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singular.idx @ 78fbaf

fieker-DuValspielwiese

Last change on this file since 78fbaf was 6cd2a5, checked in by Hans Schoenemann <hannes@…>, 4 years ago
update idx
Property mode set to `100644`
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1	! sing_36.htm#IDX101
2	!= sing_36.htm#IDX95
3	!= sing_100.htm#SEC140
4	" sing_36.htm#IDX104
5	# sing_36.htm#IDX118
6	$ sing_36.htm#IDX119
7	% sing_36.htm#IDX91
8	% sing_81.htm#SEC121
9	% sing_98.htm#SEC138
10	% sing_110.htm#SEC150
11	% sing_147.htm#SEC187
12	% sing_155.htm#SEC195
13	&& sing_36.htm#IDX102
14	&& sing_101.htm#SEC141
15	( sing_36.htm#IDX80
16	() sing_131.htm#IDX130
17	) sing_36.htm#IDX81
18	* bigintmat operations sing_36.htm#IDX89
19	* sing_81.htm#SEC121
20	* sing_87.htm#SEC127
21	* sing_93.htm#SEC133
22	* sing_98.htm#SEC138
23	* sing_106.htm#SEC146
24	* sing_110.htm#SEC150
25	* sing_137.htm#SEC177
26	* sing_142.htm#SEC182
27	* sing_147.htm#SEC187
28	* sing_155.htm#SEC195
29	** sing_36.htm#IDX93
30	+ bigintmat operations sing_36.htm#IDX85
31	+ sing_81.htm#SEC121
32	+ sing_87.htm#SEC127
33	+ sing_93.htm#SEC133
34	+ sing_98.htm#SEC138
35	+ sing_106.htm#SEC146
36	+ sing_110.htm#SEC150
37	+ sing_126.htm#SEC166
38	+ sing_137.htm#SEC177
39	+ sing_142.htm#SEC182
40	+ sing_147.htm#SEC187
41	+ sing_155.htm#SEC195
42	+ sing_169.htm#SEC209
43	+ sing_176.htm#SEC216
44	+ sing_181.htm#SEC221
45	++ sing_36.htm#IDX86
46	- bigintmat operations sing_36.htm#IDX87
47	- sing_81.htm#SEC121
48	- sing_87.htm#SEC127
49	- sing_98.htm#SEC138
50	- sing_106.htm#SEC146
51	- sing_110.htm#SEC150
52	- sing_137.htm#SEC177
53	- sing_147.htm#SEC187
54	- sing_155.htm#SEC195
55	- sing_181.htm#SEC221
56	-- sing_36.htm#IDX88
57	--MPhost sing_19.htm#IDX66
58	--MPport sing_19.htm#IDX65
59	--allow-net sing_19.htm#IDX39
60	--batch sing_19.htm#IDX64
61	--browser sing_19.htm#IDX43
62	--echo sing_19.htm#IDX35
63	--emacs sing_19.htm#IDX67
64	--emacs-dir sing_19.htm#IDX68
65	--emacs-load sing_19.htm#IDX69
66	--execute sing_19.htm#IDX56
67	--help sing_19.htm#IDX37
68	--min-time sing_19.htm#IDX61
69	--no-out sing_19.htm#IDX49
70	--no-rc sing_19.htm#IDX45
71	--no-shell sing_19.htm#IDX50
72	--no-stdlib sing_19.htm#IDX47
73	--no-tty sing_19.htm#IDX51
74	--no-warn sing_19.htm#IDX48
75	--quiet sing_19.htm#IDX53
76	--random sing_19.htm#IDX60
77	--sdb sing_19.htm#IDX32
78	--singular sing_19.htm#IDX70
79	--ticks-per-sec sing_19.htm#IDX62
80	--user-option sing_19.htm#IDX58
81	-> sing_159.htm#SEC199
82	-MPhost Command line options
83	-MPport Command line options
84	-allow-net Command line options
85	-b Command line options sing_19.htm#IDX63
86	-batch Command line options
87	-browser Command line options
88	-c Command line options sing_19.htm#IDX55
89	-d Command line options sing_19.htm#IDX31
90	-e Command line options sing_19.htm#IDX34
91	-echo Command line options
92	-emacs Command line options
93	-emacs-dir Command line options
94	-emacs-load Command line options
95	-execute Command line options
96	-h Command line options sing_19.htm#IDX36
97	-help Command line options
98	-min-time Command line options
99	-no-out Command line options
100	-no-rc Command line options
101	-no-shell Command line options
102	-no-stdlib Command line options
103	-no-tty Command line options
104	-no-warn Command line options
105	-q Command line options sing_19.htm#IDX52
106	-quiet Command line options
107	-r Command line options sing_19.htm#IDX59
108	-random Command line options
109	-sdb Command line options
110	-singular Command line options
111	-ticks-per-sec Command line options
112	-u Command line options sing_19.htm#IDX57
113	-user-option Command line options
114	-v Command line options sing_19.htm#IDX54
115	.. sing_36.htm#IDX113
116	.singularrc file sing_20.htm#IDX72
117	.singularrc file, no loading Command line options sing_19.htm#IDX46
118	/ sing_36.htm#IDX90
119	/ sing_76.htm#SEC116
120	/ sing_110.htm#SEC150
121	/ sing_137.htm#SEC177
122	/ sing_147.htm#SEC187
123	/ sing_155.htm#SEC195
124	/ sing_181.htm#SEC221
125	// sing_36.htm#IDX107
126	// sing_36.htm#IDX109
127	// sing_36.htm#IDX110
128	: sing_36.htm#IDX114
129	: sing_110.htm#SEC150
130	:: sing_36.htm#IDX115
131	:: sing_149.htm#SEC189
132	; sing_36.htm#IDX111
133	< sing_36.htm#IDX100
134	< sing_155.htm#SEC195
135	< sing_181.htm#SEC221
136	< sing_249.htm#SEC289
137	<= sing_36.htm#IDX99
138	<= sing_100.htm#SEC140
139	<= sing_147.htm#SEC187
140	<= sing_155.htm#SEC195
141	<= sing_176.htm#SEC216
142	<= sing_181.htm#SEC221
143	<> sing_36.htm#IDX96
144	<> sing_100.htm#SEC140
145	<> sing_137.htm#SEC177
146	<> sing_147.htm#SEC187
147	<> sing_155.htm#SEC195
148	<> sing_169.htm#SEC209
149	<> sing_176.htm#SEC216
150	<> sing_181.htm#SEC221
151	= sing_36.htm#IDX77
152	== sing_36.htm#IDX94
153	== sing_100.htm#SEC140
154	== sing_137.htm#SEC177
155	== sing_147.htm#SEC187
156	== sing_155.htm#SEC195
157	== sing_169.htm#SEC209
158	== sing_176.htm#SEC216
159	== sing_181.htm#SEC221
160	> sing_36.htm#IDX98
161	> sing_155.htm#SEC195
162	> sing_181.htm#SEC221
163	>= sing_36.htm#IDX97
164	>= sing_100.htm#SEC140
165	>= sing_147.htm#SEC187
166	>= sing_155.htm#SEC195
167	>= sing_176.htm#SEC216
168	>= sing_181.htm#SEC221
169	? sing_36.htm#IDX106
170	? sing_262.htm#IDX148
171	ADGT sing_1046.htm#SEC1122
172	AG codes sing_955.htm#SEC1007
173	AGcode_L sing_1916.htm#SEC1992
174	AGcode_Omega sing_1917.htm#SEC1993
175	ASCII sing_1006.htm#SEC1082
176	ASCII links sing_117.htm#SEC157
177	ASSUME sing_64.htm#SEC101
178	A_L sing_1606.htm#SEC1682
179	A_Z sing_1004.htm#SEC1080
180	A_Z_L sing_1005.htm#SEC1081
181	Access to elements of a user defined type Access to elements of a user defined type sing_186.htm#SEC226
182	Adj_div sing_1911.htm#SEC1987
183	Adjoint ideal sing_1483.htm#IDX659
184	Alexander polynomial sing_1577.htm#IDX683
185	Algebraic Geometry codes sing_1910.htm#IDX831
186	Algebraic dependence Algebraic dependence sing_934.htm#SEC986
187	Algebraic geometry sing_1458.htm#SEC1534
188	AltVarEnd sing_745.htm#SEC797
189	AltVarStart sing_744.htm#SEC796
190	Ann sing_1397.htm#SEC1473
191	Appel function sing_560.htm#IDX348
192	Appel hypergeometric function sing_560.htm#IDX349
193	Applications sing_953.htm#SEC1005
194	Arnol'd sing_2363.htm#IDX981
195	Arnold, classification. sing_2448.htm#IDX991
196	Arnold, classification. sing_2449.htm#IDX992
197	ArnoldAction sing_1699.htm#SEC1775
198	Assignments for user defined types Assignments for user defined types sing_188.htm#SEC228
199	AssocTanToEnv sing_1040.htm#SEC1116
200	Atkin sing_1999.htm#SEC2075
201	Authors sing_1.htm#IDX16
202	Automatic Deduction sing_1046.htm#IDX514
203	Automatic Demonstration sing_1046.htm#IDX515
204	BFBoundsBudur sing_598.htm#SEC650
205	BINresol sing_1496.htm#SEC1572
206	BSidealFromAnn sing_596.htm#SEC648
207	Background sing_3.htm#SEC5
208	Basic programming sing_909.htm#SEC961
209	Basic programming sing_909.htm#SEC961
210	BelongSemig sing_2444.htm#SEC2520
211	BerlekampMassey sing_2550.htm#SEC2626
212	Bern sing_2417.htm#SEC2493
213	Bernstein operator sing_537.htm#IDX330
214	Bernstein-Sato ideal sing_593.htm#IDX351
215	Bernstein-Sato polynomial sing_502.htm#IDX311
216	Bernstein-Sato polynomial sing_537.htm#IDX327
217	Bernstein-Sato polynomial sing_1640.htm#IDX714
218	Bernstein-Sato polynomial sing_1644.htm#IDX731
219	Bernstein-Sato polynomial for variety sing_601.htm#IDX359
220	BernsteinSatoIdeal sing_597.htm#SEC649
221	Betti sing_2684.htm#SEC2760
222	Betti number Syzygies and resolutions sing_971.htm#SEC1028
223	BettiNumsH sing_2581.htm#SEC2657
224	BettiNumsN sing_2589.htm#SEC2665
225	BettiNumsQp sing_2584.htm#SEC2660
226	BettiNumsS sing_2587.htm#SEC2663
227	Betty number sing_2578.htm#IDX1130
228	Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_981.htm#SEC1038
229	Bimodules Bimodules and syzygies and lifts sing_812.htm#SEC864
230	Bisyzygy Bimodules and syzygies and lifts sing_812.htm#SEC864
231	BlowingUp sing_1619.htm#SEC1695
232	Blowupcenter sing_1499.htm#SEC1575
233	BorelCheck sing_1574.htm#SEC1650
234	Bott's formula sing_2837.htm#IDX1199
235	Branches of space curve singularities Branches of space curve singularities sing_942.htm#SEC994
236	Briancon-Maisonobe algorithm sing_537.htm#IDX336
237	Brieskorn lattice sing_1640.htm#IDX710
238	Brieskorn lattice sing_1641.htm#IDX721
239	Brieskorn lattice sing_1642.htm#IDX724
240	Brieskorn lattice sing_1643.htm#IDX727
241	Brieskorn lattice sing_1644.htm#IDX730
242	Brieskorn lattice sing_1645.htm#IDX734
243	Brieskorn lattice sing_1646.htm#IDX738
244	Brieskorn lattice sing_1647.htm#IDX744
245	Brieskorn lattice sing_1648.htm#IDX752
246	Brieskorn lattice sing_1649.htm#IDX758
247	Brieskorn lattice sing_1650.htm#IDX766
248	Brieskorn lattice sing_1651.htm#IDX776
249	Brieskorn lattice sing_1662.htm#IDX782
250	Brieskorn lattice sing_1664.htm#IDX793
251	Brieskorn lattice sing_1692.htm#IDX820
252	Brill-Noether algorithm sing_1910.htm#IDX832
253	BrillNoether sing_1913.htm#SEC1989
254	Buchberger algorithm for toric ideals Buchberger algorithm sing_982.htm#SEC1039
255	Budur-Mustata-Saito approach sing_601.htm#IDX363
256	Building Singular sing_2905.htm#SEC2996
257	C programming language Major differences to the C programming language sing_413.htm#SEC453
258	C, module ordering sing_963.htm#IDX450
259	CGS sing_1027.htm#IDX463
260	CM_regularity sing_1561.htm#SEC1637 33865
261	CMtype sing_1730.htm#SEC1806
262	CRHT-ideal sing_988.htm#SEC1052
263	CSMA sing_2440.htm#SEC2516
264	CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33
265	Castelnuovo-Mumford regularity sing_1561.htm#IDX675
266	Category string sing_51.htm#SEC88
267	CenCharDec sing_646.htm#SEC698
268	Center sing_1538.htm#SEC1614
269	CenterBO sing_1545.htm#SEC1621
270	CentralQuot sing_644.htm#SEC696
271	CentralSaturation sing_645.htm#SEC697
272	Change of rings sing_9.htm#SEC15
273	Characteristic sets sing_972.htm#SEC1029
274	CharacteristicExponents CharacteristicExponents sing_1625.htm#SEC1701
275	ChernClass sing_2850.htm#SEC2926
276	ChernRootsDual sing_2396.htm#SEC2472
277	ChernRootsHom sing_2405.htm#SEC2481
278	ChernRootsProd sing_2398.htm#SEC2474
279	ChernRootsSum sing_2394.htm#SEC2470
280	ChernRootsSymm sing_2407.htm#SEC2483
281	ChernRootsWedge sing_2408.htm#SEC2484
282	Chevalley-Rosenlicht theorem sing_1477.htm#IDX644
283	Chevalley-Rosenlicht theorem sing_1478.htm#IDX647
284	Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2841.htm#IDX1204
285	ChowRing sing_2841.htm#SEC2917
286	Classification of hypersurface singularities Classification of hypersurface singularities sing_943.htm#SEC995
287	Classification of singularities sing_2810.htm#IDX1175
288	Code Codes and the decoding problem sing_987.htm#SEC1045
289	Codes and the decoding problem Codes and the decoding problem sing_987.htm#SEC1044
290	Coding theory sing_1909.htm#SEC1985
291	Coefficient rings Notes for Singular users sing_2903.htm#SEC2989
292	Command line options Command line options sing_19.htm#SEC26
293	Commands Functions and system variables sing_207.htm#SEC247
294	Commands for user defined types Commands for user defined types sing_187.htm#SEC227
295	Commutative Algebra sing_922.htm#SEC974
296	Commutative algebra sing_1210.htm#SEC1286
297	CompDecomp sing_499.htm#SEC551
298	CompInt sing_2446.htm#SEC2522
299	CompleteHomog sing_2384.htm#SEC2460
300	ComplexValue sing_2573.htm#SEC2649
301	Comprehensive Groebner System sing_1027.htm#IDX466
302	Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_918.htm#SEC970
303	ConsLevels sing_1047.htm#SEC1123
304	ContactMatrix sing_1627.htm#SEC1703
305	Conti-Traverso algorithm sing_977.htm#SEC1034
306	Contributors sing_1.htm#IDX15
307	Control structures sing_381.htm#SEC421
308	Control theory System and Control theory sing_1943.htm#SEC2019
309	Cooper philosophy sing_988.htm#SEC1050
310	Cornacchia sing_1989.htm#SEC2065
311	CornacchiaModified sing_1990.htm#SEC2066
312	Crep sing_1030.htm#SEC1106
313	Critical points sing_937.htm#SEC989
314	CurveParam sing_1621.htm#SEC1697
315	CurveRes sing_1620.htm#SEC1696
316	Curves sing_1483.htm#IDX656
317	Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36
318	Cyclic code sing_1924.htm#IDX839
319	Cyclic roots sing_915.htm#SEC967
320	D-integration sing_560.htm#IDX345
321	D-localization sing_560.htm#IDX341
322	D-localization sing_662.htm#IDX370
323	D-module purityfiltration_lib sing_502.htm#IDX309
324	D-module sing_537.htm#IDX324
325	D-module sing_560.htm#IDX338
326	D-module sing_593.htm#IDX350
327	D-module sing_601.htm#IDX357
328	D-module sing_662.htm#IDX367
329	D-module sing_772.htm#IDX385
330	D-module structure sing_537.htm#IDX325
331	D-module structure sing_593.htm#IDX353
332	D-module structure sing_601.htm#IDX358
333	D-restriction sing_560.htm#IDX343
334	DBM links sing_122.htm#SEC162
335	DISPLAY environment variable The online help system sing_16.htm#IDX28
336	DLoc sing_563.htm#SEC615
337	DLoc0 sing_565.htm#SEC617
338	Data types sing_72.htm#SEC112
339	Data types (plural) sing_426.htm#IDX295
340	Debugging tools sing_63.htm#SEC100
341	Decker, Wolfram sing_1.htm#IDX17
342	Declaration of objects of a user defined type Declaration of objects of a user defined type sing_185.htm#SEC225
343	Decoding sing_1924.htm#IDX841
344	Decoding codes with Groebner bases Decoding codes with Groebner bases sing_986.htm#SEC1043
345	Decoding method based on quadratic equations Decoding method based on quadratic equations sing_991.htm#SEC1061
346	Definition of a user defined type Definition of a user defined type sing_184.htm#SEC224
347	Deformations sing_940.htm#SEC992
348	Deformations, T1 and T2 sing_939.htm#SEC991
349	Deg sing_2687.htm#SEC2763
350	Degree sing_2688.htm#SEC2764
351	DegreePure sing_1462.htm#SEC1538
352	Degrees sing_2689.htm#SEC2765
353	Delta sing_1546.htm#SEC1622
354	DeltaList sing_1547.htm#SEC1623
355	Demo mode sing_24.htm#SEC35
356	Depth sing_929.htm#SEC981
357	Determinacy sing_2813.htm#IDX1179
358	Di Biase-Urbanke algorithm Di Biase and Urbanke sing_980.htm#SEC1037
359	DifConsLCSets sing_1050.htm#SEC1126
360	Distributed computing sing_1061.htm#IDX531
361	Dlocalization sing_663.htm#SEC715
362	Documentation Tool sing_60.htm#SEC97
363	Dp, global ordering sing_961.htm#IDX433
364	Ds, local ordering sing_962.htm#IDX443
365	DsingularLocus sing_667.htm#SEC719
366	Dynamic loading sing_71.htm#SEC111
367	Dynamic modules sing_917.htm#SEC969
368	ECPP sing_2033.htm#SEC2109
369	ECoef sing_1505.htm#SEC1581
370	EOrdlist sing_1503.htm#SEC1579
371	ERROR sing_238.htm#SEC278
372	ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33
373	Edatalist sing_1502.htm#SEC1578
374	Edelman-Reiner sing_2318.htm#IDX922
375	Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
376	Editing input sing_18.htm#SEC25
377	Elimination sing_925.htm#SEC977
378	Emacs Emacs user interface sing_21.htm#SEC28
379	Emacs, Singular demo mode sing_24.htm#SEC35
380	Emacs, a quick guide A quick guide to Emacs sing_22.htm#SEC29
381	Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC36
382	Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC37
383	Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC38
384	Emacs, overview A quick guide to Emacs sing_22.htm#SEC29
385	Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30
386	Emacs, user interface Emacs user interface sing_21.htm#SEC28
387	Emaxcont sing_1507.htm#SEC1583
388	Enumerative geometry sing_2837.htm#IDX1197
389	Equal sing_1461.htm#SEC1537
390	Eresol sing_1497.htm#SEC1573
391	EulerAff sing_2441.htm#SEC2517
392	EulerProj sing_2442.htm#SEC2518
393	Evaluation of logical expressions Evaluation of logical expressions sing_415.htm#SEC455
394	Examples sing_907.htm#SEC959
395	Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40
396	Examples of use of Letterplace Examples of use of Letterplace sing_794.htm#SEC846
397	Exp for matrices sing_1479.htm#IDX648
398	Experimental libraries Experimental libraries sing_2362.htm#SEC2438
399	Ext sing_1270.htm#SEC1346
400	Ext, computation of sing_928.htm#SEC980
401	Ext_R sing_1269.htm#SEC1345
402	Exterior sing_731.htm#SEC783
403	Extra weight vector sing_966.htm#SEC1018
404	Factorization sing_930.htm#SEC982
405	FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_1041.htm#SEC1117
406	Feynman graph sing_1246.htm#IDX564
407	Finite fields sing_924.htm#SEC976
408	First steps sing_6.htm#SEC12
409	Fitzgerald-Lax method Fitzgerald-Lax method sing_990.htm#SEC1058
410	Float sing_253.htm#SEC293
411	Flow control sing_40.htm#SEC70
412	Formal Checker sing_59.htm#SEC96
413	Formatting output sing_914.htm#SEC966
414	Free associative algebras Free associative algebras sing_808.htm#SEC860
415	Free resolution sing_926.htm#SEC978
416	Free resolution, graded Handling graded modules sing_927.htm#SEC979
417	FultonA sing_2439.htm#SEC2515
418	Functionality and release notes of Letterplace Functionality and release notes of Letterplace sing_795.htm#SEC847
419	Functions sing_208.htm#SEC248
420	Functions (letterplace) Functions (letterplace) sing_797.htm#SEC849
421	Future benefits of Singular 4 Notes for Singular users sing_2903.htm#SEC2994
422	G-algebra sing_490.htm#SEC530
423	G-algebra sing_490.htm#SEC532
424	G-algebra, setup sing_490.htm#SEC534
425	GBWeight sing_566.htm#SEC618
426	GBsolve sing_1823.htm#SEC1899
427	GIT-Fans sing_949.htm#SEC1001
428	GITcone sing_2603.htm#SEC2679
429	GITfan sing_2604.htm#SEC2680
430	GITfanFromOrbitCones GITfanFromOrbitCones sing_2605.htm#SEC2681
431	GITfanParallel sing_2606.htm#SEC2682
432	GITfanParallelSymmetric GITfanParallelSymmetric sing_2621.htm#SEC2697
433	GITfanSymmetric sing_2620.htm#SEC2696
434	GKZfan sing_2607.htm#SEC2683
435	GKZsystem sing_642.htm#SEC694
436	GKdim sing_615.htm#SEC667
437	GMP sing_1.htm#IDX3
438	GMP sing_2907.htm#SEC2998
439	GND.lib sing_2628.htm#SEC2704
440	GND_lib sing_2628.htm#SEC2704
441	GTZmod sing_1323.htm#SEC1399
442	GTZopt sing_1330.htm#SEC1406
443	G_a -Invariants sing_946.htm#SEC998
444	Gamma sing_1512.htm#SEC1588
445	Gauss-Manin connection Gauss-Manin connection sing_973.htm#SEC1030
446	Gauss-Manin connection sing_1692.htm#IDX819
447	Gauss-Manin connection sing_1739.htm#IDX822
448	Gauss-Manin system sing_1640.htm#IDX709
449	Gauss-Manin system sing_1641.htm#IDX720
450	Gauss-Manin system sing_1642.htm#IDX723
451	Gauss-Manin system sing_1643.htm#IDX726
452	Gauss-Manin system sing_1644.htm#IDX729
453	Gauss-Manin system sing_1645.htm#IDX733
454	Gauss-Manin system sing_1646.htm#IDX737
455	Gauss-Manin system sing_1647.htm#IDX743
456	Gauss-Manin system sing_1648.htm#IDX751
457	Gauss-Manin system sing_1649.htm#IDX757
458	Gauss-Manin system sing_1650.htm#IDX765
459	Gauss-Manin system sing_1651.htm#IDX775
460	Gauss-Manin system sing_1662.htm#IDX781
461	Gauss-Manin system sing_1664.htm#IDX792
462	Gelfand-Kirillov dimension sing_849.htm#IDX407
463	General command syntax General command syntax sing_35.htm#SEC59
464	General concepts sing_12.htm#SEC18
465	General purpose sing_998.htm#SEC1074
466	General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41
467	Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_492.htm#SEC542
468	Generalized Newton identities Generalized Newton identities sing_989.htm#SEC1055
469	Geometric Invariant Theory Geometric Invariant Theory sing_948.htm#SEC1000
470	Geometric Theorems sing_1046.htm#IDX516
471	Geometric genus sing_1483.htm#IDX660
472	German Umlaute sing_411.htm#IDX282
473	Getting started sing_5.htm#SEC11
474	Global orderings sing_961.htm#SEC1013
475	Goettsche's formula sing_2578.htm#IDX1131
476	GoettscheF sing_2579.htm#SEC2655
477	Graded commutative algebras Graded commutative algebras (SCA) sing_792.htm#SEC844
478	Grassmannian sing_2842.htm#SEC2918
479	Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2842.htm#IDX1205
480	Greuel, Gert-Martin sing_1.htm#IDX18
481	Grob1Levels sing_1049.htm#SEC1125
482	Groebner Bases Computing Groebner and Standard Bases sing_918.htm#SEC970
483	Groebner bases for two-sided ideals in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_810.htm#SEC862
484	Groebner bases in G-algebras Groebner bases in G-algebras sing_491.htm#SEC535
485	Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_810.htm#SEC862
486	Groebner bases, decodeGB sing_1924.htm#IDX843
487	Groebner bases, slim sing_921.htm#SEC973
488	Groebner basis conversion Groebner basis conversion sing_920.htm#SEC972
489	Groebner cover sing_1026.htm#IDX459
490	Groebner cover sing_1033.htm#IDX478
491	Groebner cover sing_1034.htm#IDX485
492	Groebner fan sing_2188.htm#IDX860
493	Groebner walk sing_1261.htm#IDX585
494	Groebner walk sing_1263.htm#IDX587
495	Groebner walk sing_2834.htm#IDX1193
496	Groebner walk sing_2835.htm#IDX1194
497	Groebner-Shirshov bases Groebner bases for two-sided ideals in free associative algebras sing_810.htm#SEC862
498	Groebner-Shirshov bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_810.htm#SEC862
499	Groebnerwalk sing_1257.htm#IDX581
500	Groebnerwalk sing_2721.htm#IDX1146
501	Groebnerwalk sing_2833.htm#IDX1192
502	Groebnerwalk sing_2876.htm#IDX1221
503	Gromov-Witten invariants sing_1246.htm#IDX561
504	Gromov-Witten invariants sing_1252.htm#IDX570
505	Gromov-Witten invariants sing_1253.htm#IDX574
506	Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2867.htm#IDX1217
507	Gromov-Witten invariants, multiple covers sing_2866.htm#IDX1216
508	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2868.htm#IDX1218
509	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2869.htm#IDX1219
510	Gromov-Witten invariants. sing_2837.htm#IDX1200
511	Gweights sing_725.htm#SEC777
512	H2basis sing_1697.htm#SEC1773
513	HHnormalForm sing_2457.htm#SEC2533
514	Hamburger-Noether expansion sing_1577.htm#IDX679
515	Hamburger-Noether expansion sing_1665.htm#IDX801
516	Hamburger-Noether expansions sing_1911.htm#IDX833
517	Handling graded modules Handling graded modules sing_927.htm#SEC979
518	Hcode sing_1599.htm#SEC1675
519	Help string sing_45.htm#SEC82
520	Hensel sing_243.htm#SEC283
521	Hilbert function sing_359.htm#IDX188
522	Hilbert function sing_970.htm#SEC1024
523	Hilbert scheme sing_2578.htm#IDX1134
524	Hilbert series sing_814.htm#IDX398
525	Hilbert series sing_970.htm#SEC1024
526	Hilbert-driven GB algorithm Groebner basis conversion sing_920.htm#SEC972
527	HilbertClassPoly sing_1996.htm#SEC2072
528	HilbertSeries sing_1792.htm#SEC1868
529	HilbertWeights sing_1793.htm#SEC1869
530	Hom sing_1273.htm#SEC1349
531	HomJJ sing_1353.htm#SEC1429
532	Hosten-Sturmfels algorithm Hosten and Sturmfels sing_979.htm#SEC1036
533	How to enter and exit How to enter and exit sing_14.htm#SEC20
534	How to use this manual How to use this manual sing_4.htm#SEC6
535	Hurwitz numbers sing_1252.htm#IDX573
536	Hurwitz numbers sing_1253.htm#IDX577
537	Hypersurface singularities, classification of Classification of hypersurface singularities sing_943.htm#SEC995
538	I-regular function sing_1033.htm#IDX484
539	IN sing_283.htm#IDX149
540	Ideal membership sing_969.htm#IDX455
541	Identifiers, syntax of sing_37.htm#SEC65
542	ImageGroup sing_1795.htm#SEC1871
543	ImageVariety sing_1794.htm#SEC1870
544	Imap, option sing_318.htm#IDX175
545	Implemented algorithms Implemented algorithms sing_33.htm#SEC47
546	Incl sing_1460.htm#SEC1536
547	Index sing_2913.htm#SEC3004
548	Info string sing_52.htm#SEC89
549	InterDiv sing_1528.htm#SEC1604
550	Interactive use sing_13.htm#SEC19
551	Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24
552	IntersectWithSub sing_647.htm#SEC699
553	Intersection theory sing_2837.htm#IDX1196
554	IntersectionMatrix sing_1626.htm#SEC1702
555	Introduction sing_2.htm#SEC4
556	Invariant Theory sing_945.htm#SEC997
557	Invariant theory sing_1744.htm#SEC1820
558	InvariantQ sing_1797.htm#SEC1873
559	InvariantRing sing_1796.htm#SEC1872
560	Invariants of a finite group Invariants of a finite group sing_947.htm#SEC999
561	Invariants of plane curve singularities Invariants of plane curve singularities sing_941.htm#SEC993
562	IsSCA sing_746.htm#SEC798
563	J-marked schemes sing_1568.htm#IDX677
564	J-marked schemes, Borel ideals sing_1573.htm#IDX678
565	JMBTest.lib sing_1568.htm#SEC1644
566	JMBTest_lib sing_1568.htm#SEC1644
567	JMSConst.lib sing_1573.htm#SEC1649
568	JMSConst_lib sing_1573.htm#SEC1649
569	JMarkedScheme sing_1575.htm#SEC1651
570	Jacobi sing_2006.htm#SEC2082
571	Jacobson form sing_1961.htm#IDX844
572	Jacobson normal form sing_1961.htm#IDX845
573	Janet basis sing_2832.htm#IDX1190
574	Janet division, Janet basis sing_2831.htm#IDX1189
575	JuReTopDim sing_1470.htm#SEC1546
576	JuReZeroDim sing_1471.htm#SEC1547
577	K-basis sing_814.htm#IDX396
578	K-dimension sing_814.htm#IDX397
579	KScoef sing_1690.htm#SEC1766
580	KSconvert sing_1688.htm#SEC1764
581	KSker sing_1687.htm#SEC1763
582	KSlinear sing_1689.htm#SEC1765
583	KSpencerKernel sing_1737.htm#SEC1813
584	KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2647.htm#SEC2723
585	Ker sing_2693.htm#SEC2769
586	Kernel of module homomorphisms Kernel of module homomorphisms sing_933.htm#SEC985
587	KoszulHomology sing_1282.htm#SEC1358
588	Kronecker module sing_2578.htm#IDX1133
589	Kronecker product sing_363.htm#SEC403
590	L, ordering sing_967.htm#SEC1019
591	LETTERPLACE sing_793.htm#SEC845
592	LETTERPLACE libraries LETTERPLACE libraries sing_813.htm#SEC865
593	LIB sing_287.htm#SEC327
594	LIB commands sing_53.htm#SEC90
595	LIBs sing_994.htm#SEC1070
596	LLL sing_361.htm#IDX218
597	LOT algorithm sing_537.htm#IDX337
598	LU-decomposition of a matrix of numbers sing_292.htm#SEC332
599	Laurent series sing_1250.htm#IDX569
600	Left and two-sided Groebner bases Left and two-sided Groebner bases sing_951.htm#SEC1003
601	Left ideal membership Groebner bases in G-algebras sing_491.htm#SEC538
602	Left normal form Groebner bases in G-algebras sing_491.htm#SEC537
603	LengthSym sing_789.htm#SEC841
604	LengthSymElement sing_788.htm#SEC840
605	Letterplace sing_793.htm#SEC845
606	Letterplace Groebner basis sing_814.htm#IDX395
607	Letterplace Groebner basis sing_849.htm#IDX405
608	Letterplace Groebner basis sing_856.htm#IDX414
609	Letterplace correspondence Letterplace correspondence sing_811.htm#SEC863
610	Letterplace libraries LETTERPLACE libraries sing_813.htm#SEC865
611	Letterplace ring sing_357.htm#SEC397
612	Levels sing_1048.htm#SEC1124
613	Lexicographic Groebner bases, computation of Groebner basis conversion sing_920.htm#SEC972
614	Libraries Writing procedures and libraries sing_48.htm#SEC85
615	Libraries sing_910.htm#SEC962
616	Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86
617	Library versioning Notes for Singular users sing_2903.htm#SEC2992
618	Lie sing_2525.htm#IDX1107
619	Lie algebra sing_1478.htm#IDX645
620	Lie bracket sing_460.htm#SEC500
621	Lie group sing_1481.htm#IDX650
622	Lie group sing_1482.htm#IDX653
623	Limitations sing_411.htm#SEC451
624	Linear algebra sing_1151.htm#SEC1227
625	Linear code sing_1924.htm#IDX840
626	LinearActionQ sing_1799.htm#SEC1875
627	LinearCombinationQ sing_1800.htm#SEC1876
628	LinearizeAction sing_1798.htm#SEC1874
629	Loading a library sing_62.htm#SEC99
630	Local orderings sing_962.htm#SEC1014
631	Log for matrices sing_1480.htm#IDX649
632	Long coefficients sing_912.htm#SEC964
633	M, ordering sing_964.htm#SEC1016
634	MVComplex sing_2479.htm#SEC2555
635	Macdonald's formula sing_2578.htm#IDX1132
636	MacdonaldF sing_2585.htm#SEC2661
637	Macintosh installation Macintosh installation instructions sing_2912.htm#SEC3003
638	Mathematical background Mathematical background sing_968.htm#SEC1020
639	Mathematical background (letterplace) Mathematical background (letterplace) sing_807.htm#SEC859
640	Mathematical background (plural) Mathematical background (plural) sing_489.htm#SEC529
641	Matrix orderings sing_964.htm#SEC1016
642	Max sing_1706.htm#SEC1782
643	Maximus sing_1570.htm#SEC1646
644	Maxord sing_1511.htm#SEC1587
645	MillerRabin sing_2016.htm#SEC2092
646	Milnor code sing_2363.htm#IDX983
647	Milnor number Milnor and Tjurina number sing_936.htm#SEC988
648	Milnor number sing_2812.htm#IDX1178
649	Min sing_1707.htm#SEC1783
650	MinMult sing_2445.htm#SEC2521
651	MinimalDecomposition MinimalDecomposition sing_1801.htm#SEC1877
652	Minimum distance sing_1924.htm#IDX842
653	Minimus sing_1569.htm#SEC1645
654	Miscellaneous libraries Miscellaneous libraries sing_2289.htm#SEC2365
655	ModEqn sing_1700.htm#SEC1776
656	Modular techniques sing_1061.htm#IDX528
657	Module orderings sing_963.htm#SEC1015
658	Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16
659	Monodromy sing_1692.htm#IDX817
660	Monomial orderings sing_958.htm#SEC1010
661	Monomial orderings on free algebras Monomial orderings on free algebras sing_809.htm#SEC861
662	Monomial orderings, Term orderings sing_31.htm#SEC44
663	Mori dream spaces sing_2372.htm#IDX986
664	Morse lemma addnondegeneratevariables sing_2811.htm#IDX1176
665	Morse lemma sing_2814.htm#IDX1180
666	MultiplicitySequence MultiplicitySequence sing_1624.htm#SEC1700
667	NF sing_337.htm#SEC377
668	NF (letterplace) reduce (letterplace) sing_802.htm#SEC854
669	NF (plural) sing_481.htm#SEC521
670	NFMora sing_2082.htm#SEC2158
671	NPos sing_1343.htm#SEC1419
672	NPos_test sing_1341.htm#SEC1417
673	NSplaces sing_1912.htm#SEC1988
674	NTL sing_1.htm#IDX4
675	NakYoshF sing_2582.htm#SEC2658
676	Names sing_37.htm#SEC65
677	Names in procedures sing_46.htm#SEC83
678	Names, indexed sing_37.htm#SEC65
679	New orderings for modules Notes for Singular users sing_2903.htm#SEC2993
680	Newton non-degenerate sing_1679.htm#IDX815
681	Newton polygon sing_1678.htm#IDX814
682	Newton polygon sing_1679.htm#IDX816
683	Newton polygons sing_2879.htm#IDX1224
684	Newton polytope sing_2188.htm#IDX859
685	Newton step sing_2815.htm#IDX1184
686	Noether position sing_1343.htm#IDX603
687	NoetherPosition sing_1337.htm#SEC1413
688	Non-commutative algebra Non-commutative algebra sing_950.htm#SEC1002
689	Non-commutative algebra sing_985.htm#SEC1042
690	Non-commutative subsystem Non-commutative subsystem sing_424.htm#SEC464
691	Nonhyp sing_1500.htm#SEC1576
692	Normalization sing_932.htm#SEC984
693	Notes for Singular users Notes for Singular users sing_2903.htm#SEC2988
694	Notes for developers Notes for developers sing_2904.htm#SEC2995
695	NullCone sing_1802.htm#SEC1878
696	NumIrrDecom sing_1474.htm#SEC1550
697	NumLocalDim sing_1463.htm#SEC1539
698	NumPrimDecom sing_1476.htm#SEC1552
699	Oaku-Takayama algorithm sing_537.htm#IDX335
700	Objects sing_38.htm#SEC66
701	Orlik-Solomon sing_2319.htm#IDX923
702	Output sing_2703.htm#IDX1144
703	Output sing_2779.htm#IDX1151
704	Output sing_2781.htm#IDX1152
705	Output sing_2782.htm#IDX1153
706	Output sing_2783.htm#IDX1154
707	Output sing_2784.htm#IDX1155
708	Output sing_2785.htm#IDX1156
709	Output sing_2786.htm#IDX1157
710	Output sing_2787.htm#IDX1158
711	Output sing_2788.htm#IDX1159
712	Output sing_2789.htm#IDX1160
713	Output sing_2790.htm#IDX1161
714	Output sing_2791.htm#IDX1162
715	Output sing_2792.htm#IDX1163
716	Output sing_2793.htm#IDX1164
717	Output sing_2794.htm#IDX1165
718	Output sing_2795.htm#IDX1166
719	Output sing_2796.htm#IDX1167
720	Output sing_2797.htm#IDX1168
721	Output sing_2798.htm#IDX1169
722	Output sing_2799.htm#IDX1170
723	Output sing_2800.htm#IDX1171
724	Output sing_2801.htm#IDX1172
725	Output sing_2802.htm#IDX1173
726	Output sing_2803.htm#IDX1174
727	Output, formatting of sing_914.htm#SEC966
728	PBW sing_516.htm#IDX323
729	PBW basis sing_490.htm#SEC531
730	PBW_eqDeg sing_534.htm#SEC586
731	PBW_maxDeg sing_535.htm#SEC587
732	PBW_maxMonom sing_536.htm#SEC588
733	PEsolve sing_1821.htm#SEC1897
734	PH_ais sing_2341.htm#SEC2417
735	PH_nais sing_2342.htm#SEC2418
736	PLURAL sing_425.htm#SEC465
737	PLURAL LIBs sing_494.htm#SEC546
738	PLURAL libraries sing_494.htm#SEC546
739	PPolyH sing_2580.htm#SEC2656
740	PPolyN sing_2588.htm#SEC2664
741	PPolyQp sing_2583.htm#SEC2659
742	PPolyS sing_2586.htm#SEC2662
743	ParToVar sing_2575.htm#SEC2651
744	Parallelization Parallelization with ssi links sing_916.htm#SEC968
745	Parallelization sing_1061.htm#IDX529
746	Parameter list sing_44.htm#SEC81
747	Parameters sing_913.htm#SEC965
748	Parametrization sing_1483.htm#IDX657
749	Parametrization, image. sing_1493.htm#IDX669
750	PartC sing_2435.htm#SEC2511
751	PartitionVar sing_2572.htm#SEC2648
752	Path names Notes for Singular users sing_2903.htm#SEC2991
753	PerfectPowerTest sing_1979.htm#SEC2055
754	Perturbation walk sing_1262.htm#IDX586
755	Pfister, Gerhard sing_1.htm#IDX19
756	Pipe links sing_121.htm#SEC161
757	PocklingtonLehmer sing_2018.htm#SEC2094
758	Poincare polynomial sing_2331.htm#IDX947
759	Polar curves sing_938.htm#SEC990
760	PollardRho sing_2019.htm#SEC2095
761	PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2344.htm#IDX963
762	PolyBoRi, Boolean Groebner Basis sing_2346.htm#IDX964
763	PolyBoRi, Boolean Groebner Basis sing_2347.htm#IDX965
764	PolyBoRi, Boolean Groebner Basis sing_2348.htm#IDX966
765	PolyBoRi, Boolean Groebner Basis sing_2349.htm#IDX967
766	PolyBoRi, Boolean Groebner Basis sing_2350.htm#IDX968
767	PolyBoRi, Boolean Groebner Basis sing_2351.htm#IDX969
768	PolyBoRi, Boolean Groebner Basis sing_2352.htm#IDX970
769	PolyBoRi, Boolean Groebner Basis sing_2353.htm#IDX971
770	PolyBoRi, Boolean Groebner Basis sing_2354.htm#IDX972
771	PolyBoRi, Boolean Groebner Basis sing_2355.htm#IDX973
772	PolyBoRi, Boolean Groebner Basis sing_2356.htm#IDX974
773	PolyBoRi, Boolean Groebner Basis sing_2357.htm#IDX975
774	PolyBoRi, Boolean Groebner Basis sing_2358.htm#IDX976
775	PolyBoRi, Boolean Groebner Basis sing_2360.htm#IDX978
776	PolyBoRi, zero-supressed decision diagram sing_2359.htm#IDX977
777	Polybori, Boolean Groebner Basis sing_2361.htm#IDX979
778	Polynomial data sing_956.htm#SEC1008
779	Pottier algorithm sing_978.htm#SEC1035
780	Preface sing_1.htm#SEC1
781	Prep sing_1031.htm#SEC1107
782	Primary decomposition Primary decomposition sing_931.htm#SEC983
783	PrimdecA sing_1319.htm#SEC1395
784	PrimdecB sing_1320.htm#SEC1396
785	Procedure definition Procedure definition sing_43.htm#SEC78
786	Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84
787	Procedures sing_42.htm#SEC77
788	Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14
789	Procedures and libraries sing_910.htm#SEC962
790	Procedures in a library Procedures in a library sing_54.htm#SEC91
791	Product orderings sing_965.htm#SEC1017
792	Programming sing_908.htm#SEC960
793	Pseudo ordering L sing_967.htm#SEC1019
794	PtoCrep sing_1032.htm#SEC1108
795	Puiseux expansion sing_1577.htm#IDX680
796	Puiseux expansion sing_1665.htm#IDX802
797	Puiseux pairs Invariants of plane curve singularities sing_941.htm#SEC993
798	Puiseux pairs sing_1671.htm#IDX807
799	QQ sing_28.htm#SEC39
800	QQ sing_75.htm#SEC115
801	Qso3Casimir sing_641.htm#SEC693
802	Quot-scheme sing_2578.htm#IDX1135
803	Quotient sing_1863.htm#SEC1939
804	QuotientEquations sing_1701.htm#SEC1777
805	Rational curves sing_1483.htm#IDX658
806	ReJunkUseHomo sing_1469.htm#SEC1545
807	ReesAlgebra sing_1436.htm#SEC1512
808	References sing_993.htm#SEC1067
809	References (plural) sing_493.htm#SEC543
810	References and history of Letterplace References and history of Letterplace sing_796.htm#SEC848
811	Release Notes sing_2899.htm#SEC2975
812	Res sing_2683.htm#SEC2759
813	ResTree sing_1529.htm#SEC1605
814	Resolution sing_11.htm#SEC17
815	Resolution of singularities Resolution of singularities sing_944.htm#SEC996
816	Resolution, free sing_926.htm#SEC978
817	ReynoldsImage sing_1803.htm#SEC1879
818	ReynoldsOperator sing_1804.htm#SEC1880
819	RiemannRochBN sing_2380.htm#SEC2456
820	RiemannRochHess sing_2666.htm#SEC2742
821	Right Groebner bases and syzygies Right Groebner bases and syzygies sing_952.htm#SEC1004
822	Ring-dependent options Notes for Singular users sing_2903.htm#SEC2990
823	Rings and orderings sing_28.htm#SEC39
824	Rings and standard bases Rings and standard bases sing_7.htm#SEC13
825	Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
826	SCA Graded commutative algebras (SCA) sing_792.htm#SEC844
827	SDB breakpoint Source code debugger sing_66.htm#SEC106
828	SDB debugger Source code debugger sing_66.htm#SEC106
829	SDLoc sing_564.htm#SEC616
830	SINGULAR libraries sing_994.htm#SEC1070
831	SINGULARHIST sing_18.htm#SEC25
832	SL sing_1807.htm#SEC1883
833	SLreynolds sing_1813.htm#SEC1889
834	SV-decoding algorithm sing_1919.htm#IDX836
835	SV-decoding algorithm, preprocessing sing_1918.htm#IDX835
836	SaitoBase sing_2893.htm#SEC2969
837	Sannfs sing_540.htm#SEC592
838	SannfsBFCT sing_549.htm#SEC601
839	SannfsVar sing_604.htm#SEC656
840	Sannfslog sing_541.htm#SEC593
841	Saturation sing_923.htm#SEC975
842	Sch@"onemann, Hans sing_1.htm#IDX20
843	Schoof sing_2030.htm#SEC2106
844	Schubert calculus sing_2837.htm#IDX1198
845	SchubertClass sing_2874.htm#SEC2950
846	SchurCh sing_2432.htm#SEC2508
847	SchurS sing_2431.htm#SEC2507
848	SegreA sing_2438.htm#SEC2514
849	Semigroup sing_1617.htm#SEC1693
850	Serre relations sing_820.htm#IDX402
851	SetDeg sing_2686.htm#SEC2762
852	Setting up a G-algebra sing_490.htm#SEC534
853	ShanksMestre sing_2029.htm#SEC2105
854	SimplifyIdeal sing_1805.htm#SEC1881
855	Singular sing_361.htm#IDX255
856	Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2901.htm#SEC2986
857	Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36
858	Singular, demo mode sing_24.htm#SEC35
859	Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
860	Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38
861	Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
862	Singular2bertini sing_1467.htm#SEC1543
863	SingularLib sing_361.htm#IDX257
864	Singularities sing_1576.htm#SEC1652
865	Singularity Theory sing_935.htm#SEC987
866	Skeletons for parallelization sing_1061.htm#IDX530
867	Smith form sing_1961.htm#IDX846
868	Smith normal form sing_1961.htm#IDX847
869	SolowayStrassen sing_2017.htm#SEC2093
870	Solving systems of polynomial equations Solving systems of polynomial equations sing_954.htm#SEC1006
871	Source sing_2675.htm#SEC2751
872	Source code debugger, invocation Command line options sing_19.htm#IDX33
873	Space curve singularities, branches of Branches of space curve singularities sing_942.htm#SEC994
874	Special characters sing_36.htm#SEC64
875	Splitting lemma addnondegeneratevariables sing_2811.htm#IDX1177
876	Splitting lemma sing_2814.htm#IDX1181
877	Ssi file links sing_119.htm#SEC159
878	Ssi links sing_118.htm#SEC158
879	Ssi tcp links sing_120.htm#SEC160
880	StabEqn sing_1702.htm#SEC1778
881	StabEqnId sing_1703.htm#SEC1779
882	StabOrder sing_1704.htm#SEC1780
883	Standard Bases Computing Groebner and Standard Bases sing_918.htm#SEC970
884	Standard bases sing_969.htm#SEC1021
885	StartOrderingV sing_1571.htm#SEC1647
886	Startup sequence sing_20.htm#SEC27
887	StringF sing_1691.htm#SEC1767
888	SymGroup sing_787.htm#SEC839
889	Symbolic-numerical solving Symbolic-numerical solving sing_954.htm#SEC1006
890	Symbolic-numerical solving sing_1818.htm#SEC1894
891	System and Control theory System and Control theory sing_1943.htm#SEC2019
892	System dependent limitations System dependent limitations sing_412.htm#SEC452
893	System variables sing_398.htm#SEC438
894	Syzygies and resolutions Syzygies and resolutions sing_971.htm#SEC1025
895	Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_492.htm#SEC539
896	Syzygy bimodule Bimodules and syzygies and lifts sing_812.htm#SEC864
897	T1 sing_939.htm#SEC991
898	T2 sing_939.htm#SEC991
899	TRACE Tracing of procedures sing_65.htm#SEC102
900	TRACE sing_407.htm#SEC447
901	T_1 sing_1724.htm#SEC1800
902	T_12 sing_1726.htm#SEC1802
903	T_2 sing_1725.htm#SEC1801
904	Target sing_2674.htm#SEC2750
905	Teaching sing_1975.htm#SEC2051
906	Template for writing a library sing_55.htm#SEC92
907	TestGRRes sing_2646.htm#SEC2722
908	TestJMark sing_1572.htm#SEC1648
909	The SINGULAR language The SINGULAR language sing_34.htm#SEC56
910	The Tran algorithm sing_1259.htm#IDX583
911	The fractal walk algorithm sing_1258.htm#IDX582
912	The fractal walk algorithm sing_2836.htm#IDX1195
913	The online help system The online help system sing_16.htm#SEC22
914	Tjurina sing_1722.htm#SEC1798
915	Tjurina number Milnor and Tjurina number sing_936.htm#SEC988
916	Tjurina number sing_1358.htm#IDX618
917	Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38
918	Tor sing_1284.htm#SEC1360
919	Toric ideals and integer programming Toric ideals and integer programming sing_974.htm#SEC1031
920	Tricks and pitfalls sing_410.htm#SEC450
921	Tropical Geometry sing_2127.htm#SEC2203
922	Type casting Type conversion and casting sing_39.htm#SEC69
923	Type conversion Type conversion and casting sing_39.htm#SEC68
924	Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98
925	U_D_O sing_1199.htm#SEC1275
926	Ufnarovski graph sing_849.htm#IDX410
927	Unix installation Unix installation instructions sing_2910.htm#SEC3001
928	UpOneMatrix sing_743.htm#SEC795
929	UpperMonomials sing_1705.htm#SEC1781
930	UseBertini sing_1466.htm#SEC1542
931	User defined types sing_183.htm#SEC223
932	V-filtration sing_1640.htm#IDX712
933	V-filtration sing_1646.htm#IDX740
934	V-filtration sing_1647.htm#IDX746
935	V-filtration sing_1648.htm#IDX754
936	V-filtration sing_1649.htm#IDX760
937	V-filtration sing_1650.htm#IDX768
938	V-filtration sing_1651.htm#IDX778
939	V-filtration sing_1662.htm#IDX784
940	V-filtration sing_1664.htm#IDX795
941	VarToPar sing_2574.htm#SEC2650
942	Variables, indexed sing_37.htm#SEC65
943	VecField.lib sing_2888.htm#SEC2964
944	VecField_lib sing_2888.htm#SEC2964
945	Version number Version schema for Singular sing_2902.htm#SEC2987
946	Version schema for Singular Version schema for Singular sing_2902.htm#SEC2987
947	Version string sing_50.htm#SEC87
948	Visualization sing_1881.htm#SEC1957
949	WLCGS sing_1044.htm#SEC1120
950	WLemma sing_1043.htm#SEC1119
951	WP, global ordering sing_961.htm#IDX437
952	WSemigroup sing_1622.htm#SEC1698
953	Weierstrass sing_1914.htm#SEC1990
954	Weierstrass semigroup sing_1910.htm#IDX830
955	Weyl sing_728.htm#SEC780
956	Weyl algebra sing_537.htm#IDX329
957	Weyl algebra sing_593.htm#IDX355
958	Weyl algebra sing_601.htm#IDX361
959	Weyl closure sing_662.htm#IDX373
960	WeylClosure sing_664.htm#SEC716
961	WeylClosure1 sing_665.htm#SEC717
962	Wibmer's Lemma sing_1043.htm#IDX513
963	Windows installation Windows installation instructions sing_2911.htm#SEC3002
964	WitSet sing_1473.htm#SEC1549
965	WitSupSet sing_1472.htm#SEC1548
966	Ws, local ordering sing_962.htm#IDX449
967	XLsolve sing_1824.htm#SEC1900
968	ZZ sing_28.htm#SEC39
969	ZZ sing_75.htm#SEC115
970	ZZ/m sing_28.htm#SEC39
971	ZZ/p sing_28.htm#SEC39
972	ZZsolve sing_1825.htm#SEC1901
973	[ sing_36.htm#IDX83
974	[] sing_142.htm#SEC182
975	[] sing_155.htm#SEC195
976	[] sing_176.htm#SEC216
977	[] sing_181.htm#SEC221
978	\ sing_36.htm#IDX112
979	] sing_36.htm#IDX84
980	^ sing_36.htm#IDX92
981	^ sing_81.htm#SEC121
982	^ sing_93.htm#SEC133
983	^ sing_147.htm#SEC187
984	^ sing_155.htm#SEC195
985	_ sing_36.htm#IDX116
986	` sing_36.htm#IDX105
987	a, ordering sing_966.htm#SEC1018
988	absFactorize sing_1212.htm#SEC1288
989	absFactorizeBCG sing_1213.htm#SEC1289
990	absPrimdecGTZ sing_1416.htm#SEC1492
991	absPrimdecGTZE sing_1417.htm#SEC1493
992	absValue sing_1007.htm#SEC1083
993	absfact.lib sing_1211.htm#SEC1287
994	absfact_lib sing_1211.htm#SEC1287
995	absolute factorization. sing_1211.htm#IDX554
996	abstract variety, projective space, Grassmannian printVariety sing_2838.htm#IDX1201
997	abstract variety, projective space, Grassmannian sing_2839.htm#IDX1202
998	abstractR sing_1555.htm#SEC1631
999	actionIsProper sing_1785.htm#SEC1861
1000	add sing_2494.htm#IDX1040
1001	add sing_2516.htm#IDX1088
1002	addLeftFractions sing_759.htm#SEC811
1003	addModules sing_2695.htm#SEC2771
1004	addNvarsTo sing_1135.htm#SEC1211
1005	addRat sing_683.htm#SEC735
1006	addSheaf sing_2857.htm#SEC2933
1007	addcol sing_1168.htm#SEC1244
1008	addcores sing_1104.htm#SEC1180
1009	addnondegeneratevariables addnondegeneratevariables sing_2814.htm#SEC2890
1010	addrow sing_1169.htm#SEC1245
1011	addvarsTo sing_1134.htm#SEC1210
1012	ademRelations sing_824.htm#SEC876
1013	adjoint sing_1193.htm#SEC1269
1014	adjointIdeal sing_1484.htm#SEC1560
1015	adjunction divisor sing_1911.htm#IDX834
1016	admissibleSub sing_719.htm#SEC771
1017	afaces sing_2599.htm#SEC2675
1018	affine code Fitzgerald-Lax method sing_990.htm#SEC1059
1019	ainvar.lib sing_1782.htm#SEC1858
1020	ainvar_lib sing_1782.htm#SEC1858
1021	aksaka.lib sing_1976.htm#SEC2052
1022	aksaka_lib sing_1976.htm#SEC2052
1023	alexanderpolynomial sing_1580.htm#SEC1656
1024	alexpoly.lib sing_1577.htm#SEC1653
1025	alexpoly_lib sing_1577.htm#SEC1653
1026	algDependent sing_1218.htm#SEC1294
1027	alg_kernel sing_1219.htm#SEC1295
1028	algebra.lib sing_1214.htm#SEC1290
1029	algebra_containment sing_1215.htm#SEC1291
1030	algebra_lib sing_1214.htm#SEC1290
1031	algebraic dependence sing_770.htm#IDX381
1032	algebraic field extension sing_1430.htm#IDX627
1033	algebraicDependence sing_1443.htm#SEC1519
1034	algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_981.htm#SEC1038
1035	algorithm of Conti and Traverso sing_977.htm#SEC1034
1036	algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_980.htm#SEC1037
1037	algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_979.htm#SEC1036
1038	algorithm of Pottier sing_978.htm#SEC1035
1039	alias General command syntax sing_35.htm#SEC59
1040	align sing_209.htm#SEC249
1041	all.lib sing_999.htm#SEC1075
1042	allDoubleExt sing_781.htm#SEC833
1043	allExtOfLeft sing_778.htm#SEC830
1044	allExtOfRight sing_779.htm#SEC831
1045	allPositive sing_513.htm#SEC565
1046	all_lib sing_999.htm#SEC1075
1047	allowing net access Command line options sing_19.htm#IDX41
1048	allprint sing_1052.htm#SEC1128
1049	allreal sing_2119.htm#SEC2195
1050	allrealst sing_2117.htm#SEC2193
1051	allsquarefree sing_1684.htm#SEC1760
1052	ambientDimension sing_2132.htm#SEC2208
1053	and Evaluation of logical expressions sing_101.htm#SEC141
1054	and sing_415.htm#SEC455
1055	annPoly sing_561.htm#SEC613
1056	annRat sing_562.htm#SEC614
1057	annRatSyz sing_672.htm#SEC724
1058	annfalphaI sing_599.htm#SEC651
1059	annfs sing_538.htm#SEC590
1060	annfs0 sing_550.htm#SEC602
1061	annfs2 sing_551.htm#SEC603
1062	annfsBMI sing_547.htm#SEC599
1063	annfsLogIdeal sing_594.htm#SEC646
1064	annfsParamBM sing_546.htm#SEC598
1065	annfsRB sing_552.htm#SEC604
1066	annfspecial sing_539.htm#SEC591
1067	annihilator of polynomial sing_560.htm#IDX339
1068	annihilator of rational function sing_560.htm#IDX340
1069	annihilator of rational function sing_662.htm#IDX376
1070	annihilatorMultiFs sing_595.htm#SEC647
1071	annil sing_1325.htm#SEC1401
1072	appelF1 sing_579.htm#SEC631
1073	appelF2 sing_580.htm#SEC632
1074	appelF4 sing_581.htm#SEC633
1075	appendWeight2Ord sing_721.htm#SEC773
1076	application sing_2522.htm#IDX1103
1077	apply sing_382.htm#SEC422
1078	applyAdF sing_529.htm#SEC581
1079	applyPermutationToIntvec applyPermutationToIntvec sing_2624.htm#SEC2700
1080	applyVecField sing_2889.htm#SEC2965
1081	arcpoint.lib sing_1590.htm#SEC1666
1082	arcpoint_lib sing_1590.htm#SEC1666
1083	areEqualLeftFractions areEqualLeftFractions sing_761.htm#SEC813
1084	areZeroElements sing_2762.htm#SEC2838
1085	argument, default sing_44.htm#SEC81
1086	argument, optional sing_44.htm#SEC81
1087	arnoldClassify sing_2367.htm#SEC2443
1088	arnoldCorank sing_2368.htm#SEC2444
1089	arnoldDeterminacy sing_2369.htm#SEC2445
1090	arnoldListAllSeries sing_2364.htm#SEC2440
1091	arnoldMilnorCode sing_2370.htm#SEC2446
1092	arnoldMorseSplit sing_2371.htm#SEC2447
1093	arnoldNormalForm sing_2366.htm#SEC2442
1094	arnoldShowSeries sing_2365.htm#SEC2441
1095	arnoldclassify.lib sing_2363.htm#SEC2439
1096	arnoldclassify_lib sing_2363.htm#SEC2439
1097	arr.lib sing_2290.htm#SEC2366
1098	arr2multarr sing_2323.htm#SEC2399
1099	arrBoolean sing_2312.htm#SEC2388
1100	arrBoundedChambers sing_2333.htm#SEC2409
1101	arrBraid sing_2313.htm#SEC2389
1102	arrCenter sing_2300.htm#SEC2376
1103	arrCentered sing_2302.htm#SEC2378
1104	arrCentral sing_2301.htm#SEC2377
1105	arrCentralize sing_2303.htm#SEC2379
1106	arrChambers sing_2332.htm#SEC2408
1107	arrCharPoly sing_2330.htm#SEC2406
1108	arrCone sing_2306.htm#SEC2382
1109	arrCoordChange sing_2304.htm#SEC2380
1110	arrCoordNormalize sing_2305.htm#SEC2381
1111	arrDecone sing_2307.htm#SEC2383
1112	arrDer sing_2320.htm#SEC2396
1113	arrEdelmanReiner sing_2318.htm#SEC2394
1114	arrEssentialize sing_2311.htm#SEC2387
1115	arrExponents sing_2322.htm#SEC2398
1116	arrFlats sing_2327.htm#SEC2403
1117	arrIsEssential sing_2310.htm#SEC2386
1118	arrIsFree sing_2321.htm#SEC2397
1119	arrLastVar sing_2299.htm#SEC2375
1120	arrLattice sing_2328.htm#SEC2404
1121	arrLocalize sing_2308.htm#SEC2384
1122	arrOrlikSolomon sing_2319.htm#SEC2395
1123	arrPoincare sing_2331.htm#SEC2407
1124	arrPrintMatrix sing_2295.htm#SEC2371
1125	arrRandom sing_2316.htm#SEC2392
1126	arrRandomCentral sing_2317.htm#SEC2393
1127	arrRestrict sing_2309.htm#SEC2385
1128	arrSet sing_2291.htm#SEC2367
1129	arrSwapVar sing_2298.htm#SEC2374
1130	arrTypeB sing_2314.htm#SEC2390
1131	arrTypeD sing_2315.htm#SEC2391
1132	arr_lib sing_2290.htm#SEC2366
1133	arrange sing_554.htm#SEC606
1134	arrangement sing_2291.htm#IDX865
1135	arrangement sing_2292.htm#IDX870
1136	arrangement sing_2323.htm#IDX932
1137	arrangement sing_2324.htm#IDX935
1138	ask sing_1984.htm#SEC2060
1139	assPrimes sing_1229.htm#SEC1305
1140	assign sing_2291.htm#IDX867
1141	assignment,custom Assignments for user defined types sing_188.htm#SEC228
1142	associated tangent FamElemsAtEnvCompPoints sing_1040.htm#IDX506
1143	associated tangent sing_1041.htm#IDX510
1144	assprimeszerodim.lib assprimeszerodim_lib sing_1227.htm#SEC1303
1145	assprimeszerodim_lib assprimeszerodim_lib sing_1227.htm#SEC1303
1146	atkins.lib sing_1985.htm#SEC2061
1147	atkins_lib sing_1985.htm#SEC2061
1148	attrib sing_210.htm#SEC250
1149	autGenWeights sing_2375.htm#SEC2451
1150	autGradAlg sing_2374.htm#SEC2450
1151	autKS sing_2373.htm#SEC2449
1152	autX sing_2378.htm#SEC2454
1153	autXhat sing_2377.htm#SEC2453
1154	autgradalg.lib sing_2372.htm#SEC2448
1155	autgradalg_lib sing_2372.htm#SEC2448
1156	automorphism group sing_2372.htm#IDX987
1157	automorphisms sing_2372.htm#IDX984
1158	autonom sing_1948.htm#SEC2024
1159	autonomDim sing_1949.htm#SEC2025
1160	awalk1 sing_1260.htm#SEC1336
1161	awalk2 sing_1261.htm#SEC1337
1162	b-function sing_502.htm#IDX312
1163	bFactor sing_584.htm#SEC636
1164	babyGiant sing_2014.htm#SEC2090
1165	backward sing_2561.htm#SEC2637
1166	bareiss sing_211.htm#SEC251
1167	base2str sing_1002.htm#SEC1078
1168	basering sing_28.htm#IDX76
1169	basering sing_88.htm#SEC128
1170	basicinvariants sing_1596.htm#SEC1672
1171	baumslagGroup sing_826.htm#SEC878
1172	baumslagSolitar sing_825.htm#SEC877
1173	belongSemigroup sing_1232.htm#SEC1308
1174	bernstein sing_1644.htm#SEC1720
1175	bernsteinBM sing_542.htm#SEC594
1176	bernsteinLift sing_543.htm#SEC595
1177	bertini sing_1459.htm#IDX631
1178	bertini sing_1464.htm#IDX638
1179	bertini2Singular sing_1468.htm#SEC1544
1180	betti sing_212.htm#SEC252
1181	betti (plural) sing_459.htm#SEC499
1182	bfct sing_503.htm#SEC555
1183	bfctAnn sing_505.htm#SEC557
1184	bfctBound sing_671.htm#SEC723
1185	bfctIdeal sing_507.htm#SEC559
1186	bfctOneGB sing_506.htm#SEC558
1187	bfctSyz sing_504.htm#SEC556
1188	bfctVarAnn sing_603.htm#SEC655
1189	bfctVarIn sing_602.htm#SEC654
1190	bfun.lib sing_502.htm#SEC554
1191	bfun_lib sing_502.htm#SEC554
1192	bigger sing_2501.htm#IDX1054
1193	bigint sing_78.htm#SEC118
1194	bigint declarations sing_79.htm#SEC119
1195	bigint expressions sing_80.htm#SEC120
1196	bigint operations sing_81.htm#SEC121
1197	bigint related functions bigint related functions sing_82.htm#SEC122
1198	bigintToBinary sing_2622.htm#SEC2698
1199	bigintmat sing_83.htm#SEC123
1200	bigintmat declarations bigintmat declarations sing_84.htm#SEC124
1201	bigintmat expressions bigintmat expressions sing_85.htm#SEC125
1202	bigintmat operations bigintmat operations sing_87.htm#SEC127
1203	bigintmat type cast sing_86.htm#SEC126
1204	bimodules sing_495.htm#IDX300
1205	bimodules.lib sing_495.htm#SEC547
1206	bimodules_lib sing_495.htm#SEC547
1207	binaryToBigint sing_2623.htm#SEC2699
1208	binary_add sing_2037.htm#SEC2113
1209	binomial sing_1008.htm#SEC1084
1210	binomials2intmat sing_1391.htm#SEC1467 58804
1211	birational map, image, inverse. sing_1485.htm#IDX663
1212	bistd sing_496.htm#SEC548
1213	bisyzygies sing_495.htm#IDX301
1214	bitrinity sing_497.htm#SEC549
1215	blackbox sing_192.htm#SEC232
1216	blackbox sing_200.htm#SEC240
1217	block sing_40.htm#SEC70
1218	block sing_381.htm#SEC421
1219	blowUp sing_1536.htm#SEC1612
1220	blowUp2 sing_1537.htm#SEC1613
1221	blowUpBO sing_1543.htm#SEC1619
1222	blowup0 sing_1237.htm#SEC1313
1223	boolean sing_2312.htm#IDX909
1224	boolean expressions sing_100.htm#SEC140
1225	boolean operations sing_101.htm#SEC141
1226	boolean_constant sing_2346.htm#SEC2422 52873
1227	boolean_ideal sing_2350.htm#SEC2426 53515
1228	boolean_poly sing_2347.htm#SEC2423 41652
1229	boolean_poly_ring sing_2345.htm#SEC2421 sprintf
1230	boolean_set sing_2351.htm#SEC2427 58235
1231	boolean_std sing_2344.htm#SEC2420 5921
1232	border basis sing_2828.htm#IDX1185
1233	borderBasis sing_2829.htm#SEC2905
1234	boundBuFou sing_2114.htm#SEC2190
1235	boundDes sing_2116.htm#SEC2192
1236	boundaryLatticePoints boundaryLatticePoints sing_2203.htm#SEC2279
1237	boundposDes sing_2115.htm#SEC2191
1238	bounds sing_2816.htm#SEC2892
1239	boxSet sing_2818.htm#SEC2894
1240	bracket sing_361.htm#IDX197
1241	bracket sing_418.htm#SEC458
1242	bracket sing_460.htm#SEC500
1243	braid sing_2313.htm#IDX911
1244	branchTo procs with different argument types sing_160.htm#SEC200
1245	break sing_383.htm#SEC423
1246	break point sing_397.htm#SEC437
1247	breakpoint sing_384.htm#SEC424
1248	brillnoether.lib sing_2379.htm#SEC2455
1249	brillnoether_lib sing_2379.htm#SEC2455
1250	brnoeth.lib sing_1910.htm#SEC1986
1251	brnoeth_lib sing_1910.htm#SEC1986
1252	browser, command line option Command line options sing_19.htm#IDX44
1253	browser, setting the sing_361.htm#IDX193
1254	browsers The online help system sing_16.htm#IDX21
1255	browsers, setting the sing_361.htm#IDX192
1256	bubblesort sing_1987.htm#SEC2063
1257	busadj sing_1191.htm#SEC1267
1258	bvar sing_2358.htm#SEC2434 52773
1259	c, module ordering sing_963.htm#IDX452
1260	cProj sing_2421.htm#SEC2497
1261	calculateI sing_1510.htm#SEC1586
1262	calculate_max_sum sing_2056.htm#SEC2132
1263	calculate_ordering sing_2034.htm#SEC2110
1264	cancelunit, option sing_318.htm#IDX171
1265	canonMap sing_1265.htm#SEC1341
1266	canoncial form sing_1030.htm#IDX473
1267	canoncial form sing_1031.htm#IDX475
1268	canoncial form sing_1032.htm#IDX477
1269	canonical sing_1026.htm#IDX461
1270	canonical form sing_1047.htm#IDX519
1271	canonical form sing_1048.htm#IDX521
1272	canonical form sing_1049.htm#IDX524
1273	canonical form sing_1050.htm#IDX526
1274	canonical, sing_1034.htm#IDX487
1275	canonicalizeCone sing_2133.htm#SEC2209
1276	canonize sing_1956.htm#SEC2032
1277	cantoradd sing_2070.htm#SEC2146
1278	cantormult sing_2073.htm#SEC2149
1279	cantorred sing_2071.htm#SEC2147
1280	cardGroup sing_1234.htm#SEC1310
1281	case No case or switch statement sing_416.htm#SEC456
1282	catNets sing_2779.htm#SEC2855
1283	cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2883.htm#SEC2959
1284	cdd sing_1.htm#IDX10
1285	cddlib sing_1.htm#IDX11
1286	center sing_516.htm#IDX319
1287	center sing_522.htm#SEC574
1288	center sing_2300.htm#IDX891
1289	center sing_2301.htm#IDX892
1290	center sing_2302.htm#IDX894
1291	center sing_2303.htm#IDX896
1292	centerRed sing_521.htm#SEC573
1293	centerVS sing_520.htm#SEC572
1294	central sing_2294.htm#IDX877
1295	central sing_2301.htm#IDX893
1296	central sing_2303.htm#IDX895
1297	central sing_2317.htm#IDX920
1298	central.lib sing_516.htm#SEC568
1299	central1st sing_2562.htm#SEC2638
1300	central2nd sing_2563.htm#SEC2639
1301	central_lib sing_516.htm#SEC568
1302	centralize sing_516.htm#IDX322
1303	centralizeSet sing_517.htm#SEC569
1304	centralizer sing_516.htm#IDX320
1305	centralizer sing_523.htm#SEC575
1306	centralizerRed sing_519.htm#SEC571
1307	centralizerVS sing_518.htm#SEC570
1308	cf_class sing_210.htm#IDX132
1309	cgs sing_1001.htm#SEC1077
1310	cgsdr sing_1027.htm#SEC1103
1311	chAll sing_2391.htm#SEC2467
1312	chAllInv sing_2392.htm#SEC2468
1313	chDual sing_2397.htm#SEC2473
1314	chHE sing_2393.htm#SEC2469
1315	chHom sing_2406.htm#SEC2482
1316	chNum sing_2387.htm#SEC2463
1317	chNumbers sing_2388.htm#SEC2464
1318	chNumbersProj sing_2425.htm#SEC2501
1319	chProd sing_2399.htm#SEC2475
1320	chProdE sing_2400.htm#SEC2476
1321	chProdL sing_2401.htm#SEC2477
1322	chProdLP sing_2402.htm#SEC2478
1323	chProdM sing_2403.htm#SEC2479
1324	chProdMP sing_2404.htm#SEC2480
1325	chProj sing_2422.htm#SEC2498
1326	chSum sing_2395.htm#SEC2471
1327	chSymm sing_2409.htm#SEC2485
1328	chSymm2L sing_2410.htm#SEC2486
1329	chSymm2LP sing_2411.htm#SEC2487
1330	chWedge sing_2412.htm#SEC2488
1331	chWedge2L sing_2413.htm#SEC2489
1332	chWedge2LP sing_2414.htm#SEC2490
1333	chaincrit sing_2084.htm#SEC2160
1334	chambers sing_2332.htm#IDX948
1335	chambers sing_2333.htm#IDX949
1336	changeCoordinates sing_2890.htm#SEC2966
1337	changeDenominator sing_1363.htm#SEC1439
1338	changechar sing_1109.htm#SEC1185
1339	changeord sing_1110.htm#SEC1186
1340	changeordTo sing_1133.htm#SEC1209
1341	changes sing_2900.htm#SEC2976
1342	changevar sing_1111.htm#SEC1187
1343	char sing_213.htm#SEC253
1344	charInfo sing_577.htm#SEC629
1345	charVariety sing_576.htm#SEC628
1346	char_series sing_214.htm#SEC254
1347	characteristic exponents sing_1584.htm#IDX687
1348	characteristic exponents sing_1585.htm#IDX692
1349	characteristic exponents sing_1586.htm#IDX695
1350	characteristic exponents sing_1587.htm#IDX699
1351	characteristic exponents sing_1671.htm#IDX805
1352	characteristic polynomial sing_2330.htm#IDX946
1353	characteristic variety sing_560.htm#IDX347
1354	characteristic variety sing_662.htm#IDX372
1355	charexp2conductor sing_1587.htm#SEC1663
1356	charexp2generators sing_1585.htm#SEC1661
1357	charexp2inter sing_1586.htm#SEC1662
1358	charexp2multseq sing_1584.htm#SEC1660
1359	charexp2poly sing_1588.htm#SEC1664
1360	charpoly sing_1192.htm#SEC1268
1361	charstr sing_215.htm#SEC255
1362	checkFactor sing_553.htm#SEC605
1363	checkRoot sing_548.htm#SEC600
1364	chern sing_2386.htm#SEC2462
1365	chern.lib sing_2381.htm#SEC2457
1366	chernCharPoly sing_2428.htm#SEC2504
1367	chernPoly sing_2427.htm#SEC2503
1368	chern_lib sing_2381.htm#SEC2457
1369	chineseRem sing_2005.htm#SEC2081
1370	chinrem sing_216.htm#SEC256
1371	chinrempoly sing_2805.htm#SEC2881
1372	chinrestp sing_2064.htm#SEC2140
1373	cimonom.lib sing_2443.htm#SEC2519
1374	cimonom_lib sing_2443.htm#SEC2519
1375	cisimplicial.lib sing_1230.htm#SEC1306
1376	cisimplicial_lib sing_1230.htm#SEC1306
1377	classification sing_2363.htm#IDX982
1378	classification sing_2447.htm#IDX990
1379	classify sing_1597.htm#SEC1673
1380	classify.lib sing_1595.htm#SEC1671
1381	classify2.lib sing_2447.htm#SEC2523
1382	classify2_lib sing_2447.htm#SEC2523
1383	classifyCeq sing_1614.htm#SEC1690
1384	classifyMapGerms.lib classifyMapGerms_lib sing_2459.htm#SEC2535
1385	classifyMapGerms_lib classifyMapGerms_lib sing_2459.htm#SEC2535
1386	classifySimpleMaps sing_2465.htm#SEC2541
1387	classifySimpleMaps1 sing_2466.htm#SEC2542
1388	classifyUnimodalMaps classifyUnimodalMaps sing_2467.htm#SEC2543
1389	classify_aeq.lib sing_2450.htm#SEC2526
1390	classify_aeq_lib sing_2450.htm#SEC2526
1391	classify_lib sing_1595.htm#SEC1671
1392	classifyceq.lib sing_1613.htm#IDX702
1393	classifyceq_lib sing_1613.htm#IDX703
1394	classifyci.lib sing_1615.htm#IDX704
1395	classifyci_lib sing_1615.htm#IDX705
1396	classifyicis sing_1616.htm#SEC1692
1397	classpoly sing_2426.htm#SEC2502
1398	cleanTmp sing_2281.htm#SEC2357
1399	cleanunit sing_1508.htm#SEC1584
1400	cleardenom sing_217.htm#SEC257
1401	close sing_218.htm#SEC258
1402	closed_points sing_1920.htm#SEC1996
1403	closetex sing_1887.htm#SEC1963
1404	closureFrac sing_1356.htm#SEC1432
1405	coDim sing_2461.htm#SEC2537
1406	coDimMap sing_2460.htm#SEC2536
1407	coHom sing_705.htm#SEC757
1408	codim sing_1709.htm#SEC1785
1409	codimension sing_2134.htm#SEC2210
1410	coding theory sing_955.htm#SEC1007
1411	coef sing_219.htm#SEC259
1412	coefficient sing_2293.htm#IDX873
1413	coefficient sing_2294.htm#IDX876
1414	coefficient sing_2295.htm#IDX880
1415	coefficient field sing_144.htm#SEC184
1416	coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45
1417	coefficients sing_2488.htm#IDX1029
1418	coefficients, long sing_912.htm#SEC964
1419	coeffmod sing_1982.htm#SEC2058
1420	coeffs sing_220.htm#SEC260
1421	coker sing_2691.htm#SEC2767
1422	colength of derivations curveColengthDerivations sing_2476.htm#IDX1010
1423	collectDiv sing_1553.htm#SEC1629
1424	colrank sing_1954.htm#SEC2030
1425	colred sing_1175.htm#SEC1251
1426	combinat.lib sing_2468.htm#SEC2544
1427	combinat_lib sing_2468.htm#SEC2544
1428	commRing sing_686.htm#SEC738
1429	comma sing_417.htm#SEC457
1430	command,custom Commands for user defined types sing_187.htm#SEC227
1431	command-line option, setting value of sing_361.htm#IDX278
1432	command-line option, value of sing_361.htm#IDX276
1433	command-line options, print all values of sing_361.htm#IDX275
1434	command-line options, short help Command line options sing_19.htm#IDX38
1435	commands (letterplace) Functions (letterplace) sing_797.htm#SEC849
1436	commands (plural) sing_458.htm#IDX299
1437	comment sing_36.htm#IDX108
1438	compare sing_2499.htm#IDX1049
1439	compare sing_2500.htm#IDX1051
1440	compare sing_2501.htm#IDX1055
1441	compare sing_2502.htm#IDX1058
1442	compare sing_2520.htm#IDX1096
1443	compare sing_2521.htm#IDX1098
1444	compareMatrix sing_2699.htm#SEC2775
1445	compareModules sing_2694.htm#SEC2770
1446	compareTasks sing_1140.htm#SEC1216
1447	compareVectors sing_2719.htm#SEC2795
1448	completeReduction sing_1787.htm#SEC1863
1449	complex sing_28.htm#IDX75
1450	complexClassify sing_2448.htm#SEC2524
1451	complexSingType sing_1611.htm#SEC1687
1452	complexType sing_2449.htm#SEC2525
1453	compregb.lib sing_1000.htm#SEC1076
1454	compregb_lib sing_1000.htm#SEC1076
1455	comprehensive Groebner system sing_1000.htm#IDX458
1456	compress sing_1153.htm#SEC1229
1457	computeAfaceOrbits sing_2609.htm#SEC2685
1458	computeConstant sing_1250.htm#SEC1326
1459	computeGromovWitten sing_1253.htm#SEC1329
1460	computeN sing_1557.htm#SEC1633
1461	computeV sing_1556.htm#SEC1632
1462	computemcm sing_1515.htm#SEC1591
1463	concat sing_1154.htm#SEC1230
1464	conductor sing_1364.htm#IDX619
1465	conductor sing_1587.htm#IDX698
1466	conductor sing_2474.htm#IDX1004
1467	conductor, degree sing_1671.htm#IDX808
1468	cone sing_189.htm#SEC229
1469	cone sing_2306.htm#IDX900
1470	cone sing_2307.htm#IDX902
1471	coneLink sing_2137.htm#SEC2213
1472	coneViaInequalities sing_2136.htm#SEC2212
1473	coneViaPoints sing_2135.htm#SEC2211
1474	conic, parametrization, rational point. sing_1492.htm#IDX668
1475	conicWithTangents sing_2257.htm#SEC2333
1476	constructH sing_1516.htm#SEC1592
1477	constructblwup sing_1517.htm#SEC1593
1478	constructible set sing_1047.htm#IDX517
1479	constructible set sing_1049.htm#IDX522
1480	constructible sets sing_1048.htm#IDX520
1481	constructible sets sing_1050.htm#IDX525
1482	constructlastblwup sing_1518.htm#SEC1594
1483	constructor derivationConstructor sing_2323.htm#IDX933
1484	constructor sing_2324.htm#IDX936
1485	constructor sing_2487.htm#IDX1025
1486	constructor sing_2510.htm#IDX1074
1487	constructor sing_2511.htm#IDX1076
1488	constructor sing_2512.htm#IDX1079
1489	constructor sing_2513.htm#IDX1082
1490	contact matrix sing_1586.htm#IDX694
1491	containedQ sing_1875.htm#SEC1951
1492	containment sing_2506.htm#IDX1065
1493	containsAsFace sing_2138.htm#SEC2214
1494	containsInCollection containsInCollection sing_2171.htm#SEC2247
1495	containsInSupport sing_2139.htm#SEC2215
1496	containsPositiveVector containsPositiveVector sing_2140.htm#SEC2216
1497	containsRelatively sing_2141.htm#SEC2217
1498	content sing_1083.htm#SEC1159
1499	contentSB, option sing_318.htm#IDX172
1500	continue Behavior of continue sing_385.htm#SEC425
1501	continue sing_419.htm#SEC459
1502	contraHom sing_706.htm#SEC758
1503	contract sing_221.htm#SEC261
1504	contraction derivationContraction sing_2523.htm#IDX1104
1505	contraction sing_2524.htm#IDX1106
1506	contraction sing_2525.htm#IDX1108
1507	contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2864.htm#IDX1214
1508	contributionBundle sing_2864.htm#SEC2940
1509	contributors sing_361.htm#IDX199
1510	control sing_1946.htm#SEC2022
1511	control.lib sing_1945.htm#SEC2021
1512	controlDim sing_1947.htm#SEC2023
1513	controlExample sing_1959.htm#SEC2035
1514	control_Matrix sing_1639.htm#SEC1715
1515	control_lib sing_1945.htm#SEC2021
1516	convertLeftToRightFraction convertLeftToRightFraction sing_758.htm#SEC810
1517	convertRightToLeftFraction convertRightToLeftFraction sing_757.htm#SEC809
1518	convertdata sing_1513.htm#SEC1589
1519	convexHull sing_2142.htm#SEC2218
1520	convexIntersection sing_2143.htm#SEC2219
1521	convloc sing_557.htm#SEC609
1522	coordinate change sing_2303.htm#IDX897
1523	coordinate change sing_2304.htm#IDX898
1524	coordinate change sing_2305.htm#IDX899
1525	coordinates sing_2102.htm#IDX850
1526	coords sing_2102.htm#SEC2178
1527	copyTask sing_1139.htm#SEC1215
1528	copyright sing_1.htm#IDX1
1529	corank sing_1598.htm#SEC1674
1530	cornerMonomials sing_1394.htm#SEC1470
1531	countPoints sing_2027.htm#SEC2103
1532	coverings sing_1252.htm#IDX572
1533	coverings sing_1253.htm#IDX576
1534	cpu sing_361.htm#IDX201
1535	cpu sing_361.htm#IDX272
1536	createBO sing_1544.htm#SEC1620
1537	createGradedRingHomomorphism createGradedRingHomomorphism sing_2738.htm#SEC2814
1538	createGroup sing_2731.htm#SEC2807
1539	createQuotientGroup sing_2732.htm#SEC2808
1540	createTask sing_1137.htm#SEC1213
1541	createTorsionFreeGroup createTorsionFreeGroup sing_2733.htm#SEC2809
1542	create_ring sing_222.htm#SEC262
1543	createlist sing_1526.htm#SEC1602
1544	cring sing_73.htm#SEC113
1545	cring declarations sing_74.htm#SEC114
1546	cring expressions sing_75.htm#SEC115
1547	cring operations sing_76.htm#SEC116
1548	cring related functions cring related functions sing_77.htm#SEC117
1549	crossprod sing_223.htm#SEC263
1550	crypto.lib sing_2000.htm#SEC2076
1551	crypto_lib sing_2000.htm#SEC2076
1552	crystallographicGroupC2MM crystallographicGroupC2MM sing_834.htm#SEC886
1553	crystallographicGroupCM crystallographicGroupCM sing_833.htm#SEC885
1554	crystallographicGroupP1 crystallographicGroupP1 sing_827.htm#SEC879
1555	crystallographicGroupP2 crystallographicGroupP2 sing_831.htm#SEC883
1556	crystallographicGroupP2GG crystallographicGroupP2GG sing_832.htm#SEC884
1557	crystallographicGroupP2MM crystallographicGroupP2MM sing_830.htm#SEC882
1558	crystallographicGroupP3 crystallographicGroupP3 sing_838.htm#SEC890
1559	crystallographicGroupP31M crystallographicGroupP31M sing_839.htm#SEC891
1560	crystallographicGroupP3M1 crystallographicGroupP3M1 sing_840.htm#SEC892
1561	crystallographicGroupP4 crystallographicGroupP4 sing_835.htm#SEC887
1562	crystallographicGroupP4GM crystallographicGroupP4GM sing_837.htm#SEC889
1563	crystallographicGroupP4MM crystallographicGroupP4MM sing_836.htm#SEC888
1564	crystallographicGroupP6 crystallographicGroupP6 sing_841.htm#SEC893
1565	crystallographicGroupP6MM crystallographicGroupP6MM sing_842.htm#SEC894
1566	crystallographicGroupPG crystallographicGroupPG sing_829.htm#SEC881
1567	crystallographicGroupPM crystallographicGroupPM sing_828.htm#SEC880
1568	cup sing_1266.htm#SEC1342
1569	cupproduct sing_1267.htm#SEC1343
1570	curve singularities sing_1577.htm#IDX681
1571	curve singularities sing_1665.htm#IDX803
1572	curve singularity sing_2472.htm#IDX999
1573	curveColengthDerivations curveColengthDerivations sing_2476.htm#SEC2552
1574	curveConductorMult sing_2474.htm#SEC2550
1575	curveDeligneNumber sing_2475.htm#SEC2551
1576	curveDeltaInv sing_2473.htm#SEC2549
1577	curveInv.lib sing_2472.htm#SEC2548
1578	curveInv_lib sing_2472.htm#SEC2548
1579	curvepar.lib sing_1618.htm#SEC1694
1580	curvepar_lib sing_1618.htm#SEC1694
1581	custom assignment Assignments for user defined types sing_188.htm#SEC228
1582	custom command Commands for user defined types sing_187.htm#SEC227
1583	custom type Definition of a user defined type sing_184.htm#SEC224
1584	customstd.lib sing_2335.htm#SEC2411
1585	customstd_lib sing_2335.htm#SEC2411
1586	cycleLength sing_2194.htm#SEC2270
1587	cyclePoints sing_2198.htm#SEC2274
1588	cyclic sing_1070.htm#SEC1146
1589	cyclic code Codes and the decoding problem sing_987.htm#SEC1046
1590	cyclotomic sing_1752.htm#SEC1828
1591	datetime sing_224.htm#SEC264
1592	dbprint sing_225.htm#SEC265
1593	deRham.lib sing_2477.htm#SEC2553
1594	deRhamCohom sing_574.htm#SEC626
1595	deRhamCohomIdeal sing_575.htm#SEC627
1596	deRhamCohomology sing_2478.htm#SEC2554
1597	deRham_lib sing_2477.htm#SEC2553
1598	debugLib, option sing_318.htm#IDX176
1599	debug_log sing_1608.htm#SEC1684
1600	debugger Source code debugger sing_66.htm#SEC103
1601	debugging library code Source code debugger sing_66.htm#SEC103
1602	dec1var sing_1324.htm#SEC1400
1603	decimal sing_2001.htm#SEC2077
1604	decode sing_1937.htm#SEC2013
1605	decodeCode sing_1939.htm#SEC2015
1606	decodeRandom sing_1938.htm#SEC2014
1607	decodeRandomFL sing_1942.htm#SEC2018
1608	decodeSV sing_1919.htm#SEC1995
1609	decodegb.lib sing_1924.htm#SEC2000
1610	decodegb_lib sing_1924.htm#SEC2000
1611	decoding, decoding problem Codes and the decoding problem sing_987.htm#SEC1047
1612	decoef sing_1967.htm#SEC2043
1613	decomposeVecField sing_2896.htm#SEC2972
1614	decomposition sing_2488.htm#IDX1027
1615	decomposition of modules sing_1317.htm#IDX602
1616	decomposition, numerical sing_1464.htm#IDX636
1617	decone sing_2306.htm#IDX901
1618	decone sing_2307.htm#IDX903
1619	def sing_88.htm#SEC128
1620	def declarations sing_89.htm#SEC129
1621	defRes, option sing_318.htm#IDX177
1622	default argument sing_44.htm#SEC81
1623	defineHomogeneous sing_2771.htm#SEC2847
1624	defined sing_226.htm#SEC266
1625	defl sing_1475.htm#SEC1551
1626	deform sing_1710.htm#SEC1786
1627	deform.lib sing_1629.htm#SEC1705
1628	deform_lib sing_1629.htm#SEC1705
1629	defring sing_1112.htm#SEC1188
1630	defringp sing_1114.htm#SEC1190
1631	defrings sing_1113.htm#SEC1189
1632	deg sing_227.htm#SEC267
1633	degBound sing_399.htm#SEC439
1634	degree Miscellaneous oddities sing_228.htm#SEC268
1635	degree sing_422.htm#IDX289
1636	degree sing_2503.htm#IDX1060
1637	degree sing_2505.htm#IDX1064
1638	degree lexicographical ordering sing_961.htm#IDX432
1639	degree of a polynomial Miscellaneous oddities sing_422.htm#IDX293
1640	degree reverse lexicographical ordering sing_961.htm#IDX430
1641	degreeDivisor sing_2534.htm#SEC2610
1642	degreeFormalDivisor sing_2542.htm#SEC2618
1643	degreepart sing_1827.htm#SEC1903
1644	delete sing_126.htm#SEC166
1645	delete sing_229.htm#SEC269
1646	delete sing_279.htm#SEC319
1647	deleteGenerator sing_589.htm#SEC641
1648	deleteSublist sing_1009.htm#SEC1085
1649	deligne number curveColengthDerivations sing_2472.htm#IDX1001
1650	deligne number sing_2475.htm#IDX1006
1651	deligne number sing_2476.htm#IDX1008
1652	delta sing_1677.htm#SEC1753
1653	delta invariant sing_1358.htm#IDX617
1654	delta invariant sing_1677.htm#IDX813
1655	delta invariant sing_2473.htm#IDX1002
1656	delta invariant. sing_1350.htm#IDX610
1657	delta invariant. sing_1351.htm#IDX613
1658	delta invariant. sing_1352.htm#IDX616
1659	deltaLoc sing_1358.htm#SEC1434
1660	denom_list sing_361.htm#IDX203
1661	denominator sing_230.htm#SEC270
1662	depth sing_1268.htm#SEC1344
1663	depthIdeal sing_1334.htm#SEC1410
1664	derivate sing_1784.htm#SEC1860
1665	derivation derivationConstructor sing_2320.htm#IDX924
1666	derivation sing_2508.htm#IDX1069
1667	derivation sing_2509.htm#IDX1073
1668	derivation sing_2510.htm#IDX1075
1669	derivation sing_2511.htm#IDX1077
1670	derivation sing_2512.htm#IDX1080
1671	derivation sing_2513.htm#IDX1083
1672	derivation sing_2522.htm#IDX1102
1673	derivationAdd sing_2516.htm#SEC2592
1674	derivationCheckList sing_2511.htm#SEC2587
1675	derivationConstructor derivationConstructor sing_2513.htm#SEC2589
1676	derivationContraction derivationContraction sing_2524.htm#SEC2600
1677	derivationContractionGen derivationContractionGen sing_2523.htm#SEC2599
1678	derivationEqu sing_2520.htm#SEC2596
1679	derivationEval sing_2522.htm#SEC2598
1680	derivationFromList sing_2510.htm#SEC2586
1681	derivationFromPoly sing_2512.htm#SEC2588
1682	derivationLie sing_2525.htm#SEC2601
1683	derivationMul sing_2519.htm#SEC2595
1684	derivationNeg sing_2518.htm#SEC2594
1685	derivationNeq sing_2521.htm#SEC2597
1686	derivationPrint sing_2515.htm#SEC2591
1687	derivationSub sing_2517.htm#SEC2593
1688	derivationToString sing_2514.htm#SEC2590
1689	desingularization sing_2628.htm#IDX1139
1690	desingularization sing_2629.htm#SEC2705
1691	det sing_231.htm#SEC271
1692	det_B sing_1194.htm#SEC1270
1693	detadj sing_1693.htm#SEC1769
1694	determinacy sing_2813.htm#SEC2889
1695	determinecenter sing_1498.htm#SEC1574
1696	detropicalise sing_2275.htm#SEC2351
1697	develop sing_1667.htm#SEC1743
1698	diag sing_1155.htm#SEC1231
1699	diagInvariants sing_1373.htm#SEC1449 62096
1700	diag_test sing_1190.htm#SEC1266
1701	diagonalizeMatrixSimul diagonalizeMatrixSimul sing_2897.htm#SEC2973
1702	diagonalizeVecField sing_2894.htm#SEC2970
1703	diagonalizeVecFieldLin diagonalizeVecFieldLin sing_2892.htm#SEC2968
1704	diff sing_232.htm#SEC272
1705	diffAlgebra sing_2481.htm#SEC2557
1706	diffAlgebraChangeOrd diffAlgebraChangeOrd sing_2485.htm#SEC2561
1707	diffAlgebraGens sing_2483.htm#SEC2559
1708	diffAlgebraListGen sing_2486.htm#SEC2562
1709	diffAlgebraStructure diffAlgebraStructure sing_2482.htm#SEC2558
1710	diffAlgebraUnivDerIdeal diffAlgebraUnivDerIdeal sing_2484.htm#SEC2560
1711	diffRat sing_685.htm#SEC737
1712	difference sing_2495.htm#IDX1043
1713	difference sing_2517.htm#IDX1091
1714	difference sing_2518.htm#IDX1093
1715	differential sing_2487.htm#IDX1026
1716	differential sing_2509.htm#IDX1071
1717	differential algebra diffAlgebraUnivDerIdeal sing_2480.htm#IDX1013
1718	differential algebra sing_2481.htm#IDX1014
1719	differential algebra sing_2482.htm#IDX1017
1720	differential algebra sing_2483.htm#IDX1018
1721	differential algebra sing_2484.htm#IDX1020
1722	differential forms sing_2480.htm#IDX1011
1723	differential forms sing_2481.htm#IDX1015
1724	differentials sing_2480.htm#IDX1012
1725	differentials sing_2481.htm#IDX1016
1726	difform.lib sing_2480.htm#SEC2556
1727	difformAdd sing_2494.htm#SEC2570
1728	difformCoef sing_2488.htm#SEC2564
1729	difformDeg sing_2503.htm#SEC2579
1730	difformDiff sing_2509.htm#SEC2585
1731	difformDiv sing_2498.htm#SEC2574
1732	difformEqu sing_2499.htm#SEC2575
1733	difformFromPoly sing_2487.htm#SEC2563
1734	difformGenToString sing_2489.htm#SEC2565
1735	difformHomogDecomp sing_2490.htm#SEC2566
1736	difformIsBigger sing_2501.htm#SEC2577
1737	difformIsGen sing_2493.htm#SEC2569
1738	difformIsHomog sing_2504.htm#SEC2580
1739	difformIsHomogDeg sing_2505.htm#SEC2581
1740	difformIsSmaller sing_2502.htm#SEC2578
1741	difformListCont sing_2506.htm#SEC2582
1742	difformListSort sing_2507.htm#SEC2583
1743	difformMul sing_2497.htm#SEC2573
1744	difformNeg sing_2496.htm#SEC2572
1745	difformNeq sing_2500.htm#SEC2576
1746	difformPrint sing_2492.htm#SEC2568
1747	difformSub sing_2495.htm#SEC2571
1748	difformToString sing_2491.htm#SEC2567
1749	difformUnivDer sing_2508.htm#SEC2584
1750	difform_lib sing_2480.htm#SEC2556
1751	difpoly2tex sing_1968.htm#SEC2044
1752	dim sing_233.htm#SEC273
1753	dim (plural) sing_461.htm#SEC501
1754	dimGradedPart sing_1566.htm#SEC1642 11262
1755	dimH sing_1565.htm#SEC1641 38534
1756	dimMon sing_1314.htm#SEC1390
1757	dimStack sing_2862.htm#SEC2938
1758	dim_slocus sing_1711.htm#SEC1787
1759	dimension sing_2144.htm#SEC2220
1760	dimension, moduli space of stable maps, rational curves dimStack sing_2862.htm#IDX1212
1761	dimensionOfLocalization dimensionOfLocalization sing_2592.htm#SEC2668
1762	direct_boolean_poly sing_2348.htm#SEC2424 49893
1763	direct_from_boolean_poly direct_from_boolean_poly sing_2354.htm#SEC2430 36941
1764	disc sing_1988.htm#SEC2064
1765	discr sing_1733.htm#SEC1809
1766	discrepancy sing_1551.htm#SEC1627
1767	discrim sing_1042.htm#SEC1118
1768	discussion of parametric ideal sing_1026.htm#IDX462
1769	disjoint sing_1027.htm#IDX464
1770	disp_zdd sing_2361.htm#SEC2437 41439
1771	displayCohom sing_1567.htm#SEC1643 22633
1772	displayHNE sing_1670.htm#SEC1746
1773	displayInvariants sing_1672.htm#SEC1748
1774	displayMultsequence sing_1674.htm#SEC1750
1775	displayPuiseuxExpansion displayPuiseuxExpansion sing_2250.htm#SEC2326
1776	displayTropicalLifting displayTropicalLifting sing_2248.htm#SEC2324
1777	distributed computing sing_1063.htm#IDX534
1778	distributed computing sing_1103.htm#IDX536
1779	distributed computing sing_1136.htm#IDX546
1780	div Miscellaneous oddities sing_81.htm#SEC121
1781	div sing_98.htm#SEC138
1782	div sing_155.htm#SEC195
1783	div sing_422.htm#IDX286
1784	divideUnits sing_1964.htm#SEC2040
1785	dividelist sing_1525.htm#SEC1601
1786	division sing_234.htm#SEC274
1787	division sing_1028.htm#IDX467
1788	division sing_1029.htm#IDX469
1789	division sing_2498.htm#IDX1048
1790	division (plural) sing_462.htm#SEC502
1791	divisor sing_2067.htm#SEC2143
1792	divisorplus sing_2528.htm#SEC2604
1793	divisors negativeformaldivisor sing_2527.htm#IDX1109
1794	divisors sing_2528.htm#IDX1110
1795	divisors sing_2529.htm#IDX1111
1796	divisors sing_2530.htm#IDX1112
1797	divisors sing_2531.htm#IDX1113
1798	divisors sing_2532.htm#IDX1114
1799	divisors sing_2533.htm#IDX1115
1800	divisors sing_2534.htm#IDX1116
1801	divisors sing_2535.htm#IDX1117
1802	divisors sing_2536.htm#IDX1118
1803	divisors sing_2537.htm#IDX1119
1804	divisors sing_2538.htm#IDX1120
1805	divisors sing_2539.htm#IDX1121
1806	divisors sing_2540.htm#IDX1122
1807	divisors sing_2541.htm#IDX1123
1808	divisors sing_2542.htm#IDX1124
1809	divisors, polyhedra sing_2543.htm#IDX1125
1810	divisors, polyhedra sing_2544.htm#IDX1126
1811	divisors, polyhedra sing_2545.htm#IDX1127
1812	divisors.lib sing_2526.htm#SEC2602
1813	divisors_lib sing_2526.htm#SEC2602
1814	dmod.lib sing_537.htm#SEC589
1815	dmodAction sing_680.htm#SEC732
1816	dmodActionRat sing_681.htm#SEC733
1817	dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_673.htm#SEC725
1818	dmod_lib sing_537.htm#SEC589
1819	dmodapp.lib sing_560.htm#SEC612
1820	dmodapp_lib sing_560.htm#SEC612
1821	dmodideal.lib sing_593.htm#SEC645
1822	dmodideal_lib sing_593.htm#SEC645
1823	dmodloc.lib sing_662.htm#IDX365
1824	dmodloc_lib sing_662.htm#IDX366
1825	dmodoublext sing_707.htm#SEC759
1826	dmodvar.lib sing_601.htm#SEC653
1827	dmodvar_lib sing_601.htm#SEC653
1828	double sing_2072.htm#SEC2148
1829	doubleExt sing_780.htm#SEC832
1830	downloading Download instructions sing_2908.htm#SEC2999
1831	dp, global ordering sing_961.htm#IDX431
1832	drawNewtonSubdivision drawNewtonSubdivision sing_2253.htm#SEC2329
1833	drawTropicalCurve sing_2252.htm#SEC2328
1834	ds, local ordering sing_962.htm#IDX441
1835	dsum sing_1156.htm#SEC1232
1836	dualCone sing_2145.htm#SEC2221
1837	dualConic sing_2277.htm#SEC2353
1838	dualPart sing_2434.htm#SEC2510
1839	dualPartition sing_2875.htm#SEC2951
1840	dualPolytope sing_2184.htm#SEC2260
1841	dualSheaf sing_2853.htm#SEC2929
1842	dual_code sing_1921.htm#SEC1997
1843	dump sing_235.htm#SEC275
1844	dyckGroup1 sing_843.htm#SEC895
1845	dyckGroup2 sing_844.htm#SEC896
1846	dyckGroup3 sing_845.htm#SEC897
1847	dynamic geometry sing_1035.htm#IDX491
1848	dynamic geometry sing_1036.htm#IDX494
1849	ecart sing_2075.htm#SEC2151
1850	echo sing_400.htm#SEC440
1851	eexgcdN sing_2002.htm#SEC2078
1852	effective sing_2536.htm#SEC2612
1853	egcdMain sing_1868.htm#SEC1944
1854	ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2204.htm#SEC2280
1855	ehrhartRing sing_1369.htm#SEC1445 16966
1856	eigenvals sing_1202.htm#SEC1278
1857	eigenvalue sing_331.htm#SEC371
1858	eigenvalue sing_1202.htm#IDX552
1859	eigenvalues sing_1452.htm#SEC1528
1860	elemSymmId sing_1071.htm#SEC1147
1861	elim sing_1239.htm#SEC1315
1862	elim.lib sing_1236.htm#SEC1312
1863	elim1 sing_1240.htm#SEC1316
1864	elim2 sing_1241.htm#SEC1317
1865	elimRing sing_1238.htm#SEC1314
1866	elimWeight sing_722.htm#SEC774
1867	elim_lib sing_1236.htm#SEC1312
1868	eliminate sing_236.htm#SEC276
1869	eliminate (plural) sing_463.htm#SEC503
1870	eliminateNC sing_717.htm#SEC769
1871	elimination sing_716.htm#IDX380
1872	elimlinearpart sing_1828.htm#SEC1904
1873	elimpart sing_1829.htm#SEC1905
1874	elimpartanyr sing_1830.htm#SEC1906
1875	elimrep sing_1506.htm#SEC1582
1876	elliptic curve sing_1249.htm#IDX568
1877	elliptic curves sing_1246.htm#IDX562
1878	elliptic curves sing_1252.htm#IDX571
1879	elliptic curves sing_1253.htm#IDX575
1880	ellipticAdd sing_2023.htm#SEC2099
1881	ellipticAllPoints sing_2028.htm#SEC2104
1882	ellipticMult sing_2024.htm#SEC2100
1883	ellipticNF sing_2201.htm#SEC2277
1884	ellipticNFDB sing_2202.htm#SEC2278
1885	ellipticRandomCurve sing_2025.htm#SEC2101
1886	ellipticRandomPoint sing_2026.htm#SEC2102
1887	ellipticcovers.lib sing_1246.htm#IDX556
1888	ellipticcovers_lib sing_1246.htm#IDX557
1889	else sing_390.htm#SEC430
1890	embedMat sing_748.htm#SEC800
1891	emptyFan sing_2172.htm#SEC2248
1892	encode sing_1929.htm#SEC2005
1893	endomorphism filtration sing_1651.htm#IDX779
1894	endvfilt sing_1651.htm#SEC1727
1895	engine sing_590.htm#SEC642
1896	ensureLeftNcfrac sing_695.htm#SEC747
1897	ensureRightNcfrac sing_696.htm#SEC748
1898	envelop FamElemsAtEnvCompPoints sing_1037.htm#SEC1113
1899	envelop sing_1037.htm#IDX497
1900	envelop sing_1038.htm#IDX500
1901	envelop sing_1040.htm#IDX505
1902	envelop sing_1041.htm#IDX509
1903	envelope sing_464.htm#SEC504
1904	enveloping algebra sing_361.htm#IDX207
1905	enveloping algebra sing_495.htm#IDX303
1906	environment variable, DISPLAY The online help system sing_16.htm#IDX29
1907	environment variables Used environment variables sing_2909.htm#SEC3000
1908	equal sing_2499.htm#IDX1050
1909	equal sing_2500.htm#IDX1052
1910	equal sing_2520.htm#IDX1097
1911	equal sing_2521.htm#IDX1099
1912	equalJinI sing_1594.htm#SEC1670
1913	equalMultiDeg sing_2764.htm#SEC2840
1914	equations sing_2146.htm#SEC2222
1915	equiRadical sing_1410.htm#SEC1486
1916	equidim sing_1412.htm#SEC1488
1917	equidimMax sing_1413.htm#SEC1489
1918	equidimMaxEHV sing_1414.htm#SEC1490
1919	equidimZ sing_1425.htm#SEC1501
1920	equising.lib sing_1634.htm#SEC1710
1921	equising_lib sing_1634.htm#SEC1710
1922	equisingular Tjurina number sing_1577.htm#IDX686
1923	equisingularity ideal sing_1636.htm#IDX706
1924	equisingularity stratum sing_1637.htm#IDX707
1925	error recovery sing_15.htm#SEC21
1926	errorInsert sing_1932.htm#SEC2008
1927	errorRand sing_1933.htm#SEC2009
1928	errormap sing_2568.htm#SEC2644
1929	esIdeal sing_1636.htm#SEC1712
1930	esStratum sing_1637.htm#SEC1713
1931	essential sing_2310.htm#IDX906
1932	essential sing_2311.htm#IDX907
1933	eta sing_2196.htm#SEC2272
1934	euler sing_1981.htm#SEC2057
1935	eulerChProj sing_2424.htm#SEC2500
1936	eval sing_237.htm#SEC277
1937	evalJacobianAtBox sing_2824.htm#SEC2900
1938	evalPolyAtBox sing_2823.htm#SEC2899
1939	evaluateFormalDivisor evaluateFormalDivisor sing_2538.htm#SEC2614
1940	evaluatePDivisor sing_2544.htm#SEC2620
1941	evaluateProduct sing_2619.htm#SEC2695
1942	evaluate_reynolds sing_1757.htm#SEC1833
1943	evaluation sing_2522.htm#IDX1101
1944	evalutateIntegral sing_1251.htm#SEC1327
1945	example sing_239.htm#SEC279
1946	example sing_2312.htm#IDX908
1947	example sing_2313.htm#IDX910
1948	example sing_2314.htm#IDX912
1949	example sing_2315.htm#IDX914
1950	example sing_2316.htm#IDX916
1951	example sing_2317.htm#IDX918
1952	example sing_2318.htm#IDX921
1953	execute sing_240.htm#SEC280
1954	exit sing_394.htm#SEC434
1955	exp2pt sing_1969.htm#SEC2045
1956	expo sing_1993.htm#SEC2069
1957	exponents sing_2322.htm#IDX929
1958	export sing_387.htm#SEC427
1959	exportNuminvs sing_1377.htm#SEC1453 10423
1960	exportto sing_388.htm#SEC428
1961	expp sing_2873.htm#SEC2949
1962	expression list sing_72.htm#IDX128
1963	expression list sing_426.htm#IDX296
1964	ext-module purityfiltration_lib sing_772.htm#IDX386
1965	extcurve sing_1915.htm#SEC1991
1966	extdevelop sing_1668.htm#SEC1744
1967	extendGC sing_1034.htm#SEC1110
1968	extendWeyl sing_674.htm#SEC726
1969	extendedTensor sing_723.htm#SEC775
1970	extendpoly sing_1033.htm#SEC1109
1971	extendring sing_1115.htm#SEC1191
1972	extension of rings sing_1430.htm#IDX628
1973	exterior basis sing_1181.htm#IDX549
1974	exterior power sing_1183.htm#IDX551
1975	exteriorBasis sing_1181.htm#SEC1257
1976	exteriorPower sing_1183.htm#SEC1259
1977	extgcd sing_241.htm#SEC281
1978	extractS sing_600.htm#SEC652
1979	fVector sing_2175.htm#SEC2251
1980	fVectorP sing_2205.htm#SEC2281
1981	facFirstShift sing_655.htm#SEC707
1982	facFirstWeyl sing_651.htm#SEC703
1983	facGBIdeal sing_1395.htm#SEC1471
1984	facShift sing_654.htm#SEC706
1985	facSubWeyl sing_653.htm#SEC705
1986	facWeyl sing_650.htm#SEC702
1987	faceContaining sing_2147.htm#SEC2223
1988	facetVertexLatticeDistances facetVertexLatticeDistances sing_2206.htm#SEC2282
1989	facetWidth sing_2207.htm#SEC2283
1990	facetWidths sing_2208.htm#SEC2284
1991	facets sing_2148.htm#SEC2224
1992	facstd sing_242.htm#SEC282
1993	factmodd sing_243.htm#SEC283
1994	factor sing_325.htm#SEC365
1995	factorH sing_1024.htm#SEC1100
1996	factorLenstraECM sing_2032.htm#SEC2108
1997	factorMain sing_1869.htm#SEC1945
1998	factorgroup sing_2754.htm#SEC2830
1999	factorial sing_1010.htm#SEC1086
2000	factorization sing_326.htm#SEC366
2001	factorization sing_1211.htm#IDX553
2002	factorize sing_244.htm#SEC284
2003	factorize sing_325.htm#SEC365
2004	factory sing_1.htm#IDX2
2005	fan sing_190.htm#SEC230
2006	fan sing_2188.htm#IDX855
2007	fanViaCones sing_2173.htm#SEC2249
2008	farey sing_245.htm#SEC285
2009	fareypoly sing_2547.htm#SEC2623
2010	fastExpt sing_1977.htm#SEC2053
2011	fastHC, option sing_318.htm#IDX153
2012	fastelim sing_1831.htm#SEC1907
2013	fetch sing_246.htm#SEC286
2014	fetch (plural) sing_465.htm#SEC505
2015	fetchall sing_1116.htm#SEC1192
2016	ffmodStd sing_2553.htm#SEC2629
2017	ffmodstd.lib sing_2546.htm#SEC2622
2018	ffmodstd_lib sing_2546.htm#SEC2622
2019	ffsolve sing_1820.htm#SEC1896
2020	ffsolve.lib sing_1819.htm#SEC1895
2021	ffsolve_lib sing_1819.htm#SEC1895
2022	fglm sing_247.htm#SEC287
2023	fglm sing_358.htm#IDX187
2024	fglm_solve sing_1847.htm#SEC1923
2025	fglmquot sing_248.htm#SEC288
2026	fibonacci sing_1011.htm#SEC1087
2027	fibonacciGroup sing_846.htm#SEC898
2028	field sing_144.htm#SEC184
2029	file, .singularrc sing_20.htm#IDX71
2030	filecmd sing_249.htm#SEC289
2031	filtration purityfiltration_lib sing_772.htm#IDX387
2032	finalCharts sing_1530.htm#SEC1606
2033	find sing_250.htm#SEC290
2034	findAuto sing_609.htm#SEC661
2035	findInvo sing_607.htm#SEC659
2036	findInvoDiag sing_608.htm#SEC660
2037	findOrientedBoundary findOrientedBoundary sing_2197.htm#SEC2273
2038	findTorsion sing_1958.htm#SEC2034
2039	find_first_primitive_root find_first_primitive_root sing_2036.htm#SEC2112
2040	find_index sing_2040.htm#SEC2116
2041	findifs.lib sing_1965.htm#SEC2041
2042	findifs_example sing_1966.htm#SEC2042
2043	findifs_lib sing_1965.htm#SEC2041
2044	findimAlgebra sing_732.htm#SEC784
2045	finduni sing_251.htm#SEC291
2046	findvars sing_1832.htm#SEC1908
2047	finite field sing_144.htm#SEC184
2048	finite field sing_1819.htm#IDX828
2049	finiteDiagInvariants finiteDiagInvariants sing_1372.htm#SEC1448 3508
2050	finitediff.lib sing_2554.htm#IDX1128
2051	finitediff_lib sing_2554.htm#IDX1129
2052	finitely presented algebra sing_814.htm#IDX394
2053	finitely presented algebra sing_820.htm#IDX400
2054	finitely presented algebra sing_849.htm#IDX403
2055	finitely presented algebra sing_856.htm#IDX415
2056	finitely presented algebra sing_870.htm#IDX416
2057	finitely presented algebra, standard finitely presented algebra Free associative algebras sing_808.htm#IDX393
2058	finitely presented group sing_820.htm#IDX401
2059	finitenessTest sing_1225.htm#SEC1301
2060	finiterep sing_1810.htm#SEC1886
2061	finvar.lib sing_1745.htm#SEC1821
2062	finvar_lib sing_1745.htm#SEC1821
2063	first index is 1 sing_421.htm#SEC461
2064	firstoct sing_1880.htm#SEC1956
2065	fitting sing_1271.htm#SEC1347
2066	fixed points, moduli space of stable maps, graph fixedPoints sing_2863.htm#IDX1213
2067	fixedPoints sing_2863.htm#SEC2939
2068	fl2poly sing_587.htm#SEC639
2069	flatten sing_1157.htm#SEC1233
2070	flatteningStrat sing_1272.htm#SEC1348
2071	flintQ sing_252.htm#SEC292
2072	floating point sing_1125.htm#IDX539
2073	for sing_389.htm#SEC429
2074	formal linear representations sing_873.htm#IDX424
2075	formaldivisorplus sing_2539.htm#SEC2615
2076	forward sing_2560.htm#SEC2636
2077	fourier sing_582.htm#SEC634
2078	fouriersystem sing_2571.htm#SEC2647
2079	fpadim.lib sing_814.htm#SEC866
2080	fpadim_lib sing_814.htm#SEC866
2081	fpalgebras.lib sing_820.htm#SEC872
2082	fpalgebras_lib sing_820.htm#SEC872
2083	fpaprops.lib sing_849.htm#SEC901
2084	fpaprops_lib sing_849.htm#SEC901
2085	fprintf sing_254.htm#SEC294
2086	fracStatus sing_753.htm#SEC805
2087	framed sheaves sing_2578.htm#IDX1136
2088	frandwalk sing_2836.htm#SEC2912
2089	free sing_2321.htm#IDX926
2090	free sing_2322.htm#IDX928
2091	free associative algebra sing_820.htm#IDX399
2092	free associative algebra sing_856.htm#IDX411
2093	free associative algebra, tensor algebra Free associative algebras sing_808.htm#SEC860
2094	free noncommutative Groebner basis sing_856.htm#IDX413
2095	freeAlgebra (letterplace) freeAlgebra (letterplace) sing_798.htm#SEC850
2096	freeModule sing_2671.htm#SEC2747
2097	freeModule2Module sing_2700.htm#SEC2776
2098	freegb.lib sing_856.htm#SEC908
2099	freegb_lib sing_856.htm#SEC908
2100	freemodule sing_255.htm#SEC295
2101	freerank sing_1073.htm#SEC1149
2102	fres sing_256.htm#SEC296
2103	from_boolean_constant from_boolean_constant sing_2352.htm#SEC2428 44881
2104	from_boolean_ideal sing_2356.htm#SEC2432 62698
2105	from_boolean_poly sing_2353.htm#SEC2429 27864
2106	from_boolean_set sing_2357.htm#SEC2433 60615
2107	frwalk sing_257.htm#SEC297
2108	full representation sing_1033.htm#IDX483
2109	full representation sing_1034.htm#IDX488
2110	fullDimImages sing_2600.htm#SEC2676
2111	fullFan sing_2174.htm#SEC2250
2112	fullSerreRelations sing_823.htm#SEC875
2113	fullSpace sing_2129.htm#SEC2205
2114	furtherInvar sing_1789.htm#SEC1865
2115	further_hn_proc sing_1685.htm#SEC1761
2116	fwalk sing_1258.htm#SEC1334
2117	galois field sing_144.htm#SEC184
2118	gauss_col sing_1166.htm#SEC1242
2119	gauss_nf sing_1197.htm#SEC1273
2120	gauss_row sing_1167.htm#SEC1243
2121	gaussred sing_1195.htm#SEC1271
2122	gaussred_pivot sing_1196.htm#SEC1272
2123	gcd sing_258.htm#SEC298
2124	gcdMon sing_1303.htm#SEC1379
2125	gcddivisor sing_2068.htm#SEC2144
2126	gen sing_259.htm#SEC299
2127	genMDSMat sing_1935.htm#SEC2011
2128	genSymId sing_1449.htm#SEC1525
2129	general error-locator polynomial sing_988.htm#SEC1053
2130	general neron. sing_2628.htm#IDX1140
2131	general weighted lexicographical ordering sing_962.htm#IDX447
2132	general weighted reverse lexicographical ordering Local orderings sing_962.htm#IDX444
2133	general.lib sing_1003.htm#SEC1079
2134	generalOrder sing_2093.htm#SEC2169
2135	general_lib sing_1003.htm#SEC1079
2136	generateG sing_2031.htm#SEC2107
2137	generator derivationContractionGen sing_2483.htm#IDX1019
2138	generator sing_2493.htm#IDX1039
2139	generator sing_2523.htm#IDX1105
2140	generators sing_1585.htm#IDX690
2141	generators sing_2486.htm#IDX1023
2142	generators sing_2488.htm#IDX1028
2143	generators sing_2489.htm#IDX1032
2144	generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2149.htm#SEC2225
2145	generatorsOfSpan sing_2150.htm#SEC2226
2146	generic representation sing_1033.htm#IDX482
2147	genericid sing_1091.htm#SEC1167
2148	genericity sing_1955.htm#SEC2031
2149	genericmat sing_1158.htm#SEC1234
2150	genoutput sing_1519.htm#SEC1595
2151	genus sing_1354.htm#SEC1430
2152	geometrical locus FamElemsAtEnvCompPoints sing_1035.htm#IDX489
2153	geometrical locus sing_1036.htm#IDX492
2154	geometrical locus sing_1037.htm#IDX495
2155	geometrical locus sing_1038.htm#IDX498
2156	geometrical locus sing_1039.htm#IDX501
2157	geometrical locus sing_1040.htm#IDX503
2158	geometrical locus sing_1041.htm#IDX507
2159	getArguments sing_1148.htm#SEC1224
2160	getCommand sing_1147.htm#SEC1223
2161	getCone sing_2176.htm#SEC2252
2162	getGradingGroup sing_2729.htm#SEC2805
2163	getLattice sing_2730.htm#SEC2806
2164	getLinearForms sing_2151.htm#SEC2227
2165	getModuleGrading sing_2740.htm#SEC2816
2166	getMultiplicity sing_2152.htm#SEC2228
2167	getOneVar sing_1362.htm#SEC1438
2168	getResult sing_1149.htm#SEC1225
2169	getSmallest sing_1361.htm#SEC1437
2170	getState sing_1150.htm#SEC1226
2171	getVariableWeights sing_2728.htm#SEC2804
2172	getcores sing_1106.htm#SEC1182
2173	getdump sing_260.htm#SEC300
2174	getenv sing_361.htm#IDX209
2175	gfan.lib sing_2128.htm#SEC2204
2176	gfan_lib sing_2128.htm#SEC2204
2177	gfanlib sing_1.htm#IDX9
2178	gitCone sing_2627.htm#SEC2703
2179	gitfan.lib sing_2597.htm#SEC2673
2180	gitfan_lib sing_2597.htm#SEC2673
2181	gkdim.lib sing_614.htm#SEC666
2182	gkdim_lib sing_614.htm#SEC666
2183	global sing_210.htm#IDX133
2184	global Bernstein-Sato ideal sing_593.htm#IDX352
2185	global Bernstein-Sato polynomial sing_502.htm#IDX310
2186	global Bernstein-Sato polynomial sing_537.htm#IDX328
2187	global Bernstein-Sato polynomial for variety sing_601.htm#IDX360
2188	global homological dimension sing_849.htm#IDX408
2189	globalSections sing_2533.htm#SEC2609
2190	gmscoeffs sing_1643.htm#SEC1719
2191	gmsnf sing_1642.htm#SEC1718
2192	gmspoly.lib sing_1662.htm#SEC1738
2193	gmspoly_lib sing_1662.htm#SEC1738
2194	gmsring sing_1641.htm#SEC1717
2195	gmssing.lib sing_1640.htm#SEC1716
2196	gmssing_lib sing_1640.htm#SEC1716
2197	goettsche.lib sing_2578.htm#SEC2654
2198	goettsche_lib sing_2578.htm#SEC2654
2199	good basis sing_1640.htm#IDX718
2200	good basis sing_1650.htm#IDX773
2201	good basis sing_1662.htm#IDX789
2202	good basis sing_1664.htm#IDX800
2203	goodBasis sing_1664.htm#SEC1740
2204	gorensteinIndex sing_2209.htm#SEC2285
2205	gorensteinVector sing_2210.htm#SEC2286
2206	graal.lib sing_2590.htm#SEC2666
2207	graalMixed sing_2591.htm#SEC2667
2208	graal_lib sing_2590.htm#SEC2666
2209	gradeNumber sing_776.htm#SEC828
2210	graded sing_2486.htm#IDX1024
2211	graded Hilbert series sing_870.htm#IDX418
2212	graded Weyl algebra sing_502.htm#IDX313
2213	graded algebra sing_2372.htm#IDX985
2214	graded module, graded piece sing_1566.htm#IDX676
2215	graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2630.htm#IDX1141
2216	graded modules, handling of Handling graded modules sing_927.htm#SEC979
2217	graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2668.htm#IDX1143
2218	gradedModules.lib sing_2630.htm#SEC2706
2219	gradedModules_lib sing_2630.htm#SEC2706
2220	gradiator sing_2773.htm#SEC2849
2221	graph sing_1247.htm#IDX566
2222	graph sing_1248.htm#IDX567
2223	graph sing_2858.htm#IDX1208
2224	graph sing_2859.htm#IDX1209
2225	graphics.lib sing_1882.htm#SEC1958
2226	graphics_lib sing_1882.htm#SEC1958
2227	graphviz sing_1.htm#IDX13
2228	graver4ti2 sing_1447.htm#SEC1523 39635
2229	grconcat sing_2653.htm#SEC2729
2230	grdeg sing_2633.htm#SEC2709
2231	grgens sing_2642.htm#SEC2718
2232	grgroebner sing_2652.htm#SEC2728
2233	grlift sing_2650.htm#SEC2726
2234	grlifting sing_2657.htm#SEC2733
2235	grlifting2 sing_2658.htm#SEC2734
2236	grlifting3 sing_2660.htm#SEC2736
2237	grneg sing_2663.htm#SEC2739
2238	grobcov sing_1026.htm#SEC1102
2239	grobcov.lib sing_1025.htm#SEC1101
2240	grobcov_lib sing_1025.htm#SEC1101
2241	grobj sing_2631.htm#SEC2707
2242	groebner sing_261.htm#SEC301
2243	groebner sing_919.htm#SEC971
2244	groebner basis computations sing_261.htm#IDX147
2245	groebnerComplex sing_2288.htm#SEC2364
2246	groebnerCone sing_2282.htm#SEC2358
2247	groebnerFan sing_2287.htm#SEC2363
2248	gromovWitten sing_1252.htm#SEC1328
2249	grorder sing_2644.htm#SEC2720
2250	ground field sing_144.htm#SEC184
2251	groupActionOnHashes sing_2615.htm#SEC2691
2252	groupActionOnQImage sing_2614.htm#SEC2690
2253	group_reynolds sing_1753.htm#SEC1829
2254	growth of algebra sing_849.htm#IDX406
2255	grpower sing_2640.htm#SEC2716
2256	grpres sing_2643.htm#SEC2719
2257	grprod sing_2651.htm#SEC2727
2258	grrange sing_2662.htm#SEC2738
2259	grres sing_2649.htm#SEC2725
2260	grrndmap sing_2655.htm#SEC2731
2261	grrndmap2 sing_2656.htm#SEC2732
2262	grrndmat sing_2654.htm#SEC2730
2263	grshift sing_2635.htm#SEC2711
2264	grsum sing_2639.htm#SEC2715
2265	grsyz sing_2648.htm#SEC2724
2266	grtest sing_2632.htm#SEC2708
2267	grtranspose sing_2641.htm#SEC2717
2268	grtranspose1 sing_2645.htm#SEC2721
2269	grtwist sing_2637.htm#SEC2713
2270	grtwists sing_2638.htm#SEC2714
2271	grview sing_2634.htm#SEC2710
2272	grwalk.lib sing_1257.htm#SEC1333
2273	grwalk_lib sing_1257.htm#SEC1333
2274	grzero sing_2636.htm#SEC2712
2275	gwalk sing_1263.htm#SEC1339
2276	hStarVector sing_2211.htm#SEC2287
2277	hVector sing_2212.htm#SEC2288
2278	h_increasing_knapsack h_increasing_knapsack sing_2054.htm#SEC2130
2279	hardware platform sing_361.htm#IDX268
2280	hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1129.htm#SEC1205
2281	hasCommutativeVars sing_1126.htm#SEC1202
2282	hasGlobalOrdering sing_1127.htm#SEC1203
2283	hasLeftDenom sing_689.htm#SEC741
2284	hasMixedOrdering sing_1128.htm#SEC1204
2285	hasNumericCoeffs sing_1125.htm#SEC1201
2286	hasRightDenom sing_690.htm#SEC742
2287	hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1130.htm#SEC1206
2288	hashToCone sing_2625.htm#SEC2701
2289	hashesToFan sing_2626.htm#SEC2702
2290	headStand sing_1179.htm#SEC1255
2291	heightZ sing_1424.htm#SEC1500
2292	help sing_262.htm#SEC302
2293	help browsers The online help system sing_16.htm#IDX22
2294	help browsers, dummy The online help system sing_16.htm#IDX25
2295	help browsers, dummy sing_16.htm#IDX27
2296	help browsers, emacs The online help system sing_16.htm#IDX26
2297	help browsers, html The online help system sing_16.htm#IDX23
2298	help browsers, setting command to use The online help system sing_16.htm#IDX30
2299	help browsers, setting the sing_361.htm#IDX194
2300	help, accessing over the net Command line options sing_19.htm#IDX42
2301	help, online help system The online help system sing_16.htm#SEC22
2302	hermiteNormalForm sing_2774.htm#SEC2850
2303	hess.lib sing_2665.htm#SEC2741
2304	hess_lib sing_2665.htm#SEC2741
2305	hessenberg sing_361.htm#IDX215
2306	hessenberg sing_1201.htm#SEC1277
2307	highcorner sing_263.htm#SEC303
2308	hilb sing_264.htm#SEC304
2309	hilbPoly sing_1089.htm#SEC1165
2310	hilbert4ti2 sing_1446.htm#SEC1522 13993
2311	hilbertBasis sing_2213.htm#SEC2289
2312	hilbertSeries sing_2776.htm#SEC2852
2313	hilbvec sing_1833.htm#SEC1909
2314	hnexpansion sing_1666.htm#SEC1742
2315	hnoether.lib sing_1665.htm#SEC1741
2316	hnoether_lib sing_1665.htm#SEC1741
2317	holonomic rank sing_662.htm#IDX368
2318	holonomicRank sing_666.htm#SEC718
2319	hom sing_2712.htm#SEC2788
2320	hom_kernel sing_1279.htm#SEC1355
2321	homog sing_265.htm#SEC305
2322	homog sing_2504.htm#IDX1062
2323	homog_part sing_2870.htm#SEC2946
2324	homog_parts sing_2871.htm#SEC2947
2325	homogeneitySpace sing_2284.htm#SEC2360
2326	homogeneous sing_2490.htm#IDX1033
2327	homogeneous sing_2504.htm#IDX1061
2328	homogeneous sing_2505.htm#IDX1063
2329	homogeneous decomposition sing_2490.htm#IDX1034
2330	homogfacFirstQWeyl sing_658.htm#SEC710
2331	homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_660.htm#SEC712
2332	homogfacNthQWeyl sing_657.htm#SEC709
2333	homogfacNthQWeyl_all homogfacNthQWeyl_all sing_659.htm#SEC711
2334	homogfacNthWeyl sing_656.htm#SEC708
2335	homolog.lib sing_1264.htm#SEC1340
2336	homolog_lib sing_1264.htm#SEC1340
2337	homology sing_1274.htm#SEC1350
2338	homomorphism sing_2696.htm#SEC2772
2339	howto, download Download instructions sing_2908.htm#SEC2999
2340	howto, install on Macintosh Macintosh installation instructions sing_2912.htm#SEC3003
2341	howto, install on Unix Unix installation instructions sing_2910.htm#SEC3001
2342	howto, install on Windows Windows installation instructions sing_2911.htm#SEC3002
2343	hres sing_266.htm#SEC306
2344	html, default help The online help system sing_16.htm#IDX24
2345	hyperel.lib sing_2061.htm#SEC2137
2346	hyperel_lib sing_2061.htm#SEC2137
2347	hyperplane sing_2291.htm#IDX866
2348	hyperplane arrangement sing_537.htm#IDX334
2349	hypersurface singularity sing_1692.htm#IDX818
2350	iMult sing_1357.htm#SEC1433
2351	id sing_2669.htm#SEC2745
2352	id2mod sing_1085.htm#SEC1161
2353	ideal sing_90.htm#SEC130
2354	ideal (plural) sing_427.htm#SEC467
2355	ideal declarations sing_91.htm#SEC131
2356	ideal declarations (plural) ideal declarations (plural) sing_428.htm#SEC468
2357	ideal expressions sing_92.htm#SEC132
2358	ideal expressions (plural) ideal expressions (plural) sing_429.htm#SEC469
2359	ideal operations sing_93.htm#SEC133
2360	ideal operations (plural) ideal operations (plural) sing_430.htm#SEC470
2361	ideal related functions ideal related functions sing_94.htm#SEC134
2362	ideal related functions (plural) ideal related functions (plural) sing_431.htm#SEC471
2363	ideal, toric sing_975.htm#SEC1032
2364	idealSplit sing_1840.htm#SEC1916
2365	ideals Miscellaneous oddities sing_422.htm#IDX290
2366	idealsimplify sing_1593.htm#SEC1669
2367	identifier Identifier resolution sing_423.htm#SEC463
2368	identifyvar sing_1501.htm#SEC1577
2369	if sing_390.htm#SEC430
2370	image sing_2692.htm#SEC2768
2371	imageLattice sing_2742.htm#SEC2818
2372	image_of_variety sing_1781.htm#SEC1857
2373	imap sing_267.htm#SEC307
2374	imap (plural) sing_466.htm#SEC506
2375	imapall sing_1117.htm#SEC1193
2376	impart sing_268.htm#SEC308
2377	importfrom sing_391.htm#SEC431
2378	inCenter sing_526.htm#SEC578
2379	inCentralizer sing_527.htm#SEC579
2380	inForm sing_569.htm#SEC621
2381	inSubring sing_1217.htm#SEC1293
2382	indSet sing_1329.htm#SEC1405
2383	indepSet sing_269.htm#SEC309
2384	indexed names sing_36.htm#IDX82
2385	indexed names sing_37.htm#SEC65
2386	indices, multi sing_37.htm#SEC65
2387	inequalities sing_2153.htm#SEC2229
2388	infRedTail, option sing_318.htm#IDX154
2389	infinitely presented algebra sing_870.htm#IDX417
2390	info The online help system sing_16.htm#SEC23
2391	iniD sing_1521.htm#SEC1597
2392	init_debug sing_1600.htm#SEC1676
2393	initial sing_2285.htm#SEC2361
2394	initial form sing_502.htm#IDX315
2395	initial ideal sing_502.htm#IDX314
2396	initial ideal approach sing_502.htm#IDX318
2397	initial ideal approach sing_601.htm#IDX364
2398	initialForm sing_2262.htm#SEC2338
2399	initialIdeal sing_2263.htm#SEC2339
2400	initialIdealW sing_568.htm#SEC620
2401	initialMalgrange sing_567.htm#SEC619
2402	injective_knapsack sing_2055.htm#SEC2131
2403	inout.lib sing_1051.htm#SEC1127
2404	inout_lib sing_1051.htm#SEC1127
2405	input sing_41.htm#SEC71
2406	insert sing_126.htm#SEC166
2407	insert sing_270.htm#SEC310
2408	insertCone sing_2177.htm#SEC2253
2409	insertGenerator sing_588.htm#SEC640
2410	instructions, Macintosh installation Macintosh installation instructions sing_2912.htm#SEC3003
2411	instructions, Unix installation Unix installation instructions sing_2910.htm#SEC3001
2412	instructions, Windows installation Windows installation instructions sing_2911.htm#SEC3002
2413	instructions, downloading Download instructions sing_2908.htm#SEC2999
2414	int sing_95.htm#SEC135
2415	int declarations sing_96.htm#SEC136
2416	int expressions sing_97.htm#SEC137
2417	int operations sing_98.htm#SEC138
2418	int related functions int related functions sing_99.htm#SEC139
2419	intInverse sing_2751.htm#SEC2827
2420	intPart sing_2009.htm#SEC2085
2421	intRank sing_2743.htm#SEC2819
2422	intRoot sing_2010.htm#SEC2086
2423	intRoots sing_585.htm#SEC637
2424	intStrategy, option sing_318.htm#IDX155
2425	intclMonIdeal sing_1370.htm#SEC1446 22338
2426	intclToricRing sing_1366.htm#SEC1442 62143
2427	integer division Miscellaneous oddities sing_422.htm#IDX285
2428	integer programming sing_983.htm#SEC1040
2429	integral sing_2845.htm#SEC2921
2430	integral basis sing_1286.htm#IDX588
2431	integral basis sing_1484.htm#IDX661
2432	integral closure sing_1350.htm#IDX609
2433	integral closure sing_1351.htm#IDX612
2434	integral closure sing_1352.htm#IDX615
2435	integral closure sing_1365.htm#IDX621
2436	integralBasis sing_1286.htm#SEC1362
2437	integralIdeal sing_572.htm#SEC624
2438	integralModule sing_573.htm#SEC625
2439	integralSection sing_2752.htm#SEC2828
2440	integralbasis.lib sing_1285.htm#SEC1361
2441	integralbasis_lib sing_1285.htm#SEC1361
2442	integration of D-module sing_560.htm#IDX346
2443	interface, Emacs Emacs user interface sing_21.htm#SEC28
2444	interiorLatticePoints interiorLatticePoints sing_2214.htm#SEC2290
2445	internalfunctions sing_1601.htm#SEC1677
2446	interpolate sing_1846.htm#SEC1922
2447	interpolation sing_271.htm#SEC311
2448	interpret sing_2714.htm#SEC2790
2449	interpretElem sing_2717.htm#SEC2793
2450	interpretInv sing_2715.htm#SEC2791
2451	interpretList sing_2718.htm#SEC2794
2452	interred sing_272.htm#SEC312
2453	intersect sing_273.htm#SEC313
2454	intersect (plural) sing_467.htm#SEC507
2455	intersectElim, option sing_318.htm#IDX173
2456	intersectLattices sing_2748.htm#SEC2824
2457	intersectLists sing_2469.htm#SEC2545
2458	intersectMon sing_1306.htm#SEC1382
2459	intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2613.htm#SEC2689
2460	intersectSyz, option sing_318.htm#IDX174
2461	intersectZ sing_1426.htm#SEC1502
2462	intersection sing_1675.htm#SEC1751
2463	intersection lattice sing_2327.htm#IDX941
2464	intersection lattice sing_2328.htm#IDX942
2465	intersection multiplicity sing_1586.htm#IDX696
2466	intersection multiplicity sing_1675.htm#IDX811
2467	intersectionDiv sing_1549.htm#SEC1625
2468	intersectionValRingIdeals intersectionValRingIdeals sing_1375.htm#SEC1451 38773
2469	intersectionValRings intersectionValRings sing_1374.htm#SEC1450 35761
2470	intersectpar sing_1045.htm#SEC1121
2471	interval arithmetic sing_2815.htm#IDX1183
2472	intmat sing_102.htm#SEC142
2473	intmat declarations sing_103.htm#SEC143
2474	intmat expressions sing_104.htm#SEC144
2475	intmat operations sing_106.htm#SEC146
2476	intmat related functions intmat related functions sing_107.htm#SEC147
2477	intmat type cast sing_105.htm#SEC145
2478	intmat2mons sing_1390.htm#SEC1466 21150
2479	intprog.lib sing_1287.htm#SEC1363
2480	intprog_lib sing_1287.htm#SEC1363
2481	intvec sing_108.htm#SEC148
2482	intvec declarations sing_109.htm#SEC149
2483	intvec expressions sing_110.htm#SEC150
2484	intvec operations sing_111.htm#SEC151
2485	intvec related functions intvec related functions sing_112.htm#SEC152
2486	invar sing_1812.htm#SEC1888
2487	invar.lib sing_1806.htm#SEC1882
2488	invar_lib sing_1806.htm#SEC1882
2489	invariant sing_2475.htm#IDX1007
2490	invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1750.htm#IDX824
2491	invariant ring minimal generating set permutation group invariant_algebra_perm sing_1751.htm#IDX825
2492	invariantRing sing_1783.htm#SEC1859
2493	invariant_algebra_perm invariant_algebra_perm sing_1751.htm#SEC1827
2494	invariant_algebra_reynolds invariant_algebra_reynolds sing_1750.htm#SEC1826
2495	invariant_basis sing_1758.htm#SEC1834
2496	invariant_basis_reynolds invariant_basis_reynolds sing_1759.htm#SEC1835
2497	invariant_ring sing_1746.htm#SEC1822
2498	invariant_ring_random invariant_ring_random sing_1747.htm#SEC1823
2499	invariants curveColengthDerivations sing_1671.htm#SEC1747
2500	invariants sing_2472.htm#IDX1000
2501	invariants sing_2476.htm#IDX1009
2502	inverse sing_1185.htm#SEC1261
2503	inverse of a matrix via its LU-decomposition sing_293.htm#SEC333
2504	inverseFourier sing_583.htm#SEC635
2505	inverse_B sing_1186.htm#SEC1262
2506	inverse_L sing_1187.htm#SEC1263
2507	inverse_modulus sing_2038.htm#SEC2114
2508	invertAlgebraMorphism invertAlgebraMorphism sing_2898.htm#SEC2974
2509	invertBirMap sing_1485.htm#SEC1561
2510	invertLeftFraction sing_763.htm#SEC815
2511	invertNcfrac sing_699.htm#SEC751
2512	invertNumberMain sing_1870.htm#SEC1946
2513	involut.lib sing_606.htm#SEC658
2514	involut_lib sing_606.htm#SEC658
2515	involution sing_611.htm#SEC663
2516	invunit sing_1694.htm#SEC1770
2517	iostruct sing_1957.htm#SEC2033
2518	irrRealizationDim sing_2244.htm#SEC2320
2519	irred_secondary_char0 irred_secondary_char0 sing_1772.htm#SEC1848
2520	irred_secondary_no_molien irred_secondary_no_molien sing_1775.htm#SEC1851
2521	irreddecMon sing_1315.htm#SEC1391
2522	irreducible power series sing_1676.htm#IDX812
2523	irreducible secondary invariant irred_secondary_char0 sing_1772.htm#IDX826
2524	isAface sing_2598.htm#SEC2674
2525	isAntiEndo sing_613.htm#SEC665
2526	isBounded sing_2215.htm#SEC2291
2527	isCI sing_210.htm#IDX139
2528	isCI sing_1235.htm#SEC1311
2529	isCM sing_210.htm#IDX140
2530	isCM sing_1275.htm#SEC1351
2531	isCMcod2 sing_1729.htm#SEC1805
2532	isCanonical sing_2216.htm#SEC2292
2533	isCartan sing_528.htm#SEC580
2534	isCentral sing_739.htm#SEC791
2535	isCommutative sing_741.htm#SEC793
2536	isCompatible sing_2178.htm#SEC2254
2537	isCompressed sing_2217.htm#SEC2293
2538	isDenom sing_711.htm#SEC763
2539	isEqualDivisor sing_2532.htm#SEC2608
2540	isEquising sing_1638.htm#SEC1714
2541	isFlat sing_1276.htm#SEC1352
2542	isFreeAlgebra sing_857.htm#SEC909
2543	isFsat sing_578.htm#SEC630
2544	isFullSpace sing_2154.htm#SEC2230
2545	isGorenstein sing_2218.htm#SEC2294
2546	isGradedRingHomomorphism isGradedRingHomomorphism sing_2737.htm#SEC2813
2547	isGroup sing_2735.htm#SEC2811
2548	isGroupHomomorphism sing_2736.htm#SEC2812
2549	isHolonomic sing_556.htm#SEC608
2550	isHomog sing_210.htm#IDX135
2551	isHomogeneous sing_2763.htm#SEC2839
2552	isInS sing_752.htm#SEC804
2553	isInt sing_591.htm#SEC643
2554	isIntegralSurjective isIntegralSurjective sing_2749.htm#SEC2825
2555	isInvertibleLeftFraction isInvertibleLeftFraction sing_762.htm#SEC814
2556	isInvertibleNcfrac sing_698.htm#SEC750
2557	isInvolution sing_612.htm#SEC664
2558	isLatticeEmpty sing_2219.htm#SEC2295
2559	isLocalizationRegular isLocalizationRegular sing_2594.htm#SEC2670
2560	isLocallyFree sing_1277.htm#SEC1353
2561	isMonomial sing_1301.htm#SEC1377
2562	isNC sing_740.htm#SEC792
2563	isNormal sing_2220.htm#SEC2296
2564	isOnCurve sing_2022.htm#SEC2098
2565	isOneFraction sing_765.htm#SEC817
2566	isOneNcfrac sing_692.htm#SEC744
2567	isOrderingShiftInvariant isOrderingShiftInvariant sing_863.htm#SEC915
2568	isOrigin sing_2155.htm#SEC2231
2569	isPositive sing_2760.htm#SEC2836
2570	isPrimitiveSublattice isPrimitiveSublattice sing_2750.htm#SEC2826
2571	isPure sing_2179.htm#SEC2255
2572	isPureTensor sing_500.htm#SEC552
2573	isQuotientRing sing_1131.htm#SEC1207
2574	isRational sing_559.htm#SEC611
2575	isReflexive sing_2221.htm#SEC2297
2576	isReg sing_1278.htm#SEC1354
2577	isSB sing_210.htm#IDX134
2578	isSimplicial sing_2156.htm#SEC2232
2579	isSmooth sing_2222.htm#SEC2298
2580	isSubModule sing_1132.htm#SEC1208
2581	isSublattice sing_2741.htm#SEC2817
2582	isSymmetric sing_1450.htm#SEC1526
2583	isTame sing_1663.htm#SEC1739
2584	isTerminal sing_2223.htm#SEC2299
2585	isTorsionFree sing_2759.htm#SEC2835
2586	isTwoSidedGB sing_501.htm#SEC553
2587	isUpperTriangular sing_720.htm#SEC772
2588	isVeryAmple sing_2224.htm#SEC2300
2589	isWeyl sing_742.htm#SEC794
2590	isZeroElement sing_2761.htm#SEC2837
2591	isZeroFraction sing_764.htm#SEC816
2592	isZeroNcfrac sing_691.htm#SEC743
2593	is_NND sing_1679.htm#SEC1755
2594	is_NP sing_1338.htm#SEC1414
2595	is_active sing_1712.htm#SEC1788
2596	is_bijective sing_1222.htm#SEC1298
2597	is_cenBimodule sing_708.htm#SEC760
2598	is_cenSubbimodule sing_709.htm#SEC761
2599	is_ci sing_1713.htm#SEC1789
2600	is_complex sing_1159.htm#SEC1235
2601	is_fix_injective sing_2059.htm#SEC2135
2602	is_h_injective sing_2058.htm#SEC2134
2603	is_injective sing_1220.htm#SEC1296
2604	is_irred sing_1676.htm#SEC1752
2605	is_is sing_1714.htm#SEC1790
2606	is_nested sing_1339.htm#SEC1415
2607	is_prime sing_2039.htm#SEC2115
2608	is_primitive_root sing_2035.htm#SEC2111
2609	is_pure sing_782.htm#SEC834
2610	is_reg sing_1715.htm#SEC1791
2611	is_regs sing_1716.htm#SEC1792
2612	is_surjective sing_1221.htm#SEC1297
2613	is_zero sing_1074.htm#SEC1150
2614	isartinianMon sing_1312.htm#SEC1388
2615	isgenericMon sing_1313.htm#SEC1389
2616	ishyper sing_2062.htm#SEC2138
2617	isirreducibleMon sing_1311.htm#SEC1387
2618	isoncurve sing_2063.htm#SEC2139
2619	isparam sing_2126.htm#SEC2202
2620	isprimaryMon sing_1310.htm#SEC1386
2621	isprimeMon sing_1309.htm#SEC1385
2622	isuni sing_2111.htm#SEC2187
2623	ivmatGaussian sing_2822.htm#SEC2898
2624	ivmatInit sing_2819.htm#SEC2895
2625	ivmatSet sing_2820.htm#SEC2896
2626	jInvariant sing_2256.htm#SEC2332
2627	jOft sing_1994.htm#SEC2070
2628	jacob sing_274.htm#SEC314
2629	jacoblift sing_1695.htm#SEC1771
2630	jacobson sing_1963.htm#SEC2039
2631	jacobson.lib sing_1961.htm#SEC2037
2632	jacobson_lib sing_1961.htm#SEC2037
2633	janet sing_275.htm#SEC315
2634	janet basis sing_2828.htm#IDX1186
2635	jet sing_276.htm#SEC316
2636	jordan sing_1206.htm#SEC1282
2637	jordanVecField sing_2891.htm#SEC2967
2638	jordanbasis sing_1207.htm#SEC1283
2639	jordanmatrix sing_1208.htm#SEC1284
2640	jordannf sing_1209.htm#SEC1285
2641	jungfib sing_1534.htm#SEC1610
2642	jungnormal sing_1533.htm#SEC1609
2643	jungresolve sing_1532.htm#SEC1608
2644	katsura sing_1072.htm#SEC1148
2645	kbase sing_277.htm#SEC317
2646	kbase (plural) sing_468.htm#SEC508
2647	keepring sing_392.htm#SEC432
2648	kerHom sing_2713.htm#SEC2789
2649	kernel sing_278.htm#SEC318
2650	kernelLattice sing_2744.htm#SEC2820
2651	kill sing_279.htm#SEC319
2652	killTask sing_1138.htm#SEC1214
2653	killall sing_1013.htm#SEC1089
2654	killattrib sing_280.htm#SEC320
2655	kmemory sing_1012.htm#SEC1088
2656	kohom sing_1280.htm#SEC1356
2657	kontrahom sing_1281.htm#SEC1357
2658	koszul sing_281.htm#SEC321
2659	kskernel.lib sing_1686.htm#SEC1762
2660	kskernel_lib sing_1686.htm#SEC1762
2661	l-adic numbers sing_32.htm#SEC46
2662	laguerre sing_282.htm#SEC322
2663	laguerre_solve sing_1842.htm#SEC1918
2664	lastvarGeneral sing_2092.htm#SEC2168
2665	latex.lib sing_1886.htm#SEC1962
2666	latex_lib sing_1886.htm#SEC1962
2667	lattice sing_2328.htm#IDX944
2668	latticeArea sing_2199.htm#SEC2275
2669	latticeBasis sing_2745.htm#SEC2821
2670	latticeCodegree sing_2225.htm#SEC2301
2671	latticeDegree sing_2226.htm#SEC2302
2672	latticePoints sing_2227.htm#SEC2303
2673	latticeVolume sing_2228.htm#SEC2304
2674	laxfrT sing_2558.htm#SEC2634
2675	laxfrX sing_2559.htm#SEC2635
2676	lazy, option sing_318.htm#IDX156
2677	lcm sing_1075.htm#SEC1151
2678	lcmMon sing_1304.htm#SEC1380
2679	lcmN sing_2003.htm#SEC2079
2680	lcmofall sing_1514.htm#SEC1590
2681	lead sing_283.htm#SEC323
2682	leadcoef sing_284.htm#SEC324
2683	leadexp sing_285.htm#SEC325
2684	leadmonom sing_286.htm#SEC326
2685	leadmonomial sing_2078.htm#SEC2154
2686	left annihilator ideal sing_537.htm#IDX326
2687	left annihilator ideal sing_593.htm#IDX354
2688	leftInverse sing_1952.htm#SEC2028
2689	leftKernel sing_1950.htm#SEC2026
2690	leftOre sing_755.htm#SEC807
2691	length sing_2817.htm#SEC2893
2692	length, option sing_318.htm#IDX157
2693	letplaceGBasis sing_865.htm#SEC917
2694	letterplace sing_296.htm#SEC336
2695	letterplace sing_337.htm#SEC377
2696	lex_solve sing_1848.htm#SEC1924
2697	lexicographical ordering sing_961.htm#IDX427
2698	lib2doc sing_60.htm#SEC97
2699	libSingular sing_2907.htm#SEC2998
2700	libcdd sing_1.htm#IDX12
2701	libfac sing_1.htm#IDX6
2702	libparse sing_69.htm#SEC109
2703	library sing_2343.htm#IDX959
2704	library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2597.htm#IDX1138
2705	library, info string sing_55.htm#IDX124
2706	library, polybori.lib sing_2343.htm#IDX956
2707	library, template sing_55.htm#SEC92
2708	library, template.lib sing_55.htm#IDX122
2709	lieBracket sing_866.htm#SEC918
2710	lift sing_288.htm#SEC328
2711	lift sing_495.htm#IDX302
2712	lift (letterplace) sing_800.htm#SEC852
2713	lift (plural) sing_469.htm#SEC509
2714	lift_kbase sing_1632.htm#SEC1708
2715	lift_rel_kb sing_1633.htm#SEC1709
2716	liftenvelope sing_498.htm#SEC550
2717	liftstd sing_289.htm#SEC329
2718	liftstd (letterplace) liftstd (letterplace) sing_801.htm#SEC853
2719	liftstd (plural) sing_470.htm#SEC510
2720	linReduce sing_510.htm#SEC562
2721	linReduceIdeal sing_511.htm#SEC563
2722	linSyzSolve sing_512.htm#SEC564
2723	linalg.lib sing_1184.htm#SEC1260
2724	linalg_lib sing_1184.htm#SEC1260
2725	linealityDimension sing_2157.htm#SEC2233
2726	linealitySpace sing_2158.htm#SEC2234
2727	linear algebra sing_211.htm#SEC251
2728	linear algebra sing_292.htm#SEC332
2729	linear algebra sing_293.htm#SEC333
2730	linear algebra sing_294.htm#SEC334
2731	linear code, dual sing_1921.htm#IDX837
2732	linear code, systematic sing_1922.htm#IDX838
2733	linear interreduction sing_502.htm#IDX317
2734	linearCombinations sing_531.htm#SEC583
2735	linearMapKernel sing_530.htm#SEC582
2736	linear_relations sing_1176.htm#SEC1252
2737	linearlyEquivalent sing_2535.htm#SEC2611
2738	linearpart sing_1834.htm#SEC1910
2739	linesHypersurface sing_2867.htm#SEC2943
2740	link Parallelization with ssi links sing_113.htm#SEC153
2741	link sing_916.htm#SEC968
2742	link declarations sing_114.htm#SEC154
2743	link expressions sing_115.htm#SEC155
2744	link related functions link related functions sing_116.htm#SEC156
2745	list sing_123.htm#SEC163
2746	list sing_2506.htm#IDX1066
2747	list sing_2507.htm#IDX1068
2748	list declarations sing_124.htm#SEC164
2749	list expressions sing_125.htm#SEC165
2750	list operations sing_126.htm#SEC166
2751	list related functions list related functions sing_127.htm#SEC167
2752	lists sing_2469.htm#IDX996
2753	lists, elements sing_2471.htm#IDX998
2754	listvar sing_290.htm#SEC330
2755	lll sing_2777.htm#SEC2853
2756	load sing_393.htm#SEC433
2757	loadLib, option sing_318.htm#IDX178
2758	loadProc, option sing_318.htm#IDX179
2759	locAtZero sing_1359.htm#SEC1435
2760	locNormal sing_1290.htm#SEC1366
2761	locStatus sing_750.htm#SEC802
2762	local methods sing_1289.htm#IDX591
2763	local methods sing_1290.htm#IDX594
2764	local names sing_46.htm#SEC83
2765	local rings, computing in Rings associated to monomial orderings sing_911.htm#SEC963
2766	local weighted lexicographical ordering sing_962.htm#IDX448
2767	local weighted reverse lexicographical ordering Local orderings sing_962.htm#IDX445
2768	localInvar sing_1788.htm#SEC1864
2769	localization Rings associated to monomial orderings sing_911.htm#SEC963
2770	localization sing_2308.htm#IDX904
2771	localization of D-module sing_560.htm#IDX342
2772	localization of D-module sing_662.htm#IDX371
2773	locally closed set sing_1030.htm#IDX472
2774	locally closed set sing_1031.htm#IDX474
2775	locally closed set sing_1032.htm#IDX476
2776	locally closed set sing_1033.htm#IDX480
2777	locally closed set sing_1047.htm#IDX518
2778	locally closed set sing_1049.htm#IDX523
2779	localstd sing_2088.htm#SEC2164
2780	locnormal.lib sing_1289.htm#SEC1365
2781	locnormal_lib sing_1289.htm#SEC1365
2782	locstd sing_1717.htm#SEC1793
2783	locus FamElemsAtEnvCompPoints sing_1035.htm#SEC1111
2784	locus sing_1035.htm#IDX490
2785	locus sing_1036.htm#IDX493
2786	locus sing_1037.htm#IDX496
2787	locus sing_1038.htm#IDX499
2788	locus sing_1039.htm#IDX502
2789	locus sing_1040.htm#IDX504
2790	locus sing_1041.htm#IDX508
2791	locusdg sing_1036.htm#SEC1112
2792	locusto sing_1038.htm#SEC1114
2793	log2 sing_1978.htm#SEC2054
2794	logarithmic annihilator ideal sing_537.htm#IDX331
2795	logarithmic annihilator ideal sing_593.htm#IDX356
2796	logg sing_2872.htm#SEC2948
2797	lp, global ordering sing_961.htm#IDX426
2798	lpCalcSubstDegBound sing_855.htm#SEC907
2799	lpDegBound sing_858.htm#SEC910
2800	lpDivision sing_861.htm#SEC913
2801	lpGBPres2Poly sing_862.htm#SEC914
2802	lpGlDimBound sing_853.htm#SEC905
2803	lpHilbert sing_818.htm#SEC870
2804	lpIsPrime sing_852.htm#SEC904
2805	lpIsSemiPrime sing_851.htm#SEC903
2806	lpKDim sing_816.htm#SEC868
2807	lpKDimCheck sing_815.htm#SEC867
2808	lpMonomialBasis sing_817.htm#SEC869
2809	lpNcgenCount sing_860.htm#SEC912
2810	lpNoetherian sing_850.htm#SEC902
2811	lpSickleDim sing_819.htm#SEC871
2812	lpSubstitute sing_854.htm#SEC906
2813	lpVarBlockSize sing_859.htm#SEC911
2814	lprint sing_1053.htm#SEC1129
2815	lres sing_291.htm#SEC331
2816	ls, local ordering sing_962.htm#IDX439
2817	lsum sing_1256.htm#SEC1332
2818	ludecomp sing_292.htm#SEC332
2819	luinverse sing_293.htm#SEC333
2820	lusolve sing_294.htm#SEC334
2821	mRes sing_2681.htm#SEC2757
2822	m_merkle_hellman_decryption m_merkle_hellman_decryption sing_2050.htm#SEC2126
2823	m_merkle_hellman_encryption m_merkle_hellman_encryption sing_2049.htm#SEC2125
2824	m_merkle_hellman_transformation m_merkle_hellman_transformation sing_2048.htm#SEC2124
2825	magnitude sing_1972.htm#SEC2048
2826	makeDivisor sing_2527.htm#SEC2603
2827	makeFormalDivisor sing_2537.htm#SEC2613
2828	makeGraph sing_1247.htm#SEC1323
2829	makeGraphVE sing_2858.htm#SEC2934
2830	makeHeisenberg sing_730.htm#SEC782
2831	makeIdeal sing_2673.htm#SEC2749
2832	makeLetterplaceRing sing_864.htm#SEC916
2833	makeMalgrange sing_605.htm#SEC657
2834	makeMatrix sing_2672.htm#SEC2748
2835	makeModElimRing sing_747.htm#SEC799
2836	makePDivisor sing_2543.htm#SEC2619
2837	makeQsl2 sing_639.htm#SEC691
2838	makeQsl3 sing_640.htm#SEC692
2839	makeQso3 sing_638.htm#SEC690
2840	makeSheaf sing_2846.htm#SEC2922
2841	makeUe6 sing_635.htm#SEC687
2842	makeUe7 sing_636.htm#SEC688
2843	makeUe8 sing_637.htm#SEC689
2844	makeUf4 sing_634.htm#SEC686
2845	makeUg2 sing_633.htm#SEC685
2846	makeUgl sing_619.htm#SEC671
2847	makeUsl sing_618.htm#SEC670
2848	makeUsl2 sing_617.htm#SEC669
2849	makeUso10 sing_625.htm#SEC677
2850	makeUso11 sing_626.htm#SEC678
2851	makeUso12 sing_627.htm#SEC679
2852	makeUso5 sing_620.htm#SEC672
2853	makeUso6 sing_621.htm#SEC673
2854	makeUso7 sing_622.htm#SEC674
2855	makeUso8 sing_623.htm#SEC675
2856	makeUso9 sing_624.htm#SEC676
2857	makeUsp1 sing_628.htm#SEC680
2858	makeUsp2 sing_629.htm#SEC681
2859	makeUsp3 sing_630.htm#SEC682
2860	makeUsp4 sing_631.htm#SEC683
2861	makeUsp5 sing_632.htm#SEC684
2862	makeVariety sing_2838.htm#SEC2914
2863	makeVector sing_2701.htm#SEC2777
2864	makeWeyl sing_729.htm#SEC781
2865	map sing_128.htm#SEC168
2866	map (plural) sing_432.htm#SEC472
2867	map declarations sing_129.htm#SEC169
2868	map declarations (plural) map declarations (plural) sing_433.htm#SEC473
2869	map expressions sing_130.htm#SEC170
2870	map expressions (plural) map expressions (plural) sing_434.htm#SEC474
2871	map operations sing_131.htm#IDX129
2872	map operations (plural) map operations (plural) sing_435.htm#IDX297
2873	map related functions map related functions sing_132.htm#IDX131
2874	map related functions (plural) map related functions (plural) sing_436.htm#IDX298
2875	mapIsFinite sing_1224.htm#SEC1300
2876	mapToRatNormCurve sing_1489.htm#SEC1565
2877	mapall sing_1118.htm#SEC1194
2878	mappingcone sing_2659.htm#SEC2735
2879	mappingcone3 sing_2661.htm#SEC2737
2880	markov4ti2 sing_1445.htm#SEC1521 9163
2881	mat2arr sing_2293.htm#SEC2369
2882	mat2carr sing_2294.htm#SEC2370
2883	mat_rk sing_1198.htm#SEC1274
2884	matbil sing_2099.htm#SEC2175
2885	mathematical objects Representation of mathematical objects sing_957.htm#SEC1009
2886	mathinit sing_1884.htm#SEC1960
2887	matmult sing_2100.htm#SEC2176
2888	matrix sing_133.htm#SEC173
2889	matrix sing_2293.htm#IDX872
2890	matrix sing_2294.htm#IDX875
2891	matrix sing_2295.htm#IDX879
2892	matrix declarations sing_134.htm#SEC174
2893	matrix diagonalization sing_1961.htm#IDX848
2894	matrix expressions sing_135.htm#SEC175
2895	matrix operations sing_137.htm#SEC177
2896	matrix related functions matrix related functions sing_138.htm#SEC178
2897	matrix type cast sing_136.htm#SEC176
2898	matrix.lib sing_1152.htm#SEC1228
2899	matrixExp sing_1479.htm#SEC1555
2900	matrixLog sing_1480.htm#SEC1556
2901	matrixT1 sing_1731.htm#SEC1807
2902	matrix_lib sing_1152.htm#SEC1228
2903	matrixpres sing_2664.htm#SEC2740
2904	matrixsystem sing_2569.htm#SEC2645
2905	max sing_295.htm#SEC335
2906	maxEord sing_1504.htm#SEC1580
2907	maxExp sing_210.htm#IDX136
2908	maxIntRoot sing_679.htm#SEC731
2909	maxZeros sing_1482.htm#SEC1558
2910	maxabs sing_2118.htm#SEC2194
2911	maxcoef sing_1076.htm#SEC1152
2912	maxdeg sing_1077.htm#SEC1153
2913	maxdeg1 sing_1078.htm#SEC1154
2914	maxideal sing_296.htm#SEC336
2915	maximalFace sing_2229.htm#SEC2305
2916	maximalGroebnerCone sing_2283.htm#SEC2359
2917	maximalValue sing_2230.htm#SEC2306
2918	maximum sing_1991.htm#SEC2067
2919	maximum number of zeroes sing_1482.htm#IDX655
2920	mdouble sing_56.htm#SEC93
2921	mem, option sing_318.htm#IDX180
2922	member sing_2471.htm#SEC2547
2923	membershipMon sing_1305.htm#SEC1381
2924	memory sing_297.htm#SEC337
2925	memory managment sing_297.htm#SEC337
2926	merkle_hellman_decryption merkle_hellman_decryption sing_2052.htm#SEC2128
2927	merkle_hellman_encryption merkle_hellman_encryption sing_2051.htm#SEC2127
2928	methods, hashtables sing_2667.htm#IDX1142
2929	methods.lib sing_2667.htm#SEC2743
2930	methods_lib sing_2667.htm#SEC2743
2931	midpoint sing_2565.htm#SEC2641
2932	milnor sing_1718.htm#SEC1794
2933	milnorcode sing_1602.htm#SEC1678
2934	milnornumber sing_2812.htm#SEC2888
2935	min sing_298.htm#SEC338
2936	minAssChar sing_1404.htm#SEC1480
2937	minAssCharE sing_1405.htm#SEC1481
2938	minAssGTZ sing_1402.htm#SEC1478
2939	minAssGTZE sing_1403.htm#SEC1479
2940	minAssZ sing_1422.htm#SEC1498
2941	minEcart sing_2081.htm#SEC2157
2942	minIntRoot sing_558.htm#SEC610
2943	minIntRoot2 sing_678.htm#SEC730
2944	minMult sing_1231.htm#SEC1307
2945	minbase sing_299.htm#SEC339
2946	minbaseMon sing_1302.htm#SEC1378
2947	mindeg sing_1079.htm#SEC1155
2948	mindeg1 sing_1080.htm#SEC1156
2949	mindist sing_1936.htm#SEC2012
2950	minimal display time, setting the sing_361.htm#IDX281
2951	minimal representations sing_873.htm#IDX425
2952	minimalAfaceOrbits sing_2610.htm#SEC2686
2953	minimalAfaces sing_2601.htm#SEC2677
2954	minimalFace sing_2231.htm#SEC2307
2955	minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2612.htm#SEC2688
2956	minimalValue sing_2232.htm#SEC2308
2957	minipoly sing_1203.htm#SEC1279
2958	minkowskiSum sing_2233.htm#SEC2309
2959	minor sing_300.htm#SEC340
2960	minpoly sing_401.htm#SEC441
2961	minres sing_301.htm#SEC341
2962	minres (plural) sing_471.htm#SEC511
2963	minus sing_2495.htm#IDX1042
2964	minus sing_2496.htm#IDX1044
2965	minus sing_2517.htm#IDX1090
2966	minus sing_2518.htm#IDX1092
2967	mirror symmetry sing_1246.htm#IDX559
2968	mixed Hodge structure sing_1640.htm#IDX711
2969	mixed Hodge structure sing_1646.htm#IDX739
2970	mixed Hodge structure sing_1647.htm#IDX745
2971	mixed Hodge structure sing_1648.htm#IDX753
2972	mixed Hodge structure sing_1649.htm#IDX759
2973	mixed Hodge structure sing_1650.htm#IDX767
2974	mixed Hodge structure sing_1651.htm#IDX777
2975	mixed Hodge structure sing_1662.htm#IDX783
2976	mixed Hodge structure sing_1664.htm#IDX794
2977	mod sing_81.htm#SEC121
2978	mod sing_98.htm#SEC138
2979	mod sing_147.htm#SEC187
2980	mod sing_155.htm#SEC195
2981	mod2id sing_1084.htm#SEC1160
2982	modBorder sing_2830.htm#SEC2906
2983	modDec sing_1321.htm#SEC1397
2984	modIntersect sing_1299.htm#SEC1375
2985	modJanet sing_2832.htm#SEC2908
2986	modNPos sing_1344.htm#SEC1420
2987	modNormal sing_1295.htm#SEC1371
2988	modNpos_test sing_1342.htm#SEC1418
2989	modQuotient sing_1292.htm#SEC1368
2990	modSagbiAlg sing_2458.htm#SEC2534
2991	modSat sing_1293.htm#SEC1369
2992	modStd sing_1297.htm#SEC1373
2993	modSyz sing_1298.htm#SEC1374
2994	modVStd sing_2463.htm#SEC2539
2995	modVStd0 sing_2464.htm#SEC2540
2996	modWalk sing_2722.htm#SEC2798
2997	mod_versal sing_1631.htm#SEC1707
2998	modality sing_1610.htm#SEC1686
2999	modberlekampMassey sing_2551.htm#SEC2627
3000	moddiq.lib sing_1291.htm#SEC1367
3001	moddiq_lib sing_1291.htm#SEC1367
3002	modfWalk sing_2724.htm#SEC2800
3003	modfrWalk sing_2725.htm#SEC2801
3004	modnormal.lib sing_1294.htm#SEC1370
3005	modnormal_lib sing_1294.htm#SEC1370
3006	modrWalk sing_2723.htm#SEC2799
3007	modrationalInterpolation modrationalInterpolation sing_2549.htm#SEC2625
3008	modregCM sing_1348.htm#SEC1424
3009	modsatiety sing_1346.htm#SEC1422
3010	modstd.lib sing_1296.htm#SEC1372
3011	modstd_lib sing_1296.htm#SEC1372
3012	modular sing_1062.htm#SEC1138
3013	modular methods sing_1289.htm#IDX592
3014	modular methods sing_1294.htm#IDX598
3015	modular methods. sing_1290.htm#IDX595
3016	modular techniques. sing_1295.htm#IDX600
3017	modular.lib sing_1061.htm#SEC1137
3018	modular_lib sing_1061.htm#SEC1137
3019	modular_lib sing_1061.htm#IDX527
3020	module sing_139.htm#SEC179
3021	module (plural) sing_437.htm#SEC477
3022	module declarations sing_140.htm#SEC180
3023	module declarations (plural) module declarations (plural) sing_438.htm#SEC478
3024	module expressions sing_141.htm#SEC181
3025	module expressions (plural) module expressions (plural) sing_439.htm#SEC479
3026	module operations sing_142.htm#SEC182
3027	module operations (plural) module operations (plural) sing_440.htm#SEC480
3028	module ordering C sing_963.htm#IDX451
3029	module ordering c sing_963.htm#IDX453
3030	module related functions module related functions sing_143.htm#SEC183
3031	module related functions (plural) module related functions (plural) sing_441.htm#SEC481
3032	module_containment sing_1216.htm#SEC1292
3033	modules.lib sing_2668.htm#SEC2744
3034	modules_lib sing_2668.htm#SEC2744
3035	moduliSpace sing_2860.htm#SEC2936
3036	modulo sing_302.htm#SEC342
3037	modulo (plural) sing_472.htm#SEC512
3038	moduloSlim sing_737.htm#SEC789
3039	modwalk.lib sing_2721.htm#SEC2797
3040	modwalk_lib sing_2721.htm#SEC2797
3041	moebius sing_2329.htm#SEC2405
3042	moebius function sing_2329.htm#IDX945
3043	molien sing_1754.htm#SEC1830
3044	mondromy.lib sing_1692.htm#SEC1768
3045	mondromy_lib sing_1692.htm#SEC1768
3046	monitor sing_303.htm#SEC343
3047	monodromy sing_1640.htm#IDX715
3048	monodromy sing_1645.htm#SEC1721
3049	monodromy sing_1645.htm#IDX735
3050	monodromy sing_1650.htm#IDX770
3051	monodromy sing_1662.htm#IDX786
3052	monodromy sing_1664.htm#IDX797
3053	monodromyB sing_1696.htm#SEC1772
3054	monomial sing_304.htm#SEC344
3055	monomial ordering sing_1127.htm#IDX541
3056	monomial orderings General definitions for orderings sing_911.htm#SEC963
3057	monomial orderings sing_960.htm#SEC1012
3058	monomial orderings introduction Introduction to orderings sing_959.htm#SEC1011
3059	monomial output sing_405.htm#SEC445
3060	monomial, write sing_405.htm#SEC445
3061	monomialInIdeal sing_676.htm#SEC728
3062	monomialLcm sing_2079.htm#SEC2155
3063	monomialabortstd sing_2336.htm#SEC2412
3064	monomialideal.lib sing_1300.htm#SEC1376
3065	monomialideal_lib sing_1300.htm#SEC1376
3066	monomials and precedence Miscellaneous oddities sing_422.htm#IDX287
3067	mons2intmat sing_1389.htm#SEC1465 15555
3068	morsesplit sing_1603.htm#SEC1679
3069	movingCone sing_2608.htm#SEC2684
3070	mp_res_mat sing_1845.htm#SEC1921
3071	mplot sing_1885.htm#SEC1961
3072	mpresmat sing_305.htm#SEC345
3073	mprimdec.lib sing_1317.htm#SEC1393
3074	mprimdec_lib sing_1317.htm#SEC1393
3075	mregular.lib sing_1332.htm#SEC1408
3076	mregular_lib sing_1332.htm#SEC1408
3077	mres sing_306.htm#SEC346
3078	mres (plural) sing_473.htm#SEC513
3079	mstd sing_307.htm#SEC347
3080	msum sing_58.htm#SEC95
3081	mtriple sing_57.htm#SEC94
3082	mult Miscellaneous oddities sing_308.htm#SEC348
3083	mult sing_422.htm#IDX288
3084	multBound sing_402.htm#SEC442
3085	multRat sing_684.htm#SEC736
3086	multarr2arr sing_2324.htm#SEC2400
3087	multarrMultRestrict sing_2326.htm#SEC2402
3088	multarrRestrict sing_2325.htm#SEC2401
3089	multcol sing_1170.htm#SEC1246
3090	multdivisor sing_2529.htm#SEC2605
3091	multformaldivisor sing_2541.htm#SEC2617
3092	multi sing_2066.htm#SEC2142
3093	multi indices sing_37.htm#SEC65
3094	multi-graded Hilbert series sing_870.htm#IDX419
3095	multiDeg sing_2756.htm#SEC2832
3096	multiDegBasis sing_2757.htm#SEC2833
3097	multiDegGroebner sing_2765.htm#SEC2841
3098	multiDegModulo sing_2767.htm#SEC2843
3099	multiDegPartition sing_2758.htm#SEC2834
3100	multiDegResolution sing_2768.htm#SEC2844
3101	multiDegSyzygy sing_2766.htm#SEC2842
3102	multiDegTensor sing_2769.htm#SEC2845
3103	multiDegTor sing_2770.htm#SEC2846
3104	multiarrangement sing_2320.htm#IDX925
3105	multiarrangement sing_2321.htm#IDX927
3106	multiarrangement sing_2322.htm#IDX930
3107	multiarrangement sing_2323.htm#IDX931
3108	multiarrangement sing_2324.htm#IDX934
3109	multiarrangement sing_2325.htm#IDX937
3110	multiarrangement sing_2326.htm#IDX939
3111	multidimensional_knapsack multidimensional_knapsack sing_2044.htm#SEC2120
3112	multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2726.htm#IDX1149
3113	multigrading.lib sing_2726.htm#IDX1147
3114	multigrading_lib sing_2726.htm#IDX1148
3115	multipleCover sing_2866.htm#SEC2942
3116	multiplication sing_2497.htm#IDX1046
3117	multiplication sing_2519.htm#IDX1094
3118	multiplicities, sequence of sing_1671.htm#IDX809
3119	multiplicity sing_2474.htm#IDX1005
3120	multiplicity sequence sing_1584.htm#IDX688
3121	multiplicity sequence sing_1587.htm#IDX700
3122	multiplicity sequence sing_1673.htm#IDX810
3123	multiplyLeftFractions multiplyLeftFractions sing_760.htm#SEC812
3124	multiplylist sing_1524.htm#SEC1600
3125	multivariate equations sing_1819.htm#IDX827
3126	multrow sing_1171.htm#SEC1247
3127	multseq2charexp sing_1583.htm#SEC1659
3128	multsequence sing_1673.htm#SEC1749
3129	nBoundaryLatticePoints nBoundaryLatticePoints sing_2234.htm#SEC2310
3130	nHilbertBasis sing_2235.htm#SEC2311
3131	nInteriorLatticePoints nInteriorLatticePoints sing_2236.htm#SEC2312
3132	nLatticePoints sing_2237.htm#SEC2313
3133	naccache_stern_decryption naccache_stern_decryption sing_2047.htm#SEC2123
3134	naccache_stern_encryption naccache_stern_encryption sing_2046.htm#SEC2122
3135	naccache_stern_generation naccache_stern_generation sing_2045.htm#SEC2121
3136	nameof sing_309.htm#SEC349
3137	names sing_310.htm#SEC350
3138	nashmult sing_1591.htm#SEC1667
3139	nblocks sing_361.htm#IDX219
3140	ncExt_R sing_703.htm#SEC755
3141	ncHilb.lib sing_870.htm#SEC922
3142	ncHilb_lib sing_870.htm#SEC922
3143	ncHom sing_704.htm#SEC756
3144	ncInit sing_874.htm#SEC926
3145	ncModslimgb.lib sing_714.htm#SEC766
3146	ncModslimgb_lib sing_714.htm#SEC766
3147	ncRelations sing_738.htm#SEC790
3148	ncVarsAdd sing_876.htm#SEC928
3149	ncVarsGet sing_875.htm#SEC927
3150	nc_algebra sing_474.htm#SEC514
3151	nc_hilb sing_361.htm#IDX221
3152	ncalg.lib sing_616.htm#SEC668
3153	ncalg_lib sing_616.htm#SEC668
3154	ncalgebra sing_475.htm#SEC515
3155	ncdecomp.lib sing_643.htm#SEC695
3156	ncdecomp_lib sing_643.htm#SEC695
3157	ncdetection sing_610.htm#SEC662
3158	ncfactor sing_649.htm#SEC701
3159	ncfactor.lib sing_648.htm#SEC700
3160	ncfactor_lib sing_648.htm#SEC700
3161	ncfrac.lib sing_688.htm#SEC740
3162	ncfrac_lib sing_688.htm#SEC740
3163	ncgen sing_799.htm#SEC851
3164	nchilb sing_871.htm#SEC923
3165	nchomolog.lib sing_702.htm#IDX377
3166	nchomolog_lib sing_702.htm#IDX378
3167	ncloc.lib sing_710.htm#SEC762
3168	ncloc_lib sing_710.htm#SEC762
3169	ncmodslimgb sing_715.htm#SEC767
3170	ncols sing_311.htm#SEC351
3171	ncones sing_2181.htm#SEC2257
3172	ncpreim.lib sing_716.htm#SEC768
3173	ncpreim_lib sing_716.htm#SEC768
3174	ncrat.lib sing_873.htm#IDX420
3175	ncratAdd sing_878.htm#SEC930
3176	ncratDefine sing_877.htm#SEC929
3177	ncratEvaluateAt sing_887.htm#SEC939
3178	ncratFromPoly sing_885.htm#SEC937
3179	ncratFromString sing_884.htm#SEC936
3180	ncratInvert sing_881.htm#SEC933
3181	ncratMultiply sing_880.htm#SEC932
3182	ncratPower sing_886.htm#SEC938
3183	ncratPrint sing_883.htm#SEC935
3184	ncratSPrint sing_882.htm#SEC934
3185	ncratSubstract sing_879.htm#SEC931
3186	ncrat_lib sing_873.htm#IDX421
3187	ncrepAdd sing_889.htm#SEC941
3188	ncrepDim sing_894.htm#SEC946
3189	ncrepEvaluate sing_896.htm#SEC948
3190	ncrepEvaluateAt sing_897.htm#SEC949
3191	ncrepGet sing_888.htm#SEC940
3192	ncrepGetRegularMinimal ncrepGetRegularMinimal sing_904.htm#SEC956
3193	ncrepGetRegularZeroMinimal ncrepGetRegularZeroMinimal sing_903.htm#SEC955
3194	ncrepInvert sing_892.htm#SEC944
3195	ncrepIsDefined sing_899.htm#SEC951
3196	ncrepIsDefinedDim sing_898.htm#SEC950
3197	ncrepIsRegular sing_900.htm#SEC952
3198	ncrepMultiply sing_891.htm#SEC943
3199	ncrepPencilCombine sing_906.htm#SEC958
3200	ncrepPencilGet sing_905.htm#SEC957
3201	ncrepPrint sing_893.htm#SEC945
3202	ncrepRegularMinimize ncrepRegularMinimize sing_902.htm#SEC954
3203	ncrepRegularZeroMinimize ncrepRegularZeroMinimize sing_901.htm#SEC953
3204	ncrepSubstitute sing_895.htm#SEC947
3205	ncrepSubstract sing_890.htm#SEC942
3206	nctools.lib sing_724.htm#SEC776
3207	nctools_lib sing_724.htm#SEC776
3208	ndcond sing_727.htm#SEC779
3209	negateNcfrac sing_697.htm#SEC749
3210	negatedCone sing_2159.htm#SEC2235
3211	negation sing_2496.htm#IDX1045
3212	negative degree lexicographical ordering sing_962.htm#IDX442
3213	negative degree reverse lexicographical ordering Local orderings sing_962.htm#IDX440
3214	negative lexicographical ordering sing_962.htm#IDX438
3215	negativedivisor sing_2530.htm#SEC2606
3216	negativeformaldivisor negativeformaldivisor sing_2540.htm#SEC2616
3217	net sing_2778.htm#IDX1150
3218	net sing_2780.htm#SEC2856
3219	net access Command line options sing_19.htm#IDX40
3220	netBigInt sing_2786.htm#SEC2862
3221	netBigIntMat sing_2781.htm#SEC2857
3222	netBigIntMatShort sing_2782.htm#SEC2858
3223	netCoefficientRing sing_2783.htm#SEC2859
3224	netIdeal sing_2784.htm#SEC2860
3225	netInt sing_2785.htm#SEC2861
3226	netIntMat sing_2787.htm#SEC2863
3227	netIntMatShort sing_2788.htm#SEC2864
3228	netIntVector sing_2789.htm#SEC2865
3229	netIntVectorShort sing_2790.htm#SEC2866
3230	netList sing_2792.htm#SEC2868
3231	netMap sing_2793.htm#SEC2869
3232	netMap2 sing_2794.htm#SEC2870
3233	netMatrix sing_2703.htm#SEC2779
3234	netNumber sing_2791.htm#SEC2867
3235	netPoly sing_2797.htm#SEC2873
3236	netPrimePower sing_2798.htm#SEC2874
3237	netRing sing_2799.htm#SEC2875
3238	netString sing_2800.htm#SEC2876
3239	netVector sing_2702.htm#SEC2778
3240	netmatrix sing_2795.htm#SEC2871
3241	netmatrixShort sing_2796.htm#SEC2872
3242	nets.lib sing_2778.htm#SEC2854
3243	nets_lib sing_2778.htm#SEC2854
3244	netvector sing_2801.htm#SEC2877
3245	netvectorShort sing_2802.htm#SEC2878
3246	newTest sing_1986.htm#SEC2062
3247	newline sing_172.htm#SEC212
3248	news sing_2900.htm#SEC2976
3249	newstruct sing_183.htm#SEC223
3250	newstruct sing_2343.htm#IDX961
3251	newtonDiag sing_1088.htm#SEC1164
3252	newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2882.htm#SEC2958
3253	newtonPolytope sing_2185.htm#SEC2261
3254	newtonPolytopeLP sing_2191.htm#SEC2267
3255	newtonPolytopeP sing_2190.htm#SEC2266
3256	newtonpoly sing_1678.htm#SEC1754
3257	nf_icis sing_1719.htm#SEC1795
3258	nfmodStd sing_2806.htm#SEC2882
3259	nfmodSyz sing_2808.htm#SEC2884
3260	nfmodstd.lib sing_2804.htm#SEC2880
3261	nfmodstd_lib sing_2804.htm#SEC2880
3262	nfmodsyz.lib sing_2807.htm#SEC2883
3263	nfmodsyz_lib sing_2807.htm#SEC2883
3264	nilpotent Lie algebras sing_1477.htm#IDX640
3265	nmaxcones sing_2180.htm#SEC2256
3266	noether sing_403.htm#SEC443
3267	noether.lib sing_1340.htm#SEC1416
3268	noetherNormal sing_1223.htm#SEC1299
3269	noether_lib sing_1340.htm#SEC1416
3270	non-english special characters sing_411.htm#IDX283
3271	nonMonomials sing_1393.htm#SEC1469
3272	nonZeroEntry sing_1226.htm#SEC1302
3273	noncommutative, rational expressions sing_873.htm#IDX422
3274	none, option sing_318.htm#IDX150
3275	norTest sing_1360.htm#SEC1436
3276	norm sing_2065.htm#SEC2141
3277	normaform (up to a bound) sing_361.htm#IDX244
3278	normal sing_1350.htm#SEC1426
3279	normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2865.htm#IDX1215
3280	normal form sing_969.htm#IDX454
3281	normal.lib sing_1349.htm#SEC1425
3282	normalBundle sing_2865.htm#SEC2941
3283	normalC sing_1352.htm#SEC1428
3284	normalConductor sing_1364.htm#SEC1440
3285	normalFan sing_2238.htm#SEC2314
3286	normalForm sing_2531.htm#SEC2607
3287	normalI sing_1437.htm#SEC1513
3288	normalP sing_1351.htm#SEC1427
3289	normalToricRing sing_1367.htm#SEC1443 29638
3290	normalToricRingFromBinomials normalToricRingFromBinomials sing_1368.htm#SEC1444 2301
3291	normal_lib sing_1349.htm#SEC1425
3292	normalform sing_1607.htm#SEC1683
3293	normalform sing_2457.htm#IDX993
3294	normaliz sing_1.htm#IDX14 18426
3295	normaliz sing_1380.htm#SEC1456
3296	normaliz.lib sing_1365.htm#SEC1441
3297	normaliz_lib sing_1365.htm#SEC1441
3298	normalization sing_1289.htm#IDX590
3299	normalization sing_1290.htm#IDX593
3300	normalization sing_1294.htm#IDX597
3301	normalization sing_1295.htm#IDX599
3302	normalization sing_1350.htm#IDX608
3303	normalization sing_1351.htm#IDX611
3304	normalization sing_1352.htm#IDX614
3305	normalization sing_1364.htm#IDX620
3306	normalization sing_1365.htm#IDX622
3307	normalization sing_2473.htm#IDX1003
3308	normalization. sing_1286.htm#IDX589
3309	normalization. sing_1484.htm#IDX662
3310	normalize sing_1081.htm#SEC1157
3311	normalizeMonoidal sing_766.htm#SEC818
3312	normalizeRational sing_767.htm#SEC819
3313	not sing_101.htm#SEC141
3314	not equal sing_2500.htm#IDX1053
3315	not equal sing_2521.htm#IDX1100
3316	notBuckets, option sing_318.htm#IDX160
3317	notRegularity, option sing_318.htm#IDX158
3318	notSugar, option sing_318.htm#IDX159
3319	notWarnSB, option sing_318.htm#IDX181
3320	npar sing_1971.htm#SEC2047
3321	npars sing_312.htm#SEC352
3322	nrRootsDeterm sing_2096.htm#SEC2172
3323	nrRootsProbab sing_2095.htm#SEC2171
3324	nres sing_313.htm#SEC353
3325	nres (plural) sing_476.htm#SEC516
3326	nrows sing_314.htm#SEC354
3327	nrroots sing_2125.htm#SEC2201
3328	nsatiety sing_1345.htm#SEC1421
3329	nselect sing_1242.htm#SEC1318
3330	nt_solve sing_1860.htm#SEC1936
3331	ntsolve.lib sing_1859.htm#SEC1935
3332	ntsolve_lib sing_1859.htm#SEC1935
3333	number sing_144.htm#SEC184
3334	number sing_2297.htm#IDX885
3335	number declarations sing_145.htm#SEC185
3336	number expressions sing_146.htm#SEC186
3337	number operations sing_147.htm#SEC187
3338	number related functions number related functions sing_148.htm#SEC188
3339	numberOfConesOfDimension numberOfConesOfDimension sing_2182.htm#SEC2258
3340	number_e sing_1014.htm#SEC1090
3341	number_pi sing_1015.htm#SEC1091
3342	numerAlg.lib sing_1459.htm#IDX629
3343	numerAlg_lib sing_1459.htm#IDX630
3344	numerAlg_lib sing_1464.htm#IDX639
3345	numerDecom.lib sing_1464.htm#IDX633
3346	numerDecom_lib sing_1459.htm#IDX632
3347	numerDecom_lib sing_1464.htm#IDX634
3348	numerator sing_315.htm#SEC355
3349	numerical irreducible decomposition sing_1464.htm#IDX635
3350	nvars sing_316.htm#SEC356
3351	olga.lib sing_749.htm#SEC801
3352	olga_lib sing_749.htm#SEC801
3353	oneDimBelongSemigroup oneDimBelongSemigroup sing_1233.htm#SEC1309
3354	oneNcfrac sing_694.htm#SEC746
3355	onesVector sing_2187.htm#SEC2263
3356	online help The online help system sing_16.htm#SEC22
3357	open sing_317.htm#SEC357
3358	opentex sing_1888.htm#SEC1964
3359	operatorAlgebra sing_821.htm#SEC873
3360	operatorBM sing_544.htm#SEC596
3361	operatorModulo sing_545.htm#SEC597
3362	oppose sing_477.htm#SEC517
3363	opposite sing_478.htm#SEC518
3364	opposite polynomial sing_361.htm#IDX229
3365	opposite ring sing_361.htm#IDX226
3366	option sing_318.htm#SEC358
3367	option(warn) sing_70.htm#SEC110
3368	optionIsSet sing_1124.htm#SEC1200
3369	or Evaluation of logical expressions sing_101.htm#SEC141
3370	or sing_415.htm#SEC455
3371	orbit sing_1477.htm#IDX642
3372	orbit sing_1478.htm#IDX646
3373	orbit sing_1481.htm#IDX651
3374	orbit sing_1482.htm#IDX654
3375	orbitConeOrbits sing_2611.htm#SEC2687
3376	orbitCones sing_2602.htm#SEC2678
3377	orbit_variety sing_1778.htm#SEC1854
3378	orbitparam.lib sing_1477.htm#SEC1553
3379	orbitparam_lib sing_1477.htm#SEC1553
3380	ord sing_319.htm#SEC359
3381	ord_test sing_1119.htm#SEC1195
3382	order ideal, border basis sing_2829.htm#IDX1187
3383	order ideal, border basis sing_2830.htm#IDX1188
3384	ordering diffAlgebraChangeOrd sing_2485.htm#IDX1022
3385	ordering sing_2501.htm#IDX1056
3386	ordering sing_2502.htm#IDX1059
3387	orderings General definitions for orderings sing_960.htm#SEC1012
3388	orderings introduction Introduction to orderings sing_959.htm#SEC1011
3389	orderings, L sing_967.htm#SEC1019
3390	orderings, M sing_964.htm#SEC1016
3391	orderings, a sing_966.htm#SEC1018
3392	orderings, global sing_961.htm#SEC1013
3393	orderings, local sing_962.htm#SEC1014
3394	orderings, product sing_965.htm#SEC1017
3395	ordstr sing_320.htm#SEC360
3396	origin sing_2130.htm#SEC2206
3397	orthogonalize sing_1189.htm#SEC1265
3398	outer sing_1160.htm#SEC1236
3399	output sing_41.htm#SEC71
3400	outputting monomials sing_405.htm#SEC445
3401	p-adic numbers sing_32.htm#SEC46
3402	pFactor sing_2020.htm#SEC2096
3403	pIntersect sing_508.htm#SEC560
3404	pIntersectSyz sing_509.htm#SEC561
3405	package sing_149.htm#SEC189
3406	package declarations package declarations sing_150.htm#SEC190
3407	package related functions package related functions sing_151.htm#SEC191
3408	pairset sing_2085.htm#SEC2161
3409	par sing_321.htm#SEC361
3410	par2varRing sing_997.htm#SEC1073
3411	paraConic sing_1492.htm#SEC1568
3412	paraPlaneCurve sing_1486.htm#SEC1562
3413	parallel skeletons sing_1063.htm#IDX533
3414	parallel.lib sing_1063.htm#SEC1139
3415	parallelTestAND sing_1067.htm#SEC1143
3416	parallelTestOR sing_1068.htm#SEC1144
3417	parallelWaitAll sing_1066.htm#SEC1142
3418	parallelWaitFirst sing_1065.htm#SEC1141
3419	parallelWaitN sing_1064.htm#SEC1140
3420	parallel_lib sing_1063.htm#SEC1139
3421	parallelization sing_1063.htm#IDX532
3422	parallelization sing_1103.htm#IDX535
3423	parallelization sing_1136.htm#IDX545
3424	param sing_1669.htm#SEC1745
3425	parameter, as numbers sing_144.htm#SEC184
3426	parameterSubstitute sing_2278.htm#SEC2354
3427	parametric annihilator sing_537.htm#IDX332
3428	parametric annihilator for variety sing_601.htm#IDX362
3429	parametric ideal sing_1026.htm#IDX460
3430	parametric ideal sing_1033.htm#IDX479
3431	parametric ideal sing_1033.htm#IDX481
3432	parametric ideal sing_1034.htm#IDX486
3433	parametrization sing_1477.htm#IDX643
3434	parametrization sing_1481.htm#IDX652
3435	parametrization sing_1669.htm#IDX804
3436	parametrizeOrbit sing_1481.htm#SEC1557
3437	paraplanecurves.lib sing_1483.htm#SEC1559
3438	paraplanecurves_lib sing_1483.htm#SEC1559
3439	pardeg sing_322.htm#SEC362
3440	parstr sing_323.htm#SEC363
3441	part sing_2433.htm#SEC2509
3442	partOver sing_2436.htm#SEC2512
3443	partUnder sing_2437.htm#SEC2513
3444	partial_molien sing_1756.htm#SEC1832
3445	partitions sing_1254.htm#SEC1330
3446	partitions sing_1254.htm#IDX578
3447	path Used environment variables sing_2909.htm#SEC3000
3448	path integral sing_1246.htm#IDX565
3449	paths Used environment variables sing_2909.htm#SEC3000
3450	pause sing_1060.htm#SEC1136
3451	pdivi sing_1028.htm#SEC1104
3452	pdivi sing_1029.htm#IDX470
3453	pdivisorplus sing_2545.htm#SEC2621
3454	permcol sing_1172.htm#SEC1248
3455	permrow sing_1173.htm#SEC1249
3456	permutationFromIntvec permutationFromIntvec sing_2617.htm#SEC2693
3457	permutationToIntvec sing_2618.htm#SEC2694
3458	permutations sing_1255.htm#IDX579
3459	permutations, sum, max, min sing_2468.htm#IDX995
3460	permute sing_1255.htm#SEC1331
3461	permute_L sing_1923.htm#SEC1999
3462	perron sing_771.htm#SEC823
3463	perron.lib sing_770.htm#SEC822
3464	perron_lib sing_770.htm#SEC822
3465	phindex.lib sing_2338.htm#IDX952
3466	phindex_lib sing_2338.htm#IDX953
3467	picksFormula sing_2200.htm#SEC2276
3468	pid sing_361.htm#IDX238
3469	plainInvariants sing_1628.htm#SEC1704
3470	planeCur sing_2455.htm#SEC2531
3471	plot sing_1901.htm#SEC1977
3472	plotRot sing_1905.htm#SEC1981
3473	plotRotated sing_1904.htm#SEC1980
3474	plotRotatedDirect sing_1907.htm#SEC1983
3475	plotRotatedList sing_1906.htm#SEC1982
3476	plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1908.htm#SEC1984
3477	plural sing_1126.htm#IDX540
3478	pmat sing_1054.htm#SEC1130
3479	pnormalf sing_1029.htm#SEC1105
3480	pointid.lib sing_1392.htm#SEC1468
3481	pointid_lib sing_1392.htm#SEC1468
3482	polSol sing_668.htm#SEC720
3483	polSolFiniteRank sing_669.htm#SEC721
3484	pollTask sing_1146.htm#SEC1222
3485	poly sing_152.htm#SEC192
3486	poly (plural) sing_442.htm#SEC482
3487	poly declarations sing_153.htm#SEC193
3488	poly declarations (plural) poly declarations (plural) sing_443.htm#SEC483
3489	poly expressions sing_154.htm#SEC194
3490	poly expressions (plural) poly expressions (plural) sing_444.htm#SEC484
3491	poly operations sing_155.htm#SEC195
3492	poly operations (plural) poly operations (plural) sing_445.htm#SEC485
3493	poly related functions poly related functions sing_156.htm#SEC196
3494	poly related functions (plural) poly related functions (plural) sing_446.htm#SEC486
3495	poly.lib sing_1069.htm#SEC1145
3496	poly2list sing_586.htm#SEC638
3497	poly2zdd sing_2359.htm#SEC2435 61839
3498	polyInterpolation sing_2548.htm#SEC2624
3499	polyVars sing_675.htm#SEC727
3500	poly_lib sing_1069.htm#SEC1145
3501	polybori sing_2343.htm#IDX957
3502	polybori.lib sing_2343.htm#IDX954
3503	polybori.lib sing_2343.htm#IDX958
3504	polybori_lib sing_2343.htm#IDX955
3505	polymake sing_2188.htm#IDX858
3506	polymake.lib sing_2188.htm#SEC2264
3507	polymakePolytope sing_2189.htm#SEC2265
3508	polymake_lib sing_2188.htm#SEC2264
3509	polynomial sing_2512.htm#IDX1081
3510	polynomial solutions sing_662.htm#IDX374
3511	polynomial, opposite sing_361.htm#IDX230
3512	polytope sing_191.htm#SEC231
3513	polytope sing_2188.htm#IDX854
3514	polytopeViaInequalities polytopeViaInequalities sing_2160.htm#SEC2236
3515	polytopeViaPoints sing_2161.htm#SEC2237
3516	pos_def sing_1200.htm#SEC1276
3517	poset sing_2328.htm#IDX943
3518	positiveOrthant sing_2131.htm#SEC2207
3519	posweight sing_1736.htm#SEC1812
3520	powSumSym sing_2390.htm#SEC2466
3521	power sing_1161.htm#SEC1237
3522	power set sing_2470.htm#IDX997
3523	powerN sing_2004.htm#SEC2080
3524	powerX sing_2013.htm#SEC2089
3525	power_products sing_1770.htm#SEC1846
3526	powerpolyX sing_1983.htm#SEC2059
3527	powersums sing_2106.htm#SEC2182
3528	preComp sing_1328.htm#SEC1404
3529	preimage sing_324.htm#SEC364
3530	preimage sing_716.htm#IDX379
3531	preimage (plural) sing_479.htm#SEC519
3532	preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1122.htm#IDX538
3533	preimageLattice sing_2746.htm#SEC2822
3534	preimageLoc sing_1122.htm#SEC1198
3535	preimageNC sing_718.htm#SEC770
3536	prepEmbDiv sing_1554.htm#SEC1630
3537	prepMat sing_1816.htm#SEC1892
3538	prepRealclassify sing_1612.htm#SEC1688
3539	prepSV sing_1918.htm#SEC1994
3540	prepareAss sing_1411.htm#SEC1487
3541	presentTree sing_1541.htm#SEC1617
3542	presentation sing_2704.htm#SEC2780
3543	presolve.lib sing_1826.htm#SEC1902
3544	presolve_lib sing_1826.htm#SEC1902
3545	primL sing_2008.htm#SEC2084
3546	primList sing_2007.htm#SEC2083
3547	primRoot sing_1451.htm#SEC1527
3548	primTest sing_1327.htm#SEC1403
3549	primary decomposition sing_1396.htm#IDX624
3550	primary decomposition sing_1419.htm#IDX625
3551	primary decomposition of modules sing_1317.htm#IDX601
3552	primary decomposition, numerical sing_1464.htm#IDX637
3553	primary_char0 sing_1760.htm#SEC1836
3554	primary_char0_no_molien primary_char0_no_molien sing_1762.htm#SEC1838
3555	primary_char0_no_molien_random primary_char0_no_molien_random sing_1767.htm#SEC1843
3556	primary_char0_random primary_char0_random sing_1765.htm#SEC1841
3557	primary_charp sing_1761.htm#SEC1837
3558	primary_charp_no_molien primary_charp_no_molien sing_1763.htm#SEC1839
3559	primary_charp_no_molien_random primary_charp_no_molien_random sing_1768.htm#SEC1844
3560	primary_charp_random primary_charp_random sing_1766.htm#SEC1842
3561	primary_charp_without primary_charp_without sing_1764.htm#SEC1840
3562	primary_charp_without_random primary_charp_without_random sing_1769.htm#SEC1845
3563	primary_invariants sing_1748.htm#SEC1824
3564	primary_invariants_random primary_invariants_random sing_1749.htm#SEC1825
3565	primdec.lib sing_1396.htm#SEC1472
3566	primdecGTZ sing_1398.htm#SEC1474
3567	primdecGTZE sing_1399.htm#SEC1475
3568	primdecMon sing_1316.htm#SEC1392
3569	primdecSY sing_1400.htm#SEC1476
3570	primdecSYE sing_1401.htm#SEC1477
3571	primdecZ sing_1420.htm#SEC1496
3572	primdecZM sing_1421.htm#SEC1497
3573	primdec_lib sing_1396.htm#SEC1472
3574	primdecint.lib sing_1419.htm#SEC1495
3575	primdecint_lib sing_1419.htm#SEC1495
3576	prime sing_325.htm#SEC365
3577	primeClosure sing_1355.htm#SEC1431
3578	primecoeffs sing_1021.htm#SEC1097
3579	primefactors sing_326.htm#SEC366
3580	primes sing_1016.htm#SEC1092
3581	primitiv.lib sing_1427.htm#SEC1503
3582	primitiv_lib sing_1427.htm#SEC1503
3583	primitive sing_1428.htm#SEC1504
3584	primitive element sing_1428.htm#IDX626
3585	primitiveSpan sing_2753.htm#SEC2829
3586	primitive_extra sing_1429.htm#SEC1505
3587	primparam sing_1623.htm#SEC1699
3588	principal intersection sing_502.htm#IDX316
3589	print sing_327.htm#SEC367
3590	print sing_2295.htm#IDX878
3591	print sing_2489.htm#IDX1031
3592	print sing_2491.htm#IDX1036
3593	print sing_2492.htm#IDX1037
3594	print sing_2514.htm#IDX1085
3595	print sing_2515.htm#IDX1086
3596	printBetti sing_2685.htm#SEC2761
3597	printFreeModule sing_2677.htm#SEC2753
3598	printGraph sing_1248.htm#SEC1324
3599	printGraphG sing_2859.htm#SEC2935
3600	printGroup sing_2734.htm#SEC2810
3601	printHom sing_2680.htm#SEC2756
3602	printMatrix sing_2676.htm#SEC2752
3603	printModule sing_2679.htm#SEC2755
3604	printMoebius sing_2334.htm#SEC2410
3605	printResolution sing_2678.htm#SEC2754
3606	printSheaf sing_2847.htm#SEC2923
3607	printStack sing_2861.htm#SEC2937
3608	printTask sing_1141.htm#SEC1217
3609	printVariety sing_2839.htm#SEC2915
3610	printf sing_328.htm#SEC368
3611	printlevel sing_404.htm#SEC444
3612	proc sing_157.htm#SEC197
3613	proc declaration sing_158.htm#SEC198
3614	proc expression sing_159.htm#SEC199
3615	procedure, ASCII help sing_56.htm#IDX125
3616	procedure, ASCII/Texinfo help sing_58.htm#IDX127
3617	procedure, texinfo help sing_57.htm#IDX126
3618	procedures, help string sing_45.htm#SEC82
3619	procedures, static Procedure definition sing_43.htm#SEC78
3620	procs with different argument types procs with different argument types sing_160.htm#SEC200
3621	prodcrit sing_2083.htm#SEC2159
3622	product sing_1017.htm#SEC1093
3623	product sing_2497.htm#IDX1047
3624	product sing_2519.htm#IDX1095
3625	product variety, abstract variety sing_2840.htm#IDX1203
3626	productVariety sing_2840.htm#SEC2916
3627	productgroup sing_2755.htm#SEC2831
3628	progress watch sing_318.htm#IDX163
3629	projectLattice sing_2747.htm#SEC2823
3630	projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2844.htm#IDX1207
3631	projective dimension purityfiltration_lib sing_772.htm#IDX388
3632	projective limes sing_32.htm#SEC46
3633	projective space, abstract variety sing_2843.htm#IDX1206
3634	projectiveBundle sing_2844.htm#SEC2920
3635	projectiveDimension sing_773.htm#SEC825
3636	projectiveSpace sing_2843.htm#SEC2919
3637	prompt sing_15.htm#SEC21
3638	prompt, option sing_318.htm#IDX182
3639	propagator sing_1246.htm#IDX563
3640	propagator sing_1249.htm#SEC1325
3641	prot, option sing_318.htm#IDX161
3642	protocol of computations sing_318.htm#IDX162
3643	proximitymatrix sing_1582.htm#SEC1658
3644	prune sing_329.htm#SEC369
3645	pruneModule sing_2711.htm#SEC2787
3646	prwalk sing_2834.htm#SEC2910
3647	psigncnd sing_1879.htm#SEC1955
3648	puiseux2generators sing_1681.htm#SEC1757
3649	puiseuxExpansion sing_2249.htm#SEC2325
3650	pure tensor sing_495.htm#IDX304
3651	purelist sing_783.htm#SEC835
3652	purity purityfiltration_lib sing_772.htm#IDX390
3653	purityFiltration sing_774.htm#SEC826
3654	purityTriang sing_775.htm#SEC827
3655	purityfiltration.lib purityfiltration_lib sing_772.htm#IDX383
3656	purityfiltration_lib purityfiltration_lib sing_772.htm#IDX384
3657	pushForward sing_2772.htm#SEC2848
3658	pwalk sing_1262.htm#SEC1338
3659	pyobject sing_192.htm#SEC232
3660	pyobject sing_2343.htm#IDX960
3661	pyobject declarations pyobject declarations sing_193.htm#SEC233
3662	pyobject expressions pyobject expressions sing_194.htm#SEC234
3663	pyobject operations sing_195.htm#SEC235
3664	pyobject related functions pyobject related functions sing_196.htm#SEC236
3665	pyramid sing_2566.htm#SEC2642
3666	python_eval sing_197.htm#SEC237
3667	python_import sing_198.htm#SEC238
3668	python_run sing_199.htm#SEC239
3669	qbase sing_2109.htm#SEC2185
3670	qepcad sing_2576.htm#SEC2652
3671	qepcadsystem sing_2577.htm#SEC2653
3672	qhmatrix sing_1734.htm#SEC1810
3673	qhmoduli.lib sing_1698.htm#SEC1774
3674	qhmoduli_lib sing_1698.htm#SEC1774
3675	qhspectrum sing_1721.htm#SEC1797
3676	qhweight sing_330.htm#SEC370
3677	qmatrix.lib sing_784.htm#SEC836
3678	qmatrix_lib sing_784.htm#SEC836
3679	qminor sing_786.htm#SEC838
3680	qrds sing_331.htm#SEC371
3681	qring Miscellaneous oddities sing_166.htm#SEC206
3682	qring sing_422.htm#IDX292
3683	qring (plural) sing_447.htm#SEC487
3684	qring declaration sing_170.htm#SEC210
3685	qring declaration (plural) qring declaration (plural) sing_448.htm#SEC488
3686	qring related functions (plural) qring related functions (plural) sing_449.htm#SEC489
3687	qring ring ideal 'factor ring' sing_1131.htm#IDX544
3688	qringNF, option sing_318.htm#IDX164
3689	qslimgb sing_996.htm#SEC1072
3690	quadraticSieve sing_2021.htm#SEC2097
3691	quantMat sing_785.htm#SEC837
3692	quickclass sing_1604.htm#SEC1680
3693	quit sing_394.htm#SEC434
3694	quotSheaf sing_2856.htm#SEC2932
3695	quote sing_332.htm#SEC372
3696	quotient sing_333.htm#SEC373
3697	quotient (plural) sing_480.htm#SEC520
3698	quotientLatticeBasis quotientLatticeBasis sing_2162.htm#SEC2238
3699	quotientMain sing_1871.htm#SEC1947
3700	quotientMon sing_1307.htm#SEC1383
3701	rHRR sing_2430.htm#SEC2506
3702	rJanet sing_2831.htm#SEC2907
3703	rMacaulay sing_1055.htm#SEC1131
3704	rad_con sing_1082.htm#SEC1158
3705	radical sing_1408.htm#SEC1484
3706	radicalEHV sing_1409.htm#SEC1485
3707	radicalMemberShip sing_2271.htm#SEC2347
3708	radicalMon sing_1308.htm#SEC1384
3709	radicalZ sing_1423.htm#SEC1499
3710	randcharpoly sing_2103.htm#SEC2179
3711	randlinpoly sing_2105.htm#SEC2181
3712	random sing_334.htm#SEC374
3713	random sing_361.htm#IDX242
3714	random sing_2316.htm#IDX917
3715	random sing_2317.htm#IDX919
3716	random number generator, seed sing_361.htm#IDX240
3717	random.lib sing_1090.htm#SEC1166
3718	randomBinomial sing_1102.htm#SEC1178
3719	randomCheck sing_1934.htm#SEC2010
3720	randomLast sing_1101.htm#SEC1177
3721	randomPoint sing_2163.htm#SEC2239
3722	randomPolyInT sing_2280.htm#SEC2356
3723	random_lib sing_1090.htm#SEC1166
3724	randomid sing_1092.htm#SEC1168
3725	randommat sing_1093.htm#SEC1169
3726	rank sing_210.htm#IDX137
3727	rank sing_335.htm#SEC375
3728	rankSheaf sing_2848.htm#SEC2924
3729	ratSol sing_670.htm#SEC722
3730	ratgb.lib sing_790.htm#IDX391
3731	ratgb_lib sing_790.htm#IDX392
3732	rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1486.htm#IDX664
3733	rational functions sing_873.htm#IDX423
3734	rational normal curve, projection. sing_1487.htm#IDX665
3735	rational normal curve, projection. sing_1490.htm#IDX666
3736	rational normal curve, projection. sing_1491.htm#IDX667
3737	rational solutions sing_662.htm#IDX375
3738	rational univariate projection sing_2103.htm#IDX851
3739	rationalCurve sing_2868.htm#SEC2944
3740	rationalPointConic sing_1488.htm#SEC1564
3741	ratstd sing_791.htm#SEC843
3742	rays sing_2164.htm#SEC2240
3743	rcolon sing_872.htm#SEC924
3744	re2squ sing_1465.htm#SEC1541
3745	read sing_336.htm#SEC376
3746	readNmzData sing_1383.htm#SEC1459 18957
3747	reading, option sing_318.htm#IDX183
3748	readline sing_1.htm#IDX5
3749	real sing_28.htm#IDX74
3750	real root isolation sing_2815.htm#IDX1182
3751	real roots, univariate polynomial sing_2110.htm#IDX853
3752	real roots, univariate projection sing_2094.htm#IDX849
3753	real roots,sign conditions sing_1877.htm#IDX829
3754	realclassify sing_2810.htm#SEC2886
3755	realclassify.lib sing_2809.htm#SEC2885
3756	realclassify_lib sing_2809.htm#SEC2885
3757	realizationDim sing_2243.htm#SEC2319
3758	realizationDimPoly sing_2245.htm#SEC2321
3759	realizationMatroids.lib realizationMatroids_lib sing_2242.htm#SEC2318
3760	realizationMatroids_lib realizationMatroids_lib sing_2242.htm#SEC2318
3761	realmorsesplit sing_2811.htm#SEC2887
3762	realpoly sing_1432.htm#SEC1508
3763	realrad sing_1434.htm#SEC1510
3764	realrad.lib sing_1431.htm#SEC1507
3765	realrad_lib sing_1431.htm#SEC1507
3766	realzero sing_1433.htm#SEC1509
3767	recursive_boolean_poly recursive_boolean_poly sing_2349.htm#SEC2425 17045
3768	recursive_from_boolean_poly recursive_from_boolean_poly sing_2355.htm#SEC2431 37794
3769	redSB, option sing_318.htm#IDX165
3770	redTail, option sing_318.htm#IDX167
3771	redThrough, option sing_318.htm#IDX168
3772	redefine, option sing_318.htm#IDX184
3773	reduce sing_337.htm#SEC377
3774	reduce sing_516.htm#IDX321
3775	reduce sing_1028.htm#IDX468
3776	reduce sing_1029.htm#IDX471
3777	reduce (letterplace) reduce (letterplace) sing_802.htm#SEC854
3778	reduce (plural) sing_481.htm#SEC521
3779	reduce (up to a bound) sing_361.htm#IDX243
3780	reduceIntChain sing_2716.htm#SEC2792
3781	reduced sing_1027.htm#IDX465
3782	reduced standard basis sing_318.htm#IDX166
3783	reduction sing_1786.htm#SEC1862
3784	reesclos.lib sing_1435.htm#SEC1511
3785	reesclos_lib sing_1435.htm#SEC1511
3786	reference sing_200.htm#SEC240
3787	reference declarations reference declarations sing_201.htm#SEC241
3788	reference expressions reference expressions sing_202.htm#SEC242
3789	reference operations reference and shared operations sing_205.htm#SEC245
3790	reference related functions reference and shared related functions sing_206.htm#SEC246
3791	regCM sing_1347.htm#SEC1423
3792	regIdeal sing_1333.htm#SEC1409
3793	regMonCurve sing_1336.htm#SEC1412
3794	regularity Syzygies and resolutions sing_338.htm#SEC378
3795	regularity sing_971.htm#SEC1028
3796	regularity sing_1347.htm#IDX606
3797	regularity sing_1348.htm#IDX607
3798	reiffen sing_555.htm#SEC607
3799	rel_orbit_variety sing_1779.htm#SEC1855
3800	relations sing_770.htm#IDX382
3801	relativeInteriorPoint relativeInteriorPoint sing_2165.htm#SEC2241
3802	relative_orbit_variety relative_orbit_variety sing_1780.htm#SEC1856
3803	relweight sing_1735.htm#SEC1811
3804	remainder sing_1864.htm#SEC1940
3805	remainderMain sing_1872.htm#SEC1948
3806	removeCone sing_2183.htm#SEC2259
3807	removepower sing_1592.htm#SEC1668
3808	repart sing_339.htm#SEC379
3809	replace sing_1973.htm#SEC2049
3810	representation, math objects Representation of mathematical objects sing_957.htm#SEC1009
3811	res sing_340.htm#SEC380
3812	resbinomial.lib sing_1495.htm#IDX670
3813	resbinomial_lib sing_1495.htm#IDX671
3814	reservedName sing_341.htm#SEC381
3815	resfunction sing_1509.htm#SEC1585
3816	resgraph.lib sing_1527.htm#SEC1603
3817	resgraph_lib sing_1527.htm#SEC1603
3818	resjung.lib sing_1531.htm#SEC1607
3819	resjung_lib sing_1531.htm#SEC1607
3820	reslist sing_1523.htm#SEC1599
3821	resolution purityfiltration_lib sing_161.htm#SEC201
3822	resolution sing_772.htm#IDX389
3823	resolution (plural) sing_450.htm#SEC490
3824	resolution declarations resolution declarations sing_162.htm#SEC202
3825	resolution declarations (plural) resolution declarations (plural) sing_451.htm#SEC491
3826	resolution expressions resolution expressions sing_163.htm#SEC203
3827	resolution expressions (plural) resolution expressions (plural) sing_452.htm#SEC492
3828	resolution graph sing_1577.htm#IDX684
3829	resolution related functions resolution related functions sing_164.htm#SEC204
3830	resolution related functions (plural) resolution related functions (plural) sing_453.htm#SEC493
3831	resolution, La Scala's method sing_291.htm#SEC331
3832	resolution, computation of sing_340.htm#IDX186
3833	resolution, hilbert-driven sing_266.htm#SEC306
3834	resolutionInLocalization resolutionInLocalization sing_2596.htm#SEC2672
3835	resolutiongraph sing_1578.htm#SEC1654
3836	resolve sing_1539.htm#SEC1615
3837	resolve.lib sing_1535.htm#SEC1611
3838	resolve_lib sing_1535.htm#SEC1611
3839	resources.lib sing_1103.htm#SEC1179
3840	resources_lib sing_1103.htm#SEC1179
3841	restriction sing_2309.htm#IDX905
3842	restriction sing_2325.htm#IDX938
3843	restriction sing_2326.htm#IDX940
3844	restriction of sing_560.htm#IDX344
3845	restrictionIdeal sing_570.htm#SEC622
3846	restrictionModule sing_571.htm#SEC623
3847	resultant sing_305.htm#SEC345
3848	resultant sing_342.htm#SEC382
3849	reszeta.lib sing_1548.htm#SEC1624
3850	reszeta_lib sing_1548.htm#SEC1624
3851	return sing_395.htm#SEC435
3852	return type of procedures Return type of procedures sing_420.htm#SEC460
3853	returnSB, option sing_318.htm#IDX152
3854	reverse sing_2124.htm#SEC2200
3855	reverse lexicographical ordering sing_961.htm#IDX429
3856	reynolds_molien sing_1755.htm#SEC1831
3857	rho sing_2015.htm#SEC2091
3858	rightInverse sing_1953.htm#SEC2029
3859	rightKernel sing_1951.htm#SEC2027
3860	rightModulo sing_736.htm#SEC788
3861	rightNF sing_735.htm#SEC787
3862	rightNFWeyl sing_687.htm#SEC739
3863	rightOre sing_756.htm#SEC808
3864	rightStd sing_734.htm#SEC786
3865	rightstd (letterplace) rightstd (letterplace) sing_803.htm#SEC855
3866	ring sing_165.htm#SEC205
3867	ring (plural) sing_454.htm#SEC494
3868	ring coefficients hasTransExtensionCoefficient sing_1129.htm#IDX542
3869	ring coefficients sing_1130.htm#IDX543
3870	ring declarations sing_167.htm#SEC207
3871	ring declarations (plural) ring declarations (plural) sing_455.htm#SEC495
3872	ring operations sing_169.htm#SEC209
3873	ring operations (plural) ring operations (plural) sing_456.htm#SEC496
3874	ring related functions ring related functions sing_168.htm#SEC208
3875	ring related functions (plural) ring related functions (plural) sing_457.htm#SEC497
3876	ring theory sing_849.htm#IDX404
3877	ring, opposite sing_361.htm#IDX227
3878	ring.lib sing_1108.htm#SEC1184
3879	ring_cf sing_210.htm#IDX138
3880	ring_lib sing_1108.htm#SEC1184
3881	ring_list sing_344.htm#SEC384
3882	ring_variable sing_2296.htm#IDX882
3883	ring_variable sing_2297.htm#IDX884
3884	ring_variable sing_2298.htm#IDX888
3885	ring_variable sing_2299.htm#IDX890
3886	ringlist sing_343.htm#SEC383
3887	ringlist (plural) sing_482.htm#SEC522
3888	ringtensor sing_1120.htm#SEC1196
3889	ringweights sing_1121.htm#SEC1197
3890	rinvar.lib sing_1791.htm#SEC1867
3891	rinvar_lib sing_1791.htm#SEC1867
3892	rmNmzFiles sing_1388.htm#SEC1464 32601
3893	rm_unitcol sing_1178.htm#SEC1254
3894	rm_unitrow sing_1177.htm#SEC1253
3895	rmx sing_1898.htm#SEC1974
3896	rncAntiCanonicalMap sing_1487.htm#SEC1563
3897	rncItProjEven sing_1491.htm#SEC1567
3898	rncItProjOdd sing_1490.htm#SEC1566
3899	root of Bernstein-Sato polynomial sing_537.htm#IDX333
3900	rootIsolation sing_2826.htm#SEC2902
3901	rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2825.htm#SEC2901
3902	rootIsolationPrimdec rootIsolationPrimdec sing_2827.htm#SEC2903
3903	rootisolation.lib sing_2815.htm#SEC2891
3904	rootisolation_lib sing_2815.htm#SEC2891
3905	rootofUnity sing_1123.htm#SEC1199
3906	roots sing_1865.htm#SEC1941
3907	rootsMain sing_1873.htm#SEC1949
3908	rootsModp sing_1997.htm#SEC2073
3909	rootsmr.lib sing_2094.htm#SEC2170
3910	rootsmr_lib sing_2094.htm#SEC2170
3911	rootsur.lib sing_2110.htm#SEC2186
3912	rootsur_lib sing_2110.htm#SEC2186
3913	round sing_1995.htm#SEC2071
3914	rowShift sing_210.htm#IDX141
3915	rowShift sing_212.htm#SEC252
3916	rowred sing_1174.htm#SEC1250
3917	rp, global ordering sing_961.htm#IDX428
3918	rstandard.lib sing_2828.htm#SEC2904
3919	rstandard_lib sing_2828.htm#SEC2904
3920	rswalk sing_2878.htm#SEC2954
3921	rtimer sing_408.htm#SEC448
3922	rvalue No rvalue of increments and assignments sing_414.htm#SEC454
3923	rvar sing_345.htm#SEC385
3924	rwalk sing_2835.htm#SEC2911
3925	rwalk.lib sing_2833.htm#SEC2909
3926	rwalk_lib sing_2833.htm#SEC2909
3927	sRes sing_2682.htm#SEC2758
3928	sa_poly_reduce sing_525.htm#SEC577
3929	sa_reduce sing_524.htm#SEC576
3930	sagbi sing_1441.htm#SEC1517
3931	sagbi basis sing_2458.htm#IDX994
3932	sagbi.lib sing_1438.htm#SEC1514
3933	sagbiAlg sing_2451.htm#SEC2527
3934	sagbiMod sing_2452.htm#SEC2528
3935	sagbiPart sing_1442.htm#SEC1518
3936	sagbiReduce sing_1440.htm#SEC1516
3937	sagbiSPoly sing_1439.htm#SEC1515
3938	sagbi_lib sing_1438.htm#SEC1514
3939	salida sing_1520.htm#SEC1596
3940	sameComponent sing_2077.htm#SEC2153
3941	sameQ sing_1876.htm#SEC1952
3942	sat sing_1243.htm#SEC1319
3943	satiety sing_1335.htm#SEC1411
3944	satstd sing_2337.htm#SEC2413
3945	saturation sing_1243.htm#IDX555
3946	saturation sing_1293.htm#IDX596
3947	saturation sing_1345.htm#IDX604
3948	saturation sing_1346.htm#IDX605
3949	sba sing_346.htm#SEC386
3950	scalarProd sing_514.htm#SEC566
3951	scheme sing_2557.htm#SEC2633
3952	schubert.lib sing_2837.htm#SEC2913
3953	schubert_lib sing_2837.htm#SEC2913
3954	sdb, source code debugger Source code debugger sing_66.htm#SEC103
3955	second degree sing_1042.htm#IDX511
3956	secondary fan sing_2188.htm#IDX856
3957	secondary polytope sing_2188.htm#IDX857
3958	secondaryPolytope sing_2193.htm#SEC2269
3959	secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1776.htm#SEC1852
3960	secondary_char0 sing_1771.htm#SEC1847
3961	secondary_charp sing_1773.htm#SEC1849
3962	secondary_no_molien sing_1774.htm#SEC1850
3963	secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1777.htm#SEC1853
3964	segre sing_2385.htm#SEC2461
3965	select sing_1244.htm#SEC1320
3966	select1 sing_1245.htm#SEC1321
3967	semaphore sing_361.htm#IDX247
3968	semaphore sing_1107.htm#SEC1183
3969	semaphores sing_1103.htm#IDX537
3970	semi-prime ideal sing_849.htm#IDX409
3971	semiCMcod2 sing_1732.htm#SEC1808
3972	semiGroup sing_2453.htm#SEC2529
3973	semiMod sing_2454.htm#SEC2530
3974	semidiv sing_2069.htm#SEC2145
3975	semigroup sing_1581.htm#SEC1657
3976	semigroup sing_1585.htm#IDX691
3977	semigroup of values sing_1671.htm#IDX806
3978	semigroupGenerator sing_2166.htm#SEC2242
3979	sep sing_1418.htm#SEC1494
3980	separateHNE sing_1682.htm#SEC1758
3981	separator sing_1318.htm#SEC1394
3982	serreRelations sing_822.htm#SEC874
3983	set sing_2291.htm#IDX868
3984	setBaseMultigrading sing_2727.htm#SEC2803
3985	setLetterplaceAttributes setLetterplaceAttributes sing_867.htm#SEC919
3986	setLinearForms sing_2167.htm#SEC2243
3987	setModuleGrading sing_2739.htm#SEC2815
3988	setMultiplicity sing_2168.htm#SEC2244
3989	setNmzDataPath sing_1385.htm#SEC1461 18123
3990	setNmzExecPath sing_1381.htm#SEC1457 38993
3991	setNmzFilename sing_1384.htm#SEC1460 20206
3992	setNmzOption sing_1378.htm#SEC1454 9012
3993	setUniformizingParameter setUniformizingParameter sing_2880.htm#SEC2956
3994	set_is_injective sing_2057.htm#SEC2133
3995	setcores sing_1105.htm#SEC1181
3996	setenv sing_361.htm#IDX250
3997	setinitials sing_2567.htm#SEC2643
3998	setring sing_347.htm#SEC387
3999	sh sing_361.htm#IDX252
4000	shared sing_200.htm#SEC240
4001	shared declarations sing_203.htm#SEC243
4002	shared expressions sing_204.htm#SEC244
4003	shared operations reference and shared operations sing_205.htm#SEC245
4004	shared related functions reference and shared related functions sing_206.htm#SEC246
4005	sheaf cohomology sing_1558.htm#IDX672
4006	sheafCoh sing_1564.htm#SEC1640 64501
4007	sheafCohBGG sing_1562.htm#SEC1638 13439
4008	sheafCohBGG2 sing_1563.htm#SEC1639 3338
4009	sheafcoh.lib sing_1558.htm#SEC1634
4010	sheafcoh_lib sing_1558.htm#SEC1634
4011	short sing_405.htm#SEC445
4012	show sing_1056.htm#SEC1132
4013	showBO sing_1540.htm#SEC1616
4014	showDataTypes sing_1542.htm#SEC1618
4015	showNmzOptions sing_1379.htm#SEC1455 64955
4016	showNuminvs sing_1376.htm#SEC1452 18934
4017	showgrades sing_777.htm#SEC829
4018	showrecursive sing_1057.htm#SEC1133
4019	signal handler sing_2907.htm#SEC2998
4020	signatureBrieskorn sing_1741.htm#SEC1817
4021	signatureL sing_2339.htm#SEC2415
4022	signatureLqf sing_2340.htm#SEC2416
4023	signatureNemethi sing_1743.htm#SEC1819
4024	signaturePuiseux sing_1742.htm#SEC1818
4025	signcnd sing_1878.htm#SEC1954
4026	signcond.lib sing_1877.htm#SEC1953
4027	signcond_lib sing_1877.htm#SEC1953
4028	simplePrune sing_2720.htm#SEC2796
4029	simplesolver sing_1822.htm#SEC1898
4030	simplex sing_348.htm#SEC388
4031	simplexOut sing_1849.htm#SEC1925
4032	simplify sing_349.htm#SEC389
4033	simplifyRat sing_682.htm#SEC734
4034	sing.lib sing_1708.htm#SEC1784
4035	sing4ti2.lib sing_1444.htm#SEC1520
4036	sing4ti2_lib sing_1444.htm#SEC1520
4037	sing_lib sing_1708.htm#SEC1784
4038	singular locus of D-module sing_662.htm#IDX369
4039	singularities sing_1640.htm#IDX708
4040	singularities sing_1641.htm#IDX719
4041	singularities sing_1642.htm#IDX722
4042	singularities sing_1643.htm#IDX725
4043	singularities sing_1644.htm#IDX728
4044	singularities sing_1645.htm#IDX732
4045	singularities sing_1646.htm#IDX736
4046	singularities sing_1647.htm#IDX742
4047	singularities sing_1648.htm#IDX750
4048	singularities sing_1649.htm#IDX756
4049	singularities sing_1650.htm#IDX764
4050	singularities sing_1651.htm#IDX774
4051	singularities sing_1739.htm#IDX821
4052	singularities sing_2363.htm#IDX980
4053	singularities sing_2447.htm#IDX989
4054	singularities, resolution of Resolution of singularities sing_944.htm#SEC996
4055	singularity sing_1605.htm#SEC1681
4056	singularrc sing_20.htm#IDX73
4057	size Miscellaneous oddities sing_350.htm#SEC390
4058	size sing_422.htm#IDX291
4059	skewmat sing_1162.htm#SEC1238
4060	sleep sing_356.htm#SEC396
4061	slimgb sing_351.htm#SEC391
4062	slimgb sing_921.htm#SEC973
4063	slimgb (plural) sing_483.htm#SEC523
4064	slocus sing_1720.htm#SEC1796
4065	smaller sing_2502.htm#IDX1057
4066	smatrix sing_171.htm#SEC211
4067	smith sing_1962.htm#SEC2038
4068	smithNormalForm sing_2775.htm#SEC2851
4069	solutionsMod2 sing_2012.htm#SEC2088
4070	solve sing_1042.htm#IDX512
4071	solve sing_1843.htm#SEC1919
4072	solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_294.htm#SEC334
4073	solve.lib sing_1841.htm#SEC1917
4074	solveTInitialFormPar solveTInitialFormPar sing_2274.htm#SEC2350
4075	solve_IP sing_1288.htm#SEC1364
4076	solve_lib sing_1841.htm#SEC1917
4077	solvelinearpart sing_1836.htm#SEC1912
4078	sort sing_1018.htm#SEC1094
4079	sort sing_2507.htm#IDX1067
4080	sortIntvec sing_592.htm#SEC644
4081	sortandmap sing_1837.htm#SEC1913
4082	sortier sing_1790.htm#SEC1866
4083	sortvars sing_1838.htm#SEC1914
4084	sortvec sing_352.htm#SEC392
4085	source sing_2698.htm#SEC2774
4086	source code debugger, sdb Source code debugger sing_66.htm#SEC103
4087	spaceCur sing_2456.htm#SEC2532
4088	spadd sing_1654.htm#SEC1730
4089	span sing_2169.htm#SEC2245
4090	sparseHomogIdeal sing_1099.htm#SEC1175
4091	sparseInterpolation sing_2552.htm#SEC2628
4092	sparseid sing_1094.htm#SEC1170
4093	sparsemat sing_1096.htm#SEC1172
4094	sparsematrix sing_1095.htm#SEC1171
4095	sparsepoly sing_1097.htm#SEC1173
4096	sparsetriag sing_1098.htm#SEC1174
4097	spcurve.lib sing_1728.htm#SEC1804
4098	spcurve_lib sing_1728.htm#SEC1804
4099	special characters, non-english sing_411.htm#IDX284
4100	spectral pairs sing_1640.htm#IDX717
4101	spectral pairs sing_1647.htm#IDX749
4102	spectral pairs sing_1649.htm#IDX763
4103	spectral pairs sing_1650.htm#IDX772
4104	spectral pairs sing_1662.htm#IDX788
4105	spectral pairs sing_1664.htm#IDX799
4106	spectralNeg sing_1550.htm#SEC1626
4107	spectrum sing_1640.htm#IDX716
4108	spectrum sing_1646.htm#SEC1722
4109	spectrum sing_1646.htm#IDX741
4110	spectrum sing_1647.htm#IDX748
4111	spectrum sing_1648.htm#IDX755
4112	spectrum sing_1649.htm#IDX762
4113	spectrum sing_1650.htm#IDX771
4114	spectrum sing_1662.htm#IDX787
4115	spectrum sing_1664.htm#IDX798
4116	spectrum sing_1739.htm#IDX823
4117	spectrum.lib sing_1738.htm#SEC1814
4118	spectrum_lib sing_1738.htm#SEC1814
4119	spectrumnd sing_1739.htm#SEC1815
4120	spgamma sing_1661.htm#SEC1737
4121	spgeomgenus sing_1660.htm#SEC1736
4122	spissemicont sing_1657.htm#SEC1733
4123	split sing_1058.htm#SEC1134
4124	splitPolygon sing_2195.htm#SEC2271
4125	splitring sing_1430.htm#SEC1506
4126	splitting sing_1326.htm#SEC1402
4127	spmilnor sing_1659.htm#SEC1735
4128	spmul sing_1656.htm#SEC1732
4129	spnf sing_1204.htm#SEC1280
4130	spoly sing_2080.htm#SEC2156
4131	sppairs sing_1647.htm#SEC1723
4132	sppnf sing_1652.htm#SEC1728
4133	sppprint sing_1653.htm#SEC1729
4134	spprint sing_1205.htm#SEC1281
4135	sprintf sing_354.htm#SEC394
4136	spsemicont sing_1658.htm#SEC1734
4137	spsub sing_1655.htm#SEC1731
4138	sqfrNorm sing_1866.htm#SEC1942
4139	sqfrNormMain sing_1874.htm#SEC1950
4140	sqr sing_1992.htm#SEC2068
4141	sqrfree sing_353.htm#SEC393
4142	squareRoot sing_2011.htm#SEC2087
4143	squarefree sing_1683.htm#SEC1759
4144	sres sing_355.htm#SEC395
4145	ssi Parallelization with ssi links sing_916.htm#SEC968
4146	stabilizer sing_2376.htm#SEC2452
4147	stack, moduli space of stable maps sing_2861.htm#IDX1211
4148	stack, moduli space of stable maps, rational curves moduliSpace sing_2860.htm#IDX1210
4149	stackNets sing_2803.htm#SEC2879
4150	staircase sing_1883.htm#SEC1959
4151	standard sing_2087.htm#SEC2163
4152	standard bases, saturation sing_2337.htm#IDX951
4153	standard bases. sing_2336.htm#IDX950
4154	standard.lib sing_995.htm#IDX456
4155	standard_lib sing_995.htm#IDX457
4156	startNmz sing_1387.htm#SEC1463 21925
4157	startTasks sing_1142.htm#SEC1218
4158	static procedures Procedure definition sing_43.htm#SEC78
4159	status sing_356.htm#SEC396
4160	std sing_357.htm#SEC397
4161	std sing_919.htm#SEC971
4162	std (letterplace) sing_804.htm#SEC856
4163	std (plural) sing_484.htm#SEC524
4164	stdfglm sing_358.htm#SEC398
4165	stdhilb sing_359.htm#SEC399
4166	stdlocus sing_1039.htm#SEC1115
4167	stopTask sing_1143.htm#SEC1219
4168	storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2616.htm#SEC2692
4169	stratify sing_1817.htm#SEC1893
4170	stratify.lib sing_1815.htm#SEC1891
4171	stratify_lib sing_1815.htm#SEC1891
4172	string Miscellaneous oddities sing_172.htm#SEC212
4173	string sing_422.htm#IDX294
4174	string sing_2489.htm#IDX1030
4175	string sing_2491.htm#IDX1035
4176	string sing_2492.htm#IDX1038
4177	string sing_2514.htm#IDX1084
4178	string sing_2515.htm#IDX1087
4179	string declarations sing_173.htm#SEC213
4180	string expressions sing_174.htm#SEC214
4181	string operations sing_176.htm#SEC216
4182	string related functions string related functions sing_177.htm#SEC217
4183	string type cast sing_175.htm#SEC215
4184	stripHNE sing_1680.htm#SEC1756
4185	structure sing_2511.htm#IDX1078
4186	sturm sing_2120.htm#SEC2196
4187	sturmha sing_2122.htm#SEC2198
4188	sturmhaseq sing_2123.htm#SEC2199
4189	sturmquery sing_2098.htm#SEC2174
4190	sturmseq sing_2121.htm#SEC2197
4191	sublists sing_2470.htm#SEC2546
4192	submat sing_1163.htm#SEC1239
4193	subquotient sing_2690.htm#SEC2766
4194	subrInterred sing_1087.htm#SEC1163
4195	subset_sum01 sing_2041.htm#SEC2117
4196	subset_sum02 sing_2042.htm#SEC2118
4197	subst sing_360.htm#SEC400
4198	subst (plural) sing_485.htm#SEC525
4199	substitute sing_1086.htm#SEC1162
4200	sugarCrit, option sing_318.htm#IDX169
4201	sum sing_1019.htm#SEC1095
4202	sum sing_2494.htm#IDX1041
4203	sum sing_2516.htm#IDX1089
4204	sum_of_powers sing_2389.htm#SEC2465
4205	sumlist sing_1522.htm#SEC1598
4206	sumofquotients sing_2869.htm#SEC2945
4207	super-commutative algebras Graded commutative algebras (SCA) sing_792.htm#SEC844
4208	superCommutative sing_733.htm#SEC785
4209	super_increasing_knapsack super_increasing_knapsack sing_2053.htm#SEC2129
4210	surf.lib sing_1900.htm#SEC1976
4211	surf_lib sing_1900.htm#SEC1976
4212	surfacesignature.lib surfacesignature_lib sing_1740.htm#SEC1816
4213	surfacesignature_lib surfacesignature_lib sing_1740.htm#SEC1816
4214	surfer sing_1.htm#IDX8
4215	surfer sing_1902.htm#SEC1978
4216	surfex sing_1.htm#IDX7
4217	surfex.lib sing_1903.htm#SEC1979
4218	surfex_lib sing_1903.htm#SEC1979
4219	suspend sing_356.htm#SEC396
4220	swalk sing_2877.htm#SEC2953
4221	swalk.lib sing_2876.htm#SEC2952
4222	swalk_lib sing_2876.htm#SEC2952
4223	swap sing_1609.htm#SEC1685
4224	swap sing_2298.htm#IDX886
4225	switch No case or switch statement sing_416.htm#SEC456
4226	switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2885.htm#SEC2961
4227	syModStd sing_1454.htm#SEC1530
4228	symNsym sing_2383.htm#SEC2459
4229	sym_gauss sing_1188.htm#SEC1264
4230	symm sing_2382.htm#SEC2458
4231	symmStd sing_1453.htm#SEC1529
4232	symmat sing_1164.htm#SEC1240
4233	symmetric basis sing_1180.htm#IDX548
4234	symmetric power sing_1182.htm#IDX550
4235	symmetric product sing_2578.htm#IDX1137
4236	symmetricBasis sing_1180.htm#SEC1256
4237	symmetricPower sing_1182.htm#SEC1258
4238	symmetricPowerSheaf sing_2855.htm#SEC2931
4239	symmetries sing_2372.htm#IDX988
4240	symmfunc sing_2107.htm#SEC2183
4241	symodstd.lib sing_1448.htm#SEC1524
4242	symodstd_lib sing_1448.htm#SEC1524
4243	sympower sing_1811.htm#SEC1887
4244	symsignature sing_2097.htm#SEC2173
4245	syndrome sing_1930.htm#SEC2006
4246	sysBin sing_1928.htm#SEC2004
4247	sysCRHT sing_1925.htm#SEC2001
4248	sysCRHTMindist sing_1926.htm#SEC2002
4249	sysFL sing_1941.htm#SEC2017
4250	sysNewton sing_1927.htm#SEC2003
4251	sysQE sing_1931.htm#SEC2007
4252	sys_code sing_1922.htm#SEC1998
4253	system sing_361.htm#SEC401
4254	system, -- sing_361.htm#IDX274
4255	system, --long_option_name sing_361.htm#IDX277
4256	system, --long_option_name=value sing_361.htm#IDX279
4257	system, HC sing_361.htm#IDX213
4258	system, LLL sing_361.htm#IDX217
4259	system, Singular sing_361.htm#IDX256
4260	system, SingularLib sing_361.htm#IDX258
4261	system, absFact sing_361.htm#IDX190
4262	system, alarm sing_361.htm#IDX189
4263	system, blackbox sing_361.htm#IDX191
4264	system, bracket sing_361.htm#IDX196
4265	system, browsers sing_361.htm#IDX195
4266	system, complexNearZero sing_361.htm#IDX198
4267	system, contributors sing_361.htm#IDX200
4268	system, cpu sing_361.htm#IDX202
4269	system, cpu sing_361.htm#IDX273
4270	system, denom_list sing_361.htm#IDX204
4271	system, eigenvals sing_361.htm#IDX205
4272	system, env sing_361.htm#IDX206
4273	system, executable sing_361.htm#IDX208
4274	system, getPrecDigits sing_361.htm#IDX211
4275	system, getenv sing_361.htm#IDX210
4276	system, gmsnf sing_361.htm#IDX212
4277	system, hessenberg sing_361.htm#IDX214
4278	system, install sing_361.htm#IDX216
4279	system, nblocks sing_361.htm#IDX220
4280	system, nc_hilb sing_361.htm#IDX222
4281	system, neworder sing_361.htm#IDX223
4282	system, newstruct sing_361.htm#IDX224
4283	system, opp sing_361.htm#IDX225
4284	system, oppose sing_361.htm#IDX228
4285	system, pcvBasis sing_361.htm#IDX237
4286	system, pcvCV2P sing_361.htm#IDX235
4287	system, pcvDim sing_361.htm#IDX236
4288	system, pcvLAddL sing_361.htm#IDX231
4289	system, pcvMinDeg sing_361.htm#IDX233
4290	system, pcvP2CV sing_361.htm#IDX234
4291	system, pcvPMulL sing_361.htm#IDX232
4292	system, pid sing_361.htm#IDX239
4293	system, random sing_361.htm#IDX241
4294	system, reserve sing_361.htm#IDX245
4295	system, reservedLink sing_361.htm#IDX246
4296	system, semaphore sing_361.htm#IDX248
4297	system, semic sing_361.htm#IDX249
4298	system, setenv sing_361.htm#IDX251
4299	system, sh sing_361.htm#IDX253
4300	system, shrinktest sing_361.htm#IDX254
4301	system, spadd sing_361.htm#IDX259
4302	system, spectrum sing_361.htm#IDX260
4303	system, spmul sing_361.htm#IDX261
4304	system, std_syz sing_361.htm#IDX262
4305	system, tensorModuleMult sing_361.htm#IDX263
4306	system, twostd sing_361.htm#IDX264
4307	system, uname sing_361.htm#IDX267
4308	system, version sing_361.htm#IDX270
4309	system, with sing_361.htm#IDX271
4310	systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2593.htm#SEC2669
4311	syz sing_362.htm#SEC402
4312	syz (letterplace) sing_805.htm#SEC857
4313	syz (plural) sing_486.htm#SEC526
4314	tDetropicalise sing_2276.htm#SEC2352
4315	tInitialForm sing_2260.htm#SEC2336
4316	tInitialFormPar sing_2272.htm#SEC2348
4317	tInitialFormParMax sing_2273.htm#SEC2349
4318	tInitialIdeal sing_2261.htm#SEC2337
4319	tab sing_1059.htm#SEC1135
4320	tail sing_2076.htm#SEC2152
4321	tame polynomial sing_1662.htm#IDX780
4322	tame polynomial sing_1663.htm#IDX790
4323	tame polynomial sing_1664.htm#IDX791
4324	tangentGens sing_1478.htm#SEC1554
4325	tangentcone sing_1727.htm#SEC1803
4326	target sing_2697.htm#SEC2773
4327	task sing_1136.htm#IDX547
4328	tasks.lib sing_1136.htm#SEC1212
4329	tasks_lib sing_1136.htm#SEC1212
4330	tau_es sing_1635.htm#SEC1711
4331	tau_es2 sing_1589.htm#SEC1665
4332	tdCf sing_2418.htm#SEC2494
4333	tdFactor sing_2420.htm#SEC2496
4334	tdProj sing_2423.htm#SEC2499
4335	tdTerms sing_2419.htm#SEC2495
4336	teachstd.lib sing_2074.htm#SEC2150
4337	teachstd_lib sing_2074.htm#SEC2150
4338	template.lib sing_55.htm#IDX120
4339	template.lib sing_55.htm#IDX123
4340	template_lib sing_55.htm#SEC92
4341	template_lib sing_55.htm#IDX121
4342	tensor sing_363.htm#SEC403
4343	tensor sing_495.htm#IDX308
4344	tensor algebra sing_856.htm#IDX412
4345	tensorFreeModule sing_2709.htm#SEC2785
4346	tensorFreemodMod sing_2708.htm#SEC2784
4347	tensorMatrix sing_2705.htm#SEC2781
4348	tensorMod sing_1283.htm#SEC1359
4349	tensorModFreemod sing_2707.htm#SEC2783
4350	tensorModule sing_2706.htm#SEC2782
4351	tensorProduct sing_2710.htm#SEC2786
4352	tensorSheaf sing_2854.htm#SEC2930
4353	term orderings General definitions for orderings sing_960.htm#SEC1012
4354	term orderings introduction Introduction to orderings sing_959.htm#SEC1011
4355	testFraction sing_754.htm#SEC806
4356	testLift sing_868.htm#SEC920
4357	testLocData sing_751.htm#SEC803
4358	testNCfac sing_652.htm#SEC704
4359	testNcfrac sing_700.htm#SEC752
4360	testNcfracExamples sing_701.htm#SEC753
4361	testNcloc sing_712.htm#SEC764
4362	testNclocExamples sing_713.htm#SEC765
4363	testOlga sing_768.htm#SEC820
4364	testOlgaExamples sing_769.htm#SEC821
4365	testParametrization sing_1493.htm#SEC1569
4366	testPointConic sing_1494.htm#SEC1570
4367	testPrimary sing_1406.htm#SEC1482
4368	testPrimaryE sing_1407.htm#SEC1483
4369	testSyz sing_869.htm#SEC921
4370	tetrahedronGroup sing_847.htm#SEC899
4371	tex sing_1889.htm#SEC1965
4372	texDrawBasic sing_2267.htm#SEC2343
4373	texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2269.htm#SEC2345
4374	texDrawTriangulation texDrawTriangulation sing_2270.htm#SEC2346
4375	texDrawTropical sing_2268.htm#SEC2344
4376	texMatrix sing_2266.htm#SEC2342
4377	texNumber sing_2264.htm#SEC2340
4378	texPolynomial sing_2265.htm#SEC2341
4379	texcoef sing_1970.htm#SEC2046
4380	texdemo sing_1890.htm#SEC1966
4381	texfactorize sing_1891.htm#SEC1967
4382	texmap sing_1892.htm#SEC1968
4383	texname sing_1893.htm#SEC1969
4384	texobj sing_1894.htm#SEC1970
4385	texpoly sing_1895.htm#SEC1971
4386	texproc sing_1896.htm#SEC1972
4387	texring sing_1897.htm#SEC1973
4388	the first alternative algorithm sing_1260.htm#IDX584
4389	three_elements sing_2060.htm#SEC2136
4390	timeFactorize sing_1023.htm#SEC1099
4391	timeStd sing_1022.htm#SEC1098
4392	timer sing_406.htm#SEC446
4393	timer resolution, setting the sing_361.htm#IDX280
4394	timestep sing_2570.htm#SEC2646
4395	tjurina sing_1723.htm#SEC1799
4396	tmatrix sing_1650.htm#SEC1726
4397	todd sing_2415.htm#SEC2491
4398	toddE sing_2416.htm#SEC2492
4399	toddPoly sing_2429.htm#SEC2505
4400	tolessvars sing_1835.htm#SEC1911
4401	topChernClass sing_2851.htm#SEC2927
4402	topological invariants sing_1577.htm#IDX682
4403	topological invariants sing_1584.htm#IDX689
4404	topological invariants sing_1585.htm#IDX693
4405	topological invariants sing_1586.htm#IDX697
4406	topological invariants sing_1587.htm#IDX701
4407	toric ideals sing_975.htm#SEC1032
4408	toric ring sing_1365.htm#IDX623
4409	toric.lib sing_1455.htm#SEC1531
4410	toric_ideal sing_1456.htm#SEC1532
4411	toric_lib sing_1455.htm#SEC1531
4412	toric_std sing_1457.htm#SEC1533
4413	torus sing_1808.htm#SEC1884
4414	torusInvariants sing_1371.htm#SEC1447 911
4415	torusrep sing_1809.htm#SEC1885
4416	torusreynolds sing_1814.htm#SEC1890
4417	total divisors sing_495.htm#IDX305
4418	total multiplicities sing_1577.htm#IDX685
4419	totalChernClass sing_2849.htm#SEC2925
4420	totalSegreClass sing_2852.htm#SEC2928
4421	totalmultiplicities sing_1579.htm#SEC1655
4422	trace sing_364.htm#SEC404
4423	tracemult sing_2101.htm#SEC2177
4424	transpose sing_365.htm#SEC405
4425	trapezoid sing_2564.htm#SEC2640
4426	triMNewton sing_1861.htm#SEC1937
4427	triagmatrix sing_1100.htm#SEC1176
4428	triang.lib sing_1854.htm#SEC1930
4429	triangL sing_1855.htm#SEC1931
4430	triangL_solve sing_1852.htm#SEC1928
4431	triangLf_solve sing_1850.htm#SEC1926
4432	triangLfak sing_1856.htm#SEC1932
4433	triangM sing_1857.htm#SEC1933
4434	triangMH sing_1858.htm#SEC1934
4435	triangM_solve sing_1851.htm#SEC1927
4436	triang_lib sing_1854.htm#SEC1930
4437	triang_solve sing_1853.htm#SEC1929
4438	triangularGroup sing_848.htm#SEC900
4439	triangulations sing_2192.htm#SEC2268
4440	tropical curves sing_2246.htm#IDX863
4441	tropical geometry sing_1246.htm#IDX558
4442	tropical geometry sing_2879.htm#IDX1222
4443	tropical mirror symmetry sing_1246.htm#IDX560
4444	tropical polynomials sing_2246.htm#IDX864
4445	tropical varieties sing_2879.htm#IDX1223
4446	tropical.lib sing_2246.htm#IDX861
4447	tropicalCurve sing_2251.htm#SEC2327
4448	tropicalJInvariant sing_2254.htm#SEC2330
4449	tropicalLifting sing_2247.htm#SEC2323
4450	tropicalLinkNewton sing_2887.htm#SEC2963
4451	tropicalNewton.lib sing_2879.htm#SEC2955
4452	tropicalNewton_lib sing_2879.htm#SEC2955
4453	tropicalPointNewton sing_2884.htm#SEC2960
4454	tropicalSubst sing_2279.htm#SEC2355
4455	tropicalVariety sing_2286.htm#SEC2362
4456	tropicalVarietyNewton tropicalVarietyNewton sing_2886.htm#SEC2962
4457	tropical_lib sing_2246.htm#IDX862
4458	tropicalise sing_2258.htm#SEC2334
4459	tropicaliseSet sing_2259.htm#SEC2335
4460	truncate sing_1559.htm#SEC1635 13545
4461	truncateFast sing_1560.htm#SEC1636 5124
4462	truncated module sing_1559.htm#IDX673
4463	truncated module sing_1560.htm#IDX674
4464	tst_ncfactor sing_661.htm#SEC713
4465	twalk sing_1259.htm#SEC1335
4466	two-sided sing_495.htm#IDX306
4467	two-sided Groebner basis sing_495.htm#IDX307
4468	twostd sing_361.htm#IDX265
4469	twostd (letterplace) twostd (letterplace) sing_806.htm#SEC858
4470	twostd (plural) sing_487.htm#SEC527
4471	type sing_366.htm#SEC406
4472	type B sing_2314.htm#IDX913
4473	type D sing_2315.htm#IDX915
4474	type,custom Definition of a user defined type sing_184.htm#SEC224
4475	type2arr sing_2292.htm#SEC2368
4476	typecasting sing_2292.htm#IDX869
4477	typecasting sing_2293.htm#IDX871
4478	typecasting sing_2294.htm#IDX874
4479	typeof sing_367.htm#SEC407
4480	u sing_2556.htm#SEC2632
4481	uname sing_361.htm#IDX266
4482	unbounded_knapsack sing_2043.htm#SEC2119
4483	unipotent groups sing_1477.htm#IDX641
4484	uniquePoint sing_2170.htm#SEC2246
4485	unitMatrix sing_2821.htm#SEC2897
4486	unitmat sing_1165.htm#SEC1241
4487	univariate sing_368.htm#SEC408
4488	univarpoly sing_2108.htm#SEC2184
4489	universal sing_2508.htm#IDX1070
4490	universal sing_2509.htm#IDX1072
4491	universal derivation diffAlgebraUnivDerIdeal sing_2484.htm#IDX1021
4492	unknown syndrome Decoding method based on quadratic equations sing_991.htm#SEC1062
4493	unset sing_279.htm#SEC319
4494	untyped definitions sing_88.htm#SEC128
4495	untyped definitions sing_427.htm#SEC467
4496	updatePairs sing_2086.htm#SEC2162
4497	ures_solve sing_1844.htm#SEC1920
4498	uressolve sing_369.htm#SEC409
4499	usage, option sing_318.htm#IDX185
4500	used environment variables Used environment variables sing_2909.htm#SEC3000
4501	user interface, Emacs Emacs user interface sing_21.htm#SEC28
4502	vStd sing_2462.htm#SEC2538
4503	val sing_2881.htm#SEC2957
4504	valvars sing_1839.htm#SEC1915
4505	vandermonde sing_370.htm#SEC410
4506	vanishId sing_1940.htm#SEC2016
4507	var sing_371.htm#SEC411
4508	varMat sing_2296.htm#SEC2372
4509	varNum sing_2297.htm#SEC2373
4510	variables sing_372.htm#SEC412
4511	variables sing_2296.htm#IDX881
4512	variables sing_2297.htm#IDX883
4513	variables sing_2298.htm#IDX887
4514	variables sing_2299.htm#IDX889
4515	variablesSorted sing_533.htm#SEC585
4516	variablesStandard sing_532.htm#SEC584
4517	vars2pars sing_677.htm#SEC729
4518	varsigns sing_2113.htm#SEC2189
4519	varstr sing_373.htm#SEC413
4520	vdim sing_374.htm#SEC414
4521	vdim (plural) sing_488.htm#SEC528
4522	vec2poly sing_515.htm#SEC567
4523	vecFieldToMatrix sing_2895.htm#SEC2971
4524	vector sing_178.htm#SEC218
4525	vector declarations sing_179.htm#SEC219
4526	vector expressions sing_180.htm#SEC220
4527	vector operations sing_181.htm#SEC221
4528	vector related functions vector related functions sing_182.htm#SEC222
4529	verify sing_2104.htm#SEC2180
4530	versal sing_1630.htm#SEC1706
4531	version sing_361.htm#IDX269
4532	vertexAdjacencyGraph vertexAdjacencyGraph sing_2239.htm#SEC2315
4533	vertexEdgeGraph sing_2240.htm#SEC2316
4534	vertices sing_2186.htm#SEC2262
4535	vfilt sing_1648.htm#SEC1724
4536	view sing_1960.htm#SEC2036
4537	visual sing_2241.htm#SEC2317
4538	visualize sing_2555.htm#SEC2631
4539	voice sing_409.htm#SEC449
4540	vwfilt sing_1649.htm#SEC1725
4541	wUnit sing_1998.htm#SEC2074
4542	waitAllTasks sing_1145.htm#SEC1221
4543	waitTasks sing_1144.htm#SEC1220
4544	waitall sing_375.htm#SEC415
4545	waitfirst sing_376.htm#SEC416
4546	walk, groebner sing_1257.htm#IDX580
4547	walk, groebner sing_2721.htm#IDX1145
4548	walk, groebner sing_2833.htm#IDX1191
4549	walk, groebner sing_2876.htm#IDX1220
4550	warkedPreimageStd sing_2595.htm#SEC2671
4551	warn, option sing_70.htm#SEC110
4552	warn, option sing_318.htm#IDX151
4553	watchdog sing_1020.htm#SEC1096
4554	wedge sing_377.htm#SEC417
4555	weierstr.lib sing_2089.htm#SEC2165
4556	weierstrDiv sing_2090.htm#SEC2166
4557	weierstrPrep sing_2091.htm#SEC2167
4558	weierstr_lib sing_2089.htm#SEC2165
4559	weierstrassForm sing_2255.htm#SEC2331
4560	weight sing_378.htm#SEC418
4561	weight filtration sing_1640.htm#IDX713
4562	weight filtration sing_1647.htm#IDX747
4563	weight filtration sing_1649.htm#IDX761
4564	weight filtration sing_1650.htm#IDX769
4565	weight filtration sing_1662.htm#IDX785
4566	weight filtration sing_1664.htm#IDX796
4567	weightKB sing_379.htm#SEC419
4568	weightM, option sing_318.htm#IDX170
4569	weighted lexicographical ordering sing_961.htm#IDX436
4570	weighted reverse lexicographical ordering Global orderings sing_961.htm#IDX434
4571	weightedRing sing_726.htm#SEC778
4572	whichvariable sing_2112.htm#SEC2188
4573	while sing_396.htm#SEC436
4574	withDim sing_210.htm#IDX145
4575	withHilb sing_210.htm#IDX143
4576	withMult sing_210.htm#IDX146
4577	withRes sing_210.htm#IDX144
4578	withSB sing_210.htm#IDX142
4579	wp, global ordering sing_961.htm#IDX435
4580	write sing_380.htm#SEC420
4581	writeNmzData sing_1382.htm#SEC1458 38467
4582	writeNmzPaths sing_1386.htm#SEC1462 sprintf
4583	writing monomials sing_405.htm#SEC445
4584	ws, local ordering sing_962.htm#IDX446
4585	wurzel sing_1980.htm#SEC2056
4586	xchange sing_1974.htm#SEC2050
4587	xdvi sing_1899.htm#SEC1975
4588	zdd sing_2343.htm#IDX962
4589	zdd2poly sing_2360.htm#SEC2436 55047
4590	zero sing_2670.htm#SEC2746
4591	zero-dimensional sing_2109.htm#IDX852
4592	zeroMod sing_1322.htm#SEC1398
4593	zeroNcfrac sing_693.htm#SEC745
4594	zeroOpt sing_1331.htm#SEC1407
4595	zeroRadical sing_1228.htm#SEC1304
4596	zeroSet sing_1867.htm#SEC1943
4597	zerodec sing_1415.htm#SEC1491
4598	zeroset.lib sing_1862.htm#SEC1938
4599	zeroset_lib sing_1862.htm#SEC1938
4600	zetaDL sing_1552.htm#SEC1628
4601	{ sing_36.htm#IDX78
4602	\|\| sing_36.htm#IDX103
4603	\|\| sing_101.htm#SEC141
4604	} sing_36.htm#IDX79
4605	~ sing_36.htm#IDX117
4606	~ sing_397.htm#SEC437

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