Changeset a070b84 in git

Timestamp:

Aug 19, 2016, 4:56:16 PM (7 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', '828514cf6e480e4bafc26df99217bf2a1ed1ef45')

Children:

32e84f5b8f065a8070d982ae939de64e4721beab

Parents:

961c76da92efc86885b6506c8c83262f14e705ff

Message:

Singular 4.0.3p3

Files:

• doc/singular.idx (modified) (23 diffs)
• kernel/mod2.h (modified) (1 diff)
• make_tar.sh (modified) (1 diff)

doc/singular.idx

@@ -9 +9 @@
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+%               sing_142.htm#SEC182     
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@@ -20 +22 @@
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@@ -28 +34 @@
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 ++              sing_36.htm#IDX86       
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@@ -35 +49 @@
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@@ -99 +117 @@
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 //              sing_36.htm#IDX107      
 //              sing_36.htm#IDX109      
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-AGcode_Omega            sing_1830.htm#SEC1906   
-ASCII           sing_936.htm#SEC1012    
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 ASCII links             sing_112.htm#SEC152     
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-A_Z             sing_935.htm#SEC1011    
+A_L             sing_1531.htm#SEC1607   
+A_Z             sing_937.htm#SEC1013    
 Access to elements of a user defined type       Access to elements of a user defined type       sing_180.htm#SEC220     
-Adj_div         sing_1824.htm#SEC1900   
-Adjoint ideal           sing_1405.htm#IDX535    
-Alexander polynomial            sing_1499.htm#IDX559    
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-Appel hypergeometric function           sing_611.htm#IDX340     
-Applications            sing_885.htm#SEC937     
-ArnoldAction            sing_1621.htm#SEC1697   
+Adj_div         sing_1827.htm#SEC1903   
+Adjoint ideal           sing_1408.htm#IDX542    
+Alexander polynomial            sing_1502.htm#IDX566    
+Algebraic Geometry codes                sing_1826.htm#IDX714    
+Algebraic dependence    Algebraic dependence    sing_870.htm#SEC922     
+Algebraic geometry              sing_1383.htm#SEC1459   
+AltVarEnd               sing_783.htm#SEC835     
+AltVarStart             sing_782.htm#SEC834     
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+Appel hypergeometric function           sing_612.htm#IDX346     
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+ArnoldAction            sing_1624.htm#SEC1700   
 Assignments for user defined types      Assignments for user defined types      sing_182.htm#SEC222     
-Atkin           sing_1912.htm#SEC1988   
+Atkin           sing_1915.htm#SEC1991   
 Authors         sing_1.htm#IDX16        
-BINresol                sing_1418.htm#SEC1494   
+BINresol                sing_1421.htm#SEC1497   
 Background              sing_3.htm#SEC5 
-Basic programming               sing_843.htm#SEC895     
-Basic programming               sing_843.htm#SEC895     
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-Bern            sing_2208.htm#SEC2284   
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-Bernstein-Sato polynomial               sing_553.htm#IDX302     
-Bernstein-Sato polynomial               sing_588.htm#IDX318     
-Bernstein-Sato polynomial               sing_1562.htm#IDX590    
-Bernstein-Sato polynomial               sing_1566.htm#IDX607    
-Bernstein-Sato polynomial for variety           sing_644.htm#IDX343     
-Betti number    Syzygies and resolutions        sing_902.htm#SEC959     
-Bigatti-La Scala-Robbiano algorithm     Bigatti and La Scala and Robbiano       sing_912.htm#SEC969     
-BlowingUp               sing_1541.htm#SEC1617   
-Blowupcenter            sing_1421.htm#SEC1497   
-BorelCheck              sing_1496.htm#SEC1572   
-Branches of space curve singularities   Branches of space curve singularities   sing_876.htm#SEC928     
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-Brieskorn lattice               sing_1564.htm#IDX600    
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-Brieskorn lattice                       sing_1569.htm#IDX620    
-Brieskorn lattice                       sing_1570.htm#IDX628    
-Brieskorn lattice                       sing_1571.htm#IDX634    
-Brieskorn lattice                       sing_1572.htm#IDX642    
-Brieskorn lattice                       sing_1573.htm#IDX652    
-Brieskorn lattice                       sing_1584.htm#IDX658    
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-Brieskorn lattice                       sing_1614.htm#IDX696    
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-BrillNoether            sing_1826.htm#SEC1902   
-Buchberger algorithm for toric ideals   Buchberger algorithm    sing_913.htm#SEC970     
-Budur-Mustata-Saito approach            sing_644.htm#IDX347     
-Building Singular               sing_2470.htm#SEC2559   
+Basic programming               sing_845.htm#SEC897     
+Basic programming               sing_845.htm#SEC897     
+BelongSemig             sing_2233.htm#SEC2309   
+BerlekampMassey         sing_2259.htm#SEC2335   
+Bern            sing_2211.htm#SEC2287   
+Bernstein operator              sing_589.htm#IDX327     
+Bernstein-Sato polynomial               sing_554.htm#IDX308     
+Bernstein-Sato polynomial               sing_589.htm#IDX324     
+Bernstein-Sato polynomial               sing_1565.htm#IDX597    
+Bernstein-Sato polynomial               sing_1569.htm#IDX614    
+Bernstein-Sato polynomial for variety           sing_645.htm#IDX349     
+Betti number    Syzygies and resolutions        sing_904.htm#SEC961     
+Bigatti-La Scala-Robbiano algorithm     Bigatti and La Scala and Robbiano       sing_914.htm#SEC971     
+BlowingUp               sing_1544.htm#SEC1620   
+Blowupcenter            sing_1424.htm#SEC1500   
+BorelCheck              sing_1499.htm#SEC1575   
+Branches of space curve singularities   Branches of space curve singularities   sing_878.htm#SEC930     
+Briancon-Maisonobe algorithm            sing_589.htm#IDX333     
+Brieskorn lattice               sing_1565.htm#IDX593    
+Brieskorn lattice               sing_1566.htm#IDX604    
+Brieskorn lattice               sing_1567.htm#IDX607    
+Brieskorn lattice               sing_1568.htm#IDX610    
+Brieskorn lattice               sing_1569.htm#IDX613    
+Brieskorn lattice               sing_1570.htm#IDX617    
+Brieskorn lattice               sing_1571.htm#IDX621    
+Brieskorn lattice                       sing_1572.htm#IDX627    
+Brieskorn lattice                       sing_1573.htm#IDX635    
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+BrillNoether            sing_1829.htm#SEC1905   
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 C programming language  Major differences to the C programming language sing_457.htm#SEC497     
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-CRHT-ideal              sing_919.htm#SEC983     
+C, module ordering              sing_897.htm#IDX407     
+CGS, disjoint, reduced, Comprehensive Groebner System   cgsdr   sing_959.htm#IDX417     
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 CYGWIN and ESingular    Running SINGULAR under Emacs    sing_23.htm#SEC33       
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+Castelnuovo-Mumford regularity          sing_1486.htm#IDX558    
 Category string         sing_51.htm#SEC88       
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-CentralSaturation               sing_737.htm#SEC789     
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-Classification of singularities         sing_2404.htm#IDX891    
-Code    Codes and the decoding problem  sing_918.htm#SEC976     
-Codes and the decoding problem  Codes and the decoding problem  sing_918.htm#SEC975     
-Coding theory           sing_1822.htm#SEC1898   
-Coefficient rings       Notes for Singular users        sing_2468.htm#SEC2551   
+Characteristic sets             sing_905.htm#SEC962     
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+ChernRootsWedge         sing_2202.htm#SEC2278   
+Chevalley-Rosenlicht theorem            sing_1402.htm#IDX527    
+Chevalley-Rosenlicht theorem            sing_1403.htm#IDX530    
+Classification of hypersurface singularities    Classification of hypersurface singularities    sing_879.htm#SEC931     
+Classification of singularities         sing_2409.htm#IDX898    
+Code    Codes and the decoding problem  sing_920.htm#SEC978     
+Codes and the decoding problem  Codes and the decoding problem  sing_920.htm#SEC977     
+Coding theory           sing_1825.htm#SEC1901   
+Coefficient rings       Notes for Singular users        sing_2473.htm#SEC2556   
 Command line options    Command line options    sing_19.htm#SEC26       
 Commands        Functions and system variables  sing_258.htm#SEC298     
 Commands for user defined types Commands for user defined types sing_181.htm#SEC221     
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-CompDecomp              sing_550.htm#SEC602     
-CompInt         sing_2232.htm#SEC2308   
-CompleteHomog           sing_2175.htm#SEC2251   
-ComplexValue            sing_2278.htm#SEC2354   
-Computing Groebner and Standard Bases   Computing Groebner and Standard Bases   sing_852.htm#SEC904     
-ConsLevels              sing_964.htm#SEC1040    
-ContactMatrix           sing_1549.htm#SEC1625   
-Conti-Traverso algorithm                sing_908.htm#SEC965     
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+Commutative algebra             sing_1141.htm#SEC1217   
+CompDecomp              sing_551.htm#SEC603     
+CompInt         sing_2235.htm#SEC2311   
+CompleteHomog           sing_2178.htm#SEC2254   
+ComplexValue            sing_2281.htm#SEC2357   
+Computing Groebner and Standard Bases   Computing Groebner and Standard Bases   sing_854.htm#SEC906     
+ConsLevels              sing_966.htm#SEC1042    
+ContactMatrix           sing_1552.htm#SEC1628   
+Conti-Traverso algorithm                sing_910.htm#SEC967     
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 Control structures              sing_425.htm#SEC465     
-Control theory  System and Control theory       sing_1856.htm#SEC1932   
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-CornacchiaModified              sing_1903.htm#SEC1979   
-Crep            sing_960.htm#SEC1036    
-Critical points         sing_871.htm#SEC923     
-CurveParam              sing_1543.htm#SEC1619   
-CurveRes                sing_1542.htm#SEC1618   
-Curves          sing_1405.htm#IDX532    
+Control theory  System and Control theory       sing_1859.htm#SEC1935   
+Cooper philosophy               sing_921.htm#SEC983     
+Cornacchia              sing_1905.htm#SEC1981   
+CornacchiaModified              sing_1906.htm#SEC1982   
+Crep            sing_962.htm#SEC1038    
+Critical points         sing_873.htm#SEC925     
+CurveParam              sing_1546.htm#SEC1622   
+CurveRes                sing_1545.htm#SEC1621   
+Curves          sing_1408.htm#IDX539    
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-Cyclic code             sing_1837.htm#IDX715    
-Cyclic roots            sing_849.htm#SEC901     
-D-integration           sing_611.htm#IDX336     
-D-localization          sing_611.htm#IDX332     
-D-localization          sing_815.htm#IDX370     
-D-module        purityfiltration_lib    sing_553.htm#IDX300     
-D-module                sing_588.htm#IDX315     
-D-module                sing_611.htm#IDX329     
-D-module                sing_644.htm#IDX341     
-D-module                sing_793.htm#IDX355     
-D-module                sing_815.htm#IDX367     
-D-module structure              sing_588.htm#IDX316     
-D-module structure              sing_644.htm#IDX342     
-D-restriction           sing_611.htm#IDX334     
+Cyclic code             sing_1840.htm#IDX722    
+Cyclic roots            sing_851.htm#SEC903     
+D-integration           sing_612.htm#IDX342     
+D-localization          sing_612.htm#IDX338     
+D-localization          sing_817.htm#IDX376     
+D-module        purityfiltration_lib    sing_554.htm#IDX306     
+D-module                sing_589.htm#IDX321     
+D-module                sing_612.htm#IDX335     
+D-module                sing_645.htm#IDX347     
+D-module                sing_795.htm#IDX361     
+D-module                sing_817.htm#IDX373     
+D-module structure              sing_589.htm#IDX322     
+D-module structure              sing_645.htm#IDX348     
+D-restriction           sing_612.htm#IDX340     
 DBM links               sing_117.htm#SEC157     
 DISPLAY environment variable    The online help system  sing_16.htm#IDX28       
-DLoc            sing_614.htm#SEC666     
-DLoc0           sing_616.htm#SEC668     
+DLoc            sing_615.htm#SEC667     
+DLoc0           sing_617.htm#SEC669     
 Data types              sing_72.htm#SEC112      
-Data types (plural)             sing_470.htm#IDX286     
+Data types (plural)             sing_471.htm#IDX292     
 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_1837.htm#IDX717    
-Decoding codes with Groebner bases      Decoding codes with Groebner bases      sing_917.htm#SEC974     
-Decoding method based on quadratic equations    Decoding method based on quadratic equations    sing_922.htm#SEC992     
+Decoding                sing_1840.htm#IDX724    
+Decoding codes with Groebner bases      Decoding codes with Groebner bases      sing_919.htm#SEC976     
+Decoding method based on quadratic equations    Decoding method based on quadratic equations    sing_924.htm#SEC994     
 Definition of a user defined type       Definition of a user defined type       sing_178.htm#SEC218     
-Deformations            sing_874.htm#SEC926     
-Deformations, T1 and T2         sing_873.htm#SEC925     
-Degree          sing_1384.htm#SEC1460   
-Delta           sing_1468.htm#SEC1544   
-DeltaList               sing_1469.htm#SEC1545   
+Deformations            sing_876.htm#SEC928     
+Deformations, T1 and T2         sing_875.htm#SEC927     
+Degree          sing_1387.htm#SEC1463   
+Delta           sing_1471.htm#SEC1547   
+DeltaList               sing_1472.htm#SEC1548   
 Demo mode               sing_24.htm#SEC35       
-Depth           sing_863.htm#SEC915     
-Determinacy             sing_2407.htm#IDX895    
-Di Biase-Urbanke algorithm      Di Biase and Urbanke    sing_911.htm#SEC968     
-Distributed computing           sing_980.htm#IDX425     
-Dlocalization           sing_816.htm#SEC868     
+Depth           sing_865.htm#SEC917     
+Determinacy             sing_2412.htm#IDX902    
+Di Biase-Urbanke algorithm      Di Biase and Urbanke    sing_913.htm#SEC970     
+Distributed computing           sing_982.htm#IDX431     
+Dlocalization           sing_818.htm#SEC870     
 Documentation Tool              sing_60.htm#SEC97       
-Dp, global ordering             sing_893.htm#IDX384     
-Ds, local ordering              sing_894.htm#IDX394     
-DsingularLocus          sing_820.htm#SEC872     
+Dp, global ordering             sing_895.htm#IDX390     
+Ds, local ordering              sing_896.htm#IDX400     
+DsingularLocus          sing_822.htm#SEC874     
 Dynamic loading         sing_71.htm#SEC111      
-Dynamic modules         sing_851.htm#SEC903     
-ECPP            sing_1946.htm#SEC2022   
-ECoef           sing_1427.htm#SEC1503   
-EOrdlist                sing_1425.htm#SEC1501   
+Dynamic modules         sing_853.htm#SEC905     
+ECPP            sing_1949.htm#SEC2025   
+ECoef           sing_1430.htm#SEC1506   
+EOrdlist                sing_1428.htm#SEC1504   
 ERROR           sing_287.htm#SEC327     
 ESingular, CYGWIN       Running SINGULAR under Emacs    sing_23.htm#SEC33       
-Edatalist               sing_1424.htm#SEC1500   
-Edelman-Reiner          sing_2153.htm#IDX826    
+Edatalist               sing_1427.htm#SEC1503   
+Edelman-Reiner          sing_2156.htm#IDX833    
 Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37       
 Editing input           sing_18.htm#SEC25       
-Elimination             sing_859.htm#SEC911     
+Elimination             sing_861.htm#SEC913     
 Emacs   Emacs user interface    sing_21.htm#SEC28       
 Emacs, Singular demo mode               sing_24.htm#SEC35       
@@ -305 +351 @@
 Emacs, running Singular under   Running SINGULAR under Emacs    sing_23.htm#SEC30       
 Emacs, user interface   Emacs user interface    sing_21.htm#SEC28       
-Emaxcont                sing_1429.htm#SEC1505   
-Equal           sing_1383.htm#SEC1459   
-Eresol          sing_1419.htm#SEC1495   
+Emaxcont                sing_1432.htm#SEC1508   
+Equal           sing_1386.htm#SEC1462   
+Eresol          sing_1422.htm#SEC1498   
 Evaluation of logical expressions       Evaluation of logical expressions       sing_459.htm#SEC499     
-Examples                sing_841.htm#SEC893     
+Examples                sing_843.htm#SEC895     
 Examples of ring declarations   Examples of ring declarations   sing_29.htm#SEC40       
-Exp for matrices                sing_1401.htm#IDX524    
-Experimental libraries  Experimental libraries  sing_2124.htm#SEC2200   
-Ext             sing_1198.htm#SEC1274   
-Ext, computation of             sing_862.htm#SEC914     
-Ext_R           sing_1197.htm#SEC1273   
-Exterior                sing_767.htm#SEC819     
-Extra weight vector             sing_898.htm#SEC950     
-Factorization           sing_864.htm#SEC916     
-Feynman graph           sing_1174.htm#IDX461    
-Finite fields           sing_858.htm#SEC910     
+Exp for matrices                sing_1404.htm#IDX531    
+Experimental libraries  Experimental libraries  sing_2127.htm#SEC2203   
+Ext             sing_1201.htm#SEC1277   
+Ext, computation of             sing_864.htm#SEC916     
+Ext_R           sing_1200.htm#SEC1276   
+Exterior                sing_769.htm#SEC821     
+Extra weight vector             sing_900.htm#SEC952     
+Factorization           sing_866.htm#SEC918     
+Feynman graph           sing_1177.htm#IDX468    
+Finite fields           sing_860.htm#SEC912     
 First steps             sing_6.htm#SEC12        
-Fitzgerald-Lax method   Fitzgerald-Lax method   sing_921.htm#SEC989     
+Fitzgerald-Lax method   Fitzgerald-Lax method   sing_923.htm#SEC991     
 Flow control            sing_40.htm#SEC70       
 Formal Checker          sing_59.htm#SEC96       
-Formatting output               sing_848.htm#SEC900     
-Free resolution         sing_860.htm#SEC912     
-Free resolution, graded Handling graded modules sing_861.htm#SEC913     
+Formatting output               sing_850.htm#SEC902     
+Free resolution         sing_862.htm#SEC914     
+Free resolution, graded Handling graded modules sing_863.htm#SEC915     
 Functions               sing_259.htm#SEC299     
-Future benefits of Singular 4   Notes for Singular users        sing_2468.htm#SEC2557   
-G-algebra               sing_534.htm#SEC574     
-G-algebra               sing_534.htm#SEC576     
-G-algebra, setup                sing_534.htm#SEC578     
-GBWeight                sing_617.htm#SEC669     
-GBsolve         sing_1736.htm#SEC1812   
-GIT             sing_2290.htm#IDX877    
-GKZsystem               sing_734.htm#SEC786     
-GKdim           sing_707.htm#SEC759     
+Future benefits of Singular 4   Notes for Singular users        sing_2473.htm#SEC2562   
+G-algebra               sing_535.htm#SEC575     
+G-algebra               sing_535.htm#SEC577     
+G-algebra, setup                sing_535.htm#SEC579     
+GBWeight                sing_618.htm#SEC670     
+GBsolve         sing_1739.htm#SEC1815   
+GIT             sing_2293.htm#IDX884    
+GKZsystem               sing_735.htm#SEC787     
+GKdim           sing_708.htm#SEC760     
 GMP             sing_1.htm#IDX3 
-GND.lib         sing_2297.htm#SEC2373   
-GND_lib         sing_2297.htm#SEC2373   
-GTZmod          sing_1246.htm#SEC1322   
-GTZopt          sing_1253.htm#SEC1329   
-G_a -Invariants         sing_880.htm#SEC932     
-Gamma           sing_1434.htm#SEC1510   
-Gauss-Manin connection  Gauss-Manin connection  sing_904.htm#SEC961     
-Gauss-Manin connection          sing_1614.htm#IDX695    
-Gauss-Manin connection                  sing_1661.htm#IDX698    
-Gauss-Manin system              sing_1562.htm#IDX585    
-Gauss-Manin system              sing_1563.htm#IDX596    
-Gauss-Manin system              sing_1564.htm#IDX599    
-Gauss-Manin system              sing_1565.htm#IDX602    
-Gauss-Manin system              sing_1566.htm#IDX605    
-Gauss-Manin system              sing_1567.htm#IDX609    
-Gauss-Manin system                      sing_1568.htm#IDX613    
-Gauss-Manin system                      sing_1569.htm#IDX619    
-Gauss-Manin system                      sing_1570.htm#IDX627    
-Gauss-Manin system                      sing_1571.htm#IDX633    
-Gauss-Manin system                      sing_1572.htm#IDX641    
-Gauss-Manin system                      sing_1573.htm#IDX651    
-Gauss-Manin system                      sing_1584.htm#IDX657    
-Gauss-Manin system                      sing_1586.htm#IDX668    
+GND.lib         sing_2300.htm#SEC2376   
+GND_lib         sing_2300.htm#SEC2376   
+GTZmod          sing_1249.htm#SEC1325   
+GTZopt          sing_1256.htm#SEC1332   
+G_a -Invariants         sing_882.htm#SEC934     
+Gamma           sing_1437.htm#SEC1513   
+Gauss-Manin connection  Gauss-Manin connection  sing_906.htm#SEC963     
+Gauss-Manin connection          sing_1617.htm#IDX702    
+Gauss-Manin connection                  sing_1664.htm#IDX705    
+Gauss-Manin system              sing_1565.htm#IDX592    
+Gauss-Manin system              sing_1566.htm#IDX603    
+Gauss-Manin system              sing_1567.htm#IDX606    
+Gauss-Manin system              sing_1568.htm#IDX609    
+Gauss-Manin system              sing_1569.htm#IDX612    
+Gauss-Manin system              sing_1570.htm#IDX616    
+Gauss-Manin system                      sing_1571.htm#IDX620    
+Gauss-Manin system                      sing_1572.htm#IDX626    
+Gauss-Manin system                      sing_1573.htm#IDX634    
+Gauss-Manin system                      sing_1574.htm#IDX640    
+Gauss-Manin system                      sing_1575.htm#IDX648    
+Gauss-Manin system                      sing_1576.htm#IDX658    
+Gauss-Manin system                      sing_1587.htm#IDX664    
+Gauss-Manin system                      sing_1589.htm#IDX675    
 General command syntax  General command syntax  sing_35.htm#SEC59       
 General concepts                sing_12.htm#SEC18       
-General purpose         sing_929.htm#SEC1005    
+General purpose         sing_931.htm#SEC1007    
 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_536.htm#SEC586     
-Generalized Newton identities   Generalized Newton identities   sing_920.htm#SEC986     
-Geometric genus         sing_1405.htm#IDX536    
-German Umlaute          sing_455.htm#IDX273     
+Generalized Hilbert Syzygy Theorem      Syzygies and resolutions (plural)       sing_537.htm#SEC587     
+Generalized Newton identities   Generalized Newton identities   sing_922.htm#SEC988     
+Geometric genus         sing_1408.htm#IDX543    
+German Umlaute          sing_455.htm#IDX279     
 Getting started         sing_5.htm#SEC11        
-Global orderings                sing_893.htm#SEC945     
-Graded commutative algebras     Graded commutative algebras (SCA)       sing_538.htm#SEC590     
+Global orderings                sing_895.htm#SEC947     
+Graded commutative algebras     Graded commutative algebras (SCA)       sing_539.htm#SEC591     
 Greuel, Gert-Martin             sing_1.htm#IDX18        
-Groebner Bases  Computing Groebner and Standard Bases   sing_852.htm#SEC904     
-Groebner bases in G-algebras    Groebner bases in G-algebras    sing_535.htm#SEC579     
-Groebner bases in free associative algebras     Groebner bases for two-sided ideals in free associative algebras        sing_541.htm#SEC593     
-Groebner bases, decodeGB                sing_1837.htm#IDX719    
-Groebner bases, slim            sing_855.htm#SEC907     
-Groebner basis conversion       Groebner basis conversion       sing_854.htm#SEC906     
-Groebner cover, parametric ideal, canonical, discussion of      extend  sing_956.htm#IDX410     
-Groebner cover, parametric ideal, canonical, discussion of              sing_963.htm#IDX414     
-Groebner fan            sing_2041.htm#IDX736    
-Groebner walk           sing_1189.htm#IDX480    
-Groebner walk           sing_1191.htm#IDX482    
-Groebner walk           sing_2397.htm#IDX888    
-Groebner walk                   sing_2398.htm#IDX889    
-Gromov-Witten invariants                sing_1174.htm#IDX458    
-Gromov-Witten invariants                sing_1180.htm#IDX467    
-Gromov-Witten invariants                sing_1181.htm#IDX471    
-Gweights                sing_761.htm#SEC813     
-H2basis         sing_1619.htm#SEC1695   
-Hamburger-Noether expansion             sing_1499.htm#IDX555    
-Hamburger-Noether expansion             sing_1587.htm#IDX677    
-Hamburger-Noether expansions            sing_1824.htm#IDX709    
-Handling graded modules Handling graded modules sing_861.htm#SEC913     
-Hcode           sing_1521.htm#SEC1597   
+Groebner Bases  Computing Groebner and Standard Bases   sing_854.htm#SEC906     
+Groebner bases in G-algebras    Groebner bases in G-algebras    sing_536.htm#SEC580     
+Groebner bases in free associative algebras     Groebner bases for two-sided ideals in free associative algebras        sing_542.htm#SEC594     
+Groebner bases, decodeGB                sing_1840.htm#IDX726    
+Groebner bases, slim            sing_857.htm#SEC909     
+Groebner basis conversion       Groebner basis conversion       sing_856.htm#SEC908     
+Groebner cover, parametric ideal, canonical, discussion of      extend  sing_958.htm#IDX416     
+Groebner cover, parametric ideal, canonical, discussion of              sing_965.htm#IDX420     
+Groebner fan            sing_2044.htm#IDX743    
+Groebner walk           sing_1192.htm#IDX487    
+Groebner walk           sing_1194.htm#IDX489    
+Groebner walk           sing_2402.htm#IDX895    
+Groebner walk                   sing_2403.htm#IDX896    
+Gromov-Witten invariants                sing_1177.htm#IDX465    
+Gromov-Witten invariants                sing_1183.htm#IDX474    
+Gromov-Witten invariants                sing_1184.htm#IDX478    
+Gweights                sing_763.htm#SEC815     
+H2basis         sing_1622.htm#SEC1698   
+Hamburger-Noether expansion             sing_1502.htm#IDX562    
+Hamburger-Noether expansion             sing_1590.htm#IDX684    
+Hamburger-Noether expansions            sing_1827.htm#IDX716    
+Handling graded modules Handling graded modules sing_863.htm#SEC915     
+Hcode           sing_1524.htm#SEC1600   
 Help string             sing_45.htm#SEC82       
 Hensel          sing_292.htm#SEC332     
-Hilbert function                sing_404.htm#IDX183     
-Hilbert function                sing_901.htm#SEC955     
-Hilbert series          sing_901.htm#SEC955     
-Hilbert-driven GB algorithm     Groebner basis conversion       sing_854.htm#SEC906     
-HilbertClassPoly                sing_1909.htm#SEC1985   
-HilbertSeries           sing_1714.htm#SEC1790   
-HilbertWeights          sing_1715.htm#SEC1791   
-Hom             sing_1201.htm#SEC1277   
-HomJJ           sing_1276.htm#SEC1352   
-Hosten-Sturmfels algorithm      Hosten and Sturmfels    sing_910.htm#SEC967     
+Hilbert function                sing_404.htm#IDX188     
+Hilbert function                sing_903.htm#SEC957     
+Hilbert series          sing_903.htm#SEC957     
+Hilbert-driven GB algorithm     Groebner basis conversion       sing_856.htm#SEC908     
+HilbertClassPoly                sing_1912.htm#SEC1988   
+HilbertSeries           sing_1717.htm#SEC1793   
+HilbertWeights          sing_1718.htm#SEC1794   
+Hom             sing_1204.htm#SEC1280   
+HomJJ           sing_1279.htm#SEC1355   
+Hosten-Sturmfels algorithm      Hosten and Sturmfels    sing_912.htm#SEC969     
 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_1180.htm#IDX470    
-Hurwitz numbers                 sing_1181.htm#IDX474    
-Hypersurface singularities, classification of   Classification of hypersurface singularities    sing_877.htm#SEC929     
-IN              sing_329.htm#IDX144     
-Ideal membership                sing_900.htm#IDX406     
+Hurwitz numbers         sing_1183.htm#IDX477    
+Hurwitz numbers                 sing_1184.htm#IDX481    
+Hypersurface singularities, classification of   Classification of hypersurface singularities    sing_879.htm#SEC931     
+IN              sing_329.htm#IDX149     
+Ideal membership                sing_902.htm#IDX412     
 Identifiers, syntax of          sing_37.htm#SEC65       
-ImageGroup              sing_1717.htm#SEC1793   
-ImageVariety            sing_1716.htm#SEC1792   
-Imap, option            sing_364.htm#IDX170     
+ImageGroup              sing_1720.htm#SEC1796   
+ImageVariety            sing_1719.htm#SEC1795   
+Imap, option            sing_364.htm#IDX175     
 Implemented algorithms  Implemented algorithms  sing_33.htm#SEC47       
-Incl            sing_1382.htm#SEC1458   
-Index           sing_2476.htm#SEC2565   
+Incl            sing_1385.htm#SEC1461   
+Index           sing_2481.htm#SEC2570   
 Info string             sing_52.htm#SEC89       
-InterDiv                sing_1450.htm#SEC1526   
+InterDiv                sing_1453.htm#SEC1529   
 Interactive use         sing_13.htm#SEC19       
 Interrupting SINGULAR   Interrupting SINGULAR   sing_17.htm#SEC24       
-IntersectWithSub                sing_739.htm#SEC791     
-IntersectionMatrix              sing_1548.htm#SEC1624   
+IntersectWithSub                sing_740.htm#SEC792     
+IntersectionMatrix              sing_1551.htm#SEC1627   
 Introduction            sing_2.htm#SEC4 
-Invariant Theory                sing_879.htm#SEC931     
-Invariant theory                sing_1666.htm#SEC1742   
-InvariantQ              sing_1719.htm#SEC1795   
-InvariantRing           sing_1718.htm#SEC1794   
-Invariants of a finite group    Invariants of a finite group    sing_881.htm#SEC933     
-Invariants of plane curve singularities Invariants of plane curve singularities sing_875.htm#SEC927     
-IsSCA           sing_782.htm#SEC834     
-J-marked schemes                sing_1490.htm#IDX553    
-J-marked schemes, Borel ideals          sing_1495.htm#IDX554    
-JMBTest.lib             sing_1490.htm#SEC1566   
-JMBTest_lib             sing_1490.htm#SEC1566   
-JMSConst.lib            sing_1495.htm#SEC1571   
-JMSConst_lib            sing_1495.htm#SEC1571   
-JMarkedScheme           sing_1497.htm#SEC1573   
-Jacobi          sing_1919.htm#SEC1995   
-Jacobson form           sing_1874.htm#IDX720    
-Jacobson normal form            sing_1874.htm#IDX721    
-JuReTopDim              sing_1392.htm#SEC1468   
-JuReZeroDim             sing_1393.htm#SEC1469   
-KScoef          sing_1612.htm#SEC1688   
-KSconvert               sing_1610.htm#SEC1686   
-KSker           sing_1609.htm#SEC1685   
-KSlinear                sing_1611.htm#SEC1687   
-KSpencerKernel          sing_1659.htm#SEC1735   
-KeneshlouMatrixPresentation     KeneshlouMatrixPresentation     sing_2316.htm#SEC2392   
-Kernel of module homomorphisms  Kernel of module homomorphisms  sing_867.htm#SEC919     
-KoszulHomology          sing_1210.htm#SEC1286   
-LETTERPLACE             sing_539.htm#SEC591     
+Invariant Theory                sing_881.htm#SEC933     
+Invariant theory                sing_1669.htm#SEC1745   
+InvariantQ              sing_1722.htm#SEC1798   
+InvariantRing           sing_1721.htm#SEC1797   
+Invariants of a finite group    Invariants of a finite group    sing_883.htm#SEC935     
+Invariants of plane curve singularities Invariants of plane curve singularities sing_877.htm#SEC929     
+IsSCA           sing_784.htm#SEC836     
+J-marked schemes                sing_1493.htm#IDX560    
+J-marked schemes, Borel ideals          sing_1498.htm#IDX561    
+JMBTest.lib             sing_1493.htm#SEC1569   
+JMBTest_lib             sing_1493.htm#SEC1569   
+JMSConst.lib            sing_1498.htm#SEC1574   
+JMSConst_lib            sing_1498.htm#SEC1574   
+JMarkedScheme           sing_1500.htm#SEC1576   
+Jacobi          sing_1922.htm#SEC1998   
+Jacobson form           sing_1877.htm#IDX727    
+Jacobson normal form            sing_1877.htm#IDX728    
+JuReTopDim              sing_1395.htm#SEC1471   
+JuReZeroDim             sing_1396.htm#SEC1472   
+KScoef          sing_1615.htm#SEC1691   
+KSconvert               sing_1613.htm#SEC1689   
+KSker           sing_1612.htm#SEC1688   
+KSlinear                sing_1614.htm#SEC1690   
+KSpencerKernel          sing_1662.htm#SEC1738   
+KeneshlouMatrixPresentation     KeneshlouMatrixPresentation     sing_2319.htm#SEC2395   
+Kernel of module homomorphisms  Kernel of module homomorphisms  sing_869.htm#SEC921     
+KoszulHomology          sing_1213.htm#SEC1289   
+LETTERPLACE             sing_540.htm#SEC592     
 LIB             sing_333.htm#SEC373     
 LIB commands            sing_53.htm#SEC90       
-LIBs            sing_925.htm#SEC1001    
-LLL             sing_406.htm#IDX213     
-LOT algorithm           sing_588.htm#IDX328     
+LIBs            sing_927.htm#SEC1003    
+LLL             sing_406.htm#IDX219     
+LOT algorithm           sing_589.htm#IDX334     
 LU-decomposition of a matrix of numbers         sing_338.htm#SEC378     
-Laurent series          sing_1178.htm#IDX466    
-Left and two-sided Groebner bases       Left and two-sided Groebner bases       sing_883.htm#SEC935     
-Left ideal membership   Groebner bases in G-algebras    sing_535.htm#SEC582     
-Left normal form        Groebner bases in G-algebras    sing_535.htm#SEC581     
-LengthSym               sing_792.htm#SEC844     
-LengthSymElement                sing_791.htm#SEC843     
-Letterplace             sing_539.htm#SEC591     
-Lexicographic Groebner bases, computation of    Groebner basis conversion       sing_854.htm#SEC906     
+Laurent series          sing_1181.htm#IDX473    
+Left and two-sided Groebner bases       Left and two-sided Groebner bases       sing_885.htm#SEC937     
+Left ideal membership   Groebner bases in G-algebras    sing_536.htm#SEC583     
+Left normal form        Groebner bases in G-algebras    sing_536.htm#SEC582     
+LengthSym               sing_794.htm#SEC846     
+LengthSymElement                sing_793.htm#SEC845     
+Letterplace             sing_540.htm#SEC592     
+Lexicographic Groebner bases, computation of    Groebner basis conversion       sing_856.htm#SEC908     
 Libraries       Writing procedures and libraries        sing_48.htm#SEC85       
-Libraries               sing_844.htm#SEC896     
+Libraries               sing_846.htm#SEC898     
 Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86       
-Library versioning      Notes for Singular users        sing_2468.htm#SEC2555   
-Lie algebra             sing_1400.htm#IDX521    
-Lie group               sing_1403.htm#IDX526    
-Lie group               sing_1404.htm#IDX529    
+Library versioning      Notes for Singular users        sing_2473.htm#SEC2560   
+Lie algebra             sing_1403.htm#IDX528    
+Lie group               sing_1406.htm#IDX533    
+Lie group               sing_1407.htm#IDX536    
 Limitations             sing_455.htm#SEC495     
-Linear algebra          sing_1078.htm#SEC1154   
-Linear code             sing_1837.htm#IDX716    
-LinearActionQ           sing_1721.htm#SEC1797   
-LinearCombinationQ              sing_1722.htm#SEC1798   
-LinearizeAction         sing_1720.htm#SEC1796   
+Linear algebra          sing_1081.htm#SEC1157   
+Linear code             sing_1840.htm#IDX723    
+LinearActionQ           sing_1724.htm#SEC1800   
+LinearCombinationQ              sing_1725.htm#SEC1801   
+LinearizeAction         sing_1723.htm#SEC1799   
 Loading a library               sing_62.htm#SEC99       
-Local orderings         sing_894.htm#SEC946     
-Log for matrices                sing_1402.htm#IDX525    
-Long coefficients               sing_846.htm#SEC898     
-M, ordering             sing_896.htm#SEC948     
-MVComplex               sing_2410.htm#SEC2486   
-Macintosh installation  Macintosh installation instructions     sing_2475.htm#SEC2564   
-Mathematical background Mathematical background sing_899.htm#SEC951     
-Mathematical background (plural)        Mathematical background (plural)        sing_533.htm#SEC573     
-Matrix orderings                sing_896.htm#SEC948     
-Max             sing_1628.htm#SEC1704   
-Maximus         sing_1492.htm#SEC1568   
-Maxord          sing_1433.htm#SEC1509   
-MillerRabin             sing_1929.htm#SEC2005   
-Milnor number   Milnor and Tjurina number       sing_870.htm#SEC922     
-Milnor number           sing_2406.htm#IDX894    
-Min             sing_1629.htm#SEC1705   
-MinMult         sing_2231.htm#SEC2307   
-MinimalDecomposition    MinimalDecomposition    sing_1723.htm#SEC1799   
-Minimum distance                sing_1837.htm#IDX718    
-Minimus         sing_1491.htm#SEC1567   
-Miscellaneous libraries Miscellaneous libraries sing_2099.htm#SEC2175   
-ModEqn          sing_1622.htm#SEC1698   
-Modular techniques              sing_980.htm#IDX422     
-Module orderings                sing_895.htm#SEC947     
+Local orderings         sing_896.htm#SEC948     
+Log for matrices                sing_1405.htm#IDX532    
+Long coefficients               sing_848.htm#SEC900     
+M, ordering             sing_898.htm#SEC950     
+MVComplex               sing_2415.htm#SEC2491   
+Macintosh installation  Macintosh installation instructions     sing_2480.htm#SEC2569   
+Mathematical background Mathematical background sing_901.htm#SEC953     
+Mathematical background (plural)        Mathematical background (plural)        sing_534.htm#SEC574     
+Matrix orderings                sing_898.htm#SEC950     
+Max             sing_1631.htm#SEC1707   
+Maximus         sing_1495.htm#SEC1571   
+Maxord          sing_1436.htm#SEC1512   
+MillerRabin             sing_1932.htm#SEC2008   
+Milnor number   Milnor and Tjurina number       sing_872.htm#SEC924     
+Milnor number           sing_2411.htm#IDX901    
+Min             sing_1632.htm#SEC1708   
+MinMult         sing_2234.htm#SEC2310   
+MinimalDecomposition    MinimalDecomposition    sing_1726.htm#SEC1802   
+Minimum distance                sing_1840.htm#IDX725    
+Minimus         sing_1494.htm#SEC1570   
+Miscellaneous libraries Miscellaneous libraries sing_2102.htm#SEC2178   
+ModEqn          sing_1625.htm#SEC1701   
+Modular techniques              sing_982.htm#IDX428     
+Module orderings                sing_897.htm#SEC949     
 Modules and and their annihilator       Modules and their annihilator   sing_10.htm#SEC16       
-Monodromy               sing_1614.htm#IDX693    
-Monomial orderings              sing_890.htm#SEC942     
+Monodromy               sing_1617.htm#IDX700    
+Monomial orderings              sing_892.htm#SEC944     
 Monomial orderings, Term orderings              sing_31.htm#SEC44       
-Morse lemma             sing_2405.htm#IDX892    
-MultiplicitySequence    MultiplicitySequence    sing_1546.htm#SEC1622   
+Morse lemma             sing_2410.htm#IDX899    
+MultiplicitySequence    MultiplicitySequence    sing_1549.htm#SEC1625   
 NF              sing_383.htm#SEC423     
-NF              sing_525.htm#SEC565     
-NFMora          sing_1995.htm#SEC2071   
-NPos            sing_1266.htm#SEC1342   
-NPos_test               sing_1264.htm#SEC1340   
-NSplaces                sing_1825.htm#SEC1901   
+NF              sing_526.htm#SEC566     
+NFMora          sing_1998.htm#SEC2074   
+NPos            sing_1269.htm#SEC1345   
+NPos_test               sing_1267.htm#SEC1343   
+NSplaces                sing_1828.htm#SEC1904   
 NTL             sing_1.htm#IDX4 
 Names           sing_37.htm#SEC65       
 Names in procedures             sing_46.htm#SEC83       
 Names, indexed          sing_37.htm#SEC65       
-New libraries depending on Singular 4   Notes for Singular users        sing_2468.htm#SEC2553   
-New orderings for modules       Notes for Singular users        sing_2468.htm#SEC2556   
-Newton non-degenerate           sing_1601.htm#IDX691    
-Newton polygon          sing_1600.htm#IDX690    
-Newton polygon          sing_1601.htm#IDX692    
-Newton polytope         sing_2041.htm#IDX735    
-NoetherPosition         sing_1260.htm#SEC1336   
-Non-commutative LIBs    Non-commutative libraries       sing_545.htm#SEC597     
-Non-commutative algebra Non-commutative algebra sing_882.htm#SEC934     
-Non-commutative algebra                 sing_916.htm#SEC973     
-Non-commutative libraries       Non-commutative libraries       sing_545.htm#SEC597     
-Non-commutative subsystem       Non-commutative subsystem       sing_468.htm#SEC508     
-Nonhyp          sing_1422.htm#SEC1498   
-Normal form             sing_900.htm#IDX405     
-Normalization           sing_866.htm#SEC918     
-Notes for Singular users        Notes for Singular users        sing_2468.htm#SEC2550   
-Notes for developers    Notes for developers    sing_2469.htm#SEC2558   
-NullCone                sing_1724.htm#SEC1800   
-NumIrrDecom             sing_1396.htm#SEC1472   
-NumLocalDim             sing_1385.htm#SEC1461   
-NumPrimDecom            sing_1398.htm#SEC1474   
-Oaku-Takayama algorithm         sing_588.htm#IDX326     
+New libraries depending on Singular 4   Notes for Singular users        sing_2473.htm#SEC2558   
+New orderings for modules       Notes for Singular users        sing_2473.htm#SEC2561   
+Newton non-degenerate           sing_1604.htm#IDX698    
+Newton polygon          sing_1603.htm#IDX697    
+Newton polygon          sing_1604.htm#IDX699    
+Newton polytope         sing_2044.htm#IDX742    
+NoetherPosition         sing_1263.htm#SEC1339   
+Non-commutative LIBs    Non-commutative libraries       sing_546.htm#SEC598     
+Non-commutative algebra Non-commutative algebra sing_884.htm#SEC936     
+Non-commutative algebra                 sing_918.htm#SEC975     
+Non-commutative libraries       Non-commutative libraries       sing_546.htm#SEC598     
+Non-commutative subsystem       Non-commutative subsystem       sing_469.htm#SEC509     
+Nonhyp          sing_1425.htm#SEC1501   
+Normal form             sing_902.htm#IDX411     
+Normalization           sing_868.htm#SEC920     
+Notes for Singular users        Notes for Singular users        sing_2473.htm#SEC2555   
+Notes for developers    Notes for developers    sing_2474.htm#SEC2563   
+NullCone                sing_1727.htm#SEC1803   
+NumIrrDecom             sing_1399.htm#SEC1475   
+NumLocalDim             sing_1388.htm#SEC1464   
+NumPrimDecom            sing_1401.htm#SEC1477   
+Oaku-Takayama algorithm         sing_589.htm#IDX332     
 Objects         sing_38.htm#SEC66       
-Orlik-Solomon           sing_2154.htm#IDX827    
-Output, formatting of           sing_848.htm#SEC900     
-PBW             sing_567.htm#IDX314     
-PBW basis               sing_534.htm#SEC575     
-PBW_eqDeg               sing_585.htm#SEC637     
-PBW_maxDeg              sing_586.htm#SEC638     
-PBW_maxMonom            sing_587.htm#SEC639     
-PEsolve         sing_1734.htm#SEC1810   
-PH_ais          sing_2103.htm#SEC2179   
-PH_nais         sing_2104.htm#SEC2180   
-PLURAL          sing_469.htm#SEC509     
-PLURAL LIBs     Non-commutative libraries       sing_545.htm#SEC597     
-ParToVar                sing_2280.htm#SEC2356   
-Parallelization Parallelization with ssi links  sing_850.htm#SEC902     
-Parallelization                 sing_980.htm#IDX423     
+Orlik-Solomon           sing_2157.htm#IDX834    
+Output, formatting of           sing_850.htm#SEC902     
+PBW             sing_568.htm#IDX320     
+PBW basis               sing_535.htm#SEC576     
+PBW_eqDeg               sing_586.htm#SEC638     
+PBW_maxDeg              sing_587.htm#SEC639     
+PBW_maxMonom            sing_588.htm#SEC640     
+PEsolve         sing_1737.htm#SEC1813   
+PH_ais          sing_2106.htm#SEC2182   
+PH_nais         sing_2107.htm#SEC2183   
+PLURAL          sing_470.htm#SEC510     
+PLURAL LIBs     Non-commutative libraries       sing_546.htm#SEC598     
+ParToVar                sing_2283.htm#SEC2359   
+Parallelization Parallelization with ssi links  sing_852.htm#SEC904     
+Parallelization                 sing_982.htm#IDX429     
 Parameter list          sing_44.htm#SEC81       
-Parameters              sing_847.htm#SEC899     
-Parametrization         sing_1405.htm#IDX533    
-Parametrization, image.         sing_1415.htm#IDX545    
-PartC           sing_2226.htm#SEC2302   
-PartitionVar            sing_2277.htm#SEC2353   
-Path names      Notes for Singular users        sing_2468.htm#SEC2554   
-PerfectPowerTest                sing_1892.htm#SEC1968   
-Perturbation walk               sing_1190.htm#IDX481    
+Parameters              sing_849.htm#SEC901     
+Parametrization         sing_1408.htm#IDX540    
+Parametrization, image.         sing_1418.htm#IDX552    
+PartC           sing_2229.htm#SEC2305   
+PartitionVar            sing_2280.htm#SEC2356   
+Path names      Notes for Singular users        sing_2473.htm#SEC2559   
+PerfectPowerTest                sing_1895.htm#SEC1971   
+Perturbation walk               sing_1193.htm#IDX488    
 Pfister, Gerhard                sing_1.htm#IDX19        
 Pipe links              sing_116.htm#SEC156     
-PocklingtonLehmer               sing_1931.htm#SEC2007   
-Poincare polynomial             sing_2166.htm#IDX851    
-Polar curves            sing_872.htm#SEC924     
-PollardRho              sing_1932.htm#SEC2008   
-PolyBoRi, Boolean Groebner Basis        recursive_from_boolean_poly     sing_2106.htm#IDX752    
-PolyBoRi, Boolean Groebner Basis                sing_2108.htm#IDX753    
-PolyBoRi, Boolean Groebner Basis                sing_2109.htm#IDX754    
-PolyBoRi, Boolean Groebner Basis                sing_2110.htm#IDX755    
-PolyBoRi, Boolean Groebner Basis                sing_2111.htm#IDX756    
-PolyBoRi, Boolean Groebner Basis                sing_2112.htm#IDX757    
-PolyBoRi, Boolean Groebner Basis                sing_2113.htm#IDX758    
-PolyBoRi, Boolean Groebner Basis                sing_2114.htm#IDX759    
-PolyBoRi, Boolean Groebner Basis                        sing_2115.htm#IDX760    
-PolyBoRi, Boolean Groebner Basis                        sing_2116.htm#IDX761    
-PolyBoRi, Boolean Groebner Basis                        sing_2117.htm#IDX762    
-PolyBoRi, Boolean Groebner Basis                        sing_2118.htm#IDX763    
-PolyBoRi, Boolean Groebner Basis                        sing_2119.htm#IDX764    
-PolyBoRi, Boolean Groebner Basis                        sing_2120.htm#IDX765    
-PolyBoRi, Boolean Groebner Basis                        sing_2122.htm#IDX767    
-PolyBoRi, zero-supressed decision diagram               sing_2121.htm#IDX766    
-Polybori, Boolean Groebner Basis                sing_2123.htm#IDX768    
-Polynomial data         sing_888.htm#SEC940     
-Pottier algorithm               sing_909.htm#SEC966     
+PocklingtonLehmer               sing_1934.htm#SEC2010   
+Poincare polynomial             sing_2169.htm#IDX858    
+Polar curves            sing_874.htm#SEC926     
+PollardRho              sing_1935.htm#SEC2011   
+PolyBoRi, Boolean Groebner Basis        recursive_from_boolean_poly     sing_2109.htm#IDX759    
+PolyBoRi, Boolean Groebner Basis                sing_2111.htm#IDX760    
+PolyBoRi, Boolean Groebner Basis                sing_2112.htm#IDX761    
+PolyBoRi, Boolean Groebner Basis                sing_2113.htm#IDX762    
+PolyBoRi, Boolean Groebner Basis                sing_2114.htm#IDX763    
+PolyBoRi, Boolean Groebner Basis                sing_2115.htm#IDX764    
+PolyBoRi, Boolean Groebner Basis                sing_2116.htm#IDX765    
+PolyBoRi, Boolean Groebner Basis                sing_2117.htm#IDX766    
+PolyBoRi, Boolean Groebner Basis                        sing_2118.htm#IDX767    
+PolyBoRi, Boolean Groebner Basis                        sing_2119.htm#IDX768    
+PolyBoRi, Boolean Groebner Basis                        sing_2120.htm#IDX769    
+PolyBoRi, Boolean Groebner Basis                        sing_2121.htm#IDX770    
+PolyBoRi, Boolean Groebner Basis                        sing_2122.htm#IDX771    
+PolyBoRi, Boolean Groebner Basis                        sing_2123.htm#IDX772    
+PolyBoRi, Boolean Groebner Basis                        sing_2125.htm#IDX774    
+PolyBoRi, zero-supressed decision diagram               sing_2124.htm#IDX773    
+Polybori, Boolean Groebner Basis                sing_2126.htm#IDX775    
+Polynomial data         sing_890.htm#SEC942     
+Pottier algorithm               sing_911.htm#SEC968     
 Preface         sing_1.htm#SEC1 
-Prep            sing_961.htm#SEC1037    
-Primary decomposition   Primary decomposition   sing_865.htm#SEC917     
-PrimdecA                sing_1242.htm#SEC1318   
-PrimdecB                sing_1243.htm#SEC1319   
+Prep            sing_963.htm#SEC1039    
+Primary decomposition   Primary decomposition   sing_867.htm#SEC919     
+PrimdecA                sing_1245.htm#SEC1321   
+PrimdecB                sing_1246.htm#SEC1322   
 Procedure definition    Procedure definition    sing_43.htm#SEC78       
 Procedure-specific commands     Procedure-specific commands     sing_47.htm#SEC84       
 Procedures              sing_42.htm#SEC77       
 Procedures and libraries        Writing procedures and libraries        sing_8.htm#SEC14        
-Procedures and libraries                sing_844.htm#SEC896     
+Procedures and libraries                sing_846.htm#SEC898     
 Procedures in a library Procedures in a library sing_54.htm#SEC91       
-Product orderings               sing_897.htm#SEC949     
-Programming             sing_842.htm#SEC894     
-PtoCrep         sing_962.htm#SEC1038    
-Puiseux expansion               sing_1499.htm#IDX556    
-Puiseux expansion               sing_1587.htm#IDX678    
-Puiseux pairs   Invariants of plane curve singularities sing_875.htm#SEC927     
-Puiseux pairs           sing_1593.htm#IDX683    
-Qso3Casimir             sing_733.htm#SEC785     
-Quotient                sing_1776.htm#SEC1852   
-QuotientEquations               sing_1623.htm#SEC1699   
-Rational curves         sing_1405.htm#IDX534    
-ReJunkUseHomo           sing_1391.htm#SEC1467   
-ReesAlgebra             sing_1358.htm#SEC1434   
-References              sing_924.htm#SEC998     
-References (plural)             sing_537.htm#SEC587     
-Release Notes           sing_2464.htm#SEC2540   
-ResTree         sing_1451.htm#SEC1527   
+Product orderings               sing_899.htm#SEC951     
+Programming             sing_844.htm#SEC896     
+PtoCrep         sing_964.htm#SEC1040    
+Puiseux expansion               sing_1502.htm#IDX563    
+Puiseux expansion               sing_1590.htm#IDX685    
+Puiseux pairs   Invariants of plane curve singularities sing_877.htm#SEC929     
+Puiseux pairs           sing_1596.htm#IDX690    
+Qso3Casimir             sing_734.htm#SEC786     
+Quotient                sing_1779.htm#SEC1855   
+QuotientEquations               sing_1626.htm#SEC1702   
+Rational curves         sing_1408.htm#IDX541    
+ReJunkUseHomo           sing_1394.htm#SEC1470   
+ReesAlgebra             sing_1361.htm#SEC1437   
+References              sing_926.htm#SEC1000    
+References (plural)             sing_538.htm#SEC588     
+Release Notes           sing_2469.htm#SEC2545   
+ResTree         sing_1454.htm#SEC1530   
 Resolution              sing_11.htm#SEC17       
-Resolution of singularities     Resolution of singularities     sing_878.htm#SEC930     
-Resolution, free                sing_860.htm#SEC912     
-ReynoldsImage           sing_1725.htm#SEC1801   
-ReynoldsOperator                sing_1726.htm#SEC1802   
-RiemannRochBN           sing_2171.htm#SEC2247   
-RiemannRochHess         sing_2335.htm#SEC2411   
-Right Groebner bases and syzygies       Right Groebner bases and syzygies       sing_884.htm#SEC936     
-Ring-dependent options  Notes for Singular users        sing_2468.htm#SEC2552   
+Resolution of singularities     Resolution of singularities     sing_880.htm#SEC932     
+Resolution, free                sing_862.htm#SEC914     
+ReynoldsImage           sing_1728.htm#SEC1804   
+ReynoldsOperator                sing_1729.htm#SEC1805   
+RiemannRochBN           sing_2174.htm#SEC2250   
+RiemannRochHess         sing_2338.htm#SEC2414   
+Right Groebner bases and syzygies       Right Groebner bases and syzygies       sing_886.htm#SEC938     
+Ring-dependent options  Notes for Singular users        sing_2473.htm#SEC2557   
 Rings and orderings             sing_28.htm#SEC39       
 Rings and standard bases        Rings and standard bases        sing_7.htm#SEC13        
 Running SINGULAR under Emacs    Running SINGULAR under Emacs    sing_23.htm#SEC30       
-SCA     Graded commutative algebras (SCA)       sing_538.htm#SEC590     
+SCA     Graded commutative algebras (SCA)       sing_539.htm#SEC591     
 SDB breakpoint  Source code debugger    sing_66.htm#SEC106      
 SDB debugger    Source code debugger    sing_66.htm#SEC106      
-SDLoc           sing_615.htm#SEC667     
-SINGULAR libraries              sing_925.htm#SEC1001    
+SDLoc           sing_616.htm#SEC668     
+SINGULAR libraries              sing_927.htm#SEC1003    
 SINGULARHIST            sing_18.htm#SEC25       
-SScontinue              sing_1062.htm#SEC1138   
-SSres           sing_1060.htm#SEC1136   
-SSsyz           sing_1061.htm#SEC1137   
-SV-decoding algorithm           sing_1832.htm#IDX712    
-SV-decoding algorithm, preprocessing            sing_1831.htm#IDX711    
-Sannfs          sing_591.htm#SEC643     
-SannfsBFCT              sing_600.htm#SEC652     
-SannfsVar               sing_647.htm#SEC699     
-Sannfslog               sing_592.htm#SEC644     
-Saturation              sing_857.htm#SEC909     
-Saturation              sing_1171.htm#IDX452    
-Saturation              sing_2463.htm#SEC2539   
+SScontinue              sing_1065.htm#SEC1141   
+SSres           sing_1063.htm#SEC1139   
+SSsyz           sing_1064.htm#SEC1140   
+SV-decoding algorithm           sing_1835.htm#IDX719    
+SV-decoding algorithm, preprocessing            sing_1834.htm#IDX718    
+Sannfs          sing_592.htm#SEC644     
+SannfsBFCT              sing_601.htm#SEC653     
+SannfsVar               sing_648.htm#SEC700     
+Sannfslog               sing_593.htm#SEC645     
+Saturation              sing_859.htm#SEC911     
+Saturation              sing_1174.htm#IDX459    
+Saturation              sing_2468.htm#SEC2544   
 Sch@"onemann, Hans              sing_1.htm#IDX20        
-Schoof          sing_1943.htm#SEC2019   
-Schreyer ordering               sing_1055.htm#IDX439    
-Schreyer resolution             sing_1055.htm#IDX440    
-SchurCh         sing_2223.htm#SEC2299   
-SchurS          sing_2222.htm#SEC2298   
-Scontinue               sing_1059.htm#SEC1135   
-Semigroup               sing_1539.htm#SEC1615   
-Setting up a G-algebra          sing_534.htm#SEC578     
-ShanksMestre            sing_1942.htm#SEC2018   
-SimplifyIdeal           sing_1727.htm#SEC1803   
-Singular                sing_406.htm#IDX245     
-Singular 3 and Singular 4       Singular 3 and Singular 4       sing_2466.htm#SEC2548   
+Schoof          sing_1946.htm#SEC2022   
+Schreyer ordering               sing_1058.htm#IDX446    
+Schreyer resolution             sing_1058.htm#IDX447    
+SchurCh         sing_2226.htm#SEC2302   
+SchurS          sing_2225.htm#SEC2301   
+Scontinue               sing_1062.htm#SEC1138   
+Semigroup               sing_1542.htm#SEC1618   
+Setting up a G-algebra          sing_535.htm#SEC579     
+ShanksMestre            sing_1945.htm#SEC2021   
+SimplifyIdeal           sing_1730.htm#SEC1806   
+Singular                sing_406.htm#IDX251     
+Singular 3 and Singular 4       Singular 3 and Singular 4       sing_2471.htm#SEC2553   
 Singular, customization of Emacs user interface Customization of the Emacs interface    sing_25.htm#SEC36       
 Singular, demo mode             sing_24.htm#SEC35       
@@ -674 +720 @@
 Singular, important commands of Emacs interface Top 20 Emacs commands   sing_27.htm#SEC38       
 Singular, running within Emacs  Running SINGULAR under Emacs    sing_23.htm#SEC30       
-Singular2bertini                sing_1389.htm#SEC1465   
-SingularLib             sing_406.htm#IDX247     
-Singularities           sing_1498.htm#SEC1574   
-Singularity Theory              sing_869.htm#SEC921     
-Skeletons for parallelization           sing_980.htm#IDX424     
-Smith form              sing_1874.htm#IDX722    
-Smith normal form               sing_1874.htm#IDX723    
-SolowayStrassen         sing_1930.htm#SEC2006   
-Solving systems of polynomial equations Solving systems of polynomial equations sing_886.htm#SEC938     
+Singular2bertini                sing_1392.htm#SEC1468   
+SingularLib             sing_406.htm#IDX253     
+Singularities           sing_1501.htm#SEC1577   
+Singularity Theory              sing_871.htm#SEC923     
+Skeletons for parallelization           sing_982.htm#IDX430     
+Smith form              sing_1877.htm#IDX729    
+Smith normal form               sing_1877.htm#IDX730    
+SolowayStrassen         sing_1933.htm#SEC2009   
+Solving systems of polynomial equations Solving systems of polynomial equations sing_888.htm#SEC940     
 Source code debugger, invocation        Command line options    sing_19.htm#IDX33       
-Space curve singularities, branches of  Branches of space curve singularities   sing_876.htm#SEC928     
+Space curve singularities, branches of  Branches of space curve singularities   sing_878.htm#SEC930     
 Special characters              sing_36.htm#SEC64       
-Splitting lemma         sing_2405.htm#IDX893    
-Sres            sing_1057.htm#SEC1133   
+Splitting lemma         sing_2410.htm#IDX900    
+Sres            sing_1060.htm#SEC1136   
 Ssi file links          sing_114.htm#SEC154     
 Ssi links               sing_113.htm#SEC153     
 Ssi tcp links           sing_115.htm#SEC155     
-Ssyz            sing_1058.htm#SEC1134   
-StabEqn         sing_1624.htm#SEC1700   
-StabEqnId               sing_1625.htm#SEC1701   
-StabOrder               sing_1626.htm#SEC1702   
-Standard Bases  Computing Groebner and Standard Bases   sing_852.htm#SEC904     
-Standard bases          sing_900.htm#SEC952     
-StartOrderingV          sing_1493.htm#SEC1569   
+Ssyz            sing_1061.htm#SEC1137   
+StabEqn         sing_1627.htm#SEC1703   
+StabEqnId               sing_1628.htm#SEC1704   
+StabOrder               sing_1629.htm#SEC1705   
+Standard Bases  Computing Groebner and Standard Bases   sing_854.htm#SEC906     
+Standard bases          sing_902.htm#SEC954     
+StartOrderingV          sing_1496.htm#SEC1572   
 Startup sequence                sing_20.htm#SEC27       
-StringF         sing_1613.htm#SEC1689   
-SymGroup                sing_790.htm#SEC842     
-Symbolic-numerical solving      Symbolic-numerical solving      sing_886.htm#SEC938     
-Symbolic-numerical solving              sing_1731.htm#SEC1807   
-System and Control theory       System and Control theory       sing_1856.htm#SEC1932   
+StringF         sing_1616.htm#SEC1692   
+SymGroup                sing_792.htm#SEC844     
+Symbolic-numerical solving      Symbolic-numerical solving      sing_888.htm#SEC940     
+Symbolic-numerical solving              sing_1734.htm#SEC1810   
+System and Control theory       System and Control theory       sing_1859.htm#SEC1935   
 System dependent limitations    System dependent limitations    sing_456.htm#SEC496     
 System variables                sing_442.htm#SEC482     
-Syzygies and resolutions        Syzygies and resolutions        sing_902.htm#SEC956     
-Syzygies and resolutions (plural)       Syzygies and resolutions (plural)       sing_536.htm#SEC583     
-T1              sing_873.htm#SEC925     
-T2              sing_873.htm#SEC925     
+Syzygies and resolutions        Syzygies and resolutions        sing_904.htm#SEC958     
+Syzygies and resolutions (plural)       Syzygies and resolutions (plural)       sing_537.htm#SEC584     
+T1              sing_875.htm#SEC927     
+T2              sing_875.htm#SEC927     
 TRACE   Tracing of procedures   sing_65.htm#SEC102      
 TRACE           sing_451.htm#SEC491     
-T_1             sing_1646.htm#SEC1722   
-T_12            sing_1648.htm#SEC1724   
-T_2             sing_1647.htm#SEC1723   
-Teaching                sing_1888.htm#SEC1964   
+T_1             sing_1649.htm#SEC1725   
+T_12            sing_1651.htm#SEC1727   
+T_2             sing_1650.htm#SEC1726   
+Teaching                sing_1891.htm#SEC1967   
 Template for writing a library          sing_55.htm#SEC92       
-TestGRRes               sing_2315.htm#SEC2391   
-TestJMark               sing_1494.htm#SEC1570   
+TestGRRes               sing_2318.htm#SEC2394   
+TestJMark               sing_1497.htm#SEC1573   
 The SINGULAR language   The SINGULAR language   sing_34.htm#SEC56       
-The Tran algorithm              sing_1187.htm#IDX478    
-The fractal walk algorithm              sing_1186.htm#IDX477    
-The fractal walk algorithm              sing_2399.htm#IDX890    
+The Tran algorithm              sing_1190.htm#IDX485    
+The fractal walk algorithm              sing_1189.htm#IDX484    
+The fractal walk algorithm              sing_2404.htm#IDX897    
 The online help system  The online help system  sing_16.htm#SEC22       
-Tjurina         sing_1644.htm#SEC1720   
-Tjurina number  Milnor and Tjurina number       sing_870.htm#SEC922     
-Tjurina number          sing_1281.htm#IDX505    
+Tjurina         sing_1647.htm#SEC1723   
+Tjurina number  Milnor and Tjurina number       sing_872.htm#SEC924     
+Tjurina number          sing_1284.htm#IDX512    
 Top 20 Emacs commands   Top 20 Emacs commands   sing_27.htm#SEC38       
-Tor             sing_1212.htm#SEC1288   
-Toric ideals and integer programming    Toric ideals and integer programming    sing_905.htm#SEC962     
+Tor             sing_1215.htm#SEC1291   
+Toric ideals and integer programming    Toric ideals and integer programming    sing_907.htm#SEC964     
 Tricks and pitfalls             sing_454.htm#SEC494     
-Tropical Geometry               sing_2040.htm#SEC2116   
+Tropical Geometry               sing_2043.htm#SEC2119   
 Type casting    Type conversion and casting     sing_39.htm#SEC69       
 Type conversion Type conversion and casting     sing_39.htm#SEC68       
 Typesetting of help and info strings    Typesetting of help and info strings    sing_61.htm#SEC98       
-U_D_O           sing_1127.htm#SEC1203   
-Unix installation       Unix installation instructions  sing_2473.htm#SEC2562   
-UpOneMatrix             sing_779.htm#SEC831     
-UpperMonomials          sing_1627.htm#SEC1703   
-UseBertini              sing_1388.htm#SEC1464   
+U_D_O           sing_1130.htm#SEC1206   
+Unix installation       Unix installation instructions  sing_2478.htm#SEC2567   
+UpOneMatrix             sing_781.htm#SEC833     
+UpperMonomials          sing_1630.htm#SEC1706   
+UseBertini              sing_1391.htm#SEC1467   
 User defined types              sing_177.htm#SEC217     
-V-filtration            sing_1562.htm#IDX588    
-V-filtration            sing_1568.htm#IDX616    
-V-filtration            sing_1569.htm#IDX622    
-V-filtration            sing_1570.htm#IDX630    
-V-filtration                    sing_1571.htm#IDX636    
-V-filtration                    sing_1572.htm#IDX644    
-V-filtration                    sing_1573.htm#IDX654    
-V-filtration                    sing_1584.htm#IDX660    
-V-filtration                    sing_1586.htm#IDX671    
-VarToPar                sing_2279.htm#SEC2355   
+V-filtration            sing_1565.htm#IDX595    
+V-filtration            sing_1571.htm#IDX623    
+V-filtration            sing_1572.htm#IDX629    
+V-filtration            sing_1573.htm#IDX637    
+V-filtration                    sing_1574.htm#IDX643    
+V-filtration                    sing_1575.htm#IDX651    
+V-filtration                    sing_1576.htm#IDX661    
+V-filtration                    sing_1587.htm#IDX667    
+V-filtration                    sing_1589.htm#IDX678    
+VarToPar                sing_2282.htm#SEC2358   
 Variables, indexed              sing_37.htm#SEC65       
-Version number  Version schema for Singular     sing_2467.htm#SEC2549   
-Version schema for Singular     Version schema for Singular     sing_2467.htm#SEC2549   
+Version number  Version schema for Singular     sing_2472.htm#SEC2554   
+Version schema for Singular     Version schema for Singular     sing_2472.htm#SEC2554   
 Version string          sing_50.htm#SEC87       
-Visualization           sing_1794.htm#SEC1870   
-WP, global ordering             sing_893.htm#IDX388     
-WSemigroup              sing_1544.htm#SEC1620   
-Weierstrass             sing_1827.htm#SEC1903   
-Weierstrass semigroup           sing_1823.htm#IDX706    
-Weyl            sing_764.htm#SEC816     
-Weyl algebra            sing_588.htm#IDX320     
-Weyl algebra            sing_644.htm#IDX345     
-Weyl closure            sing_815.htm#IDX373     
-WeylClosure             sing_817.htm#SEC869     
-WeylClosure1            sing_818.htm#SEC870     
-Windows installation    Windows installation instructions       sing_2474.htm#SEC2563   
-WitSet          sing_1395.htm#SEC1471   
-WitSupSet               sing_1394.htm#SEC1470   
-Ws, local ordering              sing_894.htm#IDX400     
-XLsolve         sing_1737.htm#SEC1813   
-ZZsolve         sing_1738.htm#SEC1814   
+Visualization           sing_1797.htm#SEC1873   
+WP, global ordering             sing_895.htm#IDX394     
+WSemigroup              sing_1547.htm#SEC1623   
+Weierstrass             sing_1830.htm#SEC1906   
+Weierstrass semigroup           sing_1826.htm#IDX713    
+Weyl            sing_766.htm#SEC818     
+Weyl algebra            sing_589.htm#IDX326     
+Weyl algebra            sing_645.htm#IDX351     
+Weyl closure            sing_817.htm#IDX379     
+WeylClosure             sing_819.htm#SEC871     
+WeylClosure1            sing_820.htm#SEC872     
+Windows installation    Windows installation instructions       sing_2479.htm#SEC2568   
+WitSet          sing_1398.htm#SEC1474   
+WitSupSet               sing_1397.htm#SEC1473   
+Ws, local ordering              sing_896.htm#IDX406     
+XLsolve         sing_1740.htm#SEC1816   
+ZZsolve         sing_1741.htm#SEC1817   
 [               sing_36.htm#IDX83       
+[]              sing_137.htm#SEC177     
+[]              sing_150.htm#SEC190     
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@@ -778 +828 @@
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+^               sing_142.htm#SEC182     
+^               sing_150.htm#SEC190     
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-absFactorizeBCG         sing_1141.htm#SEC1217   
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-absPrimdecGTZE          sing_1339.htm#SEC1415   
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-absfact_lib             sing_1139.htm#SEC1215   
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-ademRelations           sing_697.htm#SEC749     
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-adjunction divisor              sing_1824.htm#IDX710    
-admissibleSub           sing_755.htm#SEC807     
-afaces          sing_2291.htm#SEC2367   
-affine code     Fitzgerald-Lax method   sing_921.htm#SEC990     
-ainvar.lib              sing_1704.htm#SEC1780   
-ainvar_lib              sing_1704.htm#SEC1780   
-aksaka.lib              sing_1889.htm#SEC1965   
-aksaka_lib              sing_1889.htm#SEC1965   
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-alg_kernel              sing_1147.htm#SEC1223   
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-algebraic dependence            sing_785.htm#IDX351     
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-algorithm of Conti and Traverso         sing_908.htm#SEC965     
-algorithm of Di Biase and Urbanke       Di Biase and Urbanke    sing_911.htm#SEC968     
-algorithm of Hosten and Sturmfels       Hosten and Sturmfels    sing_910.htm#SEC967     
-algorithm of Pottier            sing_909.htm#SEC966     
+a, ordering             sing_900.htm#SEC952     
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+afaces          sing_2294.htm#SEC2370   
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+ainvar_lib              sing_1707.htm#SEC1783   
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+aksaka_lib              sing_1892.htm#SEC1968   
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+alg_kernel              sing_1150.htm#SEC1226   
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+algebra_lib             sing_1145.htm#SEC1221   
+algebraic dependence            sing_787.htm#IDX357     
+algebraic field extension               sing_1355.htm#IDX517    
+algebraicDependence             sing_1368.htm#SEC1444   
+algorithm of Bigatti, La Scala and Robbiano     Bigatti and La Scala and Robbiano       sing_914.htm#SEC971     
+algorithm of Conti and Traverso         sing_910.htm#SEC967     
+algorithm of Di Biase and Urbanke       Di Biase and Urbanke    sing_913.htm#SEC970     
+algorithm of Hosten and Sturmfels       Hosten and Sturmfels    sing_912.htm#SEC969     
+algorithm of Pottier            sing_911.htm#SEC968     
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-allExtOfRight           sing_800.htm#SEC852     
-allPositive             sing_564.htm#SEC616     
-all_lib         sing_930.htm#SEC1006    
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-allreal         sing_2032.htm#SEC2108   
-allrealst               sing_2030.htm#SEC2106   
-allsquarefree           sing_1606.htm#SEC1682   
+allprint                sing_973.htm#SEC1049    
+allreal         sing_2035.htm#SEC2111   
+allrealst               sing_2033.htm#SEC2109   
+allsquarefree           sing_1609.htm#SEC1685   
 ambientDimension                sing_187.htm#SEC227     
 and     Evaluation of logical expressions       sing_96.htm#SEC136      
 and             sing_459.htm#SEC499     
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-annRat          sing_613.htm#SEC665     
-annRatSyz               sing_825.htm#SEC877     
-annfs           sing_589.htm#SEC641     
-annfs0          sing_601.htm#SEC653     
-annfs2          sing_602.htm#SEC654     
-annfsBMI                sing_598.htm#SEC650     
-annfsParamBM            sing_597.htm#SEC649     
-annfsRB         sing_603.htm#SEC655     
-annfspecial             sing_590.htm#SEC642     
-annihilator of polynomial               sing_611.htm#IDX330     
-annihilator of rational function                sing_611.htm#IDX331     
-annihilator of rational function                sing_815.htm#IDX376     
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-appelF1         sing_630.htm#SEC682     
-appelF2         sing_631.htm#SEC683     
-appelF4         sing_632.htm#SEC684     
-appendWeight2Ord                sing_757.htm#SEC809     
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+annRat          sing_614.htm#SEC666     
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+annfs           sing_590.htm#SEC642     
+annfs0          sing_602.htm#SEC654     
+annfs2          sing_603.htm#SEC655     
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+annfsParamBM            sing_598.htm#SEC650     
+annfsRB         sing_604.htm#SEC656     
+annfspecial             sing_591.htm#SEC643     
+annihilator of polynomial               sing_612.htm#IDX336     
+annihilator of rational function                sing_612.htm#IDX337     
+annihilator of rational function                sing_817.htm#IDX382     
+annil           sing_1251.htm#SEC1327   
+appelF1         sing_631.htm#SEC683     
+appelF2         sing_632.htm#SEC684     
+appelF4         sing_633.htm#SEC685     
+appendWeight2Ord                sing_759.htm#SEC811     
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-applyAdF                sing_580.htm#SEC632     
-arcpoint.lib            sing_1512.htm#SEC1588   
-arcpoint_lib            sing_1512.htm#SEC1588   
-areZeroElements         sing_2377.htm#SEC2453   
+applyAdF                sing_581.htm#SEC633     
+arcpoint.lib            sing_1515.htm#SEC1591   
+arcpoint_lib            sing_1515.htm#SEC1591   
+areZeroElements         sing_2380.htm#SEC2456   
 argument, default               sing_44.htm#SEC81       
 argument, optional              sing_44.htm#SEC81       
-arr.lib         sing_2125.htm#SEC2201   
-arr2multarr             sing_2158.htm#SEC2234   
-arrBoolean              sing_2147.htm#SEC2223   
-arrBoundedChambers              sing_2168.htm#SEC2244   
-arrBraid                sing_2148.htm#SEC2224   
-arrCenter               sing_2135.htm#SEC2211   
-arrCentered             sing_2137.htm#SEC2213   
-arrCentral              sing_2136.htm#SEC2212   
-arrCentralize           sing_2138.htm#SEC2214   
-arrChambers             sing_2167.htm#SEC2243   
-arrCharPoly             sing_2165.htm#SEC2241   
-arrCone         sing_2141.htm#SEC2217   
-arrCoordChange          sing_2139.htm#SEC2215   
-arrCoordNormalize               sing_2140.htm#SEC2216   
-arrDecone               sing_2142.htm#SEC2218   
-arrDer          sing_2155.htm#SEC2231   
-arrEdelmanReiner                sing_2153.htm#SEC2229   
-arrEssentialize         sing_2146.htm#SEC2222   
-arrExponents            sing_2157.htm#SEC2233   
-arrFlats                sing_2162.htm#SEC2238   
-arrIsEssential          sing_2145.htm#SEC2221   
-arrIsFree               sing_2156.htm#SEC2232   
-arrLastVar              sing_2134.htm#SEC2210   
-arrLattice              sing_2163.htm#SEC2239   
-arrLocalize             sing_2143.htm#SEC2219   
-arrOrlikSolomon         sing_2154.htm#SEC2230   
-arrPoincare             sing_2166.htm#SEC2242   
-arrPrintMatrix          sing_2130.htm#SEC2206   
-arrRandom               sing_2151.htm#SEC2227   
-arrRandomCentral                sing_2152.htm#SEC2228   
-arrRestrict             sing_2144.htm#SEC2220   
-arrSet          sing_2126.htm#SEC2202   
-arrSwapVar              sing_2133.htm#SEC2209   
-arrTypeB                sing_2149.htm#SEC2225   
-arrTypeD                sing_2150.htm#SEC2226   
-arr_lib         sing_2125.htm#SEC2201   
-arrange         sing_605.htm#SEC657     
-arrangement             sing_2126.htm#IDX769    
-arrangement             sing_2127.htm#IDX774    
-arrangement             sing_2158.htm#IDX836    
-arrangement             sing_2159.htm#IDX839    
-ask             sing_1897.htm#SEC1973   
-assPrimes               sing_1157.htm#SEC1233   
-assign          sing_2126.htm#IDX771    
+arr.lib         sing_2128.htm#SEC2204   
+arr2multarr             sing_2161.htm#SEC2237   
+arrBoolean              sing_2150.htm#SEC2226   
+arrBoundedChambers              sing_2171.htm#SEC2247   
+arrBraid                sing_2151.htm#SEC2227   
+arrCenter               sing_2138.htm#SEC2214   
+arrCentered             sing_2140.htm#SEC2216   
+arrCentral              sing_2139.htm#SEC2215   
+arrCentralize           sing_2141.htm#SEC2217   
+arrChambers             sing_2170.htm#SEC2246   
+arrCharPoly             sing_2168.htm#SEC2244   
+arrCone         sing_2144.htm#SEC2220   
+arrCoordChange          sing_2142.htm#SEC2218   
+arrCoordNormalize               sing_2143.htm#SEC2219   
+arrDecone               sing_2145.htm#SEC2221   
+arrDer          sing_2158.htm#SEC2234   
+arrEdelmanReiner                sing_2156.htm#SEC2232   
+arrEssentialize         sing_2149.htm#SEC2225   
+arrExponents            sing_2160.htm#SEC2236   
+arrFlats                sing_2165.htm#SEC2241   
+arrIsEssential          sing_2148.htm#SEC2224   
+arrIsFree               sing_2159.htm#SEC2235   
+arrLastVar              sing_2137.htm#SEC2213   
+arrLattice              sing_2166.htm#SEC2242   
+arrLocalize             sing_2146.htm#SEC2222   
+arrOrlikSolomon         sing_2157.htm#SEC2233   
+arrPoincare             sing_2169.htm#SEC2245   
+arrPrintMatrix          sing_2133.htm#SEC2209   
+arrRandom               sing_2154.htm#SEC2230   
+arrRandomCentral                sing_2155.htm#SEC2231   
+arrRestrict             sing_2147.htm#SEC2223   
+arrSet          sing_2129.htm#SEC2205   
+arrSwapVar              sing_2136.htm#SEC2212   
+arrTypeB                sing_2152.htm#SEC2228   
+arrTypeD                sing_2153.htm#SEC2229   
+arr_lib         sing_2128.htm#SEC2204   
+arrange         sing_606.htm#SEC658     
+arrangement             sing_2129.htm#IDX776    
+arrangement             sing_2130.htm#IDX781    
+arrangement             sing_2161.htm#IDX843    
+arrangement             sing_2162.htm#IDX846    
+ask             sing_1900.htm#SEC1976   
+assPrimes               sing_1160.htm#SEC1236   
+assign          sing_2129.htm#IDX778    
 assignment,custom       Assignments for user defined types      sing_182.htm#SEC222     
-assprimeszerodim.lib    assprimeszerodim_lib    sing_1155.htm#SEC1231   
-assprimeszerodim_lib    assprimeszerodim_lib    sing_1155.htm#SEC1231   
-atkins.lib              sing_1898.htm#SEC1974   
-atkins_lib              sing_1898.htm#SEC1974   
+assprimeszerodim.lib    assprimeszerodim_lib    sing_1158.htm#SEC1234   
+assprimeszerodim_lib    assprimeszerodim_lib    sing_1158.htm#SEC1234   
+atkins.lib              sing_1901.htm#SEC1977   
+atkins_lib              sing_1901.htm#SEC1977   
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-autonom         sing_1861.htm#SEC1937   
-autonomDim              sing_1862.htm#SEC1938   
-awalk1          sing_1188.htm#SEC1264   
-awalk2          sing_1189.htm#SEC1265   
-b-function              sing_553.htm#IDX303     
-bFactor         sing_635.htm#SEC687     
-babyGiant               sing_1927.htm#SEC2003   
-backward                sing_2266.htm#SEC2342   
+autonom         sing_1864.htm#SEC1940   
+autonomDim              sing_1865.htm#SEC1941   
+awalk1          sing_1191.htm#SEC1267   
+awalk2          sing_1192.htm#SEC1268   
+b-function              sing_554.htm#IDX309     
+bFactor         sing_636.htm#SEC688     
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+backward                sing_2269.htm#SEC2345   
 bareiss         sing_262.htm#SEC302     
-base2str                sing_933.htm#SEC1009    
+base2str                sing_935.htm#SEC1011    
 basering                sing_28.htm#IDX76       
 basering                sing_83.htm#SEC123      
-basicinvariants         sing_1518.htm#SEC1594   
-belongSemigroup         sing_1160.htm#SEC1236   
-bernstein               sing_1566.htm#SEC1642   
-bernsteinBM             sing_593.htm#SEC645     
-bernsteinLift           sing_594.htm#SEC646     
-bertini2Singular                sing_1390.htm#SEC1466   
+basicinvariants         sing_1521.htm#SEC1597   
+belongSemigroup         sing_1163.htm#SEC1239   
+bernstein               sing_1569.htm#SEC1645   
+bernsteinBM             sing_594.htm#SEC646     
+bernsteinLift           sing_595.htm#SEC647     
+bertini2Singular                sing_1393.htm#SEC1469   
 betti           sing_263.htm#SEC303     
-betti (plural)          sing_503.htm#SEC543     
-bfct            sing_554.htm#SEC606     
-bfctAnn         sing_556.htm#SEC608     
-bfctBound               sing_824.htm#SEC876     
-bfctIdeal               sing_558.htm#SEC610     
-bfctOneGB               sing_557.htm#SEC609     
-bfctSyz         sing_555.htm#SEC607     
-bfctVarAnn              sing_646.htm#SEC698     
-bfctVarIn               sing_645.htm#SEC697     
-bfun.lib                sing_553.htm#SEC605     
-bfun_lib                sing_553.htm#SEC605     
+betti (plural)          sing_504.htm#SEC544     
+bfct            sing_555.htm#SEC607     
+bfctAnn         sing_557.htm#SEC609     
+bfctBound               sing_826.htm#SEC878     
+bfctIdeal               sing_559.htm#SEC611     
+bfctOneGB               sing_558.htm#SEC610     
+bfctSyz         sing_556.htm#SEC608     
+bfctVarAnn              sing_647.htm#SEC699     
+bfctVarIn               sing_646.htm#SEC698     
+bfun.lib                sing_554.htm#SEC606     
+bfun_lib                sing_554.htm#SEC606     
 bigint          sing_73.htm#SEC113      
 bigint declarations             sing_74.htm#SEC114      
@@ -954 +1006 @@
 bigintmat operations    bigintmat operations    sing_82.htm#SEC122      
 bigintmat type cast             sing_81.htm#SEC121      
-bimodules               sing_546.htm#IDX291     
-bimodules.lib           sing_546.htm#SEC598     
-bimodules_lib           sing_546.htm#SEC598     
-binary_add              sing_1950.htm#SEC2026   
-binomial                sing_938.htm#SEC1014    
-binomials2intmat                sing_1313.htm#SEC1389   58804
-birational map, image, inverse.         sing_1407.htm#IDX539    
-bistd           sing_547.htm#SEC599     
-bisyzygies              sing_546.htm#IDX292     
-bitrinity               sing_548.htm#SEC600     
+bimodules               sing_547.htm#IDX297     
+bimodules.lib           sing_547.htm#SEC599     
+bimodules_lib           sing_547.htm#SEC599     
+binary_add              sing_1953.htm#SEC2029   
+binomial                sing_940.htm#SEC1016    
+binomials2intmat                sing_1316.htm#SEC1392   58804
+birational map, image, inverse.         sing_1410.htm#IDX546    
+bistd           sing_548.htm#SEC600     
+bisyzygies              sing_547.htm#IDX298     
+bitrinity               sing_549.htm#SEC601     
 blackbox                sing_243.htm#SEC283     
 blackbox                sing_251.htm#SEC291     
 block           sing_40.htm#SEC70       
 block           sing_425.htm#SEC465     
-blowUp          sing_1458.htm#SEC1534   
-blowUp2         sing_1459.htm#SEC1535   
-blowUpBO                sing_1465.htm#SEC1541   
-blowup0         sing_1165.htm#SEC1241   
-boolean         sing_2147.htm#IDX813    
+blowUp          sing_1461.htm#SEC1537   
+blowUp2         sing_1462.htm#SEC1538   
+blowUpBO                sing_1468.htm#SEC1544   
+blowup0         sing_1168.htm#SEC1244   
+boolean         sing_2150.htm#IDX820    
 boolean expressions             sing_95.htm#SEC135      
 boolean operations              sing_96.htm#SEC136      
-boolean_constant                sing_2108.htm#SEC2184   52873
-boolean_ideal           sing_2112.htm#SEC2188   53515
-boolean_poly            sing_2109.htm#SEC2185   41652
-boolean_poly_ring               sing_2107.htm#SEC2183   sprintf
-boolean_set             sing_2113.htm#SEC2189   58235
-boolean_std             sing_2106.htm#SEC2182   5921
-boundBuFou              sing_2027.htm#SEC2103   
-boundDes                sing_2029.htm#SEC2105   
-boundaryLatticePoints   boundaryLatticePoints   sing_2422.htm#SEC2498   
-boundposDes             sing_2028.htm#SEC2104   
-bracket         sing_406.htm#IDX191     
+boolean_constant                sing_2111.htm#SEC2187   52873
+boolean_ideal           sing_2115.htm#SEC2191   53515
+boolean_poly            sing_2112.htm#SEC2188   41652
+boolean_poly_ring               sing_2110.htm#SEC2186   sprintf
+boolean_set             sing_2116.htm#SEC2192   58235
+boolean_std             sing_2109.htm#SEC2185   5921
+boundBuFou              sing_2030.htm#SEC2106   
+boundDes                sing_2032.htm#SEC2108   
+boundaryLatticePoints   boundaryLatticePoints   sing_2427.htm#SEC2503   
+boundposDes             sing_2031.htm#SEC2107   
+bracket         sing_406.htm#IDX196     
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-bracket                 sing_504.htm#SEC544     
-braid           sing_2148.htm#IDX815    
+bracket                 sing_505.htm#SEC545     
+braid           sing_2151.htm#IDX822    
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 break           sing_427.htm#SEC467     
 break point             sing_441.htm#SEC481     
 breakpoint              sing_428.htm#SEC468     
-brillnoether.lib                sing_2170.htm#SEC2246   
-brillnoether_lib                sing_2170.htm#SEC2246   
-brnoeth.lib             sing_1823.htm#SEC1899   
-brnoeth_lib             sing_1823.htm#SEC1899   
+brillnoether.lib                sing_2173.htm#SEC2249   
+brillnoether_lib                sing_2173.htm#SEC2249   
+brnoeth.lib             sing_1826.htm#SEC1902   
+brnoeth_lib             sing_1826.htm#SEC1902   
 browser, command line option    Command line options    sing_19.htm#IDX44       
-browser, setting the            sing_406.htm#IDX187     
+browser, setting the            sing_406.htm#IDX192     
 browsers        The online help system  sing_16.htm#IDX21       
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-bubblesort              sing_1900.htm#SEC1976   
-busadj          sing_1119.htm#SEC1195   
-bvar            sing_2120.htm#SEC2196   52773
-c, module ordering              sing_895.htm#IDX403     
-cProj           sing_2212.htm#SEC2288   
-calculateI              sing_1432.htm#SEC1508   
-calculate_max_sum               sing_1969.htm#SEC2045   
-calculate_ordering              sing_1947.htm#SEC2023   
-cancelunit, option              sing_364.htm#IDX166     
-canonMap                sing_1193.htm#SEC1269   
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+bubblesort              sing_1903.htm#SEC1979   
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+cProj           sing_2215.htm#SEC2291   
+calculateI              sing_1435.htm#SEC1511   
+calculate_max_sum               sing_1972.htm#SEC2048   
+calculate_ordering              sing_1950.htm#SEC2026   
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 canonicalizeCone                sing_188.htm#SEC228     
-canonize                sing_1869.htm#SEC1945   
-cantoradd               sing_1983.htm#SEC2059   
-cantormult              sing_1986.htm#SEC2062   
-cantorred               sing_1984.htm#SEC2060   
-cardGroup               sing_1162.htm#SEC1238   
+canonize                sing_1872.htm#SEC1948   
+cantoradd               sing_1986.htm#SEC2062   
+cantormult              sing_1989.htm#SEC2065   
+cantorred               sing_1987.htm#SEC2063   
+cardGroup               sing_1165.htm#SEC1241   
 case    No case or switch statement     sing_460.htm#SEC500     
 cdd             sing_1.htm#IDX10        
 cddlib          sing_1.htm#IDX11        
-center          sing_567.htm#IDX310     
-center          sing_573.htm#SEC625     
-center                  sing_2135.htm#IDX795    
-center                  sing_2136.htm#IDX796    
-center                  sing_2137.htm#IDX798    
-center                  sing_2138.htm#IDX800    
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-characteristic exponents                sing_1507.htm#IDX568    
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-command-line option, setting value of           sing_406.htm#IDX269     
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-command-line options, print all values of               sing_406.htm#IDX266     
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+command-line options, print all values of               sing_406.htm#IDX272     
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+commands (plural)               sing_503.htm#IDX296     
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-cone            sing_2142.htm#IDX806    
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 coneViaPoints           sing_184.htm#SEC224     
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 containsAsFace          sing_191.htm#SEC231     
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@@ -1188 +1241 @@
 containsPositiveVector  containsPositiveVector  sing_193.htm#SEC233     
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-coordinate change               sing_2140.htm#IDX803    
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-coverings               sing_1181.htm#IDX473    
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-createTask              sing_1064.htm#SEC1140   
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 custom type     Definition of a user defined type       sing_178.htm#SEC218     
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 datetime                sing_273.htm#SEC313     
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-deRham.lib              sing_2408.htm#IDX896    
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-debug_log               sing_1530.htm#SEC1606   
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 debugger        Source code debugger    sing_66.htm#SEC103      
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-decone          sing_2142.htm#IDX807    
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-defrings                sing_1032.htm#SEC1108   
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+defrings                sing_1034.htm#SEC1110   
 deg             sing_276.htm#SEC316     
 degBound                sing_443.htm#SEC483     
 degree  Miscellaneous oddities  sing_277.htm#SEC317     
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-degree lexicographical ordering         sing_893.htm#IDX383     
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-degree reverse lexicographical ordering         sing_893.htm#IDX381     
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-delta invariant         sing_1281.htm#IDX504    
-delta invariant                 sing_1599.htm#IDX689    
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-delta invariant.                sing_1274.htm#IDX500    
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-deltaLoc                sing_1281.htm#SEC1357   
-denom_list              sing_406.htm#IDX198     
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+degree of a polynomial  Miscellaneous oddities  sing_466.htm#IDX290     
+degree reverse lexicographical ordering         sing_895.htm#IDX387     
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 denominator             sing_279.htm#SEC319     
-depth           sing_1196.htm#SEC1272   
-depthIdeal              sing_1257.htm#SEC1333   
-derivate                sing_1706.htm#SEC1782   
-derivation              sing_2155.htm#IDX828    
-desingularization               sing_2297.htm#IDX880    
-desingularization               sing_2298.htm#SEC2374   
+depth           sing_1199.htm#SEC1275   
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-detadj          sing_1615.htm#SEC1691   
-determinacy             sing_2407.htm#SEC2483   
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-diag            sing_1082.htm#SEC1158   
-diagInvariants          sing_1295.htm#SEC1371   62096
-diag_test               sing_1118.htm#SEC1194   
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+determinacy             sing_2412.htm#SEC2488   
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+diagInvariants          sing_1298.htm#SEC1374   62096
+diag_test               sing_1121.htm#SEC1197   
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-difpoly2tex             sing_1881.htm#SEC1957   
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+difpoly2tex             sing_1884.htm#SEC1960   
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-dimGradedPart           sing_1488.htm#SEC1564   11262
-dimH            sing_1487.htm#SEC1563   38534
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-dim_slocus              sing_1633.htm#SEC1709   
+dim (plural)            sing_506.htm#SEC546     
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+dimMon          sing_1240.htm#SEC1316   
+dim_slocus              sing_1636.htm#SEC1712   
 dimension               sing_197.htm#SEC237     
-dimensionOfLocalization dimensionOfLocalization sing_2285.htm#SEC2361   
-direct_boolean_poly             sing_2110.htm#SEC2186   49893
-direct_from_boolean_poly        direct_from_boolean_poly        sing_2116.htm#SEC2192   36941
-disc            sing_1901.htm#SEC1977   
-discr           sing_1655.htm#SEC1731   
-discrepancy             sing_1473.htm#SEC1549   
-disp_zdd                sing_2123.htm#SEC2199   41439
-displayCohom            sing_1489.htm#SEC1565   22633
-displayHNE              sing_1592.htm#SEC1668   
-displayInvariants               sing_1594.htm#SEC1670   
-displayMultsequence             sing_1596.htm#SEC1672   
-displayPuiseuxExpansion displayPuiseuxExpansion sing_2067.htm#SEC2143   
-displayTropicalLifting  displayTropicalLifting  sing_2065.htm#SEC2141   
-distributed computing           sing_982.htm#IDX428     
-distributed computing           sing_1022.htm#IDX430    
-distributed computing           sing_1063.htm#IDX443    
+dimensionOfLocalization dimensionOfLocalization sing_2288.htm#SEC2364   
+direct_boolean_poly             sing_2113.htm#SEC2189   49893
+direct_from_boolean_poly        direct_from_boolean_poly        sing_2119.htm#SEC2195   36941
+disc            sing_1904.htm#SEC1980   
+discr           sing_1658.htm#SEC1734   
+discrepancy             sing_1476.htm#SEC1552   
+disp_zdd                sing_2126.htm#SEC2202   41439
+displayCohom            sing_1492.htm#SEC1568   22633
+displayHNE              sing_1595.htm#SEC1671   
+displayInvariants               sing_1597.htm#SEC1673   
+displayMultsequence             sing_1599.htm#SEC1675   
+displayPuiseuxExpansion displayPuiseuxExpansion sing_2070.htm#SEC2146   
+displayTropicalLifting  displayTropicalLifting  sing_2068.htm#SEC2144   
+distributed computing           sing_984.htm#IDX434     
+distributed computing           sing_1024.htm#IDX436    
+distributed computing           sing_1066.htm#IDX450    
 div     Miscellaneous oddities  sing_76.htm#SEC116      
 div             sing_93.htm#SEC133      
-div             sing_466.htm#IDX277     
-divideUnits             sing_1877.htm#SEC1953   
-dividelist              sing_1447.htm#SEC1523   
+div             sing_466.htm#IDX283     
+divideUnits             sing_1880.htm#SEC1956   
+dividelist              sing_1450.htm#SEC1526   
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-division (plural)               sing_506.htm#SEC546     
-division, pdivi, reduce         sing_959.htm#IDX413     
-division, reduce                sing_958.htm#IDX412     
-divisor         sing_1980.htm#SEC2056   
-divisorplus             sing_2235.htm#SEC2311   
-divisors        negativeformaldivisor   sing_2234.htm#IDX854    
-divisors                sing_2235.htm#IDX855    
-divisors                sing_2236.htm#IDX856    
-divisors                sing_2237.htm#IDX857    
-divisors                sing_2238.htm#IDX858    
-divisors                sing_2239.htm#IDX859    
-divisors                sing_2240.htm#IDX860    
-divisors                sing_2241.htm#IDX861    
-divisors                        sing_2242.htm#IDX862    
-divisors                        sing_2243.htm#IDX863    
-divisors                        sing_2244.htm#IDX864    
-divisors                        sing_2245.htm#IDX865    
-divisors                        sing_2246.htm#IDX866    
-divisors                        sing_2247.htm#IDX867    
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-divisors                        sing_2249.htm#IDX869    
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-dmod.lib                sing_588.htm#SEC640     
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-dmodapp.lib             sing_611.htm#SEC663     
-dmodapp_lib             sing_611.htm#SEC663     
-dmodloc.lib             sing_815.htm#IDX365     
-dmodloc_lib             sing_815.htm#IDX366     
-dmodoublext             sing_810.htm#SEC862     
-dmodvar.lib             sing_644.htm#SEC696     
-dmodvar_lib             sing_644.htm#SEC696     
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-doubleExt               sing_801.htm#SEC853     
-downloading     Download instructions   sing_2472.htm#SEC2561   
-dp, global ordering             sing_893.htm#IDX382     
-drawNewtonSubdivision   drawNewtonSubdivision   sing_2070.htm#SEC2146   
-drawTropicalCurve               sing_2069.htm#SEC2145   
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-dsum            sing_1083.htm#SEC1159   
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 eigenvalue              sing_377.htm#SEC417     
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-elimpart                sing_1742.htm#SEC1818   
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-elliptic curves                 sing_1180.htm#IDX468    
-elliptic curves                 sing_1181.htm#IDX472    
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-ellipticRandomCurve             sing_1938.htm#SEC2014   
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-ellipticcovers_lib              sing_1174.htm#IDX454    
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 environment variable, DISPLAY   The online help system  sing_16.htm#IDX29       
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 execute         sing_289.htm#SEC329     
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 expression list         sing_72.htm#IDX128      
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-h_increasing_knapsack   h_increasing_knapsack   sing_1967.htm#SEC2043   
-hardware platform               sing_406.htm#IDX259     
-hasAlgExtensionCoefficient      hasAlgExtensionCoefficient      sing_1049.htm#SEC1125   
-hasCommutativeVars              sing_1045.htm#SEC1121   
-hasFieldCoefficient             sing_1048.htm#SEC1124   
-hasGlobalOrdering               sing_1046.htm#SEC1122   
-hasMixedOrdering                sing_1047.htm#SEC1123   
-hasNumericCoeffs                sing_1044.htm#SEC1120   
-headStand               sing_1107.htm#SEC1183   
-heightZ         sing_1346.htm#SEC1422   
+group_reynolds          sing_1678.htm#SEC1754   
+grpower         sing_2312.htm#SEC2388   
+grpres          sing_2315.htm#SEC2391   
+grprod          sing_2323.htm#SEC2399   
+grrange         sing_2334.htm#SEC2410   
+grres           sing_2321.htm#SEC2397   
+grrndmap                sing_2327.htm#SEC2403   
+grrndmap2               sing_2328.htm#SEC2404   
+grrndmat                sing_2326.htm#SEC2402   
+grshift         sing_2307.htm#SEC2383   
+grsum           sing_2311.htm#SEC2387   
+grsyz           sing_2320.htm#SEC2396   
+grtest          sing_2304.htm#SEC2380   
+grtranspose             sing_2313.htm#SEC2389   
+grtranspose1            sing_2317.htm#SEC2393   
+grtwist         sing_2309.htm#SEC2385   
+grtwists                sing_2310.htm#SEC2386   
+grview          sing_2306.htm#SEC2382   
+grwalk.lib              sing_1188.htm#SEC1264   
+grwalk_lib              sing_1188.htm#SEC1264   
+grzero          sing_2308.htm#SEC2384   
+gwalk           sing_1194.htm#SEC1270   
+hStarVector             sing_2436.htm#SEC2512   
+hVector         sing_2437.htm#SEC2513   
+h_increasing_knapsack   h_increasing_knapsack   sing_1970.htm#SEC2046   
+hardware platform               sing_406.htm#IDX265     
+hasAlgExtensionCoefficient      hasAlgExtensionCoefficient      sing_1051.htm#SEC1127   
+hasCommutativeVars              sing_1047.htm#SEC1123   
+hasFieldCoefficient             sing_1050.htm#SEC1126   
+hasGlobalOrdering               sing_1048.htm#SEC1124   
+hasMixedOrdering                sing_1049.htm#SEC1125   
+hasNumericCoeffs                sing_1046.htm#SEC1122   
+hasTransExtensionCoefficient    hasTransExtensionCoefficient    sing_1052.htm#SEC1128   
+headStand               sing_1110.htm#SEC1186   
+heightZ         sing_1349.htm#SEC1425   
 help            sing_308.htm#SEC348     
 help browsers   The online help system  sing_16.htm#IDX22       
@@ -1783 +1840 @@
 help browsers, html     The online help system  sing_16.htm#IDX23       
 help browsers, setting command to use   The online help system  sing_16.htm#IDX30       
-help browsers, setting the              sing_406.htm#IDX188     
+help browsers, setting the              sing_406.htm#IDX193     
 help, accessing over the net    Command line options    sing_19.htm#IDX42       
 help, online help system        The online help system  sing_16.htm#SEC22       
-hermiteNormalForm               sing_2389.htm#SEC2465   
-hess.lib                sing_2334.htm#SEC2410   
-hess_lib                sing_2334.htm#SEC2410   
-hessenberg              sing_406.htm#IDX210     
-hessenberg              sing_1129.htm#SEC1205   
+hermiteNormalForm               sing_2392.htm#SEC2468   
+hess.lib                sing_2337.htm#SEC2413   
+hess_lib                sing_2337.htm#SEC2413   
+hessenberg              sing_406.htm#IDX216     
+hessenberg              sing_1132.htm#SEC1208   
 highcorner              sing_309.htm#SEC349     
 hilb            sing_310.htm#SEC350     
-hilbPoly                sing_1008.htm#SEC1084   
-hilbert4ti2             sing_1368.htm#SEC1444   13993
-hilbertBasis            sing_2430.htm#SEC2506   
-hilbertSeries           sing_2391.htm#SEC2467   
-hilbvec         sing_1746.htm#SEC1822   
-hnexpansion             sing_1588.htm#SEC1664   
-hnoether.lib            sing_1587.htm#SEC1663   
-hnoether_lib            sing_1587.htm#SEC1663   
-holonomic rank          sing_815.htm#IDX368     
-holonomicRank           sing_819.htm#SEC871     
-hom_kernel              sing_1207.htm#SEC1283   
+hilbPoly                sing_1010.htm#SEC1086   
+hilbert4ti2             sing_1371.htm#SEC1447   13993
+hilbertBasis            sing_2435.htm#SEC2511   
+hilbertSeries           sing_2394.htm#SEC2470   
+hilbvec         sing_1749.htm#SEC1825   
+hnexpansion             sing_1591.htm#SEC1667   
+hnoether.lib            sing_1590.htm#SEC1666   
+hnoether_lib            sing_1590.htm#SEC1666   
+holonomic rank          sing_817.htm#IDX374     
+holonomicRank           sing_821.htm#SEC873     
+hom_kernel              sing_1210.htm#SEC1286   
 homog           sing_311.htm#SEC351     
-homogeneitySpace                sing_2414.htm#SEC2490   
-homogfacFirstQWeyl              sing_748.htm#SEC800     
-homogfacFirstQWeyl_all  homogfacFirstQWeyl_all  sing_750.htm#SEC802     
-homogfacNthQWeyl                sing_747.htm#SEC799     
-homogfacNthQWeyl_all    homogfacNthQWeyl_all    sing_749.htm#SEC801     
-homolog.lib             sing_1192.htm#SEC1268   
-homolog_lib             sing_1192.htm#SEC1268   
-homology                sing_1202.htm#SEC1278   
-howto, download Download instructions   sing_2472.htm#SEC2561   
-howto, install on Macintosh     Macintosh installation instructions     sing_2475.htm#SEC2564   
-howto, install on Unix  Unix installation instructions  sing_2473.htm#SEC2562   
-howto, install on Windows       Windows installation instructions       sing_2474.htm#SEC2563   
+homogeneitySpace                sing_2419.htm#SEC2495   
+homogfacFirstQWeyl              sing_750.htm#SEC802     
+homogfacFirstQWeyl_all  homogfacFirstQWeyl_all  sing_752.htm#SEC804     
+homogfacNthQWeyl                sing_749.htm#SEC801     
+homogfacNthQWeyl_all    homogfacNthQWeyl_all    sing_751.htm#SEC803     
+homolog.lib             sing_1195.htm#SEC1271   
+homolog_lib             sing_1195.htm#SEC1271   
+homology                sing_1205.htm#SEC1281   
+howto, download Download instructions   sing_2477.htm#SEC2566   
+howto, install on Macintosh     Macintosh installation instructions     sing_2480.htm#SEC2569   
+howto, install on Unix  Unix installation instructions  sing_2478.htm#SEC2567   
+howto, install on Windows       Windows installation instructions       sing_2479.htm#SEC2568   
 hres            sing_312.htm#SEC352     
 html, default help      The online help system  sing_16.htm#IDX24       
-hyperel.lib             sing_1974.htm#SEC2050   
-hyperel_lib             sing_1974.htm#SEC2050   
-hyperplane              sing_2126.htm#IDX770    
-hyperplane arrangement          sing_588.htm#IDX325     
-hypersurface singularity                sing_1614.htm#IDX694    
-iMult           sing_1280.htm#SEC1356   
-id2mod          sing_1004.htm#SEC1080   
+hyperel.lib             sing_1977.htm#SEC2053   
+hyperel_lib             sing_1977.htm#SEC2053   
+hyperplane              sing_2129.htm#IDX777    
+hyperplane arrangement          sing_589.htm#IDX331     
+hypersurface singularity                sing_1617.htm#IDX701    
+iMult           sing_1283.htm#SEC1359   
+id2mod          sing_1006.htm#SEC1082   
 ideal           sing_85.htm#SEC125      
 ideal declarations              sing_86.htm#SEC126      
-ideal declarations (plural)     ideal declarations (plural)     sing_472.htm#SEC512     
+ideal declarations (plural)     ideal declarations (plural)     sing_473.htm#SEC513     
 ideal expressions               sing_87.htm#SEC127      
-ideal expressions (plural)      ideal expressions (plural)      sing_473.htm#SEC513     
+ideal expressions (plural)      ideal expressions (plural)      sing_474.htm#SEC514     
 ideal operations                sing_88.htm#SEC128      
-ideal operations (plural)       ideal operations (plural)       sing_474.htm#SEC514     
+ideal operations (plural)       ideal operations (plural)       sing_475.htm#SEC515     
 ideal related functions ideal related functions sing_89.htm#SEC129      
-ideal related functions (plural)        ideal related functions (plural)        sing_475.htm#SEC515     
-ideal, toric            sing_906.htm#SEC963     
-idealSplit              sing_1753.htm#SEC1829   
-ideals  Miscellaneous oddities  sing_466.htm#IDX281     
-idealsimplify           sing_1515.htm#SEC1591   
+ideal related functions (plural)        ideal related functions (plural)        sing_476.htm#SEC516     
+ideal, toric            sing_908.htm#SEC965     
+idealSplit              sing_1756.htm#SEC1832   
+ideals  Miscellaneous oddities  sing_466.htm#IDX287     
+idealsimplify           sing_1518.htm#SEC1594   
 identifier      Identifier resolution   sing_467.htm#SEC507     
-identifyvar             sing_1423.htm#SEC1499   
+identifyvar             sing_1426.htm#SEC1502   
 if              sing_434.htm#SEC474     
-imageLattice            sing_2357.htm#SEC2433   
-image_of_variety                sing_1703.htm#SEC1779   
+imageLattice            sing_2360.htm#SEC2436   
+image_of_variety                sing_1706.htm#SEC1782   
 imap            sing_313.htm#SEC353     
-imap (plural)           sing_510.htm#SEC550     
-imapall         sing_1036.htm#SEC1112   
+imap (plural)           sing_511.htm#SEC551     
+imapall         sing_1038.htm#SEC1114   
 impart          sing_314.htm#SEC354     
 importfrom              sing_435.htm#SEC475     
-inCenter                sing_577.htm#SEC629     
-inCentralizer           sing_578.htm#SEC630     
-inForm          sing_620.htm#SEC672     
-inSubring               sing_1145.htm#SEC1221   
-indSet          sing_1252.htm#SEC1328   
+inCenter                sing_578.htm#SEC630     
+inCentralizer           sing_579.htm#SEC631     
+inForm          sing_621.htm#SEC673     
+inSubring               sing_1148.htm#SEC1224   
+indSet          sing_1255.htm#SEC1331   
 indepSet                sing_315.htm#SEC355     
 indexed names           sing_36.htm#IDX82       
 indexed names           sing_37.htm#SEC65       
 inequalities            sing_205.htm#SEC245     
-infRedTail, option              sing_364.htm#IDX149     
+infRedTail, option              sing_364.htm#IDX154     
 info    The online help system  sing_16.htm#SEC23       
-iniD            sing_1443.htm#SEC1519   
-init_debug              sing_1522.htm#SEC1598   
-initial         sing_2413.htm#SEC2489   
-initial form            sing_553.htm#IDX306     
-initial ideal           sing_553.htm#IDX305     
-initial ideal approach          sing_553.htm#IDX309     
-initial ideal approach          sing_644.htm#IDX348     
-initialForm             sing_2079.htm#SEC2155   
-initialIdeal            sing_2080.htm#SEC2156   
-initialIdealW           sing_619.htm#SEC671     
-initialMalgrange                sing_618.htm#SEC670     
-injective_knapsack              sing_1968.htm#SEC2044   
-inout.lib               sing_970.htm#SEC1046    
-inout_lib               sing_970.htm#SEC1046    
+iniD            sing_1446.htm#SEC1522   
+init_debug              sing_1525.htm#SEC1601   
+initial         sing_2418.htm#SEC2494   
+initial form            sing_554.htm#IDX312     
+initial ideal           sing_554.htm#IDX311     
+initial ideal approach          sing_554.htm#IDX315     
+initial ideal approach          sing_645.htm#IDX354     
+initialForm             sing_2082.htm#SEC2158   
+initialIdeal            sing_2083.htm#SEC2159   
+initialIdealW           sing_620.htm#SEC672     
+initialMalgrange                sing_619.htm#SEC671     
+injective_knapsack              sing_1971.htm#SEC2047   
+inout.lib               sing_972.htm#SEC1048    
+inout_lib               sing_972.htm#SEC1048    
 input           sing_41.htm#SEC71       
-insert          sing_316.htm#SEC356     
+insert          sing_121.htm#SEC161     
+insert          sing_316.htm#SEC356     
 insertCone              sing_229.htm#SEC269     
-insertGenerator         sing_639.htm#SEC691     
-instructions, Macintosh installation    Macintosh installation instructions     sing_2475.htm#SEC2564   
-instructions, Unix installation Unix installation instructions  sing_2473.htm#SEC2562   
-instructions, Windows installation      Windows installation instructions       sing_2474.htm#SEC2563   
-instructions, downloading       Download instructions   sing_2472.htm#SEC2561   
+insertGenerator         sing_640.htm#SEC692     
+instructions, Macintosh installation    Macintosh installation instructions     sing_2480.htm#SEC2569   
+instructions, Unix installation Unix installation instructions  sing_2478.htm#SEC2567   
+instructions, Windows installation      Windows installation instructions       sing_2479.htm#SEC2568   
+instructions, downloading       Download instructions   sing_2477.htm#SEC2566   
 int             sing_90.htm#SEC130      
 int declarations                sing_91.htm#SEC131      
@@ -1887 +1945 @@
 int operations          sing_93.htm#SEC133      
 int related functions   int related functions   sing_94.htm#SEC134      
-intInverse              sing_2366.htm#SEC2442   
-intPart         sing_1922.htm#SEC1998   
-intRank         sing_2358.htm#SEC2434   
-intRoot         sing_1923.htm#SEC1999   
-intRoots                sing_636.htm#SEC688     
-intStrategy, option             sing_364.htm#IDX150     
-intclMonIdeal           sing_1292.htm#SEC1368   22338
-intclToricRing          sing_1288.htm#SEC1364   62143
-integer division        Miscellaneous oddities  sing_466.htm#IDX276     
-integer programming             sing_914.htm#SEC971     
-integral basis          sing_1214.htm#IDX483    
-integral basis          sing_1406.htm#IDX537    
-integral closure                sing_1273.htm#IDX496    
-integral closure                sing_1274.htm#IDX499    
-integral closure                sing_1275.htm#IDX502    
-integral closure                sing_1287.htm#IDX506    
-integralBasis           sing_1214.htm#SEC1290   
-integralIdeal           sing_623.htm#SEC675     
-integralModule          sing_624.htm#SEC676     
-integralSection         sing_2367.htm#SEC2443   
-integralbasis.lib               sing_1213.htm#SEC1289   
-integralbasis_lib               sing_1213.htm#SEC1289   
-integration of D-module         sing_611.htm#IDX337     
+intInverse              sing_2369.htm#SEC2445   
+intPart         sing_1925.htm#SEC2001   
+intRank         sing_2361.htm#SEC2437   
+intRoot         sing_1926.htm#SEC2002   
+intRoots                sing_637.htm#SEC689     
+intStrategy, option             sing_364.htm#IDX155     
+intclMonIdeal           sing_1295.htm#SEC1371   22338
+intclToricRing          sing_1291.htm#SEC1367   62143
+integer division        Miscellaneous oddities  sing_466.htm#IDX282     
+integer programming             sing_916.htm#SEC973     
+integral basis          sing_1217.htm#IDX490    
+integral basis          sing_1409.htm#IDX544    
+integral closure                sing_1276.htm#IDX503    
+integral closure                sing_1277.htm#IDX506    
+integral closure                sing_1278.htm#IDX509    
+integral closure                sing_1290.htm#IDX513    
+integralBasis           sing_1217.htm#SEC1293   
+integralIdeal           sing_624.htm#SEC676     
+integralModule          sing_625.htm#SEC677     
+integralSection         sing_2370.htm#SEC2446   
+integralbasis.lib               sing_1216.htm#SEC1292   
+integralbasis_lib               sing_1216.htm#SEC1292   
+integration of D-module         sing_612.htm#IDX343     
 interface, Emacs        Emacs user interface    sing_21.htm#SEC28       
-interiorLatticePoints   interiorLatticePoints   sing_2433.htm#SEC2509   
-internalfunctions               sing_1523.htm#SEC1599   
-interpolate             sing_1759.htm#SEC1835   
+interiorLatticePoints   interiorLatticePoints   sing_2438.htm#SEC2514   
+internalfunctions               sing_1526.htm#SEC1602   
+interpolate             sing_1762.htm#SEC1838   
 interpolation           sing_317.htm#SEC357     
 interred                sing_318.htm#SEC358     
 intersect               sing_319.htm#SEC359     
-intersect (plural)              sing_511.htm#SEC551     
-intersectElim, option           sing_364.htm#IDX168     
-intersectLattices               sing_2363.htm#SEC2439   
-intersectMon            sing_1229.htm#SEC1305   
-intersectSyz, option            sing_364.htm#IDX169     
-intersectZ              sing_1348.htm#SEC1424   
-intersection            sing_1597.htm#SEC1673   
-intersection lattice            sing_2162.htm#IDX845    
-intersection lattice            sing_2163.htm#IDX846    
-intersection multiplicity               sing_1508.htm#IDX572    
-intersection multiplicity               sing_1597.htm#IDX687    
-intersectionDiv         sing_1471.htm#SEC1547   
-intersectionValRingIdeals       intersectionValRingIdeals       sing_1297.htm#SEC1373   38773
-intersectionValRings    intersectionValRings    sing_1296.htm#SEC1372   35761
+intersect (plural)              sing_512.htm#SEC552     
+intersectElim, option           sing_364.htm#IDX173     
+intersectLattices               sing_2366.htm#SEC2442   
+intersectMon            sing_1232.htm#SEC1308   
+intersectSyz, option            sing_364.htm#IDX174     
+intersectZ              sing_1351.htm#SEC1427   
+intersection            sing_1600.htm#SEC1676   
+intersection lattice            sing_2165.htm#IDX852    
+intersection lattice            sing_2166.htm#IDX853    
+intersection multiplicity               sing_1511.htm#IDX579    
+intersection multiplicity               sing_1600.htm#IDX694    
+intersectionDiv         sing_1474.htm#SEC1550   
+intersectionValRingIdeals       intersectionValRingIdeals       sing_1300.htm#SEC1376   38773
+intersectionValRings    intersectionValRings    sing_1299.htm#SEC1375   35761
 intmat          sing_97.htm#SEC137      
 intmat declarations             sing_98.htm#SEC138      
@@ -1937 +1995 @@
 intmat related functions        intmat related functions        sing_102.htm#SEC142     
 intmat type cast                sing_100.htm#SEC140     
-intmat2mons             sing_1312.htm#SEC1388   21150
-intprog.lib             sing_1215.htm#SEC1291   
-intprog_lib             sing_1215.htm#SEC1291   
+intmat2mons             sing_1315.htm#SEC1391   21150
+intprog.lib             sing_1218.htm#SEC1294   
+intprog_lib             sing_1218.htm#SEC1294   
 intvec          sing_103.htm#SEC143     
 intvec declarations             sing_104.htm#SEC144     
@@ -1945 +2003 @@
 intvec operations               sing_106.htm#SEC146     
 intvec related functions        intvec related functions        sing_107.htm#SEC147     
-invariant ring minimal generating set matrix group      invariant_algebra_reynolds      sing_1672.htm#IDX700    
-invariant ring minimal generating set permutation group invariant_algebra_perm  sing_1673.htm#IDX701    
-invariantRing           sing_1705.htm#SEC1781   
-invariant_algebra_perm  invariant_algebra_perm  sing_1673.htm#SEC1749   
-invariant_algebra_reynolds      invariant_algebra_reynolds      sing_1672.htm#SEC1748   
-invariant_basis         sing_1680.htm#SEC1756   
-invariant_basis_reynolds        invariant_basis_reynolds        sing_1681.htm#SEC1757   
-invariant_ring          sing_1668.htm#SEC1744   
-invariant_ring_random   invariant_ring_random   sing_1669.htm#SEC1745   
-invariants              sing_1593.htm#SEC1669   
-inverse         sing_1113.htm#SEC1189   
+invariant ring minimal generating set matrix group      invariant_algebra_reynolds      sing_1675.htm#IDX707    
+invariant ring minimal generating set permutation group invariant_algebra_perm  sing_1676.htm#IDX708    
+invariantRing           sing_1708.htm#SEC1784   
+invariant_algebra_perm  invariant_algebra_perm  sing_1676.htm#SEC1752   
+invariant_algebra_reynolds      invariant_algebra_reynolds      sing_1675.htm#SEC1751   
+invariant_basis         sing_1683.htm#SEC1759   
+invariant_basis_reynolds        invariant_basis_reynolds        sing_1684.htm#SEC1760   
+invariant_ring          sing_1671.htm#SEC1747   
+invariant_ring_random   invariant_ring_random   sing_1672.htm#SEC1748   
+invariants              sing_1596.htm#SEC1672   
+inverse         sing_1116.htm#SEC1192   
 inverse of a matrix via its LU-decomposition            sing_339.htm#SEC379     
-inverseFourier          sing_634.htm#SEC686     
-inverse_B               sing_1114.htm#SEC1190   
-inverse_L               sing_1115.htm#SEC1191   
-inverse_modulus         sing_1951.htm#SEC2027   
-invertBirMap            sing_1407.htm#SEC1483   
-invertNumberMain                sing_1783.htm#SEC1859   
-involut.lib             sing_698.htm#SEC750     
-involut_lib             sing_698.htm#SEC750     
-involution              sing_703.htm#SEC755     
-invunit         sing_1616.htm#SEC1692   
-iostruct                sing_1870.htm#SEC1946   
-irrRealizationDim               sing_2061.htm#SEC2137   
-irred_secondary_char0   irred_secondary_char0   sing_1694.htm#SEC1770   
-irred_secondary_no_molien       irred_secondary_no_molien       sing_1697.htm#SEC1773   
-irreddecMon             sing_1238.htm#SEC1314   
-irreducible power series                sing_1598.htm#IDX688    
-irreducible secondary invariant irred_secondary_char0   sing_1694.htm#IDX702    
-isAface         sing_2295.htm#SEC2371   
-isAntiEndo              sing_705.htm#SEC757     
-isBounded               sing_2434.htm#SEC2510   
-isCI            sing_261.htm#IDX135     
-isCI            sing_1163.htm#SEC1239   
-isCM            sing_261.htm#IDX136     
-isCM            sing_1203.htm#SEC1279   
-isCMcod2                sing_1651.htm#SEC1727   
-isCanonical             sing_2435.htm#SEC2511   
-isCartan                sing_579.htm#SEC631     
-isCentral               sing_775.htm#SEC827     
-isCommutative           sing_777.htm#SEC829     
+inverseFourier          sing_635.htm#SEC687     
+inverse_B               sing_1117.htm#SEC1193   
+inverse_L               sing_1118.htm#SEC1194   
+inverse_modulus         sing_1954.htm#SEC2030   
+invertBirMap            sing_1410.htm#SEC1486   
+invertNumberMain                sing_1786.htm#SEC1862   
+involut.lib             sing_699.htm#SEC751     
+involut_lib             sing_699.htm#SEC751     
+involution              sing_704.htm#SEC756     
+invunit         sing_1619.htm#SEC1695   
+iostruct                sing_1873.htm#SEC1949   
+irrRealizationDim               sing_2064.htm#SEC2140   
+irred_secondary_char0   irred_secondary_char0   sing_1697.htm#SEC1773   
+irred_secondary_no_molien       irred_secondary_no_molien       sing_1700.htm#SEC1776   
+irreddecMon             sing_1241.htm#SEC1317   
+irreducible power series                sing_1601.htm#IDX695    
+irreducible secondary invariant irred_secondary_char0   sing_1697.htm#IDX709    
+isAface         sing_2298.htm#SEC2374   
+isAntiEndo              sing_706.htm#SEC758     
+isBounded               sing_2439.htm#SEC2515   
+isCI            sing_261.htm#IDX139     
+isCI            sing_1166.htm#SEC1242   
+isCM            sing_261.htm#IDX140     
+isCM            sing_1206.htm#SEC1282   
+isCMcod2                sing_1654.htm#SEC1730   
+isCanonical             sing_2440.htm#SEC2516   
+isCartan                sing_580.htm#SEC632     
+isCentral               sing_777.htm#SEC829     
+isCommutative           sing_779.htm#SEC831     
 isCompatible            sing_230.htm#SEC270     
-isCompressed            sing_2436.htm#SEC2512   
-isEqualDivisor          sing_2239.htm#SEC2315   
-isEquising              sing_1560.htm#SEC1636   
-isFlat          sing_1204.htm#SEC1280   
-isFsat          sing_629.htm#SEC681     
+isCompressed            sing_2441.htm#SEC2517   
+isEqualDivisor          sing_2242.htm#SEC2318   
+isEquising              sing_1563.htm#SEC1639   
+isFlat          sing_1207.htm#SEC1283   
+isFsat          sing_630.htm#SEC682     
 isFullSpace             sing_206.htm#SEC246     
-isGorenstein            sing_2437.htm#SEC2513   
-isGradedRingHomomorphism        isGradedRingHomomorphism        sing_2352.htm#SEC2428   
-isGroup         sing_2350.htm#SEC2426   
-isGroupHomomorphism             sing_2351.htm#SEC2427   
-isHolonomic             sing_607.htm#SEC659     
-isHomg          sing_261.htm#IDX132     
-isHomogeneous           sing_2378.htm#SEC2454   
-isInt           sing_642.htm#SEC694     
-isIntegralSurjective    isIntegralSurjective    sing_2364.htm#SEC2440   
-isInvolution            sing_704.htm#SEC756     
-isLatticeEmpty          sing_2438.htm#SEC2514   
-isLocalizationRegular   isLocalizationRegular   sing_2287.htm#SEC2363   
-isLocallyFree           sing_1205.htm#SEC1281   
-isMonomial              sing_1224.htm#SEC1300   
-isNC            sing_776.htm#SEC828     
-isNormal                sing_2439.htm#SEC2515   
-isOnCurve               sing_1935.htm#SEC2011   
+isGorenstein            sing_2442.htm#SEC2518   
+isGradedRingHomomorphism        isGradedRingHomomorphism        sing_2355.htm#SEC2431   
+isGroup         sing_2353.htm#SEC2429   
+isGroupHomomorphism             sing_2354.htm#SEC2430   
+isHolonomic             sing_608.htm#SEC660     
+isHomg          sing_261.htm#IDX135     
+isHomogeneous           sing_2381.htm#SEC2457   
+isInt           sing_643.htm#SEC695     
+isIntegralSurjective    isIntegralSurjective    sing_2367.htm#SEC2443   
+isInvolution            sing_705.htm#SEC757     
+isLatticeEmpty          sing_2443.htm#SEC2519   
+isLocalizationRegular   isLocalizationRegular   sing_2290.htm#SEC2366   
+isLocallyFree           sing_1208.htm#SEC1284   
+isMonomial              sing_1227.htm#SEC1303   
+isNC            sing_778.htm#SEC830     
+isNormal                sing_2444.htm#SEC2520   
+isOnCurve               sing_1938.htm#SEC2014   
 isOrigin                sing_207.htm#SEC247     
-isPositive              sing_2375.htm#SEC2451   
-isPrimitiveSublattice   isPrimitiveSublattice   sing_2365.htm#SEC2441   
+isPositive              sing_2378.htm#SEC2454   
+isPrimitiveSublattice   isPrimitiveSublattice   sing_2368.htm#SEC2444   
 isPure          sing_231.htm#SEC271     
-isPureTensor            sing_551.htm#SEC603     
-isQuotientRing          sing_1050.htm#SEC1126   
-isRational              sing_610.htm#SEC662     
-isReflexive             sing_2440.htm#SEC2516   
-isReg           sing_1206.htm#SEC1282   
-isSB            sing_261.htm#IDX131     
+isPureTensor            sing_552.htm#SEC604     
+isQuotientRing          sing_1053.htm#SEC1129   
+isRational              sing_611.htm#SEC663     
+isReflexive             sing_2445.htm#SEC2521   
+isReg           sing_1209.htm#SEC1285   
+isSB            sing_261.htm#IDX134     
 isSimplicial            sing_208.htm#SEC248     
-isSmooth                sing_2441.htm#SEC2517   
-isSubModule             sing_1051.htm#SEC1127   
-isSublattice            sing_2356.htm#SEC2432   
-isSymmetric             sing_1372.htm#SEC1448   
-isTame          sing_1585.htm#SEC1661   
-isTerminal              sing_2442.htm#SEC2518   
-isTorsionFree           sing_2374.htm#SEC2450   
-isTwoSidedGB            sing_552.htm#SEC604     
-isUpperTriangular               sing_756.htm#SEC808     
-isVar           sing_696.htm#SEC748     
-isVeryAmple             sing_2443.htm#SEC2519   
-isWeyl          sing_778.htm#SEC830     
-isZeroElement           sing_2376.htm#SEC2452   
-is_NND          sing_1601.htm#SEC1677   
-is_NP           sing_1261.htm#SEC1337   
-is_active               sing_1634.htm#SEC1710   
-is_bijective            sing_1150.htm#SEC1226   
-is_cenBimodule          sing_811.htm#SEC863     
-is_cenSubbimodule               sing_812.htm#SEC864     
-is_ci           sing_1635.htm#SEC1711   
-is_complex              sing_1086.htm#SEC1162   
-is_fix_injective                sing_1972.htm#SEC2048   
-is_h_injective          sing_1971.htm#SEC2047   
-is_injective            sing_1148.htm#SEC1224   
-is_irred                sing_1598.htm#SEC1674   
-is_is           sing_1636.htm#SEC1712   
-is_nested               sing_1262.htm#SEC1338   
-is_prime                sing_1952.htm#SEC2028   
-is_primitive_root               sing_1948.htm#SEC2024   
-is_pure         sing_803.htm#SEC855     
-is_reg          sing_1637.htm#SEC1713   
-is_regs         sing_1638.htm#SEC1714   
-is_surjective           sing_1149.htm#SEC1225   
-is_zero         sing_993.htm#SEC1069    
-isartinianMon           sing_1235.htm#SEC1311   
-isgenericMon            sing_1236.htm#SEC1312   
-ishyper         sing_1975.htm#SEC2051   
-isirreducibleMon                sing_1234.htm#SEC1310   
-isoncurve               sing_1976.htm#SEC2052   
-isparam         sing_2039.htm#SEC2115   
-isprimaryMon            sing_1233.htm#SEC1309   
-isprimeMon              sing_1232.htm#SEC1308   
-isuni           sing_2024.htm#SEC2100   
-iv2lp           sing_674.htm#SEC726     
-iv2lpList               sing_675.htm#SEC727     
-iv2lpMat                sing_676.htm#SEC728     
-ivDHilbert              sing_650.htm#SEC702     
-ivDHilbertSickle                sing_651.htm#SEC703     
-ivDimCheck              sing_652.htm#SEC704     
-ivHilbert               sing_653.htm#SEC705     
-ivKDim          sing_654.htm#SEC706     
-ivL2lpI         sing_673.htm#SEC725     
-ivMis2Base              sing_655.htm#SEC707     
-ivMis2Dim               sing_656.htm#SEC708     
-ivOrdMisLex             sing_657.htm#SEC709     
-ivSickle                sing_658.htm#SEC710     
-ivSickleDim             sing_660.htm#SEC712     
-ivSickleHil             sing_659.htm#SEC711     
-jInvariant              sing_2073.htm#SEC2149   
-jOft            sing_1907.htm#SEC1983   
+isSmooth                sing_2446.htm#SEC2522   
+isSubModule             sing_1054.htm#SEC1130   
+isSublattice            sing_2359.htm#SEC2435   
+isSymmetric             sing_1375.htm#SEC1451   
+isTame          sing_1588.htm#SEC1664   
+isTerminal              sing_2447.htm#SEC2523   
+isTorsionFree           sing_2377.htm#SEC2453   
+isTwoSidedGB            sing_553.htm#SEC605     
+isUpperTriangular               sing_758.htm#SEC810     
+isVar           sing_697.htm#SEC749     
+isVeryAmple             sing_2448.htm#SEC2524   
+isWeyl          sing_780.htm#SEC832     
+isZeroElement           sing_2379.htm#SEC2455   
+is_NND          sing_1604.htm#SEC1680   
+is_NP           sing_1264.htm#SEC1340   
+is_active               sing_1637.htm#SEC1713   
+is_bijective            sing_1153.htm#SEC1229   
+is_cenBimodule          sing_813.htm#SEC865     
+is_cenSubbimodule               sing_814.htm#SEC866     
+is_ci           sing_1638.htm#SEC1714   
+is_complex              sing_1089.htm#SEC1165   
+is_fix_injective                sing_1975.htm#SEC2051   
+is_h_injective          sing_1974.htm#SEC2050   
+is_injective            sing_1151.htm#SEC1227   
+is_irred                sing_1601.htm#SEC1677   
+is_is           sing_1639.htm#SEC1715   
+is_nested               sing_1265.htm#SEC1341   
+is_prime                sing_1955.htm#SEC2031   
+is_primitive_root               sing_1951.htm#SEC2027   
+is_pure         sing_805.htm#SEC857     
+is_reg          sing_1640.htm#SEC1716   
+is_regs         sing_1641.htm#SEC1717   
+is_surjective           sing_1152.htm#SEC1228   
+is_zero         sing_995.htm#SEC1071    
+isartinianMon           sing_1238.htm#SEC1314   
+isgenericMon            sing_1239.htm#SEC1315   
+ishyper         sing_1978.htm#SEC2054   
+isirreducibleMon                sing_1237.htm#SEC1313   
+isoncurve               sing_1979.htm#SEC2055   
+isparam         sing_2042.htm#SEC2118   
+isprimaryMon            sing_1236.htm#SEC1312   
+isprimeMon              sing_1235.htm#SEC1311   
+isuni           sing_2027.htm#SEC2103   
+iv2lp           sing_675.htm#SEC727     
+iv2lpList               sing_676.htm#SEC728     
+iv2lpMat                sing_677.htm#SEC729     
+ivDHilbert              sing_651.htm#SEC703     
+ivDHilbertSickle                sing_652.htm#SEC704     
+ivDimCheck              sing_653.htm#SEC705     
+ivHilbert               sing_654.htm#SEC706     
+ivKDim          sing_655.htm#SEC707     
+ivL2lpI         sing_674.htm#SEC726     
+ivMis2Base              sing_656.htm#SEC708     
+ivMis2Dim               sing_657.htm#SEC709     
+ivOrdMisLex             sing_658.htm#SEC710     
+ivSickle                sing_659.htm#SEC711     
+ivSickleDim             sing_661.htm#SEC713     
+ivSickleHil             sing_660.htm#SEC712     
+jInvariant              sing_2076.htm#SEC2152   
+jOft            sing_1910.htm#SEC1986   
 jacob           sing_320.htm#SEC360     
-jacoblift               sing_1617.htm#SEC1693   
-jacobson                sing_1876.htm#SEC1952   
-jacobson.lib            sing_1874.htm#SEC1950   
-jacobson_lib            sing_1874.htm#SEC1950   
+jacoblift               sing_1620.htm#SEC1696   
+jacobson                sing_1879.htm#SEC1955   
+jacobson.lib            sing_1877.htm#SEC1953   
+jacobson_lib            sing_1877.htm#SEC1953   
 janet           sing_321.htm#SEC361     
 jet             sing_322.htm#SEC362     
-jordan          sing_1134.htm#SEC1210   
-jordanbasis             sing_1135.htm#SEC1211   
-jordanmatrix            sing_1136.htm#SEC1212   
-jordannf                sing_1137.htm#SEC1213   
-jungfib         sing_1456.htm#SEC1532   
-jungnormal              sing_1455.htm#SEC1531   
-jungresolve             sing_1454.htm#SEC1530   
-katsura         sing_991.htm#SEC1067    
+jordan          sing_1137.htm#SEC1213   
+jordanbasis             sing_1138.htm#SEC1214   
+jordanmatrix            sing_1139.htm#SEC1215   
+jordannf                sing_1140.htm#SEC1216   
+jungfib         sing_1459.htm#SEC1535   
+jungnormal              sing_1458.htm#SEC1534   
+jungresolve             sing_1457.htm#SEC1533   
+katsura         sing_993.htm#SEC1069    
 kbase           sing_323.htm#SEC363     
-kbase (plural)          sing_512.htm#SEC552     
+kbase (plural)          sing_513.htm#SEC553     
 keepring                sing_436.htm#SEC476     
 kernel          sing_324.htm#SEC364     
-kernelLattice           sing_2359.htm#SEC2435   
+kernelLattice           sing_2362.htm#SEC2438   
 kill            sing_325.htm#SEC365     
-killTask                sing_1065.htm#SEC1141   
-killall         sing_943.htm#SEC1019    
+killTask                sing_1068.htm#SEC1144   
+killall         sing_945.htm#SEC1021    
 killattrib              sing_326.htm#SEC366     
-kmemory         sing_942.htm#SEC1018    
-kohom           sing_1208.htm#SEC1284   
-kontrahom               sing_1209.htm#SEC1285   
+kmemory         sing_944.htm#SEC1020    
+kohom           sing_1211.htm#SEC1287   
+kontrahom               sing_1212.htm#SEC1288   
 koszul          sing_327.htm#SEC367     
-kskernel.lib            sing_1608.htm#SEC1684   
-kskernel_lib            sing_1608.htm#SEC1684   
+kskernel.lib            sing_1611.htm#SEC1687   
+kskernel_lib            sing_1611.htm#SEC1687   
 l-adic numbers          sing_32.htm#SEC46       
 laguerre                sing_328.htm#SEC368     
-laguerre_solve          sing_1755.htm#SEC1831   
-lastvarGeneral          sing_2005.htm#SEC2081   
-latex.lib               sing_1799.htm#SEC1875   
-latex_lib               sing_1799.htm#SEC1875   
-lattice         sing_2163.htm#IDX848    
-latticeArea             sing_2055.htm#SEC2131   
-latticeBasis            sing_2360.htm#SEC2436   
-latticeCodegree         sing_2444.htm#SEC2520   
-latticeDegree           sing_2445.htm#SEC2521   
-latticePoints           sing_2446.htm#SEC2522   
-latticeVolume           sing_2447.htm#SEC2523   
-laxfrT          sing_2263.htm#SEC2339   
-laxfrX          sing_2264.htm#SEC2340   
-lazy, option            sing_364.htm#IDX151     
-lcm             sing_994.htm#SEC1070    
-lcmMon          sing_1227.htm#SEC1303   
-lcmN            sing_1916.htm#SEC1992   
-lcmofall                sing_1436.htm#SEC1512   
+laguerre_solve          sing_1758.htm#SEC1834   
+lastvarGeneral          sing_2008.htm#SEC2084   
+latex.lib               sing_1802.htm#SEC1878   
+latex_lib               sing_1802.htm#SEC1878   
+lattice         sing_2166.htm#IDX855    
+latticeArea             sing_2058.htm#SEC2134   
+latticeBasis            sing_2363.htm#SEC2439   
+latticeCodegree         sing_2449.htm#SEC2525   
+latticeDegree           sing_2450.htm#SEC2526   
+latticePoints           sing_2451.htm#SEC2527   
+latticeVolume           sing_2452.htm#SEC2528   
+laxfrT          sing_2266.htm#SEC2342   
+laxfrX          sing_2267.htm#SEC2343   
+lazy, option            sing_364.htm#IDX156     
+lcm             sing_996.htm#SEC1072    
+lcmMon          sing_1230.htm#SEC1306   
+lcmN            sing_1919.htm#SEC1995   
+lcmofall                sing_1439.htm#SEC1515   
 lead            sing_329.htm#SEC369     
 leadcoef                sing_330.htm#SEC370     
 leadexp         sing_331.htm#SEC371     
 leadmonom               sing_332.htm#SEC372     
-leadmonomial            sing_1991.htm#SEC2067   
-left annihilator ideal          sing_588.htm#IDX317     
-leftInverse             sing_1865.htm#SEC1941   
-leftKernel              sing_1863.htm#SEC1939   
-length, option          sing_364.htm#IDX152     
-letplaceGBasis          sing_682.htm#SEC734     
-letterplace correspondence      Letterplace correspondence      sing_542.htm#SEC594     
-lex_solve               sing_1761.htm#SEC1837   
-lexicographical ordering                sing_893.htm#IDX378     
+leadmonomial            sing_1994.htm#SEC2070   
+left annihilator ideal          sing_589.htm#IDX323     
+leftInverse             sing_1868.htm#SEC1944   
+leftKernel              sing_1866.htm#SEC1942   
+length, option          sing_364.htm#IDX157     
+letplaceGBasis          sing_683.htm#SEC735     
+letterplace correspondence      Letterplace correspondence      sing_543.htm#SEC595     
+lex_solve               sing_1764.htm#SEC1840   
+lexicographical ordering                sing_895.htm#IDX384     
 lib2doc         sing_60.htm#SEC97       
+libSingular             sing_468.htm#SEC508     
 libcdd          sing_1.htm#IDX12        
 libfac          sing_1.htm#IDX6 
 libparse                sing_69.htm#SEC109      
-library         sing_2105.htm#IDX748    
-library                 sing_2290.htm#IDX875    
+library         sing_2108.htm#IDX755    
+library                 sing_2293.htm#IDX882    
 library, info string            sing_55.htm#IDX124      
-library, polybori.lib           sing_2105.htm#IDX745    
+library, polybori.lib           sing_2108.htm#IDX752    
 library, template               sing_55.htm#SEC92       
 library, template.lib           sing_55.htm#IDX122      
-lieBracket              sing_693.htm#SEC745     
+lieBracket              sing_694.htm#SEC746     
 lift            sing_334.htm#SEC374     
-lift            sing_546.htm#IDX293     
-lift (plural)           sing_513.htm#SEC553     
-lift_kbase              sing_1554.htm#SEC1630   
-lift_rel_kb             sing_1555.htm#SEC1631   
-liftenvelope            sing_549.htm#SEC601     
+lift            sing_547.htm#IDX299     
+lift (plural)           sing_514.htm#SEC554     
+lift_kbase              sing_1557.htm#SEC1633   
+lift_rel_kb             sing_1558.htm#SEC1634   
+liftenvelope            sing_550.htm#SEC602     
 liftstd         sing_335.htm#SEC375     
-liftstd (plural)                sing_514.htm#SEC554     
-linReduce               sing_561.htm#SEC613     
-linReduceIdeal          sing_562.htm#SEC614     
-linSyzSolve             sing_563.htm#SEC615     
-linalg.lib              sing_1112.htm#SEC1188   
-linalg_lib              sing_1112.htm#SEC1188   
+liftstd (plural)                sing_515.htm#SEC555     
+linReduce               sing_562.htm#SEC614     
+linReduceIdeal          sing_563.htm#SEC615     
+linSyzSolve             sing_564.htm#SEC616     
+linalg.lib              sing_1115.htm#SEC1191   
+linalg_lib              sing_1115.htm#SEC1191   
 linealityDimension              sing_209.htm#SEC249     
 linealitySpace          sing_210.htm#SEC250     
@@ -2174 +2233 @@
 linear algebra                  sing_339.htm#SEC379     
 linear algebra                  sing_340.htm#SEC380     
-linear code, dual               sing_1834.htm#IDX713    
-linear code, systematic         sing_1835.htm#IDX714    
-linear interreduction           sing_553.htm#IDX308     
-linearCombinations              sing_582.htm#SEC634     
-linearMapKernel         sing_581.htm#SEC633     
-linear_relations                sing_1104.htm#SEC1180   
-linearlyEquivalent              sing_2242.htm#SEC2318   
-linearpart              sing_1747.htm#SEC1823   
+linear code, dual               sing_1837.htm#IDX720    
+linear code, systematic         sing_1838.htm#IDX721    
+linear interreduction           sing_554.htm#IDX314     
+linearCombinations              sing_583.htm#SEC635     
+linearMapKernel         sing_582.htm#SEC634     
+linear_relations                sing_1107.htm#SEC1183   
+linearlyEquivalent              sing_2245.htm#SEC2321   
+linearpart              sing_1750.htm#SEC1826   
 link    Parallelization with ssi links  sing_108.htm#SEC148     
-link            sing_850.htm#SEC902     
+link            sing_852.htm#SEC904     
 link declarations               sing_109.htm#SEC149     
 link expressions                sing_110.htm#SEC150     
@@ -2193 +2252 @@
 list related functions  list related functions  sing_122.htm#SEC162     
 listvar         sing_336.htm#SEC376     
-lll             sing_2392.htm#SEC2468   
+lll             sing_2395.htm#SEC2471   
 load            sing_437.htm#SEC477     
-loadLib, option         sing_364.htm#IDX173     
-loadProc, option                sing_364.htm#IDX174     
-locAtZero               sing_1282.htm#SEC1358   
-locNormal               sing_1218.htm#SEC1294   
-local methods           sing_1217.htm#IDX486    
-local methods           sing_1218.htm#IDX489    
+loadLib, option         sing_364.htm#IDX178     
+loadProc, option                sing_364.htm#IDX179     
+locAtZero               sing_1285.htm#SEC1361   
+locNormal               sing_1221.htm#SEC1297   
+local methods           sing_1220.htm#IDX493    
+local methods           sing_1221.htm#IDX496    
 local names             sing_46.htm#SEC83       
-local rings, computing in       Rings associated to monomial orderings  sing_845.htm#SEC897     
-local weighted lexicographical ordering         sing_894.htm#IDX399     
-local weighted reverse lexicographical ordering Local orderings sing_894.htm#IDX396     
-localInvar              sing_1710.htm#SEC1786   
-localization    Rings associated to monomial orderings  sing_845.htm#SEC897     
-localization            sing_2143.htm#IDX808    
-localization of D-module                sing_611.htm#IDX333     
-localization of D-module                sing_815.htm#IDX371     
-locally closed set, constructible set           sing_964.htm#IDX415     
-localstd                sing_2001.htm#SEC2077   
-locnormal.lib           sing_1217.htm#SEC1293   
-locnormal_lib           sing_1217.htm#SEC1293   
-locstd          sing_1639.htm#SEC1715   
-locus           sing_965.htm#SEC1041    
-locusdg         sing_966.htm#SEC1042    
-locusto         sing_969.htm#SEC1045    
-log2            sing_1891.htm#SEC1967   
-logarithmic annihilator ideal           sing_588.htm#IDX322     
-lowerHomogeneitySpace   lowerHomogeneitySpace   sing_2418.htm#SEC2494   
-lp, global ordering             sing_893.htm#IDX377     
-lp2iv           sing_677.htm#SEC729     
-lp2ivId         sing_678.htm#SEC730     
-lp2lstr         sing_689.htm#SEC741     
-lpDHilbert              sing_661.htm#SEC713     
-lpDHilbertSickle                sing_662.htm#SEC714     
-lpDimCheck              sing_664.htm#SEC716     
-lpHilbert               sing_663.htm#SEC715     
-lpId2ivLi               sing_679.htm#SEC731     
-lpKDim          sing_665.htm#SEC717     
-lpMis2Base              sing_666.htm#SEC718     
-lpMis2Dim               sing_667.htm#SEC719     
-lpMult          sing_686.htm#SEC738     
-lpNF            sing_683.htm#SEC735     
-lpOrdMisLex             sing_668.htm#SEC720     
-lpPower         sing_688.htm#SEC740     
-lpSickle                sing_669.htm#SEC721     
-lpSickleDim             sing_671.htm#SEC723     
-lpSickleHil             sing_670.htm#SEC722     
-lprint          sing_972.htm#SEC1048    
+local rings, computing in       Rings associated to monomial orderings  sing_847.htm#SEC899     
+local weighted lexicographical ordering         sing_896.htm#IDX405     
+local weighted reverse lexicographical ordering Local orderings sing_896.htm#IDX402     
+localInvar              sing_1713.htm#SEC1789   
+localization    Rings associated to monomial orderings  sing_847.htm#SEC899     
+localization            sing_2146.htm#IDX815    
+localization of D-module                sing_612.htm#IDX339     
+localization of D-module                sing_817.htm#IDX377     
+locally closed set, constructible set           sing_966.htm#IDX421     
+localstd                sing_2004.htm#SEC2080   
+locnormal.lib           sing_1220.htm#SEC1296   
+locnormal_lib           sing_1220.htm#SEC1296   
+locstd          sing_1642.htm#SEC1718   
+locus           sing_967.htm#SEC1043    
+locusdg         sing_968.htm#SEC1044    
+locusto         sing_971.htm#SEC1047    
+log2            sing_1894.htm#SEC1970   
+logarithmic annihilator ideal           sing_589.htm#IDX328     
+lowerHomogeneitySpace   lowerHomogeneitySpace   sing_2423.htm#SEC2499   
+lp, global ordering             sing_895.htm#IDX383     
+lp2iv           sing_678.htm#SEC730     
+lp2ivId         sing_679.htm#SEC731     
+lp2lstr         sing_690.htm#SEC742     
+lpDHilbert              sing_662.htm#SEC714     
+lpDHilbertSickle                sing_663.htm#SEC715     
+lpDimCheck              sing_665.htm#SEC717     
+lpHilbert               sing_664.htm#SEC716     
+lpId2ivLi               sing_680.htm#SEC732     
+lpKDim          sing_666.htm#SEC718     
+lpMis2Base              sing_667.htm#SEC719     
+lpMis2Dim               sing_668.htm#SEC720     
+lpMult          sing_687.htm#SEC739     
+lpNF            sing_684.htm#SEC736     
+lpOrdMisLex             sing_669.htm#SEC721     
+lpPower         sing_689.htm#SEC741     
+lpSickle                sing_670.htm#SEC722     
+lpSickleDim             sing_672.htm#SEC724     
+lpSickleHil             sing_671.htm#SEC723     
+lprint          sing_974.htm#SEC1050    
 lres            sing_337.htm#SEC377     
-ls, local ordering              sing_894.htm#IDX390     
-lst2str         sing_690.htm#SEC742     
-lsum            sing_1184.htm#SEC1260   
+ls, local ordering              sing_896.htm#IDX396     
+lst2str         sing_691.htm#SEC743     
+lsum            sing_1187.htm#SEC1263   
 ludecomp                sing_338.htm#SEC378     
 luinverse               sing_339.htm#SEC379     
 lusolve         sing_340.htm#SEC380     
-m_merkle_hellman_decryption     m_merkle_hellman_decryption     sing_1963.htm#SEC2039   
-m_merkle_hellman_encryption     m_merkle_hellman_encryption     sing_1962.htm#SEC2038   
-m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1961.htm#SEC2037   
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-makeFormalDivisor               sing_2244.htm#SEC2320   
-makeGraph               sing_1175.htm#SEC1251   
-makeHeisenberg          sing_766.htm#SEC818     
-makeLetterplaceRing             sing_681.htm#SEC733     
-makeMalgrange           sing_648.htm#SEC700     
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-makePDivisor            sing_2250.htm#SEC2326   
-makeQsl2                sing_731.htm#SEC783     
-makeQsl3                sing_732.htm#SEC784     
-makeQso3                sing_730.htm#SEC782     
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-makeUso11               sing_718.htm#SEC770     
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-makeUso5                sing_712.htm#SEC764     
-makeUso6                sing_713.htm#SEC765     
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-makeUso8                sing_715.htm#SEC767     
-makeUso9                sing_716.htm#SEC768     
-makeUsp1                sing_720.htm#SEC772     
-makeUsp2                sing_721.htm#SEC773     
-makeUsp3                sing_722.htm#SEC774     
-makeUsp4                sing_723.htm#SEC775     
-makeUsp5                sing_724.htm#SEC776     
-makeWeyl                sing_765.htm#SEC817     
+m_merkle_hellman_decryption     m_merkle_hellman_decryption     sing_1966.htm#SEC2042   
+m_merkle_hellman_encryption     m_merkle_hellman_encryption     sing_1965.htm#SEC2041   
+m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1964.htm#SEC2040   
+magnitude               sing_1888.htm#SEC1964   
+makeDivisor             sing_2237.htm#SEC2313   
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+makeGraph               sing_1178.htm#SEC1254   
+makeHeisenberg          sing_768.htm#SEC820     
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+makeUso5                sing_713.htm#SEC765     
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+makeUso7                sing_715.htm#SEC767     
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 map             sing_123.htm#SEC163     
-map (plural)            sing_476.htm#SEC516     
+map (plural)            sing_477.htm#SEC517     
 map declarations                sing_124.htm#SEC164     
-map declarations (plural)       map declarations (plural)       sing_477.htm#SEC517     
+map declarations (plural)       map declarations (plural)       sing_478.htm#SEC518     
 map expressions         sing_125.htm#SEC165     
-map expressions (plural)        map expressions (plural)        sing_478.htm#SEC518     
+map expressions (plural)        map expressions (plural)        sing_479.htm#SEC519     
 map operations          sing_126.htm#IDX129     
-map operations (plural) map operations (plural) sing_479.htm#IDX288     
-map related functions   map related functions   sing_127.htm#IDX130     
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-mapIsFinite             sing_1152.htm#SEC1228   
-mapToRatNormCurve               sing_1411.htm#SEC1487   
-mapall          sing_1037.htm#SEC1113   
-mappingcone             sing_2328.htm#SEC2404   
-mappingcone3            sing_2330.htm#SEC2406   
-markov4ti2              sing_1367.htm#SEC1443   9163
-mat2arr         sing_2128.htm#SEC2204   
-mat2carr                sing_2129.htm#SEC2205   
-mat_rk          sing_1126.htm#SEC1202   
-matbil          sing_2012.htm#SEC2088   
-mathematical objects    Representation of mathematical objects  sing_889.htm#SEC941     
-mathinit                sing_1797.htm#SEC1873   
-matmult         sing_2013.htm#SEC2089   
+map operations (plural) map operations (plural) sing_480.htm#IDX294     
+map related functions   map related functions   sing_127.htm#IDX131     
+map related functions  (plural) map related functions (plural)  sing_481.htm#IDX295     
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+mapall          sing_1039.htm#SEC1115   
+mappingcone             sing_2331.htm#SEC2407   
+mappingcone3            sing_2333.htm#SEC2409   
+markov4ti2              sing_1370.htm#SEC1446   9163
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+mat2carr                sing_2132.htm#SEC2208   
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+matbil          sing_2015.htm#SEC2091   
+mathematical objects    Representation of mathematical objects  sing_891.htm#SEC943     
+mathinit                sing_1800.htm#SEC1876   
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-matrix          sing_2128.htm#IDX776    
-matrix                  sing_2129.htm#IDX779    
-matrix                  sing_2130.htm#IDX783    
+matrix          sing_2131.htm#IDX783    
+matrix                  sing_2132.htm#IDX786    
+matrix                  sing_2133.htm#IDX790    
 matrix declarations             sing_129.htm#SEC169     
-matrix diagonalization          sing_1874.htm#IDX724    
+matrix diagonalization          sing_1877.htm#IDX731    
 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_1079.htm#SEC1155   
-matrixExp               sing_1401.htm#SEC1477   
-matrixLog               sing_1402.htm#SEC1478   
-matrixT1                sing_1653.htm#SEC1729   
-matrix_lib              sing_1079.htm#SEC1155   
-matrixpres              sing_2333.htm#SEC2409   
-matrixsystem            sing_2274.htm#SEC2350   
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+matrix_lib              sing_1082.htm#SEC1158   
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 max             sing_341.htm#SEC381     
-maxEord         sing_1426.htm#SEC1502   
-maxIntRoot              sing_832.htm#SEC884     
-maxZeros                sing_1404.htm#SEC1480   
-maxabs          sing_2031.htm#SEC2107   
-maxcoef         sing_995.htm#SEC1071    
-maxdeg          sing_996.htm#SEC1072    
-maxdeg1         sing_997.htm#SEC1073    
+maxEord         sing_1429.htm#SEC1505   
+maxExp          sing_261.htm#IDX136     
+maxIntRoot              sing_834.htm#SEC886     
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+maxabs          sing_2034.htm#SEC2110   
+maxcoef         sing_997.htm#SEC1073    
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 maxideal                sing_342.htm#SEC382     
-maximalFace             sing_2448.htm#SEC2524   
-maximalGroebnerCone             sing_2416.htm#SEC2492   
-maximalValue            sing_2449.htm#SEC2525   
-maximum         sing_1904.htm#SEC1980   
-maximum number of zeroes                sing_1404.htm#IDX531    
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+maximum         sing_1907.htm#SEC1983   
+maximum number of zeroes                sing_1407.htm#IDX538    
 mdouble         sing_56.htm#SEC93       
-mem, option             sing_364.htm#IDX175     
-membershipMon           sing_1228.htm#SEC1304   
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+membershipMon           sing_1231.htm#SEC1307   
 memory          sing_343.htm#SEC383     
 memory managment                sing_343.htm#SEC383     
-merkle_hellman_decryption       merkle_hellman_decryption       sing_1965.htm#SEC2041   
-merkle_hellman_encryption       merkle_hellman_encryption       sing_1964.htm#SEC2040   
-midpoint                sing_2270.htm#SEC2346   
-milnor          sing_1640.htm#SEC1716   
-milnorcode              sing_1524.htm#SEC1600   
-milnornumber            sing_2406.htm#SEC2482   
+merkle_hellman_decryption       merkle_hellman_decryption       sing_1968.htm#SEC2044   
+merkle_hellman_encryption       merkle_hellman_encryption       sing_1967.htm#SEC2043   
+midpoint                sing_2273.htm#SEC2349   
+milnor          sing_1643.htm#SEC1719   
+milnorcode              sing_1527.htm#SEC1603   
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-minAssChar              sing_1326.htm#SEC1402   
-minAssCharE             sing_1327.htm#SEC1403   
-minAssGTZ               sing_1324.htm#SEC1400   
-minAssGTZE              sing_1325.htm#SEC1401   
-minAssZ         sing_1344.htm#SEC1420   
-minEcart                sing_1994.htm#SEC2070   
-minIntRoot              sing_609.htm#SEC661     
-minIntRoot2             sing_831.htm#SEC883     
-minMult         sing_1159.htm#SEC1235   
+minAssChar              sing_1329.htm#SEC1405   
+minAssCharE             sing_1330.htm#SEC1406   
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+minEcart                sing_1997.htm#SEC2073   
+minIntRoot              sing_610.htm#SEC662     
+minIntRoot2             sing_833.htm#SEC885     
+minMult         sing_1162.htm#SEC1238   
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-minbaseMon              sing_1225.htm#SEC1301   
-mindeg          sing_998.htm#SEC1074    
-mindeg1         sing_999.htm#SEC1075    
-mindist         sing_1849.htm#SEC1925   
-minimal display time, setting the               sing_406.htm#IDX272     
-minimalFace             sing_2450.htm#SEC2526   
-minimalValue            sing_2451.htm#SEC2527   
-minipoly                sing_1131.htm#SEC1207   
-minkowskiSum            sing_2452.htm#SEC2528   
+minbaseMon              sing_1228.htm#SEC1304   
+mindeg          sing_1000.htm#SEC1076   
+mindeg1         sing_1001.htm#SEC1077   
+mindist         sing_1852.htm#SEC1928   
+minimal display time, setting the               sing_406.htm#IDX278     
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+minimalValue            sing_2456.htm#SEC2532   
+minipoly                sing_1134.htm#SEC1210   
+minkowskiSum            sing_2457.htm#SEC2533   
 minor           sing_346.htm#SEC386     
 minpoly         sing_445.htm#SEC485     
 minres          sing_347.htm#SEC387     
-minres (plural)         sing_515.htm#SEC555     
-mirror symmetry         sing_1174.htm#IDX456    
-mixed Hodge structure           sing_1562.htm#IDX587    
-mixed Hodge structure           sing_1568.htm#IDX615    
-mixed Hodge structure           sing_1569.htm#IDX621    
-mixed Hodge structure                   sing_1570.htm#IDX629    
-mixed Hodge structure                   sing_1571.htm#IDX635    
-mixed Hodge structure                   sing_1572.htm#IDX643    
-mixed Hodge structure                   sing_1573.htm#IDX653    
-mixed Hodge structure                   sing_1584.htm#IDX659    
-mixed Hodge structure                   sing_1586.htm#IDX670    
+minres (plural)         sing_516.htm#SEC556     
+mirror symmetry         sing_1177.htm#IDX463    
+mixed Hodge structure           sing_1565.htm#IDX594    
+mixed Hodge structure           sing_1571.htm#IDX622    
+mixed Hodge structure           sing_1572.htm#IDX628    
+mixed Hodge structure                   sing_1573.htm#IDX636    
+mixed Hodge structure                   sing_1574.htm#IDX642    
+mixed Hodge structure                   sing_1575.htm#IDX650    
+mixed Hodge structure                   sing_1576.htm#IDX660    
+mixed Hodge structure                   sing_1587.htm#IDX666    
+mixed Hodge structure                   sing_1589.htm#IDX677    
 mod             sing_76.htm#SEC116      
 mod             sing_93.htm#SEC133      
 mod             sing_142.htm#SEC182     
-mod2id          sing_1003.htm#SEC1079   
-mod2str         sing_691.htm#SEC743     
-modDec          sing_1244.htm#SEC1320   
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-modNormal               sing_1220.htm#SEC1296   
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-modWalk         sing_2337.htm#SEC2413   
-mod_versal              sing_1553.htm#SEC1629   
-modality                sing_1532.htm#SEC1608   
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-modnormal.lib           sing_1219.htm#SEC1295   
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-modrWalk                sing_2338.htm#SEC2414   
-modregCM                sing_1271.htm#SEC1347   
-modsatiety              sing_1269.htm#SEC1345   
-modstd.lib              sing_1221.htm#SEC1297   
-modstd_lib              sing_1221.htm#SEC1297   
-modular         sing_981.htm#SEC1057    
-modular methods         sing_1217.htm#IDX487    
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-modular methods.                sing_1218.htm#IDX490    
-modular techniques.             sing_1220.htm#IDX494    
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-modular_lib             sing_980.htm#SEC1056    
-modular_lib             sing_980.htm#IDX421     
+mod2id          sing_1005.htm#SEC1081   
+mod2str         sing_692.htm#SEC744     
+modDec          sing_1247.htm#SEC1323   
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 module          sing_134.htm#SEC174     
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 module declarations             sing_135.htm#SEC175     
-module declarations (plural)    module declarations (plural)    sing_482.htm#SEC522     
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 module expressions              sing_136.htm#SEC176     
-module expressions (plural)     module expressions (plural)     sing_483.htm#SEC523     
+module expressions (plural)     module expressions (plural)     sing_484.htm#SEC524     
 module operations               sing_137.htm#SEC177     
-module operations (plural)      module operations (plural)      sing_484.htm#SEC524     
-module ordering C               sing_895.htm#IDX402     
-module ordering c               sing_895.htm#IDX404     
+module operations (plural)      module operations (plural)      sing_485.htm#SEC525     
+module ordering C               sing_897.htm#IDX408     
+module ordering c               sing_897.htm#IDX410     
 module related functions        module related functions        sing_138.htm#SEC178     
-module related functions (plural)       module related functions (plural)       sing_485.htm#SEC525     
-module_containment              sing_1144.htm#SEC1220   
+module related functions (plural)       module related functions (plural)       sing_486.htm#SEC526     
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 modulo          sing_348.htm#SEC388     
-modulo (plural)         sing_516.htm#SEC556     
-moduloSlim              sing_773.htm#SEC825     
-modwalk.lib             sing_2336.htm#IDX883    
-modwalk_lib             sing_2336.htm#IDX884    
-moebius         sing_2164.htm#SEC2240   
-moebius function                sing_2164.htm#IDX849    
-molien          sing_1676.htm#SEC1752   
-mondromy.lib            sing_1614.htm#SEC1690   
-mondromy_lib            sing_1614.htm#SEC1690   
+modulo (plural)         sing_517.htm#SEC557     
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 monitor         sing_349.htm#SEC389     
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-monodromy               sing_1567.htm#SEC1643   
-monodromy               sing_1567.htm#IDX611    
-monodromy               sing_1572.htm#IDX646    
-monodromy               sing_1584.htm#IDX662    
-monodromy               sing_1586.htm#IDX673    
-monodromyB              sing_1618.htm#SEC1694   
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+monodromy               sing_1570.htm#IDX618    
+monodromy               sing_1575.htm#IDX653    
+monodromy               sing_1587.htm#IDX669    
+monodromy               sing_1589.htm#IDX680    
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 monomial                sing_350.htm#SEC390     
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-monomial orderings              sing_892.htm#SEC944     
-monomial orderings introduction Introduction to orderings       sing_891.htm#SEC943     
-monomialInIdeal         sing_829.htm#SEC881     
-monomialLcm             sing_1992.htm#SEC2068   
-monomialideal.lib               sing_1223.htm#SEC1299   
-monomialideal_lib               sing_1223.htm#SEC1299   
-monomials and precedence        Miscellaneous oddities  sing_466.htm#IDX278     
-mons2intmat             sing_1311.htm#SEC1387   15555
-morsesplit              sing_1525.htm#SEC1601   
-mp_res_mat              sing_1758.htm#SEC1834   
-mplot           sing_1798.htm#SEC1874   
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 mpresmat                sing_351.htm#SEC391     
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 mres            sing_352.htm#SEC392     
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 mstd            sing_353.htm#SEC393     
 msum            sing_58.htm#SEC95       
 mtriple         sing_57.htm#SEC94       
 mult    Miscellaneous oddities  sing_354.htm#SEC394     
-mult            sing_466.htm#IDX279     
+mult            sing_466.htm#IDX285     
 multBound               sing_446.htm#SEC486     
-multRat         sing_837.htm#SEC889     
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 multi indices           sing_37.htm#SEC65       
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