!		sing_36.htm#IDX101	
!=		sing_36.htm#IDX95	
!= 		sing_105.htm#SEC145	
"		sing_36.htm#IDX104	
#		sing_36.htm#IDX118	
$		sing_36.htm#IDX119	
%		sing_36.htm#IDX91	
% 		sing_81.htm#SEC121	
%  		sing_103.htm#SEC143	
%   		sing_115.htm#SEC155	
%    		sing_152.htm#SEC192	
%     		sing_160.htm#SEC200	
&&		sing_36.htm#IDX102	
&& 		sing_106.htm#SEC146	
(		sing_36.htm#IDX80	
()		sing_136.htm#IDX130	
)		sing_36.htm#IDX81	
*	bigintmat operations	sing_36.htm#IDX89	
* 		sing_81.htm#SEC121	
*  		sing_87.htm#SEC127	
*   		sing_92.htm#SEC132	
*    		sing_98.htm#SEC138	
*     		sing_103.htm#SEC143	
*      		sing_111.htm#SEC151	
*       		sing_115.htm#SEC155	
*        		sing_142.htm#SEC182	
*         		sing_147.htm#SEC187	
*          		sing_152.htm#SEC192	
*           		sing_160.htm#SEC200	
**		sing_36.htm#IDX93	
+	bigintmat operations	sing_36.htm#IDX85	
+ 		sing_81.htm#SEC121	
+  		sing_87.htm#SEC127	
+   		sing_92.htm#SEC132	
+    		sing_98.htm#SEC138	
+     		sing_103.htm#SEC143	
+      		sing_111.htm#SEC151	
+       		sing_115.htm#SEC155	
+        		sing_131.htm#SEC171	
+         		sing_142.htm#SEC182	
+          		sing_147.htm#SEC187	
+           		sing_152.htm#SEC192	
+            		sing_160.htm#SEC200	
+             		sing_174.htm#SEC214	
+              		sing_181.htm#SEC221	
+               		sing_186.htm#SEC226	
++		sing_36.htm#IDX86	
-	bigintmat operations	sing_36.htm#IDX87	
- 		sing_81.htm#SEC121	
-  		sing_87.htm#SEC127	
-   		sing_92.htm#SEC132	
-    		sing_103.htm#SEC143	
-     		sing_111.htm#SEC151	
-      		sing_115.htm#SEC155	
-       		sing_142.htm#SEC182	
-        		sing_152.htm#SEC192	
-         		sing_160.htm#SEC200	
-          		sing_186.htm#SEC226	
--		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_164.htm#SEC204	
-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	
.singular		sing_18.htm#SEC25	
.singularrc file		sing_20.htm#IDX72	
.singularrc file, no loading	Command line options	sing_19.htm#IDX46	
/		sing_36.htm#IDX90	
/ 		sing_76.htm#SEC116	
/  		sing_115.htm#SEC155	
/   		sing_142.htm#SEC182	
/    		sing_152.htm#SEC192	
/     		sing_160.htm#SEC200	
/      		sing_186.htm#SEC226	
//		sing_36.htm#IDX107	
// 		sing_36.htm#IDX109	
//  		sing_36.htm#IDX110	
:		sing_36.htm#IDX114	
: 		sing_115.htm#SEC155	
::		sing_36.htm#IDX115	
:: 		sing_154.htm#SEC194	
;		sing_36.htm#IDX111	
<		sing_36.htm#IDX100	
< 		sing_160.htm#SEC200	
<  		sing_186.htm#SEC226	
<   		sing_254.htm#SEC294	
<=		sing_36.htm#IDX99	
<= 		sing_105.htm#SEC145	
<=  		sing_152.htm#SEC192	
<=   		sing_160.htm#SEC200	
<=    		sing_181.htm#SEC221	
<=     		sing_186.htm#SEC226	
<>		sing_36.htm#IDX96	
<> 		sing_105.htm#SEC145	
<>  		sing_142.htm#SEC182	
<>   		sing_152.htm#SEC192	
<>    		sing_160.htm#SEC200	
<>     		sing_174.htm#SEC214	
<>      		sing_181.htm#SEC221	
<>       		sing_186.htm#SEC226	
=		sing_36.htm#IDX77	
==		sing_36.htm#IDX94	
== 		sing_105.htm#SEC145	
==  		sing_142.htm#SEC182	
==   		sing_152.htm#SEC192	
==    		sing_160.htm#SEC200	
==     		sing_174.htm#SEC214	
==      		sing_181.htm#SEC221	
==       		sing_186.htm#SEC226	
>		sing_36.htm#IDX98	
> 		sing_160.htm#SEC200	
>  		sing_186.htm#SEC226	
>=		sing_36.htm#IDX97	
>= 		sing_105.htm#SEC145	
>=  		sing_152.htm#SEC192	
>=   		sing_160.htm#SEC200	
>=    		sing_181.htm#SEC221	
>=     		sing_186.htm#SEC226	
?		sing_36.htm#IDX106	
? 		sing_267.htm#IDX150	
ADGT		sing_1070.htm#SEC1151	50088
AG codes		sing_979.htm#SEC1036	
AGcode_L		sing_2286.htm#SEC2367	60329
AGcode_Omega		sing_2287.htm#SEC2368	56285
ASCII		sing_1030.htm#SEC1111	26816
ASCII links		sing_122.htm#SEC162	
ASSUME		sing_64.htm#SEC101	
A_L		sing_1907.htm#SEC1988	16721
A_Z		sing_1028.htm#SEC1109	50866
A_Z_L		sing_1029.htm#SEC1110	64002
Access to elements of a user defined type	Access to elements of a user defined type	sing_191.htm#SEC231	
Adj_div		sing_2281.htm#SEC2362	44919
Adjoint ideal		sing_1732.htm#IDX747	
Alexander polynomial		sing_1868.htm#IDX795	
Algebraic Geometry codes		sing_2280.htm#IDX964	
Algebraic dependence	Algebraic dependence	sing_958.htm#SEC1015	
Algebraic geometry		sing_1601.htm#SEC1682	
AltVarEnd		sing_758.htm#SEC812	11020
AltVarStart		sing_757.htm#SEC811	21592
Ann		sing_1528.htm#SEC1609	18496
Appel function		sing_568.htm#IDX366	
Appel hypergeometric function		sing_568.htm#IDX367	
Applications		sing_977.htm#SEC1034	
Arnol'd		sing_1886.htm#IDX815	
Arnold, classification.		sing_1915.htm#IDX820	
Arnold, classification. 		sing_1916.htm#IDX821	
ArnoldAction		sing_2022.htm#SEC2103	26958
ArnoldType		sing_2794.htm#SEC2875	4729
Assignments for user defined types	Assignments for user defined types	sing_193.htm#SEC233	
AssocTanToEnv		sing_1064.htm#SEC1145	38126
Authors		sing_1.htm#IDX16	
Automatic Deduction		sing_1070.htm#IDX542	
Automatic Demonstration		sing_1070.htm#IDX543	
BFBoundsBudur		sing_605.htm#SEC659	20515
BINresol		sing_1745.htm#SEC1826	52996
BSidealFromAnn		sing_603.htm#SEC657	28160
Background		sing_3.htm#SEC5	
Basic programming		sing_933.htm#SEC990	
Basic programming 		sing_933.htm#SEC990	
BelongSemig		sing_2486.htm#SEC2567	22405
BerlekampMassey		sing_1313.htm#SEC1394	2172
Bern		sing_1640.htm#SEC1721	64051
Bernstein operator		sing_544.htm#IDX348	
Bernstein-Sato ideal		sing_600.htm#IDX369	
Bernstein-Sato polynomial		sing_509.htm#IDX329	
Bernstein-Sato polynomial 		sing_544.htm#IDX345	
Bernstein-Sato polynomial  		sing_1963.htm#IDX832	
Bernstein-Sato polynomial   		sing_1967.htm#IDX849	
Bernstein-Sato polynomial for variety		sing_608.htm#IDX377	
BernsteinSatoIdeal		sing_604.htm#SEC658	20995
Betti		sing_1373.htm#SEC1454	20012
Betti number	Syzygies and resolutions	sing_995.htm#SEC1057	
BettiNumsH		sing_1690.htm#SEC1771	18661
BettiNumsN		sing_1698.htm#SEC1779	44681
BettiNumsQp		sing_1693.htm#SEC1774	16693
BettiNumsS		sing_1696.htm#SEC1777	14964
Betty number		sing_1687.htm#IDX709	
Bigatti-La Scala-Robbiano algorithm	Bigatti and La Scala and Robbiano	sing_1005.htm#SEC1067	
Bimodules	Bimodules and syzygies and lifts	sing_831.htm#SEC885	
Bisyzygy	Bimodules and syzygies and lifts	sing_831.htm#SEC885	
BlowingUp		sing_1942.htm#SEC2023	43153
Blowupcenter		sing_1748.htm#SEC1829	3423
BorelCheck		sing_1865.htm#SEC1946	48787
Bott's formula		sing_1807.htm#IDX763	
Branches of space curve singularities	Branches of space curve singularities	sing_966.htm#SEC1023	
Briancon-Maisonobe algorithm		sing_544.htm#IDX354	
Brieskorn lattice		sing_1963.htm#IDX828	
Brieskorn lattice 		sing_1964.htm#IDX839	
Brieskorn lattice  		sing_1965.htm#IDX842	
Brieskorn lattice   		sing_1966.htm#IDX845	
Brieskorn lattice    		sing_1967.htm#IDX848	
Brieskorn lattice     		sing_1968.htm#IDX852	
Brieskorn lattice      		sing_1969.htm#IDX856	
Brieskorn lattice       		sing_1970.htm#IDX862	
Brieskorn lattice        		sing_1971.htm#IDX870	
Brieskorn lattice         		sing_1972.htm#IDX876	
Brieskorn lattice          		sing_1973.htm#IDX884	
Brieskorn lattice           		sing_1974.htm#IDX894	
Brieskorn lattice            		sing_1985.htm#IDX900	
Brieskorn lattice             		sing_1987.htm#IDX911	
Brieskorn lattice              		sing_2015.htm#IDX938	
Brill-Noether algorithm		sing_2280.htm#IDX965	
BrillNoether		sing_2283.htm#SEC2364	39919
Buchberger algorithm for toric ideals	Buchberger algorithm	sing_1006.htm#SEC1068	
Budur-Mustata-Saito approach		sing_608.htm#IDX381	
Building Singular		sing_3131.htm#SEC3236	
C programming language	Major differences to the C programming language	sing_420.htm#SEC460	
C, module ordering		sing_987.htm#IDX478	
CGS		sing_1051.htm#IDX491	
CGS, disjoint, reduced, comprehensive Groebner system	buildtree	sing_1122.htm#IDX568	
CM_regularity		sing_1849.htm#SEC1930	33865
CMtype		sing_2060.htm#SEC2141	24849
CRHT-ideal		sing_1012.htm#SEC1081	
CSMA		sing_1663.htm#SEC1744	49080
CYGWIN and ESingular	Running SINGULAR under Emacs	sing_23.htm#SEC33	
Castelnuovo-Mumford regularity		sing_1849.htm#IDX787	
Category string		sing_51.htm#SEC88	
CenCharDec		sing_653.htm#SEC707	44505
Center		sing_1787.htm#SEC1868	25541
CenterBO		sing_1794.htm#SEC1875	34701
CentralQuot		sing_651.htm#SEC705	56490
CentralSaturation		sing_652.htm#SEC706	32577
Change of rings		sing_9.htm#SEC15	
Characteristic sets		sing_996.htm#SEC1058	
CharacteristicExponents	CharacteristicExponents	sing_1948.htm#SEC2029	21795
ChernClass		sing_1820.htm#SEC1901	32965
ChernRootsDual		sing_1619.htm#SEC1700	40100
ChernRootsHom		sing_1628.htm#SEC1709	48446
ChernRootsProd		sing_1621.htm#SEC1702	13967
ChernRootsSum		sing_1617.htm#SEC1698	57286
ChernRootsSymm		sing_1630.htm#SEC1711	59304
ChernRootsWedge		sing_1631.htm#SEC1712	7239
Chevalley-Rosenlicht theorem		sing_1726.htm#IDX732	
Chevalley-Rosenlicht theorem 		sing_1727.htm#IDX735	
Chow ring, abstract variety, projective space, Grassmannian	ChowRing	sing_1811.htm#IDX768	
ChowRing		sing_1811.htm#SEC1892	57977
Classification of hypersurface singularities	Classification of hypersurface singularities	sing_967.htm#SEC1024	
Classification of singularities		sing_2032.htm#IDX939	
Code	Codes and the decoding problem	sing_1011.htm#SEC1074	
Codes and the decoding problem	Codes and the decoding problem	sing_1011.htm#SEC1073	
Coding theory		sing_2279.htm#SEC2360	
Coefficient rings	Notes for Singular users	sing_3129.htm#SEC3229	
Command line options	Command line options	sing_19.htm#SEC26	
Commands	Functions and system variables	sing_212.htm#SEC252	
Commands for user defined types	Commands for user defined types	sing_192.htm#SEC232	
Commutative Algebra		sing_946.htm#SEC1003	
Commutative algebra		sing_1249.htm#SEC1330	
CompDecomp		sing_506.htm#SEC560	9959
CompInt		sing_2488.htm#SEC2569	7518
CompleteHomog		sing_1607.htm#SEC1688	42123
ComplexValue		sing_2873.htm#SEC2954	45548
Comprehensive Groebner System		sing_1051.htm#IDX494	
Comprehensive Groebner Systems		sing_1049.htm#SEC1130	
Comprehensive Groebner Systems 		sing_1114.htm#SEC1195	
Computing Groebner and Standard Bases	Computing Groebner and Standard Bases	sing_942.htm#SEC999	
ConsLevels		sing_1071.htm#SEC1152	14282
ContactMatrix		sing_1950.htm#SEC2031	24686
Conti-Traverso algorithm		sing_1001.htm#SEC1063	
Contributors		sing_1.htm#IDX15	
Control structures		sing_388.htm#SEC428	
Control theory	System and Control theory	sing_2313.htm#SEC2394	
Cooper philosophy		sing_1012.htm#SEC1079	
CoverMult		sing_3102.htm#SEC3183	51718
Crep		sing_1054.htm#SEC1135	16717
Critical points		sing_961.htm#SEC1018	
CurveParam		sing_1944.htm#SEC2025	53605
CurveRes		sing_1943.htm#SEC2024	48848
Curves		sing_1732.htm#IDX744	
Customization of the Emacs interface	Customization of the Emacs interface	sing_25.htm#SEC36	
Cyclic code		sing_2294.htm#IDX972	
Cyclic roots		sing_939.htm#SEC996	
D-integration		sing_568.htm#IDX363	
D-localization		sing_568.htm#IDX359	
D-localization 		sing_675.htm#IDX398	
D-module	purityfiltration_lib	sing_509.htm#IDX327	
D-module 		sing_544.htm#IDX342	
D-module  		sing_568.htm#IDX356	
D-module   		sing_600.htm#IDX368	
D-module    		sing_608.htm#IDX375	
D-module     		sing_675.htm#IDX395	
D-module      		sing_785.htm#IDX413	
D-module structure		sing_544.htm#IDX343	
D-module structure 		sing_600.htm#IDX371	
D-module structure  		sing_608.htm#IDX376	
D-restriction		sing_568.htm#IDX361	
DBM links		sing_127.htm#SEC167	
DISPLAY environment variable	The online help system	sing_16.htm#IDX28	
DLoc		sing_571.htm#SEC625	5981
DLoc0		sing_573.htm#SEC627	14327
Data types		sing_72.htm#SEC112	
Data types (plural)		sing_433.htm#IDX313	
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_190.htm#SEC230	
Decoding		sing_2294.htm#IDX974	
Decoding codes with Groebner bases	Decoding codes with Groebner bases	sing_1010.htm#SEC1072	
Decoding method based on quadratic equations	Decoding method based on quadratic equations	sing_1015.htm#SEC1090	
Definition of a user defined type	Definition of a user defined type	sing_189.htm#SEC229	
Deformations		sing_964.htm#SEC1021	
Deformations, T1 and T2		sing_963.htm#SEC1020	
Deg		sing_1376.htm#SEC1457	35419
Degree		sing_1377.htm#SEC1458	48523
DegreePure		sing_1711.htm#SEC1792	33003
Degrees		sing_1378.htm#SEC1459	50349
Delta		sing_1795.htm#SEC1876	33497
DeltaList		sing_1796.htm#SEC1877	65148
Demo mode		sing_24.htm#SEC35	
Depth		sing_953.htm#SEC1010	
Determinacy		sing_2035.htm#IDX943	
Di Biase-Urbanke algorithm	Di Biase and Urbanke	sing_1004.htm#SEC1066	
DifConsLCSets		sing_1074.htm#SEC1155	sprintf
Distributed computing		sing_1085.htm#IDX559	
Dlocalization		sing_676.htm#SEC730	22140
Documentation Tool		sing_60.htm#SEC97	
Dp, global ordering		sing_985.htm#IDX461	
DrawCovers		sing_3111.htm#SEC3192	12668
Ds, local ordering		sing_986.htm#IDX471	
DsingularLocus		sing_680.htm#SEC734	46495
Dynamic loading		sing_71.htm#SEC111	
Dynamic modules		sing_941.htm#SEC998	
ECPP		sing_2390.htm#SEC2471	55777
ECoef		sing_1754.htm#SEC1835	14154
EOrdlist		sing_1752.htm#SEC1833	36329
ERROR		sing_243.htm#SEC283	
ESingular, CYGWIN	Running SINGULAR under Emacs	sing_23.htm#SEC33	
Edatalist		sing_1751.htm#SEC1832	61593
Edelman-Reiner		sing_2675.htm#IDX1056	
Editing SINGULAR input files with Emacs	Editing SINGULAR input files with Emacs	sing_26.htm#SEC37	
Editing input		sing_18.htm#SEC25	
Elimination		sing_949.htm#SEC1006	
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_1756.htm#SEC1837	47312
Enumerative geometry		sing_1807.htm#IDX761	
Equal		sing_1710.htm#SEC1791	19984
Eresol		sing_1746.htm#SEC1827	12842
EulerAff		sing_1664.htm#SEC1745	54325
EulerProj		sing_1665.htm#SEC1746	13537
Evaluation of logical expressions	Evaluation of logical expressions	sing_422.htm#SEC462	
Examples		sing_931.htm#SEC988	
Examples of ring declarations	Examples of ring declarations	sing_29.htm#SEC40	
Examples of use of LETTERPLACE	Examples of use of Letterplace	sing_807.htm#SEC861	
Examples of use of LETTERPLACE over Z	Examples of use of Letterplace over Z	sing_808.htm#SEC862	
Exp for matrices		sing_1728.htm#IDX736	
Experimental libraries	Experimental libraries	sing_2759.htm#SEC2840	
Ext		sing_1330.htm#SEC1411	21909
Ext, computation of		sing_952.htm#SEC1009	
Ext_R		sing_1329.htm#SEC1410	53310
Exterior		sing_744.htm#SEC798	23593
Extra weight vector		sing_990.htm#SEC1047	
Factorization		sing_954.htm#SEC1011	
FamElemsAtEnvCompPoints	FamElemsAtEnvCompPoints	sing_1065.htm#SEC1146	45869
Feynman graph	tropicalEllipticCovers_lib	sing_1298.htm#IDX616	
Feynman graph 		sing_3098.htm#IDX1310	
Feynman integral	tropicalEllipticCovers_lib	sing_3098.htm#IDX1311	
Feynman integral of a graph for a fixed ordering	FeynmanIntegralo	sing_3108.htm#IDX1329	
Feynman integrals		sing_3110.htm#IDX1334	
FeynmanIntegralA		sing_3110.htm#SEC3191	1897
FeynmanIntegralO		sing_3109.htm#SEC3190	23852
FeynmanIntegralo		sing_3108.htm#SEC3189	1720
Finite fields		sing_948.htm#SEC1005	
First steps		sing_6.htm#SEC12	
Fitzgerald-Lax method	Fitzgerald-Lax method	sing_1014.htm#SEC1087	
Float		sing_258.htm#SEC298	
FloorDiagrams		sing_3106.htm#SEC3187	32801
Flow control		sing_40.htm#SEC70	
Formal Checker		sing_59.htm#SEC96	
Formatting output		sing_938.htm#SEC995	
Free associative algebras	Free associative algebras	sing_828.htm#SEC882	
Free resolution		sing_950.htm#SEC1007	
Free resolution, graded	Handling graded modules	sing_951.htm#SEC1008	
FultonA		sing_1662.htm#SEC1743	33688
Functional decomposition		sing_1280.htm#IDX607	
Functionality and release notes of LETTERPLACE	Functionality and release notes of Letterplace	sing_809.htm#SEC863	
Functions		sing_213.htm#SEC253	
Functions (letterplace)	Functions (letterplace)	sing_811.htm#SEC865	
Future benefits of Singular 4	Notes for Singular users	sing_3129.htm#SEC3234	
G-algebra		sing_497.htm#SEC537	
G-algebra 		sing_497.htm#SEC539	
G-algebra  		sing_668.htm#IDX383	
G-algebra   		sing_669.htm#IDX390	
G-algebra, setup		sing_497.htm#SEC541	
GBWeight		sing_574.htm#SEC628	24641
GBsolve		sing_2153.htm#SEC2234	16830
GIT-Fans		sing_973.htm#SEC1030	
GITcone		sing_2555.htm#SEC2636	64643
GITfan		sing_2556.htm#SEC2637	56677
GITfanFromOrbitCones	GITfanFromOrbitCones	sing_2557.htm#SEC2638	63104
GITfanParallel		sing_2558.htm#SEC2639	18256
GITfanParallelSymmetric	GITfanParallelSymmetric	sing_2573.htm#SEC2654	30292
GITfanSymmetric		sing_2572.htm#SEC2653	25831
GKExp		sing_673.htm#SEC727	38541
GKZfan		sing_2559.htm#SEC2640	sprintf
GKZsystem		sing_649.htm#SEC703	20528
GKdim		sing_622.htm#SEC676	9814
GMP		sing_1.htm#IDX3	
GMP 		sing_3133.htm#SEC3238	
GND.lib		sing_2878.htm#SEC2959	
GND_lib		sing_2878.htm#SEC2959	
GTZmod		sing_1438.htm#SEC1519	30091
GTZopt		sing_1445.htm#SEC1526	14642
G_a -Invariants		sing_970.htm#SEC1027	
Gamma		sing_1761.htm#SEC1842	3820
Gauss-Manin connection	Gauss-Manin connection	sing_997.htm#SEC1059	
Gauss-Manin connection 		sing_2015.htm#IDX937	
Gauss-Manin connection  		sing_2069.htm#IDX947	
Gauss-Manin system		sing_1963.htm#IDX827	
Gauss-Manin system 		sing_1964.htm#IDX838	
Gauss-Manin system  		sing_1965.htm#IDX841	
Gauss-Manin system   		sing_1966.htm#IDX844	
Gauss-Manin system    		sing_1967.htm#IDX847	
Gauss-Manin system     		sing_1968.htm#IDX851	
Gauss-Manin system      		sing_1969.htm#IDX855	
Gauss-Manin system       		sing_1970.htm#IDX861	
Gauss-Manin system        		sing_1971.htm#IDX869	
Gauss-Manin system         		sing_1972.htm#IDX875	
Gauss-Manin system          		sing_1973.htm#IDX883	
Gauss-Manin system           		sing_1974.htm#IDX893	
Gauss-Manin system            		sing_1985.htm#IDX899	
Gauss-Manin system             		sing_1987.htm#IDX910	
Gelfand-Kirillov dimension		sing_870.htm#IDX435	
Gelfand-Kirillov dimension, G-Algebra		sing_673.htm#IDX391	
General command syntax	General command syntax	sing_35.htm#SEC59	
General concepts		sing_12.htm#SEC18	
General purpose		sing_1022.htm#SEC1103	
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_499.htm#SEC551	
Generalized Newton identities	Generalized Newton identities	sing_1013.htm#SEC1084	
Geometric Invariant Theory	Geometric Invariant Theory	sing_972.htm#SEC1029	
Geometric Theorems		sing_1070.htm#IDX544	
Geometric genus		sing_1732.htm#IDX748	
German Umlaute		sing_418.htm#IDX297	
Getting started		sing_5.htm#SEC11	
Global orderings		sing_985.htm#SEC1042	
Goettsche's formula		sing_1687.htm#IDX710	
GoettscheF		sing_1688.htm#SEC1769	27881
Graded commutative algebras	Graded commutative algebras (SCA)	sing_805.htm#SEC859	
Grassmannian		sing_1812.htm#SEC1893	43898
Grassmannian, abstract variety, Schubert calculus	Grassmannian	sing_1812.htm#IDX769	
Greuel, Gert-Martin		sing_1.htm#IDX18	
Grob1Levels		sing_1073.htm#SEC1154	50331
Groebner Bases	Computing Groebner and Standard Bases	sing_942.htm#SEC999	
Groebner bases for two-sided ideals in free associative algebras	Groebner bases for two-sided ideals in free associative algebras	sing_830.htm#SEC884	
Groebner bases in G-algebras	Groebner bases in G-algebras	sing_498.htm#SEC542	
Groebner bases in free associative algebras	Groebner bases for two-sided ideals in free associative algebras	sing_830.htm#SEC884	
Groebner bases, decodeGB		sing_2294.htm#IDX976	
Groebner bases, slim		sing_945.htm#SEC1002	
Groebner basis conversion	Groebner basis conversion	sing_944.htm#SEC1001	
Groebner cover		sing_1050.htm#IDX487	
Groebner cover 		sing_1057.htm#IDX506	
Groebner cover  		sing_1058.htm#IDX513	
Groebner fan		sing_2580.htm#IDX993	
Groebner walk		sing_1321.htm#IDX639	
Groebner walk 		sing_1323.htm#IDX641	
Groebner walk  		sing_3028.htm#IDX1284	
Groebner walk   		sing_3029.htm#IDX1285	
Groebner-Shirshov bases	Groebner bases for two-sided ideals in free associative algebras	sing_830.htm#SEC884	
Groebner-Shirshov bases in free associative algebras	Groebner bases for two-sided ideals in free associative algebras	sing_830.htm#SEC884	
Groebnerwalk		sing_1317.htm#IDX635	
Groebnerwalk 		sing_2935.htm#IDX1268	
Groebnerwalk  		sing_3027.htm#IDX1283	
Groebnerwalk   		sing_3075.htm#IDX1299	
Gromov-Witten invariants	tropicalEllipticCovers_lib	sing_1298.htm#IDX613	
Gromov-Witten invariants 		sing_1304.htm#IDX624	
Gromov-Witten invariants  		sing_1305.htm#IDX628	
Gromov-Witten invariants   		sing_3098.htm#IDX1307	
Gromov-Witten invariants    		sing_3110.htm#IDX1333	
Gromov-Witten invariants, lines on hypersurfaces	linesHypersurface	sing_1837.htm#IDX781	
Gromov-Witten invariants, multiple covers		sing_1836.htm#IDX780	
Gromov-Witten invariants, rational curves on Calabi-Yau threefolds	rationalCurve	sing_1838.htm#IDX782	
Gromov-Witten invariants, rational curves on Calabi-Yau threefolds 		sing_1839.htm#IDX783	
Gromov-Witten invariants.		sing_1807.htm#IDX764	
Gweights		sing_738.htm#SEC792	651
H2basis		sing_2020.htm#SEC2101	3414
HHnormalForm		sing_1924.htm#SEC2005	33972
Hamburger-Noether expansion		sing_1868.htm#IDX791	
Hamburger-Noether expansion 		sing_1988.htm#IDX919	
Hamburger-Noether expansions		sing_2281.htm#IDX966	
Handling graded modules	Handling graded modules	sing_951.htm#SEC1008	
Hcode		sing_1900.htm#SEC1981	26628
Help string		sing_45.htm#SEC82	
Hensel		sing_248.htm#SEC288	
Hilbert function		sing_366.htm#IDX195	
Hilbert function 		sing_668.htm#IDX384	
Hilbert function  		sing_669.htm#IDX388	
Hilbert function   		sing_994.htm#SEC1053	
Hilbert polynomial		sing_668.htm#IDX386	
Hilbert scheme		sing_1687.htm#IDX713	
Hilbert series		sing_668.htm#IDX385	
Hilbert series 		sing_669.htm#IDX389	
Hilbert series  		sing_834.htm#IDX426	
Hilbert series   		sing_994.htm#SEC1053	
Hilbert-driven GB algorithm	Groebner basis conversion	sing_944.htm#SEC1001	
HilbertClassPoly		sing_2037.htm#SEC2118	sprintf
HilbertSeries		sing_2122.htm#SEC2203	21249
HilbertWeights		sing_2123.htm#SEC2204	sprintf
Hodge ideals		sing_2915.htm#IDX1260	
Hom		sing_1333.htm#SEC1414	61434
HomJJ		sing_1475.htm#SEC1556	1525
Hosten-Sturmfels algorithm	Hosten and Sturmfels	sing_1003.htm#SEC1065	
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_1304.htm#IDX627	
Hurwitz numbers 		sing_1305.htm#IDX631	
Hypersurface singularities, classification of	Classification of hypersurface singularities	sing_967.htm#SEC1024	
I-regular function		sing_1057.htm#IDX512	
IN		sing_288.htm#IDX151	
Ideal membership		sing_993.htm#IDX483	
Ideal quotients		sing_1354.htm#IDX647	
Identifiers, syntax of		sing_37.htm#SEC65	
ImageGroup		sing_2125.htm#SEC2206	28808
ImageVariety		sing_2124.htm#SEC2205	15252
Imap, option		sing_324.htm#IDX181	
Implemented algorithms	Implemented algorithms	sing_33.htm#SEC47	
Incl		sing_1709.htm#SEC1790	7621
Index		sing_3139.htm#SEC3244	
Info string		sing_52.htm#SEC89	
InterDiv		sing_1777.htm#SEC1858	46142
Interactive use		sing_13.htm#SEC19	
Interrupting SINGULAR	Interrupting SINGULAR	sing_17.htm#SEC24	
IntersectWithSub		sing_654.htm#SEC708	56289
Intersection theory		sing_1807.htm#IDX760	
IntersectionMatrix		sing_1949.htm#SEC2030	29351
Introduction		sing_2.htm#SEC4	
Invariant Theory		sing_969.htm#SEC1026	
Invariant theory		sing_2074.htm#SEC2155	
InvariantQ		sing_2127.htm#SEC2208	53256
InvariantRing		sing_2126.htm#SEC2207	22928
Invariants of a finite group	Invariants of a finite group	sing_971.htm#SEC1028	
Invariants of plane curve singularities	Invariants of plane curve singularities	sing_965.htm#SEC1022	
IsSCA		sing_759.htm#SEC813	58445
J-marked schemes		sing_1859.htm#IDX789	
J-marked schemes, Borel ideals		sing_1864.htm#IDX790	
JMBTest.lib		sing_1859.htm#SEC1940	
JMBTest_lib		sing_1859.htm#SEC1940	
JMSConst.lib		sing_1864.htm#SEC1945	
JMSConst_lib		sing_1864.htm#SEC1945	
JMarkedScheme		sing_1866.htm#SEC1947	60696
Jacobi		sing_2363.htm#SEC2444	29843
Jacobson form		sing_2331.htm#IDX977	
Jacobson normal form		sing_2331.htm#IDX978	
Janet basis		sing_1580.htm#IDX691	
Janet division, Janet basis		sing_1579.htm#IDX690	
JuReTopDim		sing_1719.htm#SEC1800	sprintf
JuReZeroDim		sing_1720.htm#SEC1801	sprintf
Jumping numbers		sing_2915.htm#IDX1263	
K-basis		sing_834.htm#IDX424	
K-dimension		sing_834.htm#IDX425	
KScoef		sing_2013.htm#SEC2094	sprintf
KSconvert		sing_2011.htm#SEC2092	3585
KSker		sing_2010.htm#SEC2091	40166
KSlinear		sing_2012.htm#SEC2093	19896
KSpencerKernel		sing_2067.htm#SEC2148	12490
KeneshlouMatrixPresentation	KeneshlouMatrixPresentation	sing_2897.htm#SEC2978	20741
Ker		sing_1382.htm#SEC1463	58279
Kernel of module homomorphisms	Kernel of module homomorphisms	sing_957.htm#SEC1014	
KoszulHomology		sing_1342.htm#SEC1423	sprintf
Kronecker module		sing_1687.htm#IDX712	
Kronecker product		sing_370.htm#SEC410	
L, ordering		sing_991.htm#SEC1048	
LETTERPLACE		sing_806.htm#SEC860	
LETTERPLACE libraries	LETTERPLACE libraries	sing_833.htm#SEC887	
LIB		sing_292.htm#SEC332	
LIB commands		sing_53.htm#SEC90	
LIBs		sing_1018.htm#SEC1099	
LLL		sing_368.htm#IDX227	
LOT algorithm		sing_544.htm#IDX355	
LRcoef		sing_2922.htm#SEC3003	29653
LRcoprod		sing_2925.htm#SEC3006	32111
LRinstall		sing_2921.htm#SEC3002	362
LRmult		sing_2924.htm#SEC3005	31755
LRschubmult		sing_2926.htm#SEC3007	28341
LRskew		sing_2923.htm#SEC3004	46115
LTGS		sing_3032.htm#SEC3113	6595
LU-decomposition of a matrix of numbers		sing_297.htm#SEC337	
Laurent series		sing_1302.htm#IDX621	
Laurent series 		sing_1303.htm#IDX623	
Left and two-sided Groebner bases	Left and two-sided Groebner bases	sing_975.htm#SEC1032	
Left ideal membership (plural)	Groebner bases in G-algebras	sing_498.htm#SEC545	
Left normal form	Groebner bases in G-algebras	sing_498.htm#SEC544	
Leinartas		sing_2992.htm#IDX1274	
LengthSym		sing_802.htm#SEC856	16591
LengthSymElement		sing_801.htm#SEC855	28292
Letterplace		sing_806.htm#SEC860	
Letterplace Groebner basis		sing_834.htm#IDX423	
Letterplace Groebner basis 		sing_870.htm#IDX433	
Letterplace Groebner basis  		sing_879.htm#IDX442	
Letterplace correspondence	Letterplace correspondence	sing_832.htm#SEC886	
Letterplace libraries	LETTERPLACE libraries	sing_833.htm#SEC887	
Letterplace ring		sing_364.htm#SEC404	
Levels		sing_1072.htm#SEC1153	16031
Lexicographic Groebner bases, computation of	Groebner basis conversion	sing_944.htm#SEC1001	
Libraries	Writing procedures and libraries	sing_48.htm#SEC85	
Libraries 		sing_934.htm#SEC991	
Libraries in the SINGULAR Documentation	Libraries in the SINGULAR Documentation	sing_49.htm#SEC86	
Library versioning	Notes for Singular users	sing_3129.htm#SEC3232	
Lie		sing_2850.htm#IDX1251	
Lie algebra		sing_1727.htm#IDX733	
Lie bracket		sing_467.htm#SEC507	
Lie group		sing_1730.htm#IDX738	
Lie group 		sing_1731.htm#IDX741	
Limitations		sing_418.htm#SEC458	
Linear algebra		sing_1190.htm#SEC1271	
Linear code		sing_2294.htm#IDX973	
LinearActionQ		sing_2129.htm#SEC2210	62218
LinearCombinationQ		sing_2130.htm#SEC2211	59373
LinearizeAction		sing_2128.htm#SEC2209	60266
Loading a library		sing_62.htm#SEC99	
Local orderings		sing_986.htm#SEC1043	
Log for matrices		sing_1729.htm#IDX737	
Long coefficients		sing_936.htm#SEC993	
M, ordering		sing_988.htm#SEC1045	
MPGS		sing_3071.htm#SEC3152	7899
MSGB		sing_3074.htm#SEC3155	59379
MSPOLY		sing_3073.htm#SEC3154	sprintf
MVComplex		sing_1668.htm#SEC1749	62126
Macdonald's formula		sing_1687.htm#IDX711	
MacdonaldF		sing_1694.htm#SEC1775	12751
Macintosh installation	Macintosh installation instructions	sing_3138.htm#SEC3243	
Mathematical background	Mathematical background	sing_992.htm#SEC1049	
Mathematical background (letterplace)	Mathematical background (letterplace)	sing_827.htm#SEC881	
Mathematical background (plural)	Mathematical background (plural)	sing_496.htm#SEC536	
Matrix orderings		sing_988.htm#SEC1045	
Max		sing_2029.htm#SEC2110	23
Maximus		sing_1861.htm#SEC1942	10010
Maxord		sing_1760.htm#SEC1841	14124
MillerRabin		sing_2373.htm#SEC2454	15740
Milnor code		sing_1886.htm#IDX817	
Milnor number	Milnor and Tjurina number	sing_960.htm#SEC1017	
Milnor number 		sing_2034.htm#IDX942	
Min		sing_2030.htm#SEC2111	29623
MinMult		sing_2487.htm#SEC2568	39835
MinimalDecomposition	MinimalDecomposition	sing_2131.htm#SEC2212	24161
Minimum distance		sing_2294.htm#IDX975	
Minimus		sing_1860.htm#SEC1941	61721
Miscellaneous libraries	Miscellaneous libraries	sing_2646.htm#SEC2727	
ModEqn		sing_2023.htm#SEC2104	59394
Modular techniques		sing_1085.htm#IDX556	
Module orderings		sing_987.htm#SEC1044	
Modules and and their annihilator	Modules and their annihilator	sing_10.htm#SEC16	
Monodromy		sing_2015.htm#IDX935	
Monomial orderings		sing_982.htm#SEC1039	
Monomial orderings on free algebras	Monomial orderings on free algebras	sing_829.htm#SEC883	
Monomial orderings, Term orderings		sing_31.htm#SEC44	
Mori dream spaces		sing_2798.htm#IDX1152	
Morse lemma	addnondegeneratevariables	sing_2033.htm#IDX940	
Morse lemma 		sing_2036.htm#IDX944	
MultiplicitySequence	MultiplicitySequence	sing_1947.htm#SEC2028	1309
Multiplier ideals		sing_2915.htm#IDX1262	
NF		sing_344.htm#SEC384	
NF (letterplace)	reduce (letterplace)	sing_820.htm#SEC874	
NF (plural)		sing_488.htm#SEC528	
NFMora		sing_2439.htm#SEC2520	40670
NPos		sing_1463.htm#SEC1544	39857
NPos_test		sing_1461.htm#SEC1542	48172
NSplaces		sing_2282.htm#SEC2363	48675
NTL		sing_1.htm#IDX4	
NakYoshF		sing_1691.htm#SEC1772	58602
Names		sing_37.htm#SEC65	
Names in procedures		sing_46.htm#SEC83	
Names, indexed		sing_37.htm#SEC65	
New orderings for modules	Notes for Singular users	sing_3129.htm#SEC3233	
Newton non-degenerate		sing_2002.htm#IDX933	
Newton polygon		sing_2001.htm#IDX932	
Newton polygon 		sing_2002.htm#IDX934	
Newton polygons		sing_2637.htm#IDX998	
Newton polytope		sing_2580.htm#IDX992	
Newton step		sing_2219.htm#IDX961	
Noether position		sing_1463.htm#IDX653	
NoetherPosition		sing_1452.htm#SEC1533	18735
Non-commutative algebra	Non-commutative Algebra	sing_974.htm#SEC1031	
Non-commutative algebra 		sing_1009.htm#SEC1071	
Non-commutative subsystem	Non-commutative subsystem	sing_431.htm#SEC471	
Nonhyp		sing_1749.htm#SEC1830	sprintf
Normalization		sing_956.htm#SEC1013	
Notes for Singular users	Notes for Singular users	sing_3129.htm#SEC3228	
Notes for developers	Notes for developers	sing_3130.htm#SEC3235	
NullCone		sing_2132.htm#SEC2213	26449
NumIrrDecom		sing_1723.htm#SEC1804	sprintf
NumLocalDim		sing_1712.htm#SEC1793	1739
NumPrimDecom		sing_1725.htm#SEC1806	34134
Oaku-Takayama algorithm		sing_544.htm#IDX353	
Objects		sing_38.htm#SEC66	
Orlik-Solomon		sing_2676.htm#IDX1057	
Output		sing_1392.htm#IDX650	
Output 		sing_2701.htm#IDX1092	
Output  		sing_2703.htm#IDX1093	
Output   		sing_2704.htm#IDX1094	
Output    		sing_2705.htm#IDX1095	
Output     		sing_2706.htm#IDX1096	
Output      		sing_2707.htm#IDX1097	
Output       		sing_2708.htm#IDX1098	
Output        		sing_2709.htm#IDX1099	
Output         		sing_2710.htm#IDX1100	
Output          		sing_2711.htm#IDX1101	
Output           		sing_2712.htm#IDX1102	
Output            		sing_2713.htm#IDX1103	
Output             		sing_2714.htm#IDX1104	
Output              		sing_2715.htm#IDX1105	
Output               		sing_2716.htm#IDX1106	
Output                		sing_2717.htm#IDX1107	
Output                 		sing_2718.htm#IDX1108	
Output                  		sing_2719.htm#IDX1109	
Output                   		sing_2720.htm#IDX1110	
Output                    		sing_2721.htm#IDX1111	
Output                     		sing_2722.htm#IDX1112	
Output                      		sing_2723.htm#IDX1113	
Output                       		sing_2724.htm#IDX1114	
Output                        		sing_2725.htm#IDX1115	
Output, formatting of		sing_938.htm#SEC995	
PBW		sing_523.htm#IDX341	
PBW basis		sing_497.htm#SEC538	
PBW_eqDeg		sing_541.htm#SEC595	23181
PBW_maxDeg		sing_542.htm#SEC596	59566
PBW_maxMonom		sing_543.htm#SEC597	1155
PEsolve		sing_2151.htm#SEC2232	9229
PH_ais		sing_2729.htm#SEC2810	49473
PH_nais		sing_2730.htm#SEC2811	46271
PLURAL		sing_432.htm#SEC472	
PLURAL LIBs		sing_501.htm#SEC555	
PLURAL libraries		sing_501.htm#SEC555	
PPolyH		sing_1689.htm#SEC1770	25241
PPolyN		sing_1697.htm#SEC1778	39067
PPolyQp		sing_1692.htm#SEC1773	35707
PPolyS		sing_1695.htm#SEC1776	13817
ParToVar		sing_2875.htm#SEC2956	14023
Parallel computing		sing_3126.htm#SEC3224	
Parallelization	Parallelization with ssi links	sing_940.htm#SEC997	
Parallelization 		sing_1085.htm#IDX557	
Parameter list		sing_44.htm#SEC81	
Parameters		sing_937.htm#SEC994	
Parametrization		sing_1732.htm#IDX745	
Parametrization, image.		sing_1742.htm#IDX757	
PartC		sing_1658.htm#SEC1739	4327
PartitionVar		sing_2872.htm#SEC2953	41350
Path names	Notes for Singular users	sing_3129.htm#SEC3231	
PerfectPowerTest		sing_2349.htm#SEC2430	17450
Perturbation walk		sing_1322.htm#IDX640	
Pfister, Gerhard		sing_1.htm#IDX19	
Pipe links		sing_126.htm#SEC166	
PocklingtonLehmer		sing_2375.htm#SEC2456	13634
Poincare polynomial		sing_2688.htm#IDX1081	
Polar curves		sing_962.htm#SEC1019	
PollardRho		sing_2376.htm#SEC2457	49602
PolyBoRi, Boolean Groebner Basis	recursive_boolean_poly	sing_2732.htm#IDX1123	
PolyBoRi, Boolean Groebner Basis 		sing_2734.htm#IDX1124	
PolyBoRi, Boolean Groebner Basis  		sing_2735.htm#IDX1125	
PolyBoRi, Boolean Groebner Basis   		sing_2736.htm#IDX1126	
PolyBoRi, Boolean Groebner Basis    		sing_2737.htm#IDX1127	
PolyBoRi, Boolean Groebner Basis     		sing_2738.htm#IDX1128	
PolyBoRi, Boolean Groebner Basis      		sing_2739.htm#IDX1129	
PolyBoRi, Boolean Groebner Basis       		sing_2740.htm#IDX1130	
PolyBoRi, Boolean Groebner Basis        		sing_2741.htm#IDX1131	
PolyBoRi, Boolean Groebner Basis         		sing_2742.htm#IDX1132	
PolyBoRi, Boolean Groebner Basis          		sing_2743.htm#IDX1133	
PolyBoRi, Boolean Groebner Basis           		sing_2744.htm#IDX1134	
PolyBoRi, Boolean Groebner Basis            		sing_2745.htm#IDX1135	
PolyBoRi, Boolean Groebner Basis             		sing_2746.htm#IDX1136	
PolyBoRi, Boolean Groebner Basis              		sing_2748.htm#IDX1138	
PolyBoRi, zero-supressed decision diagram		sing_2747.htm#IDX1137	
Polybori, Boolean Groebner Basis		sing_2749.htm#IDX1139	
Polynomial data		sing_980.htm#SEC1037	
Pottier algorithm		sing_1002.htm#SEC1064	
Preface		sing_1.htm#SEC1	
Prep		sing_1055.htm#SEC1136	54574
Primary decomposition	Primary decomposition	sing_955.htm#SEC1012	
Primary decomposition 		sing_1352.htm#IDX646	
PrimdecA		sing_1434.htm#SEC1515	248
PrimdecB		sing_1435.htm#SEC1516	9653
Procedure definition	Procedure definition	sing_43.htm#SEC78	
Procedure-specific commands	Procedure-specific commands	sing_47.htm#SEC84	
Procedures		sing_42.htm#SEC77	
Procedures and libraries	Procedures and libraries	sing_8.htm#SEC14	
Procedures and libraries 		sing_934.htm#SEC991	
Procedures in a library	Procedures in a library	sing_54.htm#SEC91	
Product orderings		sing_989.htm#SEC1046	
Programming		sing_932.htm#SEC989	
PropagatorFunction		sing_3107.htm#SEC3188	8662
Pseudo ordering L		sing_991.htm#SEC1048	
PtoCrep		sing_1056.htm#SEC1137	52865
Puiseux expansion		sing_1868.htm#IDX792	
Puiseux expansion 		sing_1988.htm#IDX920	
Puiseux expansions		sing_3017.htm#IDX1276	
Puiseux pairs	Invariants of plane curve singularities	sing_965.htm#SEC1022	
Puiseux pairs 		sing_1994.htm#IDX925	
QPoly, quotient ring.		sing_3066.htm#IDX1294	
QQ		sing_28.htm#SEC39	
QQ 		sing_75.htm#SEC115	
Qso3Casimir		sing_648.htm#SEC702	40212
Quot-scheme		sing_1687.htm#IDX714	
Quotient		sing_2237.htm#SEC2318	47295
QuotientEquations		sing_2024.htm#SEC2105	18230
Rational curves		sing_1732.htm#IDX746	
ReJunkUseHomo		sing_1718.htm#SEC1799	10186
Reduced Comprehensive Groebner Systems		sing_1114.htm#SEC1195	
ReesAlgebra		sing_1574.htm#SEC1655	59951
References		sing_1017.htm#SEC1096	
References (plural)		sing_500.htm#SEC552	
References and history of LETTERPLACE	References and history of Letterplace	sing_810.htm#SEC864	
Release Notes		sing_3124.htm#SEC3205	
Release Notes (letterplace)	Release Notes (letterplace)	sing_930.htm#SEC984	
Res		sing_1372.htm#SEC1453	40566
ResTree		sing_1778.htm#SEC1859	58727
Resolution		sing_11.htm#SEC17	
Resolution of singularities	Resolution of singularities	sing_968.htm#SEC1025	
Resolution, free		sing_950.htm#SEC1007	
ReynoldsImage		sing_2133.htm#SEC2214	35172
ReynoldsOperator		sing_2134.htm#SEC2215	14986
RiemannRochBN		sing_1603.htm#SEC1684	20085
RiemannRochHess		sing_1707.htm#SEC1788	sprintf
Right Groebner bases and syzygies	Right Groebner bases and syzygies	sing_976.htm#SEC1033	
Right ideal membership (plural)	Groebner bases in G-algebras	sing_498.htm#SEC546	
Ring-dependent options	Notes for Singular users	sing_3129.htm#SEC3230	
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	
S-function		sing_3105.htm#IDX1322	
SCA	Graded commutative algebras (SCA)	sing_805.htm#SEC859	
SDB breakpoint	Source code debugger	sing_66.htm#SEC106	
SDB debugger	Source code debugger	sing_66.htm#SEC106	
SDLoc		sing_572.htm#SEC626	9512
SGB		sing_3035.htm#SEC3116	39045
SGNF		sing_3033.htm#SEC3114	62249
SINGULAR libraries		sing_1018.htm#SEC1099	
SINGULARHIST		sing_18.htm#SEC25	
SL		sing_2137.htm#SEC2218	37540
SLreynolds		sing_2143.htm#SEC2224	32171
SNF		sing_3072.htm#SEC3153	30632
SPOLY		sing_3034.htm#SEC3115	51574
SV-decoding algorithm		sing_2289.htm#IDX969	
SV-decoding algorithm, preprocessing		sing_2288.htm#IDX968	
Sagbi basis, initial algebra, defining ideal.	sagbiNormaliz_lib	sing_3036.htm#IDX1287	
Sagbi basis, initial algebra, defining ideal. 		sing_3042.htm#IDX1288	
SaitoBase		sing_3118.htm#SEC3199	49324
Sannfs		sing_548.htm#SEC602	42932
SannfsBFCT		sing_557.htm#SEC611	59702
SannfsVar		sing_611.htm#SEC665	37522
Sannfslog		sing_549.htm#SEC603	49313
Saturation		sing_947.htm#SEC1004	
Sch@"onemann, Hans		sing_1.htm#IDX20	
Schoof		sing_2387.htm#SEC2468	49281
Schubert calculus		sing_1807.htm#IDX762	
SchubertClass		sing_1844.htm#SEC1925	62336
SchurCh		sing_1655.htm#SEC1736	58575
SchurS		sing_1654.htm#SEC1735	46004
SegreA		sing_1661.htm#SEC1742	55776
Semigroup		sing_1931.htm#SEC2012	22323
Serre relations		sing_841.htm#IDX430	
SetDeg		sing_1375.htm#SEC1456	40543
Setting up a G-algebra		sing_497.htm#SEC541	
Sfunction		sing_3105.htm#SEC3186	4726
ShanksMestre		sing_2386.htm#SEC2467	12973
SimplifyIdeal		sing_2135.htm#SEC2216	sprintf
Singular		sing_368.htm#IDX265	
Singular 3 and Singular 4	Singular 3 and Singular 4	sing_3127.htm#SEC3226	
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_1716.htm#SEC1797	7552
SingularBin		sing_368.htm#IDX267	
SingularLib		sing_368.htm#IDX269	
Singularities		sing_1867.htm#SEC1948	
Singularity Theory		sing_959.htm#SEC1016	
SingularityDBM.lib		sing_1886.htm#SEC1967	
SingularityDBM_lib		sing_1886.htm#SEC1967	
Skeletons for parallelization		sing_1085.htm#IDX558	
Smith form		sing_2331.htm#IDX979	
Smith normal form		sing_2331.htm#IDX980	
SolowayStrassen		sing_2374.htm#SEC2455	22680
Solving systems of polynomial equations	Solving systems of polynomial equations	sing_978.htm#SEC1035	
Source		sing_1364.htm#SEC1445	10351
Source code debugger, invocation	Command line options	sing_19.htm#IDX33	
Space curve singularities, branches of	Branches of space curve singularities	sing_966.htm#SEC1023	
Special characters		sing_36.htm#SEC64	
Splitting lemma	addnondegeneratevariables	sing_2033.htm#IDX941	
Splitting lemma 		sing_2036.htm#IDX945	
Ssi file links		sing_124.htm#SEC164	
Ssi links		sing_123.htm#SEC163	
Ssi tcp links		sing_125.htm#SEC165	
StabEqn		sing_2025.htm#SEC2106	29571
StabEqnId		sing_2026.htm#SEC2107	27955
StabOrder		sing_2027.htm#SEC2108	55603
Standard Bases	Computing Groebner and Standard Bases	sing_942.htm#SEC999	
Standard bases		sing_993.htm#SEC1050	
Stanely-Reisner ideals, Stanley-Reisner rings, deformations	stanleyreisner_lib	sing_3063.htm#IDX1291	
StartOrderingV		sing_1862.htm#SEC1943	58927
Startup sequence		sing_20.htm#SEC27	
StringF		sing_2014.htm#SEC2095	11590
SymGroup		sing_800.htm#SEC854	56676
Symbolic-numerical solving	Solving systems of polynomial equations	sing_978.htm#SEC1035	
Symbolic-numerical solving 		sing_2148.htm#SEC2229	
System and Control theory	System and Control theory	sing_2313.htm#SEC2394	
System dependent limitations	System dependent limitations	sing_419.htm#SEC459	
System variables		sing_405.htm#SEC445	
Syzygies and resolutions	Syzygies and resolutions	sing_995.htm#SEC1054	
Syzygies and resolutions (plural)	Syzygies and resolutions (plural)	sing_499.htm#SEC548	
Syzygy bimodule	Bimodules and syzygies and lifts	sing_831.htm#SEC885	
T1		sing_963.htm#SEC1020	34830
T1 		sing_3064.htm#SEC3145	
T2		sing_963.htm#SEC1020	7148
T2 		sing_3065.htm#SEC3146	
TRACE	Tracing of procedures	sing_65.htm#SEC102	
TRACE 		sing_414.htm#SEC454	
T_1		sing_2054.htm#SEC2135	59277
T_12		sing_2056.htm#SEC2137	12923
T_2		sing_2055.htm#SEC2136	55781
Target		sing_1363.htm#SEC1444	16006
Teaching		sing_2345.htm#SEC2426	
Template for writing a library		sing_55.htm#SEC92	
TestGRRes		sing_2896.htm#SEC2977	8315
TestJMark		sing_1863.htm#SEC1944	41314
The SINGULAR language	The SINGULAR language	sing_34.htm#SEC56	
The Tran algorithm		sing_1319.htm#IDX637	
The fractal walk algorithm		sing_1318.htm#IDX636	
The fractal walk algorithm 		sing_3030.htm#IDX1286	
The online help system	The online help system	sing_16.htm#SEC22	
Tjurina		sing_2052.htm#SEC2133	11249
Tjurina number	Milnor and Tjurina number	sing_960.htm#SEC1017	
Tjurina number 		sing_1480.htm#IDX673	
Top 20 Emacs commands	Top 20 Emacs commands	sing_27.htm#SEC38	
Tor		sing_1344.htm#SEC1425	sprintf
Toric ideals and integer programming	Toric ideals and integer programming	sing_998.htm#SEC1060	
Tricks and pitfalls		sing_417.htm#SEC457	
TropCovandMaps		sing_3112.htm#SEC3193	50987
Tropical Geometry		sing_2484.htm#SEC2565	
Tropicalcover		sing_3103.htm#SEC3184	49186
Two-sided ideal membership (plural)	Groebner bases in G-algebras	sing_498.htm#SEC547	
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_1238.htm#SEC1319	26192
Ufnarovski graph		sing_870.htm#IDX438	
Unix installation	Unix installation instructions	sing_3136.htm#SEC3241	
UpOneMatrix		sing_756.htm#SEC810	63020
UpperMonomials		sing_2028.htm#SEC2109	20941
UseBertini		sing_1715.htm#SEC1796	43362
User defined types		sing_188.htm#SEC228	
V-filtration		sing_1963.htm#IDX830	
V-filtration 		sing_1969.htm#IDX858	
V-filtration  		sing_1970.htm#IDX864	
V-filtration   		sing_1971.htm#IDX872	
V-filtration    		sing_1972.htm#IDX878	
V-filtration     		sing_1973.htm#IDX886	
V-filtration      		sing_1974.htm#IDX896	
V-filtration       		sing_1985.htm#IDX902	
V-filtration        		sing_1987.htm#IDX913	
V-filtration         		sing_2915.htm#IDX1261	
VarToPar		sing_2874.htm#SEC2955	10524
Variables, indexed		sing_37.htm#SEC65	
VecField.lib		sing_3113.htm#SEC3194	
VecField_lib		sing_3113.htm#SEC3194	
Version number	Version schema for Singular	sing_3128.htm#SEC3227	
Version schema for Singular	Version schema for Singular	sing_3128.htm#SEC3227	
Version string		sing_50.htm#SEC87	
Vfiltration		sing_2916.htm#SEC2997	35173
Visualization		sing_2251.htm#SEC2332	
WLCGS		sing_1068.htm#SEC1149	sprintf
WLemma		sing_1067.htm#SEC1148	7302
WP, global ordering		sing_985.htm#IDX465	
WSemigroup		sing_1945.htm#SEC2026	15061
Weierstrass		sing_2284.htm#SEC2365	58220
Weierstrass semigroup		sing_2280.htm#IDX963	
Weyl		sing_741.htm#SEC795	29212
Weyl algebra		sing_544.htm#IDX347	
Weyl algebra 		sing_600.htm#IDX373	
Weyl algebra  		sing_608.htm#IDX379	
Weyl closure		sing_675.htm#IDX401	
WeylClosure		sing_677.htm#SEC731	23845
WeylClosure1		sing_678.htm#SEC732	15759
Wibmer's Lemma		sing_1067.htm#IDX541	
Windows installation	Windows installation instructions	sing_3137.htm#SEC3242	
WitSet		sing_1722.htm#SEC1803	39803
WitSupSet		sing_1721.htm#SEC1802	47758
Ws, local ordering		sing_986.htm#IDX477	
XLsolve		sing_2154.htm#SEC2235	34970
ZZ		sing_28.htm#SEC39	
ZZ 		sing_75.htm#SEC115	
ZZ/m		sing_28.htm#SEC39	
ZZ/p		sing_28.htm#SEC39	
ZZsolve		sing_2155.htm#SEC2236	18657
[		sing_36.htm#IDX83	
[]		sing_147.htm#SEC187	
[] 		sing_160.htm#SEC200	
[]  		sing_181.htm#SEC221	
[]   		sing_186.htm#SEC226	
\		sing_36.htm#IDX112	
]		sing_36.htm#IDX84	
^		sing_36.htm#IDX92	
^ 		sing_81.htm#SEC121	
^  		sing_98.htm#SEC138	
^   		sing_152.htm#SEC192	
^    		sing_160.htm#SEC200	
_		sing_36.htm#IDX116	
`		sing_36.htm#IDX105	
a, ordering		sing_990.htm#SEC1047	
absFactorize		sing_1251.htm#SEC1332	52546
absFactorizeBCG		sing_1252.htm#SEC1333	55510
absPrimdecGTZ		sing_1549.htm#SEC1630	46393
absPrimdecGTZE		sing_1550.htm#SEC1631	48005
absValue		sing_1031.htm#SEC1112	54595
absfact.lib		sing_1250.htm#SEC1331	
absfact_lib		sing_1250.htm#SEC1331	
absolute factorization.		sing_1250.htm#IDX594	
abstract variety, projective space, Grassmannian	makeVariety	sing_1808.htm#IDX765	
abstract variety, projective space, Grassmannian 		sing_1809.htm#IDX766	
abstractR		sing_1804.htm#SEC1885	22284
actionIsProper		sing_2115.htm#SEC2196	52474
add		sing_2819.htm#IDX1184	
add 		sing_2841.htm#IDX1232	
addElement		sing_2758.htm#SEC2839	53050
addLeftFractions		sing_772.htm#SEC826	38826
addModules		sing_1384.htm#SEC1465	51193
addNmzOption		sing_1507.htm#SEC1588	47404
addNvarsTo		sing_1174.htm#SEC1255	27033
addPoly		sing_3008.htm#SEC3089	sprintf
addRat		sing_696.htm#SEC750	4768
addSheaf		sing_1827.htm#SEC1908	27062
addcol		sing_1207.htm#SEC1288	52204
addcores		sing_1143.htm#SEC1224	41254
addnondegeneratevariables	addnondegeneratevariables	sing_2036.htm#SEC2117	40483
addrow		sing_1208.htm#SEC1289	47055
addvarsTo		sing_1173.htm#SEC1254	19606
ademRelations		sing_845.htm#SEC899	9651
adjoint		sing_1232.htm#SEC1313	56619
adjointIdeal		sing_1733.htm#SEC1814	11455
adjunction divisor		sing_2281.htm#IDX967	
admissibleSub		sing_732.htm#SEC786	6583
afaces		sing_2551.htm#SEC2632	28045
affine code	Fitzgerald-Lax method	sing_1014.htm#SEC1088	
ainvar.lib		sing_2112.htm#SEC2193	
ainvar_lib		sing_2112.htm#SEC2193	
aksaka.lib		sing_2346.htm#SEC2427	
aksaka_lib		sing_2346.htm#SEC2427	
alexanderpolynomial		sing_1871.htm#SEC1952	36814
alexpoly.lib		sing_1868.htm#SEC1949	
alexpoly_lib		sing_1868.htm#SEC1949	
algDependent		sing_1257.htm#SEC1338	20789
alg_kernel		sing_1258.htm#SEC1339	307
algebra.lib		sing_1253.htm#SEC1334	
algebra_containment		sing_1254.htm#SEC1335	47912
algebra_lib		sing_1253.htm#SEC1334	
algebraic dependence		sing_783.htm#IDX409	
algebraic field extension		sing_1568.htm#IDX684	
algebraic statistics		sing_2927.htm#IDX1264	
algebraicDependence		sing_1586.htm#SEC1667	38500
algorithm of Bigatti, La Scala and Robbiano	Bigatti and La Scala and Robbiano	sing_1005.htm#SEC1067	
algorithm of Conti and Traverso		sing_1001.htm#SEC1063	
algorithm of Di Biase and Urbanke	Di Biase and Urbanke	sing_1004.htm#SEC1066	
algorithm of Hosten and Sturmfels	Hosten and Sturmfels	sing_1003.htm#SEC1065	
algorithm of Pottier		sing_1002.htm#SEC1064	
alias	General command syntax	sing_35.htm#SEC59	
align		sing_214.htm#SEC254	
all.lib		sing_1023.htm#SEC1104	
allDoubleExt		sing_794.htm#SEC848	43457
allExtOfLeft		sing_791.htm#SEC845	6405
allExtOfRight		sing_792.htm#SEC846	56781
allNmzOptions		sing_1505.htm#SEC1586	58167
allPositive		sing_520.htm#SEC574	1409
all_lib		sing_1023.htm#SEC1104	
allowing net access	Command line options	sing_19.htm#IDX41	
allprint		sing_1076.htm#SEC1157	5195
allreal		sing_2476.htm#SEC2557	57232
allrealst		sing_2474.htm#SEC2555	40962
allsquarefree		sing_2007.htm#SEC2088	45545
ambientDimension		sing_2493.htm#SEC2574	18907
and	Evaluation of logical expressions	sing_106.htm#SEC146	
and 		sing_422.htm#SEC462	
annPoly		sing_569.htm#SEC623	18228
annRat		sing_570.htm#SEC624	62662
annRatSyz		sing_685.htm#SEC739	15672
annfalphaI		sing_606.htm#SEC660	5760
annfs		sing_545.htm#SEC599	38155
annfs0		sing_558.htm#SEC612	26476
annfs2		sing_559.htm#SEC613	47962
annfsBMI		sing_555.htm#SEC609	2532
annfsLogIdeal		sing_601.htm#SEC655	54611
annfsParamBM		sing_554.htm#SEC608	43587
annfsRB		sing_560.htm#SEC614	31892
annfspecial		sing_546.htm#SEC600	54522
annfspecialOld		sing_547.htm#SEC601	4490
annihilator of a module		sing_1528.htm#IDX681	
annihilator of polynomial		sing_568.htm#IDX357	
annihilator of rational function		sing_568.htm#IDX358	
annihilator of rational function 		sing_675.htm#IDX404	
annihilatorMultiFs		sing_602.htm#SEC656	2476
annil		sing_1440.htm#SEC1521	48744
appelF1		sing_587.htm#SEC641	63146
appelF2		sing_588.htm#SEC642	22460
appelF4		sing_589.htm#SEC643	6847
appendDataToSSI		sing_3055.htm#SEC3136	63198
appendWeight2Ord		sing_734.htm#SEC788	21488
application		sing_2847.htm#IDX1247	
apply		sing_389.htm#SEC429	
applyAdF		sing_536.htm#SEC590	40329
applyMatrix		sing_2161.htm#SEC2242	20788
applyPermutationToIntvec	applyPermutationToIntvec	sing_2576.htm#SEC2657	28900
applyVecField		sing_3114.htm#SEC3195	46310
arc		sing_2761.htm#SEC2842	30978
arc.lib		sing_2760.htm#SEC2841	
arc_lib		sing_2760.htm#SEC2841	
arcpoint.lib		sing_1881.htm#SEC1962	
arcpoint_lib		sing_1881.htm#SEC1962	
areEqualLeftFractions	areEqualLeftFractions	sing_774.htm#SEC828	29498
areZeroElements		sing_2976.htm#SEC3057	14728
argument, default		sing_44.htm#SEC81	
argument, optional		sing_44.htm#SEC81	
arnold.lib		sing_2762.htm#SEC2843	
arnoldClassify		sing_1890.htm#SEC1971	40812
arnoldClassify_to_string	arnoldClassify_to_string	sing_1891.htm#SEC1972	50046
arnoldCorank		sing_1892.htm#SEC1973	44841
arnoldDeterminacy		sing_1893.htm#SEC1974	22284
arnoldListAllSeries		sing_1887.htm#SEC1968	44760
arnoldMilnorCode		sing_1894.htm#SEC1975	24144
arnoldMorseSplit		sing_1895.htm#SEC1976	2792
arnoldNormalForm		sing_1889.htm#SEC1970	19102
arnoldShowSeries		sing_1888.htm#SEC1969	15643
arnold_lib		sing_2762.htm#SEC2843	
arnoldclassify.lib		sing_1886.htm#SEC1967	
arnoldclassify_lib		sing_1886.htm#SEC1967	
arr.lib		sing_2647.htm#SEC2728	
arr2multarr		sing_2680.htm#SEC2761	15063
arrBoolean		sing_2669.htm#SEC2750	63256
arrBoundedChambers		sing_2690.htm#SEC2771	18347
arrBraid		sing_2670.htm#SEC2751	34093
arrCenter		sing_2657.htm#SEC2738	24565
arrCentered		sing_2659.htm#SEC2740	15904
arrCentral		sing_2658.htm#SEC2739	14086
arrCentralize		sing_2660.htm#SEC2741	53235
arrChambers		sing_2689.htm#SEC2770	44578
arrCharPoly		sing_2687.htm#SEC2768	44881
arrCone		sing_2663.htm#SEC2744	38068
arrCoordChange		sing_2661.htm#SEC2742	61430
arrCoordNormalize		sing_2662.htm#SEC2743	57731
arrDecone		sing_2664.htm#SEC2745	54637
arrDer		sing_2677.htm#SEC2758	48815
arrEdelmanReiner		sing_2675.htm#SEC2756	59091
arrEssentialize		sing_2668.htm#SEC2749	6667
arrExponents		sing_2679.htm#SEC2760	1948
arrFlats		sing_2684.htm#SEC2765	64792
arrIsEssential		sing_2667.htm#SEC2748	34363
arrIsFree		sing_2678.htm#SEC2759	3860
arrLastVar		sing_2656.htm#SEC2737	25835
arrLattice		sing_2685.htm#SEC2766	58951
arrLocalize		sing_2665.htm#SEC2746	56070
arrOrlikSolomon		sing_2676.htm#SEC2757	31686
arrPoincare		sing_2688.htm#SEC2769	412
arrPrintMatrix		sing_2652.htm#SEC2733	21204
arrRandom		sing_2673.htm#SEC2754	59986
arrRandomCentral		sing_2674.htm#SEC2755	43698
arrRestrict		sing_2666.htm#SEC2747	sprintf
arrSet		sing_2648.htm#SEC2729	53769
arrSwapVar		sing_2655.htm#SEC2736	44919
arrTypeB		sing_2671.htm#SEC2752	22358
arrTypeD		sing_2672.htm#SEC2753	26495
arr_lib		sing_2647.htm#SEC2728	
arrange		sing_562.htm#SEC616	50350
arrangement		sing_2648.htm#IDX999	
arrangement 		sing_2649.htm#IDX1004	
arrangement  		sing_2680.htm#IDX1066	
arrangement   		sing_2681.htm#IDX1069	
ask		sing_2354.htm#SEC2435	3862
assPrimes		sing_1268.htm#SEC1349	sprintf
assign		sing_2648.htm#IDX1001	
assignment,custom	Assignments for user defined types	sing_193.htm#SEC233	
associated tangent	FamElemsAtEnvCompPoints	sing_1064.htm#IDX534	
associated tangent 		sing_1065.htm#IDX538	
assprimeszerodim.lib	assprimeszerodim_lib	sing_1266.htm#SEC1347	
assprimeszerodim_lib	assprimeszerodim_lib	sing_1266.htm#SEC1347	
attrib		sing_215.htm#SEC255	
autGenWeights		sing_2801.htm#SEC2882	32642
autGradAlg		sing_2800.htm#SEC2881	21136
autKS		sing_2799.htm#SEC2880	51607
autX		sing_2804.htm#SEC2885	43261
autXhat		sing_2803.htm#SEC2884	35932
autgradalg.lib		sing_2798.htm#SEC2879	
autgradalg_lib		sing_2798.htm#SEC2879	
automorphism group		sing_2798.htm#IDX1153	
automorphisms		sing_2798.htm#IDX1150	
autonom		sing_2318.htm#SEC2399	57044
autonomDim		sing_2319.htm#SEC2400	30055
awalk1		sing_1320.htm#SEC1401	11044
awalk2		sing_1321.htm#SEC1402	8955
b-function		sing_509.htm#IDX330	
bFactor		sing_592.htm#SEC646	15179
babyGiant		sing_2371.htm#SEC2452	41113
backward		sing_2861.htm#SEC2942	11225
bareiss		sing_216.htm#SEC256	
base2str		sing_1026.htm#SEC1107	sprintf
basering		sing_28.htm#IDX76	
basering 		sing_93.htm#SEC133	
basicinvariants		sing_1897.htm#SEC1978	32136
baumslagGroup		sing_847.htm#SEC901	14989
baumslagSolitar		sing_846.htm#SEC900	30093
beilinsonWindow		sing_3091.htm#SEC3172	1098
belongSemigroup		sing_1271.htm#SEC1352	20002
bernstein		sing_1967.htm#SEC2048	5605
bernsteinBM		sing_550.htm#SEC604	57689
bernsteinLift		sing_551.htm#SEC605	22885
bertini		sing_1708.htm#IDX719	
bertini 		sing_1713.htm#IDX726	
bertini  		sing_2201.htm#IDX958	
bertini2Singular		sing_1717.htm#SEC1798	58501
betti		sing_217.htm#SEC257	
betti (plural)		sing_466.htm#SEC506	
bfct		sing_510.htm#SEC564	29858
bfctAnn		sing_512.htm#SEC566	36658
bfctBound		sing_684.htm#SEC738	5630
bfctIdeal		sing_514.htm#SEC568	41018
bfctOneGB		sing_513.htm#SEC567	9696
bfctSyz		sing_511.htm#SEC565	26796
bfctVarAnn		sing_610.htm#SEC664	51667
bfctVarIn		sing_609.htm#SEC663	9274
bfun.lib		sing_509.htm#SEC563	
bfun_lib		sing_509.htm#SEC563	
bigger		sing_2826.htm#IDX1198	
bigint		sing_78.htm#SEC118	
bigint declarations		sing_79.htm#SEC119	
bigint expressions		sing_80.htm#SEC120	
bigint operations		sing_81.htm#SEC121	
bigint related functions	bigint related functions	sing_82.htm#SEC122	
bigintToBinary		sing_2574.htm#SEC2655	59742
bigintmat		sing_83.htm#SEC123	
bigintmat declarations	bigintmat declarations	sing_84.htm#SEC124	
bigintmat expressions	bigintmat expressions	sing_85.htm#SEC125	
bigintmat operations	bigintmat operations	sing_87.htm#SEC127	
bigintmat type cast		sing_86.htm#SEC126	
bigintvec		sing_88.htm#SEC128	
bigintvec declarations	bigintvec declarations	sing_89.htm#SEC129	
bigintvec expressions	bigintvec expressions	sing_90.htm#SEC130	
bigintvec operations	bigintvec operations	sing_92.htm#SEC132	
bigintvec type cast		sing_91.htm#SEC131	
bimodules		sing_502.htm#IDX318	
bimodules.lib		sing_502.htm#SEC556	
bimodules_lib		sing_502.htm#SEC556	
binaryToBigint		sing_2575.htm#SEC2656	sprintf
binary_add		sing_2394.htm#SEC2475	42817
binomial		sing_1032.htm#SEC1113	23208
binomials2intmat		sing_1521.htm#SEC1602	19410
birational map, image, inverse.		sing_1734.htm#IDX751	
bistd		sing_503.htm#SEC557	45237
bisyzygies		sing_502.htm#IDX319	
bitrinity		sing_504.htm#SEC558	3516
blackbox		sing_197.htm#SEC237	
blackbox 		sing_205.htm#SEC245	
block		sing_40.htm#SEC70	
block 		sing_388.htm#SEC428	
blowUp		sing_1785.htm#SEC1866	34819
blowUp2		sing_1786.htm#SEC1867	65264
blowUpBO		sing_1792.htm#SEC1873	11604
blowup0		sing_1288.htm#SEC1369	61921
boolean		sing_2669.htm#IDX1043	
boolean expressions		sing_105.htm#SEC145	
boolean operations		sing_106.htm#SEC146	
boolean_constant		sing_2734.htm#SEC2815	52873
boolean_ideal		sing_2738.htm#SEC2819	53515
boolean_poly		sing_2735.htm#SEC2816	41652
boolean_poly_ring		sing_2733.htm#SEC2814	sprintf
boolean_set		sing_2739.htm#SEC2820	58235
boolean_std		sing_2732.htm#SEC2813	5921
border basis		sing_1576.htm#IDX686	
borderBasis		sing_1577.htm#SEC1658	33172
boundBuFou		sing_2471.htm#SEC2552	26589
boundDes		sing_2473.htm#SEC2554	35149
boundposDes		sing_2472.htm#SEC2553	58854
bounds		sing_2220.htm#SEC2301	50218
bounds2		sing_2158.htm#SEC2239	20435
boxSet		sing_2222.htm#SEC2303	8552
bracket		sing_368.htm#IDX204	
bracket 		sing_425.htm#SEC465	
bracket  		sing_467.htm#SEC507	
braid		sing_2670.htm#IDX1045	
branchTo	procs with different argument types	sing_165.htm#SEC205	
break		sing_390.htm#SEC430	
break point		sing_404.htm#SEC444	
breakpoint		sing_391.htm#SEC431	
brillnoether.lib		sing_1602.htm#SEC1683	
brillnoether_lib		sing_1602.htm#SEC1683	
brnoeth.lib		sing_2280.htm#SEC2361	
brnoeth_lib		sing_2280.htm#SEC2361	
browser, command line option	Command line options	sing_19.htm#IDX44	
browser, setting the		sing_368.htm#IDX200	
browsers	The online help system	sing_16.htm#IDX21	
browsers, setting the		sing_368.htm#IDX199	
bubblesort		sing_2357.htm#SEC2438	63278
buildtree		sing_1122.htm#SEC1203	48740
buildtree, Maple		sing_1123.htm#IDX569	
buildtree, buildtreetoMaple, CGS		sing_1124.htm#IDX570	
buildtreetoMaple		sing_1123.htm#SEC1204	27880
busadj		sing_1230.htm#SEC1311	36301
bvar		sing_2746.htm#SEC2827	52773
c, module ordering		sing_987.htm#IDX480	
cProj		sing_1644.htm#SEC1725	24037
calculateI		sing_1759.htm#SEC1840	31107
calculate_max_sum		sing_2413.htm#SEC2494	4706
calculate_ordering		sing_2391.htm#SEC2472	42616
cancelunit, option		sing_324.htm#IDX177	
canonMap		sing_1325.htm#SEC1406	47599
canonical		sing_1050.htm#IDX489	
canonical form		sing_1054.htm#IDX501	
canonical form 		sing_1055.htm#IDX503	
canonical form  		sing_1056.htm#IDX505	
canonical form   		sing_1071.htm#IDX547	
canonical form    		sing_1072.htm#IDX549	
canonical form     		sing_1073.htm#IDX552	
canonical form      		sing_1074.htm#IDX554	
canonical,		sing_1058.htm#IDX515	
canonicalizeCone		sing_2494.htm#SEC2575	6251
canonize		sing_2326.htm#SEC2407	54090
cantodiffcgs		sing_1128.htm#SEC1209	6347
cantoradd		sing_2427.htm#SEC2508	55304
cantormult		sing_2430.htm#SEC2511	57569
cantorred		sing_2428.htm#SEC2509	46502
cardGroup		sing_1273.htm#SEC1354	5553
case	No case or switch statement	sing_423.htm#SEC463	
catNets		sing_2701.htm#SEC2782	24760
cccMatrixToPositiveIntvec	cccMatrixToPositiveIntvec	sing_2641.htm#SEC2722	55393
cdd		sing_1.htm#IDX10	
cddlib		sing_1.htm#IDX11	
center		sing_523.htm#IDX337	65108
center 		sing_529.htm#SEC583	
center  		sing_2657.htm#IDX1025	
center   		sing_2658.htm#IDX1026	
center    		sing_2659.htm#IDX1028	
center     		sing_2660.htm#IDX1030	
centerRed		sing_528.htm#SEC582	59910
centerVS		sing_527.htm#SEC581	27548
central		sing_2651.htm#IDX1011	
central 		sing_2658.htm#IDX1027	
central  		sing_2660.htm#IDX1029	
central   		sing_2674.htm#IDX1054	
central.lib		sing_523.htm#SEC577	
central1st		sing_2862.htm#SEC2943	29090
central2nd		sing_2863.htm#SEC2944	37545
central_lib		sing_523.htm#SEC577	
centralize		sing_523.htm#IDX340	
centralizeSet		sing_524.htm#SEC578	55737
centralizer		sing_523.htm#IDX338	65261
centralizer 		sing_530.htm#SEC584	
centralizerRed		sing_526.htm#SEC580	8209
centralizerVS		sing_525.htm#SEC579	22925
cf_class		sing_215.htm#IDX132	
cf_of		sing_3099.htm#SEC3180	59347
cgs		sing_1025.htm#SEC1106	57776
cgsdr		sing_1051.htm#SEC1132	44460
chAll		sing_1614.htm#SEC1695	2690
chAllInv		sing_1615.htm#SEC1696	57760
chDual		sing_1620.htm#SEC1701	17745
chHE		sing_1616.htm#SEC1697	63916
chHom		sing_1629.htm#SEC1710	54776
chNum		sing_1610.htm#SEC1691	54415
chNumbers		sing_1611.htm#SEC1692	42134
chNumbersProj		sing_1648.htm#SEC1729	28837
chProd		sing_1622.htm#SEC1703	40209
chProdE		sing_1623.htm#SEC1704	33460
chProdL		sing_1624.htm#SEC1705	44795
chProdLP		sing_1625.htm#SEC1706	8881
chProdM		sing_1626.htm#SEC1707	64514
chProdMP		sing_1627.htm#SEC1708	17103
chProj		sing_1645.htm#SEC1726	32311
chSum		sing_1618.htm#SEC1699	21088
chSymm		sing_1632.htm#SEC1713	24066
chSymm2L		sing_1633.htm#SEC1714	51625
chSymm2LP		sing_1634.htm#SEC1715	26099
chWedge		sing_1635.htm#SEC1716	57678
chWedge2L		sing_1636.htm#SEC1717	46597
chWedge2LP		sing_1637.htm#SEC1718	8876
chaincrit		sing_2441.htm#SEC2522	9502
chambers		sing_2689.htm#IDX1082	
chambers 		sing_2690.htm#IDX1083	
changeCoordinates		sing_3115.htm#SEC3196	4612
changeDenominator		sing_1485.htm#SEC1566	21094
changechar		sing_1148.htm#SEC1229	40388
changeord		sing_1149.htm#SEC1230	55156
changeordTo		sing_1172.htm#SEC1253	6817
changes		sing_3125.htm#SEC3206	
changevar		sing_1150.htm#SEC1231	32829
char		sing_218.htm#SEC258	
charInfo		sing_585.htm#SEC639	11034
charVariety		sing_584.htm#SEC638	18306
char_series		sing_219.htm#SEC259	
characteristic exponents		sing_1875.htm#IDX799	
characteristic exponents 		sing_1876.htm#IDX804	
characteristic exponents  		sing_1877.htm#IDX807	
characteristic exponents   		sing_1878.htm#IDX811	
characteristic exponents    		sing_1994.htm#IDX923	
characteristic polynomial		sing_2687.htm#IDX1080	
characteristic variety		sing_568.htm#IDX365	
characteristic variety 		sing_675.htm#IDX400	
charexp2conductor		sing_1878.htm#SEC1959	sprintf
charexp2generators		sing_1876.htm#SEC1957	16838
charexp2inter		sing_1877.htm#SEC1958	39881
charexp2multseq		sing_1875.htm#SEC1956	334
charexp2poly		sing_1879.htm#SEC1960	sprintf
charpoly		sing_1231.htm#SEC1312	38340
charstr		sing_220.htm#SEC260	
chebyshev		sing_1284.htm#SEC1365	15329
checkFactor		sing_561.htm#SEC615	55900
checkRoot		sing_556.htm#SEC610	37045
checkpfd		sing_2994.htm#SEC3075	23390
checkpfdMat		sing_3002.htm#SEC3083	29685
chern		sing_1609.htm#SEC1690	4916
chern.lib		sing_1604.htm#SEC1685	
chernCharPoly		sing_1651.htm#SEC1732	31610
chernPoly		sing_1650.htm#SEC1731	31316
chern_lib		sing_1604.htm#SEC1685	
chineseRem		sing_2362.htm#SEC2443	38560
chinrem		sing_221.htm#SEC261	
chinrempoly		sing_1456.htm#SEC1537	42312
chinrestp		sing_2421.htm#SEC2502	24779
cimonom.lib		sing_2485.htm#SEC2566	
cimonom_lib		sing_2485.htm#SEC2566	
cisimplicial.lib		sing_1269.htm#SEC1350	
cisimplicial_lib		sing_1269.htm#SEC1350	
classSpaceCurve		sing_1926.htm#SEC2007	sprintf
classification		sing_1886.htm#IDX816	
classification 		sing_1914.htm#IDX819	
classification  		sing_2762.htm#IDX1143	
classify		sing_1898.htm#SEC1979	4953
classify.lib		sing_1896.htm#SEC1977	
classify2.lib		sing_1914.htm#SEC1995	
classify2_lib		sing_1914.htm#SEC1995	
classifyCeq		sing_1928.htm#SEC2009	42719
classifyMapGerms.lib	classifyMapGerms_lib	sing_1932.htm#SEC2013	
classifyMapGerms_lib	classifyMapGerms_lib	sing_1932.htm#SEC2013	
classifySimpleMaps		sing_1938.htm#SEC2019	62176
classifySimpleMaps1		sing_1939.htm#SEC2020	24789
classifyUnimodalMaps	classifyUnimodalMaps	sing_1940.htm#SEC2021	63464
classify_aeq.lib		sing_1917.htm#SEC1998	
classify_aeq_lib		sing_1917.htm#SEC1998	
classify_lib		sing_1896.htm#SEC1977	
classifyceq.lib		sing_1927.htm#SEC2008	
classifyceq_lib		sing_1927.htm#SEC2008	
classifyci.lib		sing_1929.htm#SEC2010	
classifyci_lib		sing_1929.htm#SEC2010	
classifyicis		sing_1930.htm#SEC2011	37651
classpoly		sing_1649.htm#SEC1730	45724
cleanTmp		sing_2629.htm#SEC2710	14108
cleanunit		sing_1757.htm#SEC1838	sprintf
cleardenom		sing_222.htm#SEC262	
close		sing_223.htm#SEC263	
closeSSI		sing_3052.htm#SEC3133	17933
closed_points		sing_2290.htm#SEC2371	47269
closetex		sing_2257.htm#SEC2338	42334
closureFrac		sing_1478.htm#SEC1559	9252
coDim		sing_1934.htm#SEC2015	54424
coDimMap		sing_1933.htm#SEC2014	2002
coHom		sing_718.htm#SEC772	51043
codim		sing_2039.htm#SEC2120	14253
codimension		sing_2495.htm#SEC2576	32207
coding theory		sing_979.htm#SEC1036	
coef		sing_224.htm#SEC264	
coeff		sing_2765.htm#SEC2846	63901
coefficient		sing_2650.htm#IDX1007	
coefficient 		sing_2651.htm#IDX1010	
coefficient  		sing_2652.htm#IDX1014	
coefficient field		sing_149.htm#SEC189	
coefficient of a polynomial		sing_3099.htm#IDX1314	
coefficient rings, ring of integers, zero divisors, p-adic numbers	Coefficient rings	sing_32.htm#SEC45	
coefficients		sing_2813.htm#IDX1173	
coefficients, long		sing_936.htm#SEC993	
coeffmod		sing_2352.htm#SEC2433	23531
coeffs		sing_225.htm#SEC265	
cohomologyHashTable		sing_3089.htm#SEC3170	28034
cohomologyMatrix		sing_3086.htm#SEC3167	19617
cohomologyMatrixFromResolution	cohomologyMatrixFromResolution	sing_3087.htm#SEC3168	5397
coker		sing_1380.htm#SEC1461	35639
colength of derivations	curveColengthDerivations	sing_1279.htm#IDX606	
collectDiv		sing_1802.htm#SEC1883	50348
colrank		sing_2324.htm#SEC2405	52290
colred		sing_1214.htm#SEC1295	1693
combinat.lib		sing_2692.htm#SEC2773	
combinat_lib		sing_2692.htm#SEC2773	
commRing		sing_699.htm#SEC753	30892
comma		sing_424.htm#SEC464	
command,custom	Commands for user defined types	sing_192.htm#SEC232	
command-line option, setting value of		sing_368.htm#IDX293	
command-line option, value of		sing_368.htm#IDX291	
command-line options, print all values of		sing_368.htm#IDX290	
command-line options, short help	Command line options	sing_19.htm#IDX38	
commands (letterplace)	Functions (letterplace)	sing_811.htm#SEC865	
commands (plural)		sing_465.htm#IDX317	
comment		sing_36.htm#IDX108	
compare		sing_2824.htm#IDX1193	
compare 		sing_2825.htm#IDX1195	
compare  		sing_2826.htm#IDX1199	
compare   		sing_2827.htm#IDX1202	
compare    		sing_2845.htm#IDX1240	
compare     		sing_2846.htm#IDX1242	
compareMatrix		sing_1388.htm#SEC1469	49930
compareModules		sing_1383.htm#SEC1464	3692
compareTasks		sing_1179.htm#SEC1260	45157
compareVectors		sing_1408.htm#SEC1489	12881
complement		sing_2754.htm#SEC2835	55668
completeReduction		sing_2117.htm#SEC2198	57157
complex		sing_28.htm#IDX75	
complexClassify		sing_1915.htm#SEC1996	22796
complexSingType		sing_1912.htm#SEC1993	34483
complexType		sing_1916.htm#SEC1997	55772
compose		sing_1285.htm#SEC1366	50947
compregb.lib		sing_1024.htm#SEC1105	
compregb_lib		sing_1024.htm#SEC1105	
comprehensive Groebner system		sing_1024.htm#IDX486	
compress		sing_1192.htm#SEC1273	61998
computeAfaceOrbits		sing_2561.htm#SEC2642	28683
computeConstant		sing_1302.htm#SEC1383	19040
computeGromovWitten		sing_1305.htm#SEC1386	18834
computeN		sing_1806.htm#SEC1887	61628
computeV		sing_1805.htm#SEC1886	40316
computemcm		sing_1764.htm#SEC1845	36956
concat		sing_1193.htm#SEC1274	16653
conductor		sing_1277.htm#IDX600	
conductor 		sing_1486.htm#IDX674	
conductor  		sing_1878.htm#IDX810	
conductor, degree		sing_1994.htm#IDX926	
cone		sing_194.htm#SEC234	
cone 		sing_2663.htm#IDX1034	
cone  		sing_2664.htm#IDX1036	
coneLink		sing_2498.htm#SEC2579	13635
coneViaInequalities		sing_2497.htm#SEC2578	25661
coneViaPoints		sing_2496.htm#SEC2577	3386
conic, parametrization, rational point.		sing_1741.htm#IDX756	
conicWithTangents		sing_2605.htm#SEC2686	60752
constructH		sing_1765.htm#SEC1846	59577
constructblwup		sing_1766.htm#SEC1847	19326
constructible set		sing_1071.htm#IDX545	
constructible set 		sing_1073.htm#IDX550	
constructible sets		sing_1072.htm#IDX548	
constructible sets 		sing_1074.htm#IDX553	
constructlastblwup		sing_1767.htm#SEC1848	7639
constructor	derivationConstructor	sing_2680.htm#IDX1067	
constructor 		sing_2681.htm#IDX1070	
constructor  		sing_2812.htm#IDX1169	
constructor   		sing_2835.htm#IDX1218	
constructor    		sing_2836.htm#IDX1220	
constructor     		sing_2837.htm#IDX1223	
constructor      		sing_2838.htm#IDX1226	
contact matrix		sing_1877.htm#IDX806	
containedQ		sing_2249.htm#SEC2330	46718
containment		sing_2831.htm#IDX1209	
containsAsFace		sing_2499.htm#SEC2580	25159
containsInCollection	containsInCollection	sing_2532.htm#SEC2613	14368
containsInSupport		sing_2500.htm#SEC2581	32493
containsPositiveVector	containsPositiveVector	sing_2501.htm#SEC2582	27042
containsRelatively		sing_2502.htm#SEC2583	24321
content		sing_368.htm#IDX208	9095
content 		sing_1107.htm#SEC1188	
contentSB, option		sing_324.htm#IDX178	
continue	Behavior of continue	sing_392.htm#SEC432	
continue 		sing_426.htm#SEC466	
contraHom		sing_719.htm#SEC773	54270
contract		sing_226.htm#SEC266	
contraction	derivationContractionGen	sing_2848.htm#IDX1248	
contraction 		sing_2849.htm#IDX1250	
contraction  		sing_2850.htm#IDX1252	
contribution bundle, graph, multiple cover, rational curve,	contributionBundle	sing_1834.htm#IDX778	
contributionBundle		sing_1834.htm#SEC1915	32874
contributors		sing_368.htm#IDX206	
control		sing_2316.htm#SEC2397	44498
control.lib		sing_2315.htm#SEC2396	
controlDim		sing_2317.htm#SEC2398	2417
controlExample		sing_2329.htm#SEC2410	32774
control_Matrix		sing_1962.htm#SEC2043	sprintf
control_lib		sing_2315.htm#SEC2396	
convertLeftToRightFraction	convertLeftToRightFraction	sing_771.htm#SEC825	4318
convertRightToLeftFraction	convertRightToLeftFraction	sing_770.htm#SEC824	19389
convertdata		sing_1762.htm#SEC1843	54629
convexHull		sing_2503.htm#SEC2584	56690
convexIntersection		sing_2504.htm#SEC2585	27836
convloc		sing_565.htm#SEC619	19122
coordinate change		sing_2660.htm#IDX1031	
coordinate change 		sing_2661.htm#IDX1032	
coordinate change  		sing_2662.htm#IDX1033	
coordinates		sing_2459.htm#IDX983	
coords		sing_2459.htm#SEC2540	29362
copyTask		sing_1178.htm#SEC1259	65475
copyright		sing_1.htm#IDX1	
corank		sing_1899.htm#SEC1980	51503
corner (highest), option		sing_324.htm#IDX164	
corner, highest		sing_410.htm#SEC450	
cornerMonomials		sing_1525.htm#SEC1606	33995
countPoints		sing_2384.htm#SEC2465	58566
coverTuple		sing_3101.htm#SEC3182	28139
coverings		sing_1304.htm#IDX626	
coverings 		sing_1305.htm#IDX630	
cpu		sing_368.htm#IDX210	
cpu 		sing_368.htm#IDX287	
crcgs		sing_1127.htm#SEC1208	50631
createBO		sing_1793.htm#SEC1874	32669
createGradedRingHomomorphism	createGradedRingHomomorphism	sing_2952.htm#SEC3033	62177
createGroup		sing_2945.htm#SEC3026	28500
createQuotientGroup		sing_2946.htm#SEC3027	26374
createTask		sing_1176.htm#SEC1257	48404
createTorsionFreeGroup	createTorsionFreeGroup	sing_2947.htm#SEC3028	51944
create_ring		sing_227.htm#SEC267	22266
createlist		sing_1775.htm#SEC1856	61781
cring		sing_73.htm#SEC113	
cring declarations		sing_74.htm#SEC114	
cring expressions		sing_75.htm#SEC115	
cring operations		sing_76.htm#SEC116	
cring related functions	cring related functions	sing_77.htm#SEC117	
crossprod		sing_228.htm#SEC268	
crypto.lib		sing_2355.htm#SEC2436	
crypto_lib		sing_2355.htm#SEC2436	
crystallographicGroupC2MM	crystallographicGroupC2MM	sing_855.htm#SEC909	9913
crystallographicGroupCM	crystallographicGroupCM	sing_854.htm#SEC908	6581
crystallographicGroupP1	crystallographicGroupP1	sing_848.htm#SEC902	48853
crystallographicGroupP2	crystallographicGroupP2	sing_852.htm#SEC906	33660
crystallographicGroupP2GG	crystallographicGroupP2GG	sing_853.htm#SEC907	53252
crystallographicGroupP2MM	crystallographicGroupP2MM	sing_851.htm#SEC905	7901
crystallographicGroupP3	crystallographicGroupP3	sing_859.htm#SEC913	54137
crystallographicGroupP31M	crystallographicGroupP31M	sing_860.htm#SEC914	40601
crystallographicGroupP3M1	crystallographicGroupP3M1	sing_861.htm#SEC915	25851
crystallographicGroupP4	crystallographicGroupP4	sing_856.htm#SEC910	15991
crystallographicGroupP4GM	crystallographicGroupP4GM	sing_858.htm#SEC912	33875
crystallographicGroupP4MM	crystallographicGroupP4MM	sing_857.htm#SEC911	40759
crystallographicGroupP6	crystallographicGroupP6	sing_862.htm#SEC916	22732
crystallographicGroupP6MM	crystallographicGroupP6MM	sing_863.htm#SEC917	28745
crystallographicGroupPG	crystallographicGroupPG	sing_850.htm#SEC904	12116
crystallographicGroupPM	crystallographicGroupPM	sing_849.htm#SEC903	24392
cup		sing_1326.htm#SEC1407	57972
cupproduct		sing_1327.htm#SEC1408	43349
curve singularities		sing_1868.htm#IDX793	
curve singularities 		sing_1988.htm#IDX921	
curve singularity		sing_1275.htm#IDX595	
curveColengthDerivations	curveColengthDerivations	sing_1279.htm#SEC1360	2078
curveConductorMult		sing_1277.htm#SEC1358	15897
curveDeligneNumber		sing_1278.htm#SEC1359	12294
curveDeltaInv		sing_1276.htm#SEC1357	16375
curveInv.lib		sing_1275.htm#SEC1356	
curveInv_lib		sing_1275.htm#SEC1356	
curvepar.lib		sing_1941.htm#SEC2022	
curvepar_lib		sing_1941.htm#SEC2022	
custom assignment	Assignments for user defined types	sing_193.htm#SEC233	
custom command	Commands for user defined types	sing_192.htm#SEC232	
custom type	Definition of a user defined type	sing_189.htm#SEC229	
customstd.lib		sing_2696.htm#SEC2777	
customstd_lib		sing_2696.htm#SEC2777	
cycleLength		sing_2583.htm#SEC2664	16898
cyclePoints		sing_2587.htm#SEC2668	54460
cyclic		sing_1094.htm#SEC1175	21375
cyclic code	Codes and the decoding problem	sing_1011.htm#SEC1075	
cyclotomic		sing_2082.htm#SEC2163	33749
datetime		sing_229.htm#SEC269	54939
dbprint		sing_230.htm#SEC270	
deRham.lib		sing_1666.htm#SEC1747	
deRhamCohom		sing_582.htm#SEC636	58222
deRhamCohomIdeal		sing_583.htm#SEC637	42169
deRhamCohomology		sing_1667.htm#SEC1748	30823
deRham_lib		sing_1666.htm#SEC1747	
debugLib, option		sing_324.htm#IDX183	
debug_log		sing_1909.htm#SEC1990	62043
debugger	Source code debugger	sing_66.htm#SEC103	
debugging library code	Source code debugger	sing_66.htm#SEC103	
dec1var		sing_1439.htm#SEC1520	36098
decimal		sing_2358.htm#SEC2439	56066
decode		sing_2307.htm#SEC2388	64330
decodeCode		sing_2309.htm#SEC2390	28262
decodeRandom		sing_2308.htm#SEC2389	40118
decodeRandomFL		sing_2312.htm#SEC2393	29305
decodeSV		sing_2289.htm#SEC2370	37975
decodegb.lib		sing_2294.htm#SEC2375	
decodegb_lib		sing_2294.htm#SEC2375	
decoding, decoding problem	Codes and the decoding problem	sing_1011.htm#SEC1076	
decoef		sing_2337.htm#SEC2418	60284
decomp.lib		sing_1280.htm#SEC1361	
decomp_lib		sing_1280.htm#SEC1361	
decompopts		sing_1281.htm#SEC1362	40761
decompose		sing_1282.htm#SEC1363	37692
decomposeVecField		sing_3121.htm#SEC3202	50585
decomposition		sing_2813.htm#IDX1171	
decomposition 		sing_2992.htm#IDX1273	
decomposition of modules		sing_1432.htm#IDX652	
decomposition, numerical		sing_1713.htm#IDX724	
decone		sing_2663.htm#IDX1035	
decone 		sing_2664.htm#IDX1037	
def		sing_93.htm#SEC133	
def declarations		sing_94.htm#SEC134	
defRes, option		sing_324.htm#IDX184	
default argument		sing_44.htm#SEC81	
defineHomogeneous		sing_2985.htm#SEC3066	55072
defined		sing_231.htm#SEC271	
definingBinomialIdeal	definingBinomialIdeal	sing_1495.htm#SEC1576	27991
defl		sing_1724.htm#SEC1805	11825
deform		sing_2040.htm#SEC2121	5250
deform.lib		sing_1952.htm#SEC2033	
deform_lib		sing_1952.htm#SEC2033	
defring		sing_1151.htm#SEC1232	1814
defringp		sing_1153.htm#SEC1234	42905
defrings		sing_1152.htm#SEC1233	1034
deg		sing_232.htm#SEC272	
degBound		sing_406.htm#SEC446	
degree	Miscellaneous oddities	sing_233.htm#SEC273	
degree 		sing_429.htm#IDX307	
degree  		sing_2828.htm#IDX1204	
degree   		sing_2830.htm#IDX1208	
degree lexicographical ordering		sing_985.htm#IDX460	
degree of a polynomial	Miscellaneous oddities	sing_429.htm#IDX311	
degree reverse lexicographical ordering		sing_985.htm#IDX458	
degreeDivisor		sing_1677.htm#SEC1758	31751
degreeFormalDivisor		sing_1685.htm#SEC1766	42503
degreepart		sing_2166.htm#SEC2247	53036
delete		sing_131.htm#SEC171	
delete 		sing_234.htm#SEC274	
delete  		sing_284.htm#SEC324	
deleteGenerator		sing_597.htm#SEC651	24917
deleteSublist		sing_1033.htm#SEC1114	20406
deligne number	curveColengthDerivations	sing_1275.htm#IDX597	
deligne number 		sing_1278.htm#IDX602	
deligne number  		sing_1279.htm#IDX604	
delta		sing_2000.htm#SEC2081	56952
delta invariant		sing_1276.htm#IDX598	
delta invariant 		sing_1480.htm#IDX672	
delta invariant  		sing_2000.htm#IDX931	
delta invariant   		sing_2762.htm#IDX1145	
delta invariant.		sing_1470.htm#IDX660	
delta invariant. 		sing_1473.htm#IDX668	
delta invariant.  		sing_1474.htm#IDX671	
deltaLoc		sing_1480.htm#SEC1561	35192
deltaNNB		sing_2791.htm#SEC2872	23079
denom_list		sing_368.htm#IDX212	
denominator		sing_235.htm#SEC275	
depth		sing_1328.htm#SEC1409	58120
depthIdeal		sing_1449.htm#SEC1530	54782
derivate		sing_2114.htm#SEC2195	15409
derivation	derivationConstructor	sing_2677.htm#IDX1058	
derivation 		sing_2833.htm#IDX1213	
derivation  		sing_2834.htm#IDX1217	
derivation   		sing_2835.htm#IDX1219	
derivation    		sing_2836.htm#IDX1221	
derivation     		sing_2837.htm#IDX1224	
derivation      		sing_2838.htm#IDX1227	
derivation       		sing_2847.htm#IDX1246	
derivationAdd		sing_2841.htm#SEC2922	6778
derivationCheckList		sing_2836.htm#SEC2917	43492
derivationConstructor	derivationConstructor	sing_2838.htm#SEC2919	39369
derivationContraction	derivationContraction	sing_2849.htm#SEC2930	30973
derivationContractionGen	derivationContractionGen	sing_2848.htm#SEC2929	38568
derivationEqu		sing_2845.htm#SEC2926	6648
derivationEval		sing_2847.htm#SEC2928	50615
derivationFromList		sing_2835.htm#SEC2916	26077
derivationFromPoly		sing_2837.htm#SEC2918	53267
derivationLie		sing_2850.htm#SEC2931	19187
derivationMul		sing_2844.htm#SEC2925	10860
derivationNeg		sing_2843.htm#SEC2924	65108
derivationNeq		sing_2846.htm#SEC2927	12420
derivationPrint		sing_2840.htm#SEC2921	24145
derivationSub		sing_2842.htm#SEC2923	63630
derivationToString		sing_2839.htm#SEC2920	15425
desingularization		sing_2878.htm#IDX1257	59041
desingularization 		sing_2879.htm#SEC2960	
det		sing_236.htm#SEC276	
det_B		sing_1233.htm#SEC1314	60143
detadj		sing_2016.htm#SEC2097	57584
determinacy		sing_2035.htm#SEC2116	44818
determinacy bound		sing_2762.htm#IDX1146	
determinacyBound		sing_2790.htm#SEC2871	51791
determineArnoldType		sing_2793.htm#SEC2874	6585
determineExceptionalHypersurface	determineExceptionalHypersurface	sing_2779.htm#SEC2860	56884
determineGermWithSemiNormalizedNNB	determineGermWithSemiNormalizedNNB	sing_2786.htm#SEC2867	8392
determineNormalForm		sing_2777.htm#SEC2858	38783
determineNormalFormEquation	determineNormalFormEquation	sing_2781.htm#SEC2862	30923
determinecenter		sing_1747.htm#SEC1828	44496
detropicalise		sing_2623.htm#SEC2704	38025
develop		sing_1990.htm#SEC2071	48457
diag		sing_1194.htm#SEC1275	56759
diagInvariants		sing_1500.htm#SEC1581	62096
diag_test		sing_1229.htm#SEC1310	31469
diagonalizeMatrixSimul	diagonalizeMatrixSimul	sing_3122.htm#SEC3203	35203
diagonalizeVecField		sing_3119.htm#SEC3200	17203
diagonalizeVecFieldLin	diagonalizeVecFieldLin	sing_3117.htm#SEC3198	14427
diff		sing_237.htm#SEC277	
diffAlgebra		sing_2806.htm#SEC2887	sprintf
diffAlgebraChangeOrd	diffAlgebraChangeOrd	sing_2810.htm#SEC2891	14915
diffAlgebraGens		sing_2808.htm#SEC2889	15657
diffAlgebraListGen		sing_2811.htm#SEC2892	36288
diffAlgebraStructure	diffAlgebraStructure	sing_2807.htm#SEC2888	61758
diffAlgebraUnivDerIdeal	diffAlgebraUnivDerIdeal	sing_2809.htm#SEC2890	46686
diffRat		sing_698.htm#SEC752	36134
difference		sing_2820.htm#IDX1187	
difference 		sing_2842.htm#IDX1235	
difference  		sing_2843.htm#IDX1237	
differential		sing_2812.htm#IDX1170	
differential 		sing_2834.htm#IDX1215	
differential algebra	diffAlgebraStructure	sing_2805.htm#IDX1157	
differential algebra 		sing_2806.htm#IDX1158	
differential algebra  		sing_2807.htm#IDX1161	
differential algebra   		sing_2808.htm#IDX1162	
differential algebra    		sing_2809.htm#IDX1164	
differential forms		sing_2805.htm#IDX1155	
differential forms 		sing_2806.htm#IDX1159	
differentials		sing_2805.htm#IDX1156	
differentials 		sing_2806.htm#IDX1160	
difform.lib		sing_2805.htm#SEC2886	
difformAdd		sing_2819.htm#SEC2900	28830
difformCoef		sing_2813.htm#SEC2894	24261
difformDeg		sing_2828.htm#SEC2909	49895
difformDiff		sing_2834.htm#SEC2915	23157
difformDiv		sing_2823.htm#SEC2904	14615
difformEqu		sing_2824.htm#SEC2905	57529
difformFromPoly		sing_2812.htm#SEC2893	31062
difformGenToString		sing_2814.htm#SEC2895	10208
difformHomogDecomp		sing_2815.htm#SEC2896	58877
difformIsBigger		sing_2826.htm#SEC2907	57971
difformIsGen		sing_2818.htm#SEC2899	40829
difformIsHomog		sing_2829.htm#SEC2910	39513
difformIsHomogDeg		sing_2830.htm#SEC2911	29202
difformIsSmaller		sing_2827.htm#SEC2908	57933
difformListCont		sing_2831.htm#SEC2912	19777
difformListSort		sing_2832.htm#SEC2913	sprintf
difformMul		sing_2822.htm#SEC2903	23145
difformNeg		sing_2821.htm#SEC2902	33447
difformNeq		sing_2825.htm#SEC2906	10847
difformPrint		sing_2817.htm#SEC2898	61595
difformSub		sing_2820.htm#SEC2901	31870
difformToString		sing_2816.htm#SEC2897	21809
difformUnivDer		sing_2833.htm#SEC2914	60731
difform_lib		sing_2805.htm#SEC2886	
difpoly2tex		sing_2338.htm#SEC2419	6451
dim		sing_238.htm#SEC278	
dim (letterplace)		sing_812.htm#SEC866	
dim (plural)		sing_468.htm#SEC508	
dimGradedPart		sing_1857.htm#SEC1938	11262
dimH		sing_1856.htm#SEC1937	38534
dimMon		sing_1429.htm#SEC1510	39971
dimStack		sing_1832.htm#SEC1913	47772
dim_slocus		sing_2041.htm#SEC2122	47218
dimension		sing_2505.htm#SEC2586	35262
dimension, moduli space of stable maps, rational curves	dimStack	sing_1832.htm#IDX776	
dimensionOfLocalization	dimensionOfLocalization	sing_1701.htm#SEC1782	25632
direct_boolean_poly		sing_2736.htm#SEC2817	49893
direct_from_boolean_poly	direct_from_boolean_poly	sing_2742.htm#SEC2823	36941
discr		sing_2063.htm#SEC2144	9642
discrepancy		sing_1800.htm#SEC1881	5501
discrim		sing_1066.htm#SEC1147	44091
discussion of parametric ideal		sing_1050.htm#IDX490	
disjoint		sing_1051.htm#IDX492	
disp_zdd		sing_2749.htm#SEC2830	41439
displayCohom		sing_1858.htm#SEC1939	22633
displayHNE		sing_1993.htm#SEC2074	29845
displayInvariants		sing_1995.htm#SEC2076	13678
displayMultsequence		sing_1997.htm#SEC2078	16668
displayPuiseuxExpansion	displayPuiseuxExpansion	sing_2599.htm#SEC2680	560
displayTropicalLifting	displayTropicalLifting	sing_2597.htm#SEC2678	28144
displaypfd		sing_2996.htm#SEC3077	22301
displaypfd_long		sing_2997.htm#SEC3078	49396
distributed computing		sing_1087.htm#IDX562	
distributed computing 		sing_1142.htm#IDX576	
distributed computing  		sing_1175.htm#IDX586	
div	Miscellaneous oddities	sing_81.htm#SEC121	
div 		sing_103.htm#SEC143	
div  		sing_160.htm#SEC200	
div   		sing_429.htm#IDX304	
divideUnits		sing_2334.htm#SEC2415	26711
dividelist		sing_1774.htm#SEC1855	34210
division		sing_239.htm#SEC279	
division 		sing_1052.htm#IDX495	
division  		sing_1053.htm#IDX497	
division   		sing_2823.htm#IDX1192	
division (plural)		sing_469.htm#SEC509	
division, pdivi2, reduce		sing_1121.htm#IDX567	
division, reduce		sing_1118.htm#IDX564	
divisor		sing_2424.htm#SEC2505	10035
divisorplus		sing_1671.htm#SEC1752	34248
divisors	evaluateFormalDivisor	sing_1670.htm#IDX692	
divisors 		sing_1671.htm#IDX693	
divisors  		sing_1672.htm#IDX694	
divisors   		sing_1673.htm#IDX695	
divisors    		sing_1674.htm#IDX696	
divisors     		sing_1675.htm#IDX697	
divisors      		sing_1676.htm#IDX698	
divisors       		sing_1677.htm#IDX699	
divisors        		sing_1678.htm#IDX700	
divisors         		sing_1679.htm#IDX701	
divisors          		sing_1680.htm#IDX702	
divisors           		sing_1681.htm#IDX703	
divisors            		sing_1682.htm#IDX704	
divisors             		sing_1683.htm#IDX705	
divisors              		sing_1684.htm#IDX706	
divisors               		sing_1685.htm#IDX707	
divisors, polyhedra		sing_1686.htm#IDX708	
divisors.lib		sing_1669.htm#SEC1750	
divisors_lib		sing_1669.htm#SEC1750	
dmod.lib		sing_544.htm#SEC598	
dmodAction		sing_693.htm#SEC747	9763
dmodActionRat		sing_694.htm#SEC748	6277
dmodGeneralAssumptionCheck	dmodGeneralAssumptionCheck	sing_686.htm#SEC740	44337
dmod_lib		sing_544.htm#SEC598	
dmodapp.lib		sing_568.htm#SEC622	
dmodapp_lib		sing_568.htm#SEC622	
dmodideal.lib		sing_600.htm#SEC654	
dmodideal_lib		sing_600.htm#SEC654	
dmodloc.lib		sing_675.htm#IDX393	
dmodloc_lib		sing_675.htm#IDX394	
dmodoublext		sing_720.htm#SEC774	60637
dmodvar.lib		sing_608.htm#SEC662	
dmodvar_lib		sing_608.htm#SEC662	
double		sing_2429.htm#SEC2510	34697
doubleExt		sing_793.htm#SEC847	56896
downloading	Download instructions	sing_3134.htm#SEC3239	
dp, global ordering		sing_985.htm#IDX459	
drawNewtonSubdivision	drawNewtonSubdivision	sing_2602.htm#SEC2683	51416
drawTropicalCurve		sing_2601.htm#SEC2682	10441
ds, local ordering		sing_986.htm#IDX469	
dsum		sing_1195.htm#SEC1276	1303
dualCone		sing_2506.htm#SEC2587	61460
dualConic		sing_2625.htm#SEC2706	31080
dualPart		sing_1657.htm#SEC1738	13279
dualPartition		sing_1845.htm#SEC1926	24739
dualPolytope		sing_2545.htm#SEC2626	32081
dualSheaf		sing_1823.htm#SEC1904	633
dual_code		sing_2291.htm#SEC2372	57229
dump		sing_240.htm#SEC280	
dyckGroup1		sing_864.htm#SEC918	9319
dyckGroup2		sing_865.htm#SEC919	10364
dyckGroup3		sing_866.htm#SEC920	60041
dynamic geometry		sing_1059.htm#IDX519	
dynamic geometry 		sing_1060.htm#IDX522	
ecart		sing_2432.htm#SEC2513	32475
echo		sing_407.htm#SEC447	
edge, highest		sing_410.htm#SEC450	
eexgcdN		sing_2359.htm#SEC2440	53237
effective		sing_1679.htm#SEC1760	53028
egcdMain		sing_2242.htm#SEC2323	52133
ehrhartRing		sing_1493.htm#SEC1574	45502
eigenvals		sing_1241.htm#SEC1322	11228
eigenvalue		sing_338.htm#SEC378	
eigenvalue 		sing_1241.htm#IDX592	
eigenvalues		sing_1595.htm#SEC1676	2182
elemSymmId		sing_1095.htm#SEC1176	sprintf
elim		sing_1290.htm#SEC1371	26220
elim.lib		sing_1287.htm#SEC1368	
elim1		sing_1291.htm#SEC1372	21692
elim2		sing_1292.htm#SEC1373	7867
elimRing		sing_1289.htm#SEC1370	12203
elimWeight		sing_735.htm#SEC789	54297
elim_lib		sing_1287.htm#SEC1368	
eliminate		sing_241.htm#SEC281	
eliminate (plural)		sing_470.htm#SEC510	
eliminateNC		sing_730.htm#SEC784	3777
elimination		sing_729.htm#IDX408	
elimlinearpart		sing_2167.htm#SEC2248	14251
elimpart		sing_2168.htm#SEC2249	10258
elimpartanyr		sing_2169.htm#SEC2250	38450
elimrep		sing_1755.htm#SEC1836	23641
elliptic curve		sing_1301.htm#IDX620	
elliptic curve cover multiplicities		sing_3102.htm#IDX1317	
elliptic curve covers		sing_3103.htm#IDX1318	
elliptic curve draw covers		sing_3111.htm#IDX1335	
elliptic curve draw covers 		sing_3112.htm#IDX1336	
elliptic curves	tropicalEllipticCovers_lib	sing_1298.htm#IDX614	
elliptic curves 		sing_1304.htm#IDX625	
elliptic curves  		sing_1305.htm#IDX629	
elliptic curves   		sing_3098.htm#IDX1308	
elliptic curves    		sing_3104.htm#IDX1319	
elliptic curves     		sing_3105.htm#IDX1321	
elliptic curves      		sing_3106.htm#IDX1323	
elliptic curves       		sing_3107.htm#IDX1326	
elliptic curves        		sing_3108.htm#IDX1328	
elliptic curves         		sing_3109.htm#IDX1330	
elliptic curves          		sing_3110.htm#IDX1332	
ellipticAdd		sing_2380.htm#SEC2461	13279
ellipticAllPoints		sing_2385.htm#SEC2466	60770
ellipticMult		sing_2381.htm#SEC2462	1558
ellipticNF		sing_2590.htm#SEC2671	5045
ellipticRandomCurve		sing_2382.htm#SEC2463	36980
ellipticRandomPoint		sing_2383.htm#SEC2464	6866
ellipticcovers.lib		sing_1298.htm#SEC1379	
ellipticcovers_lib		sing_1298.htm#SEC1379	
else		sing_397.htm#SEC437	
embedMat		sing_761.htm#SEC815	17119
emptyFan		sing_2533.htm#SEC2614	7396
encode		sing_2299.htm#SEC2380	56687
endomorphism filtration		sing_1974.htm#IDX897	
endvfilt		sing_1974.htm#SEC2055	26670
ensureLeftNcfrac		sing_708.htm#SEC762	64571
ensureRightNcfrac		sing_709.htm#SEC763	14107
enumpoints.lib		sing_2851.htm#SEC2932	
enumpoints_lib		sing_2851.htm#SEC2932	
envelop	FamElemsAtEnvCompPoints	sing_1061.htm#SEC1142	43483
envelop 		sing_1061.htm#IDX525	
envelop  		sing_1062.htm#IDX528	
envelop   		sing_1064.htm#IDX533	
envelop    		sing_1065.htm#IDX537	
envelope		sing_471.htm#SEC511	
enveloping algebra		sing_368.htm#IDX216	
enveloping algebra 		sing_502.htm#IDX321	
environment variable, DISPLAY	The online help system	sing_16.htm#IDX29	
environment variables	Used environment variables	sing_3135.htm#SEC3240	
equal		sing_2824.htm#IDX1194	
equal 		sing_2825.htm#IDX1196	
equal  		sing_2845.htm#IDX1241	
equal   		sing_2846.htm#IDX1243	
equalJinI		sing_1885.htm#SEC1966	18502
equalMultiDeg		sing_2978.htm#SEC3059	37090
equalPoly		sing_3010.htm#SEC3091	sprintf
equations		sing_2507.htm#SEC2588	7896
equiRadical		sing_1543.htm#SEC1624	8884
equidim		sing_1545.htm#SEC1626	38541
equidimMax		sing_1546.htm#SEC1627	49289
equidimMaxEHV		sing_1547.htm#SEC1628	42650
equidimZ		sing_1563.htm#SEC1644	32547
equising.lib		sing_1957.htm#SEC2038	
equising_lib		sing_1957.htm#SEC2038	
equisingular Tjurina number		sing_1868.htm#IDX798	
equisingularity ideal		sing_1959.htm#IDX824	
equisingularity stratum		sing_1960.htm#IDX825	
error recovery		sing_15.htm#SEC21	
errorInsert		sing_2302.htm#SEC2383	59470
errorRand		sing_2303.htm#SEC2384	5727
errormap		sing_2868.htm#SEC2949	7782
esIdeal		sing_1959.htm#SEC2040	60477
esStratum		sing_1960.htm#SEC2041	21460
essential		sing_2667.htm#IDX1040	
essential 		sing_2668.htm#IDX1041	
eta		sing_2585.htm#SEC2666	53299
euler		sing_2351.htm#SEC2432	10519
eulerChProj		sing_1647.htm#SEC1728	8329
eulerPolynomialTable	eulerPolynomialTable	sing_3088.htm#SEC3169	31384
eval		sing_242.htm#SEC282	
evalJacobianAtBox		sing_2228.htm#SEC2309	42716
evalPolyAtBox		sing_2227.htm#SEC2308	10346
evalPolyAtBox2		sing_2163.htm#SEC2244	63974
evaluateFormalDivisor	evaluateFormalDivisor	sing_1681.htm#SEC1762	3535
evaluateIntegral		sing_1303.htm#SEC1384	61670
evaluateProduct		sing_2571.htm#SEC2652	54515
evaluate_reynolds		sing_2087.htm#SEC2168	46353
evaluatepfd		sing_2995.htm#SEC3076	13879
evaluation		sing_2847.htm#IDX1245	
exactness recovery		sing_2201.htm#IDX956	
example		sing_244.htm#SEC284	
example 		sing_2669.htm#IDX1042	
example  		sing_2670.htm#IDX1044	
example   		sing_2671.htm#IDX1046	
example    		sing_2672.htm#IDX1048	
example     		sing_2673.htm#IDX1050	
example      		sing_2674.htm#IDX1052	
example       		sing_2675.htm#IDX1055	
exceptionalHypersurface	exceptionalHypersurface	sing_2780.htm#SEC2861	12870
exclusionTest		sing_2164.htm#SEC2245	47250
execute		sing_245.htm#SEC285	
exit		sing_401.htm#SEC441	
exp2pt		sing_2339.htm#SEC2420	19621
expPoly		sing_3011.htm#SEC3092	sprintf
exponents		sing_2679.htm#IDX1063	
export		sing_394.htm#SEC434	
exportNuminvs		sing_1504.htm#SEC1585	10423
exportto		sing_395.htm#SEC435	
expp		sing_1843.htm#SEC1924	15751
expression list		sing_72.htm#IDX128	
expression list 		sing_433.htm#IDX314	
ext-module	purityfiltration_lib	sing_785.htm#IDX414	
extcurve		sing_2285.htm#SEC2366	6730
extdevelop		sing_1991.htm#SEC2072	51044
extendGC		sing_1058.htm#SEC1139	40951
extendWeyl		sing_687.htm#SEC741	49954
extendedTensor		sing_736.htm#SEC790	4975
extendpoly		sing_1057.htm#SEC1138	29201
extendring		sing_1154.htm#SEC1235	64781
extension of rings		sing_1568.htm#IDX685	
exterior basis		sing_1220.htm#IDX589	
exterior power		sing_1222.htm#IDX591	
exteriorBasis		sing_1220.htm#SEC1301	sprintf
exteriorPower		sing_1222.htm#SEC1303	20173
extgcd		sing_246.htm#SEC286	
extractS		sing_607.htm#SEC661	32846
fPiece		sing_3067.htm#SEC3148	35357
fVector		sing_2536.htm#SEC2617	3715
facFirstShift		sing_662.htm#SEC716	6469
facFirstWeyl		sing_658.htm#SEC712	42412
facGBIdeal		sing_1526.htm#SEC1607	5823
facShift		sing_661.htm#SEC715	48551
facSubWeyl		sing_660.htm#SEC714	9630
facWeyl		sing_657.htm#SEC711	32331
faceContaining		sing_2508.htm#SEC2589	64804
facets		sing_2509.htm#SEC2590	8112
facstd		sing_247.htm#SEC287	
factmodd		sing_248.htm#SEC288	
factor		sing_331.htm#SEC371	
factor 		sing_1119.htm#IDX565	
factorH		sing_1048.htm#SEC1129	24814
factorLenstraECM		sing_2389.htm#SEC2470	54967
factorMain		sing_2243.htm#SEC2324	65152
factorgroup		sing_2968.htm#SEC3049	59914
factorial		sing_1034.htm#SEC1115	32871
factorization		sing_332.htm#SEC372	
factorization 		sing_1250.htm#IDX593	
factorize		sing_249.htm#SEC289	
factorize 		sing_331.htm#SEC371	
factory		sing_1.htm#IDX2	
facvar		sing_1119.htm#SEC1200	28207
fan		sing_195.htm#SEC235	
fan 		sing_2580.htm#IDX989	
fanViaCones		sing_2534.htm#SEC2615	16418
farey		sing_250.htm#SEC290	
farey 		sing_418.htm#IDX302	
fareypoly		sing_1310.htm#SEC1391	12389
fastExpt		sing_2347.htm#SEC2428	43912
fastHC, option		sing_324.htm#IDX155	
fastelim		sing_2170.htm#SEC2251	7409
fetch		sing_251.htm#SEC291	
fetch (letterplace)		sing_813.htm#SEC867	
fetch (plural)		sing_472.htm#SEC512	
fetchall		sing_1155.htm#SEC1236	7537
ffmodStd		sing_1316.htm#SEC1397	29234
ffmodstd.lib		sing_1309.htm#SEC1390	
ffmodstd_lib		sing_1309.htm#SEC1390	
ffsolve		sing_2150.htm#SEC2231	20432
ffsolve.lib		sing_2149.htm#SEC2230	
ffsolve_lib		sing_2149.htm#SEC2230	
fglm		sing_252.htm#SEC292	
fglm 		sing_365.htm#IDX194	
fglm_solve		sing_2186.htm#SEC2267	51398
fglmquot		sing_253.htm#SEC293	
fibonacci		sing_1035.htm#SEC1116	24750
fibonacciGroup		sing_867.htm#SEC921	35301
field		sing_149.htm#SEC189	
file, .singularrc		sing_20.htm#IDX71	
filecmd		sing_254.htm#SEC294	
filtration	purityfiltration_lib	sing_785.htm#IDX415	
finalCharts		sing_1779.htm#SEC1860	37296
finalcases		sing_1124.htm#SEC1205	55683
find		sing_255.htm#SEC295	
findAuto		sing_616.htm#SEC670	51205
findInvo		sing_614.htm#SEC668	18177
findInvoDiag		sing_615.htm#SEC669	7365
findOrientedBoundary	findOrientedBoundary	sing_2586.htm#SEC2667	24110
findTorsion		sing_2328.htm#SEC2409	29572
findZeroPoly		sing_3023.htm#SEC3104	17366
find_first_primitive_root	find_first_primitive_root	sing_2393.htm#SEC2474	33327
find_index		sing_2397.htm#SEC2478	62564
findifs.lib		sing_2335.htm#SEC2416	
findifs_example		sing_2336.htm#SEC2417	33849
findifs_lib		sing_2335.htm#SEC2416	
findimAlgebra		sing_745.htm#SEC799	64612
finduni		sing_256.htm#SEC296	
findvars		sing_2171.htm#SEC2252	42474
finite field		sing_149.htm#SEC189	
finite field 		sing_2149.htm#IDX953	
finite field  		sing_2851.htm#IDX1254	
finiteDiagInvariants	finiteDiagInvariants	sing_1499.htm#SEC1580	3508
finitediff.lib		sing_2854.htm#IDX1255	
finitediff_lib		sing_2854.htm#IDX1256	
finitely presented algebra		sing_834.htm#IDX422	
finitely presented algebra 		sing_841.htm#IDX428	
finitely presented algebra  		sing_870.htm#IDX431	
finitely presented algebra   		sing_879.htm#IDX443	
finitely presented algebra    		sing_893.htm#IDX444	
finitely presented algebra, standard finitely presented algebra	Free associative algebras	sing_828.htm#IDX421	
finitely presented group		sing_841.htm#IDX429	
finitenessTest		sing_1264.htm#SEC1345	40633
finiterep		sing_2140.htm#SEC2221	47740
finvar.lib		sing_2075.htm#SEC2156	
finvar_lib		sing_2075.htm#SEC2156	
first index is 1		sing_428.htm#SEC468	
first order deformation		sing_3064.htm#IDX1292	
first order deformation 		sing_3067.htm#IDX1295	
firstQuadrantComplex	firstQuadrantComplex	sing_3094.htm#SEC3175	2213
firstoct		sing_2235.htm#SEC2316	11498
fitting		sing_1331.htm#SEC1412	20661
fixed points, moduli space of stable maps, graph	fixedPoints	sing_1833.htm#IDX777	
fixedPoints		sing_1833.htm#SEC1914	25366
fl2poly		sing_595.htm#SEC649	51682
flatten		sing_1196.htm#SEC1277	5964
flatteningStrat		sing_1332.htm#SEC1413	15622
flintQ		sing_257.htm#SEC297	
floating point		sing_1164.htm#IDX579	
floor diagrams		sing_3106.htm#IDX1325	
for		sing_396.htm#SEC436	
formal linear representations		sing_896.htm#IDX452	
formaldivisorplus		sing_1682.htm#SEC1763	31959
forward		sing_2860.htm#SEC2941	15383
fourier		sing_590.htm#SEC644	5326
fouriersystem		sing_2871.htm#SEC2952	43681
fpadim.lib		sing_834.htm#SEC888	
fpadim_lib		sing_834.htm#SEC888	
fpalgebras.lib		sing_841.htm#SEC895	
fpalgebras_lib		sing_841.htm#SEC895	
fpaprops.lib		sing_870.htm#SEC924	
fpaprops_lib		sing_870.htm#SEC924	
fprintf		sing_259.htm#SEC299	13662
fracStatus		sing_766.htm#SEC820	14582
framed sheaves		sing_1687.htm#IDX715	
frandwalk		sing_3030.htm#SEC3111	25555
free		sing_2678.htm#IDX1060	
free 		sing_2679.htm#IDX1062	
free associative algebra		sing_841.htm#IDX427	
free associative algebra 		sing_879.htm#IDX439	
free associative algebra, tensor algebra	Free associative algebras	sing_828.htm#SEC882	
free noncommutative Groebner basis		sing_879.htm#IDX441	
freeAlgebra (letterplace)	freeAlgebra (letterplace)	sing_814.htm#SEC868	
freeModule		sing_1360.htm#SEC1441	34173
freeModule2Module		sing_1389.htm#SEC1470	15296
freegb.lib		sing_879.htm#SEC933	
freegb_lib		sing_879.htm#SEC933	
freemodule		sing_260.htm#SEC300	
freerank		sing_1097.htm#SEC1178	52218
fres		sing_261.htm#SEC301	
from_boolean_constant	from_boolean_constant	sing_2740.htm#SEC2821	44881
from_boolean_ideal		sing_2744.htm#SEC2825	62698
from_boolean_poly		sing_2741.htm#SEC2822	27864
from_boolean_set		sing_2745.htm#SEC2826	60615
frwalk		sing_262.htm#SEC302	
full representation		sing_1057.htm#IDX511	
full representation 		sing_1058.htm#IDX516	
fullDimImages		sing_2552.htm#SEC2633	20094
fullFan		sing_2535.htm#SEC2616	7534
fullSerreRelations		sing_844.htm#SEC898	17379
fullSpace		sing_2490.htm#SEC2571	19485
furtherInvar		sing_2119.htm#SEC2200	19209
further_hn_proc		sing_2008.htm#SEC2089	63500
fwalk		sing_1318.htm#SEC1399	15070
galois field		sing_149.htm#SEC189	
gaussColWithoutPerm		sing_2207.htm#SEC2288	17188
gaussRowWithoutPerm		sing_2206.htm#SEC2287	8056
gauss_col		sing_1205.htm#SEC1286	36252
gauss_nf		sing_1236.htm#SEC1317	51060
gauss_row		sing_1206.htm#SEC1287	58877
gaussred		sing_1234.htm#SEC1315	29001
gaussred_pivot		sing_1235.htm#SEC1316	25477
gcd		sing_263.htm#SEC303	
gcdMon		sing_1418.htm#SEC1499	42448
gcdTest		sing_1555.htm#SEC1636	sprintf
gcddivisor		sing_2425.htm#SEC2506	1276
gen		sing_264.htm#SEC304	
genMDSMat		sing_2305.htm#SEC2386	3347
genSymId		sing_1592.htm#SEC1673	17521
general error-locator polynomial		sing_1012.htm#SEC1082	
general neron.		sing_2878.htm#IDX1258	
general weighted lexicographical ordering		sing_986.htm#IDX475	
general weighted reverse lexicographical ordering	Local orderings	sing_986.htm#IDX472	
general.lib		sing_1027.htm#SEC1108	
generalOrder		sing_2450.htm#SEC2531	42536
general_lib		sing_1027.htm#SEC1108	
generateG		sing_2388.htm#SEC2469	51697
generator	derivationContractionGen	sing_2808.htm#IDX1163	
generator 		sing_2818.htm#IDX1183	
generator  		sing_2848.htm#IDX1249	
generators		sing_1876.htm#IDX802	
generators 		sing_2811.htm#IDX1167	
generators  		sing_2813.htm#IDX1172	
generators   		sing_2814.htm#IDX1176	
generatorsOfLinealitySpace	generatorsOfLinealitySpace	sing_2510.htm#SEC2591	4454
generatorsOfSpan		sing_2511.htm#SEC2592	40297
generic representation		sing_1057.htm#IDX510	
genericid		sing_1130.htm#SEC1211	29731
genericity		sing_2325.htm#SEC2406	16822
genericmat		sing_1197.htm#SEC1278	35016
genoutput		sing_1768.htm#SEC1849	18973
genus		sing_1476.htm#SEC1557	sprintf
geometrical locus	FamElemsAtEnvCompPoints	sing_1059.htm#IDX517	
geometrical locus 		sing_1060.htm#IDX520	
geometrical locus  		sing_1061.htm#IDX523	
geometrical locus   		sing_1062.htm#IDX526	
geometrical locus    		sing_1063.htm#IDX529	
geometrical locus     		sing_1064.htm#IDX531	
geometrical locus      		sing_1065.htm#IDX535	
germWithNNB		sing_2785.htm#SEC2866	64985
germWithSemiNormalizedNNB	germWithSemiNormalizedNNB	sing_2787.htm#SEC2868	59276
getArguments		sing_1187.htm#SEC1268	14254
getCommand		sing_1186.htm#SEC1267	32181
getCone		sing_2537.htm#SEC2618	37551
getGradingGroup		sing_2943.htm#SEC3024	18137
getLattice		sing_2944.htm#SEC3025	7775
getLinearForms		sing_2512.htm#SEC2593	47590
getMaxPoints		sing_2930.htm#SEC3011	49225
getModuleGrading		sing_2954.htm#SEC3035	43451
getMultiplicity		sing_2513.htm#SEC2594	639
getOneVar		sing_1484.htm#SEC1565	55402
getRelations		sing_2204.htm#SEC2285	13821
getRelationsRadical		sing_2205.htm#SEC2286	45129
getResult		sing_1188.htm#SEC1269	51722
getSmallest		sing_1483.htm#SEC1564	1623
getState		sing_1189.htm#SEC1270	36453
getStringpfd		sing_2998.htm#SEC3079	35517
getStringpfd_indexed	getStringpfd_indexed	sing_2999.htm#SEC3080	29777
getVariableWeights		sing_2942.htm#SEC3023	9591
getWitnessSet		sing_2208.htm#SEC2289	48291
getcores		sing_1145.htm#SEC1226	30785
getdump		sing_265.htm#SEC305	
getenv		sing_368.htm#IDX218	
gfan.lib		sing_2489.htm#SEC2570	
gfan_lib		sing_2489.htm#SEC2570	
gfanlib		sing_1.htm#IDX9	
gitCone		sing_2579.htm#SEC2660	23853
gitfan.lib		sing_2549.htm#SEC2630	
gitfan_lib		sing_2549.htm#SEC2630	
gkdim.lib		sing_621.htm#SEC675	
gkdim_lib		sing_621.htm#SEC675	
global		sing_215.htm#IDX133	
global Bernstein-Sato ideal		sing_600.htm#IDX370	
global Bernstein-Sato polynomial		sing_509.htm#IDX328	
global Bernstein-Sato polynomial 		sing_544.htm#IDX346	
global Bernstein-Sato polynomial for variety		sing_608.htm#IDX378	
global homological dimension		sing_870.htm#IDX436	
globalSections		sing_1676.htm#SEC1757	55191
gmscoeffs		sing_1966.htm#SEC2047	13182
gmsnf		sing_1965.htm#SEC2046	44676
gmspoly.lib		sing_1985.htm#SEC2066	
gmspoly_lib		sing_1985.htm#SEC2066	
gmsring		sing_1964.htm#SEC2045	59438
gmssing.lib		sing_1963.htm#SEC2044	
gmssing_lib		sing_1963.htm#SEC2044	
goettsche.lib		sing_1687.htm#SEC1768	
goettsche_lib		sing_1687.htm#SEC1768	
good basis		sing_1963.htm#IDX836	
good basis 		sing_1973.htm#IDX891	
good basis  		sing_1985.htm#IDX907	
good basis   		sing_1987.htm#IDX918	
goodBasis		sing_1987.htm#SEC2068	41606
graal.lib		sing_1699.htm#SEC1780	
graalMixed		sing_1700.htm#SEC1781	6401
graal_lib		sing_1699.htm#SEC1780	
gradeNumber		sing_789.htm#SEC843	29956
graded		sing_2811.htm#IDX1168	
graded Hilbert series		sing_893.htm#IDX446	
graded Weyl algebra		sing_509.htm#IDX331	
graded algebra		sing_2798.htm#IDX1151	
graded module, graded piece		sing_1857.htm#IDX788	
graded modules, graded homomorphisms, syzygies	gradedModules_lib	sing_2880.htm#IDX1259	
graded modules, handling of	Handling graded modules	sing_951.htm#SEC1008	
graded piece,  second order piece		sing_3068.htm#IDX1296	
graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism	modules_lib	sing_1357.htm#IDX649	
gradedModules.lib		sing_2880.htm#SEC2961	
gradedModules_lib		sing_2880.htm#SEC2961	
gradiator		sing_2987.htm#SEC3068	53802
graph		sing_1299.htm#IDX618	
graph 		sing_1300.htm#IDX619	
graph  		sing_1828.htm#IDX772	
graph   		sing_1829.htm#IDX773	
graphics.lib		sing_2252.htm#SEC2333	
graphics_lib		sing_2252.htm#SEC2333	
graphviz		sing_1.htm#IDX13	
graver4ti2		sing_1590.htm#SEC1671	39635
grconcat		sing_2903.htm#SEC2984	16754
grdeg		sing_2883.htm#SEC2964	48886
grgens		sing_2892.htm#SEC2973	12823
grgroebner		sing_2902.htm#SEC2983	29288
grlift		sing_2900.htm#SEC2981	21656
grlifting		sing_2907.htm#SEC2988	51177
grlifting2		sing_2908.htm#SEC2989	59011
grlifting3		sing_2910.htm#SEC2991	6369
grneg		sing_2913.htm#SEC2994	64584
grobcov		sing_1050.htm#SEC1131	44826
grobcov.lib		sing_1049.htm#SEC1130	
grobcov_lib		sing_1049.htm#SEC1130	
grobj		sing_2881.htm#SEC2962	18115
groebner		sing_266.htm#SEC306	42544
groebner 		sing_943.htm#SEC1000	
groebner basis computation		sing_353.htm#SEC393	
groebner basis computations		sing_266.htm#IDX147	
groebnerBasis		sing_1497.htm#SEC1578	35106
groebnerComplex		sing_2636.htm#SEC2717	2421
groebnerCone		sing_2630.htm#SEC2711	58776
groebnerFan		sing_2635.htm#SEC2716	48157
gromovWitten		sing_1304.htm#SEC1385	28559
grorder		sing_2894.htm#SEC2975	20857
ground field		sing_149.htm#SEC189	
groupActionOnHashes		sing_2567.htm#SEC2648	30249
groupActionOnQImage		sing_2566.htm#SEC2647	53270
group_reynolds		sing_2083.htm#SEC2164	35079
growth of algebra		sing_870.htm#IDX434	
grpower		sing_2890.htm#SEC2971	3960
grpres		sing_2893.htm#SEC2974	18145
grprod		sing_2901.htm#SEC2982	41525
grrange		sing_2912.htm#SEC2993	41835
grres		sing_2899.htm#SEC2980	35795
grrndmap		sing_2905.htm#SEC2986	4054
grrndmap2		sing_2906.htm#SEC2987	50536
grrndmat		sing_2904.htm#SEC2985	42634
grshift		sing_2885.htm#SEC2966	1415
grsum		sing_2889.htm#SEC2970	60602
grsyz		sing_2898.htm#SEC2979	61843
grtest		sing_2882.htm#SEC2963	35587
grtranspose		sing_2891.htm#SEC2972	13865
grtranspose1		sing_2895.htm#SEC2976	3637
grtwist		sing_2887.htm#SEC2968	10498
grtwists		sing_2888.htm#SEC2969	56638
grview		sing_2884.htm#SEC2965	6878
grwalk.lib		sing_1317.htm#SEC1398	
grwalk_lib		sing_1317.htm#SEC1398	
grzero		sing_2886.htm#SEC2967	4212
gwalk		sing_1323.htm#SEC1404	38238
h_increasing_knapsack	h_increasing_knapsack	sing_2411.htm#SEC2492	62968
hardware platform		sing_368.htm#IDX280	
hasAlgExtensionCoefficient	hasAlgExtensionCoefficient	sing_1168.htm#SEC1249	10858
hasCommutativeVars		sing_1165.htm#SEC1246	3152
hasGlobalOrdering		sing_1166.htm#SEC1247	34053
hasLeftDenom		sing_702.htm#SEC756	47260
hasMixedOrdering		sing_1167.htm#SEC1248	29738
hasNumericCoeffs		sing_1164.htm#SEC1245	20651
hasRightDenom		sing_703.htm#SEC757	34279
hasTransExtensionCoefficient	hasTransExtensionCoefficient	sing_1169.htm#SEC1250	46638
hashToCone		sing_2577.htm#SEC2658	6929
hashesToFan		sing_2578.htm#SEC2659	26774
headStand		sing_1218.htm#SEC1299	14413
heightZ		sing_1562.htm#SEC1643	59905
help		sing_267.htm#SEC307	
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_368.htm#IDX201	
help, accessing over the net	Command line options	sing_19.htm#IDX42	
help, online help system	The online help system	sing_16.htm#SEC22	
hensel lifting.		sing_1349.htm#IDX645	
henselGlobal		sing_1349.htm#SEC1430	27452
hermiteNormalForm		sing_2988.htm#SEC3069	37225
hess.lib		sing_1706.htm#SEC1787	
hess_lib		sing_1706.htm#SEC1787	
hessenberg		sing_368.htm#IDX224	24168
hessenberg 		sing_1240.htm#SEC1321	
high corner method		sing_266.htm#IDX148	
highcorner		sing_266.htm#IDX149	
highcorner 		sing_268.htm#SEC308	
highest corner		sing_410.htm#SEC450	
highest corner, option		sing_324.htm#IDX162	
highest edge		sing_410.htm#SEC450	
hilb		sing_269.htm#SEC309	
hilbPoly		sing_1113.htm#SEC1194	36118
hilbert driven Groebner basis, option		sing_324.htm#IDX163	
hilbert4ti2		sing_1589.htm#SEC1670	13993
hilbertSeries		sing_2990.htm#SEC3071	60148
hilbvec		sing_2172.htm#SEC2253	44605
history		sing_18.htm#SEC25	
hnexpansion		sing_1989.htm#SEC2070	46990
hnoether.lib		sing_1988.htm#SEC2069	
hnoether_lib		sing_1988.htm#SEC2069	
hodge.lib		sing_2915.htm#SEC2996	
hodgeIdeals		sing_2917.htm#SEC2998	40385
hodge_lib		sing_2915.htm#SEC2996	
holonomic rank		sing_675.htm#IDX396	
holonomicRank		sing_679.htm#SEC733	41306
hom		sing_1401.htm#SEC1482	40032
hom_kernel		sing_1339.htm#SEC1420	32604
homog		sing_270.htm#SEC310	
homog 		sing_2829.htm#IDX1206	
homog_part		sing_1840.htm#SEC1921	20875
homog_parts		sing_1841.htm#SEC1922	12854
homogeneitySpace		sing_2632.htm#SEC2713	48243
homogeneous		sing_270.htm#SEC310	
homogeneous 		sing_2815.htm#IDX1177	
homogeneous  		sing_2829.htm#IDX1205	
homogeneous   		sing_2830.htm#IDX1207	
homogeneous decomposition		sing_2815.htm#IDX1178	
homogfacFirstQWeyl		sing_665.htm#SEC719	32751
homogfacFirstQWeyl_all	homogfacFirstQWeyl_all	sing_667.htm#SEC721	9014
homogfacNthQWeyl		sing_664.htm#SEC718	19238
homogfacNthQWeyl_all	homogfacNthQWeyl_all	sing_666.htm#SEC720	44838
homogfacNthWeyl		sing_663.htm#SEC717	5919
homolog.lib		sing_1324.htm#SEC1405	
homolog_lib		sing_1324.htm#SEC1405	
homology		sing_1334.htm#SEC1415	15040
homomorphism		sing_1385.htm#SEC1466	27115
howto, download	Download instructions	sing_3134.htm#SEC3239	
howto, install on Macintosh	Macintosh installation instructions	sing_3138.htm#SEC3243	
howto, install on Unix	Unix installation instructions	sing_3136.htm#SEC3241	
howto, install on Windows	Windows installation instructions	sing_3137.htm#SEC3242	
hres		sing_271.htm#SEC311	
html, default help	The online help system	sing_16.htm#IDX24	
hybrid algorithms		sing_2201.htm#IDX955	
hyperbolic sine series expansion		sing_3104.htm#IDX1320	
hyperel.lib		sing_2418.htm#SEC2499	
hyperel_lib		sing_2418.htm#SEC2499	
hyperplane		sing_2648.htm#IDX1000	
hyperplane arrangement		sing_544.htm#IDX352	
hypersurface singularity		sing_2015.htm#IDX936	
iMult		sing_1479.htm#SEC1560	22059
id		sing_1358.htm#SEC1439	47592
id2mod		sing_1109.htm#SEC1190	32918
ideal		sing_95.htm#SEC135	
ideal (plural)		sing_434.htm#SEC474	
ideal declarations		sing_96.htm#SEC136	
ideal declarations (plural)	ideal declarations (plural)	sing_435.htm#SEC475	
ideal expressions		sing_97.htm#SEC137	
ideal expressions (plural)	ideal expressions (plural)	sing_436.htm#SEC476	
ideal operations		sing_98.htm#SEC138	
ideal operations (plural)	ideal operations (plural)	sing_437.htm#SEC477	
ideal related functions	ideal related functions	sing_99.htm#SEC139	
ideal related functions (plural)	ideal related functions (plural)	sing_438.htm#SEC478	
ideal, toric		sing_999.htm#SEC1061	
idealSplit		sing_2179.htm#SEC2260	4673
ideals	Miscellaneous oddities	sing_429.htm#IDX308	
idealsEqual		sing_1554.htm#SEC1635	sprintf
idealsimplify		sing_1884.htm#SEC1965	38569
identifier	Identifier resolution	sing_430.htm#SEC470	
identifyvar		sing_1750.htm#SEC1831	11751
if		sing_397.htm#SEC437	
image		sing_1381.htm#SEC1462	43481
imageLattice		sing_2956.htm#SEC3037	15740
image_of_variety		sing_2111.htm#SEC2192	11559
imap		sing_272.htm#SEC312	
imap (letterplace)		sing_815.htm#SEC869	
imap (plural)		sing_473.htm#SEC513	
imapall		sing_1156.htm#SEC1237	16023
impart		sing_273.htm#SEC313	
importfrom		sing_398.htm#SEC438	
inCenter		sing_533.htm#SEC587	22152
inCentralizer		sing_534.htm#SEC588	49000
inForm		sing_577.htm#SEC631	5283
inSubring		sing_1256.htm#SEC1337	24817
indSet		sing_1444.htm#SEC1525	32828
indepSet		sing_274.htm#SEC314	
indexed names		sing_36.htm#IDX82	
indexed names 		sing_37.htm#SEC65	
indices, multi		sing_37.htm#SEC65	
inequalities		sing_2514.htm#SEC2595	10122
infRedTail, option		sing_324.htm#IDX156	
infinitely presented algebra		sing_893.htm#IDX445	
info	The online help system	sing_16.htm#SEC23	
iniD		sing_1770.htm#SEC1851	35084
init_debug		sing_1901.htm#SEC1982	8378
initial		sing_2633.htm#SEC2714	8678
initial form		sing_509.htm#IDX333	
initial ideal		sing_509.htm#IDX332	
initial ideal approach		sing_509.htm#IDX336	
initial ideal approach 		sing_608.htm#IDX382	
initialForm		sing_2610.htm#SEC2691	57793
initialIdeal		sing_2611.htm#SEC2692	22205
initialIdealW		sing_576.htm#SEC630	36086
initialMalgrange		sing_575.htm#SEC629	26846
injective_knapsack		sing_2412.htm#SEC2493	7619
inout.lib		sing_1075.htm#SEC1156	
inout_lib		sing_1075.htm#SEC1156	
input		sing_41.htm#SEC71	
insert		sing_131.htm#SEC171	
insert 		sing_275.htm#SEC315	
insertCone		sing_2538.htm#SEC2619	13858
insertGenerator		sing_596.htm#SEC650	13951
instructions, Macintosh installation	Macintosh installation instructions	sing_3138.htm#SEC3243	
instructions, Unix installation	Unix installation instructions	sing_3136.htm#SEC3241	
instructions, Windows installation	Windows installation instructions	sing_3137.htm#SEC3242	
instructions, downloading	Download instructions	sing_3134.htm#SEC3239	
int		sing_100.htm#SEC140	
int declarations		sing_101.htm#SEC141	
int expressions		sing_102.htm#SEC142	
int operations		sing_103.htm#SEC143	
int related functions	int related functions	sing_104.htm#SEC144	
intInverse		sing_2965.htm#SEC3046	sprintf
intPart		sing_2366.htm#SEC2447	48360
intRank		sing_2957.htm#SEC3038	1830
intRoot		sing_2367.htm#SEC2448	54582
intRoots		sing_593.htm#SEC647	24538
intStrategy, option		sing_324.htm#IDX157	
intclMonIdeal		sing_1494.htm#SEC1575	8313
intclToricRing		sing_1489.htm#SEC1570	9772
integer division	Miscellaneous oddities	sing_429.htm#IDX303	
integer programming		sing_1007.htm#SEC1069	
integral		sing_1815.htm#SEC1896	62683
integral basis		sing_1346.htm#IDX642	
integral basis 		sing_1733.htm#IDX749	
integral closure		sing_1470.htm#IDX659	
integral closure 		sing_1473.htm#IDX667	
integral closure  		sing_1474.htm#IDX670	
integral closure   		sing_1488.htm#IDX677	
integralBasis		sing_1346.htm#SEC1427	65284
integralIdeal		sing_580.htm#SEC634	29194
integralModule		sing_581.htm#SEC635	58078
integralSection		sing_2966.htm#SEC3047	sprintf
integralbasis.lib		sing_1345.htm#SEC1426	
integralbasis_lib		sing_1345.htm#SEC1426	
integration of D-module		sing_568.htm#IDX364	
interface, Emacs	Emacs user interface	sing_21.htm#SEC28	
internalfunctions		sing_1902.htm#SEC1983	61230
interpolate		sing_2185.htm#SEC2266	51502
interpolation		sing_276.htm#SEC316	
interpret		sing_1403.htm#SEC1484	48499
interpretElem		sing_1406.htm#SEC1487	51740
interpretInv		sing_1404.htm#SEC1485	6149
interpretList		sing_1407.htm#SEC1488	64061
interred		sing_277.htm#SEC317	
intersect		sing_278.htm#SEC318	
intersect (plural)		sing_474.htm#SEC514	
intersectElim, option		sing_324.htm#IDX179	
intersectLattices		sing_2962.htm#SEC3043	41354
intersectLists		sing_2693.htm#SEC2774	4153
intersectMon		sing_1421.htm#SEC1502	44572
intersectOrbitsWithMovingCone	intersectOrbitsWithMovingCone	sing_2565.htm#SEC2646	19444
intersectSyz, option		sing_324.htm#IDX180	
intersectZ		sing_1564.htm#SEC1645	sprintf
intersection		sing_1998.htm#SEC2079	46938
intersection 		sing_2753.htm#IDX1141	
intersection lattice		sing_2684.htm#IDX1075	
intersection lattice 		sing_2685.htm#IDX1076	
intersection multiplicity		sing_1877.htm#IDX808	
intersection multiplicity 		sing_1998.htm#IDX929	
intersectionDiv		sing_1798.htm#SEC1879	29017
intersectionSet		sing_2753.htm#SEC2834	60638
intersectionValRingIdeals	intersectionValRingIdeals	sing_1502.htm#SEC1583	37892
intersectionValRings	intersectionValRings	sing_1501.htm#SEC1582	35761
intersectpar		sing_1069.htm#SEC1150	2975
interval arithmetic		sing_2219.htm#IDX960	
interval.lib		sing_2156.htm#SEC2237	
interval_lib		sing_2156.htm#SEC2237	
intervalmatrixInit		sing_2159.htm#SEC2240	1323
intmat		sing_107.htm#SEC147	
intmat declarations		sing_108.htm#SEC148	
intmat expressions		sing_109.htm#SEC149	
intmat operations		sing_111.htm#SEC151	
intmat related functions	intmat related functions	sing_112.htm#SEC152	
intmat type cast		sing_110.htm#SEC150	
intmat2binomials		sing_1522.htm#SEC1603	20225
intmat2mons		sing_1520.htm#SEC1601	21150
intprog.lib		sing_1350.htm#SEC1431	
intprog_lib		sing_1350.htm#SEC1431	
intvec		sing_113.htm#SEC153	
intvec declarations		sing_114.htm#SEC154	
intvec expressions		sing_115.htm#SEC155	
intvec operations		sing_116.htm#SEC156	
intvec related functions	intvec related functions	sing_117.htm#SEC157	
invar		sing_2142.htm#SEC2223	15731
invar.lib		sing_2136.htm#SEC2217	
invar_lib		sing_2136.htm#SEC2217	
invariant		sing_1278.htm#IDX603	
invariant ring minimal generating set matrix group	invariant_algebra_reynolds	sing_2080.htm#IDX949	
invariant ring minimal generating set permutation group	invariant_algebra_perm	sing_2081.htm#IDX950	
invariantRing		sing_2113.htm#SEC2194	41016
invariant_algebra_perm	invariant_algebra_perm	sing_2081.htm#SEC2162	63525
invariant_algebra_reynolds	invariant_algebra_reynolds	sing_2080.htm#SEC2161	35705
invariant_basis		sing_2088.htm#SEC2169	21530
invariant_basis_reynolds	invariant_basis_reynolds	sing_2089.htm#SEC2170	59344
invariant_ring		sing_2076.htm#SEC2157	8059
invariant_ring_random	invariant_ring_random	sing_2077.htm#SEC2158	6986
invariants	curveColengthDerivations	sing_1275.htm#IDX596	57499
invariants 		sing_1279.htm#IDX605	
invariants  		sing_1994.htm#SEC2075	
inverse		sing_1224.htm#SEC1305	27411
inverse lexicographical ordering		sing_985.htm#IDX457	
inverse of a matrix via its LU-decomposition		sing_298.htm#SEC338	
inverseFourier		sing_591.htm#SEC645	65140
inverse_B		sing_1225.htm#SEC1306	17616
inverse_L		sing_1226.htm#SEC1307	49271
inverse_modulus		sing_2395.htm#SEC2476	60822
invertAlgebraMorphism	invertAlgebraMorphism	sing_3123.htm#SEC3204	20745
invertBirMap		sing_1734.htm#SEC1815	16086
invertLeftFraction		sing_776.htm#SEC830	51903
invertNcfrac		sing_712.htm#SEC766	50842
invertNumberMain		sing_2244.htm#SEC2325	19063
involut.lib		sing_613.htm#SEC667	
involut_lib		sing_613.htm#SEC667	
involution		sing_618.htm#SEC672	34280
invunit		sing_2017.htm#SEC2098	62398
iostruct		sing_2327.htm#SEC2408	60444
irrRealizationDim		sing_2593.htm#SEC2674	7814
irred_secondary_char0	irred_secondary_char0	sing_2102.htm#SEC2183	45051
irred_secondary_no_molien	irred_secondary_no_molien	sing_2105.htm#SEC2186	55905
irreddecMon		sing_1430.htm#SEC1511	1727
irreducible power series		sing_1999.htm#IDX930	
irreducible secondary invariant	irred_secondary_char0	sing_2102.htm#IDX951	
isAface		sing_2550.htm#SEC2631	25344
isAntiEndo		sing_620.htm#SEC674	19156
isCI		sing_215.htm#IDX139	58425
isCI 		sing_1274.htm#SEC1355	
isCM		sing_215.htm#IDX140	50469
isCM 		sing_1335.htm#SEC1416	
isCMcod2		sing_2059.htm#SEC2140	2563
isCartan		sing_535.htm#SEC589	39541
isCentral		sing_752.htm#SEC806	54650
isCommutative		sing_754.htm#SEC808	60728
isCompatible		sing_2539.htm#SEC2620	57323
isDenom		sing_724.htm#SEC778	55537
isElement		sing_2755.htm#SEC2836	10897
isEqualDivisor		sing_1675.htm#SEC1756	17569
isEquising		sing_1961.htm#SEC2042	1424
isFlat		sing_1336.htm#SEC1417	14706
isFreeAlgebra		sing_880.htm#SEC934	23925
isFsat		sing_586.htm#SEC640	28225
isFullSpace		sing_2515.htm#SEC2596	27433
isGradedRingHomomorphism	isGradedRingHomomorphism	sing_2951.htm#SEC3032	39551
isGroup		sing_2949.htm#SEC3030	55744
isGroupHomomorphism		sing_2950.htm#SEC3031	65475
isHolonomic		sing_564.htm#SEC618	30274
isHomog		sing_215.htm#IDX135	
isHomogeneous		sing_2977.htm#SEC3058	3034
isInS		sing_765.htm#SEC819	30907
isInt		sing_598.htm#SEC652	9879
isIntegralSurjective	isIntegralSurjective	sing_2963.htm#SEC3044	sprintf
isInvertibleLeftFraction	isInvertibleLeftFraction	sing_775.htm#SEC829	623
isInvertibleNcfrac		sing_711.htm#SEC765	48367
isInvolution		sing_619.htm#SEC673	13601
isLocalizationRegular	isLocalizationRegular	sing_1703.htm#SEC1784	11221
isLocallyFree		sing_1337.htm#SEC1418	46389
isMonomial		sing_1416.htm#SEC1497	57615
isNC		sing_753.htm#SEC807	57151
isNormal		sing_1487.htm#SEC1568	6152
isOnCurve		sing_2379.htm#SEC2460	36324
isOneFraction		sing_778.htm#SEC832	55015
isOneNcfrac		sing_705.htm#SEC759	12754
isOrderingShiftInvariant	isOrderingShiftInvariant	sing_886.htm#SEC940	26018
isOrigin		sing_2516.htm#SEC2597	13977
isPositive		sing_2974.htm#SEC3055	50852
isPrimitiveSublattice	isPrimitiveSublattice	sing_2964.htm#SEC3045	sprintf
isPure		sing_2540.htm#SEC2621	44002
isPureTensor		sing_507.htm#SEC561	21323
isQuotientRing		sing_1170.htm#SEC1251	sprintf
isRational		sing_567.htm#SEC621	57398
isReg		sing_1338.htm#SEC1419	40920
isSB		sing_215.htm#IDX134	
isSimplicial		sing_2517.htm#SEC2598	57789
isSubModule		sing_1171.htm#SEC1252	sprintf
isSublattice		sing_2955.htm#SEC3036	10501
isSubset		sing_2756.htm#SEC2837	33482
isSuperset		sing_2757.htm#SEC2838	sprintf
isSymmetric		sing_1593.htm#SEC1674	61363
isTame		sing_1986.htm#SEC2067	31925
isTorsionFree		sing_2973.htm#SEC3054	52228
isTwoSidedGB		sing_508.htm#SEC562	36558
isUpperTriangular		sing_733.htm#SEC787	40655
isWeyl		sing_755.htm#SEC809	28994
isZeroElement		sing_2975.htm#SEC3056	514
isZeroFraction		sing_777.htm#SEC831	1926
isZeroNcfrac		sing_704.htm#SEC758	6841
is_NND		sing_2002.htm#SEC2083	26564
is_NP		sing_1453.htm#SEC1534	43891
is_active		sing_2042.htm#SEC2123	6867
is_bijective		sing_1261.htm#SEC1342	63609
is_cenBimodule		sing_721.htm#SEC775	35450
is_cenSubbimodule		sing_722.htm#SEC776	26181
is_ci		sing_2043.htm#SEC2124	35370
is_complex		sing_1198.htm#SEC1279	1234
is_composite		sing_1283.htm#SEC1364	33233
is_fix_injective		sing_2416.htm#SEC2497	11663
is_h_injective		sing_2415.htm#SEC2496	36696
is_injective		sing_1259.htm#SEC1340	63563
is_irred		sing_1999.htm#SEC2080	51150
is_is		sing_2044.htm#SEC2125	64105
is_nested		sing_1454.htm#SEC1535	9200
is_prime		sing_2396.htm#SEC2477	29018
is_primitive_root		sing_2392.htm#SEC2473	42838
is_pure		sing_795.htm#SEC849	59105
is_reg		sing_2045.htm#SEC2126	18146
is_regs		sing_2046.htm#SEC2127	50242
is_surjective		sing_1260.htm#SEC1341	26539
is_zero		sing_1098.htm#SEC1179	24341
isartinianMon		sing_1427.htm#SEC1508	1103
isgenericMon		sing_1428.htm#SEC1509	14444
ishyper		sing_2419.htm#SEC2500	65518
isirreducibleMon		sing_1426.htm#SEC1507	22428
isoncurve		sing_2420.htm#SEC2501	16384
isparam		sing_2483.htm#SEC2564	56395
isprimaryMon		sing_1425.htm#SEC1506	57367
isprimeMon		sing_1424.htm#SEC1505	9124
isuni		sing_2468.htm#SEC2549	39427
ivmatGaussian		sing_2226.htm#SEC2307	37718
ivmatGaussian2		sing_2162.htm#SEC2243	57822
ivmatInit		sing_2223.htm#SEC2304	22774
ivmatSet		sing_2224.htm#SEC2305	53480
jacob		sing_279.htm#SEC319	
jacoblift		sing_2018.htm#SEC2099	40125
jacobson		sing_2333.htm#SEC2414	59267
jacobson.lib		sing_2331.htm#SEC2412	
jacobson_lib		sing_2331.htm#SEC2412	
janet		sing_280.htm#SEC320	
janet basis		sing_1576.htm#IDX687	
jet		sing_281.htm#SEC321	
jordan		sing_1245.htm#SEC1326	16602
jordanVecField		sing_3116.htm#SEC3197	32424
jordanbasis		sing_1246.htm#SEC1327	12736
jordanmatrix		sing_1247.htm#SEC1328	2886
jordannf		sing_1248.htm#SEC1329	20535
jungfib		sing_1783.htm#SEC1864	5432
jungnormal		sing_1782.htm#SEC1863	43561
jungresolve		sing_1781.htm#SEC1862	45004
katsura		sing_1096.htm#SEC1177	45913
kbase		sing_282.htm#SEC322	
kbase (plural)		sing_475.htm#SEC515	
keepring		sing_399.htm#SEC439	
kerHom		sing_1402.htm#SEC1483	53906
kernel		sing_283.htm#SEC323	
kernelLattice		sing_2958.htm#SEC3039	36320
kill		sing_284.htm#SEC324	
killTask		sing_1177.htm#SEC1258	39317
killall		sing_1037.htm#SEC1118	34661
killattrib		sing_285.htm#SEC325	
kmemory		sing_1036.htm#SEC1117	52193
kohom		sing_1340.htm#SEC1421	50086
kontrahom		sing_1341.htm#SEC1422	58549
koszul		sing_286.htm#SEC326	
kskernel.lib		sing_2009.htm#SEC2090	
kskernel_lib		sing_2009.htm#SEC2090	
l-adic numbers		sing_32.htm#SEC46	
laguerre		sing_287.htm#SEC327	
laguerre_solve		sing_2181.htm#SEC2262	10155
lastQuadrantComplex		sing_3095.htm#SEC3176	59799
lastvarGeneral		sing_2449.htm#SEC2530	28645
latex.lib		sing_2256.htm#SEC2337	
latex_lib		sing_2256.htm#SEC2337	
lattice		sing_2685.htm#IDX1078	
latticeArea		sing_2588.htm#SEC2669	53771
latticeBasis		sing_2959.htm#SEC3040	43162
latticeIdeal		sing_1496.htm#SEC1577	22813
latticePoints		sing_2769.htm#SEC2850	1256
latticeToMonomials		sing_2770.htm#SEC2851	62171
laxfrT		sing_2858.htm#SEC2939	60899
laxfrX		sing_2859.htm#SEC2940	57254
lazy, option		sing_324.htm#IDX158	
lcm		sing_1099.htm#SEC1180	44755
lcmMon		sing_1419.htm#SEC1500	52749
lcmN		sing_2360.htm#SEC2441	52355
lcmofall		sing_1763.htm#SEC1844	56889
lead		sing_288.htm#SEC328	
leadcoef		sing_289.htm#SEC329	
leadexp		sing_290.htm#SEC330	
leadmonom		sing_291.htm#SEC331	
leadmonomial		sing_2435.htm#SEC2516	8195
left annihilator ideal		sing_544.htm#IDX344	
left annihilator ideal 		sing_600.htm#IDX372	
leftInverse		sing_2322.htm#SEC2403	41469
leftKernel		sing_2320.htm#SEC2401	9292
leftOre		sing_768.htm#SEC822	44669
length		sing_2221.htm#SEC2302	9547
length, option		sing_324.htm#IDX159	
length2		sing_2157.htm#SEC2238	13262
letplaceGBasis		sing_888.htm#SEC942	31260
letterplace		sing_301.htm#SEC341	
letterplace 		sing_344.htm#SEC384	
lex_solve		sing_2187.htm#SEC2268	48692
lexicographical ordering		sing_985.htm#IDX455	
lib2doc		sing_60.htm#SEC97	
libSingular		sing_3133.htm#SEC3238	
libcdd		sing_1.htm#IDX12	
libfac		sing_1.htm#IDX6	
libparse		sing_69.htm#SEC109	
library		sing_2731.htm#IDX1119	
library, gitfan, GIT, geometric invariant theory, quotients	gitfan_lib	sing_2549.htm#IDX987	
library, info string		sing_55.htm#IDX124	
library, polybori.lib		sing_2731.htm#IDX1116	
library, ringgb.lib		sing_3022.htm#IDX1280	
library, template		sing_55.htm#SEC92	
library, template.lib		sing_55.htm#IDX122	
lieBracket		sing_889.htm#SEC943	62995
lift		sing_293.htm#SEC333	
lift 		sing_502.htm#IDX320	
lift (letterplace)		sing_816.htm#SEC870	
lift (plural)		sing_476.htm#SEC516	
lift_kbase		sing_1955.htm#SEC2036	10906
lift_rel_kb		sing_1956.htm#SEC2037	13673
liftenvelope		sing_505.htm#SEC559	58802
liftstd		sing_294.htm#SEC334	
liftstd (letterplace)	liftstd (letterplace)	sing_817.htm#SEC871	
liftstd (plural)		sing_477.htm#SEC517	
likeIdeal		sing_2928.htm#SEC3009	1506
likelihood ideal		sing_2927.htm#IDX1265	
linReduce		sing_517.htm#SEC571	57527
linReduceIdeal		sing_518.htm#SEC572	19076
linSyzSolve		sing_519.htm#SEC573	26185
linalg.lib		sing_1223.htm#SEC1304	
linalg_lib		sing_1223.htm#SEC1304	
linealityDimension		sing_2518.htm#SEC2599	30751
linealitySpace		sing_2519.htm#SEC2600	14489
linear algebra		sing_216.htm#SEC256	
linear algebra 		sing_297.htm#SEC337	
linear algebra  		sing_298.htm#SEC338	
linear algebra   		sing_299.htm#SEC339	
linear code, dual		sing_2291.htm#IDX970	
linear code, systematic		sing_2292.htm#IDX971	
linear interreduction		sing_509.htm#IDX335	
linearCombinations		sing_538.htm#SEC592	20514
linearMapKernel		sing_537.htm#SEC591	43761
linear_relations		sing_1215.htm#SEC1296	45983
linearlyEquivalent		sing_1678.htm#SEC1759	28351
linearpart		sing_2173.htm#SEC2254	2162
linesHypersurface		sing_1837.htm#SEC1918	9129
link	Parallelization with ssi links	sing_118.htm#SEC158	
link 		sing_940.htm#SEC997	
link declarations		sing_119.htm#SEC159	
link expressions		sing_120.htm#SEC160	
link related functions	link related functions	sing_121.htm#SEC161	
links		sing_3069.htm#IDX1297	
list		sing_128.htm#SEC168	
list 		sing_2831.htm#IDX1210	
list  		sing_2832.htm#IDX1212	
list declarations		sing_129.htm#SEC169	
list expressions		sing_130.htm#SEC170	
list operations		sing_131.htm#SEC171	
list related functions	list related functions	sing_132.htm#SEC172	
lists		sing_2693.htm#IDX1085	
lists, elements		sing_2695.htm#IDX1087	
listvar		sing_295.htm#SEC335	
lll		sing_2991.htm#SEC3072	35827
load		sing_400.htm#SEC440	
loadLib, option		sing_324.htm#IDX185	
loadProc, option		sing_324.htm#IDX186	
locAtZero		sing_1481.htm#SEC1562	5687
locNormal		sing_1471.htm#SEC1552	11813
locStatus		sing_763.htm#SEC817	54575
local methods		sing_1471.htm#IDX662	
local names		sing_46.htm#SEC83	
local rings, computing in	Rings associated to monomial orderings	sing_935.htm#SEC992	
local weighted lexicographical ordering		sing_986.htm#IDX476	
local weighted reverse lexicographical ordering	Local orderings	sing_986.htm#IDX473	
localInvar		sing_2118.htm#SEC2199	38478
localization	Rings associated to monomial orderings	sing_935.htm#SEC992	
localization 		sing_2665.htm#IDX1038	
localization of D-module		sing_568.htm#IDX360	
localization of D-module 		sing_675.htm#IDX399	
locally closed set		sing_1054.htm#IDX500	
locally closed set 		sing_1055.htm#IDX502	
locally closed set  		sing_1056.htm#IDX504	
locally closed set   		sing_1057.htm#IDX508	
locally closed set    		sing_1071.htm#IDX546	
locally closed set     		sing_1073.htm#IDX551	
localstd		sing_2445.htm#SEC2526	25562
locstd		sing_2047.htm#SEC2128	25864
locus	FamElemsAtEnvCompPoints	sing_1059.htm#SEC1140	26910
locus 		sing_1059.htm#IDX518	
locus  		sing_1060.htm#IDX521	
locus   		sing_1061.htm#IDX524	
locus    		sing_1062.htm#IDX527	
locus     		sing_1063.htm#IDX530	
locus      		sing_1064.htm#IDX532	
locus       		sing_1065.htm#IDX536	
locusdg		sing_1060.htm#SEC1141	6077
locusto		sing_1062.htm#SEC1143	730
log2		sing_2348.htm#SEC2429	40703
logHessian		sing_2929.htm#SEC3010	60859
logarithmic annihilator ideal		sing_544.htm#IDX349	
logarithmic annihilator ideal 		sing_600.htm#IDX374	
logg		sing_1842.htm#SEC1923	38736
lp, global ordering		sing_985.htm#IDX454	
lpCalcSubstDegBound		sing_878.htm#SEC932	41046
lpDegBound		sing_881.htm#SEC935	4313
lpDivision		sing_884.htm#SEC938	5546
lpGBPres2Poly		sing_885.htm#SEC939	19402
lpGkDim		sing_874.htm#SEC928	30394
lpGlDimBound		sing_876.htm#SEC930	53074
lpHilbert		sing_839.htm#SEC893	17309
lpIsPrime		sing_873.htm#SEC927	49715
lpIsSemiPrime		sing_872.htm#SEC926	20274
lpKDim		sing_836.htm#SEC890	57526
lpMonomialBasis		sing_838.htm#SEC892	24326
lpNcgenCount		sing_883.htm#SEC937	48263
lpNoetherian		sing_871.htm#SEC925	27069
lpSubstitute		sing_877.htm#SEC931	8859
lpVarBlockSize		sing_882.htm#SEC936	20447
lprint		sing_1077.htm#SEC1158	5285
lrcalc.lib		sing_2920.htm#SEC3001	
lrcalc_lib		sing_2920.htm#SEC3001	
lres		sing_296.htm#SEC336	
ls, local ordering		sing_986.htm#IDX467	
lsum		sing_1308.htm#SEC1389	50315
ludecomp		sing_297.htm#SEC337	
luinverse		sing_298.htm#SEC338	
lusolve		sing_299.htm#SEC339	
mRes		sing_1370.htm#SEC1451	6062
m_merkle_hellman_decryption	m_merkle_hellman_decryption	sing_2407.htm#SEC2488	57945
m_merkle_hellman_encryption	m_merkle_hellman_encryption	sing_2406.htm#SEC2487	33857
m_merkle_hellman_transformation	m_merkle_hellman_transformation	sing_2405.htm#SEC2486	7880
magnitude		sing_2342.htm#SEC2423	37967
makeDivisor		sing_1670.htm#SEC1751	3414
makeFormalDivisor		sing_1680.htm#SEC1761	54579
makeGraph		sing_1299.htm#SEC1380	21758
makeGraphVE		sing_1828.htm#SEC1909	sprintf
makeHeisenberg		sing_743.htm#SEC797	2050
makeIdeal		sing_1362.htm#SEC1443	57829
makeLetterplaceRing		sing_887.htm#SEC941	3721
makeLinks		sing_3069.htm#SEC3150	27210
makeMalgrange		sing_612.htm#SEC666	41377
makeMatrix		sing_1361.htm#SEC1442	32736
makeModElimRing		sing_760.htm#SEC814	52764
makePDivisor		sing_1686.htm#SEC1767	45273
makePoly		sing_3004.htm#SEC3085	34516
makePuiseux		sing_3018.htm#SEC3099	27496
makePuiseuxFromPoly		sing_3019.htm#SEC3100	22583
makeQPoly		sing_3066.htm#SEC3147	48948
makeQsl2		sing_646.htm#SEC700	3997
makeQsl3		sing_647.htm#SEC701	41249
makeQso3		sing_645.htm#SEC699	58910
makeSheaf		sing_1816.htm#SEC1897	10497
makeUe6		sing_642.htm#SEC696	58585
makeUe7		sing_643.htm#SEC697	61849
makeUe8		sing_644.htm#SEC698	64987
makeUf4		sing_641.htm#SEC695	8408
makeUg2		sing_640.htm#SEC694	34512
makeUgl		sing_626.htm#SEC680	3543
makeUsl		sing_625.htm#SEC679	24536
makeUsl2		sing_624.htm#SEC678	42637
makeUso10		sing_632.htm#SEC686	6936
makeUso11		sing_633.htm#SEC687	35873
makeUso12		sing_634.htm#SEC688	19319
makeUso5		sing_627.htm#SEC681	34378
makeUso6		sing_628.htm#SEC682	65009
makeUso7		sing_629.htm#SEC683	49142
makeUso8		sing_630.htm#SEC684	33275
makeUso9		sing_631.htm#SEC685	16896
makeUsp1		sing_635.htm#SEC689	44522
makeUsp2		sing_636.htm#SEC690	18017
makeUsp3		sing_637.htm#SEC691	57445
makeUsp4		sing_638.htm#SEC692	51690
makeUsp5		sing_639.htm#SEC693	35951
makeVariety		sing_1808.htm#SEC1889	23915
makeVector		sing_1390.htm#SEC1471	9049
makeWeyl		sing_742.htm#SEC796	8554
makedistinguished		sing_1286.htm#SEC1367	50438
map		sing_133.htm#SEC173	
map (plural)		sing_439.htm#SEC479	
map declarations		sing_134.htm#SEC174	
map declarations (plural)	map declarations (plural)	sing_440.htm#SEC480	
map expressions		sing_135.htm#SEC175	
map expressions (plural)	map expressions (plural)	sing_441.htm#SEC481	
map operations		sing_136.htm#IDX129	
map operations (plural)	map operations (plural)	sing_442.htm#IDX315	
map related functions	map related functions	sing_137.htm#IDX131	
map related functions  (plural)		sing_443.htm#IDX316	
map related functions (plural)	map related functions (plural)		
mapIsFinite		sing_1263.htm#SEC1344	60897
mapToRatNormCurve		sing_1738.htm#SEC1819	8877
mapall		sing_1157.htm#SEC1238	14907
mappingcone		sing_2909.htm#SEC2990	48219
mappingcone3		sing_2911.htm#SEC2992	58973
markov4ti2		sing_1588.htm#SEC1669	9163
mat2arr		sing_2650.htm#SEC2731	20840
mat2carr		sing_2651.htm#SEC2732	13777
mat_rk		sing_1237.htm#SEC1318	32196
matbil		sing_2456.htm#SEC2537	1611
mathematical objects	Representation of mathematical objects	sing_981.htm#SEC1038	
mathinit		sing_2254.htm#SEC2335	16793
matmult		sing_2457.htm#SEC2538	60088
matrix		sing_138.htm#SEC178	
matrix 		sing_2650.htm#IDX1006	
matrix  		sing_2651.htm#IDX1009	
matrix   		sing_2652.htm#IDX1013	
matrix declarations		sing_139.htm#SEC179	
matrix diagonalization		sing_2331.htm#IDX981	
matrix expressions		sing_140.htm#SEC180	
matrix operations		sing_142.htm#SEC182	
matrix related functions	matrix related functions	sing_143.htm#SEC183	
matrix type cast		sing_141.htm#SEC181	
matrix.lib		sing_1191.htm#SEC1272	
matrixExp		sing_1728.htm#SEC1809	53063
matrixLog		sing_1729.htm#SEC1810	26235
matrixT1		sing_2061.htm#SEC2142	15051
matrix_lib		sing_1191.htm#SEC1272	
matrixpres		sing_2914.htm#SEC2995	60645
matrixsystem		sing_2869.htm#SEC2950	38328
max		sing_300.htm#SEC340	23624
maxEord		sing_1753.htm#SEC1834	64032
maxExp		sing_215.htm#IDX136	
maxIntRoot		sing_692.htm#SEC746	37127
maxPoints		sing_2931.htm#SEC3012	64914
maxPointsProb		sing_2932.htm#SEC3013	33636
maxZeros		sing_1731.htm#SEC1812	334
maxabs		sing_2475.htm#SEC2556	64510
maxcoef		sing_1100.htm#SEC1181	50577
maxdeg		sing_1101.htm#SEC1182	39794
maxdeg1		sing_1102.htm#SEC1183	21545
maxideal		sing_301.htm#SEC341	
maximalGroebnerCone		sing_2631.htm#SEC2712	62935
maximum likelihood estimate		sing_2927.htm#IDX1266	
maximum number of zeroes		sing_1731.htm#IDX743	
maxlike.lib		sing_2927.htm#SEC3008	
maxlike_lib		sing_2927.htm#SEC3008	
mdouble		sing_56.htm#SEC93	56685
mem, option		sing_324.htm#IDX187	
member		sing_2695.htm#SEC2776	1765
memberpos		sing_1116.htm#SEC1197	15764
membershipMon		sing_1420.htm#SEC1501	40876
memory		sing_302.htm#SEC342	
memory management		sing_302.htm#SEC342	
merkle_hellman_decryption	merkle_hellman_decryption	sing_2409.htm#SEC2490	49106
merkle_hellman_encryption	merkle_hellman_encryption	sing_2408.htm#SEC2489	13645
methods, hashtables		sing_2699.htm#IDX1090	
methods.lib		sing_2699.htm#SEC2780	
methods_lib		sing_2699.htm#SEC2780	
midpoint		sing_2865.htm#SEC2946	29391
milnor		sing_2048.htm#SEC2129	23173
milnor number		sing_2762.htm#IDX1147	
milnorNNB		sing_2789.htm#SEC2870	42717
milnorcode		sing_1903.htm#SEC1984	13849
milnornumber		sing_2034.htm#SEC2115	21855
min		sing_303.htm#SEC343	56342
minAss		sing_1538.htm#SEC1619	43336
minAssChar		sing_1536.htm#SEC1617	18758
minAssCharE		sing_1537.htm#SEC1618	31570
minAssGTZ		sing_1534.htm#SEC1615	41315
minAssGTZE		sing_1535.htm#SEC1616	47474
minAssZ		sing_1560.htm#SEC1641	14250
minEcart		sing_2438.htm#SEC2519	34890
minIntRoot		sing_566.htm#SEC620	3288
minIntRoot2		sing_691.htm#SEC745	46494
minMult		sing_1270.htm#SEC1351	31978
minbase		sing_304.htm#SEC344	
minbaseMon		sing_1417.htm#SEC1498	1501
mindeg		sing_1103.htm#SEC1184	16307
mindeg1		sing_1104.htm#SEC1185	39698
mindist		sing_2306.htm#SEC2387	55281
minimal display time, setting the		sing_368.htm#IDX296	
minimal generating set		sing_304.htm#SEC344	
minimal generating set 		sing_313.htm#SEC353	
minimal representations		sing_896.htm#IDX453	
minimalAfaceOrbits		sing_2562.htm#SEC2643	2467
minimalAfaces		sing_2553.htm#SEC2634	47736
minimalOrbitConeOrbits	minimalOrbitConeOrbits	sing_2564.htm#SEC2645	11756
minipoly		sing_1242.htm#SEC1323	4927
minor		sing_305.htm#SEC345	
minpoly		sing_408.htm#SEC448	
minres		sing_306.htm#SEC346	
minres (plural)		sing_478.htm#SEC518	
minus		sing_2820.htm#IDX1186	
minus 		sing_2821.htm#IDX1188	
minus  		sing_2842.htm#IDX1234	
minus   		sing_2843.htm#IDX1236	
mirror symmetry	tropicalEllipticCovers_lib	sing_1298.htm#IDX611	
mirror symmetry 		sing_3098.htm#IDX1305	
mixed Hodge structure		sing_1963.htm#IDX829	
mixed Hodge structure 		sing_1969.htm#IDX857	
mixed Hodge structure  		sing_1970.htm#IDX863	
mixed Hodge structure   		sing_1971.htm#IDX871	
mixed Hodge structure    		sing_1972.htm#IDX877	
mixed Hodge structure     		sing_1973.htm#IDX885	
mixed Hodge structure      		sing_1974.htm#IDX895	
mixed Hodge structure       		sing_1985.htm#IDX901	
mixed Hodge structure        		sing_1987.htm#IDX912	
mod		sing_81.htm#SEC121	
mod 		sing_103.htm#SEC143	
mod  		sing_152.htm#SEC192	
mod   		sing_160.htm#SEC200	
mod2id		sing_1108.htm#SEC1189	27927
modBorder		sing_1578.htm#SEC1659	19224
modDec		sing_1436.htm#SEC1517	48578
modFinduni		sing_2934.htm#SEC3015	44354
modGB		sing_1412.htm#SEC1493	28790
modIntersect		sing_1414.htm#SEC1495	43699
modJanet		sing_1580.htm#SEC1661	8550
modNPos		sing_1464.htm#SEC1545	17138
modNormal		sing_1472.htm#SEC1553	25274
modNpos_test		sing_1462.htm#SEC1543	34326
modPrimdecGTZ		sing_1353.htm#SEC1434	23036
modQuotient		sing_1355.htm#SEC1436	49602
modSagbiAlg		sing_1925.htm#SEC2006	25025
modSat		sing_1356.htm#SEC1437	22827
modStd		sing_1411.htm#SEC1492	57853
modSyz		sing_1413.htm#SEC1494	37065
modVStd		sing_1936.htm#SEC2017	31133
modVStd0		sing_1937.htm#SEC2018	12714
modWalk		sing_2936.htm#SEC3017	sprintf
mod_versal		sing_1954.htm#SEC2035	63927
modality		sing_1911.htm#SEC1992	49951
modality 		sing_2762.htm#IDX1144	
modalityNNB		sing_2788.htm#SEC2869	37019
modberlekampMassey		sing_1314.htm#SEC1395	40818
modfWalk		sing_2938.htm#SEC3019	sprintf
modfinduni.lib		sing_2933.htm#SEC3014	
modfinduni_lib		sing_2933.htm#SEC3014	
modfrWalk		sing_2939.htm#SEC3020	sprintf
modprimdec.lib		sing_1352.htm#SEC1433	
modprimdec_lib		sing_1352.htm#SEC1433	
modquotient.lib		sing_1354.htm#SEC1435	
modquotient_lib		sing_1354.htm#SEC1435	
modrWalk		sing_2937.htm#SEC3018	sprintf
modrationalInterpolation	modrationalInterpolation	sing_1312.htm#SEC1393	13369
modregCM		sing_1468.htm#SEC1549	64933
modsatiety		sing_1466.htm#SEC1547	12335
modstd.lib		sing_1410.htm#SEC1491	
modstd_lib		sing_1410.htm#SEC1491	
modular		sing_1086.htm#SEC1167	16950
modular methods.		sing_1471.htm#IDX663	
modular techniques.		sing_1472.htm#IDX665	
modular.lib		sing_1085.htm#SEC1166	
modular_lib		sing_1085.htm#SEC1166	
modular_lib 		sing_1085.htm#IDX555	
module		sing_144.htm#SEC184	
module (plural)		sing_444.htm#SEC484	
module declarations		sing_145.htm#SEC185	
module declarations (plural)	module declarations (plural)	sing_445.htm#SEC485	
module expressions		sing_146.htm#SEC186	
module expressions (plural)	module expressions (plural)	sing_446.htm#SEC486	
module operations		sing_147.htm#SEC187	
module operations (plural)	module operations (plural)	sing_447.htm#SEC487	
module ordering C		sing_987.htm#IDX479	
module ordering c		sing_987.htm#IDX481	
module related functions	module related functions	sing_148.htm#SEC188	
module related functions (plural)	module related functions (plural)	sing_448.htm#SEC488	
module_containment		sing_1255.htm#SEC1336	31620
modules.lib		sing_1357.htm#SEC1438	
modules_lib		sing_1357.htm#SEC1438	
moduliMonomials		sing_2792.htm#SEC2873	52263
moduliSpace		sing_1830.htm#SEC1911	37013
modulo		sing_307.htm#SEC347	
modulo (letterplace)	modulo (letterplace)	sing_818.htm#SEC872	
modulo (plural)		sing_479.htm#SEC519	
moduloSlim		sing_750.htm#SEC804	52636
modwalk.lib		sing_2935.htm#SEC3016	
modwalk_lib		sing_2935.htm#SEC3016	
moebius		sing_2686.htm#SEC2767	61319
moebius function		sing_2686.htm#IDX1079	
molien		sing_2084.htm#SEC2165	23972
mondim		sing_674.htm#SEC728	6791
mondromy.lib		sing_2015.htm#SEC2096	
mondromy_lib		sing_2015.htm#SEC2096	
monic		sing_1348.htm#SEC1429	22806
monitor		sing_308.htm#SEC348	
monodromy		sing_1963.htm#IDX833	40112
monodromy 		sing_1968.htm#SEC2049	
monodromy  		sing_1968.htm#IDX853	
monodromy   		sing_1973.htm#IDX888	
monodromy    		sing_1985.htm#IDX904	
monodromy     		sing_1987.htm#IDX915	
monodromyB		sing_2019.htm#SEC2100	46517
monoideal, dimension		sing_674.htm#IDX392	
monomial		sing_309.htm#SEC349	
monomial ordering		sing_1166.htm#IDX581	
monomial orderings	Rings associated to monomial orderings	sing_935.htm#SEC992	
monomial orderings 		sing_984.htm#SEC1041	
monomial orderings introduction	Introduction to orderings	sing_983.htm#SEC1040	
monomial output		sing_412.htm#SEC452	
monomial, write		sing_412.htm#SEC452	
monomialInIdeal		sing_689.htm#SEC743	4687
monomialLcm		sing_2436.htm#SEC2517	36233
monomialabortstd		sing_2697.htm#SEC2778	14901
monomialideal.lib		sing_1415.htm#SEC1496	
monomialideal_lib		sing_1415.htm#SEC1496	
monomials		sing_2764.htm#SEC2845	57994
monomials and precedence	Miscellaneous oddities	sing_429.htm#IDX305	
mons2intmat		sing_1519.htm#SEC1600	15555
morsesplit		sing_1904.htm#SEC1985	3417
movingCone		sing_2560.htm#SEC2641	39892
mp_res_mat		sing_2184.htm#SEC2265	44453
mplot		sing_2255.htm#SEC2336	21740
mpresmat		sing_310.htm#SEC350	
mprimdec.lib		sing_1432.htm#SEC1513	
mprimdec_lib		sing_1432.htm#SEC1513	
mrcgs		sing_1125.htm#SEC1206	16597
mrcgs, rcgs, buildtree, cantreetoMaple, cantodiffcgs	crcgs	sing_1127.htm#IDX573	
mrcgs, rcgs, crcgs, Maple		sing_1128.htm#IDX574	
mregular.lib		sing_1447.htm#SEC1528	
mregular_lib		sing_1447.htm#SEC1528	
mres		sing_311.htm#SEC351	
mres (plural)		sing_480.htm#SEC520	
mresExt		sing_3061.htm#SEC3142	48962
mres_map		sing_312.htm#SEC352	
mstd		sing_313.htm#SEC353	
msum		sing_58.htm#SEC95	53344
mtriple		sing_57.htm#SEC94	55390
mult	Miscellaneous oddities	sing_314.htm#SEC354	
mult 		sing_429.htm#IDX306	
multBound		sing_409.htm#SEC449	
multIdeals		sing_2918.htm#SEC2999	21709
multPoly		sing_3009.htm#SEC3090	sprintf
multRat		sing_697.htm#SEC751	44047
multarr2arr		sing_2681.htm#SEC2762	44731
multarrMultRestrict		sing_2683.htm#SEC2764	41742
multarrRestrict		sing_2682.htm#SEC2763	sprintf
multcol		sing_1209.htm#SEC1290	21899
multdivisor		sing_1672.htm#SEC1753	65139
multformaldivisor		sing_1684.htm#SEC1765	32238
multi		sing_2423.htm#SEC2504	18473
multi indices		sing_37.htm#SEC65	
multi-graded Hilbert series		sing_893.htm#IDX447	
multiDeg		sing_2970.htm#SEC3051	7049
multiDegBasis		sing_2971.htm#SEC3052	3320
multiDegGroebner		sing_2979.htm#SEC3060	1040
multiDegModulo		sing_2981.htm#SEC3062	27244
multiDegPartition		sing_2972.htm#SEC3053	9577
multiDegResolution		sing_2982.htm#SEC3063	38535
multiDegSyzygy		sing_2980.htm#SEC3061	54075
multiDegTensor		sing_2983.htm#SEC3064	45108
multiDegTor		sing_2984.htm#SEC3065	sprintf
multiarrangement		sing_2677.htm#IDX1059	
multiarrangement 		sing_2678.htm#IDX1061	
multiarrangement  		sing_2679.htm#IDX1064	
multiarrangement   		sing_2680.htm#IDX1065	
multiarrangement    		sing_2681.htm#IDX1068	
multiarrangement     		sing_2682.htm#IDX1071	
multiarrangement      		sing_2683.htm#IDX1073	
multidimensional_knapsack	multidimensional_knapsack	sing_2401.htm#SEC2482	15647
multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra	multigrading_lib	sing_2940.htm#IDX1271	
multigrading.lib		sing_2940.htm#IDX1269	
multigrading_lib		sing_2940.htm#IDX1270	
multipleCover		sing_1836.htm#SEC1917	55988
multiplication		sing_2822.htm#IDX1190	
multiplication 		sing_2844.htm#IDX1238	
multiplicities, sequence of		sing_1994.htm#IDX927	
multiplicity		sing_668.htm#IDX387	
multiplicity 		sing_1277.htm#IDX601	
multiplicity sequence		sing_1875.htm#IDX800	
multiplicity sequence 		sing_1878.htm#IDX812	
multiplicity sequence  		sing_1996.htm#IDX928	
multiplyLeftFractions	multiplyLeftFractions	sing_773.htm#SEC827	57489
multiplylist		sing_1773.htm#SEC1854	34999
multivariate equations		sing_2149.htm#IDX952	
multivariate equations 		sing_2851.htm#IDX1253	
multrow		sing_1210.htm#SEC1291	871
multseq2charexp		sing_1874.htm#SEC1955	sprintf
multsequence		sing_1996.htm#SEC2077	35117
naccache_stern_decryption	naccache_stern_decryption	sing_2404.htm#SEC2485	31429
naccache_stern_encryption	naccache_stern_encryption	sing_2403.htm#SEC2484	60034
naccache_stern_generation	naccache_stern_generation	sing_2402.htm#SEC2483	2559
nameof		sing_315.htm#SEC355	
names		sing_316.htm#SEC356	
nashmult		sing_1882.htm#SEC1963	8491
nblocks		sing_368.htm#IDX228	
ncExt_R		sing_716.htm#SEC770	14357
ncHilb		sing_669.htm#SEC723	50352
ncHilb.lib		sing_893.htm#SEC947	
ncHilb_lib		sing_893.htm#SEC947	
ncHilbertMultiplicity	ncHilbertMultiplicity	sing_672.htm#SEC726	60811
ncHilbertPolynomial		sing_671.htm#SEC725	64989
ncHilbertSeries		sing_670.htm#SEC724	30747
ncHom		sing_717.htm#SEC771	45033
ncInit		sing_897.htm#SEC951	55321
ncModslimgb.lib		sing_727.htm#SEC781	
ncModslimgb_lib		sing_727.htm#SEC781	
ncRelations		sing_751.htm#SEC805	7225
ncVarsAdd		sing_899.htm#SEC953	55173
ncVarsGet		sing_898.htm#SEC952	41459
nc_algebra		sing_481.htm#SEC521	
nc_hilb		sing_368.htm#IDX230	
ncalg.lib		sing_623.htm#SEC677	
ncalg_lib		sing_623.htm#SEC677	
ncalgebra		sing_482.htm#SEC522	
ncdecomp.lib		sing_650.htm#SEC704	
ncdecomp_lib		sing_650.htm#SEC704	
ncdetection		sing_617.htm#SEC671	24994
ncfactor		sing_656.htm#SEC710	56995
ncfactor.lib		sing_655.htm#SEC709	
ncfactor_lib		sing_655.htm#SEC709	
ncfrac.lib		sing_701.htm#SEC755	
ncfrac_lib		sing_701.htm#SEC755	
ncgen		sing_819.htm#SEC873	
nchilb		sing_894.htm#SEC948	27003
nchilbert.lib		sing_668.htm#SEC722	
nchilbert_lib		sing_668.htm#SEC722	
nchomolog.lib		sing_715.htm#IDX405	
nchomolog_lib		sing_715.htm#IDX406	
ncloc.lib		sing_723.htm#SEC777	
ncloc_lib		sing_723.htm#SEC777	
ncmodslimgb		sing_728.htm#SEC782	61192
ncols		sing_317.htm#SEC357	
ncones		sing_2542.htm#SEC2623	48316
ncpreim.lib		sing_729.htm#SEC783	
ncpreim_lib		sing_729.htm#SEC783	
ncrat.lib		sing_896.htm#IDX448	
ncratAdd		sing_901.htm#SEC955	34791
ncratDefine		sing_900.htm#SEC954	53337
ncratEvaluateAt		sing_910.htm#SEC964	38737
ncratFromPoly		sing_908.htm#SEC962	13980
ncratFromString		sing_907.htm#SEC961	27148
ncratInvert		sing_904.htm#SEC958	41502
ncratMultiply		sing_903.htm#SEC957	36291
ncratPower		sing_909.htm#SEC963	1973
ncratPrint		sing_906.htm#SEC960	13600
ncratSPrint		sing_905.htm#SEC959	65300
ncratSubstract		sing_902.htm#SEC956	37583
ncrat_lib		sing_896.htm#IDX449	
ncrepAdd		sing_912.htm#SEC966	16569
ncrepDim		sing_917.htm#SEC971	48352
ncrepEvaluate		sing_919.htm#SEC973	53482
ncrepEvaluateAt		sing_920.htm#SEC974	21150
ncrepGet		sing_911.htm#SEC965	25651
ncrepGetRegularMinimal	ncrepGetRegularMinimal	sing_927.htm#SEC981	19538
ncrepGetRegularZeroMinimal	ncrepGetRegularZeroMinimal	sing_926.htm#SEC980	12686
ncrepInvert		sing_915.htm#SEC969	54448
ncrepIsDefined		sing_922.htm#SEC976	60090
ncrepIsDefinedDim		sing_921.htm#SEC975	6513
ncrepIsRegular		sing_923.htm#SEC977	60397
ncrepMultiply		sing_914.htm#SEC968	13469
ncrepPencilCombine		sing_929.htm#SEC983	20857
ncrepPencilGet		sing_928.htm#SEC982	61630
ncrepPrint		sing_916.htm#SEC970	65099
ncrepRegularMinimize	ncrepRegularMinimize	sing_925.htm#SEC979	25283
ncrepRegularZeroMinimize	ncrepRegularZeroMinimize	sing_924.htm#SEC978	40367
ncrepSubstitute		sing_918.htm#SEC972	977
ncrepSubstract		sing_913.htm#SEC967	46335
nctools.lib		sing_737.htm#SEC791	
nctools_lib		sing_737.htm#SEC791	
ndcond		sing_740.htm#SEC794	1006
negateNcfrac		sing_710.htm#SEC764	23626
negatedCone		sing_2520.htm#SEC2601	38527
negation		sing_2821.htm#IDX1189	
negative degree lexicographical ordering		sing_986.htm#IDX470	
negative degree reverse lexicographical ordering	Local orderings	sing_986.htm#IDX468	
negative lexicographical ordering		sing_986.htm#IDX466	
negativedivisor		sing_1673.htm#SEC1754	8274
negativeformaldivisor	negativeformaldivisor	sing_1683.htm#SEC1764	55026
net		sing_2700.htm#IDX1091	sprintf
net 		sing_2702.htm#SEC2783	
net access	Command line options	sing_19.htm#IDX40	
netBigInt		sing_2708.htm#SEC2789	63523
netBigIntMat		sing_2703.htm#SEC2784	36296
netBigIntMatShort		sing_2704.htm#SEC2785	30702
netCoefficientRing		sing_2705.htm#SEC2786	6081
netIdeal		sing_2706.htm#SEC2787	64434
netInt		sing_2707.htm#SEC2788	19545
netIntMat		sing_2709.htm#SEC2790	34242
netIntMatShort		sing_2710.htm#SEC2791	21160
netIntVector		sing_2711.htm#SEC2792	17568
netIntVectorShort		sing_2712.htm#SEC2793	16105
netList		sing_2714.htm#SEC2795	29178
netMap		sing_2715.htm#SEC2796	19115
netMap2		sing_2716.htm#SEC2797	44053
netMatrix		sing_1392.htm#SEC1473	29311
netNumber		sing_2713.htm#SEC2794	24930
netPoly		sing_2719.htm#SEC2800	7938
netPrimePower		sing_2720.htm#SEC2801	54219
netRing		sing_2721.htm#SEC2802	42246
netString		sing_2722.htm#SEC2803	43247
netVector		sing_1391.htm#SEC1472	32453
netmatrix		sing_2717.htm#SEC2798	4023
netmatrixShort		sing_2718.htm#SEC2799	24709
nets.lib		sing_2700.htm#SEC2781	
nets_lib		sing_2700.htm#SEC2781	
netvector		sing_2723.htm#SEC2804	39957
netvectorShort		sing_2724.htm#SEC2805	22053
newline		sing_177.htm#SEC217	
news		sing_3125.htm#SEC3206	
newstruct		sing_188.htm#SEC228	
newstruct 		sing_2731.htm#IDX1121	
newtonDiag		sing_1112.htm#SEC1193	56652
newtonNumber		sing_2795.htm#SEC2876	26410
newtonPolygon		sing_2766.htm#SEC2847	44826
newtonPolygonNegSlopes	newtonPolygonNegSlopes	sing_2640.htm#SEC2721	22052
newtonPolytope		sing_2546.htm#SEC2627	56291
newtonpoly		sing_2001.htm#SEC2082	31930
nextHodgeIdeal		sing_2919.htm#SEC3000	53183
nf_icis		sing_2049.htm#SEC2130	49093
nfmodStd		sing_1457.htm#SEC1538	46077
nfmodSyz		sing_1459.htm#SEC1540	55942
nfmodstd.lib		sing_1455.htm#SEC1536	
nfmodstd_lib		sing_1455.htm#SEC1536	
nfmodsyz.lib		sing_1458.htm#SEC1539	
nfmodsyz_lib		sing_1458.htm#SEC1539	
nilpotent Lie algebras		sing_1726.htm#IDX728	
nmaxcones		sing_2541.htm#SEC2622	660
noElements		sing_3026.htm#SEC3107	18469
noether		sing_410.htm#SEC450	
noether.lib		sing_1460.htm#SEC1541	
noetherNormal		sing_1262.htm#SEC1343	44522
noether_lib		sing_1460.htm#SEC1541	
non-english special characters		sing_418.htm#IDX298	
nonMonomials		sing_1524.htm#SEC1605	53124
nonZeroEntry		sing_1265.htm#SEC1346	933
noncommutative, rational expressions		sing_896.htm#IDX450	
nondegeneratePart		sing_2784.htm#SEC2865	23246
none, option		sing_324.htm#IDX152	
norTest		sing_1482.htm#SEC1563	sprintf
norm		sing_2422.htm#SEC2503	31143
normaform (up to a bound)		sing_368.htm#IDX253	
normal		sing_1470.htm#SEC1551	21287
normal bundle, graph, rational curves, multiple covers, lines on	normalBundle	sing_1835.htm#IDX779	
normal form		sing_993.htm#IDX482	
normal form 		sing_2762.htm#IDX1148	
normal form equation		sing_2762.htm#IDX1149	
normal integral closure.		sing_1487.htm#IDX676	
normal.lib		sing_1469.htm#SEC1550	
normalBundle		sing_1835.htm#SEC1916	sprintf
normalC		sing_1474.htm#SEC1555	34842
normalConductor		sing_1486.htm#SEC1567	26085
normalForm		sing_2778.htm#SEC2859	64811
normalFormDivisor		sing_1674.htm#SEC1755	13778
normalFormEquation		sing_2782.htm#SEC2863	64815
normalFormEquationUpToRescaling	normalFormEquationUpToRescaling	sing_2783.htm#SEC2864	51156
normalI		sing_1575.htm#SEC1656	7516
normalP		sing_1473.htm#SEC1554	36584
normalToricRing		sing_1490.htm#SEC1571	21021
normalToricRingFromBinomials	normalToricRingFromBinomials	sing_1491.htm#SEC1572	16737
normal_lib		sing_1469.htm#SEC1550	
normalform		sing_1908.htm#SEC1989	5550
normalform 		sing_1924.htm#IDX822	
normaliz		sing_1.htm#IDX14	sprintf
normaliz 		sing_1510.htm#SEC1591	
normaliz.lib		sing_1488.htm#SEC1569	
normaliz_lib		sing_1488.htm#SEC1569	
normalization		sing_1276.htm#IDX599	
normalization 		sing_1470.htm#IDX658	
normalization  		sing_1471.htm#IDX661	
normalization   		sing_1472.htm#IDX664	
normalization    		sing_1473.htm#IDX666	
normalization     		sing_1474.htm#IDX669	
normalization      		sing_1486.htm#IDX675	
normalization       		sing_1488.htm#IDX678	
normalization.		sing_1346.htm#IDX643	
normalization. 		sing_1733.htm#IDX750	
normalize		sing_1105.htm#SEC1186	44788
normalizeMonoidal		sing_779.htm#SEC833	33071
normalizeRational		sing_780.htm#SEC834	55177
not		sing_106.htm#SEC146	
not equal		sing_2825.htm#IDX1197	
not equal 		sing_2846.htm#IDX1244	
notBuckets, option		sing_324.htm#IDX166	
notRegularity, option		sing_324.htm#IDX160	
notSugar, option		sing_324.htm#IDX165	
notWarnSB, option		sing_324.htm#IDX188	
npar		sing_2341.htm#SEC2422	5753
npars		sing_318.htm#SEC358	
nrRootsDeterm		sing_2453.htm#SEC2534	sprintf
nrRootsProbab		sing_2452.htm#SEC2533	sprintf
nres		sing_319.htm#SEC359	
nres (plural)		sing_483.htm#SEC523	
nrows		sing_320.htm#SEC360	
nrroots		sing_2482.htm#SEC2563	54867
nsatiety		sing_1465.htm#SEC1546	56854
nselect		sing_1293.htm#SEC1374	34057
nt_solve		sing_2199.htm#SEC2280	33061
ntsolve.lib		sing_2198.htm#SEC2279	
ntsolve_lib		sing_2198.htm#SEC2279	
num_elim		sing_2216.htm#SEC2297	6781
num_elim1		sing_2217.htm#SEC2298	39629
num_prime_decom		sing_2210.htm#SEC2291	19461
num_prime_decom1		sing_2211.htm#SEC2292	51558
num_radical1		sing_2214.htm#SEC2295	14838
num_radical2		sing_2215.htm#SEC2296	4594
num_radical_via_decom	num_radical_via_decom	sing_2212.htm#SEC2293	53773
num_radical_via_randlincom	num_radical_via_randlincom	sing_2213.htm#SEC2294	62430
number		sing_149.htm#SEC189	
number 		sing_2654.htm#IDX1019	
number declarations		sing_150.htm#SEC190	
number expressions		sing_151.htm#SEC191	
number operations		sing_152.htm#SEC192	
number related functions	number related functions	sing_153.htm#SEC193	
numberOfConesOfDimension	numberOfConesOfDimension	sing_2543.htm#SEC2624	6666
number_e		sing_1038.htm#SEC1119	59152
number_pi		sing_1039.htm#SEC1120	15492
numerAlg.lib		sing_1708.htm#IDX717	
numerAlg_lib		sing_1708.htm#IDX718	
numerAlg_lib 		sing_1713.htm#IDX727	
numerDecom.lib		sing_1713.htm#IDX721	
numerDecom_lib		sing_1708.htm#IDX720	
numerDecom_lib 		sing_1713.htm#IDX722	
numerator		sing_321.htm#SEC361	
numerical algebraic geometry		sing_2201.htm#IDX954	
numerical irreducible decomposition		sing_1713.htm#IDX723	
nvars		sing_322.htm#SEC362	
olga.lib		sing_762.htm#SEC816	
olga_lib		sing_762.htm#SEC816	
oneDimBelongSemigroup	oneDimBelongSemigroup	sing_1272.htm#SEC1353	34399
oneNcfrac		sing_707.htm#SEC761	35654
onesVector		sing_2548.htm#SEC2629	17712
online help	The online help system	sing_16.htm#SEC22	
open		sing_323.htm#SEC363	
openSSI		sing_3049.htm#SEC3130	56202
opentex		sing_2258.htm#SEC2339	54236
operatorAlgebra		sing_842.htm#SEC896	36270
operatorBM		sing_552.htm#SEC606	54875
operatorModulo		sing_553.htm#SEC607	26064
oppose		sing_484.htm#SEC524	
opposite		sing_485.htm#SEC525	
opposite polynomial		sing_368.htm#IDX238	
opposite ring		sing_368.htm#IDX235	
option		sing_324.htm#SEC364	
option Imap		sing_324.htm#IDX182	
option(warn)		sing_70.htm#SEC110	
optionIsSet		sing_1163.htm#SEC1244	57325
or	Evaluation of logical expressions	sing_106.htm#SEC146	
or 		sing_422.htm#SEC462	
orbit		sing_1726.htm#IDX730	
orbit 		sing_1727.htm#IDX734	
orbit  		sing_1730.htm#IDX739	
orbit   		sing_1731.htm#IDX742	
orbitConeOrbits		sing_2563.htm#SEC2644	60979
orbitCones		sing_2554.htm#SEC2635	60528
orbit_variety		sing_2108.htm#SEC2189	7037
orbitparam.lib		sing_1726.htm#SEC1807	
orbitparam_lib		sing_1726.htm#SEC1807	
ord		sing_325.htm#SEC365	
ord_test		sing_1158.htm#SEC1239	36532
order ideal, border basis		sing_1577.htm#IDX688	
order ideal, border basis 		sing_1578.htm#IDX689	
ordering	diffAlgebraChangeOrd	sing_2810.htm#IDX1166	
ordering 		sing_2826.htm#IDX1200	
ordering  		sing_2827.htm#IDX1203	
orderings	General definitions for orderings	sing_984.htm#SEC1041	
orderings introduction	Introduction to orderings	sing_983.htm#SEC1040	
orderings, L		sing_991.htm#SEC1048	
orderings, M		sing_988.htm#SEC1045	
orderings, a		sing_990.htm#SEC1047	
orderings, global		sing_985.htm#SEC1042	
orderings, local		sing_986.htm#SEC1043	
orderings, product		sing_989.htm#SEC1046	
ordstr		sing_326.htm#SEC366	
origin		sing_2491.htm#SEC2572	31408
orthogonalize		sing_1228.htm#SEC1309	29404
outer		sing_1199.htm#SEC1280	64048
output		sing_41.htm#SEC71	
outputting monomials		sing_412.htm#SEC452	
p-adic numbers		sing_32.htm#SEC46	
pFactor		sing_2377.htm#SEC2458	31504
pIntersect		sing_515.htm#SEC569	44055
pIntersectSyz		sing_516.htm#SEC570	45608
package		sing_154.htm#SEC194	
package declarations	package declarations	sing_155.htm#SEC195	
package related functions	package related functions	sing_156.htm#SEC196	
pairset		sing_2442.htm#SEC2523	38258
par		sing_327.htm#SEC367	
par2varRing		sing_1021.htm#SEC1102	45538
paraConic		sing_1741.htm#SEC1822	9828
paraPlaneCurve		sing_1735.htm#SEC1816	34094
parallel computing		sing_3078.htm#IDX1300	
parallel skeletons		sing_1087.htm#IDX561	
parallel.lib		sing_1087.htm#SEC1168	
parallelTestAND		sing_1091.htm#SEC1172	1415
parallelTestOR		sing_1092.htm#SEC1173	14920
parallelWaitAll		sing_1090.htm#SEC1171	2017
parallelWaitFirst		sing_1089.htm#SEC1170	32
parallelWaitN		sing_1088.htm#SEC1169	38878
parallel_lib		sing_1087.htm#SEC1168	
parallelization		sing_1087.htm#IDX560	
parallelization 		sing_1142.htm#IDX575	
parallelization  		sing_1175.htm#IDX585	
parallelization   		sing_3126.htm#SEC3224	
param		sing_1992.htm#SEC2073	57220
parameter, as numbers		sing_149.htm#SEC189	
parameter, default		sing_44.htm#SEC81	
parameter, optional		sing_44.htm#SEC81	
parameterSubstitute		sing_2626.htm#SEC2707	63147
parametric annihilator		sing_544.htm#IDX350	
parametric annihilator for variety		sing_608.htm#IDX380	
parametric ideal		sing_1050.htm#IDX488	
parametric ideal 		sing_1057.htm#IDX507	
parametric ideal  		sing_1057.htm#IDX509	
parametric ideal   		sing_1058.htm#IDX514	
parametrization		sing_1726.htm#IDX731	
parametrization 		sing_1730.htm#IDX740	
parametrization  		sing_1992.htm#IDX922	
parametrizeOrbit		sing_1730.htm#SEC1811	5225
paraplanecurves.lib		sing_1732.htm#SEC1813	
paraplanecurves_lib		sing_1732.htm#SEC1813	
pardeg		sing_328.htm#SEC368	
parstr		sing_329.htm#SEC369	
part		sing_1656.htm#SEC1737	31485
partOver		sing_1659.htm#SEC1740	25555
partUnder		sing_1660.htm#SEC1741	13123
partial fraction		sing_2992.htm#IDX1272	
partial_molien		sing_2086.htm#SEC2167	21772
partitions		sing_1306.htm#SEC1387	48089
partitions 		sing_1306.htm#IDX632	
path	Used environment variables	sing_3135.htm#SEC3240	
path integral		sing_1298.htm#IDX617	
paths	Used environment variables	sing_3135.htm#SEC3240	
pause		sing_1084.htm#SEC1165	2273
pdivi		sing_1052.htm#SEC1133	21786
pdivi 		sing_1053.htm#IDX498	
pdivi2		sing_1118.htm#SEC1199	11955
permcol		sing_1211.htm#SEC1292	12886
permrow		sing_1212.htm#SEC1293	26561
permutationFromIntvec	permutationFromIntvec	sing_2569.htm#SEC2650	6533
permutationToIntvec		sing_2570.htm#SEC2651	1989
permutations		sing_1307.htm#IDX633	
permutations, sum, max, min		sing_2692.htm#IDX1084	
permute		sing_1307.htm#SEC1388	40893
permute_L		sing_2293.htm#SEC2374	10716
perron		sing_784.htm#SEC838	3782
perron.lib		sing_783.htm#SEC837	
perron_lib		sing_783.htm#SEC837	
pfd		sing_2993.htm#SEC3074	16552
pfd.lib		sing_2992.htm#SEC3073	
pfdMat		sing_3001.htm#SEC3082	58018
pfd_lib		sing_2992.htm#SEC3073	
phindex.lib		sing_2726.htm#SEC2807	
phindex_lib		sing_2726.htm#SEC2807	
picksFormula		sing_2589.htm#SEC2670	14656
pid		sing_368.htm#IDX247	
piecewiseJet		sing_2775.htm#SEC2856	53252
piecewiseOrd		sing_2773.htm#SEC2854	58014
piecewiseWeightOfPolygon	piecewiseWeightOfPolygon	sing_2772.htm#SEC2853	18162
piecewisedegree		sing_2774.htm#SEC2855	15493
plainInvariants		sing_1951.htm#SEC2032	40916
planeCur		sing_1922.htm#SEC2003	sprintf
plot		sing_2271.htm#SEC2352	46610
plotRot		sing_2275.htm#SEC2356	57150
plotRotated		sing_2274.htm#SEC2355	33009
plotRotatedDirect		sing_2277.htm#SEC2358	18202
plotRotatedList		sing_2276.htm#SEC2357	41668
plotRotatedListFromSpecifyList	plotRotatedListFromSpecifyList	sing_2278.htm#SEC2359	38856
plural		sing_1165.htm#IDX580	
pmat		sing_1078.htm#SEC1159	3857
pnormalf		sing_1053.htm#SEC1134	26174
pnormalform		sing_1121.htm#SEC1202	63529
pointid.lib		sing_1523.htm#SEC1604	
pointid_lib		sing_1523.htm#SEC1604	
points		sing_2852.htm#SEC2933	11076
polSol		sing_681.htm#SEC735	323
polSolFiniteRank		sing_682.htm#SEC736	30875
pollTask		sing_1185.htm#SEC1266	53950
poly		sing_157.htm#SEC197	
poly (plural)		sing_449.htm#SEC489	
poly declarations		sing_158.htm#SEC198	
poly declarations (plural)	poly declarations (plural)	sing_450.htm#SEC490	
poly expressions		sing_159.htm#SEC199	
poly expressions (plural)	poly expressions (plural)	sing_451.htm#SEC491	
poly operations		sing_160.htm#SEC200	
poly operations (plural)	poly operations (plural)	sing_452.htm#SEC492	
poly related functions	poly related functions	sing_161.htm#SEC201	
poly related functions (plural)	poly related functions (plural)	sing_453.htm#SEC493	
poly2list		sing_594.htm#SEC648	4960
poly2zdd		sing_2747.htm#SEC2828	61839
polyDK		sing_1347.htm#SEC1428	14357
polyInterpolation		sing_1311.htm#SEC1392	45866
polyVars		sing_688.htm#SEC742	43882
polybori		sing_2731.htm#IDX1117	
polybori.lib		sing_2731.htm#SEC2812	
polybori.lib 		sing_2731.htm#IDX1118	
polybori_lib		sing_2731.htm#SEC2812	
polyclass.lib		sing_3003.htm#SEC3084	
polyclass_lib		sing_3003.htm#SEC3084	
polylib.lib		sing_1093.htm#SEC1174	
polylib_lib		sing_1093.htm#SEC1174	
polymake.lib		sing_2580.htm#SEC2661	
polymake_lib		sing_2580.htm#SEC2661	
polynomial		sing_2837.htm#IDX1225	
polynomial functions		sing_3022.htm#IDX1279	
polynomial solutions		sing_675.htm#IDX402	
polynomial, opposite		sing_368.htm#IDX239	
polynomials		sing_3003.htm#IDX1275	
polytope		sing_196.htm#SEC236	
polytope 		sing_2580.htm#IDX988	
polytopeViaInequalities	polytopeViaInequalities	sing_2521.htm#SEC2602	52084
polytopeViaPoints		sing_2522.htm#SEC2603	281
pos_def		sing_1239.htm#SEC1320	4994
poset		sing_2685.htm#IDX1077	
poshull		sing_2763.htm#SEC2844	27537
positiveOrthant		sing_2492.htm#SEC2573	42102
posweight		sing_2066.htm#SEC2147	3364
powSumSym		sing_1613.htm#SEC1694	38369
power		sing_1200.htm#SEC1281	23365
power set		sing_2694.htm#IDX1086	
powerN		sing_2361.htm#SEC2442	20170
powerX		sing_2370.htm#SEC2451	47971
power_products		sing_2100.htm#SEC2181	54629
powerpolyX		sing_2353.htm#SEC2434	37247
powersums		sing_2463.htm#SEC2544	59049
preComp		sing_1443.htm#SEC1524	16160
precision		sing_3096.htm#IDX1303	
preim		sing_3100.htm#SEC3181	44269
preimage		sing_330.htm#SEC370	
preimage 		sing_729.htm#IDX407	
preimage  		sing_3100.htm#IDX1315	
preimage (plural)		sing_486.htm#SEC526	
preimage under a map between local rings, map between local rings, map between local and global rings	preimageLoc	sing_1161.htm#IDX578	
preimageLattice		sing_2960.htm#SEC3041	37348
preimageLoc		sing_1161.htm#SEC1242	33315
preimageNC		sing_731.htm#SEC785	16037
prepEmbDiv		sing_1803.htm#SEC1884	36708
prepMat		sing_2146.htm#SEC2227	39868
prepRealclassify		sing_1913.htm#SEC1994	10994
prepSV		sing_2288.htm#SEC2369	50095
prepareAss		sing_1544.htm#SEC1625	31988
presentTree		sing_1790.htm#SEC1871	10731
presentation		sing_1393.htm#SEC1474	40323
presolve.lib		sing_2165.htm#SEC2246	
presolve_lib		sing_2165.htm#SEC2246	
primL		sing_2365.htm#SEC2446	14513
primList		sing_2364.htm#SEC2445	6802
primRoot		sing_1594.htm#SEC1675	14210
primTest		sing_1442.htm#SEC1523	8105
primary decomposition		sing_1527.htm#IDX680	
primary decomposition 		sing_1557.htm#IDX682	
primary decomposition of modules		sing_1432.htm#IDX651	
primary decomposition, numerical		sing_1713.htm#IDX725	
primaryTest		sing_1552.htm#SEC1633	sprintf
primary_char0		sing_2090.htm#SEC2171	61413
primary_char0_no_molien	primary_char0_no_molien	sing_2092.htm#SEC2173	50477
primary_char0_no_molien_random	primary_char0_no_molien_random	sing_2097.htm#SEC2178	8422
primary_char0_random	primary_char0_random	sing_2095.htm#SEC2176	5996
primary_charp		sing_2091.htm#SEC2172	30091
primary_charp_no_molien	primary_charp_no_molien	sing_2093.htm#SEC2174	32282
primary_charp_no_molien_random	primary_charp_no_molien_random	sing_2098.htm#SEC2179	11498
primary_charp_random	primary_charp_random	sing_2096.htm#SEC2177	7352
primary_charp_without	primary_charp_without	sing_2094.htm#SEC2175	49585
primary_charp_without_random	primary_charp_without_random	sing_2099.htm#SEC2180	36998
primary_invariants		sing_2078.htm#SEC2159	5500
primary_invariants_random	primary_invariants_random	sing_2079.htm#SEC2160	28958
primdec		sing_1533.htm#SEC1614	48548
primdec.lib		sing_1527.htm#SEC1608	
primdecGTZ		sing_1529.htm#SEC1610	46615
primdecGTZE		sing_1530.htm#SEC1611	17822
primdecMon		sing_1431.htm#SEC1512	14096
primdecSY		sing_1531.htm#SEC1612	6547
primdecSYE		sing_1532.htm#SEC1613	52788
primdecZ		sing_1558.htm#SEC1639	57892
primdecZM		sing_1559.htm#SEC1640	484
primdec_lib		sing_1527.htm#SEC1608	
primdecint.lib		sing_1557.htm#SEC1638	
primdecint_lib		sing_1557.htm#SEC1638	
prime		sing_331.htm#SEC371	
primeClosure		sing_1477.htm#SEC1558	43589
primecoeffs		sing_1045.htm#SEC1126	46153
primefactors		sing_332.htm#SEC372	
primes		sing_1040.htm#SEC1121	24408
primitiv.lib		sing_1565.htm#SEC1646	
primitiv_lib		sing_1565.htm#SEC1646	
primitive		sing_1566.htm#SEC1647	36163
primitive element		sing_1566.htm#IDX683	
primitiveSpan		sing_2967.htm#SEC3048	sprintf
primitive_extra		sing_1567.htm#SEC1648	49025
primparam		sing_1946.htm#SEC2027	35357
principal intersection		sing_509.htm#IDX334	
print		sing_333.htm#SEC373	
print 		sing_2652.htm#IDX1012	
print  		sing_2814.htm#IDX1175	
print   		sing_2816.htm#IDX1180	
print    		sing_2817.htm#IDX1181	
print     		sing_2839.htm#IDX1229	
print      		sing_2840.htm#IDX1230	
printBetti		sing_1374.htm#SEC1455	28941
printFreeModule		sing_1366.htm#SEC1447	13316
printGraph		sing_1300.htm#SEC1381	45041
printGraphG		sing_1829.htm#SEC1910	48742
printGroup		sing_2948.htm#SEC3029	6791
printHom		sing_1369.htm#SEC1450	7070
printMatrix		sing_1365.htm#SEC1446	15522
printModule		sing_1368.htm#SEC1449	sprintf
printMoebius		sing_2691.htm#SEC2772	45828
printNormalForm		sing_3015.htm#SEC3096	41856
printNormalFormEquation	printNormalFormEquation	sing_3014.htm#SEC3095	61996
printPoly		sing_3007.htm#SEC3088	56858
printPolynomialRightEquivalence	printPolynomialRightEquivalence	sing_3012.htm#SEC3093	61891
printPuiseux		sing_3020.htm#SEC3101	28777
printResolution		sing_1367.htm#SEC1448	29278
printRightEquivalenceChainWithPrecision	printRightEquivalenceChainWithPrecision	sing_3013.htm#SEC3094	38655
printSheaf		sing_1817.htm#SEC1898	31762
printStack		sing_1831.htm#SEC1912	3692
printTask		sing_1180.htm#SEC1261	54549
printVariety		sing_1809.htm#SEC1890	2846
printf		sing_334.htm#SEC374	2294
printlevel		sing_411.htm#SEC451	
proc		sing_162.htm#SEC202	
proc declaration		sing_163.htm#SEC203	
proc expression		sing_164.htm#SEC204	
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_165.htm#SEC205	
prodcrit		sing_2440.htm#SEC2521	56231
product		sing_1041.htm#SEC1122	54431
product 		sing_2822.htm#IDX1191	
product  		sing_2844.htm#IDX1239	
product variety, abstract variety		sing_1810.htm#IDX767	
productOfProjectiveSpaces	productOfProjectiveSpaces	sing_3080.htm#SEC3161	52147
productVariety		sing_1810.htm#SEC1891	54191
productgroup		sing_2969.htm#SEC3050	55937
progress watch		sing_324.htm#IDX169	
projPoints		sing_2853.htm#SEC2934	sprintf
projectLattice		sing_2961.htm#SEC3042	28463
projective bundle, abstract variety, sheaf, enumeration of conics	projectiveBundle	sing_1814.htm#IDX771	
projective dimension	purityfiltration_lib	sing_785.htm#IDX416	
projective limes		sing_32.htm#SEC46	
projective space, abstract variety		sing_1813.htm#IDX770	
projectiveBundle		sing_1814.htm#SEC1895	13791
projectiveDimension		sing_786.htm#SEC840	8165
projectiveSpace		sing_1813.htm#SEC1894	21729
prompt		sing_15.htm#SEC21	
prompt, option		sing_324.htm#IDX189	
propagator	tropicalEllipticCovers_lib	sing_1298.htm#IDX615	42460
propagator 		sing_1301.htm#SEC1382	
propagator  		sing_3098.htm#IDX1309	
propagator of a graph		sing_3107.htm#IDX1327	
prot, option		sing_324.htm#IDX167	
protocol of computations		sing_324.htm#IDX168	
proximitymatrix		sing_1873.htm#SEC1954	58403
prune		sing_335.htm#SEC375	
pruneModule		sing_1400.htm#SEC1481	51437
prune_map		sing_336.htm#SEC376	
prwalk		sing_3028.htm#SEC3109	46963
psigncnd		sing_2234.htm#SEC2315	57734
puiseux		sing_3021.htm#SEC3102	11573
puiseux2generators		sing_2004.htm#SEC2085	64508
puiseuxExpansion		sing_2598.htm#SEC2679	47301
puiseuxList		sing_3017.htm#SEC3098	22896
puiseuxexpansions.lib	puiseuxexpansions_lib	sing_3016.htm#SEC3097	
puiseuxexpansions_lib	puiseuxexpansions_lib	sing_3016.htm#SEC3097	
pure tensor		sing_502.htm#IDX322	
pure_gb, option		sing_324.htm#IDX161	
purelist		sing_796.htm#SEC850	15517
purity	purityfiltration_lib	sing_785.htm#IDX418	
purityFiltration		sing_787.htm#SEC841	5742
purityTriang		sing_788.htm#SEC842	3665
purityfiltration.lib	purityfiltration_lib	sing_785.htm#IDX411	
purityfiltration_lib	purityfiltration_lib	sing_785.htm#IDX412	
pushForward		sing_2986.htm#SEC3067	26697
pwalk		sing_1322.htm#SEC1403	61187
pyobject		sing_197.htm#SEC237	
pyobject 		sing_2731.htm#IDX1120	
pyobject declarations	pyobject declarations	sing_198.htm#SEC238	
pyobject expressions	pyobject expressions	sing_199.htm#SEC239	
pyobject operations		sing_200.htm#SEC240	
pyobject related functions	pyobject related functions	sing_201.htm#SEC241	
pyramid		sing_2866.htm#SEC2947	7421
python_eval		sing_202.htm#SEC242	
python_import		sing_203.htm#SEC243	
python_run		sing_204.htm#SEC244	
qbase		sing_2466.htm#SEC2547	8633
qepcad		sing_2876.htm#SEC2957	39171
qepcadsystem		sing_2877.htm#SEC2958	31977
qhmatrix		sing_2064.htm#SEC2145	61813
qhmoduli.lib		sing_2021.htm#SEC2102	
qhmoduli_lib		sing_2021.htm#SEC2102	
qhspectrum		sing_2051.htm#SEC2132	13732
qhweight		sing_337.htm#SEC377	
qmatrix.lib		sing_797.htm#SEC851	
qmatrix_lib		sing_797.htm#SEC851	
qminor		sing_799.htm#SEC853	52670
qrds		sing_338.htm#SEC378	
qring	Miscellaneous oddities	sing_171.htm#SEC211	
qring 		sing_429.htm#IDX310	
qring (plural)		sing_454.htm#SEC494	
qring declaration		sing_175.htm#SEC215	
qring declaration (plural)	qring declaration (plural)	sing_455.htm#SEC495	
qring related functions (plural)	qring related functions (plural)	sing_456.htm#SEC496	
qring ring ideal 'factor ring'		sing_1170.htm#IDX584	
qringNF, option		sing_324.htm#IDX170	
qslimgb		sing_1020.htm#SEC1101	51999
quadraticSieve		sing_2378.htm#SEC2459	58557
quantMat		sing_798.htm#SEC852	56227
quickclass		sing_1905.htm#SEC1986	14018
quit		sing_401.htm#SEC441	
quotSheaf		sing_1826.htm#SEC1907	49619
quote		sing_339.htm#SEC379	
quotient		sing_340.htm#SEC380	
quotient (plural)		sing_487.htm#SEC527	
quotientLatticeBasis	quotientLatticeBasis	sing_2523.htm#SEC2604	15613
quotientMain		sing_2245.htm#SEC2326	17762
quotientMon		sing_1422.htm#SEC1503	57149
rHRR		sing_1653.htm#SEC1734	20131
rJanet		sing_1579.htm#SEC1660	30716
rMacaulay		sing_1079.htm#SEC1160	45499
rad_con		sing_1106.htm#SEC1187	21777
radical		sing_1541.htm#SEC1622	1407
radicalEHV		sing_1542.htm#SEC1623	33703
radicalMemberShip		sing_2619.htm#SEC2700	28527
radicalMon		sing_1423.htm#SEC1504	64912
radicalZ		sing_1561.htm#SEC1642	27420
randcharpoly		sing_2460.htm#SEC2541	37737
randlinpoly		sing_2462.htm#SEC2543	22330
random		sing_341.htm#SEC381	
random 		sing_368.htm#IDX251	
random  		sing_2673.htm#IDX1051	
random   		sing_2674.htm#IDX1053	
random number generator, seed		sing_368.htm#IDX249	
random.lib		sing_1129.htm#SEC1210	
randomBinomial		sing_1141.htm#SEC1222	17913
randomCheck		sing_2304.htm#SEC2385	20973
randomLast		sing_1140.htm#SEC1221	2046
randomPoint		sing_2524.htm#SEC2605	63952
randomPolyInT		sing_2628.htm#SEC2709	2264
random_lib		sing_1129.htm#SEC1210	
randomid		sing_1131.htm#SEC1212	7815
randommat		sing_1132.htm#SEC1213	33569
rank		sing_215.htm#IDX137	
rank 		sing_342.htm#SEC382	
rankSheaf		sing_1818.htm#SEC1899	11850
ratSol		sing_683.htm#SEC737	62488
ratgb.lib		sing_803.htm#IDX419	
ratgb_lib		sing_803.htm#IDX420	
rational curves, rational parametrization of rational curves.	paraPlaneCurve	sing_1735.htm#IDX752	
rational functions		sing_896.htm#IDX451	
rational normal curve, projection.		sing_1736.htm#IDX753	
rational normal curve, projection. 		sing_1739.htm#IDX754	
rational normal curve, projection.  		sing_1740.htm#IDX755	
rational reconstraction		sing_250.htm#SEC290	
rational solutions		sing_675.htm#IDX403	
rational univariate projection		sing_2460.htm#IDX984	
rationalCurve		sing_1838.htm#SEC1919	61201
rationalPointConic		sing_1737.htm#SEC1818	9761
ratstd		sing_804.htm#SEC858	65487
rays		sing_2525.htm#SEC2606	44445
rcgs		sing_1126.htm#SEC1207	50875
rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs	mrcgs	sing_1125.htm#IDX571	
rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs 		sing_1126.htm#IDX572	
rcolon		sing_895.htm#SEC949	1208
re2squ		sing_1714.htm#SEC1795	24350
read		sing_343.htm#SEC383	
readDataFromSSI		sing_3054.htm#SEC3135	195
readFromString		sing_3056.htm#SEC3137	4258
readInputTXT		sing_3000.htm#SEC3081	37598
readNmzData		sing_1513.htm#SEC1594	3397
readSSI		sing_3051.htm#SEC3132	16038
reading, option		sing_324.htm#IDX190	
readline		sing_1.htm#IDX5	
real		sing_28.htm#IDX74	
real root isolation		sing_2219.htm#IDX959	
real roots, univariate polynomial		sing_2467.htm#IDX986	
real roots, univariate projection		sing_2451.htm#IDX982	
real roots,sign conditions		sing_2232.htm#IDX962	
realLLL		sing_2218.htm#SEC2299	2937
realclassify		sing_2032.htm#SEC2113	51416
realclassify.lib		sing_2031.htm#SEC2112	
realclassify_lib		sing_2031.htm#SEC2112	
realizationDim		sing_2592.htm#SEC2673	37756
realizationDimPoly		sing_2594.htm#SEC2675	3611
realizationMatroids.lib	realizationMatroids_lib	sing_2591.htm#SEC2672	
realizationMatroids_lib	realizationMatroids_lib	sing_2591.htm#SEC2672	
realmorsesplit		sing_2033.htm#SEC2114	16318
realpoly		sing_1570.htm#SEC1651	9453
realrad		sing_1572.htm#SEC1653	21797
realrad.lib		sing_1569.htm#SEC1650	
realrad_lib		sing_1569.htm#SEC1650	
realzero		sing_1571.htm#SEC1652	12712
recover.lib		sing_2201.htm#SEC2282	
recover_lib		sing_2201.htm#SEC2282	
recursive_boolean_poly	recursive_boolean_poly	sing_2737.htm#SEC2818	17045
recursive_from_boolean_poly	recursive_from_boolean_poly	sing_2743.htm#SEC2824	37794
redSB, option		sing_324.htm#IDX171	
redTail, option		sing_324.htm#IDX173	
redThrough, option		sing_324.htm#IDX174	
redcgs.lib		sing_1114.htm#SEC1195	
redcgs_lib		sing_1114.htm#SEC1195	
redefine, option		sing_324.htm#IDX191	
redspec		sing_1120.htm#SEC1201	12952
reduce		sing_344.htm#SEC384	
reduce 		sing_523.htm#IDX339	
reduce  		sing_1052.htm#IDX496	
reduce   		sing_1053.htm#IDX499	
reduce (letterplace)	reduce (letterplace)	sing_820.htm#SEC874	
reduce (plural)		sing_488.htm#SEC528	
reduce (up to a bound)		sing_368.htm#IDX252	
reduceIntChain		sing_1405.htm#SEC1486	17776
reduced		sing_1051.htm#IDX493	
reduced standard basis		sing_324.htm#IDX172	
reduction		sing_2116.htm#SEC2197	31048
reesclos.lib		sing_1573.htm#SEC1654	
reesclos_lib		sing_1573.htm#SEC1654	
reference		sing_205.htm#SEC245	
reference declarations	reference declarations	sing_206.htm#SEC246	
reference expressions	reference expressions	sing_207.htm#SEC247	
reference operations	reference and shared operations	sing_210.htm#SEC250	
reference related functions	reference and shared related functions	sing_211.htm#SEC251	
regCM		sing_1467.htm#SEC1548	47140
regIdeal		sing_1448.htm#SEC1529	3827
regMonCurve		sing_1451.htm#SEC1532	41311
regionComplex		sing_3092.htm#SEC3173	27359
regularBasis		sing_2776.htm#SEC2857	63894
regularity	Syzygies and resolutions	sing_345.htm#SEC385	
regularity 		sing_995.htm#SEC1057	
regularity  		sing_1467.htm#IDX656	
regularity   		sing_1468.htm#IDX657	
reiffen		sing_563.htm#SEC617	32856
rel_orbit_variety		sing_2109.htm#SEC2190	2186
relations		sing_783.htm#IDX410	
relativeInteriorPoint	relativeInteriorPoint	sing_2526.htm#SEC2607	30097
relative_orbit_variety	relative_orbit_variety	sing_2110.htm#SEC2191	2424
relweight		sing_2065.htm#SEC2146	10658
remainder		sing_2238.htm#SEC2319	1191
remainderMain		sing_2246.htm#SEC2327	13832
removeCone		sing_2544.htm#SEC2625	33877
removepower		sing_1883.htm#SEC1964	47644
repart		sing_346.htm#SEC386	
replace		sing_2343.htm#SEC2424	50075
representation, math objects	Representation of mathematical objects	sing_981.htm#SEC1038	
res		sing_347.htm#SEC387	10393
resbinomial.lib		sing_1744.htm#IDX758	
resbinomial_lib		sing_1744.htm#IDX759	
reservedName		sing_348.htm#SEC388	
resetNmzOptions		sing_1509.htm#SEC1590	27438
resfunction		sing_1758.htm#SEC1839	59312
resgraph.lib		sing_1776.htm#SEC1857	
resgraph_lib		sing_1776.htm#SEC1857	
residue		sing_1303.htm#IDX622	
resjung.lib		sing_1780.htm#SEC1861	
resjung_lib		sing_1780.htm#SEC1861	
reslist		sing_1772.htm#SEC1853	64950
resolution	purityfiltration_lib	sing_166.htm#SEC206	
resolution 		sing_785.htm#IDX417	
resolution (plural)		sing_457.htm#SEC497	
resolution declarations	resolution declarations	sing_167.htm#SEC207	
resolution declarations (plural)	resolution declarations (plural)	sing_458.htm#SEC498	
resolution expressions	resolution expressions	sing_168.htm#SEC208	
resolution expressions (plural)	resolution expressions (plural)	sing_459.htm#SEC499	
resolution graph		sing_1868.htm#IDX796	
resolution related functions	resolution related functions	sing_169.htm#SEC209	
resolution related functions (plural)	resolution related functions (plural)	sing_460.htm#SEC500	
resolution, La Scala's method		sing_296.htm#SEC336	
resolution, computation of		sing_347.htm#IDX193	
resolution, hilbert-driven		sing_271.htm#SEC311	
resolutionInLocalization	resolutionInLocalization	sing_1705.htm#SEC1786	31106
resolutiongraph		sing_1869.htm#SEC1950	32697
resolve		sing_1788.htm#SEC1869	26235
resolve.lib		sing_1784.htm#SEC1865	
resolve_lib		sing_1784.htm#SEC1865	
resources.lib		sing_1142.htm#SEC1223	
resources_lib		sing_1142.htm#SEC1223	
restriction		sing_2666.htm#IDX1039	
restriction 		sing_2682.htm#IDX1072	
restriction  		sing_2683.htm#IDX1074	
restriction of		sing_568.htm#IDX362	
restrictionIdeal		sing_578.htm#SEC632	49796
restrictionModule		sing_579.htm#SEC633	62461
resultant		sing_310.htm#SEC350	
resultant 		sing_349.htm#SEC389	
reszeta.lib		sing_1797.htm#SEC1878	
reszeta_lib		sing_1797.htm#SEC1878	
return		sing_402.htm#SEC442	
return type of procedures	Return type of procedures	sing_427.htm#SEC467	
returnSB, option		sing_324.htm#IDX154	
reverse		sing_2481.htm#SEC2562	35880
reynolds_molien		sing_2085.htm#SEC2166	19350
rho		sing_2372.htm#SEC2453	51414
right equivalence		sing_3096.htm#IDX1301	
rightInverse		sing_2323.htm#SEC2404	6558
rightKernel		sing_2321.htm#SEC2402	46603
rightModulo		sing_749.htm#SEC803	12618
rightNF		sing_748.htm#SEC802	42610
rightNFWeyl		sing_700.htm#SEC754	35828
rightOre		sing_769.htm#SEC823	56918
rightStd		sing_747.htm#SEC801	sprintf
rightstd (letterplace)	rightstd (letterplace)	sing_821.htm#SEC875	
ring		sing_170.htm#SEC210	
ring (plural)		sing_461.htm#SEC501	
ring coefficients	hasAlgExtensionCoefficient	sing_1168.htm#IDX582	
ring coefficients 		sing_1169.htm#IDX583	
ring declarations		sing_172.htm#SEC212	
ring declarations (plural)	ring declarations (plural)	sing_462.htm#SEC502	
ring operations		sing_174.htm#SEC214	
ring operations (plural)	ring operations (plural)	sing_463.htm#SEC503	
ring related functions	ring related functions	sing_173.htm#SEC213	
ring related functions (plural)	ring related functions (plural)	sing_464.htm#SEC504	
ring theory		sing_870.htm#IDX432	
ring, opposite		sing_368.htm#IDX236	
ring, rings		sing_1115.htm#IDX563	
ring.lib		sing_1147.htm#SEC1228	
ringOf		sing_3005.htm#SEC3086	42677
ring_cf		sing_215.htm#IDX138	
ring_lib		sing_1147.htm#SEC1228	
ring_list		sing_351.htm#SEC391	
ring_variable		sing_2653.htm#IDX1016	
ring_variable 		sing_2654.htm#IDX1018	
ring_variable  		sing_2655.htm#IDX1022	
ring_variable   		sing_2656.htm#IDX1024	
ringgb.lib		sing_3022.htm#SEC3103	
ringgb.lib, functions for coefficient rings		sing_3022.htm#IDX1281	
ringgb_lib		sing_3022.htm#SEC3103	
ringlist		sing_350.htm#SEC390	
ringlist (plural)		sing_489.htm#SEC529	
ringtensor		sing_1159.htm#SEC1240	56648
ringweights		sing_1160.htm#SEC1241	33307
rinvar.lib		sing_2121.htm#SEC2202	
rinvar_lib		sing_2121.htm#SEC2202	
rmNmzFiles		sing_1518.htm#SEC1599	32601
rm_unitcol		sing_1217.htm#SEC1298	5591
rm_unitrow		sing_1216.htm#SEC1297	35694
rmx		sing_2268.htm#SEC2349	17675
rncAntiCanonicalMap		sing_1736.htm#SEC1817	41965
rncItProjEven		sing_1740.htm#SEC1821	18200
rncItProjOdd		sing_1739.htm#SEC1820	61976
root of Bernstein-Sato polynomial		sing_544.htm#IDX351	
rootIsolation		sing_2230.htm#SEC2311	34513
rootIsolationNoPreprocessing	rootIsolationNoPreprocessing	sing_2229.htm#SEC2310	42387
rootIsolationPrimdec	rootIsolationPrimdec	sing_2231.htm#SEC2312	35485
rootisolation.lib		sing_2219.htm#SEC2300	
rootisolation_lib		sing_2219.htm#SEC2300	
rootofUnity		sing_1162.htm#SEC1243	21365
roots		sing_2239.htm#SEC2320	19148
rootsMain		sing_2247.htm#SEC2328	64464
rootsmr.lib		sing_2451.htm#SEC2532	
rootsmr_lib		sing_2451.htm#SEC2532	
rootsur.lib		sing_2467.htm#SEC2548	
rootsur_lib		sing_2467.htm#SEC2548	
round		sing_2356.htm#SEC2437	9248
rowShift		sing_215.htm#IDX141	
rowShift 		sing_217.htm#SEC257	
rowred		sing_1213.htm#SEC1294	63416
rp, global ordering		sing_985.htm#IDX456	
rstandard.lib		sing_1576.htm#SEC1657	
rstandard_lib		sing_1576.htm#SEC1657	
rswalk		sing_3077.htm#SEC3158	50903
rtimer		sing_415.htm#SEC455	
rvalue	No rvalue of increments and assignments	sing_421.htm#SEC461	
rvar		sing_352.htm#SEC392	
rwalk		sing_3029.htm#SEC3110	42525
rwalk.lib		sing_3027.htm#SEC3108	
rwalk_lib		sing_3027.htm#SEC3108	
sPiece		sing_3068.htm#SEC3149	sprintf
sRes		sing_1371.htm#SEC1452	27313
sa_poly_reduce		sing_532.htm#SEC586	60856
sa_reduce		sing_531.htm#SEC585	55799
sagbi		sing_1584.htm#SEC1665	46653
sagbi basis		sing_1925.htm#IDX823	
sagbi.lib		sing_1581.htm#SEC1662	
sagbiAlg		sing_1918.htm#SEC1999	sprintf
sagbiByDegree		sing_3038.htm#SEC3119	56936
sagbiByDegree 		sing_3044.htm#SEC3125	
sagbiDefIdealByDegree	sagbiDefIdealByDegree	sing_3041.htm#SEC3122	sprintf
sagbiDefIdealByDegree 		sing_3047.htm#SEC3128	
sagbiDefIdealGeneral	sagbiDefIdealGeneral	sing_3040.htm#SEC3121	sprintf
sagbiDefIdealGeneral 		sing_3046.htm#SEC3127	
sagbiGeneral		sing_3037.htm#SEC3118	431
sagbiGeneral 		sing_3043.htm#SEC3124	
sagbiHilbControlled		sing_3039.htm#SEC3120	17149
sagbiHilbControlled 		sing_3045.htm#SEC3126	
sagbiMod		sing_1919.htm#SEC2000	sprintf
sagbiNormaliz.lib		sing_3036.htm#SEC3117	
sagbiNormaliz0.lib		sing_3042.htm#SEC3123	
sagbiNormaliz0_lib		sing_3042.htm#SEC3123	
sagbiNormaliz_lib		sing_3036.htm#SEC3117	
sagbiPart		sing_1585.htm#SEC1666	56066
sagbiReduce		sing_1583.htm#SEC1664	19036
sagbiSPoly		sing_1582.htm#SEC1663	20437
sagbi_lib		sing_1581.htm#SEC1662	
sagbigrob.lib		sing_3031.htm#SEC3112	
sagbigrob_lib		sing_3031.htm#SEC3112	
salida		sing_1769.htm#SEC1850	9839
sameComponent		sing_2434.htm#SEC2515	13540
sameQ		sing_2250.htm#SEC2331	45579
sat		sing_1294.htm#SEC1375	34230
sat_with_exp		sing_1295.htm#SEC1376	12812
satiety		sing_1450.htm#SEC1531	60238
satstd		sing_2698.htm#SEC2779	41173
saturation		sing_1294.htm#IDX608	
saturation 		sing_1295.htm#IDX609	
saturation  		sing_1354.htm#IDX648	
saturation   		sing_1465.htm#IDX654	
saturation    		sing_1466.htm#IDX655	
sba		sing_353.htm#SEC393	
scalarProd		sing_521.htm#SEC575	54488
scheme		sing_2857.htm#SEC2938	15722
schreyerSyzExt		sing_3059.htm#SEC3140	13785
schubert.lib		sing_1807.htm#SEC1888	
schubert_lib		sing_1807.htm#SEC1888	
sdb, source code debugger	Source code debugger	sing_66.htm#SEC103	
second degree		sing_1066.htm#IDX539	
second order deformation.		sing_3065.htm#IDX1293	
secondary fan		sing_2580.htm#IDX990	
secondary polytope		sing_2580.htm#IDX991	
secondaryPolytope		sing_2582.htm#SEC2663	48451
secondary_and_irreducibles_no_molien	secondary_and_irreducibles_no_molien	sing_2106.htm#SEC2187	37058
secondary_char0		sing_2101.htm#SEC2182	31029
secondary_charp		sing_2103.htm#SEC2184	17415
secondary_no_molien		sing_2104.htm#SEC2185	3616
secondary_not_cohen_macaulay	secondary_not_cohen_macaulay	sing_2107.htm#SEC2188	31675
segre		sing_1608.htm#SEC1689	44035
select		sing_1296.htm#SEC1377	17096
select1		sing_1297.htm#SEC1378	32617
semaphore		sing_368.htm#IDX257	44342
semaphore 		sing_1146.htm#SEC1227	
semaphores		sing_1142.htm#IDX577	
semi-prime ideal		sing_870.htm#IDX437	
semiCMcod2		sing_2062.htm#SEC2143	15905
semiGroup		sing_1920.htm#SEC2001	sprintf
semiMod		sing_1921.htm#SEC2002	sprintf
semidiv		sing_2426.htm#SEC2507	58107
semigroup		sing_1872.htm#SEC1953	29017
semigroup 		sing_1876.htm#IDX803	
semigroup of values		sing_1994.htm#IDX924	
semigroupGenerator		sing_2527.htm#SEC2608	59446
sep		sing_1551.htm#SEC1632	sprintf
separateHNE		sing_2005.htm#SEC2086	12052
separator		sing_1433.htm#SEC1514	33000
serialization		sing_3048.htm#IDX1290	
serreRelations		sing_843.htm#SEC897	15263
set		sing_2648.htm#IDX1002	63132
set 		sing_2751.htm#SEC2832	
set, intersectionSet, union, complement, equality, isEqual	sets_lib	sing_2750.htm#IDX1140	
setBaseMultigrading		sing_2941.htm#SEC3022	6575
setLetterplaceAttributes	setLetterplaceAttributes	sing_890.htm#SEC944	40924
setLinearForms		sing_2528.htm#SEC2609	40257
setModuleGrading		sing_2953.htm#SEC3034	59018
setMultiplicity		sing_2529.htm#SEC2610	64650
setNmzDataPath		sing_1515.htm#SEC1596	18123
setNmzExecPath		sing_1511.htm#SEC1592	38993
setNmzFilename		sing_1514.htm#SEC1595	20206
setNmzOption		sing_1506.htm#SEC1587	20172
setUniformizingParameter	setUniformizingParameter	sing_2638.htm#SEC2719	63635
set_is_injective		sing_2414.htm#SEC2495	8429
setcores		sing_1144.htm#SEC1225	49704
setenv		sing_368.htm#IDX260	
setglobalrings		sing_1115.htm#SEC1196	3471
setinitials		sing_2867.htm#SEC2948	24792
setring		sing_354.htm#SEC394	
sets.lib		sing_2750.htm#SEC2831	
sets_lib		sing_2750.htm#SEC2831	
sh		sing_368.htm#IDX262	
shared		sing_205.htm#SEC245	
shared declarations		sing_208.htm#SEC248	
shared expressions		sing_209.htm#SEC249	
shared operations	reference and shared operations	sing_210.htm#SEC250	
shared related functions	reference and shared related functions	sing_211.htm#SEC251	
sheaf cohomology		sing_1846.htm#IDX784	
sheafCoh		sing_1854.htm#SEC1935	62633
sheafCohBGG		sing_1850.htm#SEC1931	33370
sheafCohBGG2		sing_1853.htm#SEC1934	52789
sheafCohBGGregul		sing_1851.htm#SEC1932	35359
sheafCohBGGregul_w		sing_1852.htm#SEC1933	21844
sheafCohBGGsres		sing_3062.htm#SEC3143	49122
sheafCoh_w		sing_1855.htm#SEC1936	54689
sheafcoh.lib		sing_1846.htm#SEC1927	
sheafcoh_lib		sing_1846.htm#SEC1927	
short		sing_412.htm#SEC452	
show		sing_1080.htm#SEC1161	15599
showBO		sing_1789.htm#SEC1870	20089
showDataTypes		sing_1791.htm#SEC1872	4270
showNmzOptions		sing_1508.htm#SEC1589	32968
showNuminvs		sing_1503.htm#SEC1584	18934
showgrades		sing_790.htm#SEC844	48081
showrecursive		sing_1081.htm#SEC1162	50022
signal handler		sing_3133.htm#SEC3238	
signatureBrieskorn		sing_2071.htm#SEC2152	26283
signatureL		sing_2727.htm#SEC2808	65493
signatureLqf		sing_2728.htm#SEC2809	18811
signatureNemethi		sing_2073.htm#SEC2154	21981
signaturePuiseux		sing_2072.htm#SEC2153	23398
signcnd		sing_2233.htm#SEC2314	40147
signcond.lib		sing_2232.htm#SEC2313	
signcond_lib		sing_2232.htm#SEC2313	
simplePrune		sing_1409.htm#SEC1490	sprintf
simplesolver		sing_2152.htm#SEC2233	13418
simplex		sing_355.htm#SEC395	
simplexOut		sing_2188.htm#SEC2269	56099
simplify		sing_356.htm#SEC396	
simplifyRat		sing_695.htm#SEC749	52658
sing.lib		sing_2038.htm#SEC2119	
sing4ti2.lib		sing_1587.htm#SEC1668	
sing4ti2_lib		sing_1587.htm#SEC1668	
sing_lib		sing_2038.htm#SEC2119	
singular locus of D-module		sing_675.htm#IDX397	
singularities		sing_1886.htm#IDX814	
singularities 		sing_1914.htm#IDX818	
singularities  		sing_1963.htm#IDX826	
singularities   		sing_1964.htm#IDX837	
singularities    		sing_1965.htm#IDX840	
singularities     		sing_1966.htm#IDX843	
singularities      		sing_1967.htm#IDX846	
singularities       		sing_1968.htm#IDX850	
singularities        		sing_1969.htm#IDX854	
singularities         		sing_1970.htm#IDX860	
singularities          		sing_1971.htm#IDX868	
singularities           		sing_1972.htm#IDX874	
singularities            		sing_1973.htm#IDX882	
singularities             		sing_1974.htm#IDX892	
singularities              		sing_2069.htm#IDX946	
singularities               		sing_2762.htm#IDX1142	
singularities ordinary multiple point.		sing_1347.htm#IDX644	
singularities, resolution of	Resolution of singularities	sing_968.htm#SEC1025	
singularity		sing_1906.htm#SEC1987	44123
singularrc		sing_20.htm#IDX73	
sinh		sing_3104.htm#SEC3185	52331
size	Miscellaneous oddities	sing_357.htm#SEC397	
size 		sing_429.htm#IDX309	
skewmat		sing_1201.htm#SEC1282	2167
sleep		sing_363.htm#SEC403	
slimgb		sing_358.htm#SEC398	
slimgb 		sing_945.htm#SEC1002	
slimgb (plural)		sing_490.htm#SEC530	
slocus		sing_2050.htm#SEC2131	27853
smaller		sing_2827.htm#IDX1201	
smatrix		sing_176.htm#SEC216	
smith		sing_2332.htm#SEC2413	61915
smithNormalForm		sing_2989.htm#SEC3070	7174
solutionsMod2		sing_2369.htm#SEC2450	53360
solve		sing_287.htm#SEC327	3078
solve 		sing_1066.htm#IDX540	
solve  		sing_2182.htm#SEC2263	
solve a linear equation system A*x = b via the LU-decomposition of A	lusolve	sing_299.htm#SEC339	
solve.lib		sing_2180.htm#SEC2261	
solveTInitialFormPar	solveTInitialFormPar	sing_2622.htm#SEC2703	36670
solve_IP		sing_1351.htm#SEC1432	59518
solve_lib		sing_2180.htm#SEC2261	
solvelinearpart		sing_2175.htm#SEC2256	42872
solving		sing_2201.htm#IDX957	
sort		sing_1042.htm#SEC1123	58207
sort 		sing_2832.htm#IDX1211	
sortIntvec		sing_599.htm#SEC653	60798
sortandmap		sing_2176.htm#SEC2257	1198
sortier		sing_2120.htm#SEC2201	3555
sortvars		sing_2177.htm#SEC2258	8640
sortvec		sing_359.htm#SEC399	
source		sing_1387.htm#SEC1468	63163
source code debugger, sdb	Source code debugger	sing_66.htm#SEC103	
spaceCur		sing_1923.htm#SEC2004	sprintf
spadd		sing_1977.htm#SEC2058	48739
span		sing_2530.htm#SEC2611	64343
sparseHomogIdeal		sing_1138.htm#SEC1219	22631
sparseInterpolation		sing_1315.htm#SEC1396	28771
sparseid		sing_1133.htm#SEC1214	20824
sparsemat		sing_1135.htm#SEC1216	17653
sparsematrix		sing_1134.htm#SEC1215	41031
sparsepoly		sing_1136.htm#SEC1217	21649
sparsetriag		sing_1137.htm#SEC1218	50657
spcurve.lib		sing_2058.htm#SEC2139	
spcurve_lib		sing_2058.htm#SEC2139	
special characters, non-english		sing_418.htm#IDX299	
specification		sing_1120.htm#IDX566	
spectral pairs		sing_1963.htm#IDX835	
spectral pairs 		sing_1970.htm#IDX867	
spectral pairs  		sing_1972.htm#IDX881	
spectral pairs   		sing_1973.htm#IDX890	
spectral pairs    		sing_1985.htm#IDX906	
spectral pairs     		sing_1987.htm#IDX917	
spectralNeg		sing_1799.htm#SEC1880	36691
spectrum		sing_1963.htm#IDX834	47545
spectrum 		sing_1969.htm#SEC2050	
spectrum  		sing_1969.htm#IDX859	
spectrum   		sing_1970.htm#IDX866	
spectrum    		sing_1971.htm#IDX873	
spectrum     		sing_1972.htm#IDX880	
spectrum      		sing_1973.htm#IDX889	
spectrum       		sing_1985.htm#IDX905	
spectrum        		sing_1987.htm#IDX916	
spectrum         		sing_2069.htm#IDX948	
spectrum.lib		sing_2068.htm#SEC2149	
spectrum_lib		sing_2068.htm#SEC2149	
spectrumnd		sing_2069.htm#SEC2150	29943
spgamma		sing_1984.htm#SEC2065	59653
spgeomgenus		sing_1983.htm#SEC2064	57796
spissemicont		sing_1980.htm#SEC2061	23679
split		sing_1082.htm#SEC1163	29794
splitPolygon		sing_2584.htm#SEC2665	706
splitring		sing_1568.htm#SEC1649	56404
splitting		sing_1441.htm#SEC1522	34734
spmilnor		sing_1982.htm#SEC2063	32933
spmul		sing_1979.htm#SEC2060	43607
spnf		sing_1243.htm#SEC1324	57309
spoly		sing_2437.htm#SEC2518	35454
sppairs		sing_1970.htm#SEC2051	49513
sppnf		sing_1975.htm#SEC2056	16650
sppprint		sing_1976.htm#SEC2057	43682
spprint		sing_1244.htm#SEC1325	18671
sprintf		sing_361.htm#SEC401	55889
spsemicont		sing_1981.htm#SEC2062	61169
spsub		sing_1978.htm#SEC2059	54296
sqfrNorm		sing_2240.htm#SEC2321	47833
sqfrNormMain		sing_2248.htm#SEC2329	33868
sqrfree		sing_360.htm#SEC400	
squareRoot		sing_2368.htm#SEC2449	17446
squarefree		sing_2006.htm#SEC2087	48485
sres		sing_362.htm#SEC402	
sresExt		sing_3060.htm#SEC3141	19905
sresext.lib		sing_3058.htm#SEC3139	
sresext_lib		sing_3058.htm#SEC3139	
ssi	Parallelization with ssi links	sing_940.htm#SEC997	
ssi file handling		sing_3048.htm#IDX1289	
ssi.lib		sing_3048.htm#SEC3129	
ssi_lib		sing_3048.htm#SEC3129	
stabilizer		sing_2802.htm#SEC2883	36692
stack, moduli space of stable maps		sing_1831.htm#IDX775	
stack, moduli space of stable maps, rational curves	moduliSpace	sing_1830.htm#IDX774	
stackNets		sing_2725.htm#SEC2806	30974
staircase		sing_2253.htm#SEC2334	49781
standard		sing_2444.htm#SEC2525	14067
standard bases, saturation		sing_2698.htm#IDX1089	
standard bases.		sing_2697.htm#IDX1088	
standard.lib		sing_1019.htm#IDX484	
standard_lib		sing_1019.htm#IDX485	
stanleyreisner.lib		sing_3063.htm#SEC3144	
stanleyreisner_lib		sing_3063.htm#SEC3144	
startNmz		sing_1517.htm#SEC1598	21925
startTasks		sing_1181.htm#SEC1262	16715
static procedures	Procedure definition	sing_43.htm#SEC78	
status		sing_363.htm#SEC403	
std		sing_364.htm#SEC404	
std 		sing_943.htm#SEC1000	
std (letterplace)		sing_822.htm#SEC876	
std (plural)		sing_491.htm#SEC531	
stdfglm		sing_365.htm#SEC405	256
stdhilb		sing_366.htm#SEC406	63138
stdlocus		sing_1063.htm#SEC1144	25619
stdmodule.lib		sing_3070.htm#SEC3151	
stdmodule_lib		sing_3070.htm#SEC3151	
stopTask		sing_1182.htm#SEC1263	6801
storeActionOnOrbitConeIndices	storeActionOnOrbitConeIndices	sing_2568.htm#SEC2649	64428
strand		sing_3093.htm#SEC3174	27556
stratify		sing_2147.htm#SEC2228	56744
stratify.lib		sing_2145.htm#SEC2226	
stratify_lib		sing_2145.htm#SEC2226	
string	Miscellaneous oddities	sing_177.htm#SEC217	
string 		sing_429.htm#IDX312	
string  		sing_2814.htm#IDX1174	
string   		sing_2816.htm#IDX1179	
string    		sing_2817.htm#IDX1182	
string     		sing_2839.htm#IDX1228	
string      		sing_2840.htm#IDX1231	
string declarations		sing_178.htm#SEC218	
string expressions		sing_179.htm#SEC219	
string operations		sing_181.htm#SEC221	
string related functions	string related functions	sing_182.htm#SEC222	
string type cast		sing_180.htm#SEC220	
stripHNE		sing_2003.htm#SEC2084	19265
structure		sing_2836.htm#IDX1222	
sturm		sing_2477.htm#SEC2558	54353
sturmha		sing_2479.htm#SEC2560	12467
sturmhaseq		sing_2480.htm#SEC2561	59133
sturmquery		sing_2455.htm#SEC2536	10805
sturmseq		sing_2478.htm#SEC2559	23005
sublists		sing_2694.htm#SEC2775	2979
submat		sing_1202.htm#SEC1283	37665
subquotient		sing_1379.htm#SEC1460	40364
subrInterred		sing_1111.htm#SEC1192	10165
subset		sing_1117.htm#SEC1198	4326
subset_sum01		sing_2398.htm#SEC2479	60620
subset_sum02		sing_2399.htm#SEC2480	37340
subst		sing_367.htm#SEC407	
subst (letterplace)		sing_823.htm#SEC877	
subst (plural)		sing_492.htm#SEC532	
substAll		sing_2202.htm#SEC2283	62659
substitute		sing_1110.htm#SEC1191	28919
sufficientlyPositiveMultidegree	sufficientlyPositiveMultidegree	sing_3084.htm#SEC3165	38368
sugarCrit, option		sing_324.htm#IDX175	
sum		sing_1043.htm#SEC1124	555
sum 		sing_2819.htm#IDX1185	
sum  		sing_2841.htm#IDX1233	
sum of Feynman integrals		sing_3109.htm#IDX1331	
sum_of_powers		sing_1612.htm#SEC1693	12170
sumlist		sing_1771.htm#SEC1852	59918
sumofquotients		sing_1839.htm#SEC1920	4569
super-commutative algebras	Graded commutative algebras (SCA)	sing_805.htm#SEC859	
superCommutative		sing_746.htm#SEC800	45528
super_increasing_knapsack	super_increasing_knapsack	sing_2410.htm#SEC2491	9177
surf.lib		sing_2270.htm#SEC2351	
surf_lib		sing_2270.htm#SEC2351	
surfacesignature.lib	surfacesignature_lib	sing_2070.htm#SEC2151	
surfacesignature_lib	surfacesignature_lib	sing_2070.htm#SEC2151	
surfer		sing_1.htm#IDX8	14287
surfer 		sing_2272.htm#SEC2353	
surfex		sing_1.htm#IDX7	
surfex.lib		sing_2273.htm#SEC2354	
surfex_lib		sing_2273.htm#SEC2354	
suspend		sing_363.htm#SEC403	
swalk		sing_3076.htm#SEC3157	16794
swalk.lib		sing_3075.htm#SEC3156	
swalk_lib		sing_3075.htm#SEC3156	
swap		sing_1910.htm#SEC1991	15408
swap 		sing_2655.htm#IDX1020	
switch	No case or switch statement	sing_423.htm#SEC463	
switchRingsAndComputeInitialIdeal	switchRingsAndComputeInitialIdeal	sing_2643.htm#SEC2724	1827
syModStd		sing_1597.htm#SEC1678	50246
symExt		sing_3083.htm#SEC3164	37640
symNsym		sing_1606.htm#SEC1687	60973
sym_gauss		sing_1227.htm#SEC1308	5121
symm		sing_1605.htm#SEC1686	64628
symmStd		sing_1596.htm#SEC1677	39353
symmat		sing_1203.htm#SEC1284	61294
symmetric basis		sing_1219.htm#IDX588	
symmetric power		sing_1221.htm#IDX590	
symmetric product		sing_1687.htm#IDX716	
symmetricBasis		sing_1219.htm#SEC1300	sprintf
symmetricPower		sing_1221.htm#SEC1302	6542
symmetricPowerSheaf		sing_1825.htm#SEC1906	56922
symmetries		sing_2798.htm#IDX1154	
symmfunc		sing_2464.htm#SEC2545	45575
symodstd.lib		sing_1591.htm#SEC1672	
symodstd_lib		sing_1591.htm#SEC1672	
sympower		sing_2141.htm#SEC2222	48043
symsignature		sing_2454.htm#SEC2535	10520
syndrome		sing_2300.htm#SEC2381	14057
sysBin		sing_2298.htm#SEC2379	34279
sysCRHT		sing_2295.htm#SEC2376	52466
sysCRHTMindist		sing_2296.htm#SEC2377	13692
sysFL		sing_2311.htm#SEC2392	53040
sysNewton		sing_2297.htm#SEC2378	19704
sysQE		sing_2301.htm#SEC2382	61026
sys_code		sing_2292.htm#SEC2373	20220
system		sing_368.htm#SEC408	
system, --		sing_368.htm#IDX289	
system, --long_option_name		sing_368.htm#IDX292	
system, --long_option_name=value		sing_368.htm#IDX294	
system, HC		sing_368.htm#IDX222	
system, LLL		sing_368.htm#IDX226	
system, Singular		sing_368.htm#IDX266	
system, SingularBin		sing_368.htm#IDX268	
system, SingularLib		sing_368.htm#IDX270	
system, absFact		sing_368.htm#IDX197	
system, alarm		sing_368.htm#IDX196	
system, blackbox		sing_368.htm#IDX198	
system, bracket		sing_368.htm#IDX203	
system, browsers		sing_368.htm#IDX202	
system, complexNearZero		sing_368.htm#IDX205	
system, content		sing_368.htm#IDX209	
system, contributors		sing_368.htm#IDX207	
system, cpu		sing_368.htm#IDX211	
system, cpu 		sing_368.htm#IDX288	
system, denom_list		sing_368.htm#IDX213	
system, eigenvals		sing_368.htm#IDX214	
system, env		sing_368.htm#IDX215	
system, executable		sing_368.htm#IDX217	
system, getPrecDigits		sing_368.htm#IDX220	
system, getenv		sing_368.htm#IDX219	
system, gmsnf		sing_368.htm#IDX221	
system, hessenberg		sing_368.htm#IDX223	
system, install		sing_368.htm#IDX225	
system, nblocks		sing_368.htm#IDX229	
system, nc_hilb		sing_368.htm#IDX231	
system, neworder		sing_368.htm#IDX232	
system, newstruct		sing_368.htm#IDX233	
system, opp		sing_368.htm#IDX234	
system, oppose		sing_368.htm#IDX237	
system, pcvBasis		sing_368.htm#IDX246	
system, pcvCV2P		sing_368.htm#IDX244	
system, pcvDim		sing_368.htm#IDX245	
system, pcvLAddL		sing_368.htm#IDX240	
system, pcvMinDeg		sing_368.htm#IDX242	
system, pcvP2CV		sing_368.htm#IDX243	
system, pcvPMulL		sing_368.htm#IDX241	
system, pid		sing_368.htm#IDX248	
system, random		sing_368.htm#IDX250	
system, reserve		sing_368.htm#IDX254	
system, reservedLink		sing_368.htm#IDX255	
system, rref		sing_368.htm#IDX256	
system, semaphore		sing_368.htm#IDX258	
system, semic		sing_368.htm#IDX259	
system, setenv		sing_368.htm#IDX261	
system, sh		sing_368.htm#IDX263	
system, shrinktest		sing_368.htm#IDX264	
system, spadd		sing_368.htm#IDX271	
system, spectrum		sing_368.htm#IDX272	
system, spmul		sing_368.htm#IDX273	
system, std_syz		sing_368.htm#IDX274	
system, tensorModuleMult		sing_368.htm#IDX275	
system, twostd		sing_368.htm#IDX276	
system, uname		sing_368.htm#IDX279	
system, verifyGB		sing_368.htm#IDX282	
system, version		sing_368.htm#IDX285	
system, with		sing_368.htm#IDX286	
systemOfParametersOfLocalization	systemOfParametersOfLocalization	sing_1702.htm#SEC1783	63094
systhreads.lib		sing_3078.htm#SEC3159	
systhreads_lib		sing_3078.htm#SEC3159	
syz		sing_369.htm#SEC409	
syz (letterplace)		sing_824.htm#SEC878	
syz (plural)		sing_493.htm#SEC533	
tDetropicalise		sing_2624.htm#SEC2705	14907
tInitialForm		sing_2608.htm#SEC2689	24484
tInitialFormPar		sing_2620.htm#SEC2701	9584
tInitialFormParMax		sing_2621.htm#SEC2702	7829
tInitialIdeal		sing_2609.htm#SEC2690	17937
tab		sing_1083.htm#SEC1164	60407
tail		sing_2433.htm#SEC2514	13066
tame polynomial		sing_1985.htm#IDX898	
tame polynomial 		sing_1986.htm#IDX908	
tame polynomial  		sing_1987.htm#IDX909	
tangentGens		sing_1727.htm#SEC1808	61244
tangentcone		sing_2057.htm#SEC2138	20056
target		sing_1386.htm#SEC1467	18743
task		sing_1175.htm#IDX587	
tasks.lib		sing_1175.htm#SEC1256	
tasks_lib		sing_1175.htm#SEC1256	
tateProdCplxNegGrad.lib	tateProdCplxNegGrad_lib	sing_3079.htm#SEC3160	
tateProdCplxNegGrad_lib	tateProdCplxNegGrad_lib	sing_3079.htm#SEC3160	
tateResolution		sing_3085.htm#SEC3166	45794
tau_es		sing_1958.htm#SEC2039	17043
tau_es2		sing_1880.htm#SEC1961	38083
tdCf		sing_1641.htm#SEC1722	21522
tdFactor		sing_1643.htm#SEC1724	17466
tdProj		sing_1646.htm#SEC1727	38406
tdTerms		sing_1642.htm#SEC1723	30166
teach_lpGkDim		sing_875.htm#SEC929	60677
teach_lpKDim		sing_837.htm#SEC891	60416
teach_lpKDimCheck		sing_835.htm#SEC889	27509
teach_lpSickleDim		sing_840.htm#SEC894	20793
teachstd.lib		sing_2431.htm#SEC2512	
teachstd_lib		sing_2431.htm#SEC2512	
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_370.htm#SEC410	
tensor 		sing_502.htm#IDX326	
tensor algebra		sing_879.htm#IDX440	
tensorFreeModule		sing_1398.htm#SEC1479	59314
tensorFreemodMod		sing_1397.htm#SEC1478	sprintf
tensorMatrix		sing_1394.htm#SEC1475	31437
tensorMod		sing_1343.htm#SEC1424	21961
tensorModFreemod		sing_1396.htm#SEC1477	11852
tensorModule		sing_1395.htm#SEC1476	58772
tensorProduct		sing_1399.htm#SEC1480	sprintf
tensorSheaf		sing_1824.htm#SEC1905	24072
term orderings	General definitions for orderings	sing_984.htm#SEC1041	
term orderings introduction	Introduction to orderings	sing_983.htm#SEC1040	
terms		sing_2771.htm#SEC2852	23463
termsOnPolygon		sing_2768.htm#SEC2849	33692
testFraction		sing_767.htm#SEC821	28466
testLift		sing_891.htm#SEC945	20747
testLocData		sing_764.htm#SEC818	50986
testNCfac		sing_659.htm#SEC713	60394
testNcfrac		sing_713.htm#SEC767	34186
testNcfracExamples		sing_714.htm#SEC768	15399
testNcloc		sing_725.htm#SEC779	62706
testNclocExamples		sing_726.htm#SEC780	14584
testOlga		sing_781.htm#SEC835	53953
testOlgaExamples		sing_782.htm#SEC836	62869
testParametrization		sing_1742.htm#SEC1823	18686
testPointConic		sing_1743.htm#SEC1824	25315
testPrimary		sing_1539.htm#SEC1620	34254
testPrimaryE		sing_1540.htm#SEC1621	20693
testSyz		sing_892.htm#SEC946	54351
testZero		sing_3025.htm#SEC3106	11766
tetrahedronGroup		sing_868.htm#SEC922	12256
tex		sing_2259.htm#SEC2340	12226
texDrawBasic		sing_2615.htm#SEC2696	3635
texDrawNewtonSubdivision	texDrawNewtonSubdivision	sing_2617.htm#SEC2698	42021
texDrawTriangulation	texDrawTriangulation	sing_2618.htm#SEC2699	18865
texDrawTropical		sing_2616.htm#SEC2697	56051
texMatrix		sing_2614.htm#SEC2695	1334
texNumber		sing_2612.htm#SEC2693	12628
texPolynomial		sing_2613.htm#SEC2694	41136
texcoef		sing_2340.htm#SEC2421	28189
texdemo		sing_2260.htm#SEC2341	13008
texfactorize		sing_2261.htm#SEC2342	6682
texmap		sing_2262.htm#SEC2343	35265
texname		sing_2263.htm#SEC2344	1008
texobj		sing_2264.htm#SEC2345	2107
texpoly		sing_2265.htm#SEC2346	64109
texproc		sing_2266.htm#SEC2347	23626
texring		sing_2267.htm#SEC2348	38275
the first alternative algorithm		sing_1320.htm#IDX638	
three_elements		sing_2417.htm#SEC2498	513
timeFactorize		sing_1047.htm#SEC1128	31679
timeStd		sing_1046.htm#SEC1127	20654
timer		sing_413.htm#SEC453	
timer resolution, setting the		sing_368.htm#IDX295	
timestep		sing_2870.htm#SEC2951	38225
tjurina		sing_2053.htm#SEC2134	9100
tmatrix		sing_1973.htm#SEC2054	57332
todd		sing_1638.htm#SEC1719	25618
toddE		sing_1639.htm#SEC1720	17823
toddPoly		sing_1652.htm#SEC1733	65066
tolessvars		sing_2174.htm#SEC2255	56590
topChernClass		sing_1821.htm#SEC1902	17374
topological invariants		sing_1868.htm#IDX794	
topological invariants 		sing_1875.htm#IDX801	
topological invariants  		sing_1876.htm#IDX805	
topological invariants   		sing_1877.htm#IDX809	
topological invariants    		sing_1878.htm#IDX813	
toric ideals		sing_999.htm#SEC1061	
toric ring		sing_1488.htm#IDX679	
toric.lib		sing_1598.htm#SEC1679	
toricRingFromBinomials	toricRingFromBinomials	sing_1492.htm#SEC1573	59714
toric_ideal		sing_1599.htm#SEC1680	5760
toric_lib		sing_1598.htm#SEC1679	
toric_std		sing_1600.htm#SEC1681	26141
torus		sing_2138.htm#SEC2219	31169
torusInvariants		sing_1498.htm#SEC1579	911
torusrep		sing_2139.htm#SEC2220	16511
torusreynolds		sing_2144.htm#SEC2225	sprintf
total divisors		sing_502.htm#IDX323	
total multiplicities		sing_1868.htm#IDX797	
totalChernClass		sing_1819.htm#SEC1900	6153
totalSegreClass		sing_1822.htm#SEC1903	3291
totalmultiplicities		sing_1870.htm#SEC1951	54264
trace		sing_371.htm#SEC411	
tracemult		sing_2458.htm#SEC2539	58303
transWithPrecision		sing_3097.htm#SEC3178	56159
transformation		sing_3096.htm#IDX1302	
transformation.lib		sing_3096.htm#SEC3177	
transformation_lib		sing_3096.htm#SEC3177	
transformationsAfterSplit	transformationsAfterSplit	sing_2797.htm#SEC2878	39424
transformationsBeforeSplit	transformationsBeforeSplit	sing_2796.htm#SEC2877	31595
transpose		sing_372.htm#SEC412	
trapezoid		sing_2864.htm#SEC2945	61525
triMNewton		sing_2200.htm#SEC2281	62822
triagmatrix		sing_1139.htm#SEC1220	17944
triang.lib		sing_2193.htm#SEC2274	
triangL		sing_2194.htm#SEC2275	51847
triangL_solve		sing_2191.htm#SEC2272	10101
triangLf_solve		sing_2189.htm#SEC2270	49796
triangLfak		sing_2195.htm#SEC2276	50093
triangM		sing_2196.htm#SEC2277	59334
triangMH		sing_2197.htm#SEC2278	34277
triangM_solve		sing_2190.htm#SEC2271	63652
triang_lib		sing_2193.htm#SEC2274	
triang_solve		sing_2192.htm#SEC2273	64404
triangularGroup		sing_869.htm#SEC923	50365
triangulations		sing_2581.htm#SEC2662	61888
tropical covers	tropicalEllipticCovers_lib	sing_3098.htm#IDX1312	
tropical curves		sing_2595.htm#IDX994	
tropical geometry	tropicalEllipticCovers_lib	sing_1298.htm#IDX610	
tropical geometry 		sing_2637.htm#IDX996	
tropical geometry  		sing_3098.htm#IDX1304	
tropical mirror symmetry	tropicalEllipticCovers_lib	sing_1298.htm#IDX612	
tropical mirror symmetry 		sing_3098.htm#IDX1306	
tropical polynomials		sing_2595.htm#IDX995	
tropical stable maps	tropicalEllipticCovers_lib	sing_3098.htm#IDX1313	
tropical stable maps 		sing_3106.htm#IDX1324	
tropical varieties		sing_2637.htm#IDX997	
tropical.lib		sing_2595.htm#SEC2676	
tropicalCurve		sing_2600.htm#SEC2681	15715
tropicalEllipticCovers.lib	tropicalEllipticCovers_lib	sing_3098.htm#SEC3179	
tropicalEllipticCovers_lib	tropicalEllipticCovers_lib	sing_3098.htm#SEC3179	
tropicalJInvariant		sing_2603.htm#SEC2684	7621
tropicalLifting		sing_2596.htm#SEC2677	7549
tropicalLinkNewton		sing_2645.htm#SEC2726	63886
tropicalNewton.lib		sing_2637.htm#SEC2718	
tropicalNewton_lib		sing_2637.htm#SEC2718	
tropicalPointNewton		sing_2642.htm#SEC2723	18572
tropicalSubst		sing_2627.htm#SEC2708	49846
tropicalVariety		sing_2634.htm#SEC2715	39087
tropicalVarietyNewton	tropicalVarietyNewton	sing_2644.htm#SEC2725	28532
tropical_lib		sing_2595.htm#SEC2676	
tropicalise		sing_2606.htm#SEC2687	49739
tropicaliseSet		sing_2607.htm#SEC2688	35136
truncate		sing_1847.htm#SEC1928	13545
truncateCoker		sing_3082.htm#SEC3163	52846
truncateFast		sing_1848.htm#SEC1929	22046
truncateM		sing_3081.htm#SEC3162	37552
truncated module		sing_1847.htm#IDX785	
truncated module 		sing_1848.htm#IDX786	
tuple to compute a cover of elliptic curve		sing_3101.htm#IDX1316	
twalk		sing_1319.htm#SEC1400	35753
twist		sing_3090.htm#SEC3171	45852
two-sided		sing_502.htm#IDX324	
two-sided Groebner basis		sing_502.htm#IDX325	
twostd		sing_368.htm#IDX277	
twostd (letterplace)	twostd (letterplace)	sing_825.htm#SEC879	
twostd (plural)		sing_494.htm#SEC534	
type		sing_373.htm#SEC413	
type B		sing_2671.htm#IDX1047	
type D		sing_2672.htm#IDX1049	
type,custom	Definition of a user defined type	sing_189.htm#SEC229	
type2arr		sing_2649.htm#SEC2730	62624
typecasting		sing_2649.htm#IDX1003	
typecasting 		sing_2650.htm#IDX1005	
typecasting  		sing_2651.htm#IDX1008	
typeof		sing_374.htm#SEC414	
u		sing_2856.htm#SEC2937	12154
uname		sing_368.htm#IDX278	
unbounded_knapsack		sing_2400.htm#SEC2481	17226
union		sing_2752.htm#SEC2833	59870
unipotent groups		sing_1726.htm#IDX729	
uniquePoint		sing_2531.htm#SEC2612	893
unitMatrix		sing_2225.htm#SEC2306	33014
unitMatrix2		sing_2160.htm#SEC2241	23360
unitmat		sing_1204.htm#SEC1285	12862
univariate		sing_375.htm#SEC415	
univarpoly		sing_2465.htm#SEC2546	46288
universal		sing_2833.htm#IDX1214	
universal 		sing_2834.htm#IDX1216	
universal derivation	diffAlgebraUnivDerIdeal	sing_2809.htm#IDX1165	
unknown syndrome	Decoding method based on quadratic equations	sing_1015.htm#SEC1091	
unset		sing_284.htm#SEC324	
untyped definitions		sing_93.htm#SEC133	
untyped definitions 		sing_434.htm#SEC474	
updatePairs		sing_2443.htm#SEC2524	51144
ures_solve		sing_2183.htm#SEC2264	32449
uressolve		sing_376.htm#SEC416	
usage, option		sing_324.htm#IDX192	
used environment variables	Used environment variables	sing_3135.htm#SEC3240	
user interface, Emacs	Emacs user interface	sing_21.htm#SEC28	
vStd		sing_1935.htm#SEC2016	57729
val		sing_2639.htm#SEC2720	62171
valueOf		sing_3006.htm#SEC3087	55204
valvars		sing_2178.htm#SEC2259	48321
vandermonde		sing_377.htm#SEC417	
vanishId		sing_2310.htm#SEC2391	49148
vanishing polynomial		sing_3022.htm#IDX1277	
var		sing_378.htm#SEC418	
varMat		sing_2653.htm#SEC2734	51772
varNum		sing_2654.htm#SEC2735	18485
variables		sing_379.htm#SEC419	
variables 		sing_2653.htm#IDX1015	
variables  		sing_2654.htm#IDX1017	
variables   		sing_2655.htm#IDX1021	
variables    		sing_2656.htm#IDX1023	
variablesSorted		sing_540.htm#SEC594	13533
variablesStandard		sing_539.htm#SEC593	56500
vars2pars		sing_690.htm#SEC744	47343
varsigns		sing_2470.htm#SEC2551	3471
varstr		sing_380.htm#SEC420	
vdim		sing_381.htm#SEC421	
vdim (letterplace)		sing_826.htm#SEC880	
vdim (plural)		sing_495.htm#SEC535	
vec2poly		sing_522.htm#SEC576	27377
vecFieldToMatrix		sing_3120.htm#SEC3201	39951
vector		sing_183.htm#SEC223	
vector declarations		sing_184.htm#SEC224	
vector expressions		sing_185.htm#SEC225	
vector operations		sing_186.htm#SEC226	
vector related functions	vector related functions	sing_187.htm#SEC227	
verify		sing_2461.htm#SEC2542	32271
verify Groebner base		sing_368.htm#IDX281	
verifyGB		sing_368.htm#IDX283	
verifyGB 		sing_418.htm#IDX301	
veronese		sing_2203.htm#SEC2284	24550
versal		sing_1953.htm#SEC2034	46247
version		sing_368.htm#IDX284	
vertices		sing_2547.htm#SEC2628	11398
verticesOfNP		sing_2767.htm#SEC2848	51587
vfilt		sing_1971.htm#SEC2052	9283
view		sing_2330.htm#SEC2411	29284
visualize		sing_2855.htm#SEC2936	6750
voice		sing_416.htm#SEC456	
vspace		sing_418.htm#IDX300	
vwfilt		sing_1972.htm#SEC2053	8281
waitAllTasks		sing_1184.htm#SEC1265	7087
waitTasks		sing_1183.htm#SEC1264	52857
waitall		sing_382.htm#SEC422	
waitfirst		sing_383.htm#SEC423	
walk, groebner		sing_1317.htm#IDX634	
walk, groebner 		sing_2935.htm#IDX1267	
walk, groebner  		sing_3027.htm#IDX1282	
walk, groebner   		sing_3075.htm#IDX1298	
warkedPreimageStd		sing_1704.htm#SEC1785	14759
warn, option		sing_70.htm#SEC110	
warn, option 		sing_324.htm#IDX153	
watchdog		sing_1044.htm#SEC1125	sprintf
wedge		sing_384.htm#SEC424	
weierstr.lib		sing_2446.htm#SEC2527	
weierstrDiv		sing_2447.htm#SEC2528	260
weierstrPrep		sing_2448.htm#SEC2529	5752
weierstr_lib		sing_2446.htm#SEC2527	
weierstrassForm		sing_2604.htm#SEC2685	sprintf
weight		sing_385.htm#SEC425	
weight filtration		sing_1963.htm#IDX831	
weight filtration 		sing_1970.htm#IDX865	
weight filtration  		sing_1972.htm#IDX879	
weight filtration   		sing_1973.htm#IDX887	
weight filtration    		sing_1985.htm#IDX903	
weight filtration     		sing_1987.htm#IDX914	
weightKB		sing_386.htm#SEC426	21753
weightM, option		sing_324.htm#IDX176	
weighted lexicographical ordering		sing_985.htm#IDX464	
weighted reverse lexicographical ordering	Global orderings	sing_985.htm#IDX462	
weightedRing		sing_739.htm#SEC793	33786
whichvariable		sing_2469.htm#SEC2550	27122
while		sing_403.htm#SEC443	
withDim		sing_215.htm#IDX145	
withHilb		sing_215.htm#IDX143	
withMult		sing_215.htm#IDX146	
withRes		sing_215.htm#IDX144	
withSB		sing_215.htm#IDX142	
wp, global ordering		sing_985.htm#IDX463	
write		sing_387.htm#SEC427	
writeBertiniInput		sing_2209.htm#SEC2290	50918
writeDataToSSI		sing_3053.htm#SEC3134	14931
writeNmzData		sing_1512.htm#SEC1593	1733
writeNmzPaths		sing_1516.htm#SEC1597	sprintf
writeSSI		sing_3050.htm#SEC3131	26638
writeToString		sing_3057.htm#SEC3138	57139
writing monomials		sing_412.htm#SEC452	
ws, local ordering		sing_986.htm#IDX474	
wurzel		sing_2350.htm#SEC2431	12755
xchange		sing_2344.htm#SEC2425	40741
xdvi		sing_2269.htm#SEC2350	16898
zdd		sing_2731.htm#IDX1122	
zdd2poly		sing_2748.htm#SEC2829	55047
zero		sing_1359.htm#SEC1440	12060
zero-dimensional		sing_2466.htm#IDX985	
zeroMod		sing_1437.htm#SEC1518	60609
zeroNcfrac		sing_706.htm#SEC760	50840
zeroOpt		sing_1446.htm#SEC1527	19260
zeroRad		sing_1553.htm#SEC1634	29991
zeroRadical		sing_1267.htm#SEC1348	35598
zeroReduce		sing_3024.htm#SEC3105	58674
zeroSet		sing_2241.htm#SEC2322	39565
zero_decomp		sing_1556.htm#SEC1637	39163
zerodec		sing_1548.htm#SEC1629	30765
zeroreduce		sing_3022.htm#IDX1278	
zeroset.lib		sing_2236.htm#SEC2317	
zeroset_lib		sing_2236.htm#SEC2317	
zetaDL		sing_1801.htm#SEC1882	sprintf
{		sing_36.htm#IDX78	
||		sing_36.htm#IDX103	
|| 		sing_106.htm#SEC146	
}		sing_36.htm#IDX79	
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~ 		sing_404.htm#SEC444	
