!		sing_36.htm#IDX101	
!=		sing_36.htm#IDX95	
!= 		sing_95.htm#SEC135	
"		sing_36.htm#IDX104	
#		sing_36.htm#IDX118	
$		sing_36.htm#IDX119	
%		sing_36.htm#IDX91	
% 		sing_76.htm#SEC116	
%  		sing_93.htm#SEC133	
%   		sing_105.htm#SEC145	
%    		sing_142.htm#SEC182	
&&		sing_36.htm#IDX102	
&& 		sing_96.htm#SEC136	
(		sing_36.htm#IDX80	
()		sing_126.htm#IDX130	
)		sing_36.htm#IDX81	
*	bigintmat operations	sing_36.htm#IDX89	
* 		sing_76.htm#SEC116	
*  		sing_82.htm#SEC122	
*   		sing_88.htm#SEC128	
*    		sing_93.htm#SEC133	
*     		sing_101.htm#SEC141	
*      		sing_105.htm#SEC145	
*       		sing_132.htm#SEC172	
*        		sing_137.htm#SEC177	
*         		sing_142.htm#SEC182	
*          		sing_150.htm#SEC190	
**		sing_36.htm#IDX93	
+	bigintmat operations	sing_36.htm#IDX85	
+ 		sing_76.htm#SEC116	
+  		sing_82.htm#SEC122	
+   		sing_88.htm#SEC128	
+    		sing_93.htm#SEC133	
+     		sing_101.htm#SEC141	
+      		sing_105.htm#SEC145	
+       		sing_121.htm#SEC161	
+        		sing_132.htm#SEC172	
+         		sing_137.htm#SEC177	
+          		sing_142.htm#SEC182	
+           		sing_150.htm#SEC190	
+            		sing_164.htm#SEC204	
+             		sing_170.htm#SEC210	
+              		sing_175.htm#SEC215	
++		sing_36.htm#IDX86	
-	bigintmat operations	sing_36.htm#IDX87	
- 		sing_76.htm#SEC116	
-  		sing_82.htm#SEC122	
-   		sing_93.htm#SEC133	
-    		sing_101.htm#SEC141	
-     		sing_105.htm#SEC145	
-      		sing_132.htm#SEC172	
-       		sing_142.htm#SEC182	
-        		sing_150.htm#SEC190	
-         		sing_175.htm#SEC215	
--		sing_36.htm#IDX88	
--MPhost		sing_19.htm#IDX66	
--MPport		sing_19.htm#IDX65	
--allow-net		sing_19.htm#IDX39	
--batch		sing_19.htm#IDX64	
--browser		sing_19.htm#IDX43	
--echo		sing_19.htm#IDX35	
--emacs		sing_19.htm#IDX67	
--emacs-dir		sing_19.htm#IDX68	
--emacs-load		sing_19.htm#IDX69	
--execute		sing_19.htm#IDX56	
--help		sing_19.htm#IDX37	
--min-time		sing_19.htm#IDX61	
--no-out		sing_19.htm#IDX49	
--no-rc		sing_19.htm#IDX45	
--no-shell		sing_19.htm#IDX50	
--no-stdlib		sing_19.htm#IDX47	
--no-tty		sing_19.htm#IDX51	
--no-warn		sing_19.htm#IDX48	
--quiet		sing_19.htm#IDX53	
--random		sing_19.htm#IDX60	
--sdb		sing_19.htm#IDX32	
--singular		sing_19.htm#IDX70	
--ticks-per-sec		sing_19.htm#IDX62	
--user-option		sing_19.htm#IDX58	
->		sing_154.htm#SEC194	
-MPhost	Command line options		
-MPport	Command line options		
-allow-net	Command line options		
-b	Command line options	sing_19.htm#IDX63	
-batch	Command line options		
-browser	Command line options		
-c	Command line options	sing_19.htm#IDX55	
-d	Command line options	sing_19.htm#IDX31	
-e	Command line options	sing_19.htm#IDX34	
-echo	Command line options		
-emacs	Command line options		
-emacs-dir	Command line options		
-emacs-load	Command line options		
-execute	Command line options		
-h	Command line options	sing_19.htm#IDX36	
-help	Command line options		
-min-time	Command line options		
-no-out	Command line options		
-no-rc	Command line options		
-no-shell	Command line options		
-no-stdlib	Command line options		
-no-tty	Command line options		
-no-warn	Command line options		
-q	Command line options	sing_19.htm#IDX52	
-quiet	Command line options		
-r	Command line options	sing_19.htm#IDX59	
-random	Command line options		
-sdb	Command line options		
-singular	Command line options		
-ticks-per-sec	Command line options		
-u	Command line options	sing_19.htm#IDX57	
-user-option	Command line options		
-v	Command line options	sing_19.htm#IDX54	
..		sing_36.htm#IDX113	
.singularrc file		sing_20.htm#IDX72	
.singularrc file, no loading	Command line options	sing_19.htm#IDX46	
/		sing_36.htm#IDX90	
/ 		sing_105.htm#SEC145	
/  		sing_132.htm#SEC172	
/   		sing_142.htm#SEC182	
/    		sing_150.htm#SEC190	
/     		sing_175.htm#SEC215	
//		sing_36.htm#IDX107	
// 		sing_36.htm#IDX109	
//  		sing_36.htm#IDX110	
:		sing_36.htm#IDX114	
: 		sing_105.htm#SEC145	
::		sing_36.htm#IDX115	
:: 		sing_144.htm#SEC184	
;		sing_36.htm#IDX111	
<		sing_36.htm#IDX100	
< 		sing_150.htm#SEC190	
<  		sing_175.htm#SEC215	
<   		sing_298.htm#SEC338	
<=		sing_36.htm#IDX99	
<= 		sing_95.htm#SEC135	
<=  		sing_142.htm#SEC182	
<=   		sing_150.htm#SEC190	
<=    		sing_170.htm#SEC210	
<=     		sing_175.htm#SEC215	
<>		sing_36.htm#IDX96	
<> 		sing_95.htm#SEC135	
<>  		sing_132.htm#SEC172	
<>   		sing_142.htm#SEC182	
<>    		sing_150.htm#SEC190	
<>     		sing_164.htm#SEC204	
<>      		sing_170.htm#SEC210	
<>       		sing_175.htm#SEC215	
=		sing_36.htm#IDX77	
==		sing_36.htm#IDX94	
== 		sing_95.htm#SEC135	
==  		sing_132.htm#SEC172	
==   		sing_142.htm#SEC182	
==    		sing_150.htm#SEC190	
==     		sing_164.htm#SEC204	
==      		sing_170.htm#SEC210	
==       		sing_175.htm#SEC215	
>		sing_36.htm#IDX98	
> 		sing_150.htm#SEC190	
>  		sing_175.htm#SEC215	
>=		sing_36.htm#IDX97	
>= 		sing_95.htm#SEC135	
>=  		sing_142.htm#SEC182	
>=   		sing_150.htm#SEC190	
>=    		sing_170.htm#SEC210	
>=     		sing_175.htm#SEC215	
?		sing_36.htm#IDX106	
? 		sing_308.htm#IDX148	
AG codes		sing_889.htm#SEC941	
AGcode_L		sing_1832.htm#SEC1908	
AGcode_Omega		sing_1833.htm#SEC1909	
ASCII		sing_938.htm#SEC1014	
ASCII links		sing_112.htm#SEC152	
ASSUME		sing_64.htm#SEC101	
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_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	
Ann		sing_1322.htm#SEC1398	
Appel function		sing_612.htm#IDX345	
Appel hypergeometric function		sing_612.htm#IDX346	
Applications		sing_887.htm#SEC939	
ArnoldAction		sing_1624.htm#SEC1700	
Assignments for user defined types	Assignments for user defined types	sing_182.htm#SEC222	
Atkin		sing_1915.htm#SEC1991	
Authors		sing_1.htm#IDX16	
BINresol		sing_1421.htm#SEC1497	
Background		sing_3.htm#SEC5	
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	
Brieskorn lattice         		sing_1574.htm#IDX641	
Brieskorn lattice          		sing_1575.htm#IDX649	
Brieskorn lattice           		sing_1576.htm#IDX659	
Brieskorn lattice            		sing_1587.htm#IDX665	
Brieskorn lattice             		sing_1589.htm#IDX676	
Brieskorn lattice              		sing_1617.htm#IDX703	
Brill-Noether algorithm		sing_1826.htm#IDX715	
BrillNoether		sing_1829.htm#SEC1905	
Buchberger algorithm for toric ideals	Buchberger algorithm	sing_915.htm#SEC972	
Budur-Mustata-Saito approach		sing_645.htm#IDX353	
Building Singular		sing_2475.htm#SEC2564	
C programming language	Major differences to the C programming language	sing_457.htm#SEC497	
C, module ordering		sing_897.htm#IDX407	
CGS, disjoint, reduced, Comprehensive Groebner System	cgsdr	sing_959.htm#IDX417	
CM_regularity		sing_1486.htm#SEC1562	33865
CMtype		sing_1655.htm#SEC1731	
CRHT-ideal		sing_921.htm#SEC985	
CYGWIN and ESingular	Running SINGULAR under Emacs	sing_23.htm#SEC33	
Castelnuovo-Mumford regularity		sing_1486.htm#IDX558	
Category string		sing_51.htm#SEC88	
CenCharDec		sing_739.htm#SEC791	
Center		sing_1463.htm#SEC1539	
CenterBO		sing_1470.htm#SEC1546	
CentralQuot		sing_737.htm#SEC789	
CentralSaturation		sing_738.htm#SEC790	
Change of rings		sing_9.htm#SEC15	
Characteristic sets		sing_905.htm#SEC962	
CharacteristicExponents	CharacteristicExponents	sing_1550.htm#SEC1626	
ChernRootsDual		sing_2190.htm#SEC2266	
ChernRootsHom		sing_2199.htm#SEC2275	
ChernRootsProd		sing_2192.htm#SEC2268	
ChernRootsSum		sing_2188.htm#SEC2264	
ChernRootsSymm		sing_2201.htm#SEC2277	
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	
Commutative Algebra		sing_858.htm#SEC910	
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	
Contributors		sing_1.htm#IDX15	
Control structures		sing_425.htm#SEC465	
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	
Customization of the Emacs interface	Customization of the Emacs interface	sing_25.htm#SEC36	
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_615.htm#SEC667	
DLoc0		sing_617.htm#SEC669	
Data types		sing_72.htm#SEC112	
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_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_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_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_895.htm#IDX390	
Ds, local ordering		sing_896.htm#IDX400	
DsingularLocus		sing_822.htm#SEC874	
Dynamic loading		sing_71.htm#SEC111	
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_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_861.htm#SEC913	
Emacs	Emacs user interface	sing_21.htm#SEC28	
Emacs, Singular demo mode		sing_24.htm#SEC35	
Emacs, a quick guide	A quick guide to Emacs	sing_22.htm#SEC29	
Emacs, customization of Singular mode	Customization of the Emacs interface	sing_25.htm#SEC36	
Emacs, editing Singular input files	Editing SINGULAR input files with Emacs	sing_26.htm#SEC37	
Emacs, important commands	Top 20 Emacs commands	sing_27.htm#SEC38	
Emacs, overview	A quick guide to Emacs	sing_22.htm#SEC29	
Emacs, running Singular under	Running SINGULAR under Emacs	sing_23.htm#SEC30	
Emacs, user interface	Emacs user interface	sing_21.htm#SEC28	
Emaxcont		sing_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_843.htm#SEC895	
Examples of ring declarations	Examples of ring declarations	sing_29.htm#SEC40	
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_923.htm#SEC991	
Flow control		sing_40.htm#SEC70	
Formal Checker		sing_59.htm#SEC96	
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_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_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_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_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_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_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#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_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_1720.htm#SEC1796	
ImageVariety		sing_1719.htm#SEC1795	
Imap, option		sing_364.htm#IDX175	
Implemented algorithms	Implemented algorithms	sing_33.htm#SEC47	
Incl		sing_1385.htm#SEC1461	
Index		sing_2481.htm#SEC2570	
Info string		sing_52.htm#SEC89	
InterDiv		sing_1453.htm#SEC1529	
Interactive use		sing_13.htm#SEC19	
Interrupting SINGULAR	Interrupting SINGULAR	sing_17.htm#SEC24	
IntersectWithSub		sing_740.htm#SEC792	
IntersectionMatrix		sing_1551.htm#SEC1627	
Introduction		sing_2.htm#SEC4	
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_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_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_846.htm#SEC898	
Libraries in the SINGULAR Documentation	Libraries in the SINGULAR Documentation	sing_49.htm#SEC86	
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_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_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_1617.htm#IDX700	
Monomial orderings		sing_892.htm#SEC944	
Monomial orderings, Term orderings		sing_31.htm#SEC44	
Morse lemma		sing_2410.htm#IDX899	
MultiplicitySequence	MultiplicitySequence	sing_1549.htm#SEC1625	
NF		sing_383.htm#SEC423	
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_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_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_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_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_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_846.htm#SEC898	
Procedures in a library	Procedures in a library	sing_54.htm#SEC91	
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_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_539.htm#SEC591	
SDB breakpoint	Source code debugger	sing_66.htm#SEC106	
SDB debugger	Source code debugger	sing_66.htm#SEC106	
SDLoc		sing_616.htm#SEC668	
SINGULAR libraries		sing_927.htm#SEC1003	
SINGULARHIST		sing_18.htm#SEC25	
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_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	
Singular, editing input files with Emacs	Editing SINGULAR input files with Emacs	sing_26.htm#SEC37	
Singular, important commands of Emacs interface	Top 20 Emacs commands	sing_27.htm#SEC38	
Singular, running within Emacs	Running SINGULAR under Emacs	sing_23.htm#SEC30	
Singular2bertini		sing_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_878.htm#SEC930	
Special characters		sing_36.htm#SEC64	
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_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_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_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_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_2318.htm#SEC2394	
TestJMark		sing_1497.htm#SEC1573	
The SINGULAR language	The SINGULAR language	sing_34.htm#SEC56	
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_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_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_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_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_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_2472.htm#SEC2554	
Version schema for Singular	Version schema for Singular	sing_2472.htm#SEC2554	
Version string		sing_50.htm#SEC87	
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	
[]  		sing_170.htm#SEC210	
[]   		sing_175.htm#SEC215	
\		sing_36.htm#IDX112	
]		sing_36.htm#IDX84	
^		sing_36.htm#IDX92	
^ 		sing_76.htm#SEC116	
^  		sing_88.htm#SEC128	
^   		sing_142.htm#SEC182	
^    		sing_150.htm#SEC190	
_		sing_36.htm#IDX116	
`		sing_36.htm#IDX105	
a, ordering		sing_900.htm#SEC952	
absFactorize		sing_1143.htm#SEC1219	
absFactorizeBCG		sing_1144.htm#SEC1220	
absPrimdecGTZ		sing_1341.htm#SEC1417	
absPrimdecGTZE		sing_1342.htm#SEC1418	
absValue		sing_939.htm#SEC1015	
absfact.lib		sing_1142.htm#SEC1218	
absfact_lib		sing_1142.htm#SEC1218	
absolute factorization.		sing_1142.htm#IDX458	
abstractR		sing_1480.htm#SEC1556	
actionIsProper		sing_1710.htm#SEC1786	
addNvarsTo		sing_1057.htm#SEC1133	
addRat		sing_838.htm#SEC890	
addcol		sing_1099.htm#SEC1175	
addcores		sing_1025.htm#SEC1101	
addrow		sing_1100.htm#SEC1176	
addvarsTo		sing_1056.htm#SEC1132	
ademRelations		sing_698.htm#SEC750	
adjoint		sing_1124.htm#SEC1200	
adjointIdeal		sing_1409.htm#SEC1485	
adjunction divisor		sing_1827.htm#IDX717	
admissibleSub		sing_757.htm#SEC809	
afaces		sing_2294.htm#SEC2370	
affine code	Fitzgerald-Lax method	sing_923.htm#SEC992	
ainvar.lib		sing_1707.htm#SEC1783	
ainvar_lib		sing_1707.htm#SEC1783	
aksaka.lib		sing_1892.htm#SEC1968	
aksaka_lib		sing_1892.htm#SEC1968	
alexanderpolynomial		sing_1505.htm#SEC1581	
alexpoly.lib		sing_1502.htm#SEC1578	
alexpoly_lib		sing_1502.htm#SEC1578	
algDependent		sing_1149.htm#SEC1225	
alg_kernel		sing_1150.htm#SEC1226	
algebra.lib		sing_1145.htm#SEC1221	
algebra_containment		sing_1146.htm#SEC1222	
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	
align		sing_260.htm#SEC300	
all.lib		sing_932.htm#SEC1008	
allDoubleExt		sing_804.htm#SEC856	
allExtOfLeft		sing_801.htm#SEC853	
allExtOfRight		sing_802.htm#SEC854	
allPositive		sing_565.htm#SEC617	
all_lib		sing_932.htm#SEC1008	
allowing net access	Command line options	sing_19.htm#IDX41	
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	
annPoly		sing_613.htm#SEC665	
annRat		sing_614.htm#SEC666	
annRatSyz		sing_827.htm#SEC879	
annfs		sing_590.htm#SEC642	
annfs0		sing_602.htm#SEC654	
annfs2		sing_603.htm#SEC655	
annfsBMI		sing_599.htm#SEC651	
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	
apply		sing_426.htm#SEC466	
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_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_1158.htm#SEC1234	
assprimeszerodim_lib	assprimeszerodim_lib	sing_1158.htm#SEC1234	
atkins.lib		sing_1901.htm#SEC1977	
atkins_lib		sing_1901.htm#SEC1977	
attrib		sing_261.htm#SEC301	
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	
babyGiant		sing_1930.htm#SEC2006	
backward		sing_2269.htm#SEC2345	
bareiss		sing_262.htm#SEC302	
base2str		sing_935.htm#SEC1011	
basering		sing_28.htm#IDX76	
basering 		sing_83.htm#SEC123	
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_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	
bigint expressions		sing_75.htm#SEC115	
bigint operations		sing_76.htm#SEC116	
bigint related functions	bigint related functions	sing_77.htm#SEC117	
bigintmat		sing_78.htm#SEC118	
bigintmat declarations	bigintmat declarations	sing_79.htm#SEC119	
bigintmat expressions	bigintmat expressions	sing_80.htm#SEC120	
bigintmat operations	bigintmat operations	sing_82.htm#SEC122	
bigintmat type cast		sing_81.htm#SEC121	
bimodules		sing_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_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_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	
bracket 		sing_462.htm#SEC502	
bracket  		sing_505.htm#SEC545	
braid		sing_2151.htm#IDX822	
branchTo	procs with different argument types	sing_155.htm#SEC195	
break		sing_427.htm#SEC467	
break point		sing_441.htm#SEC481	
breakpoint		sing_428.htm#SEC468	
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#IDX192	
browsers	The online help system	sing_16.htm#IDX21	
browsers, setting the		sing_406.htm#IDX191	
bubblesort		sing_1903.htm#SEC1979	
busadj		sing_1122.htm#SEC1198	
bvar		sing_2123.htm#SEC2199	52773
c, module ordering		sing_897.htm#IDX409	
cProj		sing_2215.htm#SEC2291	
calculateI		sing_1435.htm#SEC1511	
calculate_max_sum		sing_1972.htm#SEC2048	
calculate_ordering		sing_1950.htm#SEC2026	
cancelunit, option		sing_364.htm#IDX171	
canonMap		sing_1196.htm#SEC1272	
canonicalizeCone		sing_188.htm#SEC228	
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_568.htm#IDX316	
center 		sing_574.htm#SEC626	
center  		sing_2138.htm#IDX802	
center   		sing_2139.htm#IDX803	
center    		sing_2140.htm#IDX805	
center     		sing_2141.htm#IDX807	
centerRed		sing_573.htm#SEC625	
centerVS		sing_572.htm#SEC624	
central		sing_2132.htm#IDX788	
central 		sing_2139.htm#IDX804	
central  		sing_2141.htm#IDX806	
central   		sing_2155.htm#IDX831	
central.lib		sing_568.htm#SEC620	
central1st		sing_2270.htm#SEC2346	
central2nd		sing_2271.htm#SEC2347	
central_lib		sing_568.htm#SEC620	
centralize		sing_568.htm#IDX319	
centralizeSet		sing_569.htm#SEC621	
centralizer		sing_568.htm#IDX317	
centralizer 		sing_575.htm#SEC627	
centralizerRed		sing_571.htm#SEC623	
centralizerVS		sing_570.htm#SEC622	
cf_class		sing_261.htm#IDX132	
cgs		sing_934.htm#SEC1010	
cgsdr		sing_959.htm#SEC1035	
chAll		sing_2185.htm#SEC2261	
chAllInv		sing_2186.htm#SEC2262	
chDual		sing_2191.htm#SEC2267	
chHE		sing_2187.htm#SEC2263	
chHom		sing_2200.htm#SEC2276	
chNum		sing_2181.htm#SEC2257	
chNumbers		sing_2182.htm#SEC2258	
chNumbersProj		sing_2219.htm#SEC2295	
chProd		sing_2193.htm#SEC2269	
chProdE		sing_2194.htm#SEC2270	
chProdL		sing_2195.htm#SEC2271	
chProdLP		sing_2196.htm#SEC2272	
chProdM		sing_2197.htm#SEC2273	
chProdMP		sing_2198.htm#SEC2274	
chProj		sing_2216.htm#SEC2292	
chSum		sing_2189.htm#SEC2265	
chSymm		sing_2203.htm#SEC2279	
chSymm2L		sing_2204.htm#SEC2280	
chSymm2LP		sing_2205.htm#SEC2281	
chWedge		sing_2206.htm#SEC2282	
chWedge2L		sing_2207.htm#SEC2283	
chWedge2LP		sing_2208.htm#SEC2284	
chaincrit		sing_2000.htm#SEC2076	
chambers		sing_2170.htm#IDX859	
chambers 		sing_2171.htm#IDX860	
changeDenominator		sing_1289.htm#SEC1365	
changechar		sing_1030.htm#SEC1106	
changeord		sing_1031.htm#SEC1107	
changeordTo		sing_1055.htm#SEC1131	
changes		sing_2470.htm#SEC2546	
changevar		sing_1032.htm#SEC1108	
char		sing_264.htm#SEC304	
charInfo		sing_629.htm#SEC681	
charVariety		sing_628.htm#SEC680	
char_series		sing_265.htm#SEC305	
characteristic exponents		sing_1509.htm#IDX570	
characteristic exponents 		sing_1510.htm#IDX575	
characteristic exponents  		sing_1511.htm#IDX578	
characteristic exponents   		sing_1512.htm#IDX582	
characteristic exponents    		sing_1596.htm#IDX688	
characteristic polynomial		sing_2168.htm#IDX857	
characteristic variety		sing_612.htm#IDX344	
characteristic variety 		sing_817.htm#IDX378	
charexp2conductor		sing_1512.htm#SEC1588	
charexp2generators		sing_1510.htm#SEC1586	
charexp2inter		sing_1511.htm#SEC1587	
charexp2multseq		sing_1509.htm#SEC1585	
charexp2poly		sing_1513.htm#SEC1589	
charpoly		sing_1123.htm#SEC1199	
charstr		sing_266.htm#SEC306	
checkFactor		sing_605.htm#SEC657	
checkRoot		sing_600.htm#SEC652	
chern		sing_2180.htm#SEC2256	
chern.lib		sing_2175.htm#SEC2251	
chernCharPoly		sing_2222.htm#SEC2298	
chernPoly		sing_2221.htm#SEC2297	
chern_lib		sing_2175.htm#SEC2251	
chineseRem		sing_1921.htm#SEC1997	
chinrem		sing_267.htm#SEC307	
chinrempoly		sing_2397.htm#SEC2473	
chinrestp		sing_1980.htm#SEC2056	
cimonom.lib		sing_2232.htm#SEC2308	
cimonom_lib		sing_2232.htm#SEC2308	
cisimplicial.lib		sing_1161.htm#SEC1237	
cisimplicial_lib		sing_1161.htm#SEC1237	
classify		sing_1522.htm#SEC1598	
classify.lib		sing_1520.htm#SEC1596	
classifyCeq		sing_1539.htm#SEC1615	
classify_lib		sing_1520.htm#SEC1596	
classifyceq.lib		sing_1538.htm#IDX585	
classifyceq_lib		sing_1538.htm#IDX586	
classifyci.lib		sing_1540.htm#IDX587	
classifyci_lib		sing_1540.htm#IDX588	
classifyicis		sing_1541.htm#SEC1617	
classpoly		sing_2220.htm#SEC2296	
cleanTmp		sing_2101.htm#SEC2177	
cleanunit		sing_1433.htm#SEC1509	
cleardenom		sing_268.htm#SEC308	
close		sing_269.htm#SEC309	
closed_points		sing_1836.htm#SEC1912	
closetex		sing_1803.htm#SEC1879	
closureFrac		sing_1282.htm#SEC1358	
coHom		sing_810.htm#SEC862	
codim		sing_1634.htm#SEC1710	
codimension		sing_189.htm#SEC229	
coding theory		sing_889.htm#SEC941	
coef		sing_270.htm#SEC310	
coefficient		sing_2131.htm#IDX784	
coefficient 		sing_2132.htm#IDX787	
coefficient  		sing_2133.htm#IDX791	
coefficient field		sing_139.htm#SEC179	
coefficient rings, ring of integers, zero divisors, p-adic numbers	Coefficient rings	sing_32.htm#SEC45	
coefficients, long		sing_848.htm#SEC900	
coeffmod		sing_1898.htm#SEC1974	
coeffs		sing_271.htm#SEC311	
collectDiv		sing_1478.htm#SEC1554	
colrank		sing_1870.htm#SEC1946	
colred		sing_1106.htm#SEC1182	
commRing		sing_841.htm#SEC893	
comma		sing_461.htm#SEC501	
command,custom	Commands for user defined types	sing_181.htm#SEC221	
command-line option, setting value of		sing_406.htm#IDX275	
command-line option, value of		sing_406.htm#IDX273	
command-line options, print all values of		sing_406.htm#IDX272	
command-line options, short help	Command line options	sing_19.htm#IDX38	
commands (plural)		sing_503.htm#IDX296	
comment		sing_36.htm#IDX108	
compareTasks		sing_1070.htm#SEC1146	
completeReduction		sing_1712.htm#SEC1788	
complex		sing_28.htm#IDX75	
complexSingType		sing_1536.htm#SEC1612	
compregb.lib		sing_933.htm#SEC1009	
compregb_lib		sing_933.htm#SEC1009	
comprehensive Groebner system		sing_933.htm#IDX415	
compress		sing_1083.htm#SEC1159	
computeConstant		sing_1181.htm#SEC1257	
computeGromovWitten		sing_1184.htm#SEC1260	
computeN		sing_1482.htm#SEC1558	
computeV		sing_1481.htm#SEC1557	
computemcm		sing_1440.htm#SEC1516	
concat		sing_1084.htm#SEC1160	
conductor		sing_1512.htm#IDX581	
conductor, degree		sing_1596.htm#IDX691	
cone		sing_183.htm#SEC223	
cone 		sing_2144.htm#IDX811	
cone  		sing_2145.htm#IDX813	
cone related functions	cone related functions	sing_186.htm#SEC226	
coneLink		sing_190.htm#SEC230	
coneViaInequalities		sing_185.htm#SEC225	
coneViaPoints		sing_184.htm#SEC224	
conic, parametrization, rational point.		sing_1417.htm#IDX551	
conicWithTangents		sing_2077.htm#SEC2153	
constructH		sing_1441.htm#SEC1517	
constructblwup		sing_1442.htm#SEC1518	
constructlastblwup		sing_1443.htm#SEC1519	
constructor		sing_2161.htm#IDX844	
constructor 		sing_2162.htm#IDX847	
contact matrix		sing_1511.htm#IDX577	
containedQ		sing_1791.htm#SEC1867	
containsAsFace		sing_191.htm#SEC231	
containsInCollection	containsInCollection	sing_223.htm#SEC263	
containsInSupport		sing_192.htm#SEC232	
containsPositiveVector	containsPositiveVector	sing_193.htm#SEC233	
containsRelatively		sing_194.htm#SEC234	
content		sing_1004.htm#SEC1080	
contentSB, option		sing_364.htm#IDX172	
continue	Behavior of continue	sing_429.htm#SEC469	
continue 		sing_463.htm#SEC503	
contraHom		sing_811.htm#SEC863	
contract		sing_272.htm#SEC312	
contributors		sing_406.htm#IDX199	
control		sing_1862.htm#SEC1938	
control.lib		sing_1861.htm#SEC1937	
controlDim		sing_1863.htm#SEC1939	
controlExample		sing_1875.htm#SEC1951	
control_Matrix		sing_1564.htm#SEC1640	
control_lib		sing_1861.htm#SEC1937	
convertdata		sing_1438.htm#SEC1514	
convex geometry		sing_2416.htm#SEC2492	
convexHull		sing_195.htm#SEC235	
convexIntersection		sing_196.htm#SEC236	
convloc		sing_609.htm#SEC661	
coordinate change		sing_2141.htm#IDX808	
coordinate change 		sing_2142.htm#IDX809	
coordinate change  		sing_2143.htm#IDX810	
coordinates		sing_2018.htm#IDX733	
coords		sing_2018.htm#SEC2094	
copyTask		sing_1069.htm#SEC1145	
copyright		sing_1.htm#IDX1	
corank		sing_1523.htm#SEC1599	
cornerMonomials		sing_1319.htm#SEC1395	
countPoints		sing_1943.htm#SEC2019	
coverings		sing_1183.htm#IDX476	
coverings 		sing_1184.htm#IDX480	
cpu		sing_406.htm#IDX201	
cpu 		sing_406.htm#IDX269	
createBO		sing_1469.htm#SEC1545	
createGradedRingHomomorphism	createGradedRingHomomorphism	sing_2356.htm#SEC2432	
createGroup		sing_2349.htm#SEC2425	
createQuotientGroup		sing_2350.htm#SEC2426	
createTask		sing_1067.htm#SEC1143	
createTorsionFreeGroup	createTorsionFreeGroup	sing_2351.htm#SEC2427	
createlist		sing_1451.htm#SEC1527	
crypto.lib		sing_1916.htm#SEC1992	
crypto_lib		sing_1916.htm#SEC1992	
cup		sing_1197.htm#SEC1273	
cupproduct		sing_1198.htm#SEC1274	
curve singularities		sing_1502.htm#IDX564	
curve singularities 		sing_1590.htm#IDX686	
curvepar.lib		sing_1543.htm#SEC1619	
curvepar_lib		sing_1543.htm#SEC1619	
custom assignment	Assignments for user defined types	sing_182.htm#SEC222	
custom command	Commands for user defined types	sing_181.htm#SEC221	
custom type	Definition of a user defined type	sing_178.htm#SEC218	
customstd.so		sing_2467.htm#SEC2543	
cycleLength		sing_2053.htm#SEC2129	
cyclePoints		sing_2057.htm#SEC2133	
cyclic		sing_991.htm#SEC1067	
cyclic code	Codes and the decoding problem	sing_920.htm#SEC979	
cyclotomic		sing_1677.htm#SEC1753	
datetime		sing_273.htm#SEC313	
dbprint		sing_274.htm#SEC314	
deRham.lib		sing_2413.htm#SEC2489	
deRhamCohom		sing_626.htm#SEC678	
deRhamCohomIdeal		sing_627.htm#SEC679	
deRhamCohomology		sing_2414.htm#SEC2490	
deRham_lib		sing_2413.htm#SEC2489	
debugLib, option		sing_364.htm#IDX176	
debug_log		sing_1533.htm#SEC1609	
debugger	Source code debugger	sing_66.htm#SEC103	
debugging library code	Source code debugger	sing_66.htm#SEC103	
dec1var		sing_1250.htm#SEC1326	
decimal		sing_1917.htm#SEC1993	
decode		sing_1853.htm#SEC1929	
decodeCode		sing_1855.htm#SEC1931	
decodeRandom		sing_1854.htm#SEC1930	
decodeRandomFL		sing_1858.htm#SEC1934	
decodeSV		sing_1835.htm#SEC1911	
decodegb.lib		sing_1840.htm#SEC1916	
decodegb_lib		sing_1840.htm#SEC1916	
decoding, decoding problem	Codes and the decoding problem	sing_920.htm#SEC980	
decoef		sing_1883.htm#SEC1959	
decone		sing_2144.htm#IDX812	
decone 		sing_2145.htm#IDX814	
def		sing_83.htm#SEC123	
def declarations		sing_84.htm#SEC124	
defRes, option		sing_364.htm#IDX177	
default argument		sing_44.htm#SEC81	
defineHomogeneous		sing_2389.htm#SEC2465	
defined		sing_275.htm#SEC315	
defl		sing_1400.htm#SEC1476	
deform		sing_1635.htm#SEC1711	
deform.lib		sing_1554.htm#SEC1630	
deform_lib		sing_1554.htm#SEC1630	
defring		sing_1033.htm#SEC1109	
defringp		sing_1035.htm#SEC1111	
defrings		sing_1034.htm#SEC1110	
deg		sing_276.htm#SEC316	
degBound		sing_443.htm#SEC483	
degree	Miscellaneous oddities	sing_277.htm#SEC317	
degree 		sing_466.htm#IDX286	
degree lexicographical ordering		sing_895.htm#IDX389	
degree of a polynomial	Miscellaneous oddities	sing_466.htm#IDX290	
degree reverse lexicographical ordering		sing_895.htm#IDX387	
degreeDivisor		sing_2244.htm#SEC2320	
degreeFormalDivisor		sing_2252.htm#SEC2328	
degreepart		sing_1743.htm#SEC1819	
delete		sing_121.htm#SEC161	
delete 		sing_278.htm#SEC318	
delete  		sing_325.htm#SEC365	
deleteGenerator		sing_641.htm#SEC693	
deleteSublist		sing_941.htm#SEC1017	
delta		sing_1602.htm#SEC1678	
delta invariant		sing_1284.htm#IDX511	
delta invariant 		sing_1602.htm#IDX696	
delta invariant.		sing_1276.htm#IDX504	
delta invariant. 		sing_1277.htm#IDX507	
delta invariant.  		sing_1278.htm#IDX510	
deltaLoc		sing_1284.htm#SEC1360	
denom_list		sing_406.htm#IDX203	
denominator		sing_279.htm#SEC319	
depth		sing_1199.htm#SEC1275	
depthIdeal		sing_1260.htm#SEC1336	
derivate		sing_1709.htm#SEC1785	
derivation		sing_2158.htm#IDX835	
desingularization		sing_2300.htm#IDX887	
desingularization 		sing_2301.htm#SEC2377	
det		sing_280.htm#SEC320	
det_B		sing_1125.htm#SEC1201	
detadj		sing_1618.htm#SEC1694	
determinacy		sing_2412.htm#SEC2488	
determinecenter		sing_1423.htm#SEC1499	
detropicalise		sing_2095.htm#SEC2171	
develop		sing_1592.htm#SEC1668	
diag		sing_1085.htm#SEC1161	
diagInvariants		sing_1298.htm#SEC1374	62096
diag_test		sing_1121.htm#SEC1197	
diff		sing_281.htm#SEC321	
diffRat		sing_840.htm#SEC892	
difpoly2tex		sing_1884.htm#SEC1960	
dim		sing_282.htm#SEC322	
dim (plural)		sing_506.htm#SEC546	
dimGradedPart		sing_1491.htm#SEC1567	11262
dimH		sing_1490.htm#SEC1566	38534
dimMon		sing_1240.htm#SEC1316	
dim_slocus		sing_1636.htm#SEC1712	
dimension		sing_197.htm#SEC237	
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#IDX283	
divideUnits		sing_1880.htm#SEC1956	
dividelist		sing_1450.htm#SEC1526	
division		sing_283.htm#SEC323	
division (plural)		sing_507.htm#SEC547	
division, pdivi, reduce		sing_961.htm#IDX419	
division, reduce		sing_960.htm#IDX418	
divisor		sing_1983.htm#SEC2059	
divisorplus		sing_2238.htm#SEC2314	
divisors	negativeformaldivisor	sing_2237.htm#IDX861	
divisors 		sing_2238.htm#IDX862	
divisors  		sing_2239.htm#IDX863	
divisors   		sing_2240.htm#IDX864	
divisors    		sing_2241.htm#IDX865	
divisors     		sing_2242.htm#IDX866	
divisors      		sing_2243.htm#IDX867	
divisors       		sing_2244.htm#IDX868	
divisors        		sing_2245.htm#IDX869	
divisors         		sing_2246.htm#IDX870	
divisors          		sing_2247.htm#IDX871	
divisors           		sing_2248.htm#IDX872	
divisors            		sing_2249.htm#IDX873	
divisors             		sing_2250.htm#IDX874	
divisors              		sing_2251.htm#IDX875	
divisors               		sing_2252.htm#IDX876	
divisors, polyhedra		sing_2253.htm#IDX877	
divisors, polyhedra 		sing_2254.htm#IDX878	
divisors, polyhedra  		sing_2255.htm#IDX879	
divisors.lib		sing_2236.htm#SEC2312	
divisors_lib		sing_2236.htm#SEC2312	
dmod.lib		sing_589.htm#SEC641	
dmodAction		sing_835.htm#SEC887	
dmodActionRat		sing_836.htm#SEC888	
dmodGeneralAssumptionCheck	dmodGeneralAssumptionCheck	sing_828.htm#SEC880	
dmod_lib		sing_589.htm#SEC641	
dmodapp.lib		sing_612.htm#SEC664	
dmodapp_lib		sing_612.htm#SEC664	
dmodloc.lib		sing_817.htm#IDX371	
dmodloc_lib		sing_817.htm#IDX372	
dmodoublext		sing_812.htm#SEC864	
dmodvar.lib		sing_645.htm#SEC697	
dmodvar_lib		sing_645.htm#SEC697	
double		sing_1988.htm#SEC2064	
doubleExt		sing_803.htm#SEC855	
downloading	Download instructions	sing_2477.htm#SEC2566	
dp, global ordering		sing_895.htm#IDX388	
drawNewtonSubdivision	drawNewtonSubdivision	sing_2073.htm#SEC2149	
drawTropicalCurve		sing_2072.htm#SEC2148	
ds, local ordering		sing_896.htm#IDX398	
dsum		sing_1086.htm#SEC1162	
dualCone		sing_198.htm#SEC238	
dualConic		sing_2097.htm#SEC2173	
dualPart		sing_2228.htm#SEC2304	
dualPolytope		sing_240.htm#SEC280	
dual_code		sing_1837.htm#SEC1913	
dump		sing_284.htm#SEC324	
ecart		sing_1991.htm#SEC2067	
echo		sing_444.htm#SEC484	
eexgcdN		sing_1918.htm#SEC1994	
effective		sing_2246.htm#SEC2322	
egcdMain		sing_1784.htm#SEC1860	
ehrhartPolynomialCoeff	ehrhartPolynomialCoeff	sing_2428.htm#SEC2504	
ehrhartRing		sing_1294.htm#SEC1370	16966
eigenvals		sing_1133.htm#SEC1209	
eigenvalue		sing_377.htm#SEC417	
eigenvalue 		sing_1133.htm#IDX456	
eigenvalues		sing_1377.htm#SEC1453	
elemSymmId		sing_992.htm#SEC1068	
elim		sing_1170.htm#SEC1246	
elim.lib		sing_1167.htm#SEC1243	
elim1		sing_1171.htm#SEC1247	
elim2		sing_1172.htm#SEC1248	
elimRing		sing_1169.htm#SEC1245	
elimWeight		sing_760.htm#SEC812	
elim_lib		sing_1167.htm#SEC1243	
eliminate		sing_285.htm#SEC325	
eliminate (plural)		sing_508.htm#SEC548	
eliminateNC		sing_755.htm#SEC807	
elimination		sing_754.htm#IDX356	
elimlinearpart		sing_1744.htm#SEC1820	
elimpart		sing_1745.htm#SEC1821	
elimpartanyr		sing_1746.htm#SEC1822	
elimrep		sing_1431.htm#SEC1507	
elliptic curve		sing_1180.htm#IDX472	
elliptic curves		sing_1177.htm#IDX466	
elliptic curves 		sing_1183.htm#IDX475	
elliptic curves  		sing_1184.htm#IDX479	
ellipticAdd		sing_1939.htm#SEC2015	
ellipticAllPoints		sing_1944.htm#SEC2020	
ellipticMult		sing_1940.htm#SEC2016	
ellipticNF		sing_2060.htm#SEC2136	
ellipticNFDB		sing_2061.htm#SEC2137	
ellipticRandomCurve		sing_1941.htm#SEC2017	
ellipticRandomPoint		sing_1942.htm#SEC2018	
ellipticcovers.lib		sing_1177.htm#IDX460	
ellipticcovers_lib		sing_1177.htm#IDX461	
else		sing_434.htm#SEC474	
embedMat		sing_786.htm#SEC838	
emptyFan		sing_224.htm#SEC264	
encode		sing_1845.htm#SEC1921	
endomorphism filtration		sing_1576.htm#IDX662	
endvfilt		sing_1576.htm#SEC1652	
engine		sing_642.htm#SEC694	
envelop		sing_969.htm#SEC1045	
envelopdg		sing_970.htm#SEC1046	
envelope		sing_509.htm#SEC549	
enveloping algebra		sing_406.htm#IDX207	
enveloping algebra 		sing_547.htm#IDX300	
environment variable, DISPLAY	The online help system	sing_16.htm#IDX29	
equalJinI		sing_1519.htm#SEC1595	
equalMultiDeg		sing_2382.htm#SEC2458	
equations		sing_199.htm#SEC239	
equiRadical		sing_1335.htm#SEC1411	
equidim		sing_1337.htm#SEC1413	
equidimMax		sing_1338.htm#SEC1414	
equidimMaxEHV		sing_1339.htm#SEC1415	
equidimZ		sing_1350.htm#SEC1426	
equising.lib		sing_1559.htm#SEC1635	
equising_lib		sing_1559.htm#SEC1635	
equisingular Tjurina number		sing_1502.htm#IDX569	
equisingularity ideal		sing_1561.htm#IDX589	
equisingularity stratum		sing_1562.htm#IDX590	
error recovery		sing_15.htm#SEC21	
errorInsert		sing_1848.htm#SEC1924	
errorRand		sing_1849.htm#SEC1925	
errormap		sing_2276.htm#SEC2352	
esIdeal		sing_1561.htm#SEC1637	
esStratum		sing_1562.htm#SEC1638	
essential		sing_2148.htm#IDX817	
essential 		sing_2149.htm#IDX818	
eta		sing_2055.htm#SEC2131	
euler		sing_1897.htm#SEC1973	
eulerChProj		sing_2218.htm#SEC2294	
eval		sing_286.htm#SEC326	
evaluateFormalDivisor	evaluateFormalDivisor	sing_2248.htm#SEC2324	
evaluatePDivisor		sing_2254.htm#SEC2330	
evaluate_reynolds		sing_1682.htm#SEC1758	
evalutateIntegral		sing_1182.htm#SEC1258	
example		sing_288.htm#SEC328	
example 		sing_2150.htm#IDX819	
example  		sing_2151.htm#IDX821	
example   		sing_2152.htm#IDX823	
example    		sing_2153.htm#IDX825	
example     		sing_2154.htm#IDX827	
example      		sing_2155.htm#IDX829	
example       		sing_2156.htm#IDX832	
execute		sing_289.htm#SEC329	
exit		sing_438.htm#SEC478	
exp2pt		sing_1885.htm#SEC1961	
expo		sing_1909.htm#SEC1985	
exponents		sing_2160.htm#IDX840	
export		sing_431.htm#SEC471	
exportNuminvs		sing_1302.htm#SEC1378	10423
exportto		sing_432.htm#SEC472	
expression list		sing_72.htm#IDX128	
expression list 		sing_471.htm#IDX293	
ext-module	purityfiltration_lib	sing_795.htm#IDX362	
extcurve		sing_1831.htm#SEC1907	
extdevelop		sing_1593.htm#SEC1669	
extend		sing_965.htm#SEC1041	
extendWeyl		sing_829.htm#SEC881	
extendedTensor		sing_761.htm#SEC813	
extendring		sing_1036.htm#SEC1112	
extension of rings		sing_1355.htm#IDX518	
exterior basis		sing_1112.htm#IDX453	
exterior power		sing_1114.htm#IDX455	
exteriorBasis		sing_1112.htm#SEC1188	
exteriorPower		sing_1114.htm#SEC1190	
extgcd		sing_290.htm#SEC330	
fVector		sing_227.htm#SEC267	
fVector 		sing_2432.htm#SEC2508	
fVectorP(polymake)		sing_2432.htm#SEC2508	
facFirstShift		sing_748.htm#SEC800	
facFirstWeyl		sing_744.htm#SEC796	
facGBIdeal		sing_1320.htm#SEC1396	
facShift		sing_747.htm#SEC799	
facSubWeyl		sing_746.htm#SEC798	
facWeyl		sing_743.htm#SEC795	
facetVertexLatticeDistances	facetVertexLatticeDistances	sing_2429.htm#SEC2505	
facetWidth		sing_2430.htm#SEC2506	
facetWidths		sing_2431.htm#SEC2507	
facets		sing_200.htm#SEC240	
facstd		sing_291.htm#SEC331	
factmodd		sing_292.htm#SEC332	
factorH		sing_956.htm#SEC1032	
factorLenstraECM		sing_1948.htm#SEC2024	
factorMain		sing_1785.htm#SEC1861	
factorgroup		sing_2372.htm#SEC2448	
factorial		sing_942.htm#SEC1018	
factorization		sing_372.htm#SEC412	
factorization 		sing_1142.htm#IDX457	
factorize		sing_293.htm#SEC333	
factory		sing_1.htm#IDX2	
fan		sing_221.htm#SEC261	
fan 		sing_2044.htm#IDX738	
fan related functions	fan related functions	sing_222.htm#SEC262	
fanViaCones		sing_225.htm#SEC265	
farey		sing_294.htm#SEC334	
fareypoly		sing_2257.htm#SEC2333	
fastExpt		sing_1893.htm#SEC1969	
fastHC, option		sing_364.htm#IDX153	
fastelim		sing_1747.htm#SEC1823	
fetch		sing_295.htm#SEC335	
fetch (plural)		sing_510.htm#SEC550	
fetchall		sing_1037.htm#SEC1113	
ffmodStd		sing_2261.htm#SEC2337	
ffmodstd.lib		sing_2256.htm#SEC2332	
ffmodstd_lib		sing_2256.htm#SEC2332	
ffsolve		sing_1736.htm#SEC1812	
ffsolve.lib		sing_1735.htm#SEC1811	
ffsolve_lib		sing_1735.htm#SEC1811	
fglm		sing_296.htm#SEC336	
fglm 		sing_403.htm#IDX187	
fglm_solve		sing_1763.htm#SEC1839	
fglmquot		sing_297.htm#SEC337	
fibonacci		sing_943.htm#SEC1019	
field		sing_139.htm#SEC179	
file, .singularrc		sing_20.htm#IDX71	
filecmd		sing_298.htm#SEC338	
filtration	purityfiltration_lib	sing_795.htm#IDX363	
finalCharts		sing_1455.htm#SEC1531	
find		sing_299.htm#SEC339	
findAuto		sing_702.htm#SEC754	
findInvo		sing_700.htm#SEC752	
findInvoDiag		sing_701.htm#SEC753	
findOrientedBoundary	findOrientedBoundary	sing_2056.htm#SEC2132	
findTorsion		sing_1874.htm#SEC1950	
find_first_primitive_root	find_first_primitive_root	sing_1952.htm#SEC2028	
find_index		sing_1956.htm#SEC2032	
findifs.lib		sing_1881.htm#SEC1957	
findifs_example		sing_1882.htm#SEC1958	
findifs_lib		sing_1881.htm#SEC1957	
findimAlgebra		sing_770.htm#SEC822	
finduni		sing_300.htm#SEC340	
findvars		sing_1748.htm#SEC1824	
finite field		sing_139.htm#SEC179	
finite field 		sing_1735.htm#IDX711	
finiteDiagInvariants	finiteDiagInvariants	sing_1297.htm#SEC1373	3508
finitediff.lib		sing_2262.htm#IDX880	
finitediff_lib		sing_2262.htm#IDX881	
finitenessTest		sing_1156.htm#SEC1232	
finvar.lib		sing_1670.htm#SEC1746	
finvar_lib		sing_1670.htm#SEC1746	
first index is 1		sing_465.htm#SEC505	
firstoct		sing_1796.htm#SEC1872	
fitting		sing_1202.htm#SEC1278	
fl2poly		sing_639.htm#SEC691	
flatten		sing_1087.htm#SEC1163	
flatteningStrat		sing_1203.htm#SEC1279	
floating point		sing_1046.htm#IDX439	
for		sing_433.htm#SEC473	
formaldivisorplus		sing_2249.htm#SEC2325	
forward		sing_2268.htm#SEC2344	
fourier		sing_634.htm#SEC686	
fouriersystem		sing_2279.htm#SEC2355	
fpadim.lib		sing_650.htm#SEC702	
fpadim_lib		sing_650.htm#SEC702	
fprintf		sing_301.htm#SEC341	
frandwalk		sing_2404.htm#SEC2480	
free		sing_2159.htm#IDX837	
free 		sing_2160.htm#IDX839	
free associative algebra, tensor algebra	Free associative algebras	sing_541.htm#SEC593	
freeGBasis		sing_685.htm#SEC737	
freegb.lib		sing_681.htm#SEC733	
freegb_lib		sing_681.htm#SEC733	
freemodule		sing_302.htm#SEC342	
freerank		sing_994.htm#SEC1070	
from_boolean_constant	from_boolean_constant	sing_2117.htm#SEC2193	44881
from_boolean_ideal		sing_2121.htm#SEC2197	62698
from_boolean_poly		sing_2118.htm#SEC2194	27864
from_boolean_set		sing_2122.htm#SEC2198	60615
frwalk		sing_303.htm#SEC343	
fullFan		sing_226.htm#SEC266	
fullSerreRelations		sing_696.htm#SEC748	
furtherInvar		sing_1714.htm#SEC1790	
further_hn_proc		sing_1610.htm#SEC1686	
fwalk		sing_1189.htm#SEC1265	
galois field		sing_139.htm#SEC179	
gauss_col		sing_1097.htm#SEC1173	
gauss_nf		sing_1128.htm#SEC1204	
gauss_row		sing_1098.htm#SEC1174	
gaussred		sing_1126.htm#SEC1202	
gaussred_pivot		sing_1127.htm#SEC1203	
gcd		sing_304.htm#SEC344	
gcdMon		sing_1229.htm#SEC1305	
gcddivisor		sing_1984.htm#SEC2060	
gen		sing_305.htm#SEC345	
genMDSMat		sing_1851.htm#SEC1927	
genSymId		sing_1374.htm#SEC1450	
general error-locator polynomial		sing_921.htm#SEC986	
general neron.		sing_2300.htm#IDX888	
general weighted lexicographical ordering		sing_896.htm#IDX404	
general weighted reverse lexicographical ordering	Local orderings	sing_896.htm#IDX401	
general.lib		sing_936.htm#SEC1012	
generalOrder		sing_2009.htm#SEC2085	
general_lib		sing_936.htm#SEC1012	
generateG		sing_1947.htm#SEC2023	
generators		sing_1510.htm#IDX573	
generatorsOfLinealitySpace	generatorsOfLinealitySpace	sing_201.htm#SEC241	
generatorsOfSpan		sing_202.htm#SEC242	
genericid		sing_1012.htm#SEC1088	
genericity		sing_1871.htm#SEC1947	
genericmat		sing_1088.htm#SEC1164	
genoutput		sing_1444.htm#SEC1520	
genus		sing_1280.htm#SEC1356	
geometric invariant theory		sing_2293.htm#IDX885	
geometrical locus, locus, loci, dynamic geometry		sing_968.htm#IDX423	
geometrical locus, locus, loci, envelop		sing_969.htm#IDX424	
geometrical locus, locus, loci, envelop.		sing_970.htm#IDX425	
geometrical locus, locus, loci.		sing_967.htm#IDX422	
geometrical locus, locus, loci. 		sing_971.htm#IDX426	
getArguments		sing_1078.htm#SEC1154	
getCommand		sing_1077.htm#SEC1153	
getCone		sing_228.htm#SEC268	
getGradingGroup		sing_2347.htm#SEC2423	
getLattice		sing_2348.htm#SEC2424	
getLinearForms		sing_203.htm#SEC243	
getModuleGrading		sing_2358.htm#SEC2434	
getMultiplicity		sing_204.htm#SEC244	
getOneVar		sing_1288.htm#SEC1364	
getResult		sing_1079.htm#SEC1155	
getSmallest		sing_1287.htm#SEC1363	
getState		sing_1080.htm#SEC1156	
getVariableWeights		sing_2346.htm#SEC2422	
getcores		sing_1027.htm#SEC1103	
getdump		sing_306.htm#SEC346	
getenv		sing_406.htm#IDX210	
gfanlib		sing_1.htm#IDX9	
gfanlib_so		sing_2417.htm#IDX903	
gitCone		sing_2295.htm#SEC2371	
gitFan		sing_2296.htm#SEC2372	
gitfan		sing_2293.htm#IDX883	
gitfan.lib		sing_2293.htm#SEC2369	
gitfan_lib		sing_2293.htm#SEC2369	
gkdim.lib		sing_707.htm#SEC759	
gkdim_lib		sing_707.htm#SEC759	
gkzFan		sing_2297.htm#SEC2373	
global		sing_261.htm#IDX133	
global Bernstein-Sato polynomial		sing_554.htm#IDX307	
global Bernstein-Sato polynomial 		sing_589.htm#IDX325	
global Bernstein-Sato polynomial for variety		sing_645.htm#IDX350	
globalSections		sing_2243.htm#SEC2319	
gmscoeffs		sing_1568.htm#SEC1644	
gmsnf		sing_1567.htm#SEC1643	
gmspoly.lib		sing_1587.htm#SEC1663	
gmspoly_lib		sing_1587.htm#SEC1663	
gmsring		sing_1566.htm#SEC1642	
gmssing.lib		sing_1565.htm#SEC1641	
gmssing_lib		sing_1565.htm#SEC1641	
good basis		sing_1565.htm#IDX601	
good basis 		sing_1575.htm#IDX656	
good basis  		sing_1587.htm#IDX672	
good basis   		sing_1589.htm#IDX683	
goodBasis		sing_1589.htm#SEC1665	
gorensteinIndex		sing_2433.htm#SEC2509	
gorensteinVector		sing_2434.htm#SEC2510	
graal.lib		sing_2286.htm#SEC2362	
graalMixed		sing_2287.htm#SEC2363	
graal_lib		sing_2286.htm#SEC2362	
gradeNumber		sing_799.htm#SEC851	
graded Weyl algebra		sing_554.htm#IDX310	
graded module, graded piece		sing_1491.htm#IDX559	
graded modules, graded homomorphisms, syzygies	gradedModules_lib	sing_2302.htm#IDX889	
graded modules, handling of	Handling graded modules	sing_863.htm#SEC915	
gradedModules.lib		sing_2302.htm#SEC2378	
gradedModules_lib		sing_2302.htm#SEC2378	
gradiator		sing_2391.htm#SEC2467	
graph		sing_1178.htm#IDX470	
graph 		sing_1179.htm#IDX471	
graphics.lib		sing_1798.htm#SEC1874	
graphics_lib		sing_1798.htm#SEC1874	
graphviz		sing_1.htm#IDX13	
graver4ti2		sing_1372.htm#SEC1448	39635
grconcat		sing_2325.htm#SEC2401	
grdeg		sing_2305.htm#SEC2381	
grgens		sing_2314.htm#SEC2390	
grgroebner		sing_2324.htm#SEC2400	
grlift		sing_2322.htm#SEC2398	
grlifting		sing_2329.htm#SEC2405	
grlifting2		sing_2330.htm#SEC2406	
grlifting3		sing_2332.htm#SEC2408	
grneg		sing_2335.htm#SEC2411	
grobcov		sing_958.htm#SEC1034	
grobcov.lib		sing_957.htm#SEC1033	
grobcov_lib		sing_957.htm#SEC1033	
grobj		sing_2303.htm#SEC2379	
groebner		sing_307.htm#SEC347	
groebner 		sing_855.htm#SEC907	
groebner basis computations		sing_307.htm#IDX147	
groebnerComplex		sing_2424.htm#SEC2500	
groebnerCone		sing_2420.htm#SEC2496	
groebnerFan		sing_2422.htm#SEC2498	
groebnerFanP		sing_2049.htm#SEC2125	
gromovWitten		sing_1183.htm#SEC1259	
grorder		sing_2316.htm#SEC2392	
ground field		sing_139.htm#SEC179	
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	
help browsers, dummy	The online help system	sing_16.htm#IDX25	
help browsers, dummy 		sing_16.htm#IDX27	
help browsers, emacs	The online help system	sing_16.htm#IDX26	
help browsers, html	The online help system	sing_16.htm#IDX23	
help browsers, setting command to use	The online help system	sing_16.htm#IDX30	
help browsers, setting the		sing_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_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_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_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_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_473.htm#SEC513	
ideal expressions		sing_87.htm#SEC127	
ideal expressions (plural)	ideal expressions (plural)	sing_474.htm#SEC514	
ideal operations		sing_88.htm#SEC128	
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_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_1426.htm#SEC1502	
if		sing_434.htm#SEC474	
imageLattice		sing_2360.htm#SEC2436	
image_of_variety		sing_1706.htm#SEC1782	
imap		sing_313.htm#SEC353	
imap (plural)		sing_511.htm#SEC551	
imapall		sing_1038.htm#SEC1114	
impart		sing_314.htm#SEC354	
importfrom		sing_435.htm#SEC475	
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#IDX154	
info	The online help system	sing_16.htm#SEC23	
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_121.htm#SEC161	
insert 		sing_316.htm#SEC356	
insertCone		sing_229.htm#SEC269	
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	
int expressions		sing_92.htm#SEC132	
int operations		sing_93.htm#SEC133	
int related functions	int related functions	sing_94.htm#SEC134	
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_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_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	
intmat expressions		sing_99.htm#SEC139	
intmat operations		sing_101.htm#SEC141	
intmat related functions	intmat related functions	sing_102.htm#SEC142	
intmat type cast		sing_100.htm#SEC140	
intmat2mons		sing_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	
intvec expressions		sing_105.htm#SEC145	
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_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_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_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_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_2378.htm#SEC2454	
isPrimitiveSublattice	isPrimitiveSublattice	sing_2368.htm#SEC2444	
isPure		sing_231.htm#SEC271	
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_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_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_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_513.htm#SEC553	
keepring		sing_436.htm#SEC476	
kernel		sing_324.htm#SEC364	
kernelLattice		sing_2362.htm#SEC2438	
kill		sing_325.htm#SEC365	
killTask		sing_1068.htm#SEC1144	
killall		sing_945.htm#SEC1021	
killattrib		sing_326.htm#SEC366	
kmemory		sing_944.htm#SEC1020	
kohom		sing_1211.htm#SEC1287	
kontrahom		sing_1212.htm#SEC1288	
koszul		sing_327.htm#SEC367	
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_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_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_2108.htm#IDX755	
library 		sing_2293.htm#IDX882	
library, info string		sing_55.htm#IDX124	
library, polybori.lib		sing_2108.htm#IDX752	
library, template		sing_55.htm#SEC92	
library, template.lib		sing_55.htm#IDX122	
lieBracket		sing_694.htm#SEC746	
lift		sing_334.htm#SEC374	
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_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	
linear algebra		sing_262.htm#SEC302	
linear algebra 		sing_338.htm#SEC378	
linear algebra  		sing_339.htm#SEC379	
linear algebra   		sing_340.htm#SEC380	
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_852.htm#SEC904	
link declarations		sing_109.htm#SEC149	
link expressions		sing_110.htm#SEC150	
link related functions	link related functions	sing_111.htm#SEC151	
list		sing_118.htm#SEC158	
list declarations		sing_119.htm#SEC159	
list expressions		sing_120.htm#SEC160	
list operations		sing_121.htm#SEC161	
list related functions	list related functions	sing_122.htm#SEC162	
listvar		sing_336.htm#SEC376	
lll		sing_2395.htm#SEC2471	
load		sing_437.htm#SEC477	
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_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_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_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	
makeFormalDivisor		sing_2247.htm#SEC2323	
makeGraph		sing_1178.htm#SEC1254	
makeHeisenberg		sing_768.htm#SEC820	
makeLetterplaceRing		sing_682.htm#SEC734	
makeMalgrange		sing_649.htm#SEC701	
makeModElimRing		sing_785.htm#SEC837	
makePDivisor		sing_2253.htm#SEC2329	
makeQsl2		sing_732.htm#SEC784	
makeQsl3		sing_733.htm#SEC785	
makeQso3		sing_731.htm#SEC783	
makeUe6		sing_728.htm#SEC780	
makeUe7		sing_729.htm#SEC781	
makeUe8		sing_730.htm#SEC782	
makeUf4		sing_727.htm#SEC779	
makeUg2		sing_726.htm#SEC778	
makeUgl		sing_712.htm#SEC764	
makeUsl		sing_711.htm#SEC763	
makeUsl2		sing_710.htm#SEC762	
makeUso10		sing_718.htm#SEC770	
makeUso11		sing_719.htm#SEC771	
makeUso12		sing_720.htm#SEC772	
makeUso5		sing_713.htm#SEC765	
makeUso6		sing_714.htm#SEC766	
makeUso7		sing_715.htm#SEC767	
makeUso8		sing_716.htm#SEC768	
makeUso9		sing_717.htm#SEC769	
makeUsp1		sing_721.htm#SEC773	
makeUsp2		sing_722.htm#SEC774	
makeUsp3		sing_723.htm#SEC775	
makeUsp4		sing_724.htm#SEC776	
makeUsp5		sing_725.htm#SEC777	
makeWeyl		sing_767.htm#SEC819	
map		sing_123.htm#SEC163	
map (plural)		sing_477.htm#SEC517	
map declarations		sing_124.htm#SEC164	
map declarations (plural)	map declarations (plural)	sing_478.htm#SEC518	
map expressions		sing_125.htm#SEC165	
map expressions (plural)	map expressions (plural)	sing_479.htm#SEC519	
map operations		sing_126.htm#IDX129	
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	
mapIsFinite		sing_1155.htm#SEC1231	
mapToRatNormCurve		sing_1414.htm#SEC1490	
mapall		sing_1039.htm#SEC1115	
mappingcone		sing_2331.htm#SEC2407	
mappingcone3		sing_2333.htm#SEC2409	
markov4ti2		sing_1370.htm#SEC1446	9163
mat2arr		sing_2131.htm#SEC2207	
mat2carr		sing_2132.htm#SEC2208	
mat_rk		sing_1129.htm#SEC1205	
matbil		sing_2015.htm#SEC2091	
mathematical objects	Representation of mathematical objects	sing_891.htm#SEC943	
mathinit		sing_1800.htm#SEC1876	
matmult		sing_2016.htm#SEC2092	
matrix		sing_128.htm#SEC168	
matrix 		sing_2131.htm#IDX783	
matrix  		sing_2132.htm#IDX786	
matrix   		sing_2133.htm#IDX790	
matrix declarations		sing_129.htm#SEC169	
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_1082.htm#SEC1158	
matrixExp		sing_1404.htm#SEC1480	
matrixLog		sing_1405.htm#SEC1481	
matrixT1		sing_1656.htm#SEC1732	
matrix_lib		sing_1082.htm#SEC1158	
matrixpres		sing_2336.htm#SEC2412	
matrixsystem		sing_2277.htm#SEC2353	
max		sing_341.htm#SEC381	
maxEord		sing_1429.htm#SEC1505	
maxExp		sing_261.htm#IDX136	
maxIntRoot		sing_834.htm#SEC886	
maxZeros		sing_1407.htm#SEC1483	
maxabs		sing_2034.htm#SEC2110	
maxcoef		sing_997.htm#SEC1073	
maxdeg		sing_998.htm#SEC1074	
maxdeg1		sing_999.htm#SEC1075	
maxideal		sing_342.htm#SEC382	
maximalFace		sing_2453.htm#SEC2529	
maximalGroebnerCone		sing_2421.htm#SEC2497	
maximalValue		sing_2454.htm#SEC2530	
maximum		sing_1907.htm#SEC1983	
maximum number of zeroes		sing_1407.htm#IDX538	
mdouble		sing_56.htm#SEC93	
mem, option		sing_364.htm#IDX180	
membershipMon		sing_1231.htm#SEC1307	
memory		sing_343.htm#SEC383	
memory managment		sing_343.htm#SEC383	
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	
milnornumber		sing_2411.htm#SEC2487	
min		sing_344.htm#SEC384	
minAssChar		sing_1329.htm#SEC1405	
minAssCharE		sing_1330.htm#SEC1406	
minAssGTZ		sing_1327.htm#SEC1403	
minAssGTZE		sing_1328.htm#SEC1404	
minAssZ		sing_1347.htm#SEC1423	
minEcart		sing_1997.htm#SEC2073	
minIntRoot		sing_610.htm#SEC662	
minIntRoot2		sing_833.htm#SEC885	
minMult		sing_1162.htm#SEC1238	
minbase		sing_345.htm#SEC385	
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	
minimalFace		sing_2455.htm#SEC2531	
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_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_1005.htm#SEC1081	
mod2str		sing_692.htm#SEC744	
modDec		sing_1247.htm#SEC1323	
modNPos		sing_1270.htm#SEC1346	
modNormal		sing_1223.htm#SEC1299	
modNpos_test		sing_1268.htm#SEC1344	
modStd		sing_1225.htm#SEC1301	
modWalk		sing_2340.htm#SEC2416	
mod_versal		sing_1556.htm#SEC1632	
modality		sing_1535.htm#SEC1611	
modfWalk		sing_2342.htm#SEC2418	
modfrWalk		sing_2343.htm#SEC2419	
modnormal.lib		sing_1222.htm#SEC1298	
modnormal_lib		sing_1222.htm#SEC1298	
modrWalk		sing_2341.htm#SEC2417	
modregCM		sing_1274.htm#SEC1350	
modsatiety		sing_1272.htm#SEC1348	
modstd.lib		sing_1224.htm#SEC1300	
modstd_lib		sing_1224.htm#SEC1300	
modular		sing_983.htm#SEC1059	
modular methods		sing_1220.htm#IDX494	
modular methods 		sing_1222.htm#IDX499	
modular methods.		sing_1221.htm#IDX497	
modular techniques.		sing_1223.htm#IDX501	
modular.lib		sing_982.htm#SEC1058	
modular_lib		sing_982.htm#SEC1058	
modular_lib 		sing_982.htm#IDX427	
module		sing_134.htm#SEC174	
module (plural)		sing_482.htm#SEC522	
module declarations		sing_135.htm#SEC175	
module declarations (plural)	module declarations (plural)	sing_483.htm#SEC523	
module expressions		sing_136.htm#SEC176	
module expressions (plural)	module expressions (plural)	sing_484.htm#SEC524	
module operations		sing_137.htm#SEC177	
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_486.htm#SEC526	
module_containment		sing_1147.htm#SEC1223	
modulo		sing_348.htm#SEC388	
modulo (plural)		sing_517.htm#SEC557	
moduloSlim		sing_775.htm#SEC827	
modwalk.lib		sing_2339.htm#IDX890	
modwalk_lib		sing_2339.htm#IDX891	
moebius		sing_2167.htm#SEC2243	
moebius function		sing_2167.htm#IDX856	
molien		sing_1679.htm#SEC1755	
mondromy.lib		sing_1617.htm#SEC1693	
mondromy_lib		sing_1617.htm#SEC1693	
monitor		sing_349.htm#SEC389	
monodromy		sing_1565.htm#IDX598	
monodromy 		sing_1570.htm#SEC1646	
monodromy  		sing_1570.htm#IDX618	
monodromy   		sing_1575.htm#IDX653	
monodromy    		sing_1587.htm#IDX669	
monodromy     		sing_1589.htm#IDX680	
monodromyB		sing_1621.htm#SEC1697	
monomial		sing_350.htm#SEC390	
monomial ordering		sing_1048.htm#IDX441	
monomial orderings	General definitions for orderings	sing_847.htm#SEC899	
monomial orderings 		sing_894.htm#SEC946	
monomial orderings introduction	Introduction to orderings	sing_893.htm#SEC945	
monomialInIdeal		sing_831.htm#SEC883	
monomialLcm		sing_1995.htm#SEC2071	
monomialideal.lib		sing_1226.htm#SEC1302	
monomialideal_lib		sing_1226.htm#SEC1302	
monomials and precedence	Miscellaneous oddities	sing_466.htm#IDX284	
mons2intmat		sing_1314.htm#SEC1390	15555
morsesplit		sing_1528.htm#SEC1604	
mp_res_mat		sing_1761.htm#SEC1837	
mplot		sing_1801.htm#SEC1877	
mpresmat		sing_351.htm#SEC391	
mprimdec.lib		sing_1243.htm#SEC1319	
mprimdec_lib		sing_1243.htm#SEC1319	
mregular.lib		sing_1258.htm#SEC1334	
mregular_lib		sing_1258.htm#SEC1334	
mres		sing_352.htm#SEC392	
mres (plural)		sing_518.htm#SEC558	
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#IDX285	
multBound		sing_446.htm#SEC486	
multRat		sing_839.htm#SEC891	
multarr2arr		sing_2162.htm#SEC2238	
multarrMultRestrict		sing_2164.htm#SEC2240	
multarrRestrict		sing_2163.htm#SEC2239	
multcol		sing_1101.htm#SEC1177	
multdivisor		sing_2239.htm#SEC2315	
multformaldivisor		sing_2251.htm#SEC2327	
multi		sing_1982.htm#SEC2058	
multi indices		sing_37.htm#SEC65	
multiDeg		sing_2374.htm#SEC2450	
multiDegBasis		sing_2375.htm#SEC2451	
multiDegGroebner		sing_2383.htm#SEC2459	
multiDegModulo		sing_2385.htm#SEC2461	
multiDegPartition		sing_2376.htm#SEC2452	
multiDegResolution		sing_2386.htm#SEC2462	
multiDegSyzygy		sing_2384.htm#SEC2460	
multiDegTensor		sing_2387.htm#SEC2463	
multiDegTor		sing_2388.htm#SEC2464	
multiarrangement		sing_2158.htm#IDX836	
multiarrangement 		sing_2159.htm#IDX838	
multiarrangement  		sing_2160.htm#IDX841	
multiarrangement   		sing_2161.htm#IDX842	
multiarrangement    		sing_2162.htm#IDX845	
multiarrangement     		sing_2163.htm#IDX848	
multiarrangement      		sing_2164.htm#IDX850	
multidimensional_knapsack	multidimensional_knapsack	sing_1960.htm#SEC2036	
multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra	multigrading_lib	sing_2344.htm#IDX894	
multigrading.lib		sing_2344.htm#IDX892	
multigrading_lib		sing_2344.htm#IDX893	
multiplicities, sequence of		sing_1596.htm#IDX692	
multiplicity sequence		sing_1509.htm#IDX571	
multiplicity sequence 		sing_1512.htm#IDX583	
multiplicity sequence  		sing_1598.htm#IDX693	
multiplylist		sing_1449.htm#SEC1525	
multivariate equations		sing_1735.htm#IDX710	
multrow		sing_1102.htm#SEC1178	
multseq2charexp		sing_1508.htm#SEC1584	
multsequence		sing_1598.htm#SEC1674	
nBoundaryLatticePoints	nBoundaryLatticePoints	sing_2458.htm#SEC2534	
nHilbertBasis		sing_2459.htm#SEC2535	
nInteriorLatticePoints	nInteriorLatticePoints	sing_2460.htm#SEC2536	
nLatticePoints		sing_2461.htm#SEC2537	
naccache_stern_decryption	naccache_stern_decryption	sing_1963.htm#SEC2039	
naccache_stern_encryption	naccache_stern_encryption	sing_1962.htm#SEC2038	
naccache_stern_generation	naccache_stern_generation	sing_1961.htm#SEC2037	
nameof		sing_355.htm#SEC395	
names		sing_356.htm#SEC396	
nashmult		sing_1516.htm#SEC1592	
nblocks		sing_406.htm#IDX220	
ncExt_R		sing_808.htm#SEC860	
ncHom		sing_809.htm#SEC861	
ncRelations		sing_776.htm#SEC828	
nc_algebra		sing_519.htm#SEC559	
ncalg.lib		sing_709.htm#SEC761	
ncalg_lib		sing_709.htm#SEC761	
ncalgebra		sing_520.htm#SEC560	
ncdecomp.lib		sing_736.htm#SEC788	
ncdecomp_lib		sing_736.htm#SEC788	
ncdetection		sing_703.htm#SEC755	
ncfactor		sing_742.htm#SEC794	
ncfactor.lib		sing_741.htm#SEC793	
ncfactor_lib		sing_741.htm#SEC793	
nchomolog.lib		sing_807.htm#IDX367	
nchomolog_lib		sing_807.htm#IDX368	
ncols		sing_357.htm#SEC397	
ncones		sing_233.htm#SEC273	
ncpreim.lib		sing_754.htm#SEC806	
ncpreim_lib		sing_754.htm#SEC806	
nctools.lib		sing_762.htm#SEC814	
nctools_lib		sing_762.htm#SEC814	
ndcond		sing_765.htm#SEC817	
negatedCone		sing_211.htm#SEC251	
negative degree lexicographical ordering		sing_896.htm#IDX399	
negative degree reverse lexicographical ordering	Local orderings	sing_896.htm#IDX397	
negative lexicographical ordering		sing_896.htm#IDX395	
negativedivisor		sing_2240.htm#SEC2316	
negativeformaldivisor	negativeformaldivisor	sing_2250.htm#SEC2326	
net access	Command line options	sing_19.htm#IDX40	
newTest		sing_1902.htm#SEC1978	
newline		sing_166.htm#SEC206	
news		sing_2470.htm#SEC2546	
newstruct		sing_177.htm#SEC217	
newstruct 		sing_2108.htm#IDX757	
newtonDiag		sing_1009.htm#SEC1085	
newtonPolytope		sing_241.htm#SEC281	
newtonPolytopeLP		sing_2047.htm#SEC2123	
newtonPolytopeP		sing_2046.htm#SEC2122	
newtonpoly		sing_1603.htm#SEC1679	
nf_icis		sing_1644.htm#SEC1720	
nfmodStd		sing_2398.htm#SEC2474	
nfmodSyz		sing_2400.htm#SEC2476	
nfmodstd.lib		sing_2396.htm#SEC2472	
nfmodstd_lib		sing_2396.htm#SEC2472	
nfmodsyz.lib		sing_2399.htm#SEC2475	
nfmodsyz_lib		sing_2399.htm#SEC2475	
nilpotent Lie algebras		sing_1402.htm#IDX523	
nmaxcones		sing_232.htm#SEC272	
noether		sing_447.htm#SEC487	
noether.lib		sing_1266.htm#SEC1342	
noetherNormal		sing_1154.htm#SEC1230	
noether_lib		sing_1266.htm#SEC1342	
non-english special characters		sing_455.htm#IDX280	
nonMonomials		sing_1318.htm#SEC1394	
nonZeroEntry		sing_1157.htm#SEC1233	
none, option		sing_364.htm#IDX150	
norTest		sing_1286.htm#SEC1362	
norm		sing_1981.htm#SEC2057	
normal		sing_1276.htm#SEC1352	
normal.lib		sing_1275.htm#SEC1351	
normalC		sing_1278.htm#SEC1354	
normalFan		sing_2462.htm#SEC2538	
normalFanL		sing_2048.htm#SEC2124	
normalForm		sing_2241.htm#SEC2317	
normalI		sing_1362.htm#SEC1438	
normalP		sing_1277.htm#SEC1353	
normalToricRing		sing_1292.htm#SEC1368	29638
normalToricRingFromBinomials	normalToricRingFromBinomials	sing_1293.htm#SEC1369	2301
normal_lib		sing_1275.htm#SEC1351	
normalform		sing_1532.htm#SEC1608	
normaliz		sing_1.htm#IDX14	18426
normaliz 		sing_1305.htm#SEC1381	
normaliz.lib		sing_1290.htm#SEC1366	
normaliz_lib		sing_1290.htm#SEC1366	
normalization		sing_1220.htm#IDX492	
normalization 		sing_1221.htm#IDX495	
normalization  		sing_1222.htm#IDX498	
normalization   		sing_1223.htm#IDX500	
normalization    		sing_1276.htm#IDX502	
normalization     		sing_1277.htm#IDX505	
normalization      		sing_1278.htm#IDX508	
normalization       		sing_1290.htm#IDX514	
normalization.		sing_1217.htm#IDX491	
normalization. 		sing_1409.htm#IDX545	
normalize		sing_1002.htm#SEC1078	
not		sing_96.htm#SEC136	
notBuckets, option		sing_364.htm#IDX160	
notRegularity, option		sing_364.htm#IDX158	
notSugar, option		sing_364.htm#IDX159	
notWarnSB, option		sing_364.htm#IDX181	
npar		sing_1887.htm#SEC1963	
npars		sing_358.htm#SEC398	
nrRootsDeterm		sing_2012.htm#SEC2088	
nrRootsProbab		sing_2011.htm#SEC2087	
nres		sing_359.htm#SEC399	
nres (plural)		sing_521.htm#SEC561	
nrows		sing_360.htm#SEC400	
nrroots		sing_2041.htm#SEC2117	
nsatiety		sing_1271.htm#SEC1347	
nselect		sing_1173.htm#SEC1249	
nt_solve		sing_1776.htm#SEC1852	
ntsolve.lib		sing_1775.htm#SEC1851	
ntsolve_lib		sing_1775.htm#SEC1851	
number		sing_139.htm#SEC179	
number 		sing_2135.htm#IDX796	
number declarations		sing_140.htm#SEC180	
number expressions		sing_141.htm#SEC181	
number operations		sing_142.htm#SEC182	
number related functions	number related functions	sing_143.htm#SEC183	
numberOfConesOfDimension	numberOfConesOfDimension	sing_234.htm#SEC274	
number_e		sing_946.htm#SEC1022	
number_pi		sing_947.htm#SEC1023	
numerAlg.lib		sing_1384.htm#IDX519	
numerAlg_lib		sing_1384.htm#IDX520	
numerDecom.lib		sing_1389.htm#IDX521	
numerDecom_lib		sing_1389.htm#IDX522	
numerator		sing_361.htm#SEC401	
nvars		sing_362.htm#SEC402	
oneDimBelongSemigroup	oneDimBelongSemigroup	sing_1164.htm#SEC1240	
online help	The online help system	sing_16.htm#SEC22	
open		sing_363.htm#SEC403	
opentex		sing_1804.htm#SEC1880	
operatorBM		sing_596.htm#SEC648	
operatorModulo		sing_597.htm#SEC649	
oppose		sing_522.htm#SEC562	
opposite		sing_523.htm#SEC563	
opposite polynomial		sing_406.htm#IDX227	
opposite ring		sing_406.htm#IDX224	
option		sing_364.htm#SEC404	
option(warn)		sing_70.htm#SEC110	
optionIsSet		sing_1045.htm#SEC1121	
or	Evaluation of logical expressions	sing_96.htm#SEC136	
or 		sing_459.htm#SEC499	
orbit		sing_1402.htm#IDX525	
orbit 		sing_1403.htm#IDX529	
orbit  		sing_1406.htm#IDX534	
orbit   		sing_1407.htm#IDX537	
orbitCones		sing_2299.htm#SEC2375	
orbit_variety		sing_1703.htm#SEC1779	
orbitparam.lib		sing_1402.htm#SEC1478	
orbitparam_lib		sing_1402.htm#SEC1478	
ord		sing_365.htm#SEC405	
ord_test		sing_1040.htm#SEC1116	
orderings	General definitions for orderings	sing_894.htm#SEC946	
orderings introduction	Introduction to orderings	sing_893.htm#SEC945	
orderings, M		sing_898.htm#SEC950	
orderings, a		sing_900.htm#SEC952	
orderings, global		sing_895.htm#SEC947	
orderings, local		sing_896.htm#SEC948	
orderings, product		sing_899.htm#SEC951	
ordstr		sing_366.htm#SEC406	
orthogonalize		sing_1120.htm#SEC1196	
outer		sing_1090.htm#SEC1166	
output		sing_41.htm#SEC71	
p-adic numbers		sing_32.htm#SEC46	
pFactor		sing_1936.htm#SEC2012	
pIntersect		sing_560.htm#SEC612	
pIntersectSyz		sing_561.htm#SEC613	
package		sing_144.htm#SEC184	
package declarations	package declarations	sing_145.htm#SEC185	
package related functions	package related functions	sing_146.htm#SEC186	
pairset		sing_2001.htm#SEC2077	
par		sing_367.htm#SEC407	
par2varRing		sing_930.htm#SEC1006	
paraConic		sing_1417.htm#SEC1493	
paraPlaneCurve		sing_1411.htm#SEC1487	
parallel skeletons		sing_984.htm#IDX433	
parallel.lib		sing_984.htm#SEC1060	
parallelTestAND		sing_988.htm#SEC1064	
parallelTestOR		sing_989.htm#SEC1065	
parallelWaitAll		sing_987.htm#SEC1063	
parallelWaitFirst		sing_986.htm#SEC1062	
parallelWaitN		sing_985.htm#SEC1061	
parallel_lib		sing_984.htm#SEC1060	
parallelization		sing_984.htm#IDX432	
parallelization 		sing_1024.htm#IDX435	
parallelization  		sing_1066.htm#IDX449	
param		sing_1594.htm#SEC1670	
parameter, as numbers		sing_139.htm#SEC179	
parameterSubstitute		sing_2098.htm#SEC2174	
parametric annihilator		sing_589.htm#IDX329	
parametric annihilator for variety		sing_645.htm#IDX352	
parametrization		sing_1402.htm#IDX526	
parametrization 		sing_1406.htm#IDX535	
parametrization  		sing_1594.htm#IDX687	
parametrizeOrbit		sing_1406.htm#SEC1482	
paraplanecurves.lib		sing_1408.htm#SEC1484	
paraplanecurves_lib		sing_1408.htm#SEC1484	
pardeg		sing_368.htm#SEC408	
parstr		sing_369.htm#SEC409	
part		sing_2227.htm#SEC2303	
partOver		sing_2230.htm#SEC2306	
partUnder		sing_2231.htm#SEC2307	
partial_molien		sing_1681.htm#SEC1757	
partitions		sing_1185.htm#SEC1261	
partitions 		sing_1185.htm#IDX482	
path integral		sing_1177.htm#IDX469	
pause		sing_981.htm#SEC1057	
pdivi		sing_960.htm#SEC1036	
pdivisorplus		sing_2255.htm#SEC2331	
permcol		sing_1103.htm#SEC1179	
permrow		sing_1104.htm#SEC1180	
permutations		sing_1186.htm#IDX483	
permute		sing_1186.htm#SEC1262	
permute_L		sing_1839.htm#SEC1915	
perron		sing_788.htm#SEC840	
perron.lib		sing_787.htm#SEC839	
perron_lib		sing_787.htm#SEC839	
phindex.lib		sing_2103.htm#IDX748	
phindex_lib		sing_2103.htm#IDX749	
picksFormula		sing_2059.htm#SEC2135	
pid		sing_406.htm#IDX236	
plainInvariants		sing_1553.htm#SEC1629	
plot		sing_1817.htm#SEC1893	
plotRot		sing_1821.htm#SEC1897	
plotRotated		sing_1820.htm#SEC1896	
plotRotatedDirect		sing_1823.htm#SEC1899	
plotRotatedList		sing_1822.htm#SEC1898	
plotRotatedListFromSpecifyList	plotRotatedListFromSpecifyList	sing_1824.htm#SEC1900	
plural		sing_1047.htm#IDX440	
pmat		sing_975.htm#SEC1051	
pnormalf		sing_961.htm#SEC1037	
pointid.lib		sing_1317.htm#SEC1393	
pointid_lib		sing_1317.htm#SEC1393	
polSol		sing_823.htm#SEC875	
polSolFiniteRank		sing_824.htm#SEC876	
pollTask		sing_1076.htm#SEC1152	
poly		sing_147.htm#SEC187	
poly (plural)		sing_487.htm#SEC527	
poly declarations		sing_148.htm#SEC188	
poly declarations (plural)	poly declarations (plural)	sing_488.htm#SEC528	
poly expressions		sing_149.htm#SEC189	
poly expressions (plural)	poly expressions (plural)	sing_489.htm#SEC529	
poly operations		sing_150.htm#SEC190	
poly operations (plural)	poly operations (plural)	sing_490.htm#SEC530	
poly related functions	poly related functions	sing_151.htm#SEC191	
poly related functions (plural)	poly related functions (plural)	sing_491.htm#SEC531	
poly.lib		sing_990.htm#SEC1066	
poly2list		sing_638.htm#SEC690	
poly2zdd		sing_2124.htm#SEC2200	61839
polyInterpolation		sing_2258.htm#SEC2334	
polyVars		sing_830.htm#SEC882	
poly_lib		sing_990.htm#SEC1066	
polybori		sing_2108.htm#IDX753	
polybori.lib		sing_2108.htm#IDX750	
polybori.lib 		sing_2108.htm#IDX754	
polybori_lib		sing_2108.htm#IDX751	
polymake		sing_2044.htm#IDX741	
polymake.lib		sing_2044.htm#SEC2120	
polymakePolytope		sing_2045.htm#SEC2121	
polymake_lib		sing_2044.htm#SEC2120	
polymake_so		sing_2426.htm#IDX904	
polynomial solutions		sing_817.htm#IDX380	
polynomial, opposite		sing_406.htm#IDX228	
polytope		sing_236.htm#SEC276	
polytope 		sing_2044.htm#IDX737	
polytope related functions	polytope related functions	sing_239.htm#SEC279	
polytopeViaInequalities	polytopeViaInequalities	sing_238.htm#SEC278	
polytopeViaPoints		sing_237.htm#SEC277	
pos_def		sing_1131.htm#SEC1207	
poset		sing_2166.htm#IDX854	
posweight		sing_1661.htm#SEC1737	
powSumSym		sing_2184.htm#SEC2260	
power		sing_1091.htm#SEC1167	
powerN		sing_1920.htm#SEC1996	
powerX		sing_1929.htm#SEC2005	
power_products		sing_1695.htm#SEC1771	
powerpolyX		sing_1899.htm#SEC1975	
powersums		sing_2022.htm#SEC2098	
preComp		sing_1254.htm#SEC1330	
preimage		sing_370.htm#SEC410	
preimage 		sing_754.htm#IDX355	
preimage (plural)		sing_524.htm#SEC564	
preimage under a map between local rings, map between local rings, map between local and global rings	preimageLoc	sing_1043.htm#IDX438	
preimageLattice		sing_2364.htm#SEC2440	
preimageLoc		sing_1043.htm#SEC1119	
preimageNC		sing_756.htm#SEC808	
prepEmbDiv		sing_1479.htm#SEC1555	
prepMat		sing_1732.htm#SEC1808	
prepRealclassify		sing_1537.htm#SEC1613	
prepSV		sing_1834.htm#SEC1910	
prepareAss		sing_1336.htm#SEC1412	
presentTree		sing_1466.htm#SEC1542	
presolve.lib		sing_1742.htm#SEC1818	
presolve_lib		sing_1742.htm#SEC1818	
primL		sing_1924.htm#SEC2000	
primList		sing_1923.htm#SEC1999	
primRoot		sing_1376.htm#SEC1452	
primTest		sing_1253.htm#SEC1329	
primary_char0		sing_1685.htm#SEC1761	
primary_char0_no_molien	primary_char0_no_molien	sing_1687.htm#SEC1763	
primary_char0_no_molien_random	primary_char0_no_molien_random	sing_1692.htm#SEC1768	
primary_char0_random	primary_char0_random	sing_1690.htm#SEC1766	
primary_charp		sing_1686.htm#SEC1762	
primary_charp_no_molien	primary_charp_no_molien	sing_1688.htm#SEC1764	
primary_charp_no_molien_random	primary_charp_no_molien_random	sing_1693.htm#SEC1769	
primary_charp_random	primary_charp_random	sing_1691.htm#SEC1767	
primary_charp_without	primary_charp_without	sing_1689.htm#SEC1765	
primary_charp_without_random	primary_charp_without_random	sing_1694.htm#SEC1770	
primary_invariants		sing_1673.htm#SEC1749	
primary_invariants_random	primary_invariants_random	sing_1674.htm#SEC1750	
primdec.lib		sing_1321.htm#SEC1397	
primdecGTZ		sing_1323.htm#SEC1399	
primdecGTZE		sing_1324.htm#SEC1400	
primdecMon		sing_1242.htm#SEC1318	
primdecSY		sing_1325.htm#SEC1401	
primdecSYE		sing_1326.htm#SEC1402	
primdecZ		sing_1345.htm#SEC1421	
primdecZM		sing_1346.htm#SEC1422	
primdec_lib		sing_1321.htm#SEC1397	
primdecint.lib		sing_1344.htm#SEC1420	
primdecint_lib		sing_1344.htm#SEC1420	
prime		sing_371.htm#SEC411	
primeClosure		sing_1281.htm#SEC1357	
primecoeffs		sing_953.htm#SEC1029	
primefactors		sing_372.htm#SEC412	
primes		sing_948.htm#SEC1024	
primitiv.lib		sing_1352.htm#SEC1428	
primitiv_lib		sing_1352.htm#SEC1428	
primitive		sing_1353.htm#SEC1429	
primitive element		sing_1353.htm#IDX516	
primitiveSpan		sing_2371.htm#SEC2447	
primitive_extra		sing_1354.htm#SEC1430	
primparam		sing_1548.htm#SEC1624	
principal intersection		sing_554.htm#IDX313	
print		sing_373.htm#SEC413	
print 		sing_2133.htm#IDX789	
printGraph		sing_1179.htm#SEC1255	
printGroup		sing_2352.htm#SEC2428	
printMoebius		sing_2172.htm#SEC2248	
printTask		sing_1071.htm#SEC1147	
printf		sing_374.htm#SEC414	
printlevel		sing_448.htm#SEC488	
proc		sing_152.htm#SEC192	
proc declaration		sing_153.htm#SEC193	
proc expression		sing_154.htm#SEC194	
procedure, ASCII help		sing_56.htm#IDX125	
procedure, ASCII/Texinfo help		sing_58.htm#IDX127	
procedure, texinfo help		sing_57.htm#IDX126	
procedures, help string		sing_45.htm#SEC82	
procedures, static	Procedure definition	sing_43.htm#SEC78	
procs with different argument types	procs with different argument types	sing_155.htm#SEC195	
prodcrit		sing_1999.htm#SEC2075	
product		sing_949.htm#SEC1025	
productgroup		sing_2373.htm#SEC2449	
progress watch		sing_364.htm#IDX163	
projectLattice		sing_2365.htm#SEC2441	
projective dimension	purityfiltration_lib	sing_795.htm#IDX364	
projective limes		sing_32.htm#SEC46	
projectiveDimension		sing_796.htm#SEC848	
prompt		sing_15.htm#SEC21	
prompt, option		sing_364.htm#IDX182	
propagator		sing_1177.htm#IDX467	
propagator 		sing_1180.htm#SEC1256	
prot, option		sing_364.htm#IDX161	
protocol of computations		sing_364.htm#IDX162	
proximitymatrix		sing_1507.htm#SEC1583	
prune		sing_375.htm#SEC415	
prwalk		sing_2402.htm#SEC2478	
psigncnd		sing_1795.htm#SEC1871	
puiseux2generators		sing_1606.htm#SEC1682	
puiseuxExpansion		sing_2069.htm#SEC2145	
pure tensor		sing_547.htm#IDX301	
purelist		sing_806.htm#SEC858	
purity	purityfiltration_lib	sing_795.htm#IDX366	
purityFiltration		sing_797.htm#SEC849	
purityTriang		sing_798.htm#SEC850	
purityfiltration.lib	purityfiltration_lib	sing_795.htm#IDX359	
purityfiltration_lib	purityfiltration_lib	sing_795.htm#IDX360	
pushForward		sing_2390.htm#SEC2466	
pwalk		sing_1193.htm#SEC1269	
pyobject		sing_243.htm#SEC283	
pyobject 		sing_2108.htm#IDX756	
pyobject declarations	pyobject declarations	sing_244.htm#SEC284	
pyobject expressions	pyobject expressions	sing_245.htm#SEC285	
pyobject operations		sing_246.htm#SEC286	
pyobject related functions	pyobject related functions	sing_247.htm#SEC287	
pyramid		sing_2274.htm#SEC2350	
python_eval		sing_248.htm#SEC288	
python_import		sing_249.htm#SEC289	
python_run		sing_250.htm#SEC290	
qbase		sing_2025.htm#SEC2101	
qepcad		sing_2284.htm#SEC2360	
qepcadsystem		sing_2285.htm#SEC2361	
qhmatrix		sing_1659.htm#SEC1735	
qhmoduli.lib		sing_1623.htm#SEC1699	
qhmoduli_lib		sing_1623.htm#SEC1699	
qhspectrum		sing_1646.htm#SEC1722	
qhweight		sing_376.htm#SEC416	
qmatrix.lib		sing_789.htm#SEC841	
qmatrix_lib		sing_789.htm#SEC841	
qminor		sing_791.htm#SEC843	
qrds		sing_377.htm#SEC417	
qring	Miscellaneous oddities	sing_161.htm#SEC201	
qring 		sing_466.htm#IDX289	
qring (plural)		sing_492.htm#SEC532	
qring declaration		sing_165.htm#SEC205	
qring declaration (plural)	qring declaration (plural)	sing_493.htm#SEC533	
qring related functions (plural)	qring related functions (plural)	sing_494.htm#SEC534	
qring ring ideal 'factor ring'		sing_1053.htm#IDX445	
qringNF, option		sing_364.htm#IDX164	
qslimgb		sing_929.htm#SEC1005	
quadraticSieve		sing_1937.htm#SEC2013	
quantMat		sing_790.htm#SEC842	
quickclass		sing_1529.htm#SEC1605	
quit		sing_438.htm#SEC478	
quote		sing_378.htm#SEC418	
quotient		sing_379.htm#SEC419	
quotient (plural)		sing_525.htm#SEC565	
quotientLatticeBasis	quotientLatticeBasis	sing_212.htm#SEC252	
quotientMain		sing_1787.htm#SEC1863	
quotientMon		sing_1233.htm#SEC1309	
quotients		sing_2293.htm#IDX886	
rHRR		sing_2224.htm#SEC2300	
rMacaulay		sing_976.htm#SEC1052	
rad_con		sing_1003.htm#SEC1079	
radical		sing_1333.htm#SEC1409	
radicalEHV		sing_1334.htm#SEC1410	
radicalMemberShip		sing_2091.htm#SEC2167	
radicalMon		sing_1234.htm#SEC1310	
radicalZ		sing_1348.htm#SEC1424	
randcharpoly		sing_2019.htm#SEC2095	
randlinpoly		sing_2021.htm#SEC2097	
random		sing_380.htm#SEC420	
random 		sing_406.htm#IDX240	
random  		sing_2154.htm#IDX828	
random   		sing_2155.htm#IDX830	
random number generator, seed		sing_406.htm#IDX238	
random.lib		sing_1011.htm#SEC1087	
randomBinomial		sing_1023.htm#SEC1099	
randomCheck		sing_1850.htm#SEC1926	
randomLast		sing_1022.htm#SEC1098	
randomPoint		sing_213.htm#SEC253	
randomPolyInT		sing_2100.htm#SEC2176	
random_lib		sing_1011.htm#SEC1087	
randomid		sing_1013.htm#SEC1089	
randommat		sing_1014.htm#SEC1090	
rank		sing_261.htm#IDX137	
rank 		sing_381.htm#SEC421	
ratSol		sing_825.htm#SEC877	
ratgb.lib		sing_815.htm#IDX369	
ratgb_lib		sing_815.htm#IDX370	
rational curves, rational parametrization of rational curves.	paraPlaneCurve	sing_1411.htm#IDX547	
rational normal curve, projection.		sing_1412.htm#IDX548	
rational normal curve, projection. 		sing_1415.htm#IDX549	
rational normal curve, projection.  		sing_1416.htm#IDX550	
rational solutions		sing_817.htm#IDX381	
rational univariate projection		sing_2019.htm#IDX734	
rationalPointConic		sing_1413.htm#SEC1489	
ratstd		sing_816.htm#SEC868	
rays		sing_214.htm#SEC254	
re2squ		sing_1390.htm#SEC1466	
read		sing_382.htm#SEC422	
readNmzData		sing_1308.htm#SEC1384	18957
reading, option		sing_364.htm#IDX183	
readline		sing_1.htm#IDX5	
real		sing_28.htm#IDX74	
real roots, univariate polynomial		sing_2026.htm#IDX736	
real roots, univariate projection		sing_2010.htm#IDX732	
real roots,sign conditions		sing_1793.htm#IDX712	
realclassify		sing_2409.htm#SEC2485	
realclassify.lib		sing_2408.htm#SEC2484	
realclassify_lib		sing_2408.htm#SEC2484	
realizationDim		sing_2063.htm#SEC2139	
realizationDimPoly		sing_2065.htm#SEC2141	
realizationMatroids.lib	realizationMatroids_lib	sing_2062.htm#SEC2138	
realizationMatroids_lib	realizationMatroids_lib	sing_2062.htm#SEC2138	
realmorsesplit		sing_2410.htm#SEC2486	
realpoly		sing_1357.htm#SEC1433	
realrad		sing_1359.htm#SEC1435	
realrad.lib		sing_1356.htm#SEC1432	
realrad_lib		sing_1356.htm#SEC1432	
realzero		sing_1358.htm#SEC1434	
recursive_boolean_poly	recursive_boolean_poly	sing_2114.htm#SEC2190	17045
recursive_from_boolean_poly	recursive_from_boolean_poly	sing_2120.htm#SEC2196	37794
redSB, option		sing_364.htm#IDX165	
redTail, option		sing_364.htm#IDX167	
redThrough, option		sing_364.htm#IDX168	
redefine, option		sing_364.htm#IDX184	
reduce		sing_383.htm#SEC423	
reduce 		sing_568.htm#IDX318	
reduce (plural)		sing_526.htm#SEC566	
reduced standard basis		sing_364.htm#IDX166	
reduction		sing_1711.htm#SEC1787	
reesclos.lib		sing_1360.htm#SEC1436	
reesclos_lib		sing_1360.htm#SEC1436	
reference		sing_251.htm#SEC291	
reference declarations	reference declarations	sing_252.htm#SEC292	
reference expressions	reference expressions	sing_253.htm#SEC293	
reference operations	reference and shared operations	sing_256.htm#SEC296	
reference related functions	reference and shared related functions	sing_257.htm#SEC297	
regCM		sing_1273.htm#SEC1349	
regIdeal		sing_1259.htm#SEC1335	
regMonCurve		sing_1262.htm#SEC1338	
regularity	Syzygies and resolutions	sing_384.htm#SEC424	
regularity 		sing_904.htm#SEC961	
reiffen		sing_607.htm#SEC659	
rel_orbit_variety		sing_1704.htm#SEC1780	
relations		sing_787.htm#IDX358	
relativeInteriorPoint	relativeInteriorPoint	sing_215.htm#SEC255	
relative_orbit_variety	relative_orbit_variety	sing_1705.htm#SEC1781	
relweight		sing_1660.htm#SEC1736	
remainder		sing_1780.htm#SEC1856	
remainderMain		sing_1788.htm#SEC1864	
removeCone		sing_235.htm#SEC275	
removepower		sing_1517.htm#SEC1593	
repart		sing_385.htm#SEC425	
replace		sing_1889.htm#SEC1965	
representation, math objects	Representation of mathematical objects	sing_891.htm#SEC943	
res		sing_386.htm#SEC426	
resbinomial.lib		sing_1420.htm#IDX553	
resbinomial_lib		sing_1420.htm#IDX554	
reservedName		sing_387.htm#SEC427	
resfunction		sing_1434.htm#SEC1510	
resgraph.lib		sing_1452.htm#SEC1528	
resgraph_lib		sing_1452.htm#SEC1528	
resjung.lib		sing_1456.htm#SEC1532	
resjung_lib		sing_1456.htm#SEC1532	
reslist		sing_1448.htm#SEC1524	
resolution	purityfiltration_lib	sing_156.htm#SEC196	
resolution 		sing_795.htm#IDX365	
resolution (plural)		sing_495.htm#SEC535	
resolution declarations	resolution declarations	sing_157.htm#SEC197	
resolution declarations (plural)	resolution declarations (plural)	sing_496.htm#SEC536	
resolution expressions	resolution expressions	sing_158.htm#SEC198	
resolution expressions (plural)	resolution expressions (plural)	sing_497.htm#SEC537	
resolution graph		sing_1502.htm#IDX567	
resolution related functions	resolution related functions	sing_159.htm#SEC199	
resolution related functions (plural)	resolution related functions (plural)	sing_498.htm#SEC538	
resolution, La Scala's method		sing_337.htm#SEC377	
resolution, computation of		sing_386.htm#IDX186	
resolution, hilbert-driven		sing_312.htm#SEC352	
resolutionInLocalization	resolutionInLocalization	sing_2292.htm#SEC2368	
resolutiongraph		sing_1503.htm#SEC1579	
resolve		sing_1464.htm#SEC1540	
resolve.lib		sing_1460.htm#SEC1536	
resolve_lib		sing_1460.htm#SEC1536	
resources.lib		sing_1024.htm#SEC1100	
resources_lib		sing_1024.htm#SEC1100	
restriction		sing_2147.htm#IDX816	
restriction 		sing_2163.htm#IDX849	
restriction  		sing_2164.htm#IDX851	
restriction of		sing_612.htm#IDX341	
restrictionIdeal		sing_622.htm#SEC674	
restrictionModule		sing_623.htm#SEC675	
resultant		sing_351.htm#SEC391	
resultant 		sing_388.htm#SEC428	
reszeta.lib		sing_1473.htm#SEC1549	
reszeta_lib		sing_1473.htm#SEC1549	
return		sing_439.htm#SEC479	
return type of procedures	Return type of procedures	sing_464.htm#SEC504	
returnSB, option		sing_364.htm#IDX152	
reverse		sing_2040.htm#SEC2116	
reverse lexicographical ordering		sing_895.htm#IDX386	
reynolds_molien		sing_1680.htm#SEC1756	
rho		sing_1931.htm#SEC2007	
rightInverse		sing_1869.htm#SEC1945	
rightKernel		sing_1867.htm#SEC1943	
rightModulo		sing_774.htm#SEC826	
rightNF		sing_773.htm#SEC825	
rightNFWeyl		sing_842.htm#SEC894	
rightStd		sing_772.htm#SEC824	
ring		sing_160.htm#SEC200	
ring (plural)		sing_499.htm#SEC539	
ring coefficients	hasTransExtensionCoefficient	sing_1050.htm#IDX442	
ring coefficients 		sing_1051.htm#IDX443	
ring coefficients  		sing_1052.htm#IDX444	
ring declarations		sing_162.htm#SEC202	
ring declarations (plural)	ring declarations (plural)	sing_500.htm#SEC540	
ring operations		sing_164.htm#SEC204	
ring operations (plural)	ring operations (plural)	sing_501.htm#SEC541	
ring related functions	ring related functions	sing_163.htm#SEC203	
ring related functions (plural)	ring related functions (plural)	sing_502.htm#SEC542	
ring, opposite		sing_406.htm#IDX225	
ring.lib		sing_1029.htm#SEC1105	
ring_cf		sing_261.htm#IDX138	
ring_lib		sing_1029.htm#SEC1105	
ring_variable		sing_2134.htm#IDX793	
ring_variable 		sing_2135.htm#IDX795	
ring_variable  		sing_2136.htm#IDX799	
ring_variable   		sing_2137.htm#IDX801	
ringlist		sing_389.htm#SEC429	
ringlist (plural)		sing_527.htm#SEC567	
ringtensor		sing_1041.htm#SEC1117	
ringweights		sing_1042.htm#SEC1118	
rinvar.lib		sing_1716.htm#SEC1792	
rinvar_lib		sing_1716.htm#SEC1792	
rmNmzFiles		sing_1313.htm#SEC1389	32601
rm_unitcol		sing_1109.htm#SEC1185	
rm_unitrow		sing_1108.htm#SEC1184	
rmx		sing_1814.htm#SEC1890	
rncAntiCanonicalMap		sing_1412.htm#SEC1488	
rncItProjEven		sing_1416.htm#SEC1492	
rncItProjOdd		sing_1415.htm#SEC1491	
root of Bernstein-Sato polynomial		sing_589.htm#IDX330	
rootofUnity		sing_1044.htm#SEC1120	
roots		sing_1781.htm#SEC1857	
rootsMain		sing_1789.htm#SEC1865	
rootsModp		sing_1913.htm#SEC1989	
rootsmr.lib		sing_2010.htm#SEC2086	
rootsmr_lib		sing_2010.htm#SEC2086	
rootsur.lib		sing_2026.htm#SEC2102	
rootsur_lib		sing_2026.htm#SEC2102	
round		sing_1911.htm#SEC1987	
rowShift		sing_261.htm#IDX141	
rowShift 		sing_263.htm#SEC303	
rowred		sing_1105.htm#SEC1181	
rp, global ordering		sing_895.htm#IDX385	
rswalk		sing_2407.htm#SEC2483	
rtimer		sing_452.htm#SEC492	
rvalue	No rvalue of increments and assignments	sing_458.htm#SEC498	
rvar		sing_390.htm#SEC430	
rwalk		sing_2403.htm#SEC2479	
rwalk.lib		sing_2401.htm#SEC2477	
rwalk_lib		sing_2401.htm#SEC2477	
s_res		sing_1059.htm#SEC1135	
sa_poly_reduce		sing_577.htm#SEC629	
sa_reduce		sing_576.htm#SEC628	
sagbi		sing_1366.htm#SEC1442	
sagbi.lib		sing_1363.htm#SEC1439	
sagbiPart		sing_1367.htm#SEC1443	
sagbiReduce		sing_1365.htm#SEC1441	
sagbiSPoly		sing_1364.htm#SEC1440	
sagbi_lib		sing_1363.htm#SEC1439	
salida		sing_1445.htm#SEC1521	
sameComponent		sing_1993.htm#SEC2069	
sameQ		sing_1792.htm#SEC1868	
sat		sing_1174.htm#SEC1250	
satiety		sing_1261.htm#SEC1337	
satstd		sing_2468.htm#SEC2544	
sba		sing_391.htm#SEC431	
scalarProd		sing_566.htm#SEC618	
scheme		sing_2265.htm#SEC2341	
schreyer.lib		sing_1058.htm#SEC1134	
schreyer_lib		sing_1058.htm#SEC1134	
sdb, source code debugger	Source code debugger	sing_66.htm#SEC103	
secondary fan		sing_2044.htm#IDX739	
secondary polytope		sing_2044.htm#IDX740	
secondaryFan		sing_2052.htm#SEC2128	
secondaryPolytope		sing_2051.htm#SEC2127	
secondary_and_irreducibles_no_molien	secondary_and_irreducibles_no_molien	sing_1701.htm#SEC1777	
secondary_char0		sing_1696.htm#SEC1772	
secondary_charp		sing_1698.htm#SEC1774	
secondary_no_molien		sing_1699.htm#SEC1775	
secondary_not_cohen_macaulay	secondary_not_cohen_macaulay	sing_1702.htm#SEC1778	
segre		sing_2179.htm#SEC2255	
select		sing_1175.htm#SEC1251	
select1		sing_1176.htm#SEC1252	
semaphore		sing_406.htm#IDX243	
semaphore 		sing_1028.htm#SEC1104	
semaphores		sing_1024.htm#IDX437	
semiCMcod2		sing_1657.htm#SEC1733	
semidiv		sing_1985.htm#SEC2061	
semigroup		sing_1506.htm#SEC1582	
semigroup 		sing_1510.htm#IDX574	
semigroup of values		sing_1596.htm#IDX689	
semigroupGenerator		sing_216.htm#SEC256	
sep		sing_1343.htm#SEC1419	
separateHNE		sing_1607.htm#SEC1683	
separator		sing_1244.htm#SEC1320	
serreRelations		sing_695.htm#SEC747	
set		sing_2129.htm#IDX779	
setBaseMultigrading		sing_2345.htm#SEC2421	
setLetterplaceAttributes	setLetterplaceAttributes	sing_686.htm#SEC738	
setLinearForms		sing_217.htm#SEC257	
setModuleGrading		sing_2357.htm#SEC2433	
setMultiplicity		sing_218.htm#SEC258	
setNmzDataPath		sing_1310.htm#SEC1386	18123
setNmzExecPath		sing_1306.htm#SEC1382	38993
setNmzFilename		sing_1309.htm#SEC1385	20206
setNmzOption		sing_1303.htm#SEC1379	9012
set_is_injective		sing_1973.htm#SEC2049	
setcores		sing_1026.htm#SEC1102	
setenv		sing_406.htm#IDX246	
setinitials		sing_2275.htm#SEC2351	
setring		sing_392.htm#SEC432	
sh		sing_406.htm#IDX248	
shared		sing_251.htm#SEC291	
shared declarations		sing_254.htm#SEC294	
shared expressions		sing_255.htm#SEC295	
shared operations	reference and shared operations	sing_256.htm#SEC296	
shared related functions	reference and shared related functions	sing_257.htm#SEC297	
sheaf cohomology		sing_1483.htm#IDX555	
sheafCoh		sing_1489.htm#SEC1565	64501
sheafCohBGG		sing_1487.htm#SEC1563	13439
sheafCohBGG2		sing_1488.htm#SEC1564	3338
sheafcoh.lib		sing_1483.htm#SEC1559	
sheafcoh_lib		sing_1483.htm#SEC1559	
shiftPoly		sing_688.htm#SEC740	
short		sing_449.htm#SEC489	
show		sing_977.htm#SEC1053	
showBO		sing_1465.htm#SEC1541	
showDataTypes		sing_1467.htm#SEC1543	
showNmzOptions		sing_1304.htm#SEC1380	64955
showNuminvs		sing_1301.htm#SEC1377	18934
showgrades		sing_800.htm#SEC852	
showrecursive		sing_978.htm#SEC1054	
sickle		sing_673.htm#SEC725	
signatureBrieskorn		sing_1666.htm#SEC1742	
signatureL		sing_2104.htm#SEC2180	
signatureLqf		sing_2105.htm#SEC2181	
signatureNemethi		sing_1668.htm#SEC1744	
signaturePuiseux		sing_1667.htm#SEC1743	
signcnd		sing_1794.htm#SEC1870	
signcond.lib		sing_1793.htm#SEC1869	
signcond_lib		sing_1793.htm#SEC1869	
simplesolver		sing_1738.htm#SEC1814	
simplex		sing_393.htm#SEC433	
simplexOut		sing_1765.htm#SEC1841	
simplify		sing_394.htm#SEC434	
simplifyRat		sing_837.htm#SEC889	
sing.lib		sing_1633.htm#SEC1709	
sing4ti2.lib		sing_1369.htm#SEC1445	
sing4ti2_lib		sing_1369.htm#SEC1445	
sing_lib		sing_1633.htm#SEC1709	
singular locus of D-module		sing_817.htm#IDX375	
singularities		sing_1565.htm#IDX591	
singularities 		sing_1566.htm#IDX602	
singularities  		sing_1567.htm#IDX605	
singularities   		sing_1568.htm#IDX608	
singularities    		sing_1569.htm#IDX611	
singularities     		sing_1570.htm#IDX615	
singularities      		sing_1571.htm#IDX619	
singularities       		sing_1572.htm#IDX625	
singularities        		sing_1573.htm#IDX633	
singularities         		sing_1574.htm#IDX639	
singularities          		sing_1575.htm#IDX647	
singularities           		sing_1576.htm#IDX657	
singularities            		sing_1664.htm#IDX704	
singularities, resolution of	Resolution of singularities	sing_880.htm#SEC932	
singularity		sing_1530.htm#SEC1606	
singularrc		sing_20.htm#IDX73	
size	Miscellaneous oddities	sing_395.htm#SEC435	
size 		sing_466.htm#IDX288	
skewmat		sing_1092.htm#SEC1168	
sleep		sing_401.htm#SEC441	
slimgb		sing_396.htm#SEC436	
slimgb 		sing_857.htm#SEC909	
slimgb (plural)		sing_528.htm#SEC568	
slocus		sing_1645.htm#SEC1721	
smith		sing_1878.htm#SEC1954	
smithNormalForm		sing_2393.htm#SEC2469	
solutionsMod2		sing_1928.htm#SEC2004	
solve		sing_1759.htm#SEC1835	
solve a linear equation system A*x = b via the LU-decomposition of A	lusolve	sing_340.htm#SEC380	
solve.lib		sing_1757.htm#SEC1833	
solveTInitialFormPar	solveTInitialFormPar	sing_2094.htm#SEC2170	
solve_IP		sing_1219.htm#SEC1295	
solve_lib		sing_1757.htm#SEC1833	
solvelinearpart		sing_1752.htm#SEC1828	
sort		sing_950.htm#SEC1026	
sortIntvec		sing_644.htm#SEC696	
sortandmap		sing_1753.htm#SEC1829	
sortier		sing_1715.htm#SEC1791	
sortvars		sing_1754.htm#SEC1830	
sortvec		sing_397.htm#SEC437	
source code debugger, sdb	Source code debugger	sing_66.htm#SEC103	
spadd		sing_1579.htm#SEC1655	
span		sing_219.htm#SEC259	
sparseHomogIdeal		sing_1020.htm#SEC1096	
sparseInterpolation		sing_2260.htm#SEC2336	
sparseid		sing_1015.htm#SEC1091	
sparsemat		sing_1017.htm#SEC1093	
sparsematrix		sing_1016.htm#SEC1092	
sparsepoly		sing_1018.htm#SEC1094	
sparsetriag		sing_1019.htm#SEC1095	
spcurve.lib		sing_1653.htm#SEC1729	
spcurve_lib		sing_1653.htm#SEC1729	
special characters, non-english		sing_455.htm#IDX281	
spectral pairs		sing_1565.htm#IDX600	
spectral pairs 		sing_1572.htm#IDX632	
spectral pairs  		sing_1574.htm#IDX646	
spectral pairs   		sing_1575.htm#IDX655	
spectral pairs    		sing_1587.htm#IDX671	
spectral pairs     		sing_1589.htm#IDX682	
spectralNeg		sing_1475.htm#SEC1551	
spectrum		sing_1565.htm#IDX599	
spectrum 		sing_1571.htm#SEC1647	
spectrum  		sing_1571.htm#IDX624	
spectrum   		sing_1572.htm#IDX631	
spectrum    		sing_1573.htm#IDX638	
spectrum     		sing_1574.htm#IDX645	
spectrum      		sing_1575.htm#IDX654	
spectrum       		sing_1587.htm#IDX670	
spectrum        		sing_1589.htm#IDX681	
spectrum         		sing_1664.htm#IDX706	
spectrum.lib		sing_1663.htm#SEC1739	
spectrum_lib		sing_1663.htm#SEC1739	
spectrumnd		sing_1664.htm#SEC1740	
spgamma		sing_1586.htm#SEC1662	
spgeomgenus		sing_1585.htm#SEC1661	
spissemicont		sing_1582.htm#SEC1658	
split		sing_979.htm#SEC1055	
splitPolygon		sing_2054.htm#SEC2130	
splitring		sing_1355.htm#SEC1431	
splitting		sing_1252.htm#SEC1328	
spmilnor		sing_1584.htm#SEC1660	
spmul		sing_1581.htm#SEC1657	
spnf		sing_1135.htm#SEC1211	
spoly		sing_1996.htm#SEC2072	
sppairs		sing_1572.htm#SEC1648	
sppnf		sing_1577.htm#SEC1653	
sppprint		sing_1578.htm#SEC1654	
spprint		sing_1136.htm#SEC1212	
sprintf		sing_399.htm#SEC439	
spsemicont		sing_1583.htm#SEC1659	
spsub		sing_1580.htm#SEC1656	
sqfrNorm		sing_1782.htm#SEC1858	
sqfrNormMain		sing_1790.htm#SEC1866	
sqr		sing_1908.htm#SEC1984	
sqrfree		sing_398.htm#SEC438	
squareRoot		sing_1927.htm#SEC2003	
squarefree		sing_1608.htm#SEC1684	
sres		sing_400.htm#SEC440	
ssi	Parallelization with ssi links	sing_852.htm#SEC904	
staircase		sing_1799.htm#SEC1875	
standard		sing_2003.htm#SEC2079	
standard.lib		sing_928.htm#IDX413	
standard_lib		sing_928.htm#IDX414	
startNmz		sing_1312.htm#SEC1388	21925
startTasks		sing_1072.htm#SEC1148	
static procedures	Procedure definition	sing_43.htm#SEC78	
status		sing_401.htm#SEC441	
std		sing_402.htm#SEC442	
std 		sing_855.htm#SEC907	
std (plural)		sing_529.htm#SEC569	
stdfglm		sing_403.htm#SEC443	
stdhilb		sing_404.htm#SEC444	
stopTask		sing_1073.htm#SEC1149	
stratify		sing_1733.htm#SEC1809	
stratify.lib		sing_1731.htm#SEC1807	
stratify_lib		sing_1731.htm#SEC1807	
string	Miscellaneous oddities	sing_166.htm#SEC206	
string 		sing_466.htm#IDX291	
string declarations		sing_167.htm#SEC207	
string expressions		sing_168.htm#SEC208	
string operations		sing_170.htm#SEC210	
string related functions	string related functions	sing_171.htm#SEC211	
string type cast		sing_169.htm#SEC209	
stripHNE		sing_1605.htm#SEC1681	
sturm		sing_2036.htm#SEC2112	
sturmha		sing_2038.htm#SEC2114	
sturmhaseq		sing_2039.htm#SEC2115	
sturmquery		sing_2014.htm#SEC2090	
sturmseq		sing_2037.htm#SEC2113	
submat		sing_1093.htm#SEC1169	
subrInterred		sing_1008.htm#SEC1084	
subset_sum01		sing_1957.htm#SEC2033	
subset_sum02		sing_1958.htm#SEC2034	
subst		sing_405.htm#SEC445	
subst (plural)		sing_530.htm#SEC570	
substitute		sing_1007.htm#SEC1083	
sugarCrit, option		sing_364.htm#IDX169	
sum		sing_951.htm#SEC1027	
sum_of_powers		sing_2183.htm#SEC2259	
sumlist		sing_1447.htm#SEC1523	
super-commutative algebras	Graded commutative algebras (SCA)	sing_539.htm#SEC591	
superCommutative		sing_771.htm#SEC823	
super_increasing_knapsack	super_increasing_knapsack	sing_1969.htm#SEC2045	
surf.lib		sing_1816.htm#SEC1892	
surf_lib		sing_1816.htm#SEC1892	
surfacesignature.lib	surfacesignature_lib	sing_1665.htm#SEC1741	
surfacesignature_lib	surfacesignature_lib	sing_1665.htm#SEC1741	
surfer		sing_1.htm#IDX8	
surfer 		sing_1818.htm#SEC1894	
surfex		sing_1.htm#IDX7	
surfex.lib		sing_1819.htm#SEC1895	
surfex_lib		sing_1819.htm#SEC1895	
suspend		sing_401.htm#SEC441	
swalk		sing_2406.htm#SEC2482	
swalk.lib		sing_2405.htm#SEC2481	
swalk_lib		sing_2405.htm#SEC2481	
swap		sing_1534.htm#SEC1610	
swap 		sing_2136.htm#IDX797	
switch	No case or switch statement	sing_460.htm#SEC500	
syModStd		sing_1379.htm#SEC1455	
symNsym		sing_2177.htm#SEC2253	
sym_gauss		sing_1119.htm#SEC1195	
symm		sing_2176.htm#SEC2252	
symmStd		sing_1378.htm#SEC1454	
symmat		sing_1094.htm#SEC1170	
symmetric basis		sing_1111.htm#IDX452	
symmetric power		sing_1113.htm#IDX454	
symmetricBasis		sing_1111.htm#SEC1187	
symmetricPower		sing_1113.htm#SEC1189	
symmfunc		sing_2023.htm#SEC2099	
symodstd.lib		sing_1373.htm#SEC1449	
symodstd_lib		sing_1373.htm#SEC1449	
symsignature		sing_2013.htm#SEC2089	
syndrome		sing_1846.htm#SEC1922	
sysBin		sing_1844.htm#SEC1920	
sysCRHT		sing_1841.htm#SEC1917	
sysCRHTMindist		sing_1842.htm#SEC1918	
sysFL		sing_1857.htm#SEC1933	
sysNewton		sing_1843.htm#SEC1919	
sysQE		sing_1847.htm#SEC1923	
sys_code		sing_1838.htm#SEC1914	
system		sing_406.htm#SEC446	
system, --		sing_406.htm#IDX271	
system, --long_option_name		sing_406.htm#IDX274	
system, --long_option_name=value		sing_406.htm#IDX276	
system, HC		sing_406.htm#IDX214	
system, LLL		sing_406.htm#IDX218	
system, Singular		sing_406.htm#IDX252	
system, SingularLib		sing_406.htm#IDX254	
system, absFact		sing_406.htm#IDX189	
system, blackbox		sing_406.htm#IDX190	
system, bracket		sing_406.htm#IDX195	
system, browsers		sing_406.htm#IDX194	
system, btest		sing_406.htm#IDX197	
system, complexNearZero		sing_406.htm#IDX198	
system, contributors		sing_406.htm#IDX200	
system, cpu		sing_406.htm#IDX202	
system, cpu 		sing_406.htm#IDX270	
system, denom_list		sing_406.htm#IDX204	
system, eigenvals		sing_406.htm#IDX205	
system, env		sing_406.htm#IDX206	
system, executable		sing_406.htm#IDX208	
system, freegb		sing_406.htm#IDX209	
system, getPrecDigits		sing_406.htm#IDX212	
system, getenv		sing_406.htm#IDX211	
system, gmsnf		sing_406.htm#IDX213	
system, hessenberg		sing_406.htm#IDX215	
system, install		sing_406.htm#IDX217	
system, nblocks		sing_406.htm#IDX221	
system, newstruct		sing_406.htm#IDX222	
system, opp		sing_406.htm#IDX223	
system, oppose		sing_406.htm#IDX226	
system, pcvBasis		sing_406.htm#IDX235	
system, pcvCV2P		sing_406.htm#IDX233	
system, pcvDim		sing_406.htm#IDX234	
system, pcvLAddL		sing_406.htm#IDX229	
system, pcvMinDeg		sing_406.htm#IDX231	
system, pcvP2CV		sing_406.htm#IDX232	
system, pcvPMulL		sing_406.htm#IDX230	
system, pid		sing_406.htm#IDX237	
system, random		sing_406.htm#IDX239	
system, reserve		sing_406.htm#IDX241	
system, reservedLink		sing_406.htm#IDX242	
system, semaphore		sing_406.htm#IDX244	
system, semic		sing_406.htm#IDX245	
system, setenv		sing_406.htm#IDX247	
system, sh		sing_406.htm#IDX249	
system, shrinktest		sing_406.htm#IDX250	
system, spadd		sing_406.htm#IDX255	
system, spectrum		sing_406.htm#IDX256	
system, spmul		sing_406.htm#IDX257	
system, std_syz		sing_406.htm#IDX258	
system, stest		sing_406.htm#IDX259	
system, tensorModuleMult		sing_406.htm#IDX260	
system, twostd		sing_406.htm#IDX261	
system, uname		sing_406.htm#IDX264	
system, version		sing_406.htm#IDX267	
system, with		sing_406.htm#IDX268	
systemOfParametersOfLocalization	systemOfParametersOfLocalization	sing_2289.htm#SEC2365	
syz		sing_407.htm#SEC447	
syz (plural)		sing_531.htm#SEC571	
syzygy		sing_1058.htm#IDX448	
tDetropicalise		sing_2096.htm#SEC2172	
tInitialForm		sing_2080.htm#SEC2156	
tInitialFormPar		sing_2092.htm#SEC2168	
tInitialFormParMax		sing_2093.htm#SEC2169	
tInitialIdeal		sing_2081.htm#SEC2157	
tab		sing_980.htm#SEC1056	
tail		sing_1992.htm#SEC2068	
tame polynomial		sing_1587.htm#IDX663	
tame polynomial 		sing_1588.htm#IDX673	
tame polynomial  		sing_1589.htm#IDX674	
tangentGens		sing_1403.htm#SEC1479	
tangentcone		sing_1652.htm#SEC1728	
task		sing_1066.htm#IDX451	
tasks.lib		sing_1066.htm#SEC1142	
tasks_lib		sing_1066.htm#SEC1142	
tau_es		sing_1560.htm#SEC1636	
tau_es2		sing_1514.htm#SEC1590	
tdCf		sing_2212.htm#SEC2288	
tdFactor		sing_2214.htm#SEC2290	
tdProj		sing_2217.htm#SEC2293	
tdTerms		sing_2213.htm#SEC2289	
teachstd.lib		sing_1990.htm#SEC2066	
teachstd_lib		sing_1990.htm#SEC2066	
template.lib		sing_55.htm#IDX120	
template.lib 		sing_55.htm#IDX123	
template_lib		sing_55.htm#SEC92	
template_lib 		sing_55.htm#IDX121	
tensor		sing_547.htm#IDX305	
tensor 		sing_1095.htm#SEC1171	
tensorMod		sing_1214.htm#SEC1290	
term orderings	General definitions for orderings	sing_894.htm#SEC946	
term orderings introduction	Introduction to orderings	sing_893.htm#SEC945	
testNCfac		sing_745.htm#SEC797	
testParametrization		sing_1418.htm#SEC1494	
testPointConic		sing_1419.htm#SEC1495	
testPrimary		sing_1331.htm#SEC1407	
testPrimaryE		sing_1332.htm#SEC1408	
tex		sing_1805.htm#SEC1881	
texDrawBasic		sing_2087.htm#SEC2163	
texDrawNewtonSubdivision	texDrawNewtonSubdivision	sing_2089.htm#SEC2165	
texDrawTriangulation	texDrawTriangulation	sing_2090.htm#SEC2166	
texDrawTropical		sing_2088.htm#SEC2164	
texMatrix		sing_2086.htm#SEC2162	
texNumber		sing_2084.htm#SEC2160	
texPolynomial		sing_2085.htm#SEC2161	
texcoef		sing_1886.htm#SEC1962	
texdemo		sing_1806.htm#SEC1882	
texfactorize		sing_1807.htm#SEC1883	
texmap		sing_1808.htm#SEC1884	
texname		sing_1809.htm#SEC1885	
texobj		sing_1810.htm#SEC1886	
texpoly		sing_1811.htm#SEC1887	
texproc		sing_1812.htm#SEC1888	
texring		sing_1813.htm#SEC1889	
the first alternative algorithm		sing_1191.htm#IDX486	
three_elements		sing_1976.htm#SEC2052	
timeFactorize		sing_955.htm#SEC1031	
timeStd		sing_954.htm#SEC1030	
timer		sing_450.htm#SEC490	
timer resolution, setting the		sing_406.htm#IDX277	
timestep		sing_2278.htm#SEC2354	
tjurina		sing_1648.htm#SEC1724	
tmatrix		sing_1575.htm#SEC1651	
todd		sing_2209.htm#SEC2285	
toddE		sing_2210.htm#SEC2286	
toddPoly		sing_2223.htm#SEC2299	
tolessvars		sing_1751.htm#SEC1827	
topological invariants		sing_1502.htm#IDX565	
topological invariants 		sing_1509.htm#IDX572	
topological invariants  		sing_1510.htm#IDX576	
topological invariants   		sing_1511.htm#IDX580	
topological invariants    		sing_1512.htm#IDX584	
toric geometry		sing_2466.htm#SEC2542	
toric ideals		sing_908.htm#SEC965	
toric ring		sing_1290.htm#IDX515	
toric.lib		sing_1380.htm#SEC1456	
toric_ideal		sing_1381.htm#SEC1457	
toric_lib		sing_1380.htm#SEC1456	
toric_std		sing_1382.htm#SEC1458	
torusInvariants		sing_1296.htm#SEC1372	911
total divisors		sing_547.htm#IDX302	
total multiplicities		sing_1502.htm#IDX568	
totalmultiplicities		sing_1504.htm#SEC1580	
trace		sing_408.htm#SEC448	
tracemult		sing_2017.htm#SEC2093	
transpose		sing_409.htm#SEC449	
trapezoid		sing_2272.htm#SEC2348	
triMNewton		sing_1777.htm#SEC1853	
triagmatrix		sing_1021.htm#SEC1097	
triang.lib		sing_1770.htm#SEC1846	
triangL		sing_1771.htm#SEC1847	
triangL_solve		sing_1768.htm#SEC1844	
triangLf_solve		sing_1766.htm#SEC1842	
triangLfak		sing_1772.htm#SEC1848	
triangM		sing_1773.htm#SEC1849	
triangMH		sing_1774.htm#SEC1850	
triangM_solve		sing_1767.htm#SEC1843	
triang_lib		sing_1770.htm#SEC1846	
triang_solve		sing_1769.htm#SEC1845	
triangulations		sing_2050.htm#SEC2126	
tropical curves		sing_2066.htm#IDX746	
tropical geometry		sing_1177.htm#IDX462	
tropical mirror symmetry		sing_1177.htm#IDX464	
tropical polynomials		sing_2066.htm#IDX747	
tropical.lib		sing_2066.htm#IDX744	
tropicalCurve		sing_2071.htm#SEC2147	
tropicalJInvariant		sing_2074.htm#SEC2150	
tropicalLifting		sing_2067.htm#SEC2143	
tropicalSubst		sing_2099.htm#SEC2175	
tropicalVariety		sing_2425.htm#SEC2501	
tropical_lib		sing_2066.htm#IDX745	
tropicalise		sing_2078.htm#SEC2154	
tropicaliseSet		sing_2079.htm#SEC2155	
truncate		sing_1484.htm#SEC1560	13545
truncateFast		sing_1485.htm#SEC1561	5124
truncated module		sing_1484.htm#IDX556	
truncated module 		sing_1485.htm#IDX557	
tst_ncfactor		sing_753.htm#SEC805	
twalk		sing_1190.htm#SEC1266	
two-sided		sing_547.htm#IDX303	
two-sided Groebner basis		sing_547.htm#IDX304	
twostd		sing_406.htm#IDX262	
twostd 		sing_532.htm#SEC572	
type		sing_410.htm#SEC450	
type B		sing_2152.htm#IDX824	
type D		sing_2153.htm#IDX826	
type,custom	Definition of a user defined type	sing_178.htm#SEC218	
type2arr		sing_2130.htm#SEC2206	
typecasting		sing_2130.htm#IDX780	
typecasting 		sing_2131.htm#IDX782	
typecasting  		sing_2132.htm#IDX785	
typeof		sing_411.htm#SEC451	
u		sing_2264.htm#SEC2340	
uname		sing_406.htm#IDX263	
unbounded_knapsack		sing_1959.htm#SEC2035	
unipotent groups		sing_1402.htm#IDX524	
uniquePoint		sing_220.htm#SEC260	
unitmat		sing_1096.htm#SEC1172	
univariate		sing_412.htm#SEC452	
univarpoly		sing_2024.htm#SEC2100	
unknown syndrome	Decoding method based on quadratic equations	sing_924.htm#SEC995	
unset		sing_325.htm#SEC365	
untyped definitions		sing_83.htm#SEC123	
untyped definitions 		sing_472.htm#SEC512	
updatePairs		sing_2002.htm#SEC2078	
ures_solve		sing_1760.htm#SEC1836	
uressolve		sing_413.htm#SEC453	
usage, option		sing_364.htm#IDX185	
user interface, Emacs	Emacs user interface	sing_21.htm#SEC28	
valvars		sing_1755.htm#SEC1831	
vandermonde		sing_414.htm#SEC454	
vanishId		sing_1856.htm#SEC1932	
var		sing_415.htm#SEC455	
varMat		sing_2134.htm#SEC2210	
varNum		sing_2135.htm#SEC2211	
variables		sing_416.htm#SEC456	
variables 		sing_2134.htm#IDX792	
variables  		sing_2135.htm#IDX794	
variables   		sing_2136.htm#IDX798	
variables    		sing_2137.htm#IDX800	
variablesSorted		sing_585.htm#SEC637	
variablesStandard		sing_584.htm#SEC636	
vars2pars		sing_832.htm#SEC884	
varsigns		sing_2029.htm#SEC2105	
varstr		sing_417.htm#SEC457	
vct2str		sing_693.htm#SEC745	
vdim		sing_418.htm#SEC458	
vdim (plural)		sing_533.htm#SEC573	
vec2poly		sing_567.htm#SEC619	
vector		sing_172.htm#SEC212	
vector declarations		sing_173.htm#SEC213	
vector expressions		sing_174.htm#SEC214	
vector operations		sing_175.htm#SEC215	
vector related functions	vector related functions	sing_176.htm#SEC216	
verify		sing_2020.htm#SEC2096	
versal		sing_1555.htm#SEC1631	
version		sing_406.htm#IDX266	
vertexAdjacencyGraph	vertexAdjacencyGraph	sing_2463.htm#SEC2539	
vertexEdgeGraph		sing_2464.htm#SEC2540	
vertices		sing_242.htm#SEC282	
vfilt		sing_1573.htm#SEC1649	
view		sing_1876.htm#SEC1952	
visual		sing_2465.htm#SEC2541	
visualize		sing_2263.htm#SEC2339	
voice		sing_453.htm#SEC493	
vwfilt		sing_1574.htm#SEC1650	
wUnit		sing_1914.htm#SEC1990	
waitAllTasks		sing_1075.htm#SEC1151	
waitTasks		sing_1074.htm#SEC1150	
waitall		sing_419.htm#SEC459	
waitfirst		sing_420.htm#SEC460	
warkedPreimageStd		sing_2291.htm#SEC2367	
warn, option		sing_70.htm#SEC110	
warn, option 		sing_364.htm#IDX151	
watchdog		sing_952.htm#SEC1028	
wedge		sing_421.htm#SEC461	
weierstr.lib		sing_2005.htm#SEC2081	
weierstrDiv		sing_2006.htm#SEC2082	
weierstrPrep		sing_2007.htm#SEC2083	
weierstr_lib		sing_2005.htm#SEC2081	
weierstrassForm		sing_2075.htm#SEC2151	
weight		sing_422.htm#SEC462	
weight filtration		sing_1565.htm#IDX596	
weight filtration 		sing_1572.htm#IDX630	
weight filtration  		sing_1574.htm#IDX644	
weight filtration   		sing_1575.htm#IDX652	
weight filtration    		sing_1587.htm#IDX668	
weight filtration     		sing_1589.htm#IDX679	
weightKB		sing_423.htm#SEC463	
weightM, option		sing_364.htm#IDX170	
weighted lexicographical ordering		sing_895.htm#IDX393	
weighted reverse lexicographical ordering	Global orderings	sing_895.htm#IDX391	
weightedRing		sing_764.htm#SEC816	
whichvariable		sing_2028.htm#SEC2104	
while		sing_440.htm#SEC480	
withDim		sing_261.htm#IDX145	
withHilb		sing_261.htm#IDX143	
withMult		sing_261.htm#IDX146	
withRes		sing_261.htm#IDX144	
withSB		sing_261.htm#IDX142	
wp, global ordering		sing_895.htm#IDX392	
write		sing_424.htm#SEC464	
writeNmzData		sing_1307.htm#SEC1383	38467
writeNmzPaths		sing_1311.htm#SEC1387	sprintf
ws, local ordering		sing_896.htm#IDX403	
wurzel		sing_1896.htm#SEC1972	
xchange		sing_1890.htm#SEC1966	
xdvi		sing_1815.htm#SEC1891	
zdd		sing_2108.htm#IDX758	
zdd2poly		sing_2125.htm#SEC2201	55047
zero-dimensional		sing_2025.htm#IDX735	
zeroMod		sing_1248.htm#SEC1324	
zeroOpt		sing_1257.htm#SEC1333	
zeroRadical		sing_1159.htm#SEC1235	
zeroSet		sing_1783.htm#SEC1859	
zerodec		sing_1340.htm#SEC1416	
zeroset.lib		sing_1778.htm#SEC1854	
zeroset_lib		sing_1778.htm#SEC1854	
zetaDL		sing_1477.htm#SEC1553	
{		sing_36.htm#IDX78	
||		sing_36.htm#IDX103	
|| 		sing_96.htm#SEC136	
}		sing_36.htm#IDX79	
~		sing_36.htm#IDX117	
~ 		sing_441.htm#SEC481	
