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singular.idx @ 54fdec1

spielwiese

Last change on this file since 54fdec1 was 54fdec1, checked in by Hans Schoenemann <hannes@…>, 7 years ago
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Property mode set to `100644`
File size: 162.0 KB

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[a719149]	1	! sing_36.htm#IDX101
	2	!= sing_36.htm#IDX95
	3	!= sing_95.htm#SEC135
	4	" sing_36.htm#IDX104
	5	# sing_36.htm#IDX118
	6	$ sing_36.htm#IDX119
	7	% sing_36.htm#IDX91
	8	% sing_76.htm#SEC116
	9	% sing_93.htm#SEC133
	10	% sing_105.htm#SEC145
[a070b84]	11	% sing_142.htm#SEC182
[a719149]	12	&& sing_36.htm#IDX102
	13	&& sing_96.htm#SEC136
	14	( sing_36.htm#IDX80
[a070b84]	15	() sing_126.htm#IDX130
[a719149]	16	) sing_36.htm#IDX81
	17	* bigintmat operations sing_36.htm#IDX89
	18	* sing_76.htm#SEC116
	19	* sing_82.htm#SEC122
	20	* sing_88.htm#SEC128
	21	* sing_93.htm#SEC133
	22	* sing_101.htm#SEC141
	23	* sing_105.htm#SEC145
[a070b84]	24	* sing_132.htm#SEC172
	25	* sing_137.htm#SEC177
	26	* sing_142.htm#SEC182
	27	* sing_150.htm#SEC190
[a719149]	28	** sing_36.htm#IDX93
	29	+ bigintmat operations sing_36.htm#IDX85
	30	+ sing_76.htm#SEC116
	31	+ sing_82.htm#SEC122
	32	+ sing_88.htm#SEC128
	33	+ sing_93.htm#SEC133
	34	+ sing_101.htm#SEC141
	35	+ sing_105.htm#SEC145
[a070b84]	36	+ sing_121.htm#SEC161
	37	+ sing_132.htm#SEC172
	38	+ sing_137.htm#SEC177
	39	+ sing_142.htm#SEC182
	40	+ sing_150.htm#SEC190
	41	+ sing_164.htm#SEC204
	42	+ sing_170.htm#SEC210
	43	+ sing_175.htm#SEC215
[a719149]	44	++ sing_36.htm#IDX86
	45	- bigintmat operations sing_36.htm#IDX87
	46	- sing_76.htm#SEC116
	47	- sing_82.htm#SEC122
	48	- sing_93.htm#SEC133
	49	- sing_101.htm#SEC141
	50	- sing_105.htm#SEC145
[a070b84]	51	- sing_132.htm#SEC172
	52	- sing_142.htm#SEC182
	53	- sing_150.htm#SEC190
	54	- sing_175.htm#SEC215
[a719149]	55	-- sing_36.htm#IDX88
	56	--MPhost sing_19.htm#IDX66
	57	--MPport sing_19.htm#IDX65
[3a9ee05]	58	--allow-net sing_19.htm#IDX39
[a719149]	59	--batch sing_19.htm#IDX64
[3a9ee05]	60	--browser sing_19.htm#IDX43
	61	--echo sing_19.htm#IDX35
[a719149]	62	--emacs sing_19.htm#IDX67
	63	--emacs-dir sing_19.htm#IDX68
	64	--emacs-load sing_19.htm#IDX69
	65	--execute sing_19.htm#IDX56
[3a9ee05]	66	--help sing_19.htm#IDX37
[a719149]	67	--min-time sing_19.htm#IDX61
[3a9ee05]	68	--no-out sing_19.htm#IDX49
	69	--no-rc sing_19.htm#IDX45
	70	--no-shell sing_19.htm#IDX50
	71	--no-stdlib sing_19.htm#IDX47
	72	--no-tty sing_19.htm#IDX51
	73	--no-warn sing_19.htm#IDX48
	74	--quiet sing_19.htm#IDX53
[a719149]	75	--random sing_19.htm#IDX60
[3a9ee05]	76	--sdb sing_19.htm#IDX32
[a719149]	77	--singular sing_19.htm#IDX70
	78	--ticks-per-sec sing_19.htm#IDX62
	79	--user-option sing_19.htm#IDX58
	80	-> sing_154.htm#SEC194
[3a9ee05]	81	-MPhost Command line options
	82	-MPport Command line options
	83	-allow-net Command line options
[a719149]	84	-b Command line options sing_19.htm#IDX63
[3a9ee05]	85	-batch Command line options
	86	-browser Command line options
[a719149]	87	-c Command line options sing_19.htm#IDX55
[3a9ee05]	88	-d Command line options sing_19.htm#IDX31
	89	-e Command line options sing_19.htm#IDX34
	90	-echo Command line options
	91	-emacs Command line options
	92	-emacs-dir Command line options
	93	-emacs-load Command line options
	94	-execute Command line options
	95	-h Command line options sing_19.htm#IDX36
	96	-help Command line options
	97	-min-time Command line options
	98	-no-out Command line options
	99	-no-rc Command line options
	100	-no-shell Command line options
	101	-no-stdlib Command line options
	102	-no-tty Command line options
	103	-no-warn Command line options
	104	-q Command line options sing_19.htm#IDX52
	105	-quiet Command line options
[a719149]	106	-r Command line options sing_19.htm#IDX59
[3a9ee05]	107	-random Command line options
	108	-sdb Command line options
	109	-singular Command line options
	110	-ticks-per-sec Command line options
[a719149]	111	-u Command line options sing_19.htm#IDX57
[3a9ee05]	112	-user-option Command line options
[a719149]	113	-v Command line options sing_19.htm#IDX54
	114	.. sing_36.htm#IDX113
	115	.singularrc file sing_20.htm#IDX72
[3a9ee05]	116	.singularrc file, no loading Command line options sing_19.htm#IDX46
[a719149]	117	/ sing_36.htm#IDX90
	118	/ sing_105.htm#SEC145
[a070b84]	119	/ sing_132.htm#SEC172
	120	/ sing_142.htm#SEC182
	121	/ sing_150.htm#SEC190
	122	/ sing_175.htm#SEC215
[a719149]	123	// sing_36.htm#IDX107
	124	// sing_36.htm#IDX109
	125	// sing_36.htm#IDX110
	126	: sing_36.htm#IDX114
	127	: sing_105.htm#SEC145
	128	:: sing_36.htm#IDX115
	129	:: sing_144.htm#SEC184
	130	; sing_36.htm#IDX111
	131	< sing_36.htm#IDX100
[a070b84]	132	< sing_150.htm#SEC190
	133	< sing_175.htm#SEC215
[cd8a2b5]	134	< sing_241.htm#SEC281
[a719149]	135	<= sing_36.htm#IDX99
	136	<= sing_95.htm#SEC135
[a070b84]	137	<= sing_142.htm#SEC182
	138	<= sing_150.htm#SEC190
	139	<= sing_170.htm#SEC210
	140	<= sing_175.htm#SEC215
[a719149]	141	<> sing_36.htm#IDX96
	142	<> sing_95.htm#SEC135
[a070b84]	143	<> sing_132.htm#SEC172
	144	<> sing_142.htm#SEC182
	145	<> sing_150.htm#SEC190
	146	<> sing_164.htm#SEC204
	147	<> sing_170.htm#SEC210
	148	<> sing_175.htm#SEC215
[a719149]	149	= sing_36.htm#IDX77
	150	== sing_36.htm#IDX94
	151	== sing_95.htm#SEC135
[a070b84]	152	== sing_132.htm#SEC172
	153	== sing_142.htm#SEC182
	154	== sing_150.htm#SEC190
	155	== sing_164.htm#SEC204
	156	== sing_170.htm#SEC210
	157	== sing_175.htm#SEC215
[a719149]	158	> sing_36.htm#IDX98
[a070b84]	159	> sing_150.htm#SEC190
	160	> sing_175.htm#SEC215
[a719149]	161	>= sing_36.htm#IDX97
	162	>= sing_95.htm#SEC135
[a070b84]	163	>= sing_142.htm#SEC182
	164	>= sing_150.htm#SEC190
	165	>= sing_170.htm#SEC210
	166	>= sing_175.htm#SEC215
[a719149]	167	? sing_36.htm#IDX106
[cd8a2b5]	168	? sing_251.htm#IDX148
[063ba1]	169	AG codes sing_832.htm#SEC884
	170	AGcode_L sing_1781.htm#SEC1857 60329
	171	AGcode_Omega sing_1782.htm#SEC1858 56285
	172	ASCII sing_881.htm#SEC957 26816
[a719149]	173	ASCII links sing_112.htm#SEC152
	174	ASSUME sing_64.htm#SEC101
[063ba1]	175	A_L sing_1480.htm#SEC1556 16721
	176	A_Z sing_880.htm#SEC956 50866
[a719149]	177	Access to elements of a user defined type Access to elements of a user defined type sing_180.htm#SEC220
[063ba1]	178	Adj_div sing_1776.htm#SEC1852 44919
	179	Adjoint ideal sing_1357.htm#IDX592
	180	Alexander polynomial sing_1451.htm#IDX616
	181	Algebraic Geometry codes sing_1775.htm#IDX764
	182	Algebraic dependence Algebraic dependence sing_813.htm#SEC865
	183	Algebraic geometry sing_1332.htm#SEC1408
	184	AltVarEnd sing_726.htm#SEC778 11020
	185	AltVarStart sing_725.htm#SEC777 21592
	186	Ann sing_1271.htm#SEC1347 61560
	187	Appel function sing_555.htm#IDX349
	188	Appel hypergeometric function sing_555.htm#IDX350
	189	Applications sing_830.htm#SEC882
	190	ArnoldAction sing_1573.htm#SEC1649 26958
[a719149]	191	Assignments for user defined types Assignments for user defined types sing_182.htm#SEC222
[063ba1]	192	AssocTanToEnv sing_917.htm#SEC993 39826
	193	Atkin sing_1864.htm#SEC1940 sprintf
[3a9ee05]	194	Authors sing_1.htm#IDX16
[063ba1]	195	BINresol sing_1370.htm#SEC1446 52996
[3a9ee05]	196	Background sing_3.htm#SEC5
[063ba1]	197	Basic programming sing_788.htm#SEC840
	198	Basic programming sing_788.htm#SEC840
[54fdec1]	199	BelongSemig sing_2295.htm#SEC2371 22405
	200	BerlekampMassey sing_2345.htm#SEC2421 2172
[063ba1]	201	Bern sing_2268.htm#SEC2344 64051
	202	Bernstein operator sing_532.htm#IDX331
	203	Bernstein-Sato polynomial sing_497.htm#IDX312
	204	Bernstein-Sato polynomial sing_532.htm#IDX328
	205	Bernstein-Sato polynomial sing_1514.htm#IDX647
	206	Bernstein-Sato polynomial sing_1518.htm#IDX664
	207	Bernstein-Sato polynomial for variety sing_588.htm#IDX353
	208	Betti number Syzygies and resolutions sing_847.htm#SEC904
[54fdec1]	209	BettiNumsH sing_2375.htm#SEC2451 18661
	210	BettiNumsS sing_2378.htm#SEC2454 14964
[063ba1]	211	Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_857.htm#SEC914
	212	BlowingUp sing_1493.htm#SEC1569 43153
	213	Blowupcenter sing_1373.htm#SEC1449 3423
	214	BorelCheck sing_1448.htm#SEC1524 48787
[54fdec1]	215	Bott's formula sing_2508.htm#IDX977
[063ba1]	216	Branches of space curve singularities Branches of space curve singularities sing_821.htm#SEC873
	217	Briancon-Maisonobe algorithm sing_532.htm#IDX337
	218	Brieskorn lattice sing_1514.htm#IDX643
	219	Brieskorn lattice sing_1515.htm#IDX654
	220	Brieskorn lattice sing_1516.htm#IDX657
	221	Brieskorn lattice sing_1517.htm#IDX660
	222	Brieskorn lattice sing_1518.htm#IDX663
	223	Brieskorn lattice sing_1519.htm#IDX667
	224	Brieskorn lattice sing_1520.htm#IDX671
	225	Brieskorn lattice sing_1521.htm#IDX677
	226	Brieskorn lattice sing_1522.htm#IDX685
	227	Brieskorn lattice sing_1523.htm#IDX691
	228	Brieskorn lattice sing_1524.htm#IDX699
	229	Brieskorn lattice sing_1525.htm#IDX709
	230	Brieskorn lattice sing_1536.htm#IDX715
	231	Brieskorn lattice sing_1538.htm#IDX726
	232	Brieskorn lattice sing_1566.htm#IDX753
	233	Brill-Noether algorithm sing_1775.htm#IDX765
	234	BrillNoether sing_1778.htm#SEC1854 39919
	235	Buchberger algorithm for toric ideals Buchberger algorithm sing_858.htm#SEC915
	236	Budur-Mustata-Saito approach sing_588.htm#IDX357
[54fdec1]	237	Building Singular sing_2562.htm#SEC2652
[7d21990]	238	C programming language Major differences to the C programming language sing_401.htm#SEC441
[063ba1]	239	C, module ordering sing_840.htm#IDX411
	240	CGS sing_903.htm#IDX426
	241	CM_regularity sing_1435.htm#SEC1511 33865
	242	CMtype sing_1604.htm#SEC1680 24849
	243	CRHT-ideal sing_864.htm#SEC928
[54fdec1]	244	CSMA sing_2291.htm#SEC2367 49080
[a719149]	245	CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33
[063ba1]	246	Castelnuovo-Mumford regularity sing_1435.htm#IDX608
[a719149]	247	Category string sing_51.htm#SEC88
[063ba1]	248	CenCharDec sing_682.htm#SEC734 44505
	249	Center sing_1412.htm#SEC1488 25541
	250	CenterBO sing_1419.htm#SEC1495 34701
	251	CentralQuot sing_680.htm#SEC732 56490
	252	CentralSaturation sing_681.htm#SEC733 31585
[3a9ee05]	253	Change of rings sing_9.htm#SEC15
[063ba1]	254	Characteristic sets sing_848.htm#SEC905
	255	CharacteristicExponents CharacteristicExponents sing_1499.htm#SEC1575 21795
[54fdec1]	256	ChernClass sing_2521.htm#SEC2597 32965
[063ba1]	257	ChernRootsDual sing_2247.htm#SEC2323 40100
	258	ChernRootsHom sing_2256.htm#SEC2332 48446
	259	ChernRootsProd sing_2249.htm#SEC2325 13967
	260	ChernRootsSum sing_2245.htm#SEC2321 57286
	261	ChernRootsSymm sing_2258.htm#SEC2334 59304
	262	ChernRootsWedge sing_2259.htm#SEC2335 7239
	263	Chevalley-Rosenlicht theorem sing_1351.htm#IDX577
	264	Chevalley-Rosenlicht theorem sing_1352.htm#IDX580
[54fdec1]	265	Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2512.htm#IDX982
	266	ChowRing sing_2512.htm#SEC2588 57977
[063ba1]	267	Classification of hypersurface singularities Classification of hypersurface singularities sing_822.htm#SEC874
[54fdec1]	268	Classification of singularities sing_2504.htm#IDX969
[063ba1]	269	Code Codes and the decoding problem sing_863.htm#SEC921
	270	Codes and the decoding problem Codes and the decoding problem sing_863.htm#SEC920
	271	Coding theory sing_1774.htm#SEC1850
[54fdec1]	272	Coefficient rings Notes for Singular users sing_2560.htm#SEC2644
[3a9ee05]	273	Command line options Command line options sing_19.htm#SEC26
[cd8a2b5]	274	Commands Functions and system variables sing_201.htm#SEC241
[a719149]	275	Commands for user defined types Commands for user defined types sing_181.htm#SEC221
[063ba1]	276	Commutative Algebra sing_801.htm#SEC853
	277	Commutative algebra sing_1089.htm#SEC1165
	278	CompDecomp sing_494.htm#SEC546 9959
[54fdec1]	279	CompInt sing_2297.htm#SEC2373 7518
[063ba1]	280	CompleteHomog sing_2235.htm#SEC2311 42123
[54fdec1]	281	ComplexValue sing_2367.htm#SEC2443 45546
[063ba1]	282	Comprehensive Groebner System sing_903.htm#IDX429
	283	Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_797.htm#SEC849
	284	ConsLevels sing_911.htm#SEC987 45986
	285	ConsLevelsToLevels sing_912.htm#SEC988 56302
	286	ContactMatrix sing_1501.htm#SEC1577 40767
	287	Conti-Traverso algorithm sing_853.htm#SEC910
[3a9ee05]	288	Contributors sing_1.htm#IDX15
[7d21990]	289	Control structures sing_369.htm#SEC409
[063ba1]	290	Control theory System and Control theory sing_1808.htm#SEC1884
	291	Cooper philosophy sing_864.htm#SEC926
	292	Cornacchia sing_1854.htm#SEC1930 63434
	293	CornacchiaModified sing_1855.htm#SEC1931 59790
	294	Crep sing_906.htm#SEC982 35724
	295	Critical points sing_816.htm#SEC868
	296	CurveParam sing_1495.htm#SEC1571 359
	297	CurveRes sing_1494.htm#SEC1570 48848
	298	Curves sing_1357.htm#IDX589
[a719149]	299	Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36
[063ba1]	300	Cyclic code sing_1789.htm#IDX772
	301	Cyclic roots sing_794.htm#SEC846
	302	D-integration sing_555.htm#IDX346
	303	D-localization sing_555.htm#IDX342
	304	D-localization sing_760.htm#IDX380
	305	D-module purityfiltration_lib sing_497.htm#IDX310
	306	D-module sing_532.htm#IDX325
	307	D-module sing_555.htm#IDX339
	308	D-module sing_588.htm#IDX351
	309	D-module sing_738.htm#IDX365
	310	D-module sing_760.htm#IDX377
	311	D-module structure sing_532.htm#IDX326
	312	D-module structure sing_588.htm#IDX352
	313	D-restriction sing_555.htm#IDX344
[a719149]	314	DBM links sing_117.htm#SEC157
[3a9ee05]	315	DISPLAY environment variable The online help system sing_16.htm#IDX28
[063ba1]	316	DLoc sing_558.htm#SEC610 5981
	317	DLoc0 sing_560.htm#SEC612 14327
[a719149]	318	Data types sing_72.htm#SEC112
[063ba1]	319	Data types (plural) sing_414.htm#IDX296
[a719149]	320	Debugging tools sing_63.htm#SEC100
[3a9ee05]	321	Decker, Wolfram sing_1.htm#IDX17
[a719149]	322	Declaration of objects of a user defined type Declaration of objects of a user defined type sing_179.htm#SEC219
[063ba1]	323	Decoding sing_1789.htm#IDX774
	324	Decoding codes with Groebner bases Decoding codes with Groebner bases sing_862.htm#SEC919
	325	Decoding method based on quadratic equations Decoding method based on quadratic equations sing_867.htm#SEC937
[a719149]	326	Definition of a user defined type Definition of a user defined type sing_178.htm#SEC218
[063ba1]	327	Deformations sing_819.htm#SEC871
	328	Deformations, T1 and T2 sing_818.htm#SEC870
	329	Degree sing_1336.htm#SEC1412 47790
	330	Delta sing_1420.htm#SEC1496 33497
	331	DeltaList sing_1421.htm#SEC1497 65148
[a719149]	332	Demo mode sing_24.htm#SEC35
[063ba1]	333	Depth sing_808.htm#SEC860
[54fdec1]	334	Determinacy sing_2507.htm#IDX973
[063ba1]	335	Di Biase-Urbanke algorithm Di Biase and Urbanke sing_856.htm#SEC913
	336	Distributed computing sing_931.htm#IDX478
	337	Dlocalization sing_761.htm#SEC813 22140
[a719149]	338	Documentation Tool sing_60.htm#SEC97
[063ba1]	339	Dp, global ordering sing_838.htm#IDX394
	340	Ds, local ordering sing_839.htm#IDX404
	341	DsingularLocus sing_765.htm#SEC817 46495
[a719149]	342	Dynamic loading sing_71.htm#SEC111
[063ba1]	343	Dynamic modules sing_796.htm#SEC848
	344	ECPP sing_1898.htm#SEC1974 55777
	345	ECoef sing_1379.htm#SEC1455 14154
	346	EOrdlist sing_1377.htm#SEC1453 36329
[cd8a2b5]	347	ERROR sing_230.htm#SEC270
[a719149]	348	ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33
[063ba1]	349	Edatalist sing_1376.htm#SEC1452 61593
	350	Edelman-Reiner sing_2185.htm#IDX855
[a719149]	351	Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
[3a9ee05]	352	Editing input sing_18.htm#SEC25
[063ba1]	353	Elimination sing_804.htm#SEC856
[3a9ee05]	354	Emacs Emacs user interface sing_21.htm#SEC28
[a719149]	355	Emacs, Singular demo mode sing_24.htm#SEC35
[3a9ee05]	356	Emacs, a quick guide A quick guide to Emacs sing_22.htm#SEC29
[a719149]	357	Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC36
	358	Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC37
	359	Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC38
[3a9ee05]	360	Emacs, overview A quick guide to Emacs sing_22.htm#SEC29
	361	Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30
	362	Emacs, user interface Emacs user interface sing_21.htm#SEC28
[063ba1]	363	Emaxcont sing_1381.htm#SEC1457 47312
[54fdec1]	364	Enumerative geometry sing_2508.htm#IDX975
[063ba1]	365	Equal sing_1335.htm#SEC1411 19984
	366	Eresol sing_1371.htm#SEC1447 12842
[54fdec1]	367	EulerAff sing_2292.htm#SEC2368 54325
	368	EulerProj sing_2293.htm#SEC2369 13537
[7d21990]	369	Evaluation of logical expressions Evaluation of logical expressions sing_403.htm#SEC443
[063ba1]	370	Examples sing_786.htm#SEC838
[a719149]	371	Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40
[063ba1]	372	Exp for matrices sing_1353.htm#IDX581
	373	Experimental libraries Experimental libraries sing_2229.htm#SEC2305
	374	Ext sing_1149.htm#SEC1225 21909
	375	Ext, computation of sing_807.htm#SEC859
	376	Ext_R sing_1148.htm#SEC1224 53310
	377	Exterior sing_712.htm#SEC764 23593
	378	Extra weight vector sing_843.htm#SEC895
	379	Factorization sing_809.htm#SEC861
	380	FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_918.htm#SEC994 61191
	381	Feynman graph sing_1125.htm#IDX514
	382	Finite fields sing_803.htm#SEC855
[3a9ee05]	383	First steps sing_6.htm#SEC12
[063ba1]	384	Fitzgerald-Lax method Fitzgerald-Lax method sing_866.htm#SEC934
[a719149]	385	Flow control sing_40.htm#SEC70
	386	Formal Checker sing_59.htm#SEC96
[063ba1]	387	Formatting output sing_793.htm#SEC845
	388	Free resolution sing_805.htm#SEC857
	389	Free resolution, graded Handling graded modules sing_806.htm#SEC858
[54fdec1]	390	FultonA sing_2290.htm#SEC2366 33688
[cd8a2b5]	391	Functions sing_202.htm#SEC242
[54fdec1]	392	Future benefits of Singular 4 Notes for Singular users sing_2560.htm#SEC2650
[063ba1]	393	G-algebra sing_478.htm#SEC518
	394	G-algebra sing_478.htm#SEC520
	395	G-algebra, setup sing_478.htm#SEC522
	396	GBWeight sing_561.htm#SEC613 24641
	397	GBsolve sing_1688.htm#SEC1764 16830
[54fdec1]	398	GIT sing_2386.htm#IDX949
[063ba1]	399	GKZsystem sing_678.htm#SEC730 20528
	400	GKdim sing_651.htm#SEC703 9814
[3a9ee05]	401	GMP sing_1.htm#IDX3
[54fdec1]	402	GMP sing_2564.htm#SEC2654
	403	GND.lib sing_2393.htm#SEC2469
	404	GND_lib sing_2393.htm#SEC2469
[063ba1]	405	GTZmod sing_1197.htm#SEC1273 30091
	406	GTZopt sing_1204.htm#SEC1280 14642
	407	G_a -Invariants sing_825.htm#SEC877
	408	Gamma sing_1386.htm#SEC1462 3820
	409	Gauss-Manin connection Gauss-Manin connection sing_849.htm#SEC906
	410	Gauss-Manin connection sing_1566.htm#IDX752
	411	Gauss-Manin connection sing_1613.htm#IDX755
	412	Gauss-Manin system sing_1514.htm#IDX642
	413	Gauss-Manin system sing_1515.htm#IDX653
	414	Gauss-Manin system sing_1516.htm#IDX656
	415	Gauss-Manin system sing_1517.htm#IDX659
	416	Gauss-Manin system sing_1518.htm#IDX662
	417	Gauss-Manin system sing_1519.htm#IDX666
	418	Gauss-Manin system sing_1520.htm#IDX670
	419	Gauss-Manin system sing_1521.htm#IDX676
	420	Gauss-Manin system sing_1522.htm#IDX684
	421	Gauss-Manin system sing_1523.htm#IDX690
	422	Gauss-Manin system sing_1524.htm#IDX698
	423	Gauss-Manin system sing_1525.htm#IDX708
	424	Gauss-Manin system sing_1536.htm#IDX714
	425	Gauss-Manin system sing_1538.htm#IDX725
[a719149]	426	General command syntax General command syntax sing_35.htm#SEC59
[3a9ee05]	427	General concepts sing_12.htm#SEC18
[063ba1]	428	General purpose sing_874.htm#SEC950
[a719149]	429	General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41
[063ba1]	430	Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_480.htm#SEC530
	431	Generalized Newton identities Generalized Newton identities sing_865.htm#SEC931
	432	Geometric genus sing_1357.htm#IDX593
	433	German Umlaute sing_399.htm#IDX283
[3a9ee05]	434	Getting started sing_5.htm#SEC11
[063ba1]	435	Global orderings sing_838.htm#SEC890
[54fdec1]	436	GoettscheF sing_2373.htm#SEC2449 27881
[063ba1]	437	Graded commutative algebras Graded commutative algebras (SCA) sing_482.htm#SEC534
[54fdec1]	438	Grassmannian sing_2513.htm#SEC2589 43898
	439	Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2513.htm#IDX983
[3a9ee05]	440	Greuel, Gert-Martin sing_1.htm#IDX18
[063ba1]	441	Groebner Bases Computing Groebner and Standard Bases sing_797.htm#SEC849
	442	Groebner bases in G-algebras Groebner bases in G-algebras sing_479.htm#SEC523
	443	Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_485.htm#SEC537
	444	Groebner bases, decodeGB sing_1789.htm#IDX776
	445	Groebner bases, slim sing_800.htm#SEC852
	446	Groebner basis conversion Groebner basis conversion sing_799.htm#SEC851
	447	Groebner cover sing_902.htm#IDX422
	448	Groebner cover sing_909.htm#IDX435
	449	Groebner cover sing_910.htm#IDX441
	450	Groebner fan sing_2052.htm#IDX793
	451	Groebner walk sing_1140.htm#IDX535
	452	Groebner walk sing_1142.htm#IDX537
[54fdec1]	453	Groebner walk sing_2497.htm#IDX964
	454	Groebner walk sing_2498.htm#IDX965
[063ba1]	455	Groebnerwalk sing_1136.htm#IDX531
[54fdec1]	456	Groebnerwalk sing_2432.htm#IDX958
	457	Groebnerwalk sing_2496.htm#IDX963
	458	Groebnerwalk sing_2500.htm#IDX968
[063ba1]	459	Gromov-Witten invariants sing_1125.htm#IDX511
	460	Gromov-Witten invariants sing_1131.htm#IDX520
	461	Gromov-Witten invariants sing_1132.htm#IDX524
[54fdec1]	462	Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2538.htm#IDX995
	463	Gromov-Witten invariants, multiple covers sing_2537.htm#IDX994
	464	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2539.htm#IDX996
	465	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2540.htm#IDX997
	466	Gromov-Witten invariants. sing_2508.htm#IDX978
[063ba1]	467	Gweights sing_706.htm#SEC758 651
	468	H2basis sing_1571.htm#SEC1647 3414
[54fdec1]	469	HHnormalForm sing_2305.htm#SEC2381 33972
[063ba1]	470	Hamburger-Noether expansion sing_1451.htm#IDX612
	471	Hamburger-Noether expansion sing_1539.htm#IDX734
	472	Hamburger-Noether expansions sing_1776.htm#IDX766
	473	Handling graded modules Handling graded modules sing_806.htm#SEC858
	474	Hcode sing_1473.htm#SEC1549 26628
[a719149]	475	Help string sing_45.htm#SEC82
[cd8a2b5]	476	Hensel sing_235.htm#SEC275
[7d21990]	477	Hilbert function sing_348.htm#IDX188
[063ba1]	478	Hilbert function sing_846.htm#SEC900
	479	Hilbert series sing_846.htm#SEC900
	480	Hilbert-driven GB algorithm Groebner basis conversion sing_799.htm#SEC851
	481	HilbertClassPoly sing_1861.htm#SEC1937 sprintf
	482	HilbertSeries sing_1666.htm#SEC1742 21249
	483	HilbertWeights sing_1667.htm#SEC1743 sprintf
	484	Hom sing_1152.htm#SEC1228 61434
	485	HomJJ sing_1227.htm#SEC1303 1525
	486	Hosten-Sturmfels algorithm Hosten and Sturmfels sing_855.htm#SEC912
[3a9ee05]	487	How to enter and exit How to enter and exit sing_14.htm#SEC20
	488	How to use this manual How to use this manual sing_4.htm#SEC6
[063ba1]	489	Hurwitz numbers sing_1131.htm#IDX523
	490	Hurwitz numbers sing_1132.htm#IDX527
	491	Hypersurface singularities, classification of Classification of hypersurface singularities sing_822.htm#SEC874
[cd8a2b5]	492	IN sing_272.htm#IDX149
[063ba1]	493	Ideal membership sing_845.htm#IDX416
[a719149]	494	Identifiers, syntax of sing_37.htm#SEC65
[063ba1]	495	ImageGroup sing_1669.htm#SEC1745 28808
	496	ImageVariety sing_1668.htm#SEC1744 15252
[cd8a2b5]	497	Imap, option sing_307.htm#IDX175
[a719149]	498	Implemented algorithms Implemented algorithms sing_33.htm#SEC47
[063ba1]	499	Incl sing_1334.htm#SEC1410 7621
[54fdec1]	500	Index sing_2569.htm#SEC2659
[a719149]	501	Info string sing_52.htm#SEC89
[063ba1]	502	InterDiv sing_1402.htm#SEC1478 46142
[3a9ee05]	503	Interactive use sing_13.htm#SEC19
	504	Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24
[063ba1]	505	IntersectWithSub sing_683.htm#SEC735 56289
[54fdec1]	506	Intersection theory sing_2508.htm#IDX974
[063ba1]	507	IntersectionMatrix sing_1500.htm#SEC1576 29351
[3a9ee05]	508	Introduction sing_2.htm#SEC4
[063ba1]	509	Invariant Theory sing_824.htm#SEC876
	510	Invariant theory sing_1618.htm#SEC1694
	511	InvariantQ sing_1671.htm#SEC1747 53256
	512	InvariantRing sing_1670.htm#SEC1746 22928
	513	Invariants of a finite group Invariants of a finite group sing_826.htm#SEC878
	514	Invariants of plane curve singularities Invariants of plane curve singularities sing_820.htm#SEC872
	515	IsSCA sing_727.htm#SEC779 58445
	516	J-marked schemes sing_1442.htm#IDX610
	517	J-marked schemes, Borel ideals sing_1447.htm#IDX611
	518	JMBTest.lib sing_1442.htm#SEC1518
	519	JMBTest_lib sing_1442.htm#SEC1518
	520	JMSConst.lib sing_1447.htm#SEC1523
	521	JMSConst_lib sing_1447.htm#SEC1523
	522	JMarkedScheme sing_1449.htm#SEC1525 60696
	523	Jacobi sing_1871.htm#SEC1947 29843
	524	Jacobson form sing_1826.htm#IDX777
	525	Jacobson normal form sing_1826.htm#IDX778
	526	JuReTopDim sing_1344.htm#SEC1420 sprintf
	527	JuReZeroDim sing_1345.htm#SEC1421 sprintf
	528	KScoef sing_1564.htm#SEC1640 sprintf
	529	KSconvert sing_1562.htm#SEC1638 3585
	530	KSker sing_1561.htm#SEC1637 40166
	531	KSlinear sing_1563.htm#SEC1639 19896
	532	KSpencerKernel sing_1611.htm#SEC1687 12490
[54fdec1]	533	KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2412.htm#SEC2488 20741
[063ba1]	534	Kernel of module homomorphisms Kernel of module homomorphisms sing_812.htm#SEC864
	535	KoszulHomology sing_1161.htm#SEC1237 sprintf
	536	LETTERPLACE sing_483.htm#SEC535
[cd8a2b5]	537	LIB sing_276.htm#SEC316
[a719149]	538	LIB commands sing_53.htm#SEC90
[063ba1]	539	LIBs sing_870.htm#SEC946
	540	LLL sing_350.htm#IDX220
	541	LOT algorithm sing_532.htm#IDX338
[cd8a2b5]	542	LU-decomposition of a matrix of numbers sing_281.htm#SEC321
[063ba1]	543	Laurent series sing_1129.htm#IDX519
	544	Left and two-sided Groebner bases Left and two-sided Groebner bases sing_828.htm#SEC880
	545	Left ideal membership Groebner bases in G-algebras sing_479.htm#SEC526
	546	Left normal form Groebner bases in G-algebras sing_479.htm#SEC525
	547	LengthSym sing_737.htm#SEC789 16591
	548	LengthSymElement sing_736.htm#SEC788 28292
	549	Letterplace sing_483.htm#SEC535
	550	Lexicographic Groebner bases, computation of Groebner basis conversion sing_799.htm#SEC851
[a719149]	551	Libraries Writing procedures and libraries sing_48.htm#SEC85
[063ba1]	552	Libraries sing_789.htm#SEC841
[a719149]	553	Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86
[54fdec1]	554	Library versioning Notes for Singular users sing_2560.htm#SEC2648
[063ba1]	555	Lie algebra sing_1352.htm#IDX578
	556	Lie group sing_1355.htm#IDX583
	557	Lie group sing_1356.htm#IDX586
[7d21990]	558	Limitations sing_399.htm#SEC439
[063ba1]	559	Linear algebra sing_1029.htm#SEC1105
	560	Linear code sing_1789.htm#IDX773
	561	LinearActionQ sing_1673.htm#SEC1749 62218
	562	LinearCombinationQ sing_1674.htm#SEC1750 59373
	563	LinearizeAction sing_1672.htm#SEC1748 60266
[a719149]	564	Loading a library sing_62.htm#SEC99
[063ba1]	565	Local orderings sing_839.htm#SEC891
	566	Log for matrices sing_1354.htm#IDX582
	567	Long coefficients sing_791.htm#SEC843
	568	M, ordering sing_841.htm#SEC893
[54fdec1]	569	MVComplex sing_2321.htm#SEC2397 62126
	570	MacdonaldF sing_2376.htm#SEC2452 12751
	571	Macintosh installation Macintosh installation instructions sing_2568.htm#SEC2658
[063ba1]	572	Mathematical background Mathematical background sing_844.htm#SEC896
	573	Mathematical background (plural) Mathematical background (plural) sing_477.htm#SEC517
	574	Matrix orderings sing_841.htm#SEC893
	575	Max sing_1580.htm#SEC1656 23
	576	Maximus sing_1444.htm#SEC1520 10010
	577	Maxord sing_1385.htm#SEC1461 14124
	578	MillerRabin sing_1881.htm#SEC1957 15740
	579	Milnor number Milnor and Tjurina number sing_815.htm#SEC867
[54fdec1]	580	Milnor number sing_2506.htm#IDX972
[063ba1]	581	Min sing_1581.htm#SEC1657 29622
[54fdec1]	582	MinMult sing_2296.htm#SEC2372 39835
[063ba1]	583	MinimalDecomposition MinimalDecomposition sing_1675.htm#SEC1751 24161
	584	Minimum distance sing_1789.htm#IDX775
	585	Minimus sing_1443.htm#SEC1519 61721
	586	Miscellaneous libraries Miscellaneous libraries sing_2156.htm#SEC2232
	587	ModEqn sing_1574.htm#SEC1650 59394
	588	Modular techniques sing_931.htm#IDX475
	589	Module orderings sing_840.htm#SEC892
[3a9ee05]	590	Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16
[063ba1]	591	Monodromy sing_1566.htm#IDX750
	592	Monomial orderings sing_835.htm#SEC887
[a719149]	593	Monomial orderings, Term orderings sing_31.htm#SEC44
[54fdec1]	594	Morse lemma sing_2505.htm#IDX970
[063ba1]	595	MultiplicitySequence MultiplicitySequence sing_1498.htm#SEC1574 1309
[cd8a2b5]	596	NF sing_326.htm#SEC366
[063ba1]	597	NF sing_469.htm#SEC509
	598	NFMora sing_1947.htm#SEC2023 40670
	599	NPos sing_1217.htm#SEC1293 15702
	600	NPos_test sing_1215.htm#SEC1291 48172
	601	NSplaces sing_1777.htm#SEC1853 48675
[3a9ee05]	602	NTL sing_1.htm#IDX4
[a719149]	603	Names sing_37.htm#SEC65
	604	Names in procedures sing_46.htm#SEC83
	605	Names, indexed sing_37.htm#SEC65
[54fdec1]	606	New libraries depending on Singular 4 Notes for Singular users sing_2560.htm#SEC2646
	607	New orderings for modules Notes for Singular users sing_2560.htm#SEC2649
[063ba1]	608	Newton non-degenerate sing_1553.htm#IDX748
	609	Newton polygon sing_1552.htm#IDX747
	610	Newton polygon sing_1553.htm#IDX749
[54fdec1]	611	Newton polygons sing_2547.htm#IDX1000
[063ba1]	612	Newton polytope sing_2052.htm#IDX792
	613	NoetherPosition sing_1211.htm#SEC1287 18735
	614	Non-commutative LIBs Non-commutative libraries sing_489.htm#SEC541
	615	Non-commutative algebra Non-commutative algebra sing_827.htm#SEC879
	616	Non-commutative algebra sing_861.htm#SEC918
	617	Non-commutative libraries Non-commutative libraries sing_489.htm#SEC541
	618	Non-commutative subsystem Non-commutative subsystem sing_412.htm#SEC452
	619	Nonhyp sing_1374.htm#SEC1450 sprintf
	620	Normal form sing_845.htm#IDX415
	621	Normalization sing_811.htm#SEC863
[54fdec1]	622	Notes for Singular users Notes for Singular users sing_2560.htm#SEC2643
	623	Notes for developers Notes for developers sing_2561.htm#SEC2651
[063ba1]	624	NullCone sing_1676.htm#SEC1752 64635
	625	NumIrrDecom sing_1348.htm#SEC1424 sprintf
	626	NumLocalDim sing_1337.htm#SEC1413 1739
	627	NumPrimDecom sing_1350.htm#SEC1426 34134
	628	Oaku-Takayama algorithm sing_532.htm#IDX336
[a719149]	629	Objects sing_38.htm#SEC66
[063ba1]	630	Orlik-Solomon sing_2186.htm#IDX856
	631	Output, formatting of sing_793.htm#SEC845
	632	PBW sing_511.htm#IDX324
	633	PBW basis sing_478.htm#SEC519
	634	PBW_eqDeg sing_529.htm#SEC581 23181
	635	PBW_maxDeg sing_530.htm#SEC582 59566
	636	PBW_maxMonom sing_531.htm#SEC583 1155
	637	PEsolve sing_1686.htm#SEC1762 9229
	638	PH_ais sing_2208.htm#SEC2284 49473
	639	PH_nais sing_2209.htm#SEC2285 46271
	640	PLURAL sing_413.htm#SEC453
	641	PLURAL LIBs Non-commutative libraries sing_489.htm#SEC541
[54fdec1]	642	PPolyH sing_2374.htm#SEC2450 25241
	643	PPolyS sing_2377.htm#SEC2453 13817
	644	ParToVar sing_2369.htm#SEC2445 13991
[063ba1]	645	Parallelization Parallelization with ssi links sing_795.htm#SEC847
	646	Parallelization sing_931.htm#IDX476
[a719149]	647	Parameter list sing_44.htm#SEC81
[063ba1]	648	Parameters sing_792.htm#SEC844
	649	Parametrization sing_1357.htm#IDX590
	650	Parametrization, image. sing_1367.htm#IDX602
	651	PartC sing_2286.htm#SEC2362 54120
[54fdec1]	652	PartitionVar sing_2366.htm#SEC2442 41350
	653	Path names Notes for Singular users sing_2560.htm#SEC2647
[063ba1]	654	PerfectPowerTest sing_1844.htm#SEC1920 17450
	655	Perturbation walk sing_1141.htm#IDX536
[3a9ee05]	656	Pfister, Gerhard sing_1.htm#IDX19
[a719149]	657	Pipe links sing_116.htm#SEC156
[063ba1]	658	PocklingtonLehmer sing_1883.htm#SEC1959 13634
	659	Poincare polynomial sing_2198.htm#IDX880
	660	Polar curves sing_817.htm#SEC869
	661	PollardRho sing_1884.htm#SEC1960 49602
	662	PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2211.htm#IDX896
	663	PolyBoRi, Boolean Groebner Basis sing_2213.htm#IDX897
	664	PolyBoRi, Boolean Groebner Basis sing_2214.htm#IDX898
	665	PolyBoRi, Boolean Groebner Basis sing_2215.htm#IDX899
	666	PolyBoRi, Boolean Groebner Basis sing_2216.htm#IDX900
	667	PolyBoRi, Boolean Groebner Basis sing_2217.htm#IDX901
	668	PolyBoRi, Boolean Groebner Basis sing_2218.htm#IDX902
	669	PolyBoRi, Boolean Groebner Basis sing_2219.htm#IDX903
	670	PolyBoRi, Boolean Groebner Basis sing_2220.htm#IDX904
	671	PolyBoRi, Boolean Groebner Basis sing_2221.htm#IDX905
	672	PolyBoRi, Boolean Groebner Basis sing_2222.htm#IDX906
	673	PolyBoRi, Boolean Groebner Basis sing_2223.htm#IDX907
	674	PolyBoRi, Boolean Groebner Basis sing_2224.htm#IDX908
	675	PolyBoRi, Boolean Groebner Basis sing_2225.htm#IDX909
	676	PolyBoRi, Boolean Groebner Basis sing_2227.htm#IDX911
	677	PolyBoRi, zero-supressed decision diagram sing_2226.htm#IDX910
	678	Polybori, Boolean Groebner Basis sing_2228.htm#IDX912
	679	Polynomial data sing_833.htm#SEC885
	680	Pottier algorithm sing_854.htm#SEC911
[3a9ee05]	681	Preface sing_1.htm#SEC1
[063ba1]	682	Prep sing_907.htm#SEC983 49657
	683	Primary decomposition Primary decomposition sing_810.htm#SEC862
	684	PrimdecA sing_1193.htm#SEC1269 248
	685	PrimdecB sing_1194.htm#SEC1270 9653
[a719149]	686	Procedure definition Procedure definition sing_43.htm#SEC78
	687	Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84
	688	Procedures sing_42.htm#SEC77
[3a9ee05]	689	Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14
[063ba1]	690	Procedures and libraries sing_789.htm#SEC841
[a719149]	691	Procedures in a library Procedures in a library sing_54.htm#SEC91
[063ba1]	692	Product orderings sing_842.htm#SEC894
	693	Programming sing_787.htm#SEC839
	694	PtoCrep sing_908.htm#SEC984 30456
	695	Puiseux expansion sing_1451.htm#IDX613
	696	Puiseux expansion sing_1539.htm#IDX735
	697	Puiseux pairs Invariants of plane curve singularities sing_820.htm#SEC872
	698	Puiseux pairs sing_1545.htm#IDX740
[7d21990]	699	QQ sing_28.htm#SEC39
[063ba1]	700	Qso3Casimir sing_677.htm#SEC729 40212
	701	Quotient sing_1728.htm#SEC1804 24888
	702	QuotientEquations sing_1575.htm#SEC1651 18230
	703	Rational curves sing_1357.htm#IDX591
	704	ReJunkUseHomo sing_1343.htm#SEC1419 10186
	705	ReesAlgebra sing_1310.htm#SEC1386 59951
	706	References sing_869.htm#SEC943
	707	References (plural) sing_481.htm#SEC531
[54fdec1]	708	Release Notes sing_2556.htm#SEC2632
[063ba1]	709	ResTree sing_1403.htm#SEC1479 58727
[3a9ee05]	710	Resolution sing_11.htm#SEC17
[063ba1]	711	Resolution of singularities Resolution of singularities sing_823.htm#SEC875
	712	Resolution, free sing_805.htm#SEC857
	713	ReynoldsImage sing_1677.htm#SEC1753 35172
	714	ReynoldsOperator sing_1678.htm#SEC1754 14986
	715	RiemannRochBN sing_2231.htm#SEC2307 20085
[54fdec1]	716	RiemannRochHess sing_2431.htm#SEC2507 sprintf
[063ba1]	717	Right Groebner bases and syzygies Right Groebner bases and syzygies sing_829.htm#SEC881
[54fdec1]	718	Ring-dependent options Notes for Singular users sing_2560.htm#SEC2645
[a719149]	719	Rings and orderings sing_28.htm#SEC39
[3a9ee05]	720	Rings and standard bases Rings and standard bases sing_7.htm#SEC13
	721	Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
[063ba1]	722	SCA Graded commutative algebras (SCA) sing_482.htm#SEC534
[a719149]	723	SDB breakpoint Source code debugger sing_66.htm#SEC106
	724	SDB debugger Source code debugger sing_66.htm#SEC106
[063ba1]	725	SDLoc sing_559.htm#SEC611 9512
	726	SINGULAR libraries sing_870.htm#SEC946
[3a9ee05]	727	SINGULARHIST sing_18.htm#SEC25
[063ba1]	728	SScontinue sing_1013.htm#SEC1089 38390
	729	SSres sing_1011.htm#SEC1087 4648
	730	SSsyz sing_1012.htm#SEC1088 34610
	731	SV-decoding algorithm sing_1784.htm#IDX769
	732	SV-decoding algorithm, preprocessing sing_1783.htm#IDX768
	733	Sannfs sing_535.htm#SEC587 42932
	734	SannfsBFCT sing_544.htm#SEC596 59702
	735	SannfsVar sing_591.htm#SEC643 37522
	736	Sannfslog sing_536.htm#SEC588 49313
	737	Saturation sing_802.htm#SEC854
	738	Saturation sing_1122.htm#IDX505
[3a9ee05]	739	Sch@"onemann, Hans sing_1.htm#IDX20
[063ba1]	740	Schoof sing_1895.htm#SEC1971 49281
	741	Schreyer ordering sing_1006.htm#IDX492
	742	Schreyer resolution sing_1006.htm#IDX493
[54fdec1]	743	Schubert calculus sing_2508.htm#IDX976
	744	SchubertClass sing_2545.htm#SEC2621 62336
[063ba1]	745	SchurCh sing_2283.htm#SEC2359 58575
	746	SchurS sing_2282.htm#SEC2358 46004
	747	Scontinue sing_1010.htm#SEC1086 11534
[54fdec1]	748	SegreA sing_2289.htm#SEC2365 55776
[063ba1]	749	Semigroup sing_1491.htm#SEC1567 22323
	750	Setting up a G-algebra sing_478.htm#SEC522
	751	ShanksMestre sing_1894.htm#SEC1970 12973
	752	SimplifyIdeal sing_1679.htm#SEC1755 sprintf
	753	Singular sing_350.htm#IDX255
[54fdec1]	754	Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2558.htm#SEC2641
[a719149]	755	Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36
	756	Singular, demo mode sing_24.htm#SEC35
	757	Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
	758	Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38
[3a9ee05]	759	Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
[063ba1]	760	Singular2bertini sing_1341.htm#SEC1417 7552
	761	SingularLib sing_350.htm#IDX257
	762	Singularities sing_1450.htm#SEC1526
	763	Singularity Theory sing_814.htm#SEC866
	764	Skeletons for parallelization sing_931.htm#IDX477
	765	Smith form sing_1826.htm#IDX779
	766	Smith normal form sing_1826.htm#IDX780
	767	SolowayStrassen sing_1882.htm#SEC1958 22680
	768	Solving systems of polynomial equations Solving systems of polynomial equations sing_831.htm#SEC883
[3a9ee05]	769	Source code debugger, invocation Command line options sing_19.htm#IDX33
[063ba1]	770	Space curve singularities, branches of Branches of space curve singularities sing_821.htm#SEC873
[a719149]	771	Special characters sing_36.htm#SEC64
[54fdec1]	772	Splitting lemma sing_2505.htm#IDX971
[063ba1]	773	Sres sing_1008.htm#SEC1084 60186
[a719149]	774	Ssi file links sing_114.htm#SEC154
	775	Ssi links sing_113.htm#SEC153
	776	Ssi tcp links sing_115.htm#SEC155
[063ba1]	777	Ssyz sing_1009.htm#SEC1085 56541
	778	StabEqn sing_1576.htm#SEC1652 28539
	779	StabEqnId sing_1577.htm#SEC1653 27955
	780	StabOrder sing_1578.htm#SEC1654 55603
	781	Standard Bases Computing Groebner and Standard Bases sing_797.htm#SEC849
	782	Standard bases sing_845.htm#SEC897
	783	StartOrderingV sing_1445.htm#SEC1521 58927
[3a9ee05]	784	Startup sequence sing_20.htm#SEC27
[063ba1]	785	StringF sing_1565.htm#SEC1641 11590
	786	SymGroup sing_735.htm#SEC787 56676
	787	Symbolic-numerical solving Symbolic-numerical solving sing_831.htm#SEC883
	788	Symbolic-numerical solving sing_1683.htm#SEC1759
	789	System and Control theory System and Control theory sing_1808.htm#SEC1884
[7d21990]	790	System dependent limitations System dependent limitations sing_400.htm#SEC440
	791	System variables sing_386.htm#SEC426
[063ba1]	792	Syzygies and resolutions Syzygies and resolutions sing_847.htm#SEC901
	793	Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_480.htm#SEC527
	794	T1 sing_818.htm#SEC870
	795	T2 sing_818.htm#SEC870
[a719149]	796	TRACE Tracing of procedures sing_65.htm#SEC102
[7d21990]	797	TRACE sing_395.htm#SEC435
[063ba1]	798	T_1 sing_1598.htm#SEC1674 59277
	799	T_12 sing_1600.htm#SEC1676 12923
	800	T_2 sing_1599.htm#SEC1675 55781
	801	Teaching sing_1840.htm#SEC1916
[a719149]	802	Template for writing a library sing_55.htm#SEC92
[54fdec1]	803	TestGRRes sing_2411.htm#SEC2487 8315
[063ba1]	804	TestJMark sing_1446.htm#SEC1522 41314
[a719149]	805	The SINGULAR language The SINGULAR language sing_34.htm#SEC56
[063ba1]	806	The Tran algorithm sing_1138.htm#IDX533
	807	The fractal walk algorithm sing_1137.htm#IDX532
[54fdec1]	808	The fractal walk algorithm sing_2499.htm#IDX966
[3a9ee05]	809	The online help system The online help system sing_16.htm#SEC22
[063ba1]	810	Tjurina sing_1596.htm#SEC1672 11249
	811	Tjurina number Milnor and Tjurina number sing_815.htm#SEC867
	812	Tjurina number sing_1232.htm#IDX560
[a719149]	813	Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38
[063ba1]	814	Tor sing_1163.htm#SEC1239 sprintf
	815	Toric ideals and integer programming Toric ideals and integer programming sing_850.htm#SEC907
[7d21990]	816	Tricks and pitfalls sing_398.htm#SEC438
[063ba1]	817	Tropical Geometry sing_1992.htm#SEC2068
[a719149]	818	Type casting Type conversion and casting sing_39.htm#SEC69
	819	Type conversion Type conversion and casting sing_39.htm#SEC68
	820	Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98
[063ba1]	821	U_D_O sing_1078.htm#SEC1154 26192
[54fdec1]	822	Unix installation Unix installation instructions sing_2566.htm#SEC2656
[063ba1]	823	UpOneMatrix sing_724.htm#SEC776 63020
	824	UpperMonomials sing_1579.htm#SEC1655 20941
	825	UseBertini sing_1340.htm#SEC1416 43362
[a719149]	826	User defined types sing_177.htm#SEC217
[063ba1]	827	V-filtration sing_1514.htm#IDX645
	828	V-filtration sing_1520.htm#IDX673
	829	V-filtration sing_1521.htm#IDX679
	830	V-filtration sing_1522.htm#IDX687
	831	V-filtration sing_1523.htm#IDX693
	832	V-filtration sing_1524.htm#IDX701
	833	V-filtration sing_1525.htm#IDX711
	834	V-filtration sing_1536.htm#IDX717
	835	V-filtration sing_1538.htm#IDX728
[54fdec1]	836	VarToPar sing_2368.htm#SEC2444 10508
[a719149]	837	Variables, indexed sing_37.htm#SEC65
[54fdec1]	838	Version number Version schema for Singular sing_2559.htm#SEC2642
	839	Version schema for Singular Version schema for Singular sing_2559.htm#SEC2642
[a719149]	840	Version string sing_50.htm#SEC87
[063ba1]	841	Visualization sing_1746.htm#SEC1822
	842	WLemma sing_920.htm#SEC996 3921
	843	WP, global ordering sing_838.htm#IDX398
	844	WSemigroup sing_1496.htm#SEC1572 57449
	845	Weierstrass sing_1779.htm#SEC1855 58220
	846	Weierstrass semigroup sing_1775.htm#IDX763
	847	Weyl sing_709.htm#SEC761 29212
	848	Weyl algebra sing_532.htm#IDX330
	849	Weyl algebra sing_588.htm#IDX355
	850	Weyl closure sing_760.htm#IDX383
	851	WeylClosure sing_762.htm#SEC814 23845
	852	WeylClosure1 sing_763.htm#SEC815 15759
	853	Wibmer's Lemma sing_920.htm#IDX473
[54fdec1]	854	Windows installation Windows installation instructions sing_2567.htm#SEC2657
[063ba1]	855	WitSet sing_1347.htm#SEC1423 39803
	856	WitSupSet sing_1346.htm#SEC1422 47758
	857	Ws, local ordering sing_839.htm#IDX410
	858	XLsolve sing_1689.htm#SEC1765 34970
[7d21990]	859	ZZ sing_28.htm#SEC39
	860	ZZ/m sing_28.htm#SEC39
	861	ZZ/p sing_28.htm#SEC39
[063ba1]	862	ZZsolve sing_1690.htm#SEC1766 18657
[a719149]	863	[ sing_36.htm#IDX83
[a070b84]	864	[] sing_137.htm#SEC177
	865	[] sing_150.htm#SEC190
	866	[] sing_170.htm#SEC210
	867	[] sing_175.htm#SEC215
[a719149]	868	\ sing_36.htm#IDX112
	869	] sing_36.htm#IDX84
	870	^ sing_36.htm#IDX92
	871	^ sing_76.htm#SEC116
	872	^ sing_88.htm#SEC128
[a070b84]	873	^ sing_142.htm#SEC182
	874	^ sing_150.htm#SEC190
[a719149]	875	_ sing_36.htm#IDX116
	876	` sing_36.htm#IDX105
[063ba1]	877	a, ordering sing_843.htm#SEC895
	878	absFactorize sing_1091.htm#SEC1167 52546
	879	absFactorizeBCG sing_1092.htm#SEC1168 55510
	880	absPrimdecGTZ sing_1290.htm#SEC1366 46393
	881	absPrimdecGTZE sing_1291.htm#SEC1367 48005
	882	absValue sing_882.htm#SEC958 54595
	883	absfact.lib sing_1090.htm#SEC1166
	884	absfact_lib sing_1090.htm#SEC1166
	885	absolute factorization. sing_1090.htm#IDX504
[54fdec1]	886	abstract variety, projective space, Grassmannian printVariety sing_2509.htm#IDX979
	887	abstract variety, projective space, Grassmannian sing_2510.htm#IDX980
[063ba1]	888	abstractR sing_1429.htm#SEC1505 22284
	889	actionIsProper sing_1659.htm#SEC1735 52474
	890	addNvarsTo sing_1005.htm#SEC1081 63123
	891	addRat sing_781.htm#SEC833 4768
[54fdec1]	892	addSheaf sing_2528.htm#SEC2604 27062
[063ba1]	893	addcol sing_1047.htm#SEC1123 52204
	894	addcores sing_974.htm#SEC1050 41254
	895	addrow sing_1048.htm#SEC1124 47055
	896	addvarsTo sing_1004.htm#SEC1080 17717
	897	ademRelations sing_641.htm#SEC693 30263
	898	adjoint sing_1072.htm#SEC1148 56619
	899	adjointIdeal sing_1358.htm#SEC1434 11455
	900	adjunction divisor sing_1776.htm#IDX767
	901	admissibleSub sing_700.htm#SEC752 6583
[54fdec1]	902	afaces sing_2387.htm#SEC2463 41634
[063ba1]	903	affine code Fitzgerald-Lax method sing_866.htm#SEC935
	904	ainvar.lib sing_1656.htm#SEC1732
	905	ainvar_lib sing_1656.htm#SEC1732
	906	aksaka.lib sing_1841.htm#SEC1917
	907	aksaka_lib sing_1841.htm#SEC1917
	908	alexanderpolynomial sing_1454.htm#SEC1530 36814
	909	alexpoly.lib sing_1451.htm#SEC1527
	910	alexpoly_lib sing_1451.htm#SEC1527
	911	algDependent sing_1097.htm#SEC1173 20789
	912	alg_kernel sing_1098.htm#SEC1174 307
	913	algebra.lib sing_1093.htm#SEC1169
	914	algebra_containment sing_1094.htm#SEC1170 47912
	915	algebra_lib sing_1093.htm#SEC1169
	916	algebraic dependence sing_730.htm#IDX361
	917	algebraic field extension sing_1304.htm#IDX567
	918	algebraicDependence sing_1317.htm#SEC1393 38500
	919	algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_857.htm#SEC914
	920	algorithm of Conti and Traverso sing_853.htm#SEC910
	921	algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_856.htm#SEC913
	922	algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_855.htm#SEC912
	923	algorithm of Pottier sing_854.htm#SEC911
[cd8a2b5]	924	align sing_203.htm#SEC243
[063ba1]	925	all.lib sing_875.htm#SEC951
	926	allDoubleExt sing_747.htm#SEC799 43457
	927	allExtOfLeft sing_744.htm#SEC796 6405
	928	allExtOfRight sing_745.htm#SEC797 56781
	929	allPositive sing_508.htm#SEC560 1409
	930	all_lib sing_875.htm#SEC951
[3a9ee05]	931	allowing net access Command line options sing_19.htm#IDX41
[063ba1]	932	allprint sing_922.htm#SEC998 5195
	933	allreal sing_1984.htm#SEC2060 57232
	934	allrealst sing_1982.htm#SEC2058 40962
	935	allsquarefree sing_1558.htm#SEC1634 45545
	936	ambientDimension sing_1997.htm#SEC2073 18907
[a719149]	937	and Evaluation of logical expressions sing_96.htm#SEC136
[7d21990]	938	and sing_403.htm#SEC443
[063ba1]	939	annPoly sing_556.htm#SEC608 18228
	940	annRat sing_557.htm#SEC609 62662
	941	annRatSyz sing_770.htm#SEC822 15672
	942	annfs sing_533.htm#SEC585 38155
	943	annfs0 sing_545.htm#SEC597 26476
	944	annfs2 sing_546.htm#SEC598 47962
	945	annfsBMI sing_542.htm#SEC594 2532
	946	annfsParamBM sing_541.htm#SEC593 43587
	947	annfsRB sing_547.htm#SEC599 31892
	948	annfspecial sing_534.htm#SEC586 27566
	949	annihilator of polynomial sing_555.htm#IDX340
	950	annihilator of rational function sing_555.htm#IDX341
	951	annihilator of rational function sing_760.htm#IDX386
	952	annil sing_1199.htm#SEC1275 48744
	953	appelF1 sing_574.htm#SEC626 63146
	954	appelF2 sing_575.htm#SEC627 22460
	955	appelF4 sing_576.htm#SEC628 6847
	956	appendWeight2Ord sing_702.htm#SEC754 21488
[7d21990]	957	apply sing_370.htm#SEC410
[063ba1]	958	applyAdF sing_524.htm#SEC576 40329
	959	arcpoint.lib sing_1464.htm#SEC1540
	960	arcpoint_lib sing_1464.htm#SEC1540
[54fdec1]	961	areZeroElements sing_2473.htm#SEC2549 14728
[a719149]	962	argument, default sing_44.htm#SEC81
	963	argument, optional sing_44.htm#SEC81
[063ba1]	964	arr.lib sing_2157.htm#SEC2233
	965	arr2multarr sing_2190.htm#SEC2266 15063
	966	arrBoolean sing_2179.htm#SEC2255 63256
	967	arrBoundedChambers sing_2200.htm#SEC2276 18347
	968	arrBraid sing_2180.htm#SEC2256 34093
	969	arrCenter sing_2167.htm#SEC2243 24565
	970	arrCentered sing_2169.htm#SEC2245 15904
	971	arrCentral sing_2168.htm#SEC2244 14086
	972	arrCentralize sing_2170.htm#SEC2246 53235
	973	arrChambers sing_2199.htm#SEC2275 44578
	974	arrCharPoly sing_2197.htm#SEC2273 44129
	975	arrCone sing_2173.htm#SEC2249 38068
	976	arrCoordChange sing_2171.htm#SEC2247 61430
	977	arrCoordNormalize sing_2172.htm#SEC2248 46273
	978	arrDecone sing_2174.htm#SEC2250 54637
	979	arrDer sing_2187.htm#SEC2263 48815
	980	arrEdelmanReiner sing_2185.htm#SEC2261 59091
	981	arrEssentialize sing_2178.htm#SEC2254 6667
	982	arrExponents sing_2189.htm#SEC2265 1948
	983	arrFlats sing_2194.htm#SEC2270 64792
	984	arrIsEssential sing_2177.htm#SEC2253 34363
	985	arrIsFree sing_2188.htm#SEC2264 3860
	986	arrLastVar sing_2166.htm#SEC2242 25835
	987	arrLattice sing_2195.htm#SEC2271 58951
	988	arrLocalize sing_2175.htm#SEC2251 56070
	989	arrOrlikSolomon sing_2186.htm#SEC2262 31686
	990	arrPoincare sing_2198.htm#SEC2274 412
	991	arrPrintMatrix sing_2162.htm#SEC2238 21204
	992	arrRandom sing_2183.htm#SEC2259 59986
	993	arrRandomCentral sing_2184.htm#SEC2260 43698
	994	arrRestrict sing_2176.htm#SEC2252 sprintf
	995	arrSet sing_2158.htm#SEC2234 53769
	996	arrSwapVar sing_2165.htm#SEC2241 44919
	997	arrTypeB sing_2181.htm#SEC2257 22358
	998	arrTypeD sing_2182.htm#SEC2258 26495
	999	arr_lib sing_2157.htm#SEC2233
	1000	arrange sing_549.htm#SEC601 50350
	1001	arrangement sing_2158.htm#IDX798
	1002	arrangement sing_2159.htm#IDX803
	1003	arrangement sing_2190.htm#IDX865
	1004	arrangement sing_2191.htm#IDX868
	1005	ask sing_1849.htm#SEC1925 3862
	1006	assPrimes sing_1108.htm#SEC1184 sprintf
	1007	assign sing_2158.htm#IDX800
[a719149]	1008	assignment,custom Assignments for user defined types sing_182.htm#SEC222
[063ba1]	1009	associated tangent FamElemsAtEnvCompPoints sing_917.htm#IDX466
	1010	associated tangent sing_918.htm#IDX470
	1011	assprimeszerodim.lib assprimeszerodim_lib sing_1106.htm#SEC1182
	1012	assprimeszerodim_lib assprimeszerodim_lib sing_1106.htm#SEC1182
	1013	atkins.lib sing_1850.htm#SEC1926
	1014	atkins_lib sing_1850.htm#SEC1926
[cd8a2b5]	1015	attrib sing_204.htm#SEC244
[063ba1]	1016	autonom sing_1813.htm#SEC1889 57044
	1017	autonomDim sing_1814.htm#SEC1890 30055
	1018	awalk1 sing_1139.htm#SEC1215 11044
	1019	awalk2 sing_1140.htm#SEC1216 8955
	1020	b-function sing_497.htm#IDX313
	1021	bFactor sing_579.htm#SEC631 15179
	1022	babyGiant sing_1879.htm#SEC1955 41113
[54fdec1]	1023	backward sing_2355.htm#SEC2431 11225
[cd8a2b5]	1024	bareiss sing_205.htm#SEC245
[063ba1]	1025	base2str sing_878.htm#SEC954 sprintf
[a719149]	1026	basering sing_28.htm#IDX76
	1027	basering sing_83.htm#SEC123
[063ba1]	1028	basicinvariants sing_1470.htm#SEC1546 32136
	1029	belongSemigroup sing_1111.htm#SEC1187 19983
	1030	bernstein sing_1518.htm#SEC1594 5605
	1031	bernsteinBM sing_537.htm#SEC589 57689
	1032	bernsteinLift sing_538.htm#SEC590 22885
	1033	bertini2Singular sing_1342.htm#SEC1418 58501
[cd8a2b5]	1034	betti sing_206.htm#SEC246
[063ba1]	1035	betti (plural) sing_447.htm#SEC487
	1036	bfct sing_498.htm#SEC550 29858
	1037	bfctAnn sing_500.htm#SEC552 36658
	1038	bfctBound sing_769.htm#SEC821 5630
	1039	bfctIdeal sing_502.htm#SEC554 41018
	1040	bfctOneGB sing_501.htm#SEC553 9696
	1041	bfctSyz sing_499.htm#SEC551 26796
	1042	bfctVarAnn sing_590.htm#SEC642 51667
	1043	bfctVarIn sing_589.htm#SEC641 9274
	1044	bfun.lib sing_497.htm#SEC549
	1045	bfun_lib sing_497.htm#SEC549
[a719149]	1046	bigint sing_73.htm#SEC113
	1047	bigint declarations sing_74.htm#SEC114
	1048	bigint expressions sing_75.htm#SEC115
	1049	bigint operations sing_76.htm#SEC116
	1050	bigint related functions bigint related functions sing_77.htm#SEC117
	1051	bigintmat sing_78.htm#SEC118
	1052	bigintmat declarations bigintmat declarations sing_79.htm#SEC119
	1053	bigintmat expressions bigintmat expressions sing_80.htm#SEC120
	1054	bigintmat operations bigintmat operations sing_82.htm#SEC122
	1055	bigintmat type cast sing_81.htm#SEC121
[063ba1]	1056	bimodules sing_490.htm#IDX301
	1057	bimodules.lib sing_490.htm#SEC542
	1058	bimodules_lib sing_490.htm#SEC542
	1059	binary_add sing_1902.htm#SEC1978 42817
	1060	binomial sing_883.htm#SEC959 23208
	1061	binomials2intmat sing_1265.htm#SEC1341 58804
	1062	birational map, image, inverse. sing_1359.htm#IDX596
	1063	bistd sing_491.htm#SEC543 45237
	1064	bisyzygies sing_490.htm#IDX302
	1065	bitrinity sing_492.htm#SEC544 3516
[cd8a2b5]	1066	blackbox sing_186.htm#SEC226
	1067	blackbox sing_194.htm#SEC234
[a719149]	1068	block sing_40.htm#SEC70
[7d21990]	1069	block sing_369.htm#SEC409
[063ba1]	1070	blowUp sing_1410.htm#SEC1486 34819
	1071	blowUp2 sing_1411.htm#SEC1487 65264
	1072	blowUpBO sing_1417.htm#SEC1493 58146
	1073	blowup0 sing_1116.htm#SEC1192 44451
	1074	boolean sing_2179.htm#IDX842
[a719149]	1075	boolean expressions sing_95.htm#SEC135
	1076	boolean operations sing_96.htm#SEC136
[063ba1]	1077	boolean_constant sing_2213.htm#SEC2289 52873
	1078	boolean_ideal sing_2217.htm#SEC2293 53515
	1079	boolean_poly sing_2214.htm#SEC2290 41652
	1080	boolean_poly_ring sing_2212.htm#SEC2288 sprintf
	1081	boolean_set sing_2218.htm#SEC2294 58235
	1082	boolean_std sing_2211.htm#SEC2287 5921
	1083	boundBuFou sing_1979.htm#SEC2055 26589
	1084	boundDes sing_1981.htm#SEC2057 35149
	1085	boundaryLatticePoints boundaryLatticePoints sing_2070.htm#SEC2146 6238
	1086	boundposDes sing_1980.htm#SEC2056 58854
	1087	bracket sing_350.htm#IDX197
[7d21990]	1088	bracket sing_406.htm#SEC446
[063ba1]	1089	bracket sing_448.htm#SEC488
	1090	braid sing_2180.htm#IDX844
[a719149]	1091	branchTo procs with different argument types sing_155.htm#SEC195
[7d21990]	1092	break sing_371.htm#SEC411
	1093	break point sing_385.htm#SEC425
	1094	breakpoint sing_372.htm#SEC412
[063ba1]	1095	brillnoether.lib sing_2230.htm#SEC2306
	1096	brillnoether_lib sing_2230.htm#SEC2306
	1097	brnoeth.lib sing_1775.htm#SEC1851
	1098	brnoeth_lib sing_1775.htm#SEC1851
[3a9ee05]	1099	browser, command line option Command line options sing_19.htm#IDX44
[063ba1]	1100	browser, setting the sing_350.htm#IDX193
[3a9ee05]	1101	browsers The online help system sing_16.htm#IDX21
[063ba1]	1102	browsers, setting the sing_350.htm#IDX192
	1103	bubblesort sing_1852.htm#SEC1928 63278
	1104	busadj sing_1070.htm#SEC1146 36301
	1105	bvar sing_2225.htm#SEC2301 52773
	1106	c, module ordering sing_840.htm#IDX413
	1107	cProj sing_2272.htm#SEC2348 24037
	1108	calculateI sing_1384.htm#SEC1460 31107
	1109	calculate_max_sum sing_1921.htm#SEC1997 4706
	1110	calculate_ordering sing_1899.htm#SEC1975 42616
[cd8a2b5]	1111	cancelunit, option sing_307.htm#IDX171
[063ba1]	1112	canonMap sing_1144.htm#SEC1220 47599
	1113	canonical sing_902.htm#IDX424
	1114	canonical form sing_911.htm#IDX447
	1115	canonical form sing_912.htm#IDX449
	1116	canonical, discussion of parametric ideal sing_910.htm#IDX443
	1117	canonicalizeCone sing_1998.htm#SEC2074 6251
	1118	canonize sing_1821.htm#SEC1897 54090
	1119	cantoradd sing_1935.htm#SEC2011 55304
	1120	cantormult sing_1938.htm#SEC2014 57569
	1121	cantorred sing_1936.htm#SEC2012 46502
	1122	cardGroup sing_1113.htm#SEC1189 5553
[7d21990]	1123	case No case or switch statement sing_404.htm#SEC444
[54fdec1]	1124	cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2551.htm#SEC2627 55393
[3a9ee05]	1125	cdd sing_1.htm#IDX10
	1126	cddlib sing_1.htm#IDX11
[063ba1]	1127	center sing_511.htm#IDX320 65108
	1128	center sing_517.htm#SEC569
	1129	center sing_2167.htm#IDX824
	1130	center sing_2168.htm#IDX825
	1131	center sing_2169.htm#IDX827
	1132	center sing_2170.htm#IDX829
	1133	centerRed sing_516.htm#SEC568 59910
	1134	centerVS sing_515.htm#SEC567 27548
	1135	central sing_2161.htm#IDX810
	1136	central sing_2168.htm#IDX826
	1137	central sing_2170.htm#IDX828
	1138	central sing_2184.htm#IDX853
	1139	central.lib sing_511.htm#SEC563
[54fdec1]	1140	central1st sing_2356.htm#SEC2432 29090
	1141	central2nd sing_2357.htm#SEC2433 37545
[063ba1]	1142	central_lib sing_511.htm#SEC563
	1143	centralize sing_511.htm#IDX323
	1144	centralizeSet sing_512.htm#SEC564 55737
	1145	centralizer sing_511.htm#IDX321 65261
	1146	centralizer sing_518.htm#SEC570
	1147	centralizerRed sing_514.htm#SEC566 8209
	1148	centralizerVS sing_513.htm#SEC565 22925
[cd8a2b5]	1149	cf_class sing_204.htm#IDX132
[063ba1]	1150	cgs sing_877.htm#SEC953 57776
	1151	cgsdr sing_903.htm#SEC979 11367
	1152	chAll sing_2242.htm#SEC2318 2690
	1153	chAllInv sing_2243.htm#SEC2319 57760
	1154	chDual sing_2248.htm#SEC2324 17745
	1155	chHE sing_2244.htm#SEC2320 63916
[54fdec1]	1156	chHom sing_2257.htm#SEC2333 54776
[063ba1]	1157	chNum sing_2238.htm#SEC2314 54415
	1158	chNumbers sing_2239.htm#SEC2315 42134
	1159	chNumbersProj sing_2276.htm#SEC2352 28837
	1160	chProd sing_2250.htm#SEC2326 40209
	1161	chProdE sing_2251.htm#SEC2327 33460
	1162	chProdL sing_2252.htm#SEC2328 44795
	1163	chProdLP sing_2253.htm#SEC2329 8881
	1164	chProdM sing_2254.htm#SEC2330 64514
	1165	chProdMP sing_2255.htm#SEC2331 17103
	1166	chProj sing_2273.htm#SEC2349 32311
	1167	chSum sing_2246.htm#SEC2322 21088
	1168	chSymm sing_2260.htm#SEC2336 24066
	1169	chSymm2L sing_2261.htm#SEC2337 51625
	1170	chSymm2LP sing_2262.htm#SEC2338 26099
	1171	chWedge sing_2263.htm#SEC2339 57678
	1172	chWedge2L sing_2264.htm#SEC2340 46597
	1173	chWedge2LP sing_2265.htm#SEC2341 8876
	1174	chaincrit sing_1949.htm#SEC2025 9502
	1175	chambers sing_2199.htm#IDX881
	1176	chambers sing_2200.htm#IDX882
	1177	changeDenominator sing_1237.htm#SEC1313 21094
	1178	changechar sing_979.htm#SEC1055 65454
	1179	changeord sing_980.htm#SEC1056 55156
	1180	changeordTo sing_1003.htm#SEC1079 41903
[54fdec1]	1181	changes sing_2557.htm#SEC2633
[063ba1]	1182	changevar sing_981.htm#SEC1057 32829
[cd8a2b5]	1183	char sing_207.htm#SEC247
[063ba1]	1184	charInfo sing_572.htm#SEC624 11034
	1185	charVariety sing_571.htm#SEC623 18306
[cd8a2b5]	1186	char_series sing_208.htm#SEC248
[063ba1]	1187	characteristic exponents sing_1458.htm#IDX620
	1188	characteristic exponents sing_1459.htm#IDX625
	1189	characteristic exponents sing_1460.htm#IDX628
	1190	characteristic exponents sing_1461.htm#IDX632
	1191	characteristic exponents sing_1545.htm#IDX738
	1192	characteristic polynomial sing_2197.htm#IDX879
	1193	characteristic variety sing_555.htm#IDX348
	1194	characteristic variety sing_760.htm#IDX382
	1195	charexp2conductor sing_1461.htm#SEC1537 sprintf
	1196	charexp2generators sing_1459.htm#SEC1535 16838
	1197	charexp2inter sing_1460.htm#SEC1536 39881
	1198	charexp2multseq sing_1458.htm#SEC1534 334
	1199	charexp2poly sing_1462.htm#SEC1538 sprintf
	1200	charpoly sing_1071.htm#SEC1147 29561
[cd8a2b5]	1201	charstr sing_209.htm#SEC249
[063ba1]	1202	checkFactor sing_548.htm#SEC600 55900
	1203	checkRoot sing_543.htm#SEC595 37045
	1204	chern sing_2237.htm#SEC2313 4916
	1205	chern.lib sing_2232.htm#SEC2308
	1206	chernCharPoly sing_2279.htm#SEC2355 31610
	1207	chernPoly sing_2278.htm#SEC2354 31316
	1208	chern_lib sing_2232.htm#SEC2308
	1209	chineseRem sing_1870.htm#SEC1946 38560
[cd8a2b5]	1210	chinrem sing_210.htm#SEC250
[54fdec1]	1211	chinrempoly sing_2492.htm#SEC2568 42312
[063ba1]	1212	chinrestp sing_1929.htm#SEC2005 24779
[54fdec1]	1213	cimonom.lib sing_2294.htm#SEC2370
	1214	cimonom_lib sing_2294.htm#SEC2370
[063ba1]	1215	cisimplicial.lib sing_1109.htm#SEC1185
	1216	cisimplicial_lib sing_1109.htm#SEC1185
	1217	classify sing_1471.htm#SEC1547 4953
	1218	classify.lib sing_1469.htm#SEC1545
	1219	classifyCeq sing_1488.htm#SEC1564 42719
[54fdec1]	1220	classifyMapGerms.lib classifyMapGerms_lib sing_2306.htm#SEC2382
	1221	classifyMapGerms_lib classifyMapGerms_lib sing_2306.htm#SEC2382
	1222	classifySimpleMaps sing_2312.htm#SEC2388 62176
	1223	classifySimpleMaps1 sing_2313.htm#SEC2389 24789
	1224	classify_aeq.lib sing_2298.htm#SEC2374
	1225	classify_aeq_lib sing_2298.htm#SEC2374
[063ba1]	1226	classify_lib sing_1469.htm#SEC1545
	1227	classifyceq.lib sing_1487.htm#IDX635
	1228	classifyceq_lib sing_1487.htm#IDX636
	1229	classifyci.lib sing_1489.htm#IDX637
	1230	classifyci_lib sing_1489.htm#IDX638
	1231	classifyicis sing_1490.htm#SEC1566 37651
	1232	classpoly sing_2277.htm#SEC2353 45724
	1233	cleanTmp sing_2148.htm#SEC2224 14108
	1234	cleanunit sing_1382.htm#SEC1458 sprintf
[cd8a2b5]	1235	cleardenom sing_211.htm#SEC251
	1236	close sing_212.htm#SEC252
[063ba1]	1237	closed_points sing_1785.htm#SEC1861 47269
	1238	closetex sing_1752.htm#SEC1828 42334
	1239	closureFrac sing_1230.htm#SEC1306 9252
[54fdec1]	1240	coDim sing_2308.htm#SEC2384 60680
	1241	coDimMap sing_2307.htm#SEC2383 2002
[063ba1]	1242	coHom sing_753.htm#SEC805 51043
	1243	codim sing_1583.htm#SEC1659 14253
	1244	codimension sing_1999.htm#SEC2075 32207
	1245	coding theory sing_832.htm#SEC884
[cd8a2b5]	1246	coef sing_213.htm#SEC253
[063ba1]	1247	coefficient sing_2160.htm#IDX806
	1248	coefficient sing_2161.htm#IDX809
	1249	coefficient sing_2162.htm#IDX813
[a719149]	1250	coefficient field sing_139.htm#SEC179
	1251	coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45
[063ba1]	1252	coefficients, long sing_791.htm#SEC843
	1253	coeffmod sing_1847.htm#SEC1923 23531
[cd8a2b5]	1254	coeffs sing_214.htm#SEC254
[54fdec1]	1255	colength of derivations curveColengthDerivations sing_2318.htm#IDX925
[063ba1]	1256	collectDiv sing_1427.htm#SEC1503 50348
	1257	colrank sing_1819.htm#SEC1895 52290
	1258	colred sing_1054.htm#SEC1130 1693
	1259	commRing sing_784.htm#SEC836 30892
[7d21990]	1260	comma sing_405.htm#SEC445
[a719149]	1261	command,custom Commands for user defined types sing_181.htm#SEC221
[063ba1]	1262	command-line option, setting value of sing_350.htm#IDX279
	1263	command-line option, value of sing_350.htm#IDX277
	1264	command-line options, print all values of sing_350.htm#IDX276
[3a9ee05]	1265	command-line options, short help Command line options sing_19.htm#IDX38
[063ba1]	1266	commands (plural) sing_446.htm#IDX300
[a719149]	1267	comment sing_36.htm#IDX108
[063ba1]	1268	compareTasks sing_1018.htm#SEC1094 45157
	1269	completeReduction sing_1661.htm#SEC1737 57157
[a719149]	1270	complex sing_28.htm#IDX75
[063ba1]	1271	complexSingType sing_1485.htm#SEC1561 34483
	1272	compregb.lib sing_876.htm#SEC952
	1273	compregb_lib sing_876.htm#SEC952
	1274	comprehensive Groebner system sing_876.htm#IDX419
	1275	compress sing_1031.htm#SEC1107 61998
	1276	computeConstant sing_1129.htm#SEC1205 55024
	1277	computeGromovWitten sing_1132.htm#SEC1208 18834
	1278	computeN sing_1431.htm#SEC1507 61628
	1279	computeV sing_1430.htm#SEC1506 40316
	1280	computemcm sing_1389.htm#SEC1465 36956
	1281	concat sing_1032.htm#SEC1108 16653
	1282	conductor sing_1238.htm#IDX561
	1283	conductor sing_1461.htm#IDX631
[54fdec1]	1284	conductor sing_2316.htm#IDX919
[063ba1]	1285	conductor, degree sing_1545.htm#IDX741
[a719149]	1286	cone sing_183.htm#SEC223
[063ba1]	1287	cone sing_2173.htm#IDX833
	1288	cone sing_2174.htm#IDX835
	1289	coneLink sing_2002.htm#SEC2078 13635
	1290	coneViaInequalities sing_2001.htm#SEC2077 25661
	1291	coneViaPoints sing_2000.htm#SEC2076 3386
	1292	conic, parametrization, rational point. sing_1366.htm#IDX601
	1293	conicWithTangents sing_2124.htm#SEC2200 60752
	1294	constructH sing_1390.htm#SEC1466 59577
	1295	constructblwup sing_1391.htm#SEC1467 19326
	1296	constructible set sing_911.htm#IDX445
	1297	constructible sets sing_912.htm#IDX448
	1298	constructlastblwup sing_1392.htm#SEC1468 7639
	1299	constructor sing_2190.htm#IDX866
	1300	constructor sing_2191.htm#IDX869
	1301	contact matrix sing_1460.htm#IDX627
	1302	containedQ sing_1740.htm#SEC1816 46718
	1303	containsAsFace sing_2003.htm#SEC2079 25159
	1304	containsInCollection containsInCollection sing_2036.htm#SEC2112 14368
	1305	containsInSupport sing_2004.htm#SEC2080 32493
	1306	containsPositiveVector containsPositiveVector sing_2005.htm#SEC2081 27042
	1307	containsRelatively sing_2006.htm#SEC2082 17126
	1308	content sing_953.htm#SEC1029 9095
[cd8a2b5]	1309	contentSB, option sing_307.htm#IDX172
[7d21990]	1310	continue Behavior of continue sing_373.htm#SEC413
	1311	continue sing_407.htm#SEC447
[063ba1]	1312	contraHom sing_754.htm#SEC806 24706
[cd8a2b5]	1313	contract sing_215.htm#SEC255
[54fdec1]	1314	contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2535.htm#IDX992
	1315	contributionBundle sing_2535.htm#SEC2611 32874
[063ba1]	1316	contributors sing_350.htm#IDX200
	1317	control sing_1811.htm#SEC1887 44498
	1318	control.lib sing_1810.htm#SEC1886
	1319	controlDim sing_1812.htm#SEC1888 2417
	1320	controlExample sing_1824.htm#SEC1900 2678
	1321	control_Matrix sing_1513.htm#SEC1589 sprintf
	1322	control_lib sing_1810.htm#SEC1886
	1323	convertdata sing_1387.htm#SEC1463 54629
	1324	convexHull sing_2007.htm#SEC2083 56690
	1325	convexIntersection sing_2008.htm#SEC2084 63587
	1326	convloc sing_552.htm#SEC604 19122
	1327	coordinate change sing_2170.htm#IDX830
	1328	coordinate change sing_2171.htm#IDX831
	1329	coordinate change sing_2172.htm#IDX832
	1330	coordinates sing_1967.htm#IDX783
	1331	coords sing_1967.htm#SEC2043 29362
	1332	copyTask sing_1017.htm#SEC1093 65331
[3a9ee05]	1333	copyright sing_1.htm#IDX1
[063ba1]	1334	corank sing_1472.htm#SEC1548 33709
	1335	cornerMonomials sing_1268.htm#SEC1344 33995
	1336	countPoints sing_1892.htm#SEC1968 58566
	1337	coverings sing_1131.htm#IDX522
	1338	coverings sing_1132.htm#IDX526
	1339	cpu sing_350.htm#IDX202
	1340	cpu sing_350.htm#IDX273
	1341	createBO sing_1418.htm#SEC1494 32669
[54fdec1]	1342	createGradedRingHomomorphism createGradedRingHomomorphism sing_2449.htm#SEC2525 62177
	1343	createGroup sing_2442.htm#SEC2518 28500
	1344	createQuotientGroup sing_2443.htm#SEC2519 26374
[063ba1]	1345	createTask sing_1015.htm#SEC1091 48404
[54fdec1]	1346	createTorsionFreeGroup createTorsionFreeGroup sing_2444.htm#SEC2520 51944
[063ba1]	1347	createlist sing_1400.htm#SEC1476 61781
	1348	crypto.lib sing_1865.htm#SEC1941
	1349	crypto_lib sing_1865.htm#SEC1941
	1350	cup sing_1145.htm#SEC1221 57972
	1351	cupproduct sing_1146.htm#SEC1222 43349
	1352	curve singularities sing_1451.htm#IDX614
	1353	curve singularities sing_1539.htm#IDX736
[54fdec1]	1354	curve singularity sing_2314.htm#IDX914
	1355	curveColengthDerivations curveColengthDerivations sing_2318.htm#SEC2394 2078
	1356	curveConductorMult sing_2316.htm#SEC2392 15897
	1357	curveDeligneNumber sing_2317.htm#SEC2393 12294
	1358	curveDeltaInv sing_2315.htm#SEC2391 16375
	1359	curveInv.lib sing_2314.htm#SEC2390
	1360	curveInv_lib sing_2314.htm#SEC2390
[063ba1]	1361	curvepar.lib sing_1492.htm#SEC1568
	1362	curvepar_lib sing_1492.htm#SEC1568
[a719149]	1363	custom assignment Assignments for user defined types sing_182.htm#SEC222
	1364	custom command Commands for user defined types sing_181.htm#SEC221
	1365	custom type Definition of a user defined type sing_178.htm#SEC218
[063ba1]	1366	customstd.lib sing_2202.htm#SEC2278
	1367	customstd_lib sing_2202.htm#SEC2278
	1368	cycleLength sing_2061.htm#SEC2137 16898
	1369	cyclePoints sing_2065.htm#SEC2141 54460
	1370	cyclic sing_940.htm#SEC1016 21375
	1371	cyclic code Codes and the decoding problem sing_863.htm#SEC922
	1372	cyclotomic sing_1626.htm#SEC1702 33749
[895ba26]	1373	datetime sing_216.htm#SEC256 50127
[cd8a2b5]	1374	dbprint sing_217.htm#SEC257
[54fdec1]	1375	deRham.lib sing_2319.htm#SEC2395
[063ba1]	1376	deRhamCohom sing_569.htm#SEC621 58222
	1377	deRhamCohomIdeal sing_570.htm#SEC622 42169
[54fdec1]	1378	deRhamCohomology sing_2320.htm#SEC2396 41947
	1379	deRham_lib sing_2319.htm#SEC2395
[cd8a2b5]	1380	debugLib, option sing_307.htm#IDX176
[063ba1]	1381	debug_log sing_1482.htm#SEC1558 62043
[a719149]	1382	debugger Source code debugger sing_66.htm#SEC103
	1383	debugging library code Source code debugger sing_66.htm#SEC103
[063ba1]	1384	dec1var sing_1198.htm#SEC1274 36098
	1385	decimal sing_1866.htm#SEC1942 56066
	1386	decode sing_1802.htm#SEC1878 64330
	1387	decodeCode sing_1804.htm#SEC1880 28262
	1388	decodeRandom sing_1803.htm#SEC1879 40118
	1389	decodeRandomFL sing_1807.htm#SEC1883 35423
	1390	decodeSV sing_1784.htm#SEC1860 37975
	1391	decodegb.lib sing_1789.htm#SEC1865
	1392	decodegb_lib sing_1789.htm#SEC1865
	1393	decoding, decoding problem Codes and the decoding problem sing_863.htm#SEC923
	1394	decoef sing_1832.htm#SEC1908 60284
	1395	decone sing_2173.htm#IDX834
	1396	decone sing_2174.htm#IDX836
[a719149]	1397	def sing_83.htm#SEC123
	1398	def declarations sing_84.htm#SEC124
[cd8a2b5]	1399	defRes, option sing_307.htm#IDX177
[a719149]	1400	default argument sing_44.htm#SEC81
[54fdec1]	1401	defineHomogeneous sing_2482.htm#SEC2558 55072
[cd8a2b5]	1402	defined sing_218.htm#SEC258
[063ba1]	1403	defl sing_1349.htm#SEC1425 11825
	1404	deform sing_1584.htm#SEC1660 5250
	1405	deform.lib sing_1503.htm#SEC1579
	1406	deform_lib sing_1503.htm#SEC1579
	1407	defring sing_982.htm#SEC1058 1814
	1408	defringp sing_984.htm#SEC1060 42905
	1409	defrings sing_983.htm#SEC1059 1034
[cd8a2b5]	1410	deg sing_219.htm#SEC259
[7d21990]	1411	degBound sing_387.htm#SEC427
[cd8a2b5]	1412	degree Miscellaneous oddities sing_220.htm#SEC260
[063ba1]	1413	degree sing_410.htm#IDX290
	1414	degree lexicographical ordering sing_838.htm#IDX393
	1415	degree of a polynomial Miscellaneous oddities sing_410.htm#IDX294
	1416	degree reverse lexicographical ordering sing_838.htm#IDX391
[54fdec1]	1417	degreeDivisor sing_2330.htm#SEC2406 31751
	1418	degreeFormalDivisor sing_2338.htm#SEC2414 42503
[063ba1]	1419	degreepart sing_1692.htm#SEC1768 53036
[a070b84]	1420	delete sing_121.htm#SEC161
[cd8a2b5]	1421	delete sing_221.htm#SEC261
	1422	delete sing_268.htm#SEC308
[063ba1]	1423	deleteGenerator sing_584.htm#SEC636 24917
	1424	deleteSublist sing_884.htm#SEC960 20406
[54fdec1]	1425	deligne number curveColengthDerivations sing_2314.htm#IDX916
	1426	deligne number sing_2317.htm#IDX921
	1427	deligne number sing_2318.htm#IDX923
[063ba1]	1428	delta sing_1551.htm#SEC1627 56952
	1429	delta invariant sing_1232.htm#IDX559
	1430	delta invariant sing_1551.htm#IDX746
[54fdec1]	1431	delta invariant sing_2315.htm#IDX917
[063ba1]	1432	delta invariant. sing_1224.htm#IDX552
	1433	delta invariant. sing_1225.htm#IDX555
	1434	delta invariant. sing_1226.htm#IDX558
	1435	deltaLoc sing_1232.htm#SEC1308 35192
	1436	denom_list sing_350.htm#IDX204
[cd8a2b5]	1437	denominator sing_222.htm#SEC262
[063ba1]	1438	depth sing_1147.htm#SEC1223 17777
	1439	depthIdeal sing_1208.htm#SEC1284 54782
	1440	derivate sing_1658.htm#SEC1734 15409
	1441	derivation sing_2187.htm#IDX857
[54fdec1]	1442	desingularization sing_2393.htm#IDX952 59041
	1443	desingularization sing_2394.htm#SEC2470
[cd8a2b5]	1444	det sing_223.htm#SEC263
[063ba1]	1445	det_B sing_1073.htm#SEC1149 60143
	1446	detadj sing_1567.htm#SEC1643 5914
[54fdec1]	1447	determinacy sing_2507.htm#SEC2583 44818
[063ba1]	1448	determinecenter sing_1372.htm#SEC1448 44496
	1449	detropicalise sing_2142.htm#SEC2218 38025
	1450	develop sing_1541.htm#SEC1617 48457
	1451	diag sing_1033.htm#SEC1109 56759
	1452	diagInvariants sing_1247.htm#SEC1323 62096
	1453	diag_test sing_1069.htm#SEC1145 31469
[cd8a2b5]	1454	diff sing_224.htm#SEC264
[063ba1]	1455	diffRat sing_783.htm#SEC835 36134
	1456	difpoly2tex sing_1833.htm#SEC1909 6451
[cd8a2b5]	1457	dim sing_225.htm#SEC265
[063ba1]	1458	dim (plural) sing_449.htm#SEC489
	1459	dimGradedPart sing_1440.htm#SEC1516 11262
	1460	dimH sing_1439.htm#SEC1515 38534
	1461	dimMon sing_1188.htm#SEC1264 39971
[54fdec1]	1462	dimStack sing_2533.htm#SEC2609 47772
[063ba1]	1463	dim_slocus sing_1585.htm#SEC1661 47218
	1464	dimension sing_2009.htm#SEC2085 35262
[54fdec1]	1465	dimension, moduli space of stable maps, rational curves dimStack sing_2533.htm#IDX990
	1466	dimensionOfLocalization dimensionOfLocalization sing_2381.htm#SEC2457 25632
[063ba1]	1467	direct_boolean_poly sing_2215.htm#SEC2291 49893
	1468	direct_from_boolean_poly direct_from_boolean_poly sing_2221.htm#SEC2297 36941
	1469	disc sing_1853.htm#SEC1929 45279
	1470	discr sing_1607.htm#SEC1683 9642
	1471	discrepancy sing_1425.htm#SEC1501 5597
	1472	discrim sing_919.htm#SEC995 21370
	1473	discussion of parametric ideal sing_902.htm#IDX425
	1474	disjoint sing_903.htm#IDX427
	1475	disp_zdd sing_2228.htm#SEC2304 41439
	1476	displayCohom sing_1441.htm#SEC1517 22633
	1477	displayHNE sing_1544.htm#SEC1620 29845
	1478	displayInvariants sing_1546.htm#SEC1622 13678
	1479	displayMultsequence sing_1548.htm#SEC1624 16668
	1480	displayPuiseuxExpansion displayPuiseuxExpansion sing_2117.htm#SEC2193 560
	1481	displayTropicalLifting displayTropicalLifting sing_2115.htm#SEC2191 28144
	1482	distributed computing sing_933.htm#IDX481
	1483	distributed computing sing_973.htm#IDX483
	1484	distributed computing sing_1014.htm#IDX496
[a719149]	1485	div Miscellaneous oddities sing_76.htm#SEC116
	1486	div sing_93.htm#SEC133
[063ba1]	1487	div sing_410.htm#IDX287
	1488	divideUnits sing_1829.htm#SEC1905 26711
	1489	dividelist sing_1399.htm#SEC1475 34210
[cd8a2b5]	1490	division sing_226.htm#SEC266
[063ba1]	1491	division sing_904.htm#IDX430
	1492	division sing_905.htm#IDX432
	1493	division (plural) sing_450.htm#SEC490
	1494	divisor sing_1932.htm#SEC2008 47231
[54fdec1]	1495	divisorplus sing_2324.htm#SEC2400 34248
	1496	divisors negativeformaldivisor sing_2323.htm#IDX926
	1497	divisors sing_2324.htm#IDX927
	1498	divisors sing_2325.htm#IDX928
	1499	divisors sing_2326.htm#IDX929
	1500	divisors sing_2327.htm#IDX930
	1501	divisors sing_2328.htm#IDX931
	1502	divisors sing_2329.htm#IDX932
	1503	divisors sing_2330.htm#IDX933
	1504	divisors sing_2331.htm#IDX934
	1505	divisors sing_2332.htm#IDX935
	1506	divisors sing_2333.htm#IDX936
	1507	divisors sing_2334.htm#IDX937
	1508	divisors sing_2335.htm#IDX938
	1509	divisors sing_2336.htm#IDX939
	1510	divisors sing_2337.htm#IDX940
	1511	divisors sing_2338.htm#IDX941
	1512	divisors, polyhedra sing_2339.htm#IDX942
	1513	divisors, polyhedra sing_2340.htm#IDX943
	1514	divisors, polyhedra sing_2341.htm#IDX944
	1515	divisors.lib sing_2322.htm#SEC2398
	1516	divisors_lib sing_2322.htm#SEC2398
[063ba1]	1517	dmod.lib sing_532.htm#SEC584
	1518	dmodAction sing_778.htm#SEC830 9763
	1519	dmodActionRat sing_779.htm#SEC831 6277
	1520	dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_771.htm#SEC823 44337
	1521	dmod_lib sing_532.htm#SEC584
	1522	dmodapp.lib sing_555.htm#SEC607
	1523	dmodapp_lib sing_555.htm#SEC607
	1524	dmodloc.lib sing_760.htm#IDX375
	1525	dmodloc_lib sing_760.htm#IDX376
	1526	dmodoublext sing_755.htm#SEC807 60637
	1527	dmodvar.lib sing_588.htm#SEC640
	1528	dmodvar_lib sing_588.htm#SEC640
	1529	double sing_1937.htm#SEC2013 34697
	1530	doubleExt sing_746.htm#SEC798 56896
[54fdec1]	1531	downloading Download instructions sing_2565.htm#SEC2655
[063ba1]	1532	dp, global ordering sing_838.htm#IDX392
	1533	drawNewtonSubdivision drawNewtonSubdivision sing_2120.htm#SEC2196 61060
	1534	drawTropicalCurve sing_2119.htm#SEC2195 27590
	1535	ds, local ordering sing_839.htm#IDX402
	1536	dsum sing_1034.htm#SEC1110 1303
	1537	dualCone sing_2010.htm#SEC2086 61460
	1538	dualConic sing_2144.htm#SEC2220 31080
	1539	dualPart sing_2285.htm#SEC2361 13279
[54fdec1]	1540	dualPartition sing_2546.htm#SEC2622 24739
[063ba1]	1541	dualPolytope sing_2049.htm#SEC2125 32081
[54fdec1]	1542	dualSheaf sing_2524.htm#SEC2600 633
[063ba1]	1543	dual_code sing_1786.htm#SEC1862 57229
[cd8a2b5]	1544	dump sing_227.htm#SEC267
[063ba1]	1545	dynamic geometry sing_913.htm#IDX452
	1546	dynamic geometry sing_914.htm#IDX455
	1547	ecart sing_1940.htm#SEC2016 32475
[7d21990]	1548	echo sing_388.htm#SEC428
[063ba1]	1549	eexgcdN sing_1867.htm#SEC1943 53237
[54fdec1]	1550	effective sing_2332.htm#SEC2408 53028
[063ba1]	1551	egcdMain sing_1733.htm#SEC1809 25359
	1552	ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2071.htm#SEC2147 38271
	1553	ehrhartRing sing_1243.htm#SEC1319 16966
	1554	eigenvals sing_1081.htm#SEC1157 11228
[cd8a2b5]	1555	eigenvalue sing_320.htm#SEC360
[063ba1]	1556	eigenvalue sing_1081.htm#IDX502
	1557	eigenvalues sing_1326.htm#SEC1402 2182
	1558	elemSymmId sing_941.htm#SEC1017 sprintf
	1559	elim sing_1118.htm#SEC1194 62585
	1560	elim.lib sing_1115.htm#SEC1191
	1561	elim1 sing_1119.htm#SEC1195 15653
	1562	elim2 sing_1120.htm#SEC1196 44749
	1563	elimRing sing_1117.htm#SEC1193 12194
	1564	elimWeight sing_703.htm#SEC755 54297
	1565	elim_lib sing_1115.htm#SEC1191
[cd8a2b5]	1566	eliminate sing_228.htm#SEC268
[063ba1]	1567	eliminate (plural) sing_451.htm#SEC491
	1568	eliminateNC sing_698.htm#SEC750 3777
	1569	elimination sing_697.htm#IDX360
	1570	elimlinearpart sing_1693.htm#SEC1769 14251
	1571	elimpart sing_1694.htm#SEC1770 10258
	1572	elimpartanyr sing_1695.htm#SEC1771 39751
	1573	elimrep sing_1380.htm#SEC1456 23641
	1574	elliptic curve sing_1128.htm#IDX518
	1575	elliptic curves sing_1125.htm#IDX512
	1576	elliptic curves sing_1131.htm#IDX521
	1577	elliptic curves sing_1132.htm#IDX525
	1578	ellipticAdd sing_1888.htm#SEC1964 13279
	1579	ellipticAllPoints sing_1893.htm#SEC1969 60770
	1580	ellipticMult sing_1889.htm#SEC1965 1558
	1581	ellipticNF sing_2068.htm#SEC2144 5045
	1582	ellipticNFDB sing_2069.htm#SEC2145 27917
	1583	ellipticRandomCurve sing_1890.htm#SEC1966 36980
	1584	ellipticRandomPoint sing_1891.htm#SEC1967 6866
	1585	ellipticcovers.lib sing_1125.htm#IDX506
	1586	ellipticcovers_lib sing_1125.htm#IDX507
[7d21990]	1587	else sing_378.htm#SEC418
[063ba1]	1588	embedMat sing_729.htm#SEC781 17119
	1589	emptyFan sing_2037.htm#SEC2113 7396
	1590	encode sing_1794.htm#SEC1870 56687
	1591	endomorphism filtration sing_1525.htm#IDX712
	1592	endvfilt sing_1525.htm#SEC1601 26670
	1593	engine sing_585.htm#SEC637 30876
	1594	envelop FamElemsAtEnvCompPoints sing_915.htm#SEC991 9501
	1595	envelop sing_915.htm#IDX458
	1596	envelop sing_916.htm#IDX461
	1597	envelop sing_917.htm#IDX465
	1598	envelop sing_918.htm#IDX469
	1599	envelope sing_452.htm#SEC492
	1600	enveloping algebra sing_350.htm#IDX208
	1601	enveloping algebra sing_490.htm#IDX304
[3a9ee05]	1602	environment variable, DISPLAY The online help system sing_16.htm#IDX29
[063ba1]	1603	equalJinI sing_1468.htm#SEC1544 18502
[54fdec1]	1604	equalMultiDeg sing_2475.htm#SEC2551 37090
[063ba1]	1605	equations sing_2011.htm#SEC2087 7896
	1606	equiRadical sing_1284.htm#SEC1360 8884
	1607	equidim sing_1286.htm#SEC1362 38541
	1608	equidimMax sing_1287.htm#SEC1363 49289
	1609	equidimMaxEHV sing_1288.htm#SEC1364 42650
	1610	equidimZ sing_1299.htm#SEC1375 49610
	1611	equising.lib sing_1508.htm#SEC1584
	1612	equising_lib sing_1508.htm#SEC1584
	1613	equisingular Tjurina number sing_1451.htm#IDX619
	1614	equisingularity ideal sing_1510.htm#IDX639
	1615	equisingularity stratum sing_1511.htm#IDX640
[3a9ee05]	1616	error recovery sing_15.htm#SEC21
[063ba1]	1617	errorInsert sing_1797.htm#SEC1873 59470
	1618	errorRand sing_1798.htm#SEC1874 5727
[54fdec1]	1619	errormap sing_2362.htm#SEC2438 7782
[063ba1]	1620	esIdeal sing_1510.htm#SEC1586 60477
	1621	esStratum sing_1511.htm#SEC1587 50094
	1622	essential sing_2177.htm#IDX839
	1623	essential sing_2178.htm#IDX840
	1624	eta sing_2063.htm#SEC2139 60729
	1625	euler sing_1846.htm#SEC1922 10519
	1626	eulerChProj sing_2275.htm#SEC2351 28549
[cd8a2b5]	1627	eval sing_229.htm#SEC269
[54fdec1]	1628	evaluateFormalDivisor evaluateFormalDivisor sing_2334.htm#SEC2410 3535
	1629	evaluatePDivisor sing_2340.htm#SEC2416 18855
[063ba1]	1630	evaluate_reynolds sing_1631.htm#SEC1707 46353
	1631	evalutateIntegral sing_1130.htm#SEC1206 sprintf
[cd8a2b5]	1632	example sing_231.htm#SEC271
[063ba1]	1633	example sing_2179.htm#IDX841
	1634	example sing_2180.htm#IDX843
	1635	example sing_2181.htm#IDX845
	1636	example sing_2182.htm#IDX847
	1637	example sing_2183.htm#IDX849
	1638	example sing_2184.htm#IDX851
	1639	example sing_2185.htm#IDX854
[cd8a2b5]	1640	execute sing_232.htm#SEC272
[7d21990]	1641	exit sing_382.htm#SEC422
[063ba1]	1642	exp2pt sing_1834.htm#SEC1910 19621
	1643	expo sing_1858.htm#SEC1934 8833
	1644	exponents sing_2189.htm#IDX862
[7d21990]	1645	export sing_375.htm#SEC415
[063ba1]	1646	exportNuminvs sing_1251.htm#SEC1327 10423
[7d21990]	1647	exportto sing_376.htm#SEC416
[54fdec1]	1648	expp sing_2544.htm#SEC2620 15751
[a719149]	1649	expression list sing_72.htm#IDX128
[063ba1]	1650	expression list sing_414.htm#IDX297
	1651	ext-module purityfiltration_lib sing_738.htm#IDX366
	1652	extcurve sing_1780.htm#SEC1856 6730
	1653	extdevelop sing_1542.htm#SEC1618 51044
	1654	extendGC sing_910.htm#SEC986 19135
	1655	extendWeyl sing_772.htm#SEC824 49954
	1656	extendedTensor sing_704.htm#SEC756 4975
	1657	extendpoly sing_909.htm#SEC985 29113
	1658	extendring sing_985.htm#SEC1061 64781
	1659	extension of rings sing_1304.htm#IDX568
	1660	exterior basis sing_1060.htm#IDX499
	1661	exterior power sing_1062.htm#IDX501
	1662	exteriorBasis sing_1060.htm#SEC1136 sprintf
	1663	exteriorPower sing_1062.htm#SEC1138 20173
[cd8a2b5]	1664	extgcd sing_233.htm#SEC273
[063ba1]	1665	fVector sing_2040.htm#SEC2116 3715
	1666	fVectorP sing_2072.htm#SEC2148 31843
	1667	facFirstShift sing_691.htm#SEC743 6469
	1668	facFirstWeyl sing_687.htm#SEC739 42412
	1669	facGBIdeal sing_1269.htm#SEC1345 9924
	1670	facShift sing_690.htm#SEC742 21253
	1671	facSubWeyl sing_689.htm#SEC741 9630
	1672	facWeyl sing_686.htm#SEC738 32331
	1673	faceContaining sing_2012.htm#SEC2088 64804
	1674	facetVertexLatticeDistances facetVertexLatticeDistances sing_2073.htm#SEC2149 60714
	1675	facetWidth sing_2074.htm#SEC2150 62810
	1676	facetWidths sing_2075.htm#SEC2151 5503
	1677	facets sing_2013.htm#SEC2089 8112
[cd8a2b5]	1678	facstd sing_234.htm#SEC274
	1679	factmodd sing_235.htm#SEC275
[7d21990]	1680	factor sing_314.htm#SEC354
[063ba1]	1681	factorH sing_899.htm#SEC975 24814
	1682	factorLenstraECM sing_1897.htm#SEC1973 54951
	1683	factorMain sing_1734.htm#SEC1810 65152
[54fdec1]	1684	factorgroup sing_2465.htm#SEC2541 59914
[063ba1]	1685	factorial sing_885.htm#SEC961 32871
[cd8a2b5]	1686	factorization sing_315.htm#SEC355
[063ba1]	1687	factorization sing_1090.htm#IDX503
[cd8a2b5]	1688	factorize sing_236.htm#SEC276
[7d21990]	1689	factorize sing_314.htm#SEC354
[3a9ee05]	1690	factory sing_1.htm#IDX2
[cd8a2b5]	1691	fan sing_184.htm#SEC224
[063ba1]	1692	fan sing_2052.htm#IDX788
	1693	fanViaCones sing_2038.htm#SEC2114 16418
[cd8a2b5]	1694	farey sing_237.htm#SEC277
[54fdec1]	1695	fareypoly sing_2343.htm#SEC2419 12389
[063ba1]	1696	fastExpt sing_1842.htm#SEC1918 43912
[cd8a2b5]	1697	fastHC, option sing_307.htm#IDX153
[063ba1]	1698	fastelim sing_1696.htm#SEC1772 7409
[cd8a2b5]	1699	fetch sing_238.htm#SEC278
[063ba1]	1700	fetch (plural) sing_453.htm#SEC493
	1701	fetchall sing_986.htm#SEC1062 7537
[54fdec1]	1702	ffmodStd sing_2347.htm#SEC2423 50680
	1703	ffmodstd.lib sing_2342.htm#SEC2418
	1704	ffmodstd_lib sing_2342.htm#SEC2418
[063ba1]	1705	ffsolve sing_1685.htm#SEC1761 20432
	1706	ffsolve.lib sing_1684.htm#SEC1760
	1707	ffsolve_lib sing_1684.htm#SEC1760
[cd8a2b5]	1708	fglm sing_239.htm#SEC279
[7d21990]	1709	fglm sing_347.htm#IDX187
[063ba1]	1710	fglm_solve sing_1712.htm#SEC1788 51398
[cd8a2b5]	1711	fglmquot sing_240.htm#SEC280
[063ba1]	1712	fibonacci sing_886.htm#SEC962 24750
[a719149]	1713	field sing_139.htm#SEC179
	1714	file, .singularrc sing_20.htm#IDX71
[cd8a2b5]	1715	filecmd sing_241.htm#SEC281
[063ba1]	1716	filtration purityfiltration_lib sing_738.htm#IDX367
	1717	finalCharts sing_1404.htm#SEC1480 37296
[cd8a2b5]	1718	find sing_242.htm#SEC282
[063ba1]	1719	findAuto sing_645.htm#SEC697 51205
	1720	findInvo sing_643.htm#SEC695 18177
	1721	findInvoDiag sing_644.htm#SEC696 7365
	1722	findOrientedBoundary findOrientedBoundary sing_2064.htm#SEC2140 24110
	1723	findTorsion sing_1823.htm#SEC1899 29572
	1724	find_first_primitive_root find_first_primitive_root sing_1901.htm#SEC1977 33327
	1725	find_index sing_1905.htm#SEC1981 62564
	1726	findifs.lib sing_1830.htm#SEC1906
	1727	findifs_example sing_1831.htm#SEC1907 33849
	1728	findifs_lib sing_1830.htm#SEC1906
	1729	findimAlgebra sing_713.htm#SEC765 64612
[cd8a2b5]	1730	finduni sing_243.htm#SEC283
[063ba1]	1731	findvars sing_1697.htm#SEC1773 54503
[a719149]	1732	finite field sing_139.htm#SEC179
[063ba1]	1733	finite field sing_1684.htm#IDX761
	1734	finiteDiagInvariants finiteDiagInvariants sing_1246.htm#SEC1322 3508
[54fdec1]	1735	finitediff.lib sing_2348.htm#IDX945
	1736	finitediff_lib sing_2348.htm#IDX946
[063ba1]	1737	finitenessTest sing_1104.htm#SEC1180 40633
	1738	finvar.lib sing_1619.htm#SEC1695
	1739	finvar_lib sing_1619.htm#SEC1695
[7d21990]	1740	first index is 1 sing_409.htm#SEC449
[063ba1]	1741	firstoct sing_1745.htm#SEC1821 11498
	1742	fitting sing_1150.htm#SEC1226 20661
[54fdec1]	1743	fixed points, moduli space of stable maps, graph fixedPoints sing_2534.htm#IDX991
	1744	fixedPoints sing_2534.htm#SEC2610 25366
[063ba1]	1745	fl2poly sing_582.htm#SEC634 51682
	1746	flatten sing_1035.htm#SEC1111 55617
	1747	flatteningStrat sing_1151.htm#SEC1227 15622
	1748	floating point sing_995.htm#IDX486
[7d21990]	1749	for sing_377.htm#SEC417
[54fdec1]	1750	formaldivisorplus sing_2335.htm#SEC2411 31959
	1751	forward sing_2354.htm#SEC2430 15383
[063ba1]	1752	fourier sing_577.htm#SEC629 5326
[54fdec1]	1753	fouriersystem sing_2365.htm#SEC2441 43681
[063ba1]	1754	fpadim.lib sing_593.htm#SEC645
	1755	fpadim_lib sing_593.htm#SEC645
[895ba26]	1756	fprintf sing_244.htm#SEC284 13662
[54fdec1]	1757	frandwalk sing_2499.htm#SEC2575 25555
[063ba1]	1758	free sing_2188.htm#IDX859
	1759	free sing_2189.htm#IDX861
	1760	free associative algebra, tensor algebra Free associative algebras sing_484.htm#SEC536
	1761	freeGBasis sing_628.htm#SEC680 43055
	1762	freegb.lib sing_624.htm#SEC676
	1763	freegb_lib sing_624.htm#SEC676
[cd8a2b5]	1764	freemodule sing_245.htm#SEC285
[063ba1]	1765	freerank sing_943.htm#SEC1019 52218
	1766	from_boolean_constant from_boolean_constant sing_2219.htm#SEC2295 44881
	1767	from_boolean_ideal sing_2223.htm#SEC2299 62698
	1768	from_boolean_poly sing_2220.htm#SEC2296 27864
	1769	from_boolean_set sing_2224.htm#SEC2300 60615
[cd8a2b5]	1770	frwalk sing_246.htm#SEC286
[063ba1]	1771	full representation sing_909.htm#IDX440
	1772	full representation sing_910.htm#IDX444
	1773	fullFan sing_2039.htm#SEC2115 7534
	1774	fullSerreRelations sing_639.htm#SEC691 27691
	1775	fullSpace sing_1994.htm#SEC2070 19485
	1776	furtherInvar sing_1663.htm#SEC1739 19209
	1777	further_hn_proc sing_1559.htm#SEC1635 63500
	1778	fwalk sing_1137.htm#SEC1213 15070
[a719149]	1779	galois field sing_139.htm#SEC179
[063ba1]	1780	gauss_col sing_1045.htm#SEC1121 36252
	1781	gauss_nf sing_1076.htm#SEC1152 51060
	1782	gauss_row sing_1046.htm#SEC1122 58877
	1783	gaussred sing_1074.htm#SEC1150 29001
	1784	gaussred_pivot sing_1075.htm#SEC1151 25477
[cd8a2b5]	1785	gcd sing_247.htm#SEC287
[063ba1]	1786	gcdMon sing_1177.htm#SEC1253 42448
	1787	gcddivisor sing_1933.htm#SEC2009 1276
[cd8a2b5]	1788	gen sing_248.htm#SEC288
[063ba1]	1789	genMDSMat sing_1800.htm#SEC1876 3347
	1790	genSymId sing_1323.htm#SEC1399 17521
	1791	general error-locator polynomial sing_864.htm#SEC929
[54fdec1]	1792	general neron. sing_2393.htm#IDX953
[063ba1]	1793	general weighted lexicographical ordering sing_839.htm#IDX408
	1794	general weighted reverse lexicographical ordering Local orderings sing_839.htm#IDX405
	1795	general.lib sing_879.htm#SEC955
	1796	generalOrder sing_1958.htm#SEC2034 42536
	1797	general_lib sing_879.htm#SEC955
	1798	generateG sing_1896.htm#SEC1972 51697
	1799	generators sing_1459.htm#IDX623
	1800	generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2014.htm#SEC2090 4454
	1801	generatorsOfSpan sing_2015.htm#SEC2091 40297
	1802	generic representation sing_909.htm#IDX439
	1803	genericid sing_961.htm#SEC1037 29731
	1804	genericity sing_1820.htm#SEC1896 16822
	1805	genericmat sing_1036.htm#SEC1112 35016
	1806	genoutput sing_1393.htm#SEC1469 18973
	1807	genus sing_1228.htm#SEC1304 sprintf
[54fdec1]	1808	geometric invariant theory sing_2386.htm#IDX950
[063ba1]	1809	geometrical locus FamElemsAtEnvCompPoints sing_913.htm#IDX450
	1810	geometrical locus sing_914.htm#IDX453
	1811	geometrical locus sing_915.htm#IDX456
	1812	geometrical locus sing_916.htm#IDX459
	1813	geometrical locus sing_917.htm#IDX463
	1814	geometrical locus sing_918.htm#IDX467
	1815	getArguments sing_1026.htm#SEC1102 14254
	1816	getCommand sing_1025.htm#SEC1101 32181
	1817	getCone sing_2041.htm#SEC2117 41394
[54fdec1]	1818	getGradingGroup sing_2440.htm#SEC2516 18137
	1819	getLattice sing_2441.htm#SEC2517 7775
[063ba1]	1820	getLinearForms sing_2016.htm#SEC2092 47590
[54fdec1]	1821	getModuleGrading sing_2451.htm#SEC2527 43451
[063ba1]	1822	getMultiplicity sing_2017.htm#SEC2093 639
	1823	getOneVar sing_1236.htm#SEC1312 55402
	1824	getResult sing_1027.htm#SEC1103 51722
	1825	getSmallest sing_1235.htm#SEC1311 1623
	1826	getState sing_1028.htm#SEC1104 36453
[54fdec1]	1827	getVariableWeights sing_2439.htm#SEC2515 9591
[063ba1]	1828	getcores sing_976.htm#SEC1052 30785
[cd8a2b5]	1829	getdump sing_249.htm#SEC289
[063ba1]	1830	getenv sing_350.htm#IDX211
	1831	gfan.lib sing_1993.htm#SEC2069
	1832	gfan_lib sing_1993.htm#SEC2069
[3a9ee05]	1833	gfanlib sing_1.htm#IDX9
[54fdec1]	1834	gitCone sing_2388.htm#SEC2464 23853
	1835	gitFan sing_2389.htm#SEC2465 sprintf
	1836	gitfan sing_2386.htm#IDX948
	1837	gitfan.lib sing_2386.htm#SEC2462
	1838	gitfan_lib sing_2386.htm#SEC2462
[063ba1]	1839	gkdim.lib sing_650.htm#SEC702
	1840	gkdim_lib sing_650.htm#SEC702
[54fdec1]	1841	gkzFan sing_2390.htm#SEC2466 35496
[cd8a2b5]	1842	global sing_204.htm#IDX133
[063ba1]	1843	global Bernstein-Sato polynomial sing_497.htm#IDX311
	1844	global Bernstein-Sato polynomial sing_532.htm#IDX329
	1845	global Bernstein-Sato polynomial for variety sing_588.htm#IDX354
[54fdec1]	1846	globalSections sing_2329.htm#SEC2405 55191
[063ba1]	1847	gmscoeffs sing_1517.htm#SEC1593 13182
	1848	gmsnf sing_1516.htm#SEC1592 44676
	1849	gmspoly.lib sing_1536.htm#SEC1612
	1850	gmspoly_lib sing_1536.htm#SEC1612
	1851	gmsring sing_1515.htm#SEC1591 59438
	1852	gmssing.lib sing_1514.htm#SEC1590
	1853	gmssing_lib sing_1514.htm#SEC1590
[54fdec1]	1854	goettsche.lib sing_2372.htm#SEC2448
	1855	goettsche_lib sing_2372.htm#SEC2448
[063ba1]	1856	good basis sing_1514.htm#IDX651
	1857	good basis sing_1524.htm#IDX706
	1858	good basis sing_1536.htm#IDX722
	1859	good basis sing_1538.htm#IDX733
	1860	goodBasis sing_1538.htm#SEC1614 41606
	1861	gorensteinIndex sing_2076.htm#SEC2152 52919
	1862	gorensteinVector sing_2077.htm#SEC2153 50407
[54fdec1]	1863	graal.lib sing_2379.htm#SEC2455
	1864	graalMixed sing_2380.htm#SEC2456 6401
	1865	graal_lib sing_2379.htm#SEC2455
[063ba1]	1866	gradeNumber sing_742.htm#SEC794 29956
	1867	graded Weyl algebra sing_497.htm#IDX314
	1868	graded module, graded piece sing_1440.htm#IDX609
[54fdec1]	1869	graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2395.htm#IDX954
[063ba1]	1870	graded modules, handling of Handling graded modules sing_806.htm#SEC858
[54fdec1]	1871	gradedModules.lib sing_2395.htm#SEC2471
	1872	gradedModules_lib sing_2395.htm#SEC2471
	1873	gradiator sing_2484.htm#SEC2560 53802
[063ba1]	1874	graph sing_1126.htm#IDX516
	1875	graph sing_1127.htm#IDX517
[54fdec1]	1876	graph sing_2529.htm#IDX986
	1877	graph sing_2530.htm#IDX987
[063ba1]	1878	graphics.lib sing_1747.htm#SEC1823
	1879	graphics_lib sing_1747.htm#SEC1823
[3a9ee05]	1880	graphviz sing_1.htm#IDX13
[063ba1]	1881	graver4ti2 sing_1321.htm#SEC1397 39635
[54fdec1]	1882	grconcat sing_2418.htm#SEC2494 16754
	1883	grdeg sing_2398.htm#SEC2474 22879
	1884	grgens sing_2407.htm#SEC2483 12823
	1885	grgroebner sing_2417.htm#SEC2493 29288
	1886	grlift sing_2415.htm#SEC2491 21656
	1887	grlifting sing_2422.htm#SEC2498 51177
	1888	grlifting2 sing_2423.htm#SEC2499 59011
	1889	grlifting3 sing_2425.htm#SEC2501 6369
	1890	grneg sing_2428.htm#SEC2504 64584
[063ba1]	1891	grobcov sing_902.htm#SEC978 27432
	1892	grobcov.lib sing_900.htm#SEC976
	1893	grobcov_lib sing_900.htm#SEC976
[54fdec1]	1894	grobj sing_2396.htm#SEC2472 18115
[895ba26]	1895	groebner sing_250.htm#SEC290 5130
[063ba1]	1896	groebner sing_798.htm#SEC850
[cd8a2b5]	1897	groebner basis computations sing_250.htm#IDX147
[063ba1]	1898	groebnerComplex sing_2155.htm#SEC2231 2421
	1899	groebnerCone sing_2149.htm#SEC2225 58776
	1900	groebnerFan sing_2154.htm#SEC2230 48157
	1901	groebnerFanP sing_2057.htm#SEC2133 5802
	1902	gromovWitten sing_1131.htm#SEC1207 28559
[54fdec1]	1903	grorder sing_2409.htm#SEC2485 20857
[a719149]	1904	ground field sing_139.htm#SEC179
[063ba1]	1905	group_reynolds sing_1627.htm#SEC1703 35079
[54fdec1]	1906	grpower sing_2405.htm#SEC2481 3960
	1907	grpres sing_2408.htm#SEC2484 18145
	1908	grprod sing_2416.htm#SEC2492 41525
	1909	grrange sing_2427.htm#SEC2503 41835
	1910	grres sing_2414.htm#SEC2490 35795
	1911	grrndmap sing_2420.htm#SEC2496 4054
	1912	grrndmap2 sing_2421.htm#SEC2497 50536
	1913	grrndmat sing_2419.htm#SEC2495 42634
	1914	grshift sing_2400.htm#SEC2476 1415
	1915	grsum sing_2404.htm#SEC2480 60602
	1916	grsyz sing_2413.htm#SEC2489 61843
	1917	grtest sing_2397.htm#SEC2473 62577
	1918	grtranspose sing_2406.htm#SEC2482 13865
	1919	grtranspose1 sing_2410.htm#SEC2486 3637
	1920	grtwist sing_2402.htm#SEC2478 10498
	1921	grtwists sing_2403.htm#SEC2479 56638
	1922	grview sing_2399.htm#SEC2475 6878
[063ba1]	1923	grwalk.lib sing_1136.htm#SEC1212
	1924	grwalk_lib sing_1136.htm#SEC1212
[54fdec1]	1925	grzero sing_2401.htm#SEC2477 4212
[063ba1]	1926	gwalk sing_1142.htm#SEC1218 38238
	1927	hStarVector sing_2078.htm#SEC2154 60821
	1928	hVector sing_2079.htm#SEC2155 46486
	1929	h_increasing_knapsack h_increasing_knapsack sing_1919.htm#SEC1995 62968
	1930	hardware platform sing_350.htm#IDX269
	1931	hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_999.htm#SEC1075 54609
	1932	hasCommutativeVars sing_996.htm#SEC1072 3152
	1933	hasGlobalOrdering sing_997.htm#SEC1073 34053
	1934	hasMixedOrdering sing_998.htm#SEC1074 29738
	1935	hasNumericCoeffs sing_995.htm#SEC1071 14522
	1936	hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1000.htm#SEC1076 56211
	1937	headStand sing_1058.htm#SEC1134 14413
	1938	heightZ sing_1298.htm#SEC1374 16800
[cd8a2b5]	1939	help sing_251.htm#SEC291
[3a9ee05]	1940	help browsers The online help system sing_16.htm#IDX22
	1941	help browsers, dummy The online help system sing_16.htm#IDX25
	1942	help browsers, dummy sing_16.htm#IDX27
	1943	help browsers, emacs The online help system sing_16.htm#IDX26
	1944	help browsers, html The online help system sing_16.htm#IDX23
	1945	help browsers, setting command to use The online help system sing_16.htm#IDX30
[063ba1]	1946	help browsers, setting the sing_350.htm#IDX194
[3a9ee05]	1947	help, accessing over the net Command line options sing_19.htm#IDX42
	1948	help, online help system The online help system sing_16.htm#SEC22
[54fdec1]	1949	hermiteNormalForm sing_2485.htm#SEC2561 37225
	1950	hess.lib sing_2430.htm#SEC2506
	1951	hess_lib sing_2430.htm#SEC2506
[063ba1]	1952	hessenberg sing_350.htm#IDX217 24168
	1953	hessenberg sing_1080.htm#SEC1156
[cd8a2b5]	1954	highcorner sing_252.htm#SEC292
	1955	hilb sing_253.htm#SEC293
[063ba1]	1956	hilbPoly sing_959.htm#SEC1035 36118
	1957	hilbert4ti2 sing_1320.htm#SEC1396 13993
	1958	hilbertBasis sing_2080.htm#SEC2156 35423
[54fdec1]	1959	hilbertSeries sing_2487.htm#SEC2563 60148
[063ba1]	1960	hilbvec sing_1698.htm#SEC1774 9204
	1961	hnexpansion sing_1540.htm#SEC1616 46990
	1962	hnoether.lib sing_1539.htm#SEC1615
	1963	hnoether_lib sing_1539.htm#SEC1615
	1964	holonomic rank sing_760.htm#IDX378
	1965	holonomicRank sing_764.htm#SEC816 41306
	1966	hom_kernel sing_1158.htm#SEC1234 32604
[cd8a2b5]	1967	homog sing_254.htm#SEC294
[54fdec1]	1968	homog_part sing_2541.htm#SEC2617 20875
	1969	homog_parts sing_2542.htm#SEC2618 12854
[063ba1]	1970	homogeneitySpace sing_2151.htm#SEC2227 48243
	1971	homogfacFirstQWeyl sing_693.htm#SEC745 32751
	1972	homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_695.htm#SEC747 9014
	1973	homogfacNthQWeyl sing_692.htm#SEC744 55267
	1974	homogfacNthQWeyl_all homogfacNthQWeyl_all sing_694.htm#SEC746 62161
	1975	homolog.lib sing_1143.htm#SEC1219
	1976	homolog_lib sing_1143.htm#SEC1219
	1977	homology sing_1153.htm#SEC1229 15040
[54fdec1]	1978	howto, download Download instructions sing_2565.htm#SEC2655
	1979	howto, install on Macintosh Macintosh installation instructions sing_2568.htm#SEC2658
	1980	howto, install on Unix Unix installation instructions sing_2566.htm#SEC2656
	1981	howto, install on Windows Windows installation instructions sing_2567.htm#SEC2657
[cd8a2b5]	1982	hres sing_255.htm#SEC295
[3a9ee05]	1983	html, default help The online help system sing_16.htm#IDX24
[063ba1]	1984	hyperel.lib sing_1926.htm#SEC2002
	1985	hyperel_lib sing_1926.htm#SEC2002
	1986	hyperplane sing_2158.htm#IDX799
	1987	hyperplane arrangement sing_532.htm#IDX335
	1988	hypersurface singularity sing_1566.htm#IDX751
	1989	iMult sing_1231.htm#SEC1307 22059
	1990	id2mod sing_955.htm#SEC1031 32918
[a719149]	1991	ideal sing_85.htm#SEC125
	1992	ideal declarations sing_86.htm#SEC126
[063ba1]	1993	ideal declarations (plural) ideal declarations (plural) sing_416.htm#SEC456
[a719149]	1994	ideal expressions sing_87.htm#SEC127
[063ba1]	1995	ideal expressions (plural) ideal expressions (plural) sing_417.htm#SEC457
[a719149]	1996	ideal operations sing_88.htm#SEC128
[063ba1]	1997	ideal operations (plural) ideal operations (plural) sing_418.htm#SEC458
[a719149]	1998	ideal related functions ideal related functions sing_89.htm#SEC129
[063ba1]	1999	ideal related functions (plural) ideal related functions (plural) sing_419.htm#SEC459
	2000	ideal, toric sing_851.htm#SEC908
	2001	idealSplit sing_1705.htm#SEC1781 4673
	2002	ideals Miscellaneous oddities sing_410.htm#IDX291
	2003	idealsimplify sing_1467.htm#SEC1543 38569
[7d21990]	2004	identifier Identifier resolution sing_411.htm#SEC451
[063ba1]	2005	identifyvar sing_1375.htm#SEC1451 59662
[7d21990]	2006	if sing_378.htm#SEC418
[54fdec1]	2007	imageLattice sing_2453.htm#SEC2529 15740
[063ba1]	2008	image_of_variety sing_1655.htm#SEC1731 43711
[cd8a2b5]	2009	imap sing_256.htm#SEC296
[063ba1]	2010	imap (plural) sing_454.htm#SEC494
	2011	imapall sing_987.htm#SEC1063 16023
[cd8a2b5]	2012	impart sing_257.htm#SEC297
[7d21990]	2013	importfrom sing_379.htm#SEC419
[063ba1]	2014	inCenter sing_521.htm#SEC573 22152
	2015	inCentralizer sing_522.htm#SEC574 49000
	2016	inForm sing_564.htm#SEC616 5283
	2017	inSubring sing_1096.htm#SEC1172 24817
	2018	indSet sing_1203.htm#SEC1279 32828
[cd8a2b5]	2019	indepSet sing_258.htm#SEC298
[a719149]	2020	indexed names sing_36.htm#IDX82
	2021	indexed names sing_37.htm#SEC65
[7d21990]	2022	indices, multi sing_37.htm#SEC65
[063ba1]	2023	inequalities sing_2018.htm#SEC2094 10122
[cd8a2b5]	2024	infRedTail, option sing_307.htm#IDX154
[3a9ee05]	2025	info The online help system sing_16.htm#SEC23
[063ba1]	2026	iniD sing_1395.htm#SEC1471 35084
	2027	init_debug sing_1474.htm#SEC1550 29863
	2028	initial sing_2152.htm#SEC2228 8678
	2029	initial form sing_497.htm#IDX316
	2030	initial ideal sing_497.htm#IDX315
	2031	initial ideal approach sing_497.htm#IDX319
	2032	initial ideal approach sing_588.htm#IDX358
	2033	initialForm sing_2129.htm#SEC2205 57793
	2034	initialIdeal sing_2130.htm#SEC2206 22205
	2035	initialIdealW sing_563.htm#SEC615 36086
	2036	initialMalgrange sing_562.htm#SEC614 26846
	2037	injective_knapsack sing_1920.htm#SEC1996 7619
	2038	inout.lib sing_921.htm#SEC997
	2039	inout_lib sing_921.htm#SEC997
[a719149]	2040	input sing_41.htm#SEC71
[a070b84]	2041	insert sing_121.htm#SEC161
[cd8a2b5]	2042	insert sing_259.htm#SEC299
[063ba1]	2043	insertCone sing_2042.htm#SEC2118 13858
	2044	insertGenerator sing_583.htm#SEC635 13951
[54fdec1]	2045	instructions, Macintosh installation Macintosh installation instructions sing_2568.htm#SEC2658
	2046	instructions, Unix installation Unix installation instructions sing_2566.htm#SEC2656
	2047	instructions, Windows installation Windows installation instructions sing_2567.htm#SEC2657
	2048	instructions, downloading Download instructions sing_2565.htm#SEC2655
[a719149]	2049	int sing_90.htm#SEC130
	2050	int declarations sing_91.htm#SEC131
	2051	int expressions sing_92.htm#SEC132
	2052	int operations sing_93.htm#SEC133
	2053	int related functions int related functions sing_94.htm#SEC134
[54fdec1]	2054	intInverse sing_2462.htm#SEC2538 sprintf
[063ba1]	2055	intPart sing_1874.htm#SEC1950 48360
[54fdec1]	2056	intRank sing_2454.htm#SEC2530 1830
[063ba1]	2057	intRoot sing_1875.htm#SEC1951 54582
	2058	intRoots sing_580.htm#SEC632 24538
[cd8a2b5]	2059	intStrategy, option sing_307.htm#IDX155
[063ba1]	2060	intclMonIdeal sing_1244.htm#SEC1320 22338
	2061	intclToricRing sing_1240.htm#SEC1316 62143
	2062	integer division Miscellaneous oddities sing_410.htm#IDX286
	2063	integer programming sing_859.htm#SEC916
[54fdec1]	2064	integral sing_2516.htm#SEC2592 62683
[063ba1]	2065	integral basis sing_1165.htm#IDX538
	2066	integral basis sing_1358.htm#IDX594
	2067	integral closure sing_1224.htm#IDX551
	2068	integral closure sing_1225.htm#IDX554
	2069	integral closure sing_1226.htm#IDX557
	2070	integral closure sing_1239.htm#IDX563
	2071	integralBasis sing_1165.htm#SEC1241 38114
	2072	integralIdeal sing_567.htm#SEC619 29194
	2073	integralModule sing_568.htm#SEC620 58078
[54fdec1]	2074	integralSection sing_2463.htm#SEC2539 sprintf
[063ba1]	2075	integralbasis.lib sing_1164.htm#SEC1240
	2076	integralbasis_lib sing_1164.htm#SEC1240
	2077	integration of D-module sing_555.htm#IDX347
[3a9ee05]	2078	interface, Emacs Emacs user interface sing_21.htm#SEC28
[063ba1]	2079	interiorLatticePoints interiorLatticePoints sing_2081.htm#SEC2157 49868
	2080	internalfunctions sing_1475.htm#SEC1551 61230
	2081	interpolate sing_1711.htm#SEC1787 51502
[cd8a2b5]	2082	interpolation sing_260.htm#SEC300
	2083	interred sing_261.htm#SEC301
	2084	intersect sing_262.htm#SEC302
[063ba1]	2085	intersect (plural) sing_455.htm#SEC495
[cd8a2b5]	2086	intersectElim, option sing_307.htm#IDX173
[54fdec1]	2087	intersectLattices sing_2459.htm#SEC2535 41354
[063ba1]	2088	intersectMon sing_1180.htm#SEC1256 44572
[cd8a2b5]	2089	intersectSyz, option sing_307.htm#IDX174
[063ba1]	2090	intersectZ sing_1300.htm#SEC1376 sprintf
	2091	intersection sing_1549.htm#SEC1625 46938
	2092	intersection lattice sing_2194.htm#IDX874
	2093	intersection lattice sing_2195.htm#IDX875
	2094	intersection multiplicity sing_1460.htm#IDX629
	2095	intersection multiplicity sing_1549.htm#IDX744
	2096	intersectionDiv sing_1423.htm#SEC1499 29017
	2097	intersectionValRingIdeals intersectionValRingIdeals sing_1249.htm#SEC1325 38773
	2098	intersectionValRings intersectionValRings sing_1248.htm#SEC1324 35761
[a719149]	2099	intmat sing_97.htm#SEC137
	2100	intmat declarations sing_98.htm#SEC138
	2101	intmat expressions sing_99.htm#SEC139
	2102	intmat operations sing_101.htm#SEC141
	2103	intmat related functions intmat related functions sing_102.htm#SEC142
	2104	intmat type cast sing_100.htm#SEC140
[063ba1]	2105	intmat2mons sing_1264.htm#SEC1340 21150
	2106	intprog.lib sing_1166.htm#SEC1242
	2107	intprog_lib sing_1166.htm#SEC1242
[a719149]	2108	intvec sing_103.htm#SEC143
	2109	intvec declarations sing_104.htm#SEC144
	2110	intvec expressions sing_105.htm#SEC145
	2111	intvec operations sing_106.htm#SEC146
	2112	intvec related functions intvec related functions sing_107.htm#SEC147
[54fdec1]	2113	invariant sing_2317.htm#IDX922
[063ba1]	2114	invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1624.htm#IDX757
	2115	invariant ring minimal generating set permutation group invariant_algebra_perm sing_1625.htm#IDX758
	2116	invariantRing sing_1657.htm#SEC1733 18582
	2117	invariant_algebra_perm invariant_algebra_perm sing_1625.htm#SEC1701 63525
	2118	invariant_algebra_reynolds invariant_algebra_reynolds sing_1624.htm#SEC1700 35705
	2119	invariant_basis sing_1632.htm#SEC1708 18343
	2120	invariant_basis_reynolds invariant_basis_reynolds sing_1633.htm#SEC1709 54788
	2121	invariant_ring sing_1620.htm#SEC1696 8059
	2122	invariant_ring_random invariant_ring_random sing_1621.htm#SEC1697 6986
	2123	invariants curveColengthDerivations sing_1545.htm#SEC1621 57499
[54fdec1]	2124	invariants sing_2314.htm#IDX915
	2125	invariants sing_2318.htm#IDX924
[063ba1]	2126	inverse sing_1064.htm#SEC1140 27411
[cd8a2b5]	2127	inverse of a matrix via its LU-decomposition sing_282.htm#SEC322
[063ba1]	2128	inverseFourier sing_578.htm#SEC630 65140
	2129	inverse_B sing_1065.htm#SEC1141 17616
	2130	inverse_L sing_1066.htm#SEC1142 49271
	2131	inverse_modulus sing_1903.htm#SEC1979 60822
	2132	invertBirMap sing_1359.htm#SEC1435 16086
	2133	invertNumberMain sing_1735.htm#SEC1811 62615
	2134	involut.lib sing_642.htm#SEC694
	2135	involut_lib sing_642.htm#SEC694
	2136	involution sing_647.htm#SEC699 34280
	2137	invunit sing_1568.htm#SEC1644 62398
	2138	iostruct sing_1822.htm#SEC1898 60444
	2139	irrRealizationDim sing_2111.htm#SEC2187 7814
	2140	irred_secondary_char0 irred_secondary_char0 sing_1646.htm#SEC1722 2943
	2141	irred_secondary_no_molien irred_secondary_no_molien sing_1649.htm#SEC1725 55905
	2142	irreddecMon sing_1189.htm#SEC1265 20160
	2143	irreducible power series sing_1550.htm#IDX745
	2144	irreducible secondary invariant irred_secondary_char0 sing_1646.htm#IDX759
[54fdec1]	2145	isAface sing_2391.htm#SEC2467 47756
[063ba1]	2146	isAntiEndo sing_649.htm#SEC701 19156
	2147	isBounded sing_2082.htm#SEC2158 28183
[895ba26]	2148	isCI sing_204.htm#IDX139 58425
[063ba1]	2149	isCI sing_1114.htm#SEC1190
[895ba26]	2150	isCM sing_204.htm#IDX140 50469
[063ba1]	2151	isCM sing_1154.htm#SEC1230
	2152	isCMcod2 sing_1603.htm#SEC1679 2563
	2153	isCanonical sing_2083.htm#SEC2159 51109
	2154	isCartan sing_523.htm#SEC575 39541
	2155	isCentral sing_720.htm#SEC772 54650
	2156	isCommutative sing_722.htm#SEC774 60728
	2157	isCompatible sing_2043.htm#SEC2119 57323
	2158	isCompressed sing_2084.htm#SEC2160 2849
[54fdec1]	2159	isEqualDivisor sing_2328.htm#SEC2404 17569
[063ba1]	2160	isEquising sing_1512.htm#SEC1588 1424
	2161	isFlat sing_1155.htm#SEC1231 14706
	2162	isFsat sing_573.htm#SEC625 28225
	2163	isFullSpace sing_2019.htm#SEC2095 27433
	2164	isGorenstein sing_2085.htm#SEC2161 24010
[54fdec1]	2165	isGradedRingHomomorphism isGradedRingHomomorphism sing_2448.htm#SEC2524 39551
	2166	isGroup sing_2446.htm#SEC2522 55744
	2167	isGroupHomomorphism sing_2447.htm#SEC2523 65475
[063ba1]	2168	isHolonomic sing_551.htm#SEC603 30274
[cd8a2b5]	2169	isHomg sing_204.htm#IDX135
[54fdec1]	2170	isHomogeneous sing_2474.htm#SEC2550 3034
[063ba1]	2171	isInt sing_586.htm#SEC638 9879
[54fdec1]	2172	isIntegralSurjective isIntegralSurjective sing_2460.htm#SEC2536 sprintf
[063ba1]	2173	isInvolution sing_648.htm#SEC700 13601
	2174	isLatticeEmpty sing_2086.htm#SEC2162 48517
[54fdec1]	2175	isLocalizationRegular isLocalizationRegular sing_2383.htm#SEC2459 11221
[063ba1]	2176	isLocallyFree sing_1156.htm#SEC1232 46389
	2177	isMonomial sing_1175.htm#SEC1251 57615
	2178	isNC sing_721.htm#SEC773 57151
	2179	isNormal sing_2087.htm#SEC2163 64236
	2180	isOnCurve sing_1887.htm#SEC1963 36324
	2181	isOrigin sing_2020.htm#SEC2096 13977
[54fdec1]	2182	isPositive sing_2471.htm#SEC2547 50852
	2183	isPrimitiveSublattice isPrimitiveSublattice sing_2461.htm#SEC2537 sprintf
[063ba1]	2184	isPure sing_2044.htm#SEC2120 44002
	2185	isPureTensor sing_495.htm#SEC547 21323
	2186	isQuotientRing sing_1001.htm#SEC1077 sprintf
	2187	isRational sing_554.htm#SEC606 57398
	2188	isReflexive sing_2088.htm#SEC2164 3991
	2189	isReg sing_1157.htm#SEC1233 40920
[cd8a2b5]	2190	isSB sing_204.htm#IDX134
[063ba1]	2191	isSimplicial sing_2021.htm#SEC2097 57789
	2192	isSmooth sing_2089.htm#SEC2165 37647
	2193	isSubModule sing_1002.htm#SEC1078 sprintf
[54fdec1]	2194	isSublattice sing_2452.htm#SEC2528 10501
[063ba1]	2195	isSymmetric sing_1324.htm#SEC1400 61363
	2196	isTame sing_1537.htm#SEC1613 31925
	2197	isTerminal sing_2090.htm#SEC2166 29416
[54fdec1]	2198	isTorsionFree sing_2470.htm#SEC2546 52228
[063ba1]	2199	isTwoSidedGB sing_496.htm#SEC548 36558
	2200	isUpperTriangular sing_701.htm#SEC753 40655
	2201	isVar sing_640.htm#SEC692 43851
	2202	isVeryAmple sing_2091.htm#SEC2167 64652
	2203	isWeyl sing_723.htm#SEC775 28994
[54fdec1]	2204	isZeroElement sing_2472.htm#SEC2548 514
[063ba1]	2205	is_NND sing_1553.htm#SEC1629 26564
	2206	is_NP sing_1212.htm#SEC1288 43891
	2207	is_active sing_1586.htm#SEC1662 6867
	2208	is_bijective sing_1101.htm#SEC1177 49512
	2209	is_cenBimodule sing_756.htm#SEC808 35450
	2210	is_cenSubbimodule sing_757.htm#SEC809 26181
	2211	is_ci sing_1587.htm#SEC1663 35370
	2212	is_complex sing_1037.htm#SEC1113 1234
	2213	is_fix_injective sing_1924.htm#SEC2000 11663
	2214	is_h_injective sing_1923.htm#SEC1999 36696
	2215	is_injective sing_1099.htm#SEC1175 15776
	2216	is_irred sing_1550.htm#SEC1626 51150
	2217	is_is sing_1588.htm#SEC1664 64105
	2218	is_nested sing_1213.htm#SEC1289 9200
	2219	is_prime sing_1904.htm#SEC1980 29018
	2220	is_primitive_root sing_1900.htm#SEC1976 42838
	2221	is_pure sing_748.htm#SEC800 59105
	2222	is_reg sing_1589.htm#SEC1665 18146
	2223	is_regs sing_1590.htm#SEC1666 50242
	2224	is_surjective sing_1100.htm#SEC1176 57044
	2225	is_zero sing_944.htm#SEC1020 24341
	2226	isartinianMon sing_1186.htm#SEC1262 1103
	2227	isgenericMon sing_1187.htm#SEC1263 14444
	2228	ishyper sing_1927.htm#SEC2003 65518
	2229	isirreducibleMon sing_1185.htm#SEC1261 22428
	2230	isoncurve sing_1928.htm#SEC2004 16384
	2231	isparam sing_1991.htm#SEC2067 56395
	2232	isprimaryMon sing_1184.htm#SEC1260 57367
	2233	isprimeMon sing_1183.htm#SEC1259 9124
	2234	isuni sing_1976.htm#SEC2052 39427
	2235	iv2lp sing_618.htm#SEC670 53390
	2236	iv2lpList sing_619.htm#SEC671 38626
	2237	iv2lpMat sing_620.htm#SEC672 41720
	2238	ivDHilbert sing_594.htm#SEC646 18825
	2239	ivDHilbertSickle sing_595.htm#SEC647 16102
	2240	ivDimCheck sing_596.htm#SEC648 42112
	2241	ivHilbert sing_597.htm#SEC649 34233
	2242	ivKDim sing_598.htm#SEC650 40986
	2243	ivL2lpI sing_617.htm#SEC669 45855
	2244	ivMis2Base sing_599.htm#SEC651 57812
	2245	ivMis2Dim sing_600.htm#SEC652 15557
	2246	ivOrdMisLex sing_601.htm#SEC653 40656
	2247	ivSickle sing_602.htm#SEC654 48016
	2248	ivSickleDim sing_604.htm#SEC656 57209
	2249	ivSickleHil sing_603.htm#SEC655 1967
	2250	jInvariant sing_2123.htm#SEC2199 2369
	2251	jOft sing_1859.htm#SEC1935 25716
[cd8a2b5]	2252	jacob sing_263.htm#SEC303
[063ba1]	2253	jacoblift sing_1569.htm#SEC1645 40125
	2254	jacobson sing_1828.htm#SEC1904 59267
	2255	jacobson.lib sing_1826.htm#SEC1902
	2256	jacobson_lib sing_1826.htm#SEC1902
[cd8a2b5]	2257	janet sing_264.htm#SEC304
	2258	jet sing_265.htm#SEC305
[063ba1]	2259	jordan sing_1085.htm#SEC1161 16602
	2260	jordanbasis sing_1086.htm#SEC1162 12736
	2261	jordanmatrix sing_1087.htm#SEC1163 2886
	2262	jordannf sing_1088.htm#SEC1164 20535
	2263	jungfib sing_1408.htm#SEC1484 5432
	2264	jungnormal sing_1407.htm#SEC1483 43561
	2265	jungresolve sing_1406.htm#SEC1482 45004
	2266	katsura sing_942.htm#SEC1018 45913
[cd8a2b5]	2267	kbase sing_266.htm#SEC306
[063ba1]	2268	kbase (plural) sing_456.htm#SEC496
[7d21990]	2269	keepring sing_380.htm#SEC420
[cd8a2b5]	2270	kernel sing_267.htm#SEC307
[54fdec1]	2271	kernelLattice sing_2455.htm#SEC2531 36320
[cd8a2b5]	2272	kill sing_268.htm#SEC308
[063ba1]	2273	killTask sing_1016.htm#SEC1092 39317
	2274	killall sing_888.htm#SEC964 34661
[cd8a2b5]	2275	killattrib sing_269.htm#SEC309
[063ba1]	2276	kmemory sing_887.htm#SEC963 52193
	2277	kohom sing_1159.htm#SEC1235 50086
	2278	kontrahom sing_1160.htm#SEC1236 58549
[cd8a2b5]	2279	koszul sing_270.htm#SEC310
[063ba1]	2280	kskernel.lib sing_1560.htm#SEC1636
	2281	kskernel_lib sing_1560.htm#SEC1636
[a719149]	2282	l-adic numbers sing_32.htm#SEC46
[cd8a2b5]	2283	laguerre sing_271.htm#SEC311
[063ba1]	2284	laguerre_solve sing_1707.htm#SEC1783 10155
	2285	lastvarGeneral sing_1957.htm#SEC2033 28645
	2286	latex.lib sing_1751.htm#SEC1827
	2287	latex_lib sing_1751.htm#SEC1827
	2288	lattice sing_2195.htm#IDX877
	2289	latticeArea sing_2066.htm#SEC2142 53771
[54fdec1]	2290	latticeBasis sing_2456.htm#SEC2532 43162
[063ba1]	2291	latticeCodegree sing_2092.htm#SEC2168 25482
	2292	latticeDegree sing_2093.htm#SEC2169 52881
	2293	latticePoints sing_2094.htm#SEC2170 41965
	2294	latticeVolume sing_2095.htm#SEC2171 42234
[54fdec1]	2295	laxfrT sing_2352.htm#SEC2428 60899
	2296	laxfrX sing_2353.htm#SEC2429 57254
[cd8a2b5]	2297	lazy, option sing_307.htm#IDX156
[063ba1]	2298	lcm sing_945.htm#SEC1021 44755
	2299	lcmMon sing_1178.htm#SEC1254 52749
	2300	lcmN sing_1868.htm#SEC1944 52355
	2301	lcmofall sing_1388.htm#SEC1464 56889
[cd8a2b5]	2302	lead sing_272.htm#SEC312
	2303	leadcoef sing_273.htm#SEC313
	2304	leadexp sing_274.htm#SEC314
	2305	leadmonom sing_275.htm#SEC315
[063ba1]	2306	leadmonomial sing_1943.htm#SEC2019 8195
	2307	left annihilator ideal sing_532.htm#IDX327
	2308	leftInverse sing_1817.htm#SEC1893 41469
	2309	leftKernel sing_1815.htm#SEC1891 9292
[cd8a2b5]	2310	length, option sing_307.htm#IDX157
[063ba1]	2311	letplaceGBasis sing_626.htm#SEC678 33757
	2312	letterplace correspondence Letterplace correspondence sing_486.htm#SEC538
	2313	lex_solve sing_1713.htm#SEC1789 48692
	2314	lexicographical ordering sing_838.htm#IDX388
[a719149]	2315	lib2doc sing_60.htm#SEC97
[54fdec1]	2316	libSingular sing_2564.htm#SEC2654
[3a9ee05]	2317	libcdd sing_1.htm#IDX12
	2318	libfac sing_1.htm#IDX6
[a719149]	2319	libparse sing_69.htm#SEC109
[063ba1]	2320	library sing_2210.htm#IDX892
[54fdec1]	2321	library sing_2386.htm#IDX947
[a719149]	2322	library, info string sing_55.htm#IDX124
[063ba1]	2323	library, polybori.lib sing_2210.htm#IDX889
[a719149]	2324	library, template sing_55.htm#SEC92
	2325	library, template.lib sing_55.htm#IDX122
[063ba1]	2326	lieBracket sing_637.htm#SEC689 50745
[cd8a2b5]	2327	lift sing_277.htm#SEC317
[063ba1]	2328	lift sing_490.htm#IDX303
	2329	lift (plural) sing_457.htm#SEC497
	2330	lift_kbase sing_1506.htm#SEC1582 10906
	2331	lift_rel_kb sing_1507.htm#SEC1583 13673
	2332	liftenvelope sing_493.htm#SEC545 58802
[cd8a2b5]	2333	liftstd sing_278.htm#SEC318
[063ba1]	2334	liftstd (plural) sing_458.htm#SEC498
	2335	linReduce sing_505.htm#SEC557 57527
	2336	linReduceIdeal sing_506.htm#SEC558 19076
	2337	linSyzSolve sing_507.htm#SEC559 26185
	2338	linalg.lib sing_1063.htm#SEC1139
	2339	linalg_lib sing_1063.htm#SEC1139
	2340	linealityDimension sing_2022.htm#SEC2098 30751
	2341	linealitySpace sing_2023.htm#SEC2099 14489
[cd8a2b5]	2342	linear algebra sing_205.htm#SEC245
	2343	linear algebra sing_281.htm#SEC321
	2344	linear algebra sing_282.htm#SEC322
	2345	linear algebra sing_283.htm#SEC323
[063ba1]	2346	linear code, dual sing_1786.htm#IDX770
	2347	linear code, systematic sing_1787.htm#IDX771
	2348	linear interreduction sing_497.htm#IDX318
	2349	linearCombinations sing_526.htm#SEC578 20514
	2350	linearMapKernel sing_525.htm#SEC577 43761
	2351	linear_relations sing_1055.htm#SEC1131 45983
[54fdec1]	2352	linearlyEquivalent sing_2331.htm#SEC2407 28351
[063ba1]	2353	linearpart sing_1699.htm#SEC1775 2162
[54fdec1]	2354	linesHypersurface sing_2538.htm#SEC2614 9129
[a719149]	2355	link Parallelization with ssi links sing_108.htm#SEC148
[063ba1]	2356	link sing_795.htm#SEC847
[a719149]	2357	link declarations sing_109.htm#SEC149
	2358	link expressions sing_110.htm#SEC150
	2359	link related functions link related functions sing_111.htm#SEC151
	2360	list sing_118.htm#SEC158
	2361	list declarations sing_119.htm#SEC159
	2362	list expressions sing_120.htm#SEC160
	2363	list operations sing_121.htm#SEC161
	2364	list related functions list related functions sing_122.htm#SEC162
[cd8a2b5]	2365	listvar sing_279.htm#SEC319
[54fdec1]	2366	lll sing_2488.htm#SEC2564 35827
[7d21990]	2367	load sing_381.htm#SEC421
[cd8a2b5]	2368	loadLib, option sing_307.htm#IDX178
	2369	loadProc, option sing_307.htm#IDX179
[063ba1]	2370	locAtZero sing_1233.htm#SEC1309 5687
	2371	locNormal sing_1169.htm#SEC1245 52237
	2372	local methods sing_1168.htm#IDX541
	2373	local methods sing_1169.htm#IDX544
[a719149]	2374	local names sing_46.htm#SEC83
[063ba1]	2375	local rings, computing in Rings associated to monomial orderings sing_790.htm#SEC842
	2376	local weighted lexicographical ordering sing_839.htm#IDX409
	2377	local weighted reverse lexicographical ordering Local orderings sing_839.htm#IDX406
	2378	localInvar sing_1662.htm#SEC1738 38478
	2379	localization Rings associated to monomial orderings sing_790.htm#SEC842
	2380	localization sing_2175.htm#IDX837
	2381	localization of D-module sing_555.htm#IDX343
	2382	localization of D-module sing_760.htm#IDX381
	2383	locally closed set sing_909.htm#IDX437
	2384	locally closed set sing_911.htm#IDX446
	2385	localstd sing_1953.htm#SEC2029 25562
	2386	locnormal.lib sing_1168.htm#SEC1244
	2387	locnormal_lib sing_1168.htm#SEC1244
	2388	locstd sing_1591.htm#SEC1667 25864
	2389	locus FamElemsAtEnvCompPoints sing_913.htm#SEC989 49563
	2390	locus sing_913.htm#IDX451
	2391	locus sing_914.htm#IDX454
	2392	locus sing_915.htm#IDX457
	2393	locus sing_916.htm#IDX460
	2394	locus sing_917.htm#IDX464
	2395	locus sing_918.htm#IDX468
	2396	locusdg sing_914.htm#SEC990 62891
	2397	locusto sing_916.htm#SEC992 17047
	2398	log2 sing_1843.htm#SEC1919 40703
	2399	logarithmic annihilator ideal sing_532.htm#IDX332
[54fdec1]	2400	logg sing_2543.htm#SEC2619 38736
[063ba1]	2401	lp, global ordering sing_838.htm#IDX387
	2402	lp2iv sing_621.htm#SEC673 26909
	2403	lp2ivId sing_622.htm#SEC674 15628
	2404	lp2lstr sing_633.htm#SEC685 24713
	2405	lpDHilbert sing_605.htm#SEC657 11075
	2406	lpDHilbertSickle sing_606.htm#SEC658 46653
	2407	lpDimCheck sing_608.htm#SEC660 50239
	2408	lpHilbert sing_607.htm#SEC659 53685
	2409	lpId2ivLi sing_623.htm#SEC675 29846
	2410	lpKDim sing_609.htm#SEC661 53650
	2411	lpMis2Base sing_610.htm#SEC662 10826
	2412	lpMis2Dim sing_611.htm#SEC663 47442
	2413	lpMult sing_630.htm#SEC682 58898
	2414	lpNF sing_627.htm#SEC679 55144
	2415	lpOrdMisLex sing_612.htm#SEC664 21260
	2416	lpPower sing_632.htm#SEC684 7325
	2417	lpSickle sing_613.htm#SEC665 19646
	2418	lpSickleDim sing_615.htm#SEC667 50163
	2419	lpSickleHil sing_614.htm#SEC666 19038
	2420	lprint sing_923.htm#SEC999 5285
[cd8a2b5]	2421	lres sing_280.htm#SEC320
[063ba1]	2422	ls, local ordering sing_839.htm#IDX400
	2423	lst2str sing_634.htm#SEC686 10088
	2424	lsum sing_1135.htm#SEC1211 50315
[cd8a2b5]	2425	ludecomp sing_281.htm#SEC321
	2426	luinverse sing_282.htm#SEC322
	2427	lusolve sing_283.htm#SEC323
[063ba1]	2428	m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1915.htm#SEC1991 57945
	2429	m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1914.htm#SEC1990 33857
	2430	m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1913.htm#SEC1989 7880
	2431	magnitude sing_1837.htm#SEC1913 37967
[54fdec1]	2432	makeDivisor sing_2323.htm#SEC2399 3414
	2433	makeFormalDivisor sing_2333.htm#SEC2409 54579
[7a419f]	2434	makeGraph sing_1126.htm#SEC1202 21758
[54fdec1]	2435	makeGraphVE sing_2529.htm#SEC2605 sprintf
[063ba1]	2436	makeHeisenberg sing_711.htm#SEC763 2050
	2437	makeLetterplaceRing sing_625.htm#SEC677 41789
	2438	makeMalgrange sing_592.htm#SEC644 41377
	2439	makeModElimRing sing_728.htm#SEC780 56092
[54fdec1]	2440	makePDivisor sing_2339.htm#SEC2415 45273
[063ba1]	2441	makeQsl2 sing_675.htm#SEC727 3997
	2442	makeQsl3 sing_676.htm#SEC728 41249
	2443	makeQso3 sing_674.htm#SEC726 58910
[54fdec1]	2444	makeSheaf sing_2517.htm#SEC2593 10497
[063ba1]	2445	makeUe6 sing_671.htm#SEC723 58585
	2446	makeUe7 sing_672.htm#SEC724 61849
	2447	makeUe8 sing_673.htm#SEC725 64987
	2448	makeUf4 sing_670.htm#SEC722 8408
	2449	makeUg2 sing_669.htm#SEC721 34512
	2450	makeUgl sing_655.htm#SEC707 3543
	2451	makeUsl sing_654.htm#SEC706 24536
	2452	makeUsl2 sing_653.htm#SEC705 42637
	2453	makeUso10 sing_661.htm#SEC713 6936
	2454	makeUso11 sing_662.htm#SEC714 35873
	2455	makeUso12 sing_663.htm#SEC715 19319
	2456	makeUso5 sing_656.htm#SEC708 34378
	2457	makeUso6 sing_657.htm#SEC709 65009
	2458	makeUso7 sing_658.htm#SEC710 49142
	2459	makeUso8 sing_659.htm#SEC711 33275
	2460	makeUso9 sing_660.htm#SEC712 16896
	2461	makeUsp1 sing_664.htm#SEC716 44522
	2462	makeUsp2 sing_665.htm#SEC717 18017
	2463	makeUsp3 sing_666.htm#SEC718 57445
	2464	makeUsp4 sing_667.htm#SEC719 51690
	2465	makeUsp5 sing_668.htm#SEC720 35951
[54fdec1]	2466	makeVariety sing_2509.htm#SEC2585 23915
[063ba1]	2467	makeWeyl sing_710.htm#SEC762 8554
[a719149]	2468	map sing_123.htm#SEC163
[063ba1]	2469	map (plural) sing_420.htm#SEC460
[a719149]	2470	map declarations sing_124.htm#SEC164
[063ba1]	2471	map declarations (plural) map declarations (plural) sing_421.htm#SEC461
[a719149]	2472	map expressions sing_125.htm#SEC165
[063ba1]	2473	map expressions (plural) map expressions (plural) sing_422.htm#SEC462
[a719149]	2474	map operations sing_126.htm#IDX129
[063ba1]	2475	map operations (plural) map operations (plural) sing_423.htm#IDX298
[a070b84]	2476	map related functions map related functions sing_127.htm#IDX131
[063ba1]	2477	map related functions (plural) map related functions (plural) sing_424.htm#IDX299
	2478	mapIsFinite sing_1103.htm#SEC1179 60897
	2479	mapToRatNormCurve sing_1363.htm#SEC1439 8877
	2480	mapall sing_988.htm#SEC1064 14907
[54fdec1]	2481	mappingcone sing_2424.htm#SEC2500 48219
	2482	mappingcone3 sing_2426.htm#SEC2502 58973
[063ba1]	2483	markov4ti2 sing_1319.htm#SEC1395 9163
	2484	mat2arr sing_2160.htm#SEC2236 20840
	2485	mat2carr sing_2161.htm#SEC2237 13777
	2486	mat_rk sing_1077.htm#SEC1153 32196
	2487	matbil sing_1964.htm#SEC2040 1611
	2488	mathematical objects Representation of mathematical objects sing_834.htm#SEC886
	2489	mathinit sing_1749.htm#SEC1825 16793
	2490	matmult sing_1965.htm#SEC2041 60088
[a719149]	2491	matrix sing_128.htm#SEC168
[063ba1]	2492	matrix sing_2160.htm#IDX805
	2493	matrix sing_2161.htm#IDX808
	2494	matrix sing_2162.htm#IDX812
[a719149]	2495	matrix declarations sing_129.htm#SEC169
[063ba1]	2496	matrix diagonalization sing_1826.htm#IDX781
[a719149]	2497	matrix expressions sing_130.htm#SEC170
	2498	matrix operations sing_132.htm#SEC172
	2499	matrix related functions matrix related functions sing_133.htm#SEC173
	2500	matrix type cast sing_131.htm#SEC171
[063ba1]	2501	matrix.lib sing_1030.htm#SEC1106
	2502	matrixExp sing_1353.htm#SEC1429 53063
	2503	matrixLog sing_1354.htm#SEC1430 26235
	2504	matrixT1 sing_1605.htm#SEC1681 15051
	2505	matrix_lib sing_1030.htm#SEC1106
[54fdec1]	2506	matrixpres sing_2429.htm#SEC2505 60645
	2507	matrixsystem sing_2363.htm#SEC2439 62950
[895ba26]	2508	max sing_284.htm#SEC324 23624
[063ba1]	2509	maxEord sing_1378.htm#SEC1454 64032
[cd8a2b5]	2510	maxExp sing_204.htm#IDX136
[063ba1]	2511	maxIntRoot sing_777.htm#SEC829 37127
	2512	maxZeros sing_1356.htm#SEC1432 35964
	2513	maxabs sing_1983.htm#SEC2059 64510
	2514	maxcoef sing_946.htm#SEC1022 50577
	2515	maxdeg sing_947.htm#SEC1023 39794
	2516	maxdeg1 sing_948.htm#SEC1024 21545
[cd8a2b5]	2517	maxideal sing_285.htm#SEC325
[063ba1]	2518	maximalFace sing_2096.htm#SEC2172 35224
	2519	maximalGroebnerCone sing_2150.htm#SEC2226 62935
	2520	maximalValue sing_2097.htm#SEC2173 32783
	2521	maximum sing_1856.htm#SEC1932 2355
	2522	maximum number of zeroes sing_1356.htm#IDX588
[895ba26]	2523	mdouble sing_56.htm#SEC93 56685
[cd8a2b5]	2524	mem, option sing_307.htm#IDX180
[063ba1]	2525	membershipMon sing_1179.htm#SEC1255 40876
[cd8a2b5]	2526	memory sing_286.htm#SEC326
	2527	memory managment sing_286.htm#SEC326
[063ba1]	2528	merkle_hellman_decryption merkle_hellman_decryption sing_1917.htm#SEC1993 49106
	2529	merkle_hellman_encryption merkle_hellman_encryption sing_1916.htm#SEC1992 13645
[54fdec1]	2530	midpoint sing_2359.htm#SEC2435 29391
[063ba1]	2531	milnor sing_1592.htm#SEC1668 23173
	2532	milnorcode sing_1476.htm#SEC1552 13849
[54fdec1]	2533	milnornumber sing_2506.htm#SEC2582 21855
[895ba26]	2534	min sing_287.htm#SEC327 56342
[063ba1]	2535	minAssChar sing_1278.htm#SEC1354 18758
	2536	minAssCharE sing_1279.htm#SEC1355 31570
	2537	minAssGTZ sing_1276.htm#SEC1352 41315
	2538	minAssGTZE sing_1277.htm#SEC1353 50867
	2539	minAssZ sing_1296.htm#SEC1372 54152
	2540	minEcart sing_1946.htm#SEC2022 34890
	2541	minIntRoot sing_553.htm#SEC605 3288
	2542	minIntRoot2 sing_776.htm#SEC828 46494
	2543	minMult sing_1110.htm#SEC1186 31978
[cd8a2b5]	2544	minbase sing_288.htm#SEC328
[063ba1]	2545	minbaseMon sing_1176.htm#SEC1252 1501
	2546	mindeg sing_949.htm#SEC1025 16307
	2547	mindeg1 sing_950.htm#SEC1026 39698
	2548	mindist sing_1801.htm#SEC1877 55281
	2549	minimal display time, setting the sing_350.htm#IDX282
	2550	minimalFace sing_2098.htm#SEC2174 40971
	2551	minimalValue sing_2099.htm#SEC2175 31262
	2552	minipoly sing_1082.htm#SEC1158 4927
	2553	minkowskiSum sing_2100.htm#SEC2176 3969
[cd8a2b5]	2554	minor sing_289.htm#SEC329
[7d21990]	2555	minpoly sing_389.htm#SEC429
[cd8a2b5]	2556	minres sing_290.htm#SEC330
[063ba1]	2557	minres (plural) sing_459.htm#SEC499
	2558	mirror symmetry sing_1125.htm#IDX509
	2559	mixed Hodge structure sing_1514.htm#IDX644
	2560	mixed Hodge structure sing_1520.htm#IDX672
	2561	mixed Hodge structure sing_1521.htm#IDX678
	2562	mixed Hodge structure sing_1522.htm#IDX686
	2563	mixed Hodge structure sing_1523.htm#IDX692
	2564	mixed Hodge structure sing_1524.htm#IDX700
	2565	mixed Hodge structure sing_1525.htm#IDX710
	2566	mixed Hodge structure sing_1536.htm#IDX716
	2567	mixed Hodge structure sing_1538.htm#IDX727
[a719149]	2568	mod sing_76.htm#SEC116
	2569	mod sing_93.htm#SEC133
	2570	mod sing_142.htm#SEC182
[063ba1]	2571	mod2id sing_954.htm#SEC1030 27927
	2572	mod2str sing_635.htm#SEC687 35236
	2573	modDec sing_1195.htm#SEC1271 48578
	2574	modNPos sing_1218.htm#SEC1294 17130
	2575	modNormal sing_1171.htm#SEC1247 39654
	2576	modNpos_test sing_1216.htm#SEC1292 34326
	2577	modStd sing_1173.htm#SEC1249 4500
[54fdec1]	2578	modVStd sing_2310.htm#SEC2386 38529
	2579	modVStd0 sing_2311.htm#SEC2387 46080
	2580	modWalk sing_2433.htm#SEC2509 sprintf
[063ba1]	2581	mod_versal sing_1505.htm#SEC1581 63927
	2582	modality sing_1484.htm#SEC1560 49951
[54fdec1]	2583	modfWalk sing_2435.htm#SEC2511 sprintf
	2584	modfrWalk sing_2436.htm#SEC2512 sprintf
[063ba1]	2585	modnormal.lib sing_1170.htm#SEC1246
	2586	modnormal_lib sing_1170.htm#SEC1246
[54fdec1]	2587	modrWalk sing_2434.htm#SEC2510 sprintf
[063ba1]	2588	modregCM sing_1222.htm#SEC1298 5049
	2589	modsatiety sing_1220.htm#SEC1296 44506
	2590	modstd.lib sing_1172.htm#SEC1248
	2591	modstd_lib sing_1172.htm#SEC1248
	2592	modular sing_932.htm#SEC1008 16950
	2593	modular methods sing_1168.htm#IDX542
	2594	modular methods sing_1170.htm#IDX547
	2595	modular methods. sing_1169.htm#IDX545
	2596	modular techniques. sing_1171.htm#IDX549
	2597	modular.lib sing_931.htm#SEC1007
	2598	modular_lib sing_931.htm#SEC1007
	2599	modular_lib sing_931.htm#IDX474
[a719149]	2600	module sing_134.htm#SEC174
[063ba1]	2601	module (plural) sing_425.htm#SEC465
[a719149]	2602	module declarations sing_135.htm#SEC175
[063ba1]	2603	module declarations (plural) module declarations (plural) sing_426.htm#SEC466
[a719149]	2604	module expressions sing_136.htm#SEC176
[063ba1]	2605	module expressions (plural) module expressions (plural) sing_427.htm#SEC467
[a719149]	2606	module operations sing_137.htm#SEC177
[063ba1]	2607	module operations (plural) module operations (plural) sing_428.htm#SEC468
	2608	module ordering C sing_840.htm#IDX412
	2609	module ordering c sing_840.htm#IDX414
[a719149]	2610	module related functions module related functions sing_138.htm#SEC178
[063ba1]	2611	module related functions (plural) module related functions (plural) sing_429.htm#SEC469
	2612	module_containment sing_1095.htm#SEC1171 31620
[54fdec1]	2613	moduliSpace sing_2531.htm#SEC2607 37013
[cd8a2b5]	2614	modulo sing_291.htm#SEC331
[063ba1]	2615	modulo (plural) sing_460.htm#SEC500
	2616	moduloSlim sing_718.htm#SEC770 52636
[54fdec1]	2617	modwalk.lib sing_2432.htm#IDX955
	2618	modwalk_lib sing_2432.htm#IDX956
[063ba1]	2619	moebius sing_2196.htm#SEC2272 61319
	2620	moebius function sing_2196.htm#IDX878
	2621	molien sing_1628.htm#SEC1704 63561
	2622	mondromy.lib sing_1566.htm#SEC1642
	2623	mondromy_lib sing_1566.htm#SEC1642
[cd8a2b5]	2624	monitor sing_292.htm#SEC332
[063ba1]	2625	monodromy sing_1514.htm#IDX648 40112
	2626	monodromy sing_1519.htm#SEC1595
	2627	monodromy sing_1519.htm#IDX668
	2628	monodromy sing_1524.htm#IDX703
	2629	monodromy sing_1536.htm#IDX719
	2630	monodromy sing_1538.htm#IDX730
	2631	monodromyB sing_1570.htm#SEC1646 46517
[cd8a2b5]	2632	monomial sing_293.htm#SEC333
[063ba1]	2633	monomial ordering sing_997.htm#IDX488
	2634	monomial orderings General definitions for orderings sing_790.htm#SEC842
	2635	monomial orderings sing_837.htm#SEC889
	2636	monomial orderings introduction Introduction to orderings sing_836.htm#SEC888
	2637	monomialInIdeal sing_774.htm#SEC826 4687
	2638	monomialLcm sing_1944.htm#SEC2020 36233
	2639	monomialabortstd sing_2203.htm#SEC2279 14901
	2640	monomialideal.lib sing_1174.htm#SEC1250
	2641	monomialideal_lib sing_1174.htm#SEC1250
	2642	monomials and precedence Miscellaneous oddities sing_410.htm#IDX288
	2643	mons2intmat sing_1263.htm#SEC1339 15555
	2644	morsesplit sing_1477.htm#SEC1553 3417
	2645	mp_res_mat sing_1710.htm#SEC1786 44453
	2646	mplot sing_1750.htm#SEC1826 21740
[cd8a2b5]	2647	mpresmat sing_294.htm#SEC334
[063ba1]	2648	mprimdec.lib sing_1191.htm#SEC1267
	2649	mprimdec_lib sing_1191.htm#SEC1267
	2650	mregular.lib sing_1206.htm#SEC1282
	2651	mregular_lib sing_1206.htm#SEC1282
[cd8a2b5]	2652	mres sing_295.htm#SEC335
[063ba1]	2653	mres (plural) sing_461.htm#SEC501
[cd8a2b5]	2654	mstd sing_296.htm#SEC336
[895ba26]	2655	msum sing_58.htm#SEC95 53344
	2656	mtriple sing_57.htm#SEC94 55390
[cd8a2b5]	2657	mult Miscellaneous oddities sing_297.htm#SEC337
[063ba1]	2658	mult sing_410.htm#IDX289
[7d21990]	2659	multBound sing_390.htm#SEC430
[063ba1]	2660	multRat sing_782.htm#SEC834 44047
	2661	multarr2arr sing_2191.htm#SEC2267 44731
	2662	multarrMultRestrict sing_2193.htm#SEC2269 41742
	2663	multarrRestrict sing_2192.htm#SEC2268 sprintf
	2664	multcol sing_1049.htm#SEC1125 21899
[54fdec1]	2665	multdivisor sing_2325.htm#SEC2401 65139
	2666	multformaldivisor sing_2337.htm#SEC2413 32238
[063ba1]	2667	multi sing_1931.htm#SEC2007 18473
[a719149]	2668	multi indices sing_37.htm#SEC65
[54fdec1]	2669	multiDeg sing_2467.htm#SEC2543 7049
	2670	multiDegBasis sing_2468.htm#SEC2544 3320
	2671	multiDegGroebner sing_2476.htm#SEC2552 1040
	2672	multiDegModulo sing_2478.htm#SEC2554 27244
	2673	multiDegPartition sing_2469.htm#SEC2545 9577
	2674	multiDegResolution sing_2479.htm#SEC2555 38535
	2675	multiDegSyzygy sing_2477.htm#SEC2553 54075
	2676	multiDegTensor sing_2480.htm#SEC2556 45108
	2677	multiDegTor sing_2481.htm#SEC2557 sprintf
[063ba1]	2678	multiarrangement sing_2187.htm#IDX858
	2679	multiarrangement sing_2188.htm#IDX860
	2680	multiarrangement sing_2189.htm#IDX863
	2681	multiarrangement sing_2190.htm#IDX864
	2682	multiarrangement sing_2191.htm#IDX867
	2683	multiarrangement sing_2192.htm#IDX870
	2684	multiarrangement sing_2193.htm#IDX872
	2685	multidimensional_knapsack multidimensional_knapsack sing_1909.htm#SEC1985 15647
[54fdec1]	2686	multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2437.htm#IDX961
	2687	multigrading.lib sing_2437.htm#IDX959
	2688	multigrading_lib sing_2437.htm#IDX960
	2689	multipleCover sing_2537.htm#SEC2613 55988
[063ba1]	2690	multiplicities, sequence of sing_1545.htm#IDX742
[54fdec1]	2691	multiplicity sing_2316.htm#IDX920
[063ba1]	2692	multiplicity sequence sing_1458.htm#IDX621
	2693	multiplicity sequence sing_1461.htm#IDX633
	2694	multiplicity sequence sing_1547.htm#IDX743
	2695	multiplylist sing_1398.htm#SEC1474 34999
	2696	multivariate equations sing_1684.htm#IDX760
	2697	multrow sing_1050.htm#SEC1126 871
	2698	multseq2charexp sing_1457.htm#SEC1533 sprintf
	2699	multsequence sing_1547.htm#SEC1623 35117
	2700	nBoundaryLatticePoints nBoundaryLatticePoints sing_2101.htm#SEC2177 49670
	2701	nHilbertBasis sing_2102.htm#SEC2178 173
	2702	nInteriorLatticePoints nInteriorLatticePoints sing_2103.htm#SEC2179 42152
	2703	nLatticePoints sing_2104.htm#SEC2180 5977
	2704	naccache_stern_decryption naccache_stern_decryption sing_1912.htm#SEC1988 31429
	2705	naccache_stern_encryption naccache_stern_encryption sing_1911.htm#SEC1987 60034
	2706	naccache_stern_generation naccache_stern_generation sing_1910.htm#SEC1986 2559
[cd8a2b5]	2707	nameof sing_298.htm#SEC338
	2708	names sing_299.htm#SEC339
[063ba1]	2709	nashmult sing_1465.htm#SEC1541 8491
	2710	nblocks sing_350.htm#IDX221
	2711	ncExt_R sing_751.htm#SEC803 14357
[54fdec1]	2712	ncHilb.lib sing_2489.htm#SEC2565
	2713	ncHilb_lib sing_2489.htm#SEC2565
[063ba1]	2714	ncHom sing_752.htm#SEC804 45033
	2715	ncRelations sing_719.htm#SEC771 7225
	2716	nc_algebra sing_462.htm#SEC502
	2717	nc_hilb sing_350.htm#IDX223
	2718	ncalg.lib sing_652.htm#SEC704
	2719	ncalg_lib sing_652.htm#SEC704
	2720	ncalgebra sing_463.htm#SEC503
	2721	ncdecomp.lib sing_679.htm#SEC731
	2722	ncdecomp_lib sing_679.htm#SEC731
	2723	ncdetection sing_646.htm#SEC698 24994
	2724	ncfactor sing_685.htm#SEC737 53809
	2725	ncfactor.lib sing_684.htm#SEC736
	2726	ncfactor_lib sing_684.htm#SEC736
[54fdec1]	2727	nchilb sing_2490.htm#SEC2566 36922
[063ba1]	2728	nchomolog.lib sing_750.htm#IDX371
	2729	nchomolog_lib sing_750.htm#IDX372
[cd8a2b5]	2730	ncols sing_300.htm#SEC340
[063ba1]	2731	ncones sing_2046.htm#SEC2122 48316
	2732	ncpreim.lib sing_697.htm#SEC749
	2733	ncpreim_lib sing_697.htm#SEC749
	2734	nctools.lib sing_705.htm#SEC757
	2735	nctools_lib sing_705.htm#SEC757
	2736	ndcond sing_708.htm#SEC760 1006
	2737	negatedCone sing_2024.htm#SEC2100 38527
	2738	negative degree lexicographical ordering sing_839.htm#IDX403
	2739	negative degree reverse lexicographical ordering Local orderings sing_839.htm#IDX401
	2740	negative lexicographical ordering sing_839.htm#IDX399
[54fdec1]	2741	negativedivisor sing_2326.htm#SEC2402 8274
	2742	negativeformaldivisor negativeformaldivisor sing_2336.htm#SEC2412 55026
[3a9ee05]	2743	net access Command line options sing_19.htm#IDX40
[063ba1]	2744	newTest sing_1851.htm#SEC1927 36655
[a719149]	2745	newline sing_166.htm#SEC206
[54fdec1]	2746	news sing_2557.htm#SEC2633
[a719149]	2747	newstruct sing_177.htm#SEC217
[063ba1]	2748	newstruct sing_2210.htm#IDX894
	2749	newtonDiag sing_958.htm#SEC1034 56652
[54fdec1]	2750	newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2550.htm#SEC2626 22052
[063ba1]	2751	newtonPolytope sing_2050.htm#SEC2126 56291
	2752	newtonPolytopeLP sing_2055.htm#SEC2131 36186
	2753	newtonPolytopeP sing_2054.htm#SEC2130 29927
	2754	newtonpoly sing_1552.htm#SEC1628 31930
	2755	nf_icis sing_1593.htm#SEC1669 49093
[54fdec1]	2756	nfmodStd sing_2493.htm#SEC2569 46077
	2757	nfmodSyz sing_2495.htm#SEC2571 55942
	2758	nfmodstd.lib sing_2491.htm#SEC2567
	2759	nfmodstd_lib sing_2491.htm#SEC2567
	2760	nfmodsyz.lib sing_2494.htm#SEC2570
	2761	nfmodsyz_lib sing_2494.htm#SEC2570
[063ba1]	2762	nilpotent Lie algebras sing_1351.htm#IDX573
	2763	nmaxcones sing_2045.htm#SEC2121 660
[7d21990]	2764	noether sing_391.htm#SEC431
[063ba1]	2765	noether.lib sing_1214.htm#SEC1290
	2766	noetherNormal sing_1102.htm#SEC1178 44522
	2767	noether_lib sing_1214.htm#SEC1290
	2768	non-english special characters sing_399.htm#IDX284
	2769	nonMonomials sing_1267.htm#SEC1343 16309
	2770	nonZeroEntry sing_1105.htm#SEC1181 933
[cd8a2b5]	2771	none, option sing_307.htm#IDX150
[063ba1]	2772	norTest sing_1234.htm#SEC1310 sprintf
	2773	norm sing_1930.htm#SEC2006 31143
	2774	normal sing_1224.htm#SEC1300 61073
[54fdec1]	2775	normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2536.htm#IDX993
[063ba1]	2776	normal.lib sing_1223.htm#SEC1299
[54fdec1]	2777	normalBundle sing_2536.htm#SEC2612 sprintf
[063ba1]	2778	normalC sing_1226.htm#SEC1302 34842
	2779	normalConductor sing_1238.htm#SEC1314 26085
	2780	normalFan sing_2105.htm#SEC2181 39216
	2781	normalFanL sing_2056.htm#SEC2132 55096
[54fdec1]	2782	normalForm sing_2327.htm#SEC2403 34962
[063ba1]	2783	normalI sing_1311.htm#SEC1387 7516
	2784	normalP sing_1225.htm#SEC1301 36584
	2785	normalToricRing sing_1241.htm#SEC1317 29638
	2786	normalToricRingFromBinomials normalToricRingFromBinomials sing_1242.htm#SEC1318 2301
	2787	normal_lib sing_1223.htm#SEC1299
	2788	normalform sing_1481.htm#SEC1557 5550
[54fdec1]	2789	normalform sing_2305.htm#IDX913
[3a9ee05]	2790	normaliz sing_1.htm#IDX14 18426
[063ba1]	2791	normaliz sing_1254.htm#SEC1330
	2792	normaliz.lib sing_1239.htm#SEC1315
	2793	normaliz_lib sing_1239.htm#SEC1315
	2794	normalization sing_1168.htm#IDX540
	2795	normalization sing_1169.htm#IDX543
	2796	normalization sing_1170.htm#IDX546
	2797	normalization sing_1171.htm#IDX548
	2798	normalization sing_1224.htm#IDX550
	2799	normalization sing_1225.htm#IDX553
	2800	normalization sing_1226.htm#IDX556
	2801	normalization sing_1238.htm#IDX562
	2802	normalization sing_1239.htm#IDX564
[54fdec1]	2803	normalization sing_2315.htm#IDX918
[063ba1]	2804	normalization. sing_1165.htm#IDX539
	2805	normalization. sing_1358.htm#IDX595
	2806	normalize sing_951.htm#SEC1027 44788
[a719149]	2807	not sing_96.htm#SEC136
[cd8a2b5]	2808	notBuckets, option sing_307.htm#IDX160
	2809	notRegularity, option sing_307.htm#IDX158
	2810	notSugar, option sing_307.htm#IDX159
	2811	notWarnSB, option sing_307.htm#IDX181
[063ba1]	2812	npar sing_1836.htm#SEC1912 5753
[cd8a2b5]	2813	npars sing_301.htm#SEC341
[063ba1]	2814	nrRootsDeterm sing_1961.htm#SEC2037 sprintf
	2815	nrRootsProbab sing_1960.htm#SEC2036 sprintf
[cd8a2b5]	2816	nres sing_302.htm#SEC342
[063ba1]	2817	nres (plural) sing_464.htm#SEC504
[cd8a2b5]	2818	nrows sing_303.htm#SEC343
[063ba1]	2819	nrroots sing_1990.htm#SEC2066 54867
	2820	nsatiety sing_1219.htm#SEC1295 53333
	2821	nselect sing_1121.htm#SEC1197 34057
	2822	nt_solve sing_1725.htm#SEC1801 33061
	2823	ntsolve.lib sing_1724.htm#SEC1800
	2824	ntsolve_lib sing_1724.htm#SEC1800
[a719149]	2825	number sing_139.htm#SEC179
[063ba1]	2826	number sing_2164.htm#IDX818
[a719149]	2827	number declarations sing_140.htm#SEC180
	2828	number expressions sing_141.htm#SEC181
	2829	number operations sing_142.htm#SEC182
	2830	number related functions number related functions sing_143.htm#SEC183
[063ba1]	2831	numberOfConesOfDimension numberOfConesOfDimension sing_2047.htm#SEC2123 5905
	2832	number_e sing_889.htm#SEC965 59152
	2833	number_pi sing_890.htm#SEC966 15492
	2834	numerAlg.lib sing_1333.htm#IDX569
	2835	numerAlg_lib sing_1333.htm#IDX570
	2836	numerDecom.lib sing_1338.htm#IDX571
	2837	numerDecom_lib sing_1338.htm#IDX572
[cd8a2b5]	2838	numerator sing_304.htm#SEC344
	2839	nvars sing_305.htm#SEC345
[063ba1]	2840	oneDimBelongSemigroup oneDimBelongSemigroup sing_1112.htm#SEC1188 34399
[3a9ee05]	2841	online help The online help system sing_16.htm#SEC22
[cd8a2b5]	2842	open sing_306.htm#SEC346
[063ba1]	2843	opentex sing_1753.htm#SEC1829 54236
	2844	operatorBM sing_539.htm#SEC591 54875
	2845	operatorModulo sing_540.htm#SEC592 26064
	2846	oppose sing_465.htm#SEC505
	2847	opposite sing_466.htm#SEC506
	2848	opposite polynomial sing_350.htm#IDX231
	2849	opposite ring sing_350.htm#IDX228
[cd8a2b5]	2850	option sing_307.htm#SEC347
[a719149]	2851	option(warn) sing_70.htm#SEC110
[063ba1]	2852	optionIsSet sing_994.htm#SEC1070 57325
[a719149]	2853	or Evaluation of logical expressions sing_96.htm#SEC136
[7d21990]	2854	or sing_403.htm#SEC443
[063ba1]	2855	orbit sing_1351.htm#IDX575
	2856	orbit sing_1352.htm#IDX579
	2857	orbit sing_1355.htm#IDX584
	2858	orbit sing_1356.htm#IDX587
[54fdec1]	2859	orbitCones sing_2392.htm#SEC2468 5522
[063ba1]	2860	orbit_variety sing_1652.htm#SEC1728 22665
	2861	orbitparam.lib sing_1351.htm#SEC1427
	2862	orbitparam_lib sing_1351.htm#SEC1427
[cd8a2b5]	2863	ord sing_308.htm#SEC348
[063ba1]	2864	ord_test sing_989.htm#SEC1065 36532
	2865	orderings General definitions for orderings sing_837.htm#SEC889
	2866	orderings introduction Introduction to orderings sing_836.htm#SEC888
	2867	orderings, M sing_841.htm#SEC893
	2868	orderings, a sing_843.htm#SEC895
	2869	orderings, global sing_838.htm#SEC890
	2870	orderings, local sing_839.htm#SEC891
	2871	orderings, product sing_842.htm#SEC894
[cd8a2b5]	2872	ordstr sing_309.htm#SEC349
[063ba1]	2873	origin sing_1995.htm#SEC2071 31408
	2874	orthogonalize sing_1068.htm#SEC1144 63711
	2875	outer sing_1038.htm#SEC1114 64048
[a719149]	2876	output sing_41.htm#SEC71
	2877	p-adic numbers sing_32.htm#SEC46
[063ba1]	2878	pFactor sing_1885.htm#SEC1961 31504
	2879	pIntersect sing_503.htm#SEC555 44055
	2880	pIntersectSyz sing_504.htm#SEC556 45608
[a719149]	2881	package sing_144.htm#SEC184
	2882	package declarations package declarations sing_145.htm#SEC185
	2883	package related functions package related functions sing_146.htm#SEC186
[063ba1]	2884	pairset sing_1950.htm#SEC2026 38258
[cd8a2b5]	2885	par sing_310.htm#SEC350
[063ba1]	2886	par2varRing sing_873.htm#SEC949 44769
	2887	paraConic sing_1366.htm#SEC1442 9828
	2888	paraPlaneCurve sing_1360.htm#SEC1436 34094
	2889	parallel skeletons sing_933.htm#IDX480
	2890	parallel.lib sing_933.htm#SEC1009
	2891	parallelTestAND sing_937.htm#SEC1013 1415
	2892	parallelTestOR sing_938.htm#SEC1014 14920
	2893	parallelWaitAll sing_936.htm#SEC1012 2017
	2894	parallelWaitFirst sing_935.htm#SEC1011 32
	2895	parallelWaitN sing_934.htm#SEC1010 38878
	2896	parallel_lib sing_933.htm#SEC1009
	2897	parallelization sing_933.htm#IDX479
	2898	parallelization sing_973.htm#IDX482
	2899	parallelization sing_1014.htm#IDX495
	2900	param sing_1543.htm#SEC1619 57220
[a719149]	2901	parameter, as numbers sing_139.htm#SEC179
[063ba1]	2902	parameterSubstitute sing_2145.htm#SEC2221 63147
	2903	parametric annihilator sing_532.htm#IDX333
	2904	parametric annihilator for variety sing_588.htm#IDX356
	2905	parametric ideal sing_902.htm#IDX423
	2906	parametric ideal sing_909.htm#IDX436
	2907	parametric ideal sing_909.htm#IDX438
	2908	parametric ideal sing_910.htm#IDX442
	2909	parametrization sing_1351.htm#IDX576
	2910	parametrization sing_1355.htm#IDX585
	2911	parametrization sing_1543.htm#IDX737
	2912	parametrizeOrbit sing_1355.htm#SEC1431 26969
	2913	paraplanecurves.lib sing_1357.htm#SEC1433
	2914	paraplanecurves_lib sing_1357.htm#SEC1433
[cd8a2b5]	2915	pardeg sing_311.htm#SEC351
	2916	parstr sing_312.htm#SEC352
[7a419f]	2917	part sing_2284.htm#SEC2360 31485
[063ba1]	2918	partOver sing_2287.htm#SEC2363 25555
	2919	partUnder sing_2288.htm#SEC2364 13123
	2920	partial_molien sing_1630.htm#SEC1706 21772
	2921	partitions sing_1133.htm#SEC1209 48089
	2922	partitions sing_1133.htm#IDX528
	2923	path integral sing_1125.htm#IDX515
	2924	pause sing_930.htm#SEC1006 2273
	2925	pdivi sing_904.htm#SEC980 39081
	2926	pdivi sing_905.htm#IDX433
[54fdec1]	2927	pdivisorplus sing_2341.htm#SEC2417 47486
[063ba1]	2928	permcol sing_1051.htm#SEC1127 12886
	2929	permrow sing_1052.htm#SEC1128 26561
	2930	permutations sing_1134.htm#IDX529
	2931	permute sing_1134.htm#SEC1210 40893
	2932	permute_L sing_1788.htm#SEC1864 10716
	2933	perron sing_731.htm#SEC783 3782
	2934	perron.lib sing_730.htm#SEC782
	2935	perron_lib sing_730.htm#SEC782
	2936	phindex.lib sing_2205.htm#IDX885
	2937	phindex_lib sing_2205.htm#IDX886
	2938	picksFormula sing_2067.htm#SEC2143 14656
	2939	pid sing_350.htm#IDX240
	2940	plainInvariants sing_1502.htm#SEC1578 40916
[54fdec1]	2941	planeCur sing_2303.htm#SEC2379 sprintf
[063ba1]	2942	plot sing_1766.htm#SEC1842 46610
	2943	plotRot sing_1770.htm#SEC1846 57150
	2944	plotRotated sing_1769.htm#SEC1845 33009
	2945	plotRotatedDirect sing_1772.htm#SEC1848 18202
	2946	plotRotatedList sing_1771.htm#SEC1847 41668
	2947	plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1773.htm#SEC1849 38856
	2948	plural sing_996.htm#IDX487
	2949	pmat sing_924.htm#SEC1000 3857
	2950	pnormalf sing_905.htm#SEC981 34068
	2951	pointid.lib sing_1266.htm#SEC1342
	2952	pointid_lib sing_1266.htm#SEC1342
	2953	polSol sing_766.htm#SEC818 323
	2954	polSolFiniteRank sing_767.htm#SEC819 30875
	2955	pollTask sing_1024.htm#SEC1100 53950
[a719149]	2956	poly sing_147.htm#SEC187
[063ba1]	2957	poly (plural) sing_430.htm#SEC470
[a719149]	2958	poly declarations sing_148.htm#SEC188
[063ba1]	2959	poly declarations (plural) poly declarations (plural) sing_431.htm#SEC471
[a719149]	2960	poly expressions sing_149.htm#SEC189
[063ba1]	2961	poly expressions (plural) poly expressions (plural) sing_432.htm#SEC472
[a719149]	2962	poly operations sing_150.htm#SEC190
[063ba1]	2963	poly operations (plural) poly operations (plural) sing_433.htm#SEC473
[a719149]	2964	poly related functions poly related functions sing_151.htm#SEC191
[063ba1]	2965	poly related functions (plural) poly related functions (plural) sing_434.htm#SEC474
	2966	poly.lib sing_939.htm#SEC1015
	2967	poly2list sing_581.htm#SEC633 4960
	2968	poly2zdd sing_2226.htm#SEC2302 61839
[54fdec1]	2969	polyInterpolation sing_2344.htm#SEC2420 45866
[063ba1]	2970	polyVars sing_773.htm#SEC825 43882
	2971	poly_lib sing_939.htm#SEC1015
	2972	polybori sing_2210.htm#IDX890
	2973	polybori.lib sing_2210.htm#IDX887
	2974	polybori.lib sing_2210.htm#IDX891
	2975	polybori_lib sing_2210.htm#IDX888
	2976	polymake sing_2052.htm#IDX791
	2977	polymake.lib sing_2052.htm#SEC2128
	2978	polymakePolytope sing_2053.htm#SEC2129 47302
	2979	polymake_lib sing_2052.htm#SEC2128
	2980	polynomial solutions sing_760.htm#IDX384
	2981	polynomial, opposite sing_350.htm#IDX232
[cd8a2b5]	2982	polytope sing_185.htm#SEC225
[063ba1]	2983	polytope sing_2052.htm#IDX787
	2984	polytopeViaInequalities polytopeViaInequalities sing_2025.htm#SEC2101 52084
	2985	polytopeViaPoints sing_2026.htm#SEC2102 281
	2986	pos_def sing_1079.htm#SEC1155 4994
	2987	poset sing_2195.htm#IDX876
	2988	positiveOrthant sing_1996.htm#SEC2072 42102
	2989	posweight sing_1610.htm#SEC1686 3364
	2990	powSumSym sing_2241.htm#SEC2317 2339
	2991	power sing_1039.htm#SEC1115 23365
	2992	powerN sing_1869.htm#SEC1945 20170
	2993	powerX sing_1878.htm#SEC1954 47971
	2994	power_products sing_1644.htm#SEC1720 54629
	2995	powerpolyX sing_1848.htm#SEC1924 37247
	2996	powersums sing_1971.htm#SEC2047 59049
	2997	preComp sing_1202.htm#SEC1278 16160
[cd8a2b5]	2998	preimage sing_313.htm#SEC353
[063ba1]	2999	preimage sing_697.htm#IDX359
	3000	preimage (plural) sing_467.htm#SEC507
	3001	preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_992.htm#IDX485
[54fdec1]	3002	preimageLattice sing_2457.htm#SEC2533 37348
[063ba1]	3003	preimageLoc sing_992.htm#SEC1068 33315
	3004	preimageNC sing_699.htm#SEC751 16037
	3005	prepEmbDiv sing_1428.htm#SEC1504 36708
	3006	prepMat sing_1681.htm#SEC1757 39868
	3007	prepRealclassify sing_1486.htm#SEC1562 10994
	3008	prepSV sing_1783.htm#SEC1859 50095
	3009	prepareAss sing_1285.htm#SEC1361 21802
	3010	presentTree sing_1415.htm#SEC1491 10731
	3011	presolve.lib sing_1691.htm#SEC1767
	3012	presolve_lib sing_1691.htm#SEC1767
	3013	primL sing_1873.htm#SEC1949 14513
	3014	primList sing_1872.htm#SEC1948 6802
	3015	primRoot sing_1325.htm#SEC1401 14210
	3016	primTest sing_1201.htm#SEC1277 8105
	3017	primary_char0 sing_1634.htm#SEC1710 61413
	3018	primary_char0_no_molien primary_char0_no_molien sing_1636.htm#SEC1712 50477
	3019	primary_char0_no_molien_random primary_char0_no_molien_random sing_1641.htm#SEC1717 8422
	3020	primary_char0_random primary_char0_random sing_1639.htm#SEC1715 5996
	3021	primary_charp sing_1635.htm#SEC1711 37863
	3022	primary_charp_no_molien primary_charp_no_molien sing_1637.htm#SEC1713 32282
	3023	primary_charp_no_molien_random primary_charp_no_molien_random sing_1642.htm#SEC1718 11498
	3024	primary_charp_random primary_charp_random sing_1640.htm#SEC1716 24739
	3025	primary_charp_without primary_charp_without sing_1638.htm#SEC1714 49585
	3026	primary_charp_without_random primary_charp_without_random sing_1643.htm#SEC1719 36998
	3027	primary_invariants sing_1622.htm#SEC1698 5500
	3028	primary_invariants_random primary_invariants_random sing_1623.htm#SEC1699 28958
	3029	primdec.lib sing_1270.htm#SEC1346
	3030	primdecGTZ sing_1272.htm#SEC1348 6091
	3031	primdecGTZE sing_1273.htm#SEC1349 64882
	3032	primdecMon sing_1190.htm#SEC1266 3856
	3033	primdecSY sing_1274.htm#SEC1350 6547
	3034	primdecSYE sing_1275.htm#SEC1351 52788
	3035	primdecZ sing_1294.htm#SEC1370 48194
	3036	primdecZM sing_1295.htm#SEC1371 17214
	3037	primdec_lib sing_1270.htm#SEC1346
	3038	primdecint.lib sing_1293.htm#SEC1369
	3039	primdecint_lib sing_1293.htm#SEC1369
[cd8a2b5]	3040	prime sing_314.htm#SEC354
[063ba1]	3041	primeClosure sing_1229.htm#SEC1305 43589
	3042	primecoeffs sing_896.htm#SEC972 46153
[cd8a2b5]	3043	primefactors sing_315.htm#SEC355
[063ba1]	3044	primes sing_891.htm#SEC967 24408
	3045	primitiv.lib sing_1301.htm#SEC1377
	3046	primitiv_lib sing_1301.htm#SEC1377
	3047	primitive sing_1302.htm#SEC1378 36163
	3048	primitive element sing_1302.htm#IDX566
[54fdec1]	3049	primitiveSpan sing_2464.htm#SEC2540 sprintf
[063ba1]	3050	primitive_extra sing_1303.htm#SEC1379 49025
	3051	primparam sing_1497.htm#SEC1573 35357
	3052	principal intersection sing_497.htm#IDX317
[cd8a2b5]	3053	print sing_316.htm#SEC356
[063ba1]	3054	print sing_2162.htm#IDX811
[7a419f]	3055	printGraph sing_1127.htm#SEC1203 45041
[54fdec1]	3056	printGraphG sing_2530.htm#SEC2606 48742
	3057	printGroup sing_2445.htm#SEC2521 6791
[063ba1]	3058	printMoebius sing_2201.htm#SEC2277 45828
[54fdec1]	3059	printSheaf sing_2518.htm#SEC2594 31762
	3060	printStack sing_2532.htm#SEC2608 3692
[063ba1]	3061	printTask sing_1019.htm#SEC1095 54549
[54fdec1]	3062	printVariety sing_2510.htm#SEC2586 2846
[895ba26]	3063	printf sing_317.htm#SEC357 2294
[7d21990]	3064	printlevel sing_392.htm#SEC432
[a719149]	3065	proc sing_152.htm#SEC192
	3066	proc declaration sing_153.htm#SEC193
	3067	proc expression sing_154.htm#SEC194
	3068	procedure, ASCII help sing_56.htm#IDX125
	3069	procedure, ASCII/Texinfo help sing_58.htm#IDX127
	3070	procedure, texinfo help sing_57.htm#IDX126
	3071	procedures, help string sing_45.htm#SEC82
	3072	procedures, static Procedure definition sing_43.htm#SEC78
	3073	procs with different argument types procs with different argument types sing_155.htm#SEC195
[063ba1]	3074	prodcrit sing_1948.htm#SEC2024 56231
	3075	product sing_892.htm#SEC968 54431
[54fdec1]	3076	product variety, abstract variety sing_2511.htm#IDX981
	3077	productVariety sing_2511.htm#SEC2587 54191
	3078	productgroup sing_2466.htm#SEC2542 55937
[cd8a2b5]	3079	progress watch sing_307.htm#IDX163
[54fdec1]	3080	projectLattice sing_2458.htm#SEC2534 28463
	3081	projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2515.htm#IDX985
[063ba1]	3082	projective dimension purityfiltration_lib sing_738.htm#IDX368
[a719149]	3083	projective limes sing_32.htm#SEC46
[54fdec1]	3084	projective space, abstract variety sing_2514.htm#IDX984
	3085	projectiveBundle sing_2515.htm#SEC2591 13791
[063ba1]	3086	projectiveDimension sing_739.htm#SEC791 8165
[54fdec1]	3087	projectiveSpace sing_2514.htm#SEC2590 21729
[3a9ee05]	3088	prompt sing_15.htm#SEC21
[cd8a2b5]	3089	prompt, option sing_307.htm#IDX182
[063ba1]	3090	propagator sing_1125.htm#IDX513 42460
	3091	propagator sing_1128.htm#SEC1204
[cd8a2b5]	3092	prot, option sing_307.htm#IDX161
	3093	protocol of computations sing_307.htm#IDX162
[063ba1]	3094	proximitymatrix sing_1456.htm#SEC1532 58403
[cd8a2b5]	3095	prune sing_318.htm#SEC358
[54fdec1]	3096	prwalk sing_2497.htm#SEC2573 46963
[063ba1]	3097	psigncnd sing_1744.htm#SEC1820 57734
	3098	puiseux2generators sing_1555.htm#SEC1631 64508
	3099	puiseuxExpansion sing_2116.htm#SEC2192 46277
	3100	pure tensor sing_490.htm#IDX305
	3101	purelist sing_749.htm#SEC801 15517
	3102	purity purityfiltration_lib sing_738.htm#IDX370
	3103	purityFiltration sing_740.htm#SEC792 5742
	3104	purityTriang sing_741.htm#SEC793 3665
	3105	purityfiltration.lib purityfiltration_lib sing_738.htm#IDX363
	3106	purityfiltration_lib purityfiltration_lib sing_738.htm#IDX364
[54fdec1]	3107	pushForward sing_2483.htm#SEC2559 26697
[063ba1]	3108	pwalk sing_1141.htm#SEC1217 61187
[cd8a2b5]	3109	pyobject sing_186.htm#SEC226
[063ba1]	3110	pyobject sing_2210.htm#IDX893
[cd8a2b5]	3111	pyobject declarations pyobject declarations sing_187.htm#SEC227
	3112	pyobject expressions pyobject expressions sing_188.htm#SEC228
	3113	pyobject operations sing_189.htm#SEC229
	3114	pyobject related functions pyobject related functions sing_190.htm#SEC230
[54fdec1]	3115	pyramid sing_2360.htm#SEC2436 7421
[cd8a2b5]	3116	python_eval sing_191.htm#SEC231
	3117	python_import sing_192.htm#SEC232
	3118	python_run sing_193.htm#SEC233
[063ba1]	3119	qbase sing_1974.htm#SEC2050 8633
[54fdec1]	3120	qepcad sing_2370.htm#SEC2446 39171
	3121	qepcadsystem sing_2371.htm#SEC2447 31977
[063ba1]	3122	qhmatrix sing_1608.htm#SEC1684 61813
	3123	qhmoduli.lib sing_1572.htm#SEC1648
	3124	qhmoduli_lib sing_1572.htm#SEC1648
	3125	qhspectrum sing_1595.htm#SEC1671 13732
[cd8a2b5]	3126	qhweight sing_319.htm#SEC359
[063ba1]	3127	qmatrix.lib sing_732.htm#SEC784
	3128	qmatrix_lib sing_732.htm#SEC784
	3129	qminor sing_734.htm#SEC786 52670
[cd8a2b5]	3130	qrds sing_320.htm#SEC360
[a719149]	3131	qring Miscellaneous oddities sing_161.htm#SEC201
[063ba1]	3132	qring sing_410.htm#IDX293
	3133	qring (plural) sing_435.htm#SEC475
[a719149]	3134	qring declaration sing_165.htm#SEC205
[063ba1]	3135	qring declaration (plural) qring declaration (plural) sing_436.htm#SEC476
	3136	qring related functions (plural) qring related functions (plural) sing_437.htm#SEC477
	3137	qring ring ideal 'factor ring' sing_1001.htm#IDX491
[cd8a2b5]	3138	qringNF, option sing_307.htm#IDX164
[063ba1]	3139	qslimgb sing_872.htm#SEC948 51999
	3140	quadraticSieve sing_1886.htm#SEC1962 58557
	3141	quantMat sing_733.htm#SEC785 56227
	3142	quickclass sing_1478.htm#SEC1554 14018
[7d21990]	3143	quit sing_382.htm#SEC422
[54fdec1]	3144	quotSheaf sing_2527.htm#SEC2603 49619
[cd8a2b5]	3145	quote sing_321.htm#SEC361
	3146	quotient sing_322.htm#SEC362
[063ba1]	3147	quotient (plural) sing_468.htm#SEC508
	3148	quotientLatticeBasis quotientLatticeBasis sing_2027.htm#SEC2103 15613
	3149	quotientMain sing_1736.htm#SEC1812 39870
	3150	quotientMon sing_1181.htm#SEC1257 57149
[54fdec1]	3151	quotients sing_2386.htm#IDX951
[063ba1]	3152	rHRR sing_2281.htm#SEC2357 20131
	3153	rMacaulay sing_925.htm#SEC1001 45499
	3154	rad_con sing_952.htm#SEC1028 21777
	3155	radical sing_1282.htm#SEC1358 1407
	3156	radicalEHV sing_1283.htm#SEC1359 33703
	3157	radicalMemberShip sing_2138.htm#SEC2214 28527
	3158	radicalMon sing_1182.htm#SEC1258 64912
	3159	radicalZ sing_1297.htm#SEC1373 5783
	3160	randcharpoly sing_1968.htm#SEC2044 37737
	3161	randlinpoly sing_1970.htm#SEC2046 22330
[cd8a2b5]	3162	random sing_323.htm#SEC363
[063ba1]	3163	random sing_350.htm#IDX244
	3164	random sing_2183.htm#IDX850
	3165	random sing_2184.htm#IDX852
	3166	random number generator, seed sing_350.htm#IDX242
	3167	random.lib sing_960.htm#SEC1036
	3168	randomBinomial sing_972.htm#SEC1048 17913
	3169	randomCheck sing_1799.htm#SEC1875 20973
	3170	randomLast sing_971.htm#SEC1047 2046
	3171	randomPoint sing_2028.htm#SEC2104 22561
	3172	randomPolyInT sing_2147.htm#SEC2223 2264
	3173	random_lib sing_960.htm#SEC1036
	3174	randomid sing_962.htm#SEC1038 7815
	3175	randommat sing_963.htm#SEC1039 33569
[cd8a2b5]	3176	rank sing_204.htm#IDX137
	3177	rank sing_324.htm#SEC364
[54fdec1]	3178	rankSheaf sing_2519.htm#SEC2595 11850
[063ba1]	3179	ratSol sing_768.htm#SEC820 62488
	3180	ratgb.lib sing_758.htm#IDX373
	3181	ratgb_lib sing_758.htm#IDX374
	3182	rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1360.htm#IDX597
	3183	rational normal curve, projection. sing_1361.htm#IDX598
	3184	rational normal curve, projection. sing_1364.htm#IDX599
	3185	rational normal curve, projection. sing_1365.htm#IDX600
	3186	rational solutions sing_760.htm#IDX385
	3187	rational univariate projection sing_1968.htm#IDX784
[54fdec1]	3188	rationalCurve sing_2539.htm#SEC2615 61201
[063ba1]	3189	rationalPointConic sing_1362.htm#SEC1438 9761
	3190	ratstd sing_759.htm#SEC811 61346
	3191	rays sing_2029.htm#SEC2105 44445
	3192	re2squ sing_1339.htm#SEC1415 24350
[cd8a2b5]	3193	read sing_325.htm#SEC365
[063ba1]	3194	readNmzData sing_1257.htm#SEC1333 18957
[cd8a2b5]	3195	reading, option sing_307.htm#IDX183
[3a9ee05]	3196	readline sing_1.htm#IDX5
[a719149]	3197	real sing_28.htm#IDX74
[063ba1]	3198	real roots, univariate polynomial sing_1975.htm#IDX786
	3199	real roots, univariate projection sing_1959.htm#IDX782
	3200	real roots,sign conditions sing_1742.htm#IDX762
[54fdec1]	3201	realclassify sing_2504.htm#SEC2580 60279
	3202	realclassify.lib sing_2503.htm#SEC2579
	3203	realclassify_lib sing_2503.htm#SEC2579
[063ba1]	3204	realizationDim sing_2110.htm#SEC2186 37756
	3205	realizationDimPoly sing_2112.htm#SEC2188 3611
	3206	realizationMatroids.lib realizationMatroids_lib sing_2109.htm#SEC2185
	3207	realizationMatroids_lib realizationMatroids_lib sing_2109.htm#SEC2185
[54fdec1]	3208	realmorsesplit sing_2505.htm#SEC2581 16318
[063ba1]	3209	realpoly sing_1306.htm#SEC1382 9453
	3210	realrad sing_1308.htm#SEC1384 43381
	3211	realrad.lib sing_1305.htm#SEC1381
	3212	realrad_lib sing_1305.htm#SEC1381
	3213	realzero sing_1307.htm#SEC1383 12712
	3214	recursive_boolean_poly recursive_boolean_poly sing_2216.htm#SEC2292 17045
	3215	recursive_from_boolean_poly recursive_from_boolean_poly sing_2222.htm#SEC2298 37794
[cd8a2b5]	3216	redSB, option sing_307.htm#IDX165
	3217	redTail, option sing_307.htm#IDX167
	3218	redThrough, option sing_307.htm#IDX168
	3219	redefine, option sing_307.htm#IDX184
	3220	reduce sing_326.htm#SEC366
[063ba1]	3221	reduce sing_511.htm#IDX322
	3222	reduce sing_904.htm#IDX431
	3223	reduce sing_905.htm#IDX434
	3224	reduce (plural) sing_469.htm#SEC509
	3225	reduced sing_903.htm#IDX428
[cd8a2b5]	3226	reduced standard basis sing_307.htm#IDX166
[063ba1]	3227	reduction sing_1660.htm#SEC1736 31048
	3228	reesclos.lib sing_1309.htm#SEC1385
	3229	reesclos_lib sing_1309.htm#SEC1385
[cd8a2b5]	3230	reference sing_194.htm#SEC234
	3231	reference declarations reference declarations sing_195.htm#SEC235
	3232	reference expressions reference expressions sing_196.htm#SEC236
	3233	reference operations reference and shared operations sing_199.htm#SEC239
	3234	reference related functions reference and shared related functions sing_200.htm#SEC240
[063ba1]	3235	regCM sing_1221.htm#SEC1297 25488
	3236	regIdeal sing_1207.htm#SEC1283 3827
	3237	regMonCurve sing_1210.htm#SEC1286 41311
[cd8a2b5]	3238	regularity Syzygies and resolutions sing_327.htm#SEC367
[063ba1]	3239	regularity sing_847.htm#SEC904
	3240	reiffen sing_550.htm#SEC602 32856
	3241	rel_orbit_variety sing_1653.htm#SEC1729 34278
	3242	relations sing_730.htm#IDX362
	3243	relativeInteriorPoint relativeInteriorPoint sing_2030.htm#SEC2106 30097
	3244	relative_orbit_variety relative_orbit_variety sing_1654.htm#SEC1730 32995
	3245	relweight sing_1609.htm#SEC1685 10658
	3246	remainder sing_1729.htm#SEC1805 1191
	3247	remainderMain sing_1737.htm#SEC1813 3532
	3248	removeCone sing_2048.htm#SEC2124 33877
	3249	removepower sing_1466.htm#SEC1542 47644
[cd8a2b5]	3250	repart sing_328.htm#SEC368
[063ba1]	3251	replace sing_1838.htm#SEC1914 50075
	3252	representation, math objects Representation of mathematical objects sing_834.htm#SEC886
[895ba26]	3253	res sing_329.htm#SEC369 53499
[063ba1]	3254	resbinomial.lib sing_1369.htm#IDX603
	3255	resbinomial_lib sing_1369.htm#IDX604
[cd8a2b5]	3256	reservedName sing_330.htm#SEC370
[063ba1]	3257	resfunction sing_1383.htm#SEC1459 59312
	3258	resgraph.lib sing_1401.htm#SEC1477
	3259	resgraph_lib sing_1401.htm#SEC1477
	3260	resjung.lib sing_1405.htm#SEC1481
	3261	resjung_lib sing_1405.htm#SEC1481
	3262	reslist sing_1397.htm#SEC1473 64950
[a719149]	3263	resolution purityfiltration_lib sing_156.htm#SEC196
[063ba1]	3264	resolution sing_738.htm#IDX369
	3265	resolution (plural) sing_438.htm#SEC478
[a719149]	3266	resolution declarations resolution declarations sing_157.htm#SEC197
[063ba1]	3267	resolution declarations (plural) resolution declarations (plural) sing_439.htm#SEC479
[a719149]	3268	resolution expressions resolution expressions sing_158.htm#SEC198
[063ba1]	3269	resolution expressions (plural) resolution expressions (plural) sing_440.htm#SEC480
	3270	resolution graph sing_1451.htm#IDX617
[a719149]	3271	resolution related functions resolution related functions sing_159.htm#SEC199
[063ba1]	3272	resolution related functions (plural) resolution related functions (plural) sing_441.htm#SEC481
[cd8a2b5]	3273	resolution, La Scala's method sing_280.htm#SEC320
	3274	resolution, computation of sing_329.htm#IDX186
	3275	resolution, hilbert-driven sing_255.htm#SEC295
[54fdec1]	3276	resolutionInLocalization resolutionInLocalization sing_2385.htm#SEC2461 31106
[063ba1]	3277	resolutiongraph sing_1452.htm#SEC1528 32697
	3278	resolve sing_1413.htm#SEC1489 27374
	3279	resolve.lib sing_1409.htm#SEC1485
	3280	resolve_lib sing_1409.htm#SEC1485
	3281	resources.lib sing_973.htm#SEC1049
	3282	resources_lib sing_973.htm#SEC1049
	3283	restriction sing_2176.htm#IDX838
	3284	restriction sing_2192.htm#IDX871
	3285	restriction sing_2193.htm#IDX873
	3286	restriction of sing_555.htm#IDX345
	3287	restrictionIdeal sing_565.htm#SEC617 49796
	3288	restrictionModule sing_566.htm#SEC618 62461
[cd8a2b5]	3289	resultant sing_294.htm#SEC334
	3290	resultant sing_331.htm#SEC371
[063ba1]	3291	reszeta.lib sing_1422.htm#SEC1498
	3292	reszeta_lib sing_1422.htm#SEC1498
[7d21990]	3293	return sing_383.htm#SEC423
	3294	return type of procedures Return type of procedures sing_408.htm#SEC448
[cd8a2b5]	3295	returnSB, option sing_307.htm#IDX152
[063ba1]	3296	reverse sing_1989.htm#SEC2065 35880
	3297	reverse lexicographical ordering sing_838.htm#IDX390
	3298	reynolds_molien sing_1629.htm#SEC1705 45316
	3299	rho sing_1880.htm#SEC1956 51414
	3300	rightInverse sing_1818.htm#SEC1894 6558
	3301	rightKernel sing_1816.htm#SEC1892 46603
	3302	rightModulo sing_717.htm#SEC769 12618
	3303	rightNF sing_716.htm#SEC768 42610
	3304	rightNFWeyl sing_785.htm#SEC837 35828
	3305	rightStd sing_715.htm#SEC767 5740
[a719149]	3306	ring sing_160.htm#SEC200
[063ba1]	3307	ring sing_901.htm#IDX420
	3308	ring (plural) sing_442.htm#SEC482
	3309	ring coefficients hasTransExtensionCoefficient sing_999.htm#IDX489
	3310	ring coefficients sing_1000.htm#IDX490
[a719149]	3311	ring declarations sing_162.htm#SEC202
[063ba1]	3312	ring declarations (plural) ring declarations (plural) sing_443.htm#SEC483
[a719149]	3313	ring operations sing_164.htm#SEC204
[063ba1]	3314	ring operations (plural) ring operations (plural) sing_444.htm#SEC484
[a719149]	3315	ring related functions ring related functions sing_163.htm#SEC203
[063ba1]	3316	ring related functions (plural) ring related functions (plural) sing_445.htm#SEC485
	3317	ring, opposite sing_350.htm#IDX229
	3318	ring.lib sing_978.htm#SEC1054
[cd8a2b5]	3319	ring_cf sing_204.htm#IDX138
[063ba1]	3320	ring_lib sing_978.htm#SEC1054
[7d21990]	3321	ring_list sing_333.htm#SEC373
[063ba1]	3322	ring_variable sing_2163.htm#IDX815
	3323	ring_variable sing_2164.htm#IDX817
	3324	ring_variable sing_2165.htm#IDX821
	3325	ring_variable sing_2166.htm#IDX823
[cd8a2b5]	3326	ringlist sing_332.htm#SEC372
[063ba1]	3327	ringlist (plural) sing_470.htm#SEC510
	3328	rings sing_901.htm#IDX421
	3329	ringtensor sing_990.htm#SEC1066 56648
	3330	ringweights sing_991.htm#SEC1067 33307
	3331	rinvar.lib sing_1665.htm#SEC1741
	3332	rinvar_lib sing_1665.htm#SEC1741
	3333	rmNmzFiles sing_1262.htm#SEC1338 32601
	3334	rm_unitcol sing_1057.htm#SEC1133 5591
	3335	rm_unitrow sing_1056.htm#SEC1132 35694
	3336	rmx sing_1763.htm#SEC1839 17675
	3337	rncAntiCanonicalMap sing_1361.htm#SEC1437 41965
	3338	rncItProjEven sing_1365.htm#SEC1441 18200
	3339	rncItProjOdd sing_1364.htm#SEC1440 61976
	3340	root of Bernstein-Sato polynomial sing_532.htm#IDX334
	3341	rootofUnity sing_993.htm#SEC1069 21365
	3342	roots sing_1730.htm#SEC1806 18436
	3343	rootsMain sing_1738.htm#SEC1814 54934
	3344	rootsModp sing_1862.htm#SEC1938 47315
	3345	rootsmr.lib sing_1959.htm#SEC2035
	3346	rootsmr_lib sing_1959.htm#SEC2035
	3347	rootsur.lib sing_1975.htm#SEC2051
	3348	rootsur_lib sing_1975.htm#SEC2051
	3349	round sing_1860.htm#SEC1936 9248
[cd8a2b5]	3350	rowShift sing_204.htm#IDX141
	3351	rowShift sing_206.htm#SEC246
[063ba1]	3352	rowred sing_1053.htm#SEC1129 63416
	3353	rp, global ordering sing_838.htm#IDX389
[54fdec1]	3354	rswalk sing_2502.htm#SEC2578 50903
[7d21990]	3355	rtimer sing_396.htm#SEC436
	3356	rvalue No rvalue of increments and assignments sing_402.htm#SEC442
	3357	rvar sing_334.htm#SEC374
[54fdec1]	3358	rwalk sing_2498.htm#SEC2574 42525
	3359	rwalk.lib sing_2496.htm#SEC2572
	3360	rwalk_lib sing_2496.htm#SEC2572
[063ba1]	3361	s_res sing_1007.htm#SEC1083 47429
	3362	sa_poly_reduce sing_520.htm#SEC572 60856
	3363	sa_reduce sing_519.htm#SEC571 55799
	3364	sagbi sing_1315.htm#SEC1391 46653
	3365	sagbi.lib sing_1312.htm#SEC1388
[54fdec1]	3366	sagbiAlg sing_2299.htm#SEC2375 sprintf
	3367	sagbiMod sing_2300.htm#SEC2376 sprintf
[063ba1]	3368	sagbiPart sing_1316.htm#SEC1392 56066
	3369	sagbiReduce sing_1314.htm#SEC1390 19036
	3370	sagbiSPoly sing_1313.htm#SEC1389 17365
	3371	sagbi_lib sing_1312.htm#SEC1388
	3372	salida sing_1394.htm#SEC1470 9839
	3373	sameComponent sing_1942.htm#SEC2018 13540
	3374	sameQ sing_1741.htm#SEC1817 45579
	3375	sat sing_1122.htm#SEC1198 6266
	3376	satiety sing_1209.htm#SEC1285 34323
	3377	satstd sing_2204.htm#SEC2280 63657
[7d21990]	3378	sba sing_335.htm#SEC375
[063ba1]	3379	scalarProd sing_509.htm#SEC561 54488
[54fdec1]	3380	scheme sing_2351.htm#SEC2427 15722
[063ba1]	3381	schreyer.lib sing_1006.htm#SEC1082
	3382	schreyer_lib sing_1006.htm#SEC1082
[54fdec1]	3383	schubert.lib sing_2508.htm#SEC2584
	3384	schubert_lib sing_2508.htm#SEC2584
[a719149]	3385	sdb, source code debugger Source code debugger sing_66.htm#SEC103
[063ba1]	3386	second degree sing_919.htm#IDX471
	3387	secondary fan sing_2052.htm#IDX789
	3388	secondary polytope sing_2052.htm#IDX790
	3389	secondaryFan sing_2060.htm#SEC2136 43205
	3390	secondaryPolytope sing_2059.htm#SEC2135 48451
	3391	secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1650.htm#SEC1726 37058
	3392	secondary_char0 sing_1645.htm#SEC1721 31029
	3393	secondary_charp sing_1647.htm#SEC1723 16364
	3394	secondary_no_molien sing_1648.htm#SEC1724 3616
	3395	secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1651.htm#SEC1727 31675
	3396	segre sing_2236.htm#SEC2312 44035
	3397	select sing_1123.htm#SEC1199 17096
	3398	select1 sing_1124.htm#SEC1200 32617
	3399	semaphore sing_350.htm#IDX247 44342
	3400	semaphore sing_977.htm#SEC1053
	3401	semaphores sing_973.htm#IDX484
	3402	semiCMcod2 sing_1606.htm#SEC1682 15905
[54fdec1]	3403	semiGroup sing_2301.htm#SEC2377 sprintf
	3404	semiMod sing_2302.htm#SEC2378 sprintf
[063ba1]	3405	semidiv sing_1934.htm#SEC2010 58107
	3406	semigroup sing_1455.htm#SEC1531 29045
	3407	semigroup sing_1459.htm#IDX624
	3408	semigroup of values sing_1545.htm#IDX739
	3409	semigroupGenerator sing_2031.htm#SEC2107 59446
	3410	sep sing_1292.htm#SEC1368 sprintf
	3411	separateHNE sing_1556.htm#SEC1632 12052
	3412	separator sing_1192.htm#SEC1268 33000
	3413	serreRelations sing_638.htm#SEC690 33994
	3414	set sing_2158.htm#IDX801
[54fdec1]	3415	setBaseMultigrading sing_2438.htm#SEC2514 6575
[063ba1]	3416	setLetterplaceAttributes setLetterplaceAttributes sing_629.htm#SEC681 5759
	3417	setLinearForms sing_2032.htm#SEC2108 62731
[54fdec1]	3418	setModuleGrading sing_2450.htm#SEC2526 59018
[063ba1]	3419	setMultiplicity sing_2033.htm#SEC2109 27537
	3420	setNmzDataPath sing_1259.htm#SEC1335 18123
	3421	setNmzExecPath sing_1255.htm#SEC1331 38993
	3422	setNmzFilename sing_1258.htm#SEC1334 20206
	3423	setNmzOption sing_1252.htm#SEC1328 9012
[54fdec1]	3424	setUniformizingParameter setUniformizingParameter sing_2548.htm#SEC2624 63635
[063ba1]	3425	set_is_injective sing_1922.htm#SEC1998 8429
	3426	setcores sing_975.htm#SEC1051 49704
	3427	setenv sing_350.htm#IDX250
	3428	setglobalrings sing_901.htm#SEC977 33379
[54fdec1]	3429	setinitials sing_2361.htm#SEC2437 24792
[7d21990]	3430	setring sing_336.htm#SEC376
[063ba1]	3431	sh sing_350.htm#IDX252
[cd8a2b5]	3432	shared sing_194.htm#SEC234
	3433	shared declarations sing_197.htm#SEC237
	3434	shared expressions sing_198.htm#SEC238
	3435	shared operations reference and shared operations sing_199.htm#SEC239
	3436	shared related functions reference and shared related functions sing_200.htm#SEC240
[063ba1]	3437	sheaf cohomology sing_1432.htm#IDX605
	3438	sheafCoh sing_1438.htm#SEC1514 64501
	3439	sheafCohBGG sing_1436.htm#SEC1512 13439
	3440	sheafCohBGG2 sing_1437.htm#SEC1513 3338
	3441	sheafcoh.lib sing_1432.htm#SEC1508
	3442	sheafcoh_lib sing_1432.htm#SEC1508
	3443	shiftPoly sing_631.htm#SEC683 65223
[7d21990]	3444	short sing_393.htm#SEC433
[063ba1]	3445	show sing_926.htm#SEC1002 15599
	3446	showBO sing_1414.htm#SEC1490 20089
	3447	showDataTypes sing_1416.htm#SEC1492 4270
	3448	showNmzOptions sing_1253.htm#SEC1329 64955
	3449	showNuminvs sing_1250.htm#SEC1326 18934
	3450	showgrades sing_743.htm#SEC795 48081
	3451	showrecursive sing_927.htm#SEC1003 6127
	3452	sickle sing_616.htm#SEC668 17166
[54fdec1]	3453	signal handler sing_2564.htm#SEC2654
[063ba1]	3454	signatureBrieskorn sing_1615.htm#SEC1691 26283
	3455	signatureL sing_2206.htm#SEC2282 65493
	3456	signatureLqf sing_2207.htm#SEC2283 18811
	3457	signatureNemethi sing_1617.htm#SEC1693 21981
	3458	signaturePuiseux sing_1616.htm#SEC1692 23398
	3459	signcnd sing_1743.htm#SEC1819 40147
	3460	signcond.lib sing_1742.htm#SEC1818
	3461	signcond_lib sing_1742.htm#SEC1818
	3462	simplesolver sing_1687.htm#SEC1763 13418
[7d21990]	3463	simplex sing_337.htm#SEC377
[063ba1]	3464	simplexOut sing_1714.htm#SEC1790 56099
[7d21990]	3465	simplify sing_338.htm#SEC378
[063ba1]	3466	simplifyRat sing_780.htm#SEC832 52658
	3467	sing.lib sing_1582.htm#SEC1658
	3468	sing4ti2.lib sing_1318.htm#SEC1394
	3469	sing4ti2_lib sing_1318.htm#SEC1394
	3470	sing_lib sing_1582.htm#SEC1658
	3471	singular locus of D-module sing_760.htm#IDX379
	3472	singularities sing_1514.htm#IDX641
	3473	singularities sing_1515.htm#IDX652
	3474	singularities sing_1516.htm#IDX655
	3475	singularities sing_1517.htm#IDX658
	3476	singularities sing_1518.htm#IDX661
	3477	singularities sing_1519.htm#IDX665
	3478	singularities sing_1520.htm#IDX669
	3479	singularities sing_1521.htm#IDX675
	3480	singularities sing_1522.htm#IDX683
	3481	singularities sing_1523.htm#IDX689
	3482	singularities sing_1524.htm#IDX697
	3483	singularities sing_1525.htm#IDX707
	3484	singularities sing_1613.htm#IDX754
	3485	singularities, resolution of Resolution of singularities sing_823.htm#SEC875
	3486	singularity sing_1479.htm#SEC1555 23002
[a719149]	3487	singularrc sing_20.htm#IDX73
[7d21990]	3488	size Miscellaneous oddities sing_339.htm#SEC379
[063ba1]	3489	size sing_410.htm#IDX292
	3490	skewmat sing_1040.htm#SEC1116 2167
[7d21990]	3491	sleep sing_345.htm#SEC385
	3492	slimgb sing_340.htm#SEC380
[063ba1]	3493	slimgb sing_800.htm#SEC852
	3494	slimgb (plural) sing_471.htm#SEC511
	3495	slocus sing_1594.htm#SEC1670 27853
	3496	smith sing_1827.htm#SEC1903 61915
[54fdec1]	3497	smithNormalForm sing_2486.htm#SEC2562 7174
[063ba1]	3498	solutionsMod2 sing_1877.htm#SEC1953 53360
	3499	solve sing_919.htm#IDX472 3078
	3500	solve sing_1708.htm#SEC1784
[cd8a2b5]	3501	solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_283.htm#SEC323
[063ba1]	3502	solve.lib sing_1706.htm#SEC1782
	3503	solveTInitialFormPar solveTInitialFormPar sing_2141.htm#SEC2217 36670
	3504	solve_IP sing_1167.htm#SEC1243 59518
	3505	solve_lib sing_1706.htm#SEC1782
	3506	solvelinearpart sing_1701.htm#SEC1777 42872
	3507	sort sing_893.htm#SEC969 58207
	3508	sortIntvec sing_587.htm#SEC639 60798
	3509	sortandmap sing_1702.htm#SEC1778 10314
	3510	sortier sing_1664.htm#SEC1740 3555
	3511	sortvars sing_1703.htm#SEC1779 61778
[7d21990]	3512	sortvec sing_341.htm#SEC381
[a719149]	3513	source code debugger, sdb Source code debugger sing_66.htm#SEC103
[54fdec1]	3514	spaceCur sing_2304.htm#SEC2380 sprintf
[063ba1]	3515	spadd sing_1528.htm#SEC1604 48739
	3516	span sing_2034.htm#SEC2110 64343
	3517	sparseHomogIdeal sing_969.htm#SEC1045 22631
[54fdec1]	3518	sparseInterpolation sing_2346.htm#SEC2422 28771
[063ba1]	3519	sparseid sing_964.htm#SEC1040 20824
	3520	sparsemat sing_966.htm#SEC1042 17653
	3521	sparsematrix sing_965.htm#SEC1041 41031
	3522	sparsepoly sing_967.htm#SEC1043 21649
	3523	sparsetriag sing_968.htm#SEC1044 50657
	3524	spcurve.lib sing_1602.htm#SEC1678
	3525	spcurve_lib sing_1602.htm#SEC1678
	3526	special characters, non-english sing_399.htm#IDX285
	3527	spectral pairs sing_1514.htm#IDX650
	3528	spectral pairs sing_1521.htm#IDX682
	3529	spectral pairs sing_1523.htm#IDX696
	3530	spectral pairs sing_1524.htm#IDX705
	3531	spectral pairs sing_1536.htm#IDX721
	3532	spectral pairs sing_1538.htm#IDX732
	3533	spectralNeg sing_1424.htm#SEC1500 36691
	3534	spectrum sing_1514.htm#IDX649 47545
	3535	spectrum sing_1520.htm#SEC1596
	3536	spectrum sing_1520.htm#IDX674
	3537	spectrum sing_1521.htm#IDX681
	3538	spectrum sing_1522.htm#IDX688
	3539	spectrum sing_1523.htm#IDX695
	3540	spectrum sing_1524.htm#IDX704
	3541	spectrum sing_1536.htm#IDX720
	3542	spectrum sing_1538.htm#IDX731
	3543	spectrum sing_1613.htm#IDX756
	3544	spectrum.lib sing_1612.htm#SEC1688
	3545	spectrum_lib sing_1612.htm#SEC1688
	3546	spectrumnd sing_1613.htm#SEC1689 29943
	3547	spgamma sing_1535.htm#SEC1611 59653
	3548	spgeomgenus sing_1534.htm#SEC1610 57796
	3549	spissemicont sing_1531.htm#SEC1607 23679
	3550	split sing_928.htm#SEC1004 29794
	3551	splitPolygon sing_2062.htm#SEC2138 706
	3552	splitring sing_1304.htm#SEC1380 56404
	3553	splitting sing_1200.htm#SEC1276 34734
	3554	spmilnor sing_1533.htm#SEC1609 32933
	3555	spmul sing_1530.htm#SEC1606 43607
	3556	spnf sing_1083.htm#SEC1159 57309
	3557	spoly sing_1945.htm#SEC2021 35454
	3558	sppairs sing_1521.htm#SEC1597 49513
	3559	sppnf sing_1526.htm#SEC1602 16650
	3560	sppprint sing_1527.htm#SEC1603 43682
	3561	spprint sing_1084.htm#SEC1160 18671
[895ba26]	3562	sprintf sing_343.htm#SEC383 55889
[063ba1]	3563	spsemicont sing_1532.htm#SEC1608 61169
	3564	spsub sing_1529.htm#SEC1605 54296
	3565	sqfrNorm sing_1731.htm#SEC1807 20546
	3566	sqfrNormMain sing_1739.htm#SEC1815 9890
	3567	sqr sing_1857.htm#SEC1933 sprintf
[7d21990]	3568	sqrfree sing_342.htm#SEC382
[063ba1]	3569	squareRoot sing_1876.htm#SEC1952 17446
	3570	squarefree sing_1557.htm#SEC1633 48485
[7d21990]	3571	sres sing_344.htm#SEC384
[063ba1]	3572	ssi Parallelization with ssi links sing_795.htm#SEC847
[54fdec1]	3573	stack, moduli space of stable maps sing_2532.htm#IDX989
	3574	stack, moduli space of stable maps, rational curves moduliSpace sing_2531.htm#IDX988
[063ba1]	3575	staircase sing_1748.htm#SEC1824 49781
	3576	standard sing_1952.htm#SEC2028 14067
	3577	standard bases. sing_2203.htm#IDX883
	3578	standard bases. sing_2204.htm#IDX884
	3579	standard.lib sing_871.htm#IDX417
	3580	standard_lib sing_871.htm#IDX418
	3581	startNmz sing_1261.htm#SEC1337 21925
	3582	startTasks sing_1020.htm#SEC1096 16715
[a719149]	3583	static procedures Procedure definition sing_43.htm#SEC78
[7d21990]	3584	status sing_345.htm#SEC385
	3585	std sing_346.htm#SEC386
[063ba1]	3586	std sing_798.htm#SEC850
	3587	std (plural) sing_472.htm#SEC512
[895ba26]	3588	stdfglm sing_347.htm#SEC387 256
	3589	stdhilb sing_348.htm#SEC388 63138
[063ba1]	3590	stopTask sing_1021.htm#SEC1097 6801
	3591	stratify sing_1682.htm#SEC1758 56744
	3592	stratify.lib sing_1680.htm#SEC1756
	3593	stratify_lib sing_1680.htm#SEC1756
[a719149]	3594	string Miscellaneous oddities sing_166.htm#SEC206
[063ba1]	3595	string sing_410.htm#IDX295
	3596	string sing_916.htm#IDX462
[a719149]	3597	string declarations sing_167.htm#SEC207
	3598	string expressions sing_168.htm#SEC208
	3599	string operations sing_170.htm#SEC210
	3600	string related functions string related functions sing_171.htm#SEC211
	3601	string type cast sing_169.htm#SEC209
[063ba1]	3602	stripHNE sing_1554.htm#SEC1630 19265
	3603	sturm sing_1985.htm#SEC2061 54353
	3604	sturmha sing_1987.htm#SEC2063 12467
	3605	sturmhaseq sing_1988.htm#SEC2064 59133
	3606	sturmquery sing_1963.htm#SEC2039 10805
	3607	sturmseq sing_1986.htm#SEC2062 23005
	3608	submat sing_1041.htm#SEC1117 37665
	3609	subrInterred sing_957.htm#SEC1033 10165
	3610	subset_sum01 sing_1906.htm#SEC1982 60620
	3611	subset_sum02 sing_1907.htm#SEC1983 37340
[7d21990]	3612	subst sing_349.htm#SEC389
[063ba1]	3613	subst (plural) sing_473.htm#SEC513
	3614	substitute sing_956.htm#SEC1032 28919
[cd8a2b5]	3615	sugarCrit, option sing_307.htm#IDX169
[063ba1]	3616	sum sing_894.htm#SEC970 555
	3617	sum_of_powers sing_2240.htm#SEC2316 12170
	3618	sumlist sing_1396.htm#SEC1472 59918
[54fdec1]	3619	sumofquotients sing_2540.htm#SEC2616 4569
[063ba1]	3620	super-commutative algebras Graded commutative algebras (SCA) sing_482.htm#SEC534
	3621	superCommutative sing_714.htm#SEC766 45528
	3622	super_increasing_knapsack super_increasing_knapsack sing_1918.htm#SEC1994 9177
	3623	surf.lib sing_1765.htm#SEC1841
	3624	surf_lib sing_1765.htm#SEC1841
	3625	surfacesignature.lib surfacesignature_lib sing_1614.htm#SEC1690
	3626	surfacesignature_lib surfacesignature_lib sing_1614.htm#SEC1690
[895ba26]	3627	surfer sing_1.htm#IDX8 14287
[063ba1]	3628	surfer sing_1767.htm#SEC1843
[3a9ee05]	3629	surfex sing_1.htm#IDX7
[063ba1]	3630	surfex.lib sing_1768.htm#SEC1844
	3631	surfex_lib sing_1768.htm#SEC1844
[7d21990]	3632	suspend sing_345.htm#SEC385
[54fdec1]	3633	swalk sing_2501.htm#SEC2577 16794
	3634	swalk.lib sing_2500.htm#SEC2576
	3635	swalk_lib sing_2500.htm#SEC2576
[063ba1]	3636	swap sing_1483.htm#SEC1559 15408
	3637	swap sing_2165.htm#IDX819
[7d21990]	3638	switch No case or switch statement sing_404.htm#SEC444
[54fdec1]	3639	switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2553.htm#SEC2629 1827
[063ba1]	3640	syModStd sing_1328.htm#SEC1404 50246
	3641	symNsym sing_2234.htm#SEC2310 55230
	3642	sym_gauss sing_1067.htm#SEC1143 5121
	3643	symm sing_2233.htm#SEC2309 64628
	3644	symmStd sing_1327.htm#SEC1403 39353
	3645	symmat sing_1042.htm#SEC1118 61294
	3646	symmetric basis sing_1059.htm#IDX498
	3647	symmetric power sing_1061.htm#IDX500
	3648	symmetricBasis sing_1059.htm#SEC1135 sprintf
	3649	symmetricPower sing_1061.htm#SEC1137 6542
[54fdec1]	3650	symmetricPowerSheaf sing_2526.htm#SEC2602 56922
[063ba1]	3651	symmfunc sing_1972.htm#SEC2048 45575
	3652	symodstd.lib sing_1322.htm#SEC1398
	3653	symodstd_lib sing_1322.htm#SEC1398
	3654	symsignature sing_1962.htm#SEC2038 10520
	3655	syndrome sing_1795.htm#SEC1871 14057
	3656	sysBin sing_1793.htm#SEC1869 41948
	3657	sysCRHT sing_1790.htm#SEC1866 58930
	3658	sysCRHTMindist sing_1791.htm#SEC1867 13692
	3659	sysFL sing_1806.htm#SEC1882 53040
	3660	sysNewton sing_1792.htm#SEC1868 19704
	3661	sysQE sing_1796.htm#SEC1872 61026
	3662	sys_code sing_1787.htm#SEC1863 20220
[7d21990]	3663	system sing_350.htm#SEC390
[063ba1]	3664	system, -- sing_350.htm#IDX275
	3665	system, --long_option_name sing_350.htm#IDX278
	3666	system, --long_option_name=value sing_350.htm#IDX280
	3667	system, HC sing_350.htm#IDX215
	3668	system, LLL sing_350.htm#IDX219
	3669	system, Singular sing_350.htm#IDX256
	3670	system, SingularLib sing_350.htm#IDX258
	3671	system, absFact sing_350.htm#IDX190
	3672	system, alarm sing_350.htm#IDX189
	3673	system, blackbox sing_350.htm#IDX191
	3674	system, bracket sing_350.htm#IDX196
	3675	system, browsers sing_350.htm#IDX195
	3676	system, btest sing_350.htm#IDX198
	3677	system, complexNearZero sing_350.htm#IDX199
	3678	system, contributors sing_350.htm#IDX201
	3679	system, cpu sing_350.htm#IDX203
	3680	system, cpu sing_350.htm#IDX274
	3681	system, denom_list sing_350.htm#IDX205
	3682	system, eigenvals sing_350.htm#IDX206
	3683	system, env sing_350.htm#IDX207
	3684	system, executable sing_350.htm#IDX209
	3685	system, freegb sing_350.htm#IDX210
	3686	system, getPrecDigits sing_350.htm#IDX213
	3687	system, getenv sing_350.htm#IDX212
	3688	system, gmsnf sing_350.htm#IDX214
	3689	system, hessenberg sing_350.htm#IDX216
	3690	system, install sing_350.htm#IDX218
	3691	system, nblocks sing_350.htm#IDX222
	3692	system, nc_hilb sing_350.htm#IDX224
	3693	system, neworder sing_350.htm#IDX225
	3694	system, newstruct sing_350.htm#IDX226
	3695	system, opp sing_350.htm#IDX227
	3696	system, oppose sing_350.htm#IDX230
	3697	system, pcvBasis sing_350.htm#IDX239
	3698	system, pcvCV2P sing_350.htm#IDX237
	3699	system, pcvDim sing_350.htm#IDX238
	3700	system, pcvLAddL sing_350.htm#IDX233
	3701	system, pcvMinDeg sing_350.htm#IDX235
	3702	system, pcvP2CV sing_350.htm#IDX236
	3703	system, pcvPMulL sing_350.htm#IDX234
	3704	system, pid sing_350.htm#IDX241
	3705	system, random sing_350.htm#IDX243
	3706	system, reserve sing_350.htm#IDX245
	3707	system, reservedLink sing_350.htm#IDX246
	3708	system, semaphore sing_350.htm#IDX248
	3709	system, semic sing_350.htm#IDX249
	3710	system, setenv sing_350.htm#IDX251
	3711	system, sh sing_350.htm#IDX253
	3712	system, shrinktest sing_350.htm#IDX254
	3713	system, spadd sing_350.htm#IDX259
	3714	system, spectrum sing_350.htm#IDX260
	3715	system, spmul sing_350.htm#IDX261
	3716	system, std_syz sing_350.htm#IDX262
	3717	system, stest sing_350.htm#IDX263
	3718	system, tensorModuleMult sing_350.htm#IDX264
	3719	system, twostd sing_350.htm#IDX265
	3720	system, uname sing_350.htm#IDX268
	3721	system, version sing_350.htm#IDX271
	3722	system, with sing_350.htm#IDX272
[54fdec1]	3723	systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2382.htm#SEC2458 63094
[7d21990]	3724	syz sing_351.htm#SEC391
[063ba1]	3725	syz (plural) sing_474.htm#SEC514
	3726	syzygy sing_1006.htm#IDX494
	3727	tDetropicalise sing_2143.htm#SEC2219 23532
	3728	tInitialForm sing_2127.htm#SEC2203 24484
	3729	tInitialFormPar sing_2139.htm#SEC2215 9584
	3730	tInitialFormParMax sing_2140.htm#SEC2216 7829
	3731	tInitialIdeal sing_2128.htm#SEC2204 17937
	3732	tab sing_929.htm#SEC1005 60407
	3733	tail sing_1941.htm#SEC2017 13066
	3734	tame polynomial sing_1536.htm#IDX713
	3735	tame polynomial sing_1537.htm#IDX723
	3736	tame polynomial sing_1538.htm#IDX724
	3737	tangentGens sing_1352.htm#SEC1428 37797
	3738	tangentcone sing_1601.htm#SEC1677 20056
	3739	task sing_1014.htm#IDX497
	3740	tasks.lib sing_1014.htm#SEC1090
	3741	tasks_lib sing_1014.htm#SEC1090
	3742	tau_es sing_1509.htm#SEC1585 17043
	3743	tau_es2 sing_1463.htm#SEC1539 38083
	3744	tdCf sing_2269.htm#SEC2345 21522
	3745	tdFactor sing_2271.htm#SEC2347 37910
	3746	tdProj sing_2274.htm#SEC2350 38406
	3747	tdTerms sing_2270.htm#SEC2346 30166
	3748	teachstd.lib sing_1939.htm#SEC2015
	3749	teachstd_lib sing_1939.htm#SEC2015
[a719149]	3750	template.lib sing_55.htm#IDX120
	3751	template.lib sing_55.htm#IDX123
	3752	template_lib sing_55.htm#SEC92
	3753	template_lib sing_55.htm#IDX121
[063ba1]	3754	tensor sing_490.htm#IDX309 65451
	3755	tensor sing_1043.htm#SEC1119
	3756	tensorMod sing_1162.htm#SEC1238 21961
[54fdec1]	3757	tensorSheaf sing_2525.htm#SEC2601 24072
[063ba1]	3758	term orderings General definitions for orderings sing_837.htm#SEC889
	3759	term orderings introduction Introduction to orderings sing_836.htm#SEC888
	3760	testNCfac sing_688.htm#SEC740 60394
	3761	testParametrization sing_1367.htm#SEC1443 18686
	3762	testPointConic sing_1368.htm#SEC1444 25315
	3763	testPrimary sing_1280.htm#SEC1356 34254
	3764	testPrimaryE sing_1281.htm#SEC1357 20693
	3765	tex sing_1754.htm#SEC1830 12226
	3766	texDrawBasic sing_2134.htm#SEC2210 3635
	3767	texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2136.htm#SEC2212 42021
	3768	texDrawTriangulation texDrawTriangulation sing_2137.htm#SEC2213 18865
	3769	texDrawTropical sing_2135.htm#SEC2211 58447
	3770	texMatrix sing_2133.htm#SEC2209 1334
	3771	texNumber sing_2131.htm#SEC2207 12628
	3772	texPolynomial sing_2132.htm#SEC2208 41136
	3773	texcoef sing_1835.htm#SEC1911 28189
	3774	texdemo sing_1755.htm#SEC1831 13008
	3775	texfactorize sing_1756.htm#SEC1832 6682
	3776	texmap sing_1757.htm#SEC1833 35265
	3777	texname sing_1758.htm#SEC1834 1008
	3778	texobj sing_1759.htm#SEC1835 2107
	3779	texpoly sing_1760.htm#SEC1836 64109
	3780	texproc sing_1761.htm#SEC1837 23626
	3781	texring sing_1762.htm#SEC1838 38275
	3782	the first alternative algorithm sing_1139.htm#IDX534
	3783	three_elements sing_1925.htm#SEC2001 513
	3784	timeFactorize sing_898.htm#SEC974 49531
	3785	timeStd sing_897.htm#SEC973 31506
[7d21990]	3786	timer sing_394.htm#SEC434
[063ba1]	3787	timer resolution, setting the sing_350.htm#IDX281
[54fdec1]	3788	timestep sing_2364.htm#SEC2440 38225
[063ba1]	3789	tjurina sing_1597.htm#SEC1673 9100
	3790	tmatrix sing_1524.htm#SEC1600 57332
	3791	todd sing_2266.htm#SEC2342 25618
	3792	toddE sing_2267.htm#SEC2343 17823
	3793	toddPoly sing_2280.htm#SEC2356 65066
	3794	tolessvars sing_1700.htm#SEC1776 56590
[54fdec1]	3795	topChernClass sing_2522.htm#SEC2598 17374
[063ba1]	3796	topological invariants sing_1451.htm#IDX615
	3797	topological invariants sing_1458.htm#IDX622
	3798	topological invariants sing_1459.htm#IDX626
	3799	topological invariants sing_1460.htm#IDX630
	3800	topological invariants sing_1461.htm#IDX634
	3801	toric ideals sing_851.htm#SEC908
	3802	toric ring sing_1239.htm#IDX565
	3803	toric.lib sing_1329.htm#SEC1405
	3804	toric_ideal sing_1330.htm#SEC1406 2041
	3805	toric_lib sing_1329.htm#SEC1405
	3806	toric_std sing_1331.htm#SEC1407 26141
	3807	torusInvariants sing_1245.htm#SEC1321 911
	3808	total divisors sing_490.htm#IDX306
	3809	total multiplicities sing_1451.htm#IDX618
[54fdec1]	3810	totalChernClass sing_2520.htm#SEC2596 6153
	3811	totalSegreClass sing_2523.htm#SEC2599 3291
[063ba1]	3812	totalmultiplicities sing_1453.htm#SEC1529 58264
[7d21990]	3813	trace sing_352.htm#SEC392
[063ba1]	3814	tracemult sing_1966.htm#SEC2042 58303
[7d21990]	3815	transpose sing_353.htm#SEC393
[54fdec1]	3816	trapezoid sing_2358.htm#SEC2434 61525
[063ba1]	3817	triMNewton sing_1726.htm#SEC1802 62822
	3818	triagmatrix sing_970.htm#SEC1046 17944
	3819	triang.lib sing_1719.htm#SEC1795
	3820	triangL sing_1720.htm#SEC1796 51847
	3821	triangL_solve sing_1717.htm#SEC1793 10101
	3822	triangLf_solve sing_1715.htm#SEC1791 49796
	3823	triangLfak sing_1721.htm#SEC1797 50093
	3824	triangM sing_1722.htm#SEC1798 59334
	3825	triangMH sing_1723.htm#SEC1799 34277
	3826	triangM_solve sing_1716.htm#SEC1792 63652
	3827	triang_lib sing_1719.htm#SEC1795
	3828	triang_solve sing_1718.htm#SEC1794 64404
	3829	triangulations sing_2058.htm#SEC2134 61888
	3830	tropical curves sing_2113.htm#IDX796
	3831	tropical geometry sing_1125.htm#IDX508
[54fdec1]	3832	tropical geometry sing_2547.htm#IDX998
[063ba1]	3833	tropical mirror symmetry sing_1125.htm#IDX510
	3834	tropical polynomials sing_2113.htm#IDX797
[54fdec1]	3835	tropical varieties sing_2547.htm#IDX999
[063ba1]	3836	tropical.lib sing_2113.htm#IDX794
	3837	tropicalCurve sing_2118.htm#SEC2194 16865
	3838	tropicalJInvariant sing_2121.htm#SEC2197 40395
	3839	tropicalLifting sing_2114.htm#SEC2190 7052
[54fdec1]	3840	tropicalLinkNewton sing_2555.htm#SEC2631 63886
	3841	tropicalNewton.lib sing_2547.htm#SEC2623
	3842	tropicalNewton_lib sing_2547.htm#SEC2623
	3843	tropicalPointNewton sing_2552.htm#SEC2628 18572
[063ba1]	3844	tropicalSubst sing_2146.htm#SEC2222 49846
	3845	tropicalVariety sing_2153.htm#SEC2229 39087
[54fdec1]	3846	tropicalVarietyNewton tropicalVarietyNewton sing_2554.htm#SEC2630 28532
[063ba1]	3847	tropical_lib sing_2113.htm#IDX795
	3848	tropicalise sing_2125.htm#SEC2201 49739
	3849	tropicaliseSet sing_2126.htm#SEC2202 35136
	3850	truncate sing_1433.htm#SEC1509 13545
	3851	truncateFast sing_1434.htm#SEC1510 5124
	3852	truncated module sing_1433.htm#IDX606
	3853	truncated module sing_1434.htm#IDX607
	3854	tst_ncfactor sing_696.htm#SEC748 3339
	3855	twalk sing_1138.htm#SEC1214 35753
	3856	two-sided sing_490.htm#IDX307
	3857	two-sided Groebner basis sing_490.htm#IDX308
	3858	twostd sing_350.htm#IDX266
	3859	twostd sing_475.htm#SEC515
[7d21990]	3860	type sing_354.htm#SEC394
[063ba1]	3861	type B sing_2181.htm#IDX846
	3862	type D sing_2182.htm#IDX848
[a719149]	3863	type,custom Definition of a user defined type sing_178.htm#SEC218
[063ba1]	3864	type2arr sing_2159.htm#SEC2235 62624
	3865	typecasting sing_2159.htm#IDX802
	3866	typecasting sing_2160.htm#IDX804
	3867	typecasting sing_2161.htm#IDX807
[7d21990]	3868	typeof sing_355.htm#SEC395
[54fdec1]	3869	u sing_2350.htm#SEC2426 12154
[063ba1]	3870	uname sing_350.htm#IDX267
	3871	unbounded_knapsack sing_1908.htm#SEC1984 17226
	3872	unipotent groups sing_1351.htm#IDX574
	3873	uniquePoint sing_2035.htm#SEC2111 893
	3874	unitmat sing_1044.htm#SEC1120 12862
[7d21990]	3875	univariate sing_356.htm#SEC396
[063ba1]	3876	univarpoly sing_1973.htm#SEC2049 46288
	3877	unknown syndrome Decoding method based on quadratic equations sing_867.htm#SEC938
[cd8a2b5]	3878	unset sing_268.htm#SEC308
[a719149]	3879	untyped definitions sing_83.htm#SEC123
[063ba1]	3880	untyped definitions sing_415.htm#SEC455
	3881	updatePairs sing_1951.htm#SEC2027 51144
	3882	ures_solve sing_1709.htm#SEC1785 32449
[7d21990]	3883	uressolve sing_357.htm#SEC397
[cd8a2b5]	3884	usage, option sing_307.htm#IDX185
[3a9ee05]	3885	user interface, Emacs Emacs user interface sing_21.htm#SEC28
[54fdec1]	3886	vStd sing_2309.htm#SEC2385 12321
	3887	val sing_2549.htm#SEC2625 62171
[063ba1]	3888	valvars sing_1704.htm#SEC1780 15723
[7d21990]	3889	vandermonde sing_358.htm#SEC398
[063ba1]	3890	vanishId sing_1805.htm#SEC1881 49148
[7d21990]	3891	var sing_359.htm#SEC399
[063ba1]	3892	varMat sing_2163.htm#SEC2239 51772
	3893	varNum sing_2164.htm#SEC2240 18485
[7d21990]	3894	variables sing_360.htm#SEC400
[063ba1]	3895	variables sing_2163.htm#IDX814
	3896	variables sing_2164.htm#IDX816
	3897	variables sing_2165.htm#IDX820
	3898	variables sing_2166.htm#IDX822
	3899	variablesSorted sing_528.htm#SEC580 13533
	3900	variablesStandard sing_527.htm#SEC579 56500
	3901	vars2pars sing_775.htm#SEC827 47343
	3902	varsigns sing_1978.htm#SEC2054 3471
[7d21990]	3903	varstr sing_361.htm#SEC401
[063ba1]	3904	vct2str sing_636.htm#SEC688 51983
[7d21990]	3905	vdim sing_362.htm#SEC402
[063ba1]	3906	vdim (plural) sing_476.htm#SEC516
	3907	vec2poly sing_510.htm#SEC562 27377
[a719149]	3908	vector sing_172.htm#SEC212
	3909	vector declarations sing_173.htm#SEC213
	3910	vector expressions sing_174.htm#SEC214
	3911	vector operations sing_175.htm#SEC215
	3912	vector related functions vector related functions sing_176.htm#SEC216
[063ba1]	3913	verify sing_1969.htm#SEC2045 32271
	3914	versal sing_1504.htm#SEC1580 46247
	3915	version sing_350.htm#IDX270
	3916	vertexAdjacencyGraph vertexAdjacencyGraph sing_2106.htm#SEC2182 60102
	3917	vertexEdgeGraph sing_2107.htm#SEC2183 32816
	3918	vertices sing_2051.htm#SEC2127 11398
	3919	vfilt sing_1522.htm#SEC1598 9283
	3920	view sing_1825.htm#SEC1901 29284
	3921	visual sing_2108.htm#SEC2184 51434
[54fdec1]	3922	visualize sing_2349.htm#SEC2425 6750
[7d21990]	3923	voice sing_397.htm#SEC437
[063ba1]	3924	vwfilt sing_1523.htm#SEC1599 8281
	3925	wUnit sing_1863.htm#SEC1939 27198
	3926	waitAllTasks sing_1023.htm#SEC1099 7087
	3927	waitTasks sing_1022.htm#SEC1098 52857
[7d21990]	3928	waitall sing_363.htm#SEC403
	3929	waitfirst sing_364.htm#SEC404
[063ba1]	3930	walk, groebner sing_1136.htm#IDX530
[54fdec1]	3931	walk, groebner sing_2432.htm#IDX957
	3932	walk, groebner sing_2496.htm#IDX962
	3933	walk, groebner sing_2500.htm#IDX967
	3934	warkedPreimageStd sing_2384.htm#SEC2460 14759
[a719149]	3935	warn, option sing_70.htm#SEC110
[cd8a2b5]	3936	warn, option sing_307.htm#IDX151
[063ba1]	3937	watchdog sing_895.htm#SEC971 sprintf
[7d21990]	3938	wedge sing_365.htm#SEC405
[063ba1]	3939	weierstr.lib sing_1954.htm#SEC2030
	3940	weierstrDiv sing_1955.htm#SEC2031 260
	3941	weierstrPrep sing_1956.htm#SEC2032 5752
	3942	weierstr_lib sing_1954.htm#SEC2030
	3943	weierstrassForm sing_2122.htm#SEC2198 60874
[7d21990]	3944	weight sing_366.htm#SEC406
[063ba1]	3945	weight filtration sing_1514.htm#IDX646
	3946	weight filtration sing_1521.htm#IDX680
	3947	weight filtration sing_1523.htm#IDX694
	3948	weight filtration sing_1524.htm#IDX702
	3949	weight filtration sing_1536.htm#IDX718
	3950	weight filtration sing_1538.htm#IDX729
[895ba26]	3951	weightKB sing_367.htm#SEC407 21753
[cd8a2b5]	3952	weightM, option sing_307.htm#IDX170
[063ba1]	3953	weighted lexicographical ordering sing_838.htm#IDX397
	3954	weighted reverse lexicographical ordering Global orderings sing_838.htm#IDX395
	3955	weightedRing sing_707.htm#SEC759 33786
	3956	whichvariable sing_1977.htm#SEC2053 27122
[7d21990]	3957	while sing_384.htm#SEC424
[cd8a2b5]	3958	withDim sing_204.htm#IDX145
	3959	withHilb sing_204.htm#IDX143
	3960	withMult sing_204.htm#IDX146
	3961	withRes sing_204.htm#IDX144
	3962	withSB sing_204.htm#IDX142
[063ba1]	3963	wp, global ordering sing_838.htm#IDX396
[7d21990]	3964	write sing_368.htm#SEC408
[063ba1]	3965	writeNmzData sing_1256.htm#SEC1332 38467
	3966	writeNmzPaths sing_1260.htm#SEC1336 sprintf
	3967	ws, local ordering sing_839.htm#IDX407
	3968	wurzel sing_1845.htm#SEC1921 12755
	3969	xchange sing_1839.htm#SEC1915 40741
	3970	xdvi sing_1764.htm#SEC1840 16898
	3971	zdd sing_2210.htm#IDX895
	3972	zdd2poly sing_2227.htm#SEC2303 55047
	3973	zero-dimensional sing_1974.htm#IDX785
	3974	zeroMod sing_1196.htm#SEC1272 60609
	3975	zeroOpt sing_1205.htm#SEC1281 19260
	3976	zeroRadical sing_1107.htm#SEC1183 35598
	3977	zeroSet sing_1732.htm#SEC1808 60030
	3978	zerodec sing_1289.htm#SEC1365 30765
	3979	zeroset.lib sing_1727.htm#SEC1803
	3980	zeroset_lib sing_1727.htm#SEC1803
	3981	zetaDL sing_1426.htm#SEC1502 sprintf
[a719149]	3982	{ sing_36.htm#IDX78
	3983	\|\| sing_36.htm#IDX103
	3984	\|\| sing_96.htm#SEC136
	3985	} sing_36.htm#IDX79
	3986	~ sing_36.htm#IDX117
[7d21990]	3987	~ sing_385.htm#SEC425

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