<1>: intvec expressions ! Special characters sing_36.htm#IDX171 != boolean expressions sing_36.htm#IDX165 != sing_86.htm#SEC127 " Special characters sing_36.htm#IDX174 # Special characters sing_36.htm#IDX187 $ Special characters sing_36.htm#IDX188 % intvec expressions sing_36.htm#IDX161 % sing_84.htm#SEC125 % sing_96.htm#SEC137 && boolean operations sing_36.htm#IDX172 && sing_87.htm#SEC128 ( Special characters sing_36.htm#IDX150 ) Special characters sing_36.htm#IDX151 * intvec expressions sing_36.htm#IDX159 * sing_72.htm#SEC113 * sing_79.htm#SEC120 * sing_84.htm#SEC125 * sing_92.htm#SEC133 * sing_96.htm#SEC137 ** Special characters sing_36.htm#IDX163 + intvec expressions sing_36.htm#IDX155 + sing_72.htm#SEC113 + sing_79.htm#SEC120 + sing_84.htm#SEC125 + sing_92.htm#SEC133 + sing_96.htm#SEC137 ++ Special characters sing_36.htm#IDX156 - intvec expressions sing_36.htm#IDX157 - sing_72.htm#SEC113 - sing_84.htm#SEC125 - sing_92.htm#SEC133 - sing_96.htm#SEC137 -- sing_36.htm#IDX158 --MPhost sing_19.htm#IDX136 --MPport sing_19.htm#IDX135 --allow-net sing_19.htm#IDX109 --batch sing_19.htm#IDX134 --browser sing_19.htm#IDX113 --echo sing_19.htm#IDX105 --emacs sing_19.htm#IDX137 --emacs-dir sing_19.htm#IDX138 --emacs-load sing_19.htm#IDX139 --execute sing_19.htm#IDX126 --help sing_19.htm#IDX107 --min-time sing_19.htm#IDX131 --no-out sing_19.htm#IDX119 --no-rc sing_19.htm#IDX115 --no-stdlib sing_19.htm#IDX117 --no-tty sing_19.htm#IDX120 --no-warn sing_19.htm#IDX118 --quiet sing_19.htm#IDX122 --random sing_19.htm#IDX130 --sdb sing_19.htm#IDX102 --singular sing_19.htm#IDX140 --ticks-per-sec sing_19.htm#IDX132 --user-option sing_19.htm#IDX128 --verbose sing_19.htm#IDX123 -MPhost Command line options -MPport Command line options -allow-net Command line options -b Command line options sing_19.htm#IDX133 -batch Command line options -browser Command line options -c Command line options sing_19.htm#IDX125 -d Command line options sing_19.htm#IDX101 -e Command line options sing_19.htm#IDX104 -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#IDX106 -help Command line options -min-time Command line options -no-out Command line options -no-rc 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#IDX121 -quiet Command line options -r Command line options sing_19.htm#IDX129 -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#IDX127 -user-option Command line options -v Command line options sing_19.htm#IDX124 -verbose Command line options .. Special characters sing_36.htm#IDX182 .singularrc file Startup sequence sing_20.htm#IDX142 .singularrc file, no loading Command line options sing_19.htm#IDX116 / intvec expressions sing_36.htm#IDX160 / sing_72.htm#SEC113 / sing_84.htm#SEC125 / sing_96.htm#SEC137 // Special characters sing_36.htm#IDX177 // sing_36.htm#IDX178 // sing_36.htm#IDX179 : Special characters sing_36.htm#IDX183 : sing_96.htm#SEC137 :: Special characters sing_36.htm#IDX184 :: sing_134.htm#SEC175 ; Special characters sing_36.htm#IDX180 < filecmd sing_36.htm#IDX170 < sing_200.htm#SEC241 <= boolean expressions sing_36.htm#IDX169 <= sing_86.htm#SEC127 <> boolean expressions sing_36.htm#IDX166 <> sing_86.htm#SEC127 = Special characters sing_36.htm#IDX147 == boolean expressions sing_36.htm#IDX164 == sing_86.htm#SEC127 > Special characters sing_36.htm#IDX168 >= boolean expressions sing_36.htm#IDX167 >= sing_86.htm#SEC127 ? help sing_36.htm#IDX176 ? sing_210.htm#IDX205 AG codes AG codes sing_646.htm#SEC699 AGcode_L AGcode_L sing_1344.htm#SEC1421 60329 AGcode_Omega AGcode_Omega sing_1345.htm#SEC1422 56285 ASCII ASCII sing_695.htm#SEC772 26816 ASCII links ASCII links sing_103.htm#SEC144 A_L A_L sing_1065.htm#SEC1142 16721 A_Z A_Z sing_694.htm#SEC771 50866 Adj_div Adj_div sing_1339.htm#SEC1416 44919 Alexander polynomial alexpoly_lib sing_1036.htm#IDX398 Algebraic Geometry codes brnoeth_lib sing_1338.htm#IDX503 Algebraic dependence Algebraic dependence sing_627.htm#SEC680 AltVarEnd AltVarEnd sing_589.htm#SEC642 47763 AltVarStart AltVarStart sing_588.htm#SEC641 22648 Andres, Daniel Preface sing_1.htm#IDX36 Ann Ann sing_965.htm#SEC1042 61560 Applications Applications sing_644.htm#SEC697 ArnoldAction ArnoldAction sing_1144.htm#SEC1221 26958 Atkin Atkin sing_1417.htm#SEC1494 sprintf Authors Preface sing_1.htm#IDX11 Bachmann, Olaf Preface sing_1.htm#IDX23 Background Background sing_3.htm#SEC5 Basic programming Basic programming sing_602.htm#SEC655 Basic programming sing_602.htm#SEC655 Bayer, Thomas Preface sing_1.htm#IDX37 Becker, Markus Preface sing_1.htm#IDX39 BelongSemig BelongSemig sing_870.htm#SEC947 22405 Bermejo, Isabelle Preface sing_1.htm#IDX38 Bernstein polynomial bernstein sing_1089.htm#IDX431 Betti number Syzygies and resolutions sing_661.htm#SEC719 Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_671.htm#SEC729 BinDir Loading a library sing_48.htm#SEC86 BlowingUp BlowingUp sing_1070.htm#SEC1147 49897 Branches of space curve singularities Branches of space curve singularities sing_635.htm#SEC688 Brickenstein, Michael Preface sing_1.htm#IDX15 Brieskorn lattice mondromy_lib sing_1085.htm#IDX421 Brieskorn lattice sing_1086.htm#IDX430 Brieskorn lattice sing_1107.htm#IDX454 Brieskorn lattice sing_1109.htm#IDX465 Brieskorn lattice sing_1137.htm#IDX492 Brill-Noether algorithm brnoeth_lib sing_1338.htm#IDX504 BrillNoether BrillNoether sing_1341.htm#SEC1418 39919 Buchberger algorithm for toric ideals Buchberger algorithm sing_672.htm#SEC730 Bulygin, Stanislav Preface sing_1.htm#IDX40 C programming language Major differences to the C programming language sing_345.htm#SEC386 C, module ordering Module orderings sing_654.htm#IDX348 CGS, disjoint, reduced, comprehensive Groebner system buildtree sing_770.htm#IDX362 CM_regularity CM_regularity sing_1021.htm#SEC1098 33865 CMtype CMtype sing_1175.htm#SEC1252 24849 CRHT-ideal Cooper philosophy sing_678.htm#SEC743 Castelnuovo-Mumford regularity CM_regularity sing_1021.htm#IDX392 CenCharDec CenCharDec sing_568.htm#SEC621 44505 Center Center sing_994.htm#SEC1071 25541 CenterBO CenterBO sing_1001.htm#SEC1078 34701 CentralQuot CentralQuot sing_566.htm#SEC619 49392 CentralSaturation CentralSaturation sing_567.htm#SEC620 31585 Change of rings Change of rings sing_9.htm#SEC15 Characteristic sets Characteristic sets sing_662.htm#SEC720 Classification of hypersurface singularities Classification of hypersurface singularities sing_636.htm#SEC689 Code Codes and the decoding problem sing_677.htm#SEC736 Codes and the decoding problem Codes and the decoding problem sing_677.htm#SEC735 Coding theory Coding theory sing_1337.htm#SEC1414 Command line options Command line options sing_19.htm#SEC26 Commands Functions and system variables sing_165.htm#SEC206 Commutative Algebra Commutative Algebra sing_615.htm#SEC668 Commutative algebra Commutative algebra sing_853.htm#SEC930 CompInt CompInt sing_872.htm#SEC949 7518 Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_611.htm#SEC664 Conti-Traverso algorithm Conti and Traverso sing_667.htm#SEC725 Contributed libraries Contributed sing_1575.htm#SEC1652 Contributors Preface sing_1.htm#IDX10 Control structures Control structures sing_314.htm#SEC355 Control theory System and Control theory sing_1371.htm#SEC1448 Cooper philosophy Cooper philosophy sing_678.htm#SEC741 Cornacchia Cornacchia sing_1407.htm#SEC1484 63434 CornacchiaModified CornacchiaModified sing_1408.htm#SEC1485 59790 Cremer, Nadine Preface sing_1.htm#IDX41 Critical points Critical points sing_630.htm#SEC683 Cuntz, Michael Preface sing_1.htm#IDX42 CurveParam CurveParam sing_1072.htm#SEC1149 38213 CurveRes CurveRes sing_1071.htm#SEC1148 16352 Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC35 Cyclic code decodegb_lib sing_1352.htm#IDX511 Cyclic roots Cyclic roots sing_608.htm#SEC661 DBM links DBM links sing_107.htm#SEC148 DISPLAY environment variable The online help system sing_16.htm#IDX98 DLoc DLoc sing_501.htm#SEC554 38935 DLoc0 DLoc0 sing_503.htm#SEC556 55563 Data types Data types sing_68.htm#SEC109 Data types (plural) Data types (plural) sing_358.htm#IDX288 Debugging tools Debugging tools sing_61.htm#SEC99 Decker, Wolfram Preface sing_1.htm#IDX16 Decoding decodegb_lib sing_1352.htm#IDX513 Decoding codes with Groebner bases Decoding codes with Groebner bases sing_676.htm#SEC734 Decoding method based on quadratic equations Decoding method based on quadratic equations sing_681.htm#SEC752 DefaultDir Loading a library sing_48.htm#SEC86 Deformations Deformations sing_633.htm#SEC686 Deformations, T1 and T2 T1 and T2 sing_632.htm#SEC685 Dehmann, Kai Preface sing_1.htm#IDX43 Delta Delta sing_1002.htm#SEC1079 33497 DeltaList DeltaList sing_1003.htm#SEC1080 65148 Demo mode Demo mode sing_24.htm#SEC34 Depth Depth sing_622.htm#SEC675 Di Biase-Urbanke algorithm Di Biase and Urbanke sing_670.htm#SEC728 Documentation of a library Documentation of a library sing_52.htm#SEC90 Dp, global ordering Global orderings sing_652.htm#IDX331 Dreyer, Alexander Preface sing_1.htm#IDX17 Ds, local ordering Local orderings sing_653.htm#IDX341 Dumnicki, Marcin Preface sing_1.htm#IDX44 Dynamic loading Dynamic loading sing_67.htm#SEC108 Dynamic modules Dynamic modules sing_610.htm#SEC663 ECPP ECPP sing_1453.htm#SEC1530 55777 ERROR ERROR sing_191.htm#SEC232 ESingular, no prompt Unix installation instructions sing_1584.htm#IDX535 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC36 Editing input Editing input sing_18.htm#SEC25 Elimination Elimination sing_618.htm#SEC671 Emacs Emacs user interface sing_21.htm#SEC28 Emacs, Singular demo mode Demo mode sing_24.htm#SEC34 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#SEC35 Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC36 Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC37 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 Endrass, Stephan Preface sing_1.htm#IDX45 Evaluation of logical expressions Evaluation of logical expressions sing_347.htm#SEC388 Examples Examples sing_600.htm#SEC653 Examples of ring declarations Examples of ring declarations sing_29.htm#SEC39 Ext Ext sing_895.htm#SEC972 21909 Ext, computation of Computation of Ext sing_621.htm#SEC674 Ext_R Ext_R sing_894.htm#SEC971 53310 Exterior Exterior sing_577.htm#SEC630 23593 Extra weight vector Extra weight vector sing_657.htm#SEC710 Factorization Factorization sing_623.htm#SEC676 Farran, Jose Ignacio Preface sing_1.htm#IDX46 Finite fields Finite fields sing_617.htm#SEC670 First steps First steps sing_6.htm#SEC12 Fitzgerald-Lax method Fitzgerald-Lax method sing_680.htm#SEC749 Flow control Flow control sing_40.htm#SEC69 Format of a library Format of a library sing_49.htm#SEC87 Formatting output Formatting output sing_607.htm#SEC660 Fr@"uhbis-Kr@"uger, Anne sing_1.htm#IDX18 Free resolution Free resolution sing_619.htm#SEC672 Free resolution, graded Handling graded modules sing_620.htm#SEC673 Fru"hbis-Kru"ger, Anne Preface Functions Functions sing_166.htm#SEC207 G-algebra G-algebras sing_420.htm#SEC461 G-algebra sing_420.htm#SEC463 G-algebra, setup G-algebras sing_420.htm#SEC465 GKZsystem GKZsystem sing_564.htm#SEC617 791 GKdim GKdim sing_537.htm#SEC590 9814 GMP Preface sing_1.htm#IDX3 GTZmod GTZmod sing_924.htm#SEC1001 30091 GTZopt GTZopt sing_931.htm#SEC1008 14642 G_a -Invariants G_a -Invariants sing_639.htm#SEC692 Garcia-Marco, I. Preface sing_1.htm#IDX47 Gauss-Manin connection spectrumnd sing_663.htm#SEC721 Gauss-Manin connection sing_1137.htm#IDX491 Gauss-Manin connection sing_1184.htm#IDX494 Gauss-Manin system goodBasis sing_1085.htm#IDX420 Gauss-Manin system sing_1086.htm#IDX429 Gauss-Manin system sing_1107.htm#IDX453 Gauss-Manin system sing_1109.htm#IDX464 General command syntax General command syntax sing_35.htm#SEC58 General concepts General concepts sing_12.htm#SEC18 General purpose General purpose sing_688.htm#SEC765 General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC40 Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_422.htm#SEC473 Generalized Newton identities Generalized Newton identities sing_679.htm#SEC746 Gerdt, Vladimir Preface sing_1.htm#IDX48 German Umlaute Limitations sing_343.htm#IDX275 Getting started Getting started sing_5.htm#SEC11 Gimenez, Philippe Preface sing_1.htm#IDX49 Global orderings Global orderings sing_652.htm#SEC705 Gorzel, Christian Preface sing_1.htm#IDX50 Grassmann, Hubert Preface sing_1.htm#IDX51 Greuel, Gert-Martin Preface sing_1.htm#IDX12 Groebner Bases Computing Groebner and Standard Bases sing_611.htm#SEC664 Groebner bases decodegb_lib sing_1352.htm#IDX515 Groebner bases in G-algebras Groebner bases in G-algebras sing_421.htm#SEC466 Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_427.htm#SEC480 Groebner bases, slim slim Groebner bases sing_614.htm#SEC667 Groebner basis conversion Groebner basis conversion sing_613.htm#SEC666 Groebner fan polymake_lib sing_1521.htm#IDX527 Groebner walk gwalk sing_887.htm#IDX378 Groebner walk sing_889.htm#IDX380 Guidelines for writing a library Guidelines for writing a library sing_50.htm#SEC88 Gweights Gweights sing_571.htm#SEC624 651 H2basis H2basis sing_1142.htm#SEC1219 3414 Hamburger-Noether expansion hnoether_lib sing_1036.htm#IDX394 Hamburger-Noether expansion sing_1110.htm#IDX473 Hamburger-Noether expansions Adj_div sing_1339.htm#IDX505 Handling graded modules Handling graded modules sing_620.htm#SEC673 Hashemi, Amir Preface sing_1.htm#IDX52 Hcode Hcode sing_1058.htm#SEC1135 26628 Hernando, Fernando Preface sing_1.htm#IDX53 Heydtmann, Agnes Preface sing_1.htm#IDX54 Hilbert function Hilbert function sing_295.htm#IDX237 Hilbert function sing_660.htm#SEC715 Hilbert series Hilbert function sing_660.htm#SEC715 Hilbert-driven GB algorithm Groebner basis conversion sing_613.htm#SEC666 HilbertClassPoly HilbertClassPoly sing_1414.htm#SEC1491 sprintf HilbertSeries HilbertSeries sing_1233.htm#SEC1310 21249 HilbertWeights HilbertWeights sing_1234.htm#SEC1311 sprintf Hillebrand, Dietmar Preface sing_1.htm#IDX55 Hirsch, Tobias Preface sing_1.htm#IDX56 Hochstetter, Markus Preface sing_1.htm#IDX57 Hom Hom sing_898.htm#SEC975 61434 HomJJ HomJJ sing_952.htm#SEC1029 1525 Hosten-Sturmfels algorithm Hosten and Sturmfels sing_669.htm#SEC727 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 Hypersurface singularities, classification of Classification of hypersurface singularities sing_636.htm#SEC689 IN lead sing_231.htm#IDX206 Ideal membership Standard bases sing_659.htm#IDX353 Identifiers, syntax of Names sing_37.htm#SEC64 Iena, Oleksandr Preface sing_1.htm#IDX58 ImageGroup ImageGroup sing_1236.htm#SEC1313 28808 ImageVariety ImageVariety sing_1235.htm#SEC1312 15252 Imap, option option sing_259.htm#IDX226 Implemented algorithms Implemented algorithms sing_33.htm#SEC46 Index Index sing_1587.htm#SEC1690 InterDiv InterDiv sing_1326.htm#SEC1403 45354 Interactive use Interactive use sing_13.htm#SEC19 Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24 IntersectWithSub IntersectWithSub sing_569.htm#SEC622 19793 Introduction Introduction sing_2.htm#SEC4 Invariant Theory Invariant Theory sing_638.htm#SEC691 Invariant theory Invariant theory sing_1185.htm#SEC1262 InvariantQ InvariantQ sing_1238.htm#SEC1315 53256 InvariantRing InvariantRing sing_1237.htm#SEC1314 22928 Invariants of a finite group Invariants of a finite group sing_640.htm#SEC693 Invariants of plane curve singularities Invariants of plane curve singularities sing_634.htm#SEC687 IsSCA IsSCA sing_590.htm#SEC643 21962 Jacobi Jacobi sing_1426.htm#SEC1503 29843 KScoef KScoef sing_1135.htm#SEC1212 sprintf KSconvert KSconvert sing_1133.htm#SEC1210 3585 KSker KSker sing_1132.htm#SEC1209 40166 KSlinear KSlinear sing_1134.htm#SEC1211 19896 KSpencerKernel KSpencerKernel sing_1182.htm#SEC1259 12490 Kauers, Manuel Preface sing_1.htm#IDX59 Kernel of module homomorphisms Kernel of module homomorphisms sing_626.htm#SEC679 King, Simon Preface sing_1.htm#IDX60 KoszulHomology KoszulHomology sing_907.htm#SEC984 sprintf Kr@"uger, Kai sing_1.htm#IDX24 Kru"ger, Kai Preface LETTERPLACE LETTERPLACE sing_425.htm#SEC478 LIB LIB sing_235.htm#SEC276 LIBs SINGULAR libraries sing_684.htm#SEC761 LLL LLL sing_913.htm#SEC990 32748 Lakhal, Anen Preface sing_1.htm#IDX61 Lamm, Martin Preface sing_1.htm#IDX62 Laplagne, Santiago Preface sing_1.htm#IDX63 Lecerf, Gregoire Preface sing_1.htm#IDX64 Left and two-sided Groebner bases Left and two-sided Groebner bases sing_642.htm#SEC695 Left ideal membership Groebner bases in G-algebras sing_421.htm#SEC469 Left normal form Groebner bases in G-algebras sing_421.htm#SEC468 LengthSym LengthSym sing_599.htm#SEC652 16591 LengthSymElement LengthSymElement sing_598.htm#SEC651 28292 Letterplace LETTERPLACE sing_425.htm#SEC478 Levandovskyy, Viktor Preface sing_1.htm#IDX19 Lexicographic Groebner bases, computation of Groebner basis conversion sing_613.htm#SEC666 Libraries Writing procedures and libraries sing_47.htm#SEC85 Libraries sing_603.htm#SEC656 Limitations Limitations sing_343.htm#SEC384 Linear algebra Linear algebra sing_793.htm#SEC870 Linear code decodegb_lib sing_1352.htm#IDX512 LinearActionQ LinearActionQ sing_1240.htm#SEC1317 62218 LinearCombinationQ LinearCombinationQ sing_1241.htm#SEC1318 59373 LinearizeAction LinearizeAction sing_1239.htm#SEC1316 60266 Loading a library Loading a library sing_48.htm#SEC86 Lobillo, Javier Preface sing_1.htm#IDX65 Local orderings Local orderings sing_653.htm#SEC706 Long coefficients Long coefficients sing_605.htm#SEC658 Lossen, Christoph Preface sing_1.htm#IDX25 M, ordering Matrix orderings sing_655.htm#SEC708 MP Preface sing_1.htm#IDX4 MP links MP links sing_104.htm#SEC145 MP, groebner basis computations groebner sing_209.htm#IDX204 MPfile links MPfile links sing_105.htm#SEC146 MPtcp Parallelization with MPtcp links sing_609.htm#SEC662 MPtcp links MPtcp links sing_106.htm#SEC147 Macintosh installation Macintosh installation instructions sing_1586.htm#SEC1689 Mang, Christoph Preface sing_1.htm#IDX66 Markwig, Thomas Preface sing_1.htm#IDX67 Martin, Bernd Preface sing_1.htm#IDX68 Mathematical background Mathematical background sing_658.htm#SEC711 Mathematical background (plural) Mathematical background (plural) sing_419.htm#SEC460 Matrix orderings Matrix orderings sing_655.htm#SEC708 Max Max sing_1151.htm#SEC1228 22 Messollen, Michael Preface sing_1.htm#IDX69 MillerRabin MillerRabin sing_1436.htm#SEC1513 15740 Milnor number Milnor and Tjurina number sing_629.htm#SEC682 Min Min sing_1152.htm#SEC1229 29622 MinMult MinMult sing_871.htm#SEC948 39835 Mindnich, Andrea Preface sing_1.htm#IDX70 MinimalDecomposition MinimalDecomposition sing_1242.htm#SEC1319 24161 Minimum distance decodegb_lib sing_1352.htm#IDX514 ModEqn ModEqn sing_1145.htm#SEC1222 59394 Module orderings Module orderings sing_654.htm#SEC707 Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16 Monodromy mondromy_lib sing_1137.htm#IDX489 Monomial orderings Monomial orderings sing_649.htm#SEC702 Monomial orderings, Term orderings Term orderings sing_31.htm#SEC43 Morales, Jorge Martin Preface sing_1.htm#IDX71 Motsak, Oleksandr Preface sing_1.htm#IDX20 N@"ussler, Thomas sing_1.htm#IDX72 NF reduce (plural) sing_275.htm#SEC316 NF sing_411.htm#SEC452 NFMora NFMora sing_1475.htm#SEC1552 40670 NPos NPos sing_944.htm#SEC1021 15702 NPos_test NPos_test sing_942.htm#SEC1019 48172 NSplaces NSplaces sing_1340.htm#SEC1417 48675 NTL Preface sing_1.htm#IDX5 Names Names sing_37.htm#SEC64 Names in procedures Names in procedures sing_44.htm#SEC82 Names, indexed Names sing_37.htm#SEC64 Neumann, Wolfgang Preface sing_1.htm#IDX26 Newton non-degenerate is_NND sing_1124.htm#IDX487 Newton polygon is_NND sing_1123.htm#IDX486 Newton polygon sing_1124.htm#IDX488 Newton polytope polymake_lib sing_1521.htm#IDX526 NoetherPosition NoetherPosition sing_938.htm#SEC1015 18735 Non-commutative LIBs Non-commutative libraries sing_431.htm#SEC484 Non-commutative algebra Non-commutative algebra sing_641.htm#SEC694 Non-commutative algebra sing_675.htm#SEC733 Non-commutative libraries Non-commutative libraries sing_431.htm#SEC484 Non-commutative subsystem Non-commutative subsystem sing_356.htm#SEC397 Normal form Standard bases sing_659.htm#IDX352 Normalization Normalization sing_625.htm#SEC678 Nu"ssler, Thomas Preface NullCone NullCone sing_1243.htm#SEC1320 64635 Objects Objects sing_38.htm#SEC65 Output, formatting of Formatting output sing_607.htm#SEC660 PBW central_lib sing_446.htm#IDX301 PBW basis G-algebras sing_420.htm#SEC462 PBW_eqDeg PBW_eqDeg sing_464.htm#SEC517 23181 PBW_maxDeg PBW_maxDeg sing_465.htm#SEC518 59566 PBW_maxMonom PBW_maxMonom sing_466.htm#SEC519 1155 PH_ais PH_ais sing_1579.htm#SEC1656 49473 PH_nais PH_nais sing_1580.htm#SEC1657 46271 PLURAL PLURAL sing_357.htm#SEC398 PLURAL LIBs Non-commutative libraries sing_431.htm#SEC484 Parallelization Parallelization with MPtcp links sing_609.htm#SEC662 Parameter list Parameter list sing_45.htm#SEC83 Parameters Parameters sing_606.htm#SEC659 PerfectPowerTest PerfectPowerTest sing_1397.htm#SEC1474 17450 Perling, Markus Preface sing_1.htm#IDX27 Perturbation walk pwalk sing_888.htm#IDX379 Pfister, Gerhard Preface sing_1.htm#IDX13 PocklingtonLehmer PocklingtonLehmer sing_1438.htm#SEC1515 13634 Pohl, Wilfred Preface sing_1.htm#IDX28 Polar curves Polar curves sing_631.htm#SEC684 PollardRho PollardRho sing_1439.htm#SEC1516 38835 Polynomial data Polynomial data sing_647.htm#SEC700 Pottier algorithm Pottier sing_668.htm#SEC726 Povalyaeva, Tetyana Preface sing_1.htm#IDX73 Preface Preface sing_1.htm#SEC1 Primary decomposition Primary decomposition sing_624.htm#SEC677 PrimdecA PrimdecA sing_920.htm#SEC997 248 PrimdecB PrimdecB sing_921.htm#SEC998 9653 Procedure commands Procedure commands sing_46.htm#SEC84 Procedure definition Procedure definition sing_43.htm#SEC78 Procedures Procedures sing_42.htm#SEC77 Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14 Procedures and libraries sing_603.htm#SEC656 Procedures in a library Procedures in a library sing_51.htm#SEC89 Product orderings Product orderings sing_656.htm#SEC709 Programming Programming sing_601.htm#SEC654 Puiseux expansion hnoether_lib sing_1036.htm#IDX395 Puiseux expansion sing_1110.htm#IDX474 Puiseux pairs invariants sing_634.htm#SEC687 Puiseux pairs sing_1116.htm#IDX479 Qso3Casimir Qso3Casimir sing_563.htm#SEC616 40212 Quotient Quotient sing_1288.htm#SEC1365 10390 QuotientEquations QuotientEquations sing_1146.htm#SEC1223 18230 Rabelo, Carlos Preface sing_1.htm#IDX74 ReesAlgebra ReesAlgebra sing_989.htm#SEC1066 59951 References References sing_683.htm#SEC758 References (plural) References (plural) sing_423.htm#SEC474 Release Notes Release Notes sing_1581.htm#SEC1658 ResTree ResTree sing_1327.htm#SEC1404 55897 Resolution Resolution sing_11.htm#SEC17 Resolution of singularities Resolution of singularities sing_637.htm#SEC690 Resolution, free Free resolution sing_619.htm#SEC672 ReynoldsImage ReynoldsImage sing_1244.htm#SEC1321 35172 ReynoldsOperator ReynoldsOperator sing_1245.htm#SEC1322 14986 Right Groebner bases and syzygies Right Groebner bases and syzygies sing_643.htm#SEC696 Rings and orderings Rings and orderings sing_28.htm#SEC38 Rings and standard bases Rings and standard bases sing_7.htm#SEC13 RootDir Loading a library sing_48.htm#SEC86 Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 SCA, Super-commutative algebras, Z_2-graded algebras Super-commutative algebras sing_424.htm#SEC477 SDB breakpoint Source code debugger sing_63.htm#SEC104 SDB debugger Source code debugger sing_63.htm#SEC104 SDLoc SDLoc sing_502.htm#SEC555 41981 SINGULAR libraries SINGULAR libraries sing_684.htm#SEC761 SINGULARHIST Editing input sing_18.htm#SEC25 SINGULARPATH Loading a library sing_48.htm#SEC86 SV-decoding algorithm decodeSV sing_1347.htm#IDX508 SV-decoding algorithm, preprocessing prepSV sing_1346.htm#IDX507 Salazar-Gonzalez, J.-J. Preface sing_1.htm#IDX75 Sanchez-Navarro, Alfredo Preface sing_1.htm#IDX76 Sannfs Sannfs sing_470.htm#SEC523 37497 SannfsBFCT SannfsBFCT sing_482.htm#SEC535 19127 SannfsBM SannfsBM sing_481.htm#SEC534 60484 SannfsLOT SannfsLOT sing_483.htm#SEC536 24161 SannfsOT SannfsOT sing_484.htm#SEC537 60244 Sannfslog Sannfslog sing_471.htm#SEC524 35542 Saturation Saturation sing_616.htm#SEC669 Saynisch, Ivor Preface sing_1.htm#IDX77 Sch@"onemann, Hans sing_1.htm#IDX14 Schindelar, Kristina Preface sing_1.htm#IDX78 Schmidt, Jens Preface sing_1.htm#IDX29 Scho"nemann, Hans Preface Schoof Schoof sing_1450.htm#SEC1527 49281 Schulze, Mathias Preface sing_1.htm#IDX21 Schulze, Mathias sing_1.htm#IDX30 SearchPath Loading a library sing_48.htm#SEC86 Seelisch, Frank Preface sing_1.htm#IDX22 Setting up a G-algebra G-algebras sing_420.htm#SEC465 ShanksMestre ShanksMestre sing_1449.htm#SEC1526 12973 Siebert, Thomas Preface sing_1.htm#IDX31 SimplifyIdeal SimplifyIdeal sing_1246.htm#SEC1323 sprintf Singular system sing_297.htm#IDX258 Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC35 Singular, demo mode Demo mode sing_24.htm#SEC34 Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC36 Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC37 Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30 SingularLib system sing_297.htm#IDX260 Singularities Singularities sing_1035.htm#SEC1112 Singularity Theory Singularity Theory sing_628.htm#SEC681 SolowayStrassen SolowayStrassen sing_1437.htm#SEC1514 22680 Solving systems of polynomial equations Solving systems of polynomial equations sing_645.htm#SEC698 Source code debugger, invocation Command line options sing_19.htm#IDX103 Space curve singularities, branches of Branches of space curve singularities sing_635.htm#SEC688 Spang, Silke Preface sing_1.htm#IDX79 Special characters Special characters sing_36.htm#SEC63 StabEqn StabEqn sing_1147.htm#SEC1224 28539 StabEqnId StabEqnId sing_1148.htm#SEC1225 27955 StabOrder StabOrder sing_1149.htm#SEC1226 55603 Standard Bases Computing Groebner and Standard Bases sing_611.htm#SEC664 Standard bases Standard bases sing_659.htm#SEC712 Startup sequence Startup sequence sing_20.htm#SEC27 Steidel, Stefan Preface sing_1.htm#IDX80 Stobbe, R@"udiger sing_1.htm#IDX32 Stobbe, Ru"diger Preface StringF StringF sing_1136.htm#SEC1213 11590 Strohmayer, Henrik Preface sing_1.htm#IDX81 Stussak, Christian Preface sing_1.htm#IDX82 SuSE, ESingular bug Unix installation instructions sing_1584.htm#IDX534 Sulandra, Imade Preface sing_1.htm#IDX83 Suzuki, Akira Preface sing_1.htm#IDX84 SymGroup SymGroup sing_597.htm#SEC650 56676 Symbolic-numerical solving Symbolic-numerical solving sing_645.htm#SEC698 Symbolic-numerical solving sing_1250.htm#SEC1327 System and Control theory System and Control theory sing_1371.htm#SEC1448 System dependent limitations System dependent limitations sing_344.htm#SEC385 System variables System variables sing_330.htm#SEC371 Syzygies and resolutions Syzygies and resolutions sing_661.htm#SEC716 Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_422.htm#SEC470 T1 T1 and T2 sing_632.htm#SEC685 T2 T1 and T2 sing_632.htm#SEC685 TRACE TRACE var sing_339.htm#SEC380 T_1 T_1 sing_1169.htm#SEC1246 59277 T_12 T_12 sing_1171.htm#SEC1248 12923 T_2 T_2 sing_1170.htm#SEC1247 55781 Teaching Teaching sing_1393.htm#SEC1470 Template for writing a library template_lib sing_57.htm#SEC95 The SINGULAR language The SINGULAR language sing_34.htm#SEC55 The Tran algorithm twalk sing_885.htm#IDX376 The fractal walk algorithm fwalk sing_884.htm#IDX375 The online help system The online help system sing_16.htm#SEC22 Theis, Christine Preface sing_1.htm#IDX86 Tjurina Tjurina sing_1167.htm#SEC1244 11249 Tjurina number deltaLoc sing_629.htm#SEC682 Tjurina number sing_957.htm#IDX385 Tobis, Enrique Preface sing_1.htm#IDX85 Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC37 Tor Tor sing_909.htm#SEC986 sprintf Toric ideals and integer programming Toric ideals and integer programming sing_664.htm#SEC722 Tricks and pitfalls Tricks and pitfalls sing_342.htm#SEC383 Tropical Geometry Tropical Geometry sing_1520.htm#SEC1597 Type casting Type conversion and casting sing_39.htm#SEC68 Type conversion Type conversion and casting sing_39.htm#SEC67 Typesetting of help strings Typesetting of help strings sing_54.htm#SEC92 U_D_O U_D_O sing_842.htm#SEC919 26192 Unix installation Unix installation instructions sing_1584.htm#SEC1683 UpOneMatrix UpOneMatrix sing_587.htm#SEC640 63020 UpperMonomials UpperMonomials sing_1150.htm#SEC1227 20941 V-filtration goodBasis sing_1085.htm#IDX423 V-filtration sing_1091.htm#IDX434 V-filtration sing_1092.htm#IDX437 V-filtration sing_1093.htm#IDX442 V-filtration sing_1094.htm#IDX445 V-filtration sing_1096.htm#IDX450 V-filtration sing_1107.htm#IDX456 V-filtration sing_1109.htm#IDX467 Variables, indexed Names sing_37.htm#SEC64 Viazovska, Maryna Preface sing_1.htm#IDX87 Vigneron-Tenorio, Alberto Preface sing_1.htm#IDX88 Visualization Visualization sing_1306.htm#SEC1383 WP, global ordering Global orderings sing_652.htm#IDX335 WSemigroup WSemigroup sing_1073.htm#SEC1150 31355 Weierstrass Weierstrass sing_1342.htm#SEC1419 58220 Weierstrass semigroup brnoeth_lib sing_1338.htm#IDX502 Wenk, Moritz Preface sing_1.htm#IDX89 Westenberger, Eric Preface sing_1.htm#IDX33 Weyl Weyl sing_574.htm#SEC627 29212 Wichmann, Tim Preface sing_1.htm#IDX34 Wienand, Oliver Preface sing_1.htm#IDX35 Windows installation Windows installation instructions sing_1585.htm#SEC1686 Ws, local ordering Local orderings sing_653.htm#IDX347 Yanovich, Denis Preface sing_1.htm#IDX90 [ Special characters sing_36.htm#IDX153 \ Special characters sing_36.htm#IDX181 ] Special characters sing_36.htm#IDX154 ^ ideal operations sing_36.htm#IDX162 ^ sing_72.htm#SEC113 ^ sing_79.htm#SEC120 _ Special characters sing_36.htm#IDX185 ` Special characters sing_36.htm#IDX175 a, ordering Extra weight vector sing_657.htm#SEC710 absFactorize absFactorize sing_855.htm#SEC932 52546 absPrimdecGTZ absPrimdecGTZ sing_979.htm#SEC1056 27310 absValue absValue sing_696.htm#SEC773 54595 absfact.lib absfact_lib sing_854.htm#SEC931 absfact_lib absfact_lib sing_854.htm#SEC931 abstractR abstractR sing_1011.htm#SEC1088 22284 actionIsProper actionIsProper sing_1226.htm#SEC1303 52474 addcol addcol sing_811.htm#SEC888 52204 addrow addrow sing_812.htm#SEC889 44143 ademRelations ademRelations sing_529.htm#SEC582 30263 adjoint adjoint sing_836.htm#SEC913 56619 adjunction divisor Adj_div sing_1339.htm#IDX506 affine code Fitzgerald-Lax method sing_680.htm#SEC750 ainvar.lib ainvar_lib sing_1223.htm#SEC1300 ainvar_lib ainvar_lib sing_1223.htm#SEC1300 aksaka.lib aksaka_lib sing_1394.htm#SEC1471 aksaka_lib aksaka_lib sing_1394.htm#SEC1471 alexanderpolynomial alexanderpolynomial sing_1039.htm#SEC1116 36814 alexpoly.lib alexpoly_lib sing_1036.htm#SEC1113 alexpoly_lib alexpoly_lib sing_1036.htm#SEC1113 algDependent algDependent sing_860.htm#SEC937 8272 alg_kernel alg_kernel sing_861.htm#SEC938 307 algebra.lib algebra_lib sing_856.htm#SEC933 algebra_containment algebra_containment sing_857.htm#SEC934 47912 algebra_lib algebra_lib sing_856.htm#SEC933 algebraic dependence perron_lib sing_592.htm#IDX320 algebraic field extension splitring sing_983.htm#IDX387 algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_671.htm#SEC729 algorithm of Conti and Traverso Conti and Traverso sing_667.htm#SEC725 algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_670.htm#SEC728 algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_669.htm#SEC727 algorithm of Pottier Pottier sing_668.htm#SEC726 all.lib all_lib sing_689.htm#SEC766 allPositive allPositive sing_443.htm#SEC496 1409 all_lib all_lib sing_689.htm#SEC766 allowing net access Command line options sing_19.htm#IDX111 allprint allprint sing_717.htm#SEC794 5195 allreal allreal sing_1512.htm#SEC1589 57232 allrealst allrealst sing_1510.htm#SEC1587 40962 allsquarefree allsquarefree sing_1129.htm#SEC1206 45545 and Evaluation of logical expressions sing_87.htm#SEC128 and sing_347.htm#SEC388 annPoly annPoly sing_499.htm#SEC552 26354 annRat annRat sing_500.htm#SEC553 26896 annfs annfs sing_468.htm#SEC521 32230 annfs0 annfs0 sing_485.htm#SEC538 26168 annfs2 annfs2 sing_486.htm#SEC539 55516 annfsBM annfsBM sing_478.htm#SEC531 37487 annfsBMI annfsBMI sing_476.htm#SEC529 27724 annfsLOT annfsLOT sing_479.htm#SEC532 46556 annfsOT annfsOT sing_480.htm#SEC533 5190 annfsParamBM annfsParamBM sing_475.htm#SEC528 43587 annfsRB annfsRB sing_487.htm#SEC540 38418 annfspecial annfspecial sing_469.htm#SEC522 57568 annil annil sing_926.htm#SEC1003 48744 appelF1 appelF1 sing_509.htm#SEC562 17783 appelF2 appelF2 sing_510.htm#SEC563 sprintf appelF4 appelF4 sing_511.htm#SEC564 35194 applyAdF applyAdF sing_459.htm#SEC512 40329 arcpoint.lib arcpoint_lib sing_1049.htm#SEC1126 arcpoint_lib arcpoint_lib sing_1049.htm#SEC1126 argument, default Parameter list sing_45.htm#SEC83 argument, optional Parameter list sing_45.htm#SEC83 arrange arrange sing_491.htm#SEC544 50350 ask ask sing_1402.htm#SEC1479 3862 atkins.lib atkins_lib sing_1403.htm#SEC1480 atkins_lib atkins_lib sing_1403.htm#SEC1480 attrib attrib sing_167.htm#SEC208 autonom autonom sing_1376.htm#SEC1453 57044 autonomDim autonomDim sing_1377.htm#SEC1454 30055 awalk1 awalk1 sing_886.htm#SEC963 11044 awalk2 awalk2 sing_887.htm#SEC964 8955 bFactor bFactor sing_508.htm#SEC561 28801 babyGiant babyGiant sing_1434.htm#SEC1511 41113 bareiss bareiss sing_168.htm#SEC209 base2str base2str sing_692.htm#SEC769 sprintf basering def sing_28.htm#IDX146 basering sing_74.htm#SEC115 basicinvariants basicinvariants sing_1055.htm#SEC1132 32136 bernstein bernstein sing_1089.htm#SEC1166 34280 bernsteinBM bernsteinBM sing_472.htm#SEC525 19828 betti betti sing_169.htm#SEC210 betti (plural) betti (plural) sing_391.htm#SEC432 bfct bfct sing_433.htm#SEC486 5953 bfctAnn bfctAnn sing_435.htm#SEC488 52517 bfctIdeal bfctIdeal sing_437.htm#SEC490 53572 bfctOneGB bfctOneGB sing_436.htm#SEC489 32422 bfctSyz bfctSyz sing_434.htm#SEC487 15690 bfun.lib bfun_lib sing_432.htm#SEC485 bfun.lib sing_432.htm#IDX293 bfun_lib bfun_lib sing_432.htm#SEC485 bfun_lib sing_432.htm#IDX294 bigint bigint sing_69.htm#SEC110 bigint declarations bigint declarations sing_70.htm#SEC111 bigint expressions bigint expressions sing_71.htm#SEC112 bigint operations bigint operations sing_72.htm#SEC113 bigint related functions bigint related functions sing_73.htm#SEC114 binomial binomial sing_697.htm#SEC774 48021 block Control structures sing_40.htm#SEC69 block sing_314.htm#SEC355 blowUp blowUp sing_992.htm#SEC1069 34819 blowUp2 blowUp2 sing_993.htm#SEC1070 65264 blowUpBO blowUpBO sing_999.htm#SEC1076 58146 blowup0 blowup0 sing_874.htm#SEC951 44451 boolean expressions boolean expressions sing_86.htm#SEC127 boolean operations boolean operations sing_87.htm#SEC128 boundBuFou boundBuFou sing_1507.htm#SEC1584 26589 boundDes boundDes sing_1509.htm#SEC1586 35149 boundposDes boundposDes sing_1508.htm#SEC1585 58854 bracket bracket sing_350.htm#SEC391 bracket sing_392.htm#SEC433 break break sing_315.htm#SEC356 break point ~ sing_329.htm#SEC370 breakpoint breakpoint sing_316.htm#SEC357 brnoeth.lib brnoeth_lib sing_1338.htm#SEC1415 brnoeth_lib brnoeth_lib sing_1338.htm#SEC1415 browser, command line option Command line options sing_19.htm#IDX114 browser, setting the system sing_297.htm#IDX270 browsers The online help system sing_16.htm#IDX91 browsers, setting the system sing_297.htm#IDX269 bubblesort bubblesort sing_1405.htm#SEC1482 63278 bug, ESingular Unix installation instructions sing_1584.htm#IDX536 buildtree buildtree sing_770.htm#SEC847 24362 buildtree, Maple buildtreetoMaple sing_771.htm#IDX363 buildtree, buildtreetoMaple, CGS finalcases sing_772.htm#IDX364 buildtreetoMaple buildtreetoMaple sing_771.htm#SEC848 27880 busadj busadj sing_834.htm#SEC911 36301 c, module ordering Module orderings sing_654.htm#IDX350 canonize canonize sing_1384.htm#SEC1461 54090 cantodiffcgs cantodiffcgs sing_776.htm#SEC853 6347 cantoradd cantoradd sing_1463.htm#SEC1540 55304 cantormult cantormult sing_1466.htm#SEC1543 57569 cantorred cantorred sing_1464.htm#SEC1541 46502 case No case or switch statement sing_348.htm#SEC389 category in a library Format of a library sing_49.htm#IDX191 center center sing_446.htm#IDX297 65108 center sing_452.htm#SEC505 centerRed centerRed sing_451.htm#SEC504 59910 centerVS centerVS sing_450.htm#SEC503 27548 central.lib central_lib sing_446.htm#SEC499 central.lib sing_446.htm#IDX295 central_lib central_lib sing_446.htm#SEC499 central_lib sing_446.htm#IDX296 centralize central_lib sing_446.htm#IDX300 centralizeSet centralizeSet sing_447.htm#SEC500 55737 centralizer centralizer sing_446.htm#IDX298 65261 centralizer sing_453.htm#SEC506 centralizerRed centralizerRed sing_449.htm#SEC502 8209 centralizerVS centralizerVS sing_448.htm#SEC501 22925 cgs cgs sing_691.htm#SEC768 57776 chaincrit chaincrit sing_1477.htm#SEC1554 9502 changechar changechar sing_778.htm#SEC855 49849 changeord changeord sing_779.htm#SEC856 47708 changes News and changes sing_1582.htm#SEC1659 changevar changevar sing_780.htm#SEC857 32829 char char sing_170.htm#SEC211 char_series char_series sing_171.htm#SEC212 characteristic exponents invariants sing_1043.htm#IDX402 characteristic exponents sing_1044.htm#IDX407 characteristic exponents sing_1045.htm#IDX410 characteristic exponents sing_1046.htm#IDX414 characteristic exponents sing_1116.htm#IDX477 charexp2conductor charexp2conductor sing_1046.htm#SEC1123 sprintf charexp2generators charexp2generators sing_1044.htm#SEC1121 16838 charexp2inter charexp2inter sing_1045.htm#SEC1122 39881 charexp2multseq charexp2multseq sing_1043.htm#SEC1120 334 charexp2poly charexp2poly sing_1047.htm#SEC1124 sprintf charpoly charpoly sing_835.htm#SEC912 29561 charstr charstr sing_172.htm#SEC213 checkFactor checkFactor sing_490.htm#SEC543 60779 checkRoot checkRoot sing_477.htm#SEC530 33063 checkRoot1 checkRoot1 sing_488.htm#SEC541 5957 checkRoot2 checkRoot2 sing_489.htm#SEC542 53691 chineseRem chineseRem sing_1425.htm#SEC1502 38560 chinrem chinrem sing_173.htm#SEC214 chinrestp chinrestp sing_1457.htm#SEC1534 24779 cimonom.lib cimonom_lib sing_869.htm#SEC946 cimonom_lib cimonom_lib sing_869.htm#SEC946 classify classify sing_1056.htm#SEC1133 17008 classify.lib classify_lib sing_1054.htm#SEC1131 classify_lib classify_lib sing_1054.htm#SEC1131 cleanTmp cleanTmp sing_1574.htm#SEC1651 14108 cleardenom cleardenom sing_174.htm#SEC215 close close sing_175.htm#SEC216 closed_points closed_points sing_1348.htm#SEC1425 47269 closetex closetex sing_1312.htm#SEC1389 42334 closureFrac closureFrac sing_955.htm#SEC1032 9252 codim codim sing_1154.htm#SEC1231 14253 coding theory AG codes sing_646.htm#SEC699 coef coef sing_176.htm#SEC217 coefficient field number sing_129.htm#SEC170 coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC44 coefficients, long Long coefficients sing_605.htm#SEC658 coeffmod coeffmod sing_1400.htm#SEC1477 23531 coeffs coeffs sing_177.htm#SEC218 collectDiv collectDiv sing_1009.htm#SEC1086 50348 colrank colrank sing_1382.htm#SEC1459 52290 colred colred sing_818.htm#SEC895 1693 comma Usage of commas sing_349.htm#SEC390 command-line option, setting value of system sing_297.htm#IDX266 command-line option, value of system sing_297.htm#IDX264 command-line options, print all values of system sing_297.htm#IDX263 command-line options, short help Command line options sing_19.htm#IDX108 commands (plural) Functions (plural) sing_390.htm#IDX292 completeReduction completeReduction sing_1228.htm#SEC1305 57157 complex Rings and orderings sing_28.htm#IDX145 compregb.lib compregb_lib sing_690.htm#SEC767 compregb_lib compregb_lib sing_690.htm#SEC767 comprehensive Groebner system compregb_lib sing_690.htm#IDX356 compress compress sing_795.htm#SEC872 61998 concat concat sing_796.htm#SEC873 16653 conductor charexp2conductor sing_1046.htm#IDX413 conductor, degree invariants sing_1116.htm#IDX480 conicWithTangents conicWithTangents sing_1551.htm#SEC1628 23506 contact matrix charexp2inter sing_1045.htm#IDX409 containedQ containedQ sing_1300.htm#SEC1377 46718 content content sing_740.htm#SEC817 9095 continue Behavior of continue sing_317.htm#SEC358 continue sing_351.htm#SEC392 contract contract sing_178.htm#SEC219 contributors system sing_297.htm#IDX253 control control sing_1374.htm#SEC1451 44498 control.lib control_lib sing_1373.htm#SEC1450 controlDim controlDim sing_1375.htm#SEC1452 2417 controlExample controlExample sing_1387.htm#SEC1464 2678 control_Matrix control_Matrix sing_1084.htm#SEC1161 sprintf control_lib control_lib sing_1373.htm#SEC1450 convloc convloc sing_494.htm#SEC547 19122 coordinates coords sing_1495.htm#IDX517 coords coords sing_1495.htm#SEC1572 29362 copyright Preface sing_1.htm#IDX1 corank corank sing_1057.htm#SEC1134 33709 cornerMonomials cornerMonomials sing_962.htm#SEC1039 33995 countPoints countPoints sing_1447.htm#SEC1524 58566 crcgs crcgs sing_775.htm#SEC852 53348 createBO createBO sing_1000.htm#SEC1077 32669 crypto.lib crypto_lib sing_1418.htm#SEC1495 crypto_lib crypto_lib sing_1418.htm#SEC1495 cup cup sing_891.htm#SEC968 57972 cupproduct cupproduct sing_892.htm#SEC969 62854 curve singularities hnoether_lib sing_1036.htm#IDX396 curve singularities sing_1110.htm#IDX475 curvepar.lib curvepar_lib sing_1069.htm#SEC1146 curvepar_lib curvepar_lib sing_1069.htm#SEC1146 cycleLength cycleLength sing_1532.htm#SEC1609 26458 cyclePoints cyclePoints sing_1536.htm#SEC1613 63110 cyclic cyclic sing_728.htm#SEC805 21375 cyclic code Codes and the decoding problem sing_677.htm#SEC737 cyclotomic cyclotomic sing_1193.htm#SEC1270 33749 dbprint dbprint sing_179.htm#SEC220 debugLib, option option sing_259.htm#IDX228 debug_log debug_log sing_1067.htm#SEC1144 62043 debugger Source code debugger sing_63.htm#SEC101 debugging library code Source code debugger sing_63.htm#SEC101 dec1var dec1var sing_925.htm#SEC1002 36098 decimal decimal sing_1419.htm#SEC1496 56066 decode decode sing_1365.htm#SEC1442 64330 decodeCode decodeCode sing_1367.htm#SEC1444 28262 decodeRandom decodeRandom sing_1366.htm#SEC1443 40118 decodeRandomFL decodeRandomFL sing_1370.htm#SEC1447 35423 decodeSV decodeSV sing_1347.htm#SEC1424 37975 decodegb.lib decodegb_lib sing_1352.htm#SEC1429 decodegb_lib decodegb_lib sing_1352.htm#SEC1429 decoding, decoding problem Codes and the decoding problem sing_677.htm#SEC738 def def sing_74.htm#SEC115 def declarations def declarations sing_75.htm#SEC116 default argument Parameter list sing_45.htm#SEC83 defined defined sing_180.htm#SEC221 deform deform sing_1155.htm#SEC1232 5250 deform.lib deform_lib sing_1074.htm#SEC1151 deform_lib deform_lib sing_1074.htm#SEC1151 defring defring sing_781.htm#SEC858 1814 defringp defringp sing_783.htm#SEC860 42905 defrings defrings sing_782.htm#SEC859 1034 deg deg sing_181.htm#SEC222 degBound degBound sing_331.htm#SEC372 degree Miscellaneous oddities sing_182.htm#SEC223 degree sing_354.htm#IDX282 degree lexicographical ordering Global orderings sing_652.htm#IDX330 degree of a polynomial Miscellaneous oddities sing_354.htm#IDX286 degree reverse lexicographical ordering Global orderings sing_652.htm#IDX328 degreepart degreepart sing_1252.htm#SEC1329 53036 delete delete sing_183.htm#SEC224 deleteGenerator deleteGenerator sing_516.htm#SEC569 53465 deleteSublist deleteSublist sing_698.htm#SEC775 20406 delta delta sing_1122.htm#SEC1199 56952 delta invariant delta sing_957.htm#IDX384 delta invariant sing_1122.htm#IDX485 delta invariant. normal sing_951.htm#IDX383 deltaLoc deltaLoc sing_957.htm#SEC1034 35192 denominator denominator sing_742.htm#SEC819 51847 depth depth sing_893.htm#SEC970 17777 depthIdeal depthIdeal sing_935.htm#SEC1012 54782 derivate derivate sing_1225.htm#SEC1302 15409 det det sing_184.htm#SEC225 det_B det_B sing_837.htm#SEC914 60143 detadj detadj sing_1138.htm#SEC1215 5914 detropicalise detropicalise sing_1569.htm#SEC1646 34237 develop develop sing_1112.htm#SEC1189 48457 diag diag sing_797.htm#SEC874 56759 diag_test diag_test sing_833.htm#SEC910 31469 diff diff sing_185.htm#SEC226 dim dim sing_186.htm#SEC227 dimGradedPart dimGradedPart sing_1026.htm#SEC1103 11262 dimH dimH sing_1025.htm#SEC1102 38534 dim_slocus dim_slocus sing_1156.htm#SEC1233 47218 disc disc sing_1406.htm#SEC1483 45279 discr discr sing_1178.htm#SEC1255 9642 discrepancy discrepancy sing_1007.htm#SEC1084 5597 displayCohom displayCohom sing_1027.htm#SEC1104 22633 displayHNE displayHNE sing_1115.htm#SEC1192 29845 displayInvariants displayInvariants sing_1117.htm#SEC1194 13678 displayMultsequence displayMultsequence sing_1119.htm#SEC1196 16668 displayTropicalLifting displayTropicalLifting sing_1544.htm#SEC1621 28144 div Miscellaneous oddities sing_72.htm#SEC113 div sing_84.htm#SEC125 div sing_354.htm#IDX279 divideUnits divideUnits sing_1392.htm#SEC1469 26711 division division sing_187.htm#SEC228 division, pdivi, reduce pnormalform sing_769.htm#IDX361 division, reduce pdivi sing_766.htm#IDX358 divisor divisor sing_1460.htm#SEC1537 38158 dmod.lib dmod_lib sing_467.htm#SEC520 dmod.lib sing_467.htm#IDX302 dmod_lib dmod_lib sing_467.htm#SEC520 dmod_lib sing_467.htm#IDX303 dmodapp.lib dmodapp_lib sing_498.htm#SEC551 dmodapp.lib sing_498.htm#IDX304 dmodapp_lib dmodapp_lib sing_498.htm#SEC551 dmodapp_lib sing_498.htm#IDX305 double double sing_1465.htm#SEC1542 34697 downloading Download instructions sing_1583.htm#SEC1679 dp, global ordering Global orderings sing_652.htm#IDX329 drawNewtonSubdivision drawNewtonSubdivision sing_1547.htm#SEC1624 18504 drawTropicalCurve drawTropicalCurve sing_1546.htm#SEC1623 41581 ds, local ordering Local orderings sing_653.htm#IDX339 dsum dsum sing_798.htm#SEC875 1303 dualConic dualConic sing_1570.htm#SEC1647 31080 dual_code dual_code sing_1349.htm#SEC1426 57229 dump dump sing_188.htm#SEC229 ecart ecart sing_1468.htm#SEC1545 32475 echo echo sing_332.htm#SEC373 eexgcdN eexgcdN sing_1421.htm#SEC1498 53237 egcdMain egcdMain sing_1293.htm#SEC1370 25359 eigenvals eigenvals sing_845.htm#SEC922 7626 elim elim sing_876.htm#SEC953 30059 elim.lib elim_lib sing_873.htm#SEC950 elim1 elim1 sing_877.htm#SEC954 15653 elim2 elim2 sing_878.htm#SEC955 44749 elimRing elimRing sing_875.htm#SEC952 12194 elim_lib elim_lib sing_873.htm#SEC950 eliminate eliminate sing_189.htm#SEC230 eliminate (plural) eliminate (plural) sing_393.htm#SEC434 elimlinearpart elimlinearpart sing_1253.htm#SEC1330 14251 elimpart elimpart sing_1254.htm#SEC1331 10258 elimpartanyr elimpartanyr sing_1255.htm#SEC1332 39751 ellipticAdd ellipticAdd sing_1443.htm#SEC1520 13279 ellipticAllPoints ellipticAllPoints sing_1448.htm#SEC1525 60770 ellipticMult ellipticMult sing_1444.htm#SEC1521 1558 ellipticNF ellipticNF sing_1539.htm#SEC1616 3056 ellipticNFDB ellipticNFDB sing_1540.htm#SEC1617 7965 ellipticRandomCurve ellipticRandomCurve sing_1445.htm#SEC1522 36980 ellipticRandomPoint ellipticRandomPoint sing_1446.htm#SEC1523 6866 else if sing_322.htm#SEC363 encode encode sing_1357.htm#SEC1434 56687 endomorphism filtration endvfilt sing_1096.htm#IDX451 endvfilt endvfilt sing_1096.htm#SEC1173 36204 engine engine sing_512.htm#SEC565 4183 envelope envelope sing_394.htm#SEC435 environment variable, DISPLAY The online help system sing_16.htm#IDX99 equalJinI equalJinI sing_1053.htm#SEC1130 18502 equiRadical equiRadical sing_973.htm#SEC1050 8884 equidim equidim sing_975.htm#SEC1052 20125 equidimMax equidimMax sing_976.htm#SEC1053 49289 equidimMaxEHV equidimMaxEHV sing_977.htm#SEC1054 42650 equising.lib equising_lib sing_1079.htm#SEC1156 equising_lib equising_lib sing_1079.htm#SEC1156 equisingular Tjurina number alexpoly_lib sing_1036.htm#IDX401 equisingularity ideal esIdeal sing_1081.htm#IDX417 equisingularity stratum esStratum sing_1082.htm#IDX418 error recovery The SINGULAR prompt sing_15.htm#SEC21 errorInsert errorInsert sing_1360.htm#SEC1437 23547 errorRand errorRand sing_1361.htm#SEC1438 5727 esIdeal esIdeal sing_1081.htm#SEC1158 60477 esStratum esStratum sing_1082.htm#SEC1159 3628 eta eta sing_1534.htm#SEC1611 1400 euler euler sing_1399.htm#SEC1476 26390 eval eval sing_190.htm#SEC231 evaluate_reynolds evaluate_reynolds sing_1198.htm#SEC1275 46353 example example sing_192.htm#SEC233 execute execute sing_193.htm#SEC234 exgcdN exgcdN sing_1420.htm#SEC1497 23525 exit quit sing_326.htm#SEC367 expo expo sing_1411.htm#SEC1488 8833 export export sing_319.htm#SEC360 exportto exportto sing_320.htm#SEC361 expression list Data types (plural) sing_68.htm#IDX200 expression list sing_358.htm#IDX289 extcurve extcurve sing_1343.htm#SEC1420 6730 extdevelop extdevelop sing_1113.htm#SEC1190 51044 extendring extendring sing_784.htm#SEC861 64781 extension of rings splitring sing_983.htm#IDX388 exterior basis exteriorBasis sing_824.htm#IDX371 exterior power exteriorPower sing_826.htm#IDX373 exteriorBasis exteriorBasis sing_824.htm#SEC901 sprintf exteriorPower exteriorPower sing_826.htm#SEC903 20173 extgcd extgcd sing_194.htm#SEC235 facGBIdeal facGBIdeal sing_963.htm#SEC1040 9924 facstd facstd sing_195.htm#SEC236 factor facvar sing_767.htm#IDX359 factorH factorH sing_715.htm#SEC792 24814 factorLenstraECM factorLenstraECM sing_1452.htm#SEC1529 54951 factorMain factorMain sing_1294.htm#SEC1371 65152 factorial factorial sing_699.htm#SEC776 32871 factorization, absolute factorization. absfact_lib sing_854.htm#IDX374 factorize factorize sing_196.htm#SEC237 factory Preface sing_1.htm#IDX2 facvar facvar sing_767.htm#SEC844 28207 fan polymake_lib sing_1521.htm#IDX522 fastExpt fastExpt sing_1395.htm#SEC1472 43912 fastHC, option option sing_259.htm#IDX209 fastelim fastelim sing_1256.htm#SEC1333 7409 fetch fetch sing_197.htm#SEC238 fetch (plural) fetch (plural) sing_395.htm#SEC436 fetchall fetchall sing_785.htm#SEC862 58389 fglm stdfglm sing_198.htm#SEC239 fglm sing_294.htm#IDX236 fglm_solve fglm_solve sing_1272.htm#SEC1349 51398 fglmquot fglmquot sing_199.htm#SEC240 fibonacci fibonacci sing_700.htm#SEC777 24750 field number sing_129.htm#SEC170 file, .singularrc Startup sequence sing_20.htm#IDX141 filecmd filecmd sing_200.htm#SEC241 finalCharts finalCharts sing_1328.htm#SEC1405 57151 finalcases finalcases sing_772.htm#SEC849 55683 find find sing_201.htm#SEC242 findAuto findAuto sing_533.htm#SEC586 56092 findInvo findInvo sing_531.htm#SEC584 9975 findInvoDiag findInvoDiag sing_532.htm#SEC585 42010 findOrientedBoundary findOrientedBoundary sing_1535.htm#SEC1612 24110 findTorsion findTorsion sing_1386.htm#SEC1463 29572 findimAlgebra findimAlgebra sing_578.htm#SEC631 612 finduni finduni sing_202.htm#SEC243 findvars findvars sing_1257.htm#SEC1334 20191 finite field number sing_129.htm#SEC170 finitenessTest finitenessTest sing_867.htm#SEC944 40633 finvar.lib finvar_lib sing_1186.htm#SEC1263 finvar_lib finvar_lib sing_1186.htm#SEC1263 first index is 1 First index is 1 sing_353.htm#SEC394 firstoct firstoct sing_1305.htm#SEC1382 11498 fitting fitting sing_896.htm#SEC973 20661 fl2poly fl2poly sing_514.htm#SEC567 32611 flatten flatten sing_799.htm#SEC876 55617 flatteningStrat flatteningStrat sing_897.htm#SEC974 15622 for for sing_321.htm#SEC362 fprintf fprintf sing_203.htm#SEC244 13662 free associative algebra, tensor algebra Free associative algebras sing_426.htm#SEC479 freeGBasis freeGBasis sing_519.htm#SEC572 1642 freegb.lib freegb_lib sing_517.htm#SEC570 freegb.lib sing_517.htm#IDX306 freegb_lib freegb_lib sing_517.htm#SEC570 freegb_lib sing_517.htm#IDX307 freemodule freemodule sing_204.htm#SEC245 freerank freerank sing_730.htm#SEC807 52218 frwalk frwalk sing_205.htm#SEC246 furtherInvar furtherInvar sing_1230.htm#SEC1307 19209 further_hn_proc further_hn_proc sing_1130.htm#SEC1207 63500 fwalk fwalk sing_884.htm#SEC961 15070 galois field number sing_129.htm#SEC170 gauss_col gauss_col sing_809.htm#SEC886 36252 gauss_nf gauss_nf sing_840.htm#SEC917 51060 gauss_row gauss_row sing_810.htm#SEC887 58877 gaussred gaussred sing_838.htm#SEC915 29001 gaussred_pivot gaussred_pivot sing_839.htm#SEC916 25477 gcd gcd sing_206.htm#SEC247 gcdN gcdN sing_1422.htm#SEC1499 63954 gcddivisor gcddivisor sing_1461.htm#SEC1538 1276 gen gen sing_207.htm#SEC248 genMDSMat genMDSMat sing_1363.htm#SEC1440 3347 general error-locator polynomial Cooper philosophy sing_678.htm#SEC744 general weighted lexicographical ordering Local orderings sing_653.htm#IDX345 general weighted reverse lexicographical ordering Local orderings sing_653.htm#IDX342 general.lib general_lib sing_693.htm#SEC770 generalOrder generalOrder sing_1486.htm#SEC1563 42536 general_lib general_lib sing_693.htm#SEC770 generateG generateG sing_1451.htm#SEC1528 18714 generators charexp2generators sing_1044.htm#IDX405 genericid genericid sing_750.htm#SEC827 29731 genericity genericity sing_1383.htm#SEC1460 16822 genericmat genericmat sing_800.htm#SEC877 35016 genus genus sing_953.htm#SEC1030 4162 getdump getdump sing_208.htm#SEC249 getenv system sing_297.htm#IDX245 gkdim.lib gkdim_lib sing_536.htm#SEC589 gkdim.lib sing_536.htm#IDX310 gkdim_lib gkdim_lib sing_536.htm#SEC589 gkdim_lib sing_536.htm#IDX311 gmscoeffs gmscoeffs sing_1088.htm#SEC1165 31907 gmsnf gmsnf sing_1087.htm#SEC1164 33925 gmspoly.lib gmspoly_lib sing_1107.htm#SEC1184 gmspoly_lib gmspoly_lib sing_1107.htm#SEC1184 gmsring gmsring sing_1086.htm#SEC1163 55582 gmssing.lib gmssing_lib sing_1085.htm#SEC1162 gmssing_lib gmssing_lib sing_1085.htm#SEC1162 good basis goodBasis sing_1085.htm#IDX428 good basis sing_1095.htm#IDX449 good basis sing_1107.htm#IDX461 good basis sing_1109.htm#IDX472 goodBasis goodBasis sing_1109.htm#SEC1186 37512 graded module, graded piece dimGradedPart sing_1026.htm#IDX393 graded modules, handling of Handling graded modules sing_620.htm#SEC673 graphics.lib graphics_lib sing_1307.htm#SEC1384 graphics_lib graphics_lib sing_1307.htm#SEC1384 graver4ti2 graver4ti2 sing_1031.htm#SEC1108 39635 groebner groebner and std sing_209.htm#SEC250 14733 groebner sing_612.htm#SEC665 groebnerFan groebnerFan sing_1526.htm#SEC1603 41834 ground field number sing_129.htm#SEC170 group_reynolds group_reynolds sing_1194.htm#SEC1271 35079 grwalk.lib grwalk_lib sing_883.htm#SEC960 grwalk_lib grwalk_lib sing_883.htm#SEC960 gwalk gwalk sing_889.htm#SEC966 38238 hardware platform system sing_297.htm#IDX244 headStand headStand sing_822.htm#SEC899 14413 help help sing_210.htm#SEC251 help browsers The online help system sing_16.htm#IDX92 help browsers, dummy The online help system sing_16.htm#IDX95 help browsers, dummy sing_16.htm#IDX97 help browsers, emacs The online help system sing_16.htm#IDX96 help browsers, html The online help system sing_16.htm#IDX93 help browsers, setting command to use The online help system sing_16.htm#IDX100 help browsers, setting the system sing_297.htm#IDX271 help string of a library The help string of a library sing_55.htm#SEC93 help string of a procedure The help string of procedures sing_56.htm#SEC94 help, accessing over the net Command line options sing_19.htm#IDX112 help, online help system The online help system sing_16.htm#SEC22 hessenberg hessenberg sing_844.htm#SEC921 1885 highcorner highcorner sing_211.htm#SEC252 hilb hilb sing_212.htm#SEC253 hilbPoly hilbPoly sing_748.htm#SEC825 36118 hilbert4ti2 hilbert4ti2 sing_1030.htm#SEC1107 13993 hilbvec hilbvec sing_1258.htm#SEC1335 9204 hnexpansion hnexpansion sing_1111.htm#SEC1188 46990 hnoether.lib hnoether_lib sing_1110.htm#SEC1187 hnoether_lib hnoether_lib sing_1110.htm#SEC1187 hom_kernel hom_kernel sing_904.htm#SEC981 32604 homog homog sing_213.htm#SEC254 homolog.lib homolog_lib sing_890.htm#SEC967 homolog_lib homolog_lib sing_890.htm#SEC967 homology homology sing_899.htm#SEC976 15040 howto, download Download instructions sing_1583.htm#SEC1679 howto, install on Macintosh Macintosh installation instructions sing_1586.htm#SEC1689 howto, install on Unix Unix installation instructions sing_1584.htm#SEC1683 howto, install on Windows Windows installation instructions sing_1585.htm#SEC1686 hres hres sing_214.htm#SEC255 html, default help The online help system sing_16.htm#IDX94 hyperel.lib hyperel_lib sing_1454.htm#SEC1531 hyperel_lib hyperel_lib sing_1454.htm#SEC1531 hypersurface singularity mondromy_lib sing_1137.htm#IDX490 iMult iMult sing_956.htm#SEC1033 22059 id2mod id2mod sing_744.htm#SEC821 32918 ideal ideal sing_76.htm#SEC117 ideal declarations ideal declarations sing_77.htm#SEC118 ideal declarations (plural) ideal declarations (plural) sing_360.htm#SEC401 ideal expressions ideal expressions sing_78.htm#SEC119 ideal expressions (plural) ideal expressions (plural) sing_361.htm#SEC402 ideal operations ideal operations sing_79.htm#SEC120 ideal operations (plural) ideal operations (plural) sing_362.htm#SEC403 ideal related functions ideal related functions sing_80.htm#SEC121 ideal related functions (plural) ideal related functions (plural) sing_363.htm#SEC404 ideal, toric Toric ideals sing_665.htm#SEC723 idealSplit idealSplit sing_1265.htm#SEC1342 4673 ideals Miscellaneous oddities sing_354.htm#IDX283 idealsimplify idealsimplify sing_1052.htm#SEC1129 38569 identifier Identifier resolution sing_355.htm#SEC396 if if sing_322.htm#SEC363 image_of_variety image_of_variety sing_1222.htm#SEC1299 43711 imap imap sing_215.htm#SEC256 imap (plural) imap (plural) sing_396.htm#SEC437 imapall imapall sing_786.htm#SEC863 4854 impart impart sing_216.htm#SEC257 importfrom importfrom sing_323.htm#SEC364 inCenter inCenter sing_456.htm#SEC509 22152 inCentralizer inCentralizer sing_457.htm#SEC510 49000 inForm inForm sing_506.htm#SEC559 8280 inSubring inSubring sing_859.htm#SEC936 5728 indSet indSet sing_930.htm#SEC1007 32828 indepSet indepSet sing_217.htm#SEC258 indexed names Names sing_36.htm#IDX152 indexed names sing_37.htm#SEC64 info The online help system sing_16.htm#SEC23 info in a library Format of a library sing_49.htm#IDX189 info string of a library The help string of a library sing_55.htm#SEC93 init_debug init_debug sing_1059.htm#SEC1136 29863 initialForm initialForm sing_1556.htm#SEC1633 57793 initialIdeal initialIdeal sing_1557.htm#SEC1634 22205 initialIdealW initialIdealW sing_505.htm#SEC558 31696 initialMalgrange initialMalgrange sing_504.htm#SEC557 2166 inout.lib inout_lib sing_716.htm#SEC793 inout_lib inout_lib sing_716.htm#SEC793 input Input and output sing_41.htm#SEC70 insert insert sing_218.htm#SEC259 insertGenerator insertGenerator sing_515.htm#SEC568 58067 instructions, Macintosh installation Macintosh installation instructions sing_1586.htm#SEC1689 instructions, Unix installation Unix installation instructions sing_1584.htm#SEC1683 instructions, Windows installation Windows installation instructions sing_1585.htm#SEC1686 instructions, downloading Download instructions sing_1583.htm#SEC1679 int int sing_81.htm#SEC122 int declarations int declarations sing_82.htm#SEC123 int expressions int expressions sing_83.htm#SEC124 int operations int operations sing_84.htm#SEC125 int related functions int related functions sing_85.htm#SEC126 intPart intPart sing_1429.htm#SEC1506 48360 intRoot intRoot sing_1430.htm#SEC1507 54582 intStrategy, option option sing_259.htm#IDX210 integer division Miscellaneous oddities sing_354.htm#IDX278 integer programming Integer programming sing_673.htm#SEC731 integral closure normal sing_951.htm#IDX382 interface, Emacs Emacs user interface sing_21.htm#SEC28 internalfunctions internalfunctions sing_1060.htm#SEC1137 61230 interpolate interpolate sing_1271.htm#SEC1348 51502 interpolation interpolation sing_219.htm#SEC260 interred interred sing_220.htm#SEC261 intersect intersect sing_221.htm#SEC262 intersect (plural) intersect (plural) sing_397.htm#SEC438 intersection intersection sing_1120.htm#SEC1197 46938 intersection multiplicity intersection sing_1045.htm#IDX411 intersection multiplicity sing_1120.htm#IDX483 intersectionDiv intersectionDiv sing_1005.htm#SEC1082 29017 intmat intmat sing_88.htm#SEC129 intmat declarations intmat declarations sing_89.htm#SEC130 intmat expressions intmat expressions sing_90.htm#SEC131 intmat operations intmat operations sing_92.htm#SEC133 intmat related functions intmat related functions sing_93.htm#SEC134 intmat type cast intmat type cast sing_91.htm#SEC132 intmatToPolymake intmatToPolymake sing_1527.htm#SEC1604 7182 intprog.lib intprog_lib sing_910.htm#SEC987 intprog_lib intprog_lib sing_910.htm#SEC987 intvec intvec sing_94.htm#SEC135 intvec declarations intvec declarations sing_95.htm#SEC136 intvec expressions intvec expressions sing_96.htm#SEC137 intvec operations intvec operations sing_97.htm#SEC138 intvec related functions intvec related functions sing_98.htm#SEC139 invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1191.htm#IDX496 invariant ring minimal generating set permutation group invariant_algebra_perm sing_1192.htm#IDX497 invariantRing invariantRing sing_1224.htm#SEC1301 18582 invariant_algebra_perm invariant_algebra_perm sing_1192.htm#SEC1269 63525 invariant_algebra_reynolds invariant_algebra_reynolds sing_1191.htm#SEC1268 35705 invariant_basis invariant_basis sing_1199.htm#SEC1276 18343 invariant_basis_reynolds invariant_basis_reynolds sing_1200.htm#SEC1277 54788 invariant_ring invariant_ring sing_1187.htm#SEC1264 8059 invariant_ring_random invariant_ring_random sing_1188.htm#SEC1265 6986 invariants invariants sing_1116.htm#SEC1193 57499 inverse inverse sing_828.htm#SEC905 27411 inverse_B inverse_B sing_829.htm#SEC906 17616 inverse_L inverse_L sing_830.htm#SEC907 49271 invertNumberMain invertNumberMain sing_1295.htm#SEC1372 62615 involut.lib involut_lib sing_530.htm#SEC583 involut.lib sing_530.htm#IDX308 involut_lib involut_lib sing_530.htm#SEC583 involut_lib sing_530.htm#IDX309 involution involution sing_535.htm#SEC588 4213 invunit invunit sing_1139.htm#SEC1216 62398 iostruct iostruct sing_1385.htm#SEC1462 60444 irred_secondary_char0 irred_secondary_char0 sing_1213.htm#SEC1290 2943 irred_secondary_no_molien irred_secondary_no_molien sing_1216.htm#SEC1293 55905 irreducible power series is_irred sing_1121.htm#IDX484 irreducible secondary invariant irred_secondary_char0 sing_1213.htm#IDX498 isCM isCM sing_900.htm#SEC977 50469 isCMcod2 isCMcod2 sing_1174.htm#SEC1251 2563 isCartan isCartan sing_458.htm#SEC511 39541 isCentral isCentral sing_583.htm#SEC636 54650 isCommutative isCommutative sing_585.htm#SEC638 60728 isEquising isEquising sing_1083.htm#SEC1160 1424 isFlat isFlat sing_901.htm#SEC978 14706 isFsat isFsat sing_507.htm#SEC560 49578 isHolonomic isHolonomic sing_493.htm#SEC546 23650 isLocallyFree isLocallyFree sing_902.htm#SEC979 46389 isNC isNC sing_584.htm#SEC637 57151 isOnCurve isOnCurve sing_1442.htm#SEC1519 36324 isRational isRational sing_497.htm#SEC550 10732 isReg isReg sing_903.htm#SEC980 40920 isTame isTame sing_1108.htm#SEC1185 42180 isVar isVar sing_528.htm#SEC581 21360 isWeyl isWeyl sing_586.htm#SEC639 28994 is_NND is_NND sing_1124.htm#SEC1201 26564 is_NP is_NP sing_939.htm#SEC1016 43891 is_active is_active sing_1157.htm#SEC1234 6867 is_bijective is_bijective sing_864.htm#SEC941 49512 is_ci is_ci sing_1158.htm#SEC1235 35370 is_complex is_complex sing_801.htm#SEC878 1234 is_injective is_injective sing_862.htm#SEC939 13127 is_irred is_irred sing_1121.htm#SEC1198 51150 is_is is_is sing_1159.htm#SEC1236 64105 is_nested is_nested sing_940.htm#SEC1017 9200 is_reg is_reg sing_1160.htm#SEC1237 18146 is_regs is_regs sing_1161.htm#SEC1238 50242 is_surjective is_surjective sing_863.htm#SEC940 57044 is_zero is_zero sing_731.htm#SEC808 24341 ishyper ishyper sing_1455.htm#SEC1532 65518 isoncurve isoncurve sing_1456.htm#SEC1533 16384 isparam isparam sing_1519.htm#SEC1596 56395 isuni isuni sing_1504.htm#SEC1581 39427 jInvariant jInvariant sing_1550.htm#SEC1627 37364 jOft jOft sing_1412.htm#SEC1489 25716 jacob jacob sing_222.htm#SEC263 jacoblift jacoblift sing_1140.htm#SEC1217 40125 jacobson jacobson sing_1391.htm#SEC1468 56107 jacobson.lib jacobson_lib sing_1389.htm#SEC1466 jacobson_lib jacobson_lib sing_1389.htm#SEC1466 janet janet sing_223.htm#SEC264 jet jet sing_224.htm#SEC265 jordan jordan sing_849.htm#SEC926 16602 jordanbasis jordanbasis sing_850.htm#SEC927 12736 jordanmatrix jordanmatrix sing_851.htm#SEC928 2886 jordannf jordannf sing_852.htm#SEC929 20535 katsura katsura sing_729.htm#SEC806 45913 kbase kbase sing_225.htm#SEC266 kbase (plural) kbase (plural) sing_398.htm#SEC439 keepring keepring sing_324.htm#SEC365 kernel kernel sing_226.htm#SEC267 kill kill sing_227.htm#SEC268 killall killall sing_702.htm#SEC779 34661 killattrib killattrib sing_228.htm#SEC269 kmemory kmemory sing_701.htm#SEC778 52193 kohom kohom sing_905.htm#SEC982 50086 kontrahom kontrahom sing_906.htm#SEC983 58549 koszul koszul sing_229.htm#SEC270 kskernel.lib kskernel_lib sing_1131.htm#SEC1208 kskernel_lib kskernel_lib sing_1131.htm#SEC1208 laguerre laguerre sing_230.htm#SEC271 laguerre_solve laguerre_solve sing_1267.htm#SEC1344 10155 lastvarGeneral lastvarGeneral sing_1485.htm#SEC1562 28645 latex.lib latex_lib sing_1311.htm#SEC1388 latex_lib latex_lib sing_1311.htm#SEC1388 latticeArea latticeArea sing_1537.htm#SEC1614 2068 lazy, option option sing_259.htm#IDX211 lcm lcm sing_732.htm#SEC809 44755 lcmN lcmN sing_1423.htm#SEC1500 52355 lead lead sing_231.htm#SEC272 leadcoef leadcoef sing_232.htm#SEC273 leadexp leadexp sing_233.htm#SEC274 leadmonom leadmonom sing_234.htm#SEC275 leadmonomial leadmonomial sing_1471.htm#SEC1548 8195 leftInverse leftInverse sing_1380.htm#SEC1457 41469 leftKernel leftKernel sing_1378.htm#SEC1455 9292 length, option option sing_259.htm#IDX212 letterplace correspondence Letterplace correspondence sing_428.htm#SEC481 lex_solve lex_solve sing_1273.htm#SEC1350 48692 lexicographical ordering Global orderings sing_652.htm#IDX325 lib2doc lib2doc sing_53.htm#SEC91 libfac Preface sing_1.htm#IDX7 libparse libparse sing_66.htm#SEC107 library, Guidelines for writing Guidelines for writing a library sing_50.htm#SEC88 library, documentation Documentation of a library sing_52.htm#SEC90 library, help string The help string of a library sing_55.htm#SEC93 library, info string template_lib sing_55.htm#SEC93 library, info string sing_57.htm#IDX196 library, procedures Procedures in a library sing_51.htm#SEC89 library, template template_lib sing_57.htm#SEC95 library, template.lib template_lib sing_57.htm#IDX194 library, typesetting of help strings Typesetting of help strings sing_54.htm#SEC92 lieBracket lieBracket sing_526.htm#SEC579 32736 lift lift sing_236.htm#SEC277 lift (plural) lift (plural) sing_399.htm#SEC440 lift_kbase lift_kbase sing_1077.htm#SEC1154 10906 lift_rel_kb lift_rel_kb sing_1078.htm#SEC1155 13673 liftstd liftstd sing_237.htm#SEC278 liftstd (plural) liftstd (plural) sing_400.htm#SEC441 linReduce linReduce sing_440.htm#SEC493 64913 linReduceIdeal linReduceIdeal sing_441.htm#SEC494 19076 linSyzSolve linSyzSolve sing_442.htm#SEC495 26185 linalg.lib linalg_lib sing_827.htm#SEC904 linalg_lib linalg_lib sing_827.htm#SEC904 linear code, dual dual_code sing_1349.htm#IDX509 linear code, systematic sys_code sing_1350.htm#IDX510 linearCombinations linearCombinations sing_461.htm#SEC514 20514 linearMapKernel linearMapKernel sing_460.htm#SEC513 43761 linear_relations linear_relations sing_819.htm#SEC896 45983 linearpart linearpart sing_1259.htm#SEC1336 2162 link Parallelization with MPtcp links sing_99.htm#SEC140 link sing_609.htm#SEC662 link declarations link declarations sing_100.htm#SEC141 link expressions link expressions sing_101.htm#SEC142 link related functions link related functions sing_102.htm#SEC143 list list sing_108.htm#SEC149 list declarations list declarations sing_109.htm#SEC150 list expressions list expressions sing_110.htm#SEC151 list operations list operations sing_111.htm#SEC152 list related functions list related functions sing_112.htm#SEC153 listvar listvar sing_238.htm#SEC279 lll.lib lll_lib sing_912.htm#SEC989 lll_lib lll_lib sing_912.htm#SEC989 load load sing_325.htm#SEC366 loadLib, option option sing_259.htm#IDX227 loadProc, option option sing_259.htm#IDX229 locAtZero locAtZero sing_958.htm#SEC1035 5687 local names Names in procedures sing_44.htm#SEC82 local rings, computing in Rings associated to monomial orderings sing_604.htm#SEC657 local weighted lexicographical ordering Local orderings sing_653.htm#IDX346 local weighted reverse lexicographical ordering Local orderings sing_653.htm#IDX343 localInvar localInvar sing_1229.htm#SEC1306 38478 localization Rings associated to monomial orderings sing_604.htm#SEC657 localstd localstd sing_1481.htm#SEC1558 25562 locstd locstd sing_1162.htm#SEC1239 25864 log2 log2 sing_1396.htm#SEC1473 40703 lp, global ordering Global orderings sing_652.htm#IDX324 lp2lstr lp2lstr sing_522.htm#SEC575 24713 lpMult lpMult sing_521.htm#SEC574 58898 lprint lprint sing_718.htm#SEC795 5285 lres lres sing_239.htm#SEC280 ls, local ordering Local orderings sing_653.htm#IDX337 lst2str lst2str sing_523.htm#SEC576 10088 makeHeisenberg makeHeisenberg sing_576.htm#SEC629 2050 makeLetterplaceRing makeLetterplaceRing sing_518.htm#SEC571 53638 makeModElimRing makeModElimRing sing_591.htm#SEC644 30412 makeQsl2 makeQsl2 sing_561.htm#SEC614 3997 makeQsl3 makeQsl3 sing_562.htm#SEC615 41249 makeQso3 makeQso3 sing_560.htm#SEC613 58910 makeUe6 makeUe6 sing_557.htm#SEC610 58585 makeUe7 makeUe7 sing_558.htm#SEC611 61849 makeUe8 makeUe8 sing_559.htm#SEC612 64987 makeUf4 makeUf4 sing_556.htm#SEC609 8408 makeUg2 makeUg2 sing_555.htm#SEC608 34512 makeUgl makeUgl sing_541.htm#SEC594 3543 makeUsl makeUsl sing_540.htm#SEC593 24536 makeUsl2 makeUsl2 sing_539.htm#SEC592 42637 makeUso10 makeUso10 sing_547.htm#SEC600 6936 makeUso11 makeUso11 sing_548.htm#SEC601 35873 makeUso12 makeUso12 sing_549.htm#SEC602 19319 makeUso5 makeUso5 sing_542.htm#SEC595 34378 makeUso6 makeUso6 sing_543.htm#SEC596 65009 makeUso7 makeUso7 sing_544.htm#SEC597 49142 makeUso8 makeUso8 sing_545.htm#SEC598 33275 makeUso9 makeUso9 sing_546.htm#SEC599 16896 makeUsp1 makeUsp1 sing_550.htm#SEC603 44522 makeUsp2 makeUsp2 sing_551.htm#SEC604 18017 makeUsp3 makeUsp3 sing_552.htm#SEC605 57445 makeUsp4 makeUsp4 sing_553.htm#SEC606 51690 makeUsp5 makeUsp5 sing_554.htm#SEC607 35951 makeWeyl makeWeyl sing_575.htm#SEC628 8554 map map sing_113.htm#SEC154 map (plural) map (plural) sing_364.htm#SEC405 map declarations map declarations sing_114.htm#SEC155 map declarations (plural) map declarations (plural) sing_365.htm#SEC406 map expressions map expressions sing_115.htm#SEC156 map expressions (plural) map expressions (plural) sing_366.htm#SEC407 map operations map operations sing_116.htm#IDX201 map operations (plural) map operations (plural) sing_367.htm#IDX290 map related functions map related functions sing_117.htm#IDX202 map related functions (plural) map related functions (plural) sing_368.htm#IDX291 mapIsFinite mapIsFinite sing_866.htm#SEC943 60897 mapall mapall sing_787.htm#SEC864 41330 markov4ti2 markov4ti2 sing_1029.htm#SEC1106 9163 mat_rk mat_rk sing_841.htm#SEC918 32196 matbil matbil sing_1492.htm#SEC1569 1611 mathematical objects Representation of mathematical objects sing_648.htm#SEC701 mathinit mathinit sing_1309.htm#SEC1386 16793 matmult matmult sing_1493.htm#SEC1570 60088 matrix matrix sing_118.htm#SEC159 matrix declarations matrix declarations sing_119.htm#SEC160 matrix expressions matrix expressions sing_120.htm#SEC161 matrix operations matrix operations sing_122.htm#SEC163 matrix related functions matrix related functions sing_123.htm#SEC164 matrix type cast matrix type cast sing_121.htm#SEC162 matrix.lib matrix_lib sing_794.htm#SEC871 matrixT1 matrixT1 sing_1176.htm#SEC1253 15051 matrix_lib matrix_lib sing_794.htm#SEC871 maxabs maxabs sing_1511.htm#SEC1588 64510 maxcoef maxcoef sing_733.htm#SEC810 50577 maxdeg maxdeg sing_734.htm#SEC811 39794 maxdeg1 maxdeg1 sing_735.htm#SEC812 21545 maxideal maxideal sing_240.htm#SEC281 maximum maximum sing_1409.htm#SEC1486 2355 mdouble mdouble sing_58.htm#SEC96 63216 mem, option option sing_259.htm#IDX230 memberpos memberpos sing_764.htm#SEC841 15764 memory memory sing_241.htm#SEC282 memory managment memory sing_241.htm#SEC282 milnor milnor sing_1163.htm#SEC1240 23173 milnorcode milnorcode sing_1061.htm#SEC1138 13849 minAssChar minAssChar sing_969.htm#SEC1046 50088 minAssGTZ minAssGTZ sing_968.htm#SEC1045 6194 minEcart minEcart sing_1474.htm#SEC1551 34890 minIntRoot minIntRoot sing_495.htm#SEC548 3288 minbase minbase sing_242.htm#SEC283 mindeg mindeg sing_736.htm#SEC813 16307 mindeg1 mindeg1 sing_737.htm#SEC814 39698 mindist mindist sing_1364.htm#SEC1441 15194 minimal display time, setting the system sing_297.htm#IDX273 minipoly minipoly sing_846.htm#SEC923 4927 minor minor sing_243.htm#SEC284 minpoly minpoly sing_333.htm#SEC374 minres minres sing_244.htm#SEC285 minres (plural) minres (plural) sing_401.htm#SEC442 mixed Hodge structure goodBasis sing_1085.htm#IDX422 mixed Hodge structure sing_1091.htm#IDX433 mixed Hodge structure sing_1092.htm#IDX436 mixed Hodge structure sing_1093.htm#IDX441 mixed Hodge structure sing_1094.htm#IDX444 mixed Hodge structure sing_1107.htm#IDX455 mixed Hodge structure sing_1109.htm#IDX466 mod number operations sing_72.htm#SEC113 mod sing_84.htm#SEC125 mod sing_132.htm#SEC173 mod2id mod2id sing_743.htm#SEC820 27927 mod2str mod2str sing_524.htm#SEC577 35236 modDec modDec sing_922.htm#SEC999 48578 modNPos modNPos sing_945.htm#SEC1022 17130 modNpos_test modNpos_test sing_943.htm#SEC1020 34326 modS modS sing_916.htm#SEC993 30873 modStd modStd sing_915.htm#SEC992 58071 mod_versal mod_versal sing_1076.htm#SEC1153 63927 modregCM modregCM sing_949.htm#SEC1026 5049 modsatiety modsatiety sing_947.htm#SEC1024 44506 modstd.lib modstd_lib sing_914.htm#SEC991 modstd_lib modstd_lib sing_914.htm#SEC991 module module sing_124.htm#SEC165 module (plural) module (plural) sing_369.htm#SEC410 module declarations module declarations sing_125.htm#SEC166 module declarations (plural) module declarations (plural) sing_370.htm#SEC411 module expressions module expressions sing_126.htm#SEC167 module expressions (plural) module expressions (plural) sing_371.htm#SEC412 module operations module operations sing_127.htm#SEC168 module operations (plural) module operations (plural) sing_372.htm#SEC413 module ordering C Module orderings sing_654.htm#IDX349 module ordering c Module orderings sing_654.htm#IDX351 module related functions module related functions sing_128.htm#SEC169 module related functions (plural) module related functions (plural) sing_373.htm#SEC414 module_containment module_containment sing_858.htm#SEC935 31620 modulo modulo sing_245.htm#SEC286 modulo (plural) modulo (plural) sing_402.htm#SEC443 moduloSlim moduloSlim sing_581.htm#SEC634 52636 molien molien sing_1195.htm#SEC1272 63561 mondromy.lib mondromy_lib sing_1137.htm#SEC1214 mondromy_lib mondromy_lib sing_1137.htm#SEC1214 monitor monitor sing_246.htm#SEC287 monodromy goodBasis sing_1085.htm#IDX425 43893 monodromy sing_1090.htm#SEC1167 monodromy sing_1090.htm#IDX432 monodromy sing_1107.htm#IDX458 monodromy sing_1109.htm#IDX469 monodromyB monodromyB sing_1141.htm#SEC1218 46517 monomial orderings Rings associated to monomial orderings sing_604.htm#SEC657 monomial orderings sing_651.htm#SEC704 monomial orderings introduction Introduction to orderings sing_650.htm#SEC703 monomialLcm monomialLcm sing_1472.htm#SEC1549 36233 monomials and precedence Miscellaneous oddities sing_354.htm#IDX280 morsesplit morsesplit sing_1062.htm#SEC1139 3417 mp_res_mat mp_res_mat sing_1270.htm#SEC1347 44453 mplot mplot sing_1310.htm#SEC1387 21740 mpresmat mpresmat sing_247.htm#SEC288 mprimdec.lib mprimdec_lib sing_918.htm#SEC995 mprimdec_lib mprimdec_lib sing_918.htm#SEC995 mrcgs mrcgs sing_773.htm#SEC850 2281 mrcgs, rcgs, buildtree, cantreetoMaple, cantodiffcgs crcgs sing_775.htm#IDX367 mrcgs, rcgs, crcgs, Maple cantodiffcgs sing_776.htm#IDX368 mregular.lib mregular_lib sing_933.htm#SEC1010 mregular_lib mregular_lib sing_933.htm#SEC1010 mres mres sing_248.htm#SEC289 mres (plural) mres (plural) sing_403.htm#SEC444 mstd mstd sing_249.htm#SEC290 msum msum sing_60.htm#SEC98 37953 mtripple mtripple sing_59.htm#SEC97 30800 mult Miscellaneous oddities sing_250.htm#SEC291 mult sing_354.htm#IDX281 multBound multBound sing_334.htm#SEC375 multcol multcol sing_813.htm#SEC890 14330 multi multi sing_1459.htm#SEC1536 18473 multi indices Names sing_37.htm#SEC64 multiplicities, sequence of invariants sing_1116.htm#IDX481 multiplicity sequence multsequence sing_1043.htm#IDX403 multiplicity sequence sing_1046.htm#IDX415 multiplicity sequence sing_1118.htm#IDX482 multrow multrow sing_814.htm#SEC891 871 multseq2charexp multseq2charexp sing_1042.htm#SEC1119 sprintf multsequence multsequence sing_1118.htm#SEC1195 35117 nameof nameof sing_251.htm#SEC292 names names sing_252.htm#SEC293 nashmult nashmult sing_1050.htm#SEC1127 8491 nblocks system sing_297.htm#IDX256 ncRelations ncRelations sing_582.htm#SEC635 7225 nc_algebra nc_algebra sing_404.htm#SEC445 ncalg.lib ncalg_lib sing_538.htm#SEC591 ncalg.lib sing_538.htm#IDX312 ncalg_lib ncalg_lib sing_538.htm#SEC591 ncalg_lib sing_538.htm#IDX313 ncalgebra ncalgebra sing_405.htm#SEC446 ncdecomp.lib ncdecomp_lib sing_565.htm#SEC618 ncdecomp.lib sing_565.htm#IDX314 ncdecomp_lib ncdecomp_lib sing_565.htm#SEC618 ncdecomp_lib sing_565.htm#IDX315 ncdetection ncdetection sing_534.htm#SEC587 24994 ncols ncols sing_253.htm#SEC294 nctools.lib nctools_lib sing_570.htm#SEC623 nctools.lib sing_570.htm#IDX316 nctools_lib nctools_lib sing_570.htm#SEC623 nctools_lib sing_570.htm#IDX317 ndcond ndcond sing_573.htm#SEC626 1006 negative degree lexicographical ordering Local orderings sing_653.htm#IDX340 negative degree reverse lexicographical ordering Local orderings sing_653.htm#IDX338 negative lexicographical ordering Local orderings sing_653.htm#IDX336 net access Command line options sing_19.htm#IDX110 newTest newTest sing_1404.htm#SEC1481 36655 newline string sing_154.htm#SEC195 news News and changes sing_1582.htm#SEC1659 newtonDiag newtonDiag sing_747.htm#SEC824 56652 newtonPolytope newtonPolytope sing_1523.htm#SEC1600 63019 newtonPolytopeLP newtonPolytopeLP sing_1524.htm#SEC1601 12201 newtonpoly newtonpoly sing_1123.htm#SEC1200 31930 nf_icis nf_icis sing_1164.htm#SEC1241 49093 noether noether sing_335.htm#SEC376 noether.lib noether_lib sing_941.htm#SEC1018 noetherNormal noetherNormal sing_865.htm#SEC942 26007 noether_lib noether_lib sing_941.htm#SEC1018 non-english special characters Limitations sing_343.htm#IDX276 nonMonomials nonMonomials sing_961.htm#SEC1038 16309 nonZeroEntry nonZeroEntry sing_868.htm#SEC945 933 none, option option sing_259.htm#IDX207 norTest norTest sing_959.htm#SEC1036 sprintf norm norm sing_1458.htm#SEC1535 31143 normal normal sing_951.htm#SEC1028 62868 normal.lib normal_lib sing_950.htm#SEC1027 normalFan normalFan sing_1525.htm#SEC1602 59351 normalI normalI sing_990.htm#SEC1067 7663 normal_lib normal_lib sing_950.htm#SEC1027 normalform normalform sing_1066.htm#SEC1143 5550 normalization normal sing_951.htm#IDX381 normalize normalize sing_738.htm#SEC815 44788 not boolean operations sing_87.htm#SEC128 notBuckets, option option sing_259.htm#IDX215 notRegularity, option option sing_259.htm#IDX213 notSugar, option option sing_259.htm#IDX214 npars npars sing_254.htm#SEC295 nrRootsDeterm nrRootsDeterm sing_1489.htm#SEC1566 sprintf nrRootsProbab nrRootsProbab sing_1488.htm#SEC1565 sprintf nres nres sing_255.htm#SEC296 nres (plural) nres (plural) sing_406.htm#SEC447 nrows nrows sing_256.htm#SEC297 nrroots nrroots sing_1518.htm#SEC1595 54867 nsatiety nsatiety sing_946.htm#SEC1023 53333 nselect nselect sing_879.htm#SEC956 34057 nt_solve nt_solve sing_1285.htm#SEC1362 33061 ntsolve.lib ntsolve_lib sing_1284.htm#SEC1361 ntsolve_lib ntsolve_lib sing_1284.htm#SEC1361 number number sing_129.htm#SEC170 number declarations number declarations sing_130.htm#SEC171 number expressions number expressions sing_131.htm#SEC172 number operations number operations sing_132.htm#SEC173 number related functions number related functions sing_133.htm#SEC174 number_e number_e sing_703.htm#SEC780 59152 number_pi number_pi sing_704.htm#SEC781 15492 numerator numerator sing_741.htm#SEC818 27025 nvars nvars sing_257.htm#SEC298 oldStd, option option sing_259.htm#IDX216 online help The online help system sing_16.htm#SEC22 open open sing_258.htm#SEC299 opentex opentex sing_1313.htm#SEC1390 54236 operatorBM operatorBM sing_473.htm#SEC526 4459 operatorModulo operatorModulo sing_474.htm#SEC527 2619 oppose oppose sing_407.htm#SEC448 opposite opposite sing_408.htm#SEC449 option option sing_259.htm#SEC300 or Evaluation of logical expressions sing_87.htm#SEC128 or sing_347.htm#SEC388 orbit_variety orbit_variety sing_1219.htm#SEC1296 22665 ord ord sing_260.htm#SEC301 ord_test ord_test sing_788.htm#SEC865 57202 orderings General definitions for orderings sing_651.htm#SEC704 orderings introduction Introduction to orderings sing_650.htm#SEC703 orderings, M Matrix orderings sing_655.htm#SEC708 orderings, a Extra weight vector sing_657.htm#SEC710 orderings, global Global orderings sing_652.htm#SEC705 orderings, local Local orderings sing_653.htm#SEC706 orderings, product Product orderings sing_656.htm#SEC709 ordstr ordstr sing_261.htm#SEC302 orthogonalize orthogonalize sing_832.htm#SEC909 63711 outer outer sing_802.htm#SEC879 64048 output Input and output sing_41.htm#SEC70 p-adic numbers, l-adic numbers, projective limes Coefficient rings sing_32.htm#SEC45 pFactor pFactor sing_1440.htm#SEC1517 33542 pIntersect pIntersect sing_438.htm#SEC491 44055 pIntersectSyz pIntersectSyz sing_439.htm#SEC492 28446 package package sing_134.htm#SEC175 package declarations package declarations sing_135.htm#SEC176 package related functions package related functions sing_136.htm#SEC177 pairset pairset sing_1478.htm#SEC1555 38258 par par sing_262.htm#SEC303 par2varRing par2varRing sing_687.htm#SEC764 44769 param param sing_1114.htm#SEC1191 57220 parameter, as numbers number sing_129.htm#SEC170 parameterSubstitute parameterSubstitute sing_1571.htm#SEC1648 38314 parametrization param sing_1114.htm#IDX476 pardeg pardeg sing_263.htm#SEC304 parstr parstr sing_264.htm#SEC305 partial_molien partial_molien sing_1197.htm#SEC1274 21772 path Loading a library sing_48.htm#SEC86 pause pause sing_726.htm#SEC803 2273 pdivi pdivi sing_766.htm#SEC843 19679 permcol permcol sing_815.htm#SEC892 12886 permrow permrow sing_816.htm#SEC893 26561 permute_L permute_L sing_1351.htm#SEC1428 10716 perron perron sing_593.htm#SEC646 3782 perron.lib perron_lib sing_592.htm#SEC645 perron.lib sing_592.htm#IDX318 perron_lib perron_lib sing_592.htm#SEC645 perron_lib sing_592.htm#IDX319 phindex.lib phindex_lib sing_1576.htm#IDX532 phindex_lib phindex_lib sing_1576.htm#SEC1653 phindex_lib sing_1576.htm#IDX533 picksFormula picksFormula sing_1538.htm#SEC1615 53613 pid system sing_297.htm#IDX240 plot plot sing_1330.htm#SEC1407 51767 plotRot plotRot sing_1333.htm#SEC1410 57150 plotRotated plotRotated sing_1332.htm#SEC1409 33009 plotRotatedDirect plotRotatedDirect sing_1335.htm#SEC1412 18202 plotRotatedList plotRotatedList sing_1334.htm#SEC1411 41668 plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1336.htm#SEC1413 38856 pmat pmat sing_719.htm#SEC796 3857 pnormalform pnormalform sing_769.htm#SEC846 6751 pointid.lib pointid_lib sing_960.htm#SEC1037 pointid_lib pointid_lib sing_960.htm#SEC1037 poly poly sing_137.htm#SEC178 poly (plural) poly (plural) sing_374.htm#SEC415 poly declarations poly declarations sing_138.htm#SEC179 poly declarations (plural) poly declarations (plural) sing_375.htm#SEC416 poly expressions poly expressions sing_139.htm#SEC180 poly expressions (plural) poly expressions (plural) sing_376.htm#SEC417 poly operations poly operations sing_140.htm#SEC181 poly operations (plural) poly operations (plural) sing_377.htm#SEC418 poly related functions poly related functions sing_141.htm#SEC182 poly related functions (plural) poly related functions (plural) sing_378.htm#SEC419 poly.lib poly_lib sing_727.htm#SEC804 poly2list poly2list sing_513.htm#SEC566 24267 poly_lib poly_lib sing_727.htm#SEC804 polymake polymake_lib sing_1521.htm#IDX525 polymake.lib polymake_lib sing_1521.htm#SEC1598 polymakeKeepTmpFiles polymakeKeepTmpFiles sing_1541.htm#SEC1618 20979 polymakePolytope polymakePolytope sing_1522.htm#SEC1599 11504 polymakeToIntmat polymakeToIntmat sing_1528.htm#SEC1605 24343 polymake_lib polymake_lib sing_1521.htm#SEC1598 polymake_lib sing_1521.htm#SEC1598 polytope polymake_lib sing_1521.htm#IDX521 pos_def pos_def sing_843.htm#SEC920 4994 posweight posweight sing_1181.htm#SEC1258 3364 power power sing_803.htm#SEC880 3196 powerN powerN sing_1424.htm#SEC1501 20170 powerX powerX sing_1433.htm#SEC1510 47971 power_products power_products sing_1211.htm#SEC1288 54629 powerpolyX powerpolyX sing_1401.htm#SEC1478 37247 powersums powersums sing_1499.htm#SEC1576 59049 preComp preComp sing_929.htm#SEC1006 16160 preimage preimage sing_265.htm#SEC306 preimage (plural) preimage (plural) sing_409.htm#SEC450 preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_791.htm#IDX369 preimageLoc preimageLoc sing_791.htm#SEC868 33315 prepEmbDiv prepEmbDiv sing_1010.htm#SEC1087 36708 prepMat prepMat sing_1248.htm#SEC1325 39868 prepSV prepSV sing_1346.htm#SEC1423 50095 prepareAss prepareAss sing_974.htm#SEC1051 21802 presentTree presentTree sing_997.htm#SEC1074 10731 presolve.lib presolve_lib sing_1251.htm#SEC1328 presolve_lib presolve_lib sing_1251.htm#SEC1328 primL primL sing_1428.htm#SEC1505 45709 primList primList sing_1427.htm#SEC1504 6802 primTest primTest sing_928.htm#SEC1005 8105 primary_char0 primary_char0 sing_1201.htm#SEC1278 61413 primary_char0_no_molien primary_char0_no_molien sing_1203.htm#SEC1280 50477 primary_char0_no_molien_random primary_char0_no_molien_random sing_1208.htm#SEC1285 8422 primary_char0_random primary_char0_random sing_1206.htm#SEC1283 5996 primary_charp primary_charp sing_1202.htm#SEC1279 37863 primary_charp_no_molien primary_charp_no_molien sing_1204.htm#SEC1281 32282 primary_charp_no_molien_random primary_charp_no_molien_random sing_1209.htm#SEC1286 11498 primary_charp_random primary_charp_random sing_1207.htm#SEC1284 24739 primary_charp_without primary_charp_without sing_1205.htm#SEC1282 49585 primary_charp_without_random primary_charp_without_random sing_1210.htm#SEC1287 36998 primary_invariants primary_invariants sing_1189.htm#SEC1266 5500 primary_invariants_random primary_invariants_random sing_1190.htm#SEC1267 28958 primdec.lib primdec_lib sing_964.htm#SEC1041 primdecGTZ primdecGTZ sing_966.htm#SEC1043 10548 primdecSY primdecSY sing_967.htm#SEC1044 40294 primdec_lib primdec_lib sing_964.htm#SEC1041 prime prime sing_266.htm#SEC307 primeClosure primeClosure sing_954.htm#SEC1031 61884 primeList primeList sing_917.htm#SEC994 26450 primecoeffs primecoeffs sing_711.htm#SEC788 33334 primefactors primefactors sing_712.htm#SEC789 30122 primes primes sing_705.htm#SEC782 24408 primitiv.lib primitiv_lib sing_980.htm#SEC1057 primitiv_lib primitiv_lib sing_980.htm#SEC1057 primitive primitive sing_981.htm#SEC1058 36163 primitive element primitive sing_981.htm#IDX386 primitive_extra primitive_extra sing_982.htm#SEC1059 49025 print print sing_267.htm#SEC308 printf printf sing_268.htm#SEC309 2294 printlevel printlevel sing_336.htm#SEC377 proc proc sing_142.htm#SEC183 proc declaration proc declaration sing_143.htm#SEC184 procedure, ASCII help mdouble sing_58.htm#IDX197 procedure, ASCII/Texinfo help msum sing_60.htm#IDX199 procedure, texinfo help mtripple sing_59.htm#IDX198 procedures, help string The help string of procedures sing_56.htm#SEC94 procedures, static Procedure definition sing_43.htm#SEC78 prodcrit prodcrit sing_1476.htm#SEC1553 56231 product product sing_706.htm#SEC783 54431 progress watch option sing_259.htm#IDX219 prompt The SINGULAR prompt sing_15.htm#SEC21 prompt, option option sing_259.htm#IDX231 prot, option option sing_259.htm#IDX217 protocol of computations option sing_259.htm#IDX218 proximitymatrix proximitymatrix sing_1041.htm#SEC1118 58403 prune prune sing_269.htm#SEC310 psigncnd psigncnd sing_1304.htm#SEC1381 57734 puiseux2generators puiseux2generators sing_1126.htm#SEC1203 64508 pwalk pwalk sing_888.htm#SEC965 61187 qbase qbase sing_1502.htm#SEC1579 8633 qhmatrix qhmatrix sing_1179.htm#SEC1256 61813 qhmoduli.lib qhmoduli_lib sing_1143.htm#SEC1220 qhmoduli_lib qhmoduli_lib sing_1143.htm#SEC1220 qhspectrum qhspectrum sing_1166.htm#SEC1243 13732 qhweight qhweight sing_270.htm#SEC311 qmatrix.lib qmatrix_lib sing_594.htm#SEC647 qmatrix.lib sing_594.htm#IDX322 qmatrix_lib qmatrix_lib sing_594.htm#SEC647 qmatrix_lib sing_594.htm#IDX323 qminor qminor sing_596.htm#SEC649 52670 qring Miscellaneous oddities sing_144.htm#SEC185 qring sing_354.htm#IDX285 qring (plural) qring (plural) sing_379.htm#SEC420 qring declaration qring declaration sing_145.htm#SEC186 qring declaration (plural) qring declaration (plural) sing_380.htm#SEC421 qring related functions (plural) qring related functions (plural) sing_381.htm#SEC422 qslimgb qslimgb sing_686.htm#SEC763 51999 quadraticSieve quadraticSieve sing_1441.htm#SEC1518 58557 quantMat quantMat sing_595.htm#SEC648 56227 quickclass quickclass sing_1063.htm#SEC1140 14018 quit quit sing_326.htm#SEC367 quote quote sing_271.htm#SEC312 quotient quotient sing_272.htm#SEC313 quotient (plural) quotient (plural) sing_410.htm#SEC451 quotientMain quotientMain sing_1296.htm#SEC1373 39870 rMacaulay rMacaulay sing_720.htm#SEC797 45499 rad_con rad_con sing_739.htm#SEC816 21777 radical radical sing_971.htm#SEC1048 1407 radicalEHV radicalEHV sing_972.htm#SEC1049 33703 radicalMemberShip radicalMemberShip sing_1565.htm#SEC1642 28527 randcharpoly randcharpoly sing_1496.htm#SEC1573 37737 randlinpoly randlinpoly sing_1498.htm#SEC1575 22330 random random sing_273.htm#SEC314 random number generator, seed system sing_297.htm#IDX268 random.lib random_lib sing_749.htm#SEC826 randomBinomial randomBinomial sing_761.htm#SEC838 39056 randomCheck randomCheck sing_1362.htm#SEC1439 20973 randomLast randomLast sing_760.htm#SEC837 2046 randomPoly randomPoly sing_1573.htm#SEC1650 6278 random_lib random_lib sing_749.htm#SEC826 randomid randomid sing_751.htm#SEC828 7815 randommat randommat sing_752.htm#SEC829 33569 rational univariate projection randcharpoly sing_1496.htm#IDX518 rcgs rcgs sing_774.htm#SEC851 3560 rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs rcgs sing_773.htm#IDX365 rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs sing_774.htm#IDX366 read read sing_274.htm#SEC315 reading, option option sing_259.htm#IDX232 readline Preface sing_1.htm#IDX6 real Rings and orderings sing_28.htm#IDX144 real roots, univariate polynomial rootsur_lib sing_1503.htm#IDX520 real roots, univariate projection rootsmr_lib sing_1487.htm#IDX516 real roots,sign conditions signcond_lib sing_1302.htm#IDX499 realpoly realpoly sing_985.htm#SEC1062 9453 realrad realrad sing_987.htm#SEC1064 43381 realrad.lib realrad_lib sing_984.htm#SEC1061 realrad_lib realrad_lib sing_984.htm#SEC1061 realzero realzero sing_986.htm#SEC1063 12712 redSB, option option sing_259.htm#IDX220 redTail, option option sing_259.htm#IDX222 redThrough, option option sing_259.htm#IDX223 redcgs.lib redcgs_lib sing_762.htm#SEC839 redcgs_lib redcgs_lib sing_762.htm#SEC839 redefine, option option sing_259.htm#IDX233 redspec redspec sing_768.htm#SEC845 12952 reduce central_lib sing_275.htm#SEC316 reduce sing_446.htm#IDX299 reduce (plural) reduce (plural) sing_411.htm#SEC452 reduced standard basis option sing_259.htm#IDX221 reduction reduction sing_1227.htm#SEC1304 31048 reesclos.lib reesclos_lib sing_988.htm#SEC1065 reesclos_lib reesclos_lib sing_988.htm#SEC1065 regCM regCM sing_948.htm#SEC1025 sprintf regIdeal regIdeal sing_934.htm#SEC1011 3827 regMonCurve regMonCurve sing_937.htm#SEC1014 41311 regularity Syzygies and resolutions sing_276.htm#SEC317 regularity sing_661.htm#SEC719 reiffen reiffen sing_492.htm#SEC545 32856 rel_orbit_variety rel_orbit_variety sing_1220.htm#SEC1297 34278 relations perron_lib sing_592.htm#IDX321 relative_orbit_variety relative_orbit_variety sing_1221.htm#SEC1298 32995 relweight relweight sing_1180.htm#SEC1257 10658 remainder remainder sing_1289.htm#SEC1366 1191 remainderMain remainderMain sing_1297.htm#SEC1374 3532 removepower removepower sing_1051.htm#SEC1128 47644 repart repart sing_277.htm#SEC318 representation, math objects Representation of mathematical objects sing_648.htm#SEC701 res res sing_278.htm#SEC319 53499 reservedName reservedName sing_279.htm#SEC320 resgraph.lib resgraph_lib sing_1325.htm#SEC1402 resgraph_lib resgraph_lib sing_1325.htm#SEC1402 resolution resolution sing_146.htm#SEC187 resolution (plural) resolution (plural) sing_382.htm#SEC423 resolution declarations resolution declarations sing_147.htm#SEC188 resolution declarations (plural) resolution declarations (plural) sing_383.htm#SEC424 resolution expressions resolution expressions sing_148.htm#SEC189 resolution expressions (plural) resolution expressions (plural) sing_384.htm#SEC425 resolution graph alexpoly_lib sing_1036.htm#IDX399 resolution related functions resolution related functions sing_149.htm#SEC190 resolution related functions (plural) resolution related functions (plural) sing_385.htm#SEC426 resolution, La Scala's method lres sing_239.htm#SEC280 resolution, computation of res sing_278.htm#IDX235 resolution, hilbert-driven hres sing_214.htm#SEC255 resolutiongraph resolutiongraph sing_1037.htm#SEC1114 32697 resolve resolve sing_995.htm#SEC1072 8099 resolve.lib resolve_lib sing_991.htm#SEC1068 resolve_lib resolve_lib sing_991.htm#SEC1068 resultant resultant sing_280.htm#SEC321 reszeta.lib reszeta_lib sing_1004.htm#SEC1081 reszeta_lib reszeta_lib sing_1004.htm#SEC1081 return return sing_327.htm#SEC368 return type of procedures Return type of procedures sing_352.htm#SEC393 returnSB, option option sing_259.htm#IDX208 reverse reverse sing_1517.htm#SEC1594 35880 reverse lexicographical ordering Global orderings sing_652.htm#IDX327 reynolds_molien reynolds_molien sing_1196.htm#SEC1273 45316 rho rho sing_1435.htm#SEC1512 51414 rightInverse rightInverse sing_1381.htm#SEC1458 6558 rightKernel rightKernel sing_1379.htm#SEC1456 46603 rightStd rightStd sing_580.htm#SEC633 5740 ring ring sing_150.htm#SEC191 ring (plural) ring (plural) sing_386.htm#SEC427 ring declarations ring declarations sing_151.htm#SEC192 ring declarations (plural) ring declarations (plural) sing_387.htm#SEC428 ring operations ring operations sing_153.htm#SEC194 ring operations (plural) ring operations (plural) sing_388.htm#SEC429 ring related functions ring related functions sing_152.htm#SEC193 ring related functions (plural) ring related functions (plural) sing_389.htm#SEC430 ring, rings setglobalrings sing_763.htm#IDX357 ring.lib ring_lib sing_777.htm#SEC854 ring_lib ring_lib sing_777.htm#SEC854 ringlist ringlist sing_281.htm#SEC322 ringlist (plural) ringlist (plural) sing_412.htm#SEC453 ringtensor ringtensor sing_789.htm#SEC866 56648 ringweights ringweights sing_790.htm#SEC867 33307 rinvar.lib rinvar_lib sing_1232.htm#SEC1309 rinvar_lib rinvar_lib sing_1232.htm#SEC1309 rm_unitcol rm_unitcol sing_821.htm#SEC898 5591 rm_unitrow rm_unitrow sing_820.htm#SEC897 35694 rmx rmx sing_1323.htm#SEC1400 17675 rootofUnity rootofUnity sing_792.htm#SEC869 21365 roots roots sing_1290.htm#SEC1367 18436 rootsMain rootsMain sing_1298.htm#SEC1375 54934 rootsModp rootsModp sing_1415.htm#SEC1492 24252 rootsmr.lib rootsmr_lib sing_1487.htm#SEC1564 rootsmr_lib rootsmr_lib sing_1487.htm#SEC1564 rootsur.lib rootsur_lib sing_1503.htm#SEC1580 rootsur_lib rootsur_lib sing_1503.htm#SEC1580 round round sing_1413.htm#SEC1490 9248 rowred rowred sing_817.htm#SEC894 63416 rp, global ordering Global orderings sing_652.htm#IDX326 rvalue No rvalue of increments and assignments sing_346.htm#SEC387 rvar rvar sing_282.htm#SEC323 sa_poly_reduce sa_poly_reduce sing_455.htm#SEC508 60856 sa_reduce sa_reduce sing_454.htm#SEC507 55799 sagbi sagbi sing_1016.htm#SEC1093 48546 sagbi.lib sagbi_lib sing_1012.htm#SEC1089 sagbiNF sagbiNF sing_1015.htm#SEC1092 19752 sagbiPart sagbiPart sing_1017.htm#SEC1094 28068 sagbiRreduction sagbiRreduction sing_1013.htm#SEC1090 sprintf sagbiSPoly sagbiSPoly sing_1014.htm#SEC1091 34863 sagbi_lib sagbi_lib sing_1012.htm#SEC1089 sameComponent sameComponent sing_1470.htm#SEC1547 13540 sameQ sameQ sing_1301.htm#SEC1378 45579 sat sat sing_880.htm#SEC957 34991 satiety satiety sing_936.htm#SEC1013 34323 scalarProd scalarProd sing_444.htm#SEC497 54488 sdb, source code debugger Source code debugger sing_63.htm#SEC101 secondary fan polymake_lib sing_1521.htm#IDX523 secondary polytope polymake_lib sing_1521.htm#IDX524 secondaryFan secondaryFan sing_1531.htm#SEC1608 17938 secondaryPolytope secondaryPolytope sing_1530.htm#SEC1607 6405 secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1217.htm#SEC1294 37058 secondary_char0 secondary_char0 sing_1212.htm#SEC1289 31029 secondary_charp secondary_charp sing_1214.htm#SEC1291 16364 secondary_no_molien secondary_no_molien sing_1215.htm#SEC1292 3616 secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1218.htm#SEC1295 31675 select select sing_881.htm#SEC958 17096 select1 select1 sing_882.htm#SEC959 32617 semiCMcod2 semiCMcod2 sing_1177.htm#SEC1254 15905 semidiv semidiv sing_1462.htm#SEC1539 58107 semigroup charexp2generators sing_1040.htm#SEC1117 29045 semigroup sing_1044.htm#IDX406 semigroup of values invariants sing_1116.htm#IDX478 separateHNE separateHNE sing_1127.htm#SEC1204 12052 separator separator sing_919.htm#SEC996 33000 serreRelations serreRelations sing_527.htm#SEC580 33994 setLetterplaceAttributes setLetterplaceAttributes sing_520.htm#SEC573 49210 setenv system sing_297.htm#IDX247 setglobalrings setglobalrings sing_763.htm#SEC840 3471 setring setring sing_283.htm#SEC324 sh system sing_297.htm#IDX238 sheaf cohomology sheafcoh_lib sing_1018.htm#IDX389 sheafCoh sheafCoh sing_1024.htm#SEC1101 64501 sheafCohBGG sheafCohBGG sing_1022.htm#SEC1099 13439 sheafCohBGG2 sheafCohBGG2 sing_1023.htm#SEC1100 3338 sheafcoh.lib sheafcoh_lib sing_1018.htm#SEC1095 sheafcoh_lib sheafcoh_lib sing_1018.htm#SEC1095 short short sing_337.htm#SEC378 show show sing_721.htm#SEC798 15599 showBO showBO sing_996.htm#SEC1073 20089 showDataTypes showDataTypes sing_998.htm#SEC1075 4270 showrecursive showrecursive sing_722.htm#SEC799 6127 signatureL signatureL sing_1577.htm#SEC1654 65493 signatureLqf signatureLqf sing_1578.htm#SEC1655 18811 signcnd signcnd sing_1303.htm#SEC1380 40147 signcond.lib signcond_lib sing_1302.htm#SEC1379 signcond_lib signcond_lib sing_1302.htm#SEC1379 simplex simplex sing_284.htm#SEC325 simplexOut simplexOut sing_1274.htm#SEC1351 56099 simplify simplify sing_285.htm#SEC326 sing.lib sing_lib sing_1153.htm#SEC1230 sing4ti2.lib sing4ti2_lib sing_1028.htm#SEC1105 sing4ti2_lib sing4ti2_lib sing_1028.htm#SEC1105 sing_lib sing_lib sing_1153.htm#SEC1230 singularities spectrumnd sing_1085.htm#IDX419 singularities sing_1184.htm#IDX493 singularities, resolution of Resolution of singularities sing_637.htm#SEC690 singularity singularity sing_1064.htm#SEC1141 23002 singularrc Startup sequence sing_20.htm#IDX143 size Miscellaneous oddities sing_286.htm#SEC327 size sing_354.htm#IDX284 skewmat skewmat sing_804.htm#SEC881 2167 sleep status sing_292.htm#SEC333 slimgb slim Groebner bases sing_287.htm#SEC328 slimgb sing_614.htm#SEC667 slimgb (plural) slimgb (plural) sing_413.htm#SEC454 slocus slocus sing_1165.htm#SEC1242 33229 smith smith sing_1390.htm#SEC1467 31292 solutionsMod2 solutionsMod2 sing_1432.htm#SEC1509 53360 solve solve sing_1268.htm#SEC1345 3078 solve.lib solve_lib sing_1266.htm#SEC1343 solveTInitialFormPar solveTInitialFormPar sing_1568.htm#SEC1645 31360 solve_IP solve_IP sing_911.htm#SEC988 59518 solve_lib solve_lib sing_1266.htm#SEC1343 solvelinearpart solvelinearpart sing_1261.htm#SEC1338 42872 sort sort sing_707.htm#SEC784 49553 sortandmap sortandmap sing_1262.htm#SEC1339 10314 sortier sortier sing_1231.htm#SEC1308 3555 sortvars sortvars sing_1263.htm#SEC1340 61778 sortvec sortvec sing_288.htm#SEC329 source code debugger, sdb Source code debugger sing_63.htm#SEC101 spadd spadd sing_1099.htm#SEC1176 48739 sparseHomogIdeal sparseHomogIdeal sing_758.htm#SEC835 34709 sparseid sparseid sing_753.htm#SEC830 20824 sparsemat sparsemat sing_755.htm#SEC832 17653 sparsematrix sparsematrix sing_754.htm#SEC831 41031 sparsepoly sparsepoly sing_756.htm#SEC833 21649 sparsetriag sparsetriag sing_757.htm#SEC834 50657 spcurve.lib spcurve_lib sing_1173.htm#SEC1250 spcurve_lib spcurve_lib sing_1173.htm#SEC1250 special characters, non-english Limitations sing_343.htm#IDX277 specification redspec sing_768.htm#IDX360 spectral pairs goodBasis sing_1085.htm#IDX427 spectral pairs sing_1092.htm#IDX440 spectral pairs sing_1094.htm#IDX448 spectral pairs sing_1107.htm#IDX460 spectral pairs sing_1109.htm#IDX471 spectralNeg spectralNeg sing_1006.htm#SEC1083 36691 spectrum spectrumnd sing_1085.htm#IDX426 33857 spectrum sing_1091.htm#SEC1168 spectrum sing_1091.htm#IDX435 spectrum sing_1092.htm#IDX439 spectrum sing_1093.htm#IDX443 spectrum sing_1094.htm#IDX447 spectrum sing_1107.htm#IDX459 spectrum sing_1109.htm#IDX470 spectrum sing_1184.htm#IDX495 spectrum.lib spectrum_lib sing_1183.htm#SEC1260 spectrum_lib spectrum_lib sing_1183.htm#SEC1260 spectrumnd spectrumnd sing_1184.htm#SEC1261 29943 spgamma spgamma sing_1106.htm#SEC1183 59653 spgeomgenus spgeomgenus sing_1105.htm#SEC1182 57796 spissemicont spissemicont sing_1102.htm#SEC1179 23679 split split sing_723.htm#SEC800 29794 splitPolygon splitPolygon sing_1533.htm#SEC1610 2411 splitring splitring sing_983.htm#SEC1060 56404 splitting splitting sing_927.htm#SEC1004 34734 spmilnor spmilnor sing_1104.htm#SEC1181 32933 spmul spmul sing_1101.htm#SEC1178 43607 spnf spnf sing_847.htm#SEC924 29592 spoly spoly sing_1473.htm#SEC1550 35454 sppairs sppairs sing_1092.htm#SEC1169 18918 sppnf sppnf sing_1097.htm#SEC1174 16650 sppprint sppprint sing_1098.htm#SEC1175 43682 spprint spprint sing_848.htm#SEC925 18671 sprintf sprintf sing_290.htm#SEC331 55889 spsemicont spsemicont sing_1103.htm#SEC1180 61169 spsub spsub sing_1100.htm#SEC1177 54296 sqfrNorm sqfrNorm sing_1291.htm#SEC1368 20546 sqfrNormMain sqfrNormMain sing_1299.htm#SEC1376 9890 sqr sqr sing_1410.htm#SEC1487 sprintf sqrfree sqrfree sing_289.htm#SEC330 squareRoot squareRoot sing_1431.htm#SEC1508 17446 squarefree squarefree sing_1128.htm#SEC1205 48485 sres sres sing_291.htm#SEC332 staircase staircase sing_1308.htm#SEC1385 49781 standard standard sing_1480.htm#SEC1557 14067 standard.lib standard_lib sing_685.htm#IDX354 standard_lib standard_lib sing_685.htm#IDX355 static procedures Procedure definition sing_43.htm#SEC78 status status sing_292.htm#SEC333 std groebner and std sing_293.htm#SEC334 std sing_612.htm#SEC665 std (plural) std (plural) sing_414.htm#SEC455 stdfglm stdfglm sing_294.htm#SEC335 256 stdhilb stdhilb sing_295.htm#SEC336 63138 stratify stratify sing_1249.htm#SEC1326 56744 stratify.lib stratify_lib sing_1247.htm#SEC1324 stratify_lib stratify_lib sing_1247.htm#SEC1324 string Miscellaneous oddities sing_154.htm#SEC195 string sing_354.htm#IDX287 string declarations string declarations sing_155.htm#SEC196 string expressions string expressions sing_156.htm#SEC197 string operations string operations sing_158.htm#SEC199 string related functions string related functions sing_159.htm#SEC200 string type cast string type cast sing_157.htm#SEC198 stripHNE stripHNE sing_1125.htm#SEC1202 19265 sturm sturm sing_1513.htm#SEC1590 54353 sturmha sturmha sing_1515.htm#SEC1592 12467 sturmhaseq sturmhaseq sing_1516.htm#SEC1593 59133 sturmquery sturmquery sing_1491.htm#SEC1568 10805 sturmseq sturmseq sing_1514.htm#SEC1591 23005 submat submat sing_805.htm#SEC882 37665 subrInterred subrInterred sing_746.htm#SEC823 10165 subset subset sing_765.htm#SEC842 4326 subst subst sing_296.htm#SEC337 subst (plural) subst (plural) sing_415.htm#SEC456 substitute substitute sing_745.htm#SEC822 28919 sugarCrit, option option sing_259.htm#IDX224 sum sum sing_708.htm#SEC785 555 superCommutative superCommutative sing_579.htm#SEC632 26299 surf.lib surf_lib sing_1329.htm#IDX500 surf_lib surf_lib sing_1329.htm#IDX501 surfer Preface sing_1.htm#IDX9 surfex Preface sing_1.htm#IDX8 surfex.lib surfex_lib sing_1331.htm#SEC1408 surfex_lib surfex_lib sing_1331.htm#SEC1408 suspend status sing_292.htm#SEC333 swap swap sing_1068.htm#SEC1145 15408 switch No case or switch statement sing_348.htm#SEC389 sym_gauss sym_gauss sing_831.htm#SEC908 5121 symmat symmat sing_806.htm#SEC883 61294 symmetric basis symmetricBasis sing_823.htm#IDX370 symmetric power symmetricPower sing_825.htm#IDX372 symmetricBasis symmetricBasis sing_823.htm#SEC900 sprintf symmetricPower symmetricPower sing_825.htm#SEC902 6542 symmfunc symmfunc sing_1500.htm#SEC1577 45575 symsignature symsignature sing_1490.htm#SEC1567 10520 syndrome syndrome sing_1358.htm#SEC1435 14057 sysBin sysBin sing_1356.htm#SEC1433 41948 sysCRHT sysCRHT sing_1353.htm#SEC1430 58930 sysCRHTMindist sysCRHTMindist sing_1354.htm#SEC1431 13692 sysFL sysFL sing_1369.htm#SEC1446 53040 sysNewton sysNewton sing_1355.htm#SEC1432 19704 sysQE sysQE sing_1359.htm#SEC1436 61026 sys_code sys_code sing_1350.htm#SEC1427 20220 system system sing_297.htm#SEC338 system, - system system, -- sing_297.htm#IDX262 system, --long_option_name sing_297.htm#IDX265 system, --long_option_name=value sing_297.htm#IDX267 system, -long_option_name system system, -long_option_name=value system system, Singular system sing_297.htm#IDX259 system, SingularLib system sing_297.htm#IDX261 system, browsers system sing_297.htm#IDX274 system, contributors system sing_297.htm#IDX254 system, gen system sing_297.htm#IDX255 system, getenv system sing_297.htm#IDX246 system, nblocks system sing_297.htm#IDX257 system, pid system sing_297.htm#IDX241 system, setenv system sing_297.htm#IDX248 system, sh system sing_297.htm#IDX239 system, tty system sing_297.htm#IDX250 system, uname system sing_297.htm#IDX243 system, version system sing_297.htm#IDX252 syz syz sing_298.htm#SEC339 syz (plural) syz (plural) sing_416.htm#SEC457 tInitialForm tInitialForm sing_1554.htm#SEC1631 42727 tInitialFormPar tInitialFormPar sing_1566.htm#SEC1643 9584 tInitialFormParMax tInitialFormParMax sing_1567.htm#SEC1644 7829 tInitialIdeal tInitialIdeal sing_1555.htm#SEC1632 48112 tab tab sing_724.htm#SEC801 60407 tail tail sing_1469.htm#SEC1546 13066 tame polynomial goodBasis sing_1107.htm#IDX452 tame polynomial sing_1108.htm#IDX462 tame polynomial sing_1109.htm#IDX463 tangentcone tangentcone sing_1172.htm#SEC1249 20056 tau_es tau_es sing_1080.htm#SEC1157 17043 tau_es2 tau_es2 sing_1048.htm#SEC1125 38083 teachstd.lib teachstd_lib sing_1467.htm#SEC1544 teachstd_lib teachstd_lib sing_1467.htm#SEC1544 template.lib template_lib sing_57.htm#IDX192 template.lib sing_57.htm#IDX195 template_lib template_lib sing_57.htm#SEC95 template_lib sing_57.htm#IDX193 tensor tensor sing_807.htm#SEC884 65451 tensorMod tensorMod sing_908.htm#SEC985 21961 term orderings General definitions for orderings sing_651.htm#SEC704 term orderings introduction Introduction to orderings sing_650.htm#SEC703 testPrimary testPrimary sing_970.htm#SEC1047 34254 tex tex sing_1314.htm#SEC1391 12226 texDrawBasic texDrawBasic sing_1561.htm#SEC1638 35239 texDrawNewtonSubdivision texDrawNewtonSubdivision sing_1563.htm#SEC1640 16439 texDrawTriangulation texDrawTriangulation sing_1564.htm#SEC1641 21307 texDrawTropical texDrawTropical sing_1562.htm#SEC1639 20453 texMatrix texMatrix sing_1560.htm#SEC1637 1334 texNumber texNumber sing_1558.htm#SEC1635 12628 texPolynomial texPolynomial sing_1559.htm#SEC1636 41136 texdemo texdemo sing_1315.htm#SEC1392 56734 texfactorize texfactorize sing_1316.htm#SEC1393 6682 texmap texmap sing_1317.htm#SEC1394 35265 texname texname sing_1318.htm#SEC1395 1008 texobj texobj sing_1319.htm#SEC1396 2107 texpoly texpoly sing_1320.htm#SEC1397 64109 texproc texproc sing_1321.htm#SEC1398 45412 texring texring sing_1322.htm#SEC1399 38275 the first alternative algorithm awalk1 sing_886.htm#IDX377 time limit on computations groebner sing_209.htm#IDX203 timeFactorize timeFactorize sing_714.htm#SEC791 49531 timeStd timeStd sing_713.htm#SEC790 31506 timer rtimer sing_338.htm#SEC379 timer sing_340.htm#SEC381 timer resolution, setting the system sing_297.htm#IDX272 tjurina tjurina sing_1168.htm#SEC1245 9100 tmatrix tmatrix sing_1095.htm#SEC1172 4402 tolessvars tolessvars sing_1260.htm#SEC1337 56590 topological invariants charexp2conductor sing_1036.htm#IDX397 topological invariants sing_1043.htm#IDX404 topological invariants sing_1044.htm#IDX408 topological invariants sing_1045.htm#IDX412 topological invariants sing_1046.htm#IDX416 toric ideals Toric ideals sing_665.htm#SEC723 toric.lib toric_lib sing_1032.htm#SEC1109 toric_ideal toric_ideal sing_1033.htm#SEC1110 2041 toric_lib toric_lib sing_1032.htm#SEC1109 toric_std toric_std sing_1034.htm#SEC1111 26141 total multiplicities alexpoly_lib sing_1036.htm#IDX400 totalmultiplicities totalmultiplicities sing_1038.htm#SEC1115 58264 trace trace sing_299.htm#SEC340 tracemult tracemult sing_1494.htm#SEC1571 58303 transpose transpose sing_300.htm#SEC341 triMNewton triMNewton sing_1286.htm#SEC1363 62822 triagmatrix triagmatrix sing_759.htm#SEC836 17944 triang.lib triang_lib sing_1279.htm#SEC1356 triangL triangL sing_1280.htm#SEC1357 51847 triangL_solve triangL_solve sing_1277.htm#SEC1354 10101 triangLf_solve triangLf_solve sing_1275.htm#SEC1352 49796 triangLfak triangLfak sing_1281.htm#SEC1358 50093 triangM triangM sing_1282.htm#SEC1359 59334 triangMH triangMH sing_1283.htm#SEC1360 34277 triangM_solve triangM_solve sing_1276.htm#SEC1353 63652 triang_lib triang_lib sing_1279.htm#SEC1356 triang_solve triang_solve sing_1278.htm#SEC1355 64404 triangulations triangulations sing_1529.htm#SEC1606 28771 tropical curves tropical_lib sing_1542.htm#IDX530 tropical polynomials tropical_lib sing_1542.htm#IDX531 tropical.lib tropical_lib sing_1542.htm#IDX528 tropicalCurve tropicalCurve sing_1545.htm#SEC1622 44084 tropicalJInvariant tropicalJInvariant sing_1548.htm#SEC1625 25480 tropicalLifting tropicalLifting sing_1543.htm#SEC1620 47777 tropicalSubst tropicalSubst sing_1572.htm#SEC1649 49846 tropical_lib tropical_lib sing_1542.htm#SEC1619 tropical_lib sing_1542.htm#IDX529 tropicalise tropicalise sing_1552.htm#SEC1629 56771 tropicaliseSet tropicaliseSet sing_1553.htm#SEC1630 35136 truncate truncate sing_1019.htm#SEC1096 13545 truncateFast truncateFast sing_1020.htm#SEC1097 5124 truncated module truncateFast sing_1019.htm#IDX390 truncated module sing_1020.htm#IDX391 tty system sing_297.htm#IDX249 twalk twalk sing_885.htm#SEC962 35753 twostd twostd sing_417.htm#SEC458 type type sing_301.htm#SEC342 typeof typeof sing_302.htm#SEC343 uname system sing_297.htm#IDX242 unitmat unitmat sing_808.htm#SEC885 12862 univariate univariate sing_303.htm#SEC344 univarpoly univarpoly sing_1501.htm#SEC1578 46288 unknown syndrome Decoding method based on quadratic equations sing_681.htm#SEC753 untyped definitions ideal (plural) sing_74.htm#SEC115 untyped definitions sing_359.htm#SEC400 updatePairs updatePairs sing_1479.htm#SEC1556 51144 ures_solve ures_solve sing_1269.htm#SEC1346 32449 uressolve uressolve sing_304.htm#SEC345 usage, option option sing_259.htm#IDX234 user interface, Emacs Emacs user interface sing_21.htm#SEC28 valvars valvars sing_1264.htm#SEC1341 15723 vandermonde vandermonde 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weightedRing weightedRing sing_572.htm#SEC625 33786 which which sing_710.htm#SEC787 14271 whichvariable whichvariable sing_1505.htm#SEC1582 27122 while while sing_328.htm#SEC369 wp, global ordering Global orderings sing_652.htm#IDX333 write write sing_313.htm#SEC354 writelist writelist sing_725.htm#SEC802 29998 ws, local ordering Local orderings sing_653.htm#IDX344 wurzel wurzel sing_1398.htm#SEC1475 12755 xdvi xdvi sing_1324.htm#SEC1401 16898 zero-dimensional qbase sing_1502.htm#IDX519 zeroMod zeroMod sing_923.htm#SEC1000 60609 zeroOpt zeroOpt sing_932.htm#SEC1009 19260 zeroSet zeroSet sing_1292.htm#SEC1369 60030 zerodec zerodec sing_978.htm#SEC1055 30765 zeroset.lib zeroset_lib sing_1287.htm#SEC1364 zeroset_lib zeroset_lib sing_1287.htm#SEC1364 zetaDL zetaDL sing_1008.htm#SEC1085 sprintf { Special characters sing_36.htm#IDX148 || boolean operations sing_36.htm#IDX173 || sing_87.htm#SEC128 } Special characters sing_36.htm#IDX149 ~ ~ sing_36.htm#IDX186 ~ sing_329.htm#SEC370