!		sing_36.htm#IDX101	
!=		sing_36.htm#IDX95	
!= 		sing_100.htm#SEC140	
"		sing_36.htm#IDX104	
#		sing_36.htm#IDX118	
$		sing_36.htm#IDX119	
%		sing_36.htm#IDX91	
% 		sing_81.htm#SEC121	
%  		sing_98.htm#SEC138	
%   		sing_110.htm#SEC150	
%    		sing_147.htm#SEC187	
%     		sing_155.htm#SEC195	
&&		sing_36.htm#IDX102	
&& 		sing_101.htm#SEC141	
(		sing_36.htm#IDX80	
()		sing_131.htm#IDX130	
)		sing_36.htm#IDX81	
*	bigintmat operations	sing_36.htm#IDX89	
* 		sing_81.htm#SEC121	
*  		sing_87.htm#SEC127	
*   		sing_93.htm#SEC133	
*    		sing_98.htm#SEC138	
*     		sing_106.htm#SEC146	
*      		sing_110.htm#SEC150	
*       		sing_137.htm#SEC177	
*        		sing_142.htm#SEC182	
*         		sing_147.htm#SEC187	
*          		sing_155.htm#SEC195	
**		sing_36.htm#IDX93	
+	bigintmat operations	sing_36.htm#IDX85	
+ 		sing_81.htm#SEC121	
+  		sing_87.htm#SEC127	
+   		sing_93.htm#SEC133	
+    		sing_98.htm#SEC138	
+     		sing_106.htm#SEC146	
+      		sing_110.htm#SEC150	
+       		sing_126.htm#SEC166	
+        		sing_137.htm#SEC177	
+         		sing_142.htm#SEC182	
+          		sing_147.htm#SEC187	
+           		sing_155.htm#SEC195	
+            		sing_169.htm#SEC209	
+             		sing_175.htm#SEC215	
+              		sing_180.htm#SEC220	
++		sing_36.htm#IDX86	
-	bigintmat operations	sing_36.htm#IDX87	
- 		sing_81.htm#SEC121	
-  		sing_87.htm#SEC127	
-   		sing_98.htm#SEC138	
-    		sing_106.htm#SEC146	
-     		sing_110.htm#SEC150	
-      		sing_137.htm#SEC177	
-       		sing_147.htm#SEC187	
-        		sing_155.htm#SEC195	
-         		sing_180.htm#SEC220	
--		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_159.htm#SEC199	
-MPhost	Command line options		
-MPport	Command line options		
-allow-net	Command line options		
-b	Command line options	sing_19.htm#IDX63	
-batch	Command line options		
-browser	Command line options		
-c	Command line options	sing_19.htm#IDX55	
-d	Command line options	sing_19.htm#IDX31	
-e	Command line options	sing_19.htm#IDX34	
-echo	Command line options		
-emacs	Command line options		
-emacs-dir	Command line options		
-emacs-load	Command line options		
-execute	Command line options		
-h	Command line options	sing_19.htm#IDX36	
-help	Command line options		
-min-time	Command line options		
-no-out	Command line options		
-no-rc	Command line options		
-no-shell	Command line options		
-no-stdlib	Command line options		
-no-tty	Command line options		
-no-warn	Command line options		
-q	Command line options	sing_19.htm#IDX52	
-quiet	Command line options		
-r	Command line options	sing_19.htm#IDX59	
-random	Command line options		
-sdb	Command line options		
-singular	Command line options		
-ticks-per-sec	Command line options		
-u	Command line options	sing_19.htm#IDX57	
-user-option	Command line options		
-v	Command line options	sing_19.htm#IDX54	
..		sing_36.htm#IDX113	
.singularrc file		sing_20.htm#IDX72	
.singularrc file, no loading	Command line options	sing_19.htm#IDX46	
/		sing_36.htm#IDX90	
/ 		sing_76.htm#SEC116	
/  		sing_110.htm#SEC150	
/   		sing_137.htm#SEC177	
/    		sing_147.htm#SEC187	
/     		sing_155.htm#SEC195	
/      		sing_180.htm#SEC220	
//		sing_36.htm#IDX107	
// 		sing_36.htm#IDX109	
//  		sing_36.htm#IDX110	
:		sing_36.htm#IDX114	
: 		sing_110.htm#SEC150	
::		sing_36.htm#IDX115	
:: 		sing_149.htm#SEC189	
;		sing_36.htm#IDX111	
<		sing_36.htm#IDX100	
< 		sing_155.htm#SEC195	
<  		sing_180.htm#SEC220	
<   		sing_247.htm#SEC287	
<=		sing_36.htm#IDX99	
<= 		sing_100.htm#SEC140	
<=  		sing_147.htm#SEC187	
<=   		sing_155.htm#SEC195	
<=    		sing_175.htm#SEC215	
<=     		sing_180.htm#SEC220	
<>		sing_36.htm#IDX96	
<> 		sing_100.htm#SEC140	
<>  		sing_137.htm#SEC177	
<>   		sing_147.htm#SEC187	
<>    		sing_155.htm#SEC195	
<>     		sing_169.htm#SEC209	
<>      		sing_175.htm#SEC215	
<>       		sing_180.htm#SEC220	
=		sing_36.htm#IDX77	
==		sing_36.htm#IDX94	
== 		sing_100.htm#SEC140	
==  		sing_137.htm#SEC177	
==   		sing_147.htm#SEC187	
==    		sing_155.htm#SEC195	
==     		sing_169.htm#SEC209	
==      		sing_175.htm#SEC215	
==       		sing_180.htm#SEC220	
>		sing_36.htm#IDX98	
> 		sing_155.htm#SEC195	
>  		sing_180.htm#SEC220	
>=		sing_36.htm#IDX97	
>= 		sing_100.htm#SEC140	
>=  		sing_147.htm#SEC187	
>=   		sing_155.htm#SEC195	
>=    		sing_175.htm#SEC215	
>=     		sing_180.htm#SEC220	
?		sing_36.htm#IDX106	
? 		sing_259.htm#IDX148	
ADGT		sing_945.htm#SEC1021	65350
AG codes		sing_854.htm#SEC906	
AGcode_L		sing_1800.htm#SEC1876	60329
AGcode_Omega		sing_1801.htm#SEC1877	56285
ASCII		sing_904.htm#SEC980	26816
ASCII links		sing_117.htm#SEC157	
ASSUME		sing_64.htm#SEC101	
A_L		sing_1499.htm#SEC1575	16721
A_Z		sing_903.htm#SEC979	50866
Access to elements of a user defined type	Access to elements of a user defined type	sing_185.htm#SEC225	
Adj_div		sing_1795.htm#SEC1871	44919
Adjoint ideal		sing_1376.htm#IDX611	
Alexander polynomial		sing_1470.htm#IDX635	
Algebraic Geometry codes		sing_1794.htm#IDX783	
Algebraic dependence	Algebraic dependence	sing_833.htm#SEC885	
Algebraic geometry		sing_1351.htm#SEC1427	
AltVarEnd		sing_746.htm#SEC798	11020
AltVarStart		sing_745.htm#SEC797	21592
Ann		sing_1290.htm#SEC1366	61560
Appel function		sing_563.htm#IDX351	
Appel hypergeometric function		sing_563.htm#IDX352	
Applications		sing_852.htm#SEC904	
Arnold, classification.		sing_2322.htm#IDX939	
Arnold, classification. 		sing_2323.htm#IDX940	
ArnoldAction		sing_1592.htm#SEC1668	26958
Assignments for user defined types	Assignments for user defined types	sing_187.htm#SEC227	
AssocTanToEnv		sing_940.htm#SEC1016	46214
Atkin		sing_1883.htm#SEC1959	sprintf
Authors		sing_1.htm#IDX16	
Automatic Deduction		sing_945.htm#IDX482	
Automatic Demonstration		sing_945.htm#IDX483	
BINresol		sing_1389.htm#SEC1465	52996
Background		sing_3.htm#SEC5	
Basic programming		sing_808.htm#SEC860	
Basic programming 		sing_808.htm#SEC860	
BelongSemig		sing_2318.htm#SEC2394	22405
BerlekampMassey		sing_2377.htm#SEC2453	2172
Bern		sing_2291.htm#SEC2367	64051
Bernstein operator		sing_540.htm#IDX333	
Bernstein-Sato polynomial		sing_505.htm#IDX314	
Bernstein-Sato polynomial 		sing_540.htm#IDX330	
Bernstein-Sato polynomial  		sing_1533.htm#IDX666	
Bernstein-Sato polynomial   		sing_1537.htm#IDX683	
Bernstein-Sato polynomial for variety		sing_596.htm#IDX355	
Betti		sing_2507.htm#SEC2583	21134
Betti number	Syzygies and resolutions	sing_870.htm#SEC927	
BettiNumsH		sing_2407.htm#SEC2483	18661
BettiNumsN		sing_2412.htm#SEC2488	44681
BettiNumsS		sing_2410.htm#SEC2486	14964
Bigatti-La Scala-Robbiano algorithm	Bigatti and La Scala and Robbiano	sing_880.htm#SEC937	
BlowingUp		sing_1512.htm#SEC1588	43153
Blowupcenter		sing_1392.htm#SEC1468	3423
BorelCheck		sing_1467.htm#SEC1543	48787
Bott's formula		sing_2702.htm#IDX1045	
Branches of space curve singularities	Branches of space curve singularities	sing_841.htm#SEC893	
Briancon-Maisonobe algorithm		sing_540.htm#IDX339	
Brieskorn lattice		sing_1533.htm#IDX662	
Brieskorn lattice 		sing_1534.htm#IDX673	
Brieskorn lattice  		sing_1535.htm#IDX676	
Brieskorn lattice   		sing_1536.htm#IDX679	
Brieskorn lattice    		sing_1537.htm#IDX682	
Brieskorn lattice     		sing_1538.htm#IDX686	
Brieskorn lattice      		sing_1539.htm#IDX690	
Brieskorn lattice       		sing_1540.htm#IDX696	
Brieskorn lattice        		sing_1541.htm#IDX704	
Brieskorn lattice         		sing_1542.htm#IDX710	
Brieskorn lattice          		sing_1543.htm#IDX718	
Brieskorn lattice           		sing_1544.htm#IDX728	
Brieskorn lattice            		sing_1555.htm#IDX734	
Brieskorn lattice             		sing_1557.htm#IDX745	
Brieskorn lattice              		sing_1585.htm#IDX772	
Brill-Noether algorithm		sing_1794.htm#IDX784	
BrillNoether		sing_1797.htm#SEC1873	39919
Buchberger algorithm for toric ideals	Buchberger algorithm	sing_881.htm#SEC938	
Budur-Mustata-Saito approach		sing_596.htm#IDX359	
Building Singular		sing_2759.htm#SEC2848	
C programming language	Major differences to the C programming language	sing_409.htm#SEC449	
C, module ordering		sing_862.htm#IDX413	
CGS		sing_925.htm#IDX426	
CM_regularity		sing_1454.htm#SEC1530	33865
CMtype		sing_1623.htm#SEC1699	24849
CRHT-ideal		sing_887.htm#SEC951	
CSMA		sing_2314.htm#SEC2390	49080
CYGWIN and ESingular	Running SINGULAR under Emacs	sing_23.htm#SEC33	
Castelnuovo-Mumford regularity		sing_1454.htm#IDX627	
Category string		sing_51.htm#SEC88	
CenCharDec		sing_702.htm#SEC754	44505
Center		sing_1431.htm#SEC1507	25541
CenterBO		sing_1438.htm#SEC1514	34701
CentralQuot		sing_700.htm#SEC752	56490
CentralSaturation		sing_701.htm#SEC753	31585
Change of rings		sing_9.htm#SEC15	
Characteristic sets		sing_871.htm#SEC928	
CharacteristicExponents	CharacteristicExponents	sing_1518.htm#SEC1594	21795
ChernClass		sing_2715.htm#SEC2791	32965
ChernRootsDual		sing_2270.htm#SEC2346	40100
ChernRootsHom		sing_2279.htm#SEC2355	48446
ChernRootsProd		sing_2272.htm#SEC2348	13967
ChernRootsSum		sing_2268.htm#SEC2344	57286
ChernRootsSymm		sing_2281.htm#SEC2357	59304
ChernRootsWedge		sing_2282.htm#SEC2358	7239
Chevalley-Rosenlicht theorem		sing_1370.htm#IDX596	
Chevalley-Rosenlicht theorem 		sing_1371.htm#IDX599	
Chow ring, abstract variety, projective space, Grassmannian	ChowRing	sing_2706.htm#IDX1050	
ChowRing		sing_2706.htm#SEC2782	57977
Classification of hypersurface singularities	Classification of hypersurface singularities	sing_842.htm#SEC894	
Classification of singularities		sing_2675.htm#IDX1021	
Code	Codes and the decoding problem	sing_886.htm#SEC944	
Codes and the decoding problem	Codes and the decoding problem	sing_886.htm#SEC943	
Coding theory		sing_1793.htm#SEC1869	
Coefficient rings	Notes for Singular users	sing_2757.htm#SEC2841	
Command line options	Command line options	sing_19.htm#SEC26	
Commands	Functions and system variables	sing_206.htm#SEC246	
Commands for user defined types	Commands for user defined types	sing_186.htm#SEC226	
Commutative Algebra		sing_821.htm#SEC873	
Commutative algebra		sing_1106.htm#SEC1182	
CompDecomp		sing_502.htm#SEC554	9959
CompInt		sing_2320.htm#SEC2396	7518
CompleteHomog		sing_2258.htm#SEC2334	42123
ComplexValue		sing_2399.htm#SEC2475	45546
Comprehensive Groebner System		sing_925.htm#IDX429	
Computing Groebner and Standard Bases	Computing Groebner and Standard Bases	sing_817.htm#SEC869	
ConsLevels		sing_933.htm#SEC1009	14282
ContactMatrix		sing_1520.htm#SEC1596	40767
Conti-Traverso algorithm		sing_876.htm#SEC933	
Contributors		sing_1.htm#IDX15	
Control structures		sing_377.htm#SEC417	
Control theory	System and Control theory	sing_1827.htm#SEC1903	
Cooper philosophy		sing_887.htm#SEC949	
Cornacchia		sing_1873.htm#SEC1949	63434
CornacchiaModified		sing_1874.htm#SEC1950	59790
Crep		sing_928.htm#SEC1004	17485
Critical points		sing_836.htm#SEC888	
CurveParam		sing_1514.htm#SEC1590	53605
CurveRes		sing_1513.htm#SEC1589	48848
Curves		sing_1376.htm#IDX608	
Customization of the Emacs interface	Customization of the Emacs interface	sing_25.htm#SEC36	
Cyclic code		sing_1808.htm#IDX791	
Cyclic roots		sing_814.htm#SEC866	
D-integration		sing_563.htm#IDX348	
D-localization		sing_563.htm#IDX344	
D-localization 		sing_780.htm#IDX382	
D-module	purityfiltration_lib	sing_505.htm#IDX312	
D-module 		sing_540.htm#IDX327	
D-module  		sing_563.htm#IDX341	
D-module   		sing_596.htm#IDX353	
D-module    		sing_758.htm#IDX367	
D-module     		sing_780.htm#IDX379	
D-module structure		sing_540.htm#IDX328	
D-module structure 		sing_596.htm#IDX354	
D-restriction		sing_563.htm#IDX346	
DBM links		sing_122.htm#SEC162	
DISPLAY environment variable	The online help system	sing_16.htm#IDX28	
DLoc		sing_566.htm#SEC618	5981
DLoc0		sing_568.htm#SEC620	14327
Data types		sing_72.htm#SEC112	
Data types (plural)		sing_422.htm#IDX298	
Debugging tools		sing_63.htm#SEC100	
Decker, Wolfram		sing_1.htm#IDX17	
Declaration of objects of a user defined type	Declaration of objects of a user defined type	sing_184.htm#SEC224	
Decoding		sing_1808.htm#IDX793	
Decoding codes with Groebner bases	Decoding codes with Groebner bases	sing_885.htm#SEC942	
Decoding method based on quadratic equations	Decoding method based on quadratic equations	sing_890.htm#SEC960	
Definition of a user defined type	Definition of a user defined type	sing_183.htm#SEC223	
Deformations		sing_839.htm#SEC891	
Deformations, T1 and T2		sing_838.htm#SEC890	
Deg		sing_2510.htm#SEC2586	35419
Degree		sing_2511.htm#SEC2587	48523
DegreePure		sing_1355.htm#SEC1431	33003
Degrees		sing_2512.htm#SEC2588	50349
Delta		sing_1439.htm#SEC1515	33497
DeltaList		sing_1440.htm#SEC1516	65148
Demo mode		sing_24.htm#SEC35	
Depth		sing_828.htm#SEC880	
Determinacy		sing_2678.htm#IDX1025	
Di Biase-Urbanke algorithm	Di Biase and Urbanke	sing_879.htm#SEC936	
Distributed computing		sing_956.htm#IDX489	
Dlocalization		sing_781.htm#SEC833	22140
Documentation Tool		sing_60.htm#SEC97	
Dp, global ordering		sing_860.htm#IDX396	
Ds, local ordering		sing_861.htm#IDX406	
DsingularLocus		sing_785.htm#SEC837	46495
Dynamic loading		sing_71.htm#SEC111	
Dynamic modules		sing_816.htm#SEC868	
ECPP		sing_1917.htm#SEC1993	55777
ECoef		sing_1398.htm#SEC1474	14154
EOrdlist		sing_1396.htm#SEC1472	36329
ERROR		sing_236.htm#SEC276	
ESingular, CYGWIN	Running SINGULAR under Emacs	sing_23.htm#SEC33	
Edatalist		sing_1395.htm#SEC1471	61593
Edelman-Reiner		sing_2201.htm#IDX874	
Editing SINGULAR input files with Emacs	Editing SINGULAR input files with Emacs	sing_26.htm#SEC37	
Editing input		sing_18.htm#SEC25	
Elimination		sing_824.htm#SEC876	
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_1400.htm#SEC1476	47312
Enumerative geometry		sing_2702.htm#IDX1043	
Equal		sing_1354.htm#SEC1430	19984
Eresol		sing_1390.htm#SEC1466	12842
EulerAff		sing_2315.htm#SEC2391	54325
EulerProj		sing_2316.htm#SEC2392	13537
Evaluation of logical expressions	Evaluation of logical expressions	sing_411.htm#SEC451	
Examples		sing_806.htm#SEC858	
Examples of ring declarations	Examples of ring declarations	sing_29.htm#SEC40	
Exp for matrices		sing_1372.htm#IDX600	
Experimental libraries	Experimental libraries	sing_2245.htm#SEC2321	
Ext		sing_1166.htm#SEC1242	21909
Ext, computation of		sing_827.htm#SEC879	
Ext_R		sing_1165.htm#SEC1241	53310
Exterior		sing_732.htm#SEC784	23593
Extra weight vector		sing_865.htm#SEC917	
Factorization		sing_829.htm#SEC881	
FamElemsAtEnvCompPoints	FamElemsAtEnvCompPoints	sing_941.htm#SEC1017	18153
Feynman graph		sing_1142.htm#IDX522	
Finite fields		sing_823.htm#SEC875	
First steps		sing_6.htm#SEC12	
Fitzgerald-Lax method	Fitzgerald-Lax method	sing_889.htm#SEC957	
Float		sing_250.htm#SEC290	
Flow control		sing_40.htm#SEC70	
Formal Checker		sing_59.htm#SEC96	
Formatting output		sing_813.htm#SEC865	
Free resolution		sing_825.htm#SEC877	
Free resolution, graded	Handling graded modules	sing_826.htm#SEC878	
FultonA		sing_2313.htm#SEC2389	33688
Functions		sing_207.htm#SEC247	
Future benefits of Singular 4	Notes for Singular users	sing_2757.htm#SEC2846	
G-algebra		sing_486.htm#SEC526	
G-algebra 		sing_486.htm#SEC528	
G-algebra, setup		sing_486.htm#SEC530	
GBWeight		sing_569.htm#SEC621	24641
GBsolve		sing_1707.htm#SEC1783	16830
GIT-Fans		sing_848.htm#SEC900	
GITcone		sing_2426.htm#SEC2502	64643
GITfan		sing_2427.htm#SEC2503	32549
GITfanFromOrbitCones	GITfanFromOrbitCones	sing_2428.htm#SEC2504	63104
GITfanParallel		sing_2429.htm#SEC2505	53071
GITfanParallelSymmetric	GITfanParallelSymmetric	sing_2444.htm#SEC2520	30232
GITfanSymmetric		sing_2443.htm#SEC2519	25831
GKZfan		sing_2430.htm#SEC2506	sprintf
GKZsystem		sing_698.htm#SEC750	20528
GKdim		sing_671.htm#SEC723	9814
GMP		sing_1.htm#IDX3	
GMP 		sing_2761.htm#SEC2850	
GND.lib		sing_2451.htm#SEC2527	
GND_lib		sing_2451.htm#SEC2527	
GTZmod		sing_1216.htm#SEC1292	30091
GTZopt		sing_1223.htm#SEC1299	14642
G_a -Invariants		sing_845.htm#SEC897	
Gamma		sing_1405.htm#SEC1481	3820
Gauss-Manin connection	Gauss-Manin connection	sing_872.htm#SEC929	
Gauss-Manin connection 		sing_1585.htm#IDX771	
Gauss-Manin connection  		sing_1632.htm#IDX774	
Gauss-Manin system		sing_1533.htm#IDX661	
Gauss-Manin system 		sing_1534.htm#IDX672	
Gauss-Manin system  		sing_1535.htm#IDX675	
Gauss-Manin system   		sing_1536.htm#IDX678	
Gauss-Manin system    		sing_1537.htm#IDX681	
Gauss-Manin system     		sing_1538.htm#IDX685	
Gauss-Manin system      		sing_1539.htm#IDX689	
Gauss-Manin system       		sing_1540.htm#IDX695	
Gauss-Manin system        		sing_1541.htm#IDX703	
Gauss-Manin system         		sing_1542.htm#IDX709	
Gauss-Manin system          		sing_1543.htm#IDX717	
Gauss-Manin system           		sing_1544.htm#IDX727	
Gauss-Manin system            		sing_1555.htm#IDX733	
Gauss-Manin system             		sing_1557.htm#IDX744	
General command syntax	General command syntax	sing_35.htm#SEC59	
General concepts		sing_12.htm#SEC18	
General purpose		sing_897.htm#SEC973	
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_488.htm#SEC538	
Generalized Newton identities	Generalized Newton identities	sing_888.htm#SEC954	
Geometric Invariant Theory	Geometric Invariant Theory	sing_847.htm#SEC899	
Geometric Theorems		sing_945.htm#IDX484	
Geometric genus		sing_1376.htm#IDX612	
German Umlaute		sing_407.htm#IDX285	
Getting started		sing_5.htm#SEC11	
Global orderings		sing_860.htm#SEC912	
Goettsche's formula		sing_2404.htm#IDX981	
GoettscheF		sing_2405.htm#SEC2481	27881
Graded commutative algebras	Graded commutative algebras (SCA)	sing_490.htm#SEC542	
Grassmannian		sing_2707.htm#SEC2783	43898
Grassmannian, abstract variety, Schubert calculus	Grassmannian	sing_2707.htm#IDX1051	
Greuel, Gert-Martin		sing_1.htm#IDX18	
Groebner Bases	Computing Groebner and Standard Bases	sing_817.htm#SEC869	
Groebner bases in G-algebras	Groebner bases in G-algebras	sing_487.htm#SEC531	
Groebner bases in free associative algebras	Groebner bases for two-sided ideals in free associative algebras	sing_493.htm#SEC545	
Groebner bases, decodeGB		sing_1808.htm#IDX795	
Groebner bases, slim		sing_820.htm#SEC872	
Groebner basis conversion	Groebner basis conversion	sing_819.htm#SEC871	
Groebner cover		sing_924.htm#IDX422	
Groebner cover 		sing_931.htm#IDX441	
Groebner cover  		sing_932.htm#IDX448	
Groebner fan		sing_2071.htm#IDX812	
Groebner walk		sing_1157.htm#IDX543	
Groebner walk 		sing_1159.htm#IDX545	
Groebner walk  		sing_2699.htm#IDX1039	
Groebner walk   		sing_2700.htm#IDX1040	
Groebnerwalk		sing_1153.htm#IDX539	
Groebnerwalk 		sing_2544.htm#IDX992	
Groebnerwalk  		sing_2698.htm#IDX1038	
Groebnerwalk   		sing_2741.htm#IDX1067	
Gromov-Witten invariants		sing_1142.htm#IDX519	
Gromov-Witten invariants 		sing_1148.htm#IDX528	
Gromov-Witten invariants  		sing_1149.htm#IDX532	
Gromov-Witten invariants, lines on hypersurfaces	linesHypersurface	sing_2732.htm#IDX1063	
Gromov-Witten invariants, multiple covers		sing_2731.htm#IDX1062	
Gromov-Witten invariants, rational curves on Calabi-Yau threefolds	sumofquotients	sing_2733.htm#IDX1064	
Gromov-Witten invariants, rational curves on Calabi-Yau threefolds 		sing_2734.htm#IDX1065	
Gromov-Witten invariants.		sing_2702.htm#IDX1046	
Gweights		sing_726.htm#SEC778	651
H2basis		sing_1590.htm#SEC1666	3414
HHnormalForm		sing_2331.htm#SEC2407	33972
Hamburger-Noether expansion		sing_1470.htm#IDX631	
Hamburger-Noether expansion 		sing_1558.htm#IDX753	
Hamburger-Noether expansions		sing_1795.htm#IDX785	
Handling graded modules	Handling graded modules	sing_826.htm#SEC878	
Hcode		sing_1492.htm#SEC1568	26628
Help string		sing_45.htm#SEC82	
Hensel		sing_241.htm#SEC281	
Hilbert function		sing_356.htm#IDX188	
Hilbert function 		sing_869.htm#SEC923	
Hilbert series		sing_869.htm#SEC923	
Hilbert-driven GB algorithm	Groebner basis conversion	sing_819.htm#SEC871	
HilbertClassPoly		sing_1880.htm#SEC1956	sprintf
HilbertSeries		sing_1685.htm#SEC1761	21249
HilbertWeights		sing_1686.htm#SEC1762	sprintf
Hom		sing_1169.htm#SEC1245	61434
HomJJ		sing_1246.htm#SEC1322	1525
Hosten-Sturmfels algorithm	Hosten and Sturmfels	sing_878.htm#SEC935	
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_1148.htm#IDX531	
Hurwitz numbers 		sing_1149.htm#IDX535	
Hypersurface singularities, classification of	Classification of hypersurface singularities	sing_842.htm#SEC894	
I-regular function		sing_931.htm#IDX447	
IN		sing_280.htm#IDX149	
Ideal membership		sing_868.htm#IDX418	
Identifiers, syntax of		sing_37.htm#SEC65	
ImageGroup		sing_1688.htm#SEC1764	28808
ImageVariety		sing_1687.htm#SEC1763	15252
Imap, option		sing_315.htm#IDX175	
Implemented algorithms	Implemented algorithms	sing_33.htm#SEC47	
Incl		sing_1353.htm#SEC1429	7621
Index		sing_2766.htm#SEC2855	
Info string		sing_52.htm#SEC89	
InterDiv		sing_1421.htm#SEC1497	46142
Interactive use		sing_13.htm#SEC19	
Interrupting SINGULAR	Interrupting SINGULAR	sing_17.htm#SEC24	
IntersectWithSub		sing_703.htm#SEC755	56289
Intersection theory		sing_2702.htm#IDX1042	
IntersectionMatrix		sing_1519.htm#SEC1595	29351
Introduction		sing_2.htm#SEC4	
Invariant Theory		sing_844.htm#SEC896	
Invariant theory		sing_1637.htm#SEC1713	
InvariantQ		sing_1690.htm#SEC1766	53256
InvariantRing		sing_1689.htm#SEC1765	22928
Invariants of a finite group	Invariants of a finite group	sing_846.htm#SEC898	
Invariants of plane curve singularities	Invariants of plane curve singularities	sing_840.htm#SEC892	
IsSCA		sing_747.htm#SEC799	58445
J-marked schemes		sing_1461.htm#IDX629	
J-marked schemes, Borel ideals		sing_1466.htm#IDX630	
JMBTest.lib		sing_1461.htm#SEC1537	
JMBTest_lib		sing_1461.htm#SEC1537	
JMSConst.lib		sing_1466.htm#SEC1542	
JMSConst_lib		sing_1466.htm#SEC1542	
JMarkedScheme		sing_1468.htm#SEC1544	60696
Jacobi		sing_1890.htm#SEC1966	29843
Jacobson form		sing_1845.htm#IDX796	
Jacobson normal form		sing_1845.htm#IDX797	
Janet basis		sing_2697.htm#IDX1036	
Janet division, Janet basis		sing_2696.htm#IDX1035	
JuReTopDim		sing_1363.htm#SEC1439	sprintf
JuReZeroDim		sing_1364.htm#SEC1440	sprintf
KScoef		sing_1583.htm#SEC1659	sprintf
KSconvert		sing_1581.htm#SEC1657	3585
KSker		sing_1580.htm#SEC1656	40166
KSlinear		sing_1582.htm#SEC1658	19896
KSpencerKernel		sing_1630.htm#SEC1706	12490
KeneshlouMatrixPresentation	KeneshlouMatrixPresentation	sing_2470.htm#SEC2546	20741
Ker		sing_2516.htm#SEC2592	58279
Kernel of module homomorphisms	Kernel of module homomorphisms	sing_832.htm#SEC884	
KoszulHomology		sing_1178.htm#SEC1254	sprintf
Kronecker modules		sing_2404.htm#IDX983	
L, ordering		sing_866.htm#SEC918	
LETTERPLACE		sing_491.htm#SEC543	
LIB		sing_284.htm#SEC324	
LIB commands		sing_53.htm#SEC90	
LIBs		sing_893.htm#SEC969	
LLL		sing_358.htm#IDX220	
LOT algorithm		sing_540.htm#IDX340	
LU-decomposition of a matrix of numbers		sing_289.htm#SEC329	
Laurent series		sing_1146.htm#IDX527	
Left and two-sided Groebner bases	Left and two-sided Groebner bases	sing_850.htm#SEC902	
Left ideal membership	Groebner bases in G-algebras	sing_487.htm#SEC534	
Left normal form	Groebner bases in G-algebras	sing_487.htm#SEC533	
LengthSym		sing_757.htm#SEC809	16591
LengthSymElement		sing_756.htm#SEC808	28292
Letterplace		sing_491.htm#SEC543	
Levels		sing_934.htm#SEC1010	16031
Lexicographic Groebner bases, computation of	Groebner basis conversion	sing_819.htm#SEC871	
Libraries	Writing procedures and libraries	sing_48.htm#SEC85	
Libraries 		sing_809.htm#SEC861	
Libraries in the SINGULAR Documentation	Libraries in the SINGULAR Documentation	sing_49.htm#SEC86	
Library versioning	Notes for Singular users	sing_2757.htm#SEC2844	
Lie algebra		sing_1371.htm#IDX597	
Lie group		sing_1374.htm#IDX602	
Lie group 		sing_1375.htm#IDX605	
Limitations		sing_407.htm#SEC447	
Linear algebra		sing_1046.htm#SEC1122	
Linear code		sing_1808.htm#IDX792	
LinearActionQ		sing_1692.htm#SEC1768	62218
LinearCombinationQ		sing_1693.htm#SEC1769	59373
LinearizeAction		sing_1691.htm#SEC1767	60266
Loading a library		sing_62.htm#SEC99	
Local orderings		sing_861.htm#SEC913	
Log for matrices		sing_1373.htm#IDX601	
Long coefficients		sing_811.htm#SEC863	
M, ordering		sing_863.htm#SEC915	
MVComplex		sing_2353.htm#SEC2429	62126
Macdonald's formula		sing_2404.htm#IDX982	
MacdonaldF		sing_2408.htm#SEC2484	12751
Macintosh installation	Macintosh installation instructions	sing_2765.htm#SEC2854	
Mathematical background	Mathematical background	sing_867.htm#SEC919	
Mathematical background (plural)	Mathematical background (plural)	sing_485.htm#SEC525	
Matrix orderings		sing_863.htm#SEC915	
Max		sing_1599.htm#SEC1675	23
Maximus		sing_1463.htm#SEC1539	10010
Maxord		sing_1404.htm#SEC1480	14124
MillerRabin		sing_1900.htm#SEC1976	15740
Milnor number	Milnor and Tjurina number	sing_835.htm#SEC887	
Milnor number 		sing_2677.htm#IDX1024	
Min		sing_1600.htm#SEC1676	29622
MinMult		sing_2319.htm#SEC2395	39835
MinimalDecomposition	MinimalDecomposition	sing_1694.htm#SEC1770	24161
Minimum distance		sing_1808.htm#IDX794	
Minimus		sing_1462.htm#SEC1538	61721
Miscellaneous libraries	Miscellaneous libraries	sing_2172.htm#SEC2248	
ModEqn		sing_1593.htm#SEC1669	59394
Modular techniques		sing_956.htm#IDX486	
Module orderings		sing_862.htm#SEC914	
Modules and and their annihilator	Modules and their annihilator	sing_10.htm#SEC16	
Monodromy		sing_1585.htm#IDX769	
Monomial orderings		sing_857.htm#SEC909	
Monomial orderings, Term orderings		sing_31.htm#SEC44	
Mori dream spaces		sing_2246.htm#IDX934	
Morse lemma	addnondegeneratevariables	sing_2676.htm#IDX1022	
Morse lemma 		sing_2679.htm#IDX1026	
MultiplicitySequence	MultiplicitySequence	sing_1517.htm#SEC1593	1309
NF		sing_334.htm#SEC374	
NF 		sing_477.htm#SEC517	
NFMora		sing_1966.htm#SEC2042	40670
NPos		sing_1236.htm#SEC1312	15702
NPos_test		sing_1234.htm#SEC1310	48172
NSplaces		sing_1796.htm#SEC1872	48675
NTL		sing_1.htm#IDX4	
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_2757.htm#SEC2845	
Newton non-degenerate		sing_1572.htm#IDX767	
Newton polygon		sing_1571.htm#IDX766	
Newton polygon 		sing_1572.htm#IDX768	
Newton polygons		sing_2744.htm#IDX1070	
Newton polytope		sing_2071.htm#IDX811	
Newton step		sing_2680.htm#IDX1030	
NoetherPosition		sing_1230.htm#SEC1306	18735
Non-commutative LIBs	Non-commutative libraries	sing_497.htm#SEC549	
Non-commutative algebra	Non-commutative algebra	sing_849.htm#SEC901	
Non-commutative algebra 		sing_884.htm#SEC941	
Non-commutative libraries	Non-commutative libraries	sing_497.htm#SEC549	
Non-commutative subsystem	Non-commutative subsystem	sing_420.htm#SEC460	
Nonhyp		sing_1393.htm#SEC1469	sprintf
Normalization		sing_831.htm#SEC883	
Notes for Singular users	Notes for Singular users	sing_2757.htm#SEC2840	
Notes for developers	Notes for developers	sing_2758.htm#SEC2847	
NullCone		sing_1695.htm#SEC1771	64635
NumIrrDecom		sing_1367.htm#SEC1443	sprintf
NumLocalDim		sing_1356.htm#SEC1432	1739
NumPrimDecom		sing_1369.htm#SEC1445	34134
Oaku-Takayama algorithm		sing_540.htm#IDX338	
Objects		sing_38.htm#SEC66	
Orlik-Solomon		sing_2202.htm#IDX875	
Output		sing_2526.htm#IDX990	
Output 		sing_2623.htm#IDX997	
Output  		sing_2625.htm#IDX998	
Output   		sing_2626.htm#IDX999	
Output    		sing_2627.htm#IDX1000	
Output     		sing_2628.htm#IDX1001	
Output      		sing_2629.htm#IDX1002	
Output       		sing_2630.htm#IDX1003	
Output        		sing_2631.htm#IDX1004	
Output         		sing_2632.htm#IDX1005	
Output          		sing_2633.htm#IDX1006	
Output           		sing_2634.htm#IDX1007	
Output            		sing_2635.htm#IDX1008	
Output             		sing_2636.htm#IDX1009	
Output              		sing_2637.htm#IDX1010	
Output               		sing_2638.htm#IDX1011	
Output                		sing_2639.htm#IDX1012	
Output                 		sing_2640.htm#IDX1013	
Output                  		sing_2641.htm#IDX1014	
Output                   		sing_2642.htm#IDX1015	
Output                    		sing_2643.htm#IDX1016	
Output                     		sing_2644.htm#IDX1017	
Output                      		sing_2645.htm#IDX1018	
Output                       		sing_2646.htm#IDX1019	
Output                        		sing_2647.htm#IDX1020	
Output, formatting of		sing_813.htm#SEC865	
PBW		sing_519.htm#IDX326	
PBW basis		sing_486.htm#SEC527	
PBW_eqDeg		sing_537.htm#SEC589	23181
PBW_maxDeg		sing_538.htm#SEC590	59566
PBW_maxMonom		sing_539.htm#SEC591	1155
PEsolve		sing_1705.htm#SEC1781	9229
PH_ais		sing_2224.htm#SEC2300	49473
PH_nais		sing_2225.htm#SEC2301	46271
PLURAL		sing_421.htm#SEC461	
PLURAL LIBs	Non-commutative libraries	sing_497.htm#SEC549	
PPolyH		sing_2406.htm#SEC2482	25241
PPolyN		sing_2411.htm#SEC2487	39067
PPolyS		sing_2409.htm#SEC2485	13817
ParToVar		sing_2401.htm#SEC2477	13991
Parallelization	Parallelization with ssi links	sing_815.htm#SEC867	
Parallelization 		sing_956.htm#IDX487	
Parameter list		sing_44.htm#SEC81	
Parameters		sing_812.htm#SEC864	
Parametrization		sing_1376.htm#IDX609	
Parametrization, image.		sing_1386.htm#IDX621	
PartC		sing_2309.htm#SEC2385	54120
PartitionVar		sing_2398.htm#SEC2474	41350
Path names	Notes for Singular users	sing_2757.htm#SEC2843	
PerfectPowerTest		sing_1863.htm#SEC1939	17450
Perturbation walk		sing_1158.htm#IDX544	
Pfister, Gerhard		sing_1.htm#IDX19	
Pipe links		sing_121.htm#SEC161	
PocklingtonLehmer		sing_1902.htm#SEC1978	13634
Poincare polynomial		sing_2214.htm#IDX899	
Polar curves		sing_837.htm#SEC889	
PollardRho		sing_1903.htm#SEC1979	49602
PolyBoRi, Boolean Groebner Basis	recursive_from_boolean_poly	sing_2227.htm#IDX915	
PolyBoRi, Boolean Groebner Basis 		sing_2229.htm#IDX916	
PolyBoRi, Boolean Groebner Basis  		sing_2230.htm#IDX917	
PolyBoRi, Boolean Groebner Basis   		sing_2231.htm#IDX918	
PolyBoRi, Boolean Groebner Basis    		sing_2232.htm#IDX919	
PolyBoRi, Boolean Groebner Basis     		sing_2233.htm#IDX920	
PolyBoRi, Boolean Groebner Basis      		sing_2234.htm#IDX921	
PolyBoRi, Boolean Groebner Basis       		sing_2235.htm#IDX922	
PolyBoRi, Boolean Groebner Basis        		sing_2236.htm#IDX923	
PolyBoRi, Boolean Groebner Basis         		sing_2237.htm#IDX924	
PolyBoRi, Boolean Groebner Basis          		sing_2238.htm#IDX925	
PolyBoRi, Boolean Groebner Basis           		sing_2239.htm#IDX926	
PolyBoRi, Boolean Groebner Basis            		sing_2240.htm#IDX927	
PolyBoRi, Boolean Groebner Basis             		sing_2241.htm#IDX928	
PolyBoRi, Boolean Groebner Basis              		sing_2243.htm#IDX930	
PolyBoRi, zero-supressed decision diagram		sing_2242.htm#IDX929	
Polybori, Boolean Groebner Basis		sing_2244.htm#IDX931	
Polynomial data		sing_855.htm#SEC907	
Pottier algorithm		sing_877.htm#SEC934	
Preface		sing_1.htm#SEC1	
Prep		sing_929.htm#SEC1005	55342
Primary decomposition	Primary decomposition	sing_830.htm#SEC882	
PrimdecA		sing_1212.htm#SEC1288	248
PrimdecB		sing_1213.htm#SEC1289	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	Writing procedures and libraries	sing_8.htm#SEC14	
Procedures and libraries 		sing_809.htm#SEC861	
Procedures in a library	Procedures in a library	sing_54.htm#SEC91	
Product orderings		sing_864.htm#SEC916	
Programming		sing_807.htm#SEC859	
Pseudo ordering L		sing_866.htm#SEC918	
PtoCrep		sing_930.htm#SEC1006	52961
Puiseux expansion		sing_1470.htm#IDX632	
Puiseux expansion 		sing_1558.htm#IDX754	
Puiseux pairs	Invariants of plane curve singularities	sing_840.htm#SEC892	
Puiseux pairs 		sing_1564.htm#IDX759	
QQ		sing_28.htm#SEC39	
Qso3Casimir		sing_697.htm#SEC749	40212
Quotient		sing_1747.htm#SEC1823	24888
QuotientEquations		sing_1594.htm#SEC1670	18230
Rational curves		sing_1376.htm#IDX610	
ReJunkUseHomo		sing_1362.htm#SEC1438	10186
ReesAlgebra		sing_1329.htm#SEC1405	59951
References		sing_892.htm#SEC966	
References (plural)		sing_489.htm#SEC539	
Release Notes		sing_2753.htm#SEC2829	
Res		sing_2506.htm#SEC2582	92
ResTree		sing_1422.htm#SEC1498	58727
Resolution		sing_11.htm#SEC17	
Resolution of singularities	Resolution of singularities	sing_843.htm#SEC895	
Resolution, free		sing_825.htm#SEC877	
ReynoldsImage		sing_1696.htm#SEC1772	35172
ReynoldsOperator		sing_1697.htm#SEC1773	14986
RiemannRochBN		sing_2254.htm#SEC2330	20085
RiemannRochHess		sing_2489.htm#SEC2565	sprintf
Right Groebner bases and syzygies	Right Groebner bases and syzygies	sing_851.htm#SEC903	
Ring-dependent options	Notes for Singular users	sing_2757.htm#SEC2842	
Rings and orderings		sing_28.htm#SEC39	
Rings and standard bases	Rings and standard bases	sing_7.htm#SEC13	
Running SINGULAR under Emacs	Running SINGULAR under Emacs	sing_23.htm#SEC30	
SCA	Graded commutative algebras (SCA)	sing_490.htm#SEC542	
SDB breakpoint	Source code debugger	sing_66.htm#SEC106	
SDB debugger	Source code debugger	sing_66.htm#SEC106	
SDLoc		sing_567.htm#SEC619	9512
SINGULAR libraries		sing_893.htm#SEC969	
SINGULARHIST		sing_18.htm#SEC25	
SV-decoding algorithm		sing_1803.htm#IDX788	
SV-decoding algorithm, preprocessing		sing_1802.htm#IDX787	
Sannfs		sing_543.htm#SEC595	42932
SannfsBFCT		sing_552.htm#SEC604	59702
SannfsVar		sing_599.htm#SEC651	37522
Sannfslog		sing_544.htm#SEC596	49313
Saturation		sing_822.htm#SEC874	
Saturation 		sing_1139.htm#IDX513	
Sch@"onemann, Hans		sing_1.htm#IDX20	
Schoof		sing_1914.htm#SEC1990	49281
Schubert calculus		sing_2702.htm#IDX1044	
SchubertClass		sing_2739.htm#SEC2815	62336
SchurCh		sing_2306.htm#SEC2382	58575
SchurS		sing_2305.htm#SEC2381	46004
SegreA		sing_2312.htm#SEC2388	55776
Semigroup		sing_1510.htm#SEC1586	22323
SetDeg		sing_2509.htm#SEC2585	40547
Setting up a G-algebra		sing_486.htm#SEC530	
ShanksMestre		sing_1913.htm#SEC1989	12973
SimplifyIdeal		sing_1698.htm#SEC1774	sprintf
Singular		sing_358.htm#IDX257	
Singular 3 and Singular 4	Singular 3 and Singular 4	sing_2755.htm#SEC2838	
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_1360.htm#SEC1436	7552
SingularLib		sing_358.htm#IDX259	
Singularities		sing_1469.htm#SEC1545	
Singularity Theory		sing_834.htm#SEC886	
Skeletons for parallelization		sing_956.htm#IDX488	
Smith form		sing_1845.htm#IDX798	
Smith normal form		sing_1845.htm#IDX799	
SolowayStrassen		sing_1901.htm#SEC1977	22680
Solving systems of polynomial equations	Solving systems of polynomial equations	sing_853.htm#SEC905	
Source		sing_2498.htm#SEC2574	10351
Source code debugger, invocation	Command line options	sing_19.htm#IDX33	
Space curve singularities, branches of	Branches of space curve singularities	sing_841.htm#SEC893	
Special characters		sing_36.htm#SEC64	
Splitting lemma	addnondegeneratevariables	sing_2676.htm#IDX1023	
Splitting lemma 		sing_2679.htm#IDX1027	
Ssi file links		sing_119.htm#SEC159	
Ssi links		sing_118.htm#SEC158	
Ssi tcp links		sing_120.htm#SEC160	
StabEqn		sing_1595.htm#SEC1671	28539
StabEqnId		sing_1596.htm#SEC1672	27955
StabOrder		sing_1597.htm#SEC1673	55603
Standard Bases	Computing Groebner and Standard Bases	sing_817.htm#SEC869	
Standard bases		sing_868.htm#SEC920	
StartOrderingV		sing_1464.htm#SEC1540	58927
Startup sequence		sing_20.htm#SEC27	
StringF		sing_1584.htm#SEC1660	11590
SymGroup		sing_755.htm#SEC807	56676
Symbolic-numerical solving	Symbolic-numerical solving	sing_853.htm#SEC905	
Symbolic-numerical solving 		sing_1702.htm#SEC1778	
System and Control theory	System and Control theory	sing_1827.htm#SEC1903	
System dependent limitations	System dependent limitations	sing_408.htm#SEC448	
System variables		sing_394.htm#SEC434	
Syzygies and resolutions	Syzygies and resolutions	sing_870.htm#SEC924	
Syzygies and resolutions (plural)	Syzygies and resolutions (plural)	sing_488.htm#SEC535	
T1		sing_838.htm#SEC890	
T2		sing_838.htm#SEC890	
TRACE	Tracing of procedures	sing_65.htm#SEC102	
TRACE 		sing_403.htm#SEC443	
T_1		sing_1617.htm#SEC1693	59277
T_12		sing_1619.htm#SEC1695	12923
T_2		sing_1618.htm#SEC1694	55781
Target		sing_2497.htm#SEC2573	16006
Teaching		sing_1859.htm#SEC1935	
Template for writing a library		sing_55.htm#SEC92	
TestGRRes		sing_2469.htm#SEC2545	8315
TestJMark		sing_1465.htm#SEC1541	41314
The SINGULAR language	The SINGULAR language	sing_34.htm#SEC56	
The Tran algorithm		sing_1155.htm#IDX541	
The fractal walk algorithm		sing_1154.htm#IDX540	
The fractal walk algorithm 		sing_2701.htm#IDX1041	
The online help system	The online help system	sing_16.htm#SEC22	
Tjurina		sing_1615.htm#SEC1691	11249
Tjurina number	Milnor and Tjurina number	sing_835.htm#SEC887	
Tjurina number 		sing_1251.htm#IDX570	
Top 20 Emacs commands	Top 20 Emacs commands	sing_27.htm#SEC38	
Tor		sing_1180.htm#SEC1256	sprintf
Toric ideals and integer programming	Toric ideals and integer programming	sing_873.htm#SEC930	
Tricks and pitfalls		sing_406.htm#SEC446	
Tropical Geometry		sing_2011.htm#SEC2087	
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_1095.htm#SEC1171	26192
Unix installation	Unix installation instructions	sing_2763.htm#SEC2852	
UpOneMatrix		sing_744.htm#SEC796	63020
UpperMonomials		sing_1598.htm#SEC1674	20941
UseBertini		sing_1359.htm#SEC1435	43362
User defined types		sing_182.htm#SEC222	
V-filtration		sing_1533.htm#IDX664	
V-filtration 		sing_1539.htm#IDX692	
V-filtration  		sing_1540.htm#IDX698	
V-filtration   		sing_1541.htm#IDX706	
V-filtration    		sing_1542.htm#IDX712	
V-filtration     		sing_1543.htm#IDX720	
V-filtration      		sing_1544.htm#IDX730	
V-filtration       		sing_1555.htm#IDX736	
V-filtration        		sing_1557.htm#IDX747	
VarToPar		sing_2400.htm#SEC2476	10508
Variables, indexed		sing_37.htm#SEC65	
Version number	Version schema for Singular	sing_2756.htm#SEC2839	
Version schema for Singular	Version schema for Singular	sing_2756.htm#SEC2839	
Version string		sing_50.htm#SEC87	
Visualization		sing_1765.htm#SEC1841	
WLemma		sing_943.htm#SEC1019	7302
WP, global ordering		sing_860.htm#IDX400	
WSemigroup		sing_1515.htm#SEC1591	57449
Weierstrass		sing_1798.htm#SEC1874	58220
Weierstrass semigroup		sing_1794.htm#IDX782	
Weyl		sing_729.htm#SEC781	29212
Weyl algebra		sing_540.htm#IDX332	
Weyl algebra 		sing_596.htm#IDX357	
Weyl closure		sing_780.htm#IDX385	
WeylClosure		sing_782.htm#SEC834	23845
WeylClosure1		sing_783.htm#SEC835	15759
Wibmer's Lemma		sing_943.htm#IDX481	
Windows installation	Windows installation instructions	sing_2764.htm#SEC2853	
WitSet		sing_1366.htm#SEC1442	39803
WitSupSet		sing_1365.htm#SEC1441	47758
Ws, local ordering		sing_861.htm#IDX412	
XLsolve		sing_1708.htm#SEC1784	34970
ZZ		sing_28.htm#SEC39	
ZZ/m		sing_28.htm#SEC39	
ZZ/p		sing_28.htm#SEC39	
ZZsolve		sing_1709.htm#SEC1785	18657
[		sing_36.htm#IDX83	
[]		sing_142.htm#SEC182	
[] 		sing_155.htm#SEC195	
[]  		sing_175.htm#SEC215	
[]   		sing_180.htm#SEC220	
\		sing_36.htm#IDX112	
]		sing_36.htm#IDX84	
^		sing_36.htm#IDX92	
^ 		sing_81.htm#SEC121	
^  		sing_93.htm#SEC133	
^   		sing_147.htm#SEC187	
^    		sing_155.htm#SEC195	
_		sing_36.htm#IDX116	
`		sing_36.htm#IDX105	
a, ordering		sing_865.htm#SEC917	
absFactorize		sing_1108.htm#SEC1184	52546
absFactorizeBCG		sing_1109.htm#SEC1185	55510
absPrimdecGTZ		sing_1309.htm#SEC1385	46393
absPrimdecGTZE		sing_1310.htm#SEC1386	48005
absValue		sing_905.htm#SEC981	54595
absfact.lib		sing_1107.htm#SEC1183	
absfact_lib		sing_1107.htm#SEC1183	
absolute factorization.		sing_1107.htm#IDX512	
abstract variety, projective space, Grassmannian	printVariety	sing_2703.htm#IDX1047	
abstract variety, projective space, Grassmannian 		sing_2704.htm#IDX1048	
abstractR		sing_1448.htm#SEC1524	22284
actionIsProper		sing_1678.htm#SEC1754	52474
addLeftFractions		sing_2663.htm#SEC2739	38826
addModules		sing_2518.htm#SEC2594	51193
addNvarsTo		sing_1030.htm#SEC1106	63123
addRat		sing_801.htm#SEC853	4768
addSheaf		sing_2722.htm#SEC2798	27062
addcol		sing_1064.htm#SEC1140	52204
addcores		sing_999.htm#SEC1075	41254
addnondegeneratevariables	addnondegeneratevariables	sing_2679.htm#SEC2755	40483
addrow		sing_1065.htm#SEC1141	47055
addvarsTo		sing_1029.htm#SEC1105	17717
ademRelations		sing_661.htm#SEC713	30263
adjoint		sing_1089.htm#SEC1165	56619
adjointIdeal		sing_1377.htm#SEC1453	11455
adjunction divisor		sing_1795.htm#IDX786	
admissibleSub		sing_720.htm#SEC772	6583
afaces		sing_2422.htm#SEC2498	28045
affine code	Fitzgerald-Lax method	sing_889.htm#SEC958	
ainvar.lib		sing_1675.htm#SEC1751	
ainvar_lib		sing_1675.htm#SEC1751	
aksaka.lib		sing_1860.htm#SEC1936	
aksaka_lib		sing_1860.htm#SEC1936	
alexanderpolynomial		sing_1473.htm#SEC1549	36814
alexpoly.lib		sing_1470.htm#SEC1546	
alexpoly_lib		sing_1470.htm#SEC1546	
algDependent		sing_1114.htm#SEC1190	20789
alg_kernel		sing_1115.htm#SEC1191	307
algebra.lib		sing_1110.htm#SEC1186	
algebra_containment		sing_1111.htm#SEC1187	47912
algebra_lib		sing_1110.htm#SEC1186	
algebraic dependence		sing_750.htm#IDX363	
algebraic field extension		sing_1323.htm#IDX579	
algebraicDependence		sing_1336.htm#SEC1412	38500
algorithm of Bigatti, La Scala and Robbiano	Bigatti and La Scala and Robbiano	sing_880.htm#SEC937	
algorithm of Conti and Traverso		sing_876.htm#SEC933	
algorithm of Di Biase and Urbanke	Di Biase and Urbanke	sing_879.htm#SEC936	
algorithm of Hosten and Sturmfels	Hosten and Sturmfels	sing_878.htm#SEC935	
algorithm of Pottier		sing_877.htm#SEC934	
alias	General command syntax	sing_35.htm#SEC59	
align		sing_208.htm#SEC248	
all.lib		sing_898.htm#SEC974	
allDoubleExt		sing_767.htm#SEC819	43457
allExtOfLeft		sing_764.htm#SEC816	6405
allExtOfRight		sing_765.htm#SEC817	56781
allPositive		sing_516.htm#SEC568	1409
all_lib		sing_898.htm#SEC974	
allowing net access	Command line options	sing_19.htm#IDX41	
allprint		sing_947.htm#SEC1023	5195
allreal		sing_2003.htm#SEC2079	57232
allrealst		sing_2001.htm#SEC2077	40962
allsquarefree		sing_1577.htm#SEC1653	45545
ambientDimension		sing_2016.htm#SEC2092	18907
and	Evaluation of logical expressions	sing_101.htm#SEC141	
and 		sing_411.htm#SEC451	
annPoly		sing_564.htm#SEC616	18228
annRat		sing_565.htm#SEC617	62662
annRatSyz		sing_790.htm#SEC842	15672
annfs		sing_541.htm#SEC593	38155
annfs0		sing_553.htm#SEC605	26476
annfs2		sing_554.htm#SEC606	47962
annfsBMI		sing_550.htm#SEC602	2532
annfsParamBM		sing_549.htm#SEC601	43587
annfsRB		sing_555.htm#SEC607	31892
annfspecial		sing_542.htm#SEC594	27566
annihilator of polynomial		sing_563.htm#IDX342	
annihilator of rational function		sing_563.htm#IDX343	
annihilator of rational function 		sing_780.htm#IDX388	
annil		sing_1218.htm#SEC1294	48744
appelF1		sing_582.htm#SEC634	63146
appelF2		sing_583.htm#SEC635	22460
appelF4		sing_584.htm#SEC636	6847
appendWeight2Ord		sing_722.htm#SEC774	21488
apply		sing_378.htm#SEC418	
applyAdF		sing_532.htm#SEC584	40329
applyPermutationToIntvec	applyPermutationToIntvec	sing_2447.htm#SEC2523	28900
arcpoint.lib		sing_1483.htm#SEC1559	
arcpoint_lib		sing_1483.htm#SEC1559	
areEqualLeftFractions	areEqualLeftFractions	sing_2665.htm#SEC2741	29498
areZeroElements		sing_2585.htm#SEC2661	14728
argument, default		sing_44.htm#SEC81	
argument, optional		sing_44.htm#SEC81	
arr.lib		sing_2173.htm#SEC2249	
arr2multarr		sing_2206.htm#SEC2282	15063
arrBoolean		sing_2195.htm#SEC2271	63256
arrBoundedChambers		sing_2216.htm#SEC2292	18347
arrBraid		sing_2196.htm#SEC2272	34093
arrCenter		sing_2183.htm#SEC2259	24565
arrCentered		sing_2185.htm#SEC2261	15904
arrCentral		sing_2184.htm#SEC2260	14086
arrCentralize		sing_2186.htm#SEC2262	53235
arrChambers		sing_2215.htm#SEC2291	44578
arrCharPoly		sing_2213.htm#SEC2289	44129
arrCone		sing_2189.htm#SEC2265	38068
arrCoordChange		sing_2187.htm#SEC2263	61430
arrCoordNormalize		sing_2188.htm#SEC2264	46273
arrDecone		sing_2190.htm#SEC2266	54637
arrDer		sing_2203.htm#SEC2279	48815
arrEdelmanReiner		sing_2201.htm#SEC2277	59091
arrEssentialize		sing_2194.htm#SEC2270	6667
arrExponents		sing_2205.htm#SEC2281	1948
arrFlats		sing_2210.htm#SEC2286	64792
arrIsEssential		sing_2193.htm#SEC2269	34363
arrIsFree		sing_2204.htm#SEC2280	3860
arrLastVar		sing_2182.htm#SEC2258	25835
arrLattice		sing_2211.htm#SEC2287	58951
arrLocalize		sing_2191.htm#SEC2267	56070
arrOrlikSolomon		sing_2202.htm#SEC2278	31686
arrPoincare		sing_2214.htm#SEC2290	412
arrPrintMatrix		sing_2178.htm#SEC2254	21204
arrRandom		sing_2199.htm#SEC2275	59986
arrRandomCentral		sing_2200.htm#SEC2276	43698
arrRestrict		sing_2192.htm#SEC2268	sprintf
arrSet		sing_2174.htm#SEC2250	53769
arrSwapVar		sing_2181.htm#SEC2257	44919
arrTypeB		sing_2197.htm#SEC2273	22358
arrTypeD		sing_2198.htm#SEC2274	26495
arr_lib		sing_2173.htm#SEC2249	
arrange		sing_557.htm#SEC609	50350
arrangement		sing_2174.htm#IDX817	
arrangement 		sing_2175.htm#IDX822	
arrangement  		sing_2206.htm#IDX884	
arrangement   		sing_2207.htm#IDX887	
ask		sing_1868.htm#SEC1944	3862
assPrimes		sing_1125.htm#SEC1201	sprintf
assign		sing_2174.htm#IDX819	
assignment,custom	Assignments for user defined types	sing_187.htm#SEC227	
associated tangent	FamElemsAtEnvCompPoints	sing_940.htm#IDX474	
associated tangent 		sing_941.htm#IDX478	
assprimeszerodim.lib	assprimeszerodim_lib	sing_1123.htm#SEC1199	
assprimeszerodim_lib	assprimeszerodim_lib	sing_1123.htm#SEC1199	
atkins.lib		sing_1869.htm#SEC1945	
atkins_lib		sing_1869.htm#SEC1945	
attrib		sing_209.htm#SEC249	
autGenWeights		sing_2249.htm#SEC2325	32642
autGradAlg		sing_2248.htm#SEC2324	21136
autKS		sing_2247.htm#SEC2323	51607
autX		sing_2252.htm#SEC2328	43261
autXhat		sing_2251.htm#SEC2327	35932
autgradalg.lib		sing_2246.htm#SEC2322	
autgradalg_lib		sing_2246.htm#SEC2322	
automorphism group		sing_2246.htm#IDX935	
automorphisms		sing_2246.htm#IDX932	
autonom		sing_1832.htm#SEC1908	57044
autonomDim		sing_1833.htm#SEC1909	30055
awalk1		sing_1156.htm#SEC1232	11044
awalk2		sing_1157.htm#SEC1233	8955
b-function		sing_505.htm#IDX315	
bFactor		sing_587.htm#SEC639	15179
babyGiant		sing_1898.htm#SEC1974	41113
backward		sing_2387.htm#SEC2463	11225
bareiss		sing_210.htm#SEC250	
base2str		sing_901.htm#SEC977	sprintf
basering		sing_28.htm#IDX76	
basering 		sing_88.htm#SEC128	
basicinvariants		sing_1489.htm#SEC1565	32136
belongSemigroup		sing_1128.htm#SEC1204	19983
bernstein		sing_1537.htm#SEC1613	5605
bernsteinBM		sing_545.htm#SEC597	57689
bernsteinLift		sing_546.htm#SEC598	22885
bertini		sing_1352.htm#IDX583	
bertini 		sing_1357.htm#IDX590	
bertini2Singular		sing_1361.htm#SEC1437	58501
betti		sing_211.htm#SEC251	
betti (plural)		sing_455.htm#SEC495	
betti number		sing_2404.htm#IDX980	
bfct		sing_506.htm#SEC558	29858
bfctAnn		sing_508.htm#SEC560	36658
bfctBound		sing_789.htm#SEC841	5630
bfctIdeal		sing_510.htm#SEC562	41018
bfctOneGB		sing_509.htm#SEC561	9696
bfctSyz		sing_507.htm#SEC559	26796
bfctVarAnn		sing_598.htm#SEC650	51667
bfctVarIn		sing_597.htm#SEC649	9274
bfun.lib		sing_505.htm#SEC557	
bfun_lib		sing_505.htm#SEC557	
bigint		sing_78.htm#SEC118	
bigint declarations		sing_79.htm#SEC119	
bigint expressions		sing_80.htm#SEC120	
bigint operations		sing_81.htm#SEC121	
bigint related functions	bigint related functions	sing_82.htm#SEC122	
bigintToBinary		sing_2445.htm#SEC2521	59742
bigintmat		sing_83.htm#SEC123	
bigintmat declarations	bigintmat declarations	sing_84.htm#SEC124	
bigintmat expressions	bigintmat expressions	sing_85.htm#SEC125	
bigintmat operations	bigintmat operations	sing_87.htm#SEC127	
bigintmat type cast		sing_86.htm#SEC126	
bimodules		sing_498.htm#IDX303	
bimodules.lib		sing_498.htm#SEC550	
bimodules_lib		sing_498.htm#SEC550	
binaryToBigint		sing_2446.htm#SEC2522	sprintf
binary_add		sing_1921.htm#SEC1997	42817
binomial		sing_906.htm#SEC982	23208
binomials2intmat		sing_1284.htm#SEC1360	58804
birational map, image, inverse.		sing_1378.htm#IDX615	
bistd		sing_499.htm#SEC551	45237
bisyzygies		sing_498.htm#IDX304	
bitrinity		sing_500.htm#SEC552	3516
blackbox		sing_191.htm#SEC231	
blackbox 		sing_199.htm#SEC239	
block		sing_40.htm#SEC70	
block 		sing_377.htm#SEC417	
blowUp		sing_1429.htm#SEC1505	34819
blowUp2		sing_1430.htm#SEC1506	65264
blowUpBO		sing_1436.htm#SEC1512	58146
blowup0		sing_1133.htm#SEC1209	44451
boolean		sing_2195.htm#IDX861	
boolean expressions		sing_100.htm#SEC140	
boolean operations		sing_101.htm#SEC141	
boolean_constant		sing_2229.htm#SEC2305	52873
boolean_ideal		sing_2233.htm#SEC2309	53515
boolean_poly		sing_2230.htm#SEC2306	41652
boolean_poly_ring		sing_2228.htm#SEC2304	sprintf
boolean_set		sing_2234.htm#SEC2310	58235
boolean_std		sing_2227.htm#SEC2303	5921
border basis		sing_2693.htm#IDX1031	
borderBasis		sing_2694.htm#SEC2770	33172
boundBuFou		sing_1998.htm#SEC2074	26589
boundDes		sing_2000.htm#SEC2076	35149
boundaryLatticePoints	boundaryLatticePoints	sing_2086.htm#SEC2162	6238
boundposDes		sing_1999.htm#SEC2075	58854
bounds		sing_2681.htm#SEC2757	50218
boxSet		sing_2683.htm#SEC2759	8552
bracket		sing_358.htm#IDX197	
bracket 		sing_414.htm#SEC454	
bracket  		sing_456.htm#SEC496	
braid		sing_2196.htm#IDX863	
branchTo	procs with different argument types	sing_160.htm#SEC200	
break		sing_379.htm#SEC419	
break point		sing_393.htm#SEC433	
breakpoint		sing_380.htm#SEC420	
brillnoether.lib		sing_2253.htm#SEC2329	
brillnoether_lib		sing_2253.htm#SEC2329	
brnoeth.lib		sing_1794.htm#SEC1870	
brnoeth_lib		sing_1794.htm#SEC1870	
browser, command line option	Command line options	sing_19.htm#IDX44	
browser, setting the		sing_358.htm#IDX193	
browsers	The online help system	sing_16.htm#IDX21	
browsers, setting the		sing_358.htm#IDX192	
bubblesort		sing_1871.htm#SEC1947	63278
busadj		sing_1087.htm#SEC1163	36301
bvar		sing_2241.htm#SEC2317	52773
c, module ordering		sing_862.htm#IDX415	
cProj		sing_2295.htm#SEC2371	24037
calculateI		sing_1403.htm#SEC1479	31107
calculate_max_sum		sing_1940.htm#SEC2016	4706
calculate_ordering		sing_1918.htm#SEC1994	42616
cancelunit, option		sing_315.htm#IDX171	
canonMap		sing_1161.htm#SEC1237	47599
canoncial form		sing_928.htm#IDX436	
canoncial form 		sing_929.htm#IDX438	
canoncial form  		sing_930.htm#IDX440	
canonical		sing_924.htm#IDX424	
canonical form		sing_933.htm#IDX454	
canonical form 		sing_934.htm#IDX456	
canonical,		sing_932.htm#IDX450	
canonicalizeCone		sing_2017.htm#SEC2093	6251
canonize		sing_1840.htm#SEC1916	54090
cantoradd		sing_1954.htm#SEC2030	55304
cantormult		sing_1957.htm#SEC2033	57569
cantorred		sing_1955.htm#SEC2031	46502
cardGroup		sing_1130.htm#SEC1206	5553
case	No case or switch statement	sing_412.htm#SEC452	
catNets		sing_2623.htm#SEC2699	24760
cccMatrixToPositiveIntvec	cccMatrixToPositiveIntvec	sing_2748.htm#SEC2824	55393
cdd		sing_1.htm#IDX10	
cddlib		sing_1.htm#IDX11	
center		sing_519.htm#IDX322	65108
center 		sing_525.htm#SEC577	
center  		sing_2183.htm#IDX843	
center   		sing_2184.htm#IDX844	
center    		sing_2185.htm#IDX846	
center     		sing_2186.htm#IDX848	
centerRed		sing_524.htm#SEC576	59910
centerVS		sing_523.htm#SEC575	27548
central		sing_2177.htm#IDX829	
central 		sing_2184.htm#IDX845	
central  		sing_2186.htm#IDX847	
central   		sing_2200.htm#IDX872	
central.lib		sing_519.htm#SEC571	
central1st		sing_2388.htm#SEC2464	29090
central2nd		sing_2389.htm#SEC2465	37545
central_lib		sing_519.htm#SEC571	
centralize		sing_519.htm#IDX325	
centralizeSet		sing_520.htm#SEC572	55737
centralizer		sing_519.htm#IDX323	65261
centralizer 		sing_526.htm#SEC578	
centralizerRed		sing_522.htm#SEC574	8209
centralizerVS		sing_521.htm#SEC573	22925
cf_class		sing_209.htm#IDX132	
cgs		sing_900.htm#SEC976	57776
cgsdr		sing_925.htm#SEC1001	44460
chAll		sing_2265.htm#SEC2341	2690
chAllInv		sing_2266.htm#SEC2342	57760
chDual		sing_2271.htm#SEC2347	17745
chHE		sing_2267.htm#SEC2343	63916
chHom		sing_2280.htm#SEC2356	54776
chNum		sing_2261.htm#SEC2337	54415
chNumbers		sing_2262.htm#SEC2338	42134
chNumbersProj		sing_2299.htm#SEC2375	28837
chProd		sing_2273.htm#SEC2349	40209
chProdE		sing_2274.htm#SEC2350	33460
chProdL		sing_2275.htm#SEC2351	44795
chProdLP		sing_2276.htm#SEC2352	8881
chProdM		sing_2277.htm#SEC2353	64514
chProdMP		sing_2278.htm#SEC2354	17103
chProj		sing_2296.htm#SEC2372	32311
chSum		sing_2269.htm#SEC2345	21088
chSymm		sing_2283.htm#SEC2359	24066
chSymm2L		sing_2284.htm#SEC2360	51625
chSymm2LP		sing_2285.htm#SEC2361	26099
chWedge		sing_2286.htm#SEC2362	57678
chWedge2L		sing_2287.htm#SEC2363	46597
chWedge2LP		sing_2288.htm#SEC2364	8876
chaincrit		sing_1968.htm#SEC2044	9502
chambers		sing_2215.htm#IDX900	
chambers 		sing_2216.htm#IDX901	
changeDenominator		sing_1256.htm#SEC1332	21094
changechar		sing_1004.htm#SEC1080	65454
changeord		sing_1005.htm#SEC1081	55156
changeordTo		sing_1028.htm#SEC1104	41903
changes		sing_2754.htm#SEC2830	
changevar		sing_1006.htm#SEC1082	32829
char		sing_212.htm#SEC252	
charInfo		sing_580.htm#SEC632	11034
charVariety		sing_579.htm#SEC631	18306
char_series		sing_213.htm#SEC253	
characteristic exponents		sing_1477.htm#IDX639	
characteristic exponents 		sing_1478.htm#IDX644	
characteristic exponents  		sing_1479.htm#IDX647	
characteristic exponents   		sing_1480.htm#IDX651	
characteristic exponents    		sing_1564.htm#IDX757	
characteristic polynomial		sing_2213.htm#IDX898	
characteristic variety		sing_563.htm#IDX350	
characteristic variety 		sing_780.htm#IDX384	
charexp2conductor		sing_1480.htm#SEC1556	sprintf
charexp2generators		sing_1478.htm#SEC1554	16838
charexp2inter		sing_1479.htm#SEC1555	39881
charexp2multseq		sing_1477.htm#SEC1553	334
charexp2poly		sing_1481.htm#SEC1557	sprintf
charpoly		sing_1088.htm#SEC1164	29561
charstr		sing_214.htm#SEC254	
checkFactor		sing_556.htm#SEC608	55900
checkRoot		sing_551.htm#SEC603	37045
chern		sing_2260.htm#SEC2336	4916
chern.lib		sing_2255.htm#SEC2331	
chernCharPoly		sing_2302.htm#SEC2378	31610
chernPoly		sing_2301.htm#SEC2377	31316
chern_lib		sing_2255.htm#SEC2331	
chineseRem		sing_1889.htm#SEC1965	38560
chinrem		sing_215.htm#SEC255	
chinrempoly		sing_2649.htm#SEC2725	42312
chinrestp		sing_1948.htm#SEC2024	24779
cimonom.lib		sing_2317.htm#SEC2393	
cimonom_lib		sing_2317.htm#SEC2393	
cisimplicial.lib		sing_1126.htm#SEC1202	
cisimplicial_lib		sing_1126.htm#SEC1202	
classification		sing_2321.htm#IDX938	
classify		sing_1490.htm#SEC1566	4953
classify.lib		sing_1488.htm#SEC1564	
classify2.lib		sing_2321.htm#SEC2397	
classify2_lib		sing_2321.htm#SEC2397	
classifyCeq		sing_1507.htm#SEC1583	42719
classifyMapGerms.lib	classifyMapGerms_lib	sing_2333.htm#SEC2409	
classifyMapGerms_lib	classifyMapGerms_lib	sing_2333.htm#SEC2409	
classifySimpleMaps		sing_2339.htm#SEC2415	62176
classifySimpleMaps1		sing_2340.htm#SEC2416	24789
classifyUnimodalMaps	classifyUnimodalMaps	sing_2341.htm#SEC2417	63464
classify_aeq.lib		sing_2324.htm#SEC2400	
classify_aeq_lib		sing_2324.htm#SEC2400	
classify_lib		sing_1488.htm#SEC1564	
classifyceq.lib		sing_1506.htm#IDX654	
classifyceq_lib		sing_1506.htm#IDX655	
classifyci.lib		sing_1508.htm#IDX656	
classifyci_lib		sing_1508.htm#IDX657	
classifyicis		sing_1509.htm#SEC1585	37651
classpoly		sing_2300.htm#SEC2376	45724
cleanTmp		sing_2164.htm#SEC2240	14108
cleanunit		sing_1401.htm#SEC1477	sprintf
cleardenom		sing_216.htm#SEC256	
close		sing_217.htm#SEC257	
closed_points		sing_1804.htm#SEC1880	47269
closetex		sing_1771.htm#SEC1847	42334
closureFrac		sing_1249.htm#SEC1325	9252
coDim		sing_2335.htm#SEC2411	60680
coDimMap		sing_2334.htm#SEC2410	2002
coHom		sing_773.htm#SEC825	51043
codim		sing_1602.htm#SEC1678	14253
codimension		sing_2018.htm#SEC2094	32207
coding theory		sing_854.htm#SEC906	
coef		sing_218.htm#SEC258	
coefficient		sing_2176.htm#IDX825	
coefficient 		sing_2177.htm#IDX828	
coefficient  		sing_2178.htm#IDX832	
coefficient field		sing_144.htm#SEC184	
coefficient rings, ring of integers, zero divisors, p-adic numbers	Coefficient rings	sing_32.htm#SEC45	
coefficients, long		sing_811.htm#SEC863	
coeffmod		sing_1866.htm#SEC1942	23531
coeffs		sing_219.htm#SEC259	
coker		sing_2514.htm#SEC2590	35639
colength of derivations	curveColengthDerivations	sing_2350.htm#IDX958	
collectDiv		sing_1446.htm#SEC1522	50348
colrank		sing_1838.htm#SEC1914	52290
colred		sing_1071.htm#SEC1147	1693
combinat.lib		sing_2342.htm#SEC2418	
combinat_lib		sing_2342.htm#SEC2418	
commRing		sing_804.htm#SEC856	30892
comma		sing_413.htm#SEC453	
command,custom	Commands for user defined types	sing_186.htm#SEC226	
command-line option, setting value of		sing_358.htm#IDX281	
command-line option, value of		sing_358.htm#IDX279	
command-line options, print all values of		sing_358.htm#IDX278	
command-line options, short help	Command line options	sing_19.htm#IDX38	
commands (plural)		sing_454.htm#IDX302	
comment		sing_36.htm#IDX108	
compareMatrix		sing_2522.htm#SEC2598	49930
compareModules		sing_2517.htm#SEC2593	3692
compareTasks		sing_1035.htm#SEC1111	45157
compareVectors		sing_2542.htm#SEC2618	12881
completeReduction		sing_1680.htm#SEC1756	57157
complex		sing_28.htm#IDX75	
complexClassify		sing_2322.htm#SEC2398	22796
complexSingType		sing_1504.htm#SEC1580	34483
complexType		sing_2323.htm#SEC2399	55772
compregb.lib		sing_899.htm#SEC975	
compregb_lib		sing_899.htm#SEC975	
comprehensive Groebner system		sing_899.htm#IDX421	
compress		sing_1048.htm#SEC1124	61998
computeAfaceOrbits		sing_2432.htm#SEC2508	28683
computeConstant		sing_1146.htm#SEC1222	55024
computeGromovWitten		sing_1149.htm#SEC1225	18834
computeN		sing_1450.htm#SEC1526	61628
computeV		sing_1449.htm#SEC1525	40316
computemcm		sing_1408.htm#SEC1484	36956
concat		sing_1049.htm#SEC1125	16653
conductor		sing_1257.htm#IDX571	
conductor 		sing_1480.htm#IDX650	
conductor  		sing_2348.htm#IDX952	
conductor, degree		sing_1564.htm#IDX760	
cone		sing_188.htm#SEC228	
cone 		sing_2189.htm#IDX852	
cone  		sing_2190.htm#IDX854	
coneLink		sing_2021.htm#SEC2097	13635
coneViaInequalities		sing_2020.htm#SEC2096	25661
coneViaPoints		sing_2019.htm#SEC2095	3386
conic, parametrization, rational point.		sing_1385.htm#IDX620	
conicWithTangents		sing_2140.htm#SEC2216	60752
constructH		sing_1409.htm#SEC1485	59577
constructblwup		sing_1410.htm#SEC1486	19326
constructible set		sing_933.htm#IDX452	
constructible sets		sing_934.htm#IDX455	
constructlastblwup		sing_1411.htm#SEC1487	7639
constructor		sing_2206.htm#IDX885	
constructor 		sing_2207.htm#IDX888	
contact matrix		sing_1479.htm#IDX646	
containedQ		sing_1759.htm#SEC1835	46718
containsAsFace		sing_2022.htm#SEC2098	25159
containsInCollection	containsInCollection	sing_2055.htm#SEC2131	14368
containsInSupport		sing_2023.htm#SEC2099	32493
containsPositiveVector	containsPositiveVector	sing_2024.htm#SEC2100	27042
containsRelatively		sing_2025.htm#SEC2101	17126
content		sing_978.htm#SEC1054	9095
contentSB, option		sing_315.htm#IDX172	
continue	Behavior of continue	sing_381.htm#SEC421	
continue 		sing_415.htm#SEC455	
contraHom		sing_774.htm#SEC826	54270
contract		sing_220.htm#SEC260	
contribution bundle, graph, multiple cover, rational curve,	contributionBundle	sing_2729.htm#IDX1060	
contributionBundle		sing_2729.htm#SEC2805	32874
contributors		sing_358.htm#IDX200	
control		sing_1830.htm#SEC1906	44498
control.lib		sing_1829.htm#SEC1905	
controlDim		sing_1831.htm#SEC1907	2417
controlExample		sing_1843.htm#SEC1919	2678
control_Matrix		sing_1532.htm#SEC1608	sprintf
control_lib		sing_1829.htm#SEC1905	
convertLeftToRightFraction	convertLeftToRightFraction	sing_2662.htm#SEC2738	4318
convertRightToLeftFraction	convertRightToLeftFraction	sing_2661.htm#SEC2737	19389
convertdata		sing_1406.htm#SEC1482	54629
convexHull		sing_2026.htm#SEC2102	56690
convexIntersection		sing_2027.htm#SEC2103	63587
convloc		sing_560.htm#SEC612	19122
coordinate change		sing_2186.htm#IDX849	
coordinate change 		sing_2187.htm#IDX850	
coordinate change  		sing_2188.htm#IDX851	
coordinates		sing_1986.htm#IDX802	
coords		sing_1986.htm#SEC2062	29362
copyTask		sing_1034.htm#SEC1110	65331
copyright		sing_1.htm#IDX1	
corank		sing_1491.htm#SEC1567	33709
cornerMonomials		sing_1287.htm#SEC1363	33995
countPoints		sing_1911.htm#SEC1987	58566
coverings		sing_1148.htm#IDX530	
coverings 		sing_1149.htm#IDX534	
cpu		sing_358.htm#IDX202	
cpu 		sing_358.htm#IDX275	
createBO		sing_1437.htm#SEC1513	32669
createGradedRingHomomorphism	createGradedRingHomomorphism	sing_2561.htm#SEC2637	62177
createGroup		sing_2554.htm#SEC2630	28500
createQuotientGroup		sing_2555.htm#SEC2631	26374
createTask		sing_1032.htm#SEC1108	48404
createTorsionFreeGroup	createTorsionFreeGroup	sing_2556.htm#SEC2632	51944
createlist		sing_1419.htm#SEC1495	61781
cring		sing_73.htm#SEC113	
cring declarations		sing_74.htm#SEC114	
cring expressions		sing_75.htm#SEC115	
cring operations		sing_76.htm#SEC116	
cring related functions	cring related functions	sing_77.htm#SEC117	
crossprod		sing_221.htm#SEC261	
crypto.lib		sing_1884.htm#SEC1960	
crypto_lib		sing_1884.htm#SEC1960	
cup		sing_1162.htm#SEC1238	57972
cupproduct		sing_1163.htm#SEC1239	43349
curve singularities		sing_1470.htm#IDX633	
curve singularities 		sing_1558.htm#IDX755	
curve singularity		sing_2346.htm#IDX947	
curveColengthDerivations	curveColengthDerivations	sing_2350.htm#SEC2426	2078
curveConductorMult		sing_2348.htm#SEC2424	15897
curveDeligneNumber		sing_2349.htm#SEC2425	12294
curveDeltaInv		sing_2347.htm#SEC2423	16375
curveInv.lib		sing_2346.htm#SEC2422	
curveInv_lib		sing_2346.htm#SEC2422	
curvepar.lib		sing_1511.htm#SEC1587	
curvepar_lib		sing_1511.htm#SEC1587	
custom assignment	Assignments for user defined types	sing_187.htm#SEC227	
custom command	Commands for user defined types	sing_186.htm#SEC226	
custom type	Definition of a user defined type	sing_183.htm#SEC223	
customstd.lib		sing_2218.htm#SEC2294	
customstd_lib		sing_2218.htm#SEC2294	
cycleLength		sing_2077.htm#SEC2153	16898
cyclePoints		sing_2081.htm#SEC2157	54460
cyclic		sing_965.htm#SEC1041	21375
cyclic code	Codes and the decoding problem	sing_886.htm#SEC945	
cyclotomic		sing_1645.htm#SEC1721	33749
datetime		sing_222.htm#SEC262	50127
dbprint		sing_223.htm#SEC263	
deRham.lib		sing_2351.htm#SEC2427	
deRhamCohom		sing_577.htm#SEC629	58222
deRhamCohomIdeal		sing_578.htm#SEC630	42169
deRhamCohomology		sing_2352.htm#SEC2428	41947
deRham_lib		sing_2351.htm#SEC2427	
debugLib, option		sing_315.htm#IDX176	
debug_log		sing_1501.htm#SEC1577	62043
debugger	Source code debugger	sing_66.htm#SEC103	
debugging library code	Source code debugger	sing_66.htm#SEC103	
dec1var		sing_1217.htm#SEC1293	36098
decimal		sing_1885.htm#SEC1961	56066
decode		sing_1821.htm#SEC1897	64330
decodeCode		sing_1823.htm#SEC1899	28262
decodeRandom		sing_1822.htm#SEC1898	40118
decodeRandomFL		sing_1826.htm#SEC1902	35423
decodeSV		sing_1803.htm#SEC1879	37975
decodegb.lib		sing_1808.htm#SEC1884	
decodegb_lib		sing_1808.htm#SEC1884	
decoding, decoding problem	Codes and the decoding problem	sing_886.htm#SEC946	
decoef		sing_1851.htm#SEC1927	60284
decomposition of modules		sing_1210.htm#IDX559	
decomposition, numerical		sing_1357.htm#IDX588	
decone		sing_2189.htm#IDX853	
decone 		sing_2190.htm#IDX855	
def		sing_88.htm#SEC128	
def declarations		sing_89.htm#SEC129	
defRes, option		sing_315.htm#IDX177	
default argument		sing_44.htm#SEC81	
defineHomogeneous		sing_2594.htm#SEC2670	55072
defined		sing_224.htm#SEC264	
defl		sing_1368.htm#SEC1444	11825
deform		sing_1603.htm#SEC1679	5250
deform.lib		sing_1522.htm#SEC1598	
deform_lib		sing_1522.htm#SEC1598	
defring		sing_1007.htm#SEC1083	1814
defringp		sing_1009.htm#SEC1085	42905
defrings		sing_1008.htm#SEC1084	1034
deg		sing_225.htm#SEC265	
degBound		sing_395.htm#SEC435	
degree	Miscellaneous oddities	sing_226.htm#SEC266	
degree 		sing_418.htm#IDX292	
degree lexicographical ordering		sing_860.htm#IDX395	
degree of a polynomial	Miscellaneous oddities	sing_418.htm#IDX296	
degree reverse lexicographical ordering		sing_860.htm#IDX393	
degreeDivisor		sing_2362.htm#SEC2438	31751
degreeFormalDivisor		sing_2370.htm#SEC2446	42503
degreepart		sing_1711.htm#SEC1787	53036
delete		sing_126.htm#SEC166	
delete 		sing_227.htm#SEC267	
delete  		sing_276.htm#SEC316	
deleteGenerator		sing_592.htm#SEC644	24917
deleteSublist		sing_907.htm#SEC983	20406
deligne number	curveColengthDerivations	sing_2346.htm#IDX949	
deligne number 		sing_2349.htm#IDX954	
deligne number  		sing_2350.htm#IDX956	
delta		sing_1570.htm#SEC1646	56952
delta invariant		sing_1251.htm#IDX569	
delta invariant 		sing_1570.htm#IDX765	
delta invariant  		sing_2347.htm#IDX950	
delta invariant.		sing_1243.htm#IDX562	
delta invariant. 		sing_1244.htm#IDX565	
delta invariant.  		sing_1245.htm#IDX568	
deltaLoc		sing_1251.htm#SEC1327	35192
denom_list		sing_358.htm#IDX204	
denominator		sing_228.htm#SEC268	
depth		sing_1164.htm#SEC1240	17777
depthIdeal		sing_1227.htm#SEC1303	54782
derivate		sing_1677.htm#SEC1753	15409
derivation		sing_2203.htm#IDX876	
desingularization		sing_2451.htm#IDX985	59041
desingularization 		sing_2452.htm#SEC2528	
det		sing_229.htm#SEC269	
det_B		sing_1090.htm#SEC1166	60143
detadj		sing_1586.htm#SEC1662	5914
determinacy		sing_2678.htm#SEC2754	44818
determinecenter		sing_1391.htm#SEC1467	44496
detropicalise		sing_2158.htm#SEC2234	38025
develop		sing_1560.htm#SEC1636	48457
diag		sing_1050.htm#SEC1126	56759
diagInvariants		sing_1266.htm#SEC1342	62096
diag_test		sing_1086.htm#SEC1162	31469
diff		sing_230.htm#SEC270	
diffRat		sing_803.htm#SEC855	36134
difpoly2tex		sing_1852.htm#SEC1928	6451
dim		sing_231.htm#SEC271	
dim (plural)		sing_457.htm#SEC497	
dimGradedPart		sing_1459.htm#SEC1535	11262
dimH		sing_1458.htm#SEC1534	38534
dimMon		sing_1207.htm#SEC1283	39971
dimStack		sing_2727.htm#SEC2803	47772
dim_slocus		sing_1604.htm#SEC1680	47218
dimension		sing_2028.htm#SEC2104	35262
dimension, moduli space of stable maps, rational curves	dimStack	sing_2727.htm#IDX1058	
dimensionOfLocalization	dimensionOfLocalization	sing_2415.htm#SEC2491	25632
direct_boolean_poly		sing_2231.htm#SEC2307	49893
direct_from_boolean_poly	direct_from_boolean_poly	sing_2237.htm#SEC2313	36941
disc		sing_1872.htm#SEC1948	45279
discr		sing_1626.htm#SEC1702	9642
discrepancy		sing_1444.htm#SEC1520	5597
discrim		sing_942.htm#SEC1018	44091
discussion of parametric ideal		sing_924.htm#IDX425	
disjoint		sing_925.htm#IDX427	
disp_zdd		sing_2244.htm#SEC2320	41439
displayCohom		sing_1460.htm#SEC1536	22633
displayHNE		sing_1563.htm#SEC1639	29845
displayInvariants		sing_1565.htm#SEC1641	13678
displayMultsequence		sing_1567.htm#SEC1643	16668
displayPuiseuxExpansion	displayPuiseuxExpansion	sing_2133.htm#SEC2209	560
displayTropicalLifting	displayTropicalLifting	sing_2131.htm#SEC2207	28144
distributed computing		sing_958.htm#IDX492	
distributed computing 		sing_998.htm#IDX494	
distributed computing  		sing_1031.htm#IDX504	
div	Miscellaneous oddities	sing_81.htm#SEC121	
div 		sing_98.htm#SEC138	
div  		sing_155.htm#SEC195	
div   		sing_418.htm#IDX289	
divideUnits		sing_1848.htm#SEC1924	26711
dividelist		sing_1418.htm#SEC1494	34210
division		sing_232.htm#SEC272	
division 		sing_926.htm#IDX430	
division  		sing_927.htm#IDX432	
division (plural)		sing_458.htm#SEC498	
divisor		sing_1951.htm#SEC2027	47231
divisorplus		sing_2356.htm#SEC2432	34248
divisors	negativeformaldivisor	sing_2355.htm#IDX959	
divisors 		sing_2356.htm#IDX960	
divisors  		sing_2357.htm#IDX961	
divisors   		sing_2358.htm#IDX962	
divisors    		sing_2359.htm#IDX963	
divisors     		sing_2360.htm#IDX964	
divisors      		sing_2361.htm#IDX965	
divisors       		sing_2362.htm#IDX966	
divisors        		sing_2363.htm#IDX967	
divisors         		sing_2364.htm#IDX968	
divisors          		sing_2365.htm#IDX969	
divisors           		sing_2366.htm#IDX970	
divisors            		sing_2367.htm#IDX971	
divisors             		sing_2368.htm#IDX972	
divisors              		sing_2369.htm#IDX973	
divisors               		sing_2370.htm#IDX974	
divisors, polyhedra		sing_2371.htm#IDX975	
divisors, polyhedra 		sing_2372.htm#IDX976	
divisors, polyhedra  		sing_2373.htm#IDX977	
divisors.lib		sing_2354.htm#SEC2430	
divisors_lib		sing_2354.htm#SEC2430	
dmod.lib		sing_540.htm#SEC592	
dmodAction		sing_798.htm#SEC850	9763
dmodActionRat		sing_799.htm#SEC851	6277
dmodGeneralAssumptionCheck	dmodGeneralAssumptionCheck	sing_791.htm#SEC843	44337
dmod_lib		sing_540.htm#SEC592	
dmodapp.lib		sing_563.htm#SEC615	
dmodapp_lib		sing_563.htm#SEC615	
dmodloc.lib		sing_780.htm#IDX377	
dmodloc_lib		sing_780.htm#IDX378	
dmodoublext		sing_775.htm#SEC827	60637
dmodvar.lib		sing_596.htm#SEC648	
dmodvar_lib		sing_596.htm#SEC648	
double		sing_1956.htm#SEC2032	34697
doubleExt		sing_766.htm#SEC818	56896
downloading	Download instructions	sing_2762.htm#SEC2851	
dp, global ordering		sing_860.htm#IDX394	
drawNewtonSubdivision	drawNewtonSubdivision	sing_2136.htm#SEC2212	50904
drawTropicalCurve		sing_2135.htm#SEC2211	10441
ds, local ordering		sing_861.htm#IDX404	
dsum		sing_1051.htm#SEC1127	1303
dualCone		sing_2029.htm#SEC2105	61460
dualConic		sing_2160.htm#SEC2236	31080
dualPart		sing_2308.htm#SEC2384	13279
dualPartition		sing_2740.htm#SEC2816	24739
dualPolytope		sing_2068.htm#SEC2144	32081
dualSheaf		sing_2718.htm#SEC2794	633
dual_code		sing_1805.htm#SEC1881	57229
dump		sing_233.htm#SEC273	
dynamic geometry		sing_935.htm#IDX459	
dynamic geometry 		sing_936.htm#IDX462	
ecart		sing_1959.htm#SEC2035	32475
echo		sing_396.htm#SEC436	
eexgcdN		sing_1886.htm#SEC1962	53237
effective		sing_2364.htm#SEC2440	53028
egcdMain		sing_1752.htm#SEC1828	25359
ehrhartPolynomialCoeff	ehrhartPolynomialCoeff	sing_2087.htm#SEC2163	38271
ehrhartRing		sing_1262.htm#SEC1338	16966
eigenvals		sing_1098.htm#SEC1174	11228
eigenvalue		sing_328.htm#SEC368	
eigenvalue 		sing_1098.htm#IDX510	
eigenvalues		sing_1345.htm#SEC1421	2182
elemSymmId		sing_966.htm#SEC1042	sprintf
elim		sing_1135.htm#SEC1211	62585
elim.lib		sing_1132.htm#SEC1208	
elim1		sing_1136.htm#SEC1212	15653
elim2		sing_1137.htm#SEC1213	44749
elimRing		sing_1134.htm#SEC1210	12194
elimWeight		sing_723.htm#SEC775	54297
elim_lib		sing_1132.htm#SEC1208	
eliminate		sing_234.htm#SEC274	
eliminate (plural)		sing_459.htm#SEC499	
eliminateNC		sing_718.htm#SEC770	3777
elimination		sing_717.htm#IDX362	
elimlinearpart		sing_1712.htm#SEC1788	14251
elimpart		sing_1713.htm#SEC1789	10258
elimpartanyr		sing_1714.htm#SEC1790	39751
elimrep		sing_1399.htm#SEC1475	23641
elliptic curve		sing_1145.htm#IDX526	
elliptic curves		sing_1142.htm#IDX520	
elliptic curves 		sing_1148.htm#IDX529	
elliptic curves  		sing_1149.htm#IDX533	
ellipticAdd		sing_1907.htm#SEC1983	13279
ellipticAllPoints		sing_1912.htm#SEC1988	60770
ellipticMult		sing_1908.htm#SEC1984	1558
ellipticNF		sing_2084.htm#SEC2160	5045
ellipticNFDB		sing_2085.htm#SEC2161	27917
ellipticRandomCurve		sing_1909.htm#SEC1985	36980
ellipticRandomPoint		sing_1910.htm#SEC1986	6866
ellipticcovers.lib		sing_1142.htm#IDX514	
ellipticcovers_lib		sing_1142.htm#IDX515	
else		sing_386.htm#SEC426	
embedMat		sing_749.htm#SEC801	17119
emptyFan		sing_2056.htm#SEC2132	7396
encode		sing_1813.htm#SEC1889	56687
endomorphism filtration		sing_1544.htm#IDX731	
endvfilt		sing_1544.htm#SEC1620	26670
engine		sing_593.htm#SEC645	30876
ensureLeftNcfrac		sing_2611.htm#SEC2687	64571
ensureRightNcfrac		sing_2612.htm#SEC2688	14107
envelop	FamElemsAtEnvCompPoints	sing_937.htm#SEC1013	27362
envelop 		sing_937.htm#IDX465	
envelop  		sing_938.htm#IDX468	
envelop   		sing_940.htm#IDX473	
envelop    		sing_941.htm#IDX477	
envelope		sing_460.htm#SEC500	
enveloping algebra		sing_358.htm#IDX208	
enveloping algebra 		sing_498.htm#IDX306	
environment variable, DISPLAY	The online help system	sing_16.htm#IDX29	
equalJinI		sing_1487.htm#SEC1563	18502
equalMultiDeg		sing_2587.htm#SEC2663	37090
equations		sing_2030.htm#SEC2106	7896
equiRadical		sing_1303.htm#SEC1379	8884
equidim		sing_1305.htm#SEC1381	38541
equidimMax		sing_1306.htm#SEC1382	49289
equidimMaxEHV		sing_1307.htm#SEC1383	42650
equidimZ		sing_1318.htm#SEC1394	49610
equising.lib		sing_1527.htm#SEC1603	
equising_lib		sing_1527.htm#SEC1603	
equisingular Tjurina number		sing_1470.htm#IDX638	
equisingularity ideal		sing_1529.htm#IDX658	
equisingularity stratum		sing_1530.htm#IDX659	
error recovery		sing_15.htm#SEC21	
errorInsert		sing_1816.htm#SEC1892	59470
errorRand		sing_1817.htm#SEC1893	5727
errormap		sing_2394.htm#SEC2470	7782
esIdeal		sing_1529.htm#SEC1605	60477
esStratum		sing_1530.htm#SEC1606	50094
essential		sing_2193.htm#IDX858	
essential 		sing_2194.htm#IDX859	
eta		sing_2079.htm#SEC2155	60729
euler		sing_1865.htm#SEC1941	10519
eulerChProj		sing_2298.htm#SEC2374	28549
eval		sing_235.htm#SEC275	
evalJacobianAtBox		sing_2689.htm#SEC2765	42716
evalPolyAtBox		sing_2688.htm#SEC2764	43040
evaluateFormalDivisor	evaluateFormalDivisor	sing_2366.htm#SEC2442	3535
evaluatePDivisor		sing_2372.htm#SEC2448	18855
evaluateProduct		sing_2442.htm#SEC2518	54515
evaluate_reynolds		sing_1650.htm#SEC1726	46353
evalutateIntegral		sing_1147.htm#SEC1223	sprintf
example		sing_237.htm#SEC277	
example 		sing_2195.htm#IDX860	
example  		sing_2196.htm#IDX862	
example   		sing_2197.htm#IDX864	
example    		sing_2198.htm#IDX866	
example     		sing_2199.htm#IDX868	
example      		sing_2200.htm#IDX870	
example       		sing_2201.htm#IDX873	
execute		sing_238.htm#SEC278	
exit		sing_390.htm#SEC430	
exp2pt		sing_1853.htm#SEC1929	19621
expo		sing_1877.htm#SEC1953	8833
exponents		sing_2205.htm#IDX881	
export		sing_383.htm#SEC423	
exportNuminvs		sing_1270.htm#SEC1346	10423
exportto		sing_384.htm#SEC424	
expp		sing_2738.htm#SEC2814	15751
expression list		sing_72.htm#IDX128	
expression list 		sing_422.htm#IDX299	
ext-module	purityfiltration_lib	sing_758.htm#IDX368	
extcurve		sing_1799.htm#SEC1875	6730
extdevelop		sing_1561.htm#SEC1637	51044
extendGC		sing_932.htm#SEC1008	40951
extendWeyl		sing_792.htm#SEC844	49954
extendedTensor		sing_724.htm#SEC776	4975
extendpoly		sing_931.htm#SEC1007	29201
extendring		sing_1010.htm#SEC1086	64781
extension of rings		sing_1323.htm#IDX580	
exterior basis		sing_1077.htm#IDX507	
exterior power		sing_1079.htm#IDX509	
exteriorBasis		sing_1077.htm#SEC1153	sprintf
exteriorPower		sing_1079.htm#SEC1155	20173
extgcd		sing_239.htm#SEC279	
fVector		sing_2059.htm#SEC2135	3715
fVectorP		sing_2088.htm#SEC2164	31843
facFirstShift		sing_711.htm#SEC763	6469
facFirstWeyl		sing_707.htm#SEC759	42412
facGBIdeal		sing_1288.htm#SEC1364	9924
facShift		sing_710.htm#SEC762	48551
facSubWeyl		sing_709.htm#SEC761	9630
facWeyl		sing_706.htm#SEC758	32331
faceContaining		sing_2031.htm#SEC2107	64804
facetVertexLatticeDistances	facetVertexLatticeDistances	sing_2089.htm#SEC2165	60714
facetWidth		sing_2090.htm#SEC2166	62810
facetWidths		sing_2091.htm#SEC2167	5503
facets		sing_2032.htm#SEC2108	8112
facstd		sing_240.htm#SEC280	
factmodd		sing_241.htm#SEC281	
factor		sing_322.htm#SEC362	
factorH		sing_922.htm#SEC998	24814
factorLenstraECM		sing_1916.htm#SEC1992	54951
factorMain		sing_1753.htm#SEC1829	65152
factorgroup		sing_2577.htm#SEC2653	59914
factorial		sing_908.htm#SEC984	32871
factorization		sing_323.htm#SEC363	
factorization 		sing_1107.htm#IDX511	
factorize		sing_242.htm#SEC282	
factorize 		sing_322.htm#SEC362	
factory		sing_1.htm#IDX2	
fan		sing_189.htm#SEC229	
fan 		sing_2071.htm#IDX807	
fanViaCones		sing_2057.htm#SEC2133	16418
farey		sing_243.htm#SEC283	
fareypoly		sing_2375.htm#SEC2451	12389
fastExpt		sing_1861.htm#SEC1937	43912
fastHC, option		sing_315.htm#IDX153	
fastelim		sing_1715.htm#SEC1791	7409
fetch		sing_244.htm#SEC284	
fetch (plural)		sing_461.htm#SEC501	
fetchall		sing_1011.htm#SEC1087	7537
ffmodStd		sing_2379.htm#SEC2455	50680
ffmodstd.lib		sing_2374.htm#SEC2450	
ffmodstd_lib		sing_2374.htm#SEC2450	
ffsolve		sing_1704.htm#SEC1780	20432
ffsolve.lib		sing_1703.htm#SEC1779	
ffsolve_lib		sing_1703.htm#SEC1779	
fglm		sing_245.htm#SEC285	
fglm 		sing_355.htm#IDX187	
fglm_solve		sing_1731.htm#SEC1807	51398
fglmquot		sing_246.htm#SEC286	
fibonacci		sing_909.htm#SEC985	24750
field		sing_144.htm#SEC184	
file, .singularrc		sing_20.htm#IDX71	
filecmd		sing_247.htm#SEC287	
filtration	purityfiltration_lib	sing_758.htm#IDX369	
finalCharts		sing_1423.htm#SEC1499	37296
find		sing_248.htm#SEC288	
findAuto		sing_665.htm#SEC717	51205
findInvo		sing_663.htm#SEC715	18177
findInvoDiag		sing_664.htm#SEC716	7365
findOrientedBoundary	findOrientedBoundary	sing_2080.htm#SEC2156	24110
findTorsion		sing_1842.htm#SEC1918	29572
find_first_primitive_root	find_first_primitive_root	sing_1920.htm#SEC1996	33327
find_index		sing_1924.htm#SEC2000	62564
findifs.lib		sing_1849.htm#SEC1925	
findifs_example		sing_1850.htm#SEC1926	33849
findifs_lib		sing_1849.htm#SEC1925	
findimAlgebra		sing_733.htm#SEC785	64612
finduni		sing_249.htm#SEC289	
findvars		sing_1716.htm#SEC1792	54503
finite field		sing_144.htm#SEC184	
finite field 		sing_1703.htm#IDX780	
finiteDiagInvariants	finiteDiagInvariants	sing_1265.htm#SEC1341	3508
finitediff.lib		sing_2380.htm#IDX978	
finitediff_lib		sing_2380.htm#IDX979	
finitenessTest		sing_1121.htm#SEC1197	40633
finvar.lib		sing_1638.htm#SEC1714	
finvar_lib		sing_1638.htm#SEC1714	
first index is 1		sing_417.htm#SEC457	
firstoct		sing_1764.htm#SEC1840	11498
fitting		sing_1167.htm#SEC1243	20661
fixed points, moduli space of stable maps, graph	fixedPoints	sing_2728.htm#IDX1059	
fixedPoints		sing_2728.htm#SEC2804	25366
fl2poly		sing_590.htm#SEC642	51682
flatten		sing_1052.htm#SEC1128	55617
flatteningStrat		sing_1168.htm#SEC1244	15622
floating point		sing_1020.htm#IDX497	
for		sing_385.htm#SEC425	
formaldivisorplus		sing_2367.htm#SEC2443	31959
forward		sing_2386.htm#SEC2462	15383
fourier		sing_585.htm#SEC637	5326
fouriersystem		sing_2397.htm#SEC2473	43681
fpadim.lib		sing_601.htm#SEC653	
fpadim_lib		sing_601.htm#SEC653	
fpaprops.lib		sing_635.htm#SEC687	
fpaprops_lib		sing_635.htm#SEC687	
fprintf		sing_251.htm#SEC291	13662
fracStatus		sing_2657.htm#SEC2733	14582
frandwalk		sing_2701.htm#SEC2777	25555
free		sing_2204.htm#IDX878	
free 		sing_2205.htm#IDX880	
free associative algebra, tensor algebra	Free associative algebras	sing_492.htm#SEC544	
freeGBasis		sing_649.htm#SEC701	43055
freeModule		sing_2494.htm#SEC2570	34173
freeModule2Module		sing_2523.htm#SEC2599	15296
freegb.lib		sing_644.htm#SEC696	
freegb_lib		sing_644.htm#SEC696	
freemodule		sing_252.htm#SEC292	
freerank		sing_968.htm#SEC1044	52218
fres		sing_253.htm#SEC293	
from_boolean_constant	from_boolean_constant	sing_2235.htm#SEC2311	44881
from_boolean_ideal		sing_2239.htm#SEC2315	62698
from_boolean_poly		sing_2236.htm#SEC2312	27864
from_boolean_set		sing_2240.htm#SEC2316	60615
frwalk		sing_254.htm#SEC294	
full representation		sing_931.htm#IDX446	
full representation 		sing_932.htm#IDX451	
fullDimImages		sing_2423.htm#SEC2499	20094
fullFan		sing_2058.htm#SEC2134	7534
fullSerreRelations		sing_659.htm#SEC711	27691
fullSpace		sing_2013.htm#SEC2089	19485
furtherInvar		sing_1682.htm#SEC1758	19209
further_hn_proc		sing_1578.htm#SEC1654	63500
fwalk		sing_1154.htm#SEC1230	15070
galois field		sing_144.htm#SEC184	
gauss_col		sing_1062.htm#SEC1138	36252
gauss_nf		sing_1093.htm#SEC1169	51060
gauss_row		sing_1063.htm#SEC1139	58877
gaussred		sing_1091.htm#SEC1167	29001
gaussred_pivot		sing_1092.htm#SEC1168	25477
gcd		sing_255.htm#SEC295	
gcdMon		sing_1196.htm#SEC1272	42448
gcddivisor		sing_1952.htm#SEC2028	1276
gen		sing_256.htm#SEC296	
genMDSMat		sing_1819.htm#SEC1895	3347
genSymId		sing_1342.htm#SEC1418	17521
general error-locator polynomial		sing_887.htm#SEC952	
general neron.		sing_2451.htm#IDX986	
general weighted lexicographical ordering		sing_861.htm#IDX410	
general weighted reverse lexicographical ordering	Local orderings	sing_861.htm#IDX407	
general.lib		sing_902.htm#SEC978	
generalOrder		sing_1977.htm#SEC2053	42536
general_lib		sing_902.htm#SEC978	
generateG		sing_1915.htm#SEC1991	51697
generators		sing_1478.htm#IDX642	
generatorsOfLinealitySpace	generatorsOfLinealitySpace	sing_2033.htm#SEC2109	4454
generatorsOfSpan		sing_2034.htm#SEC2110	40297
generic representation		sing_931.htm#IDX445	
genericid		sing_986.htm#SEC1062	29731
genericity		sing_1839.htm#SEC1915	16822
genericmat		sing_1053.htm#SEC1129	35016
genoutput		sing_1412.htm#SEC1488	18973
genus		sing_1247.htm#SEC1323	sprintf
geometrical locus	FamElemsAtEnvCompPoints	sing_935.htm#IDX457	
geometrical locus 		sing_936.htm#IDX460	
geometrical locus  		sing_937.htm#IDX463	
geometrical locus   		sing_938.htm#IDX466	
geometrical locus    		sing_939.htm#IDX469	
geometrical locus     		sing_940.htm#IDX471	
geometrical locus      		sing_941.htm#IDX475	
getArguments		sing_1043.htm#SEC1119	14254
getCommand		sing_1042.htm#SEC1118	32181
getCone		sing_2060.htm#SEC2136	41394
getGradingGroup		sing_2552.htm#SEC2628	18137
getLattice		sing_2553.htm#SEC2629	7775
getLinearForms		sing_2035.htm#SEC2111	47590
getModuleGrading		sing_2563.htm#SEC2639	43451
getMultiplicity		sing_2036.htm#SEC2112	639
getOneVar		sing_1255.htm#SEC1331	55402
getResult		sing_1044.htm#SEC1120	51722
getSmallest		sing_1254.htm#SEC1330	1623
getState		sing_1045.htm#SEC1121	36453
getVariableWeights		sing_2551.htm#SEC2627	9591
getcores		sing_1001.htm#SEC1077	30785
getdump		sing_257.htm#SEC297	
getenv		sing_358.htm#IDX211	
gfan.lib		sing_2012.htm#SEC2088	
gfan_lib		sing_2012.htm#SEC2088	
gfanlib		sing_1.htm#IDX9	
gitCone		sing_2450.htm#SEC2526	23853
gitfan.lib		sing_2420.htm#SEC2496	
gitfan_lib		sing_2420.htm#SEC2496	
gkdim.lib		sing_670.htm#SEC722	
gkdim_lib		sing_670.htm#SEC722	
global		sing_209.htm#IDX133	
global Bernstein-Sato polynomial		sing_505.htm#IDX313	
global Bernstein-Sato polynomial 		sing_540.htm#IDX331	
global Bernstein-Sato polynomial for variety		sing_596.htm#IDX356	
globalSections		sing_2361.htm#SEC2437	55191
gmscoeffs		sing_1536.htm#SEC1612	13182
gmsnf		sing_1535.htm#SEC1611	44676
gmspoly.lib		sing_1555.htm#SEC1631	
gmspoly_lib		sing_1555.htm#SEC1631	
gmsring		sing_1534.htm#SEC1610	59438
gmssing.lib		sing_1533.htm#SEC1609	
gmssing_lib		sing_1533.htm#SEC1609	
goettsche.lib		sing_2404.htm#SEC2480	
goettsche_lib		sing_2404.htm#SEC2480	
good basis		sing_1533.htm#IDX670	
good basis 		sing_1543.htm#IDX725	
good basis  		sing_1555.htm#IDX741	
good basis   		sing_1557.htm#IDX752	
goodBasis		sing_1557.htm#SEC1633	41606
gorensteinIndex		sing_2092.htm#SEC2168	52919
gorensteinVector		sing_2093.htm#SEC2169	50407
graal.lib		sing_2413.htm#SEC2489	
graalMixed		sing_2414.htm#SEC2490	6401
graal_lib		sing_2413.htm#SEC2489	
gradeNumber		sing_762.htm#SEC814	29956
graded Weyl algebra		sing_505.htm#IDX316	
graded algebra		sing_2246.htm#IDX933	
graded module, graded piece		sing_1459.htm#IDX628	
graded modules, graded homomorphisms, syzygies	gradedModules_lib	sing_2453.htm#IDX987	
graded modules, handling of	Handling graded modules	sing_826.htm#SEC878	
graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism	modules_lib	sing_2491.htm#IDX989	
gradedModules.lib		sing_2453.htm#SEC2529	
gradedModules_lib		sing_2453.htm#SEC2529	
gradiator		sing_2596.htm#SEC2672	53802
graph		sing_1143.htm#IDX524	
graph 		sing_1144.htm#IDX525	
graph  		sing_2723.htm#IDX1054	
graph   		sing_2724.htm#IDX1055	
graphics.lib		sing_1766.htm#SEC1842	
graphics_lib		sing_1766.htm#SEC1842	
graphviz		sing_1.htm#IDX13	
graver4ti2		sing_1340.htm#SEC1416	39635
grconcat		sing_2476.htm#SEC2552	16754
grdeg		sing_2456.htm#SEC2532	22879
grgens		sing_2465.htm#SEC2541	12823
grgroebner		sing_2475.htm#SEC2551	29288
grlift		sing_2473.htm#SEC2549	21656
grlifting		sing_2480.htm#SEC2556	51177
grlifting2		sing_2481.htm#SEC2557	59011
grlifting3		sing_2483.htm#SEC2559	6369
grneg		sing_2486.htm#SEC2562	64584
grobcov		sing_924.htm#SEC1000	44826
grobcov.lib		sing_923.htm#SEC999	
grobcov_lib		sing_923.htm#SEC999	
grobj		sing_2454.htm#SEC2530	18115
groebner		sing_258.htm#SEC298	53038
groebner 		sing_818.htm#SEC870	
groebner basis computations		sing_258.htm#IDX147	
groebnerComplex		sing_2171.htm#SEC2247	2421
groebnerCone		sing_2165.htm#SEC2241	58776
groebnerFan		sing_2170.htm#SEC2246	48157
gromovWitten		sing_1148.htm#SEC1224	28559
grorder		sing_2467.htm#SEC2543	20857
ground field		sing_144.htm#SEC184	
groupActionOnHashes		sing_2438.htm#SEC2514	406
groupActionOnQImage		sing_2437.htm#SEC2513	53270
group_reynolds		sing_1646.htm#SEC1722	35079
grpower		sing_2463.htm#SEC2539	3960
grpres		sing_2466.htm#SEC2542	18145
grprod		sing_2474.htm#SEC2550	41525
grrange		sing_2485.htm#SEC2561	41835
grres		sing_2472.htm#SEC2548	35795
grrndmap		sing_2478.htm#SEC2554	4054
grrndmap2		sing_2479.htm#SEC2555	50536
grrndmat		sing_2477.htm#SEC2553	42634
grshift		sing_2458.htm#SEC2534	1415
grsum		sing_2462.htm#SEC2538	60602
grsyz		sing_2471.htm#SEC2547	61843
grtest		sing_2455.htm#SEC2531	62577
grtranspose		sing_2464.htm#SEC2540	13865
grtranspose1		sing_2468.htm#SEC2544	3637
grtwist		sing_2460.htm#SEC2536	10498
grtwists		sing_2461.htm#SEC2537	56638
grview		sing_2457.htm#SEC2533	6878
grwalk.lib		sing_1153.htm#SEC1229	
grwalk_lib		sing_1153.htm#SEC1229	
grzero		sing_2459.htm#SEC2535	4212
gwalk		sing_1159.htm#SEC1235	38238
hStarVector		sing_2094.htm#SEC2170	60821
hVector		sing_2095.htm#SEC2171	46486
h_increasing_knapsack	h_increasing_knapsack	sing_1938.htm#SEC2014	62968
hardware platform		sing_358.htm#IDX271	
hasAlgExtensionCoefficient	hasAlgExtensionCoefficient	sing_1024.htm#SEC1100	54609
hasCommutativeVars		sing_1021.htm#SEC1097	3152
hasGlobalOrdering		sing_1022.htm#SEC1098	34053
hasLeftDenom		sing_2605.htm#SEC2681	47260
hasMixedOrdering		sing_1023.htm#SEC1099	29738
hasNumericCoeffs		sing_1020.htm#SEC1096	14522
hasRightDenom		sing_2606.htm#SEC2682	34279
hasTransExtensionCoefficient	hasTransExtensionCoefficient	sing_1025.htm#SEC1101	56211
hashToCone		sing_2448.htm#SEC2524	6929
hashesToFan		sing_2449.htm#SEC2525	26774
headStand		sing_1075.htm#SEC1151	14413
heightZ		sing_1317.htm#SEC1393	16800
help		sing_259.htm#SEC299	
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_358.htm#IDX194	
help, accessing over the net	Command line options	sing_19.htm#IDX42	
help, online help system	The online help system	sing_16.htm#SEC22	
hermiteNormalForm		sing_2597.htm#SEC2673	37225
hess.lib		sing_2488.htm#SEC2564	
hess_lib		sing_2488.htm#SEC2564	
hessenberg		sing_358.htm#IDX217	24168
hessenberg 		sing_1097.htm#SEC1173	
highcorner		sing_260.htm#SEC300	
hilb		sing_261.htm#SEC301	
hilbPoly		sing_984.htm#SEC1060	36118
hilbert4ti2		sing_1339.htm#SEC1415	13993
hilbertBasis		sing_2096.htm#SEC2172	35423
hilbertSeries		sing_2599.htm#SEC2675	60148
hilbvec		sing_1717.htm#SEC1793	9204
hnexpansion		sing_1559.htm#SEC1635	46990
hnoether.lib		sing_1558.htm#SEC1634	
hnoether_lib		sing_1558.htm#SEC1634	
holonomic rank		sing_780.htm#IDX380	
holonomicRank		sing_784.htm#SEC836	41306
hom		sing_2535.htm#SEC2611	40032
hom_kernel		sing_1175.htm#SEC1251	32604
homog		sing_262.htm#SEC302	
homog_part		sing_2735.htm#SEC2811	20875
homog_parts		sing_2736.htm#SEC2812	12854
homogeneitySpace		sing_2167.htm#SEC2243	48243
homogfacFirstQWeyl		sing_713.htm#SEC765	32751
homogfacFirstQWeyl_all	homogfacFirstQWeyl_all	sing_715.htm#SEC767	9014
homogfacNthQWeyl		sing_712.htm#SEC764	19238
homogfacNthQWeyl_all	homogfacNthQWeyl_all	sing_714.htm#SEC766	56179
homolog.lib		sing_1160.htm#SEC1236	
homolog_lib		sing_1160.htm#SEC1236	
homology		sing_1170.htm#SEC1246	15040
homomorphism		sing_2519.htm#SEC2595	27115
howto, download	Download instructions	sing_2762.htm#SEC2851	
howto, install on Macintosh	Macintosh installation instructions	sing_2765.htm#SEC2854	
howto, install on Unix	Unix installation instructions	sing_2763.htm#SEC2852	
howto, install on Windows	Windows installation instructions	sing_2764.htm#SEC2853	
hres		sing_263.htm#SEC303	
html, default help	The online help system	sing_16.htm#IDX24	
hyperel.lib		sing_1945.htm#SEC2021	
hyperel_lib		sing_1945.htm#SEC2021	
hyperplane		sing_2174.htm#IDX818	
hyperplane arrangement		sing_540.htm#IDX337	
hypersurface singularity		sing_1585.htm#IDX770	
iMult		sing_1250.htm#SEC1326	22059
id		sing_2492.htm#SEC2568	47592
id2mod		sing_980.htm#SEC1056	32918
ideal		sing_90.htm#SEC130	
ideal declarations		sing_91.htm#SEC131	
ideal declarations (plural)	ideal declarations (plural)	sing_424.htm#SEC464	
ideal expressions		sing_92.htm#SEC132	
ideal expressions (plural)	ideal expressions (plural)	sing_425.htm#SEC465	
ideal operations		sing_93.htm#SEC133	
ideal operations (plural)	ideal operations (plural)	sing_426.htm#SEC466	
ideal related functions	ideal related functions	sing_94.htm#SEC134	
ideal related functions (plural)	ideal related functions (plural)	sing_427.htm#SEC467	
ideal, toric		sing_874.htm#SEC931	
idealSplit		sing_1724.htm#SEC1800	4673
ideals	Miscellaneous oddities	sing_418.htm#IDX293	
idealsimplify		sing_1486.htm#SEC1562	38569
identifier	Identifier resolution	sing_419.htm#SEC459	
identifyvar		sing_1394.htm#SEC1470	59662
if		sing_386.htm#SEC426	
image		sing_2515.htm#SEC2591	43481
imageLattice		sing_2565.htm#SEC2641	15740
image_of_variety		sing_1674.htm#SEC1750	43711
imap		sing_264.htm#SEC304	
imap (plural)		sing_462.htm#SEC502	
imapall		sing_1012.htm#SEC1088	16023
impart		sing_265.htm#SEC305	
importfrom		sing_387.htm#SEC427	
inCenter		sing_529.htm#SEC581	22152
inCentralizer		sing_530.htm#SEC582	49000
inForm		sing_572.htm#SEC624	5283
inSubring		sing_1113.htm#SEC1189	24817
indSet		sing_1222.htm#SEC1298	32828
indepSet		sing_266.htm#SEC306	
indexed names		sing_36.htm#IDX82	
indexed names 		sing_37.htm#SEC65	
indices, multi		sing_37.htm#SEC65	
inequalities		sing_2037.htm#SEC2113	10122
infRedTail, option		sing_315.htm#IDX154	
info	The online help system	sing_16.htm#SEC23	
iniD		sing_1414.htm#SEC1490	35084
init_debug		sing_1493.htm#SEC1569	29863
initial		sing_2168.htm#SEC2244	8678
initial form		sing_505.htm#IDX318	
initial ideal		sing_505.htm#IDX317	
initial ideal approach		sing_505.htm#IDX321	
initial ideal approach 		sing_596.htm#IDX360	
initialForm		sing_2145.htm#SEC2221	57793
initialIdeal		sing_2146.htm#SEC2222	22205
initialIdealW		sing_571.htm#SEC623	36086
initialMalgrange		sing_570.htm#SEC622	26846
injective_knapsack		sing_1939.htm#SEC2015	7619
inout.lib		sing_946.htm#SEC1022	
inout_lib		sing_946.htm#SEC1022	
input		sing_41.htm#SEC71	
insert		sing_126.htm#SEC166	
insert 		sing_267.htm#SEC307	
insertCone		sing_2061.htm#SEC2137	13858
insertGenerator		sing_591.htm#SEC643	13951
instructions, Macintosh installation	Macintosh installation instructions	sing_2765.htm#SEC2854	
instructions, Unix installation	Unix installation instructions	sing_2763.htm#SEC2852	
instructions, Windows installation	Windows installation instructions	sing_2764.htm#SEC2853	
instructions, downloading	Download instructions	sing_2762.htm#SEC2851	
int		sing_95.htm#SEC135	
int declarations		sing_96.htm#SEC136	
int expressions		sing_97.htm#SEC137	
int operations		sing_98.htm#SEC138	
int related functions	int related functions	sing_99.htm#SEC139	
intInverse		sing_2574.htm#SEC2650	sprintf
intPart		sing_1893.htm#SEC1969	48360
intRank		sing_2566.htm#SEC2642	1830
intRoot		sing_1894.htm#SEC1970	54582
intRoots		sing_588.htm#SEC640	24538
intStrategy, option		sing_315.htm#IDX155	
intclMonIdeal		sing_1263.htm#SEC1339	22338
intclToricRing		sing_1259.htm#SEC1335	62143
integer division	Miscellaneous oddities	sing_418.htm#IDX288	
integer programming		sing_882.htm#SEC939	
integral		sing_2710.htm#SEC2786	62683
integral basis		sing_1182.htm#IDX546	
integral basis 		sing_1377.htm#IDX613	
integral closure		sing_1243.htm#IDX561	
integral closure 		sing_1244.htm#IDX564	
integral closure  		sing_1245.htm#IDX567	
integral closure   		sing_1258.htm#IDX573	
integralBasis		sing_1182.htm#SEC1258	38114
integralIdeal		sing_575.htm#SEC627	29194
integralModule		sing_576.htm#SEC628	58078
integralSection		sing_2575.htm#SEC2651	sprintf
integralbasis.lib		sing_1181.htm#SEC1257	
integralbasis_lib		sing_1181.htm#SEC1257	
integration of D-module		sing_563.htm#IDX349	
interface, Emacs	Emacs user interface	sing_21.htm#SEC28	
interiorLatticePoints	interiorLatticePoints	sing_2097.htm#SEC2173	49868
internalfunctions		sing_1494.htm#SEC1570	61230
interpolate		sing_1730.htm#SEC1806	51502
interpolation		sing_268.htm#SEC308	
interpret		sing_2537.htm#SEC2613	48499
interpretElem		sing_2540.htm#SEC2616	51740
interpretInv		sing_2538.htm#SEC2614	6149
interpretList		sing_2541.htm#SEC2617	64061
interred		sing_269.htm#SEC309	
intersect		sing_270.htm#SEC310	
intersect (plural)		sing_463.htm#SEC503	
intersectElim, option		sing_315.htm#IDX173	
intersectLattices		sing_2571.htm#SEC2647	41354
intersectLists		sing_2343.htm#SEC2419	4153
intersectMon		sing_1199.htm#SEC1275	44572
intersectOrbitsWithMovingCone	intersectOrbitsWithMovingCone	sing_2436.htm#SEC2512	19444
intersectSyz, option		sing_315.htm#IDX174	
intersectZ		sing_1319.htm#SEC1395	sprintf
intersection		sing_1568.htm#SEC1644	46938
intersection lattice		sing_2210.htm#IDX893	
intersection lattice 		sing_2211.htm#IDX894	
intersection multiplicity		sing_1479.htm#IDX648	
intersection multiplicity 		sing_1568.htm#IDX763	
intersectionDiv		sing_1442.htm#SEC1518	29017
intersectionValRingIdeals	intersectionValRingIdeals	sing_1268.htm#SEC1344	38773
intersectionValRings	intersectionValRings	sing_1267.htm#SEC1343	35761
intersectpar		sing_944.htm#SEC1020	2975
interval arithmetic		sing_2680.htm#IDX1029	
intmat		sing_102.htm#SEC142	
intmat declarations		sing_103.htm#SEC143	
intmat expressions		sing_104.htm#SEC144	
intmat operations		sing_106.htm#SEC146	
intmat related functions	intmat related functions	sing_107.htm#SEC147	
intmat type cast		sing_105.htm#SEC145	
intmat2mons		sing_1283.htm#SEC1359	21150
intprog.lib		sing_1183.htm#SEC1259	
intprog_lib		sing_1183.htm#SEC1259	
intvec		sing_108.htm#SEC148	
intvec declarations		sing_109.htm#SEC149	
intvec expressions		sing_110.htm#SEC150	
intvec operations		sing_111.htm#SEC151	
intvec related functions	intvec related functions	sing_112.htm#SEC152	
invariant		sing_2349.htm#IDX955	
invariant ring minimal generating set matrix group	invariant_algebra_reynolds	sing_1643.htm#IDX776	
invariant ring minimal generating set permutation group	invariant_algebra_perm	sing_1644.htm#IDX777	
invariantRing		sing_1676.htm#SEC1752	18582
invariant_algebra_perm	invariant_algebra_perm	sing_1644.htm#SEC1720	63525
invariant_algebra_reynolds	invariant_algebra_reynolds	sing_1643.htm#SEC1719	35705
invariant_basis		sing_1651.htm#SEC1727	18343
invariant_basis_reynolds	invariant_basis_reynolds	sing_1652.htm#SEC1728	54788
invariant_ring		sing_1639.htm#SEC1715	8059
invariant_ring_random	invariant_ring_random	sing_1640.htm#SEC1716	6986
invariants	curveColengthDerivations	sing_1564.htm#SEC1640	57499
invariants 		sing_2346.htm#IDX948	
invariants  		sing_2350.htm#IDX957	
inverse		sing_1081.htm#SEC1157	27411
inverse of a matrix via its LU-decomposition		sing_290.htm#SEC330	
inverseFourier		sing_586.htm#SEC638	65140
inverse_B		sing_1082.htm#SEC1158	17616
inverse_L		sing_1083.htm#SEC1159	49271
inverse_modulus		sing_1922.htm#SEC1998	60822
invertBirMap		sing_1378.htm#SEC1454	16086
invertLeftFraction		sing_2667.htm#SEC2743	51903
invertNcfrac		sing_2615.htm#SEC2691	50842
invertNumberMain		sing_1754.htm#SEC1830	62615
involut.lib		sing_662.htm#SEC714	
involut_lib		sing_662.htm#SEC714	
involution		sing_667.htm#SEC719	34280
invunit		sing_1587.htm#SEC1663	62398
iostruct		sing_1841.htm#SEC1917	60444
irrRealizationDim		sing_2127.htm#SEC2203	7814
irred_secondary_char0	irred_secondary_char0	sing_1665.htm#SEC1741	2943
irred_secondary_no_molien	irred_secondary_no_molien	sing_1668.htm#SEC1744	55905
irreddecMon		sing_1208.htm#SEC1284	20160
irreducible power series		sing_1569.htm#IDX764	
irreducible secondary invariant	irred_secondary_char0	sing_1665.htm#IDX778	
isAface		sing_2421.htm#SEC2497	25344
isAntiEndo		sing_669.htm#SEC721	19156
isBounded		sing_2098.htm#SEC2174	28183
isCI		sing_209.htm#IDX139	58425
isCI 		sing_1131.htm#SEC1207	
isCM		sing_209.htm#IDX140	50469
isCM 		sing_1171.htm#SEC1247	
isCMcod2		sing_1622.htm#SEC1698	2563
isCanonical		sing_2099.htm#SEC2175	51109
isCartan		sing_531.htm#SEC583	39541
isCentral		sing_740.htm#SEC792	54650
isCommutative		sing_742.htm#SEC794	60728
isCompatible		sing_2062.htm#SEC2138	57323
isCompressed		sing_2100.htm#SEC2176	2849
isDenom		sing_2619.htm#SEC2695	55537
isEqualDivisor		sing_2360.htm#SEC2436	17569
isEquising		sing_1531.htm#SEC1607	1424
isFlat		sing_1172.htm#SEC1248	14706
isFsat		sing_581.htm#SEC633	28225
isFullSpace		sing_2038.htm#SEC2114	27433
isGorenstein		sing_2101.htm#SEC2177	24010
isGradedRingHomomorphism	isGradedRingHomomorphism	sing_2560.htm#SEC2636	39551
isGroup		sing_2558.htm#SEC2634	55744
isGroupHomomorphism		sing_2559.htm#SEC2635	65475
isHolonomic		sing_559.htm#SEC611	30274
isHomg		sing_209.htm#IDX135	
isHomogeneous		sing_2586.htm#SEC2662	3034
isInS		sing_2656.htm#SEC2732	30907
isInt		sing_594.htm#SEC646	9879
isIntegralSurjective	isIntegralSurjective	sing_2572.htm#SEC2648	sprintf
isInvertibleLeftFraction	isInvertibleLeftFraction	sing_2666.htm#SEC2742	623
isInvertibleNcfrac		sing_2614.htm#SEC2690	48367
isInvolution		sing_668.htm#SEC720	13601
isLatticeEmpty		sing_2102.htm#SEC2178	48517
isLocalizationRegular	isLocalizationRegular	sing_2417.htm#SEC2493	11221
isLocallyFree		sing_1173.htm#SEC1249	46389
isMonomial		sing_1194.htm#SEC1270	57615
isNC		sing_741.htm#SEC793	57151
isNormal		sing_2103.htm#SEC2179	64236
isOnCurve		sing_1906.htm#SEC1982	36324
isOneFraction		sing_2669.htm#SEC2745	55015
isOneNcfrac		sing_2608.htm#SEC2684	12754
isOrigin		sing_2039.htm#SEC2115	13977
isPositive		sing_2583.htm#SEC2659	50852
isPrimitiveSublattice	isPrimitiveSublattice	sing_2573.htm#SEC2649	sprintf
isPure		sing_2063.htm#SEC2139	44002
isPureTensor		sing_503.htm#SEC555	21323
isQuotientRing		sing_1026.htm#SEC1102	sprintf
isRational		sing_562.htm#SEC614	57398
isReflexive		sing_2104.htm#SEC2180	3991
isReg		sing_1174.htm#SEC1250	40920
isSB		sing_209.htm#IDX134	
isSimplicial		sing_2040.htm#SEC2116	57789
isSmooth		sing_2105.htm#SEC2181	37647
isSubModule		sing_1027.htm#SEC1103	sprintf
isSublattice		sing_2564.htm#SEC2640	10501
isSymmetric		sing_1343.htm#SEC1419	61363
isTame		sing_1556.htm#SEC1632	31925
isTerminal		sing_2106.htm#SEC2182	29416
isTorsionFree		sing_2582.htm#SEC2658	52228
isTwoSidedGB		sing_504.htm#SEC556	36558
isUpperTriangular		sing_721.htm#SEC773	40655
isVar		sing_660.htm#SEC712	43851
isVeryAmple		sing_2107.htm#SEC2183	64652
isWeyl		sing_743.htm#SEC795	28994
isZeroElement		sing_2584.htm#SEC2660	514
isZeroFraction		sing_2668.htm#SEC2744	1926
isZeroNcfrac		sing_2607.htm#SEC2683	6841
is_NND		sing_1572.htm#SEC1648	26564
is_NP		sing_1231.htm#SEC1307	43891
is_active		sing_1605.htm#SEC1681	6867
is_bijective		sing_1118.htm#SEC1194	49512
is_cenBimodule		sing_776.htm#SEC828	35450
is_cenSubbimodule		sing_777.htm#SEC829	26181
is_ci		sing_1606.htm#SEC1682	35370
is_complex		sing_1054.htm#SEC1130	1234
is_fix_injective		sing_1943.htm#SEC2019	11663
is_h_injective		sing_1942.htm#SEC2018	36696
is_injective		sing_1116.htm#SEC1192	15776
is_irred		sing_1569.htm#SEC1645	51150
is_is		sing_1607.htm#SEC1683	64105
is_nested		sing_1232.htm#SEC1308	9200
is_prime		sing_1923.htm#SEC1999	29018
is_primitive_root		sing_1919.htm#SEC1995	42838
is_pure		sing_768.htm#SEC820	59105
is_reg		sing_1608.htm#SEC1684	18146
is_regs		sing_1609.htm#SEC1685	50242
is_surjective		sing_1117.htm#SEC1193	57044
is_zero		sing_969.htm#SEC1045	24341
isartinianMon		sing_1205.htm#SEC1281	1103
isgenericMon		sing_1206.htm#SEC1282	14444
ishyper		sing_1946.htm#SEC2022	65518
isirreducibleMon		sing_1204.htm#SEC1280	22428
isoncurve		sing_1947.htm#SEC2023	16384
isparam		sing_2010.htm#SEC2086	56395
isprimaryMon		sing_1203.htm#SEC1279	57367
isprimeMon		sing_1202.htm#SEC1278	9124
isuni		sing_1995.htm#SEC2071	39427
iv2lp		sing_629.htm#SEC681	59849
iv2lpList		sing_630.htm#SEC682	18518
iv2lpMat		sing_631.htm#SEC683	21612
ivDHilbert		sing_609.htm#SEC661	56709
ivDHilbertSickle		sing_610.htm#SEC662	43194
ivDimCheck		sing_611.htm#SEC663	258
ivHilbert		sing_612.htm#SEC664	37184
ivKDim		sing_613.htm#SEC665	26109
ivL2lpI		sing_628.htm#SEC680	2454
ivMaxIdeal		sing_625.htm#SEC677	48114
ivMis2Base		sing_614.htm#SEC666	57812
ivMis2Dim		sing_615.htm#SEC667	42072
ivOrdMisLex		sing_616.htm#SEC668	27789
ivSickle		sing_617.htm#SEC669	42888
ivSickleDim		sing_619.htm#SEC671	64347
ivSickleHil		sing_618.htm#SEC670	41396
ivmatGaussian		sing_2687.htm#SEC2763	37718
ivmatInit		sing_2684.htm#SEC2760	22774
ivmatSet		sing_2685.htm#SEC2761	53480
jInvariant		sing_2139.htm#SEC2215	2369
jOft		sing_1878.htm#SEC1954	25716
jacob		sing_271.htm#SEC311	
jacoblift		sing_1588.htm#SEC1664	40125
jacobson		sing_1847.htm#SEC1923	59267
jacobson.lib		sing_1845.htm#SEC1921	
jacobson_lib		sing_1845.htm#SEC1921	
janet		sing_272.htm#SEC312	
janet basis		sing_2693.htm#IDX1032	
jet		sing_273.htm#SEC313	
jordan		sing_1102.htm#SEC1178	16602
jordanbasis		sing_1103.htm#SEC1179	12736
jordanmatrix		sing_1104.htm#SEC1180	2886
jordannf		sing_1105.htm#SEC1181	20535
jungfib		sing_1427.htm#SEC1503	5432
jungnormal		sing_1426.htm#SEC1502	43561
jungresolve		sing_1425.htm#SEC1501	45004
katsura		sing_967.htm#SEC1043	45913
kbase		sing_274.htm#SEC314	
kbase (plural)		sing_464.htm#SEC504	
keepring		sing_388.htm#SEC428	
kerHom		sing_2536.htm#SEC2612	53906
kernel		sing_275.htm#SEC315	
kernelLattice		sing_2567.htm#SEC2643	36320
kill		sing_276.htm#SEC316	
killTask		sing_1033.htm#SEC1109	39317
killall		sing_911.htm#SEC987	34661
killattrib		sing_277.htm#SEC317	
kmemory		sing_910.htm#SEC986	52193
kohom		sing_1176.htm#SEC1252	50086
kontrahom		sing_1177.htm#SEC1253	58549
koszul		sing_278.htm#SEC318	
kskernel.lib		sing_1579.htm#SEC1655	
kskernel_lib		sing_1579.htm#SEC1655	
l-adic numbers		sing_32.htm#SEC46	
laguerre		sing_279.htm#SEC319	
laguerre_solve		sing_1726.htm#SEC1802	10155
lastvarGeneral		sing_1976.htm#SEC2052	28645
latex.lib		sing_1770.htm#SEC1846	
latex_lib		sing_1770.htm#SEC1846	
lattice		sing_2211.htm#IDX896	
latticeArea		sing_2082.htm#SEC2158	53771
latticeBasis		sing_2568.htm#SEC2644	43162
latticeCodegree		sing_2108.htm#SEC2184	25482
latticeDegree		sing_2109.htm#SEC2185	52881
latticePoints		sing_2110.htm#SEC2186	41965
latticeVolume		sing_2111.htm#SEC2187	42234
laxfrT		sing_2384.htm#SEC2460	60899
laxfrX		sing_2385.htm#SEC2461	57254
lazy, option		sing_315.htm#IDX156	
lcm		sing_970.htm#SEC1046	44755
lcmMon		sing_1197.htm#SEC1273	52749
lcmN		sing_1887.htm#SEC1963	52355
lcmofall		sing_1407.htm#SEC1483	56889
lead		sing_280.htm#SEC320	
leadcoef		sing_281.htm#SEC321	
leadexp		sing_282.htm#SEC322	
leadmonom		sing_283.htm#SEC323	
leadmonomial		sing_1962.htm#SEC2038	8195
left annihilator ideal		sing_540.htm#IDX329	
leftInverse		sing_1836.htm#SEC1912	41469
leftKernel		sing_1834.htm#SEC1910	9292
leftOre		sing_2659.htm#SEC2735	44669
length		sing_2682.htm#SEC2758	9547
length, option		sing_315.htm#IDX157	
letplaceGBasis		sing_646.htm#SEC698	33757
letterplace correspondence	Letterplace correspondence	sing_494.htm#SEC546	
lex_solve		sing_1732.htm#SEC1808	48692
lexicographical ordering		sing_860.htm#IDX390	
lib2doc		sing_60.htm#SEC97	
libSingular		sing_2761.htm#SEC2850	
libcdd		sing_1.htm#IDX12	
libfac		sing_1.htm#IDX6	
libparse		sing_69.htm#SEC109	
library		sing_2226.htm#IDX911	
library, gitfan, GIT, geometric invariant theory, quotients	gitfan_lib	sing_2420.htm#IDX984	
library, info string		sing_55.htm#IDX124	
library, polybori.lib		sing_2226.htm#IDX908	
library, template		sing_55.htm#SEC92	
library, template.lib		sing_55.htm#IDX122	
lieBracket		sing_653.htm#SEC705	50745
lift		sing_285.htm#SEC325	
lift 		sing_498.htm#IDX305	
lift (plural)		sing_465.htm#SEC505	
lift_kbase		sing_1525.htm#SEC1601	10906
lift_rel_kb		sing_1526.htm#SEC1602	13673
liftenvelope		sing_501.htm#SEC553	58802
liftstd		sing_286.htm#SEC326	
liftstd (plural)		sing_466.htm#SEC506	
linReduce		sing_513.htm#SEC565	57527
linReduceIdeal		sing_514.htm#SEC566	19076
linSyzSolve		sing_515.htm#SEC567	26185
linalg.lib		sing_1080.htm#SEC1156	
linalg_lib		sing_1080.htm#SEC1156	
linealityDimension		sing_2041.htm#SEC2117	30751
linealitySpace		sing_2042.htm#SEC2118	14489
linear algebra		sing_210.htm#SEC250	
linear algebra 		sing_289.htm#SEC329	
linear algebra  		sing_290.htm#SEC330	
linear algebra   		sing_291.htm#SEC331	
linear code, dual		sing_1805.htm#IDX789	
linear code, systematic		sing_1806.htm#IDX790	
linear interreduction		sing_505.htm#IDX320	
linearCombinations		sing_534.htm#SEC586	20514
linearMapKernel		sing_533.htm#SEC585	43761
linear_relations		sing_1072.htm#SEC1148	45983
linearlyEquivalent		sing_2363.htm#SEC2439	28351
linearpart		sing_1718.htm#SEC1794	2162
linesHypersurface		sing_2732.htm#SEC2808	9129
link	Parallelization with ssi links	sing_113.htm#SEC153	
link 		sing_815.htm#SEC867	
link declarations		sing_114.htm#SEC154	
link expressions		sing_115.htm#SEC155	
link related functions	link related functions	sing_116.htm#SEC156	
list		sing_123.htm#SEC163	
list declarations		sing_124.htm#SEC164	
list expressions		sing_125.htm#SEC165	
list operations		sing_126.htm#SEC166	
list related functions	list related functions	sing_127.htm#SEC167	
lists		sing_2343.htm#IDX944	
lists, elements		sing_2345.htm#IDX946	
listvar		sing_287.htm#SEC327	
lll		sing_2600.htm#SEC2676	35827
load		sing_389.htm#SEC429	
loadLib, option		sing_315.htm#IDX178	
loadProc, option		sing_315.htm#IDX179	
locAtZero		sing_1252.htm#SEC1328	5687
locNormal		sing_1186.htm#SEC1262	52237
locStatus		sing_2654.htm#SEC2730	54575
local methods		sing_1185.htm#IDX549	
local methods 		sing_1186.htm#IDX552	
local names		sing_46.htm#SEC83	
local rings, computing in	Rings associated to monomial orderings	sing_810.htm#SEC862	
local weighted lexicographical ordering		sing_861.htm#IDX411	
local weighted reverse lexicographical ordering	Local orderings	sing_861.htm#IDX408	
localInvar		sing_1681.htm#SEC1757	38478
localization	Rings associated to monomial orderings	sing_810.htm#SEC862	
localization 		sing_2191.htm#IDX856	
localization of D-module		sing_563.htm#IDX345	
localization of D-module 		sing_780.htm#IDX383	
locally closed set		sing_928.htm#IDX435	
locally closed set 		sing_929.htm#IDX437	
locally closed set  		sing_930.htm#IDX439	
locally closed set   		sing_931.htm#IDX443	
locally closed set    		sing_933.htm#IDX453	
localstd		sing_1972.htm#SEC2048	25562
locnormal.lib		sing_1185.htm#SEC1261	
locnormal_lib		sing_1185.htm#SEC1261	
locstd		sing_1610.htm#SEC1686	25864
locus	FamElemsAtEnvCompPoints	sing_935.htm#SEC1011	22530
locus 		sing_935.htm#IDX458	
locus  		sing_936.htm#IDX461	
locus   		sing_937.htm#IDX464	
locus    		sing_938.htm#IDX467	
locus     		sing_939.htm#IDX470	
locus      		sing_940.htm#IDX472	
locus       		sing_941.htm#IDX476	
locusdg		sing_936.htm#SEC1012	6077
locusto		sing_938.htm#SEC1014	730
log2		sing_1862.htm#SEC1938	40703
logarithmic annihilator ideal		sing_540.htm#IDX334	
logg		sing_2737.htm#SEC2813	38736
lp, global ordering		sing_860.htm#IDX389	
lp2iv		sing_632.htm#SEC684	17398
lp2ivId		sing_633.htm#SEC685	16290
lp2lstr		sing_654.htm#SEC706	24713
lpCalcSubstDegBound		sing_642.htm#SEC694	46179
lpCalcSubstDegBounds	lpCalcSubstDegBounds	sing_643.htm#SEC695	56500
lpDHilbert		sing_607.htm#SEC659	10461
lpDHilbertSickle		sing_608.htm#SEC660	41445
lpDimCheck		sing_604.htm#SEC656	9807
lpGkDim		sing_639.htm#SEC691	10351
lpGlDimBound		sing_640.htm#SEC692	53074
lpHilbert		sing_606.htm#SEC658	44093
lpId2ivLi		sing_634.htm#SEC686	13273
lpIsPrime		sing_638.htm#SEC690	27562
lpIsSemiPrime		sing_637.htm#SEC689	27642
lpKDim		sing_603.htm#SEC655	18278
lpMaxIdeal		sing_626.htm#SEC678	37571
lpMis2Base		sing_605.htm#SEC657	10826
lpMis2Dim		sing_602.htm#SEC654	39947
lpMult		sing_650.htm#SEC702	58898
lpNF		sing_647.htm#SEC699	2851
lpNoetherian		sing_636.htm#SEC688	43125
lpOrdMisLex		sing_620.htm#SEC672	30943
lpPower		sing_652.htm#SEC704	7325
lpSickle		sing_621.htm#SEC673	288
lpSickleDim		sing_623.htm#SEC675	61018
lpSickleHil		sing_622.htm#SEC674	55268
lpSubstitute		sing_641.htm#SEC693	54386
lprint		sing_948.htm#SEC1024	5285
lres		sing_288.htm#SEC328	
ls, local ordering		sing_861.htm#IDX402	
lst2str		sing_655.htm#SEC707	10088
lsum		sing_1152.htm#SEC1228	50315
ludecomp		sing_289.htm#SEC329	
luinverse		sing_290.htm#SEC330	
lusolve		sing_291.htm#SEC331	
mRes		sing_2504.htm#SEC2580	58702
m_merkle_hellman_decryption	m_merkle_hellman_decryption	sing_1934.htm#SEC2010	57945
m_merkle_hellman_encryption	m_merkle_hellman_encryption	sing_1933.htm#SEC2009	33857
m_merkle_hellman_transformation	m_merkle_hellman_transformation	sing_1932.htm#SEC2008	7880
magnitude		sing_1856.htm#SEC1932	37967
makeDivisor		sing_2355.htm#SEC2431	3414
makeFormalDivisor		sing_2365.htm#SEC2441	54579
makeGraph		sing_1143.htm#SEC1219	21758
makeGraphVE		sing_2723.htm#SEC2799	sprintf
makeHeisenberg		sing_731.htm#SEC783	2050
makeIdeal		sing_2496.htm#SEC2572	57829
makeLetterplaceRing		sing_645.htm#SEC697	1592
makeMalgrange		sing_600.htm#SEC652	41377
makeMatrix		sing_2495.htm#SEC2571	64348
makeModElimRing		sing_748.htm#SEC800	56092
makePDivisor		sing_2371.htm#SEC2447	45273
makeQsl2		sing_695.htm#SEC747	3997
makeQsl3		sing_696.htm#SEC748	41249
makeQso3		sing_694.htm#SEC746	58910
makeSheaf		sing_2711.htm#SEC2787	10497
makeUe6		sing_691.htm#SEC743	58585
makeUe7		sing_692.htm#SEC744	61849
makeUe8		sing_693.htm#SEC745	64987
makeUf4		sing_690.htm#SEC742	8408
makeUg2		sing_689.htm#SEC741	34512
makeUgl		sing_675.htm#SEC727	3543
makeUsl		sing_674.htm#SEC726	24536
makeUsl2		sing_673.htm#SEC725	42637
makeUso10		sing_681.htm#SEC733	6936
makeUso11		sing_682.htm#SEC734	35873
makeUso12		sing_683.htm#SEC735	19319
makeUso5		sing_676.htm#SEC728	34378
makeUso6		sing_677.htm#SEC729	65009
makeUso7		sing_678.htm#SEC730	49142
makeUso8		sing_679.htm#SEC731	33275
makeUso9		sing_680.htm#SEC732	16896
makeUsp1		sing_684.htm#SEC736	44522
makeUsp2		sing_685.htm#SEC737	18017
makeUsp3		sing_686.htm#SEC738	57445
makeUsp4		sing_687.htm#SEC739	51690
makeUsp5		sing_688.htm#SEC740	35951
makeVariety		sing_2703.htm#SEC2779	23915
makeVector		sing_2524.htm#SEC2600	9049
makeWeyl		sing_730.htm#SEC782	8554
map		sing_128.htm#SEC168	
map (plural)		sing_428.htm#SEC468	
map declarations		sing_129.htm#SEC169	
map declarations (plural)	map declarations (plural)	sing_429.htm#SEC469	
map expressions		sing_130.htm#SEC170	
map expressions (plural)	map expressions (plural)	sing_430.htm#SEC470	
map operations		sing_131.htm#IDX129	
map operations (plural)	map operations (plural)	sing_431.htm#IDX300	
map related functions	map related functions	sing_132.htm#IDX131	
map related functions  (plural)	map related functions (plural)	sing_432.htm#IDX301	
mapIsFinite		sing_1120.htm#SEC1196	60897
mapToRatNormCurve		sing_1382.htm#SEC1458	8877
mapall		sing_1013.htm#SEC1089	14907
mappingcone		sing_2482.htm#SEC2558	48219
mappingcone3		sing_2484.htm#SEC2560	58973
markov4ti2		sing_1338.htm#SEC1414	9163
mat2arr		sing_2176.htm#SEC2252	20840
mat2carr		sing_2177.htm#SEC2253	13777
mat_rk		sing_1094.htm#SEC1170	32196
matbil		sing_1983.htm#SEC2059	1611
mathematical objects	Representation of mathematical objects	sing_856.htm#SEC908	
mathinit		sing_1768.htm#SEC1844	16793
matmult		sing_1984.htm#SEC2060	60088
matrix		sing_133.htm#SEC173	
matrix 		sing_2176.htm#IDX824	
matrix  		sing_2177.htm#IDX827	
matrix   		sing_2178.htm#IDX831	
matrix declarations		sing_134.htm#SEC174	
matrix diagonalization		sing_1845.htm#IDX800	
matrix expressions		sing_135.htm#SEC175	
matrix operations		sing_137.htm#SEC177	
matrix related functions	matrix related functions	sing_138.htm#SEC178	
matrix type cast		sing_136.htm#SEC176	
matrix.lib		sing_1047.htm#SEC1123	
matrixExp		sing_1372.htm#SEC1448	53063
matrixLog		sing_1373.htm#SEC1449	26235
matrixT1		sing_1624.htm#SEC1700	15051
matrix_lib		sing_1047.htm#SEC1123	
matrixpres		sing_2487.htm#SEC2563	60645
matrixsystem		sing_2395.htm#SEC2471	62950
max		sing_292.htm#SEC332	23624
maxEord		sing_1397.htm#SEC1473	64032
maxExp		sing_209.htm#IDX136	
maxIntRoot		sing_797.htm#SEC849	37127
maxZeros		sing_1375.htm#SEC1451	35964
maxabs		sing_2002.htm#SEC2078	64510
maxcoef		sing_971.htm#SEC1047	50577
maxdeg		sing_972.htm#SEC1048	39794
maxdeg1		sing_973.htm#SEC1049	21545
maxideal		sing_293.htm#SEC333	
maximalFace		sing_2112.htm#SEC2188	35224
maximalGroebnerCone		sing_2166.htm#SEC2242	62935
maximalValue		sing_2113.htm#SEC2189	32783
maximum		sing_1875.htm#SEC1951	2355
maximum number of zeroes		sing_1375.htm#IDX607	
mdouble		sing_56.htm#SEC93	56685
mem, option		sing_315.htm#IDX180	
member		sing_2345.htm#SEC2421	1765
membershipMon		sing_1198.htm#SEC1274	40876
memory		sing_294.htm#SEC334	
memory managment		sing_294.htm#SEC334	
merkle_hellman_decryption	merkle_hellman_decryption	sing_1936.htm#SEC2012	49106
merkle_hellman_encryption	merkle_hellman_encryption	sing_1935.htm#SEC2011	13645
methods, hashtables		sing_2490.htm#IDX988	
methods.lib		sing_2490.htm#SEC2566	
methods_lib		sing_2490.htm#SEC2566	
midpoint		sing_2391.htm#SEC2467	29391
milnor		sing_1611.htm#SEC1687	23173
milnorcode		sing_1495.htm#SEC1571	13849
milnornumber		sing_2677.htm#SEC2753	21855
min		sing_295.htm#SEC335	56342
minAssChar		sing_1297.htm#SEC1373	18758
minAssCharE		sing_1298.htm#SEC1374	31570
minAssGTZ		sing_1295.htm#SEC1371	41315
minAssGTZE		sing_1296.htm#SEC1372	50867
minAssZ		sing_1315.htm#SEC1391	54152
minEcart		sing_1965.htm#SEC2041	34890
minIntRoot		sing_561.htm#SEC613	3288
minIntRoot2		sing_796.htm#SEC848	46494
minMult		sing_1127.htm#SEC1203	31978
minbase		sing_296.htm#SEC336	
minbaseMon		sing_1195.htm#SEC1271	1501
mindeg		sing_974.htm#SEC1050	16307
mindeg1		sing_975.htm#SEC1051	39698
mindist		sing_1820.htm#SEC1896	55281
minimal display time, setting the		sing_358.htm#IDX284	
minimalAfaceOrbits		sing_2433.htm#SEC2509	2467
minimalAfaces		sing_2424.htm#SEC2500	47736
minimalFace		sing_2114.htm#SEC2190	40971
minimalOrbitConeOrbits	minimalOrbitConeOrbits	sing_2435.htm#SEC2511	11756
minimalValue		sing_2115.htm#SEC2191	31262
minipoly		sing_1099.htm#SEC1175	4927
minkowskiSum		sing_2116.htm#SEC2192	3969
minor		sing_297.htm#SEC337	
minpoly		sing_397.htm#SEC437	
minres		sing_298.htm#SEC338	
minres (plural)		sing_467.htm#SEC507	
mirror symmetry		sing_1142.htm#IDX517	
mixed Hodge structure		sing_1533.htm#IDX663	
mixed Hodge structure 		sing_1539.htm#IDX691	
mixed Hodge structure  		sing_1540.htm#IDX697	
mixed Hodge structure   		sing_1541.htm#IDX705	
mixed Hodge structure    		sing_1542.htm#IDX711	
mixed Hodge structure     		sing_1543.htm#IDX719	
mixed Hodge structure      		sing_1544.htm#IDX729	
mixed Hodge structure       		sing_1555.htm#IDX735	
mixed Hodge structure        		sing_1557.htm#IDX746	
mod		sing_81.htm#SEC121	
mod 		sing_98.htm#SEC138	
mod  		sing_147.htm#SEC187	
mod   		sing_155.htm#SEC195	
mod2id		sing_979.htm#SEC1055	27927
mod2str		sing_656.htm#SEC708	35236
modBorder		sing_2695.htm#SEC2771	19224
modDec		sing_1214.htm#SEC1290	48578
modIntersect		sing_1192.htm#SEC1268	43699
modJanet		sing_2697.htm#SEC2773	8550
modNPos		sing_1237.htm#SEC1313	17130
modNormal		sing_1188.htm#SEC1264	39654
modNpos_test		sing_1235.htm#SEC1311	34326
modSagbiAlg		sing_2332.htm#SEC2408	25025
modStd		sing_1190.htm#SEC1266	7824
modSyz		sing_1191.htm#SEC1267	37065
modVStd		sing_2337.htm#SEC2413	38529
modVStd0		sing_2338.htm#SEC2414	46080
modWalk		sing_2545.htm#SEC2621	sprintf
mod_versal		sing_1524.htm#SEC1600	63927
modality		sing_1503.htm#SEC1579	49951
modfWalk		sing_2547.htm#SEC2623	sprintf
modfrWalk		sing_2548.htm#SEC2624	sprintf
modnormal.lib		sing_1187.htm#SEC1263	
modnormal_lib		sing_1187.htm#SEC1263	
modrWalk		sing_2546.htm#SEC2622	sprintf
modregCM		sing_1241.htm#SEC1317	5049
modsatiety		sing_1239.htm#SEC1315	44506
modstd.lib		sing_1189.htm#SEC1265	
modstd_lib		sing_1189.htm#SEC1265	
modular		sing_957.htm#SEC1033	16950
modular methods		sing_1185.htm#IDX550	
modular methods 		sing_1187.htm#IDX555	
modular methods.		sing_1186.htm#IDX553	
modular techniques.		sing_1188.htm#IDX557	
modular.lib		sing_956.htm#SEC1032	
modular_lib		sing_956.htm#SEC1032	
modular_lib 		sing_956.htm#IDX485	
module		sing_139.htm#SEC179	
module (plural)		sing_433.htm#SEC473	
module declarations		sing_140.htm#SEC180	
module declarations (plural)	module declarations (plural)	sing_434.htm#SEC474	
module expressions		sing_141.htm#SEC181	
module expressions (plural)	module expressions (plural)	sing_435.htm#SEC475	
module operations		sing_142.htm#SEC182	
module operations (plural)	module operations (plural)	sing_436.htm#SEC476	
module ordering C		sing_862.htm#IDX414	
module ordering c		sing_862.htm#IDX416	
module related functions	module related functions	sing_143.htm#SEC183	
module related functions (plural)	module related functions (plural)	sing_437.htm#SEC477	
module_containment		sing_1112.htm#SEC1188	31620
modules.lib		sing_2491.htm#SEC2567	
modules_lib		sing_2491.htm#SEC2567	
moduliSpace		sing_2725.htm#SEC2801	37013
modulo		sing_299.htm#SEC339	
modulo (plural)		sing_468.htm#SEC508	
moduloSlim		sing_738.htm#SEC790	52636
modwalk.lib		sing_2544.htm#SEC2620	
modwalk_lib		sing_2544.htm#SEC2620	
moebius		sing_2212.htm#SEC2288	61319
moebius function		sing_2212.htm#IDX897	
molien		sing_1647.htm#SEC1723	63561
mondromy.lib		sing_1585.htm#SEC1661	
mondromy_lib		sing_1585.htm#SEC1661	
monitor		sing_300.htm#SEC340	
monodromy		sing_1533.htm#IDX667	40112
monodromy 		sing_1538.htm#SEC1614	
monodromy  		sing_1538.htm#IDX687	
monodromy   		sing_1543.htm#IDX722	
monodromy    		sing_1555.htm#IDX738	
monodromy     		sing_1557.htm#IDX749	
monodromyB		sing_1589.htm#SEC1665	46517
monomial		sing_301.htm#SEC341	
monomial ordering		sing_1022.htm#IDX499	
monomial orderings	General definitions for orderings	sing_810.htm#SEC862	
monomial orderings 		sing_859.htm#SEC911	
monomial orderings introduction	Introduction to orderings	sing_858.htm#SEC910	
monomialBasis		sing_627.htm#SEC679	14185
monomialInIdeal		sing_794.htm#SEC846	4687
monomialLcm		sing_1963.htm#SEC2039	36233
monomialabortstd		sing_2219.htm#SEC2295	14901
monomialideal.lib		sing_1193.htm#SEC1269	
monomialideal_lib		sing_1193.htm#SEC1269	
monomials and precedence	Miscellaneous oddities	sing_418.htm#IDX290	
mons2intmat		sing_1282.htm#SEC1358	15555
morsesplit		sing_1496.htm#SEC1572	3417
movingCone		sing_2431.htm#SEC2507	39892
mp_res_mat		sing_1729.htm#SEC1805	44453
mplot		sing_1769.htm#SEC1845	21740
mpresmat		sing_302.htm#SEC342	
mprimdec.lib		sing_1210.htm#SEC1286	
mprimdec_lib		sing_1210.htm#SEC1286	
mregular.lib		sing_1225.htm#SEC1301	
mregular_lib		sing_1225.htm#SEC1301	
mres		sing_303.htm#SEC343	
mres (plural)		sing_469.htm#SEC509	
mstd		sing_304.htm#SEC344	
msum		sing_58.htm#SEC95	53344
mtriple		sing_57.htm#SEC94	55390
mult	Miscellaneous oddities	sing_305.htm#SEC345	
mult 		sing_418.htm#IDX291	
multBound		sing_398.htm#SEC438	
multRat		sing_802.htm#SEC854	44047
multarr2arr		sing_2207.htm#SEC2283	44731
multarrMultRestrict		sing_2209.htm#SEC2285	41742
multarrRestrict		sing_2208.htm#SEC2284	sprintf
multcol		sing_1066.htm#SEC1142	21899
multdivisor		sing_2357.htm#SEC2433	65139
multformaldivisor		sing_2369.htm#SEC2445	32238
multi		sing_1950.htm#SEC2026	18473
multi indices		sing_37.htm#SEC65	
multiDeg		sing_2579.htm#SEC2655	7049
multiDegBasis		sing_2580.htm#SEC2656	3320
multiDegGroebner		sing_2588.htm#SEC2664	1040
multiDegModulo		sing_2590.htm#SEC2666	27244
multiDegPartition		sing_2581.htm#SEC2657	9577
multiDegResolution		sing_2591.htm#SEC2667	38535
multiDegSyzygy		sing_2589.htm#SEC2665	54075
multiDegTensor		sing_2592.htm#SEC2668	45108
multiDegTor		sing_2593.htm#SEC2669	sprintf
multiarrangement		sing_2203.htm#IDX877	
multiarrangement 		sing_2204.htm#IDX879	
multiarrangement  		sing_2205.htm#IDX882	
multiarrangement   		sing_2206.htm#IDX883	
multiarrangement    		sing_2207.htm#IDX886	
multiarrangement     		sing_2208.htm#IDX889	
multiarrangement      		sing_2209.htm#IDX891	
multidimensional_knapsack	multidimensional_knapsack	sing_1928.htm#SEC2004	15647
multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra	multigrading_lib	sing_2549.htm#IDX995	
multigrading.lib		sing_2549.htm#IDX993	
multigrading_lib		sing_2549.htm#IDX994	
multipleCover		sing_2731.htm#SEC2807	55988
multiplicities, sequence of		sing_1564.htm#IDX761	
multiplicity		sing_2348.htm#IDX953	
multiplicity sequence		sing_1477.htm#IDX640	
multiplicity sequence 		sing_1480.htm#IDX652	
multiplicity sequence  		sing_1566.htm#IDX762	
multiplyLeftFractions	multiplyLeftFractions	sing_2664.htm#SEC2740	57489
multiplylist		sing_1417.htm#SEC1493	34999
multivariate equations		sing_1703.htm#IDX779	
multrow		sing_1067.htm#SEC1143	871
multseq2charexp		sing_1476.htm#SEC1552	sprintf
multsequence		sing_1566.htm#SEC1642	35117
nBoundaryLatticePoints	nBoundaryLatticePoints	sing_2117.htm#SEC2193	49670
nHilbertBasis		sing_2118.htm#SEC2194	173
nInteriorLatticePoints	nInteriorLatticePoints	sing_2119.htm#SEC2195	42152
nLatticePoints		sing_2120.htm#SEC2196	5977
naccache_stern_decryption	naccache_stern_decryption	sing_1931.htm#SEC2007	31429
naccache_stern_encryption	naccache_stern_encryption	sing_1930.htm#SEC2006	60034
naccache_stern_generation	naccache_stern_generation	sing_1929.htm#SEC2005	2559
nameof		sing_306.htm#SEC346	
names		sing_307.htm#SEC347	
nashmult		sing_1484.htm#SEC1560	8491
nblocks		sing_358.htm#IDX221	
ncExt_R		sing_771.htm#SEC823	14357
ncHilb.lib		sing_2601.htm#SEC2677	
ncHilb_lib		sing_2601.htm#SEC2677	
ncHom		sing_772.htm#SEC824	45033
ncRelations		sing_739.htm#SEC791	7225
nc_algebra		sing_470.htm#SEC510	
nc_hilb		sing_358.htm#IDX223	
ncalg.lib		sing_672.htm#SEC724	
ncalg_lib		sing_672.htm#SEC724	
ncalgebra		sing_471.htm#SEC511	
ncdecomp.lib		sing_699.htm#SEC751	
ncdecomp_lib		sing_699.htm#SEC751	
ncdetection		sing_666.htm#SEC718	24994
ncfactor		sing_705.htm#SEC757	53809
ncfactor.lib		sing_704.htm#SEC756	
ncfactor_lib		sing_704.htm#SEC756	
ncfrac.lib		sing_2604.htm#SEC2680	
ncfrac_lib		sing_2604.htm#SEC2680	
nchilb		sing_2602.htm#SEC2678	40517
nchomolog.lib		sing_770.htm#IDX373	
nchomolog_lib		sing_770.htm#IDX374	
ncloc.lib		sing_2618.htm#SEC2694	
ncloc_lib		sing_2618.htm#SEC2694	
ncols		sing_308.htm#SEC348	
ncones		sing_2065.htm#SEC2141	48316
ncpreim.lib		sing_717.htm#SEC769	
ncpreim_lib		sing_717.htm#SEC769	
nctools.lib		sing_725.htm#SEC777	
nctools_lib		sing_725.htm#SEC777	
ndcond		sing_728.htm#SEC780	1006
negateNcfrac		sing_2613.htm#SEC2689	23626
negatedCone		sing_2043.htm#SEC2119	38527
negative degree lexicographical ordering		sing_861.htm#IDX405	
negative degree reverse lexicographical ordering	Local orderings	sing_861.htm#IDX403	
negative lexicographical ordering		sing_861.htm#IDX401	
negativedivisor		sing_2358.htm#SEC2434	8274
negativeformaldivisor	negativeformaldivisor	sing_2368.htm#SEC2444	55026
net		sing_2622.htm#IDX996	sprintf
net 		sing_2624.htm#SEC2700	
net access	Command line options	sing_19.htm#IDX40	
netBigInt		sing_2630.htm#SEC2706	63523
netBigIntMat		sing_2625.htm#SEC2701	36296
netBigIntMatShort		sing_2626.htm#SEC2702	30702
netCoefficientRing		sing_2627.htm#SEC2703	6081
netIdeal		sing_2628.htm#SEC2704	64434
netInt		sing_2629.htm#SEC2705	19545
netIntMat		sing_2631.htm#SEC2707	34242
netIntMatShort		sing_2632.htm#SEC2708	21160
netIntVector		sing_2633.htm#SEC2709	17568
netIntVectorShort		sing_2634.htm#SEC2710	16105
netList		sing_2636.htm#SEC2712	29178
netMap		sing_2637.htm#SEC2713	19115
netMap2		sing_2638.htm#SEC2714	44053
netMatrix		sing_2526.htm#SEC2602	29311
netNumber		sing_2635.htm#SEC2711	24930
netPoly		sing_2641.htm#SEC2717	7938
netPrimePower		sing_2642.htm#SEC2718	54219
netRing		sing_2643.htm#SEC2719	42246
netString		sing_2644.htm#SEC2720	43247
netVector		sing_2525.htm#SEC2601	32453
netmatrix		sing_2639.htm#SEC2715	4023
netmatrixShort		sing_2640.htm#SEC2716	24709
nets.lib		sing_2622.htm#SEC2698	
nets_lib		sing_2622.htm#SEC2698	
netvector		sing_2645.htm#SEC2721	39957
netvectorShort		sing_2646.htm#SEC2722	22053
newTest		sing_1870.htm#SEC1946	36655
newline		sing_171.htm#SEC211	
news		sing_2754.htm#SEC2830	
newstruct		sing_182.htm#SEC222	
newstruct 		sing_2226.htm#IDX913	
newtonDiag		sing_983.htm#SEC1059	56652
newtonPolygonNegSlopes	newtonPolygonNegSlopes	sing_2747.htm#SEC2823	22052
newtonPolytope		sing_2069.htm#SEC2145	56291
newtonPolytopeLP		sing_2074.htm#SEC2150	36186
newtonPolytopeP		sing_2073.htm#SEC2149	29927
newtonpoly		sing_1571.htm#SEC1647	31930
nf_icis		sing_1612.htm#SEC1688	49093
nfmodStd		sing_2650.htm#SEC2726	46077
nfmodSyz		sing_2652.htm#SEC2728	55942
nfmodstd.lib		sing_2648.htm#SEC2724	
nfmodstd_lib		sing_2648.htm#SEC2724	
nfmodsyz.lib		sing_2651.htm#SEC2727	
nfmodsyz_lib		sing_2651.htm#SEC2727	
nilpotent Lie algebras		sing_1370.htm#IDX592	
nmaxcones		sing_2064.htm#SEC2140	660
noether		sing_399.htm#SEC439	
noether.lib		sing_1233.htm#SEC1309	
noetherNormal		sing_1119.htm#SEC1195	44522
noether_lib		sing_1233.htm#SEC1309	
non-english special characters		sing_407.htm#IDX286	
nonMonomials		sing_1286.htm#SEC1362	16309
nonZeroEntry		sing_1122.htm#SEC1198	933
none, option		sing_315.htm#IDX150	
norTest		sing_1253.htm#SEC1329	sprintf
norm		sing_1949.htm#SEC2025	31143
normaform (up to a bound)		sing_358.htm#IDX246	
normal		sing_1243.htm#SEC1319	61073
normal bundle, graph, rational curves, mutiple covers, lines on	normalBundle	sing_2730.htm#IDX1061	
normal form		sing_868.htm#IDX417	
normal.lib		sing_1242.htm#SEC1318	
normalBundle		sing_2730.htm#SEC2806	sprintf
normalC		sing_1245.htm#SEC1321	34842
normalConductor		sing_1257.htm#SEC1333	26085
normalFan		sing_2121.htm#SEC2197	39216
normalForm		sing_2359.htm#SEC2435	34962
normalI		sing_1330.htm#SEC1406	7516
normalP		sing_1244.htm#SEC1320	36584
normalToricRing		sing_1260.htm#SEC1336	29638
normalToricRingFromBinomials	normalToricRingFromBinomials	sing_1261.htm#SEC1337	2301
normal_lib		sing_1242.htm#SEC1318	
normalform		sing_1500.htm#SEC1576	5550
normalform 		sing_2331.htm#IDX941	
normaliz		sing_1.htm#IDX14	18426
normaliz 		sing_1273.htm#SEC1349	
normaliz.lib		sing_1258.htm#SEC1334	
normaliz_lib		sing_1258.htm#SEC1334	
normalization		sing_1185.htm#IDX548	
normalization 		sing_1186.htm#IDX551	
normalization  		sing_1187.htm#IDX554	
normalization   		sing_1188.htm#IDX556	
normalization    		sing_1243.htm#IDX560	
normalization     		sing_1244.htm#IDX563	
normalization      		sing_1245.htm#IDX566	
normalization       		sing_1257.htm#IDX572	
normalization        		sing_1258.htm#IDX574	
normalization         		sing_2347.htm#IDX951	
normalization.		sing_1182.htm#IDX547	
normalization. 		sing_1377.htm#IDX614	
normalize		sing_976.htm#SEC1052	44788
normalizeMonoidal		sing_2670.htm#SEC2746	33071
normalizeRational		sing_2671.htm#SEC2747	55177
not		sing_101.htm#SEC141	
notBuckets, option		sing_315.htm#IDX160	
notRegularity, option		sing_315.htm#IDX158	
notSugar, option		sing_315.htm#IDX159	
notWarnSB, option		sing_315.htm#IDX181	
npar		sing_1855.htm#SEC1931	5753
npars		sing_309.htm#SEC349	
nrRootsDeterm		sing_1980.htm#SEC2056	sprintf
nrRootsProbab		sing_1979.htm#SEC2055	sprintf
nres		sing_310.htm#SEC350	
nres (plural)		sing_472.htm#SEC512	
nrows		sing_311.htm#SEC351	
nrroots		sing_2009.htm#SEC2085	54867
nsatiety		sing_1238.htm#SEC1314	53333
nselect		sing_1138.htm#SEC1214	34057
nt_solve		sing_1744.htm#SEC1820	33061
ntsolve.lib		sing_1743.htm#SEC1819	
ntsolve_lib		sing_1743.htm#SEC1819	
number		sing_144.htm#SEC184	
number 		sing_2180.htm#IDX837	
number declarations		sing_145.htm#SEC185	
number expressions		sing_146.htm#SEC186	
number operations		sing_147.htm#SEC187	
number related functions	number related functions	sing_148.htm#SEC188	
numberOfConesOfDimension	numberOfConesOfDimension	sing_2066.htm#SEC2142	5905
number_e		sing_912.htm#SEC988	59152
number_pi		sing_913.htm#SEC989	15492
numerAlg.lib		sing_1352.htm#IDX581	
numerAlg_lib		sing_1352.htm#IDX582	
numerAlg_lib 		sing_1357.htm#IDX591	
numerDecom.lib		sing_1357.htm#IDX585	
numerDecom_lib		sing_1352.htm#IDX584	
numerDecom_lib 		sing_1357.htm#IDX586	
numerator		sing_312.htm#SEC352	
numerical irreducible decomposition		sing_1357.htm#IDX587	
nvars		sing_313.htm#SEC353	
olga.lib		sing_2653.htm#SEC2729	
olga_lib		sing_2653.htm#SEC2729	
oneDimBelongSemigroup	oneDimBelongSemigroup	sing_1129.htm#SEC1205	34399
oneNcfrac		sing_2610.htm#SEC2686	35654
online help	The online help system	sing_16.htm#SEC22	
open		sing_314.htm#SEC354	
opentex		sing_1772.htm#SEC1848	54236
operatorBM		sing_547.htm#SEC599	54875
operatorModulo		sing_548.htm#SEC600	26064
oppose		sing_473.htm#SEC513	
opposite		sing_474.htm#SEC514	
opposite polynomial		sing_358.htm#IDX231	
opposite ring		sing_358.htm#IDX228	
option		sing_315.htm#SEC355	
option(warn)		sing_70.htm#SEC110	
optionIsSet		sing_1019.htm#SEC1095	57325
or	Evaluation of logical expressions	sing_101.htm#SEC141	
or 		sing_411.htm#SEC451	
orbit		sing_1370.htm#IDX594	
orbit 		sing_1371.htm#IDX598	
orbit  		sing_1374.htm#IDX603	
orbit   		sing_1375.htm#IDX606	
orbitConeOrbits		sing_2434.htm#SEC2510	60979
orbitCones		sing_2425.htm#SEC2501	60528
orbit_variety		sing_1671.htm#SEC1747	22665
orbitparam.lib		sing_1370.htm#SEC1446	
orbitparam_lib		sing_1370.htm#SEC1446	
ord		sing_316.htm#SEC356	
ord_test		sing_1014.htm#SEC1090	36532
order ideal, border basis		sing_2694.htm#IDX1033	
order ideal, border basis 		sing_2695.htm#IDX1034	
orderings	General definitions for orderings	sing_859.htm#SEC911	
orderings introduction	Introduction to orderings	sing_858.htm#SEC910	
orderings, L		sing_866.htm#SEC918	
orderings, M		sing_863.htm#SEC915	
orderings, a		sing_865.htm#SEC917	
orderings, global		sing_860.htm#SEC912	
orderings, local		sing_861.htm#SEC913	
orderings, product		sing_864.htm#SEC916	
ordstr		sing_317.htm#SEC357	
origin		sing_2014.htm#SEC2090	31408
orthogonalize		sing_1085.htm#SEC1161	63711
outer		sing_1055.htm#SEC1131	64048
output		sing_41.htm#SEC71	
p-adic numbers		sing_32.htm#SEC46	
pFactor		sing_1904.htm#SEC1980	31504
pIntersect		sing_511.htm#SEC563	44055
pIntersectSyz		sing_512.htm#SEC564	45608
package		sing_149.htm#SEC189	
package declarations	package declarations	sing_150.htm#SEC190	
package related functions	package related functions	sing_151.htm#SEC191	
pairset		sing_1969.htm#SEC2045	38258
par		sing_318.htm#SEC358	
par2varRing		sing_896.htm#SEC972	44769
paraConic		sing_1385.htm#SEC1461	9828
paraPlaneCurve		sing_1379.htm#SEC1455	34094
parallel skeletons		sing_958.htm#IDX491	
parallel.lib		sing_958.htm#SEC1034	
parallelTestAND		sing_962.htm#SEC1038	1415
parallelTestOR		sing_963.htm#SEC1039	14920
parallelWaitAll		sing_961.htm#SEC1037	2017
parallelWaitFirst		sing_960.htm#SEC1036	32
parallelWaitN		sing_959.htm#SEC1035	38878
parallel_lib		sing_958.htm#SEC1034	
parallelization		sing_958.htm#IDX490	
parallelization 		sing_998.htm#IDX493	
parallelization  		sing_1031.htm#IDX503	
param		sing_1562.htm#SEC1638	57220
parameter, as numbers		sing_144.htm#SEC184	
parameterSubstitute		sing_2161.htm#SEC2237	63147
parametric annihilator		sing_540.htm#IDX335	
parametric annihilator for variety		sing_596.htm#IDX358	
parametric ideal		sing_924.htm#IDX423	
parametric ideal 		sing_931.htm#IDX442	
parametric ideal  		sing_931.htm#IDX444	
parametric ideal   		sing_932.htm#IDX449	
parametrization		sing_1370.htm#IDX595	
parametrization 		sing_1374.htm#IDX604	
parametrization  		sing_1562.htm#IDX756	
parametrizeOrbit		sing_1374.htm#SEC1450	26969
paraplanecurves.lib		sing_1376.htm#SEC1452	
paraplanecurves_lib		sing_1376.htm#SEC1452	
pardeg		sing_319.htm#SEC359	
parstr		sing_320.htm#SEC360	
part		sing_2307.htm#SEC2383	31485
partOver		sing_2310.htm#SEC2386	25555
partUnder		sing_2311.htm#SEC2387	13123
partial_molien		sing_1649.htm#SEC1725	21772
partitions		sing_1150.htm#SEC1226	48089
partitions 		sing_1150.htm#IDX536	
path integral		sing_1142.htm#IDX523	
pause		sing_955.htm#SEC1031	2273
pdivi		sing_926.htm#SEC1002	21786
pdivi 		sing_927.htm#IDX433	
pdivisorplus		sing_2373.htm#SEC2449	47486
permcol		sing_1068.htm#SEC1144	12886
permrow		sing_1069.htm#SEC1145	26561
permutationFromIntvec	permutationFromIntvec	sing_2440.htm#SEC2516	6533
permutationToIntvec		sing_2441.htm#SEC2517	1989
permutations		sing_1151.htm#IDX537	
permutations, sum, max, min		sing_2342.htm#IDX943	
permute		sing_1151.htm#SEC1227	40893
permute_L		sing_1807.htm#SEC1883	10716
perron		sing_751.htm#SEC803	3782
perron.lib		sing_750.htm#SEC802	
perron_lib		sing_750.htm#SEC802	
phindex.lib		sing_2221.htm#IDX904	
phindex_lib		sing_2221.htm#IDX905	
picksFormula		sing_2083.htm#SEC2159	14656
pid		sing_358.htm#IDX240	
plainInvariants		sing_1521.htm#SEC1597	40916
planeCur		sing_2329.htm#SEC2405	sprintf
plot		sing_1785.htm#SEC1861	46610
plotRot		sing_1789.htm#SEC1865	57150
plotRotated		sing_1788.htm#SEC1864	33009
plotRotatedDirect		sing_1791.htm#SEC1867	18202
plotRotatedList		sing_1790.htm#SEC1866	41668
plotRotatedListFromSpecifyList	plotRotatedListFromSpecifyList	sing_1792.htm#SEC1868	38856
plural		sing_1021.htm#IDX498	
pmat		sing_949.htm#SEC1025	3857
pnormalf		sing_927.htm#SEC1003	26174
pointid.lib		sing_1285.htm#SEC1361	
pointid_lib		sing_1285.htm#SEC1361	
polSol		sing_786.htm#SEC838	323
polSolFiniteRank		sing_787.htm#SEC839	30875
pollTask		sing_1041.htm#SEC1117	53950
poly		sing_152.htm#SEC192	
poly (plural)		sing_438.htm#SEC478	
poly declarations		sing_153.htm#SEC193	
poly declarations (plural)	poly declarations (plural)	sing_439.htm#SEC479	
poly expressions		sing_154.htm#SEC194	
poly expressions (plural)	poly expressions (plural)	sing_440.htm#SEC480	
poly operations		sing_155.htm#SEC195	
poly operations (plural)	poly operations (plural)	sing_441.htm#SEC481	
poly related functions	poly related functions	sing_156.htm#SEC196	
poly related functions (plural)	poly related functions (plural)	sing_442.htm#SEC482	
poly.lib		sing_964.htm#SEC1040	
poly2list		sing_589.htm#SEC641	4960
poly2zdd		sing_2242.htm#SEC2318	61839
polyInterpolation		sing_2376.htm#SEC2452	45866
polyVars		sing_793.htm#SEC845	43882
poly_lib		sing_964.htm#SEC1040	
polybori		sing_2226.htm#IDX909	
polybori.lib		sing_2226.htm#IDX906	
polybori.lib 		sing_2226.htm#IDX910	
polybori_lib		sing_2226.htm#IDX907	
polymake		sing_2071.htm#IDX810	
polymake.lib		sing_2071.htm#SEC2147	
polymakePolytope		sing_2072.htm#SEC2148	47302
polymake_lib		sing_2071.htm#SEC2147	
polynomial solutions		sing_780.htm#IDX386	
polynomial, opposite		sing_358.htm#IDX232	
polytope		sing_190.htm#SEC230	
polytope 		sing_2071.htm#IDX806	
polytopeViaInequalities	polytopeViaInequalities	sing_2044.htm#SEC2120	52084
polytopeViaPoints		sing_2045.htm#SEC2121	281
pos_def		sing_1096.htm#SEC1172	4994
poset		sing_2211.htm#IDX895	
positiveOrthant		sing_2015.htm#SEC2091	42102
posweight		sing_1629.htm#SEC1705	3364
powSumSym		sing_2264.htm#SEC2340	2339
power		sing_1056.htm#SEC1132	23365
power set		sing_2344.htm#IDX945	
powerN		sing_1888.htm#SEC1964	20170
powerX		sing_1897.htm#SEC1973	47971
power_products		sing_1663.htm#SEC1739	54629
powerpolyX		sing_1867.htm#SEC1943	37247
powersums		sing_1990.htm#SEC2066	59049
preComp		sing_1221.htm#SEC1297	16160
preimage		sing_321.htm#SEC361	
preimage 		sing_717.htm#IDX361	
preimage (plural)		sing_475.htm#SEC515	
preimage under a map between local rings, map between local rings, map between local and global rings	preimageLoc	sing_1017.htm#IDX496	
preimageLattice		sing_2569.htm#SEC2645	37348
preimageLoc		sing_1017.htm#SEC1093	33315
preimageNC		sing_719.htm#SEC771	16037
prepEmbDiv		sing_1447.htm#SEC1523	36708
prepMat		sing_1700.htm#SEC1776	39868
prepRealclassify		sing_1505.htm#SEC1581	10994
prepSV		sing_1802.htm#SEC1878	50095
prepareAss		sing_1304.htm#SEC1380	21802
presentTree		sing_1434.htm#SEC1510	10731
presentation		sing_2527.htm#SEC2603	40323
presolve.lib		sing_1710.htm#SEC1786	
presolve_lib		sing_1710.htm#SEC1786	
primL		sing_1892.htm#SEC1968	14513
primList		sing_1891.htm#SEC1967	6802
primRoot		sing_1344.htm#SEC1420	14210
primTest		sing_1220.htm#SEC1296	8105
primary decomposition		sing_1289.htm#IDX576	
primary decomposition 		sing_1312.htm#IDX577	
primary decomposition of modules		sing_1210.htm#IDX558	
primary decomposition, numerical		sing_1357.htm#IDX589	
primary_char0		sing_1653.htm#SEC1729	61413
primary_char0_no_molien	primary_char0_no_molien	sing_1655.htm#SEC1731	50477
primary_char0_no_molien_random	primary_char0_no_molien_random	sing_1660.htm#SEC1736	8422
primary_char0_random	primary_char0_random	sing_1658.htm#SEC1734	5996
primary_charp		sing_1654.htm#SEC1730	37863
primary_charp_no_molien	primary_charp_no_molien	sing_1656.htm#SEC1732	32282
primary_charp_no_molien_random	primary_charp_no_molien_random	sing_1661.htm#SEC1737	11498
primary_charp_random	primary_charp_random	sing_1659.htm#SEC1735	24739
primary_charp_without	primary_charp_without	sing_1657.htm#SEC1733	49585
primary_charp_without_random	primary_charp_without_random	sing_1662.htm#SEC1738	36998
primary_invariants		sing_1641.htm#SEC1717	5500
primary_invariants_random	primary_invariants_random	sing_1642.htm#SEC1718	28958
primdec.lib		sing_1289.htm#SEC1365	
primdecGTZ		sing_1291.htm#SEC1367	6091
primdecGTZE		sing_1292.htm#SEC1368	64882
primdecMon		sing_1209.htm#SEC1285	3856
primdecSY		sing_1293.htm#SEC1369	6547
primdecSYE		sing_1294.htm#SEC1370	52788
primdecZ		sing_1313.htm#SEC1389	48194
primdecZM		sing_1314.htm#SEC1390	17214
primdec_lib		sing_1289.htm#SEC1365	
primdecint.lib		sing_1312.htm#SEC1388	
primdecint_lib		sing_1312.htm#SEC1388	
prime		sing_322.htm#SEC362	
primeClosure		sing_1248.htm#SEC1324	43589
primecoeffs		sing_919.htm#SEC995	46153
primefactors		sing_323.htm#SEC363	
primes		sing_914.htm#SEC990	24408
primitiv.lib		sing_1320.htm#SEC1396	
primitiv_lib		sing_1320.htm#SEC1396	
primitive		sing_1321.htm#SEC1397	36163
primitive element		sing_1321.htm#IDX578	
primitiveSpan		sing_2576.htm#SEC2652	sprintf
primitive_extra		sing_1322.htm#SEC1398	49025
primparam		sing_1516.htm#SEC1592	35357
principal intersection		sing_505.htm#IDX319	
print		sing_324.htm#SEC364	
print 		sing_2178.htm#IDX830	
printBetti		sing_2508.htm#SEC2584	28941
printFreeModule		sing_2500.htm#SEC2576	13316
printGraph		sing_1144.htm#SEC1220	45041
printGraphG		sing_2724.htm#SEC2800	48742
printGroup		sing_2557.htm#SEC2633	6791
printHom		sing_2503.htm#SEC2579	7070
printMatrix		sing_2499.htm#SEC2575	15522
printModule		sing_2502.htm#SEC2578	sprintf
printMoebius		sing_2217.htm#SEC2293	45828
printResolution		sing_2501.htm#SEC2577	29278
printSheaf		sing_2712.htm#SEC2788	31762
printStack		sing_2726.htm#SEC2802	3692
printTask		sing_1036.htm#SEC1112	54549
printVariety		sing_2704.htm#SEC2780	2846
printf		sing_325.htm#SEC365	2294
printlevel		sing_400.htm#SEC440	
proc		sing_157.htm#SEC197	
proc declaration		sing_158.htm#SEC198	
proc expression		sing_159.htm#SEC199	
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_160.htm#SEC200	
prodcrit		sing_1967.htm#SEC2043	56231
product		sing_915.htm#SEC991	54431
product variety, abstract variety		sing_2705.htm#IDX1049	
productVariety		sing_2705.htm#SEC2781	54191
productgroup		sing_2578.htm#SEC2654	55937
progress watch		sing_315.htm#IDX163	
projectLattice		sing_2570.htm#SEC2646	28463
projective bundle, abstract variety, sheaf, enumeration of conics	projectiveBundle	sing_2709.htm#IDX1053	
projective dimension	purityfiltration_lib	sing_758.htm#IDX370	
projective limes		sing_32.htm#SEC46	
projective space, abstract variety		sing_2708.htm#IDX1052	
projectiveBundle		sing_2709.htm#SEC2785	13791
projectiveDimension		sing_759.htm#SEC811	8165
projectiveSpace		sing_2708.htm#SEC2784	21729
prompt		sing_15.htm#SEC21	
prompt, option		sing_315.htm#IDX182	
propagator		sing_1142.htm#IDX521	42460
propagator 		sing_1145.htm#SEC1221	
prot, option		sing_315.htm#IDX161	
protocol of computations		sing_315.htm#IDX162	
proximitymatrix		sing_1475.htm#SEC1551	58403
prune		sing_326.htm#SEC366	
pruneModule		sing_2534.htm#SEC2610	51453
prwalk		sing_2699.htm#SEC2775	46963
psigncnd		sing_1763.htm#SEC1839	57734
puiseux2generators		sing_1574.htm#SEC1650	64508
puiseuxExpansion		sing_2132.htm#SEC2208	46277
pure tensor		sing_498.htm#IDX307	
purelist		sing_769.htm#SEC821	15517
purity	purityfiltration_lib	sing_758.htm#IDX372	
purityFiltration		sing_760.htm#SEC812	5742
purityTriang		sing_761.htm#SEC813	3665
purityfiltration.lib	purityfiltration_lib	sing_758.htm#IDX365	
purityfiltration_lib	purityfiltration_lib	sing_758.htm#IDX366	
pushForward		sing_2595.htm#SEC2671	26697
pwalk		sing_1158.htm#SEC1234	61187
pyobject		sing_191.htm#SEC231	
pyobject 		sing_2226.htm#IDX912	
pyobject declarations	pyobject declarations	sing_192.htm#SEC232	
pyobject expressions	pyobject expressions	sing_193.htm#SEC233	
pyobject operations		sing_194.htm#SEC234	
pyobject related functions	pyobject related functions	sing_195.htm#SEC235	
pyramid		sing_2392.htm#SEC2468	7421
python_eval		sing_196.htm#SEC236	
python_import		sing_197.htm#SEC237	
python_run		sing_198.htm#SEC238	
qbase		sing_1993.htm#SEC2069	8633
qepcad		sing_2402.htm#SEC2478	39171
qepcadsystem		sing_2403.htm#SEC2479	31977
qhmatrix		sing_1627.htm#SEC1703	61813
qhmoduli.lib		sing_1591.htm#SEC1667	
qhmoduli_lib		sing_1591.htm#SEC1667	
qhspectrum		sing_1614.htm#SEC1690	13732
qhweight		sing_327.htm#SEC367	
qmatrix.lib		sing_752.htm#SEC804	
qmatrix_lib		sing_752.htm#SEC804	
qminor		sing_754.htm#SEC806	52670
qrds		sing_328.htm#SEC368	
qring	Miscellaneous oddities	sing_166.htm#SEC206	
qring 		sing_418.htm#IDX295	
qring (plural)		sing_443.htm#SEC483	
qring declaration		sing_170.htm#SEC210	
qring declaration (plural)	qring declaration (plural)	sing_444.htm#SEC484	
qring related functions (plural)	qring related functions (plural)	sing_445.htm#SEC485	
qring ring ideal 'factor ring'		sing_1026.htm#IDX502	
qringNF, option		sing_315.htm#IDX164	
qslimgb		sing_895.htm#SEC971	51999
quadraticSieve		sing_1905.htm#SEC1981	58557
quantMat		sing_753.htm#SEC805	56227
quickclass		sing_1497.htm#SEC1573	14018
quit		sing_390.htm#SEC430	
quotSheaf		sing_2721.htm#SEC2797	49619
quote		sing_329.htm#SEC369	
quotient		sing_330.htm#SEC370	
quotient (plural)		sing_476.htm#SEC516	
quotientLatticeBasis	quotientLatticeBasis	sing_2046.htm#SEC2122	15613
quotientMain		sing_1755.htm#SEC1831	39870
quotientMon		sing_1200.htm#SEC1276	57149
rHRR		sing_2304.htm#SEC2380	20131
rJanet		sing_2696.htm#SEC2772	30716
rMacaulay		sing_950.htm#SEC1026	45499
rad_con		sing_977.htm#SEC1053	21777
radical		sing_1301.htm#SEC1377	1407
radicalEHV		sing_1302.htm#SEC1378	33703
radicalMemberShip		sing_2154.htm#SEC2230	28527
radicalMon		sing_1201.htm#SEC1277	64912
radicalZ		sing_1316.htm#SEC1392	5783
randcharpoly		sing_1987.htm#SEC2063	37737
randlinpoly		sing_1989.htm#SEC2065	22330
random		sing_331.htm#SEC371	
random 		sing_358.htm#IDX244	
random  		sing_2199.htm#IDX869	
random   		sing_2200.htm#IDX871	
random number generator, seed		sing_358.htm#IDX242	
random.lib		sing_985.htm#SEC1061	
randomBinomial		sing_997.htm#SEC1073	17913
randomCheck		sing_1818.htm#SEC1894	20973
randomLast		sing_996.htm#SEC1072	2046
randomPoint		sing_2047.htm#SEC2123	22561
randomPolyInT		sing_2163.htm#SEC2239	2264
random_lib		sing_985.htm#SEC1061	
randomid		sing_987.htm#SEC1063	7815
randommat		sing_988.htm#SEC1064	33569
rank		sing_209.htm#IDX137	
rank 		sing_332.htm#SEC372	
rankSheaf		sing_2713.htm#SEC2789	11850
ratSol		sing_788.htm#SEC840	62488
ratgb.lib		sing_778.htm#IDX375	
ratgb_lib		sing_778.htm#IDX376	
rational curves, rational parametrization of rational curves.	paraPlaneCurve	sing_1379.htm#IDX616	
rational normal curve, projection.		sing_1380.htm#IDX617	
rational normal curve, projection. 		sing_1383.htm#IDX618	
rational normal curve, projection.  		sing_1384.htm#IDX619	
rational solutions		sing_780.htm#IDX387	
rational univariate projection		sing_1987.htm#IDX803	
rationalCurve		sing_2733.htm#SEC2809	61201
rationalPointConic		sing_1381.htm#SEC1457	9761
ratstd		sing_779.htm#SEC831	61346
rays		sing_2048.htm#SEC2124	44445
rcolon		sing_2603.htm#SEC2679	1208
re2squ		sing_1358.htm#SEC1434	24350
read		sing_333.htm#SEC373	
readNmzData		sing_1276.htm#SEC1352	18957
reading, option		sing_315.htm#IDX183	
readline		sing_1.htm#IDX5	
real		sing_28.htm#IDX74	
real root isolation		sing_2680.htm#IDX1028	
real roots, univariate polynomial		sing_1994.htm#IDX805	
real roots, univariate projection		sing_1978.htm#IDX801	
real roots,sign conditions		sing_1761.htm#IDX781	
realclassify		sing_2675.htm#SEC2751	51416
realclassify.lib		sing_2674.htm#SEC2750	
realclassify_lib		sing_2674.htm#SEC2750	
realizationDim		sing_2126.htm#SEC2202	37756
realizationDimPoly		sing_2128.htm#SEC2204	3611
realizationMatroids.lib	realizationMatroids_lib	sing_2125.htm#SEC2201	
realizationMatroids_lib	realizationMatroids_lib	sing_2125.htm#SEC2201	
realmorsesplit		sing_2676.htm#SEC2752	16318
realpoly		sing_1325.htm#SEC1401	9453
realrad		sing_1327.htm#SEC1403	43381
realrad.lib		sing_1324.htm#SEC1400	
realrad_lib		sing_1324.htm#SEC1400	
realzero		sing_1326.htm#SEC1402	12712
recursive_boolean_poly	recursive_boolean_poly	sing_2232.htm#SEC2308	17045
recursive_from_boolean_poly	recursive_from_boolean_poly	sing_2238.htm#SEC2314	37794
redSB, option		sing_315.htm#IDX165	
redTail, option		sing_315.htm#IDX167	
redThrough, option		sing_315.htm#IDX168	
redefine, option		sing_315.htm#IDX184	
reduce		sing_334.htm#SEC374	
reduce 		sing_519.htm#IDX324	
reduce  		sing_926.htm#IDX431	
reduce   		sing_927.htm#IDX434	
reduce (plural)		sing_477.htm#SEC517	
reduce (up to a bound)		sing_358.htm#IDX245	
reduceIntChain		sing_2539.htm#SEC2615	17776
reduced		sing_925.htm#IDX428	
reduced standard basis		sing_315.htm#IDX166	
reduction		sing_1679.htm#SEC1755	31048
reesclos.lib		sing_1328.htm#SEC1404	
reesclos_lib		sing_1328.htm#SEC1404	
reference		sing_199.htm#SEC239	
reference declarations	reference declarations	sing_200.htm#SEC240	
reference expressions	reference expressions	sing_201.htm#SEC241	
reference operations	reference and shared operations	sing_204.htm#SEC244	
reference related functions	reference and shared related functions	sing_205.htm#SEC245	
regCM		sing_1240.htm#SEC1316	25488
regIdeal		sing_1226.htm#SEC1302	3827
regMonCurve		sing_1229.htm#SEC1305	41311
regularity	Syzygies and resolutions	sing_335.htm#SEC375	
regularity 		sing_870.htm#SEC927	
reiffen		sing_558.htm#SEC610	32856
rel_orbit_variety		sing_1672.htm#SEC1748	34278
relations		sing_750.htm#IDX364	
relativeInteriorPoint	relativeInteriorPoint	sing_2049.htm#SEC2125	30097
relative_orbit_variety	relative_orbit_variety	sing_1673.htm#SEC1749	32995
relweight		sing_1628.htm#SEC1704	10658
remainder		sing_1748.htm#SEC1824	1191
remainderMain		sing_1756.htm#SEC1832	3532
removeCone		sing_2067.htm#SEC2143	33877
removepower		sing_1485.htm#SEC1561	47644
repart		sing_336.htm#SEC376	
replace		sing_1857.htm#SEC1933	50075
representation, math objects	Representation of mathematical objects	sing_856.htm#SEC908	
res		sing_337.htm#SEC377	10393
resbinomial.lib		sing_1388.htm#IDX622	
resbinomial_lib		sing_1388.htm#IDX623	
reservedName		sing_338.htm#SEC378	
resfunction		sing_1402.htm#SEC1478	59312
resgraph.lib		sing_1420.htm#SEC1496	
resgraph_lib		sing_1420.htm#SEC1496	
resjung.lib		sing_1424.htm#SEC1500	
resjung_lib		sing_1424.htm#SEC1500	
reslist		sing_1416.htm#SEC1492	64950
resolution	purityfiltration_lib	sing_161.htm#SEC201	
resolution 		sing_758.htm#IDX371	
resolution (plural)		sing_446.htm#SEC486	
resolution declarations	resolution declarations	sing_162.htm#SEC202	
resolution declarations (plural)	resolution declarations (plural)	sing_447.htm#SEC487	
resolution expressions	resolution expressions	sing_163.htm#SEC203	
resolution expressions (plural)	resolution expressions (plural)	sing_448.htm#SEC488	
resolution graph		sing_1470.htm#IDX636	
resolution related functions	resolution related functions	sing_164.htm#SEC204	
resolution related functions (plural)	resolution related functions (plural)	sing_449.htm#SEC489	
resolution, La Scala's method		sing_288.htm#SEC328	
resolution, computation of		sing_337.htm#IDX186	
resolution, hilbert-driven		sing_263.htm#SEC303	
resolutionInLocalization	resolutionInLocalization	sing_2419.htm#SEC2495	31106
resolutiongraph		sing_1471.htm#SEC1547	32697
resolve		sing_1432.htm#SEC1508	27374
resolve.lib		sing_1428.htm#SEC1504	
resolve_lib		sing_1428.htm#SEC1504	
resources.lib		sing_998.htm#SEC1074	
resources_lib		sing_998.htm#SEC1074	
restriction		sing_2192.htm#IDX857	
restriction 		sing_2208.htm#IDX890	
restriction  		sing_2209.htm#IDX892	
restriction of		sing_563.htm#IDX347	
restrictionIdeal		sing_573.htm#SEC625	49796
restrictionModule		sing_574.htm#SEC626	62461
resultant		sing_302.htm#SEC342	
resultant 		sing_339.htm#SEC379	
reszeta.lib		sing_1441.htm#SEC1517	
reszeta_lib		sing_1441.htm#SEC1517	
return		sing_391.htm#SEC431	
return type of procedures	Return type of procedures	sing_416.htm#SEC456	
returnSB, option		sing_315.htm#IDX152	
reverse		sing_2008.htm#SEC2084	35880
reverse lexicographical ordering		sing_860.htm#IDX392	
reynolds_molien		sing_1648.htm#SEC1724	45316
rho		sing_1899.htm#SEC1975	51414
rightInverse		sing_1837.htm#SEC1913	6558
rightKernel		sing_1835.htm#SEC1911	46603
rightModulo		sing_737.htm#SEC789	12618
rightNF		sing_736.htm#SEC788	42610
rightNFWeyl		sing_805.htm#SEC857	35828
rightOre		sing_2660.htm#SEC2736	56918
rightStd		sing_735.htm#SEC787	5740
ring		sing_165.htm#SEC205	
ring (plural)		sing_450.htm#SEC490	
ring coefficients	hasTransExtensionCoefficient	sing_1024.htm#IDX500	
ring coefficients 		sing_1025.htm#IDX501	
ring declarations		sing_167.htm#SEC207	
ring declarations (plural)	ring declarations (plural)	sing_451.htm#SEC491	
ring operations		sing_169.htm#SEC209	
ring operations (plural)	ring operations (plural)	sing_452.htm#SEC492	
ring related functions	ring related functions	sing_168.htm#SEC208	
ring related functions (plural)	ring related functions (plural)	sing_453.htm#SEC493	
ring, opposite		sing_358.htm#IDX229	
ring.lib		sing_1003.htm#SEC1079	
ring_cf		sing_209.htm#IDX138	
ring_lib		sing_1003.htm#SEC1079	
ring_list		sing_341.htm#SEC381	
ring_variable		sing_2179.htm#IDX834	
ring_variable 		sing_2180.htm#IDX836	
ring_variable  		sing_2181.htm#IDX840	
ring_variable   		sing_2182.htm#IDX842	
ringlist		sing_340.htm#SEC380	
ringlist (plural)		sing_478.htm#SEC518	
ringtensor		sing_1015.htm#SEC1091	56648
ringweights		sing_1016.htm#SEC1092	33307
rinvar.lib		sing_1684.htm#SEC1760	
rinvar_lib		sing_1684.htm#SEC1760	
rmNmzFiles		sing_1281.htm#SEC1357	32601
rm_unitcol		sing_1074.htm#SEC1150	5591
rm_unitrow		sing_1073.htm#SEC1149	35694
rmx		sing_1782.htm#SEC1858	17675
rncAntiCanonicalMap		sing_1380.htm#SEC1456	41965
rncItProjEven		sing_1384.htm#SEC1460	18200
rncItProjOdd		sing_1383.htm#SEC1459	61976
root of Bernstein-Sato polynomial		sing_540.htm#IDX336	
rootIsolation		sing_2691.htm#SEC2767	34513
rootIsolationNoPreprocessing	rootIsolationNoPreprocessing	sing_2690.htm#SEC2766	42387
rootIsolationPrimdec	rootIsolationPrimdec	sing_2692.htm#SEC2768	35485
rootisolation.lib		sing_2680.htm#SEC2756	
rootisolation_lib		sing_2680.htm#SEC2756	
rootofUnity		sing_1018.htm#SEC1094	21365
roots		sing_1749.htm#SEC1825	18436
rootsMain		sing_1757.htm#SEC1833	54934
rootsModp		sing_1881.htm#SEC1957	47315
rootsmr.lib		sing_1978.htm#SEC2054	
rootsmr_lib		sing_1978.htm#SEC2054	
rootsur.lib		sing_1994.htm#SEC2070	
rootsur_lib		sing_1994.htm#SEC2070	
round		sing_1879.htm#SEC1955	9248
rowShift		sing_209.htm#IDX141	
rowShift 		sing_211.htm#SEC251	
rowred		sing_1070.htm#SEC1146	63416
rp, global ordering		sing_860.htm#IDX391	
rstandard.lib		sing_2693.htm#SEC2769	
rstandard_lib		sing_2693.htm#SEC2769	
rswalk		sing_2743.htm#SEC2819	50903
rtimer		sing_404.htm#SEC444	
rvalue	No rvalue of increments and assignments	sing_410.htm#SEC450	
rvar		sing_342.htm#SEC382	
rwalk		sing_2700.htm#SEC2776	42525
rwalk.lib		sing_2698.htm#SEC2774	
rwalk_lib		sing_2698.htm#SEC2774	
sRes		sing_2505.htm#SEC2581	23381
sa_poly_reduce		sing_528.htm#SEC580	60856
sa_reduce		sing_527.htm#SEC579	55799
sagbi		sing_1334.htm#SEC1410	46653
sagbi basis		sing_2332.htm#IDX942	
sagbi.lib		sing_1331.htm#SEC1407	
sagbiAlg		sing_2325.htm#SEC2401	sprintf
sagbiMod		sing_2326.htm#SEC2402	sprintf
sagbiPart		sing_1335.htm#SEC1411	56066
sagbiReduce		sing_1333.htm#SEC1409	19036
sagbiSPoly		sing_1332.htm#SEC1408	17365
sagbi_lib		sing_1331.htm#SEC1407	
salida		sing_1413.htm#SEC1489	9839
sameComponent		sing_1961.htm#SEC2037	13540
sameQ		sing_1760.htm#SEC1836	45579
sat		sing_1139.htm#SEC1215	6266
satiety		sing_1228.htm#SEC1304	34323
satstd		sing_2220.htm#SEC2296	16128
sba		sing_343.htm#SEC383	
scalarProd		sing_517.htm#SEC569	54488
scheme		sing_2383.htm#SEC2459	15722
schubert.lib		sing_2702.htm#SEC2778	
schubert_lib		sing_2702.htm#SEC2778	
sdb, source code debugger	Source code debugger	sing_66.htm#SEC103	
second degree		sing_942.htm#IDX479	
secondary fan		sing_2071.htm#IDX808	
secondary polytope		sing_2071.htm#IDX809	
secondaryPolytope		sing_2076.htm#SEC2152	48451
secondary_and_irreducibles_no_molien	secondary_and_irreducibles_no_molien	sing_1669.htm#SEC1745	37058
secondary_char0		sing_1664.htm#SEC1740	31029
secondary_charp		sing_1666.htm#SEC1742	16364
secondary_no_molien		sing_1667.htm#SEC1743	3616
secondary_not_cohen_macaulay	secondary_not_cohen_macaulay	sing_1670.htm#SEC1746	31675
segre		sing_2259.htm#SEC2335	44035
select		sing_1140.htm#SEC1216	17096
select1		sing_1141.htm#SEC1217	32617
semaphore		sing_358.htm#IDX249	44342
semaphore 		sing_1002.htm#SEC1078	
semaphores		sing_998.htm#IDX495	
semiCMcod2		sing_1625.htm#SEC1701	15905
semiGroup		sing_2327.htm#SEC2403	sprintf
semiMod		sing_2328.htm#SEC2404	sprintf
semidiv		sing_1953.htm#SEC2029	58107
semigroup		sing_1474.htm#SEC1550	29045
semigroup 		sing_1478.htm#IDX643	
semigroup of values		sing_1564.htm#IDX758	
semigroupGenerator		sing_2050.htm#SEC2126	59446
sep		sing_1311.htm#SEC1387	sprintf
separateHNE		sing_1575.htm#SEC1651	12052
separator		sing_1211.htm#SEC1287	33000
serreRelations		sing_658.htm#SEC710	33994
set		sing_2174.htm#IDX820	
setBaseMultigrading		sing_2550.htm#SEC2626	6575
setLetterplaceAttributes	setLetterplaceAttributes	sing_648.htm#SEC700	5759
setLinearForms		sing_2051.htm#SEC2127	62731
setModuleGrading		sing_2562.htm#SEC2638	59018
setMultiplicity		sing_2052.htm#SEC2128	27537
setNmzDataPath		sing_1278.htm#SEC1354	18123
setNmzExecPath		sing_1274.htm#SEC1350	38993
setNmzFilename		sing_1277.htm#SEC1353	20206
setNmzOption		sing_1271.htm#SEC1347	9012
setUniformizingParameter	setUniformizingParameter	sing_2745.htm#SEC2821	63635
set_is_injective		sing_1941.htm#SEC2017	8429
setcores		sing_1000.htm#SEC1076	49704
setenv		sing_358.htm#IDX252	
setinitials		sing_2393.htm#SEC2469	24792
setring		sing_344.htm#SEC384	
sh		sing_358.htm#IDX254	
shared		sing_199.htm#SEC239	
shared declarations		sing_202.htm#SEC242	
shared expressions		sing_203.htm#SEC243	
shared operations	reference and shared operations	sing_204.htm#SEC244	
shared related functions	reference and shared related functions	sing_205.htm#SEC245	
sheaf cohomology		sing_1451.htm#IDX624	
sheafCoh		sing_1457.htm#SEC1533	64501
sheafCohBGG		sing_1455.htm#SEC1531	13439
sheafCohBGG2		sing_1456.htm#SEC1532	3338
sheafcoh.lib		sing_1451.htm#SEC1527	
sheafcoh_lib		sing_1451.htm#SEC1527	
shiftPoly		sing_651.htm#SEC703	65223
short		sing_401.htm#SEC441	
show		sing_951.htm#SEC1027	15599
showBO		sing_1433.htm#SEC1509	20089
showDataTypes		sing_1435.htm#SEC1511	4270
showNmzOptions		sing_1272.htm#SEC1348	64955
showNuminvs		sing_1269.htm#SEC1345	18934
showgrades		sing_763.htm#SEC815	48081
showrecursive		sing_952.htm#SEC1028	6127
sickle		sing_624.htm#SEC676	54811
signal handler		sing_2761.htm#SEC2850	
signatureBrieskorn		sing_1634.htm#SEC1710	26283
signatureL		sing_2222.htm#SEC2298	65493
signatureLqf		sing_2223.htm#SEC2299	18811
signatureNemethi		sing_1636.htm#SEC1712	21981
signaturePuiseux		sing_1635.htm#SEC1711	23398
signcnd		sing_1762.htm#SEC1838	40147
signcond.lib		sing_1761.htm#SEC1837	
signcond_lib		sing_1761.htm#SEC1837	
simplePrune		sing_2543.htm#SEC2619	sprintf
simplesolver		sing_1706.htm#SEC1782	13418
simplex		sing_345.htm#SEC385	
simplexOut		sing_1733.htm#SEC1809	56099
simplify		sing_346.htm#SEC386	
simplifyRat		sing_800.htm#SEC852	52658
sing.lib		sing_1601.htm#SEC1677	
sing4ti2.lib		sing_1337.htm#SEC1413	
sing4ti2_lib		sing_1337.htm#SEC1413	
sing_lib		sing_1601.htm#SEC1677	
singular locus of D-module		sing_780.htm#IDX381	
singularities		sing_1533.htm#IDX660	
singularities 		sing_1534.htm#IDX671	
singularities  		sing_1535.htm#IDX674	
singularities   		sing_1536.htm#IDX677	
singularities    		sing_1537.htm#IDX680	
singularities     		sing_1538.htm#IDX684	
singularities      		sing_1539.htm#IDX688	
singularities       		sing_1540.htm#IDX694	
singularities        		sing_1541.htm#IDX702	
singularities         		sing_1542.htm#IDX708	
singularities          		sing_1543.htm#IDX716	
singularities           		sing_1544.htm#IDX726	
singularities            		sing_1632.htm#IDX773	
singularities             		sing_2321.htm#IDX937	
singularities, resolution of	Resolution of singularities	sing_843.htm#SEC895	
singularity		sing_1498.htm#SEC1574	23002
singularrc		sing_20.htm#IDX73	
size	Miscellaneous oddities	sing_347.htm#SEC387	
size 		sing_418.htm#IDX294	
skewmat		sing_1057.htm#SEC1133	2167
sleep		sing_353.htm#SEC393	
slimgb		sing_348.htm#SEC388	
slimgb 		sing_820.htm#SEC872	
slimgb (plural)		sing_479.htm#SEC519	
slocus		sing_1613.htm#SEC1689	27853
smith		sing_1846.htm#SEC1922	61915
smithNormalForm		sing_2598.htm#SEC2674	7174
solutionsMod2		sing_1896.htm#SEC1972	53360
solve		sing_942.htm#IDX480	3078
solve 		sing_1727.htm#SEC1803	
solve a linear equation system A*x = b via the LU-decomposition of A	lusolve	sing_291.htm#SEC331	
solve.lib		sing_1725.htm#SEC1801	
solveTInitialFormPar	solveTInitialFormPar	sing_2157.htm#SEC2233	36670
solve_IP		sing_1184.htm#SEC1260	59518
solve_lib		sing_1725.htm#SEC1801	
solvelinearpart		sing_1720.htm#SEC1796	42872
sort		sing_916.htm#SEC992	58207
sortIntvec		sing_595.htm#SEC647	60798
sortandmap		sing_1721.htm#SEC1797	10314
sortier		sing_1683.htm#SEC1759	3555
sortvars		sing_1722.htm#SEC1798	61778
sortvec		sing_349.htm#SEC389	
source		sing_2521.htm#SEC2597	63163
source code debugger, sdb	Source code debugger	sing_66.htm#SEC103	
spaceCur		sing_2330.htm#SEC2406	sprintf
spadd		sing_1547.htm#SEC1623	48739
span		sing_2053.htm#SEC2129	64343
sparseHomogIdeal		sing_994.htm#SEC1070	22631
sparseInterpolation		sing_2378.htm#SEC2454	28771
sparseid		sing_989.htm#SEC1065	20824
sparsemat		sing_991.htm#SEC1067	17653
sparsematrix		sing_990.htm#SEC1066	41031
sparsepoly		sing_992.htm#SEC1068	21649
sparsetriag		sing_993.htm#SEC1069	50657
spcurve.lib		sing_1621.htm#SEC1697	
spcurve_lib		sing_1621.htm#SEC1697	
special characters, non-english		sing_407.htm#IDX287	
spectral pairs		sing_1533.htm#IDX669	
spectral pairs 		sing_1540.htm#IDX701	
spectral pairs  		sing_1542.htm#IDX715	
spectral pairs   		sing_1543.htm#IDX724	
spectral pairs    		sing_1555.htm#IDX740	
spectral pairs     		sing_1557.htm#IDX751	
spectralNeg		sing_1443.htm#SEC1519	36691
spectrum		sing_1533.htm#IDX668	47545
spectrum 		sing_1539.htm#SEC1615	
spectrum  		sing_1539.htm#IDX693	
spectrum   		sing_1540.htm#IDX700	
spectrum    		sing_1541.htm#IDX707	
spectrum     		sing_1542.htm#IDX714	
spectrum      		sing_1543.htm#IDX723	
spectrum       		sing_1555.htm#IDX739	
spectrum        		sing_1557.htm#IDX750	
spectrum         		sing_1632.htm#IDX775	
spectrum.lib		sing_1631.htm#SEC1707	
spectrum_lib		sing_1631.htm#SEC1707	
spectrumnd		sing_1632.htm#SEC1708	29943
spgamma		sing_1554.htm#SEC1630	59653
spgeomgenus		sing_1553.htm#SEC1629	57796
spissemicont		sing_1550.htm#SEC1626	23679
split		sing_953.htm#SEC1029	29794
splitPolygon		sing_2078.htm#SEC2154	706
splitring		sing_1323.htm#SEC1399	56404
splitting		sing_1219.htm#SEC1295	34734
spmilnor		sing_1552.htm#SEC1628	32933
spmul		sing_1549.htm#SEC1625	43607
spnf		sing_1100.htm#SEC1176	57309
spoly		sing_1964.htm#SEC2040	35454
sppairs		sing_1540.htm#SEC1616	49513
sppnf		sing_1545.htm#SEC1621	16650
sppprint		sing_1546.htm#SEC1622	43682
spprint		sing_1101.htm#SEC1177	18671
sprintf		sing_351.htm#SEC391	55889
spsemicont		sing_1551.htm#SEC1627	61169
spsub		sing_1548.htm#SEC1624	54296
sqfrNorm		sing_1750.htm#SEC1826	20546
sqfrNormMain		sing_1758.htm#SEC1834	9890
sqr		sing_1876.htm#SEC1952	sprintf
sqrfree		sing_350.htm#SEC390	
squareRoot		sing_1895.htm#SEC1971	17446
squarefree		sing_1576.htm#SEC1652	48485
sres		sing_352.htm#SEC392	
ssi	Parallelization with ssi links	sing_815.htm#SEC867	
stabilizer		sing_2250.htm#SEC2326	36692
stack, moduli space of stable maps		sing_2726.htm#IDX1057	
stack, moduli space of stable maps, rational curves	moduliSpace	sing_2725.htm#IDX1056	
stackNets		sing_2647.htm#SEC2723	30974
staircase		sing_1767.htm#SEC1843	49781
standard		sing_1971.htm#SEC2047	14067
standard bases, saturation		sing_2220.htm#IDX903	
standard bases.		sing_2219.htm#IDX902	
standard.lib		sing_894.htm#IDX419	
standard_lib		sing_894.htm#IDX420	
startNmz		sing_1280.htm#SEC1356	21925
startTasks		sing_1037.htm#SEC1113	16715
static procedures	Procedure definition	sing_43.htm#SEC78	
status		sing_353.htm#SEC393	
std		sing_354.htm#SEC394	
std 		sing_818.htm#SEC870	
std (plural)		sing_480.htm#SEC520	
stdfglm		sing_355.htm#SEC395	256
stdhilb		sing_356.htm#SEC396	63138
stdlocus		sing_939.htm#SEC1015	25619
stopTask		sing_1038.htm#SEC1114	6801
storeActionOnOrbitConeIndices	storeActionOnOrbitConeIndices	sing_2439.htm#SEC2515	64428
stratify		sing_1701.htm#SEC1777	56744
stratify.lib		sing_1699.htm#SEC1775	
stratify_lib		sing_1699.htm#SEC1775	
string	Miscellaneous oddities	sing_171.htm#SEC211	
string 		sing_418.htm#IDX297	
string declarations		sing_172.htm#SEC212	
string expressions		sing_173.htm#SEC213	
string operations		sing_175.htm#SEC215	
string related functions	string related functions	sing_176.htm#SEC216	
string type cast		sing_174.htm#SEC214	
stripHNE		sing_1573.htm#SEC1649	19265
sturm		sing_2004.htm#SEC2080	54353
sturmha		sing_2006.htm#SEC2082	12467
sturmhaseq		sing_2007.htm#SEC2083	59133
sturmquery		sing_1982.htm#SEC2058	10805
sturmseq		sing_2005.htm#SEC2081	23005
sublists		sing_2344.htm#SEC2420	2979
submat		sing_1058.htm#SEC1134	37665
subquotient		sing_2513.htm#SEC2589	40364
subrInterred		sing_982.htm#SEC1058	10165
subset_sum01		sing_1925.htm#SEC2001	60620
subset_sum02		sing_1926.htm#SEC2002	37340
subst		sing_357.htm#SEC397	
subst (plural)		sing_481.htm#SEC521	
substitute		sing_981.htm#SEC1057	28919
sugarCrit, option		sing_315.htm#IDX169	
sum		sing_917.htm#SEC993	555
sum_of_powers		sing_2263.htm#SEC2339	12170
sumlist		sing_1415.htm#SEC1491	59918
sumofquotients		sing_2734.htm#SEC2810	4569
super-commutative algebras	Graded commutative algebras (SCA)	sing_490.htm#SEC542	
superCommutative		sing_734.htm#SEC786	45528
super_increasing_knapsack	super_increasing_knapsack	sing_1937.htm#SEC2013	9177
surf.lib		sing_1784.htm#SEC1860	
surf_lib		sing_1784.htm#SEC1860	
surfacesignature.lib	surfacesignature_lib	sing_1633.htm#SEC1709	
surfacesignature_lib	surfacesignature_lib	sing_1633.htm#SEC1709	
surfer		sing_1.htm#IDX8	14287
surfer 		sing_1786.htm#SEC1862	
surfex		sing_1.htm#IDX7	
surfex.lib		sing_1787.htm#SEC1863	
surfex_lib		sing_1787.htm#SEC1863	
suspend		sing_353.htm#SEC393	
swalk		sing_2742.htm#SEC2818	16794
swalk.lib		sing_2741.htm#SEC2817	
swalk_lib		sing_2741.htm#SEC2817	
swap		sing_1502.htm#SEC1578	15408
swap 		sing_2181.htm#IDX838	
switch	No case or switch statement	sing_412.htm#SEC452	
switchRingsAndComputeInitialIdeal	switchRingsAndComputeInitialIdeal	sing_2750.htm#SEC2826	1827
syModStd		sing_1347.htm#SEC1423	50246
symNsym		sing_2257.htm#SEC2333	55230
sym_gauss		sing_1084.htm#SEC1160	5121
symm		sing_2256.htm#SEC2332	64628
symmStd		sing_1346.htm#SEC1422	39353
symmat		sing_1059.htm#SEC1135	61294
symmetric basis		sing_1076.htm#IDX506	
symmetric power		sing_1078.htm#IDX508	
symmetricBasis		sing_1076.htm#SEC1152	sprintf
symmetricPower		sing_1078.htm#SEC1154	6542
symmetricPowerSheaf		sing_2720.htm#SEC2796	56922
symmetries		sing_2246.htm#IDX936	
symmfunc		sing_1991.htm#SEC2067	45575
symodstd.lib		sing_1341.htm#SEC1417	
symodstd_lib		sing_1341.htm#SEC1417	
symsignature		sing_1981.htm#SEC2057	10520
syndrome		sing_1814.htm#SEC1890	14057
sysBin		sing_1812.htm#SEC1888	41948
sysCRHT		sing_1809.htm#SEC1885	58930
sysCRHTMindist		sing_1810.htm#SEC1886	13692
sysFL		sing_1825.htm#SEC1901	53040
sysNewton		sing_1811.htm#SEC1887	19704
sysQE		sing_1815.htm#SEC1891	61026
sys_code		sing_1806.htm#SEC1882	20220
system		sing_358.htm#SEC398	
system, --		sing_358.htm#IDX277	
system, --long_option_name		sing_358.htm#IDX280	
system, --long_option_name=value		sing_358.htm#IDX282	
system, HC		sing_358.htm#IDX215	
system, LLL		sing_358.htm#IDX219	
system, Singular		sing_358.htm#IDX258	
system, SingularLib		sing_358.htm#IDX260	
system, absFact		sing_358.htm#IDX190	
system, alarm		sing_358.htm#IDX189	
system, blackbox		sing_358.htm#IDX191	
system, bracket		sing_358.htm#IDX196	
system, browsers		sing_358.htm#IDX195	
system, btest		sing_358.htm#IDX198	
system, complexNearZero		sing_358.htm#IDX199	
system, contributors		sing_358.htm#IDX201	
system, cpu		sing_358.htm#IDX203	
system, cpu 		sing_358.htm#IDX276	
system, denom_list		sing_358.htm#IDX205	
system, eigenvals		sing_358.htm#IDX206	
system, env		sing_358.htm#IDX207	
system, executable		sing_358.htm#IDX209	
system, freegb		sing_358.htm#IDX210	
system, getPrecDigits		sing_358.htm#IDX213	
system, getenv		sing_358.htm#IDX212	
system, gmsnf		sing_358.htm#IDX214	
system, hessenberg		sing_358.htm#IDX216	
system, install		sing_358.htm#IDX218	
system, nblocks		sing_358.htm#IDX222	
system, nc_hilb		sing_358.htm#IDX224	
system, neworder		sing_358.htm#IDX225	
system, newstruct		sing_358.htm#IDX226	
system, opp		sing_358.htm#IDX227	
system, oppose		sing_358.htm#IDX230	
system, pcvBasis		sing_358.htm#IDX239	
system, pcvCV2P		sing_358.htm#IDX237	
system, pcvDim		sing_358.htm#IDX238	
system, pcvLAddL		sing_358.htm#IDX233	
system, pcvMinDeg		sing_358.htm#IDX235	
system, pcvP2CV		sing_358.htm#IDX236	
system, pcvPMulL		sing_358.htm#IDX234	
system, pid		sing_358.htm#IDX241	
system, random		sing_358.htm#IDX243	
system, reserve		sing_358.htm#IDX247	
system, reservedLink		sing_358.htm#IDX248	
system, semaphore		sing_358.htm#IDX250	
system, semic		sing_358.htm#IDX251	
system, setenv		sing_358.htm#IDX253	
system, sh		sing_358.htm#IDX255	
system, shrinktest		sing_358.htm#IDX256	
system, spadd		sing_358.htm#IDX261	
system, spectrum		sing_358.htm#IDX262	
system, spmul		sing_358.htm#IDX263	
system, std_syz		sing_358.htm#IDX264	
system, stest		sing_358.htm#IDX265	
system, tensorModuleMult		sing_358.htm#IDX266	
system, twostd		sing_358.htm#IDX267	
system, uname		sing_358.htm#IDX270	
system, version		sing_358.htm#IDX273	
system, with		sing_358.htm#IDX274	
systemOfParametersOfLocalization	systemOfParametersOfLocalization	sing_2416.htm#SEC2492	63094
syz		sing_359.htm#SEC399	
syz (plural)		sing_482.htm#SEC522	
tDetropicalise		sing_2159.htm#SEC2235	23532
tInitialForm		sing_2143.htm#SEC2219	24484
tInitialFormPar		sing_2155.htm#SEC2231	9584
tInitialFormParMax		sing_2156.htm#SEC2232	7829
tInitialIdeal		sing_2144.htm#SEC2220	17937
tab		sing_954.htm#SEC1030	60407
tail		sing_1960.htm#SEC2036	13066
tame polynomial		sing_1555.htm#IDX732	
tame polynomial 		sing_1556.htm#IDX742	
tame polynomial  		sing_1557.htm#IDX743	
tangentGens		sing_1371.htm#SEC1447	37797
tangentcone		sing_1620.htm#SEC1696	20056
target		sing_2520.htm#SEC2596	18743
task		sing_1031.htm#IDX505	
tasks.lib		sing_1031.htm#SEC1107	
tasks_lib		sing_1031.htm#SEC1107	
tau_es		sing_1528.htm#SEC1604	17043
tau_es2		sing_1482.htm#SEC1558	38083
tdCf		sing_2292.htm#SEC2368	21522
tdFactor		sing_2294.htm#SEC2370	37910
tdProj		sing_2297.htm#SEC2373	38406
tdTerms		sing_2293.htm#SEC2369	30166
teachstd.lib		sing_1958.htm#SEC2034	
teachstd_lib		sing_1958.htm#SEC2034	
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_498.htm#IDX311	65451
tensor 		sing_1060.htm#SEC1136	
tensorFreeModule		sing_2532.htm#SEC2608	59314
tensorFreemodMod		sing_2531.htm#SEC2607	sprintf
tensorMatrix		sing_2528.htm#SEC2604	31437
tensorMod		sing_1179.htm#SEC1255	21961
tensorModFreemod		sing_2530.htm#SEC2606	11852
tensorModule		sing_2529.htm#SEC2605	58772
tensorProduct		sing_2533.htm#SEC2609	sprintf
tensorSheaf		sing_2719.htm#SEC2795	24072
term orderings	General definitions for orderings	sing_859.htm#SEC911	
term orderings introduction	Introduction to orderings	sing_858.htm#SEC910	
testFraction		sing_2658.htm#SEC2734	28466
testLocData		sing_2655.htm#SEC2731	50986
testNCfac		sing_708.htm#SEC760	60394
testNcfrac		sing_2616.htm#SEC2692	34186
testNcfracExamples		sing_2617.htm#SEC2693	15399
testNcloc		sing_2620.htm#SEC2696	62706
testNclocExamples		sing_2621.htm#SEC2697	14584
testOlga		sing_2672.htm#SEC2748	53953
testOlgaExamples		sing_2673.htm#SEC2749	62869
testParametrization		sing_1386.htm#SEC1462	18686
testPointConic		sing_1387.htm#SEC1463	25315
testPrimary		sing_1299.htm#SEC1375	34254
testPrimaryE		sing_1300.htm#SEC1376	20693
tex		sing_1773.htm#SEC1849	12226
texDrawBasic		sing_2150.htm#SEC2226	3635
texDrawNewtonSubdivision	texDrawNewtonSubdivision	sing_2152.htm#SEC2228	42021
texDrawTriangulation	texDrawTriangulation	sing_2153.htm#SEC2229	18865
texDrawTropical		sing_2151.htm#SEC2227	58447
texMatrix		sing_2149.htm#SEC2225	1334
texNumber		sing_2147.htm#SEC2223	12628
texPolynomial		sing_2148.htm#SEC2224	41136
texcoef		sing_1854.htm#SEC1930	28189
texdemo		sing_1774.htm#SEC1850	13008
texfactorize		sing_1775.htm#SEC1851	6682
texmap		sing_1776.htm#SEC1852	35265
texname		sing_1777.htm#SEC1853	1008
texobj		sing_1778.htm#SEC1854	2107
texpoly		sing_1779.htm#SEC1855	64109
texproc		sing_1780.htm#SEC1856	23626
texring		sing_1781.htm#SEC1857	38275
the first alternative algorithm		sing_1156.htm#IDX542	
three_elements		sing_1944.htm#SEC2020	513
timeFactorize		sing_921.htm#SEC997	49531
timeStd		sing_920.htm#SEC996	31506
timer		sing_402.htm#SEC442	
timer resolution, setting the		sing_358.htm#IDX283	
timestep		sing_2396.htm#SEC2472	38225
tjurina		sing_1616.htm#SEC1692	9100
tmatrix		sing_1543.htm#SEC1619	57332
todd		sing_2289.htm#SEC2365	25618
toddE		sing_2290.htm#SEC2366	17823
toddPoly		sing_2303.htm#SEC2379	65066
tolessvars		sing_1719.htm#SEC1795	56590
topChernClass		sing_2716.htm#SEC2792	17374
topological invariants		sing_1470.htm#IDX634	
topological invariants 		sing_1477.htm#IDX641	
topological invariants  		sing_1478.htm#IDX645	
topological invariants   		sing_1479.htm#IDX649	
topological invariants    		sing_1480.htm#IDX653	
toric ideals		sing_874.htm#SEC931	
toric ring		sing_1258.htm#IDX575	
toric.lib		sing_1348.htm#SEC1424	
toric_ideal		sing_1349.htm#SEC1425	5760
toric_lib		sing_1348.htm#SEC1424	
toric_std		sing_1350.htm#SEC1426	26141
torusInvariants		sing_1264.htm#SEC1340	911
total divisors		sing_498.htm#IDX308	
total multiplicities		sing_1470.htm#IDX637	
totalChernClass		sing_2714.htm#SEC2790	6153
totalSegreClass		sing_2717.htm#SEC2793	3291
totalmultiplicities		sing_1472.htm#SEC1548	58264
trace		sing_360.htm#SEC400	
tracemult		sing_1985.htm#SEC2061	58303
transpose		sing_361.htm#SEC401	
trapezoid		sing_2390.htm#SEC2466	61525
triMNewton		sing_1745.htm#SEC1821	62822
triagmatrix		sing_995.htm#SEC1071	17944
triang.lib		sing_1738.htm#SEC1814	
triangL		sing_1739.htm#SEC1815	51847
triangL_solve		sing_1736.htm#SEC1812	10101
triangLf_solve		sing_1734.htm#SEC1810	49796
triangLfak		sing_1740.htm#SEC1816	50093
triangM		sing_1741.htm#SEC1817	59334
triangMH		sing_1742.htm#SEC1818	34277
triangM_solve		sing_1735.htm#SEC1811	63652
triang_lib		sing_1738.htm#SEC1814	
triang_solve		sing_1737.htm#SEC1813	64404
triangulations		sing_2075.htm#SEC2151	61888
tropical curves		sing_2129.htm#IDX815	
tropical geometry		sing_1142.htm#IDX516	
tropical geometry 		sing_2744.htm#IDX1068	
tropical mirror symmetry		sing_1142.htm#IDX518	
tropical polynomials		sing_2129.htm#IDX816	
tropical varieties		sing_2744.htm#IDX1069	
tropical.lib		sing_2129.htm#IDX813	
tropicalCurve		sing_2134.htm#SEC2210	16865
tropicalJInvariant		sing_2137.htm#SEC2213	40395
tropicalLifting		sing_2130.htm#SEC2206	7052
tropicalLinkNewton		sing_2752.htm#SEC2828	63886
tropicalNewton.lib		sing_2744.htm#SEC2820	
tropicalNewton_lib		sing_2744.htm#SEC2820	
tropicalPointNewton		sing_2749.htm#SEC2825	18572
tropicalSubst		sing_2162.htm#SEC2238	49846
tropicalVariety		sing_2169.htm#SEC2245	39087
tropicalVarietyNewton	tropicalVarietyNewton	sing_2751.htm#SEC2827	28532
tropical_lib		sing_2129.htm#IDX814	
tropicalise		sing_2141.htm#SEC2217	49739
tropicaliseSet		sing_2142.htm#SEC2218	35136
truncate		sing_1452.htm#SEC1528	13545
truncateFast		sing_1453.htm#SEC1529	5124
truncated module		sing_1452.htm#IDX625	
truncated module 		sing_1453.htm#IDX626	
tst_ncfactor		sing_716.htm#SEC768	3339
twalk		sing_1155.htm#SEC1231	35753
two-sided		sing_498.htm#IDX309	
two-sided Groebner basis		sing_498.htm#IDX310	
twostd		sing_358.htm#IDX268	
twostd 		sing_483.htm#SEC523	
type		sing_362.htm#SEC402	
type B		sing_2197.htm#IDX865	
type D		sing_2198.htm#IDX867	
type,custom	Definition of a user defined type	sing_183.htm#SEC223	
type2arr		sing_2175.htm#SEC2251	62624
typecasting		sing_2175.htm#IDX821	
typecasting 		sing_2176.htm#IDX823	
typecasting  		sing_2177.htm#IDX826	
typeof		sing_363.htm#SEC403	
u		sing_2382.htm#SEC2458	12154
uname		sing_358.htm#IDX269	
unbounded_knapsack		sing_1927.htm#SEC2003	17226
unipotent groups		sing_1370.htm#IDX593	
uniquePoint		sing_2054.htm#SEC2130	893
unitMatrix		sing_2686.htm#SEC2762	33014
unitmat		sing_1061.htm#SEC1137	12862
univariate		sing_364.htm#SEC404	
univarpoly		sing_1992.htm#SEC2068	46288
unknown syndrome	Decoding method based on quadratic equations	sing_890.htm#SEC961	
unset		sing_276.htm#SEC316	
untyped definitions		sing_88.htm#SEC128	
untyped definitions 		sing_423.htm#SEC463	
updatePairs		sing_1970.htm#SEC2046	51144
ures_solve		sing_1728.htm#SEC1804	32449
uressolve		sing_365.htm#SEC405	
usage, option		sing_315.htm#IDX185	
user interface, Emacs	Emacs user interface	sing_21.htm#SEC28	
vStd		sing_2336.htm#SEC2412	12321
val		sing_2746.htm#SEC2822	62171
valvars		sing_1723.htm#SEC1799	15723
vandermonde		sing_366.htm#SEC406	
vanishId		sing_1824.htm#SEC1900	49148
var		sing_367.htm#SEC407	
varMat		sing_2179.htm#SEC2255	51772
varNum		sing_2180.htm#SEC2256	18485
variables		sing_368.htm#SEC408	
variables 		sing_2179.htm#IDX833	
variables  		sing_2180.htm#IDX835	
variables   		sing_2181.htm#IDX839	
variables    		sing_2182.htm#IDX841	
variablesSorted		sing_536.htm#SEC588	13533
variablesStandard		sing_535.htm#SEC587	56500
vars2pars		sing_795.htm#SEC847	47343
varsigns		sing_1997.htm#SEC2073	3471
varstr		sing_369.htm#SEC409	
vct2str		sing_657.htm#SEC709	51983
vdim		sing_370.htm#SEC410	
vdim (plural)		sing_484.htm#SEC524	
vec2poly		sing_518.htm#SEC570	27377
vector		sing_177.htm#SEC217	
vector declarations		sing_178.htm#SEC218	
vector expressions		sing_179.htm#SEC219	
vector operations		sing_180.htm#SEC220	
vector related functions	vector related functions	sing_181.htm#SEC221	
verify		sing_1988.htm#SEC2064	32271
versal		sing_1523.htm#SEC1599	46247
version		sing_358.htm#IDX272	
vertexAdjacencyGraph	vertexAdjacencyGraph	sing_2122.htm#SEC2198	60102
vertexEdgeGraph		sing_2123.htm#SEC2199	32816
vertices		sing_2070.htm#SEC2146	11398
vfilt		sing_1541.htm#SEC1617	9283
view		sing_1844.htm#SEC1920	29284
visual		sing_2124.htm#SEC2200	51434
visualize		sing_2381.htm#SEC2457	6750
voice		sing_405.htm#SEC445	
vwfilt		sing_1542.htm#SEC1618	8281
wUnit		sing_1882.htm#SEC1958	27198
waitAllTasks		sing_1040.htm#SEC1116	7087
waitTasks		sing_1039.htm#SEC1115	52857
waitall		sing_371.htm#SEC411	
waitfirst		sing_372.htm#SEC412	
walk, groebner		sing_1153.htm#IDX538	
walk, groebner 		sing_2544.htm#IDX991	
walk, groebner  		sing_2698.htm#IDX1037	
walk, groebner   		sing_2741.htm#IDX1066	
warkedPreimageStd		sing_2418.htm#SEC2494	14759
warn, option		sing_70.htm#SEC110	
warn, option 		sing_315.htm#IDX151	
watchdog		sing_918.htm#SEC994	sprintf
wedge		sing_373.htm#SEC413	
weierstr.lib		sing_1973.htm#SEC2049	
weierstrDiv		sing_1974.htm#SEC2050	260
weierstrPrep		sing_1975.htm#SEC2051	5752
weierstr_lib		sing_1973.htm#SEC2049	
weierstrassForm		sing_2138.htm#SEC2214	60874
weight		sing_374.htm#SEC414	
weight filtration		sing_1533.htm#IDX665	
weight filtration 		sing_1540.htm#IDX699	
weight filtration  		sing_1542.htm#IDX713	
weight filtration   		sing_1543.htm#IDX721	
weight filtration    		sing_1555.htm#IDX737	
weight filtration     		sing_1557.htm#IDX748	
weightKB		sing_375.htm#SEC415	21753
weightM, option		sing_315.htm#IDX170	
weighted lexicographical ordering		sing_860.htm#IDX399	
weighted reverse lexicographical ordering	Global orderings	sing_860.htm#IDX397	
weightedRing		sing_727.htm#SEC779	33786
whichvariable		sing_1996.htm#SEC2072	27122
while		sing_392.htm#SEC432	
withDim		sing_209.htm#IDX145	
withHilb		sing_209.htm#IDX143	
withMult		sing_209.htm#IDX146	
withRes		sing_209.htm#IDX144	
withSB		sing_209.htm#IDX142	
wp, global ordering		sing_860.htm#IDX398	
write		sing_376.htm#SEC416	
writeNmzData		sing_1275.htm#SEC1351	38467
writeNmzPaths		sing_1279.htm#SEC1355	sprintf
ws, local ordering		sing_861.htm#IDX409	
wurzel		sing_1864.htm#SEC1940	12755
xchange		sing_1858.htm#SEC1934	40741
xdvi		sing_1783.htm#SEC1859	16898
zdd		sing_2226.htm#IDX914	
zdd2poly		sing_2243.htm#SEC2319	55047
zero		sing_2493.htm#SEC2569	12060
zero-dimensional		sing_1993.htm#IDX804	
zeroMod		sing_1215.htm#SEC1291	60609
zeroNcfrac		sing_2609.htm#SEC2685	50840
zeroOpt		sing_1224.htm#SEC1300	19260
zeroRadical		sing_1124.htm#SEC1200	35598
zeroSet		sing_1751.htm#SEC1827	60030
zerodec		sing_1308.htm#SEC1384	30765
zeroset.lib		sing_1746.htm#SEC1822	
zeroset_lib		sing_1746.htm#SEC1822	
zetaDL		sing_1445.htm#SEC1521	sprintf
{		sing_36.htm#IDX78	
||		sing_36.htm#IDX103	
|| 		sing_101.htm#SEC141	
}		sing_36.htm#IDX79	
~		sing_36.htm#IDX117	
~ 		sing_393.htm#SEC433	
