! 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_248.htm#SEC288 <= 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_260.htm#IDX148 ADGT sing_1008.htm#SEC1084 1598 AG codes sing_917.htm#SEC969 AGcode_L sing_1862.htm#SEC1938 60329 AGcode_Omega sing_1863.htm#SEC1939 56285 ASCII sing_967.htm#SEC1043 26816 ASCII links sing_117.htm#SEC157 ASSUME sing_64.htm#SEC101 A_L sing_1561.htm#SEC1637 16721 A_Z sing_966.htm#SEC1042 50866 Access to elements of a user defined type Access to elements of a user defined type sing_186.htm#SEC226 Adj_div sing_1857.htm#SEC1933 44919 Adjoint ideal sing_1438.htm#IDX617 Alexander polynomial sing_1532.htm#IDX641 Algebraic Geometry codes sing_1856.htm#IDX789 Algebraic dependence Algebraic dependence sing_896.htm#SEC948 Algebraic geometry sing_1413.htm#SEC1489 AltVarEnd sing_775.htm#SEC827 11020 AltVarStart sing_774.htm#SEC826 21592 Ann sing_1352.htm#SEC1428 61560 Appel function sing_565.htm#IDX351 Appel hypergeometric function sing_565.htm#IDX352 Applications sing_915.htm#SEC967 Arnold, classification. sing_2384.htm#IDX945 Arnold, classification. sing_2385.htm#IDX946 ArnoldAction sing_1654.htm#SEC1730 26958 Assignments for user defined types Assignments for user defined types sing_188.htm#SEC228 AssocTanToEnv sing_1003.htm#SEC1079 46214 Atkin sing_1945.htm#SEC2021 sprintf Authors sing_1.htm#IDX16 Automatic Deduction sing_1008.htm#IDX488 Automatic Demonstration sing_1008.htm#IDX489 BINresol sing_1451.htm#SEC1527 52996 Background sing_3.htm#SEC5 Basic programming sing_871.htm#SEC923 Basic programming sing_871.htm#SEC923 BelongSemig sing_2380.htm#SEC2456 22405 BerlekampMassey sing_2439.htm#SEC2515 2172 Bern sing_2353.htm#SEC2429 64051 Bernstein operator sing_542.htm#IDX333 Bernstein-Sato polynomial sing_507.htm#IDX314 Bernstein-Sato polynomial sing_542.htm#IDX330 Bernstein-Sato polynomial sing_1595.htm#IDX672 Bernstein-Sato polynomial sing_1599.htm#IDX689 Bernstein-Sato polynomial for variety sing_598.htm#IDX355 Betti sing_2572.htm#SEC2648 21134 Betti number Syzygies and resolutions sing_933.htm#SEC990 BettiNumsH sing_2469.htm#SEC2545 18661 BettiNumsN sing_2477.htm#SEC2553 44681 BettiNumsQp sing_2472.htm#SEC2548 16693 BettiNumsS sing_2475.htm#SEC2551 14964 Betty number sing_2466.htm#IDX986 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_943.htm#SEC1000 BlowingUp sing_1574.htm#SEC1650 43153 Blowupcenter sing_1454.htm#SEC1530 3423 BorelCheck sing_1529.htm#SEC1605 48787 Bott's formula sing_2767.htm#IDX1055 Branches of space curve singularities Branches of space curve singularities sing_904.htm#SEC956 Briancon-Maisonobe algorithm sing_542.htm#IDX339 Brieskorn lattice sing_1595.htm#IDX668 Brieskorn lattice sing_1596.htm#IDX679 Brieskorn lattice sing_1597.htm#IDX682 Brieskorn lattice sing_1598.htm#IDX685 Brieskorn lattice sing_1599.htm#IDX688 Brieskorn lattice sing_1600.htm#IDX692 Brieskorn lattice sing_1601.htm#IDX696 Brieskorn lattice sing_1602.htm#IDX702 Brieskorn lattice sing_1603.htm#IDX710 Brieskorn lattice sing_1604.htm#IDX716 Brieskorn lattice sing_1605.htm#IDX724 Brieskorn lattice sing_1606.htm#IDX734 Brieskorn lattice sing_1617.htm#IDX740 Brieskorn lattice sing_1619.htm#IDX751 Brieskorn lattice sing_1647.htm#IDX778 Brill-Noether algorithm sing_1856.htm#IDX790 BrillNoether sing_1859.htm#SEC1935 39919 Buchberger algorithm for toric ideals Buchberger algorithm sing_944.htm#SEC1001 Budur-Mustata-Saito approach sing_598.htm#IDX359 Building Singular sing_2824.htm#SEC2914 C programming language Major differences to the C programming language sing_411.htm#SEC451 C, module ordering sing_925.htm#IDX419 CGS sing_988.htm#IDX432 CM_regularity sing_1516.htm#SEC1592 33865 CMtype sing_1685.htm#SEC1761 24849 CRHT-ideal sing_950.htm#SEC1014 CSMA sing_2376.htm#SEC2452 49080 CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33 Castelnuovo-Mumford regularity sing_1516.htm#IDX633 Category string sing_51.htm#SEC88 CenCharDec sing_731.htm#SEC783 44505 Center sing_1493.htm#SEC1569 25541 CenterBO sing_1500.htm#SEC1576 34701 CentralQuot sing_729.htm#SEC781 56490 CentralSaturation sing_730.htm#SEC782 31585 Change of rings sing_9.htm#SEC15 Characteristic sets sing_934.htm#SEC991 CharacteristicExponents CharacteristicExponents sing_1580.htm#SEC1656 21795 ChernClass sing_2780.htm#SEC2856 32965 ChernRootsDual sing_2332.htm#SEC2408 40100 ChernRootsHom sing_2341.htm#SEC2417 48446 ChernRootsProd sing_2334.htm#SEC2410 13967 ChernRootsSum sing_2330.htm#SEC2406 57286 ChernRootsSymm sing_2343.htm#SEC2419 59304 ChernRootsWedge sing_2344.htm#SEC2420 7239 Chevalley-Rosenlicht theorem sing_1432.htm#IDX602 Chevalley-Rosenlicht theorem sing_1433.htm#IDX605 Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2771.htm#IDX1060 ChowRing sing_2771.htm#SEC2847 57977 Classification of hypersurface singularities Classification of hypersurface singularities sing_905.htm#SEC957 Classification of singularities sing_2740.htm#IDX1031 Code Codes and the decoding problem sing_949.htm#SEC1007 Codes and the decoding problem Codes and the decoding problem sing_949.htm#SEC1006 Coding theory sing_1855.htm#SEC1931 Coefficient rings Notes for Singular users sing_2822.htm#SEC2907 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_884.htm#SEC936 Commutative algebra sing_1168.htm#SEC1244 CompDecomp sing_504.htm#SEC556 9959 CompInt sing_2382.htm#SEC2458 7518 CompleteHomog sing_2320.htm#SEC2396 42123 ComplexValue sing_2461.htm#SEC2537 45546 Comprehensive Groebner System sing_988.htm#IDX435 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_880.htm#SEC932 ConsLevels sing_996.htm#SEC1072 14282 ContactMatrix sing_1582.htm#SEC1658 40767 Conti-Traverso algorithm sing_939.htm#SEC996 Contributors sing_1.htm#IDX15 Control structures sing_379.htm#SEC419 Control theory System and Control theory sing_1889.htm#SEC1965 Cooper philosophy sing_950.htm#SEC1012 Cornacchia sing_1935.htm#SEC2011 63434 CornacchiaModified sing_1936.htm#SEC2012 59790 Crep sing_991.htm#SEC1067 17485 Critical points sing_899.htm#SEC951 CurveParam sing_1576.htm#SEC1652 53605 CurveRes sing_1575.htm#SEC1651 48848 Curves sing_1438.htm#IDX614 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36 Cyclic code sing_1870.htm#IDX797 Cyclic roots sing_877.htm#SEC929 D-integration sing_565.htm#IDX348 D-localization sing_565.htm#IDX344 D-localization sing_843.htm#IDX388 D-module purityfiltration_lib sing_507.htm#IDX312 D-module sing_542.htm#IDX327 D-module sing_565.htm#IDX341 D-module sing_598.htm#IDX353 D-module sing_787.htm#IDX367 D-module sing_843.htm#IDX385 D-module structure sing_542.htm#IDX328 D-module structure sing_598.htm#IDX354 D-restriction sing_565.htm#IDX346 DBM links sing_122.htm#SEC162 DISPLAY environment variable The online help system sing_16.htm#IDX28 DLoc sing_568.htm#SEC620 5981 DLoc0 sing_570.htm#SEC622 14327 Data types sing_72.htm#SEC112 Data types (plural) sing_424.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_1870.htm#IDX799 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_948.htm#SEC1005 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_953.htm#SEC1023 Definition of a user defined type Definition of a user defined type sing_184.htm#SEC224 Deformations sing_902.htm#SEC954 Deformations, T1 and T2 sing_901.htm#SEC953 Deg sing_2575.htm#SEC2651 35419 Degree sing_2576.htm#SEC2652 48523 DegreePure sing_1417.htm#SEC1493 33003 Degrees sing_2577.htm#SEC2653 50349 Delta sing_1501.htm#SEC1577 33497 DeltaList sing_1502.htm#SEC1578 65148 Demo mode sing_24.htm#SEC35 Depth sing_891.htm#SEC943 Determinacy sing_2743.htm#IDX1035 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_942.htm#SEC999 Distributed computing sing_1019.htm#IDX495 Dlocalization sing_844.htm#SEC896 22140 Documentation Tool sing_60.htm#SEC97 Dp, global ordering sing_923.htm#IDX402 Ds, local ordering sing_924.htm#IDX412 DsingularLocus sing_848.htm#SEC900 46495 Dynamic loading sing_71.htm#SEC111 Dynamic modules sing_879.htm#SEC931 ECPP sing_1979.htm#SEC2055 55777 ECoef sing_1460.htm#SEC1536 14154 EOrdlist sing_1458.htm#SEC1534 36329 ERROR sing_237.htm#SEC277 ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33 Edatalist sing_1457.htm#SEC1533 61593 Edelman-Reiner sing_2263.htm#IDX880 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37 Editing input sing_18.htm#SEC25 Elimination sing_887.htm#SEC939 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_1462.htm#SEC1538 47312 Enumerative geometry sing_2767.htm#IDX1053 Equal sing_1416.htm#SEC1492 19984 Eresol sing_1452.htm#SEC1528 12842 EulerAff sing_2377.htm#SEC2453 54325 EulerProj sing_2378.htm#SEC2454 13537 Evaluation of logical expressions Evaluation of logical expressions sing_413.htm#SEC453 Examples sing_869.htm#SEC921 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40 Exp for matrices sing_1434.htm#IDX606 Experimental libraries Experimental libraries sing_2307.htm#SEC2383 Ext sing_1228.htm#SEC1304 21909 Ext, computation of sing_890.htm#SEC942 Ext_R sing_1227.htm#SEC1303 53310 Exterior sing_761.htm#SEC813 23593 Extra weight vector sing_928.htm#SEC980 Factorization sing_892.htm#SEC944 FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_1004.htm#SEC1080 18153 Feynman graph sing_1204.htm#IDX528 Finite fields sing_886.htm#SEC938 First steps sing_6.htm#SEC12 Fitzgerald-Lax method Fitzgerald-Lax method sing_952.htm#SEC1020 Float sing_251.htm#SEC291 Flow control sing_40.htm#SEC70 Formal Checker sing_59.htm#SEC96 Formatting output sing_876.htm#SEC928 Free resolution sing_888.htm#SEC940 Free resolution, graded Handling graded modules sing_889.htm#SEC941 FultonA sing_2375.htm#SEC2451 33688 Functions sing_208.htm#SEC248 Future benefits of Singular 4 Notes for Singular users sing_2822.htm#SEC2912 G-algebra sing_488.htm#SEC528 G-algebra sing_488.htm#SEC530 G-algebra, setup sing_488.htm#SEC532 GBWeight sing_571.htm#SEC623 24641 GBsolve sing_1769.htm#SEC1845 16830 GIT-Fans sing_911.htm#SEC963 GITcone sing_2491.htm#SEC2567 64643 GITfan sing_2492.htm#SEC2568 32549 GITfanFromOrbitCones GITfanFromOrbitCones sing_2493.htm#SEC2569 63104 GITfanParallel sing_2494.htm#SEC2570 53071 GITfanParallelSymmetric GITfanParallelSymmetric sing_2509.htm#SEC2585 30232 GITfanSymmetric sing_2508.htm#SEC2584 25831 GKZfan sing_2495.htm#SEC2571 sprintf GKZsystem sing_727.htm#SEC779 20528 GKdim sing_700.htm#SEC752 9814 GMP sing_1.htm#IDX3 GMP sing_2826.htm#SEC2916 GND.lib sing_2516.htm#SEC2592 GND_lib sing_2516.htm#SEC2592 GTZmod sing_1278.htm#SEC1354 30091 GTZopt sing_1285.htm#SEC1361 14642 G_a -Invariants sing_908.htm#SEC960 Gamma sing_1467.htm#SEC1543 3820 Gauss-Manin connection Gauss-Manin connection sing_935.htm#SEC992 Gauss-Manin connection sing_1647.htm#IDX777 Gauss-Manin connection sing_1694.htm#IDX780 Gauss-Manin system sing_1595.htm#IDX667 Gauss-Manin system sing_1596.htm#IDX678 Gauss-Manin system sing_1597.htm#IDX681 Gauss-Manin system sing_1598.htm#IDX684 Gauss-Manin system sing_1599.htm#IDX687 Gauss-Manin system sing_1600.htm#IDX691 Gauss-Manin system sing_1601.htm#IDX695 Gauss-Manin system sing_1602.htm#IDX701 Gauss-Manin system sing_1603.htm#IDX709 Gauss-Manin system sing_1604.htm#IDX715 Gauss-Manin system sing_1605.htm#IDX723 Gauss-Manin system sing_1606.htm#IDX733 Gauss-Manin system sing_1617.htm#IDX739 Gauss-Manin system sing_1619.htm#IDX750 General command syntax General command syntax sing_35.htm#SEC59 General concepts sing_12.htm#SEC18 General purpose sing_960.htm#SEC1036 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_490.htm#SEC540 Generalized Newton identities Generalized Newton identities sing_951.htm#SEC1017 Geometric Invariant Theory Geometric Invariant Theory sing_910.htm#SEC962 Geometric Theorems sing_1008.htm#IDX490 Geometric genus sing_1438.htm#IDX618 German Umlaute sing_409.htm#IDX285 Getting started sing_5.htm#SEC11 Global orderings sing_923.htm#SEC975 Goettsche's formula sing_2466.htm#IDX987 GoettscheF sing_2467.htm#SEC2543 27881 Graded commutative algebras Graded commutative algebras (SCA) sing_492.htm#SEC544 Grassmannian sing_2772.htm#SEC2848 43898 Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2772.htm#IDX1061 Greuel, Gert-Martin sing_1.htm#IDX18 Groebner Bases Computing Groebner and Standard Bases sing_880.htm#SEC932 Groebner bases in G-algebras Groebner bases in G-algebras sing_489.htm#SEC533 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_495.htm#SEC547 Groebner bases, decodeGB sing_1870.htm#IDX801 Groebner bases, slim sing_883.htm#SEC935 Groebner basis conversion Groebner basis conversion sing_882.htm#SEC934 Groebner cover sing_987.htm#IDX428 Groebner cover sing_994.htm#IDX447 Groebner cover sing_995.htm#IDX454 Groebner fan sing_2133.htm#IDX818 Groebner walk sing_1219.htm#IDX549 Groebner walk sing_1221.htm#IDX551 Groebner walk sing_2764.htm#IDX1049 Groebner walk sing_2765.htm#IDX1050 Groebnerwalk sing_1215.htm#IDX545 Groebnerwalk sing_2609.htm#IDX1002 Groebnerwalk sing_2763.htm#IDX1048 Groebnerwalk sing_2806.htm#IDX1077 Gromov-Witten invariants sing_1204.htm#IDX525 Gromov-Witten invariants sing_1210.htm#IDX534 Gromov-Witten invariants sing_1211.htm#IDX538 Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2797.htm#IDX1073 Gromov-Witten invariants, multiple covers sing_2796.htm#IDX1072 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2798.htm#IDX1074 Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2799.htm#IDX1075 Gromov-Witten invariants. sing_2767.htm#IDX1056 Gweights sing_755.htm#SEC807 651 H2basis sing_1652.htm#SEC1728 3414 HHnormalForm sing_2393.htm#SEC2469 33972 Hamburger-Noether expansion sing_1532.htm#IDX637 Hamburger-Noether expansion sing_1620.htm#IDX759 Hamburger-Noether expansions sing_1857.htm#IDX791 Handling graded modules Handling graded modules sing_889.htm#SEC941 Hcode sing_1554.htm#SEC1630 26628 Help string sing_45.htm#SEC82 Hensel sing_242.htm#SEC282 Hilbert function sing_357.htm#IDX188 Hilbert function sing_932.htm#SEC986 Hilbert scheme sing_2466.htm#IDX990 Hilbert series sing_932.htm#SEC986 Hilbert-driven GB algorithm Groebner basis conversion sing_882.htm#SEC934 HilbertClassPoly sing_1942.htm#SEC2018 sprintf HilbertSeries sing_1747.htm#SEC1823 21249 HilbertWeights sing_1748.htm#SEC1824 sprintf Hom sing_1231.htm#SEC1307 61434 HomJJ sing_1308.htm#SEC1384 1525 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_941.htm#SEC998 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_1210.htm#IDX537 Hurwitz numbers sing_1211.htm#IDX541 Hypersurface singularities, classification of Classification of hypersurface singularities sing_905.htm#SEC957 I-regular function sing_994.htm#IDX453 IN sing_281.htm#IDX149 Ideal membership sing_931.htm#IDX424 Identifiers, syntax of sing_37.htm#SEC65 ImageGroup sing_1750.htm#SEC1826 28808 ImageVariety sing_1749.htm#SEC1825 15252 Imap, option sing_316.htm#IDX175 Implemented algorithms Implemented algorithms sing_33.htm#SEC47 Incl sing_1415.htm#SEC1491 7621 Index sing_2831.htm#SEC2921 Info string sing_52.htm#SEC89 InterDiv sing_1483.htm#SEC1559 46142 Interactive use sing_13.htm#SEC19 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 IntersectWithSub sing_732.htm#SEC784 56289 Intersection theory sing_2767.htm#IDX1052 IntersectionMatrix sing_1581.htm#SEC1657 29351 Introduction sing_2.htm#SEC4 Invariant Theory sing_907.htm#SEC959 Invariant theory sing_1699.htm#SEC1775 InvariantQ sing_1752.htm#SEC1828 53256 InvariantRing sing_1751.htm#SEC1827 22928 Invariants of a finite group Invariants of a finite group sing_909.htm#SEC961 Invariants of plane curve singularities Invariants of plane curve singularities sing_903.htm#SEC955 IsSCA sing_776.htm#SEC828 58445 J-marked schemes sing_1523.htm#IDX635 J-marked schemes, Borel ideals sing_1528.htm#IDX636 JMBTest.lib sing_1523.htm#SEC1599 JMBTest_lib sing_1523.htm#SEC1599 JMSConst.lib sing_1528.htm#SEC1604 JMSConst_lib sing_1528.htm#SEC1604 JMarkedScheme sing_1530.htm#SEC1606 60696 Jacobi sing_1952.htm#SEC2028 29843 Jacobson form sing_1907.htm#IDX802 Jacobson normal form sing_1907.htm#IDX803 Janet basis sing_2762.htm#IDX1046 Janet division, Janet basis sing_2761.htm#IDX1045 JuReTopDim sing_1425.htm#SEC1501 sprintf JuReZeroDim sing_1426.htm#SEC1502 sprintf KScoef sing_1645.htm#SEC1721 sprintf KSconvert sing_1643.htm#SEC1719 3585 KSker sing_1642.htm#SEC1718 40166 KSlinear sing_1644.htm#SEC1720 19896 KSpencerKernel sing_1692.htm#SEC1768 12490 KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2535.htm#SEC2611 20741 Ker sing_2581.htm#SEC2657 58279 Kernel of module homomorphisms Kernel of module homomorphisms sing_895.htm#SEC947 KoszulHomology sing_1240.htm#SEC1316 sprintf Kronecker module sing_2466.htm#IDX989 Kronecker product sing_361.htm#SEC401 L, ordering sing_929.htm#SEC981 LETTERPLACE sing_493.htm#SEC545 LIB sing_285.htm#SEC325 LIB commands sing_53.htm#SEC90 LIBs sing_956.htm#SEC1032 LLL sing_359.htm#IDX220 LOT algorithm sing_542.htm#IDX340 LU-decomposition of a matrix of numbers sing_290.htm#SEC330 Laurent series sing_1208.htm#IDX533 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_913.htm#SEC965 Left ideal membership Groebner bases in G-algebras sing_489.htm#SEC536 Left normal form Groebner bases in G-algebras sing_489.htm#SEC535 LengthSym sing_786.htm#SEC838 16591 LengthSymElement sing_785.htm#SEC837 28292 Letterplace sing_493.htm#SEC545 Levels sing_997.htm#SEC1073 16031 Lexicographic Groebner bases, computation of Groebner basis conversion sing_882.htm#SEC934 Libraries Writing procedures and libraries sing_48.htm#SEC85 Libraries sing_872.htm#SEC924 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86 Library versioning Notes for Singular users sing_2822.htm#SEC2910 Lie algebra sing_1433.htm#IDX603 Lie group sing_1436.htm#IDX608 Lie group sing_1437.htm#IDX611 Limitations sing_409.htm#SEC449 Linear algebra sing_1109.htm#SEC1185 Linear code sing_1870.htm#IDX798 LinearActionQ sing_1754.htm#SEC1830 62218 LinearCombinationQ sing_1755.htm#SEC1831 59373 LinearizeAction sing_1753.htm#SEC1829 60266 Loading a library sing_62.htm#SEC99 Local orderings sing_924.htm#SEC976 Log for matrices sing_1435.htm#IDX607 Long coefficients sing_874.htm#SEC926 M, ordering sing_926.htm#SEC978 MVComplex sing_2415.htm#SEC2491 62126 Macdonald's formula sing_2466.htm#IDX988 MacdonaldF sing_2473.htm#SEC2549 12751 Macintosh installation Macintosh installation instructions sing_2830.htm#SEC2920 Mathematical background Mathematical background sing_930.htm#SEC982 Mathematical background (plural) Mathematical background (plural) sing_487.htm#SEC527 Matrix orderings sing_926.htm#SEC978 Max sing_1661.htm#SEC1737 23 Maximus sing_1525.htm#SEC1601 10010 Maxord sing_1466.htm#SEC1542 14124 MillerRabin sing_1962.htm#SEC2038 15740 Milnor number Milnor and Tjurina number sing_898.htm#SEC950 Milnor number sing_2742.htm#IDX1034 Min sing_1662.htm#SEC1738 29622 MinMult sing_2381.htm#SEC2457 39835 MinimalDecomposition MinimalDecomposition sing_1756.htm#SEC1832 24161 Minimum distance sing_1870.htm#IDX800 Minimus sing_1524.htm#SEC1600 61721 Miscellaneous libraries Miscellaneous libraries sing_2234.htm#SEC2310 ModEqn sing_1655.htm#SEC1731 59394 Modular techniques sing_1019.htm#IDX492 Module orderings sing_925.htm#SEC977 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 Monodromy sing_1647.htm#IDX775 Monomial orderings sing_920.htm#SEC972 Monomial orderings, Term orderings sing_31.htm#SEC44 Mori dream spaces sing_2308.htm#IDX940 Morse lemma addnondegeneratevariables sing_2741.htm#IDX1032 Morse lemma sing_2744.htm#IDX1036 MultiplicitySequence MultiplicitySequence sing_1579.htm#SEC1655 1309 NF sing_335.htm#SEC375 NF sing_479.htm#SEC519 NFMora sing_2028.htm#SEC2104 40670 NPos sing_1298.htm#SEC1374 15702 NPos_test sing_1296.htm#SEC1372 48172 NSplaces sing_1858.htm#SEC1934 48675 NTL sing_1.htm#IDX4 NakYoshF sing_2470.htm#SEC2546 58602 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_2822.htm#SEC2911 Newton non-degenerate sing_1634.htm#IDX773 Newton polygon sing_1633.htm#IDX772 Newton polygon sing_1634.htm#IDX774 Newton polygons sing_2809.htm#IDX1080 Newton polytope sing_2133.htm#IDX817 Newton step sing_2745.htm#IDX1040 NoetherPosition sing_1292.htm#SEC1368 18735 Non-commutative LIBs Non-commutative libraries sing_499.htm#SEC551 Non-commutative algebra Non-commutative algebra sing_912.htm#SEC964 Non-commutative algebra sing_947.htm#SEC1004 Non-commutative libraries Non-commutative libraries sing_499.htm#SEC551 Non-commutative subsystem Non-commutative subsystem sing_422.htm#SEC462 Nonhyp sing_1455.htm#SEC1531 sprintf Normalization sing_894.htm#SEC946 Notes for Singular users Notes for Singular users sing_2822.htm#SEC2906 Notes for developers Notes for developers sing_2823.htm#SEC2913 NullCone sing_1757.htm#SEC1833 64635 NumIrrDecom sing_1429.htm#SEC1505 sprintf NumLocalDim sing_1418.htm#SEC1494 1739 NumPrimDecom sing_1431.htm#SEC1507 34134 Oaku-Takayama algorithm sing_542.htm#IDX338 Objects sing_38.htm#SEC66 Orlik-Solomon sing_2264.htm#IDX881 Output sing_2591.htm#IDX1000 Output sing_2688.htm#IDX1007 Output sing_2690.htm#IDX1008 Output sing_2691.htm#IDX1009 Output sing_2692.htm#IDX1010 Output sing_2693.htm#IDX1011 Output sing_2694.htm#IDX1012 Output sing_2695.htm#IDX1013 Output sing_2696.htm#IDX1014 Output sing_2697.htm#IDX1015 Output sing_2698.htm#IDX1016 Output sing_2699.htm#IDX1017 Output sing_2700.htm#IDX1018 Output sing_2701.htm#IDX1019 Output sing_2702.htm#IDX1020 Output sing_2703.htm#IDX1021 Output sing_2704.htm#IDX1022 Output sing_2705.htm#IDX1023 Output sing_2706.htm#IDX1024 Output sing_2707.htm#IDX1025 Output sing_2708.htm#IDX1026 Output sing_2709.htm#IDX1027 Output sing_2710.htm#IDX1028 Output sing_2711.htm#IDX1029 Output sing_2712.htm#IDX1030 Output, formatting of sing_876.htm#SEC928 PBW sing_521.htm#IDX326 PBW basis sing_488.htm#SEC529 PBW_eqDeg sing_539.htm#SEC591 23181 PBW_maxDeg sing_540.htm#SEC592 59566 PBW_maxMonom sing_541.htm#SEC593 1155 PEsolve sing_1767.htm#SEC1843 9229 PH_ais sing_2286.htm#SEC2362 49473 PH_nais sing_2287.htm#SEC2363 46271 PLURAL sing_423.htm#SEC463 PLURAL LIBs Non-commutative libraries sing_499.htm#SEC551 PPolyH sing_2468.htm#SEC2544 25241 PPolyN sing_2476.htm#SEC2552 39067 PPolyQp sing_2471.htm#SEC2547 35707 PPolyS sing_2474.htm#SEC2550 13817 ParToVar sing_2463.htm#SEC2539 13991 Parallelization Parallelization with ssi links sing_878.htm#SEC930 Parallelization sing_1019.htm#IDX493 Parameter list sing_44.htm#SEC81 Parameters sing_875.htm#SEC927 Parametrization sing_1438.htm#IDX615 Parametrization, image. sing_1448.htm#IDX627 PartC sing_2371.htm#SEC2447 54120 PartitionVar sing_2460.htm#SEC2536 41350 Path names Notes for Singular users sing_2822.htm#SEC2909 PerfectPowerTest sing_1925.htm#SEC2001 17450 Perturbation walk sing_1220.htm#IDX550 Pfister, Gerhard sing_1.htm#IDX19 Pipe links sing_121.htm#SEC161 PocklingtonLehmer sing_1964.htm#SEC2040 13634 Poincare polynomial sing_2276.htm#IDX905 Polar curves sing_900.htm#SEC952 PollardRho sing_1965.htm#SEC2041 49602 PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2289.htm#IDX921 PolyBoRi, Boolean Groebner Basis sing_2291.htm#IDX922 PolyBoRi, Boolean Groebner Basis sing_2292.htm#IDX923 PolyBoRi, Boolean Groebner Basis sing_2293.htm#IDX924 PolyBoRi, Boolean Groebner Basis sing_2294.htm#IDX925 PolyBoRi, Boolean Groebner Basis sing_2295.htm#IDX926 PolyBoRi, Boolean Groebner Basis sing_2296.htm#IDX927 PolyBoRi, Boolean Groebner Basis sing_2297.htm#IDX928 PolyBoRi, Boolean Groebner Basis sing_2298.htm#IDX929 PolyBoRi, Boolean Groebner Basis sing_2299.htm#IDX930 PolyBoRi, Boolean Groebner Basis sing_2300.htm#IDX931 PolyBoRi, Boolean Groebner Basis sing_2301.htm#IDX932 PolyBoRi, Boolean Groebner Basis sing_2302.htm#IDX933 PolyBoRi, Boolean Groebner Basis sing_2303.htm#IDX934 PolyBoRi, Boolean Groebner Basis sing_2305.htm#IDX936 PolyBoRi, zero-supressed decision diagram sing_2304.htm#IDX935 Polybori, Boolean Groebner Basis sing_2306.htm#IDX937 Polynomial data sing_918.htm#SEC970 Pottier algorithm sing_940.htm#SEC997 Preface sing_1.htm#SEC1 Prep sing_992.htm#SEC1068 55342 Primary decomposition Primary decomposition sing_893.htm#SEC945 PrimdecA sing_1274.htm#SEC1350 248 PrimdecB sing_1275.htm#SEC1351 9653 Procedure definition Procedure definition sing_43.htm#SEC78 Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84 Procedures sing_42.htm#SEC77 Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14 Procedures and libraries sing_872.htm#SEC924 Procedures in a library Procedures in a library sing_54.htm#SEC91 Product orderings sing_927.htm#SEC979 Programming sing_870.htm#SEC922 Pseudo ordering L sing_929.htm#SEC981 PtoCrep sing_993.htm#SEC1069 52961 Puiseux expansion sing_1532.htm#IDX638 Puiseux expansion sing_1620.htm#IDX760 Puiseux pairs Invariants of plane curve singularities sing_903.htm#SEC955 Puiseux pairs sing_1626.htm#IDX765 QQ sing_28.htm#SEC39 Qso3Casimir sing_726.htm#SEC778 40212 Quot-scheme sing_2466.htm#IDX991 Quotient sing_1809.htm#SEC1885 24888 QuotientEquations sing_1656.htm#SEC1732 18230 Rational curves sing_1438.htm#IDX616 ReJunkUseHomo sing_1424.htm#SEC1500 10186 ReesAlgebra sing_1391.htm#SEC1467 59951 References sing_955.htm#SEC1029 References (plural) sing_491.htm#SEC541 Release Notes sing_2818.htm#SEC2894 Res sing_2571.htm#SEC2647 92 ResTree sing_1484.htm#SEC1560 58727 Resolution sing_11.htm#SEC17 Resolution of singularities Resolution of singularities sing_906.htm#SEC958 Resolution, free sing_888.htm#SEC940 ReynoldsImage sing_1758.htm#SEC1834 35172 ReynoldsOperator sing_1759.htm#SEC1835 14986 RiemannRochBN sing_2316.htm#SEC2392 20085 RiemannRochHess sing_2554.htm#SEC2630 sprintf Right Groebner bases and syzygies Right Groebner bases and syzygies sing_914.htm#SEC966 Ring-dependent options Notes for Singular users sing_2822.htm#SEC2908 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_492.htm#SEC544 SDB breakpoint Source code debugger sing_66.htm#SEC106 SDB debugger Source code debugger sing_66.htm#SEC106 SDLoc sing_569.htm#SEC621 9512 SINGULAR libraries sing_956.htm#SEC1032 SINGULARHIST sing_18.htm#SEC25 SV-decoding algorithm sing_1865.htm#IDX794 SV-decoding algorithm, preprocessing sing_1864.htm#IDX793 Sannfs sing_545.htm#SEC597 42932 SannfsBFCT sing_554.htm#SEC606 59702 SannfsVar sing_601.htm#SEC653 37522 Sannfslog sing_546.htm#SEC598 49313 Saturation sing_885.htm#SEC937 Saturation sing_1201.htm#IDX519 Sch@"onemann, Hans sing_1.htm#IDX20 Schoof sing_1976.htm#SEC2052 49281 Schubert calculus sing_2767.htm#IDX1054 SchubertClass sing_2804.htm#SEC2880 62336 SchurCh sing_2368.htm#SEC2444 58575 SchurS sing_2367.htm#SEC2443 46004 SegreA sing_2374.htm#SEC2450 55776 Semigroup sing_1572.htm#SEC1648 22323 SetDeg sing_2574.htm#SEC2650 40547 Setting up a G-algebra sing_488.htm#SEC532 ShanksMestre sing_1975.htm#SEC2051 12973 SimplifyIdeal sing_1760.htm#SEC1836 sprintf Singular sing_359.htm#IDX257 Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2820.htm#SEC2904 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_1422.htm#SEC1498 7552 SingularLib sing_359.htm#IDX259 Singularities sing_1531.htm#SEC1607 Singularity Theory sing_897.htm#SEC949 Skeletons for parallelization sing_1019.htm#IDX494 Smith form sing_1907.htm#IDX804 Smith normal form sing_1907.htm#IDX805 SolowayStrassen sing_1963.htm#SEC2039 22680 Solving systems of polynomial equations Solving systems of polynomial equations sing_916.htm#SEC968 Source sing_2563.htm#SEC2639 10351 Source code debugger, invocation Command line options sing_19.htm#IDX33 Space curve singularities, branches of Branches of space curve singularities sing_904.htm#SEC956 Special characters sing_36.htm#SEC64 Splitting lemma addnondegeneratevariables sing_2741.htm#IDX1033 Splitting lemma sing_2744.htm#IDX1037 Ssi file links sing_119.htm#SEC159 Ssi links sing_118.htm#SEC158 Ssi tcp links sing_120.htm#SEC160 StabEqn sing_1657.htm#SEC1733 28539 StabEqnId sing_1658.htm#SEC1734 27955 StabOrder sing_1659.htm#SEC1735 55603 Standard Bases Computing Groebner and Standard Bases sing_880.htm#SEC932 Standard bases sing_931.htm#SEC983 StartOrderingV sing_1526.htm#SEC1602 58927 Startup sequence sing_20.htm#SEC27 StringF sing_1646.htm#SEC1722 11590 SymGroup sing_784.htm#SEC836 56676 Symbolic-numerical solving Symbolic-numerical solving sing_916.htm#SEC968 Symbolic-numerical solving sing_1764.htm#SEC1840 System and Control theory System and Control theory sing_1889.htm#SEC1965 System dependent limitations System dependent limitations sing_410.htm#SEC450 System variables sing_396.htm#SEC436 Syzygies and resolutions Syzygies and resolutions sing_933.htm#SEC987 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_490.htm#SEC537 T1 sing_901.htm#SEC953 T2 sing_901.htm#SEC953 TRACE Tracing of procedures sing_65.htm#SEC102 TRACE sing_405.htm#SEC445 T_1 sing_1679.htm#SEC1755 59277 T_12 sing_1681.htm#SEC1757 12923 T_2 sing_1680.htm#SEC1756 55781 Target sing_2562.htm#SEC2638 16006 Teaching sing_1921.htm#SEC1997 Template for writing a library sing_55.htm#SEC92 TestGRRes sing_2534.htm#SEC2610 8315 TestJMark sing_1527.htm#SEC1603 41314 The SINGULAR language The SINGULAR language sing_34.htm#SEC56 The Tran algorithm sing_1217.htm#IDX547 The fractal walk algorithm sing_1216.htm#IDX546 The fractal walk algorithm sing_2766.htm#IDX1051 The online help system The online help system sing_16.htm#SEC22 Tjurina sing_1677.htm#SEC1753 11249 Tjurina number Milnor and Tjurina number sing_898.htm#SEC950 Tjurina number sing_1313.htm#IDX576 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38 Tor sing_1242.htm#SEC1318 sprintf Toric ideals and integer programming Toric ideals and integer programming sing_936.htm#SEC993 Tricks and pitfalls sing_408.htm#SEC448 Tropical Geometry sing_2073.htm#SEC2149 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_1157.htm#SEC1233 26192 Unix installation Unix installation instructions sing_2828.htm#SEC2918 UpOneMatrix sing_773.htm#SEC825 63020 UpperMonomials sing_1660.htm#SEC1736 20941 UseBertini sing_1421.htm#SEC1497 43362 User defined types sing_183.htm#SEC223 V-filtration sing_1595.htm#IDX670 V-filtration sing_1601.htm#IDX698 V-filtration sing_1602.htm#IDX704 V-filtration sing_1603.htm#IDX712 V-filtration sing_1604.htm#IDX718 V-filtration sing_1605.htm#IDX726 V-filtration sing_1606.htm#IDX736 V-filtration sing_1617.htm#IDX742 V-filtration sing_1619.htm#IDX753 VarToPar sing_2462.htm#SEC2538 10508 Variables, indexed sing_37.htm#SEC65 Version number Version schema for Singular sing_2821.htm#SEC2905 Version schema for Singular Version schema for Singular sing_2821.htm#SEC2905 Version string sing_50.htm#SEC87 Visualization sing_1827.htm#SEC1903 WLemma sing_1006.htm#SEC1082 7302 WP, global ordering sing_923.htm#IDX406 WSemigroup sing_1577.htm#SEC1653 57449 Weierstrass sing_1860.htm#SEC1936 58220 Weierstrass semigroup sing_1856.htm#IDX788 Weyl sing_758.htm#SEC810 29212 Weyl algebra sing_542.htm#IDX332 Weyl algebra sing_598.htm#IDX357 Weyl closure sing_843.htm#IDX391 WeylClosure sing_845.htm#SEC897 23845 WeylClosure1 sing_846.htm#SEC898 15759 Wibmer's Lemma sing_1006.htm#IDX487 Windows installation Windows installation instructions sing_2829.htm#SEC2919 WitSet sing_1428.htm#SEC1504 39803 WitSupSet sing_1427.htm#SEC1503 47758 Ws, local ordering sing_924.htm#IDX418 XLsolve sing_1770.htm#SEC1846 34970 ZZ sing_28.htm#SEC39 ZZ/m sing_28.htm#SEC39 ZZ/p sing_28.htm#SEC39 ZZsolve sing_1771.htm#SEC1847 18657 [ 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_928.htm#SEC980 absFactorize sing_1170.htm#SEC1246 52546 absFactorizeBCG sing_1171.htm#SEC1247 55510 absPrimdecGTZ sing_1371.htm#SEC1447 46393 absPrimdecGTZE sing_1372.htm#SEC1448 48005 absValue sing_968.htm#SEC1044 54595 absfact.lib sing_1169.htm#SEC1245 absfact_lib sing_1169.htm#SEC1245 absolute factorization. sing_1169.htm#IDX518 abstract variety, projective space, Grassmannian printVariety sing_2768.htm#IDX1057 abstract variety, projective space, Grassmannian sing_2769.htm#IDX1058 abstractR sing_1510.htm#SEC1586 22284 actionIsProper sing_1740.htm#SEC1816 52474 addLeftFractions sing_2728.htm#SEC2804 38826 addModules sing_2583.htm#SEC2659 51193 addNvarsTo sing_1093.htm#SEC1169 63123 addRat sing_864.htm#SEC916 4768 addSheaf sing_2787.htm#SEC2863 27062 addcol sing_1126.htm#SEC1202 52204 addcores sing_1062.htm#SEC1138 41254 addnondegeneratevariables addnondegeneratevariables sing_2744.htm#SEC2820 40483 addrow sing_1127.htm#SEC1203 47055 addvarsTo sing_1092.htm#SEC1168 17717 ademRelations sing_689.htm#SEC741 30263 adjoint sing_1151.htm#SEC1227 56619 adjointIdeal sing_1439.htm#SEC1515 11455 adjunction divisor sing_1857.htm#IDX792 admissibleSub sing_749.htm#SEC801 6583 afaces sing_2487.htm#SEC2563 28045 affine code Fitzgerald-Lax method sing_952.htm#SEC1021 ainvar.lib sing_1737.htm#SEC1813 ainvar_lib sing_1737.htm#SEC1813 aksaka.lib sing_1922.htm#SEC1998 aksaka_lib sing_1922.htm#SEC1998 alexanderpolynomial sing_1535.htm#SEC1611 36814 alexpoly.lib sing_1532.htm#SEC1608 alexpoly_lib sing_1532.htm#SEC1608 algDependent sing_1176.htm#SEC1252 20789 alg_kernel sing_1177.htm#SEC1253 307 algebra.lib sing_1172.htm#SEC1248 algebra_containment sing_1173.htm#SEC1249 47912 algebra_lib sing_1172.htm#SEC1248 algebraic dependence sing_779.htm#IDX363 algebraic field extension sing_1385.htm#IDX585 algebraicDependence sing_1398.htm#SEC1474 38500 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_943.htm#SEC1000 algorithm of Conti and Traverso sing_939.htm#SEC996 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_942.htm#SEC999 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_941.htm#SEC998 algorithm of Pottier sing_940.htm#SEC997 alias General command syntax sing_35.htm#SEC59 align sing_209.htm#SEC249 all.lib sing_961.htm#SEC1037 allDoubleExt sing_796.htm#SEC848 43457 allExtOfLeft sing_793.htm#SEC845 6405 allExtOfRight sing_794.htm#SEC846 56781 allPositive sing_518.htm#SEC570 1409 all_lib sing_961.htm#SEC1037 allowing net access Command line options sing_19.htm#IDX41 allprint sing_1010.htm#SEC1086 5195 allreal sing_2065.htm#SEC2141 57232 allrealst sing_2063.htm#SEC2139 40962 allsquarefree sing_1639.htm#SEC1715 45545 ambientDimension sing_2078.htm#SEC2154 18907 and Evaluation of logical expressions sing_101.htm#SEC141 and sing_413.htm#SEC453 annPoly sing_566.htm#SEC618 18228 annRat sing_567.htm#SEC619 62662 annRatSyz sing_853.htm#SEC905 15672 annfs sing_543.htm#SEC595 38155 annfs0 sing_555.htm#SEC607 26476 annfs2 sing_556.htm#SEC608 47962 annfsBMI sing_552.htm#SEC604 2532 annfsParamBM sing_551.htm#SEC603 43587 annfsRB sing_557.htm#SEC609 31892 annfspecial sing_544.htm#SEC596 27566 annihilator of polynomial sing_565.htm#IDX342 annihilator of rational function sing_565.htm#IDX343 annihilator of rational function sing_843.htm#IDX394 annil sing_1280.htm#SEC1356 48744 appelF1 sing_584.htm#SEC636 63146 appelF2 sing_585.htm#SEC637 22460 appelF4 sing_586.htm#SEC638 6847 appendWeight2Ord sing_751.htm#SEC803 21488 apply sing_380.htm#SEC420 applyAdF sing_534.htm#SEC586 40329 applyPermutationToIntvec applyPermutationToIntvec sing_2512.htm#SEC2588 28900 arcpoint.lib sing_1545.htm#SEC1621 arcpoint_lib sing_1545.htm#SEC1621 areEqualLeftFractions areEqualLeftFractions sing_2730.htm#SEC2806 29498 areZeroElements sing_2650.htm#SEC2726 14728 argument, default sing_44.htm#SEC81 argument, optional sing_44.htm#SEC81 arr.lib sing_2235.htm#SEC2311 arr2multarr sing_2268.htm#SEC2344 15063 arrBoolean sing_2257.htm#SEC2333 63256 arrBoundedChambers sing_2278.htm#SEC2354 18347 arrBraid sing_2258.htm#SEC2334 34093 arrCenter sing_2245.htm#SEC2321 24565 arrCentered sing_2247.htm#SEC2323 15904 arrCentral sing_2246.htm#SEC2322 14086 arrCentralize sing_2248.htm#SEC2324 53235 arrChambers sing_2277.htm#SEC2353 44578 arrCharPoly sing_2275.htm#SEC2351 44129 arrCone sing_2251.htm#SEC2327 38068 arrCoordChange sing_2249.htm#SEC2325 61430 arrCoordNormalize sing_2250.htm#SEC2326 45861 arrDecone sing_2252.htm#SEC2328 54637 arrDer sing_2265.htm#SEC2341 48815 arrEdelmanReiner sing_2263.htm#SEC2339 59091 arrEssentialize sing_2256.htm#SEC2332 6667 arrExponents sing_2267.htm#SEC2343 1948 arrFlats sing_2272.htm#SEC2348 64792 arrIsEssential sing_2255.htm#SEC2331 34363 arrIsFree sing_2266.htm#SEC2342 3860 arrLastVar sing_2244.htm#SEC2320 25835 arrLattice sing_2273.htm#SEC2349 58951 arrLocalize sing_2253.htm#SEC2329 56070 arrOrlikSolomon sing_2264.htm#SEC2340 31686 arrPoincare sing_2276.htm#SEC2352 412 arrPrintMatrix sing_2240.htm#SEC2316 21204 arrRandom sing_2261.htm#SEC2337 59986 arrRandomCentral sing_2262.htm#SEC2338 43698 arrRestrict sing_2254.htm#SEC2330 sprintf arrSet sing_2236.htm#SEC2312 53769 arrSwapVar sing_2243.htm#SEC2319 44919 arrTypeB sing_2259.htm#SEC2335 22358 arrTypeD sing_2260.htm#SEC2336 26495 arr_lib sing_2235.htm#SEC2311 arrange sing_559.htm#SEC611 50350 arrangement sing_2236.htm#IDX823 arrangement sing_2237.htm#IDX828 arrangement sing_2268.htm#IDX890 arrangement sing_2269.htm#IDX893 ask sing_1930.htm#SEC2006 3862 assPrimes sing_1187.htm#SEC1263 sprintf assign sing_2236.htm#IDX825 assignment,custom Assignments for user defined types sing_188.htm#SEC228 associated tangent FamElemsAtEnvCompPoints sing_1003.htm#IDX480 associated tangent sing_1004.htm#IDX484 assprimeszerodim.lib assprimeszerodim_lib sing_1185.htm#SEC1261 assprimeszerodim_lib assprimeszerodim_lib sing_1185.htm#SEC1261 atkins.lib sing_1931.htm#SEC2007 atkins_lib sing_1931.htm#SEC2007 attrib sing_210.htm#SEC250 autGenWeights sing_2311.htm#SEC2387 32642 autGradAlg sing_2310.htm#SEC2386 21136 autKS sing_2309.htm#SEC2385 51607 autX sing_2314.htm#SEC2390 43261 autXhat sing_2313.htm#SEC2389 35932 autgradalg.lib sing_2308.htm#SEC2384 autgradalg_lib sing_2308.htm#SEC2384 automorphism group sing_2308.htm#IDX941 automorphisms sing_2308.htm#IDX938 autonom sing_1894.htm#SEC1970 57044 autonomDim sing_1895.htm#SEC1971 30055 awalk1 sing_1218.htm#SEC1294 11044 awalk2 sing_1219.htm#SEC1295 8955 b-function sing_507.htm#IDX315 bFactor sing_589.htm#SEC641 15179 babyGiant sing_1960.htm#SEC2036 41113 backward sing_2449.htm#SEC2525 11225 bareiss sing_211.htm#SEC251 base2str sing_964.htm#SEC1040 sprintf basering sing_28.htm#IDX76 basering sing_88.htm#SEC128 basicinvariants sing_1551.htm#SEC1627 32136 baumslagGroup sing_640.htm#SEC692 64086 baumslagSolitar sing_639.htm#SEC691 53837 belongSemigroup sing_1190.htm#SEC1266 19983 bernstein sing_1599.htm#SEC1675 5605 bernsteinBM sing_547.htm#SEC599 57689 bernsteinLift sing_548.htm#SEC600 22885 bertini sing_1414.htm#IDX589 bertini sing_1419.htm#IDX596 bertini2Singular sing_1423.htm#SEC1499 58501 betti sing_212.htm#SEC252 betti (plural) sing_457.htm#SEC497 bfct sing_508.htm#SEC560 29858 bfctAnn sing_510.htm#SEC562 36658 bfctBound sing_852.htm#SEC904 5630 bfctIdeal sing_512.htm#SEC564 41018 bfctOneGB sing_511.htm#SEC563 9696 bfctSyz sing_509.htm#SEC561 26796 bfctVarAnn sing_600.htm#SEC652 51667 bfctVarIn sing_599.htm#SEC651 9274 bfun.lib sing_507.htm#SEC559 bfun_lib sing_507.htm#SEC559 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_2510.htm#SEC2586 59742 bigintmat sing_83.htm#SEC123 bigintmat declarations bigintmat declarations sing_84.htm#SEC124 bigintmat expressions bigintmat expressions sing_85.htm#SEC125 bigintmat operations bigintmat operations sing_87.htm#SEC127 bigintmat type cast sing_86.htm#SEC126 bimodules sing_500.htm#IDX303 bimodules.lib sing_500.htm#SEC552 bimodules_lib sing_500.htm#SEC552 binaryToBigint sing_2511.htm#SEC2587 sprintf binary_add sing_1983.htm#SEC2059 42817 binomial sing_969.htm#SEC1045 23208 binomials2intmat sing_1346.htm#SEC1422 58804 birational map, image, inverse. sing_1440.htm#IDX621 bistd sing_501.htm#SEC553 45237 bisyzygies sing_500.htm#IDX304 bitrinity sing_502.htm#SEC554 3516 blackbox sing_192.htm#SEC232 blackbox sing_200.htm#SEC240 block sing_40.htm#SEC70 block sing_379.htm#SEC419 blowUp sing_1491.htm#SEC1567 34819 blowUp2 sing_1492.htm#SEC1568 65264 blowUpBO sing_1498.htm#SEC1574 58146 blowup0 sing_1195.htm#SEC1271 44451 boolean sing_2257.htm#IDX867 boolean expressions sing_100.htm#SEC140 boolean operations sing_101.htm#SEC141 boolean_constant sing_2291.htm#SEC2367 52873 boolean_ideal sing_2295.htm#SEC2371 53515 boolean_poly sing_2292.htm#SEC2368 41652 boolean_poly_ring sing_2290.htm#SEC2366 sprintf boolean_set sing_2296.htm#SEC2372 58235 boolean_std sing_2289.htm#SEC2365 5921 border basis sing_2758.htm#IDX1041 borderBasis sing_2759.htm#SEC2835 33172 boundBuFou sing_2060.htm#SEC2136 26589 boundDes sing_2062.htm#SEC2138 35149 boundaryLatticePoints boundaryLatticePoints sing_2148.htm#SEC2224 6238 boundposDes sing_2061.htm#SEC2137 58854 bounds sing_2746.htm#SEC2822 50218 boxSet sing_2748.htm#SEC2824 8552 bracket sing_359.htm#IDX197 bracket sing_416.htm#SEC456 bracket sing_458.htm#SEC498 braid sing_2258.htm#IDX869 branchTo procs with different argument types sing_160.htm#SEC200 break sing_381.htm#SEC421 break point sing_395.htm#SEC435 breakpoint sing_382.htm#SEC422 brillnoether.lib sing_2315.htm#SEC2391 brillnoether_lib sing_2315.htm#SEC2391 brnoeth.lib sing_1856.htm#SEC1932 brnoeth_lib sing_1856.htm#SEC1932 browser, command line option Command line options sing_19.htm#IDX44 browser, setting the sing_359.htm#IDX193 browsers The online help system sing_16.htm#IDX21 browsers, setting the sing_359.htm#IDX192 bubblesort sing_1933.htm#SEC2009 63278 busadj sing_1149.htm#SEC1225 36301 bvar sing_2303.htm#SEC2379 52773 c, module ordering sing_925.htm#IDX421 cProj sing_2357.htm#SEC2433 24037 calculateI sing_1465.htm#SEC1541 31107 calculate_max_sum sing_2002.htm#SEC2078 4706 calculate_ordering sing_1980.htm#SEC2056 42616 cancelunit, option sing_316.htm#IDX171 canonMap sing_1223.htm#SEC1299 47599 canoncial form sing_991.htm#IDX442 canoncial form sing_992.htm#IDX444 canoncial form sing_993.htm#IDX446 canonical sing_987.htm#IDX430 canonical form sing_996.htm#IDX460 canonical form sing_997.htm#IDX462 canonical, sing_995.htm#IDX456 canonicalizeCone sing_2079.htm#SEC2155 6251 canonize sing_1902.htm#SEC1978 54090 cantoradd sing_2016.htm#SEC2092 55304 cantormult sing_2019.htm#SEC2095 57569 cantorred sing_2017.htm#SEC2093 46502 cardGroup sing_1192.htm#SEC1268 5553 case No case or switch statement sing_414.htm#SEC454 catNets sing_2688.htm#SEC2764 24760 cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2813.htm#SEC2889 55393 cdd sing_1.htm#IDX10 cddlib sing_1.htm#IDX11 center sing_521.htm#IDX322 65108 center sing_527.htm#SEC579 center sing_2245.htm#IDX849 center sing_2246.htm#IDX850 center sing_2247.htm#IDX852 center sing_2248.htm#IDX854 centerRed sing_526.htm#SEC578 59910 centerVS sing_525.htm#SEC577 27548 central sing_2239.htm#IDX835 central sing_2246.htm#IDX851 central sing_2248.htm#IDX853 central sing_2262.htm#IDX878 central.lib sing_521.htm#SEC573 central1st sing_2450.htm#SEC2526 29090 central2nd sing_2451.htm#SEC2527 37545 central_lib sing_521.htm#SEC573 centralize sing_521.htm#IDX325 centralizeSet sing_522.htm#SEC574 55737 centralizer sing_521.htm#IDX323 65261 centralizer sing_528.htm#SEC580 centralizerRed sing_524.htm#SEC576 8209 centralizerVS sing_523.htm#SEC575 22925 cf_class sing_210.htm#IDX132 cgs sing_963.htm#SEC1039 57776 cgsdr sing_988.htm#SEC1064 44460 chAll sing_2327.htm#SEC2403 2690 chAllInv sing_2328.htm#SEC2404 57760 chDual sing_2333.htm#SEC2409 17745 chHE sing_2329.htm#SEC2405 63916 chHom sing_2342.htm#SEC2418 54776 chNum sing_2323.htm#SEC2399 54415 chNumbers sing_2324.htm#SEC2400 42134 chNumbersProj sing_2361.htm#SEC2437 28837 chProd sing_2335.htm#SEC2411 40209 chProdE sing_2336.htm#SEC2412 33460 chProdL sing_2337.htm#SEC2413 44795 chProdLP sing_2338.htm#SEC2414 8881 chProdM sing_2339.htm#SEC2415 64514 chProdMP sing_2340.htm#SEC2416 17103 chProj sing_2358.htm#SEC2434 32311 chSum sing_2331.htm#SEC2407 21088 chSymm sing_2345.htm#SEC2421 24066 chSymm2L sing_2346.htm#SEC2422 51625 chSymm2LP sing_2347.htm#SEC2423 26099 chWedge sing_2348.htm#SEC2424 57678 chWedge2L sing_2349.htm#SEC2425 46597 chWedge2LP sing_2350.htm#SEC2426 8876 chaincrit sing_2030.htm#SEC2106 9502 chambers sing_2277.htm#IDX906 chambers sing_2278.htm#IDX907 changeDenominator sing_1318.htm#SEC1394 21094 changechar sing_1067.htm#SEC1143 65454 changeord sing_1068.htm#SEC1144 55156 changeordTo sing_1091.htm#SEC1167 41903 changes sing_2819.htm#SEC2895 changevar sing_1069.htm#SEC1145 32829 char sing_213.htm#SEC253 charInfo sing_582.htm#SEC634 11034 charVariety sing_581.htm#SEC633 18306 char_series sing_214.htm#SEC254 characteristic exponents sing_1539.htm#IDX645 characteristic exponents sing_1540.htm#IDX650 characteristic exponents sing_1541.htm#IDX653 characteristic exponents sing_1542.htm#IDX657 characteristic exponents sing_1626.htm#IDX763 characteristic polynomial sing_2275.htm#IDX904 characteristic variety sing_565.htm#IDX350 characteristic variety sing_843.htm#IDX390 charexp2conductor sing_1542.htm#SEC1618 sprintf charexp2generators sing_1540.htm#SEC1616 16838 charexp2inter sing_1541.htm#SEC1617 39881 charexp2multseq sing_1539.htm#SEC1615 334 charexp2poly sing_1543.htm#SEC1619 sprintf charpoly sing_1150.htm#SEC1226 29561 charstr sing_215.htm#SEC255 checkFactor sing_558.htm#SEC610 55900 checkRoot sing_553.htm#SEC605 37045 chern sing_2322.htm#SEC2398 4916 chern.lib sing_2317.htm#SEC2393 chernCharPoly sing_2364.htm#SEC2440 31610 chernPoly sing_2363.htm#SEC2439 31316 chern_lib sing_2317.htm#SEC2393 chineseRem sing_1951.htm#SEC2027 38560 chinrem sing_216.htm#SEC256 chinrempoly sing_2714.htm#SEC2790 42312 chinrestp sing_2010.htm#SEC2086 24779 cimonom.lib sing_2379.htm#SEC2455 cimonom_lib sing_2379.htm#SEC2455 cisimplicial.lib sing_1188.htm#SEC1264 cisimplicial_lib sing_1188.htm#SEC1264 classification sing_2383.htm#IDX944 classify sing_1552.htm#SEC1628 4953 classify.lib sing_1550.htm#SEC1626 classify2.lib sing_2383.htm#SEC2459 classify2_lib sing_2383.htm#SEC2459 classifyCeq sing_1569.htm#SEC1645 42719 classifyMapGerms.lib classifyMapGerms_lib sing_2395.htm#SEC2471 classifyMapGerms_lib classifyMapGerms_lib sing_2395.htm#SEC2471 classifySimpleMaps sing_2401.htm#SEC2477 62176 classifySimpleMaps1 sing_2402.htm#SEC2478 24789 classifyUnimodalMaps classifyUnimodalMaps sing_2403.htm#SEC2479 63464 classify_aeq.lib sing_2386.htm#SEC2462 classify_aeq_lib sing_2386.htm#SEC2462 classify_lib sing_1550.htm#SEC1626 classifyceq.lib sing_1568.htm#IDX660 classifyceq_lib sing_1568.htm#IDX661 classifyci.lib sing_1570.htm#IDX662 classifyci_lib sing_1570.htm#IDX663 classifyicis sing_1571.htm#SEC1647 37651 classpoly sing_2362.htm#SEC2438 45724 cleanTmp sing_2226.htm#SEC2302 14108 cleanunit sing_1463.htm#SEC1539 sprintf cleardenom sing_217.htm#SEC257 close sing_218.htm#SEC258 closed_points sing_1866.htm#SEC1942 47269 closetex sing_1833.htm#SEC1909 42334 closureFrac sing_1311.htm#SEC1387 9252 coDim sing_2397.htm#SEC2473 60680 coDimMap sing_2396.htm#SEC2472 2002 coHom sing_802.htm#SEC854 51043 codim sing_1664.htm#SEC1740 14253 codimension sing_2080.htm#SEC2156 32207 coding theory sing_917.htm#SEC969 coef sing_219.htm#SEC259 coefficient sing_2238.htm#IDX831 coefficient sing_2239.htm#IDX834 coefficient sing_2240.htm#IDX838 coefficient field sing_144.htm#SEC184 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45 coefficients, long sing_874.htm#SEC926 coeffmod sing_1928.htm#SEC2004 23531 coeffs sing_220.htm#SEC260 coker sing_2579.htm#SEC2655 35639 colength of derivations curveColengthDerivations sing_2412.htm#IDX964 collectDiv sing_1508.htm#SEC1584 50348 colrank sing_1900.htm#SEC1976 52290 colred sing_1133.htm#SEC1209 1693 combinat.lib sing_2404.htm#SEC2480 combinat_lib sing_2404.htm#SEC2480 commRing sing_867.htm#SEC919 30892 comma sing_415.htm#SEC455 command,custom Commands for user defined types sing_187.htm#SEC227 command-line option, setting value of sing_359.htm#IDX281 command-line option, value of sing_359.htm#IDX279 command-line options, print all values of sing_359.htm#IDX278 command-line options, short help Command line options sing_19.htm#IDX38 commands (plural) sing_456.htm#IDX302 comment sing_36.htm#IDX108 compareMatrix sing_2587.htm#SEC2663 49930 compareModules sing_2582.htm#SEC2658 3692 compareTasks sing_1098.htm#SEC1174 45157 compareVectors sing_2607.htm#SEC2683 12881 completeReduction sing_1742.htm#SEC1818 57157 complex sing_28.htm#IDX75 complexClassify sing_2384.htm#SEC2460 22796 complexSingType sing_1566.htm#SEC1642 34483 complexType sing_2385.htm#SEC2461 55772 compregb.lib sing_962.htm#SEC1038 compregb_lib sing_962.htm#SEC1038 comprehensive Groebner system sing_962.htm#IDX427 compress sing_1111.htm#SEC1187 61998 computeAfaceOrbits sing_2497.htm#SEC2573 28683 computeConstant sing_1208.htm#SEC1284 55024 computeGromovWitten sing_1211.htm#SEC1287 18834 computeN sing_1512.htm#SEC1588 61628 computeV sing_1511.htm#SEC1587 40316 computemcm sing_1470.htm#SEC1546 36956 concat sing_1112.htm#SEC1188 16653 conductor sing_1319.htm#IDX577 conductor sing_1542.htm#IDX656 conductor sing_2410.htm#IDX958 conductor, degree sing_1626.htm#IDX766 cone sing_189.htm#SEC229 cone sing_2251.htm#IDX858 cone sing_2252.htm#IDX860 coneLink sing_2083.htm#SEC2159 13635 coneViaInequalities sing_2082.htm#SEC2158 25661 coneViaPoints sing_2081.htm#SEC2157 3386 conic, parametrization, rational point. sing_1447.htm#IDX626 conicWithTangents sing_2202.htm#SEC2278 60752 constructH sing_1471.htm#SEC1547 59577 constructblwup sing_1472.htm#SEC1548 19326 constructible set sing_996.htm#IDX458 constructible sets sing_997.htm#IDX461 constructlastblwup sing_1473.htm#SEC1549 7639 constructor sing_2268.htm#IDX891 constructor sing_2269.htm#IDX894 contact matrix sing_1541.htm#IDX652 containedQ sing_1821.htm#SEC1897 46718 containsAsFace sing_2084.htm#SEC2160 25159 containsInCollection containsInCollection sing_2117.htm#SEC2193 14368 containsInSupport sing_2085.htm#SEC2161 32493 containsPositiveVector containsPositiveVector sing_2086.htm#SEC2162 27042 containsRelatively sing_2087.htm#SEC2163 17126 content sing_1041.htm#SEC1117 9095 contentSB, option sing_316.htm#IDX172 continue Behavior of continue sing_383.htm#SEC423 continue sing_417.htm#SEC457 contraHom sing_803.htm#SEC855 54270 contract sing_221.htm#SEC261 contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2794.htm#IDX1070 contributionBundle sing_2794.htm#SEC2870 32874 contributors sing_359.htm#IDX200 control sing_1892.htm#SEC1968 44498 control.lib sing_1891.htm#SEC1967 controlDim sing_1893.htm#SEC1969 2417 controlExample sing_1905.htm#SEC1981 2678 control_Matrix sing_1594.htm#SEC1670 sprintf control_lib sing_1891.htm#SEC1967 convertLeftToRightFraction convertLeftToRightFraction sing_2727.htm#SEC2803 4318 convertRightToLeftFraction convertRightToLeftFraction sing_2726.htm#SEC2802 19389 convertdata sing_1468.htm#SEC1544 54629 convexHull sing_2088.htm#SEC2164 56690 convexIntersection sing_2089.htm#SEC2165 63587 convloc sing_562.htm#SEC614 19122 coordinate change sing_2248.htm#IDX855 coordinate change sing_2249.htm#IDX856 coordinate change sing_2250.htm#IDX857 coordinates sing_2048.htm#IDX808 coords sing_2048.htm#SEC2124 29362 copyTask sing_1097.htm#SEC1173 65331 copyright sing_1.htm#IDX1 corank sing_1553.htm#SEC1629 33709 cornerMonomials sing_1349.htm#SEC1425 33995 countPoints sing_1973.htm#SEC2049 58566 coverings sing_1210.htm#IDX536 coverings sing_1211.htm#IDX540 cpu sing_359.htm#IDX202 cpu sing_359.htm#IDX275 createBO sing_1499.htm#SEC1575 32669 createGradedRingHomomorphism createGradedRingHomomorphism sing_2626.htm#SEC2702 62177 createGroup sing_2619.htm#SEC2695 28500 createQuotientGroup sing_2620.htm#SEC2696 26374 createTask sing_1095.htm#SEC1171 48404 createTorsionFreeGroup createTorsionFreeGroup sing_2621.htm#SEC2697 51944 createlist sing_1481.htm#SEC1557 61781 cring sing_73.htm#SEC113 cring declarations sing_74.htm#SEC114 cring expressions sing_75.htm#SEC115 cring operations sing_76.htm#SEC116 cring related functions cring related functions sing_77.htm#SEC117 crossprod sing_222.htm#SEC262 crypto.lib sing_1946.htm#SEC2022 crypto_lib sing_1946.htm#SEC2022 crystallographicGroupC2MM crystallographicGroupC2MM sing_648.htm#SEC700 41262 crystallographicGroupCM crystallographicGroupCM sing_647.htm#SEC699 24754 crystallographicGroupP1 crystallographicGroupP1 sing_641.htm#SEC693 48853 crystallographicGroupP2 crystallographicGroupP2 sing_645.htm#SEC697 35903 crystallographicGroupP2GG crystallographicGroupP2GG sing_646.htm#SEC698 27952 crystallographicGroupP2MM crystallographicGroupP2MM sing_644.htm#SEC696 13909 crystallographicGroupP3 crystallographicGroupP3 sing_652.htm#SEC704 10088 crystallographicGroupP31M crystallographicGroupP31M sing_653.htm#SEC705 31189 crystallographicGroupP3M1 crystallographicGroupP3M1 sing_654.htm#SEC706 1687 crystallographicGroupP4 crystallographicGroupP4 sing_649.htm#SEC701 39932 crystallographicGroupP4GM crystallographicGroupP4GM sing_651.htm#SEC703 52244 crystallographicGroupP4MM crystallographicGroupP4MM sing_650.htm#SEC702 3914 crystallographicGroupP6 crystallographicGroupP6 sing_655.htm#SEC707 38438 crystallographicGroupP6MM crystallographicGroupP6MM sing_656.htm#SEC708 30180 crystallographicGroupPG crystallographicGroupPG sing_643.htm#SEC695 39728 crystallographicGroupPM crystallographicGroupPM sing_642.htm#SEC694 10105 cup sing_1224.htm#SEC1300 57972 cupproduct sing_1225.htm#SEC1301 43349 curve singularities sing_1532.htm#IDX639 curve singularities sing_1620.htm#IDX761 curve singularity sing_2408.htm#IDX953 curveColengthDerivations curveColengthDerivations sing_2412.htm#SEC2488 2078 curveConductorMult sing_2410.htm#SEC2486 15897 curveDeligneNumber sing_2411.htm#SEC2487 12294 curveDeltaInv sing_2409.htm#SEC2485 16375 curveInv.lib sing_2408.htm#SEC2484 curveInv_lib sing_2408.htm#SEC2484 curvepar.lib sing_1573.htm#SEC1649 curvepar_lib sing_1573.htm#SEC1649 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_2280.htm#SEC2356 customstd_lib sing_2280.htm#SEC2356 cycleLength sing_2139.htm#SEC2215 16898 cyclePoints sing_2143.htm#SEC2219 54460 cyclic sing_1028.htm#SEC1104 21375 cyclic code Codes and the decoding problem sing_949.htm#SEC1008 cyclotomic sing_1707.htm#SEC1783 33749 datetime sing_223.htm#SEC263 50127 dbprint sing_224.htm#SEC264 deRham.lib sing_2413.htm#SEC2489 deRhamCohom sing_579.htm#SEC631 58222 deRhamCohomIdeal sing_580.htm#SEC632 42169 deRhamCohomology sing_2414.htm#SEC2490 41947 deRham_lib sing_2413.htm#SEC2489 debugLib, option sing_316.htm#IDX176 debug_log sing_1563.htm#SEC1639 62043 debugger Source code debugger sing_66.htm#SEC103 debugging library code Source code debugger sing_66.htm#SEC103 dec1var sing_1279.htm#SEC1355 36098 decimal sing_1947.htm#SEC2023 56066 decode sing_1883.htm#SEC1959 64330 decodeCode sing_1885.htm#SEC1961 28262 decodeRandom sing_1884.htm#SEC1960 40118 decodeRandomFL sing_1888.htm#SEC1964 35423 decodeSV sing_1865.htm#SEC1941 37975 decodegb.lib sing_1870.htm#SEC1946 decodegb_lib sing_1870.htm#SEC1946 decoding, decoding problem Codes and the decoding problem sing_949.htm#SEC1009 decoef sing_1913.htm#SEC1989 60284 decomposition of modules sing_1272.htm#IDX565 decomposition, numerical sing_1419.htm#IDX594 decone sing_2251.htm#IDX859 decone sing_2252.htm#IDX861 def sing_88.htm#SEC128 def declarations sing_89.htm#SEC129 defRes, option sing_316.htm#IDX177 default argument sing_44.htm#SEC81 defineHomogeneous sing_2659.htm#SEC2735 55072 defined sing_225.htm#SEC265 defl sing_1430.htm#SEC1506 11825 deform sing_1665.htm#SEC1741 5250 deform.lib sing_1584.htm#SEC1660 deform_lib sing_1584.htm#SEC1660 defring sing_1070.htm#SEC1146 1814 defringp sing_1072.htm#SEC1148 42905 defrings sing_1071.htm#SEC1147 1034 deg sing_226.htm#SEC266 degBound sing_397.htm#SEC437 degree Miscellaneous oddities sing_227.htm#SEC267 degree sing_420.htm#IDX292 degree lexicographical ordering sing_923.htm#IDX401 degree of a polynomial Miscellaneous oddities sing_420.htm#IDX296 degree reverse lexicographical ordering sing_923.htm#IDX399 degreeDivisor sing_2424.htm#SEC2500 31751 degreeFormalDivisor sing_2432.htm#SEC2508 42503 degreepart sing_1773.htm#SEC1849 53036 delete sing_126.htm#SEC166 delete sing_228.htm#SEC268 delete sing_277.htm#SEC317 deleteGenerator sing_594.htm#SEC646 24917 deleteSublist sing_970.htm#SEC1046 20406 deligne number curveColengthDerivations sing_2408.htm#IDX955 deligne number sing_2411.htm#IDX960 deligne number sing_2412.htm#IDX962 delta sing_1632.htm#SEC1708 56952 delta invariant sing_1313.htm#IDX575 delta invariant sing_1632.htm#IDX771 delta invariant sing_2409.htm#IDX956 delta invariant. sing_1305.htm#IDX568 delta invariant. sing_1306.htm#IDX571 delta invariant. sing_1307.htm#IDX574 deltaLoc sing_1313.htm#SEC1389 35192 denom_list sing_359.htm#IDX204 denominator sing_229.htm#SEC269 depth sing_1226.htm#SEC1302 17777 depthIdeal sing_1289.htm#SEC1365 54782 derivate sing_1739.htm#SEC1815 15409 derivation sing_2265.htm#IDX882 desingularization sing_2516.htm#IDX995 59041 desingularization sing_2517.htm#SEC2593 det sing_230.htm#SEC270 det_B sing_1152.htm#SEC1228 60143 detadj sing_1648.htm#SEC1724 5914 determinacy sing_2743.htm#SEC2819 44818 determinecenter sing_1453.htm#SEC1529 44496 detropicalise sing_2220.htm#SEC2296 38025 develop sing_1622.htm#SEC1698 48457 diag sing_1113.htm#SEC1189 56759 diagInvariants sing_1328.htm#SEC1404 62096 diag_test sing_1148.htm#SEC1224 31469 diff sing_231.htm#SEC271 diffRat sing_866.htm#SEC918 36134 difpoly2tex sing_1914.htm#SEC1990 6451 dim sing_232.htm#SEC272 dim (plural) sing_459.htm#SEC499 dimGradedPart sing_1521.htm#SEC1597 11262 dimH sing_1520.htm#SEC1596 38534 dimMon sing_1269.htm#SEC1345 39971 dimStack sing_2792.htm#SEC2868 47772 dim_slocus sing_1666.htm#SEC1742 47218 dimension sing_2090.htm#SEC2166 35262 dimension, moduli space of stable maps, rational curves dimStack sing_2792.htm#IDX1068 dimensionOfLocalization dimensionOfLocalization sing_2480.htm#SEC2556 25632 direct_boolean_poly sing_2293.htm#SEC2369 49893 direct_from_boolean_poly direct_from_boolean_poly sing_2299.htm#SEC2375 36941 disc sing_1934.htm#SEC2010 45279 discr sing_1688.htm#SEC1764 9642 discrepancy sing_1506.htm#SEC1582 5597 discrim sing_1005.htm#SEC1081 44091 discussion of parametric ideal sing_987.htm#IDX431 disjoint sing_988.htm#IDX433 disp_zdd sing_2306.htm#SEC2382 41439 displayCohom sing_1522.htm#SEC1598 22633 displayHNE sing_1625.htm#SEC1701 29845 displayInvariants sing_1627.htm#SEC1703 13678 displayMultsequence sing_1629.htm#SEC1705 16668 displayPuiseuxExpansion displayPuiseuxExpansion sing_2195.htm#SEC2271 560 displayTropicalLifting displayTropicalLifting sing_2193.htm#SEC2269 28144 distributed computing sing_1021.htm#IDX498 distributed computing sing_1061.htm#IDX500 distributed computing sing_1094.htm#IDX510 div Miscellaneous oddities sing_81.htm#SEC121 div sing_98.htm#SEC138 div sing_155.htm#SEC195 div sing_420.htm#IDX289 divideUnits sing_1910.htm#SEC1986 26711 dividelist sing_1480.htm#SEC1556 34210 division sing_233.htm#SEC273 division sing_989.htm#IDX436 division sing_990.htm#IDX438 division (plural) sing_460.htm#SEC500 divisor sing_2013.htm#SEC2089 47231 divisorplus sing_2418.htm#SEC2494 34248 divisors negativeformaldivisor sing_2417.htm#IDX965 divisors sing_2418.htm#IDX966 divisors sing_2419.htm#IDX967 divisors sing_2420.htm#IDX968 divisors sing_2421.htm#IDX969 divisors sing_2422.htm#IDX970 divisors sing_2423.htm#IDX971 divisors sing_2424.htm#IDX972 divisors sing_2425.htm#IDX973 divisors sing_2426.htm#IDX974 divisors sing_2427.htm#IDX975 divisors sing_2428.htm#IDX976 divisors sing_2429.htm#IDX977 divisors sing_2430.htm#IDX978 divisors sing_2431.htm#IDX979 divisors sing_2432.htm#IDX980 divisors, polyhedra sing_2433.htm#IDX981 divisors, polyhedra sing_2434.htm#IDX982 divisors, polyhedra sing_2435.htm#IDX983 divisors.lib sing_2416.htm#SEC2492 divisors_lib sing_2416.htm#SEC2492 dmod.lib sing_542.htm#SEC594 dmodAction sing_861.htm#SEC913 9763 dmodActionRat sing_862.htm#SEC914 6277 dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_854.htm#SEC906 44337 dmod_lib sing_542.htm#SEC594 dmodapp.lib sing_565.htm#SEC617 dmodapp_lib sing_565.htm#SEC617 dmodloc.lib sing_843.htm#IDX383 dmodloc_lib sing_843.htm#IDX384 dmodoublext sing_804.htm#SEC856 60637 dmodvar.lib sing_598.htm#SEC650 dmodvar_lib sing_598.htm#SEC650 double sing_2018.htm#SEC2094 34697 doubleExt sing_795.htm#SEC847 56896 downloading Download instructions sing_2827.htm#SEC2917 dp, global ordering sing_923.htm#IDX400 drawNewtonSubdivision drawNewtonSubdivision sing_2198.htm#SEC2274 50904 drawTropicalCurve sing_2197.htm#SEC2273 10441 ds, local ordering sing_924.htm#IDX410 dsum sing_1114.htm#SEC1190 1303 dualCone sing_2091.htm#SEC2167 61460 dualConic sing_2222.htm#SEC2298 31080 dualPart sing_2370.htm#SEC2446 13279 dualPartition sing_2805.htm#SEC2881 24739 dualPolytope sing_2130.htm#SEC2206 32081 dualSheaf sing_2783.htm#SEC2859 633 dual_code sing_1867.htm#SEC1943 57229 dump sing_234.htm#SEC274 dyckGroup1 sing_657.htm#SEC709 62819 dyckGroup2 sing_658.htm#SEC710 13793 dyckGroup3 sing_659.htm#SEC711 42596 dynamic geometry sing_998.htm#IDX465 dynamic geometry sing_999.htm#IDX468 ecart sing_2021.htm#SEC2097 32475 echo sing_398.htm#SEC438 eexgcdN sing_1948.htm#SEC2024 53237 effective sing_2426.htm#SEC2502 53028 egcdMain sing_1814.htm#SEC1890 25359 ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2149.htm#SEC2225 38271 ehrhartRing sing_1324.htm#SEC1400 16966 eigenvals sing_1160.htm#SEC1236 11228 eigenvalue sing_329.htm#SEC369 eigenvalue sing_1160.htm#IDX516 eigenvalues sing_1407.htm#SEC1483 2182 elemSymmId sing_1029.htm#SEC1105 sprintf elim sing_1197.htm#SEC1273 62585 elim.lib sing_1194.htm#SEC1270 elim1 sing_1198.htm#SEC1274 15653 elim2 sing_1199.htm#SEC1275 44749 elimRing sing_1196.htm#SEC1272 12194 elimWeight sing_752.htm#SEC804 54297 elim_lib sing_1194.htm#SEC1270 eliminate sing_235.htm#SEC275 eliminate (plural) sing_461.htm#SEC501 eliminateNC sing_747.htm#SEC799 3777 elimination sing_746.htm#IDX362 elimlinearpart sing_1774.htm#SEC1850 14251 elimpart sing_1775.htm#SEC1851 10258 elimpartanyr sing_1776.htm#SEC1852 39751 elimrep sing_1461.htm#SEC1537 23641 elliptic curve sing_1207.htm#IDX532 elliptic curves sing_1204.htm#IDX526 elliptic curves sing_1210.htm#IDX535 elliptic curves sing_1211.htm#IDX539 ellipticAdd sing_1969.htm#SEC2045 13279 ellipticAllPoints sing_1974.htm#SEC2050 60770 ellipticMult sing_1970.htm#SEC2046 1558 ellipticNF sing_2146.htm#SEC2222 5045 ellipticNFDB sing_2147.htm#SEC2223 27917 ellipticRandomCurve sing_1971.htm#SEC2047 36980 ellipticRandomPoint sing_1972.htm#SEC2048 6866 ellipticcovers.lib sing_1204.htm#IDX520 ellipticcovers_lib sing_1204.htm#IDX521 else sing_388.htm#SEC428 embedMat sing_778.htm#SEC830 17119 emptyFan sing_2118.htm#SEC2194 7396 encode sing_1875.htm#SEC1951 56687 endomorphism filtration sing_1606.htm#IDX737 endvfilt sing_1606.htm#SEC1682 26670 engine sing_595.htm#SEC647 30876 ensureLeftNcfrac sing_2676.htm#SEC2752 64571 ensureRightNcfrac sing_2677.htm#SEC2753 14107 envelop FamElemsAtEnvCompPoints sing_1000.htm#SEC1076 27362 envelop sing_1000.htm#IDX471 envelop sing_1001.htm#IDX474 envelop sing_1003.htm#IDX479 envelop sing_1004.htm#IDX483 envelope sing_462.htm#SEC502 enveloping algebra sing_359.htm#IDX208 enveloping algebra sing_500.htm#IDX306 environment variable, DISPLAY The online help system sing_16.htm#IDX29 equalJinI sing_1549.htm#SEC1625 18502 equalMultiDeg sing_2652.htm#SEC2728 37090 equations sing_2092.htm#SEC2168 7896 equiRadical sing_1365.htm#SEC1441 8884 equidim sing_1367.htm#SEC1443 38541 equidimMax sing_1368.htm#SEC1444 49289 equidimMaxEHV sing_1369.htm#SEC1445 42650 equidimZ sing_1380.htm#SEC1456 49610 equising.lib sing_1589.htm#SEC1665 equising_lib sing_1589.htm#SEC1665 equisingular Tjurina number sing_1532.htm#IDX644 equisingularity ideal sing_1591.htm#IDX664 equisingularity stratum sing_1592.htm#IDX665 error recovery sing_15.htm#SEC21 errorInsert sing_1878.htm#SEC1954 59470 errorRand sing_1879.htm#SEC1955 5727 errormap sing_2456.htm#SEC2532 7782 esIdeal sing_1591.htm#SEC1667 60477 esStratum sing_1592.htm#SEC1668 50094 essential sing_2255.htm#IDX864 essential sing_2256.htm#IDX865 eta sing_2141.htm#SEC2217 60729 euler sing_1927.htm#SEC2003 10519 eulerChProj sing_2360.htm#SEC2436 28549 eval sing_236.htm#SEC276 evalJacobianAtBox sing_2754.htm#SEC2830 42716 evalPolyAtBox sing_2753.htm#SEC2829 43040 evaluateFormalDivisor evaluateFormalDivisor sing_2428.htm#SEC2504 3535 evaluatePDivisor sing_2434.htm#SEC2510 18855 evaluateProduct sing_2507.htm#SEC2583 54515 evaluate_reynolds sing_1712.htm#SEC1788 46353 evalutateIntegral sing_1209.htm#SEC1285 sprintf example sing_238.htm#SEC278 example sing_2257.htm#IDX866 example sing_2258.htm#IDX868 example sing_2259.htm#IDX870 example sing_2260.htm#IDX872 example sing_2261.htm#IDX874 example sing_2262.htm#IDX876 example sing_2263.htm#IDX879 execute sing_239.htm#SEC279 exit sing_392.htm#SEC432 exp2pt sing_1915.htm#SEC1991 19621 expo sing_1939.htm#SEC2015 8833 exponents sing_2267.htm#IDX887 export sing_385.htm#SEC425 exportNuminvs sing_1332.htm#SEC1408 10423 exportto sing_386.htm#SEC426 expp sing_2803.htm#SEC2879 15751 expression list sing_72.htm#IDX128 expression list sing_424.htm#IDX299 ext-module purityfiltration_lib sing_787.htm#IDX368 extcurve sing_1861.htm#SEC1937 6730 extdevelop sing_1623.htm#SEC1699 51044 extendGC sing_995.htm#SEC1071 40951 extendWeyl sing_855.htm#SEC907 49954 extendedTensor sing_753.htm#SEC805 4975 extendpoly sing_994.htm#SEC1070 29201 extendring sing_1073.htm#SEC1149 64781 extension of rings sing_1385.htm#IDX586 exterior basis sing_1139.htm#IDX513 exterior power sing_1141.htm#IDX515 exteriorBasis sing_1139.htm#SEC1215 sprintf exteriorPower sing_1141.htm#SEC1217 20173 extgcd sing_240.htm#SEC280 fVector sing_2121.htm#SEC2197 3715 fVectorP sing_2150.htm#SEC2226 31843 facFirstShift sing_740.htm#SEC792 6469 facFirstWeyl sing_736.htm#SEC788 42412 facGBIdeal sing_1350.htm#SEC1426 9924 facShift sing_739.htm#SEC791 48551 facSubWeyl sing_738.htm#SEC790 9630 facWeyl sing_735.htm#SEC787 32331 faceContaining sing_2093.htm#SEC2169 64804 facetVertexLatticeDistances facetVertexLatticeDistances sing_2151.htm#SEC2227 60714 facetWidth sing_2152.htm#SEC2228 62810 facetWidths sing_2153.htm#SEC2229 5503 facets sing_2094.htm#SEC2170 8112 facstd sing_241.htm#SEC281 factmodd sing_242.htm#SEC282 factor sing_323.htm#SEC363 factorH sing_985.htm#SEC1061 24814 factorLenstraECM sing_1978.htm#SEC2054 54951 factorMain sing_1815.htm#SEC1891 65152 factorgroup sing_2642.htm#SEC2718 59914 factorial sing_971.htm#SEC1047 32871 factorization sing_324.htm#SEC364 factorization sing_1169.htm#IDX517 factorize sing_243.htm#SEC283 factorize sing_323.htm#SEC363 factory sing_1.htm#IDX2 fan sing_190.htm#SEC230 fan sing_2133.htm#IDX813 fanViaCones sing_2119.htm#SEC2195 16418 farey sing_244.htm#SEC284 fareypoly sing_2437.htm#SEC2513 12389 fastExpt sing_1923.htm#SEC1999 43912 fastHC, option sing_316.htm#IDX153 fastelim sing_1777.htm#SEC1853 7409 fetch sing_245.htm#SEC285 fetch (plural) sing_463.htm#SEC503 fetchall sing_1074.htm#SEC1150 7537 ffmodStd sing_2441.htm#SEC2517 50680 ffmodstd.lib sing_2436.htm#SEC2512 ffmodstd_lib sing_2436.htm#SEC2512 ffsolve sing_1766.htm#SEC1842 20432 ffsolve.lib sing_1765.htm#SEC1841 ffsolve_lib sing_1765.htm#SEC1841 fglm sing_246.htm#SEC286 fglm sing_356.htm#IDX187 fglm_solve sing_1793.htm#SEC1869 51398 fglmquot sing_247.htm#SEC287 fibonacci sing_972.htm#SEC1048 24750 fibonacciGroup sing_660.htm#SEC712 25145 field sing_144.htm#SEC184 file, .singularrc sing_20.htm#IDX71 filecmd sing_248.htm#SEC288 filtration purityfiltration_lib sing_787.htm#IDX369 finalCharts sing_1485.htm#SEC1561 37296 find sing_249.htm#SEC289 findAuto sing_694.htm#SEC746 51205 findInvo sing_692.htm#SEC744 18177 findInvoDiag sing_693.htm#SEC745 7365 findOrientedBoundary findOrientedBoundary sing_2142.htm#SEC2218 24110 findTorsion sing_1904.htm#SEC1980 29572 find_first_primitive_root find_first_primitive_root sing_1982.htm#SEC2058 33327 find_index sing_1986.htm#SEC2062 62564 findifs.lib sing_1911.htm#SEC1987 findifs_example sing_1912.htm#SEC1988 33849 findifs_lib sing_1911.htm#SEC1987 findimAlgebra sing_762.htm#SEC814 64612 finduni sing_250.htm#SEC290 findvars sing_1778.htm#SEC1854 54503 finite field sing_144.htm#SEC184 finite field sing_1765.htm#IDX786 finiteDiagInvariants finiteDiagInvariants sing_1327.htm#SEC1403 3508 finitediff.lib sing_2442.htm#IDX984 finitediff_lib sing_2442.htm#IDX985 finitenessTest sing_1183.htm#SEC1259 40633 finvar.lib sing_1700.htm#SEC1776 finvar_lib sing_1700.htm#SEC1776 first index is 1 sing_419.htm#SEC459 firstoct sing_1826.htm#SEC1902 11498 fitting sing_1229.htm#SEC1305 20661 fixed points, moduli space of stable maps, graph fixedPoints sing_2793.htm#IDX1069 fixedPoints sing_2793.htm#SEC2869 25366 fl2poly sing_592.htm#SEC644 51682 flatten sing_1115.htm#SEC1191 58972 flatteningStrat sing_1230.htm#SEC1306 15622 floating point sing_1083.htm#IDX503 for sing_387.htm#SEC427 formal linear representations sing_807.htm#IDX379 formaldivisorplus sing_2429.htm#SEC2505 31959 forward sing_2448.htm#SEC2524 15383 fourier sing_587.htm#SEC639 5326 fouriersystem sing_2459.htm#SEC2535 43681 fpadim.lib sing_603.htm#SEC655 fpadim_lib sing_603.htm#SEC655 fpalgebras.lib sing_637.htm#SEC689 fpalgebras_lib sing_637.htm#SEC689 fpaprops.lib sing_663.htm#SEC715 fpaprops_lib sing_663.htm#SEC715 fprintf sing_252.htm#SEC292 13662 fracStatus sing_2722.htm#SEC2798 14582 framed sheaves sing_2466.htm#IDX992 frandwalk sing_2766.htm#SEC2842 25555 free sing_2266.htm#IDX884 free sing_2267.htm#IDX886 free associative algebra, tensor algebra Free associative algebras sing_494.htm#SEC546 freeGBasis sing_677.htm#SEC729 43055 freeModule sing_2559.htm#SEC2635 34173 freeModule2Module sing_2588.htm#SEC2664 15296 freegb.lib sing_672.htm#SEC724 freegb_lib sing_672.htm#SEC724 freemodule sing_253.htm#SEC293 freerank sing_1031.htm#SEC1107 52218 fres sing_254.htm#SEC294 from_boolean_constant from_boolean_constant sing_2297.htm#SEC2373 44881 from_boolean_ideal sing_2301.htm#SEC2377 62698 from_boolean_poly sing_2298.htm#SEC2374 27864 from_boolean_set sing_2302.htm#SEC2378 60615 frwalk sing_255.htm#SEC295 full representation sing_994.htm#IDX452 full representation sing_995.htm#IDX457 fullDimImages sing_2488.htm#SEC2564 20094 fullFan sing_2120.htm#SEC2196 7534 fullSerreRelations sing_687.htm#SEC739 27691 fullSpace sing_2075.htm#SEC2151 19485 furtherInvar sing_1744.htm#SEC1820 19209 further_hn_proc sing_1640.htm#SEC1716 63500 fwalk sing_1216.htm#SEC1292 15070 galois field sing_144.htm#SEC184 gauss_col sing_1124.htm#SEC1200 36252 gauss_nf sing_1155.htm#SEC1231 51060 gauss_row sing_1125.htm#SEC1201 58877 gaussred sing_1153.htm#SEC1229 29001 gaussred_pivot sing_1154.htm#SEC1230 25477 gcd sing_256.htm#SEC296 gcdMon sing_1258.htm#SEC1334 42448 gcddivisor sing_2014.htm#SEC2090 1276 gen sing_257.htm#SEC297 genMDSMat sing_1881.htm#SEC1957 3347 genSymId sing_1404.htm#SEC1480 17521 general error-locator polynomial sing_950.htm#SEC1015 general neron. sing_2516.htm#IDX996 general weighted lexicographical ordering sing_924.htm#IDX416 general weighted reverse lexicographical ordering Local orderings sing_924.htm#IDX413 general.lib sing_965.htm#SEC1041 generalOrder sing_2039.htm#SEC2115 42536 general_lib sing_965.htm#SEC1041 generateG sing_1977.htm#SEC2053 51697 generators sing_1540.htm#IDX648 generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2095.htm#SEC2171 4454 generatorsOfSpan sing_2096.htm#SEC2172 40297 generic representation sing_994.htm#IDX451 genericid sing_1049.htm#SEC1125 29731 genericity sing_1901.htm#SEC1977 16822 genericmat sing_1116.htm#SEC1192 35016 genoutput sing_1474.htm#SEC1550 18973 genus sing_1309.htm#SEC1385 sprintf geometrical locus FamElemsAtEnvCompPoints sing_998.htm#IDX463 geometrical locus sing_999.htm#IDX466 geometrical locus sing_1000.htm#IDX469 geometrical locus sing_1001.htm#IDX472 geometrical locus sing_1002.htm#IDX475 geometrical locus sing_1003.htm#IDX477 geometrical locus sing_1004.htm#IDX481 getArguments sing_1106.htm#SEC1182 14254 getCommand sing_1105.htm#SEC1181 32181 getCone sing_2122.htm#SEC2198 41394 getGradingGroup sing_2617.htm#SEC2693 18137 getLattice sing_2618.htm#SEC2694 7775 getLinearForms sing_2097.htm#SEC2173 47590 getModuleGrading sing_2628.htm#SEC2704 43451 getMultiplicity sing_2098.htm#SEC2174 639 getOneVar sing_1317.htm#SEC1393 55402 getResult sing_1107.htm#SEC1183 51722 getSmallest sing_1316.htm#SEC1392 1623 getState sing_1108.htm#SEC1184 36453 getVariableWeights sing_2616.htm#SEC2692 9591 getcores sing_1064.htm#SEC1140 30785 getdump sing_258.htm#SEC298 getenv sing_359.htm#IDX211 gfan.lib sing_2074.htm#SEC2150 gfan_lib sing_2074.htm#SEC2150 gfanlib sing_1.htm#IDX9 gitCone sing_2515.htm#SEC2591 23853 gitfan.lib sing_2485.htm#SEC2561 gitfan_lib sing_2485.htm#SEC2561 gkdim.lib sing_699.htm#SEC751 gkdim_lib sing_699.htm#SEC751 global sing_210.htm#IDX133 global Bernstein-Sato polynomial sing_507.htm#IDX313 global Bernstein-Sato polynomial sing_542.htm#IDX331 global Bernstein-Sato polynomial for variety sing_598.htm#IDX356 globalSections sing_2423.htm#SEC2499 55191 gmscoeffs sing_1598.htm#SEC1674 13182 gmsnf sing_1597.htm#SEC1673 44676 gmspoly.lib sing_1617.htm#SEC1693 gmspoly_lib sing_1617.htm#SEC1693 gmsring sing_1596.htm#SEC1672 59438 gmssing.lib sing_1595.htm#SEC1671 gmssing_lib sing_1595.htm#SEC1671 goettsche.lib sing_2466.htm#SEC2542 goettsche_lib sing_2466.htm#SEC2542 good basis sing_1595.htm#IDX676 good basis sing_1605.htm#IDX731 good basis sing_1617.htm#IDX747 good basis sing_1619.htm#IDX758 goodBasis sing_1619.htm#SEC1695 41606 gorensteinIndex sing_2154.htm#SEC2230 52919 gorensteinVector sing_2155.htm#SEC2231 50407 graal.lib sing_2478.htm#SEC2554 graalMixed sing_2479.htm#SEC2555 6401 graal_lib sing_2478.htm#SEC2554 gradeNumber sing_791.htm#SEC843 29956 graded Weyl algebra sing_507.htm#IDX316 graded algebra sing_2308.htm#IDX939 graded module, graded piece sing_1521.htm#IDX634 graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2518.htm#IDX997 graded modules, handling of Handling graded modules sing_889.htm#SEC941 graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2556.htm#IDX999 gradedModules.lib sing_2518.htm#SEC2594 gradedModules_lib sing_2518.htm#SEC2594 gradiator sing_2661.htm#SEC2737 53802 graph sing_1205.htm#IDX530 graph sing_1206.htm#IDX531 graph sing_2788.htm#IDX1064 graph sing_2789.htm#IDX1065 graphics.lib sing_1828.htm#SEC1904 graphics_lib sing_1828.htm#SEC1904 graphviz sing_1.htm#IDX13 graver4ti2 sing_1402.htm#SEC1478 39635 grconcat sing_2541.htm#SEC2617 16754 grdeg sing_2521.htm#SEC2597 22879 grgens sing_2530.htm#SEC2606 12823 grgroebner sing_2540.htm#SEC2616 29288 grlift sing_2538.htm#SEC2614 21656 grlifting sing_2545.htm#SEC2621 51177 grlifting2 sing_2546.htm#SEC2622 59011 grlifting3 sing_2548.htm#SEC2624 6369 grneg sing_2551.htm#SEC2627 64584 grobcov sing_987.htm#SEC1063 40493 grobcov.lib sing_986.htm#SEC1062 grobcov_lib sing_986.htm#SEC1062 grobj sing_2519.htm#SEC2595 18115 groebner sing_259.htm#SEC299 53038 groebner sing_881.htm#SEC933 groebner basis computations sing_259.htm#IDX147 groebnerComplex sing_2233.htm#SEC2309 2421 groebnerCone sing_2227.htm#SEC2303 58776 groebnerFan sing_2232.htm#SEC2308 48157 gromovWitten sing_1210.htm#SEC1286 28559 grorder sing_2532.htm#SEC2608 20857 ground field sing_144.htm#SEC184 groupActionOnHashes sing_2503.htm#SEC2579 406 groupActionOnQImage sing_2502.htm#SEC2578 53270 group_reynolds sing_1708.htm#SEC1784 35079 grpower sing_2528.htm#SEC2604 3960 grpres sing_2531.htm#SEC2607 18145 grprod sing_2539.htm#SEC2615 41525 grrange sing_2550.htm#SEC2626 41835 grres sing_2537.htm#SEC2613 35795 grrndmap sing_2543.htm#SEC2619 4054 grrndmap2 sing_2544.htm#SEC2620 50536 grrndmat sing_2542.htm#SEC2618 42634 grshift sing_2523.htm#SEC2599 1415 grsum sing_2527.htm#SEC2603 60602 grsyz sing_2536.htm#SEC2612 61843 grtest sing_2520.htm#SEC2596 62577 grtranspose sing_2529.htm#SEC2605 13865 grtranspose1 sing_2533.htm#SEC2609 3637 grtwist sing_2525.htm#SEC2601 10498 grtwists sing_2526.htm#SEC2602 56638 grview sing_2522.htm#SEC2598 6878 grwalk.lib sing_1215.htm#SEC1291 grwalk_lib sing_1215.htm#SEC1291 grzero sing_2524.htm#SEC2600 4212 gwalk sing_1221.htm#SEC1297 38238 hStarVector sing_2156.htm#SEC2232 60821 hVector sing_2157.htm#SEC2233 46486 h_increasing_knapsack h_increasing_knapsack sing_2000.htm#SEC2076 62968 hardware platform sing_359.htm#IDX271 hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1087.htm#SEC1163 54609 hasCommutativeVars sing_1084.htm#SEC1160 3152 hasGlobalOrdering sing_1085.htm#SEC1161 34053 hasLeftDenom sing_2670.htm#SEC2746 47260 hasMixedOrdering sing_1086.htm#SEC1162 29738 hasNumericCoeffs sing_1083.htm#SEC1159 14522 hasRightDenom sing_2671.htm#SEC2747 34279 hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1088.htm#SEC1164 56211 hashToCone sing_2513.htm#SEC2589 6929 hashesToFan sing_2514.htm#SEC2590 26774 headStand sing_1137.htm#SEC1213 14413 heightZ sing_1379.htm#SEC1455 16800 help sing_260.htm#SEC300 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_359.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_2662.htm#SEC2738 37225 hess.lib sing_2553.htm#SEC2629 hess_lib sing_2553.htm#SEC2629 hessenberg sing_359.htm#IDX217 24168 hessenberg sing_1159.htm#SEC1235 highcorner sing_261.htm#SEC301 hilb sing_262.htm#SEC302 hilbPoly sing_1047.htm#SEC1123 36118 hilbert4ti2 sing_1401.htm#SEC1477 13993 hilbertBasis sing_2158.htm#SEC2234 35423 hilbertSeries sing_2664.htm#SEC2740 60148 hilbvec sing_1779.htm#SEC1855 9204 hnexpansion sing_1621.htm#SEC1697 46990 hnoether.lib sing_1620.htm#SEC1696 hnoether_lib sing_1620.htm#SEC1696 holonomic rank sing_843.htm#IDX386 holonomicRank sing_847.htm#SEC899 41306 hom sing_2600.htm#SEC2676 40032 hom_kernel sing_1237.htm#SEC1313 32604 homog sing_263.htm#SEC303 homog_part sing_2800.htm#SEC2876 20875 homog_parts sing_2801.htm#SEC2877 12854 homogeneitySpace sing_2229.htm#SEC2305 48243 homogfacFirstQWeyl sing_742.htm#SEC794 32751 homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_744.htm#SEC796 9014 homogfacNthQWeyl sing_741.htm#SEC793 19238 homogfacNthQWeyl_all homogfacNthQWeyl_all sing_743.htm#SEC795 56179 homolog.lib sing_1222.htm#SEC1298 homolog_lib sing_1222.htm#SEC1298 homology sing_1232.htm#SEC1308 15040 homomorphism sing_2584.htm#SEC2660 27115 howto, download Download instructions sing_2827.htm#SEC2917 howto, install on Macintosh Macintosh installation instructions sing_2830.htm#SEC2920 howto, install on Unix Unix installation instructions sing_2828.htm#SEC2918 howto, install on Windows Windows installation instructions sing_2829.htm#SEC2919 hres sing_264.htm#SEC304 html, default help The online help system sing_16.htm#IDX24 hyperel.lib sing_2007.htm#SEC2083 hyperel_lib sing_2007.htm#SEC2083 hyperplane sing_2236.htm#IDX824 hyperplane arrangement sing_542.htm#IDX337 hypersurface singularity sing_1647.htm#IDX776 iMult sing_1312.htm#SEC1388 22059 id sing_2557.htm#SEC2633 47592 id2mod sing_1043.htm#SEC1119 32918 ideal sing_90.htm#SEC130 ideal declarations sing_91.htm#SEC131 ideal declarations (plural) ideal declarations (plural) sing_426.htm#SEC466 ideal expressions sing_92.htm#SEC132 ideal expressions (plural) ideal expressions (plural) sing_427.htm#SEC467 ideal operations sing_93.htm#SEC133 ideal operations (plural) ideal operations (plural) sing_428.htm#SEC468 ideal related functions ideal related functions sing_94.htm#SEC134 ideal related functions (plural) ideal related functions (plural) sing_429.htm#SEC469 ideal, toric sing_937.htm#SEC994 idealSplit sing_1786.htm#SEC1862 4673 ideals Miscellaneous oddities sing_420.htm#IDX293 idealsimplify sing_1548.htm#SEC1624 38569 identifier Identifier resolution sing_421.htm#SEC461 identifyvar sing_1456.htm#SEC1532 59662 if sing_388.htm#SEC428 image sing_2580.htm#SEC2656 43481 imageLattice sing_2630.htm#SEC2706 15740 image_of_variety sing_1736.htm#SEC1812 43711 imap sing_265.htm#SEC305 imap (plural) sing_464.htm#SEC504 imapall sing_1075.htm#SEC1151 16023 impart sing_266.htm#SEC306 importfrom sing_389.htm#SEC429 inCenter sing_531.htm#SEC583 22152 inCentralizer sing_532.htm#SEC584 49000 inForm sing_574.htm#SEC626 5283 inSubring sing_1175.htm#SEC1251 24817 indSet sing_1284.htm#SEC1360 32828 indepSet sing_267.htm#SEC307 indexed names sing_36.htm#IDX82 indexed names sing_37.htm#SEC65 indices, multi sing_37.htm#SEC65 inequalities sing_2099.htm#SEC2175 10122 infRedTail, option sing_316.htm#IDX154 info The online help system sing_16.htm#SEC23 iniD sing_1476.htm#SEC1552 35084 init_debug sing_1555.htm#SEC1631 29863 initial sing_2230.htm#SEC2306 8678 initial form sing_507.htm#IDX318 initial ideal sing_507.htm#IDX317 initial ideal approach sing_507.htm#IDX321 initial ideal approach sing_598.htm#IDX360 initialForm sing_2207.htm#SEC2283 57793 initialIdeal sing_2208.htm#SEC2284 22205 initialIdealW sing_573.htm#SEC625 36086 initialMalgrange sing_572.htm#SEC624 26846 injective_knapsack sing_2001.htm#SEC2077 7619 inout.lib sing_1009.htm#SEC1085 inout_lib sing_1009.htm#SEC1085 input sing_41.htm#SEC71 insert sing_126.htm#SEC166 insert sing_268.htm#SEC308 insertCone sing_2123.htm#SEC2199 13858 insertGenerator sing_593.htm#SEC645 13951 instructions, Macintosh installation Macintosh installation instructions sing_2830.htm#SEC2920 instructions, Unix installation Unix installation instructions sing_2828.htm#SEC2918 instructions, Windows installation Windows installation instructions sing_2829.htm#SEC2919 instructions, downloading Download instructions sing_2827.htm#SEC2917 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_2639.htm#SEC2715 sprintf intPart sing_1955.htm#SEC2031 48360 intRank sing_2631.htm#SEC2707 1830 intRoot sing_1956.htm#SEC2032 54582 intRoots sing_590.htm#SEC642 24538 intStrategy, option sing_316.htm#IDX155 intclMonIdeal sing_1325.htm#SEC1401 22338 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2975 interval arithmetic sing_2745.htm#IDX1039 intmat sing_102.htm#SEC142 intmat declarations sing_103.htm#SEC143 intmat expressions sing_104.htm#SEC144 intmat operations sing_106.htm#SEC146 intmat related functions intmat related functions sing_107.htm#SEC147 intmat type cast sing_105.htm#SEC145 intmat2mons sing_1345.htm#SEC1421 21150 intprog.lib sing_1245.htm#SEC1321 intprog_lib sing_1245.htm#SEC1321 intvec sing_108.htm#SEC148 intvec declarations sing_109.htm#SEC149 intvec expressions sing_110.htm#SEC150 intvec operations sing_111.htm#SEC151 intvec related functions intvec related functions sing_112.htm#SEC152 invariant sing_2411.htm#IDX961 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1705.htm#IDX782 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1706.htm#IDX783 invariantRing sing_1738.htm#SEC1814 18582 invariant_algebra_perm invariant_algebra_perm sing_1706.htm#SEC1782 63525 invariant_algebra_reynolds 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sing_1903.htm#SEC1979 60444 irrRealizationDim sing_2189.htm#SEC2265 7814 irred_secondary_char0 irred_secondary_char0 sing_1727.htm#SEC1803 2943 irred_secondary_no_molien irred_secondary_no_molien sing_1730.htm#SEC1806 55905 irreddecMon sing_1270.htm#SEC1346 20160 irreducible power series sing_1631.htm#IDX770 irreducible secondary invariant irred_secondary_char0 sing_1727.htm#IDX784 isAface sing_2486.htm#SEC2562 25344 isAntiEndo sing_698.htm#SEC750 19156 isBounded sing_2160.htm#SEC2236 28183 isCI sing_210.htm#IDX139 58425 isCI sing_1193.htm#SEC1269 isCM sing_210.htm#IDX140 50469 isCM sing_1233.htm#SEC1309 isCMcod2 sing_1684.htm#SEC1760 2563 isCanonical sing_2161.htm#SEC2237 51109 isCartan sing_533.htm#SEC585 39541 isCentral sing_769.htm#SEC821 54650 isCommutative sing_771.htm#SEC823 60728 isCompatible sing_2124.htm#SEC2200 57323 isCompressed sing_2162.htm#SEC2238 2849 isDenom sing_2684.htm#SEC2760 55537 isEqualDivisor sing_2422.htm#SEC2498 17569 isEquising sing_1593.htm#SEC1669 1424 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sing_1968.htm#SEC2044 36324 isOneFraction sing_2734.htm#SEC2810 55015 isOneNcfrac sing_2673.htm#SEC2749 12754 isOrigin sing_2101.htm#SEC2177 13977 isPositive sing_2648.htm#SEC2724 50852 isPrimitiveSublattice isPrimitiveSublattice sing_2638.htm#SEC2714 sprintf isPure sing_2125.htm#SEC2201 44002 isPureTensor sing_505.htm#SEC557 21323 isQuotientRing sing_1089.htm#SEC1165 sprintf isRational sing_564.htm#SEC616 57398 isReflexive sing_2166.htm#SEC2242 3991 isReg sing_1236.htm#SEC1312 40920 isSB sing_210.htm#IDX134 isSimplicial sing_2102.htm#SEC2178 57789 isSmooth sing_2167.htm#SEC2243 37647 isSubModule sing_1090.htm#SEC1166 sprintf isSublattice sing_2629.htm#SEC2705 10501 isSymmetric sing_1405.htm#SEC1481 61363 isTame sing_1618.htm#SEC1694 31925 isTerminal sing_2168.htm#SEC2244 29416 isTorsionFree sing_2647.htm#SEC2723 52228 isTwoSidedGB sing_506.htm#SEC558 36558 isUpperTriangular sing_750.htm#SEC802 40655 isVar sing_688.htm#SEC740 43851 isVeryAmple sing_2169.htm#SEC2245 64652 isWeyl sing_772.htm#SEC824 28994 isZeroElement sing_2649.htm#SEC2725 514 isZeroFraction sing_2733.htm#SEC2809 1926 isZeroNcfrac sing_2672.htm#SEC2748 6841 is_NND sing_1634.htm#SEC1710 26564 is_NP sing_1293.htm#SEC1369 43891 is_active sing_1667.htm#SEC1743 6867 is_bijective sing_1180.htm#SEC1256 49512 is_cenBimodule sing_805.htm#SEC857 35450 is_cenSubbimodule sing_806.htm#SEC858 26181 is_ci sing_1668.htm#SEC1744 35370 is_complex sing_1117.htm#SEC1193 1234 is_fix_injective sing_2005.htm#SEC2081 11663 is_h_injective sing_2004.htm#SEC2080 36696 is_injective sing_1178.htm#SEC1254 15776 is_irred sing_1631.htm#SEC1707 51150 is_is sing_1669.htm#SEC1745 64105 is_nested sing_1294.htm#SEC1370 9200 is_prime sing_1985.htm#SEC2061 29018 is_primitive_root sing_1981.htm#SEC2057 42838 is_pure sing_797.htm#SEC849 59105 is_reg sing_1670.htm#SEC1746 18146 is_regs sing_1671.htm#SEC1747 50242 is_surjective sing_1179.htm#SEC1255 57044 is_zero sing_1032.htm#SEC1108 24341 isartinianMon sing_1267.htm#SEC1343 1103 isgenericMon sing_1268.htm#SEC1344 14444 ishyper sing_2008.htm#SEC2084 65518 isirreducibleMon sing_1266.htm#SEC1342 22428 isoncurve sing_2009.htm#SEC2085 16384 isparam sing_2072.htm#SEC2148 56395 isprimaryMon sing_1265.htm#SEC1341 57367 isprimeMon sing_1264.htm#SEC1340 9124 isuni sing_2057.htm#SEC2133 39427 iv2lp sing_631.htm#SEC683 59849 iv2lpList sing_632.htm#SEC684 18518 iv2lpMat sing_633.htm#SEC685 21612 ivDHilbert sing_611.htm#SEC663 56709 ivDHilbertSickle sing_612.htm#SEC664 43194 ivDimCheck sing_613.htm#SEC665 258 ivHilbert sing_614.htm#SEC666 37184 ivKDim sing_615.htm#SEC667 26109 ivL2lpI sing_630.htm#SEC682 2454 ivMaxIdeal sing_627.htm#SEC679 48114 ivMis2Base sing_616.htm#SEC668 57812 ivMis2Dim sing_617.htm#SEC669 42072 ivOrdMisLex sing_618.htm#SEC670 27789 ivSickle sing_619.htm#SEC671 42888 ivSickleDim sing_621.htm#SEC673 64347 ivSickleHil sing_620.htm#SEC672 41396 ivmatGaussian sing_2752.htm#SEC2828 37718 ivmatInit sing_2749.htm#SEC2825 22774 ivmatSet sing_2750.htm#SEC2826 53480 jInvariant sing_2201.htm#SEC2277 2369 jOft sing_1940.htm#SEC2016 25716 jacob sing_272.htm#SEC312 jacoblift sing_1650.htm#SEC1726 40125 jacobson sing_1909.htm#SEC1985 59267 jacobson.lib sing_1907.htm#SEC1983 jacobson_lib sing_1907.htm#SEC1983 janet sing_273.htm#SEC313 janet basis sing_2758.htm#IDX1042 jet sing_274.htm#SEC314 jordan sing_1164.htm#SEC1240 16602 jordanbasis sing_1165.htm#SEC1241 12736 jordanmatrix sing_1166.htm#SEC1242 2886 jordannf sing_1167.htm#SEC1243 20535 jungfib sing_1489.htm#SEC1565 5432 jungnormal sing_1488.htm#SEC1564 43561 jungresolve sing_1487.htm#SEC1563 45004 katsura sing_1030.htm#SEC1106 45913 kbase sing_275.htm#SEC315 kbase (plural) sing_466.htm#SEC506 keepring sing_390.htm#SEC430 kerHom sing_2601.htm#SEC2677 53906 kernel sing_276.htm#SEC316 kernelLattice sing_2632.htm#SEC2708 36320 kill sing_277.htm#SEC317 killTask sing_1096.htm#SEC1172 39317 killall sing_974.htm#SEC1050 34661 killattrib sing_278.htm#SEC318 kmemory sing_973.htm#SEC1049 52193 kohom sing_1238.htm#SEC1314 50086 kontrahom sing_1239.htm#SEC1315 58549 koszul sing_279.htm#SEC319 kskernel.lib sing_1641.htm#SEC1717 kskernel_lib sing_1641.htm#SEC1717 l-adic numbers sing_32.htm#SEC46 laguerre sing_280.htm#SEC320 laguerre_solve sing_1788.htm#SEC1864 10155 lastvarGeneral sing_2038.htm#SEC2114 28645 latex.lib sing_1832.htm#SEC1908 latex_lib sing_1832.htm#SEC1908 lattice sing_2273.htm#IDX902 latticeArea sing_2144.htm#SEC2220 53771 latticeBasis sing_2633.htm#SEC2709 43162 latticeCodegree sing_2170.htm#SEC2246 25482 latticeDegree sing_2171.htm#SEC2247 52881 latticePoints sing_2172.htm#SEC2248 41965 latticeVolume sing_2173.htm#SEC2249 42234 laxfrT sing_2446.htm#SEC2522 60899 laxfrX sing_2447.htm#SEC2523 57254 lazy, option sing_316.htm#IDX156 lcm sing_1033.htm#SEC1109 44755 lcmMon sing_1259.htm#SEC1335 52749 lcmN sing_1949.htm#SEC2025 52355 lcmofall sing_1469.htm#SEC1545 56889 lead sing_281.htm#SEC321 leadcoef sing_282.htm#SEC322 leadexp sing_283.htm#SEC323 leadmonom sing_284.htm#SEC324 leadmonomial sing_2024.htm#SEC2100 8195 left annihilator ideal sing_542.htm#IDX329 leftInverse sing_1898.htm#SEC1974 41469 leftKernel sing_1896.htm#SEC1972 9292 leftOre sing_2724.htm#SEC2800 44669 length sing_2747.htm#SEC2823 9547 length, option sing_316.htm#IDX157 letplaceGBasis sing_674.htm#SEC726 64298 letterplace correspondence Letterplace correspondence sing_496.htm#SEC548 lex_solve sing_1794.htm#SEC1870 48692 lexicographical ordering sing_923.htm#IDX396 lib2doc sing_60.htm#SEC97 libSingular sing_2826.htm#SEC2916 libcdd sing_1.htm#IDX12 libfac sing_1.htm#IDX6 libparse sing_69.htm#SEC109 library sing_2288.htm#IDX917 library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2485.htm#IDX994 library, info string sing_55.htm#IDX124 library, polybori.lib sing_2288.htm#IDX914 library, template sing_55.htm#SEC92 library, template.lib sing_55.htm#IDX122 lieBracket sing_681.htm#SEC733 50745 lift sing_286.htm#SEC326 lift sing_500.htm#IDX305 lift (plural) sing_467.htm#SEC507 lift_kbase sing_1587.htm#SEC1663 10906 lift_rel_kb sing_1588.htm#SEC1664 13673 liftenvelope sing_503.htm#SEC555 58802 liftstd sing_287.htm#SEC327 liftstd (plural) sing_468.htm#SEC508 linReduce sing_515.htm#SEC567 57527 linReduceIdeal sing_516.htm#SEC568 19076 linSyzSolve sing_517.htm#SEC569 26185 linalg.lib sing_1142.htm#SEC1218 linalg_lib sing_1142.htm#SEC1218 linealityDimension sing_2103.htm#SEC2179 30751 linealitySpace sing_2104.htm#SEC2180 14489 linear algebra sing_211.htm#SEC251 linear algebra sing_290.htm#SEC330 linear algebra sing_291.htm#SEC331 linear algebra sing_292.htm#SEC332 linear code, dual sing_1867.htm#IDX795 linear code, systematic sing_1868.htm#IDX796 linear interreduction sing_507.htm#IDX320 linearCombinations sing_536.htm#SEC588 20514 linearMapKernel sing_535.htm#SEC587 43761 linear_relations sing_1134.htm#SEC1210 45983 linearlyEquivalent sing_2425.htm#SEC2501 28351 linearpart sing_1780.htm#SEC1856 2162 linesHypersurface sing_2797.htm#SEC2873 9129 link Parallelization with ssi links sing_113.htm#SEC153 link sing_878.htm#SEC930 link declarations sing_114.htm#SEC154 link expressions sing_115.htm#SEC155 link related functions link related functions sing_116.htm#SEC156 list sing_123.htm#SEC163 list declarations sing_124.htm#SEC164 list expressions sing_125.htm#SEC165 list operations sing_126.htm#SEC166 list related functions list related functions sing_127.htm#SEC167 lists sing_2405.htm#IDX950 lists, elements sing_2407.htm#IDX952 listvar sing_288.htm#SEC328 lll sing_2665.htm#SEC2741 35827 load sing_391.htm#SEC431 loadLib, option sing_316.htm#IDX178 loadProc, option sing_316.htm#IDX179 locAtZero sing_1314.htm#SEC1390 5687 locNormal sing_1248.htm#SEC1324 52237 locStatus sing_2719.htm#SEC2795 54575 local methods sing_1247.htm#IDX555 local methods sing_1248.htm#IDX558 local names sing_46.htm#SEC83 local rings, computing in Rings associated to monomial orderings sing_873.htm#SEC925 local weighted lexicographical ordering sing_924.htm#IDX417 local weighted reverse lexicographical ordering Local orderings sing_924.htm#IDX414 localInvar sing_1743.htm#SEC1819 38478 localization Rings associated to monomial orderings sing_873.htm#SEC925 localization sing_2253.htm#IDX862 localization of D-module sing_565.htm#IDX345 localization of D-module sing_843.htm#IDX389 locally closed set sing_991.htm#IDX441 locally closed set sing_992.htm#IDX443 locally closed set sing_993.htm#IDX445 locally closed set sing_994.htm#IDX449 locally closed set sing_996.htm#IDX459 localstd sing_2034.htm#SEC2110 25562 locnormal.lib sing_1247.htm#SEC1323 locnormal_lib sing_1247.htm#SEC1323 locstd sing_1672.htm#SEC1748 25864 locus FamElemsAtEnvCompPoints sing_998.htm#SEC1074 22530 locus sing_998.htm#IDX464 locus sing_999.htm#IDX467 locus sing_1000.htm#IDX470 locus sing_1001.htm#IDX473 locus sing_1002.htm#IDX476 locus sing_1003.htm#IDX478 locus sing_1004.htm#IDX482 locusdg sing_999.htm#SEC1075 6077 locusto sing_1001.htm#SEC1077 730 log2 sing_1924.htm#SEC2000 40703 logarithmic annihilator ideal sing_542.htm#IDX334 logg sing_2802.htm#SEC2878 38736 lp, global ordering sing_923.htm#IDX395 lp2iv sing_634.htm#SEC686 17398 lp2ivId sing_635.htm#SEC687 16290 lp2lstr sing_682.htm#SEC734 24713 lpCalcSubstDegBound sing_670.htm#SEC722 46179 lpCalcSubstDegBounds lpCalcSubstDegBounds sing_671.htm#SEC723 56500 lpDHilbert sing_609.htm#SEC661 10461 lpDHilbertSickle sing_610.htm#SEC662 41445 lpDimCheck sing_606.htm#SEC658 9807 lpGkDim sing_667.htm#SEC719 10351 lpGlDimBound sing_668.htm#SEC720 53074 lpHilbert sing_608.htm#SEC660 44093 lpId2ivLi sing_636.htm#SEC688 13273 lpIsPrime sing_666.htm#SEC718 40779 lpIsSemiPrime sing_665.htm#SEC717 41065 lpKDim sing_605.htm#SEC657 18278 lpMaxIdeal sing_628.htm#SEC680 37571 lpMis2Base sing_607.htm#SEC659 10826 lpMis2Dim sing_604.htm#SEC656 39947 lpMult sing_678.htm#SEC730 58898 lpNF sing_675.htm#SEC727 2851 lpNoetherian sing_664.htm#SEC716 44964 lpOrdMisLex sing_622.htm#SEC674 30943 lpPower sing_680.htm#SEC732 7325 lpPrint sing_690.htm#SEC742 35540 lpSickle sing_623.htm#SEC675 288 lpSickleDim sing_625.htm#SEC677 61018 lpSickleHil sing_624.htm#SEC676 55268 lpSubstitute sing_669.htm#SEC721 54386 lprint sing_1011.htm#SEC1087 5285 lres sing_289.htm#SEC329 ls, local ordering sing_924.htm#IDX408 lst2str sing_683.htm#SEC735 10088 lsum sing_1214.htm#SEC1290 50315 ludecomp sing_290.htm#SEC330 luinverse sing_291.htm#SEC331 lusolve sing_292.htm#SEC332 mRes sing_2569.htm#SEC2645 58702 m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1996.htm#SEC2072 57945 m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1995.htm#SEC2071 33857 m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1994.htm#SEC2070 7880 magnitude sing_1918.htm#SEC1994 37967 makeDivisor sing_2417.htm#SEC2493 3414 makeFormalDivisor sing_2427.htm#SEC2503 54579 makeGraph sing_1205.htm#SEC1281 21758 makeGraphVE sing_2788.htm#SEC2864 sprintf makeHeisenberg sing_760.htm#SEC812 2050 makeIdeal sing_2561.htm#SEC2637 57829 makeLetterplaceRing sing_673.htm#SEC725 1592 makeMalgrange sing_602.htm#SEC654 41377 makeMatrix sing_2560.htm#SEC2636 64348 makeModElimRing sing_777.htm#SEC829 56092 makePDivisor sing_2433.htm#SEC2509 45273 makeQsl2 sing_724.htm#SEC776 3997 makeQsl3 sing_725.htm#SEC777 41249 makeQso3 sing_723.htm#SEC775 58910 makeSheaf sing_2776.htm#SEC2852 10497 makeUe6 sing_720.htm#SEC772 58585 makeUe7 sing_721.htm#SEC773 61849 makeUe8 sing_722.htm#SEC774 64987 makeUf4 sing_719.htm#SEC771 8408 makeUg2 sing_718.htm#SEC770 34512 makeUgl sing_704.htm#SEC756 3543 makeUsl sing_703.htm#SEC755 24536 makeUsl2 sing_702.htm#SEC754 42637 makeUso10 sing_710.htm#SEC762 6936 makeUso11 sing_711.htm#SEC763 35873 makeUso12 sing_712.htm#SEC764 19319 makeUso5 sing_705.htm#SEC757 34378 makeUso6 sing_706.htm#SEC758 65009 makeUso7 sing_707.htm#SEC759 49142 makeUso8 sing_708.htm#SEC760 33275 makeUso9 sing_709.htm#SEC761 16896 makeUsp1 sing_713.htm#SEC765 44522 makeUsp2 sing_714.htm#SEC766 18017 makeUsp3 sing_715.htm#SEC767 57445 makeUsp4 sing_716.htm#SEC768 51690 makeUsp5 sing_717.htm#SEC769 35951 makeVariety sing_2768.htm#SEC2844 23915 makeVector sing_2589.htm#SEC2665 9049 makeWeyl sing_759.htm#SEC811 8554 map sing_128.htm#SEC168 map (plural) sing_430.htm#SEC470 map declarations sing_129.htm#SEC169 map declarations (plural) map declarations (plural) sing_431.htm#SEC471 map expressions sing_130.htm#SEC170 map expressions (plural) map expressions (plural) sing_432.htm#SEC472 map operations sing_131.htm#IDX129 map operations (plural) map operations (plural) sing_433.htm#IDX300 map related functions map related functions sing_132.htm#IDX131 map related functions (plural) map related functions (plural) sing_434.htm#IDX301 mapIsFinite sing_1182.htm#SEC1258 60897 mapToRatNormCurve sing_1444.htm#SEC1520 8877 mapall sing_1076.htm#SEC1152 14907 mappingcone sing_2547.htm#SEC2623 48219 mappingcone3 sing_2549.htm#SEC2625 58973 markov4ti2 sing_1400.htm#SEC1476 9163 mat2arr sing_2238.htm#SEC2314 20840 mat2carr sing_2239.htm#SEC2315 13777 mat_rk sing_1156.htm#SEC1232 32196 matbil sing_2045.htm#SEC2121 1611 mathematical objects Representation of mathematical objects sing_919.htm#SEC971 mathinit sing_1830.htm#SEC1906 16793 matmult sing_2046.htm#SEC2122 60088 matrix sing_133.htm#SEC173 matrix sing_2238.htm#IDX830 matrix sing_2239.htm#IDX833 matrix sing_2240.htm#IDX837 matrix declarations sing_134.htm#SEC174 matrix diagonalization sing_1907.htm#IDX806 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_1110.htm#SEC1186 matrixExp sing_1434.htm#SEC1510 53063 matrixLog sing_1435.htm#SEC1511 26235 matrixT1 sing_1686.htm#SEC1762 15051 matrix_lib sing_1110.htm#SEC1186 matrixpres sing_2552.htm#SEC2628 60645 matrixsystem sing_2457.htm#SEC2533 62950 max sing_293.htm#SEC333 23624 maxEord sing_1459.htm#SEC1535 64032 maxExp sing_210.htm#IDX136 maxIntRoot sing_860.htm#SEC912 37127 maxZeros sing_1437.htm#SEC1513 35964 maxabs sing_2064.htm#SEC2140 64510 maxcoef sing_1034.htm#SEC1110 50577 maxdeg sing_1035.htm#SEC1111 39794 maxdeg1 sing_1036.htm#SEC1112 21545 maxideal sing_294.htm#SEC334 maximalFace sing_2174.htm#SEC2250 35224 maximalGroebnerCone sing_2228.htm#SEC2304 62935 maximalValue sing_2175.htm#SEC2251 32783 maximum sing_1937.htm#SEC2013 2355 maximum number of zeroes sing_1437.htm#IDX613 mdouble sing_56.htm#SEC93 56685 mem, option sing_316.htm#IDX180 member sing_2407.htm#SEC2483 1765 membershipMon sing_1260.htm#SEC1336 40876 memory sing_295.htm#SEC335 memory managment sing_295.htm#SEC335 merkle_hellman_decryption merkle_hellman_decryption sing_1998.htm#SEC2074 49106 merkle_hellman_encryption merkle_hellman_encryption sing_1997.htm#SEC2073 13645 methods, hashtables sing_2555.htm#IDX998 methods.lib sing_2555.htm#SEC2631 methods_lib sing_2555.htm#SEC2631 midpoint sing_2453.htm#SEC2529 29391 milnor sing_1673.htm#SEC1749 23173 milnorcode sing_1557.htm#SEC1633 13849 milnornumber sing_2742.htm#SEC2818 21855 min sing_296.htm#SEC336 56342 minAssChar sing_1359.htm#SEC1435 18758 minAssCharE sing_1360.htm#SEC1436 31570 minAssGTZ sing_1357.htm#SEC1433 41315 minAssGTZE sing_1358.htm#SEC1434 50867 minAssZ sing_1377.htm#SEC1453 54152 minEcart sing_2027.htm#SEC2103 34890 minIntRoot sing_563.htm#SEC615 3288 minIntRoot2 sing_859.htm#SEC911 46494 minMult sing_1189.htm#SEC1265 31978 minbase sing_297.htm#SEC337 minbaseMon sing_1257.htm#SEC1333 1501 mindeg sing_1037.htm#SEC1113 16307 mindeg1 sing_1038.htm#SEC1114 39698 mindist sing_1882.htm#SEC1958 55281 minimal display time, setting the sing_359.htm#IDX284 minimal representations sing_807.htm#IDX380 minimalAfaceOrbits sing_2498.htm#SEC2574 2467 minimalAfaces sing_2489.htm#SEC2565 47736 minimalFace sing_2176.htm#SEC2252 40971 minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2500.htm#SEC2576 11756 minimalValue sing_2177.htm#SEC2253 31262 minipoly sing_1161.htm#SEC1237 4927 minkowskiSum sing_2178.htm#SEC2254 3969 minor sing_298.htm#SEC338 minpoly sing_399.htm#SEC439 minres sing_299.htm#SEC339 minres (plural) sing_469.htm#SEC509 mirror symmetry sing_1204.htm#IDX523 mixed Hodge structure sing_1595.htm#IDX669 mixed Hodge structure sing_1601.htm#IDX697 mixed Hodge structure sing_1602.htm#IDX703 mixed Hodge structure sing_1603.htm#IDX711 mixed Hodge structure sing_1604.htm#IDX717 mixed Hodge structure sing_1605.htm#IDX725 mixed Hodge structure sing_1606.htm#IDX735 mixed Hodge structure sing_1617.htm#IDX741 mixed Hodge structure sing_1619.htm#IDX752 mod sing_81.htm#SEC121 mod sing_98.htm#SEC138 mod sing_147.htm#SEC187 mod sing_155.htm#SEC195 mod2id sing_1042.htm#SEC1118 27927 mod2str sing_684.htm#SEC736 35236 modBorder sing_2760.htm#SEC2836 19224 modDec sing_1276.htm#SEC1352 48578 modIntersect sing_1254.htm#SEC1330 43699 modJanet sing_2762.htm#SEC2838 8550 modNPos sing_1299.htm#SEC1375 17130 modNormal sing_1250.htm#SEC1326 39654 modNpos_test sing_1297.htm#SEC1373 34326 modSagbiAlg sing_2394.htm#SEC2470 25025 modStd sing_1252.htm#SEC1328 7824 modSyz sing_1253.htm#SEC1329 37065 modVStd sing_2399.htm#SEC2475 38529 modVStd0 sing_2400.htm#SEC2476 46080 modWalk sing_2610.htm#SEC2686 sprintf mod_versal sing_1586.htm#SEC1662 63927 modality sing_1565.htm#SEC1641 49951 modfWalk sing_2612.htm#SEC2688 sprintf modfrWalk sing_2613.htm#SEC2689 sprintf modnormal.lib sing_1249.htm#SEC1325 modnormal_lib sing_1249.htm#SEC1325 modrWalk sing_2611.htm#SEC2687 sprintf modregCM sing_1303.htm#SEC1379 5049 modsatiety sing_1301.htm#SEC1377 44506 modstd.lib sing_1251.htm#SEC1327 modstd_lib sing_1251.htm#SEC1327 modular sing_1020.htm#SEC1096 16950 modular methods sing_1247.htm#IDX556 modular methods sing_1249.htm#IDX561 modular methods. sing_1248.htm#IDX559 modular techniques. sing_1250.htm#IDX563 modular.lib sing_1019.htm#SEC1095 modular_lib sing_1019.htm#SEC1095 modular_lib sing_1019.htm#IDX491 module sing_139.htm#SEC179 module (plural) sing_435.htm#SEC475 module declarations sing_140.htm#SEC180 module declarations (plural) module declarations (plural) sing_436.htm#SEC476 module expressions sing_141.htm#SEC181 module expressions (plural) module expressions (plural) sing_437.htm#SEC477 module operations sing_142.htm#SEC182 module operations (plural) module operations (plural) sing_438.htm#SEC478 module ordering C sing_925.htm#IDX420 module ordering c sing_925.htm#IDX422 module related functions module related functions sing_143.htm#SEC183 module related functions (plural) module related functions (plural) sing_439.htm#SEC479 module_containment sing_1174.htm#SEC1250 31620 modules.lib sing_2556.htm#SEC2632 modules_lib sing_2556.htm#SEC2632 moduliSpace sing_2790.htm#SEC2866 37013 modulo sing_300.htm#SEC340 modulo (plural) sing_470.htm#SEC510 moduloSlim sing_767.htm#SEC819 52636 modwalk.lib sing_2609.htm#SEC2685 modwalk_lib sing_2609.htm#SEC2685 moebius sing_2274.htm#SEC2350 61319 moebius function sing_2274.htm#IDX903 molien sing_1709.htm#SEC1785 63561 mondromy.lib sing_1647.htm#SEC1723 mondromy_lib sing_1647.htm#SEC1723 monitor sing_301.htm#SEC341 monodromy sing_1595.htm#IDX673 40112 monodromy sing_1600.htm#SEC1676 monodromy sing_1600.htm#IDX693 monodromy sing_1605.htm#IDX728 monodromy sing_1617.htm#IDX744 monodromy sing_1619.htm#IDX755 monodromyB sing_1651.htm#SEC1727 46517 monomial sing_302.htm#SEC342 monomial ordering sing_1085.htm#IDX505 monomial orderings General definitions for orderings sing_873.htm#SEC925 monomial orderings sing_922.htm#SEC974 monomial orderings introduction Introduction to orderings sing_921.htm#SEC973 monomialBasis sing_629.htm#SEC681 14185 monomialInIdeal sing_857.htm#SEC909 4687 monomialLcm sing_2025.htm#SEC2101 36233 monomialabortstd sing_2281.htm#SEC2357 14901 monomialideal.lib sing_1255.htm#SEC1331 monomialideal_lib sing_1255.htm#SEC1331 monomials and precedence Miscellaneous oddities sing_420.htm#IDX290 mons2intmat sing_1344.htm#SEC1420 15555 morsesplit sing_1558.htm#SEC1634 3417 movingCone sing_2496.htm#SEC2572 39892 mp_res_mat sing_1791.htm#SEC1867 44453 mplot sing_1831.htm#SEC1907 21740 mpresmat sing_303.htm#SEC343 mprimdec.lib sing_1272.htm#SEC1348 mprimdec_lib sing_1272.htm#SEC1348 mregular.lib sing_1287.htm#SEC1363 mregular_lib sing_1287.htm#SEC1363 mres sing_304.htm#SEC344 mres (plural) sing_471.htm#SEC511 mstd sing_305.htm#SEC345 msum sing_58.htm#SEC95 53344 mtriple sing_57.htm#SEC94 55390 mult Miscellaneous oddities sing_306.htm#SEC346 mult sing_420.htm#IDX291 multBound sing_400.htm#SEC440 multRat sing_865.htm#SEC917 44047 multarr2arr sing_2269.htm#SEC2345 44731 multarrMultRestrict sing_2271.htm#SEC2347 41742 multarrRestrict sing_2270.htm#SEC2346 sprintf multcol sing_1128.htm#SEC1204 21899 multdivisor sing_2419.htm#SEC2495 65139 multformaldivisor sing_2431.htm#SEC2507 32238 multi sing_2012.htm#SEC2088 18473 multi indices sing_37.htm#SEC65 multiDeg sing_2644.htm#SEC2720 7049 multiDegBasis sing_2645.htm#SEC2721 3320 multiDegGroebner sing_2653.htm#SEC2729 1040 multiDegModulo sing_2655.htm#SEC2731 27244 multiDegPartition sing_2646.htm#SEC2722 9577 multiDegResolution sing_2656.htm#SEC2732 38535 multiDegSyzygy sing_2654.htm#SEC2730 54075 multiDegTensor sing_2657.htm#SEC2733 45108 multiDegTor sing_2658.htm#SEC2734 sprintf multiarrangement sing_2265.htm#IDX883 multiarrangement sing_2266.htm#IDX885 multiarrangement sing_2267.htm#IDX888 multiarrangement sing_2268.htm#IDX889 multiarrangement sing_2269.htm#IDX892 multiarrangement sing_2270.htm#IDX895 multiarrangement sing_2271.htm#IDX897 multidimensional_knapsack multidimensional_knapsack sing_1990.htm#SEC2066 15647 multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2614.htm#IDX1005 multigrading.lib sing_2614.htm#IDX1003 multigrading_lib sing_2614.htm#IDX1004 multipleCover sing_2796.htm#SEC2872 55988 multiplicities, sequence of sing_1626.htm#IDX767 multiplicity sing_2410.htm#IDX959 multiplicity sequence sing_1539.htm#IDX646 multiplicity sequence sing_1542.htm#IDX658 multiplicity sequence sing_1628.htm#IDX768 multiplyLeftFractions multiplyLeftFractions sing_2729.htm#SEC2805 57489 multiplylist sing_1479.htm#SEC1555 34999 multivariate equations sing_1765.htm#IDX785 multrow sing_1129.htm#SEC1205 871 multseq2charexp sing_1538.htm#SEC1614 sprintf multsequence sing_1628.htm#SEC1704 35117 nBoundaryLatticePoints nBoundaryLatticePoints sing_2179.htm#SEC2255 49670 nHilbertBasis sing_2180.htm#SEC2256 173 nInteriorLatticePoints nInteriorLatticePoints sing_2181.htm#SEC2257 42152 nLatticePoints sing_2182.htm#SEC2258 5977 naccache_stern_decryption naccache_stern_decryption sing_1993.htm#SEC2069 31429 naccache_stern_encryption naccache_stern_encryption sing_1992.htm#SEC2068 60034 naccache_stern_generation naccache_stern_generation sing_1991.htm#SEC2067 2559 nameof sing_307.htm#SEC347 names sing_308.htm#SEC348 nashmult sing_1546.htm#SEC1622 8491 nblocks sing_359.htm#IDX221 ncExt_R sing_800.htm#SEC852 14357 ncHilb.lib sing_2666.htm#SEC2742 ncHilb_lib sing_2666.htm#SEC2742 ncHom sing_801.htm#SEC853 45033 ncInit sing_808.htm#SEC860 55321 ncRelations sing_768.htm#SEC820 7225 ncVarsAdd sing_810.htm#SEC862 55173 ncVarsGet sing_809.htm#SEC861 41459 nc_algebra sing_472.htm#SEC512 nc_hilb sing_359.htm#IDX223 ncalg.lib sing_701.htm#SEC753 ncalg_lib sing_701.htm#SEC753 ncalgebra sing_473.htm#SEC513 ncdecomp.lib sing_728.htm#SEC780 ncdecomp_lib sing_728.htm#SEC780 ncdetection sing_695.htm#SEC747 24994 ncfactor sing_734.htm#SEC786 53809 ncfactor.lib sing_733.htm#SEC785 ncfactor_lib sing_733.htm#SEC785 ncfrac.lib sing_2669.htm#SEC2745 ncfrac_lib sing_2669.htm#SEC2745 nchilb sing_2667.htm#SEC2743 40517 nchomolog.lib sing_799.htm#IDX373 nchomolog_lib sing_799.htm#IDX374 ncloc.lib sing_2683.htm#SEC2759 ncloc_lib sing_2683.htm#SEC2759 ncols sing_309.htm#SEC349 ncones sing_2127.htm#SEC2203 48316 ncpreim.lib sing_746.htm#SEC798 ncpreim_lib sing_746.htm#SEC798 ncrat.lib sing_807.htm#IDX375 ncratAdd sing_812.htm#SEC864 34791 ncratDefine sing_811.htm#SEC863 53337 ncratEvaluateAt sing_821.htm#SEC873 38737 ncratFromPoly sing_819.htm#SEC871 13980 ncratFromString sing_818.htm#SEC870 27148 ncratInvert sing_815.htm#SEC867 41502 ncratMultiply sing_814.htm#SEC866 36291 ncratPower sing_820.htm#SEC872 1973 ncratPrint sing_817.htm#SEC869 13600 ncratSPrint sing_816.htm#SEC868 65300 ncratSubstract sing_813.htm#SEC865 37583 ncrat_lib sing_807.htm#IDX376 ncrepAdd sing_823.htm#SEC875 16569 ncrepDim sing_828.htm#SEC880 48352 ncrepEvaluate sing_830.htm#SEC882 53482 ncrepEvaluateAt sing_831.htm#SEC883 21150 ncrepGet sing_822.htm#SEC874 25651 ncrepGetRegularMinimal ncrepGetRegularMinimal sing_838.htm#SEC890 43477 ncrepGetRegularZeroMinimal ncrepGetRegularZeroMinimal sing_837.htm#SEC889 17269 ncrepInvert sing_826.htm#SEC878 54448 ncrepIsDefined sing_833.htm#SEC885 60090 ncrepIsDefinedDim sing_832.htm#SEC884 6513 ncrepIsRegular sing_834.htm#SEC886 60397 ncrepMultiply sing_825.htm#SEC877 13469 ncrepPencilCombine sing_840.htm#SEC892 20857 ncrepPencilGet sing_839.htm#SEC891 64708 ncrepPrint sing_827.htm#SEC879 65099 ncrepRegularMinimize ncrepRegularMinimize sing_836.htm#SEC888 36893 ncrepRegularZeroMinimize ncrepRegularZeroMinimize sing_835.htm#SEC887 17270 ncrepSubstitute sing_829.htm#SEC881 977 ncrepSubstract sing_824.htm#SEC876 46335 nctools.lib sing_754.htm#SEC806 nctools_lib sing_754.htm#SEC806 ndcond sing_757.htm#SEC809 1006 negateNcfrac sing_2678.htm#SEC2754 23626 negatedCone sing_2105.htm#SEC2181 38527 negative degree lexicographical ordering sing_924.htm#IDX411 negative degree reverse lexicographical ordering Local orderings sing_924.htm#IDX409 negative lexicographical ordering sing_924.htm#IDX407 negativedivisor sing_2420.htm#SEC2496 8274 negativeformaldivisor negativeformaldivisor sing_2430.htm#SEC2506 55026 net sing_2687.htm#IDX1006 sprintf net sing_2689.htm#SEC2765 net access Command line options sing_19.htm#IDX40 netBigInt sing_2695.htm#SEC2771 63523 netBigIntMat sing_2690.htm#SEC2766 36296 netBigIntMatShort sing_2691.htm#SEC2767 30702 netCoefficientRing sing_2692.htm#SEC2768 6081 netIdeal sing_2693.htm#SEC2769 64434 netInt sing_2694.htm#SEC2770 19545 netIntMat sing_2696.htm#SEC2772 34242 netIntMatShort sing_2697.htm#SEC2773 21160 netIntVector sing_2698.htm#SEC2774 17568 netIntVectorShort sing_2699.htm#SEC2775 16105 netList sing_2701.htm#SEC2777 29178 netMap sing_2702.htm#SEC2778 19115 netMap2 sing_2703.htm#SEC2779 44053 netMatrix sing_2591.htm#SEC2667 29311 netNumber sing_2700.htm#SEC2776 24930 netPoly sing_2706.htm#SEC2782 7938 netPrimePower sing_2707.htm#SEC2783 54219 netRing sing_2708.htm#SEC2784 42246 netString sing_2709.htm#SEC2785 43247 netVector sing_2590.htm#SEC2666 32453 netmatrix sing_2704.htm#SEC2780 4023 netmatrixShort sing_2705.htm#SEC2781 24709 nets.lib sing_2687.htm#SEC2763 nets_lib sing_2687.htm#SEC2763 netvector sing_2710.htm#SEC2786 39957 netvectorShort sing_2711.htm#SEC2787 22053 newTest sing_1932.htm#SEC2008 36655 newline sing_172.htm#SEC212 news sing_2819.htm#SEC2895 newstruct sing_183.htm#SEC223 newstruct sing_2288.htm#IDX919 newtonDiag sing_1046.htm#SEC1122 56652 newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2812.htm#SEC2888 22052 newtonPolytope sing_2131.htm#SEC2207 56291 newtonPolytopeLP sing_2136.htm#SEC2212 36186 newtonPolytopeP sing_2135.htm#SEC2211 29927 newtonpoly sing_1633.htm#SEC1709 31930 nf_icis sing_1674.htm#SEC1750 49093 nfmodStd sing_2715.htm#SEC2791 46077 nfmodSyz sing_2717.htm#SEC2793 55942 nfmodstd.lib sing_2713.htm#SEC2789 nfmodstd_lib sing_2713.htm#SEC2789 nfmodsyz.lib sing_2716.htm#SEC2792 nfmodsyz_lib sing_2716.htm#SEC2792 nilpotent Lie algebras sing_1432.htm#IDX598 nmaxcones sing_2126.htm#SEC2202 660 noether sing_401.htm#SEC441 noether.lib sing_1295.htm#SEC1371 noetherNormal sing_1181.htm#SEC1257 44522 noether_lib sing_1295.htm#SEC1371 non-english special characters sing_409.htm#IDX286 nonMonomials sing_1348.htm#SEC1424 16309 nonZeroEntry sing_1184.htm#SEC1260 933 noncommutative, rational expressions sing_807.htm#IDX377 none, option sing_316.htm#IDX150 norTest sing_1315.htm#SEC1391 sprintf norm sing_2011.htm#SEC2087 31143 normaform (up to a bound) sing_359.htm#IDX246 normal sing_1305.htm#SEC1381 61073 normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2795.htm#IDX1071 normal form sing_931.htm#IDX423 normal.lib sing_1304.htm#SEC1380 normalBundle sing_2795.htm#SEC2871 sprintf normalC sing_1307.htm#SEC1383 34842 normalConductor sing_1319.htm#SEC1395 26085 normalFan sing_2183.htm#SEC2259 39216 normalForm sing_2421.htm#SEC2497 34962 normalI sing_1392.htm#SEC1468 7516 normalP sing_1306.htm#SEC1382 36584 normalToricRing sing_1322.htm#SEC1398 29638 normalToricRingFromBinomials normalToricRingFromBinomials sing_1323.htm#SEC1399 2301 normal_lib sing_1304.htm#SEC1380 normalform sing_1562.htm#SEC1638 5550 normalform sing_2393.htm#IDX947 normaliz sing_1.htm#IDX14 18426 normaliz sing_1335.htm#SEC1411 normaliz.lib sing_1320.htm#SEC1396 normaliz_lib sing_1320.htm#SEC1396 normalization sing_1247.htm#IDX554 normalization sing_1248.htm#IDX557 normalization sing_1249.htm#IDX560 normalization sing_1250.htm#IDX562 normalization sing_1305.htm#IDX566 normalization sing_1306.htm#IDX569 normalization sing_1307.htm#IDX572 normalization sing_1319.htm#IDX578 normalization sing_1320.htm#IDX580 normalization sing_2409.htm#IDX957 normalization. sing_1244.htm#IDX553 normalization. sing_1439.htm#IDX620 normalize sing_1039.htm#SEC1115 44788 normalizeMonoidal sing_2735.htm#SEC2811 33071 normalizeRational sing_2736.htm#SEC2812 55177 not sing_101.htm#SEC141 notBuckets, option sing_316.htm#IDX160 notRegularity, option sing_316.htm#IDX158 notSugar, option sing_316.htm#IDX159 notWarnSB, option sing_316.htm#IDX181 npar sing_1917.htm#SEC1993 5753 npars sing_310.htm#SEC350 nrRootsDeterm sing_2042.htm#SEC2118 sprintf nrRootsProbab sing_2041.htm#SEC2117 sprintf nres sing_311.htm#SEC351 nres (plural) sing_474.htm#SEC514 nrows sing_312.htm#SEC352 nrroots sing_2071.htm#SEC2147 54867 nsatiety sing_1300.htm#SEC1376 53333 nselect sing_1200.htm#SEC1276 34057 nt_solve sing_1806.htm#SEC1882 33061 ntsolve.lib sing_1805.htm#SEC1881 ntsolve_lib sing_1805.htm#SEC1881 number sing_144.htm#SEC184 number sing_2242.htm#IDX843 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_2128.htm#SEC2204 5905 number_e sing_975.htm#SEC1051 59152 number_pi sing_976.htm#SEC1052 15492 numerAlg.lib sing_1414.htm#IDX587 numerAlg_lib sing_1414.htm#IDX588 numerAlg_lib sing_1419.htm#IDX597 numerDecom.lib sing_1419.htm#IDX591 numerDecom_lib sing_1414.htm#IDX590 numerDecom_lib sing_1419.htm#IDX592 numerator sing_313.htm#SEC353 numerical irreducible decomposition sing_1419.htm#IDX593 nvars sing_314.htm#SEC354 olga.lib sing_2718.htm#SEC2794 olga_lib sing_2718.htm#SEC2794 oneDimBelongSemigroup oneDimBelongSemigroup sing_1191.htm#SEC1267 34399 oneNcfrac sing_2675.htm#SEC2751 35654 online help The online help system sing_16.htm#SEC22 open sing_315.htm#SEC355 opentex sing_1834.htm#SEC1910 54236 operatorAlgebra sing_638.htm#SEC690 36252 operatorBM sing_549.htm#SEC601 54875 operatorModulo sing_550.htm#SEC602 26064 oppose sing_475.htm#SEC515 opposite sing_476.htm#SEC516 opposite polynomial sing_359.htm#IDX231 opposite ring sing_359.htm#IDX228 option sing_316.htm#SEC356 option(warn) sing_70.htm#SEC110 optionIsSet sing_1082.htm#SEC1158 57325 or Evaluation of logical expressions sing_101.htm#SEC141 or sing_413.htm#SEC453 orbit sing_1432.htm#IDX600 orbit sing_1433.htm#IDX604 orbit sing_1436.htm#IDX609 orbit sing_1437.htm#IDX612 orbitConeOrbits sing_2499.htm#SEC2575 60979 orbitCones sing_2490.htm#SEC2566 60528 orbit_variety sing_1733.htm#SEC1809 22665 orbitparam.lib sing_1432.htm#SEC1508 orbitparam_lib sing_1432.htm#SEC1508 ord sing_317.htm#SEC357 ord_test sing_1077.htm#SEC1153 36532 order ideal, border basis sing_2759.htm#IDX1043 order ideal, border basis sing_2760.htm#IDX1044 orderings General definitions for orderings sing_922.htm#SEC974 orderings introduction Introduction to orderings sing_921.htm#SEC973 orderings, L sing_929.htm#SEC981 orderings, M sing_926.htm#SEC978 orderings, a sing_928.htm#SEC980 orderings, global sing_923.htm#SEC975 orderings, local sing_924.htm#SEC976 orderings, product sing_927.htm#SEC979 ordstr sing_318.htm#SEC358 origin sing_2076.htm#SEC2152 31408 orthogonalize sing_1147.htm#SEC1223 63711 outer sing_1118.htm#SEC1194 64048 output sing_41.htm#SEC71 p-adic numbers sing_32.htm#SEC46 pFactor sing_1966.htm#SEC2042 31504 pIntersect sing_513.htm#SEC565 44055 pIntersectSyz sing_514.htm#SEC566 45608 package sing_149.htm#SEC189 package declarations package declarations sing_150.htm#SEC190 package related functions package related functions sing_151.htm#SEC191 pairset sing_2031.htm#SEC2107 38258 par sing_319.htm#SEC359 par2varRing sing_959.htm#SEC1035 44769 paraConic sing_1447.htm#SEC1523 9828 paraPlaneCurve sing_1441.htm#SEC1517 34094 parallel skeletons sing_1021.htm#IDX497 parallel.lib sing_1021.htm#SEC1097 parallelTestAND sing_1025.htm#SEC1101 1415 parallelTestOR sing_1026.htm#SEC1102 14920 parallelWaitAll sing_1024.htm#SEC1100 2017 parallelWaitFirst sing_1023.htm#SEC1099 32 parallelWaitN sing_1022.htm#SEC1098 38878 parallel_lib sing_1021.htm#SEC1097 parallelization sing_1021.htm#IDX496 parallelization sing_1061.htm#IDX499 parallelization sing_1094.htm#IDX509 param sing_1624.htm#SEC1700 57220 parameter, as numbers sing_144.htm#SEC184 parameterSubstitute sing_2223.htm#SEC2299 63147 parametric annihilator sing_542.htm#IDX335 parametric annihilator for variety sing_598.htm#IDX358 parametric ideal sing_987.htm#IDX429 parametric ideal sing_994.htm#IDX448 parametric ideal sing_994.htm#IDX450 parametric ideal sing_995.htm#IDX455 parametrization sing_1432.htm#IDX601 parametrization sing_1436.htm#IDX610 parametrization sing_1624.htm#IDX762 parametrizeOrbit sing_1436.htm#SEC1512 26969 paraplanecurves.lib sing_1438.htm#SEC1514 paraplanecurves_lib sing_1438.htm#SEC1514 pardeg sing_320.htm#SEC360 parstr sing_321.htm#SEC361 part sing_2369.htm#SEC2445 31485 partOver sing_2372.htm#SEC2448 25555 partUnder sing_2373.htm#SEC2449 13123 partial_molien sing_1711.htm#SEC1787 21772 partitions sing_1212.htm#SEC1288 48089 partitions sing_1212.htm#IDX542 path integral sing_1204.htm#IDX529 pause sing_1018.htm#SEC1094 2273 pdivi sing_989.htm#SEC1065 21786 pdivi sing_990.htm#IDX439 pdivisorplus sing_2435.htm#SEC2511 47486 permcol sing_1130.htm#SEC1206 12886 permrow sing_1131.htm#SEC1207 26561 permutationFromIntvec permutationFromIntvec sing_2505.htm#SEC2581 6533 permutationToIntvec sing_2506.htm#SEC2582 1989 permutations sing_1213.htm#IDX543 permutations, sum, max, min sing_2404.htm#IDX949 permute sing_1213.htm#SEC1289 40893 permute_L sing_1869.htm#SEC1945 10716 perron sing_780.htm#SEC832 3782 perron.lib sing_779.htm#SEC831 perron_lib sing_779.htm#SEC831 phindex.lib sing_2283.htm#IDX910 phindex_lib sing_2283.htm#IDX911 picksFormula sing_2145.htm#SEC2221 14656 pid sing_359.htm#IDX240 plainInvariants sing_1583.htm#SEC1659 40916 planeCur sing_2391.htm#SEC2467 sprintf plot sing_1847.htm#SEC1923 46610 plotRot sing_1851.htm#SEC1927 57150 plotRotated sing_1850.htm#SEC1926 33009 plotRotatedDirect sing_1853.htm#SEC1929 18202 plotRotatedList sing_1852.htm#SEC1928 41668 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1854.htm#SEC1930 38856 plural sing_1084.htm#IDX504 pmat sing_1012.htm#SEC1088 3857 pnormalf sing_990.htm#SEC1066 26174 pointid.lib sing_1347.htm#SEC1423 pointid_lib sing_1347.htm#SEC1423 polSol sing_849.htm#SEC901 323 polSolFiniteRank sing_850.htm#SEC902 30875 pollTask sing_1104.htm#SEC1180 53950 poly sing_152.htm#SEC192 poly (plural) sing_440.htm#SEC480 poly declarations sing_153.htm#SEC193 poly declarations (plural) poly declarations (plural) sing_441.htm#SEC481 poly expressions sing_154.htm#SEC194 poly expressions (plural) poly expressions (plural) sing_442.htm#SEC482 poly operations sing_155.htm#SEC195 poly operations (plural) poly operations (plural) sing_443.htm#SEC483 poly related functions poly related functions sing_156.htm#SEC196 poly related functions (plural) poly related functions (plural) sing_444.htm#SEC484 poly.lib sing_1027.htm#SEC1103 poly2list sing_591.htm#SEC643 4960 poly2zdd sing_2304.htm#SEC2380 61839 polyInterpolation sing_2438.htm#SEC2514 45866 polyVars sing_856.htm#SEC908 43882 poly_lib sing_1027.htm#SEC1103 polybori sing_2288.htm#IDX915 polybori.lib sing_2288.htm#IDX912 polybori.lib sing_2288.htm#IDX916 polybori_lib sing_2288.htm#IDX913 polymake sing_2133.htm#IDX816 polymake.lib sing_2133.htm#SEC2209 polymakePolytope sing_2134.htm#SEC2210 47302 polymake_lib sing_2133.htm#SEC2209 polynomial solutions sing_843.htm#IDX392 polynomial, opposite sing_359.htm#IDX232 polytope sing_191.htm#SEC231 polytope sing_2133.htm#IDX812 polytopeViaInequalities polytopeViaInequalities sing_2106.htm#SEC2182 52084 polytopeViaPoints sing_2107.htm#SEC2183 281 pos_def sing_1158.htm#SEC1234 4994 poset sing_2273.htm#IDX901 positiveOrthant sing_2077.htm#SEC2153 42102 posweight sing_1691.htm#SEC1767 3364 powSumSym sing_2326.htm#SEC2402 2339 power sing_1119.htm#SEC1195 23365 power set sing_2406.htm#IDX951 powerN sing_1950.htm#SEC2026 20170 powerX sing_1959.htm#SEC2035 47971 power_products sing_1725.htm#SEC1801 54629 powerpolyX sing_1929.htm#SEC2005 37247 powersums sing_2052.htm#SEC2128 59049 preComp sing_1283.htm#SEC1359 16160 preimage sing_322.htm#SEC362 preimage sing_746.htm#IDX361 preimage (plural) sing_477.htm#SEC517 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1080.htm#IDX502 preimageLattice sing_2634.htm#SEC2710 37348 preimageLoc sing_1080.htm#SEC1156 33315 preimageNC sing_748.htm#SEC800 16037 prepEmbDiv sing_1509.htm#SEC1585 36708 prepMat sing_1762.htm#SEC1838 39868 prepRealclassify sing_1567.htm#SEC1643 10994 prepSV sing_1864.htm#SEC1940 50095 prepareAss sing_1366.htm#SEC1442 21802 presentTree sing_1496.htm#SEC1572 10731 presentation sing_2592.htm#SEC2668 40323 presolve.lib sing_1772.htm#SEC1848 presolve_lib sing_1772.htm#SEC1848 primL sing_1954.htm#SEC2030 14513 primList sing_1953.htm#SEC2029 6802 primRoot sing_1406.htm#SEC1482 14210 primTest sing_1282.htm#SEC1358 8105 primary decomposition sing_1351.htm#IDX582 primary decomposition sing_1374.htm#IDX583 primary decomposition of modules sing_1272.htm#IDX564 primary decomposition, numerical sing_1419.htm#IDX595 primary_char0 sing_1715.htm#SEC1791 61413 primary_char0_no_molien primary_char0_no_molien sing_1717.htm#SEC1793 50477 primary_char0_no_molien_random primary_char0_no_molien_random sing_1722.htm#SEC1798 8422 primary_char0_random primary_char0_random sing_1720.htm#SEC1796 5996 primary_charp sing_1716.htm#SEC1792 37863 primary_charp_no_molien primary_charp_no_molien sing_1718.htm#SEC1794 32282 primary_charp_no_molien_random primary_charp_no_molien_random sing_1723.htm#SEC1799 11498 primary_charp_random primary_charp_random sing_1721.htm#SEC1797 24739 primary_charp_without primary_charp_without sing_1719.htm#SEC1795 49585 primary_charp_without_random primary_charp_without_random sing_1724.htm#SEC1800 36998 primary_invariants sing_1703.htm#SEC1779 5500 primary_invariants_random primary_invariants_random sing_1704.htm#SEC1780 28958 primdec.lib sing_1351.htm#SEC1427 primdecGTZ sing_1353.htm#SEC1429 6091 primdecGTZE sing_1354.htm#SEC1430 64882 primdecMon sing_1271.htm#SEC1347 3856 primdecSY sing_1355.htm#SEC1431 6547 primdecSYE sing_1356.htm#SEC1432 52788 primdecZ sing_1375.htm#SEC1451 48194 primdecZM sing_1376.htm#SEC1452 17214 primdec_lib sing_1351.htm#SEC1427 primdecint.lib sing_1374.htm#SEC1450 primdecint_lib sing_1374.htm#SEC1450 prime sing_323.htm#SEC363 primeClosure sing_1310.htm#SEC1386 43589 primecoeffs sing_982.htm#SEC1058 46153 primefactors sing_324.htm#SEC364 primes sing_977.htm#SEC1053 24408 primitiv.lib sing_1382.htm#SEC1458 primitiv_lib sing_1382.htm#SEC1458 primitive sing_1383.htm#SEC1459 36163 primitive element sing_1383.htm#IDX584 primitiveSpan sing_2641.htm#SEC2717 sprintf primitive_extra sing_1384.htm#SEC1460 49025 primparam sing_1578.htm#SEC1654 35357 principal intersection sing_507.htm#IDX319 print sing_325.htm#SEC365 print sing_2240.htm#IDX836 printBetti sing_2573.htm#SEC2649 28941 printFreeModule sing_2565.htm#SEC2641 13316 printGraph sing_1206.htm#SEC1282 45041 printGraphG sing_2789.htm#SEC2865 48742 printGroup sing_2622.htm#SEC2698 6791 printHom sing_2568.htm#SEC2644 7070 printMatrix sing_2564.htm#SEC2640 15522 printModule sing_2567.htm#SEC2643 sprintf printMoebius sing_2279.htm#SEC2355 45828 printResolution sing_2566.htm#SEC2642 29278 printSheaf sing_2777.htm#SEC2853 31762 printStack sing_2791.htm#SEC2867 3692 printTask sing_1099.htm#SEC1175 54549 printVariety sing_2769.htm#SEC2845 2846 printf sing_326.htm#SEC366 2294 printlevel sing_402.htm#SEC442 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_2029.htm#SEC2105 56231 product sing_978.htm#SEC1054 54431 product variety, abstract variety sing_2770.htm#IDX1059 productVariety sing_2770.htm#SEC2846 54191 productgroup sing_2643.htm#SEC2719 55937 progress watch sing_316.htm#IDX163 projectLattice sing_2635.htm#SEC2711 28463 projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2774.htm#IDX1063 projective dimension purityfiltration_lib sing_787.htm#IDX370 projective limes sing_32.htm#SEC46 projective space, abstract variety sing_2773.htm#IDX1062 projectiveBundle sing_2774.htm#SEC2850 13791 projectiveDimension sing_788.htm#SEC840 8165 projectiveSpace sing_2773.htm#SEC2849 21729 prompt sing_15.htm#SEC21 prompt, option sing_316.htm#IDX182 propagator sing_1204.htm#IDX527 42460 propagator sing_1207.htm#SEC1283 prot, option sing_316.htm#IDX161 protocol of computations sing_316.htm#IDX162 proximitymatrix sing_1537.htm#SEC1613 58403 prune sing_327.htm#SEC367 pruneModule sing_2599.htm#SEC2675 51453 prwalk sing_2764.htm#SEC2840 46963 psigncnd sing_1825.htm#SEC1901 57734 puiseux2generators sing_1636.htm#SEC1712 64508 puiseuxExpansion sing_2194.htm#SEC2270 46277 pure tensor sing_500.htm#IDX307 purelist sing_798.htm#SEC850 15517 purity purityfiltration_lib sing_787.htm#IDX372 purityFiltration sing_789.htm#SEC841 5742 purityTriang sing_790.htm#SEC842 3665 purityfiltration.lib purityfiltration_lib sing_787.htm#IDX365 purityfiltration_lib purityfiltration_lib sing_787.htm#IDX366 pushForward sing_2660.htm#SEC2736 26697 pwalk sing_1220.htm#SEC1296 61187 pyobject sing_192.htm#SEC232 pyobject sing_2288.htm#IDX918 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_2454.htm#SEC2530 7421 python_eval sing_197.htm#SEC237 python_import sing_198.htm#SEC238 python_run sing_199.htm#SEC239 qbase sing_2055.htm#SEC2131 8633 qepcad sing_2464.htm#SEC2540 39171 qepcadsystem sing_2465.htm#SEC2541 31977 qhmatrix sing_1689.htm#SEC1765 61813 qhmoduli.lib sing_1653.htm#SEC1729 qhmoduli_lib sing_1653.htm#SEC1729 qhspectrum sing_1676.htm#SEC1752 13732 qhweight sing_328.htm#SEC368 qmatrix.lib sing_781.htm#SEC833 qmatrix_lib sing_781.htm#SEC833 qminor sing_783.htm#SEC835 52670 qrds sing_329.htm#SEC369 qring Miscellaneous oddities sing_166.htm#SEC206 qring sing_420.htm#IDX295 qring (plural) sing_445.htm#SEC485 qring declaration sing_170.htm#SEC210 qring declaration (plural) qring declaration (plural) sing_446.htm#SEC486 qring related functions (plural) qring related functions (plural) sing_447.htm#SEC487 qring ring ideal 'factor ring' sing_1089.htm#IDX508 qringNF, option sing_316.htm#IDX164 qslimgb sing_958.htm#SEC1034 51999 quadraticSieve sing_1967.htm#SEC2043 58557 quantMat sing_782.htm#SEC834 56227 quickclass sing_1559.htm#SEC1635 14018 quit sing_392.htm#SEC432 quotSheaf sing_2786.htm#SEC2862 49619 quote sing_330.htm#SEC370 quotient sing_331.htm#SEC371 quotient (plural) sing_478.htm#SEC518 quotientLatticeBasis quotientLatticeBasis sing_2108.htm#SEC2184 15613 quotientMain sing_1817.htm#SEC1893 39870 quotientMon sing_1262.htm#SEC1338 57149 rHRR sing_2366.htm#SEC2442 20131 rJanet sing_2761.htm#SEC2837 30716 rMacaulay sing_1013.htm#SEC1089 45499 rad_con sing_1040.htm#SEC1116 21777 radical sing_1363.htm#SEC1439 1407 radicalEHV sing_1364.htm#SEC1440 33703 radicalMemberShip sing_2216.htm#SEC2292 28527 radicalMon sing_1263.htm#SEC1339 64912 radicalZ sing_1378.htm#SEC1454 5783 randcharpoly sing_2049.htm#SEC2125 37737 randlinpoly sing_2051.htm#SEC2127 22330 random sing_332.htm#SEC372 random sing_359.htm#IDX244 random sing_2261.htm#IDX875 random sing_2262.htm#IDX877 random number generator, seed sing_359.htm#IDX242 random.lib sing_1048.htm#SEC1124 randomBinomial sing_1060.htm#SEC1136 17913 randomCheck sing_1880.htm#SEC1956 20973 randomLast sing_1059.htm#SEC1135 2046 randomPoint sing_2109.htm#SEC2185 22561 randomPolyInT sing_2225.htm#SEC2301 2264 random_lib sing_1048.htm#SEC1124 randomid sing_1050.htm#SEC1126 7815 randommat sing_1051.htm#SEC1127 33569 rank sing_210.htm#IDX137 rank sing_333.htm#SEC373 rankSheaf sing_2778.htm#SEC2854 11850 ratSol sing_851.htm#SEC903 62488 ratgb.lib sing_841.htm#IDX381 ratgb_lib sing_841.htm#IDX382 rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1441.htm#IDX622 rational functions sing_807.htm#IDX378 rational normal curve, projection. sing_1442.htm#IDX623 rational normal curve, projection. sing_1445.htm#IDX624 rational normal curve, projection. sing_1446.htm#IDX625 rational solutions sing_843.htm#IDX393 rational univariate projection sing_2049.htm#IDX809 rationalCurve sing_2798.htm#SEC2874 61201 rationalPointConic sing_1443.htm#SEC1519 9761 ratstd sing_842.htm#SEC894 61346 rays sing_2110.htm#SEC2186 44445 rcolon sing_2668.htm#SEC2744 1208 re2squ sing_1420.htm#SEC1496 24350 read sing_334.htm#SEC374 readNmzData sing_1338.htm#SEC1414 18957 reading, option sing_316.htm#IDX183 readline sing_1.htm#IDX5 real sing_28.htm#IDX74 real root isolation sing_2745.htm#IDX1038 real roots, univariate polynomial sing_2056.htm#IDX811 real roots, univariate projection sing_2040.htm#IDX807 real roots,sign conditions sing_1823.htm#IDX787 realclassify sing_2740.htm#SEC2816 51416 realclassify.lib sing_2739.htm#SEC2815 realclassify_lib sing_2739.htm#SEC2815 realizationDim sing_2188.htm#SEC2264 37756 realizationDimPoly sing_2190.htm#SEC2266 3611 realizationMatroids.lib realizationMatroids_lib sing_2187.htm#SEC2263 realizationMatroids_lib realizationMatroids_lib sing_2187.htm#SEC2263 realmorsesplit sing_2741.htm#SEC2817 16318 realpoly sing_1387.htm#SEC1463 9453 realrad sing_1389.htm#SEC1465 43381 realrad.lib sing_1386.htm#SEC1462 realrad_lib sing_1386.htm#SEC1462 realzero sing_1388.htm#SEC1464 12712 recursive_boolean_poly recursive_boolean_poly sing_2294.htm#SEC2370 17045 recursive_from_boolean_poly recursive_from_boolean_poly sing_2300.htm#SEC2376 37794 redSB, option sing_316.htm#IDX165 redTail, option sing_316.htm#IDX167 redThrough, option sing_316.htm#IDX168 redefine, option sing_316.htm#IDX184 reduce sing_335.htm#SEC375 reduce sing_521.htm#IDX324 reduce sing_989.htm#IDX437 reduce sing_990.htm#IDX440 reduce (plural) sing_479.htm#SEC519 reduce (up to a bound) sing_359.htm#IDX245 reduceIntChain sing_2604.htm#SEC2680 17776 reduced sing_988.htm#IDX434 reduced standard basis sing_316.htm#IDX166 reduction sing_1741.htm#SEC1817 31048 reesclos.lib sing_1390.htm#SEC1466 reesclos_lib sing_1390.htm#SEC1466 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_1302.htm#SEC1378 25488 regIdeal sing_1288.htm#SEC1364 3827 regMonCurve sing_1291.htm#SEC1367 41311 regularity Syzygies and resolutions sing_336.htm#SEC376 regularity sing_933.htm#SEC990 reiffen sing_560.htm#SEC612 32856 rel_orbit_variety sing_1734.htm#SEC1810 34278 relations sing_779.htm#IDX364 relativeInteriorPoint relativeInteriorPoint sing_2111.htm#SEC2187 30097 relative_orbit_variety relative_orbit_variety sing_1735.htm#SEC1811 32995 relweight sing_1690.htm#SEC1766 10658 remainder sing_1810.htm#SEC1886 1191 remainderMain sing_1818.htm#SEC1894 3532 removeCone sing_2129.htm#SEC2205 33877 removepower sing_1547.htm#SEC1623 47644 repart sing_337.htm#SEC377 replace sing_1919.htm#SEC1995 50075 representation, math objects Representation of mathematical objects sing_919.htm#SEC971 res sing_338.htm#SEC378 10393 resbinomial.lib sing_1450.htm#IDX628 resbinomial_lib sing_1450.htm#IDX629 reservedName sing_339.htm#SEC379 resfunction sing_1464.htm#SEC1540 59312 resgraph.lib sing_1482.htm#SEC1558 resgraph_lib sing_1482.htm#SEC1558 resjung.lib sing_1486.htm#SEC1562 resjung_lib sing_1486.htm#SEC1562 reslist sing_1478.htm#SEC1554 64950 resolution purityfiltration_lib sing_161.htm#SEC201 resolution sing_787.htm#IDX371 resolution (plural) sing_448.htm#SEC488 resolution declarations resolution declarations sing_162.htm#SEC202 resolution declarations (plural) resolution declarations (plural) sing_449.htm#SEC489 resolution expressions resolution expressions sing_163.htm#SEC203 resolution expressions (plural) resolution expressions (plural) sing_450.htm#SEC490 resolution graph sing_1532.htm#IDX642 resolution related functions resolution related functions sing_164.htm#SEC204 resolution related functions (plural) resolution related functions (plural) sing_451.htm#SEC491 resolution, La Scala's method sing_289.htm#SEC329 resolution, computation of sing_338.htm#IDX186 resolution, hilbert-driven sing_264.htm#SEC304 resolutionInLocalization resolutionInLocalization sing_2484.htm#SEC2560 31106 resolutiongraph sing_1533.htm#SEC1609 32697 resolve sing_1494.htm#SEC1570 27374 resolve.lib sing_1490.htm#SEC1566 resolve_lib sing_1490.htm#SEC1566 resources.lib sing_1061.htm#SEC1137 resources_lib sing_1061.htm#SEC1137 restriction sing_2254.htm#IDX863 restriction sing_2270.htm#IDX896 restriction sing_2271.htm#IDX898 restriction of sing_565.htm#IDX347 restrictionIdeal sing_575.htm#SEC627 49796 restrictionModule sing_576.htm#SEC628 62461 resultant sing_303.htm#SEC343 resultant sing_340.htm#SEC380 reszeta.lib sing_1503.htm#SEC1579 reszeta_lib sing_1503.htm#SEC1579 return sing_393.htm#SEC433 return type of procedures Return type of procedures sing_418.htm#SEC458 returnSB, option sing_316.htm#IDX152 reverse sing_2070.htm#SEC2146 35880 reverse lexicographical ordering sing_923.htm#IDX398 reynolds_molien sing_1710.htm#SEC1786 45316 rho sing_1961.htm#SEC2037 51414 rightInverse sing_1899.htm#SEC1975 6558 rightKernel sing_1897.htm#SEC1973 46603 rightModulo sing_766.htm#SEC818 12618 rightNF sing_765.htm#SEC817 42610 rightNFWeyl sing_868.htm#SEC920 35828 rightOre sing_2725.htm#SEC2801 56918 rightStd sing_764.htm#SEC816 5740 ring sing_165.htm#SEC205 ring (plural) sing_452.htm#SEC492 ring coefficients hasTransExtensionCoefficient sing_1087.htm#IDX506 ring coefficients sing_1088.htm#IDX507 ring declarations sing_167.htm#SEC207 ring declarations (plural) ring declarations (plural) sing_453.htm#SEC493 ring operations sing_169.htm#SEC209 ring operations (plural) ring operations (plural) sing_454.htm#SEC494 ring related functions ring related functions sing_168.htm#SEC208 ring related functions (plural) ring related functions (plural) sing_455.htm#SEC495 ring, opposite sing_359.htm#IDX229 ring.lib sing_1066.htm#SEC1142 ring_cf sing_210.htm#IDX138 ring_lib sing_1066.htm#SEC1142 ring_list sing_342.htm#SEC382 ring_variable sing_2241.htm#IDX840 ring_variable sing_2242.htm#IDX842 ring_variable sing_2243.htm#IDX846 ring_variable sing_2244.htm#IDX848 ringlist sing_341.htm#SEC381 ringlist (plural) sing_480.htm#SEC520 ringtensor sing_1078.htm#SEC1154 56648 ringweights sing_1079.htm#SEC1155 33307 rinvar.lib sing_1746.htm#SEC1822 rinvar_lib sing_1746.htm#SEC1822 rmNmzFiles sing_1343.htm#SEC1419 32601 rm_unitcol sing_1136.htm#SEC1212 5591 rm_unitrow sing_1135.htm#SEC1211 35694 rmx sing_1844.htm#SEC1920 17675 rncAntiCanonicalMap sing_1442.htm#SEC1518 41965 rncItProjEven sing_1446.htm#SEC1522 18200 rncItProjOdd 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sing_412.htm#SEC452 rvar sing_343.htm#SEC383 rwalk sing_2765.htm#SEC2841 42525 rwalk.lib sing_2763.htm#SEC2839 rwalk_lib sing_2763.htm#SEC2839 sRes sing_2570.htm#SEC2646 23381 sa_poly_reduce sing_530.htm#SEC582 60856 sa_reduce sing_529.htm#SEC581 55799 sagbi sing_1396.htm#SEC1472 46653 sagbi basis sing_2394.htm#IDX948 sagbi.lib sing_1393.htm#SEC1469 sagbiAlg sing_2387.htm#SEC2463 sprintf sagbiMod sing_2388.htm#SEC2464 sprintf sagbiPart sing_1397.htm#SEC1473 56066 sagbiReduce sing_1395.htm#SEC1471 19036 sagbiSPoly sing_1394.htm#SEC1470 17365 sagbi_lib sing_1393.htm#SEC1469 salida sing_1475.htm#SEC1551 9839 sameComponent sing_2023.htm#SEC2099 13540 sameQ sing_1822.htm#SEC1898 45579 sat sing_1201.htm#SEC1277 6266 satiety sing_1290.htm#SEC1366 34323 satstd sing_2282.htm#SEC2358 16128 sba sing_344.htm#SEC384 scalarProd sing_519.htm#SEC571 54488 scheme sing_2445.htm#SEC2521 15722 schubert.lib sing_2767.htm#SEC2843 schubert_lib sing_2767.htm#SEC2843 sdb, source code debugger Source code debugger sing_66.htm#SEC103 second degree sing_1005.htm#IDX485 secondary fan sing_2133.htm#IDX814 secondary polytope sing_2133.htm#IDX815 secondaryPolytope sing_2138.htm#SEC2214 48451 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1731.htm#SEC1807 37058 secondary_char0 sing_1726.htm#SEC1802 31029 secondary_charp sing_1728.htm#SEC1804 16364 secondary_no_molien sing_1729.htm#SEC1805 3616 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1732.htm#SEC1808 31675 segre sing_2321.htm#SEC2397 44035 select sing_1202.htm#SEC1278 17096 select1 sing_1203.htm#SEC1279 32617 semaphore sing_359.htm#IDX249 44342 semaphore sing_1065.htm#SEC1141 semaphores sing_1061.htm#IDX501 semiCMcod2 sing_1687.htm#SEC1763 15905 semiGroup sing_2389.htm#SEC2465 sprintf semiMod sing_2390.htm#SEC2466 sprintf semidiv sing_2015.htm#SEC2091 58107 semigroup sing_1536.htm#SEC1612 29045 semigroup sing_1540.htm#IDX649 semigroup of values sing_1626.htm#IDX764 semigroupGenerator sing_2112.htm#SEC2188 59446 sep sing_1373.htm#SEC1449 sprintf separateHNE sing_1637.htm#SEC1713 12052 separator sing_1273.htm#SEC1349 33000 serreRelations sing_686.htm#SEC738 33994 set sing_2236.htm#IDX826 setBaseMultigrading sing_2615.htm#SEC2691 6575 setLetterplaceAttributes setLetterplaceAttributes sing_676.htm#SEC728 5759 setLinearForms sing_2113.htm#SEC2189 62731 setModuleGrading sing_2627.htm#SEC2703 59018 setMultiplicity sing_2114.htm#SEC2190 27537 setNmzDataPath sing_1340.htm#SEC1416 18123 setNmzExecPath sing_1336.htm#SEC1412 38993 setNmzFilename sing_1339.htm#SEC1415 20206 setNmzOption sing_1333.htm#SEC1409 9012 setUniformizingParameter setUniformizingParameter sing_2810.htm#SEC2886 63635 set_is_injective sing_2003.htm#SEC2079 8429 setcores sing_1063.htm#SEC1139 49704 setenv sing_359.htm#IDX252 setinitials sing_2455.htm#SEC2531 24792 setring sing_345.htm#SEC385 sh sing_359.htm#IDX254 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_1513.htm#IDX630 sheafCoh sing_1519.htm#SEC1595 64501 sheafCohBGG sing_1517.htm#SEC1593 13439 sheafCohBGG2 sing_1518.htm#SEC1594 3338 sheafcoh.lib sing_1513.htm#SEC1589 sheafcoh_lib sing_1513.htm#SEC1589 shiftPoly sing_679.htm#SEC731 65223 short sing_403.htm#SEC443 show sing_1014.htm#SEC1090 15599 showBO sing_1495.htm#SEC1571 20089 showDataTypes sing_1497.htm#SEC1573 4270 showNmzOptions sing_1334.htm#SEC1410 64955 showNuminvs sing_1331.htm#SEC1407 18934 showgrades sing_792.htm#SEC844 48081 showrecursive sing_1015.htm#SEC1091 6127 sickle sing_626.htm#SEC678 54811 signal handler sing_2826.htm#SEC2916 signatureBrieskorn sing_1696.htm#SEC1772 26283 signatureL sing_2284.htm#SEC2360 65493 signatureLqf sing_2285.htm#SEC2361 18811 signatureNemethi sing_1698.htm#SEC1774 21981 signaturePuiseux sing_1697.htm#SEC1773 23398 signcnd sing_1824.htm#SEC1900 40147 signcond.lib sing_1823.htm#SEC1899 signcond_lib sing_1823.htm#SEC1899 simplePrune sing_2608.htm#SEC2684 sprintf simplesolver sing_1768.htm#SEC1844 13418 simplex sing_346.htm#SEC386 simplexOut sing_1795.htm#SEC1871 56099 simplify sing_347.htm#SEC387 simplifyRat sing_863.htm#SEC915 52658 sing.lib sing_1663.htm#SEC1739 sing4ti2.lib sing_1399.htm#SEC1475 sing4ti2_lib sing_1399.htm#SEC1475 sing_lib sing_1663.htm#SEC1739 singular locus of D-module sing_843.htm#IDX387 singularities sing_1595.htm#IDX666 singularities sing_1596.htm#IDX677 singularities sing_1597.htm#IDX680 singularities sing_1598.htm#IDX683 singularities sing_1599.htm#IDX686 singularities sing_1600.htm#IDX690 singularities sing_1601.htm#IDX694 singularities sing_1602.htm#IDX700 singularities sing_1603.htm#IDX708 singularities sing_1604.htm#IDX714 singularities sing_1605.htm#IDX722 singularities sing_1606.htm#IDX732 singularities sing_1694.htm#IDX779 singularities 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sing_597.htm#SEC649 60798 sortandmap sing_1783.htm#SEC1859 10314 sortier sing_1745.htm#SEC1821 3555 sortvars sing_1784.htm#SEC1860 61778 sortvec sing_350.htm#SEC390 source sing_2586.htm#SEC2662 63163 source code debugger, sdb Source code debugger sing_66.htm#SEC103 spaceCur sing_2392.htm#SEC2468 sprintf spadd sing_1609.htm#SEC1685 48739 span sing_2115.htm#SEC2191 64343 sparseHomogIdeal sing_1057.htm#SEC1133 22631 sparseInterpolation sing_2440.htm#SEC2516 28771 sparseid sing_1052.htm#SEC1128 20824 sparsemat sing_1054.htm#SEC1130 17653 sparsematrix sing_1053.htm#SEC1129 41031 sparsepoly sing_1055.htm#SEC1131 21649 sparsetriag sing_1056.htm#SEC1132 50657 spcurve.lib sing_1683.htm#SEC1759 spcurve_lib sing_1683.htm#SEC1759 special characters, non-english sing_409.htm#IDX287 spectral pairs sing_1595.htm#IDX675 spectral pairs sing_1602.htm#IDX707 spectral pairs sing_1604.htm#IDX721 spectral pairs sing_1605.htm#IDX730 spectral pairs sing_1617.htm#IDX746 spectral pairs sing_1619.htm#IDX757 spectralNeg sing_1505.htm#SEC1581 36691 spectrum sing_1595.htm#IDX674 47545 spectrum sing_1601.htm#SEC1677 spectrum sing_1601.htm#IDX699 spectrum sing_1602.htm#IDX706 spectrum sing_1603.htm#IDX713 spectrum sing_1604.htm#IDX720 spectrum sing_1605.htm#IDX729 spectrum sing_1617.htm#IDX745 spectrum sing_1619.htm#IDX756 spectrum sing_1694.htm#IDX781 spectrum.lib sing_1693.htm#SEC1769 spectrum_lib sing_1693.htm#SEC1769 spectrumnd sing_1694.htm#SEC1770 29943 spgamma sing_1616.htm#SEC1692 59653 spgeomgenus sing_1615.htm#SEC1691 57796 spissemicont sing_1612.htm#SEC1688 23679 split sing_1016.htm#SEC1092 29794 splitPolygon sing_2140.htm#SEC2216 706 splitring sing_1385.htm#SEC1461 56404 splitting sing_1281.htm#SEC1357 34734 spmilnor sing_1614.htm#SEC1690 32933 spmul sing_1611.htm#SEC1687 43607 spnf sing_1162.htm#SEC1238 57309 spoly sing_2026.htm#SEC2102 35454 sppairs sing_1602.htm#SEC1678 49513 sppnf sing_1607.htm#SEC1683 16650 sppprint sing_1608.htm#SEC1684 43682 spprint sing_1163.htm#SEC1239 18671 sprintf sing_352.htm#SEC392 55889 spsemicont sing_1613.htm#SEC1689 61169 spsub sing_1610.htm#SEC1686 54296 sqfrNorm sing_1812.htm#SEC1888 20546 sqfrNormMain sing_1820.htm#SEC1896 9890 sqr sing_1938.htm#SEC2014 sprintf sqrfree sing_351.htm#SEC391 squareRoot sing_1957.htm#SEC2033 17446 squarefree sing_1638.htm#SEC1714 48485 sres sing_353.htm#SEC393 ssi Parallelization with ssi links sing_878.htm#SEC930 stabilizer sing_2312.htm#SEC2388 36692 stack, moduli space of stable maps sing_2791.htm#IDX1067 stack, moduli space of stable maps, rational curves moduliSpace sing_2790.htm#IDX1066 stackNets sing_2712.htm#SEC2788 30974 staircase sing_1829.htm#SEC1905 49781 standard sing_2033.htm#SEC2109 14067 standard bases, saturation sing_2282.htm#IDX909 standard bases. sing_2281.htm#IDX908 standard.lib sing_957.htm#IDX425 standard_lib sing_957.htm#IDX426 startNmz sing_1342.htm#SEC1418 21925 startTasks sing_1100.htm#SEC1176 16715 static procedures Procedure definition sing_43.htm#SEC78 status sing_354.htm#SEC394 std sing_355.htm#SEC395 std sing_881.htm#SEC933 std (plural) sing_482.htm#SEC522 stdfglm sing_356.htm#SEC396 256 stdhilb sing_357.htm#SEC397 63138 stdlocus sing_1002.htm#SEC1078 25619 stopTask sing_1101.htm#SEC1177 6801 storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2504.htm#SEC2580 64428 stratify sing_1763.htm#SEC1839 56744 stratify.lib sing_1761.htm#SEC1837 stratify_lib sing_1761.htm#SEC1837 string Miscellaneous oddities sing_172.htm#SEC212 string sing_420.htm#IDX297 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_1635.htm#SEC1711 19265 sturm sing_2066.htm#SEC2142 54353 sturmha sing_2068.htm#SEC2144 12467 sturmhaseq sing_2069.htm#SEC2145 59133 sturmquery sing_2044.htm#SEC2120 10805 sturmseq sing_2067.htm#SEC2143 23005 sublists sing_2406.htm#SEC2482 2979 submat sing_1121.htm#SEC1197 37665 subquotient sing_2578.htm#SEC2654 40364 subrInterred sing_1045.htm#SEC1121 10165 subset_sum01 sing_1987.htm#SEC2063 60620 subset_sum02 sing_1988.htm#SEC2064 37340 subst sing_358.htm#SEC398 subst (plural) sing_483.htm#SEC523 substitute sing_1044.htm#SEC1120 28919 sugarCrit, option sing_316.htm#IDX169 sum sing_980.htm#SEC1056 555 sum_of_powers sing_2325.htm#SEC2401 12170 sumlist sing_1477.htm#SEC1553 59918 sumofquotients sing_2799.htm#SEC2875 4569 super-commutative algebras Graded commutative algebras (SCA) sing_492.htm#SEC544 superCommutative sing_763.htm#SEC815 45528 super_increasing_knapsack super_increasing_knapsack sing_1999.htm#SEC2075 9177 surf.lib sing_1846.htm#SEC1922 surf_lib sing_1846.htm#SEC1922 surfacesignature.lib surfacesignature_lib sing_1695.htm#SEC1771 surfacesignature_lib surfacesignature_lib sing_1695.htm#SEC1771 surfer sing_1.htm#IDX8 14287 surfer sing_1848.htm#SEC1924 surfex sing_1.htm#IDX7 surfex.lib sing_1849.htm#SEC1925 surfex_lib sing_1849.htm#SEC1925 suspend sing_354.htm#SEC394 swalk sing_2807.htm#SEC2883 16794 swalk.lib sing_2806.htm#SEC2882 swalk_lib sing_2806.htm#SEC2882 swap sing_1564.htm#SEC1640 15408 swap sing_2243.htm#IDX844 switch No case or switch statement sing_414.htm#SEC454 switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2815.htm#SEC2891 1827 syModStd sing_1409.htm#SEC1485 50246 symNsym sing_2319.htm#SEC2395 55230 sym_gauss sing_1146.htm#SEC1222 5121 symm sing_2318.htm#SEC2394 64628 symmStd sing_1408.htm#SEC1484 39353 symmat sing_1122.htm#SEC1198 61294 symmetric basis sing_1138.htm#IDX512 symmetric power sing_1140.htm#IDX514 symmetric product sing_2466.htm#IDX993 symmetricBasis sing_1138.htm#SEC1214 sprintf symmetricPower sing_1140.htm#SEC1216 6542 symmetricPowerSheaf sing_2785.htm#SEC2861 56922 symmetries sing_2308.htm#IDX942 symmfunc sing_2053.htm#SEC2129 45575 symodstd.lib sing_1403.htm#SEC1479 symodstd_lib sing_1403.htm#SEC1479 symsignature sing_2043.htm#SEC2119 10520 syndrome sing_1876.htm#SEC1952 14057 sysBin sing_1874.htm#SEC1950 41948 sysCRHT sing_1871.htm#SEC1947 58930 sysCRHTMindist sing_1872.htm#SEC1948 13692 sysFL sing_1887.htm#SEC1963 53040 sysNewton sing_1873.htm#SEC1949 19704 sysQE sing_1877.htm#SEC1953 61026 sys_code sing_1868.htm#SEC1944 20220 system sing_359.htm#SEC399 system, -- sing_359.htm#IDX277 system, --long_option_name sing_359.htm#IDX280 system, --long_option_name=value sing_359.htm#IDX282 system, HC sing_359.htm#IDX215 system, LLL sing_359.htm#IDX219 system, Singular sing_359.htm#IDX258 system, SingularLib sing_359.htm#IDX260 system, absFact sing_359.htm#IDX190 system, alarm sing_359.htm#IDX189 system, blackbox sing_359.htm#IDX191 system, bracket sing_359.htm#IDX196 system, browsers sing_359.htm#IDX195 system, btest sing_359.htm#IDX198 system, complexNearZero sing_359.htm#IDX199 system, contributors sing_359.htm#IDX201 system, cpu sing_359.htm#IDX203 system, cpu sing_359.htm#IDX276 system, denom_list sing_359.htm#IDX205 system, eigenvals sing_359.htm#IDX206 system, env sing_359.htm#IDX207 system, executable sing_359.htm#IDX209 system, freegb sing_359.htm#IDX210 system, getPrecDigits sing_359.htm#IDX213 system, getenv sing_359.htm#IDX212 system, gmsnf sing_359.htm#IDX214 system, hessenberg sing_359.htm#IDX216 system, install sing_359.htm#IDX218 system, nblocks sing_359.htm#IDX222 system, nc_hilb sing_359.htm#IDX224 system, neworder sing_359.htm#IDX225 system, newstruct sing_359.htm#IDX226 system, opp sing_359.htm#IDX227 system, oppose sing_359.htm#IDX230 system, pcvBasis sing_359.htm#IDX239 system, pcvCV2P sing_359.htm#IDX237 system, pcvDim sing_359.htm#IDX238 system, pcvLAddL sing_359.htm#IDX233 system, pcvMinDeg sing_359.htm#IDX235 system, pcvP2CV sing_359.htm#IDX236 system, pcvPMulL sing_359.htm#IDX234 system, pid sing_359.htm#IDX241 system, random sing_359.htm#IDX243 system, reserve sing_359.htm#IDX247 system, reservedLink sing_359.htm#IDX248 system, semaphore sing_359.htm#IDX250 system, semic sing_359.htm#IDX251 system, setenv sing_359.htm#IDX253 system, sh sing_359.htm#IDX255 system, shrinktest sing_359.htm#IDX256 system, spadd sing_359.htm#IDX261 system, spectrum sing_359.htm#IDX262 system, spmul sing_359.htm#IDX263 system, std_syz sing_359.htm#IDX264 system, stest sing_359.htm#IDX265 system, tensorModuleMult sing_359.htm#IDX266 system, twostd sing_359.htm#IDX267 system, uname sing_359.htm#IDX270 system, version sing_359.htm#IDX273 system, with sing_359.htm#IDX274 systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2481.htm#SEC2557 63094 syz sing_360.htm#SEC400 syz (plural) sing_484.htm#SEC524 tDetropicalise sing_2221.htm#SEC2297 23532 tInitialForm sing_2205.htm#SEC2281 24484 tInitialFormPar sing_2217.htm#SEC2293 9584 tInitialFormParMax sing_2218.htm#SEC2294 7829 tInitialIdeal sing_2206.htm#SEC2282 17937 tab sing_1017.htm#SEC1093 60407 tail sing_2022.htm#SEC2098 13066 tame polynomial sing_1617.htm#IDX738 tame polynomial sing_1618.htm#IDX748 tame polynomial sing_1619.htm#IDX749 tangentGens sing_1433.htm#SEC1509 37797 tangentcone sing_1682.htm#SEC1758 20056 target sing_2585.htm#SEC2661 18743 task sing_1094.htm#IDX511 tasks.lib sing_1094.htm#SEC1170 tasks_lib sing_1094.htm#SEC1170 tau_es sing_1590.htm#SEC1666 17043 tau_es2 sing_1544.htm#SEC1620 38083 tdCf sing_2354.htm#SEC2430 21522 tdFactor sing_2356.htm#SEC2432 37910 tdProj sing_2359.htm#SEC2435 38406 tdTerms sing_2355.htm#SEC2431 30166 teachstd.lib sing_2020.htm#SEC2096 teachstd_lib sing_2020.htm#SEC2096 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_361.htm#SEC401 tensor sing_500.htm#IDX311 tensorFreeModule sing_2597.htm#SEC2673 59314 tensorFreemodMod sing_2596.htm#SEC2672 sprintf tensorMatrix sing_2593.htm#SEC2669 31437 tensorMod sing_1241.htm#SEC1317 21961 tensorModFreemod sing_2595.htm#SEC2671 11852 tensorModule sing_2594.htm#SEC2670 58772 tensorProduct sing_2598.htm#SEC2674 sprintf tensorSheaf sing_2784.htm#SEC2860 24072 term orderings General definitions for orderings sing_922.htm#SEC974 term orderings introduction Introduction to orderings sing_921.htm#SEC973 testFraction sing_2723.htm#SEC2799 28466 testLocData sing_2720.htm#SEC2796 50986 testNCfac sing_737.htm#SEC789 60394 testNcfrac sing_2681.htm#SEC2757 34186 testNcfracExamples sing_2682.htm#SEC2758 15399 testNcloc sing_2685.htm#SEC2761 62706 testNclocExamples sing_2686.htm#SEC2762 14584 testOlga sing_2737.htm#SEC2813 53953 testOlgaExamples sing_2738.htm#SEC2814 62869 testParametrization sing_1448.htm#SEC1524 18686 testPointConic sing_1449.htm#SEC1525 25315 testPrimary sing_1361.htm#SEC1437 34254 testPrimaryE sing_1362.htm#SEC1438 20693 tetrahedronGroup sing_661.htm#SEC713 16398 tex sing_1835.htm#SEC1911 12226 texDrawBasic sing_2212.htm#SEC2288 3635 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2214.htm#SEC2290 42021 texDrawTriangulation texDrawTriangulation sing_2215.htm#SEC2291 18865 texDrawTropical sing_2213.htm#SEC2289 58447 texMatrix sing_2211.htm#SEC2287 1334 texNumber sing_2209.htm#SEC2285 12628 texPolynomial sing_2210.htm#SEC2286 41136 texcoef sing_1916.htm#SEC1992 28189 texdemo sing_1836.htm#SEC1912 13008 texfactorize sing_1837.htm#SEC1913 6682 texmap sing_1838.htm#SEC1914 35265 texname sing_1839.htm#SEC1915 1008 texobj sing_1840.htm#SEC1916 2107 texpoly sing_1841.htm#SEC1917 64109 texproc sing_1842.htm#SEC1918 23626 texring sing_1843.htm#SEC1919 38275 the first alternative algorithm sing_1218.htm#IDX548 three_elements sing_2006.htm#SEC2082 513 timeFactorize sing_984.htm#SEC1060 49531 timeStd sing_983.htm#SEC1059 31506 timer sing_404.htm#SEC444 timer resolution, setting the sing_359.htm#IDX283 timestep sing_2458.htm#SEC2534 38225 tjurina sing_1678.htm#SEC1754 9100 tmatrix sing_1605.htm#SEC1681 57332 todd sing_2351.htm#SEC2427 25618 toddE sing_2352.htm#SEC2428 17823 toddPoly sing_2365.htm#SEC2441 65066 tolessvars sing_1781.htm#SEC1857 56590 topChernClass sing_2781.htm#SEC2857 17374 topological invariants sing_1532.htm#IDX640 topological invariants sing_1539.htm#IDX647 topological invariants sing_1540.htm#IDX651 topological invariants sing_1541.htm#IDX655 topological invariants sing_1542.htm#IDX659 toric ideals sing_937.htm#SEC994 toric ring sing_1320.htm#IDX581 toric.lib sing_1410.htm#SEC1486 toric_ideal sing_1411.htm#SEC1487 5760 toric_lib sing_1410.htm#SEC1486 toric_std sing_1412.htm#SEC1488 26141 torusInvariants sing_1326.htm#SEC1402 911 total divisors sing_500.htm#IDX308 total multiplicities sing_1532.htm#IDX643 totalChernClass sing_2779.htm#SEC2855 6153 totalSegreClass sing_2782.htm#SEC2858 3291 totalmultiplicities sing_1534.htm#SEC1610 58264 trace sing_362.htm#SEC402 tracemult sing_2047.htm#SEC2123 58303 transpose sing_363.htm#SEC403 trapezoid sing_2452.htm#SEC2528 61525 triMNewton sing_1807.htm#SEC1883 62822 triagmatrix sing_1058.htm#SEC1134 17944 triang.lib sing_1800.htm#SEC1876 triangL sing_1801.htm#SEC1877 51847 triangL_solve sing_1798.htm#SEC1874 10101 triangLf_solve sing_1796.htm#SEC1872 49796 triangLfak sing_1802.htm#SEC1878 50093 triangM sing_1803.htm#SEC1879 59334 triangMH sing_1804.htm#SEC1880 34277 triangM_solve sing_1797.htm#SEC1873 63652 triang_lib sing_1800.htm#SEC1876 triang_solve sing_1799.htm#SEC1875 64404 triangularGroup sing_662.htm#SEC714 23560 triangulations sing_2137.htm#SEC2213 61888 tropical curves sing_2191.htm#IDX821 tropical geometry sing_1204.htm#IDX522 tropical geometry sing_2809.htm#IDX1078 tropical mirror symmetry sing_1204.htm#IDX524 tropical polynomials sing_2191.htm#IDX822 tropical varieties sing_2809.htm#IDX1079 tropical.lib sing_2191.htm#IDX819 tropicalCurve sing_2196.htm#SEC2272 16865 tropicalJInvariant sing_2199.htm#SEC2275 40395 tropicalLifting sing_2192.htm#SEC2268 7052 tropicalLinkNewton sing_2817.htm#SEC2893 63886 tropicalNewton.lib sing_2809.htm#SEC2885 tropicalNewton_lib sing_2809.htm#SEC2885 tropicalPointNewton sing_2814.htm#SEC2890 18572 tropicalSubst sing_2224.htm#SEC2300 49846 tropicalVariety sing_2231.htm#SEC2307 39087 tropicalVarietyNewton tropicalVarietyNewton sing_2816.htm#SEC2892 28532 tropical_lib sing_2191.htm#IDX820 tropicalise sing_2203.htm#SEC2279 49739 tropicaliseSet sing_2204.htm#SEC2280 35136 truncate sing_1514.htm#SEC1590 13545 truncateFast sing_1515.htm#SEC1591 5124 truncated module sing_1514.htm#IDX631 truncated module sing_1515.htm#IDX632 tst_ncfactor sing_745.htm#SEC797 3339 twalk sing_1217.htm#SEC1293 35753 two-sided sing_500.htm#IDX309 two-sided Groebner basis sing_500.htm#IDX310 twostd sing_359.htm#IDX268 twostd sing_485.htm#SEC525 type sing_364.htm#SEC404 type B sing_2259.htm#IDX871 type D sing_2260.htm#IDX873 type,custom Definition of a user defined type sing_184.htm#SEC224 type2arr sing_2237.htm#SEC2313 62624 typecasting sing_2237.htm#IDX827 typecasting sing_2238.htm#IDX829 typecasting sing_2239.htm#IDX832 typeof sing_365.htm#SEC405 u sing_2444.htm#SEC2520 12154 uname sing_359.htm#IDX269 unbounded_knapsack sing_1989.htm#SEC2065 17226 unipotent groups sing_1432.htm#IDX599 uniquePoint sing_2116.htm#SEC2192 893 unitMatrix sing_2751.htm#SEC2827 33014 unitmat sing_1123.htm#SEC1199 12862 univariate sing_366.htm#SEC406 univarpoly sing_2054.htm#SEC2130 46288 unknown syndrome Decoding method based on quadratic equations sing_953.htm#SEC1024 unset sing_277.htm#SEC317 untyped definitions sing_88.htm#SEC128 untyped definitions sing_425.htm#SEC465 updatePairs sing_2032.htm#SEC2108 51144 ures_solve sing_1790.htm#SEC1866 32449 uressolve sing_367.htm#SEC407 usage, option sing_316.htm#IDX185 user interface, Emacs Emacs user interface sing_21.htm#SEC28 vStd sing_2398.htm#SEC2474 12321 val sing_2811.htm#SEC2887 62171 valvars sing_1785.htm#SEC1861 15723 vandermonde sing_368.htm#SEC408 vanishId sing_1886.htm#SEC1962 49148 var sing_369.htm#SEC409 varMat sing_2241.htm#SEC2317 51772 varNum sing_2242.htm#SEC2318 18485 variables sing_370.htm#SEC410 variables sing_2241.htm#IDX839 variables sing_2242.htm#IDX841 variables sing_2243.htm#IDX845 variables sing_2244.htm#IDX847 variablesSorted sing_538.htm#SEC590 13533 variablesStandard sing_537.htm#SEC589 56500 vars2pars sing_858.htm#SEC910 47343 varsigns sing_2059.htm#SEC2135 3471 varstr sing_371.htm#SEC411 vct2str sing_685.htm#SEC737 51983 vdim sing_372.htm#SEC412 vdim (plural) sing_486.htm#SEC526 vec2poly sing_520.htm#SEC572 27377 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_2050.htm#SEC2126 32271 versal sing_1585.htm#SEC1661 46247 version sing_359.htm#IDX272 vertexAdjacencyGraph vertexAdjacencyGraph sing_2184.htm#SEC2260 60102 vertexEdgeGraph sing_2185.htm#SEC2261 32816 vertices sing_2132.htm#SEC2208 11398 vfilt sing_1603.htm#SEC1679 9283 view sing_1906.htm#SEC1982 29284 visual sing_2186.htm#SEC2262 51434 visualize sing_2443.htm#SEC2519 6750 voice sing_407.htm#SEC447 vwfilt sing_1604.htm#SEC1680 8281 wUnit sing_1944.htm#SEC2020 27198 waitAllTasks sing_1103.htm#SEC1179 7087 waitTasks sing_1102.htm#SEC1178 52857 waitall sing_373.htm#SEC413 waitfirst sing_374.htm#SEC414 walk, groebner sing_1215.htm#IDX544 walk, groebner sing_2609.htm#IDX1001 walk, groebner sing_2763.htm#IDX1047 walk, groebner sing_2806.htm#IDX1076 warkedPreimageStd sing_2483.htm#SEC2559 14759 warn, option sing_70.htm#SEC110 warn, option sing_316.htm#IDX151 watchdog sing_981.htm#SEC1057 sprintf wedge sing_375.htm#SEC415 weierstr.lib sing_2035.htm#SEC2111 weierstrDiv sing_2036.htm#SEC2112 260 weierstrPrep sing_2037.htm#SEC2113 5752 weierstr_lib sing_2035.htm#SEC2111 weierstrassForm sing_2200.htm#SEC2276 60874 weight sing_376.htm#SEC416 weight filtration sing_1595.htm#IDX671 weight filtration sing_1602.htm#IDX705 weight filtration sing_1604.htm#IDX719 weight filtration sing_1605.htm#IDX727 weight filtration sing_1617.htm#IDX743 weight filtration sing_1619.htm#IDX754 weightKB sing_377.htm#SEC417 21753 weightM, option sing_316.htm#IDX170 weighted lexicographical ordering sing_923.htm#IDX405 weighted reverse lexicographical ordering Global orderings sing_923.htm#IDX403 weightedRing sing_756.htm#SEC808 33786 whichvariable sing_2058.htm#SEC2134 27122 while sing_394.htm#SEC434 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_923.htm#IDX404 write sing_378.htm#SEC418 writeNmzData sing_1337.htm#SEC1413 38467 writeNmzPaths sing_1341.htm#SEC1417 sprintf ws, local ordering sing_924.htm#IDX415 wurzel sing_1926.htm#SEC2002 12755 xchange sing_1920.htm#SEC1996 40741 xdvi sing_1845.htm#SEC1921 16898 zdd sing_2288.htm#IDX920 zdd2poly sing_2305.htm#SEC2381 55047 zero sing_2558.htm#SEC2634 12060 zero-dimensional sing_2055.htm#IDX810 zeroMod sing_1277.htm#SEC1353 60609 zeroNcfrac sing_2674.htm#SEC2750 50840 zeroOpt sing_1286.htm#SEC1362 19260 zeroRadical sing_1186.htm#SEC1262 35598 zeroSet sing_1813.htm#SEC1889 60030 zerodec sing_1370.htm#SEC1446 30765 zeroset.lib sing_1808.htm#SEC1884 zeroset_lib sing_1808.htm#SEC1884 zetaDL sing_1507.htm#SEC1583 sprintf { sing_36.htm#IDX78 || sing_36.htm#IDX103 || sing_101.htm#SEC141 } sing_36.htm#IDX79 ~ sing_36.htm#IDX117 ~ sing_395.htm#SEC435