Changeset 1c5b54 in git

Timestamp:

Jan 12, 2018, 7:07:33 PM (5 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', '8d54773d6c9e2f1d2593a28bc68b7eeab54ed529')

Children:

a959dfcb571533a94c05b115085bd177e3b7f8fa

Parents:

ce4b2fb5302493784ac68ec931cfb54f96e899ff

Message:

doc: new build: singular.idx hlp-cmpl.el

Files:

• doc/singular.idx (modified) (7 diffs)
• emacs/hlp-cmpl.el (modified) (134 diffs)

doc/singular.idx

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+Critical points         sing_833.htm#SEC885     
+CurveParam              sing_1509.htm#SEC1585   53605
+CurveRes                sing_1508.htm#SEC1584   48848
+Curves          sing_1371.htm#IDX615    
 Customization of the Emacs interface    Customization of the Emacs interface    sing_25.htm#SEC36       
-Cyclic code             sing_1789.htm#IDX772    
-Cyclic roots            sing_794.htm#SEC846     
-D-integration           sing_555.htm#IDX346     
-D-localization          sing_555.htm#IDX342     
-D-localization          sing_760.htm#IDX380     
-D-module        purityfiltration_lib    sing_497.htm#IDX310     
-D-module                sing_532.htm#IDX325     
-D-module                sing_555.htm#IDX339     
-D-module                sing_588.htm#IDX351     
-D-module                sing_738.htm#IDX365     
-D-module                sing_760.htm#IDX377     
-D-module structure              sing_532.htm#IDX326     
-D-module structure              sing_588.htm#IDX352     
-D-restriction           sing_555.htm#IDX344     
-DBM links               sing_117.htm#SEC157     
+Cyclic code             sing_1803.htm#IDX798    
+Cyclic roots            sing_811.htm#SEC863     
+D-integration           sing_563.htm#IDX348     
+D-localization          sing_563.htm#IDX344     
+D-localization          sing_777.htm#IDX382     
+D-module        purityfiltration_lib    sing_505.htm#IDX312     
+D-module                sing_540.htm#IDX327     
+D-module                sing_563.htm#IDX341     
+D-module                sing_596.htm#IDX353     
+D-module                sing_755.htm#IDX367     
+D-module                sing_777.htm#IDX379     
+D-module structure              sing_540.htm#IDX328     
+D-module structure              sing_596.htm#IDX354     
+D-restriction           sing_563.htm#IDX346     
+DBM links               sing_122.htm#SEC162     
 DISPLAY environment variable    The online help system  sing_16.htm#IDX28       
-DLoc            sing_558.htm#SEC610     5981
-DLoc0           sing_560.htm#SEC612     14327
+DLoc            sing_566.htm#SEC618     5981
+DLoc0           sing_568.htm#SEC620     14327
 Data types              sing_72.htm#SEC112      
-Data types (plural)             sing_414.htm#IDX296     
+Data types (plural)             sing_422.htm#IDX298     
 Debugging tools         sing_63.htm#SEC100      
 Decker, Wolfram         sing_1.htm#IDX17        
-Declaration of objects of a user defined type   Declaration of objects of a user defined type   sing_179.htm#SEC219     
-Decoding                sing_1789.htm#IDX774    
-Decoding codes with Groebner bases      Decoding codes with Groebner bases      sing_862.htm#SEC919     
-Decoding method based on quadratic equations    Decoding method based on quadratic equations    sing_867.htm#SEC937     
-Definition of a user defined type       Definition of a user defined type       sing_178.htm#SEC218     
-Deformations            sing_819.htm#SEC871     
-Deformations, T1 and T2         sing_818.htm#SEC870     
-Degree          sing_1336.htm#SEC1412   47790
-Delta           sing_1420.htm#SEC1496   33497
-DeltaList               sing_1421.htm#SEC1497   65148
+Declaration of objects of a user defined type   Declaration of objects of a user defined type   sing_184.htm#SEC224     
+Decoding                sing_1803.htm#IDX800    
+Decoding codes with Groebner bases      Decoding codes with Groebner bases      sing_882.htm#SEC939     
+Decoding method based on quadratic equations    Decoding method based on quadratic equations    sing_887.htm#SEC957     
+Definition of a user defined type       Definition of a user defined type       sing_183.htm#SEC223     
+Deformations            sing_836.htm#SEC888     
+Deformations, T1 and T2         sing_835.htm#SEC887     
+Deg             sing_2500.htm#SEC2576   35419
+Degree          sing_2501.htm#SEC2577   48523
+DegreePure              sing_1350.htm#SEC1426   33003
+Degrees         sing_2502.htm#SEC2578   50349
+Delta           sing_1434.htm#SEC1510   33497
+DeltaList               sing_1435.htm#SEC1511   65148
 Demo mode               sing_24.htm#SEC35       
-Depth           sing_808.htm#SEC860     
-Determinacy             sing_2500.htm#IDX966    
-Di Biase-Urbanke algorithm      Di Biase and Urbanke    sing_856.htm#SEC913     
-Distributed computing           sing_931.htm#IDX478     
-Dlocalization           sing_761.htm#SEC813     22140
+Depth           sing_825.htm#SEC877     
+Determinacy             sing_2668.htm#IDX1027   
+Di Biase-Urbanke algorithm      Di Biase and Urbanke    sing_876.htm#SEC933     
+Distributed computing           sing_951.htm#IDX496     
+Dlocalization           sing_778.htm#SEC830     22140
 Documentation Tool              sing_60.htm#SEC97       
-Dp, global ordering             sing_838.htm#IDX394     
-Ds, local ordering              sing_839.htm#IDX404     
-DsingularLocus          sing_765.htm#SEC817     46495
+Dp, global ordering             sing_857.htm#IDX396     
+Ds, local ordering              sing_858.htm#IDX406     
+DsingularLocus          sing_782.htm#SEC834     46495
+Dynamic Geometry                sing_920.htm#IDX427     
 Dynamic loading         sing_71.htm#SEC111      
-Dynamic modules         sing_796.htm#SEC848     
-ECPP            sing_1898.htm#SEC1974   55777
-ECoef           sing_1379.htm#SEC1455   14154
-EOrdlist                sing_1377.htm#SEC1453   36329
-ERROR           sing_230.htm#SEC270     
+Dynamic modules         sing_813.htm#SEC865     
+ECPP            sing_1912.htm#SEC1988   55777
+ECoef           sing_1393.htm#SEC1469   14154
+EOrdlist                sing_1391.htm#SEC1467   36329
+ERROR           sing_236.htm#SEC276     
 ESingular, CYGWIN       Running SINGULAR under Emacs    sing_23.htm#SEC33       
-Edatalist               sing_1376.htm#SEC1452   61593
-Edelman-Reiner          sing_2185.htm#IDX855    
+Edatalist               sing_1390.htm#SEC1466   61593
+Edelman-Reiner          sing_2196.htm#IDX881    
 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37       
 Editing input           sing_18.htm#SEC25       
-Elimination             sing_804.htm#SEC856     
+Elimination             sing_821.htm#SEC873     
 Emacs   Emacs user interface    sing_21.htm#SEC28       
 Emacs, Singular demo mode               sing_24.htm#SEC35       
@@ -361 +375 @@
 Emacs, running Singular under   Running SINGULAR under Emacs    sing_23.htm#SEC30       
 Emacs, user interface   Emacs user interface    sing_21.htm#SEC28       
-Emaxcont                sing_1381.htm#SEC1457   47312
-Enumerative geometry            sing_2510.htm#IDX977    
-Equal           sing_1335.htm#SEC1411   19984
-Eresol          sing_1371.htm#SEC1447   12842
-EulerAff                sing_2292.htm#SEC2368   54325
-EulerProj               sing_2293.htm#SEC2369   13537
-Evaluation of logical expressions       Evaluation of logical expressions       sing_403.htm#SEC443     
-Examples                sing_786.htm#SEC838     
+Emaxcont                sing_1395.htm#SEC1471   47312
+Enumerative geometry            sing_2692.htm#IDX1045   
+Envelope                sing_920.htm#IDX429     
+Equal           sing_1349.htm#SEC1425   19984
+Eresol          sing_1385.htm#SEC1461   12842
+EulerAff                sing_2310.htm#SEC2386   54325
+EulerProj               sing_2311.htm#SEC2387   13537
+Evaluation of logical expressions       Evaluation of logical expressions       sing_411.htm#SEC451     
+Examples                sing_803.htm#SEC855     
 Examples of ring declarations   Examples of ring declarations   sing_29.htm#SEC40       
-Exp for matrices                sing_1353.htm#IDX581    
-Experimental libraries  Experimental libraries  sing_2229.htm#SEC2305   
-Ext             sing_1149.htm#SEC1225   21909
-Ext, computation of             sing_807.htm#SEC859     
-Ext_R           sing_1148.htm#SEC1224   53310
-Exterior                sing_712.htm#SEC764     23593
-Extra weight vector             sing_843.htm#SEC895     
-Factorization           sing_809.htm#SEC861     
-FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_918.htm#SEC994     61191
-Feynman graph           sing_1125.htm#IDX514    
-Finite fields           sing_803.htm#SEC855     
+Exp for matrices                sing_1367.htm#IDX607    
+Experimental libraries  Experimental libraries  sing_2240.htm#SEC2316   
+Ext             sing_1161.htm#SEC1237   21909
+Ext, computation of             sing_824.htm#SEC876     
+Ext_R           sing_1160.htm#SEC1236   53310
+Exterior                sing_729.htm#SEC781     23593
+Extra weight vector             sing_862.htm#SEC914     
+Factorization           sing_826.htm#SEC878     
+FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_938.htm#SEC1014    18153
+Feynman graph           sing_1137.htm#IDX529    
+Finite fields           sing_820.htm#SEC872     
 First steps             sing_6.htm#SEC12        
-Fitzgerald-Lax method   Fitzgerald-Lax method   sing_866.htm#SEC934     
+Fitzgerald-Lax method   Fitzgerald-Lax method   sing_886.htm#SEC954     
+Float           sing_250.htm#SEC290     
 Flow control            sing_40.htm#SEC70       
 Formal Checker          sing_59.htm#SEC96       
-Formatting output               sing_793.htm#SEC845     
-Free resolution         sing_805.htm#SEC857     
-Free resolution, graded Handling graded modules sing_806.htm#SEC858     
-FultonA         sing_2290.htm#SEC2366   33688
-Functions               sing_202.htm#SEC242     
-Future benefits of Singular 4   Notes for Singular users        sing_2565.htm#SEC2655   
-G-algebra               sing_478.htm#SEC518     
-G-algebra               sing_478.htm#SEC520     
-G-algebra, setup                sing_478.htm#SEC522     
-GBWeight                sing_561.htm#SEC613     24641
-GBsolve         sing_1688.htm#SEC1764   16830
-GIT             sing_2386.htm#IDX949    
-GKZsystem               sing_678.htm#SEC730     20528
-GKdim           sing_651.htm#SEC703     9814
+Formatting output               sing_810.htm#SEC862     
+Free resolution         sing_822.htm#SEC874     
+Free resolution, graded Handling graded modules sing_823.htm#SEC875     
+FultonA         sing_2308.htm#SEC2384   33688
+Functions               sing_207.htm#SEC247     
+Future benefits of Singular 4   Notes for Singular users        sing_2747.htm#SEC2836   
+G-algebra               sing_486.htm#SEC526     
+G-algebra               sing_486.htm#SEC528     
+G-algebra, setup                sing_486.htm#SEC530     
+GBWeight                sing_569.htm#SEC621     24641
+GBsolve         sing_1702.htm#SEC1778   16830
+GIT-Fans                sing_845.htm#SEC897     
+GITcone         sing_2417.htm#SEC2493   64643
+GITfan          sing_2418.htm#SEC2494   32549
+GITfanFromOrbitCones    GITfanFromOrbitCones    sing_2419.htm#SEC2495   63104
+GITfanParallel          sing_2420.htm#SEC2496   53071
+GITfanParallelSymmetric GITfanParallelSymmetric sing_2435.htm#SEC2511   30232
+GITfanSymmetric         sing_2434.htm#SEC2510   25831
+GKZfan          sing_2421.htm#SEC2497   sprintf
+GKZsystem               sing_695.htm#SEC747     20528
+GKdim           sing_668.htm#SEC720     9814
 GMP             sing_1.htm#IDX3 
-GMP             sing_2569.htm#SEC2659   
-GND.lib         sing_2393.htm#SEC2469   
-GND_lib         sing_2393.htm#SEC2469   
-GTZmod          sing_1197.htm#SEC1273   30091
-GTZopt          sing_1204.htm#SEC1280   14642
-G_a -Invariants         sing_825.htm#SEC877     
-Gamma           sing_1386.htm#SEC1462   3820
-Gauss-Manin connection  Gauss-Manin connection  sing_849.htm#SEC906     
-Gauss-Manin connection          sing_1566.htm#IDX752    
-Gauss-Manin connection                  sing_1613.htm#IDX755    
-Gauss-Manin system              sing_1514.htm#IDX642    
-Gauss-Manin system              sing_1515.htm#IDX653    
-Gauss-Manin system              sing_1516.htm#IDX656    
-Gauss-Manin system              sing_1517.htm#IDX659    
-Gauss-Manin system              sing_1518.htm#IDX662    
-Gauss-Manin system              sing_1519.htm#IDX666    
-Gauss-Manin system                      sing_1520.htm#IDX670    
-Gauss-Manin system                      sing_1521.htm#IDX676    
-Gauss-Manin system                      sing_1522.htm#IDX684    
-Gauss-Manin system                      sing_1523.htm#IDX690    
-Gauss-Manin system                      sing_1524.htm#IDX698    
-Gauss-Manin system                      sing_1525.htm#IDX708    
-Gauss-Manin system                      sing_1536.htm#IDX714    
-Gauss-Manin system                      sing_1538.htm#IDX725    
+GMP             sing_2751.htm#SEC2840   
+GND.lib         sing_2442.htm#SEC2518   
+GND_lib         sing_2442.htm#SEC2518   
+GTZmod          sing_1211.htm#SEC1287   30091
+GTZopt          sing_1218.htm#SEC1294   14642
+G_a -Invariants         sing_842.htm#SEC894     
+Gamma           sing_1400.htm#SEC1476   3820
+Gauss-Manin connection  Gauss-Manin connection  sing_869.htm#SEC926     
+Gauss-Manin connection          sing_1580.htm#IDX778    
+Gauss-Manin connection                  sing_1627.htm#IDX781    
+Gauss-Manin system              sing_1528.htm#IDX668    
+Gauss-Manin system              sing_1529.htm#IDX679    
+Gauss-Manin system              sing_1530.htm#IDX682    
+Gauss-Manin system              sing_1531.htm#IDX685    
+Gauss-Manin system              sing_1532.htm#IDX688    
+Gauss-Manin system              sing_1533.htm#IDX692    
+Gauss-Manin system                      sing_1534.htm#IDX696    
+Gauss-Manin system                      sing_1535.htm#IDX702    
+Gauss-Manin system                      sing_1536.htm#IDX710    
+Gauss-Manin system                      sing_1537.htm#IDX716    
+Gauss-Manin system                      sing_1538.htm#IDX724    
+Gauss-Manin system                      sing_1539.htm#IDX734    
+Gauss-Manin system                      sing_1550.htm#IDX740    
+Gauss-Manin system                      sing_1552.htm#IDX751    
 General command syntax  General command syntax  sing_35.htm#SEC59       
 General concepts                sing_12.htm#SEC18       
-General purpose         sing_874.htm#SEC950     
+General purpose         sing_894.htm#SEC970     
 General syntax of a ring declaration    General syntax of a ring declaration    sing_30.htm#SEC41       
-Generalized Hilbert Syzygy Theorem      Syzygies and resolutions (plural)       sing_480.htm#SEC530     
-Generalized Newton identities   Generalized Newton identities   sing_865.htm#SEC931     
-Geometric genus         sing_1357.htm#IDX593    
-German Umlaute          sing_399.htm#IDX283     
+Generalized Hilbert Syzygy Theorem      Syzygies and resolutions (plural)       sing_488.htm#SEC538     
+Generalized Newton identities   Generalized Newton identities   sing_885.htm#SEC951     
+Geometric Invariant Theory      Geometric Invariant Theory      sing_844.htm#SEC896     
+Geometric genus         sing_1371.htm#IDX619    
+German Umlaute          sing_407.htm#IDX285     
 Getting started         sing_5.htm#SEC11        
-Global orderings                sing_838.htm#SEC890     
-GoettscheF              sing_2373.htm#SEC2449   27881
-Graded commutative algebras     Graded commutative algebras (SCA)       sing_482.htm#SEC534     
-Grassmannian            sing_2515.htm#SEC2591   43898
-Grassmannian, abstract variety, Schubert calculus       Grassmannian    sing_2515.htm#IDX985    
+Global orderings                sing_857.htm#SEC909     
+Goettsche's formula             sing_2395.htm#IDX984    
+GoettscheF              sing_2396.htm#SEC2472   27881
+Graded commutative algebras     Graded commutative algebras (SCA)       sing_490.htm#SEC542     
+Grassmannian            sing_2697.htm#SEC2773   43898
+Grassmannian, abstract variety, Schubert calculus       Grassmannian    sing_2697.htm#IDX1053   
 Greuel, Gert-Martin             sing_1.htm#IDX18        
-Groebner Bases  Computing Groebner and Standard Bases   sing_797.htm#SEC849     
-Groebner bases in G-algebras    Groebner bases in G-algebras    sing_479.htm#SEC523     
-Groebner bases in free associative algebras     Groebner bases for two-sided ideals in free associative algebras        sing_485.htm#SEC537     
-Groebner bases, decodeGB                sing_1789.htm#IDX776    
-Groebner bases, slim            sing_800.htm#SEC852     
-Groebner basis conversion       Groebner basis conversion       sing_799.htm#SEC851     
-Groebner cover          sing_902.htm#IDX422     
-Groebner cover          sing_909.htm#IDX435     
-Groebner cover                  sing_910.htm#IDX441     
-Groebner fan            sing_2052.htm#IDX793    
-Groebner walk           sing_1140.htm#IDX535    
-Groebner walk           sing_1142.htm#IDX537    
-Groebner walk           sing_2507.htm#IDX973    
-Groebner walk                   sing_2508.htm#IDX974    
-Groebnerwalk            sing_1136.htm#IDX531    
-Groebnerwalk            sing_2432.htm#IDX958    
-Groebnerwalk            sing_2506.htm#IDX972    
-Groebnerwalk            sing_2549.htm#IDX1001   
-Gromov-Witten invariants                sing_1125.htm#IDX511    
-Gromov-Witten invariants                sing_1131.htm#IDX520    
-Gromov-Witten invariants                sing_1132.htm#IDX524    
-Gromov-Witten invariants, lines on hypersurfaces        linesHypersurface       sing_2540.htm#IDX997    
-Gromov-Witten invariants, multiple covers               sing_2539.htm#IDX996    
-Gromov-Witten invariants, rational curves on Calabi-Yau threefolds      sumofquotients  sing_2541.htm#IDX998    
-Gromov-Witten invariants, rational curves on Calabi-Yau threefolds              sing_2542.htm#IDX999    
-Gromov-Witten invariants.               sing_2510.htm#IDX980    
-Gweights                sing_706.htm#SEC758     651
-H2basis         sing_1571.htm#SEC1647   3414
-HHnormalForm            sing_2305.htm#SEC2381   33972
-Hamburger-Noether expansion             sing_1451.htm#IDX612    
-Hamburger-Noether expansion             sing_1539.htm#IDX734    
-Hamburger-Noether expansions            sing_1776.htm#IDX766    
-Handling graded modules Handling graded modules sing_806.htm#SEC858     
-Hcode           sing_1473.htm#SEC1549   26628
+Groebner Bases  Computing Groebner and Standard Bases   sing_814.htm#SEC866     
+Groebner Cover          sing_920.htm#IDX423     
+Groebner bases in G-algebras    Groebner bases in G-algebras    sing_487.htm#SEC531     
+Groebner bases in free associative algebras     Groebner bases for two-sided ideals in free associative algebras        sing_493.htm#SEC545     
+Groebner bases, decodeGB                sing_1803.htm#IDX802    
+Groebner bases, slim            sing_817.htm#SEC869     
+Groebner basis conversion       Groebner basis conversion       sing_816.htm#SEC868     
+Groebner cover          sing_921.htm#IDX431     
+Groebner cover          sing_928.htm#IDX450     
+Groebner cover                  sing_929.htm#IDX457     
+Groebner fan            sing_2066.htm#IDX819    
+Groebner walk           sing_1152.htm#IDX550    
+Groebner walk           sing_1154.htm#IDX552    
+Groebner walk           sing_2689.htm#IDX1041   
+Groebner walk                   sing_2690.htm#IDX1042   
+Groebnerwalk            sing_1148.htm#IDX546    
+Groebnerwalk            sing_2534.htm#IDX994    
+Groebnerwalk            sing_2688.htm#IDX1040   
+Groebnerwalk            sing_2731.htm#IDX1069   
+Gromov-Witten invariants                sing_1137.htm#IDX526    
+Gromov-Witten invariants                sing_1143.htm#IDX535    
+Gromov-Witten invariants                sing_1144.htm#IDX539    
+Gromov-Witten invariants, lines on hypersurfaces        linesHypersurface       sing_2722.htm#IDX1065   
+Gromov-Witten invariants, multiple covers               sing_2721.htm#IDX1064   
+Gromov-Witten invariants, rational curves on Calabi-Yau threefolds      sumofquotients  sing_2723.htm#IDX1066   
+Gromov-Witten invariants, rational curves on Calabi-Yau threefolds              sing_2724.htm#IDX1067   
+Gromov-Witten invariants.               sing_2692.htm#IDX1048   
+Gweights                sing_723.htm#SEC775     651
+H2basis         sing_1585.htm#SEC1661   3414
+HHnormalForm            sing_2326.htm#SEC2402   33972
+Hamburger-Noether expansion             sing_1465.htm#IDX638    
+Hamburger-Noether expansion             sing_1553.htm#IDX760    
+Hamburger-Noether expansions            sing_1790.htm#IDX792    
+Handling graded modules Handling graded modules sing_823.htm#SEC875     
+Hcode           sing_1487.htm#SEC1563   26628
 Help string             sing_45.htm#SEC82       
-Hensel          sing_235.htm#SEC275     
-Hilbert function                sing_348.htm#IDX188     
-Hilbert function                sing_846.htm#SEC900     
-Hilbert series          sing_846.htm#SEC900     
-Hilbert-driven GB algorithm     Groebner basis conversion       sing_799.htm#SEC851     
-HilbertClassPoly                sing_1861.htm#SEC1937   sprintf
-HilbertSeries           sing_1666.htm#SEC1742   21249
-HilbertWeights          sing_1667.htm#SEC1743   sprintf
-Hom             sing_1152.htm#SEC1228   61434
-HomJJ           sing_1227.htm#SEC1303   1525
-Hosten-Sturmfels algorithm      Hosten and Sturmfels    sing_855.htm#SEC912     
+Hensel          sing_241.htm#SEC281     
+Hilbert function                sing_356.htm#IDX188     
+Hilbert function                sing_866.htm#SEC920     
+Hilbert series          sing_866.htm#SEC920     
+Hilbert-driven GB algorithm     Groebner basis conversion       sing_816.htm#SEC868     
+HilbertClassPoly                sing_1875.htm#SEC1951   sprintf
+HilbertSeries           sing_1680.htm#SEC1756   21249
+HilbertWeights          sing_1681.htm#SEC1757   sprintf
+Hom             sing_1164.htm#SEC1240   61434
+HomJJ           sing_1241.htm#SEC1317   1525
+Hosten-Sturmfels algorithm      Hosten and Sturmfels    sing_875.htm#SEC932     
 How to enter and exit   How to enter and exit   sing_14.htm#SEC20       
 How to use this manual  How to use this manual  sing_4.htm#SEC6 
-Hurwitz numbers         sing_1131.htm#IDX523    
-Hurwitz numbers                 sing_1132.htm#IDX527    
-Hypersurface singularities, classification of   Classification of hypersurface singularities    sing_822.htm#SEC874     
-IN              sing_272.htm#IDX149     
-Ideal membership                sing_845.htm#IDX416     
+Hurwitz numbers         sing_1143.htm#IDX538    
+Hurwitz numbers                 sing_1144.htm#IDX542    
+Hypersurface singularities, classification of   Classification of hypersurface singularities    sing_839.htm#SEC891     
+I-regular function              sing_928.htm#IDX456     
+IN              sing_280.htm#IDX149     
+Ideal membership                sing_865.htm#IDX418     
 Identifiers, syntax of          sing_37.htm#SEC65       
-ImageGroup              sing_1669.htm#SEC1745   28808
-ImageVariety            sing_1668.htm#SEC1744   15252
-Imap, option            sing_307.htm#IDX175     
+ImageGroup              sing_1683.htm#SEC1759   28808
+ImageVariety            sing_1682.htm#SEC1758   15252
+Imap, option            sing_315.htm#IDX175     
 Implemented algorithms  Implemented algorithms  sing_33.htm#SEC47       
-Incl            sing_1334.htm#SEC1410   7621
-Index           sing_2574.htm#SEC2664   
+Incl            sing_1348.htm#SEC1424   7621
+Index           sing_2756.htm#SEC2845   
 Info string             sing_52.htm#SEC89       
-InterDiv                sing_1402.htm#SEC1478   46142
+InterDiv                sing_1416.htm#SEC1492   46142
 Interactive use         sing_13.htm#SEC19       
 Interrupting SINGULAR   Interrupting SINGULAR   sing_17.htm#SEC24       
-IntersectWithSub                sing_683.htm#SEC735     56289
-Intersection theory             sing_2510.htm#IDX976    
-IntersectionMatrix              sing_1500.htm#SEC1576   29351
+IntersectWithSub                sing_700.htm#SEC752     56289
+Intersection theory             sing_2692.htm#IDX1044   
+IntersectionMatrix              sing_1514.htm#SEC1590   29351
 Introduction            sing_2.htm#SEC4 
-Invariant Theory                sing_824.htm#SEC876     
-Invariant theory                sing_1618.htm#SEC1694   
-InvariantQ              sing_1671.htm#SEC1747   53256
-InvariantRing           sing_1670.htm#SEC1746   22928
-Invariants of a finite group    Invariants of a finite group    sing_826.htm#SEC878     
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-Modular techniques              sing_931.htm#IDX475     
-Module orderings                sing_840.htm#SEC892     
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+Macdonald's formula             sing_2395.htm#IDX985    
+MacdonaldF              sing_2399.htm#SEC2475   12751
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+Matrix orderings                sing_860.htm#SEC912     
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+Milnor number   Milnor and Tjurina number       sing_832.htm#SEC884     
+Milnor number           sing_2667.htm#IDX1026   
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+Module orderings                sing_859.htm#SEC911     
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-Oaku-Takayama algorithm         sing_532.htm#IDX336     
+New orderings for modules       Notes for Singular users        sing_2747.htm#SEC2835   
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+Output                  sing_2619.htm#IDX1004   
+Output                  sing_2620.htm#IDX1005   
+Output                  sing_2621.htm#IDX1006   
+Output                  sing_2622.htm#IDX1007   
+Output                          sing_2623.htm#IDX1008   
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+RiemannRochHess         sing_2480.htm#SEC2556   sprintf
+Right Groebner bases and syzygies       Right Groebner bases and syzygies       sing_848.htm#SEC900     
+Ring-dependent options  Notes for Singular users        sing_2747.htm#SEC2832   
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 Running SINGULAR under Emacs    Running SINGULAR under Emacs    sing_23.htm#SEC30       
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+SCA     Graded commutative algebras (SCA)       sing_490.htm#SEC542     
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 SDB debugger    Source code debugger    sing_66.htm#SEC106      
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+SDLoc           sing_567.htm#SEC619     9512
+SINGULAR libraries              sing_890.htm#SEC966     
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+Semigroup               sing_1505.htm#SEC1581   22323
+SetDeg          sing_2499.htm#SEC2575   40547
+Setting up a G-algebra          sing_486.htm#SEC530     
+ShanksMestre            sing_1908.htm#SEC1984   12973
+SimplifyIdeal           sing_1693.htm#SEC1769   sprintf
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+Singular 3 and Singular 4       Singular 3 and Singular 4       sing_2745.htm#SEC2828   
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-Solving systems of polynomial equations Solving systems of polynomial equations sing_831.htm#SEC883     
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+Singularities           sing_1464.htm#SEC1540   
+Singularity Theory              sing_831.htm#SEC883     
+Skeletons for parallelization           sing_951.htm#IDX495     
+Smith form              sing_1840.htm#IDX805    
+Smith normal form               sing_1840.htm#IDX806    
+SolowayStrassen         sing_1896.htm#SEC1972   22680
+Solving systems of polynomial equations Solving systems of polynomial equations sing_850.htm#SEC902     
+Source          sing_2488.htm#SEC2564   10351
 Source code debugger, invocation        Command line options    sing_19.htm#IDX33       
-Space curve singularities, branches of  Branches of space curve singularities   sing_821.htm#SEC873     
+Space curve singularities, branches of  Branches of space curve singularities   sing_838.htm#SEC890     
 Special characters              sing_36.htm#SEC64       
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-Ssi links               sing_113.htm#SEC153     
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-Standard bases          sing_845.htm#SEC897     
-StartOrderingV          sing_1445.htm#SEC1521   58927
+Splitting lemma addnondegeneratevariables       sing_2666.htm#IDX1025   
+Splitting lemma                 sing_2669.htm#IDX1029   
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+Ssi links               sing_118.htm#SEC158     
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+Standard Bases  Computing Groebner and Standard Bases   sing_814.htm#SEC866     
+Standard bases          sing_865.htm#SEC917     
+StartOrderingV          sing_1459.htm#SEC1535   58927
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-Symbolic-numerical solving              sing_1683.htm#SEC1759   
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-System dependent limitations    System dependent limitations    sing_400.htm#SEC440     
-System variables                sing_386.htm#SEC426     
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-Syzygies and resolutions (plural)       Syzygies and resolutions (plural)       sing_480.htm#SEC527     
-T1              sing_818.htm#SEC870     
-T2              sing_818.htm#SEC870     
+StringF         sing_1579.htm#SEC1655   11590
+SymGroup                sing_752.htm#SEC804     56676
+Symbolic-numerical solving      Symbolic-numerical solving      sing_850.htm#SEC902     
+Symbolic-numerical solving              sing_1697.htm#SEC1773   
+System and Control theory       System and Control theory       sing_1822.htm#SEC1898   
+System dependent limitations    System dependent limitations    sing_408.htm#SEC448     
+System variables                sing_394.htm#SEC434     
+Syzygies and resolutions        Syzygies and resolutions        sing_867.htm#SEC921     
+Syzygies and resolutions (plural)       Syzygies and resolutions (plural)       sing_488.htm#SEC535     
+T1              sing_835.htm#SEC887     
+T2              sing_835.htm#SEC887     
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-T_2             sing_1599.htm#SEC1675   55781
-Teaching                sing_1840.htm#SEC1916   
+TRACE           sing_403.htm#SEC443     
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+Target          sing_2487.htm#SEC2563   16006
+Teaching                sing_1854.htm#SEC1930   
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-TestGRRes               sing_2411.htm#SEC2487   8315
-TestJMark               sing_1446.htm#SEC1522   41314
+TestGRRes               sing_2460.htm#SEC2536   8315
+TestJMark               sing_1460.htm#SEC1536   41314
 The SINGULAR language   The SINGULAR language   sing_34.htm#SEC56       
-The Tran algorithm              sing_1138.htm#IDX533    
-The fractal walk algorithm              sing_1137.htm#IDX532    
-The fractal walk algorithm              sing_2509.htm#IDX975    
+The Tran algorithm              sing_1150.htm#IDX548    
+The fractal walk algorithm              sing_1149.htm#IDX547    
+The fractal walk algorithm              sing_2691.htm#IDX1043   
 The online help system  The online help system  sing_16.htm#SEC22       
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-Tjurina number          sing_1232.htm#IDX560    
+Tjurina         sing_1610.htm#SEC1686   11249
+Tjurina number  Milnor and Tjurina number       sing_832.htm#SEC884     
+Tjurina number          sing_1246.htm#IDX577    
 Top 20 Emacs commands   Top 20 Emacs commands   sing_27.htm#SEC38       
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-Toric ideals and integer programming    Toric ideals and integer programming    sing_850.htm#SEC907     
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-Tropical Geometry               sing_1992.htm#SEC2068   
+Tor             sing_1175.htm#SEC1251   sprintf
+Toric ideals and integer programming    Toric ideals and integer programming    sing_870.htm#SEC927     
+Tricks and pitfalls             sing_406.htm#SEC446     
+Tropical Geometry               sing_2006.htm#SEC2082   
 Type casting    Type conversion and casting     sing_39.htm#SEC69       
 Type conversion Type conversion and casting     sing_39.htm#SEC68       
 Typesetting of help and info strings    Typesetting of help and info strings    sing_61.htm#SEC98       
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-V-filtration            sing_1520.htm#IDX673    
-V-filtration            sing_1521.htm#IDX679    
-V-filtration            sing_1522.htm#IDX687    
-V-filtration                    sing_1523.htm#IDX693    
-V-filtration                    sing_1524.htm#IDX701    
-V-filtration                    sing_1525.htm#IDX711    
-V-filtration                    sing_1536.htm#IDX717    
-V-filtration                    sing_1538.htm#IDX728    
-VarToPar                sing_2368.htm#SEC2444   10508
+U_D_O           sing_1090.htm#SEC1166   26192
+Unix installation       Unix installation instructions  sing_2753.htm#SEC2842   
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+V-filtration            sing_1534.htm#IDX699    
+V-filtration            sing_1535.htm#IDX705    
+V-filtration            sing_1536.htm#IDX713    
+V-filtration                    sing_1537.htm#IDX719    
+V-filtration                    sing_1538.htm#IDX727    
+V-filtration                    sing_1539.htm#IDX737    
+V-filtration                    sing_1550.htm#IDX743    
+V-filtration                    sing_1552.htm#IDX754    
+VarToPar                sing_2391.htm#SEC2467   10508
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-Version schema for Singular     Version schema for Singular     sing_2564.htm#SEC2647   
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+Version schema for Singular     Version schema for Singular     sing_2746.htm#SEC2829   
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-Weyl algebra            sing_588.htm#IDX355     
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+WLemma          sing_940.htm#SEC1016    7302
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+Weyl algebra            sing_540.htm#IDX332     
+Weyl algebra            sing_596.htm#IDX357     
+Weyl closure            sing_777.htm#IDX385     
+WeylClosure             sing_779.htm#SEC831     23845
+WeylClosure1            sing_780.htm#SEC832     15759
+Wibmer's Lemma          sing_940.htm#IDX491     
+Windows installation    Windows installation instructions       sing_2754.htm#SEC2843   
+WitSet          sing_1361.htm#SEC1437   39803
+WitSupSet               sing_1360.htm#SEC1436   47758
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+XLsolve         sing_1703.htm#SEC1779   34970
 ZZ              sing_28.htm#SEC39       
 ZZ/m            sing_28.htm#SEC39       
 ZZ/p            sing_28.htm#SEC39       
-ZZsolve         sing_1690.htm#SEC1766   18657
+ZZsolve         sing_1704.htm#SEC1780   18657
 [               sing_36.htm#IDX83       
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-[]              sing_150.htm#SEC190     
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 _               sing_36.htm#IDX116      
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-affine code     Fitzgerald-Lax method   sing_866.htm#SEC935     
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-ainvar_lib              sing_1656.htm#SEC1732   
-aksaka.lib              sing_1841.htm#SEC1917   
-aksaka_lib              sing_1841.htm#SEC1917   
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-alexpoly_lib            sing_1451.htm#SEC1527   
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+ainvar_lib              sing_1670.htm#SEC1746   
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+algebra_lib             sing_1105.htm#SEC1181   
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+algebraic field extension               sing_1318.htm#IDX586    
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+algorithm of Pottier            sing_874.htm#SEC931     
+alias   General command syntax  sing_35.htm#SEC59       
+align           sing_208.htm#SEC248     
+all.lib         sing_895.htm#SEC971     
+allDoubleExt            sing_764.htm#SEC816     43457
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+allPositive             sing_516.htm#SEC568     1409
+all_lib         sing_895.htm#SEC971     
 allowing net access     Command line options    sing_19.htm#IDX41       
-allprint                sing_922.htm#SEC998     5195
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-allrealst               sing_1982.htm#SEC2058   40962
-allsquarefree           sing_1558.htm#SEC1634   45545
-ambientDimension                sing_1997.htm#SEC2073   18907
-and     Evaluation of logical expressions       sing_96.htm#SEC136      
-and             sing_403.htm#SEC443     
-annPoly         sing_556.htm#SEC608     18228
-annRat          sing_557.htm#SEC609     62662
-annRatSyz               sing_770.htm#SEC822     15672
-annfs           sing_533.htm#SEC585     38155
-annfs0          sing_545.htm#SEC597     26476
-annfs2          sing_546.htm#SEC598     47962
-annfsBMI                sing_542.htm#SEC594     2532
-annfsParamBM            sing_541.htm#SEC593     43587
-annfsRB         sing_547.htm#SEC599     31892
-annfspecial             sing_534.htm#SEC586     27566
-annihilator of polynomial               sing_555.htm#IDX340     
-annihilator of rational function                sing_555.htm#IDX341     
-annihilator of rational function                sing_760.htm#IDX386     
-annil           sing_1199.htm#SEC1275   48744
-appelF1         sing_574.htm#SEC626     63146
-appelF2         sing_575.htm#SEC627     22460
-appelF4         sing_576.htm#SEC628     6847
-appendWeight2Ord                sing_702.htm#SEC754     21488
-apply           sing_370.htm#SEC410     
-applyAdF                sing_524.htm#SEC576     40329
-arcpoint.lib            sing_1464.htm#SEC1540   
-arcpoint_lib            sing_1464.htm#SEC1540   
-areZeroElements         sing_2473.htm#SEC2549   14728
+allprint                sing_942.htm#SEC1018    5195
+allreal         sing_1998.htm#SEC2074   57232
+allrealst               sing_1996.htm#SEC2072   40962
+allsquarefree           sing_1572.htm#SEC1648   45545
+ambientDimension                sing_2011.htm#SEC2087   18907
+and     Evaluation of logical expressions       sing_101.htm#SEC141     
+and             sing_411.htm#SEC451     
+annPoly         sing_564.htm#SEC616     18228
+annRat          sing_565.htm#SEC617     62662
+annRatSyz               sing_787.htm#SEC839     15672
+annfs           sing_541.htm#SEC593     38155
+annfs0          sing_553.htm#SEC605     26476
+annfs2          sing_554.htm#SEC606     47962
+annfsBMI                sing_550.htm#SEC602     2532
+annfsParamBM            sing_549.htm#SEC601     43587
+annfsRB         sing_555.htm#SEC607     31892
+annfspecial             sing_542.htm#SEC594     27566
+annihilator of polynomial               sing_563.htm#IDX342     
+annihilator of rational function                sing_563.htm#IDX343     
+annihilator of rational function                sing_777.htm#IDX388     
+annil           sing_1213.htm#SEC1289   48744
+appelF1         sing_582.htm#SEC634     63146
+appelF2         sing_583.htm#SEC635     22460
+appelF4         sing_584.htm#SEC636     6847
+appendWeight2Ord                sing_719.htm#SEC771     21488
+apply           sing_378.htm#SEC418     
+applyAdF                sing_532.htm#SEC584     40329
+applyPermutationToIntvec        applyPermutationToIntvec        sing_2438.htm#SEC2514   28900
+arcpoint.lib            sing_1478.htm#SEC1554   
+arcpoint_lib            sing_1478.htm#SEC1554   
+areEqualLeftFractions   areEqualLeftFractions   sing_2655.htm#SEC2731   29498
+areZeroElements         sing_2575.htm#SEC2651   14728
 argument, default               sing_44.htm#SEC81       
 argument, optional              sing_44.htm#SEC81       
-arr.lib         sing_2157.htm#SEC2233   
-arr2multarr             sing_2190.htm#SEC2266   15063
-arrBoolean              sing_2179.htm#SEC2255   63256
-arrBoundedChambers              sing_2200.htm#SEC2276   18347
-arrBraid                sing_2180.htm#SEC2256   34093
-arrCenter               sing_2167.htm#SEC2243   24565
-arrCentered             sing_2169.htm#SEC2245   15904
-arrCentral              sing_2168.htm#SEC2244   14086
-arrCentralize           sing_2170.htm#SEC2246   53235
-arrChambers             sing_2199.htm#SEC2275   44578
-arrCharPoly             sing_2197.htm#SEC2273   44129
-arrCone         sing_2173.htm#SEC2249   38068
-arrCoordChange          sing_2171.htm#SEC2247   61430
-arrCoordNormalize               sing_2172.htm#SEC2248   46273
-arrDecone               sing_2174.htm#SEC2250   54637
-arrDer          sing_2187.htm#SEC2263   48815
-arrEdelmanReiner                sing_2185.htm#SEC2261   59091
-arrEssentialize         sing_2178.htm#SEC2254   6667
-arrExponents            sing_2189.htm#SEC2265   1948
-arrFlats                sing_2194.htm#SEC2270   64792
-arrIsEssential          sing_2177.htm#SEC2253   34363
-arrIsFree               sing_2188.htm#SEC2264   3860
-arrLastVar              sing_2166.htm#SEC2242   25835
-arrLattice              sing_2195.htm#SEC2271   58951
-arrLocalize             sing_2175.htm#SEC2251   56070
-arrOrlikSolomon         sing_2186.htm#SEC2262   31686
-arrPoincare             sing_2198.htm#SEC2274   412
-arrPrintMatrix          sing_2162.htm#SEC2238   21204
-arrRandom               sing_2183.htm#SEC2259   59986
-arrRandomCentral                sing_2184.htm#SEC2260   43698
-arrRestrict             sing_2176.htm#SEC2252   sprintf
-arrSet          sing_2158.htm#SEC2234   53769
-arrSwapVar              sing_2165.htm#SEC2241   44919
-arrTypeB                sing_2181.htm#SEC2257   22358
-arrTypeD                sing_2182.htm#SEC2258   26495
-arr_lib         sing_2157.htm#SEC2233   
-arrange         sing_549.htm#SEC601     50350
-arrangement             sing_2158.htm#IDX798    
-arrangement             sing_2159.htm#IDX803    
-arrangement             sing_2190.htm#IDX865    
-arrangement             sing_2191.htm#IDX868    
-ask             sing_1849.htm#SEC1925   3862
-assPrimes               sing_1108.htm#SEC1184   sprintf
-assign          sing_2158.htm#IDX800    
-assignment,custom       Assignments for user defined types      sing_182.htm#SEC222     
-associated tangent      FamElemsAtEnvCompPoints sing_917.htm#IDX466     
-associated tangent              sing_918.htm#IDX470     
-assprimeszerodim.lib    assprimeszerodim_lib    sing_1106.htm#SEC1182   
-assprimeszerodim_lib    assprimeszerodim_lib    sing_1106.htm#SEC1182   
-atkins.lib              sing_1850.htm#SEC1926   
-atkins_lib              sing_1850.htm#SEC1926   
-attrib          sing_204.htm#SEC244     
-autonom         sing_1813.htm#SEC1889   57044
-autonomDim              sing_1814.htm#SEC1890   30055
-awalk1          sing_1139.htm#SEC1215   11044
-awalk2          sing_1140.htm#SEC1216   8955
-b-function              sing_497.htm#IDX313     
-bFactor         sing_579.htm#SEC631     15179
-babyGiant               sing_1879.htm#SEC1955   41113
-backward                sing_2355.htm#SEC2431   11225
-bareiss         sing_205.htm#SEC245     
-base2str                sing_878.htm#SEC954     sprintf
+arr.lib         sing_2168.htm#SEC2244   
+arr2multarr             sing_2201.htm#SEC2277   15063
+arrBoolean              sing_2190.htm#SEC2266   63256
+arrBoundedChambers              sing_2211.htm#SEC2287   18347
+arrBraid                sing_2191.htm#SEC2267   34093
+arrCenter               sing_2178.htm#SEC2254   24565
+arrCentered             sing_2180.htm#SEC2256   15904
+arrCentral              sing_2179.htm#SEC2255   14086
+arrCentralize           sing_2181.htm#SEC2257   53235
+arrChambers             sing_2210.htm#SEC2286   44578
+arrCharPoly             sing_2208.htm#SEC2284   44129
+arrCone         sing_2184.htm#SEC2260   38068
+arrCoordChange          sing_2182.htm#SEC2258   61430
+arrCoordNormalize               sing_2183.htm#SEC2259   46273
+arrDecone               sing_2185.htm#SEC2261   54637
+arrDer          sing_2198.htm#SEC2274   48815
+arrEdelmanReiner                sing_2196.htm#SEC2272   59091
+arrEssentialize         sing_2189.htm#SEC2265   6667
+arrExponents            sing_2200.htm#SEC2276   1948
+arrFlats                sing_2205.htm#SEC2281   64792
+arrIsEssential          sing_2188.htm#SEC2264   34363
+arrIsFree               sing_2199.htm#SEC2275   3860
+arrLastVar              sing_2177.htm#SEC2253   25835
+arrLattice              sing_2206.htm#SEC2282   58951
+arrLocalize             sing_2186.htm#SEC2262   56070
+arrOrlikSolomon         sing_2197.htm#SEC2273   31686
+arrPoincare             sing_2209.htm#SEC2285   412
+arrPrintMatrix          sing_2173.htm#SEC2249   21204
+arrRandom               sing_2194.htm#SEC2270   59986
+arrRandomCentral                sing_2195.htm#SEC2271   43698
+arrRestrict             sing_2187.htm#SEC2263   sprintf
+arrSet          sing_2169.htm#SEC2245   53769
+arrSwapVar              sing_2176.htm#SEC2252   44919
+arrTypeB                sing_2192.htm#SEC2268   22358
+arrTypeD                sing_2193.htm#SEC2269   26495
+arr_lib         sing_2168.htm#SEC2244   
+arrange         sing_557.htm#SEC609     50350
+arrangement             sing_2169.htm#IDX824    
+arrangement             sing_2170.htm#IDX829    
+arrangement             sing_2201.htm#IDX891    
+arrangement             sing_2202.htm#IDX894    
+ask             sing_1863.htm#SEC1939   3862
+assPrimes               sing_1120.htm#SEC1196   sprintf
+assign          sing_2169.htm#IDX826    
+assignment,custom       Assignments for user defined types      sing_187.htm#SEC227     
+associated tangent      FamElemsAtEnvCompPoints sing_937.htm#IDX484     
+associated tangent              sing_938.htm#IDX488     
+assprimeszerodim.lib    assprimeszerodim_lib    sing_1118.htm#SEC1194   
+assprimeszerodim_lib    assprimeszerodim_lib    sing_1118.htm#SEC1194   
+atkins.lib              sing_1864.htm#SEC1940   
+atkins_lib              sing_1864.htm#SEC1940   
+attrib          sing_209.htm#SEC249     
+autGenWeights           sing_2244.htm#SEC2320   32642
+autGradAlg              sing_2243.htm#SEC2319   21136
+autKS           sing_2242.htm#SEC2318   51607
+autX            sing_2247.htm#SEC2323   43261
+autXhat         sing_2246.htm#SEC2322   35932
+autgradalg.lib          sing_2241.htm#SEC2317   
+autgradalg_lib          sing_2241.htm#SEC2317   
+automorphism group              sing_2241.htm#IDX942    
+automorphisms           sing_2241.htm#IDX939    
+autonom         sing_1827.htm#SEC1903   57044
+autonomDim              sing_1828.htm#SEC1904   30055
+awalk1          sing_1151.htm#SEC1227   11044
+awalk2          sing_1152.htm#SEC1228   8955
+b-function              sing_505.htm#IDX315     
+bFactor         sing_587.htm#SEC639     15179
+babyGiant               sing_1893.htm#SEC1969   41113
+backward                sing_2378.htm#SEC2454   11225
+bareiss         sing_210.htm#SEC250     
+base2str                sing_898.htm#SEC974     sprintf
 basering                sing_28.htm#IDX76       
-basering                sing_83.htm#SEC123      
-basicinvariants         sing_1470.htm#SEC1546   32136
-belongSemigroup         sing_1111.htm#SEC1187   19983
-bernstein               sing_1518.htm#SEC1594   5605
-bernsteinBM             sing_537.htm#SEC589     57689
-bernsteinLift           sing_538.htm#SEC590     22885
-bertini2Singular                sing_1342.htm#SEC1418   58501
-betti           sing_206.htm#SEC246     
-betti (plural)          sing_447.htm#SEC487     
-bfct            sing_498.htm#SEC550     29858
-bfctAnn         sing_500.htm#SEC552     36658
-bfctBound               sing_769.htm#SEC821     5630
-bfctIdeal               sing_502.htm#SEC554     41018
-bfctOneGB               sing_501.htm#SEC553     9696
-bfctSyz         sing_499.htm#SEC551     26796
-bfctVarAnn              sing_590.htm#SEC642     51667
-bfctVarIn               sing_589.htm#SEC641     9274
-bfun.lib                sing_497.htm#SEC549     
-bfun_lib                sing_497.htm#SEC549     
-bigint          sing_73.htm#SEC113      
-bigint declarations             sing_74.htm#SEC114      
-bigint expressions              sing_75.htm#SEC115      
-bigint operations               sing_76.htm#SEC116      
-bigint related functions        bigint related functions        sing_77.htm#SEC117      
-bigintmat               sing_78.htm#SEC118      
-bigintmat declarations  bigintmat declarations  sing_79.htm#SEC119      
-bigintmat expressions   bigintmat expressions   sing_80.htm#SEC120      
-bigintmat operations    bigintmat operations    sing_82.htm#SEC122      
-bigintmat type cast             sing_81.htm#SEC121      
-bimodules               sing_490.htm#IDX301     
-bimodules.lib           sing_490.htm#SEC542     
-bimodules_lib           sing_490.htm#SEC542     
-binary_add              sing_1902.htm#SEC1978   42817
-binomial                sing_883.htm#SEC959     23208
-binomials2intmat                sing_1265.htm#SEC1341   58804
-birational map, image, inverse.         sing_1359.htm#IDX596    
-bistd           sing_491.htm#SEC543     45237
-bisyzygies              sing_490.htm#IDX302     
-bitrinity               sing_492.htm#SEC544     3516
-blackbox                sing_186.htm#SEC226     
-blackbox                sing_194.htm#SEC234     
+basering                sing_88.htm#SEC128      
+basicinvariants         sing_1484.htm#SEC1560   32136
+belongSemigroup         sing_1123.htm#SEC1199   19983
+bernstein               sing_1532.htm#SEC1608   5605
+bernsteinBM             sing_545.htm#SEC597     57689
+bernsteinLift           sing_546.htm#SEC598     22885
+bertini         sing_1347.htm#IDX590    
+bertini                 sing_1352.htm#IDX597    
+bertini2Singular                sing_1356.htm#SEC1432   58501
+betti           sing_211.htm#SEC251     
+betti (plural)          sing_455.htm#SEC495     
+betti number            sing_2395.htm#IDX983    
+bfct            sing_506.htm#SEC558     29858
+bfctAnn         sing_508.htm#SEC560     36658
+bfctBound               sing_786.htm#SEC838     5630
+bfctIdeal               sing_510.htm#SEC562     41018
+bfctOneGB               sing_509.htm#SEC561     9696
+bfctSyz         sing_507.htm#SEC559     26796
+bfctVarAnn              sing_598.htm#SEC650     51667
+bfctVarIn               sing_597.htm#SEC649     9274
+bfun.lib                sing_505.htm#SEC557     
+bfun_lib                sing_505.htm#SEC557     
+bigint          sing_78.htm#SEC118      
+bigint declarations             sing_79.htm#SEC119      
+bigint expressions              sing_80.htm#SEC120      
+bigint operations               sing_81.htm#SEC121      
+bigint related functions        bigint related functions        sing_82.htm#SEC122      
+bigintToBinary          sing_2436.htm#SEC2512   59742
+bigintmat               sing_83.htm#SEC123      
+bigintmat declarations  bigintmat declarations  sing_84.htm#SEC124      
+bigintmat expressions   bigintmat expressions   sing_85.htm#SEC125      
+bigintmat operations    bigintmat operations    sing_87.htm#SEC127      
+bigintmat type cast             sing_86.htm#SEC126      
+bimodules               sing_498.htm#IDX303     
+bimodules.lib           sing_498.htm#SEC550     
+bimodules_lib           sing_498.htm#SEC550     
+binaryToBigint          sing_2437.htm#SEC2513   sprintf
+binary_add              sing_1916.htm#SEC1992   42817
+binomial                sing_903.htm#SEC979     23208
+binomials2intmat                sing_1279.htm#SEC1355   58804
+birational map, image, inverse.         sing_1373.htm#IDX622    
+bistd           sing_499.htm#SEC551     45237
+bisyzygies              sing_498.htm#IDX304     
+bitrinity               sing_500.htm#SEC552     3516
+blackbox                sing_191.htm#SEC231     
+blackbox                sing_199.htm#SEC239     
 block           sing_40.htm#SEC70       
-block           sing_369.htm#SEC409     
-blowUp          sing_1410.htm#SEC1486   34819
-blowUp2         sing_1411.htm#SEC1487   65264
-blowUpBO                sing_1417.htm#SEC1493   58146
-blowup0         sing_1116.htm#SEC1192   44451
-boolean         sing_2179.htm#IDX842    
-boolean expressions             sing_95.htm#SEC135      
-boolean operations              sing_96.htm#SEC136      
-boolean_constant                sing_2213.htm#SEC2289   52873
-boolean_ideal           sing_2217.htm#SEC2293   53515
-boolean_poly            sing_2214.htm#SEC2290   41652
-boolean_poly_ring               sing_2212.htm#SEC2288   sprintf
-boolean_set             sing_2218.htm#SEC2294   58235
-boolean_std             sing_2211.htm#SEC2287   5921
-borderBasis             sing_2502.htm#SEC2578   33172
-boundBuFou              sing_1979.htm#SEC2055   26589
-boundDes                sing_1981.htm#SEC2057   35149
-boundaryLatticePoints   boundaryLatticePoints   sing_2070.htm#SEC2146   6238
-boundposDes             sing_1980.htm#SEC2056   58854
-bracket         sing_350.htm#IDX197     
-bracket                 sing_406.htm#SEC446     
-bracket                 sing_448.htm#SEC488     
-braid           sing_2180.htm#IDX844    
-branchTo        procs with different argument types     sing_155.htm#SEC195     
-break           sing_371.htm#SEC411     
-break point             sing_385.htm#SEC425     
-breakpoint              sing_372.htm#SEC412     
-brillnoether.lib                sing_2230.htm#SEC2306   
-brillnoether_lib                sing_2230.htm#SEC2306   
-brnoeth.lib             sing_1775.htm#SEC1851   
-brnoeth_lib             sing_1775.htm#SEC1851   
+block           sing_377.htm#SEC417     
+blowUp          sing_1424.htm#SEC1500   34819
+blowUp2         sing_1425.htm#SEC1501   65264
+blowUpBO                sing_1431.htm#SEC1507   58146
+blowup0         sing_1128.htm#SEC1204   44451
+boolean         sing_2190.htm#IDX868    
+boolean expressions             sing_100.htm#SEC140     
+boolean operations              sing_101.htm#SEC141     
+boolean_constant                sing_2224.htm#SEC2300   52873
+boolean_ideal           sing_2228.htm#SEC2304   53515
+boolean_poly            sing_2225.htm#SEC2301   41652
+boolean_poly_ring               sing_2223.htm#SEC2299   sprintf
+boolean_set             sing_2229.htm#SEC2305   58235
+boolean_std             sing_2222.htm#SEC2298   5921
+border basis            sing_2683.htm#IDX1033   
+borderBasis             sing_2684.htm#SEC2760   33172
+boundBuFou              sing_1993.htm#SEC2069   26589
+boundDes                sing_1995.htm#SEC2071   35149
+boundaryLatticePoints   boundaryLatticePoints   sing_2081.htm#SEC2157   6238
+boundposDes             sing_1994.htm#SEC2070   58854
+bounds          sing_2671.htm#SEC2747   50218
+boxSet          sing_2673.htm#SEC2749   8552
+bracket         sing_358.htm#IDX197     
+bracket                 sing_414.htm#SEC454     
+bracket                 sing_456.htm#SEC496     
+braid           sing_2191.htm#IDX870    
+branchTo        procs with different argument types     sing_160.htm#SEC200     
+break           sing_379.htm#SEC419     
+break point             sing_393.htm#SEC433     
+breakpoint              sing_380.htm#SEC420     
+brillnoether.lib                sing_2248.htm#SEC2324   
+brillnoether_lib                sing_2248.htm#SEC2324   
+brnoeth.lib             sing_1789.htm#SEC1865   
+brnoeth_lib             sing_1789.htm#SEC1865   
 browser, command line option    Command line options    sing_19.htm#IDX44       
-browser, setting the            sing_350.htm#IDX193     
+browser, setting the            sing_358.htm#IDX193     
 browsers        The online help system  sing_16.htm#IDX21       
-browsers, setting the           sing_350.htm#IDX192     
-bubblesort              sing_1852.htm#SEC1928   63278
-busadj          sing_1070.htm#SEC1146   36301
-bvar            sing_2225.htm#SEC2301   52773
-c, module ordering              sing_840.htm#IDX413     
-cProj           sing_2272.htm#SEC2348   24037
-calculateI              sing_1384.htm#SEC1460   31107
-calculate_max_sum               sing_1921.htm#SEC1997   4706
-calculate_ordering              sing_1899.htm#SEC1975   42616
-cancelunit, option              sing_307.htm#IDX171     
-canonMap                sing_1144.htm#SEC1220   47599
-canonical               sing_902.htm#IDX424     
-canonical form          sing_911.htm#IDX447     
-canonical form          sing_912.htm#IDX449     
-canonical, discussion of parametric ideal               sing_910.htm#IDX443     
-canonicalizeCone                sing_1998.htm#SEC2074   6251
-canonize                sing_1821.htm#SEC1897   54090
-cantoradd               sing_1935.htm#SEC2011   55304
-cantormult              sing_1938.htm#SEC2014   57569
-cantorred               sing_1936.htm#SEC2012   46502
-cardGroup               sing_1113.htm#SEC1189   5553
-case    No case or switch statement     sing_404.htm#SEC444     
-cccMatrixToPositiveIntvec       cccMatrixToPositiveIntvec       sing_2556.htm#SEC2632   55393
+browsers, setting the           sing_358.htm#IDX192     
+bubblesort              sing_1866.htm#SEC1942   63278
+busadj          sing_1082.htm#SEC1158   36301
+bvar            sing_2236.htm#SEC2312   52773
+c, module ordering              sing_859.htm#IDX415     
+cProj           sing_2290.htm#SEC2366   24037
+calculateI              sing_1398.htm#SEC1474   31107
+calculate_max_sum               sing_1935.htm#SEC2011   4706
+calculate_ordering              sing_1913.htm#SEC1989   42616
+cancelunit, option              sing_315.htm#IDX171     
+canonMap                sing_1156.htm#SEC1232   47599
+canoncial form          sing_925.htm#IDX445     
+canoncial form          sing_926.htm#IDX447     
+canoncial form                  sing_927.htm#IDX449     
+canonical               sing_921.htm#IDX433     
+canonical               sing_929.htm#IDX459     
+canonical form          sing_930.htm#IDX464     
+canonical form          sing_931.htm#IDX466     
+canonicalizeCone                sing_2012.htm#SEC2088   6251
+canonize                sing_1835.htm#SEC1911   54090
+cantoradd               sing_1949.htm#SEC2025   55304
+cantormult              sing_1952.htm#SEC2028   57569
+cantorred               sing_1950.htm#SEC2026   46502
+cardGroup               sing_1125.htm#SEC1201   5553
+case    No case or switch statement     sing_412.htm#SEC452     
+catNets         sing_2613.htm#SEC2689   24760
+cccMatrixToPositiveIntvec       cccMatrixToPositiveIntvec       sing_2738.htm#SEC2814   55393
 cdd             sing_1.htm#IDX10        
 cddlib          sing_1.htm#IDX11        
-center          sing_511.htm#IDX320     65108
-center          sing_517.htm#SEC569     
-center                  sing_2167.htm#IDX824    
-center                  sing_2168.htm#IDX825    
-center                  sing_2169.htm#IDX827    
-center                  sing_2170.htm#IDX829    
-centerRed               sing_516.htm#SEC568     59910
-centerVS                sing_515.htm#SEC567     27548
-central         sing_2161.htm#IDX810    
-central                 sing_2168.htm#IDX826    
-central                 sing_2170.htm#IDX828    
-central                 sing_2184.htm#IDX853    
-central.lib             sing_511.htm#SEC563     
-central1st              sing_2356.htm#SEC2432   29090
-central2nd              sing_2357.htm#SEC2433   37545
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-command-line option, setting value of           sing_350.htm#IDX279     
-command-line option, value of           sing_350.htm#IDX277     
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+commands (plural)               sing_454.htm#IDX302     
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-complexSingType         sing_1485.htm#SEC1561   34483
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-compregb_lib            sing_876.htm#SEC952     
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-compress                sing_1031.htm#SEC1107   61998
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-conductor               sing_1461.htm#IDX631    
-conductor               sing_2316.htm#IDX919    
-conductor, degree               sing_1545.htm#IDX741    
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-cone            sing_2173.htm#IDX833    
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-constructible set               sing_911.htm#IDX445     
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-constructor             sing_2191.htm#IDX869    
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-containedQ              sing_1740.htm#SEC1816   46718
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-contentSB, option               sing_307.htm#IDX172     
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-contributionBundle              sing_2537.htm#SEC2613   32874
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-controlDim              sing_1812.htm#SEC1888   2417
-controlExample          sing_1824.htm#SEC1900   2678
-control_Matrix          sing_1513.htm#SEC1589   sprintf
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-convexHull              sing_2007.htm#SEC2083   56690
-convexIntersection              sing_2008.htm#SEC2084   63587
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-coordinate change               sing_2170.htm#IDX830    
-coordinate change               sing_2171.htm#IDX831    
-coordinate change               sing_2172.htm#IDX832    
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+content         sing_973.htm#SEC1049    9095
+contentSB, option               sing_315.htm#IDX172     
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-cup             sing_1145.htm#SEC1221   57972
-cupproduct              sing_1146.htm#SEC1222   43349
-curve singularities             sing_1451.htm#IDX614    
-curve singularities             sing_1539.htm#IDX736    
-curve singularity               sing_2314.htm#IDX914    
-curveColengthDerivations        curveColengthDerivations        sing_2318.htm#SEC2394   2078
-curveConductorMult              sing_2316.htm#SEC2392   15897
-curveDeligneNumber              sing_2317.htm#SEC2393   12294
-curveDeltaInv           sing_2315.htm#SEC2391   16375
-curveInv.lib            sing_2314.htm#SEC2390   
-curveInv_lib            sing_2314.htm#SEC2390   
-curvepar.lib            sing_1492.htm#SEC1568   
-curvepar_lib            sing_1492.htm#SEC1568   
-custom assignment       Assignments for user defined types      sing_182.htm#SEC222     
-custom command  Commands for user defined types sing_181.htm#SEC221     
-custom type     Definition of a user defined type       sing_178.htm#SEC218     
-customstd.lib           sing_2202.htm#SEC2278   
-customstd_lib           sing_2202.htm#SEC2278   
-cycleLength             sing_2061.htm#SEC2137   16898
-cyclePoints             sing_2065.htm#SEC2141   54460
-cyclic          sing_940.htm#SEC1016    21375
-cyclic code     Codes and the decoding problem  sing_863.htm#SEC922     
-cyclotomic              sing_1626.htm#SEC1702   33749
-datetime                sing_216.htm#SEC256     50127
-dbprint         sing_217.htm#SEC257     
-deRham.lib              sing_2319.htm#SEC2395   
-deRhamCohom             sing_569.htm#SEC621     58222
-deRhamCohomIdeal                sing_570.htm#SEC622     42169
-deRhamCohomology                sing_2320.htm#SEC2396   41947
-deRham_lib              sing_2319.htm#SEC2395   
-debugLib, option                sing_307.htm#IDX176     
-debug_log               sing_1482.htm#SEC1558   62043
+corank          sing_1486.htm#SEC1562   33709
+cornerMonomials         sing_1282.htm#SEC1358   33995
+countPoints             sing_1906.htm#SEC1982   58566
+coverings               sing_1143.htm#IDX537    
+coverings               sing_1144.htm#IDX541    
+cpu             sing_358.htm#IDX202     
+cpu             sing_358.htm#IDX275     
+createBO                sing_1432.htm#SEC1508   32669
+createGradedRingHomomorphism    createGradedRingHomomorphism    sing_2551.htm#SEC2627   62177
+createGroup             sing_2544.htm#SEC2620   28500
+createQuotientGroup             sing_2545.htm#SEC2621   26374
+createTask              sing_1027.htm#SEC1103   48404
+createTorsionFreeGroup  createTorsionFreeGroup  sing_2546.htm#SEC2622   51944
+createlist              sing_1414.htm#SEC1490   61781
+cring           sing_73.htm#SEC113      
+cring declarations              sing_74.htm#SEC114      
+cring expressions               sing_75.htm#SEC115      
+cring operations                sing_76.htm#SEC116      
+cring related functions cring related functions sing_77.htm#SEC117      
+crossprod               sing_221.htm#SEC261     
+crypto.lib              sing_1879.htm#SEC1955   
+crypto_lib              sing_1879.htm#SEC1955   
+cup             sing_1157.htm#SEC1233   57972
+cupproduct              sing_1158.htm#SEC1234   43349
+curve singularities             sing_1465.htm#IDX640    
+curve singularities             sing_1553.htm#IDX762    
+curve singularity               sing_2337.htm#IDX950    
+curveColengthDerivations        curveColengthDerivations        sing_2341.htm#SEC2417   2078
+curveConductorMult              sing_2339.htm#SEC2415   15897
+curveDeligneNumber              sing_2340.htm#SEC2416   12294
+curveDeltaInv           sing_2338.htm#SEC2414   16375
+curveInv.lib            sing_2337.htm#SEC2413   
+curveInv_lib            sing_2337.htm#SEC2413   
+curvepar.lib            sing_1506.htm#SEC1582   
+curvepar_lib            sing_1506.htm#SEC1582   
+custom assignment       Assignments for user defined types      sing_187.htm#SEC227     
+custom command  Commands for user defined types sing_186.htm#SEC226     
+custom type     Definition of a user defined type       sing_183.htm#SEC223     
+customstd.lib           sing_2213.htm#SEC2289   
+customstd_lib           sing_2213.htm#SEC2289   
+cycleLength             sing_2072.htm#SEC2148   16898
+cyclePoints             sing_2076.htm#SEC2152   54460
+cyclic          sing_960.htm#SEC1036    21375
+cyclic code     Codes and the decoding problem  sing_883.htm#SEC942     
+cyclotomic              sing_1640.htm#SEC1716   33749
+datetime                sing_222.htm#SEC262     50127
+dbprint         sing_223.htm#SEC263     
+deRham.lib              sing_2342.htm#SEC2418   
+deRhamCohom             sing_577.htm#SEC629     58222
+deRhamCohomIdeal                sing_578.htm#SEC630     42169
+deRhamCohomology                sing_2343.htm#SEC2419   41947
+deRham_lib              sing_2342.htm#SEC2418   
+debugLib, option                sing_315.htm#IDX176     
+debug_log               sing_1496.htm#SEC1572   62043
 debugger        Source code debugger    sing_66.htm#SEC103      
 debugging library code  Source code debugger    sing_66.htm#SEC103      
-dec1var         sing_1198.htm#SEC1274   36098
-decimal         sing_1866.htm#SEC1942   56066
-decode          sing_1802.htm#SEC1878   64330
-decodeCode              sing_1804.htm#SEC1880   28262
-decodeRandom            sing_1803.htm#SEC1879   40118
-decodeRandomFL          sing_1807.htm#SEC1883   35423
-decodeSV                sing_1784.htm#SEC1860   37975
-decodegb.lib            sing_1789.htm#SEC1865   
-decodegb_lib            sing_1789.htm#SEC1865   
-decoding, decoding problem      Codes and the decoding problem  sing_863.htm#SEC923     
-decoef          sing_1832.htm#SEC1908   60284
-decone          sing_2173.htm#IDX834    
-decone          sing_2174.htm#IDX836    
-def             sing_83.htm#SEC123      
-def declarations                sing_84.htm#SEC124      
-defRes, option          sing_307.htm#IDX177     
+dec1var         sing_1212.htm#SEC1288   36098
+decimal         sing_1880.htm#SEC1956   56066
+decode          sing_1816.htm#SEC1892   64330
+decodeCode              sing_1818.htm#SEC1894   28262
+decodeRandom            sing_1817.htm#SEC1893   40118
+decodeRandomFL          sing_1821.htm#SEC1897   35423
+decodeSV                sing_1798.htm#SEC1874   37975
+decodegb.lib            sing_1803.htm#SEC1879   
+decodegb_lib            sing_1803.htm#SEC1879   
+decoding, decoding problem      Codes and the decoding problem  sing_883.htm#SEC943     
+decoef          sing_1846.htm#SEC1922   60284
+decomposition of modules                sing_1205.htm#IDX566    
+decomposition, numerical                sing_1352.htm#IDX595    
+decone          sing_2184.htm#IDX860    
+decone          sing_2185.htm#IDX862    
+def             sing_88.htm#SEC128      
+def declarations                sing_89.htm#SEC129      
+defRes, option          sing_315.htm#IDX177     
 default argument                sing_44.htm#SEC81       
-defineHomogeneous               sing_2482.htm#SEC2558   55072
-defined         sing_218.htm#SEC258     
-defl            sing_1349.htm#SEC1425   11825
-deform          sing_1584.htm#SEC1660   5250
-deform.lib              sing_1503.htm#SEC1579   
-deform_lib              sing_1503.htm#SEC1579   
-defring         sing_982.htm#SEC1058    1814
-defringp                sing_984.htm#SEC1060    42905
-defrings                sing_983.htm#SEC1059    1034
-deg             sing_219.htm#SEC259     
-degBound                sing_387.htm#SEC427     
-degree  Miscellaneous oddities  sing_220.htm#SEC260     
-degree          sing_410.htm#IDX290     
-degree lexicographical ordering         sing_838.htm#IDX393     
-degree of a polynomial  Miscellaneous oddities  sing_410.htm#IDX294     
-degree reverse lexicographical ordering         sing_838.htm#IDX391     
-degreeDivisor           sing_2330.htm#SEC2406   31751
-degreeFormalDivisor             sing_2338.htm#SEC2414   42503
-degreepart              sing_1692.htm#SEC1768   53036
-delete          sing_121.htm#SEC161     
-delete          sing_221.htm#SEC261     
-delete                  sing_268.htm#SEC308     
-deleteGenerator         sing_584.htm#SEC636     24917
-deleteSublist           sing_884.htm#SEC960     20406
-deligne number  curveColengthDerivations        sing_2314.htm#IDX916    
-deligne number          sing_2317.htm#IDX921    
-deligne number                  sing_2318.htm#IDX923    
-delta           sing_1551.htm#SEC1627   56952
-delta invariant         sing_1232.htm#IDX559    
-delta invariant                 sing_1551.htm#IDX746    
-delta invariant                 sing_2315.htm#IDX917    
-delta invariant.                sing_1224.htm#IDX552    
-delta invariant.                sing_1225.htm#IDX555    
-delta invariant.                sing_1226.htm#IDX558    
-deltaLoc                sing_1232.htm#SEC1308   35192
-denom_list              sing_350.htm#IDX204     
-denominator             sing_222.htm#SEC262     
-depth           sing_1147.htm#SEC1223   17777
-depthIdeal              sing_1208.htm#SEC1284   54782
-derivate                sing_1658.htm#SEC1734   15409
-derivation              sing_2187.htm#IDX857    
-desingularization               sing_2393.htm#IDX952    59041
-desingularization               sing_2394.htm#SEC2470   
-det             sing_223.htm#SEC263     
-det_B           sing_1073.htm#SEC1149   60143
-detadj          sing_1567.htm#SEC1643   5914
-determinacy             sing_2500.htm#SEC2576   44818
-determinecenter         sing_1372.htm#SEC1448   44496
-detropicalise           sing_2142.htm#SEC2218   38025
-develop         sing_1541.htm#SEC1617   48457
-diag            sing_1033.htm#SEC1109   56759
-diagInvariants          sing_1247.htm#SEC1323   62096
-diag_test               sing_1069.htm#SEC1145   31469
-diff            sing_224.htm#SEC264     
-diffRat         sing_783.htm#SEC835     36134
-difpoly2tex             sing_1833.htm#SEC1909   6451
-dim             sing_225.htm#SEC265     
-dim (plural)            sing_449.htm#SEC489     
-dimGradedPart           sing_1440.htm#SEC1516   11262
-dimH            sing_1439.htm#SEC1515   38534
-dimMon          sing_1188.htm#SEC1264   39971
-dimStack                sing_2535.htm#SEC2611   47772
-dim_slocus              sing_1585.htm#SEC1661   47218
-dimension               sing_2009.htm#SEC2085   35262
-dimension, moduli space of stable maps, rational curves dimStack        sing_2535.htm#IDX992    
-dimensionOfLocalization dimensionOfLocalization sing_2381.htm#SEC2457   25632
-direct_boolean_poly             sing_2215.htm#SEC2291   49893
-direct_from_boolean_poly        direct_from_boolean_poly        sing_2221.htm#SEC2297   36941
-disc            sing_1853.htm#SEC1929   45279
-discr           sing_1607.htm#SEC1683   9642
-discrepancy             sing_1425.htm#SEC1501   5597
-discrim         sing_919.htm#SEC995     21370
-discussion of parametric ideal          sing_902.htm#IDX425     
-disjoint                sing_903.htm#IDX427     
-disp_zdd                sing_2228.htm#SEC2304   41439
-displayCohom            sing_1441.htm#SEC1517   22633
-displayHNE              sing_1544.htm#SEC1620   29845
-displayInvariants               sing_1546.htm#SEC1622   13678
-displayMultsequence             sing_1548.htm#SEC1624   16668
-displayPuiseuxExpansion displayPuiseuxExpansion sing_2117.htm#SEC2193   560
-displayTropicalLifting  displayTropicalLifting  sing_2115.htm#SEC2191   28144
-distributed computing           sing_933.htm#IDX481     
-distributed computing           sing_973.htm#IDX483     
-distributed computing           sing_1014.htm#IDX496    
-div     Miscellaneous oddities  sing_76.htm#SEC116      
-div             sing_93.htm#SEC133      
-div             sing_410.htm#IDX287     
-divideUnits             sing_1829.htm#SEC1905   26711
-dividelist              sing_1399.htm#SEC1475   34210
-division                sing_226.htm#SEC266     
-division                sing_904.htm#IDX430     
-division                sing_905.htm#IDX432     
-division (plural)               sing_450.htm#SEC490     
-divisor         sing_1932.htm#SEC2008   47231
-divisorplus             sing_2324.htm#SEC2400   34248
-divisors        negativeformaldivisor   sing_2323.htm#IDX926    
-divisors                sing_2324.htm#IDX927    
-divisors                sing_2325.htm#IDX928    
-divisors                sing_2326.htm#IDX929    
-divisors                sing_2327.htm#IDX930    
-divisors                sing_2328.htm#IDX931    
-divisors                sing_2329.htm#IDX932    
-divisors                sing_2330.htm#IDX933    
-divisors                        sing_2331.htm#IDX934    
-divisors                        sing_2332.htm#IDX935    
-divisors                        sing_2333.htm#IDX936    
-divisors                        sing_2334.htm#IDX937    
-divisors                        sing_2335.htm#IDX938    
-divisors                        sing_2336.htm#IDX939    
-divisors                        sing_2337.htm#IDX940    
-divisors                        sing_2338.htm#IDX941    
-divisors, polyhedra             sing_2339.htm#IDX942    
-divisors, polyhedra             sing_2340.htm#IDX943    
-divisors, polyhedra             sing_2341.htm#IDX944    
-divisors.lib            sing_2322.htm#SEC2398   
-divisors_lib            sing_2322.htm#SEC2398   
-dmod.lib                sing_532.htm#SEC584     
-dmodAction              sing_778.htm#SEC830     9763
-dmodActionRat           sing_779.htm#SEC831     6277
-dmodGeneralAssumptionCheck      dmodGeneralAssumptionCheck      sing_771.htm#SEC823     44337
-dmod_lib                sing_532.htm#SEC584     
-dmodapp.lib             sing_555.htm#SEC607     
-dmodapp_lib             sing_555.htm#SEC607     
-dmodloc.lib             sing_760.htm#IDX375     
-dmodloc_lib             sing_760.htm#IDX376     
-dmodoublext             sing_755.htm#SEC807     60637
-dmodvar.lib             sing_588.htm#SEC640     
-dmodvar_lib             sing_588.htm#SEC640     
-double          sing_1937.htm#SEC2013   34697
-doubleExt               sing_746.htm#SEC798     56896
-downloading     Download instructions   sing_2570.htm#SEC2660   
-dp, global ordering             sing_838.htm#IDX392     
-drawNewtonSubdivision   drawNewtonSubdivision   sing_2120.htm#SEC2196   50904
-drawTropicalCurve               sing_2119.htm#SEC2195   10441
-ds, local ordering              sing_839.htm#IDX402     
-dsum            sing_1034.htm#SEC1110   1303
-dualCone                sing_2010.htm#SEC2086   61460
-dualConic               sing_2144.htm#SEC2220   31080
-dualPart                sing_2285.htm#SEC2361   13279
-dualPartition           sing_2548.htm#SEC2624   24739
-dualPolytope            sing_2049.htm#SEC2125   32081
-dualSheaf               sing_2526.htm#SEC2602   633
-dual_code               sing_1786.htm#SEC1862   57229
-dump            sing_227.htm#SEC267     
-dynamic geometry                sing_913.htm#IDX452     
-dynamic geometry                sing_914.htm#IDX455     
-ecart           sing_1940.htm#SEC2016   32475
-echo            sing_388.htm#SEC428     
-eexgcdN         sing_1867.htm#SEC1943   53237
-effective               sing_2332.htm#SEC2408   53028
-egcdMain                sing_1733.htm#SEC1809   25359
-ehrhartPolynomialCoeff  ehrhartPolynomialCoeff  sing_2071.htm#SEC2147   38271
-ehrhartRing             sing_1243.htm#SEC1319   16966
-eigenvals               sing_1081.htm#SEC1157   11228
-eigenvalue              sing_320.htm#SEC360     
-eigenvalue              sing_1081.htm#IDX502    
-eigenvalues             sing_1326.htm#SEC1402   2182
-elemSymmId              sing_941.htm#SEC1017    sprintf
-elim            sing_1118.htm#SEC1194   62585
-elim.lib                sing_1115.htm#SEC1191   
-elim1           sing_1119.htm#SEC1195   15653
-elim2           sing_1120.htm#SEC1196   44749
-elimRing                sing_1117.htm#SEC1193   12194
-elimWeight              sing_703.htm#SEC755     54297
-elim_lib                sing_1115.htm#SEC1191   
-eliminate               sing_228.htm#SEC268     
-eliminate (plural)              sing_451.htm#SEC491     
-eliminateNC             sing_698.htm#SEC750     3777
-elimination             sing_697.htm#IDX360     
-elimlinearpart          sing_1693.htm#SEC1769   14251
-elimpart                sing_1694.htm#SEC1770   10258
-elimpartanyr            sing_1695.htm#SEC1771   39751
-elimrep         sing_1380.htm#SEC1456   23641
-elliptic curve          sing_1128.htm#IDX518    
-elliptic curves         sing_1125.htm#IDX512    
-elliptic curves                 sing_1131.htm#IDX521    
-elliptic curves                 sing_1132.htm#IDX525    
-ellipticAdd             sing_1888.htm#SEC1964   13279
-ellipticAllPoints               sing_1893.htm#SEC1969   60770
-ellipticMult            sing_1889.htm#SEC1965   1558
-ellipticNF              sing_2068.htm#SEC2144   5045
-ellipticNFDB            sing_2069.htm#SEC2145   27917
-ellipticRandomCurve             sing_1890.htm#SEC1966   36980
-ellipticRandomPoint             sing_1891.htm#SEC1967   6866
-ellipticcovers.lib              sing_1125.htm#IDX506    
-ellipticcovers_lib              sing_1125.htm#IDX507    
-else            sing_378.htm#SEC418     
-embedMat                sing_729.htm#SEC781     17119
-emptyFan                sing_2037.htm#SEC2113   7396
-encode          sing_1794.htm#SEC1870   56687
-endomorphism filtration         sing_1525.htm#IDX712    
-endvfilt                sing_1525.htm#SEC1601   26670
-engine          sing_585.htm#SEC637     30876
-envelop FamElemsAtEnvCompPoints sing_915.htm#SEC991     9501
-envelop                 sing_915.htm#IDX458     
-envelop                 sing_916.htm#IDX461     
-envelop                 sing_917.htm#IDX465     
-envelop                 sing_918.htm#IDX469     
-envelope                sing_452.htm#SEC492     
-enveloping algebra              sing_350.htm#IDX208     
-enveloping algebra              sing_490.htm#IDX304     
+defineHomogeneous               sing_2584.htm#SEC2660   55072
+defined         sing_224.htm#SEC264     
+defl            sing_1363.htm#SEC1439   11825
+deform          sing_1598.htm#SEC1674   5250
+deform.lib              sing_1517.htm#SEC1593   
+deform_lib              sing_1517.htm#SEC1593   
+defring         sing_1002.htm#SEC1078   1814
+defringp                sing_1004.htm#SEC1080   42905
+defrings                sing_1003.htm#SEC1079   1034
+deg             sing_225.htm#SEC265     
+degBound                sing_395.htm#SEC435     
+degree  Miscellaneous oddities  sing_226.htm#SEC266     
+degree          sing_418.htm#IDX292     
+degree lexicographical ordering         sing_857.htm#IDX395     
+degree of a polynomial  Miscellaneous oddities  sing_418.htm#IDX296     
+degree reverse lexicographical ordering         sing_857.htm#IDX393     
+degreeDivisor           sing_2353.htm#SEC2429   31751
+degreeFormalDivisor             sing_2361.htm#SEC2437   42503
+degreepart              sing_1706.htm#SEC1782   53036
+delete          sing_126.htm#SEC166     
+delete          sing_227.htm#SEC267     
+delete                  sing_276.htm#SEC316     
+deleteGenerator         sing_592.htm#SEC644     24917
+deleteSublist           sing_904.htm#SEC980     20406
+deligne number  curveColengthDerivations        sing_2337.htm#IDX952    
+deligne number          sing_2340.htm#IDX957    
+deligne number                  sing_2341.htm#IDX959    
+delta           sing_1565.htm#SEC1641   56952
+delta invariant         sing_1246.htm#IDX576    
+delta invariant                 sing_1565.htm#IDX772    
+delta invariant                 sing_2338.htm#IDX953    
+delta invariant.                sing_1238.htm#IDX569    
+delta invariant.                sing_1239.htm#IDX572    
+delta invariant.                sing_1240.htm#IDX575    
+deltaLoc                sing_1246.htm#SEC1322   35192
+denom_list              sing_358.htm#IDX204     
+denominator             sing_228.htm#SEC268     
+depth           sing_1159.htm#SEC1235   17777
+depthIdeal              sing_1222.htm#SEC1298   54782
+derivate                sing_1672.htm#SEC1748   15409
+derivation              sing_2198.htm#IDX883    
+desingularization               sing_2442.htm#IDX988    59041
+desingularization               sing_2443.htm#SEC2519   
+det             sing_229.htm#SEC269     
+det_B           sing_1085.htm#SEC1161   60143
+detadj          sing_1581.htm#SEC1657   5914
+determinacy             sing_2668.htm#SEC2744   44818
+determinecenter         sing_1386.htm#SEC1462   44496
+detropicalise           sing_2153.htm#SEC2229   38025
+develop         sing_1555.htm#SEC1631   48457
+diag            sing_1045.htm#SEC1121   56759
+diagInvariants          sing_1261.htm#SEC1337   62096
+diag_test               sing_1081.htm#SEC1157   31469
+diff            sing_230.htm#SEC270     
+diffRat         sing_800.htm#SEC852     36134
+difpoly2tex             sing_1847.htm#SEC1923   6451
+dim             sing_231.htm#SEC271     
+dim (plural)            sing_457.htm#SEC497     
+dimGradedPart           sing_1454.htm#SEC1530   11262
+dimH            sing_1453.htm#SEC1529   38534
+dimMon          sing_1202.htm#SEC1278   39971
+dimStack                sing_2717.htm#SEC2793   47772
+dim_slocus              sing_1599.htm#SEC1675   47218
+dimension               sing_2023.htm#SEC2099   35262
+dimension, moduli space of stable maps, rational curves dimStack        sing_2717.htm#IDX1060   
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+direct_boolean_poly             sing_2226.htm#SEC2302   49893
+direct_from_boolean_poly        direct_from_boolean_poly        sing_2232.htm#SEC2308   36941
+disc            sing_1867.htm#SEC1943   45279
+discr           sing_1621.htm#SEC1697   9642
+discrepancy             sing_1439.htm#SEC1515   5597
+discrim         sing_939.htm#SEC1015    44091
+discussion of parametric ideal          sing_921.htm#IDX434     
+discussion of parametric ideal          sing_929.htm#IDX460     
+disjoint                sing_922.htm#IDX436     
+disp_zdd                sing_2239.htm#SEC2315   41439
+displayCohom            sing_1455.htm#SEC1531   22633
+displayHNE              sing_1558.htm#SEC1634   29845
+displayInvariants               sing_1560.htm#SEC1636   13678
+displayMultsequence             sing_1562.htm#SEC1638   16668
+displayPuiseuxExpansion displayPuiseuxExpansion sing_2128.htm#SEC2204   560
+displayTropicalLifting  displayTropicalLifting  sing_2126.htm#SEC2202   28144
+distributed computing           sing_953.htm#IDX499     
+distributed computing           sing_993.htm#IDX501     
+distributed computing           sing_1026.htm#IDX511    
+div     Miscellaneous oddities  sing_81.htm#SEC121      
+div             sing_98.htm#SEC138      
+div             sing_155.htm#SEC195     
+div             sing_418.htm#IDX289     
+divideUnits             sing_1843.htm#SEC1919   26711
+dividelist              sing_1413.htm#SEC1489   34210
+division                sing_232.htm#SEC272     
+division                sing_923.htm#IDX439     
+division                sing_924.htm#IDX441     
+division (plural)               sing_458.htm#SEC498     
+divisor         sing_1946.htm#SEC2022   47231
+divisorplus             sing_2347.htm#SEC2423   34248
+divisors        negativeformaldivisor   sing_2346.htm#IDX962    
+divisors                sing_2347.htm#IDX963    
+divisors                sing_2348.htm#IDX964    
+divisors                sing_2349.htm#IDX965    
+divisors                sing_2350.htm#IDX966    
+divisors                sing_2351.htm#IDX967    
+divisors                sing_2352.htm#IDX968    
+divisors                sing_2353.htm#IDX969    
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+dmodvar_lib             sing_596.htm#SEC648     
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+eigenvalue              sing_1093.htm#IDX517    
+eigenvalues             sing_1340.htm#SEC1416   2182
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+elim1           sing_1131.htm#SEC1207   15653
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+enveloping algebra              sing_498.htm#IDX306     
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-equidimZ                sing_1299.htm#SEC1375   49610
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-equising_lib            sing_1508.htm#SEC1584   
-equisingular Tjurina number             sing_1451.htm#IDX619    
-equisingularity ideal           sing_1510.htm#IDX639    
-equisingularity stratum         sing_1511.htm#IDX640    
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+equidimZ                sing_1313.htm#SEC1389   49610
+equising.lib            sing_1522.htm#SEC1598   
+equising_lib            sing_1522.htm#SEC1598   
+equisingular Tjurina number             sing_1465.htm#IDX645    
+equisingularity ideal           sing_1524.htm#IDX665    
+equisingularity stratum         sing_1525.htm#IDX666    
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-errormap                sing_2362.htm#SEC2438   7782
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-esStratum               sing_1511.htm#SEC1587   50094
-essential               sing_2177.htm#IDX839    
-essential               sing_2178.htm#IDX840    
-eta             sing_2063.htm#SEC2139   60729
-euler           sing_1846.htm#SEC1922   10519
-eulerChProj             sing_2275.htm#SEC2351   28549
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-evaluatePDivisor                sing_2340.htm#SEC2416   18855
-evaluate_reynolds               sing_1631.htm#SEC1707   46353
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-example                 sing_2179.htm#IDX841    
-example                 sing_2180.htm#IDX843    
-example                 sing_2181.htm#IDX845    
-example                 sing_2182.htm#IDX847    
-example                 sing_2183.htm#IDX849    
-example                 sing_2184.htm#IDX851    
-example                 sing_2185.htm#IDX854    
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-expo            sing_1858.htm#SEC1934   8833
-exponents               sing_2189.htm#IDX862    
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-exportNuminvs           sing_1251.htm#SEC1327   10423
-exportto                sing_376.htm#SEC416     
-expp            sing_2546.htm#SEC2622   15751
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+errormap                sing_2385.htm#SEC2461   7782
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+esStratum               sing_1525.htm#SEC1601   50094
+essential               sing_2188.htm#IDX865    
+essential               sing_2189.htm#IDX866    
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+euler           sing_1860.htm#SEC1936   10519
+eulerChProj             sing_2293.htm#SEC2369   28549
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+evaluatePDivisor                sing_2363.htm#SEC2439   18855
+evaluateProduct         sing_2433.htm#SEC2509   54515
+evaluate_reynolds               sing_1645.htm#SEC1721   46353
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+example                 sing_2190.htm#IDX867    
+example                 sing_2191.htm#IDX869    
+example                 sing_2192.htm#IDX871    
+example                 sing_2193.htm#IDX873    
+example                 sing_2194.htm#IDX875    
+example                 sing_2195.htm#IDX877    
+example                 sing_2196.htm#IDX880    
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+exit            sing_390.htm#SEC430     
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+expo            sing_1872.htm#SEC1948   8833
+exponents               sing_2200.htm#IDX888    
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+exportto                sing_384.htm#SEC424     
+expp            sing_2728.htm#SEC2804   15751
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-expression list                 sing_414.htm#IDX297     
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-extdevelop              sing_1542.htm#SEC1618   51044
-extendGC                sing_910.htm#SEC986     19135
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-extendedTensor          sing_704.htm#SEC756     4975
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-exterior basis          sing_1060.htm#IDX499    
-exterior power          sing_1062.htm#IDX501    
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-extgcd          sing_233.htm#SEC273     
-fVector         sing_2040.htm#SEC2116   3715
-fVectorP                sing_2072.htm#SEC2148   31843
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-facWeyl         sing_686.htm#SEC738     32331
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-factorH         sing_899.htm#SEC975     24814
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+fVectorP                sing_2083.htm#SEC2159   31843
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-ffmodStd                sing_2347.htm#SEC2423   50680
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-ffmodstd_lib            sing_2342.htm#SEC2418   
-ffsolve         sing_1685.htm#SEC1761   20432
-ffsolve.lib             sing_1684.htm#SEC1760   
-ffsolve_lib             sing_1684.htm#SEC1760   
-fglm            sing_239.htm#SEC279     
-fglm            sing_347.htm#IDX187     
-fglm_solve              sing_1712.htm#SEC1788   51398
-fglmquot                sing_240.htm#SEC280     
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-field           sing_139.htm#SEC179     
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+fglm            sing_355.htm#IDX187     
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 file, .singularrc               sing_20.htm#IDX71       
-filecmd         sing_241.htm#SEC281     
-filtration      purityfiltration_lib    sing_738.htm#IDX367     
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-finitediff_lib          sing_2348.htm#IDX946    
-finitenessTest          sing_1104.htm#SEC1180   40633
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-freerank                sing_943.htm#SEC1019    52218
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-geometrical locus               sing_914.htm#IDX453     
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-geometrical locus               sing_917.htm#IDX463     
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+hnoether.lib            sing_1553.htm#SEC1629   
+hnoether_lib            sing_1553.htm#SEC1629   
+holonomic rank          sing_777.htm#IDX380     
+holonomicRank           sing_781.htm#SEC833     41306
+hom             sing_2525.htm#SEC2601   40032
+hom_kernel              sing_1170.htm#SEC1246   32604
+homog           sing_262.htm#SEC302     
+homog_part              sing_2725.htm#SEC2801   20875
+homog_parts             sing_2726.htm#SEC2802   12854
+homogeneitySpace                sing_2162.htm#SEC2238   48243
+homogfacFirstQWeyl              sing_710.htm#SEC762     32751
+homogfacFirstQWeyl_all  homogfacFirstQWeyl_all  sing_712.htm#SEC764     9014
+homogfacNthQWeyl                sing_709.htm#SEC761     19238
+homogfacNthQWeyl_all    homogfacNthQWeyl_all    sing_711.htm#SEC763     2523
+homolog.lib             sing_1155.htm#SEC1231   
+homolog_lib             sing_1155.htm#SEC1231   
+homology                sing_1165.htm#SEC1241   15040
+homomorphism            sing_2509.htm#SEC2585   27115
+howto, download Download instructions   sing_2752.htm#SEC2841   
+howto, install on Macintosh     Macintosh installation instructions     sing_2755.htm#SEC2844   
+howto, install on Unix  Unix installation instructions  sing_2753.htm#SEC2842   
+howto, install on Windows       Windows installation instructions       sing_2754.htm#SEC2843   
+hres            sing_263.htm#SEC303     
 html, default help      The online help system  sing_16.htm#IDX24       
-hyperel.lib             sing_1926.htm#SEC2002   
-hyperel_lib             sing_1926.htm#SEC2002   
-hyperplane              sing_2158.htm#IDX799    
-hyperplane arrangement          sing_532.htm#IDX335     
-hypersurface singularity                sing_1566.htm#IDX751    
-iMult           sing_1231.htm#SEC1307   22059
-id2mod          sing_955.htm#SEC1031    32918
-ideal           sing_85.htm#SEC125      
-ideal declarations              sing_86.htm#SEC126      
-ideal declarations (plural)     ideal declarations (plural)     sing_416.htm#SEC456     
-ideal expressions               sing_87.htm#SEC127      
-ideal expressions (plural)      ideal expressions (plural)      sing_417.htm#SEC457     
-ideal operations                sing_88.htm#SEC128      
-ideal operations (plural)       ideal operations (plural)       sing_418.htm#SEC458     
-ideal related functions ideal related functions sing_89.htm#SEC129      
-ideal related functions (plural)        ideal related functions (plural)        sing_419.htm#SEC459     
-ideal, toric            sing_851.htm#SEC908     
-idealSplit              sing_1705.htm#SEC1781   4673
-ideals  Miscellaneous oddities  sing_410.htm#IDX291     
-idealsimplify           sing_1467.htm#SEC1543   38569
-identifier      Identifier resolution   sing_411.htm#SEC451     
-identifyvar             sing_1375.htm#SEC1451   59662
-if              sing_378.htm#SEC418     
-imageLattice            sing_2453.htm#SEC2529   15740
-image_of_variety                sing_1655.htm#SEC1731   43711
-imap            sing_256.htm#SEC296     
-imap (plural)           sing_454.htm#SEC494     
-imapall         sing_987.htm#SEC1063    16023
-impart          sing_257.htm#SEC297     
-importfrom              sing_379.htm#SEC419     
-inCenter                sing_521.htm#SEC573     22152
-inCentralizer           sing_522.htm#SEC574     49000
-inForm          sing_564.htm#SEC616     5283
-inSubring               sing_1096.htm#SEC1172   24817
-indSet          sing_1203.htm#SEC1279   32828
-indepSet                sing_258.htm#SEC298     
+hyperel.lib             sing_1940.htm#SEC2016   
+hyperel_lib             sing_1940.htm#SEC2016   
+hyperplane              sing_2169.htm#IDX825    
+hyperplane arrangement          sing_540.htm#IDX337     
+hypersurface singularity                sing_1580.htm#IDX777    
+iMult           sing_1245.htm#SEC1321   22059
+id              sing_2482.htm#SEC2558   47592
+id2mod          sing_975.htm#SEC1051    32918
+ideal           sing_90.htm#SEC130      
+ideal declarations              sing_91.htm#SEC131      
+ideal declarations (plural)     ideal declarations (plural)     sing_424.htm#SEC464     
+ideal expressions               sing_92.htm#SEC132      
+ideal expressions (plural)      ideal expressions (plural)      sing_425.htm#SEC465     
+ideal operations                sing_93.htm#SEC133      
+ideal operations (plural)       ideal operations (plural)       sing_426.htm#SEC466     
+ideal related functions ideal related functions sing_94.htm#SEC134      
+ideal related functions (plural)        ideal related functions (plural)        sing_427.htm#SEC467     
+ideal, toric            sing_871.htm#SEC928     
+idealSplit              sing_1719.htm#SEC1795   4673
+ideals  Miscellaneous oddities  sing_418.htm#IDX293     
+idealsimplify           sing_1481.htm#SEC1557   38569
+identifier      Identifier resolution   sing_419.htm#SEC459     
+identifyvar             sing_1389.htm#SEC1465   59662
+if              sing_386.htm#SEC426     
+image           sing_2505.htm#SEC2581   43481
+imageLattice            sing_2555.htm#SEC2631   15740
+image_of_variety                sing_1669.htm#SEC1745   43711
+imap            sing_264.htm#SEC304     
+imap (plural)           sing_462.htm#SEC502     
+imapall         sing_1007.htm#SEC1083   16023
+impart          sing_265.htm#SEC305     
+importfrom              sing_387.htm#SEC427     
+inCenter                sing_529.htm#SEC581     22152
+inCentralizer           sing_530.htm#SEC582     49000
+inForm          sing_572.htm#SEC624     5283
+inSubring               sing_1108.htm#SEC1184   24817
+indSet          sing_1217.htm#SEC1293   32828
+indepSet                sing_266.htm#SEC306     
 indexed names           sing_36.htm#IDX82       
 indexed names           sing_37.htm#SEC65       
 indices, multi          sing_37.htm#SEC65       
-inequalities            sing_2018.htm#SEC2094   10122
-infRedTail, option              sing_307.htm#IDX154     
+inequalities            sing_2032.htm#SEC2108   10122
+infRedTail, option              sing_315.htm#IDX154     
 info    The online help system  sing_16.htm#SEC23       
-iniD            sing_1395.htm#SEC1471   35084
-init_debug              sing_1474.htm#SEC1550   29863
-initial         sing_2152.htm#SEC2228   8678
-initial form            sing_497.htm#IDX316     
-initial ideal           sing_497.htm#IDX315     
-initial ideal approach          sing_497.htm#IDX319     
-initial ideal approach          sing_588.htm#IDX358     
-initialForm             sing_2129.htm#SEC2205   57793
-initialIdeal            sing_2130.htm#SEC2206   22205
-initialIdealW           sing_563.htm#SEC615     36086
-initialMalgrange                sing_562.htm#SEC614     26846
-injective_knapsack              sing_1920.htm#SEC1996   7619
-inout.lib               sing_921.htm#SEC997     
-inout_lib               sing_921.htm#SEC997     
+iniD            sing_1409.htm#SEC1485   35084
+init_debug              sing_1488.htm#SEC1564   29863
+initial         sing_2163.htm#SEC2239   8678
+initial form            sing_505.htm#IDX318     
+initial ideal           sing_505.htm#IDX317     
+initial ideal approach          sing_505.htm#IDX321     
+initial ideal approach          sing_596.htm#IDX360     
+initialForm             sing_2140.htm#SEC2216   57793
+initialIdeal            sing_2141.htm#SEC2217   22205
+initialIdealW           sing_571.htm#SEC623     36086
+initialMalgrange                sing_570.htm#SEC622     26846
+injective_knapsack              sing_1934.htm#SEC2010   7619
+inout.lib               sing_941.htm#SEC1017    
+inout_lib               sing_941.htm#SEC1017    
 input           sing_41.htm#SEC71       
-insert          sing_121.htm#SEC161     
-insert          sing_259.htm#SEC299     
-insertCone              sing_2042.htm#SEC2118   13858
-insertGenerator         sing_583.htm#SEC635     13951
-instructions, Macintosh installation    Macintosh installation instructions     sing_2573.htm#SEC2663   
-instructions, Unix installation Unix installation instructions  sing_2571.htm#SEC2661   
-instructions, Windows installation      Windows installation instructions       sing_2572.htm#SEC2662   
-instructions, downloading       Download instructions   sing_2570.htm#SEC2660   
-int             sing_90.htm#SEC130      
-int declarations                sing_91.htm#SEC131      
-int expressions         sing_92.htm#SEC132      
-int operations          sing_93.htm#SEC133      
-int related functions   int related functions   sing_94.htm#SEC134      
-intInverse              sing_2462.htm#SEC2538   sprintf
-intPart         sing_1874.htm#SEC1950   48360
-intRank         sing_2454.htm#SEC2530   1830
-intRoot         sing_1875.htm#SEC1951   54582
-intRoots                sing_580.htm#SEC632     24538
-intStrategy, option             sing_307.htm#IDX155     
-intclMonIdeal           sing_1244.htm#SEC1320   22338
-intclToricRing          sing_1240.htm#SEC1316   62143
-integer division        Miscellaneous oddities  sing_410.htm#IDX286     
-integer programming             sing_859.htm#SEC916     
-integral                sing_2518.htm#SEC2594   62683
-integral basis          sing_1165.htm#IDX538    
-integral basis          sing_1358.htm#IDX594    
-integral closure                sing_1224.htm#IDX551    
-integral closure                sing_1225.htm#IDX554    
-integral closure                sing_1226.htm#IDX557    
-integral closure                sing_1239.htm#IDX563    
-integralBasis           sing_1165.htm#SEC1241   38114
-integralIdeal           sing_567.htm#SEC619     29194
-integralModule          sing_568.htm#SEC620     58078
-integralSection         sing_2463.htm#SEC2539   sprintf
-integralbasis.lib               sing_1164.htm#SEC1240   
-integralbasis_lib               sing_1164.htm#SEC1240   
-integration of D-module         sing_555.htm#IDX347     
+insert          sing_126.htm#SEC166     
+insert          sing_267.htm#SEC307     
+insertCone              sing_2056.htm#SEC2132   13858
+insertGenerator         sing_591.htm#SEC643     13951
+instructions, Macintosh installation    Macintosh installation instructions     sing_2755.htm#SEC2844   
+instructions, Unix installation Unix installation instructions  sing_2753.htm#SEC2842   
+instructions, Windows installation      Windows installation instructions       sing_2754.htm#SEC2843   
+instructions, downloading       Download instructions   sing_2752.htm#SEC2841   
+int             sing_95.htm#SEC135      
+int declarations                sing_96.htm#SEC136      
+int expressions         sing_97.htm#SEC137      
+int operations          sing_98.htm#SEC138      
+int related functions   int related functions   sing_99.htm#SEC139      
+intInverse              sing_2564.htm#SEC2640   sprintf
+intPart         sing_1888.htm#SEC1964   48360
+intRank         sing_2556.htm#SEC2632   1830
+intRoot         sing_1889.htm#SEC1965   54582
+intRoots                sing_588.htm#SEC640     24538
+intStrategy, option             sing_315.htm#IDX155     
+intclMonIdeal           sing_1258.htm#SEC1334   22338
+intclToricRing          sing_1254.htm#SEC1330   62143
+integer division        Miscellaneous oddities  sing_418.htm#IDX288     
+integer programming             sing_879.htm#SEC936     
+integral                sing_2700.htm#SEC2776   62683
+integral basis          sing_1177.htm#IDX553    
+integral basis          sing_1372.htm#IDX620    
+integral closure                sing_1238.htm#IDX568    
+integral closure                sing_1239.htm#IDX571    
+integral closure                sing_1240.htm#IDX574    
+integral closure                sing_1253.htm#IDX580    
+integralBasis           sing_1177.htm#SEC1253   38114
+integralIdeal           sing_575.htm#SEC627     29194
+integralModule          sing_576.htm#SEC628     58078
+integralSection         sing_2565.htm#SEC2641   sprintf
+integralbasis.lib               sing_1176.htm#SEC1252   
+integralbasis_lib               sing_1176.htm#SEC1252   
+integration of D-module         sing_563.htm#IDX349     
 interface, Emacs        Emacs user interface    sing_21.htm#SEC28       
-interiorLatticePoints   interiorLatticePoints   sing_2081.htm#SEC2157   49868
-internalfunctions               sing_1475.htm#SEC1551   61230
-interpolate             sing_1711.htm#SEC1787   51502
-interpolation           sing_260.htm#SEC300     
-interred                sing_261.htm#SEC301     
-intersect               sing_262.htm#SEC302     
-intersect (plural)              sing_455.htm#SEC495     
-intersectElim, option           sing_307.htm#IDX173     
-intersectLattices               sing_2459.htm#SEC2535   41354
-intersectMon            sing_1180.htm#SEC1256   44572
-intersectSyz, option            sing_307.htm#IDX174     
-intersectZ              sing_1300.htm#SEC1376   sprintf
-intersection            sing_1549.htm#SEC1625   46938
-intersection lattice            sing_2194.htm#IDX874    
-intersection lattice            sing_2195.htm#IDX875    
-intersection multiplicity               sing_1460.htm#IDX629    
-intersection multiplicity               sing_1549.htm#IDX744    
-intersectionDiv         sing_1423.htm#SEC1499   29017
-intersectionValRingIdeals       intersectionValRingIdeals       sing_1249.htm#SEC1325   38773
-intersectionValRings    intersectionValRings    sing_1248.htm#SEC1324   35761
-intmat          sing_97.htm#SEC137      
-intmat declarations             sing_98.htm#SEC138      
-intmat expressions              sing_99.htm#SEC139      
-intmat operations               sing_101.htm#SEC141     
-intmat related functions        intmat related functions        sing_102.htm#SEC142     
-intmat type cast                sing_100.htm#SEC140     
-intmat2mons             sing_1264.htm#SEC1340   21150
-intprog.lib             sing_1166.htm#SEC1242   
-intprog_lib             sing_1166.htm#SEC1242   
-intvec          sing_103.htm#SEC143     
-intvec declarations             sing_104.htm#SEC144     
-intvec expressions              sing_105.htm#SEC145     
-intvec operations               sing_106.htm#SEC146     
-intvec related functions        intvec related functions        sing_107.htm#SEC147     
-invariant               sing_2317.htm#IDX922    
-invariant ring minimal generating set matrix group      invariant_algebra_reynolds      sing_1624.htm#IDX757    
-invariant ring minimal generating set permutation group invariant_algebra_perm  sing_1625.htm#IDX758    
-invariantRing           sing_1657.htm#SEC1733   18582
-invariant_algebra_perm  invariant_algebra_perm  sing_1625.htm#SEC1701   63525
-invariant_algebra_reynolds      invariant_algebra_reynolds      sing_1624.htm#SEC1700   35705
-invariant_basis         sing_1632.htm#SEC1708   18343
-invariant_basis_reynolds        invariant_basis_reynolds        sing_1633.htm#SEC1709   54788
-invariant_ring          sing_1620.htm#SEC1696   8059
-invariant_ring_random   invariant_ring_random   sing_1621.htm#SEC1697   6986
-invariants      curveColengthDerivations        sing_1545.htm#SEC1621   57499
-invariants              sing_2314.htm#IDX915    
-invariants              sing_2318.htm#IDX924    
-inverse         sing_1064.htm#SEC1140   27411
-inverse of a matrix via its LU-decomposition            sing_282.htm#SEC322     
-inverseFourier          sing_578.htm#SEC630     65140
-inverse_B               sing_1065.htm#SEC1141   17616
-inverse_L               sing_1066.htm#SEC1142   49271
-inverse_modulus         sing_1903.htm#SEC1979   60822
-invertBirMap            sing_1359.htm#SEC1435   16086
-invertNumberMain                sing_1735.htm#SEC1811   62615
-involut.lib             sing_642.htm#SEC694     
-involut_lib             sing_642.htm#SEC694     
-involution              sing_647.htm#SEC699     34280
-invunit         sing_1568.htm#SEC1644   62398
-iostruct                sing_1822.htm#SEC1898   60444
-irrRealizationDim               sing_2111.htm#SEC2187   7814
-irred_secondary_char0   irred_secondary_char0   sing_1646.htm#SEC1722   2943
-irred_secondary_no_molien       irred_secondary_no_molien       sing_1649.htm#SEC1725   55905
-irreddecMon             sing_1189.htm#SEC1265   20160
-irreducible power series                sing_1550.htm#IDX745    
-irreducible secondary invariant irred_secondary_char0   sing_1646.htm#IDX759    
-isAface         sing_2391.htm#SEC2467   47756
-isAntiEndo              sing_649.htm#SEC701     19156
-isBounded               sing_2082.htm#SEC2158   28183
-isCI            sing_204.htm#IDX139     58425
-isCI            sing_1114.htm#SEC1190   
-isCM            sing_204.htm#IDX140     50469
-isCM            sing_1154.htm#SEC1230   
-isCMcod2                sing_1603.htm#SEC1679   2563
-isCanonical             sing_2083.htm#SEC2159   51109
-isCartan                sing_523.htm#SEC575     39541
-isCentral               sing_720.htm#SEC772     54650
-isCommutative           sing_722.htm#SEC774     60728
-isCompatible            sing_2043.htm#SEC2119   57323
-isCompressed            sing_2084.htm#SEC2160   2849
-isEqualDivisor          sing_2328.htm#SEC2404   17569
-isEquising              sing_1512.htm#SEC1588   1424
-isFlat          sing_1155.htm#SEC1231   14706
-isFsat          sing_573.htm#SEC625     28225
-isFullSpace             sing_2019.htm#SEC2095   27433
-isGorenstein            sing_2085.htm#SEC2161   24010
-isGradedRingHomomorphism        isGradedRingHomomorphism        sing_2448.htm#SEC2524   39551
-isGroup         sing_2446.htm#SEC2522   55744
-isGroupHomomorphism             sing_2447.htm#SEC2523   65475
-isHolonomic             sing_551.htm#SEC603     30274
-isHomg          sing_204.htm#IDX135     
-isHomogeneous           sing_2474.htm#SEC2550   3034
-isInt           sing_586.htm#SEC638     9879
-isIntegralSurjective    isIntegralSurjective    sing_2460.htm#SEC2536   sprintf
-isInvolution            sing_648.htm#SEC700     13601
-isLatticeEmpty          sing_2086.htm#SEC2162   48517
-isLocalizationRegular   isLocalizationRegular   sing_2383.htm#SEC2459   11221
-isLocallyFree           sing_1156.htm#SEC1232   46389
-isMonomial              sing_1175.htm#SEC1251   57615
-isNC            sing_721.htm#SEC773     57151
-isNormal                sing_2087.htm#SEC2163   64236
-isOnCurve               sing_1887.htm#SEC1963   36324
-isOrigin                sing_2020.htm#SEC2096   13977
-isPositive              sing_2471.htm#SEC2547   50852
-isPrimitiveSublattice   isPrimitiveSublattice   sing_2461.htm#SEC2537   sprintf
-isPure          sing_2044.htm#SEC2120   44002
-isPureTensor            sing_495.htm#SEC547     21323
-isQuotientRing          sing_1001.htm#SEC1077   sprintf
-isRational              sing_554.htm#SEC606     57398
-isReflexive             sing_2088.htm#SEC2164   3991
-isReg           sing_1157.htm#SEC1233   40920
-isSB            sing_204.htm#IDX134     
-isSimplicial            sing_2021.htm#SEC2097   57789
-isSmooth                sing_2089.htm#SEC2165   37647
-isSubModule             sing_1002.htm#SEC1078   sprintf
-isSublattice            sing_2452.htm#SEC2528   10501
-isSymmetric             sing_1324.htm#SEC1400   61363
-isTame          sing_1537.htm#SEC1613   31925
-isTerminal              sing_2090.htm#SEC2166   29416
-isTorsionFree           sing_2470.htm#SEC2546   52228
-isTwoSidedGB            sing_496.htm#SEC548     36558
-isUpperTriangular               sing_701.htm#SEC753     40655
-isVar           sing_640.htm#SEC692     43851
-isVeryAmple             sing_2091.htm#SEC2167   64652
-isWeyl          sing_723.htm#SEC775     28994
-isZeroElement           sing_2472.htm#SEC2548   514
-is_NND          sing_1553.htm#SEC1629   26564
-is_NP           sing_1212.htm#SEC1288   43891
-is_active               sing_1586.htm#SEC1662   6867
-is_bijective            sing_1101.htm#SEC1177   49512
-is_cenBimodule          sing_756.htm#SEC808     35450
-is_cenSubbimodule               sing_757.htm#SEC809     26181
-is_ci           sing_1587.htm#SEC1663   35370
-is_complex              sing_1037.htm#SEC1113   1234
-is_fix_injective                sing_1924.htm#SEC2000   11663
-is_h_injective          sing_1923.htm#SEC1999   36696
-is_injective            sing_1099.htm#SEC1175   15776
-is_irred                sing_1550.htm#SEC1626   51150
-is_is           sing_1588.htm#SEC1664   64105
-is_nested               sing_1213.htm#SEC1289   9200
-is_prime                sing_1904.htm#SEC1980   29018
-is_primitive_root               sing_1900.htm#SEC1976   42838
-is_pure         sing_748.htm#SEC800     59105
-is_reg          sing_1589.htm#SEC1665   18146
-is_regs         sing_1590.htm#SEC1666   50242
-is_surjective           sing_1100.htm#SEC1176   57044
-is_zero         sing_944.htm#SEC1020    24341
-isartinianMon           sing_1186.htm#SEC1262   1103
-isgenericMon            sing_1187.htm#SEC1263   14444
-ishyper         sing_1927.htm#SEC2003   65518
-isirreducibleMon                sing_1185.htm#SEC1261   22428
-isoncurve               sing_1928.htm#SEC2004   16384
-isparam         sing_1991.htm#SEC2067   56395
-isprimaryMon            sing_1184.htm#SEC1260   57367
-isprimeMon              sing_1183.htm#SEC1259   9124
-isuni           sing_1976.htm#SEC2052   39427
-iv2lp           sing_618.htm#SEC670     53390
-iv2lpList               sing_619.htm#SEC671     38626
-iv2lpMat                sing_620.htm#SEC672     41720
-ivDHilbert              sing_594.htm#SEC646     18825
-ivDHilbertSickle                sing_595.htm#SEC647     16102
-ivDimCheck              sing_596.htm#SEC648     42112
-ivHilbert               sing_597.htm#SEC649     34233
-ivKDim          sing_598.htm#SEC650     40986
-ivL2lpI         sing_617.htm#SEC669     45855
-ivMis2Base              sing_599.htm#SEC651     57812
-ivMis2Dim               sing_600.htm#SEC652     15557
-ivOrdMisLex             sing_601.htm#SEC653     40656
-ivSickle                sing_602.htm#SEC654     48016
-ivSickleDim             sing_604.htm#SEC656     57209
-ivSickleHil             sing_603.htm#SEC655     1967
-jInvariant              sing_2123.htm#SEC2199   2369
-jOft            sing_1859.htm#SEC1935   25716
-jacob           sing_263.htm#SEC303     
-jacoblift               sing_1569.htm#SEC1645   40125
-jacobson                sing_1828.htm#SEC1904   59267
-jacobson.lib            sing_1826.htm#SEC1902   
-jacobson_lib            sing_1826.htm#SEC1902   
-janet           sing_264.htm#SEC304     
-jet             sing_265.htm#SEC305     
-jordan          sing_1085.htm#SEC1161   16602
-jordanbasis             sing_1086.htm#SEC1162   12736
-jordanmatrix            sing_1087.htm#SEC1163   2886
-jordannf                sing_1088.htm#SEC1164   20535
-jungfib         sing_1408.htm#SEC1484   5432
-jungnormal              sing_1407.htm#SEC1483   43561
-jungresolve             sing_1406.htm#SEC1482   45004
-katsura         sing_942.htm#SEC1018    45913
-kbase           sing_266.htm#SEC306     
-kbase (plural)          sing_456.htm#SEC496     
-keepring                sing_380.htm#SEC420     
-kernel          sing_267.htm#SEC307     
-kernelLattice           sing_2455.htm#SEC2531   36320
-kill            sing_268.htm#SEC308     
-killTask                sing_1016.htm#SEC1092   39317
-killall         sing_888.htm#SEC964     34661
-killattrib              sing_269.htm#SEC309     
-kmemory         sing_887.htm#SEC963     52193
-kohom           sing_1159.htm#SEC1235   50086
-kontrahom               sing_1160.htm#SEC1236   58549
-koszul          sing_270.htm#SEC310     
-kskernel.lib            sing_1560.htm#SEC1636   
-kskernel_lib            sing_1560.htm#SEC1636   
+interiorLatticePoints   interiorLatticePoints   sing_2092.htm#SEC2168   49868
+internalfunctions               sing_1489.htm#SEC1565   61230
+interpolate             sing_1725.htm#SEC1801   51502
+interpolation           sing_268.htm#SEC308     
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-logg            sing_2545.htm#SEC2621   38736
-lp, global ordering             sing_838.htm#IDX387     
-lp2iv           sing_621.htm#SEC673     26909
-lp2ivId         sing_622.htm#SEC674     15628
-lp2lstr         sing_633.htm#SEC685     24713
-lpDHilbert              sing_605.htm#SEC657     11075
-lpDHilbertSickle                sing_606.htm#SEC658     46653
-lpDimCheck              sing_608.htm#SEC660     50239
-lpHilbert               sing_607.htm#SEC659     53685
-lpId2ivLi               sing_623.htm#SEC675     29846
-lpKDim          sing_609.htm#SEC661     53650
-lpMis2Base              sing_610.htm#SEC662     10826
-lpMis2Dim               sing_611.htm#SEC663     47442
-lpMult          sing_630.htm#SEC682     58898
-lpNF            sing_627.htm#SEC679     55144
-lpOrdMisLex             sing_612.htm#SEC664     21260
-lpPower         sing_632.htm#SEC684     7325
-lpSickle                sing_613.htm#SEC665     19646
-lpSickleDim             sing_615.htm#SEC667     50163
-lpSickleHil             sing_614.htm#SEC666     19038
-lprint          sing_923.htm#SEC999     5285
-lres            sing_280.htm#SEC320     
-ls, local ordering              sing_839.htm#IDX400     
-lst2str         sing_634.htm#SEC686     10088
-lsum            sing_1135.htm#SEC1211   50315
-ludecomp                sing_281.htm#SEC321     
-luinverse               sing_282.htm#SEC322     
-lusolve         sing_283.htm#SEC323     
-m_merkle_hellman_decryption     m_merkle_hellman_decryption     sing_1915.htm#SEC1991   57945
-m_merkle_hellman_encryption     m_merkle_hellman_encryption     sing_1914.htm#SEC1990   33857
-m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1913.htm#SEC1989   7880
-magnitude               sing_1837.htm#SEC1913   37967
-makeDivisor             sing_2323.htm#SEC2399   3414
-makeFormalDivisor               sing_2333.htm#SEC2409   54579
-makeGraph               sing_1126.htm#SEC1202   21758
-makeGraphVE             sing_2531.htm#SEC2607   sprintf
-makeHeisenberg          sing_711.htm#SEC763     2050
-makeLetterplaceRing             sing_625.htm#SEC677     41789
-makeMalgrange           sing_592.htm#SEC644     41377
-makeModElimRing         sing_728.htm#SEC780     56092
-makePDivisor            sing_2339.htm#SEC2415   45273
-makeQsl2                sing_675.htm#SEC727     3997
-makeQsl3                sing_676.htm#SEC728     41249
-makeQso3                sing_674.htm#SEC726     58910
-makeSheaf               sing_2519.htm#SEC2595   10497
-makeUe6         sing_671.htm#SEC723     58585
-makeUe7         sing_672.htm#SEC724     61849
-makeUe8         sing_673.htm#SEC725     64987
-makeUf4         sing_670.htm#SEC722     8408
-makeUg2         sing_669.htm#SEC721     34512
-makeUgl         sing_655.htm#SEC707     3543
-makeUsl         sing_654.htm#SEC706     24536
-makeUsl2                sing_653.htm#SEC705     42637
-makeUso10               sing_661.htm#SEC713     6936
-makeUso11               sing_662.htm#SEC714     35873
-makeUso12               sing_663.htm#SEC715     19319
-makeUso5                sing_656.htm#SEC708     34378
-makeUso6                sing_657.htm#SEC709     65009
-makeUso7                sing_658.htm#SEC710     49142
-makeUso8                sing_659.htm#SEC711     33275
-makeUso9                sing_660.htm#SEC712     16896
-makeUsp1                sing_664.htm#SEC716     44522
-makeUsp2                sing_665.htm#SEC717     18017
-makeUsp3                sing_666.htm#SEC718     57445
-makeUsp4                sing_667.htm#SEC719     51690
-makeUsp5                sing_668.htm#SEC720     35951
-makeVariety             sing_2511.htm#SEC2587   23915
-makeWeyl                sing_710.htm#SEC762     8554
-map             sing_123.htm#SEC163     
-map (plural)            sing_420.htm#SEC460     
-map declarations                sing_124.htm#SEC164     
-map declarations (plural)       map declarations (plural)       sing_421.htm#SEC461     
-map expressions         sing_125.htm#SEC165     
-map expressions (plural)        map expressions (plural)        sing_422.htm#SEC462     
-map operations          sing_126.htm#IDX129     
-map operations (plural) map operations (plural) sing_423.htm#IDX298     
-map related functions   map related functions   sing_127.htm#IDX131     
-map related functions  (plural) map related functions (plural)  sing_424.htm#IDX299     
-mapIsFinite             sing_1103.htm#SEC1179   60897
-mapToRatNormCurve               sing_1363.htm#SEC1439   8877
-mapall          sing_988.htm#SEC1064    14907
-mappingcone             sing_2424.htm#SEC2500   48219
-mappingcone3            sing_2426.htm#SEC2502   58973
-markov4ti2              sing_1319.htm#SEC1395   9163
-mat2arr         sing_2160.htm#SEC2236   20840
-mat2carr                sing_2161.htm#SEC2237   13777
-mat_rk          sing_1077.htm#SEC1153   32196
-matbil          sing_1964.htm#SEC2040   1611
-mathematical objects    Representation of mathematical objects  sing_834.htm#SEC886     
-mathinit                sing_1749.htm#SEC1825   16793
-matmult         sing_1965.htm#SEC2041   60088
-matrix          sing_128.htm#SEC168     
-matrix          sing_2160.htm#IDX805    
-matrix                  sing_2161.htm#IDX808    
-matrix                  sing_2162.htm#IDX812    
-matrix declarations             sing_129.htm#SEC169     
-matrix diagonalization          sing_1826.htm#IDX781    
-matrix expressions              sing_130.htm#SEC170     
-matrix operations               sing_132.htm#SEC172     
-matrix related functions        matrix related functions        sing_133.htm#SEC173     
-matrix type cast                sing_131.htm#SEC171     
-matrix.lib              sing_1030.htm#SEC1106   
-matrixExp               sing_1353.htm#SEC1429   53063
-matrixLog               sing_1354.htm#SEC1430   26235
-matrixT1                sing_1605.htm#SEC1681   15051
-matrix_lib              sing_1030.htm#SEC1106   
-matrixpr