htm#IDX347 restrictionIdeal sing_570.htm#SEC624 restrictionModule sing_571.htm#SEC625 resultant sing_305.htm#SEC345 resultant sing_342.htm#SEC382 reszeta.lib sing_1683.htm#SEC1764 reszeta_lib sing_1683.htm#SEC1764 return sing_395.htm#SEC435 return type of procedures Return type of procedures sing_420.htm#SEC460 returnSB, option sing_318.htm#IDX152 reverse sing_2367.htm#SEC2448 reverse lexicographical ordering sing_969.htm#IDX442 reynolds_molien sing_1966.htm#SEC2047 rho sing_2258.htm#SEC2339 rightInverse sing_2196.htm#SEC2277 rightKernel sing_2194.htm#SEC2275 rightModulo sing_742.htm#SEC796 rightNF sing_741.htm#SEC795 rightNFWeyl sing_693.htm#SEC747 rightOre sing_762.htm#SEC816 rightStd sing_740.htm#SEC794 rightstd (letterplace) rightstd (letterplace) sing_810.htm#SEC864 ring sing_165.htm#SEC205 ring (plural) sing_454.htm#SEC494 ring coefficients hasTransExtensionCoefficient sing_1152.htm#IDX567 ring coefficients sing_1153.htm#IDX568 ring declarations sing_167.htm#SEC207 ring declarations (plural) ring declarations (plural) sing_455.htm#SEC495 ring operations sing_169.htm#SEC209 ring operations (plural) ring operations (plural) sing_456.htm#SEC496 ring related functions ring related functions sing_168.htm#SEC208 ring related functions (plural) ring related functions (plural) sing_457.htm#SEC497 ring theory sing_856.htm#IDX417 ring, opposite sing_361.htm#IDX227 ring, rings sing_1099.htm#IDX548 ring.lib sing_1131.htm#SEC1212 ring_cf sing_210.htm#IDX138 ring_lib sing_1131.htm#SEC1212 ring_list sing_344.htm#SEC384 ring_variable sing_2583.htm#IDX989 ring_variable sing_2584.htm#IDX991 ring_variable sing_2585.htm#IDX995 ring_variable sing_2586.htm#IDX997 ringgb.lib sing_2945.htm#SEC3026 ringgb.lib, functions for coefficient rings sing_2945.htm#IDX1251 ringgb_lib sing_2945.htm#SEC3026 ringlist sing_343.htm#SEC383 ringlist (plural) sing_482.htm#SEC522 ringtensor sing_1143.htm#SEC1224 ringweights sing_1144.htm#SEC1225 rinvar.lib sing_2002.htm#SEC2083 rinvar_lib sing_2002.htm#SEC2083 rmNmzFiles sing_1429.htm#SEC1510 32601 rm_unitcol sing_1201.htm#SEC1282 rm_unitrow sing_1200.htm#SEC1281 rmx sing_2141.htm#SEC2222 rncAntiCanonicalMap sing_1622.htm#SEC1703 rncItProjEven sing_1626.htm#SEC1707 rncItProjOdd sing_1625.htm#SEC1706 root of Bernstein-Sato polynomial sing_537.htm#IDX336 rootIsolation sing_2103.htm#SEC2184 rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2102.htm#SEC2183 rootIsolationPrimdec rootIsolationPrimdec sing_2104.htm#SEC2185 rootisolation.lib sing_2092.htm#SEC2173 rootisolation_lib sing_2092.htm#SEC2173 rootofUnity sing_1146.htm#SEC1227 roots sing_2112.htm#SEC2193 rootsMain sing_2120.htm#SEC2201 rootsModp sing_2240.htm#SEC2321 rootsmr.lib sing_2337.htm#SEC2418 rootsmr_lib sing_2337.htm#SEC2418 rootsur.lib sing_2353.htm#SEC2434 rootsur_lib sing_2353.htm#SEC2434 round sing_2238.htm#SEC2319 rowShift sing_210.htm#IDX141 rowShift sing_212.htm#SEC252 rowred sing_1197.htm#SEC1278 rp, global ordering sing_969.htm#IDX441 rstandard.lib sing_1479.htm#SEC1560 rstandard_lib sing_1479.htm#SEC1560 rswalk sing_2972.htm#SEC3053 rtimer sing_408.htm#SEC448 rvalue No rvalue of increments and assignments sing_414.htm#SEC454 rvar sing_345.htm#SEC385 rwalk sing_2952.htm#SEC3033 rwalk.lib sing_2950.htm#SEC3031 rwalk_lib sing_2950.htm#SEC3031 sPiece sing_2968.htm#SEC3049 sRes sing_2808.htm#SEC2889 sa_poly_reduce sing_525.htm#SEC579 sa_reduce sing_524.htm#SEC578 sagbi sing_1487.htm#SEC1568 sagbi basis sing_1807.htm#IDX795 sagbi.lib sing_1484.htm#SEC1565 sagbiAlg sing_1800.htm#SEC1881 sagbiMod sing_1801.htm#SEC1882 sagbiPart sing_1488.htm#SEC1569 sagbiReduce sing_1486.htm#SEC1567 sagbiSPoly sing_1485.htm#SEC1566 sagbi_lib sing_1484.htm#SEC1565 salida sing_1655.htm#SEC1736 sameComponent sing_2320.htm#SEC2401 sameQ sing_2123.htm#SEC2204 sat sing_1271.htm#SEC1352 satiety sing_1371.htm#SEC1452 satstd sing_2624.htm#SEC2705 saturation sing_1271.htm#IDX592 saturation sing_1329.htm#IDX631 saturation sing_1386.htm#IDX639 saturation sing_1387.htm#IDX640 sba sing_346.htm#SEC386 scalarProd sing_514.htm#SEC568 scheme sing_2710.htm#SEC2791 schubert.lib sing_1693.htm#SEC1774 schubert_lib sing_1693.htm#SEC1774 sdb, source code debugger Source code debugger sing_66.htm#SEC103 second degree sing_1050.htm#IDX524 second order deformation. sing_2965.htm#IDX1261 secondary fan sing_2466.htm#IDX962 secondary polytope sing_2466.htm#IDX963 secondaryPolytope sing_2471.htm#SEC2552 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1987.htm#SEC2068 secondary_char0 sing_1982.htm#SEC2063 secondary_charp sing_1984.htm#SEC2065 secondary_no_molien sing_1985.htm#SEC2066 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1988.htm#SEC2069 segre sing_1511.htm#SEC1592 select sing_1272.htm#SEC1353 select1 sing_1273.htm#SEC1354 semaphore sing_361.htm#IDX247 semaphore sing_1130.htm#SEC1211 semaphores sing_1126.htm#IDX562 semi-prime ideal sing_856.htm#IDX422 semiCMcod2 sing_1943.htm#SEC2024 semiGroup sing_1802.htm#SEC1883 semiMod sing_1803.htm#SEC1884 semidiv sing_2312.htm#SEC2393 semigroup sing_1755.htm#SEC1836 semigroup sing_1759.htm#IDX775 semigroup of values sing_1876.htm#IDX896 semigroupGenerator sing_2413.htm#SEC2494 sep sing_1459.htm#SEC1540 separateHNE sing_1887.htm#SEC1968 separator sing_1354.htm#SEC1435 serreRelations sing_829.htm#SEC883 set sing_2578.htm#IDX975 set sing_2955.htm#SEC3036 set, intersectionSet, union, complement, equality, isEqual sets_lib sing_2954.htm#IDX1257 setBaseMultigrading sing_2853.htm#SEC2934 setLetterplaceAttributes setLetterplaceAttributes sing_874.htm#SEC928 setLinearForms sing_2414.htm#SEC2495 setModuleGrading sing_2865.htm#SEC2946 setMultiplicity sing_2415.htm#SEC2496 setNmzDataPath sing_1426.htm#SEC1507 18123 setNmzExecPath sing_1422.htm#SEC1503 38993 setNmzFilename sing_1425.htm#SEC1506 20206 setNmzOption sing_1419.htm#SEC1500 9012 setUniformizingParameter setUniformizingParameter sing_2568.htm#SEC2649 set_is_injective sing_2300.htm#SEC2381 setcores sing_1128.htm#SEC1209 setenv sing_361.htm#IDX250 setglobalrings sing_1099.htm#SEC1180 setinitials sing_2720.htm#SEC2801 setring sing_347.htm#SEC387 sets.lib sing_2954.htm#SEC3035 sets_lib sing_2954.htm#SEC3035 sh sing_361.htm#IDX252 shared sing_200.htm#SEC240 shared declarations sing_203.htm#SEC243 shared expressions sing_204.htm#SEC244 shared operations reference and shared operations sing_205.htm#SEC245 shared related functions reference and shared related functions sing_206.htm#SEC246 sheaf cohomology sing_1732.htm#IDX756 sheafCoh sing_1738.htm#SEC1819 64501 sheafCohBGG sing_1736.htm#SEC1817 13439 sheafCohBGG2 sing_1737.htm#SEC1818 3338 sheafcoh.lib sing_1732.htm#SEC1813 sheafcoh_lib sing_1732.htm#SEC1813 short sing_405.htm#SEC445 show sing_1064.htm#SEC1145 showBO sing_1675.htm#SEC1756 showDataTypes sing_1677.htm#SEC1758 showNmzOptions sing_1420.htm#SEC1501 64955 showNuminvs sing_1417.htm#SEC1498 18934 showgrades sing_783.htm#SEC837 showrecursive sing_1065.htm#SEC1146 signal handler sing_2993.htm#SEC3090 signatureBrieskorn sing_1952.htm#SEC2033 signatureL sing_2626.htm#SEC2707 signatureLqf sing_2627.htm#SEC2708 signatureNemethi sing_1954.htm#SEC2035 signaturePuiseux sing_1953.htm#SEC2034 signcnd sing_2106.htm#SEC2187 signcond.lib sing_2105.htm#SEC2186 signcond_lib sing_2105.htm#SEC2186 simplePrune sing_2846.htm#SEC2927 simplesolver sing_2033.htm#SEC2114 simplex sing_348.htm#SEC388 simplexOut sing_2061.htm#SEC2142 simplify sing_349.htm#SEC389 simplifyRat sing_688.htm#SEC742 sing.lib sing_1919.htm#SEC2000 sing4ti2.lib sing_1490.htm#SEC1571 sing4ti2_lib sing_1490.htm#SEC1571 sing_lib sing_1919.htm#SEC2000 singular locus of D-module sing_668.htm#IDX382 singularities sing_1769.htm#IDX786 singularities sing_1796.htm#IDX790 singularities sing_1845.htm#IDX798 singularities sing_1846.htm#IDX809 singularities sing_1847.htm#IDX812 singularities sing_1848.htm#IDX815 singularities sing_1849.htm#IDX818 singularities sing_1850.htm#IDX822 singularities sing_1851.htm#IDX826 singularities sing_1852.htm#IDX832 singularities sing_1853.htm#IDX840 singularities sing_1854.htm#IDX846 singularities sing_1855.htm#IDX854 singularities sing_1856.htm#IDX864 singularities sing_1950.htm#IDX918 singularities, resolution of Resolution of singularities sing_952.htm#SEC1009 singularity sing_1788.htm#SEC1869 singularrc sing_20.htm#IDX73 size Miscellaneous oddities sing_350.htm#SEC390 size sing_422.htm#IDX294 skewmat sing_1185.htm#SEC1266 sleep sing_356.htm#SEC396 slimgb sing_351.htm#SEC391 slimgb sing_929.htm#SEC986 slimgb (plural) sing_483.htm#SEC523 slocus sing_1931.htm#SEC2012 smaller sing_2683.htm#IDX1142 smatrix sing_171.htm#SEC211 smith sing_2205.htm#SEC2286 smithNormalForm sing_2901.htm#SEC2982 solutionsMod2 sing_2255.htm#SEC2336 solve sing_282.htm#SEC322 solve sing_1050.htm#IDX525 solve sing_2055.htm#SEC2136 solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_294.htm#SEC334 solve.lib sing_2053.htm#SEC2134 solveTInitialFormPar solveTInitialFormPar sing_2552.htm#SEC2633 solve_IP sing_1324.htm#SEC1405 solve_lib sing_2053.htm#SEC2134 solvelinearpart sing_2048.htm#SEC2129 solving sing_2074.htm#IDX929 sort sing_1026.htm#SEC1107 sort sing_2688.htm#IDX1152 sortIntvec sing_591.htm#SEC645 sortandmap sing_2049.htm#SEC2130 sortier sing_2001.htm#SEC2082 sortvars sing_2050.htm#SEC2131 sortvec sing_352.htm#SEC392 source sing_2824.htm#SEC2905 source code debugger, sdb Source code debugger sing_66.htm#SEC103 spaceCur sing_1805.htm#SEC1886 spadd sing_1859.htm#SEC1940 span sing_2416.htm#SEC2497 sparseHomogIdeal sing_1122.htm#SEC1203 sparseInterpolation sing_1291.htm#SEC1372 sparseid sing_1117.htm#SEC1198 sparsemat sing_1119.htm#SEC1200 sparsematrix sing_1118.htm#SEC1199 sparsepoly sing_1120.htm#SEC1201 sparsetriag sing_1121.htm#SEC1202 spcurve.lib sing_1939.htm#SEC2020 spcurve_lib sing_1939.htm#SEC2020 special characters, non-english sing_411.htm#IDX287 specification sing_1104.htm#IDX551 spectral pairs sing_1845.htm#IDX807 spectral pairs sing_1852.htm#IDX839 spectral pairs sing_1854.htm#IDX853 spectral pairs sing_1855.htm#IDX862 spectral pairs sing_1867.htm#IDX878 spectral pairs sing_1869.htm#IDX889 spectralNeg sing_1685.htm#SEC1766 spectrum sing_1845.htm#IDX806 spectrum sing_1851.htm#SEC1932 spectrum sing_1851.htm#IDX831 spectrum sing_1852.htm#IDX838 spectrum sing_1853.htm#IDX845 spectrum sing_1854.htm#IDX852 spectrum sing_1855.htm#IDX861 spectrum sing_1867.htm#IDX877 spectrum sing_1869.htm#IDX888 spectrum sing_1950.htm#IDX920 spectrum.lib sing_1949.htm#SEC2030 spectrum_lib sing_1949.htm#SEC2030 spectrumnd sing_1950.htm#SEC2031 spgamma sing_1866.htm#SEC1947 spgeomgenus sing_1865.htm#SEC1946 spissemicont sing_1862.htm#SEC1943 split sing_1066.htm#SEC1147 splitPolygon sing_2473.htm#SEC2554 splitring sing_1471.htm#SEC1552 splitting sing_1362.htm#SEC1443 spmilnor sing_1864.htm#SEC1945 spmul sing_1861.htm#SEC1942 spnf sing_1227.htm#SEC1308 spoly sing_2323.htm#SEC2404 sppairs sing_1852.htm#SEC1933 sppnf sing_1857.htm#SEC1938 sppprint sing_1858.htm#SEC1939 spprint sing_1228.htm#SEC1309 sprintf sing_354.htm#SEC394 spsemicont sing_1863.htm#SEC1944 spsub sing_1860.htm#SEC1941 sqfrNorm sing_2113.htm#SEC2194 sqfrNormMain sing_2121.htm#SEC2202 sqr sing_2235.htm#SEC2316 sqrfree sing_353.htm#SEC393 squareRoot sing_2254.htm#SEC2335 squarefree sing_1888.htm#SEC1969 sres sing_355.htm#SEC395 ssi Parallelization with ssi links sing_924.htm#SEC981 stabilizer sing_2654.htm#SEC2735 stack, moduli space of stable maps sing_1717.htm#IDX747 stack, moduli space of stable maps, rational curves moduliSpace sing_1716.htm#IDX746 stackNets sing_2929.htm#SEC3010 staircase sing_2126.htm#SEC2207 standard sing_2330.htm#SEC2411 standard bases, saturation sing_2624.htm#IDX1058 standard bases. sing_2623.htm#IDX1057 standard.lib sing_1003.htm#IDX469 standard_lib sing_1003.htm#IDX470 stanleyreisner.lib sing_2963.htm#SEC3044 stanleyreisner_lib sing_2963.htm#SEC3044 startNmz sing_1428.htm#SEC1509 21925 startTasks sing_1165.htm#SEC1246 static procedures Procedure definition sing_43.htm#SEC78 status sing_356.htm#SEC396 std sing_357.htm#SEC397 std sing_927.htm#SEC984 std (letterplace) sing_811.htm#SEC865 std (plural) sing_484.htm#SEC524 stdfglm sing_358.htm#SEC398 stdhilb sing_359.htm#SEC399 stdlocus sing_1047.htm#SEC1128 stopTask sing_1166.htm#SEC1247 storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2454.htm#SEC2535 stratify sing_2028.htm#SEC2109 stratify.lib sing_2026.htm#SEC2107 stratify_lib sing_2026.htm#SEC2107 string Miscellaneous oddities sing_172.htm#SEC212 string sing_422.htm#IDX297 string sing_2670.htm#IDX1115 string sing_2672.htm#IDX1120 string sing_2673.htm#IDX1123 string sing_2695.htm#IDX1169 string sing_2696.htm#IDX1172 string declarations sing_173.htm#SEC213 string expressions sing_174.htm#SEC214 string operations sing_176.htm#SEC216 string related functions string related functions sing_177.htm#SEC217 string type cast sing_175.htm#SEC215 stripHNE sing_1885.htm#SEC1966 structure sing_2692.htm#IDX1163 sturm sing_2363.htm#SEC2444 sturmha sing_2365.htm#SEC2446 sturmhaseq sing_2366.htm#SEC2447 sturmquery sing_2341.htm#SEC2422 sturmseq sing_2364.htm#SEC2445 sublists sing_2659.htm#SEC2740 submat sing_1186.htm#SEC1267 subquotient sing_2816.htm#SEC2897 subrInterred sing_1095.htm#SEC1176 subset sing_1101.htm#SEC1182 subset_sum01 sing_2284.htm#SEC2365 subset_sum02 sing_2285.htm#SEC2366 subst sing_360.htm#SEC400 subst (plural) sing_485.htm#SEC525 substAll sing_2075.htm#SEC2156 substitute sing_1094.htm#SEC1175 sugarCrit, option sing_318.htm#IDX169 sum sing_1027.htm#SEC1108 sum sing_2675.htm#IDX1126 sum sing_2697.htm#IDX1174 sum_of_powers sing_1515.htm#SEC1596 sumlist sing_1657.htm#SEC1738 sumofquotients sing_1725.htm#SEC1806 super-commutative algebras Graded commutative algebras (SCA) sing_798.htm#SEC852 superCommutative sing_739.htm#SEC793 super_increasing_knapsack super_increasing_knapsack sing_2296.htm#SEC2377 surf.lib sing_2143.htm#SEC2224 surf_lib sing_2143.htm#SEC2224 surfacesignature.lib surfacesignature_lib sing_1951.htm#SEC2032 surfacesignature_lib surfacesignature_lib sing_1951.htm#SEC2032 surfer sing_1.htm#IDX8 surfer sing_2145.htm#SEC2226 surfex sing_1.htm#IDX7 surfex.lib sing_2146.htm#SEC2227 surfex_lib sing_2146.htm#SEC2227 suspend sing_356.htm#SEC396 swalk sing_2971.htm#SEC3052 swalk.lib sing_2970.htm#SEC3051 swalk_lib sing_2970.htm#SEC3051 swap sing_1792.htm#SEC1873 swap sing_2585.htm#IDX993 switch No case or switch statement sing_416.htm#SEC456 switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2573.htm#SEC2654 syModStd sing_1500.htm#SEC1581 symNsym sing_1509.htm#SEC1590 sym_gauss sing_1211.htm#SEC1292 symm sing_1508.htm#SEC1589 symmStd sing_1499.htm#SEC1580 symmat sing_1187.htm#SEC1268 symmetric basis sing_1203.htm#IDX573 symmetric power sing_1205.htm#IDX575 symmetric product sing_2731.htm#IDX1203 symmetricBasis sing_1203.htm#SEC1284 symmetricPower sing_1205.htm#SEC1286 symmetricPowerSheaf sing_1711.htm#SEC1792 symmetries sing_2650.htm#IDX1091 symmfunc sing_2350.htm#SEC2431 symodstd.lib sing_1494.htm#SEC1575 symodstd_lib sing_1494.htm#SEC1575 sympower sing_2022.htm#SEC2103 symsignature sing_2340.htm#SEC2421 syndrome sing_2173.htm#SEC2254 sysBin sing_2171.htm#SEC2252 sysCRHT sing_2168.htm#SEC2249 sysCRHTMindist sing_2169.htm#SEC2250 sysFL sing_2184.htm#SEC2265 sysNewton sing_2170.htm#SEC2251 sysQE sing_2174.htm#SEC2255 sys_code sing_2165.htm#SEC2246 system sing_361.htm#SEC401 system, -- sing_361.htm#IDX277 system, --long_option_name sing_361.htm#IDX280 system, --long_option_name=value sing_361.htm#IDX282 system, HC sing_361.htm#IDX213 system, LLL sing_361.htm#IDX217 system, Singular sing_361.htm#IDX256 system, SingularLib sing_361.htm#IDX258 system, absFact sing_361.htm#IDX190 system, alarm sing_361.htm#IDX189 system, blackbox sing_361.htm#IDX191 system, bracket sing_361.htm#IDX196 system, browsers sing_361.htm#IDX195 system, complexNearZero sing_361.htm#IDX198 system, contributors sing_361.htm#IDX200 system, cpu sing_361.htm#IDX202 system, cpu sing_361.htm#IDX276 system, denom_list sing_361.htm#IDX204 system, eigenvals sing_361.htm#IDX205 system, env sing_361.htm#IDX206 system, executable sing_361.htm#IDX208 system, getPrecDigits sing_361.htm#IDX211 system, getenv sing_361.htm#IDX210 system, gmsnf sing_361.htm#IDX212 system, hessenberg sing_361.htm#IDX214 system, install sing_361.htm#IDX216 system, nblocks sing_361.htm#IDX220 system, nc_hilb sing_361.htm#IDX222 system, neworder sing_361.htm#IDX223 system, newstruct sing_361.htm#IDX224 system, opp sing_361.htm#IDX225 system, oppose sing_361.htm#IDX228 system, pcvBasis sing_361.htm#IDX237 system, pcvCV2P sing_361.htm#IDX235 system, pcvDim sing_361.htm#IDX236 system, pcvLAddL sing_361.htm#IDX231 system, pcvMinDeg sing_361.htm#IDX233 system, pcvP2CV sing_361.htm#IDX234 system, pcvPMulL sing_361.htm#IDX232 system, pid sing_361.htm#IDX239 system, random sing_361.htm#IDX241 system, reserve sing_361.htm#IDX245 system, reservedLink sing_361.htm#IDX246 system, semaphore sing_361.htm#IDX248 system, semic sing_361.htm#IDX249 system, setenv sing_361.htm#IDX251 system, sh sing_361.htm#IDX253 system, shrinktest sing_361.htm#IDX254 system, spadd sing_361.htm#IDX259 system, spectrum sing_361.htm#IDX260 system, spmul sing_361.htm#IDX261 system, std_syz sing_361.htm#IDX262 system, tensorModuleMult sing_361.htm#IDX263 system, twostd sing_361.htm#IDX264 system, uname sing_361.htm#IDX267 system, verifyGB sing_361.htm#IDX270 system, version sing_361.htm#IDX273 system, with sing_361.htm#IDX274 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2746.htm#SEC2827 systhreads.lib sing_2973.htm#SEC3054 systhreads_lib sing_2973.htm#SEC3054 syz sing_362.htm#SEC402 syz (letterplace) sing_812.htm#SEC866 syz (plural) sing_486.htm#SEC526 tDetropicalise sing_2554.htm#SEC2635 tInitialForm sing_2538.htm#SEC2619 tInitialFormPar sing_2550.htm#SEC2631 tInitialFormParMax sing_2551.htm#SEC2632 tInitialIdeal sing_2539.htm#SEC2620 tab sing_1067.htm#SEC1148 tail sing_2319.htm#SEC2400 tame polynomial sing_1867.htm#IDX870 tame polynomial sing_1868.htm#IDX880 tame polynomial sing_1869.htm#IDX881 tangentGens sing_1613.htm#SEC1694 tangentcone sing_1938.htm#SEC2019 target sing_2823.htm#SEC2904 task sing_1159.htm#IDX572 tasks.lib sing_1159.htm#SEC1240 tasks_lib sing_1159.htm#SEC1240 tau_es sing_1840.htm#SEC1921 tau_es2 sing_1763.htm#SEC1844 tdCf sing_1544.htm#SEC1625 tdFactor sing_1546.htm#SEC1627 tdProj sing_1549.htm#SEC1630 tdTerms sing_1545.htm#SEC1626 teachstd.lib sing_2317.htm#SEC2398 teachstd_lib sing_2317.htm#SEC2398 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_363.htm#SEC403 tensor sing_495.htm#IDX311 tensor algebra sing_863.htm#IDX425 tensorFreeModule sing_2835.htm#SEC2916 tensorFreemodMod sing_2834.htm#SEC2915 tensorMatrix sing_2831.htm#SEC2912 tensorMod sing_1319.htm#SEC1400 tensorModFreemod sing_2833.htm#SEC2914 tensorModule sing_2832.htm#SEC2913 tensorProduct sing_2836.htm#SEC2917 tensorSheaf sing_1710.htm#SEC1791 term orderings General definitions for orderings sing_968.htm#SEC1025 term orderings introduction Introduction to orderings sing_967.htm#SEC1024 testFraction sing_760.htm#SEC814 testLift sing_875.htm#SEC929 testLocData sing_757.htm#SEC811 testNCfac sing_651.htm#SEC705 testNcfrac sing_706.htm#SEC760 testNcfracExamples sing_707.htm#SEC761 testNcloc sing_718.htm#SEC772 testNclocExamples sing_719.htm#SEC773 testOlga sing_774.htm#SEC828 testOlgaExamples sing_775.htm#SEC829 testParametrization sing_1628.htm#SEC1709 testPointConic sing_1629.htm#SEC1710 testPrimary sing_1447.htm#SEC1528 testPrimaryE sing_1448.htm#SEC1529 testSyz sing_876.htm#SEC930 testZero sing_2948.htm#SEC3029 tetrahedronGroup sing_854.htm#SEC908 tex sing_2132.htm#SEC2213 texDrawBasic sing_2545.htm#SEC2626 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2547.htm#SEC2628 texDrawTriangulation texDrawTriangulation sing_2548.htm#SEC2629 texDrawTropical sing_2546.htm#SEC2627 texMatrix sing_2544.htm#SEC2625 texNumber sing_2542.htm#SEC2623 texPolynomial sing_2543.htm#SEC2624 texcoef sing_2213.htm#SEC2294 texdemo sing_2133.htm#SEC2214 texfactorize sing_2134.htm#SEC2215 texmap sing_2135.htm#SEC2216 texname sing_2136.htm#SEC2217 texobj sing_2137.htm#SEC2218 texpoly sing_2138.htm#SEC2219 texproc sing_2139.htm#SEC2220 texring sing_2140.htm#SEC2221 the first alternative algorithm sing_1296.htm#IDX619 three_elements sing_2303.htm#SEC2384 timeFactorize sing_1031.htm#SEC1112 timeStd sing_1030.htm#SEC1111 timer sing_406.htm#SEC446 timer resolution, setting the sing_361.htm#IDX283 timestep sing_2723.htm#SEC2804 tjurina sing_1934.htm#SEC2015 tmatrix sing_1855.htm#SEC1936 todd sing_1541.htm#SEC1622 toddE sing_1542.htm#SEC1623 toddPoly sing_1555.htm#SEC1636 tolessvars sing_2047.htm#SEC2128 topChernClass sing_1707.htm#SEC1788 topological invariants sing_1751.htm#IDX766 topological invariants sing_1758.htm#IDX773 topological invariants sing_1759.htm#IDX777 topological invariants sing_1760.htm#IDX781 topological invariants sing_1761.htm#IDX785 toric ideals sing_983.htm#SEC1045 toric ring sing_1406.htm#IDX658 toric.lib sing_1501.htm#SEC1582 toric_ideal sing_1502.htm#SEC1583 toric_lib sing_1501.htm#SEC1582 toric_std sing_1503.htm#SEC1584 torus sing_2019.htm#SEC2100 torusInvariants sing_1412.htm#SEC1493 911 torusrep sing_2020.htm#SEC2101 torusreynolds sing_2025.htm#SEC2106 total divisors sing_495.htm#IDX308 total multiplicities sing_1751.htm#IDX769 totalChernClass sing_1705.htm#SEC1786 totalSegreClass sing_1708.htm#SEC1789 totalmultiplicities sing_1753.htm#SEC1834 trace sing_364.htm#SEC404 tracemult sing_2344.htm#SEC2425 transpose sing_365.htm#SEC405 trapezoid sing_2717.htm#SEC2798 triMNewton sing_2073.htm#SEC2154 triagmatrix sing_1123.htm#SEC1204 triang.lib sing_2066.htm#SEC2147 triangL sing_2067.htm#SEC2148 triangL_solve sing_2064.htm#SEC2145 triangLf_solve sing_2062.htm#SEC2143 triangLfak sing_2068.htm#SEC2149 triangM sing_2069.htm#SEC2150 triangMH sing_2070.htm#SEC2151 triangM_solve sing_2063.htm#SEC2144 triang_lib sing_2066.htm#SEC2147 triang_solve sing_2065.htm#SEC2146 triangularGroup sing_855.htm#SEC909 triangulations sing_2470.htm#SEC2551 tropical curves sing_2524.htm#IDX967 tropical geometry sing_1274.htm#IDX593 tropical geometry sing_2567.htm#IDX969 tropical mirror symmetry sing_1274.htm#IDX595 tropical polynomials sing_2524.htm#IDX968 tropical varieties sing_2567.htm#IDX970 tropical.lib sing_2524.htm#SEC2605 tropicalCurve sing_2529.htm#SEC2610 tropicalJInvariant sing_2532.htm#SEC2613 tropicalLifting sing_2525.htm#SEC2606 tropicalLinkNewton sing_2575.htm#SEC2656 tropicalNewton.lib sing_2567.htm#SEC2648 tropicalNewton_lib sing_2567.htm#SEC2648 tropicalPointNewton sing_2572.htm#SEC2653 tropicalSubst sing_2557.htm#SEC2638 tropicalVariety sing_2564.htm#SEC2645 tropicalVarietyNewton tropicalVarietyNewton sing_2574.htm#SEC2655 tropical_lib sing_2524.htm#SEC2605 tropicalise sing_2536.htm#SEC2617 tropicaliseSet sing_2537.htm#SEC2618 truncate sing_1733.htm#SEC1814 13545 truncateFast sing_1734.htm#SEC1815 22046 truncated module sing_1733.htm#IDX757 truncated module sing_1734.htm#IDX758 tst_ncfactor sing_660.htm#SEC714 twalk sing_1295.htm#SEC1376 two-sided sing_495.htm#IDX309 two-sided Groebner basis sing_495.htm#IDX310 twostd sing_361.htm#IDX265 twostd (letterplace) twostd (letterplace) sing_813.htm#SEC867 twostd (plural) sing_487.htm#SEC527 type sing_366.htm#SEC406 type B sing_2601.htm#IDX1020 type D sing_2602.htm#IDX1022 type,custom Definition of a user defined type sing_184.htm#SEC224 type2arr sing_2579.htm#SEC2660 typecasting sing_2579.htm#IDX976 typecasting sing_2580.htm#IDX978 typecasting sing_2581.htm#IDX981 typeof sing_367.htm#SEC407 u sing_2709.htm#SEC2790 uname sing_361.htm#IDX266 unbounded_knapsack sing_2286.htm#SEC2367 union sing_2956.htm#SEC3037 unipotent groups sing_1612.htm#IDX701 uniquePoint sing_2417.htm#SEC2498 unitMatrix sing_2098.htm#SEC2179 unitmat sing_1188.htm#SEC1269 univariate sing_368.htm#SEC408 univarpoly sing_2351.htm#SEC2432 universal sing_2689.htm#IDX1155 universal sing_2690.htm#IDX1157 universal derivation diffAlgebraUnivDerIdeal sing_2665.htm#IDX1106 unknown syndrome Decoding method based on quadratic equations sing_999.htm#SEC1075 unset sing_279.htm#SEC319 untyped definitions sing_88.htm#SEC128 untyped definitions sing_427.htm#SEC467 updatePairs sing_2329.htm#SEC2410 ures_solve sing_2056.htm#SEC2137 uressolve sing_369.htm#SEC409 usage, option sing_318.htm#IDX185 used environment variables Used environment variables sing_2995.htm#SEC3092 user interface, Emacs Emacs user interface sing_21.htm#SEC28 vStd sing_1817.htm#SEC1898 val sing_2569.htm#SEC2650 valvars sing_2051.htm#SEC2132 vandermonde sing_370.htm#SEC410 vanishId sing_2183.htm#SEC2264 vanishing polynomial sing_2945.htm#IDX1247 var sing_371.htm#SEC411 varMat sing_2583.htm#SEC2664 varNum sing_2584.htm#SEC2665 variables sing_372.htm#SEC412 variables sing_2583.htm#IDX988 variables sing_2584.htm#IDX990 variables sing_2585.htm#IDX994 variables sing_2586.htm#IDX996 variablesSorted sing_533.htm#SEC587 variablesStandard sing_532.htm#SEC586 vars2pars sing_683.htm#SEC737 varsigns sing_2356.htm#SEC2437 varstr sing_373.htm#SEC413 vdim sing_374.htm#SEC414 vdim (plural) sing_488.htm#SEC528 vec2poly sing_515.htm#SEC569 vecFieldToMatrix sing_2981.htm#SEC3062 vector sing_178.htm#SEC218 vector declarations sing_179.htm#SEC219 vector expressions sing_180.htm#SEC220 vector operations sing_181.htm#SEC221 vector related functions vector related functions sing_182.htm#SEC222 verify sing_2347.htm#SEC2428 verify Groebner base sing_361.htm#IDX269 verifyGB sing_361.htm#IDX271 veronese sing_2076.htm#SEC2157 versal sing_1835.htm#SEC1916 version sing_361.htm#IDX272 vertexAdjacencyGraph vertexAdjacencyGraph sing_2517.htm#SEC2598 vertexEdgeGraph sing_2518.htm#SEC2599 vertices sing_2433.htm#SEC2514 vfilt sing_1853.htm#SEC1934 view sing_2203.htm#SEC2284 visual sing_2519.htm#SEC2600 visualize sing_2708.htm#SEC2789 voice sing_409.htm#SEC449 vwfilt sing_1854.htm#SEC1935 wUnit sing_2241.htm#SEC2322 waitAllTasks sing_1168.htm#SEC1249 waitTasks sing_1167.htm#SEC1248 waitall sing_375.htm#SEC415 waitfirst sing_376.htm#SEC416 walk, groebner sing_1293.htm#IDX615 walk, groebner sing_2847.htm#IDX1213 walk, groebner sing_2950.htm#IDX1252 walk, groebner sing_2970.htm#IDX1266 warkedPreimageStd sing_2748.htm#SEC2829 warn, option sing_70.htm#SEC110 warn, option sing_318.htm#IDX151 watchdog sing_1028.htm#SEC1109 wedge sing_377.htm#SEC417 weierstr.lib sing_2332.htm#SEC2413 weierstrDiv sing_2333.htm#SEC2414 weierstrPrep sing_2334.htm#SEC2415 weierstr_lib sing_2332.htm#SEC2413 weierstrassForm sing_2533.htm#SEC2614 weight sing_378.htm#SEC418 weight filtration sing_1845.htm#IDX803 weight filtration sing_1852.htm#IDX837 weight filtration sing_1854.htm#IDX851 weight filtration sing_1855.htm#IDX859 weight filtration sing_1867.htm#IDX875 weight filtration sing_1869.htm#IDX886 weightKB sing_379.htm#SEC419 weightM, option sing_318.htm#IDX170 weighted lexicographical ordering sing_969.htm#IDX449 weighted reverse lexicographical ordering Global orderings sing_969.htm#IDX447 weightedRing sing_732.htm#SEC786 whichvariable sing_2355.htm#SEC2436 while sing_396.htm#SEC436 withDim sing_210.htm#IDX145 withHilb sing_210.htm#IDX143 withMult sing_210.htm#IDX146 withRes sing_210.htm#IDX144 withSB sing_210.htm#IDX142 wp, global ordering sing_969.htm#IDX448 write sing_380.htm#SEC420 writeBertiniInput sing_2082.htm#SEC2163 writeNmzData sing_1423.htm#SEC1504 38467 writeNmzPaths sing_1427.htm#SEC1508 sprintf writing monomials sing_405.htm#SEC445 ws, local ordering sing_970.htm#IDX459 wurzel sing_2223.htm#SEC2304 xchange sing_2217.htm#SEC2298 xdvi sing_2142.htm#SEC2223 zdd sing_2630.htm#IDX1069 zdd2poly sing_2647.htm#SEC2728 55047 zero sing_2796.htm#SEC2877 zero-dimensional sing_2352.htm#IDX957 zeroMod sing_1358.htm#SEC1439 zeroNcfrac sing_699.htm#SEC753 zeroOpt sing_1367.htm#SEC1448 zeroRadical sing_1251.htm#SEC1332 zeroReduce sing_2947.htm#SEC3028 zeroSet sing_2114.htm#SEC2195 zerodec sing_1456.htm#SEC1537 zeroreduce sing_2945.htm#IDX1248 zeroset.lib sing_2109.htm#SEC2190 zeroset_lib sing_2109.htm#SEC2190 zetaDL sing_1687.htm#SEC1768 { sing_36.htm#IDX78 || sing_36.htm#IDX103 || sing_101.htm#SEC141 } sing_36.htm#IDX79 ~ sing_36.htm#IDX117 ~ sing_397.htm#SEC437