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singular.idx @ 662704

spielwiese

Last change on this file since 662704 was 2e69cf, checked in by Hans Schoenemann <hannes@…>, 4 years ago
4.1.3p2
Property mode set to `100644`
File size: 180.1 KB

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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_1047.htm#SEC1128
172	AG codes sing_956.htm#SEC1013
173	AGcode_L sing_1917.htm#SEC1998
174	AGcode_Omega sing_1918.htm#SEC1999
175	ASCII sing_1007.htm#SEC1088
176	ASCII links sing_117.htm#SEC157
177	ASSUME sing_64.htm#SEC101
178	A_L sing_1607.htm#SEC1688
179	A_Z sing_1005.htm#SEC1086
180	A_Z_L sing_1006.htm#SEC1087
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_1912.htm#SEC1993
183	Adjoint ideal sing_1484.htm#IDX659
184	Alexander polynomial sing_1578.htm#IDX683
185	Algebraic Geometry codes sing_1911.htm#IDX831
186	Algebraic dependence Algebraic dependence sing_935.htm#SEC992
187	Algebraic geometry sing_1459.htm#SEC1540
188	AltVarEnd sing_744.htm#SEC798
189	AltVarStart sing_743.htm#SEC797
190	Ann sing_1398.htm#SEC1479
191	Appel function sing_560.htm#IDX348
192	Appel hypergeometric function sing_560.htm#IDX349
193	Applications sing_954.htm#SEC1011
194	Arnol'd sing_2364.htm#IDX981
195	Arnold, classification. sing_2449.htm#IDX991
196	Arnold, classification. sing_2450.htm#IDX992
197	ArnoldAction sing_1700.htm#SEC1781
198	Assignments for user defined types Assignments for user defined types sing_188.htm#SEC228
199	AssocTanToEnv sing_1041.htm#SEC1122
200	Atkin sing_2000.htm#SEC2081
201	Authors sing_1.htm#IDX16
202	Automatic Deduction sing_1047.htm#IDX514
203	Automatic Demonstration sing_1047.htm#IDX515
204	BFBoundsBudur sing_597.htm#SEC651
205	BINresol sing_1497.htm#SEC1578
206	BSidealFromAnn sing_595.htm#SEC649
207	Background sing_3.htm#SEC5
208	Basic programming sing_910.htm#SEC967
209	Basic programming sing_910.htm#SEC967
210	BelongSemig sing_2445.htm#SEC2526
211	BerlekampMassey sing_2551.htm#SEC2632
212	Bern sing_2418.htm#SEC2499
213	Bernstein operator sing_537.htm#IDX330
214	Bernstein-Sato ideal sing_592.htm#IDX351
215	Bernstein-Sato polynomial sing_502.htm#IDX311
216	Bernstein-Sato polynomial sing_537.htm#IDX327
217	Bernstein-Sato polynomial sing_1641.htm#IDX714
218	Bernstein-Sato polynomial sing_1645.htm#IDX731
219	Bernstein-Sato polynomial for variety sing_600.htm#IDX359
220	BernsteinSatoIdeal sing_596.htm#SEC650
221	Betti sing_2685.htm#SEC2766
222	Betti number Syzygies and resolutions sing_972.htm#SEC1034
223	BettiNumsH sing_2582.htm#SEC2663
224	BettiNumsN sing_2590.htm#SEC2671
225	BettiNumsQp sing_2585.htm#SEC2666
226	BettiNumsS sing_2588.htm#SEC2669
227	Betty number sing_2579.htm#IDX1130
228	Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_982.htm#SEC1044
229	Bimodules Bimodules and syzygies and lifts sing_811.htm#SEC865
230	Bisyzygy Bimodules and syzygies and lifts sing_811.htm#SEC865
231	BlowingUp sing_1620.htm#SEC1701
232	Blowupcenter sing_1500.htm#SEC1581
233	BorelCheck sing_1575.htm#SEC1656
234	Bott's formula sing_2838.htm#IDX1199
235	Branches of space curve singularities Branches of space curve singularities sing_943.htm#SEC1000
236	Briancon-Maisonobe algorithm sing_537.htm#IDX336
237	Brieskorn lattice sing_1641.htm#IDX710
238	Brieskorn lattice sing_1642.htm#IDX721
239	Brieskorn lattice sing_1643.htm#IDX724
240	Brieskorn lattice sing_1644.htm#IDX727
241	Brieskorn lattice sing_1645.htm#IDX730
242	Brieskorn lattice sing_1646.htm#IDX734
243	Brieskorn lattice sing_1647.htm#IDX738
244	Brieskorn lattice sing_1648.htm#IDX744
245	Brieskorn lattice sing_1649.htm#IDX752
246	Brieskorn lattice sing_1650.htm#IDX758
247	Brieskorn lattice sing_1651.htm#IDX766
248	Brieskorn lattice sing_1652.htm#IDX776
249	Brieskorn lattice sing_1663.htm#IDX782
250	Brieskorn lattice sing_1665.htm#IDX793
251	Brieskorn lattice sing_1693.htm#IDX820
252	Brill-Noether algorithm sing_1911.htm#IDX832
253	BrillNoether sing_1914.htm#SEC1995
254	Buchberger algorithm for toric ideals Buchberger algorithm sing_983.htm#SEC1045
255	Budur-Mustata-Saito approach sing_600.htm#IDX363
256	Building Singular sing_2906.htm#SEC3003
257	C programming language Major differences to the C programming language sing_413.htm#SEC453
258	C, module ordering sing_964.htm#IDX450
259	CGS sing_1028.htm#IDX463
260	CM_regularity sing_1562.htm#SEC1643 33865
261	CMtype sing_1731.htm#SEC1812
262	CRHT-ideal sing_989.htm#SEC1058
263	CSMA sing_2441.htm#SEC2522
264	CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33
265	Castelnuovo-Mumford regularity sing_1562.htm#IDX675
266	Category string sing_51.htm#SEC88
267	CenCharDec sing_645.htm#SEC699
268	Center sing_1539.htm#SEC1620
269	CenterBO sing_1546.htm#SEC1627
270	CentralQuot sing_643.htm#SEC697
271	CentralSaturation sing_644.htm#SEC698
272	Change of rings sing_9.htm#SEC15
273	Characteristic sets sing_973.htm#SEC1035
274	CharacteristicExponents CharacteristicExponents sing_1626.htm#SEC1707
275	ChernClass sing_2851.htm#SEC2932
276	ChernRootsDual sing_2397.htm#SEC2478
277	ChernRootsHom sing_2406.htm#SEC2487
278	ChernRootsProd sing_2399.htm#SEC2480
279	ChernRootsSum sing_2395.htm#SEC2476
280	ChernRootsSymm sing_2408.htm#SEC2489
281	ChernRootsWedge sing_2409.htm#SEC2490
282	Chevalley-Rosenlicht theorem sing_1478.htm#IDX644
283	Chevalley-Rosenlicht theorem sing_1479.htm#IDX647
284	Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2842.htm#IDX1204
285	ChowRing sing_2842.htm#SEC2923
286	Classification of hypersurface singularities Classification of hypersurface singularities sing_944.htm#SEC1001
287	Classification of singularities sing_2811.htm#IDX1175
288	Code Codes and the decoding problem sing_988.htm#SEC1051
289	Codes and the decoding problem Codes and the decoding problem sing_988.htm#SEC1050
290	Coding theory sing_1910.htm#SEC1991
291	Coefficient rings Notes for Singular users sing_2904.htm#SEC2996
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_923.htm#SEC980
296	Commutative algebra sing_1211.htm#SEC1292
297	CompDecomp sing_499.htm#SEC553
298	CompInt sing_2447.htm#SEC2528
299	CompleteHomog sing_2385.htm#SEC2466
300	ComplexValue sing_2574.htm#SEC2655
301	Comprehensive Groebner System sing_1028.htm#IDX466
302	Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_919.htm#SEC976
303	ConsLevels sing_1048.htm#SEC1129
304	ContactMatrix sing_1628.htm#SEC1709
305	Conti-Traverso algorithm sing_978.htm#SEC1040
306	Contributors sing_1.htm#IDX15
307	Control structures sing_381.htm#SEC421
308	Control theory System and Control theory sing_1944.htm#SEC2025
309	Cooper philosophy sing_989.htm#SEC1056
310	Cornacchia sing_1990.htm#SEC2071
311	CornacchiaModified sing_1991.htm#SEC2072
312	Crep sing_1031.htm#SEC1112
313	Critical points sing_938.htm#SEC995
314	CurveParam sing_1622.htm#SEC1703
315	CurveRes sing_1621.htm#SEC1702
316	Curves sing_1484.htm#IDX656
317	Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36
318	Cyclic code sing_1925.htm#IDX839
319	Cyclic roots sing_916.htm#SEC973
320	D-integration sing_560.htm#IDX345
321	D-localization sing_560.htm#IDX341
322	D-localization sing_661.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_592.htm#IDX350
327	D-module sing_600.htm#IDX357
328	D-module sing_661.htm#IDX367
329	D-module sing_771.htm#IDX385
330	D-module structure sing_537.htm#IDX325
331	D-module structure sing_592.htm#IDX353
332	D-module structure sing_600.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#SEC617
337	DLoc0 sing_565.htm#SEC619
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_1925.htm#IDX841
344	Decoding codes with Groebner bases Decoding codes with Groebner bases sing_987.htm#SEC1049
345	Decoding method based on quadratic equations Decoding method based on quadratic equations sing_992.htm#SEC1067
346	Definition of a user defined type Definition of a user defined type sing_184.htm#SEC224
347	Deformations sing_941.htm#SEC998
348	Deformations, T1 and T2 sing_940.htm#SEC997
349	Deg sing_2688.htm#SEC2769
350	Degree sing_2689.htm#SEC2770
351	DegreePure sing_1463.htm#SEC1544
352	Degrees sing_2690.htm#SEC2771
353	Delta sing_1547.htm#SEC1628
354	DeltaList sing_1548.htm#SEC1629
355	Demo mode sing_24.htm#SEC35
356	Depth sing_930.htm#SEC987
357	Determinacy sing_2814.htm#IDX1179
358	Di Biase-Urbanke algorithm Di Biase and Urbanke sing_981.htm#SEC1043
359	DifConsLCSets sing_1051.htm#SEC1132
360	Distributed computing sing_1062.htm#IDX531
361	Dlocalization sing_662.htm#SEC716
362	Documentation Tool sing_60.htm#SEC97
363	Dp, global ordering sing_962.htm#IDX433
364	Ds, local ordering sing_963.htm#IDX443
365	DsingularLocus sing_666.htm#SEC720
366	Dynamic loading sing_71.htm#SEC111
367	Dynamic modules sing_918.htm#SEC975
368	ECPP sing_2034.htm#SEC2115
369	ECoef sing_1506.htm#SEC1587
370	EOrdlist sing_1504.htm#SEC1585
371	ERROR sing_238.htm#SEC278
372	ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33
373	Edatalist sing_1503.htm#SEC1584
374	Edelman-Reiner sing_2319.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_926.htm#SEC983
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_1508.htm#SEC1589
388	Enumerative geometry sing_2838.htm#IDX1197
389	Equal sing_1462.htm#SEC1543
390	Eresol sing_1498.htm#SEC1579
391	EulerAff sing_2442.htm#SEC2523
392	EulerProj sing_2443.htm#SEC2524
393	Evaluation of logical expressions Evaluation of logical expressions sing_415.htm#SEC455
394	Examples sing_908.htm#SEC965
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_793.htm#SEC847
397	Examples of use of Letterplace over Z Examples of use of Letterplace over Z sing_794.htm#SEC848
398	Exp for matrices sing_1480.htm#IDX648
399	Experimental libraries Experimental libraries sing_2363.htm#SEC2444
400	Ext sing_1271.htm#SEC1352
401	Ext, computation of sing_929.htm#SEC986
402	Ext_R sing_1270.htm#SEC1351
403	Exterior sing_730.htm#SEC784
404	Extra weight vector sing_967.htm#SEC1024
405	Factorization sing_931.htm#SEC988
406	FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_1042.htm#SEC1123
407	Feynman graph sing_1247.htm#IDX564
408	Finite fields sing_925.htm#SEC982
409	First steps sing_6.htm#SEC12
410	Fitzgerald-Lax method Fitzgerald-Lax method sing_991.htm#SEC1064
411	Float sing_253.htm#SEC293
412	Flow control sing_40.htm#SEC70
413	Formal Checker sing_59.htm#SEC96
414	Formatting output sing_915.htm#SEC972
415	Free associative algebras Free associative algebras sing_808.htm#SEC862
416	Free resolution sing_927.htm#SEC984
417	Free resolution, graded Handling graded modules sing_928.htm#SEC985
418	FultonA sing_2440.htm#SEC2521
419	Functionality and release notes of Letterplace Functionality and release notes of Letterplace sing_795.htm#SEC849
420	Functions sing_208.htm#SEC248
421	Functions (letterplace) Functions (letterplace) sing_797.htm#SEC851
422	Future benefits of Singular 4 Notes for Singular users sing_2904.htm#SEC3001
423	G-algebra sing_490.htm#SEC530
424	G-algebra sing_490.htm#SEC532
425	G-algebra, setup sing_490.htm#SEC534
426	GBWeight sing_566.htm#SEC620
427	GBsolve sing_1824.htm#SEC1905
428	GIT-Fans sing_950.htm#SEC1007
429	GITcone sing_2604.htm#SEC2685
430	GITfan sing_2605.htm#SEC2686
431	GITfanFromOrbitCones GITfanFromOrbitCones sing_2606.htm#SEC2687
432	GITfanParallel sing_2607.htm#SEC2688
433	GITfanParallelSymmetric GITfanParallelSymmetric sing_2622.htm#SEC2703
434	GITfanSymmetric sing_2621.htm#SEC2702
435	GKZfan sing_2608.htm#SEC2689
436	GKZsystem sing_641.htm#SEC695
437	GKdim sing_614.htm#SEC668
438	GMP sing_1.htm#IDX3
439	GMP sing_2908.htm#SEC3005
440	GND.lib sing_2629.htm#SEC2710
441	GND_lib sing_2629.htm#SEC2710
442	GTZmod sing_1324.htm#SEC1405
443	GTZopt sing_1331.htm#SEC1412
444	G_a -Invariants sing_947.htm#SEC1004
445	Gamma sing_1513.htm#SEC1594
446	Gauss-Manin connection Gauss-Manin connection sing_974.htm#SEC1036
447	Gauss-Manin connection sing_1693.htm#IDX819
448	Gauss-Manin connection sing_1740.htm#IDX822
449	Gauss-Manin system sing_1641.htm#IDX709
450	Gauss-Manin system sing_1642.htm#IDX720
451	Gauss-Manin system sing_1643.htm#IDX723
452	Gauss-Manin system sing_1644.htm#IDX726
453	Gauss-Manin system sing_1645.htm#IDX729
454	Gauss-Manin system sing_1646.htm#IDX733
455	Gauss-Manin system sing_1647.htm#IDX737
456	Gauss-Manin system sing_1648.htm#IDX743
457	Gauss-Manin system sing_1649.htm#IDX751
458	Gauss-Manin system sing_1650.htm#IDX757
459	Gauss-Manin system sing_1651.htm#IDX765
460	Gauss-Manin system sing_1652.htm#IDX775
461	Gauss-Manin system sing_1663.htm#IDX781
462	Gauss-Manin system sing_1665.htm#IDX792
463	Gelfand-Kirillov dimension sing_849.htm#IDX407
464	General command syntax General command syntax sing_35.htm#SEC59
465	General concepts sing_12.htm#SEC18
466	General purpose sing_999.htm#SEC1080
467	General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41
468	Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_492.htm#SEC544
469	Generalized Newton identities Generalized Newton identities sing_990.htm#SEC1061
470	Geometric Invariant Theory Geometric Invariant Theory sing_949.htm#SEC1006
471	Geometric Theorems sing_1047.htm#IDX516
472	Geometric genus sing_1484.htm#IDX660
473	German Umlaute sing_411.htm#IDX282
474	Getting started sing_5.htm#SEC11
475	Global orderings sing_962.htm#SEC1019
476	Goettsche's formula sing_2579.htm#IDX1131
477	GoettscheF sing_2580.htm#SEC2661
478	Graded commutative algebras Graded commutative algebras (SCA) sing_791.htm#SEC845
479	Grassmannian sing_2843.htm#SEC2924
480	Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2843.htm#IDX1205
481	Greuel, Gert-Martin sing_1.htm#IDX18
482	Grob1Levels sing_1050.htm#SEC1131
483	Groebner Bases Computing Groebner and Standard Bases sing_919.htm#SEC976
484	Groebner bases for two-sided ideals in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_810.htm#SEC864
485	Groebner bases in G-algebras Groebner bases in G-algebras sing_491.htm#SEC535
486	Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_810.htm#SEC864
487	Groebner bases, decodeGB sing_1925.htm#IDX843
488	Groebner bases, slim sing_922.htm#SEC979
489	Groebner basis conversion Groebner basis conversion sing_921.htm#SEC978
490	Groebner cover sing_1027.htm#IDX459
491	Groebner cover sing_1034.htm#IDX478
492	Groebner cover sing_1035.htm#IDX485
493	Groebner fan sing_2189.htm#IDX860
494	Groebner walk sing_1262.htm#IDX585
495	Groebner walk sing_1264.htm#IDX587
496	Groebner walk sing_2835.htm#IDX1193
497	Groebner walk sing_2836.htm#IDX1194
498	Groebner-Shirshov bases Groebner bases for two-sided ideals in free associative algebras sing_810.htm#SEC864
499	Groebner-Shirshov bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_810.htm#SEC864
500	Groebnerwalk sing_1258.htm#IDX581
501	Groebnerwalk sing_2722.htm#IDX1146
502	Groebnerwalk sing_2834.htm#IDX1192
503	Groebnerwalk sing_2877.htm#IDX1221
504	Gromov-Witten invariants sing_1247.htm#IDX561
505	Gromov-Witten invariants sing_1253.htm#IDX570
506	Gromov-Witten invariants sing_1254.htm#IDX574
507	Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2868.htm#IDX1217
508	Gromov-Witten invariants, multiple covers sing_2867.htm#IDX1216
509	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2869.htm#IDX1218
510	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2870.htm#IDX1219
511	Gromov-Witten invariants. sing_2838.htm#IDX1200
512	Gweights sing_724.htm#SEC778
513	H2basis sing_1698.htm#SEC1779
514	HHnormalForm sing_2458.htm#SEC2539
515	Hamburger-Noether expansion sing_1578.htm#IDX679
516	Hamburger-Noether expansion sing_1666.htm#IDX801
517	Hamburger-Noether expansions sing_1912.htm#IDX833
518	Handling graded modules Handling graded modules sing_928.htm#SEC985
519	Hcode sing_1600.htm#SEC1681
520	Help string sing_45.htm#SEC82
521	Hensel sing_243.htm#SEC283
522	Hilbert function sing_359.htm#IDX188
523	Hilbert function sing_971.htm#SEC1030
524	Hilbert scheme sing_2579.htm#IDX1134
525	Hilbert series sing_814.htm#IDX398
526	Hilbert series sing_971.htm#SEC1030
527	Hilbert-driven GB algorithm Groebner basis conversion sing_921.htm#SEC978
528	HilbertClassPoly sing_1997.htm#SEC2078
529	HilbertSeries sing_1793.htm#SEC1874
530	HilbertWeights sing_1794.htm#SEC1875
531	Hom sing_1274.htm#SEC1355
532	HomJJ sing_1354.htm#SEC1435
533	Hosten-Sturmfels algorithm Hosten and Sturmfels sing_980.htm#SEC1042
534	How to enter and exit How to enter and exit sing_14.htm#SEC20
535	How to use this manual How to use this manual sing_4.htm#SEC6
536	Hurwitz numbers sing_1253.htm#IDX573
537	Hurwitz numbers sing_1254.htm#IDX577
538	Hypersurface singularities, classification of Classification of hypersurface singularities sing_944.htm#SEC1001
539	I-regular function sing_1034.htm#IDX484
540	IN sing_283.htm#IDX149
541	Ideal membership sing_970.htm#IDX455
542	Identifiers, syntax of sing_37.htm#SEC65
543	ImageGroup sing_1796.htm#SEC1877
544	ImageVariety sing_1795.htm#SEC1876
545	Imap, option sing_318.htm#IDX175
546	Implemented algorithms Implemented algorithms sing_33.htm#SEC47
547	Incl sing_1461.htm#SEC1542
548	Index sing_2914.htm#SEC3011
549	Info string sing_52.htm#SEC89
550	InterDiv sing_1529.htm#SEC1610
551	Interactive use sing_13.htm#SEC19
552	Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24
553	IntersectWithSub sing_646.htm#SEC700
554	Intersection theory sing_2838.htm#IDX1196
555	IntersectionMatrix sing_1627.htm#SEC1708
556	Introduction sing_2.htm#SEC4
557	Invariant Theory sing_946.htm#SEC1003
558	Invariant theory sing_1745.htm#SEC1826
559	InvariantQ sing_1798.htm#SEC1879
560	InvariantRing sing_1797.htm#SEC1878
561	Invariants of a finite group Invariants of a finite group sing_948.htm#SEC1005
562	Invariants of plane curve singularities Invariants of plane curve singularities sing_942.htm#SEC999
563	IsSCA sing_745.htm#SEC799
564	J-marked schemes sing_1569.htm#IDX677
565	J-marked schemes, Borel ideals sing_1574.htm#IDX678
566	JMBTest.lib sing_1569.htm#SEC1650
567	JMBTest_lib sing_1569.htm#SEC1650
568	JMSConst.lib sing_1574.htm#SEC1655
569	JMSConst_lib sing_1574.htm#SEC1655
570	JMarkedScheme sing_1576.htm#SEC1657
571	Jacobi sing_2007.htm#SEC2088
572	Jacobson form sing_1962.htm#IDX844
573	Jacobson normal form sing_1962.htm#IDX845
574	Janet basis sing_2833.htm#IDX1190
575	Janet division, Janet basis sing_2832.htm#IDX1189
576	JuReTopDim sing_1471.htm#SEC1552
577	JuReZeroDim sing_1472.htm#SEC1553
578	K-basis sing_814.htm#IDX396
579	K-dimension sing_814.htm#IDX397
580	KScoef sing_1691.htm#SEC1772
581	KSconvert sing_1689.htm#SEC1770
582	KSker sing_1688.htm#SEC1769
583	KSlinear sing_1690.htm#SEC1771
584	KSpencerKernel sing_1738.htm#SEC1819
585	KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2648.htm#SEC2729
586	Ker sing_2694.htm#SEC2775
587	Kernel of module homomorphisms Kernel of module homomorphisms sing_934.htm#SEC991
588	KoszulHomology sing_1283.htm#SEC1364
589	Kronecker module sing_2579.htm#IDX1133
590	Kronecker product sing_363.htm#SEC403
591	L, ordering sing_968.htm#SEC1025
592	LETTERPLACE sing_792.htm#SEC846
593	LETTERPLACE libraries LETTERPLACE libraries sing_813.htm#SEC867
594	LIB sing_287.htm#SEC327
595	LIB commands sing_53.htm#SEC90
596	LIBs sing_995.htm#SEC1076
597	LLL sing_361.htm#IDX218
598	LOT algorithm sing_537.htm#IDX337
599	LU-decomposition of a matrix of numbers sing_292.htm#SEC332
600	Laurent series sing_1251.htm#IDX569
601	Left and two-sided Groebner bases Left and two-sided Groebner bases sing_952.htm#SEC1009
602	Left ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC538
603	Left normal form Groebner bases in G-algebras sing_491.htm#SEC537
604	LengthSym sing_788.htm#SEC842
605	LengthSymElement sing_787.htm#SEC841
606	Letterplace sing_792.htm#SEC846
607	Letterplace Groebner basis sing_814.htm#IDX395
608	Letterplace Groebner basis sing_849.htm#IDX405
609	Letterplace Groebner basis sing_856.htm#IDX414
610	Letterplace correspondence Letterplace correspondence sing_812.htm#SEC866
611	Letterplace libraries LETTERPLACE libraries sing_813.htm#SEC867
612	Letterplace ring sing_357.htm#SEC397
613	Levels sing_1049.htm#SEC1130
614	Lexicographic Groebner bases, computation of Groebner basis conversion sing_921.htm#SEC978
615	Libraries Writing procedures and libraries sing_48.htm#SEC85
616	Libraries sing_911.htm#SEC968
617	Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86
618	Library versioning Notes for Singular users sing_2904.htm#SEC2999
619	Lie sing_2526.htm#IDX1107
620	Lie algebra sing_1479.htm#IDX645
621	Lie bracket sing_460.htm#SEC500
622	Lie group sing_1482.htm#IDX650
623	Lie group sing_1483.htm#IDX653
624	Limitations sing_411.htm#SEC451
625	Linear algebra sing_1152.htm#SEC1233
626	Linear code sing_1925.htm#IDX840
627	LinearActionQ sing_1800.htm#SEC1881
628	LinearCombinationQ sing_1801.htm#SEC1882
629	LinearizeAction sing_1799.htm#SEC1880
630	Loading a library sing_62.htm#SEC99
631	Local orderings sing_963.htm#SEC1020
632	Log for matrices sing_1481.htm#IDX649
633	Long coefficients sing_913.htm#SEC970
634	M, ordering sing_965.htm#SEC1022
635	MVComplex sing_2480.htm#SEC2561
636	Macdonald's formula sing_2579.htm#IDX1132
637	MacdonaldF sing_2586.htm#SEC2667
638	Macintosh installation Macintosh installation instructions sing_2913.htm#SEC3010
639	Mathematical background Mathematical background sing_969.htm#SEC1026
640	Mathematical background (letterplace) Mathematical background (letterplace) sing_807.htm#SEC861
641	Mathematical background (plural) Mathematical background (plural) sing_489.htm#SEC529
642	Matrix orderings sing_965.htm#SEC1022
643	Max sing_1707.htm#SEC1788
644	Maximus sing_1571.htm#SEC1652
645	Maxord sing_1512.htm#SEC1593
646	MillerRabin sing_2017.htm#SEC2098
647	Milnor code sing_2364.htm#IDX983
648	Milnor number Milnor and Tjurina number sing_937.htm#SEC994
649	Milnor number sing_2813.htm#IDX1178
650	Min sing_1708.htm#SEC1789
651	MinMult sing_2446.htm#SEC2527
652	MinimalDecomposition MinimalDecomposition sing_1802.htm#SEC1883
653	Minimum distance sing_1925.htm#IDX842
654	Minimus sing_1570.htm#SEC1651
655	Miscellaneous libraries Miscellaneous libraries sing_2290.htm#SEC2371
656	ModEqn sing_1701.htm#SEC1782
657	Modular techniques sing_1062.htm#IDX528
658	Module orderings sing_964.htm#SEC1021
659	Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16
660	Monodromy sing_1693.htm#IDX817
661	Monomial orderings sing_959.htm#SEC1016
662	Monomial orderings on free algebras Monomial orderings on free algebras sing_809.htm#SEC863
663	Monomial orderings, Term orderings sing_31.htm#SEC44
664	Mori dream spaces sing_2373.htm#IDX986
665	Morse lemma addnondegeneratevariables sing_2812.htm#IDX1176
666	Morse lemma sing_2815.htm#IDX1180
667	MultiplicitySequence MultiplicitySequence sing_1625.htm#SEC1706
668	NF sing_337.htm#SEC377
669	NF (letterplace) reduce (letterplace) sing_802.htm#SEC856
670	NF (plural) sing_481.htm#SEC521
671	NFMora sing_2083.htm#SEC2164
672	NPos sing_1344.htm#SEC1425
673	NPos_test sing_1342.htm#SEC1423
674	NSplaces sing_1913.htm#SEC1994
675	NTL sing_1.htm#IDX4
676	NakYoshF sing_2583.htm#SEC2664
677	Names sing_37.htm#SEC65
678	Names in procedures sing_46.htm#SEC83
679	Names, indexed sing_37.htm#SEC65
680	New orderings for modules Notes for Singular users sing_2904.htm#SEC3000
681	Newton non-degenerate sing_1680.htm#IDX815
682	Newton polygon sing_1679.htm#IDX814
683	Newton polygon sing_1680.htm#IDX816
684	Newton polygons sing_2880.htm#IDX1224
685	Newton polytope sing_2189.htm#IDX859
686	Newton step sing_2816.htm#IDX1184
687	Noether position sing_1344.htm#IDX603
688	NoetherPosition sing_1338.htm#SEC1419
689	Non-commutative algebra Non-commutative algebra sing_951.htm#SEC1008
690	Non-commutative algebra sing_986.htm#SEC1048
691	Non-commutative subsystem Non-commutative subsystem sing_424.htm#SEC464
692	Nonhyp sing_1501.htm#SEC1582
693	Normalization sing_933.htm#SEC990
694	Notes for Singular users Notes for Singular users sing_2904.htm#SEC2995
695	Notes for developers Notes for developers sing_2905.htm#SEC3002
696	NullCone sing_1803.htm#SEC1884
697	NumIrrDecom sing_1475.htm#SEC1556
698	NumLocalDim sing_1464.htm#SEC1545
699	NumPrimDecom sing_1477.htm#SEC1558
700	Oaku-Takayama algorithm sing_537.htm#IDX335
701	Objects sing_38.htm#SEC66
702	Orlik-Solomon sing_2320.htm#IDX923
703	Output sing_2704.htm#IDX1144
704	Output sing_2780.htm#IDX1151
705	Output sing_2782.htm#IDX1152
706	Output sing_2783.htm#IDX1153
707	Output sing_2784.htm#IDX1154
708	Output sing_2785.htm#IDX1155
709	Output sing_2786.htm#IDX1156
710	Output sing_2787.htm#IDX1157
711	Output sing_2788.htm#IDX1158
712	Output sing_2789.htm#IDX1159
713	Output sing_2790.htm#IDX1160
714	Output sing_2791.htm#IDX1161
715	Output sing_2792.htm#IDX1162
716	Output sing_2793.htm#IDX1163
717	Output sing_2794.htm#IDX1164
718	Output sing_2795.htm#IDX1165
719	Output sing_2796.htm#IDX1166
720	Output sing_2797.htm#IDX1167
721	Output sing_2798.htm#IDX1168
722	Output sing_2799.htm#IDX1169
723	Output sing_2800.htm#IDX1170
724	Output sing_2801.htm#IDX1171
725	Output sing_2802.htm#IDX1172
726	Output sing_2803.htm#IDX1173
727	Output sing_2804.htm#IDX1174
728	Output, formatting of sing_915.htm#SEC972
729	PBW sing_516.htm#IDX323
730	PBW basis sing_490.htm#SEC531
731	PBW_eqDeg sing_534.htm#SEC588
732	PBW_maxDeg sing_535.htm#SEC589
733	PBW_maxMonom sing_536.htm#SEC590
734	PEsolve sing_1822.htm#SEC1903
735	PH_ais sing_2342.htm#SEC2423
736	PH_nais sing_2343.htm#SEC2424
737	PLURAL sing_425.htm#SEC465
738	PLURAL LIBs sing_494.htm#SEC548
739	PLURAL libraries sing_494.htm#SEC548
740	PPolyH sing_2581.htm#SEC2662
741	PPolyN sing_2589.htm#SEC2670
742	PPolyQp sing_2584.htm#SEC2665
743	PPolyS sing_2587.htm#SEC2668
744	ParToVar sing_2576.htm#SEC2657
745	Parallelization Parallelization with ssi links sing_917.htm#SEC974
746	Parallelization sing_1062.htm#IDX529
747	Parameter list sing_44.htm#SEC81
748	Parameters sing_914.htm#SEC971
749	Parametrization sing_1484.htm#IDX657
750	Parametrization, image. sing_1494.htm#IDX669
751	PartC sing_2436.htm#SEC2517
752	PartitionVar sing_2573.htm#SEC2654
753	Path names Notes for Singular users sing_2904.htm#SEC2998
754	PerfectPowerTest sing_1980.htm#SEC2061
755	Perturbation walk sing_1263.htm#IDX586
756	Pfister, Gerhard sing_1.htm#IDX19
757	Pipe links sing_121.htm#SEC161
758	PocklingtonLehmer sing_2019.htm#SEC2100
759	Poincare polynomial sing_2332.htm#IDX947
760	Polar curves sing_939.htm#SEC996
761	PollardRho sing_2020.htm#SEC2101
762	PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2345.htm#IDX963
763	PolyBoRi, Boolean Groebner Basis sing_2347.htm#IDX964
764	PolyBoRi, Boolean Groebner Basis sing_2348.htm#IDX965
765	PolyBoRi, Boolean Groebner Basis sing_2349.htm#IDX966
766	PolyBoRi, Boolean Groebner Basis sing_2350.htm#IDX967
767	PolyBoRi, Boolean Groebner Basis sing_2351.htm#IDX968
768	PolyBoRi, Boolean Groebner Basis sing_2352.htm#IDX969
769	PolyBoRi, Boolean Groebner Basis sing_2353.htm#IDX970
770	PolyBoRi, Boolean Groebner Basis sing_2354.htm#IDX971
771	PolyBoRi, Boolean Groebner Basis sing_2355.htm#IDX972
772	PolyBoRi, Boolean Groebner Basis sing_2356.htm#IDX973
773	PolyBoRi, Boolean Groebner Basis sing_2357.htm#IDX974
774	PolyBoRi, Boolean Groebner Basis sing_2358.htm#IDX975
775	PolyBoRi, Boolean Groebner Basis sing_2359.htm#IDX976
776	PolyBoRi, Boolean Groebner Basis sing_2361.htm#IDX978
777	PolyBoRi, zero-supressed decision diagram sing_2360.htm#IDX977
778	Polybori, Boolean Groebner Basis sing_2362.htm#IDX979
779	Polynomial data sing_957.htm#SEC1014
780	Pottier algorithm sing_979.htm#SEC1041
781	Preface sing_1.htm#SEC1
782	Prep sing_1032.htm#SEC1113
783	Primary decomposition Primary decomposition sing_932.htm#SEC989
784	PrimdecA sing_1320.htm#SEC1401
785	PrimdecB sing_1321.htm#SEC1402
786	Procedure definition Procedure definition sing_43.htm#SEC78
787	Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84
788	Procedures sing_42.htm#SEC77
789	Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14
790	Procedures and libraries sing_911.htm#SEC968
791	Procedures in a library Procedures in a library sing_54.htm#SEC91
792	Product orderings sing_966.htm#SEC1023
793	Programming sing_909.htm#SEC966
794	Pseudo ordering L sing_968.htm#SEC1025
795	PtoCrep sing_1033.htm#SEC1114
796	Puiseux expansion sing_1578.htm#IDX680
797	Puiseux expansion sing_1666.htm#IDX802
798	Puiseux pairs Invariants of plane curve singularities sing_942.htm#SEC999
799	Puiseux pairs sing_1672.htm#IDX807
800	QQ sing_28.htm#SEC39
801	QQ sing_75.htm#SEC115
802	Qso3Casimir sing_640.htm#SEC694
803	Quot-scheme sing_2579.htm#IDX1135
804	Quotient sing_1864.htm#SEC1945
805	QuotientEquations sing_1702.htm#SEC1783
806	Rational curves sing_1484.htm#IDX658
807	ReJunkUseHomo sing_1470.htm#SEC1551
808	ReesAlgebra sing_1437.htm#SEC1518
809	References sing_994.htm#SEC1073
810	References (plural) sing_493.htm#SEC545
811	References and history of Letterplace References and history of Letterplace sing_796.htm#SEC850
812	Release Notes sing_2900.htm#SEC2981
813	Release Notes (letterplace) Release Notes (letterplace) sing_907.htm#SEC961
814	Res sing_2684.htm#SEC2765
815	ResTree sing_1530.htm#SEC1611
816	Resolution sing_11.htm#SEC17
817	Resolution of singularities Resolution of singularities sing_945.htm#SEC1002
818	Resolution, free sing_927.htm#SEC984
819	ReynoldsImage sing_1804.htm#SEC1885
820	ReynoldsOperator sing_1805.htm#SEC1886
821	RiemannRochBN sing_2381.htm#SEC2462
822	RiemannRochHess sing_2667.htm#SEC2748
823	Right Groebner bases and syzygies Right Groebner bases and syzygies sing_953.htm#SEC1010
824	Right ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC539
825	Ring-dependent options Notes for Singular users sing_2904.htm#SEC2997
826	Rings and orderings sing_28.htm#SEC39
827	Rings and standard bases Rings and standard bases sing_7.htm#SEC13
828	Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
829	SCA Graded commutative algebras (SCA) sing_791.htm#SEC845
830	SDB breakpoint Source code debugger sing_66.htm#SEC106
831	SDB debugger Source code debugger sing_66.htm#SEC106
832	SDLoc sing_564.htm#SEC618
833	SINGULAR libraries sing_995.htm#SEC1076
834	SINGULARHIST sing_18.htm#SEC25
835	SL sing_1808.htm#SEC1889
836	SLreynolds sing_1814.htm#SEC1895
837	SV-decoding algorithm sing_1920.htm#IDX836
838	SV-decoding algorithm, preprocessing sing_1919.htm#IDX835
839	SaitoBase sing_2894.htm#SEC2975
840	Sannfs sing_540.htm#SEC594
841	SannfsBFCT sing_549.htm#SEC603
842	SannfsVar sing_603.htm#SEC657
843	Sannfslog sing_541.htm#SEC595
844	Saturation sing_924.htm#SEC981
845	Sch@"onemann, Hans sing_1.htm#IDX20
846	Schoof sing_2031.htm#SEC2112
847	Schubert calculus sing_2838.htm#IDX1198
848	SchubertClass sing_2875.htm#SEC2956
849	SchurCh sing_2433.htm#SEC2514
850	SchurS sing_2432.htm#SEC2513
851	SegreA sing_2439.htm#SEC2520
852	Semigroup sing_1618.htm#SEC1699
853	Serre relations sing_820.htm#IDX402
854	SetDeg sing_2687.htm#SEC2768
855	Setting up a G-algebra sing_490.htm#SEC534
856	ShanksMestre sing_2030.htm#SEC2111
857	SimplifyIdeal sing_1806.htm#SEC1887
858	Singular sing_361.htm#IDX255
859	Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2902.htm#SEC2993
860	Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36
861	Singular, demo mode sing_24.htm#SEC35
862	Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
863	Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38
864	Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
865	Singular2bertini sing_1468.htm#SEC1549
866	SingularLib sing_361.htm#IDX257
867	Singularities sing_1577.htm#SEC1658
868	Singularity Theory sing_936.htm#SEC993
869	Skeletons for parallelization sing_1062.htm#IDX530
870	Smith form sing_1962.htm#IDX846
871	Smith normal form sing_1962.htm#IDX847
872	SolowayStrassen sing_2018.htm#SEC2099
873	Solving systems of polynomial equations Solving systems of polynomial equations sing_955.htm#SEC1012
874	Source sing_2676.htm#SEC2757
875	Source code debugger, invocation Command line options sing_19.htm#IDX33
876	Space curve singularities, branches of Branches of space curve singularities sing_943.htm#SEC1000
877	Special characters sing_36.htm#SEC64
878	Splitting lemma addnondegeneratevariables sing_2812.htm#IDX1177
879	Splitting lemma sing_2815.htm#IDX1181
880	Ssi file links sing_119.htm#SEC159
881	Ssi links sing_118.htm#SEC158
882	Ssi tcp links sing_120.htm#SEC160
883	StabEqn sing_1703.htm#SEC1784
884	StabEqnId sing_1704.htm#SEC1785
885	StabOrder sing_1705.htm#SEC1786
886	Standard Bases Computing Groebner and Standard Bases sing_919.htm#SEC976
887	Standard bases sing_970.htm#SEC1027
888	StartOrderingV sing_1572.htm#SEC1653
889	Startup sequence sing_20.htm#SEC27
890	StringF sing_1692.htm#SEC1773
891	SymGroup sing_786.htm#SEC840
892	Symbolic-numerical solving Symbolic-numerical solving sing_955.htm#SEC1012
893	Symbolic-numerical solving sing_1819.htm#SEC1900
894	System and Control theory System and Control theory sing_1944.htm#SEC2025
895	System dependent limitations System dependent limitations sing_412.htm#SEC452
896	System variables sing_398.htm#SEC438
897	Syzygies and resolutions Syzygies and resolutions sing_972.htm#SEC1031
898	Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_492.htm#SEC541
899	Syzygy bimodule Bimodules and syzygies and lifts sing_811.htm#SEC865
900	T1 sing_940.htm#SEC997
901	T2 sing_940.htm#SEC997
902	TRACE Tracing of procedures sing_65.htm#SEC102
903	TRACE sing_407.htm#SEC447
904	T_1 sing_1725.htm#SEC1806
905	T_12 sing_1727.htm#SEC1808
906	T_2 sing_1726.htm#SEC1807
907	Target sing_2675.htm#SEC2756
908	Teaching sing_1976.htm#SEC2057
909	Template for writing a library sing_55.htm#SEC92
910	TestGRRes sing_2647.htm#SEC2728
911	TestJMark sing_1573.htm#SEC1654
912	The SINGULAR language The SINGULAR language sing_34.htm#SEC56
913	The Tran algorithm sing_1260.htm#IDX583
914	The fractal walk algorithm sing_1259.htm#IDX582
915	The fractal walk algorithm sing_2837.htm#IDX1195
916	The online help system The online help system sing_16.htm#SEC22
917	Tjurina sing_1723.htm#SEC1804
918	Tjurina number Milnor and Tjurina number sing_937.htm#SEC994
919	Tjurina number sing_1359.htm#IDX618
920	Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38
921	Tor sing_1285.htm#SEC1366
922	Toric ideals and integer programming Toric ideals and integer programming sing_975.htm#SEC1037
923	Tricks and pitfalls sing_410.htm#SEC450
924	Tropical Geometry sing_2128.htm#SEC2209
925	Two-sided ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC540
926	Type casting Type conversion and casting sing_39.htm#SEC69
927	Type conversion Type conversion and casting sing_39.htm#SEC68
928	Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98
929	U_D_O sing_1200.htm#SEC1281
930	Ufnarovski graph sing_849.htm#IDX410
931	Unix installation Unix installation instructions sing_2911.htm#SEC3008
932	UpOneMatrix sing_742.htm#SEC796
933	UpperMonomials sing_1706.htm#SEC1787
934	UseBertini sing_1467.htm#SEC1548
935	User defined types sing_183.htm#SEC223
936	V-filtration sing_1641.htm#IDX712
937	V-filtration sing_1647.htm#IDX740
938	V-filtration sing_1648.htm#IDX746
939	V-filtration sing_1649.htm#IDX754
940	V-filtration sing_1650.htm#IDX760
941	V-filtration sing_1651.htm#IDX768
942	V-filtration sing_1652.htm#IDX778
943	V-filtration sing_1663.htm#IDX784
944	V-filtration sing_1665.htm#IDX795
945	VarToPar sing_2575.htm#SEC2656
946	Variables, indexed sing_37.htm#SEC65
947	VecField.lib sing_2889.htm#SEC2970
948	VecField_lib sing_2889.htm#SEC2970
949	Version number Version schema for Singular sing_2903.htm#SEC2994
950	Version schema for Singular Version schema for Singular sing_2903.htm#SEC2994
951	Version string sing_50.htm#SEC87
952	Visualization sing_1882.htm#SEC1963
953	WLCGS sing_1045.htm#SEC1126
954	WLemma sing_1044.htm#SEC1125
955	WP, global ordering sing_962.htm#IDX437
956	WSemigroup sing_1623.htm#SEC1704
957	Weierstrass sing_1915.htm#SEC1996
958	Weierstrass semigroup sing_1911.htm#IDX830
959	Weyl sing_727.htm#SEC781
960	Weyl algebra sing_537.htm#IDX329
961	Weyl algebra sing_592.htm#IDX355
962	Weyl algebra sing_600.htm#IDX361
963	Weyl closure sing_661.htm#IDX373
964	WeylClosure sing_663.htm#SEC717
965	WeylClosure1 sing_664.htm#SEC718
966	Wibmer's Lemma sing_1044.htm#IDX513
967	Windows installation Windows installation instructions sing_2912.htm#SEC3009
968	WitSet sing_1474.htm#SEC1555
969	WitSupSet sing_1473.htm#SEC1554
970	Ws, local ordering sing_963.htm#IDX449
971	XLsolve sing_1825.htm#SEC1906
972	ZZ sing_28.htm#SEC39
973	ZZ sing_75.htm#SEC115
974	ZZ/m sing_28.htm#SEC39
975	ZZ/p sing_28.htm#SEC39
976	ZZsolve sing_1826.htm#SEC1907
977	[ sing_36.htm#IDX83
978	[] sing_142.htm#SEC182
979	[] sing_155.htm#SEC195
980	[] sing_176.htm#SEC216
981	[] sing_181.htm#SEC221
982	\ sing_36.htm#IDX112
983	] sing_36.htm#IDX84
984	^ sing_36.htm#IDX92
985	^ sing_81.htm#SEC121
986	^ sing_93.htm#SEC133
987	^ sing_147.htm#SEC187
988	^ sing_155.htm#SEC195
989	_ sing_36.htm#IDX116
990	` sing_36.htm#IDX105
991	a, ordering sing_967.htm#SEC1024
992	absFactorize sing_1213.htm#SEC1294
993	absFactorizeBCG sing_1214.htm#SEC1295
994	absPrimdecGTZ sing_1417.htm#SEC1498
995	absPrimdecGTZE sing_1418.htm#SEC1499
996	absValue sing_1008.htm#SEC1089
997	absfact.lib sing_1212.htm#SEC1293
998	absfact_lib sing_1212.htm#SEC1293
999	absolute factorization. sing_1212.htm#IDX554
1000	abstract variety, projective space, Grassmannian printVariety sing_2839.htm#IDX1201
1001	abstract variety, projective space, Grassmannian sing_2840.htm#IDX1202
1002	abstractR sing_1556.htm#SEC1637
1003	actionIsProper sing_1786.htm#SEC1867
1004	add sing_2495.htm#IDX1040
1005	add sing_2517.htm#IDX1088
1006	addLeftFractions sing_758.htm#SEC812
1007	addModules sing_2696.htm#SEC2777
1008	addNvarsTo sing_1136.htm#SEC1217
1009	addRat sing_682.htm#SEC736
1010	addSheaf sing_2858.htm#SEC2939
1011	addcol sing_1169.htm#SEC1250
1012	addcores sing_1105.htm#SEC1186
1013	addnondegeneratevariables addnondegeneratevariables sing_2815.htm#SEC2896
1014	addrow sing_1170.htm#SEC1251
1015	addvarsTo sing_1135.htm#SEC1216
1016	ademRelations sing_824.htm#SEC878
1017	adjoint sing_1194.htm#SEC1275
1018	adjointIdeal sing_1485.htm#SEC1566
1019	adjunction divisor sing_1912.htm#IDX834
1020	admissibleSub sing_718.htm#SEC772
1021	afaces sing_2600.htm#SEC2681
1022	affine code Fitzgerald-Lax method sing_991.htm#SEC1065
1023	ainvar.lib sing_1783.htm#SEC1864
1024	ainvar_lib sing_1783.htm#SEC1864
1025	aksaka.lib sing_1977.htm#SEC2058
1026	aksaka_lib sing_1977.htm#SEC2058
1027	alexanderpolynomial sing_1581.htm#SEC1662
1028	alexpoly.lib sing_1578.htm#SEC1659
1029	alexpoly_lib sing_1578.htm#SEC1659
1030	algDependent sing_1219.htm#SEC1300
1031	alg_kernel sing_1220.htm#SEC1301
1032	algebra.lib sing_1215.htm#SEC1296
1033	algebra_containment sing_1216.htm#SEC1297
1034	algebra_lib sing_1215.htm#SEC1296
1035	algebraic dependence sing_769.htm#IDX381
1036	algebraic field extension sing_1431.htm#IDX627
1037	algebraicDependence sing_1444.htm#SEC1525
1038	algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_982.htm#SEC1044
1039	algorithm of Conti and Traverso sing_978.htm#SEC1040
1040	algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_981.htm#SEC1043
1041	algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_980.htm#SEC1042
1042	algorithm of Pottier sing_979.htm#SEC1041
1043	alias General command syntax sing_35.htm#SEC59
1044	align sing_209.htm#SEC249
1045	all.lib sing_1000.htm#SEC1081
1046	allDoubleExt sing_780.htm#SEC834
1047	allExtOfLeft sing_777.htm#SEC831
1048	allExtOfRight sing_778.htm#SEC832
1049	allPositive sing_513.htm#SEC567
1050	all_lib sing_1000.htm#SEC1081
1051	allowing net access Command line options sing_19.htm#IDX41
1052	allprint sing_1053.htm#SEC1134
1053	allreal sing_2120.htm#SEC2201
1054	allrealst sing_2118.htm#SEC2199
1055	allsquarefree sing_1685.htm#SEC1766
1056	ambientDimension sing_2133.htm#SEC2214
1057	and Evaluation of logical expressions sing_101.htm#SEC141
1058	and sing_415.htm#SEC455
1059	annPoly sing_561.htm#SEC615
1060	annRat sing_562.htm#SEC616
1061	annRatSyz sing_671.htm#SEC725
1062	annfalphaI sing_598.htm#SEC652
1063	annfs sing_538.htm#SEC592
1064	annfs0 sing_550.htm#SEC604
1065	annfs2 sing_551.htm#SEC605
1066	annfsBMI sing_547.htm#SEC601
1067	annfsLogIdeal sing_593.htm#SEC647
1068	annfsParamBM sing_546.htm#SEC600
1069	annfsRB sing_552.htm#SEC606
1070	annfspecial sing_539.htm#SEC593
1071	annihilator of polynomial sing_560.htm#IDX339
1072	annihilator of rational function sing_560.htm#IDX340
1073	annihilator of rational function sing_661.htm#IDX376
1074	annihilatorMultiFs sing_594.htm#SEC648
1075	annil sing_1326.htm#SEC1407
1076	appelF1 sing_579.htm#SEC633
1077	appelF2 sing_580.htm#SEC634
1078	appelF4 sing_581.htm#SEC635
1079	appendWeight2Ord sing_720.htm#SEC774
1080	application sing_2523.htm#IDX1103
1081	apply sing_382.htm#SEC422
1082	applyAdF sing_529.htm#SEC583
1083	applyPermutationToIntvec applyPermutationToIntvec sing_2625.htm#SEC2706
1084	applyVecField sing_2890.htm#SEC2971
1085	arcpoint.lib sing_1591.htm#SEC1672
1086	arcpoint_lib sing_1591.htm#SEC1672
1087	areEqualLeftFractions areEqualLeftFractions sing_760.htm#SEC814
1088	areZeroElements sing_2763.htm#SEC2844
1089	argument, default sing_44.htm#SEC81
1090	argument, optional sing_44.htm#SEC81
1091	arnoldClassify sing_2368.htm#SEC2449
1092	arnoldCorank sing_2369.htm#SEC2450
1093	arnoldDeterminacy sing_2370.htm#SEC2451
1094	arnoldListAllSeries sing_2365.htm#SEC2446
1095	arnoldMilnorCode sing_2371.htm#SEC2452
1096	arnoldMorseSplit sing_2372.htm#SEC2453
1097	arnoldNormalForm sing_2367.htm#SEC2448
1098	arnoldShowSeries sing_2366.htm#SEC2447
1099	arnoldclassify.lib sing_2364.htm#SEC2445
1100	arnoldclassify_lib sing_2364.htm#SEC2445
1101	arr.lib sing_2291.htm#SEC2372
1102	arr2multarr sing_2324.htm#SEC2405
1103	arrBoolean sing_2313.htm#SEC2394
1104	arrBoundedChambers sing_2334.htm#SEC2415
1105	arrBraid sing_2314.htm#SEC2395
1106	arrCenter sing_2301.htm#SEC2382
1107	arrCentered sing_2303.htm#SEC2384
1108	arrCentral sing_2302.htm#SEC2383
1109	arrCentralize sing_2304.htm#SEC2385
1110	arrChambers sing_2333.htm#SEC2414
1111	arrCharPoly sing_2331.htm#SEC2412
1112	arrCone sing_2307.htm#SEC2388
1113	arrCoordChange sing_2305.htm#SEC2386
1114	arrCoordNormalize sing_2306.htm#SEC2387
1115	arrDecone sing_2308.htm#SEC2389
1116	arrDer sing_2321.htm#SEC2402
1117	arrEdelmanReiner sing_2319.htm#SEC2400
1118	arrEssentialize sing_2312.htm#SEC2393
1119	arrExponents sing_2323.htm#SEC2404
1120	arrFlats sing_2328.htm#SEC2409
1121	arrIsEssential sing_2311.htm#SEC2392
1122	arrIsFree sing_2322.htm#SEC2403
1123	arrLastVar sing_2300.htm#SEC2381
1124	arrLattice sing_2329.htm#SEC2410
1125	arrLocalize sing_2309.htm#SEC2390
1126	arrOrlikSolomon sing_2320.htm#SEC2401
1127	arrPoincare sing_2332.htm#SEC2413
1128	arrPrintMatrix sing_2296.htm#SEC2377
1129	arrRandom sing_2317.htm#SEC2398
1130	arrRandomCentral sing_2318.htm#SEC2399
1131	arrRestrict sing_2310.htm#SEC2391
1132	arrSet sing_2292.htm#SEC2373
1133	arrSwapVar sing_2299.htm#SEC2380
1134	arrTypeB sing_2315.htm#SEC2396
1135	arrTypeD sing_2316.htm#SEC2397
1136	arr_lib sing_2291.htm#SEC2372
1137	arrange sing_554.htm#SEC608
1138	arrangement sing_2292.htm#IDX865
1139	arrangement sing_2293.htm#IDX870
1140	arrangement sing_2324.htm#IDX932
1141	arrangement sing_2325.htm#IDX935
1142	ask sing_1985.htm#SEC2066
1143	assPrimes sing_1230.htm#SEC1311
1144	assign sing_2292.htm#IDX867
1145	assignment,custom Assignments for user defined types sing_188.htm#SEC228
1146	associated tangent FamElemsAtEnvCompPoints sing_1041.htm#IDX506
1147	associated tangent sing_1042.htm#IDX510
1148	assprimeszerodim.lib assprimeszerodim_lib sing_1228.htm#SEC1309
1149	assprimeszerodim_lib assprimeszerodim_lib sing_1228.htm#SEC1309
1150	atkins.lib sing_1986.htm#SEC2067
1151	atkins_lib sing_1986.htm#SEC2067
1152	attrib sing_210.htm#SEC250
1153	autGenWeights sing_2376.htm#SEC2457
1154	autGradAlg sing_2375.htm#SEC2456
1155	autKS sing_2374.htm#SEC2455
1156	autX sing_2379.htm#SEC2460
1157	autXhat sing_2378.htm#SEC2459
1158	autgradalg.lib sing_2373.htm#SEC2454
1159	autgradalg_lib sing_2373.htm#SEC2454
1160	automorphism group sing_2373.htm#IDX987
1161	automorphisms sing_2373.htm#IDX984
1162	autonom sing_1949.htm#SEC2030
1163	autonomDim sing_1950.htm#SEC2031
1164	awalk1 sing_1261.htm#SEC1342
1165	awalk2 sing_1262.htm#SEC1343
1166	b-function sing_502.htm#IDX312
1167	bFactor sing_584.htm#SEC638
1168	babyGiant sing_2015.htm#SEC2096
1169	backward sing_2562.htm#SEC2643
1170	bareiss sing_211.htm#SEC251
1171	base2str sing_1003.htm#SEC1084
1172	basering sing_28.htm#IDX76
1173	basering sing_88.htm#SEC128
1174	basicinvariants sing_1597.htm#SEC1678
1175	baumslagGroup sing_826.htm#SEC880
1176	baumslagSolitar sing_825.htm#SEC879
1177	belongSemigroup sing_1233.htm#SEC1314
1178	bernstein sing_1645.htm#SEC1726
1179	bernsteinBM sing_542.htm#SEC596
1180	bernsteinLift sing_543.htm#SEC597
1181	bertini sing_1460.htm#IDX631
1182	bertini sing_1465.htm#IDX638
1183	bertini2Singular sing_1469.htm#SEC1550
1184	betti sing_212.htm#SEC252
1185	betti (plural) sing_459.htm#SEC499
1186	bfct sing_503.htm#SEC557
1187	bfctAnn sing_505.htm#SEC559
1188	bfctBound sing_670.htm#SEC724
1189	bfctIdeal sing_507.htm#SEC561
1190	bfctOneGB sing_506.htm#SEC560
1191	bfctSyz sing_504.htm#SEC558
1192	bfctVarAnn sing_602.htm#SEC656
1193	bfctVarIn sing_601.htm#SEC655
1194	bfun.lib sing_502.htm#SEC556
1195	bfun_lib sing_502.htm#SEC556
1196	bigger sing_2502.htm#IDX1054
1197	bigint sing_78.htm#SEC118
1198	bigint declarations sing_79.htm#SEC119
1199	bigint expressions sing_80.htm#SEC120
1200	bigint operations sing_81.htm#SEC121
1201	bigint related functions bigint related functions sing_82.htm#SEC122
1202	bigintToBinary sing_2623.htm#SEC2704
1203	bigintmat sing_83.htm#SEC123
1204	bigintmat declarations bigintmat declarations sing_84.htm#SEC124
1205	bigintmat expressions bigintmat expressions sing_85.htm#SEC125
1206	bigintmat operations bigintmat operations sing_87.htm#SEC127
1207	bigintmat type cast sing_86.htm#SEC126
1208	bimodules sing_495.htm#IDX300
1209	bimodules.lib sing_495.htm#SEC549
1210	bimodules_lib sing_495.htm#SEC549
1211	binaryToBigint sing_2624.htm#SEC2705
1212	binary_add sing_2038.htm#SEC2119
1213	binomial sing_1009.htm#SEC1090
1214	binomials2intmat sing_1392.htm#SEC1473 58804
1215	birational map, image, inverse. sing_1486.htm#IDX663
1216	bistd sing_496.htm#SEC550
1217	bisyzygies sing_495.htm#IDX301
1218	bitrinity sing_497.htm#SEC551
1219	blackbox sing_192.htm#SEC232
1220	blackbox sing_200.htm#SEC240
1221	block sing_40.htm#SEC70
1222	block sing_381.htm#SEC421
1223	blowUp sing_1537.htm#SEC1618
1224	blowUp2 sing_1538.htm#SEC1619
1225	blowUpBO sing_1544.htm#SEC1625
1226	blowup0 sing_1238.htm#SEC1319
1227	boolean sing_2313.htm#IDX909
1228	boolean expressions sing_100.htm#SEC140
1229	boolean operations sing_101.htm#SEC141
1230	boolean_constant sing_2347.htm#SEC2428 52873
1231	boolean_ideal sing_2351.htm#SEC2432 53515
1232	boolean_poly sing_2348.htm#SEC2429 41652
1233	boolean_poly_ring sing_2346.htm#SEC2427 sprintf
1234	boolean_set sing_2352.htm#SEC2433 58235
1235	boolean_std sing_2345.htm#SEC2426 5921
1236	border basis sing_2829.htm#IDX1185
1237	borderBasis sing_2830.htm#SEC2911
1238	boundBuFou sing_2115.htm#SEC2196
1239	boundDes sing_2117.htm#SEC2198
1240	boundaryLatticePoints boundaryLatticePoints sing_2204.htm#SEC2285
1241	boundposDes sing_2116.htm#SEC2197
1242	bounds sing_2817.htm#SEC2898
1243	boxSet sing_2819.htm#SEC2900
1244	bracket sing_361.htm#IDX197
1245	bracket sing_418.htm#SEC458
1246	bracket sing_460.htm#SEC500
1247	braid sing_2314.htm#IDX911
1248	branchTo procs with different argument types sing_160.htm#SEC200
1249	break sing_383.htm#SEC423
1250	break point sing_397.htm#SEC437
1251	breakpoint sing_384.htm#SEC424
1252	brillnoether.lib sing_2380.htm#SEC2461
1253	brillnoether_lib sing_2380.htm#SEC2461
1254	brnoeth.lib sing_1911.htm#SEC1992
1255	brnoeth_lib sing_1911.htm#SEC1992
1256	browser, command line option Command line options sing_19.htm#IDX44
1257	browser, setting the sing_361.htm#IDX193
1258	browsers The online help system sing_16.htm#IDX21
1259	browsers, setting the sing_361.htm#IDX192
1260	bubblesort sing_1988.htm#SEC2069
1261	busadj sing_1192.htm#SEC1273
1262	bvar sing_2359.htm#SEC2440 52773
1263	c, module ordering sing_964.htm#IDX452
1264	cProj sing_2422.htm#SEC2503
1265	calculateI sing_1511.htm#SEC1592
1266	calculate_max_sum sing_2057.htm#SEC2138
1267	calculate_ordering sing_2035.htm#SEC2116
1268	cancelunit, option sing_318.htm#IDX171
1269	canonMap sing_1266.htm#SEC1347
1270	canonical sing_1027.htm#IDX461
1271	canonical form sing_1031.htm#IDX473
1272	canonical form sing_1032.htm#IDX475
1273	canonical form sing_1033.htm#IDX477
1274	canonical form sing_1048.htm#IDX519
1275	canonical form sing_1049.htm#IDX521
1276	canonical form sing_1050.htm#IDX524
1277	canonical form sing_1051.htm#IDX526
1278	canonical, sing_1035.htm#IDX487
1279	canonicalizeCone sing_2134.htm#SEC2215
1280	canonize sing_1957.htm#SEC2038
1281	cantoradd sing_2071.htm#SEC2152
1282	cantormult sing_2074.htm#SEC2155
1283	cantorred sing_2072.htm#SEC2153
1284	cardGroup sing_1235.htm#SEC1316
1285	case No case or switch statement sing_416.htm#SEC456
1286	catNets sing_2780.htm#SEC2861
1287	cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2884.htm#SEC2965
1288	cdd sing_1.htm#IDX10
1289	cddlib sing_1.htm#IDX11
1290	center sing_516.htm#IDX319
1291	center sing_522.htm#SEC576
1292	center sing_2301.htm#IDX891
1293	center sing_2302.htm#IDX892
1294	center sing_2303.htm#IDX894
1295	center sing_2304.htm#IDX896
1296	centerRed sing_521.htm#SEC575
1297	centerVS sing_520.htm#SEC574
1298	central sing_2295.htm#IDX877
1299	central sing_2302.htm#IDX893
1300	central sing_2304.htm#IDX895
1301	central sing_2318.htm#IDX920
1302	central.lib sing_516.htm#SEC570
1303	central1st sing_2563.htm#SEC2644
1304	central2nd sing_2564.htm#SEC2645
1305	central_lib sing_516.htm#SEC570
1306	centralize sing_516.htm#IDX322
1307	centralizeSet sing_517.htm#SEC571
1308	centralizer sing_516.htm#IDX320
1309	centralizer sing_523.htm#SEC577
1310	centralizerRed sing_519.htm#SEC573
1311	centralizerVS sing_518.htm#SEC572
1312	cf_class sing_210.htm#IDX132
1313	cgs sing_1002.htm#SEC1083
1314	cgsdr sing_1028.htm#SEC1109
1315	chAll sing_2392.htm#SEC2473
1316	chAllInv sing_2393.htm#SEC2474
1317	chDual sing_2398.htm#SEC2479
1318	chHE sing_2394.htm#SEC2475
1319	chHom sing_2407.htm#SEC2488
1320	chNum sing_2388.htm#SEC2469
1321	chNumbers sing_2389.htm#SEC2470
1322	chNumbersProj sing_2426.htm#SEC2507
1323	chProd sing_2400.htm#SEC2481
1324	chProdE sing_2401.htm#SEC2482
1325	chProdL sing_2402.htm#SEC2483
1326	chProdLP sing_2403.htm#SEC2484
1327	chProdM sing_2404.htm#SEC2485
1328	chProdMP sing_2405.htm#SEC2486
1329	chProj sing_2423.htm#SEC2504
1330	chSum sing_2396.htm#SEC2477
1331	chSymm sing_2410.htm#SEC2491
1332	chSymm2L sing_2411.htm#SEC2492
1333	chSymm2LP sing_2412.htm#SEC2493
1334	chWedge sing_2413.htm#SEC2494
1335	chWedge2L sing_2414.htm#SEC2495
1336	chWedge2LP sing_2415.htm#SEC2496
1337	chaincrit sing_2085.htm#SEC2166
1338	chambers sing_2333.htm#IDX948
1339	chambers sing_2334.htm#IDX949
1340	changeCoordinates sing_2891.htm#SEC2972
1341	changeDenominator sing_1364.htm#SEC1445
1342	changechar sing_1110.htm#SEC1191
1343	changeord sing_1111.htm#SEC1192
1344	changeordTo sing_1134.htm#SEC1215
1345	changes sing_2901.htm#SEC2982
1346	changevar sing_1112.htm#SEC1193
1347	char sing_213.htm#SEC253
1348	charInfo sing_577.htm#SEC631
1349	charVariety sing_576.htm#SEC630
1350	char_series sing_214.htm#SEC254
1351	characteristic exponents sing_1585.htm#IDX687
1352	characteristic exponents sing_1586.htm#IDX692
1353	characteristic exponents sing_1587.htm#IDX695
1354	characteristic exponents sing_1588.htm#IDX699
1355	characteristic exponents sing_1672.htm#IDX805
1356	characteristic polynomial sing_2331.htm#IDX946
1357	characteristic variety sing_560.htm#IDX347
1358	characteristic variety sing_661.htm#IDX372
1359	charexp2conductor sing_1588.htm#SEC1669
1360	charexp2generators sing_1586.htm#SEC1667
1361	charexp2inter sing_1587.htm#SEC1668
1362	charexp2multseq sing_1585.htm#SEC1666
1363	charexp2poly sing_1589.htm#SEC1670
1364	charpoly sing_1193.htm#SEC1274
1365	charstr sing_215.htm#SEC255
1366	checkFactor sing_553.htm#SEC607
1367	checkRoot sing_548.htm#SEC602
1368	chern sing_2387.htm#SEC2468
1369	chern.lib sing_2382.htm#SEC2463
1370	chernCharPoly sing_2429.htm#SEC2510
1371	chernPoly sing_2428.htm#SEC2509
1372	chern_lib sing_2382.htm#SEC2463
1373	chineseRem sing_2006.htm#SEC2087
1374	chinrem sing_216.htm#SEC256
1375	chinrempoly sing_2806.htm#SEC2887
1376	chinrestp sing_2065.htm#SEC2146
1377	cimonom.lib sing_2444.htm#SEC2525
1378	cimonom_lib sing_2444.htm#SEC2525
1379	cisimplicial.lib sing_1231.htm#SEC1312
1380	cisimplicial_lib sing_1231.htm#SEC1312
1381	classification sing_2364.htm#IDX982
1382	classification sing_2448.htm#IDX990
1383	classify sing_1598.htm#SEC1679
1384	classify.lib sing_1596.htm#SEC1677
1385	classify2.lib sing_2448.htm#SEC2529
1386	classify2_lib sing_2448.htm#SEC2529
1387	classifyCeq sing_1615.htm#SEC1696
1388	classifyMapGerms.lib classifyMapGerms_lib sing_2460.htm#SEC2541
1389	classifyMapGerms_lib classifyMapGerms_lib sing_2460.htm#SEC2541
1390	classifySimpleMaps sing_2466.htm#SEC2547
1391	classifySimpleMaps1 sing_2467.htm#SEC2548
1392	classifyUnimodalMaps classifyUnimodalMaps sing_2468.htm#SEC2549
1393	classify_aeq.lib sing_2451.htm#SEC2532
1394	classify_aeq_lib sing_2451.htm#SEC2532
1395	classify_lib sing_1596.htm#SEC1677
1396	classifyceq.lib sing_1614.htm#IDX702
1397	classifyceq_lib sing_1614.htm#IDX703
1398	classifyci.lib sing_1616.htm#IDX704
1399	classifyci_lib sing_1616.htm#IDX705
1400	classifyicis sing_1617.htm#SEC1698
1401	classpoly sing_2427.htm#SEC2508
1402	cleanTmp sing_2282.htm#SEC2363
1403	cleanunit sing_1509.htm#SEC1590
1404	cleardenom sing_217.htm#SEC257
1405	close sing_218.htm#SEC258
1406	closed_points sing_1921.htm#SEC2002
1407	closetex sing_1888.htm#SEC1969
1408	closureFrac sing_1357.htm#SEC1438
1409	coDim sing_2462.htm#SEC2543
1410	coDimMap sing_2461.htm#SEC2542
1411	coHom sing_704.htm#SEC758
1412	codim sing_1710.htm#SEC1791
1413	codimension sing_2135.htm#SEC2216
1414	coding theory sing_956.htm#SEC1013
1415	coef sing_219.htm#SEC259
1416	coefficient sing_2294.htm#IDX873
1417	coefficient sing_2295.htm#IDX876
1418	coefficient sing_2296.htm#IDX880
1419	coefficient field sing_144.htm#SEC184
1420	coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45
1421	coefficients sing_2489.htm#IDX1029
1422	coefficients, long sing_913.htm#SEC970
1423	coeffmod sing_1983.htm#SEC2064
1424	coeffs sing_220.htm#SEC260
1425	coker sing_2692.htm#SEC2773
1426	colength of derivations curveColengthDerivations sing_2477.htm#IDX1010
1427	collectDiv sing_1554.htm#SEC1635
1428	colrank sing_1955.htm#SEC2036
1429	colred sing_1176.htm#SEC1257
1430	combinat.lib sing_2469.htm#SEC2550
1431	combinat_lib sing_2469.htm#SEC2550
1432	commRing sing_685.htm#SEC739
1433	comma sing_417.htm#SEC457
1434	command,custom Commands for user defined types sing_187.htm#SEC227
1435	command-line option, setting value of sing_361.htm#IDX278
1436	command-line option, value of sing_361.htm#IDX276
1437	command-line options, print all values of sing_361.htm#IDX275
1438	command-line options, short help Command line options sing_19.htm#IDX38
1439	commands (letterplace) Functions (letterplace) sing_797.htm#SEC851
1440	commands (plural) sing_458.htm#IDX299
1441	comment sing_36.htm#IDX108
1442	compare sing_2500.htm#IDX1049
1443	compare sing_2501.htm#IDX1051
1444	compare sing_2502.htm#IDX1055
1445	compare sing_2503.htm#IDX1058
1446	compare sing_2521.htm#IDX1096
1447	compare sing_2522.htm#IDX1098
1448	compareMatrix sing_2700.htm#SEC2781
1449	compareModules sing_2695.htm#SEC2776
1450	compareTasks sing_1141.htm#SEC1222
1451	compareVectors sing_2720.htm#SEC2801
1452	completeReduction sing_1788.htm#SEC1869
1453	complex sing_28.htm#IDX75
1454	complexClassify sing_2449.htm#SEC2530
1455	complexSingType sing_1612.htm#SEC1693
1456	complexType sing_2450.htm#SEC2531
1457	compregb.lib sing_1001.htm#SEC1082
1458	compregb_lib sing_1001.htm#SEC1082
1459	comprehensive Groebner system sing_1001.htm#IDX458
1460	compress sing_1154.htm#SEC1235
1461	computeAfaceOrbits sing_2610.htm#SEC2691
1462	computeConstant sing_1251.htm#SEC1332
1463	computeGromovWitten sing_1254.htm#SEC1335
1464	computeN sing_1558.htm#SEC1639
1465	computeV sing_1557.htm#SEC1638
1466	computemcm sing_1516.htm#SEC1597
1467	concat sing_1155.htm#SEC1236
1468	conductor sing_1365.htm#IDX619
1469	conductor sing_1588.htm#IDX698
1470	conductor sing_2475.htm#IDX1004
1471	conductor, degree sing_1672.htm#IDX808
1472	cone sing_189.htm#SEC229
1473	cone sing_2307.htm#IDX900
1474	cone sing_2308.htm#IDX902
1475	coneLink sing_2138.htm#SEC2219
1476	coneViaInequalities sing_2137.htm#SEC2218
1477	coneViaPoints sing_2136.htm#SEC2217
1478	conic, parametrization, rational point. sing_1493.htm#IDX668
1479	conicWithTangents sing_2258.htm#SEC2339
1480	constructH sing_1517.htm#SEC1598
1481	constructblwup sing_1518.htm#SEC1599
1482	constructible set sing_1048.htm#IDX517
1483	constructible set sing_1050.htm#IDX522
1484	constructible sets sing_1049.htm#IDX520
1485	constructible sets sing_1051.htm#IDX525
1486	constructlastblwup sing_1519.htm#SEC1600
1487	constructor derivationConstructor sing_2324.htm#IDX933
1488	constructor sing_2325.htm#IDX936
1489	constructor sing_2488.htm#IDX1025
1490	constructor sing_2511.htm#IDX1074
1491	constructor sing_2512.htm#IDX1076
1492	constructor sing_2513.htm#IDX1079
1493	constructor sing_2514.htm#IDX1082
1494	contact matrix sing_1587.htm#IDX694
1495	containedQ sing_1876.htm#SEC1957
1496	containment sing_2507.htm#IDX1065
1497	containsAsFace sing_2139.htm#SEC2220
1498	containsInCollection containsInCollection sing_2172.htm#SEC2253
1499	containsInSupport sing_2140.htm#SEC2221
1500	containsPositiveVector containsPositiveVector sing_2141.htm#SEC2222
1501	containsRelatively sing_2142.htm#SEC2223
1502	content sing_1084.htm#SEC1165
1503	contentSB, option sing_318.htm#IDX172
1504	continue Behavior of continue sing_385.htm#SEC425
1505	continue sing_419.htm#SEC459
1506	contraHom sing_705.htm#SEC759
1507	contract sing_221.htm#SEC261
1508	contraction derivationContraction sing_2524.htm#IDX1104
1509	contraction sing_2525.htm#IDX1106
1510	contraction sing_2526.htm#IDX1108
1511	contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2865.htm#IDX1214
1512	contributionBundle sing_2865.htm#SEC2946
1513	contributors sing_361.htm#IDX199
1514	control sing_1947.htm#SEC2028
1515	control.lib sing_1946.htm#SEC2027
1516	controlDim sing_1948.htm#SEC2029
1517	controlExample sing_1960.htm#SEC2041
1518	control_Matrix sing_1640.htm#SEC1721
1519	control_lib sing_1946.htm#SEC2027
1520	convertLeftToRightFraction convertLeftToRightFraction sing_757.htm#SEC811
1521	convertRightToLeftFraction convertRightToLeftFraction sing_756.htm#SEC810
1522	convertdata sing_1514.htm#SEC1595
1523	convexHull sing_2143.htm#SEC2224
1524	convexIntersection sing_2144.htm#SEC2225
1525	convloc sing_557.htm#SEC611
1526	coordinate change sing_2304.htm#IDX897
1527	coordinate change sing_2305.htm#IDX898
1528	coordinate change sing_2306.htm#IDX899
1529	coordinates sing_2103.htm#IDX850
1530	coords sing_2103.htm#SEC2184
1531	copyTask sing_1140.htm#SEC1221
1532	copyright sing_1.htm#IDX1
1533	corank sing_1599.htm#SEC1680
1534	cornerMonomials sing_1395.htm#SEC1476
1535	countPoints sing_2028.htm#SEC2109
1536	coverings sing_1253.htm#IDX572
1537	coverings sing_1254.htm#IDX576
1538	cpu sing_361.htm#IDX201
1539	cpu sing_361.htm#IDX272
1540	createBO sing_1545.htm#SEC1626
1541	createGradedRingHomomorphism createGradedRingHomomorphism sing_2739.htm#SEC2820
1542	createGroup sing_2732.htm#SEC2813
1543	createQuotientGroup sing_2733.htm#SEC2814
1544	createTask sing_1138.htm#SEC1219
1545	createTorsionFreeGroup createTorsionFreeGroup sing_2734.htm#SEC2815
1546	create_ring sing_222.htm#SEC262
1547	createlist sing_1527.htm#SEC1608
1548	cring sing_73.htm#SEC113
1549	cring declarations sing_74.htm#SEC114
1550	cring expressions sing_75.htm#SEC115
1551	cring operations sing_76.htm#SEC116
1552	cring related functions cring related functions sing_77.htm#SEC117
1553	crossprod sing_223.htm#SEC263
1554	crypto.lib sing_2001.htm#SEC2082
1555	crypto_lib sing_2001.htm#SEC2082
1556	crystallographicGroupC2MM crystallographicGroupC2MM sing_834.htm#SEC888
1557	crystallographicGroupCM crystallographicGroupCM sing_833.htm#SEC887
1558	crystallographicGroupP1 crystallographicGroupP1 sing_827.htm#SEC881
1559	crystallographicGroupP2 crystallographicGroupP2 sing_831.htm#SEC885
1560	crystallographicGroupP2GG crystallographicGroupP2GG sing_832.htm#SEC886
1561	crystallographicGroupP2MM crystallographicGroupP2MM sing_830.htm#SEC884
1562	crystallographicGroupP3 crystallographicGroupP3 sing_838.htm#SEC892
1563	crystallographicGroupP31M crystallographicGroupP31M sing_839.htm#SEC893
1564	crystallographicGroupP3M1 crystallographicGroupP3M1 sing_840.htm#SEC894
1565	crystallographicGroupP4 crystallographicGroupP4 sing_835.htm#SEC889
1566	crystallographicGroupP4GM crystallographicGroupP4GM sing_837.htm#SEC891
1567	crystallographicGroupP4MM crystallographicGroupP4MM sing_836.htm#SEC890
1568	crystallographicGroupP6 crystallographicGroupP6 sing_841.htm#SEC895
1569	crystallographicGroupP6MM crystallographicGroupP6MM sing_842.htm#SEC896
1570	crystallographicGroupPG crystallographicGroupPG sing_829.htm#SEC883
1571	crystallographicGroupPM crystallographicGroupPM sing_828.htm#SEC882
1572	cup sing_1267.htm#SEC1348
1573	cupproduct sing_1268.htm#SEC1349
1574	curve singularities sing_1578.htm#IDX681
1575	curve singularities sing_1666.htm#IDX803
1576	curve singularity sing_2473.htm#IDX999
1577	curveColengthDerivations curveColengthDerivations sing_2477.htm#SEC2558
1578	curveConductorMult sing_2475.htm#SEC2556
1579	curveDeligneNumber sing_2476.htm#SEC2557
1580	curveDeltaInv sing_2474.htm#SEC2555
1581	curveInv.lib sing_2473.htm#SEC2554
1582	curveInv_lib sing_2473.htm#SEC2554
1583	curvepar.lib sing_1619.htm#SEC1700
1584	curvepar_lib sing_1619.htm#SEC1700
1585	custom assignment Assignments for user defined types sing_188.htm#SEC228
1586	custom command Commands for user defined types sing_187.htm#SEC227
1587	custom type Definition of a user defined type sing_184.htm#SEC224
1588	customstd.lib sing_2336.htm#SEC2417
1589	customstd_lib sing_2336.htm#SEC2417
1590	cycleLength sing_2195.htm#SEC2276
1591	cyclePoints sing_2199.htm#SEC2280
1592	cyclic sing_1071.htm#SEC1152
1593	cyclic code Codes and the decoding problem sing_988.htm#SEC1052
1594	cyclotomic sing_1753.htm#SEC1834
1595	datetime sing_224.htm#SEC264
1596	dbprint sing_225.htm#SEC265
1597	deRham.lib sing_2478.htm#SEC2559
1598	deRhamCohom sing_574.htm#SEC628
1599	deRhamCohomIdeal sing_575.htm#SEC629
1600	deRhamCohomology sing_2479.htm#SEC2560
1601	deRham_lib sing_2478.htm#SEC2559
1602	debugLib, option sing_318.htm#IDX176
1603	debug_log sing_1609.htm#SEC1690
1604	debugger Source code debugger sing_66.htm#SEC103
1605	debugging library code Source code debugger sing_66.htm#SEC103
1606	dec1var sing_1325.htm#SEC1406
1607	decimal sing_2002.htm#SEC2083
1608	decode sing_1938.htm#SEC2019
1609	decodeCode sing_1940.htm#SEC2021
1610	decodeRandom sing_1939.htm#SEC2020
1611	decodeRandomFL sing_1943.htm#SEC2024
1612	decodeSV sing_1920.htm#SEC2001
1613	decodegb.lib sing_1925.htm#SEC2006
1614	decodegb_lib sing_1925.htm#SEC2006
1615	decoding, decoding problem Codes and the decoding problem sing_988.htm#SEC1053
1616	decoef sing_1968.htm#SEC2049
1617	decomposeVecField sing_2897.htm#SEC2978
1618	decomposition sing_2489.htm#IDX1027
1619	decomposition of modules sing_1318.htm#IDX602
1620	decomposition, numerical sing_1465.htm#IDX636
1621	decone sing_2307.htm#IDX901
1622	decone sing_2308.htm#IDX903
1623	def sing_88.htm#SEC128
1624	def declarations sing_89.htm#SEC129
1625	defRes, option sing_318.htm#IDX177
1626	default argument sing_44.htm#SEC81
1627	defineHomogeneous sing_2772.htm#SEC2853
1628	defined sing_226.htm#SEC266
1629	defl sing_1476.htm#SEC1557
1630	deform sing_1711.htm#SEC1792
1631	deform.lib sing_1630.htm#SEC1711
1632	deform_lib sing_1630.htm#SEC1711
1633	defring sing_1113.htm#SEC1194
1634	defringp sing_1115.htm#SEC1196
1635	defrings sing_1114.htm#SEC1195
1636	deg sing_227.htm#SEC267
1637	degBound sing_399.htm#SEC439
1638	degree Miscellaneous oddities sing_228.htm#SEC268
1639	degree sing_422.htm#IDX289
1640	degree sing_2504.htm#IDX1060
1641	degree sing_2506.htm#IDX1064
1642	degree lexicographical ordering sing_962.htm#IDX432
1643	degree of a polynomial Miscellaneous oddities sing_422.htm#IDX293
1644	degree reverse lexicographical ordering sing_962.htm#IDX430
1645	degreeDivisor sing_2535.htm#SEC2616
1646	degreeFormalDivisor sing_2543.htm#SEC2624
1647	degreepart sing_1828.htm#SEC1909
1648	delete sing_126.htm#SEC166
1649	delete sing_229.htm#SEC269
1650	delete sing_279.htm#SEC319
1651	deleteGenerator sing_589.htm#SEC643
1652	deleteSublist sing_1010.htm#SEC1091
1653	deligne number curveColengthDerivations sing_2473.htm#IDX1001
1654	deligne number sing_2476.htm#IDX1006
1655	deligne number sing_2477.htm#IDX1008
1656	delta sing_1678.htm#SEC1759
1657	delta invariant sing_1359.htm#IDX617
1658	delta invariant sing_1678.htm#IDX813
1659	delta invariant sing_2474.htm#IDX1002
1660	delta invariant. sing_1351.htm#IDX610
1661	delta invariant. sing_1352.htm#IDX613
1662	delta invariant. sing_1353.htm#IDX616
1663	deltaLoc sing_1359.htm#SEC1440
1664	denom_list sing_361.htm#IDX203
1665	denominator sing_230.htm#SEC270
1666	depth sing_1269.htm#SEC1350
1667	depthIdeal sing_1335.htm#SEC1416
1668	derivate sing_1785.htm#SEC1866
1669	derivation derivationConstructor sing_2321.htm#IDX924
1670	derivation sing_2509.htm#IDX1069
1671	derivation sing_2510.htm#IDX1073
1672	derivation sing_2511.htm#IDX1075
1673	derivation sing_2512.htm#IDX1077
1674	derivation sing_2513.htm#IDX1080
1675	derivation sing_2514.htm#IDX1083
1676	derivation sing_2523.htm#IDX1102
1677	derivationAdd sing_2517.htm#SEC2598
1678	derivationCheckList sing_2512.htm#SEC2593
1679	derivationConstructor derivationConstructor sing_2514.htm#SEC2595
1680	derivationContraction derivationContraction sing_2525.htm#SEC2606
1681	derivationContractionGen derivationContractionGen sing_2524.htm#SEC2605
1682	derivationEqu sing_2521.htm#SEC2602
1683	derivationEval sing_2523.htm#SEC2604
1684	derivationFromList sing_2511.htm#SEC2592
1685	derivationFromPoly sing_2513.htm#SEC2594
1686	derivationLie sing_2526.htm#SEC2607
1687	derivationMul sing_2520.htm#SEC2601
1688	derivationNeg sing_2519.htm#SEC2600
1689	derivationNeq sing_2522.htm#SEC2603
1690	derivationPrint sing_2516.htm#SEC2597
1691	derivationSub sing_2518.htm#SEC2599
1692	derivationToString sing_2515.htm#SEC2596
1693	desingularization sing_2629.htm#IDX1139
1694	desingularization sing_2630.htm#SEC2711
1695	det sing_231.htm#SEC271
1696	det_B sing_1195.htm#SEC1276
1697	detadj sing_1694.htm#SEC1775
1698	determinacy sing_2814.htm#SEC2895
1699	determinecenter sing_1499.htm#SEC1580
1700	detropicalise sing_2276.htm#SEC2357
1701	develop sing_1668.htm#SEC1749
1702	diag sing_1156.htm#SEC1237
1703	diagInvariants sing_1374.htm#SEC1455 62096
1704	diag_test sing_1191.htm#SEC1272
1705	diagonalizeMatrixSimul diagonalizeMatrixSimul sing_2898.htm#SEC2979
1706	diagonalizeVecField sing_2895.htm#SEC2976
1707	diagonalizeVecFieldLin diagonalizeVecFieldLin sing_2893.htm#SEC2974
1708	diff sing_232.htm#SEC272
1709	diffAlgebra sing_2482.htm#SEC2563
1710	diffAlgebraChangeOrd diffAlgebraChangeOrd sing_2486.htm#SEC2567
1711	diffAlgebraGens sing_2484.htm#SEC2565
1712	diffAlgebraListGen sing_2487.htm#SEC2568
1713	diffAlgebraStructure diffAlgebraStructure sing_2483.htm#SEC2564
1714	diffAlgebraUnivDerIdeal diffAlgebraUnivDerIdeal sing_2485.htm#SEC2566
1715	diffRat sing_684.htm#SEC738
1716	difference sing_2496.htm#IDX1043
1717	difference sing_2518.htm#IDX1091
1718	difference sing_2519.htm#IDX1093
1719	differential sing_2488.htm#IDX1026
1720	differential sing_2510.htm#IDX1071
1721	differential algebra diffAlgebraUnivDerIdeal sing_2481.htm#IDX1013
1722	differential algebra sing_2482.htm#IDX1014
1723	differential algebra sing_2483.htm#IDX1017
1724	differential algebra sing_2484.htm#IDX1018
1725	differential algebra sing_2485.htm#IDX1020
1726	differential forms sing_2481.htm#IDX1011
1727	differential forms sing_2482.htm#IDX1015
1728	differentials sing_2481.htm#IDX1012
1729	differentials sing_2482.htm#IDX1016
1730	difform.lib sing_2481.htm#SEC2562
1731	difformAdd sing_2495.htm#SEC2576
1732	difformCoef sing_2489.htm#SEC2570
1733	difformDeg sing_2504.htm#SEC2585
1734	difformDiff sing_2510.htm#SEC2591
1735	difformDiv sing_2499.htm#SEC2580
1736	difformEqu sing_2500.htm#SEC2581
1737	difformFromPoly sing_2488.htm#SEC2569
1738	difformGenToString sing_2490.htm#SEC2571
1739	difformHomogDecomp sing_2491.htm#SEC2572
1740	difformIsBigger sing_2502.htm#SEC2583
1741	difformIsGen sing_2494.htm#SEC2575
1742	difformIsHomog sing_2505.htm#SEC2586
1743	difformIsHomogDeg sing_2506.htm#SEC2587
1744	difformIsSmaller sing_2503.htm#SEC2584
1745	difformListCont sing_2507.htm#SEC2588
1746	difformListSort sing_2508.htm#SEC2589
1747	difformMul sing_2498.htm#SEC2579
1748	difformNeg sing_2497.htm#SEC2578
1749	difformNeq sing_2501.htm#SEC2582
1750	difformPrint sing_2493.htm#SEC2574
1751	difformSub sing_2496.htm#SEC2577
1752	difformToString sing_2492.htm#SEC2573
1753	difformUnivDer sing_2509.htm#SEC2590
1754	difform_lib sing_2481.htm#SEC2562
1755	difpoly2tex sing_1969.htm#SEC2050
1756	dim sing_233.htm#SEC273
1757	dim (plural) sing_461.htm#SEC501
1758	dimGradedPart sing_1567.htm#SEC1648 11262
1759	dimH sing_1566.htm#SEC1647 38534
1760	dimMon sing_1315.htm#SEC1396
1761	dimStack sing_2863.htm#SEC2944
1762	dim_slocus sing_1712.htm#SEC1793
1763	dimension sing_2145.htm#SEC2226
1764	dimension, moduli space of stable maps, rational curves dimStack sing_2863.htm#IDX1212
1765	dimensionOfLocalization dimensionOfLocalization sing_2593.htm#SEC2674
1766	direct_boolean_poly sing_2349.htm#SEC2430 49893
1767	direct_from_boolean_poly direct_from_boolean_poly sing_2355.htm#SEC2436 36941
1768	disc sing_1989.htm#SEC2070
1769	discr sing_1734.htm#SEC1815
1770	discrepancy sing_1552.htm#SEC1633
1771	discrim sing_1043.htm#SEC1124
1772	discussion of parametric ideal sing_1027.htm#IDX462
1773	disjoint sing_1028.htm#IDX464
1774	disp_zdd sing_2362.htm#SEC2443 41439
1775	displayCohom sing_1568.htm#SEC1649 22633
1776	displayHNE sing_1671.htm#SEC1752
1777	displayInvariants sing_1673.htm#SEC1754
1778	displayMultsequence sing_1675.htm#SEC1756
1779	displayPuiseuxExpansion displayPuiseuxExpansion sing_2251.htm#SEC2332
1780	displayTropicalLifting displayTropicalLifting sing_2249.htm#SEC2330
1781	distributed computing sing_1064.htm#IDX534
1782	distributed computing sing_1104.htm#IDX536
1783	distributed computing sing_1137.htm#IDX546
1784	div Miscellaneous oddities sing_81.htm#SEC121
1785	div sing_98.htm#SEC138
1786	div sing_155.htm#SEC195
1787	div sing_422.htm#IDX286
1788	divideUnits sing_1965.htm#SEC2046
1789	dividelist sing_1526.htm#SEC1607
1790	division sing_234.htm#SEC274
1791	division sing_1029.htm#IDX467
1792	division sing_1030.htm#IDX469
1793	division sing_2499.htm#IDX1048
1794	division (plural) sing_462.htm#SEC502
1795	divisor sing_2068.htm#SEC2149
1796	divisorplus sing_2529.htm#SEC2610
1797	divisors negativeformaldivisor sing_2528.htm#IDX1109
1798	divisors sing_2529.htm#IDX1110
1799	divisors sing_2530.htm#IDX1111
1800	divisors sing_2531.htm#IDX1112
1801	divisors sing_2532.htm#IDX1113
1802	divisors sing_2533.htm#IDX1114
1803	divisors sing_2534.htm#IDX1115
1804	divisors sing_2535.htm#IDX1116
1805	divisors sing_2536.htm#IDX1117
1806	divisors sing_2537.htm#IDX1118
1807	divisors sing_2538.htm#IDX1119
1808	divisors sing_2539.htm#IDX1120
1809	divisors sing_2540.htm#IDX1121
1810	divisors sing_2541.htm#IDX1122
1811	divisors sing_2542.htm#IDX1123
1812	divisors sing_2543.htm#IDX1124
1813	divisors, polyhedra sing_2544.htm#IDX1125
1814	divisors, polyhedra sing_2545.htm#IDX1126
1815	divisors, polyhedra sing_2546.htm#IDX1127
1816	divisors.lib sing_2527.htm#SEC2608
1817	divisors_lib sing_2527.htm#SEC2608
1818	dmod.lib sing_537.htm#SEC591
1819	dmodAction sing_679.htm#SEC733
1820	dmodActionRat sing_680.htm#SEC734
1821	dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_672.htm#SEC726
1822	dmod_lib sing_537.htm#SEC591
1823	dmodapp.lib sing_560.htm#SEC614
1824	dmodapp_lib sing_560.htm#SEC614
1825	dmodideal.lib sing_592.htm#SEC646
1826	dmodideal_lib sing_592.htm#SEC646
1827	dmodloc.lib sing_661.htm#IDX365
1828	dmodloc_lib sing_661.htm#IDX366
1829	dmodoublext sing_706.htm#SEC760
1830	dmodvar.lib sing_600.htm#SEC654
1831	dmodvar_lib sing_600.htm#SEC654
1832	double sing_2073.htm#SEC2154
1833	doubleExt sing_779.htm#SEC833
1834	downloading Download instructions sing_2909.htm#SEC3006
1835	dp, global ordering sing_962.htm#IDX431
1836	drawNewtonSubdivision drawNewtonSubdivision sing_2254.htm#SEC2335
1837	drawTropicalCurve sing_2253.htm#SEC2334
1838	ds, local ordering sing_963.htm#IDX441
1839	dsum sing_1157.htm#SEC1238
1840	dualCone sing_2146.htm#SEC2227
1841	dualConic sing_2278.htm#SEC2359
1842	dualPart sing_2435.htm#SEC2516
1843	dualPartition sing_2876.htm#SEC2957
1844	dualPolytope sing_2185.htm#SEC2266
1845	dualSheaf sing_2854.htm#SEC2935
1846	dual_code sing_1922.htm#SEC2003
1847	dump sing_235.htm#SEC275
1848	dyckGroup1 sing_843.htm#SEC897
1849	dyckGroup2 sing_844.htm#SEC898
1850	dyckGroup3 sing_845.htm#SEC899
1851	dynamic geometry sing_1036.htm#IDX491
1852	dynamic geometry sing_1037.htm#IDX494
1853	ecart sing_2076.htm#SEC2157
1854	echo sing_400.htm#SEC440
1855	eexgcdN sing_2003.htm#SEC2084
1856	effective sing_2537.htm#SEC2618
1857	egcdMain sing_1869.htm#SEC1950
1858	ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2205.htm#SEC2286
1859	ehrhartRing sing_1370.htm#SEC1451 16966
1860	eigenvals sing_1203.htm#SEC1284
1861	eigenvalue sing_331.htm#SEC371
1862	eigenvalue sing_1203.htm#IDX552
1863	eigenvalues sing_1453.htm#SEC1534
1864	elemSymmId sing_1072.htm#SEC1153
1865	elim sing_1240.htm#SEC1321
1866	elim.lib sing_1237.htm#SEC1318
1867	elim1 sing_1241.htm#SEC1322
1868	elim2 sing_1242.htm#SEC1323
1869	elimRing sing_1239.htm#SEC1320
1870	elimWeight sing_721.htm#SEC775
1871	elim_lib sing_1237.htm#SEC1318
1872	eliminate sing_236.htm#SEC276
1873	eliminate (plural) sing_463.htm#SEC503
1874	eliminateNC sing_716.htm#SEC770
1875	elimination sing_715.htm#IDX380
1876	elimlinearpart sing_1829.htm#SEC1910
1877	elimpart sing_1830.htm#SEC1911
1878	elimpartanyr sing_1831.htm#SEC1912
1879	elimrep sing_1507.htm#SEC1588
1880	elliptic curve sing_1250.htm#IDX568
1881	elliptic curves sing_1247.htm#IDX562
1882	elliptic curves sing_1253.htm#IDX571
1883	elliptic curves sing_1254.htm#IDX575
1884	ellipticAdd sing_2024.htm#SEC2105
1885	ellipticAllPoints sing_2029.htm#SEC2110
1886	ellipticMult sing_2025.htm#SEC2106
1887	ellipticNF sing_2202.htm#SEC2283
1888	ellipticNFDB sing_2203.htm#SEC2284
1889	ellipticRandomCurve sing_2026.htm#SEC2107
1890	ellipticRandomPoint sing_2027.htm#SEC2108
1891	ellipticcovers.lib sing_1247.htm#IDX556
1892	ellipticcovers_lib sing_1247.htm#IDX557
1893	else sing_390.htm#SEC430
1894	embedMat sing_747.htm#SEC801
1895	emptyFan sing_2173.htm#SEC2254
1896	encode sing_1930.htm#SEC2011
1897	endomorphism filtration sing_1652.htm#IDX779
1898	endvfilt sing_1652.htm#SEC1733
1899	ensureLeftNcfrac sing_694.htm#SEC748
1900	ensureRightNcfrac sing_695.htm#SEC749
1901	envelop FamElemsAtEnvCompPoints sing_1038.htm#SEC1119
1902	envelop sing_1038.htm#IDX497
1903	envelop sing_1039.htm#IDX500
1904	envelop sing_1041.htm#IDX505
1905	envelop sing_1042.htm#IDX509
1906	envelope sing_464.htm#SEC504
1907	enveloping algebra sing_361.htm#IDX207
1908	enveloping algebra sing_495.htm#IDX303
1909	environment variable, DISPLAY The online help system sing_16.htm#IDX29
1910	environment variables Used environment variables sing_2910.htm#SEC3007
1911	equal sing_2500.htm#IDX1050
1912	equal sing_2501.htm#IDX1052
1913	equal sing_2521.htm#IDX1097
1914	equal sing_2522.htm#IDX1099
1915	equalJinI sing_1595.htm#SEC1676
1916	equalMultiDeg sing_2765.htm#SEC2846
1917	equations sing_2147.htm#SEC2228
1918	equiRadical sing_1411.htm#SEC1492
1919	equidim sing_1413.htm#SEC1494
1920	equidimMax sing_1414.htm#SEC1495
1921	equidimMaxEHV sing_1415.htm#SEC1496
1922	equidimZ sing_1426.htm#SEC1507
1923	equising.lib sing_1635.htm#SEC1716
1924	equising_lib sing_1635.htm#SEC1716
1925	equisingular Tjurina number sing_1578.htm#IDX686
1926	equisingularity ideal sing_1637.htm#IDX706
1927	equisingularity stratum sing_1638.htm#IDX707
1928	error recovery sing_15.htm#SEC21
1929	errorInsert sing_1933.htm#SEC2014
1930	errorRand sing_1934.htm#SEC2015
1931	errormap sing_2569.htm#SEC2650
1932	esIdeal sing_1637.htm#SEC1718
1933	esStratum sing_1638.htm#SEC1719
1934	essential sing_2311.htm#IDX906
1935	essential sing_2312.htm#IDX907
1936	eta sing_2197.htm#SEC2278
1937	euler sing_1982.htm#SEC2063
1938	eulerChProj sing_2425.htm#SEC2506
1939	eval sing_237.htm#SEC277
1940	evalJacobianAtBox sing_2825.htm#SEC2906
1941	evalPolyAtBox sing_2824.htm#SEC2905
1942	evaluateFormalDivisor evaluateFormalDivisor sing_2539.htm#SEC2620
1943	evaluatePDivisor sing_2545.htm#SEC2626
1944	evaluateProduct sing_2620.htm#SEC2701
1945	evaluate_reynolds sing_1758.htm#SEC1839
1946	evaluation sing_2523.htm#IDX1101
1947	evalutateIntegral sing_1252.htm#SEC1333
1948	example sing_239.htm#SEC279
1949	example sing_2313.htm#IDX908
1950	example sing_2314.htm#IDX910
1951	example sing_2315.htm#IDX912
1952	example sing_2316.htm#IDX914
1953	example sing_2317.htm#IDX916
1954	example sing_2318.htm#IDX918
1955	example sing_2319.htm#IDX921
1956	execute sing_240.htm#SEC280
1957	exit sing_394.htm#SEC434
1958	exp2pt sing_1970.htm#SEC2051
1959	expo sing_1994.htm#SEC2075
1960	exponents sing_2323.htm#IDX929
1961	export sing_387.htm#SEC427
1962	exportNuminvs sing_1378.htm#SEC1459 10423
1963	exportto sing_388.htm#SEC428
1964	expp sing_2874.htm#SEC2955
1965	expression list sing_72.htm#IDX128
1966	expression list sing_426.htm#IDX296
1967	ext-module purityfiltration_lib sing_771.htm#IDX386
1968	extcurve sing_1916.htm#SEC1997
1969	extdevelop sing_1669.htm#SEC1750
1970	extendGC sing_1035.htm#SEC1116
1971	extendWeyl sing_673.htm#SEC727
1972	extendedTensor sing_722.htm#SEC776
1973	extendpoly sing_1034.htm#SEC1115
1974	extendring sing_1116.htm#SEC1197
1975	extension of rings sing_1431.htm#IDX628
1976	exterior basis sing_1182.htm#IDX549
1977	exterior power sing_1184.htm#IDX551
1978	exteriorBasis sing_1182.htm#SEC1263
1979	exteriorPower sing_1184.htm#SEC1265
1980	extgcd sing_241.htm#SEC281
1981	extractS sing_599.htm#SEC653
1982	fVector sing_2176.htm#SEC2257
1983	fVectorP sing_2206.htm#SEC2287
1984	facFirstShift sing_654.htm#SEC708
1985	facFirstWeyl sing_650.htm#SEC704
1986	facGBIdeal sing_1396.htm#SEC1477
1987	facShift sing_653.htm#SEC707
1988	facSubWeyl sing_652.htm#SEC706
1989	facWeyl sing_649.htm#SEC703
1990	faceContaining sing_2148.htm#SEC2229
1991	facetVertexLatticeDistances facetVertexLatticeDistances sing_2207.htm#SEC2288
1992	facetWidth sing_2208.htm#SEC2289
1993	facetWidths sing_2209.htm#SEC2290
1994	facets sing_2149.htm#SEC2230
1995	facstd sing_242.htm#SEC282
1996	factmodd sing_243.htm#SEC283
1997	factor sing_325.htm#SEC365
1998	factorH sing_1025.htm#SEC1106
1999	factorLenstraECM sing_2033.htm#SEC2114
2000	factorMain sing_1870.htm#SEC1951
2001	factorgroup sing_2755.htm#SEC2836
2002	factorial sing_1011.htm#SEC1092
2003	factorization sing_326.htm#SEC366
2004	factorization sing_1212.htm#IDX553
2005	factorize sing_244.htm#SEC284
2006	factorize sing_325.htm#SEC365
2007	factory sing_1.htm#IDX2
2008	fan sing_190.htm#SEC230
2009	fan sing_2189.htm#IDX855
2010	fanViaCones sing_2174.htm#SEC2255
2011	farey sing_245.htm#SEC285
2012	fareypoly sing_2548.htm#SEC2629
2013	fastExpt sing_1978.htm#SEC2059
2014	fastHC, option sing_318.htm#IDX153
2015	fastelim sing_1832.htm#SEC1913
2016	fetch sing_246.htm#SEC286
2017	fetch (plural) sing_465.htm#SEC505
2018	fetchall sing_1117.htm#SEC1198
2019	ffmodStd sing_2554.htm#SEC2635
2020	ffmodstd.lib sing_2547.htm#SEC2628
2021	ffmodstd_lib sing_2547.htm#SEC2628
2022	ffsolve sing_1821.htm#SEC1902
2023	ffsolve.lib sing_1820.htm#SEC1901
2024	ffsolve_lib sing_1820.htm#SEC1901
2025	fglm sing_247.htm#SEC287
2026	fglm sing_358.htm#IDX187
2027	fglm_solve sing_1848.htm#SEC1929
2028	fglmquot sing_248.htm#SEC288
2029	fibonacci sing_1012.htm#SEC1093
2030	fibonacciGroup sing_846.htm#SEC900
2031	field sing_144.htm#SEC184
2032	file, .singularrc sing_20.htm#IDX71
2033	filecmd sing_249.htm#SEC289
2034	filtration purityfiltration_lib sing_771.htm#IDX387
2035	finalCharts sing_1531.htm#SEC1612
2036	find sing_250.htm#SEC290
2037	findAuto sing_608.htm#SEC662
2038	findInvo sing_606.htm#SEC660
2039	findInvoDiag sing_607.htm#SEC661
2040	findOrientedBoundary findOrientedBoundary sing_2198.htm#SEC2279
2041	findTorsion sing_1959.htm#SEC2040
2042	find_first_primitive_root find_first_primitive_root sing_2037.htm#SEC2118
2043	find_index sing_2041.htm#SEC2122
2044	findifs.lib sing_1966.htm#SEC2047
2045	findifs_example sing_1967.htm#SEC2048
2046	findifs_lib sing_1966.htm#SEC2047
2047	findimAlgebra sing_731.htm#SEC785
2048	finduni sing_251.htm#SEC291
2049	findvars sing_1833.htm#SEC1914
2050	finite field sing_144.htm#SEC184
2051	finite field sing_1820.htm#IDX828
2052	finiteDiagInvariants finiteDiagInvariants sing_1373.htm#SEC1454 3508
2053	finitediff.lib sing_2555.htm#IDX1128
2054	finitediff_lib sing_2555.htm#IDX1129
2055	finitely presented algebra sing_814.htm#IDX394
2056	finitely presented algebra sing_820.htm#IDX400
2057	finitely presented algebra sing_849.htm#IDX403
2058	finitely presented algebra sing_856.htm#IDX415
2059	finitely presented algebra sing_870.htm#IDX416
2060	finitely presented algebra, standard finitely presented algebra Free associative algebras sing_808.htm#IDX393
2061	finitely presented group sing_820.htm#IDX401
2062	finitenessTest sing_1226.htm#SEC1307
2063	finiterep sing_1811.htm#SEC1892
2064	finvar.lib sing_1746.htm#SEC1827
2065	finvar_lib sing_1746.htm#SEC1827
2066	first index is 1 sing_421.htm#SEC461
2067	firstoct sing_1881.htm#SEC1962
2068	fitting sing_1272.htm#SEC1353
2069	fixed points, moduli space of stable maps, graph fixedPoints sing_2864.htm#IDX1213
2070	fixedPoints sing_2864.htm#SEC2945
2071	fl2poly sing_587.htm#SEC641
2072	flatten sing_1158.htm#SEC1239
2073	flatteningStrat sing_1273.htm#SEC1354
2074	flintQ sing_252.htm#SEC292
2075	floating point sing_1126.htm#IDX539
2076	for sing_389.htm#SEC429
2077	formal linear representations sing_873.htm#IDX424
2078	formaldivisorplus sing_2540.htm#SEC2621
2079	forward sing_2561.htm#SEC2642
2080	fourier sing_582.htm#SEC636
2081	fouriersystem sing_2572.htm#SEC2653
2082	fpadim.lib sing_814.htm#SEC868
2083	fpadim_lib sing_814.htm#SEC868
2084	fpalgebras.lib sing_820.htm#SEC874
2085	fpalgebras_lib sing_820.htm#SEC874
2086	fpaprops.lib sing_849.htm#SEC903
2087	fpaprops_lib sing_849.htm#SEC903
2088	fprintf sing_254.htm#SEC294
2089	fracStatus sing_752.htm#SEC806
2090	framed sheaves sing_2579.htm#IDX1136
2091	frandwalk sing_2837.htm#SEC2918
2092	free sing_2322.htm#IDX926
2093	free sing_2323.htm#IDX928
2094	free associative algebra sing_820.htm#IDX399
2095	free associative algebra sing_856.htm#IDX411
2096	free associative algebra, tensor algebra Free associative algebras sing_808.htm#SEC862
2097	free noncommutative Groebner basis sing_856.htm#IDX413
2098	freeAlgebra (letterplace) freeAlgebra (letterplace) sing_798.htm#SEC852
2099	freeModule sing_2672.htm#SEC2753
2100	freeModule2Module sing_2701.htm#SEC2782
2101	freegb.lib sing_856.htm#SEC910
2102	freegb_lib sing_856.htm#SEC910
2103	freemodule sing_255.htm#SEC295
2104	freerank sing_1074.htm#SEC1155
2105	fres sing_256.htm#SEC296
2106	from_boolean_constant from_boolean_constant sing_2353.htm#SEC2434 44881
2107	from_boolean_ideal sing_2357.htm#SEC2438 62698
2108	from_boolean_poly sing_2354.htm#SEC2435 27864
2109	from_boolean_set sing_2358.htm#SEC2439 60615
2110	frwalk sing_257.htm#SEC297
2111	full representation sing_1034.htm#IDX483
2112	full representation sing_1035.htm#IDX488
2113	fullDimImages sing_2601.htm#SEC2682
2114	fullFan sing_2175.htm#SEC2256
2115	fullSerreRelations sing_823.htm#SEC877
2116	fullSpace sing_2130.htm#SEC2211
2117	furtherInvar sing_1790.htm#SEC1871
2118	further_hn_proc sing_1686.htm#SEC1767
2119	fwalk sing_1259.htm#SEC1340
2120	galois field sing_144.htm#SEC184
2121	gauss_col sing_1167.htm#SEC1248
2122	gauss_nf sing_1198.htm#SEC1279
2123	gauss_row sing_1168.htm#SEC1249
2124	gaussred sing_1196.htm#SEC1277
2125	gaussred_pivot sing_1197.htm#SEC1278
2126	gcd sing_258.htm#SEC298
2127	gcdMon sing_1304.htm#SEC1385
2128	gcddivisor sing_2069.htm#SEC2150
2129	gen sing_259.htm#SEC299
2130	genMDSMat sing_1936.htm#SEC2017
2131	genSymId sing_1450.htm#SEC1531
2132	general error-locator polynomial sing_989.htm#SEC1059
2133	general neron. sing_2629.htm#IDX1140
2134	general weighted lexicographical ordering sing_963.htm#IDX447
2135	general weighted reverse lexicographical ordering Local orderings sing_963.htm#IDX444
2136	general.lib sing_1004.htm#SEC1085
2137	generalOrder sing_2094.htm#SEC2175
2138	general_lib sing_1004.htm#SEC1085
2139	generateG sing_2032.htm#SEC2113
2140	generator derivationContractionGen sing_2484.htm#IDX1019
2141	generator sing_2494.htm#IDX1039
2142	generator sing_2524.htm#IDX1105
2143	generators sing_1586.htm#IDX690
2144	generators sing_2487.htm#IDX1023
2145	generators sing_2489.htm#IDX1028
2146	generators sing_2490.htm#IDX1032
2147	generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2150.htm#SEC2231
2148	generatorsOfSpan sing_2151.htm#SEC2232
2149	generic representation sing_1034.htm#IDX482
2150	genericid sing_1092.htm#SEC1173
2151	genericity sing_1956.htm#SEC2037
2152	genericmat sing_1159.htm#SEC1240
2153	genoutput sing_1520.htm#SEC1601
2154	genus sing_1355.htm#SEC1436
2155	geometrical locus FamElemsAtEnvCompPoints sing_1036.htm#IDX489
2156	geometrical locus sing_1037.htm#IDX492
2157	geometrical locus sing_1038.htm#IDX495
2158	geometrical locus sing_1039.htm#IDX498
2159	geometrical locus sing_1040.htm#IDX501
2160	geometrical locus sing_1041.htm#IDX503
2161	geometrical locus sing_1042.htm#IDX507
2162	getArguments sing_1149.htm#SEC1230
2163	getCommand sing_1148.htm#SEC1229
2164	getCone sing_2177.htm#SEC2258
2165	getGradingGroup sing_2730.htm#SEC2811
2166	getLattice sing_2731.htm#SEC2812
2167	getLinearForms sing_2152.htm#SEC2233
2168	getModuleGrading sing_2741.htm#SEC2822
2169	getMultiplicity sing_2153.htm#SEC2234
2170	getOneVar sing_1363.htm#SEC1444
2171	getResult sing_1150.htm#SEC1231
2172	getSmallest sing_1362.htm#SEC1443
2173	getState sing_1151.htm#SEC1232
2174	getVariableWeights sing_2729.htm#SEC2810
2175	getcores sing_1107.htm#SEC1188
2176	getdump sing_260.htm#SEC300
2177	getenv sing_361.htm#IDX209
2178	gfan.lib sing_2129.htm#SEC2210
2179	gfan_lib sing_2129.htm#SEC2210
2180	gfanlib sing_1.htm#IDX9
2181	gitCone sing_2628.htm#SEC2709
2182	gitfan.lib sing_2598.htm#SEC2679
2183	gitfan_lib sing_2598.htm#SEC2679
2184	gkdim.lib sing_613.htm#SEC667
2185	gkdim_lib sing_613.htm#SEC667
2186	global sing_210.htm#IDX133
2187	global Bernstein-Sato ideal sing_592.htm#IDX352
2188	global Bernstein-Sato polynomial sing_502.htm#IDX310
2189	global Bernstein-Sato polynomial sing_537.htm#IDX328
2190	global Bernstein-Sato polynomial for variety sing_600.htm#IDX360
2191	global homological dimension sing_849.htm#IDX408
2192	globalSections sing_2534.htm#SEC2615
2193	gmscoeffs sing_1644.htm#SEC1725
2194	gmsnf sing_1643.htm#SEC1724
2195	gmspoly.lib sing_1663.htm#SEC1744
2196	gmspoly_lib sing_1663.htm#SEC1744
2197	gmsring sing_1642.htm#SEC1723
2198	gmssing.lib sing_1641.htm#SEC1722
2199	gmssing_lib sing_1641.htm#SEC1722
2200	goettsche.lib sing_2579.htm#SEC2660
2201	goettsche_lib sing_2579.htm#SEC2660
2202	good basis sing_1641.htm#IDX718
2203	good basis sing_1651.htm#IDX773
2204	good basis sing_1663.htm#IDX789
2205	good basis sing_1665.htm#IDX800
2206	goodBasis sing_1665.htm#SEC1746
2207	gorensteinIndex sing_2210.htm#SEC2291
2208	gorensteinVector sing_2211.htm#SEC2292
2209	graal.lib sing_2591.htm#SEC2672
2210	graalMixed sing_2592.htm#SEC2673
2211	graal_lib sing_2591.htm#SEC2672
2212	gradeNumber sing_775.htm#SEC829
2213	graded sing_2487.htm#IDX1024
2214	graded Hilbert series sing_870.htm#IDX418
2215	graded Weyl algebra sing_502.htm#IDX313
2216	graded algebra sing_2373.htm#IDX985
2217	graded module, graded piece sing_1567.htm#IDX676
2218	graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2631.htm#IDX1141
2219	graded modules, handling of Handling graded modules sing_928.htm#SEC985
2220	graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2669.htm#IDX1143
2221	gradedModules.lib sing_2631.htm#SEC2712
2222	gradedModules_lib sing_2631.htm#SEC2712
2223	gradiator sing_2774.htm#SEC2855
2224	graph sing_1248.htm#IDX566
2225	graph sing_1249.htm#IDX567
2226	graph sing_2859.htm#IDX1208
2227	graph sing_2860.htm#IDX1209
2228	graphics.lib sing_1883.htm#SEC1964
2229	graphics_lib sing_1883.htm#SEC1964
2230	graphviz sing_1.htm#IDX13
2231	graver4ti2 sing_1448.htm#SEC1529 39635
2232	grconcat sing_2654.htm#SEC2735
2233	grdeg sing_2634.htm#SEC2715
2234	grgens sing_2643.htm#SEC2724
2235	grgroebner sing_2653.htm#SEC2734
2236	grlift sing_2651.htm#SEC2732
2237	grlifting sing_2658.htm#SEC2739
2238	grlifting2 sing_2659.htm#SEC2740
2239	grlifting3 sing_2661.htm#SEC2742
2240	grneg sing_2664.htm#SEC2745
2241	grobcov sing_1027.htm#SEC1108
2242	grobcov.lib sing_1026.htm#SEC1107
2243	grobcov_lib sing_1026.htm#SEC1107
2244	grobj sing_2632.htm#SEC2713
2245	groebner sing_261.htm#SEC301
2246	groebner sing_920.htm#SEC977
2247	groebner basis computations sing_261.htm#IDX147
2248	groebnerComplex sing_2289.htm#SEC2370
2249	groebnerCone sing_2283.htm#SEC2364
2250	groebnerFan sing_2288.htm#SEC2369
2251	gromovWitten sing_1253.htm#SEC1334
2252	grorder sing_2645.htm#SEC2726
2253	ground field sing_144.htm#SEC184
2254	groupActionOnHashes sing_2616.htm#SEC2697
2255	groupActionOnQImage sing_2615.htm#SEC2696
2256	group_reynolds sing_1754.htm#SEC1835
2257	growth of algebra sing_849.htm#IDX406
2258	grpower sing_2641.htm#SEC2722
2259	grpres sing_2644.htm#SEC2725
2260	grprod sing_2652.htm#SEC2733
2261	grrange sing_2663.htm#SEC2744
2262	grres sing_2650.htm#SEC2731
2263	grrndmap sing_2656.htm#SEC2737
2264	grrndmap2 sing_2657.htm#SEC2738
2265	grrndmat sing_2655.htm#SEC2736
2266	grshift sing_2636.htm#SEC2717
2267	grsum sing_2640.htm#SEC2721
2268	grsyz sing_2649.htm#SEC2730
2269	grtest sing_2633.htm#SEC2714
2270	grtranspose sing_2642.htm#SEC2723
2271	grtranspose1 sing_2646.htm#SEC2727
2272	grtwist sing_2638.htm#SEC2719
2273	grtwists sing_2639.htm#SEC2720
2274	grview sing_2635.htm#SEC2716
2275	grwalk.lib sing_1258.htm#SEC1339
2276	grwalk_lib sing_1258.htm#SEC1339
2277	grzero sing_2637.htm#SEC2718
2278	gwalk sing_1264.htm#SEC1345
2279	hStarVector sing_2212.htm#SEC2293
2280	hVector sing_2213.htm#SEC2294
2281	h_increasing_knapsack h_increasing_knapsack sing_2055.htm#SEC2136
2282	hardware platform sing_361.htm#IDX268
2283	hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1130.htm#SEC1211
2284	hasCommutativeVars sing_1127.htm#SEC1208
2285	hasGlobalOrdering sing_1128.htm#SEC1209
2286	hasLeftDenom sing_688.htm#SEC742
2287	hasMixedOrdering sing_1129.htm#SEC1210
2288	hasNumericCoeffs sing_1126.htm#SEC1207
2289	hasRightDenom sing_689.htm#SEC743
2290	hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1131.htm#SEC1212
2291	hashToCone sing_2626.htm#SEC2707
2292	hashesToFan sing_2627.htm#SEC2708
2293	headStand sing_1180.htm#SEC1261
2294	heightZ sing_1425.htm#SEC1506
2295	help sing_262.htm#SEC302
2296	help browsers The online help system sing_16.htm#IDX22
2297	help browsers, dummy The online help system sing_16.htm#IDX25
2298	help browsers, dummy sing_16.htm#IDX27
2299	help browsers, emacs The online help system sing_16.htm#IDX26
2300	help browsers, html The online help system sing_16.htm#IDX23
2301	help browsers, setting command to use The online help system sing_16.htm#IDX30
2302	help browsers, setting the sing_361.htm#IDX194
2303	help, accessing over the net Command line options sing_19.htm#IDX42
2304	help, online help system The online help system sing_16.htm#SEC22
2305	hermiteNormalForm sing_2775.htm#SEC2856
2306	hess.lib sing_2666.htm#SEC2747
2307	hess_lib sing_2666.htm#SEC2747
2308	hessenberg sing_361.htm#IDX215
2309	hessenberg sing_1202.htm#SEC1283
2310	highcorner sing_263.htm#SEC303
2311	hilb sing_264.htm#SEC304
2312	hilbPoly sing_1090.htm#SEC1171
2313	hilbert4ti2 sing_1447.htm#SEC1528 13993
2314	hilbertBasis sing_2214.htm#SEC2295
2315	hilbertSeries sing_2777.htm#SEC2858
2316	hilbvec sing_1834.htm#SEC1915
2317	hnexpansion sing_1667.htm#SEC1748
2318	hnoether.lib sing_1666.htm#SEC1747
2319	hnoether_lib sing_1666.htm#SEC1747
2320	holonomic rank sing_661.htm#IDX368
2321	holonomicRank sing_665.htm#SEC719
2322	hom sing_2713.htm#SEC2794
2323	hom_kernel sing_1280.htm#SEC1361
2324	homog sing_265.htm#SEC305
2325	homog sing_2505.htm#IDX1062
2326	homog_part sing_2871.htm#SEC2952
2327	homog_parts sing_2872.htm#SEC2953
2328	homogeneitySpace sing_2285.htm#SEC2366
2329	homogeneous sing_2491.htm#IDX1033
2330	homogeneous sing_2505.htm#IDX1061
2331	homogeneous sing_2506.htm#IDX1063
2332	homogeneous decomposition sing_2491.htm#IDX1034
2333	homogfacFirstQWeyl sing_657.htm#SEC711
2334	homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_659.htm#SEC713
2335	homogfacNthQWeyl sing_656.htm#SEC710
2336	homogfacNthQWeyl_all homogfacNthQWeyl_all sing_658.htm#SEC712
2337	homogfacNthWeyl sing_655.htm#SEC709
2338	homolog.lib sing_1265.htm#SEC1346
2339	homolog_lib sing_1265.htm#SEC1346
2340	homology sing_1275.htm#SEC1356
2341	homomorphism sing_2697.htm#SEC2778
2342	howto, download Download instructions sing_2909.htm#SEC3006
2343	howto, install on Macintosh Macintosh installation instructions sing_2913.htm#SEC3010
2344	howto, install on Unix Unix installation instructions sing_2911.htm#SEC3008
2345	howto, install on Windows Windows installation instructions sing_2912.htm#SEC3009
2346	hres sing_266.htm#SEC306
2347	html, default help The online help system sing_16.htm#IDX24
2348	hyperel.lib sing_2062.htm#SEC2143
2349	hyperel_lib sing_2062.htm#SEC2143
2350	hyperplane sing_2292.htm#IDX866
2351	hyperplane arrangement sing_537.htm#IDX334
2352	hypersurface singularity sing_1693.htm#IDX818
2353	iMult sing_1358.htm#SEC1439
2354	id sing_2670.htm#SEC2751
2355	id2mod sing_1086.htm#SEC1167
2356	ideal sing_90.htm#SEC130
2357	ideal (plural) sing_427.htm#SEC467
2358	ideal declarations sing_91.htm#SEC131
2359	ideal declarations (plural) ideal declarations (plural) sing_428.htm#SEC468
2360	ideal expressions sing_92.htm#SEC132
2361	ideal expressions (plural) ideal expressions (plural) sing_429.htm#SEC469
2362	ideal operations sing_93.htm#SEC133
2363	ideal operations (plural) ideal operations (plural) sing_430.htm#SEC470
2364	ideal related functions ideal related functions sing_94.htm#SEC134
2365	ideal related functions (plural) ideal related functions (plural) sing_431.htm#SEC471
2366	ideal, toric sing_976.htm#SEC1038
2367	idealSplit sing_1841.htm#SEC1922
2368	ideals Miscellaneous oddities sing_422.htm#IDX290
2369	idealsimplify sing_1594.htm#SEC1675
2370	identifier Identifier resolution sing_423.htm#SEC463
2371	identifyvar sing_1502.htm#SEC1583
2372	if sing_390.htm#SEC430
2373	image sing_2693.htm#SEC2774
2374	imageLattice sing_2743.htm#SEC2824
2375	image_of_variety sing_1782.htm#SEC1863
2376	imap sing_267.htm#SEC307
2377	imap (plural) sing_466.htm#SEC506
2378	imapall sing_1118.htm#SEC1199
2379	impart sing_268.htm#SEC308
2380	importfrom sing_391.htm#SEC431
2381	inCenter sing_526.htm#SEC580
2382	inCentralizer sing_527.htm#SEC581
2383	inForm sing_569.htm#SEC623
2384	inSubring sing_1218.htm#SEC1299
2385	indSet sing_1330.htm#SEC1411
2386	indepSet sing_269.htm#SEC309
2387	indexed names sing_36.htm#IDX82
2388	indexed names sing_37.htm#SEC65
2389	indices, multi sing_37.htm#SEC65
2390	inequalities sing_2154.htm#SEC2235
2391	infRedTail, option sing_318.htm#IDX154
2392	infinitely presented algebra sing_870.htm#IDX417
2393	info The online help system sing_16.htm#SEC23
2394	iniD sing_1522.htm#SEC1603
2395	init_debug sing_1601.htm#SEC1682
2396	initial sing_2286.htm#SEC2367
2397	initial form sing_502.htm#IDX315
2398	initial ideal sing_502.htm#IDX314
2399	initial ideal approach sing_502.htm#IDX318
2400	initial ideal approach sing_600.htm#IDX364
2401	initialForm sing_2263.htm#SEC2344
2402	initialIdeal sing_2264.htm#SEC2345
2403	initialIdealW sing_568.htm#SEC622
2404	initialMalgrange sing_567.htm#SEC621
2405	injective_knapsack sing_2056.htm#SEC2137
2406	inout.lib sing_1052.htm#SEC1133
2407	inout_lib sing_1052.htm#SEC1133
2408	input sing_41.htm#SEC71
2409	insert sing_126.htm#SEC166
2410	insert sing_270.htm#SEC310
2411	insertCone sing_2178.htm#SEC2259
2412	insertGenerator sing_588.htm#SEC642
2413	instructions, Macintosh installation Macintosh installation instructions sing_2913.htm#SEC3010
2414	instructions, Unix installation Unix installation instructions sing_2911.htm#SEC3008
2415	instructions, Windows installation Windows installation instructions sing_2912.htm#SEC3009
2416	instructions, downloading Download instructions sing_2909.htm#SEC3006
2417	int sing_95.htm#SEC135
2418	int declarations sing_96.htm#SEC136
2419	int expressions sing_97.htm#SEC137
2420	int operations sing_98.htm#SEC138
2421	int related functions int related functions sing_99.htm#SEC139
2422	intInverse sing_2752.htm#SEC2833
2423	intPart sing_2010.htm#SEC2091
2424	intRank sing_2744.htm#SEC2825
2425	intRoot sing_2011.htm#SEC2092
2426	intRoots sing_585.htm#SEC639
2427	intStrategy, option sing_318.htm#IDX155
2428	intclMonIdeal sing_1371.htm#SEC1452 62182
2429	intclToricRing sing_1367.htm#SEC1448 62143
2430	integer division Miscellaneous oddities sing_422.htm#IDX285
2431	integer programming sing_984.htm#SEC1046
2432	integral sing_2846.htm#SEC2927
2433	integral basis sing_1287.htm#IDX588
2434	integral basis sing_1485.htm#IDX661
2435	integral closure sing_1351.htm#IDX609
2436	integral closure sing_1352.htm#IDX612
2437	integral closure sing_1353.htm#IDX615
2438	integral closure sing_1366.htm#IDX621
2439	integralBasis sing_1287.htm#SEC1368
2440	integralIdeal sing_572.htm#SEC626
2441	integralModule sing_573.htm#SEC627
2442	integralSection sing_2753.htm#SEC2834
2443	integralbasis.lib sing_1286.htm#SEC1367
2444	integralbasis_lib sing_1286.htm#SEC1367
2445	integration of D-module sing_560.htm#IDX346
2446	interface, Emacs Emacs user interface sing_21.htm#SEC28
2447	interiorLatticePoints interiorLatticePoints sing_2215.htm#SEC2296
2448	internalfunctions sing_1602.htm#SEC1683
2449	interpolate sing_1847.htm#SEC1928
2450	interpolation sing_271.htm#SEC311
2451	interpret sing_2715.htm#SEC2796
2452	interpretElem sing_2718.htm#SEC2799
2453	interpretInv sing_2716.htm#SEC2797
2454	interpretList sing_2719.htm#SEC2800
2455	interred sing_272.htm#SEC312
2456	intersect sing_273.htm#SEC313
2457	intersect (plural) sing_467.htm#SEC507
2458	intersectElim, option sing_318.htm#IDX173
2459	intersectLattices sing_2749.htm#SEC2830
2460	intersectLists sing_2470.htm#SEC2551
2461	intersectMon sing_1307.htm#SEC1388
2462	intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2614.htm#SEC2695
2463	intersectSyz, option sing_318.htm#IDX174
2464	intersectZ sing_1427.htm#SEC1508
2465	intersection sing_1676.htm#SEC1757
2466	intersection lattice sing_2328.htm#IDX941
2467	intersection lattice sing_2329.htm#IDX942
2468	intersection multiplicity sing_1587.htm#IDX696
2469	intersection multiplicity sing_1676.htm#IDX811
2470	intersectionDiv sing_1550.htm#SEC1631
2471	intersectionValRingIdeals intersectionValRingIdeals sing_1376.htm#SEC1457 38773
2472	intersectionValRings intersectionValRings sing_1375.htm#SEC1456 35761
2473	intersectpar sing_1046.htm#SEC1127
2474	interval arithmetic sing_2816.htm#IDX1183
2475	intmat sing_102.htm#SEC142
2476	intmat declarations sing_103.htm#SEC143
2477	intmat expressions sing_104.htm#SEC144
2478	intmat operations sing_106.htm#SEC146
2479	intmat related functions intmat related functions sing_107.htm#SEC147
2480	intmat type cast sing_105.htm#SEC145
2481	intmat2mons sing_1391.htm#SEC1472 21150
2482	intprog.lib sing_1288.htm#SEC1369
2483	intprog_lib sing_1288.htm#SEC1369
2484	intvec sing_108.htm#SEC148
2485	intvec declarations sing_109.htm#SEC149
2486	intvec expressions sing_110.htm#SEC150
2487	intvec operations sing_111.htm#SEC151
2488	intvec related functions intvec related functions sing_112.htm#SEC152
2489	invar sing_1813.htm#SEC1894
2490	invar.lib sing_1807.htm#SEC1888
2491	invar_lib sing_1807.htm#SEC1888
2492	invariant sing_2476.htm#IDX1007
2493	invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1751.htm#IDX824
2494	invariant ring minimal generating set permutation group invariant_algebra_perm sing_1752.htm#IDX825
2495	invariantRing sing_1784.htm#SEC1865
2496	invariant_algebra_perm invariant_algebra_perm sing_1752.htm#SEC1833
2497	invariant_algebra_reynolds invariant_algebra_reynolds sing_1751.htm#SEC1832
2498	invariant_basis sing_1759.htm#SEC1840
2499	invariant_basis_reynolds invariant_basis_reynolds sing_1760.htm#SEC1841
2500	invariant_ring sing_1747.htm#SEC1828
2501	invariant_ring_random invariant_ring_random sing_1748.htm#SEC1829
2502	invariants curveColengthDerivations sing_1672.htm#SEC1753
2503	invariants sing_2473.htm#IDX1000
2504	invariants sing_2477.htm#IDX1009
2505	inverse sing_1186.htm#SEC1267
2506	inverse of a matrix via its LU-decomposition sing_293.htm#SEC333
2507	inverseFourier sing_583.htm#SEC637
2508	inverse_B sing_1187.htm#SEC1268
2509	inverse_L sing_1188.htm#SEC1269
2510	inverse_modulus sing_2039.htm#SEC2120
2511	invertAlgebraMorphism invertAlgebraMorphism sing_2899.htm#SEC2980
2512	invertBirMap sing_1486.htm#SEC1567
2513	invertLeftFraction sing_762.htm#SEC816
2514	invertNcfrac sing_698.htm#SEC752
2515	invertNumberMain sing_1871.htm#SEC1952
2516	involut.lib sing_605.htm#SEC659
2517	involut_lib sing_605.htm#SEC659
2518	involution sing_610.htm#SEC664
2519	invunit sing_1695.htm#SEC1776
2520	iostruct sing_1958.htm#SEC2039
2521	irrRealizationDim sing_2245.htm#SEC2326
2522	irred_secondary_char0 irred_secondary_char0 sing_1773.htm#SEC1854
2523	irred_secondary_no_molien irred_secondary_no_molien sing_1776.htm#SEC1857
2524	irreddecMon sing_1316.htm#SEC1397
2525	irreducible power series sing_1677.htm#IDX812
2526	irreducible secondary invariant irred_secondary_char0 sing_1773.htm#IDX826
2527	isAface sing_2599.htm#SEC2680
2528	isAntiEndo sing_612.htm#SEC666
2529	isBounded sing_2216.htm#SEC2297
2530	isCI sing_210.htm#IDX139
2531	isCI sing_1236.htm#SEC1317
2532	isCM sing_210.htm#IDX140
2533	isCM sing_1276.htm#SEC1357
2534	isCMcod2 sing_1730.htm#SEC1811
2535	isCanonical sing_2217.htm#SEC2298
2536	isCartan sing_528.htm#SEC582
2537	isCentral sing_738.htm#SEC792
2538	isCommutative sing_740.htm#SEC794
2539	isCompatible sing_2179.htm#SEC2260
2540	isCompressed sing_2218.htm#SEC2299
2541	isDenom sing_710.htm#SEC764
2542	isEqualDivisor sing_2533.htm#SEC2614
2543	isEquising sing_1639.htm#SEC1720
2544	isFlat sing_1277.htm#SEC1358
2545	isFreeAlgebra sing_857.htm#SEC911
2546	isFsat sing_578.htm#SEC632
2547	isFullSpace sing_2155.htm#SEC2236
2548	isGorenstein sing_2219.htm#SEC2300
2549	isGradedRingHomomorphism isGradedRingHomomorphism sing_2738.htm#SEC2819
2550	isGroup sing_2736.htm#SEC2817
2551	isGroupHomomorphism sing_2737.htm#SEC2818
2552	isHolonomic sing_556.htm#SEC610
2553	isHomog sing_210.htm#IDX135
2554	isHomogeneous sing_2764.htm#SEC2845
2555	isInS sing_751.htm#SEC805
2556	isInt sing_590.htm#SEC644
2557	isIntegralSurjective isIntegralSurjective sing_2750.htm#SEC2831
2558	isInvertibleLeftFraction isInvertibleLeftFraction sing_761.htm#SEC815
2559	isInvertibleNcfrac sing_697.htm#SEC751
2560	isInvolution sing_611.htm#SEC665
2561	isLatticeEmpty sing_2220.htm#SEC2301
2562	isLocalizationRegular isLocalizationRegular sing_2595.htm#SEC2676
2563	isLocallyFree sing_1278.htm#SEC1359
2564	isMonomial sing_1302.htm#SEC1383
2565	isNC sing_739.htm#SEC793
2566	isNormal sing_2221.htm#SEC2302
2567	isOnCurve sing_2023.htm#SEC2104
2568	isOneFraction sing_764.htm#SEC818
2569	isOneNcfrac sing_691.htm#SEC745
2570	isOrderingShiftInvariant isOrderingShiftInvariant sing_863.htm#SEC917
2571	isOrigin sing_2156.htm#SEC2237
2572	isPositive sing_2761.htm#SEC2842
2573	isPrimitiveSublattice isPrimitiveSublattice sing_2751.htm#SEC2832
2574	isPure sing_2180.htm#SEC2261
2575	isPureTensor sing_500.htm#SEC554
2576	isQuotientRing sing_1132.htm#SEC1213
2577	isRational sing_559.htm#SEC613
2578	isReflexive sing_2222.htm#SEC2303
2579	isReg sing_1279.htm#SEC1360
2580	isSB sing_210.htm#IDX134
2581	isSimplicial sing_2157.htm#SEC2238
2582	isSmooth sing_2223.htm#SEC2304
2583	isSubModule sing_1133.htm#SEC1214
2584	isSublattice sing_2742.htm#SEC2823
2585	isSymmetric sing_1451.htm#SEC1532
2586	isTame sing_1664.htm#SEC1745
2587	isTerminal sing_2224.htm#SEC2305
2588	isTorsionFree sing_2760.htm#SEC2841
2589	isTwoSidedGB sing_501.htm#SEC555
2590	isUpperTriangular sing_719.htm#SEC773
2591	isVeryAmple sing_2225.htm#SEC2306
2592	isWeyl sing_741.htm#SEC795
2593	isZeroElement sing_2762.htm#SEC2843
2594	isZeroFraction sing_763.htm#SEC817
2595	isZeroNcfrac sing_690.htm#SEC744
2596	is_NND sing_1680.htm#SEC1761
2597	is_NP sing_1339.htm#SEC1420
2598	is_active sing_1713.htm#SEC1794
2599	is_bijective sing_1223.htm#SEC1304
2600	is_cenBimodule sing_707.htm#SEC761
2601	is_cenSubbimodule sing_708.htm#SEC762
2602	is_ci sing_1714.htm#SEC1795
2603	is_complex sing_1160.htm#SEC1241
2604	is_fix_injective sing_2060.htm#SEC2141
2605	is_h_injective sing_2059.htm#SEC2140
2606	is_injective sing_1221.htm#SEC1302
2607	is_irred sing_1677.htm#SEC1758
2608	is_is sing_1715.htm#SEC1796
2609	is_nested sing_1340.htm#SEC1421
2610	is_prime sing_2040.htm#SEC2121
2611	is_primitive_root sing_2036.htm#SEC2117
2612	is_pure sing_781.htm#SEC835
2613	is_reg sing_1716.htm#SEC1797
2614	is_regs sing_1717.htm#SEC1798
2615	is_surjective sing_1222.htm#SEC1303
2616	is_zero sing_1075.htm#SEC1156
2617	isartinianMon sing_1313.htm#SEC1394
2618	isgenericMon sing_1314.htm#SEC1395
2619	ishyper sing_2063.htm#SEC2144
2620	isirreducibleMon sing_1312.htm#SEC1393
2621	isoncurve sing_2064.htm#SEC2145
2622	isparam sing_2127.htm#SEC2208
2623	isprimaryMon sing_1311.htm#SEC1392
2624	isprimeMon sing_1310.htm#SEC1391
2625	isuni sing_2112.htm#SEC2193
2626	ivmatGaussian sing_2823.htm#SEC2904
2627	ivmatInit sing_2820.htm#SEC2901
2628	ivmatSet sing_2821.htm#SEC2902
2629	jInvariant sing_2257.htm#SEC2338
2630	jOft sing_1995.htm#SEC2076
2631	jacob sing_274.htm#SEC314
2632	jacoblift sing_1696.htm#SEC1777
2633	jacobson sing_1964.htm#SEC2045
2634	jacobson.lib sing_1962.htm#SEC2043
2635	jacobson_lib sing_1962.htm#SEC2043
2636	janet sing_275.htm#SEC315
2637	janet basis sing_2829.htm#IDX1186
2638	jet sing_276.htm#SEC316
2639	jordan sing_1207.htm#SEC1288
2640	jordanVecField sing_2892.htm#SEC2973
2641	jordanbasis sing_1208.htm#SEC1289
2642	jordanmatrix sing_1209.htm#SEC1290
2643	jordannf sing_1210.htm#SEC1291
2644	jungfib sing_1535.htm#SEC1616
2645	jungnormal sing_1534.htm#SEC1615
2646	jungresolve sing_1533.htm#SEC1614
2647	katsura sing_1073.htm#SEC1154
2648	kbase sing_277.htm#SEC317
2649	kbase (plural) sing_468.htm#SEC508
2650	keepring sing_392.htm#SEC432
2651	kerHom sing_2714.htm#SEC2795
2652	kernel sing_278.htm#SEC318
2653	kernelLattice sing_2745.htm#SEC2826
2654	kill sing_279.htm#SEC319
2655	killTask sing_1139.htm#SEC1220
2656	killall sing_1014.htm#SEC1095
2657	killattrib sing_280.htm#SEC320
2658	kmemory sing_1013.htm#SEC1094
2659	kohom sing_1281.htm#SEC1362
2660	kontrahom sing_1282.htm#SEC1363
2661	koszul sing_281.htm#SEC321
2662	kskernel.lib sing_1687.htm#SEC1768
2663	kskernel_lib sing_1687.htm#SEC1768
2664	l-adic numbers sing_32.htm#SEC46
2665	laguerre sing_282.htm#SEC322
2666	laguerre_solve sing_1843.htm#SEC1924
2667	lastvarGeneral sing_2093.htm#SEC2174
2668	latex.lib sing_1887.htm#SEC1968
2669	latex_lib sing_1887.htm#SEC1968
2670	lattice sing_2329.htm#IDX944
2671	latticeArea sing_2200.htm#SEC2281
2672	latticeBasis sing_2746.htm#SEC2827
2673	latticeCodegree sing_2226.htm#SEC2307
2674	latticeDegree sing_2227.htm#SEC2308
2675	latticePoints sing_2228.htm#SEC2309
2676	latticeVolume sing_2229.htm#SEC2310
2677	laxfrT sing_2559.htm#SEC2640
2678	laxfrX sing_2560.htm#SEC2641
2679	lazy, option sing_318.htm#IDX156
2680	lcm sing_1076.htm#SEC1157
2681	lcmMon sing_1305.htm#SEC1386
2682	lcmN sing_2004.htm#SEC2085
2683	lcmofall sing_1515.htm#SEC1596
2684	lead sing_283.htm#SEC323
2685	leadcoef sing_284.htm#SEC324
2686	leadexp sing_285.htm#SEC325
2687	leadmonom sing_286.htm#SEC326
2688	leadmonomial sing_2079.htm#SEC2160
2689	left annihilator ideal sing_537.htm#IDX326
2690	left annihilator ideal sing_592.htm#IDX354
2691	leftInverse sing_1953.htm#SEC2034
2692	leftKernel sing_1951.htm#SEC2032
2693	leftOre sing_754.htm#SEC808
2694	length sing_2818.htm#SEC2899
2695	length, option sing_318.htm#IDX157
2696	letplaceGBasis sing_865.htm#SEC919
2697	letterplace sing_296.htm#SEC336
2698	letterplace sing_337.htm#SEC377
2699	lex_solve sing_1849.htm#SEC1930
2700	lexicographical ordering sing_962.htm#IDX427
2701	lib2doc sing_60.htm#SEC97
2702	libSingular sing_2908.htm#SEC3005
2703	libcdd sing_1.htm#IDX12
2704	libfac sing_1.htm#IDX6
2705	libparse sing_69.htm#SEC109
2706	library sing_2344.htm#IDX959
2707	library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2598.htm#IDX1138
2708	library, info string sing_55.htm#IDX124
2709	library, polybori.lib sing_2344.htm#IDX956
2710	library, template sing_55.htm#SEC92
2711	library, template.lib sing_55.htm#IDX122
2712	lieBracket sing_866.htm#SEC920
2713	lift sing_288.htm#SEC328
2714	lift sing_495.htm#IDX302
2715	lift (letterplace) sing_799.htm#SEC853
2716	lift (plural) sing_469.htm#SEC509
2717	lift_kbase sing_1633.htm#SEC1714
2718	lift_rel_kb sing_1634.htm#SEC1715
2719	liftenvelope sing_498.htm#SEC552
2720	liftstd sing_289.htm#SEC329
2721	liftstd (letterplace) liftstd (letterplace) sing_800.htm#SEC854
2722	liftstd (plural) sing_470.htm#SEC510
2723	linReduce sing_510.htm#SEC564
2724	linReduceIdeal sing_511.htm#SEC565
2725	linSyzSolve sing_512.htm#SEC566
2726	linalg.lib sing_1185.htm#SEC1266
2727	linalg_lib sing_1185.htm#SEC1266
2728	linealityDimension sing_2158.htm#SEC2239
2729	linealitySpace sing_2159.htm#SEC2240
2730	linear algebra sing_211.htm#SEC251
2731	linear algebra sing_292.htm#SEC332
2732	linear algebra sing_293.htm#SEC333
2733	linear algebra sing_294.htm#SEC334
2734	linear code, dual sing_1922.htm#IDX837
2735	linear code, systematic sing_1923.htm#IDX838
2736	linear interreduction sing_502.htm#IDX317
2737	linearCombinations sing_531.htm#SEC585
2738	linearMapKernel sing_530.htm#SEC584
2739	linear_relations sing_1177.htm#SEC1258
2740	linearlyEquivalent sing_2536.htm#SEC2617
2741	linearpart sing_1835.htm#SEC1916
2742	linesHypersurface sing_2868.htm#SEC2949
2743	link Parallelization with ssi links sing_113.htm#SEC153
2744	link sing_917.htm#SEC974
2745	link declarations sing_114.htm#SEC154
2746	link expressions sing_115.htm#SEC155
2747	link related functions link related functions sing_116.htm#SEC156
2748	list sing_123.htm#SEC163
2749	list sing_2507.htm#IDX1066
2750	list sing_2508.htm#IDX1068
2751	list declarations sing_124.htm#SEC164
2752	list expressions sing_125.htm#SEC165
2753	list operations sing_126.htm#SEC166
2754	list related functions list related functions sing_127.htm#SEC167
2755	lists sing_2470.htm#IDX996
2756	lists, elements sing_2472.htm#IDX998
2757	listvar sing_290.htm#SEC330
2758	lll sing_2778.htm#SEC2859
2759	load sing_393.htm#SEC433
2760	loadLib, option sing_318.htm#IDX178
2761	loadProc, option sing_318.htm#IDX179
2762	locAtZero sing_1360.htm#SEC1441
2763	locNormal sing_1291.htm#SEC1372
2764	locStatus sing_749.htm#SEC803
2765	local methods sing_1290.htm#IDX591
2766	local methods sing_1291.htm#IDX594
2767	local names sing_46.htm#SEC83
2768	local rings, computing in Rings associated to monomial orderings sing_912.htm#SEC969
2769	local weighted lexicographical ordering sing_963.htm#IDX448
2770	local weighted reverse lexicographical ordering Local orderings sing_963.htm#IDX445
2771	localInvar sing_1789.htm#SEC1870
2772	localization Rings associated to monomial orderings sing_912.htm#SEC969
2773	localization sing_2309.htm#IDX904
2774	localization of D-module sing_560.htm#IDX342
2775	localization of D-module sing_661.htm#IDX371
2776	locally closed set sing_1031.htm#IDX472
2777	locally closed set sing_1032.htm#IDX474
2778	locally closed set sing_1033.htm#IDX476
2779	locally closed set sing_1034.htm#IDX480
2780	locally closed set sing_1048.htm#IDX518
2781	locally closed set sing_1050.htm#IDX523
2782	localstd sing_2089.htm#SEC2170
2783	locnormal.lib sing_1290.htm#SEC1371
2784	locnormal_lib sing_1290.htm#SEC1371
2785	locstd sing_1718.htm#SEC1799
2786	locus FamElemsAtEnvCompPoints sing_1036.htm#SEC1117
2787	locus sing_1036.htm#IDX490
2788	locus sing_1037.htm#IDX493
2789	locus sing_1038.htm#IDX496
2790	locus sing_1039.htm#IDX499
2791	locus sing_1040.htm#IDX502
2792	locus sing_1041.htm#IDX504
2793	locus sing_1042.htm#IDX508
2794	locusdg sing_1037.htm#SEC1118
2795	locusto sing_1039.htm#SEC1120
2796	log2 sing_1979.htm#SEC2060
2797	logarithmic annihilator ideal sing_537.htm#IDX331
2798	logarithmic annihilator ideal sing_592.htm#IDX356
2799	logg sing_2873.htm#SEC2954
2800	lp, global ordering sing_962.htm#IDX426
2801	lpCalcSubstDegBound sing_855.htm#SEC909
2802	lpDegBound sing_858.htm#SEC912
2803	lpDivision sing_861.htm#SEC915
2804	lpGBPres2Poly sing_862.htm#SEC916
2805	lpGlDimBound sing_853.htm#SEC907
2806	lpHilbert sing_818.htm#SEC872
2807	lpIsPrime sing_852.htm#SEC906
2808	lpIsSemiPrime sing_851.htm#SEC905
2809	lpKDim sing_816.htm#SEC870
2810	lpKDimCheck sing_815.htm#SEC869
2811	lpMonomialBasis sing_817.htm#SEC871
2812	lpNcgenCount sing_860.htm#SEC914
2813	lpNoetherian sing_850.htm#SEC904
2814	lpSickleDim sing_819.htm#SEC873
2815	lpSubstitute sing_854.htm#SEC908
2816	lpVarBlockSize sing_859.htm#SEC913
2817	lprint sing_1054.htm#SEC1135
2818	lres sing_291.htm#SEC331
2819	ls, local ordering sing_963.htm#IDX439
2820	lsum sing_1257.htm#SEC1338
2821	ludecomp sing_292.htm#SEC332
2822	luinverse sing_293.htm#SEC333
2823	lusolve sing_294.htm#SEC334
2824	mRes sing_2682.htm#SEC2763
2825	m_merkle_hellman_decryption m_merkle_hellman_decryption sing_2051.htm#SEC2132
2826	m_merkle_hellman_encryption m_merkle_hellman_encryption sing_2050.htm#SEC2131
2827	m_merkle_hellman_transformation m_merkle_hellman_transformation sing_2049.htm#SEC2130
2828	magnitude sing_1973.htm#SEC2054
2829	makeDivisor sing_2528.htm#SEC2609
2830	makeFormalDivisor sing_2538.htm#SEC2619
2831	makeGraph sing_1248.htm#SEC1329
2832	makeGraphVE sing_2859.htm#SEC2940
2833	makeHeisenberg sing_729.htm#SEC783
2834	makeIdeal sing_2674.htm#SEC2755
2835	makeLetterplaceRing sing_864.htm#SEC918
2836	makeMalgrange sing_604.htm#SEC658
2837	makeMatrix sing_2673.htm#SEC2754
2838	makeModElimRing sing_746.htm#SEC800
2839	makePDivisor sing_2544.htm#SEC2625
2840	makeQsl2 sing_638.htm#SEC692
2841	makeQsl3 sing_639.htm#SEC693
2842	makeQso3 sing_637.htm#SEC691
2843	makeSheaf sing_2847.htm#SEC2928
2844	makeUe6 sing_634.htm#SEC688
2845	makeUe7 sing_635.htm#SEC689
2846	makeUe8 sing_636.htm#SEC690
2847	makeUf4 sing_633.htm#SEC687
2848	makeUg2 sing_632.htm#SEC686
2849	makeUgl sing_618.htm#SEC672
2850	makeUsl sing_617.htm#SEC671
2851	makeUsl2 sing_616.htm#SEC670
2852	makeUso10 sing_624.htm#SEC678
2853	makeUso11 sing_625.htm#SEC679
2854	makeUso12 sing_626.htm#SEC680
2855	makeUso5 sing_619.htm#SEC673
2856	makeUso6 sing_620.htm#SEC674
2857	makeUso7 sing_621.htm#SEC675
2858	makeUso8 sing_622.htm#SEC676
2859	makeUso9 sing_623.htm#SEC677
2860	makeUsp1 sing_627.htm#SEC681
2861	makeUsp2 sing_628.htm#SEC682
2862	makeUsp3 sing_629.htm#SEC683
2863	makeUsp4 sing_630.htm#SEC684
2864	makeUsp5 sing_631.htm#SEC685
2865	makeVariety sing_2839.htm#SEC2920
2866	makeVector sing_2702.htm#SEC2783
2867	makeWeyl sing_728.htm#SEC782
2868	map sing_128.htm#SEC168
2869	map (plural) sing_432.htm#SEC472
2870	map declarations sing_129.htm#SEC169
2871	map declarations (plural) map declarations (plural) sing_433.htm#SEC473
2872	map expressions sing_130.htm#SEC170
2873	map expressions (plural) map expressions (plural) sing_434.htm#SEC474
2874	map operations sing_131.htm#IDX129
2875	map operations (plural) map operations (plural) sing_435.htm#IDX297
2876	map related functions map related functions sing_132.htm#IDX131
2877	map related functions (plural) map related functions (plural) sing_436.htm#IDX298
2878	mapIsFinite sing_1225.htm#SEC1306
2879	mapToRatNormCurve sing_1490.htm#SEC1571
2880	mapall sing_1119.htm#SEC1200
2881	mappingcone sing_2660.htm#SEC2741
2882	mappingcone3 sing_2662.htm#SEC2743
2883	markov4ti2 sing_1446.htm#SEC1527 9163
2884	mat2arr sing_2294.htm#SEC2375
2885	mat2carr sing_2295.htm#SEC2376
2886	mat_rk sing_1199.htm#SEC1280
2887	matbil sing_2100.htm#SEC2181
2888	mathematical objects Representation of mathematical objects sing_958.htm#SEC1015
2889	mathinit sing_1885.htm#SEC1966
2890	matmult sing_2101.htm#SEC2182
2891	matrix sing_133.htm#SEC173
2892	matrix sing_2294.htm#IDX872
2893	matrix sing_2295.htm#IDX875
2894	matrix sing_2296.htm#IDX879
2895	matrix declarations sing_134.htm#SEC174
2896	matrix diagonalization sing_1962.htm#IDX848
2897	matrix expressions sing_135.htm#SEC175
2898	matrix operations sing_137.htm#SEC177
2899	matrix related functions matrix related functions sing_138.htm#SEC178
2900	matrix type cast sing_136.htm#SEC176
2901	matrix.lib sing_1153.htm#SEC1234
2902	matrixExp sing_1480.htm#SEC1561
2903	matrixLog sing_1481.htm#SEC1562
2904	matrixT1 sing_1732.htm#SEC1813
2905	matrix_lib sing_1153.htm#SEC1234
2906	matrixpres sing_2665.htm#SEC2746
2907	matrixsystem sing_2570.htm#SEC2651
2908	max sing_295.htm#SEC335
2909	maxEord sing_1505.htm#SEC1586
2910	maxExp sing_210.htm#IDX136
2911	maxIntRoot sing_678.htm#SEC732
2912	maxZeros sing_1483.htm#SEC1564
2913	maxabs sing_2119.htm#SEC2200
2914	maxcoef sing_1077.htm#SEC1158
2915	maxdeg sing_1078.htm#SEC1159
2916	maxdeg1 sing_1079.htm#SEC1160
2917	maxideal sing_296.htm#SEC336
2918	maximalFace sing_2230.htm#SEC2311
2919	maximalGroebnerCone sing_2284.htm#SEC2365
2920	maximalValue sing_2231.htm#SEC2312
2921	maximum sing_1992.htm#SEC2073
2922	maximum number of zeroes sing_1483.htm#IDX655
2923	mdouble sing_56.htm#SEC93
2924	mem, option sing_318.htm#IDX180
2925	member sing_2472.htm#SEC2553
2926	membershipMon sing_1306.htm#SEC1387
2927	memory sing_297.htm#SEC337
2928	memory management sing_297.htm#SEC337
2929	merkle_hellman_decryption merkle_hellman_decryption sing_2053.htm#SEC2134
2930	merkle_hellman_encryption merkle_hellman_encryption sing_2052.htm#SEC2133
2931	methods, hashtables sing_2668.htm#IDX1142
2932	methods.lib sing_2668.htm#SEC2749
2933	methods_lib sing_2668.htm#SEC2749
2934	midpoint sing_2566.htm#SEC2647
2935	milnor sing_1719.htm#SEC1800
2936	milnorcode sing_1603.htm#SEC1684
2937	milnornumber sing_2813.htm#SEC2894
2938	min sing_298.htm#SEC338
2939	minAssChar sing_1405.htm#SEC1486
2940	minAssCharE sing_1406.htm#SEC1487
2941	minAssGTZ sing_1403.htm#SEC1484
2942	minAssGTZE sing_1404.htm#SEC1485
2943	minAssZ sing_1423.htm#SEC1504
2944	minEcart sing_2082.htm#SEC2163
2945	minIntRoot sing_558.htm#SEC612
2946	minIntRoot2 sing_677.htm#SEC731
2947	minMult sing_1232.htm#SEC1313
2948	minbase sing_299.htm#SEC339
2949	minbaseMon sing_1303.htm#SEC1384
2950	mindeg sing_1080.htm#SEC1161
2951	mindeg1 sing_1081.htm#SEC1162
2952	mindist sing_1937.htm#SEC2018
2953	minimal display time, setting the sing_361.htm#IDX281
2954	minimal representations sing_873.htm#IDX425
2955	minimalAfaceOrbits sing_2611.htm#SEC2692
2956	minimalAfaces sing_2602.htm#SEC2683
2957	minimalFace sing_2232.htm#SEC2313
2958	minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2613.htm#SEC2694
2959	minimalValue sing_2233.htm#SEC2314
2960	minipoly sing_1204.htm#SEC1285
2961	minkowskiSum sing_2234.htm#SEC2315
2962	minor sing_300.htm#SEC340
2963	minpoly sing_401.htm#SEC441
2964	minres sing_301.htm#SEC341
2965	minres (plural) sing_471.htm#SEC511
2966	minus sing_2496.htm#IDX1042
2967	minus sing_2497.htm#IDX1044
2968	minus sing_2518.htm#IDX1090
2969	minus sing_2519.htm#IDX1092
2970	mirror symmetry sing_1247.htm#IDX559
2971	mixed Hodge structure sing_1641.htm#IDX711
2972	mixed Hodge structure sing_1647.htm#IDX739
2973	mixed Hodge structure sing_1648.htm#IDX745
2974	mixed Hodge structure sing_1649.htm#IDX753
2975	mixed Hodge structure sing_1650.htm#IDX759
2976	mixed Hodge structure sing_1651.htm#IDX767
2977	mixed Hodge structure sing_1652.htm#IDX777
2978	mixed Hodge structure sing_1663.htm#IDX783
2979	mixed Hodge structure sing_1665.htm#IDX794
2980	mod sing_81.htm#SEC121
2981	mod sing_98.htm#SEC138
2982	mod sing_147.htm#SEC187
2983	mod sing_155.htm#SEC195
2984	mod2id sing_1085.htm#SEC1166
2985	modBorder sing_2831.htm#SEC2912
2986	modDec sing_1322.htm#SEC1403
2987	modIntersect sing_1300.htm#SEC1381
2988	modJanet sing_2833.htm#SEC2914
2989	modNPos sing_1345.htm#SEC1426
2990	modNormal sing_1296.htm#SEC1377
2991	modNpos_test sing_1343.htm#SEC1424
2992	modQuotient sing_1293.htm#SEC1374
2993	modSagbiAlg sing_2459.htm#SEC2540
2994	modSat sing_1294.htm#SEC1375
2995	modStd sing_1298.htm#SEC1379
2996	modSyz sing_1299.htm#SEC1380
2997	modVStd sing_2464.htm#SEC2545
2998	modVStd0 sing_2465.htm#SEC2546
2999	modWalk sing_2723.htm#SEC2804
3000	mod_versal sing_1632.htm#SEC1713
3001	modality sing_1611.htm#SEC1692
3002	modberlekampMassey sing_2552.htm#SEC2633
3003	moddiq.lib sing_1292.htm#SEC1373
3004	moddiq_lib sing_1292.htm#SEC1373
3005	modfWalk sing_2725.htm#SEC2806
3006	modfrWalk sing_2726.htm#SEC2807
3007	modnormal.lib sing_1295.htm#SEC1376
3008	modnormal_lib sing_1295.htm#SEC1376
3009	modrWalk sing_2724.htm#SEC2805
3010	modrationalInterpolation modrationalInterpolation sing_2550.htm#SEC2631
3011	modregCM sing_1349.htm#SEC1430
3012	modsatiety sing_1347.htm#SEC1428
3013	modstd.lib sing_1297.htm#SEC1378
3014	modstd_lib sing_1297.htm#SEC1378
3015	modular sing_1063.htm#SEC1144
3016	modular methods sing_1290.htm#IDX592
3017	modular methods sing_1295.htm#IDX598
3018	modular methods. sing_1291.htm#IDX595
3019	modular techniques. sing_1296.htm#IDX600
3020	modular.lib sing_1062.htm#SEC1143
3021	modular_lib sing_1062.htm#SEC1143
3022	modular_lib sing_1062.htm#IDX527
3023	module sing_139.htm#SEC179
3024	module (plural) sing_437.htm#SEC477
3025	module declarations sing_140.htm#SEC180
3026	module declarations (plural) module declarations (plural) sing_438.htm#SEC478
3027	module expressions sing_141.htm#SEC181
3028	module expressions (plural) module expressions (plural) sing_439.htm#SEC479
3029	module operations sing_142.htm#SEC182
3030	module operations (plural) module operations (plural) sing_440.htm#SEC480
3031	module ordering C sing_964.htm#IDX451
3032	module ordering c sing_964.htm#IDX453
3033	module related functions module related functions sing_143.htm#SEC183
3034	module related functions (plural) module related functions (plural) sing_441.htm#SEC481
3035	module_containment sing_1217.htm#SEC1298
3036	modules.lib sing_2669.htm#SEC2750
3037	modules_lib sing_2669.htm#SEC2750
3038	moduliSpace sing_2861.htm#SEC2942
3039	modulo sing_302.htm#SEC342
3040	modulo (plural) sing_472.htm#SEC512
3041	moduloSlim sing_736.htm#SEC790
3042	modwalk.lib sing_2722.htm#SEC2803
3043	modwalk_lib sing_2722.htm#SEC2803
3044	moebius sing_2330.htm#SEC2411
3045	moebius function sing_2330.htm#IDX945
3046	molien sing_1755.htm#SEC1836
3047	mondromy.lib sing_1693.htm#SEC1774
3048	mondromy_lib sing_1693.htm#SEC1774
3049	monitor sing_303.htm#SEC343
3050	monodromy sing_1641.htm#IDX715
3051	monodromy sing_1646.htm#SEC1727
3052	monodromy sing_1646.htm#IDX735
3053	monodromy sing_1651.htm#IDX770
3054	monodromy sing_1663.htm#IDX786
3055	monodromy sing_1665.htm#IDX797
3056	monodromyB sing_1697.htm#SEC1778
3057	monomial sing_304.htm#SEC344
3058	monomial ordering sing_1128.htm#IDX541
3059	monomial orderings General definitions for orderings sing_912.htm#SEC969
3060	monomial orderings sing_961.htm#SEC1018
3061	monomial orderings introduction Introduction to orderings sing_960.htm#SEC1017
3062	monomial output sing_405.htm#SEC445
3063	monomial, write sing_405.htm#SEC445
3064	monomialInIdeal sing_675.htm#SEC729
3065	monomialLcm sing_2080.htm#SEC2161
3066	monomialabortstd sing_2337.htm#SEC2418
3067	monomialideal.lib sing_1301.htm#SEC1382
3068	monomialideal_lib sing_1301.htm#SEC1382
3069	monomials and precedence Miscellaneous oddities sing_422.htm#IDX287
3070	mons2intmat sing_1390.htm#SEC1471 15555
3071	morsesplit sing_1604.htm#SEC1685
3072	movingCone sing_2609.htm#SEC2690
3073	mp_res_mat sing_1846.htm#SEC1927
3074	mplot sing_1886.htm#SEC1967
3075	mpresmat sing_305.htm#SEC345
3076	mprimdec.lib sing_1318.htm#SEC1399
3077	mprimdec_lib sing_1318.htm#SEC1399
3078	mregular.lib sing_1333.htm#SEC1414
3079	mregular_lib sing_1333.htm#SEC1414
3080	mres sing_306.htm#SEC346
3081	mres (plural) sing_473.htm#SEC513
3082	mstd sing_307.htm#SEC347
3083	msum sing_58.htm#SEC95
3084	mtriple sing_57.htm#SEC94
3085	mult Miscellaneous oddities sing_308.htm#SEC348
3086	mult sing_422.htm#IDX288
3087	multBound sing_402.htm#SEC442
3088	multRat sing_683.htm#SEC737
3089	multarr2arr sing_2325.htm#SEC2406
3090	multarrMultRestrict sing_2327.htm#SEC2408
3091	multarrRestrict sing_2326.htm#SEC2407
3092	multcol sing_1171.htm#SEC1252
3093	multdivisor sing_2530.htm#SEC2611
3094	multformaldivisor sing_2542.htm#SEC2623
3095	multi sing_2067.htm#SEC2148
3096	multi indices sing_37.htm#SEC65
3097	multi-graded Hilbert series sing_870.htm#IDX419
3098	multiDeg sing_2757.htm#SEC2838
3099	multiDegBasis sing_2758.htm#SEC2839
3100	multiDegGroebner sing_2766.htm#SEC2847
3101	multiDegModulo sing_2768.htm#SEC2849
3102	multiDegPartition sing_2759.htm#SEC2840
3103	multiDegResolution sing_2769.htm#SEC2850
3104	multiDegSyzygy sing_2767.htm#SEC2848
3105	multiDegTensor sing_2770.htm#SEC2851
3106	multiDegTor sing_2771.htm#SEC2852
3107	multiarrangement sing_2321.htm#IDX925
3108	multiarrangement sing_2322.htm#IDX927
3109	multiarrangement sing_2323.htm#IDX930
3110	multiarrangement sing_2324.htm#IDX931
3111	multiarrangement sing_2325.htm#IDX934
3112	multiarrangement sing_2326.htm#IDX937
3113	multiarrangement sing_2327.htm#IDX939
3114	multidimensional_knapsack multidimensional_knapsack sing_2045.htm#SEC2126
3115	multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2727.htm#IDX1149
3116	multigrading.lib sing_2727.htm#IDX1147
3117	multigrading_lib sing_2727.htm#IDX1148
3118	multipleCover sing_2867.htm#SEC2948
3119	multiplication sing_2498.htm#IDX1046
3120	multiplication sing_2520.htm#IDX1094
3121	multiplicities, sequence of sing_1672.htm#IDX809
3122	multiplicity sing_2475.htm#IDX1005
3123	multiplicity sequence sing_1585.htm#IDX688
3124	multiplicity sequence sing_1588.htm#IDX700
3125	multiplicity sequence sing_1674.htm#IDX810
3126	multiplyLeftFractions multiplyLeftFractions sing_759.htm#SEC813
3127	multiplylist sing_1525.htm#SEC1606
3128	multivariate equations sing_1820.htm#IDX827
3129	multrow sing_1172.htm#SEC1253
3130	multseq2charexp sing_1584.htm#SEC1665
3131	multsequence sing_1674.htm#SEC1755
3132	nBoundaryLatticePoints nBoundaryLatticePoints sing_2235.htm#SEC2316
3133	nHilbertBasis sing_2236.htm#SEC2317
3134	nInteriorLatticePoints nInteriorLatticePoints sing_2237.htm#SEC2318
3135	nLatticePoints sing_2238.htm#SEC2319
3136	naccache_stern_decryption naccache_stern_decryption sing_2048.htm#SEC2129
3137	naccache_stern_encryption naccache_stern_encryption sing_2047.htm#SEC2128
3138	naccache_stern_generation naccache_stern_generation sing_2046.htm#SEC2127
3139	nameof sing_309.htm#SEC349
3140	names sing_310.htm#SEC350
3141	nashmult sing_1592.htm#SEC1673
3142	nblocks sing_361.htm#IDX219
3143	ncExt_R sing_702.htm#SEC756
3144	ncHilb.lib sing_870.htm#SEC924
3145	ncHilb_lib sing_870.htm#SEC924
3146	ncHom sing_703.htm#SEC757
3147	ncInit sing_874.htm#SEC928
3148	ncModslimgb.lib sing_713.htm#SEC767
3149	ncModslimgb_lib sing_713.htm#SEC767
3150	ncRelations sing_737.htm#SEC791
3151	ncVarsAdd sing_876.htm#SEC930
3152	ncVarsGet sing_875.htm#SEC929
3153	nc_algebra sing_474.htm#SEC514
3154	nc_hilb sing_361.htm#IDX221
3155	ncalg.lib sing_615.htm#SEC669
3156	ncalg_lib sing_615.htm#SEC669
3157	ncalgebra sing_475.htm#SEC515
3158	ncdecomp.lib sing_642.htm#SEC696
3159	ncdecomp_lib sing_642.htm#SEC696
3160	ncdetection sing_609.htm#SEC663
3161	ncfactor sing_648.htm#SEC702
3162	ncfactor.lib sing_647.htm#SEC701
3163	ncfactor_lib sing_647.htm#SEC701
3164	ncfrac.lib sing_687.htm#SEC741
3165	ncfrac_lib sing_687.htm#SEC741
3166	ncgen sing_801.htm#SEC855
3167	nchilb sing_871.htm#SEC925
3168	nchomolog.lib sing_701.htm#IDX377
3169	nchomolog_lib sing_701.htm#IDX378
3170	ncloc.lib sing_709.htm#SEC763
3171	ncloc_lib sing_709.htm#SEC763
3172	ncmodslimgb sing_714.htm#SEC768
3173	ncols sing_311.htm#SEC351
3174	ncones sing_2182.htm#SEC2263
3175	ncpreim.lib sing_715.htm#SEC769
3176	ncpreim_lib sing_715.htm#SEC769
3177	ncrat.lib sing_873.htm#IDX420
3178	ncratAdd sing_878.htm#SEC932
3179	ncratDefine sing_877.htm#SEC931
3180	ncratEvaluateAt sing_887.htm#SEC941
3181	ncratFromPoly sing_885.htm#SEC939
3182	ncratFromString sing_884.htm#SEC938
3183	ncratInvert sing_881.htm#SEC935
3184	ncratMultiply sing_880.htm#SEC934
3185	ncratPower sing_886.htm#SEC940
3186	ncratPrint sing_883.htm#SEC937
3187	ncratSPrint sing_882.htm#SEC936
3188	ncratSubstract sing_879.htm#SEC933
3189	ncrat_lib sing_873.htm#IDX421
3190	ncrepAdd sing_889.htm#SEC943
3191	ncrepDim sing_894.htm#SEC948
3192	ncrepEvaluate sing_896.htm#SEC950
3193	ncrepEvaluateAt sing_897.htm#SEC951
3194	ncrepGet sing_888.htm#SEC942
3195	ncrepGetRegularMinimal ncrepGetRegularMinimal sing_904.htm#SEC958
3196	ncrepGetRegularZeroMinimal ncrepGetRegularZeroMinimal sing_903.htm#SEC957
3197	ncrepInvert sing_892.htm#SEC946
3198	ncrepIsDefined sing_899.htm#SEC953
3199	ncrepIsDefinedDim sing_898.htm#SEC952
3200	ncrepIsRegular sing_900.htm#SEC954
3201	ncrepMultiply sing_891.htm#SEC945
3202	ncrepPencilCombine sing_906.htm#SEC960
3203	ncrepPencilGet sing_905.htm#SEC959
3204	ncrepPrint sing_893.htm#SEC947
3205	ncrepRegularMinimize ncrepRegularMinimize sing_902.htm#SEC956
3206	ncrepRegularZeroMinimize ncrepRegularZeroMinimize sing_901.htm#SEC955
3207	ncrepSubstitute sing_895.htm#SEC949
3208	ncrepSubstract sing_890.htm#SEC944
3209	nctools.lib sing_723.htm#SEC777
3210	nctools_lib sing_723.htm#SEC777
3211	ndcond sing_726.htm#SEC780
3212	negateNcfrac sing_696.htm#SEC750
3213	negatedCone sing_2160.htm#SEC2241
3214	negation sing_2497.htm#IDX1045
3215	negative degree lexicographical ordering sing_963.htm#IDX442
3216	negative degree reverse lexicographical ordering Local orderings sing_963.htm#IDX440
3217	negative lexicographical ordering sing_963.htm#IDX438
3218	negativedivisor sing_2531.htm#SEC2612
3219	negativeformaldivisor negativeformaldivisor sing_2541.htm#SEC2622
3220	net sing_2779.htm#IDX1150
3221	net sing_2781.htm#SEC2862
3222	net access Command line options sing_19.htm#IDX40
3223	netBigInt sing_2787.htm#SEC2868
3224	netBigIntMat sing_2782.htm#SEC2863
3225	netBigIntMatShort sing_2783.htm#SEC2864
3226	netCoefficientRing sing_2784.htm#SEC2865
3227	netIdeal sing_2785.htm#SEC2866
3228	netInt sing_2786.htm#SEC2867
3229	netIntMat sing_2788.htm#SEC2869
3230	netIntMatShort sing_2789.htm#SEC2870
3231	netIntVector sing_2790.htm#SEC2871
3232	netIntVectorShort sing_2791.htm#SEC2872
3233	netList sing_2793.htm#SEC2874
3234	netMap sing_2794.htm#SEC2875
3235	netMap2 sing_2795.htm#SEC2876
3236	netMatrix sing_2704.htm#SEC2785
3237	netNumber sing_2792.htm#SEC2873
3238	netPoly sing_2798.htm#SEC2879
3239	netPrimePower sing_2799.htm#SEC2880
3240	netRing sing_2800.htm#SEC2881
3241	netString sing_2801.htm#SEC2882
3242	netVector sing_2703.htm#SEC2784
3243	netmatrix sing_2796.htm#SEC2877
3244	netmatrixShort sing_2797.htm#SEC2878
3245	nets.lib sing_2779.htm#SEC2860
3246	nets_lib sing_2779.htm#SEC2860
3247	netvector sing_2802.htm#SEC2883
3248	netvectorShort sing_2803.htm#SEC2884
3249	newTest sing_1987.htm#SEC2068
3250	newline sing_172.htm#SEC212
3251	news sing_2901.htm#SEC2982
3252	newstruct sing_183.htm#SEC223
3253	newstruct sing_2344.htm#IDX961
3254	newtonDiag sing_1089.htm#SEC1170
3255	newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2883.htm#SEC2964
3256	newtonPolytope sing_2186.htm#SEC2267
3257	newtonPolytopeLP sing_2192.htm#SEC2273
3258	newtonPolytopeP sing_2191.htm#SEC2272
3259	newtonpoly sing_1679.htm#SEC1760
3260	nf_icis sing_1720.htm#SEC1801
3261	nfmodStd sing_2807.htm#SEC2888
3262	nfmodSyz sing_2809.htm#SEC2890
3263	nfmodstd.lib sing_2805.htm#SEC2886
3264	nfmodstd_lib sing_2805.htm#SEC2886
3265	nfmodsyz.lib sing_2808.htm#SEC2889
3266	nfmodsyz_lib sing_2808.htm#SEC2889
3267	nilpotent Lie algebras sing_1478.htm#IDX640
3268	nmaxcones sing_2181.htm#SEC2262
3269	noether sing_403.htm#SEC443
3270	noether.lib sing_1341.htm#SEC1422
3271	noetherNormal sing_1224.htm#SEC1305
3272	noether_lib sing_1341.htm#SEC1422
3273	non-english special characters sing_411.htm#IDX283
3274	nonMonomials sing_1394.htm#SEC1475
3275	nonZeroEntry sing_1227.htm#SEC1308
3276	noncommutative, rational expressions sing_873.htm#IDX422
3277	none, option sing_318.htm#IDX150
3278	norTest sing_1361.htm#SEC1442
3279	norm sing_2066.htm#SEC2147
3280	normaform (up to a bound) sing_361.htm#IDX244
3281	normal sing_1351.htm#SEC1432
3282	normal bundle, graph, rational curves, multiple covers, lines on normalBundle sing_2866.htm#IDX1215
3283	normal form sing_970.htm#IDX454
3284	normal.lib sing_1350.htm#SEC1431
3285	normalBundle sing_2866.htm#SEC2947
3286	normalC sing_1353.htm#SEC1434
3287	normalConductor sing_1365.htm#SEC1446
3288	normalFan sing_2239.htm#SEC2320
3289	normalForm sing_2532.htm#SEC2613
3290	normalI sing_1438.htm#SEC1519
3291	normalP sing_1352.htm#SEC1433
3292	normalToricRing sing_1368.htm#SEC1449 29638
3293	normalToricRingFromBinomials normalToricRingFromBinomials sing_1369.htm#SEC1450 2301
3294	normal_lib sing_1350.htm#SEC1431
3295	normalform sing_1608.htm#SEC1689
3296	normalform sing_2458.htm#IDX993
3297	normaliz sing_1.htm#IDX14 18426
3298	normaliz sing_1381.htm#SEC1462
3299	normaliz.lib sing_1366.htm#SEC1447
3300	normaliz_lib sing_1366.htm#SEC1447
3301	normalization sing_1290.htm#IDX590
3302	normalization sing_1291.htm#IDX593
3303	normalization sing_1295.htm#IDX597
3304	normalization sing_1296.htm#IDX599
3305	normalization sing_1351.htm#IDX608
3306	normalization sing_1352.htm#IDX611
3307	normalization sing_1353.htm#IDX614
3308	normalization sing_1365.htm#IDX620
3309	normalization sing_1366.htm#IDX622
3310	normalization sing_2474.htm#IDX1003
3311	normalization. sing_1287.htm#IDX589
3312	normalization. sing_1485.htm#IDX662
3313	normalize sing_1082.htm#SEC1163
3314	normalizeMonoidal sing_765.htm#SEC819
3315	normalizeRational sing_766.htm#SEC820
3316	not sing_101.htm#SEC141
3317	not equal sing_2501.htm#IDX1053
3318	not equal sing_2522.htm#IDX1100
3319	notBuckets, option sing_318.htm#IDX160
3320	notRegularity, option sing_318.htm#IDX158
3321	notSugar, option sing_318.htm#IDX159
3322	notWarnSB, option sing_318.htm#IDX181
3323	npar sing_1972.htm#SEC2053
3324	npars sing_312.htm#SEC352
3325	nrRootsDeterm sing_2097.htm#SEC2178
3326	nrRootsProbab sing_2096.htm#SEC2177
3327	nres sing_313.htm#SEC353
3328	nres (plural) sing_476.htm#SEC516
3329	nrows sing_314.htm#SEC354
3330	nrroots sing_2126.htm#SEC2207
3331	nsatiety sing_1346.htm#SEC1427
3332	nselect sing_1243.htm#SEC1324
3333	nt_solve sing_1861.htm#SEC1942
3334	ntsolve.lib sing_1860.htm#SEC1941
3335	ntsolve_lib sing_1860.htm#SEC1941
3336	number sing_144.htm#SEC184
3337	number sing_2298.htm#IDX885
3338	number declarations sing_145.htm#SEC185
3339	number expressions sing_146.htm#SEC186
3340	number operations sing_147.htm#SEC187
3341	number related functions number related functions sing_148.htm#SEC188
3342	numberOfConesOfDimension numberOfConesOfDimension sing_2183.htm#SEC2264
3343	number_e sing_1015.htm#SEC1096
3344	number_pi sing_1016.htm#SEC1097
3345	numerAlg.lib sing_1460.htm#IDX629
3346	numerAlg_lib sing_1460.htm#IDX630
3347	numerAlg_lib sing_1465.htm#IDX639
3348	numerDecom.lib sing_1465.htm#IDX633
3349	numerDecom_lib sing_1460.htm#IDX632
3350	numerDecom_lib sing_1465.htm#IDX634
3351	numerator sing_315.htm#SEC355
3352	numerical irreducible decomposition sing_1465.htm#IDX635
3353	nvars sing_316.htm#SEC356
3354	olga.lib sing_748.htm#SEC802
3355	olga_lib sing_748.htm#SEC802
3356	oneDimBelongSemigroup oneDimBelongSemigroup sing_1234.htm#SEC1315
3357	oneNcfrac sing_693.htm#SEC747
3358	onesVector sing_2188.htm#SEC2269
3359	online help The online help system sing_16.htm#SEC22
3360	open sing_317.htm#SEC357
3361	opentex sing_1889.htm#SEC1970
3362	operatorAlgebra sing_821.htm#SEC875
3363	operatorBM sing_544.htm#SEC598
3364	operatorModulo sing_545.htm#SEC599
3365	oppose sing_477.htm#SEC517
3366	opposite sing_478.htm#SEC518
3367	opposite polynomial sing_361.htm#IDX229
3368	opposite ring sing_361.htm#IDX226
3369	option sing_318.htm#SEC358
3370	option(warn) sing_70.htm#SEC110
3371	optionIsSet sing_1125.htm#SEC1206
3372	or Evaluation of logical expressions sing_101.htm#SEC141
3373	or sing_415.htm#SEC455
3374	orbit sing_1478.htm#IDX642
3375	orbit sing_1479.htm#IDX646
3376	orbit sing_1482.htm#IDX651
3377	orbit sing_1483.htm#IDX654
3378	orbitConeOrbits sing_2612.htm#SEC2693
3379	orbitCones sing_2603.htm#SEC2684
3380	orbit_variety sing_1779.htm#SEC1860
3381	orbitparam.lib sing_1478.htm#SEC1559
3382	orbitparam_lib sing_1478.htm#SEC1559
3383	ord sing_319.htm#SEC359
3384	ord_test sing_1120.htm#SEC1201
3385	order ideal, border basis sing_2830.htm#IDX1187
3386	order ideal, border basis sing_2831.htm#IDX1188
3387	ordering diffAlgebraChangeOrd sing_2486.htm#IDX1022
3388	ordering sing_2502.htm#IDX1056
3389	ordering sing_2503.htm#IDX1059
3390	orderings General definitions for orderings sing_961.htm#SEC1018
3391	orderings introduction Introduction to orderings sing_960.htm#SEC1017
3392	orderings, L sing_968.htm#SEC1025
3393	orderings, M sing_965.htm#SEC1022
3394	orderings, a sing_967.htm#SEC1024
3395	orderings, global sing_962.htm#SEC1019
3396	orderings, local sing_963.htm#SEC1020
3397	orderings, product sing_966.htm#SEC1023
3398	ordstr sing_320.htm#SEC360
3399	origin sing_2131.htm#SEC2212
3400	orthogonalize sing_1190.htm#SEC1271
3401	outer sing_1161.htm#SEC1242
3402	output sing_41.htm#SEC71
3403	outputting monomials sing_405.htm#SEC445
3404	p-adic numbers sing_32.htm#SEC46
3405	pFactor sing_2021.htm#SEC2102
3406	pIntersect sing_508.htm#SEC562
3407	pIntersectSyz sing_509.htm#SEC563
3408	package sing_149.htm#SEC189
3409	package declarations package declarations sing_150.htm#SEC190
3410	package related functions package related functions sing_151.htm#SEC191
3411	pairset sing_2086.htm#SEC2167
3412	par sing_321.htm#SEC361
3413	par2varRing sing_998.htm#SEC1079
3414	paraConic sing_1493.htm#SEC1574
3415	paraPlaneCurve sing_1487.htm#SEC1568
3416	parallel skeletons sing_1064.htm#IDX533
3417	parallel.lib sing_1064.htm#SEC1145
3418	parallelTestAND sing_1068.htm#SEC1149
3419	parallelTestOR sing_1069.htm#SEC1150
3420	parallelWaitAll sing_1067.htm#SEC1148
3421	parallelWaitFirst sing_1066.htm#SEC1147
3422	parallelWaitN sing_1065.htm#SEC1146
3423	parallel_lib sing_1064.htm#SEC1145
3424	parallelization sing_1064.htm#IDX532
3425	parallelization sing_1104.htm#IDX535
3426	parallelization sing_1137.htm#IDX545
3427	param sing_1670.htm#SEC1751
3428	parameter, as numbers sing_144.htm#SEC184
3429	parameterSubstitute sing_2279.htm#SEC2360
3430	parametric annihilator sing_537.htm#IDX332
3431	parametric annihilator for variety sing_600.htm#IDX362
3432	parametric ideal sing_1027.htm#IDX460
3433	parametric ideal sing_1034.htm#IDX479
3434	parametric ideal sing_1034.htm#IDX481
3435	parametric ideal sing_1035.htm#IDX486
3436	parametrization sing_1478.htm#IDX643
3437	parametrization sing_1482.htm#IDX652
3438	parametrization sing_1670.htm#IDX804
3439	parametrizeOrbit sing_1482.htm#SEC1563
3440	paraplanecurves.lib sing_1484.htm#SEC1565
3441	paraplanecurves_lib sing_1484.htm#SEC1565
3442	pardeg sing_322.htm#SEC362
3443	parstr sing_323.htm#SEC363
3444	part sing_2434.htm#SEC2515
3445	partOver sing_2437.htm#SEC2518
3446	partUnder sing_2438.htm#SEC2519
3447	partial_molien sing_1757.htm#SEC1838
3448	partitions sing_1255.htm#SEC1336
3449	partitions sing_1255.htm#IDX578
3450	path Used environment variables sing_2910.htm#SEC3007
3451	path integral sing_1247.htm#IDX565
3452	paths Used environment variables sing_2910.htm#SEC3007
3453	pause sing_1061.htm#SEC1142
3454	pdivi sing_1029.htm#SEC1110
3455	pdivi sing_1030.htm#IDX470
3456	pdivisorplus sing_2546.htm#SEC2627
3457	permcol sing_1173.htm#SEC1254
3458	permrow sing_1174.htm#SEC1255
3459	permutationFromIntvec permutationFromIntvec sing_2618.htm#SEC2699
3460	permutationToIntvec sing_2619.htm#SEC2700
3461	permutations sing_1256.htm#IDX579
3462	permutations, sum, max, min sing_2469.htm#IDX995
3463	permute sing_1256.htm#SEC1337
3464	permute_L sing_1924.htm#SEC2005
3465	perron sing_770.htm#SEC824
3466	perron.lib sing_769.htm#SEC823
3467	perron_lib sing_769.htm#SEC823
3468	phindex.lib sing_2339.htm#IDX952
3469	phindex_lib sing_2339.htm#IDX953
3470	picksFormula sing_2201.htm#SEC2282
3471	pid sing_361.htm#IDX238
3472	plainInvariants sing_1629.htm#SEC1710
3473	planeCur sing_2456.htm#SEC2537
3474	plot sing_1902.htm#SEC1983
3475	plotRot sing_1906.htm#SEC1987
3476	plotRotated sing_1905.htm#SEC1986
3477	plotRotatedDirect sing_1908.htm#SEC1989
3478	plotRotatedList sing_1907.htm#SEC1988
3479	plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1909.htm#SEC1990
3480	plural sing_1127.htm#IDX540
3481	pmat sing_1055.htm#SEC1136
3482	pnormalf sing_1030.htm#SEC1111
3483	pointid.lib sing_1393.htm#SEC1474
3484	pointid_lib sing_1393.htm#SEC1474
3485	polSol sing_667.htm#SEC721
3486	polSolFiniteRank sing_668.htm#SEC722
3487	pollTask sing_1147.htm#SEC1228
3488	poly sing_152.htm#SEC192
3489	poly (plural) sing_442.htm#SEC482
3490	poly declarations sing_153.htm#SEC193
3491	poly declarations (plural) poly declarations (plural) sing_443.htm#SEC483
3492	poly expressions sing_154.htm#SEC194
3493	poly expressions (plural) poly expressions (plural) sing_444.htm#SEC484
3494	poly operations sing_155.htm#SEC195
3495	poly operations (plural) poly operations (plural) sing_445.htm#SEC485
3496	poly related functions poly related functions sing_156.htm#SEC196
3497	poly related functions (plural) poly related functions (plural) sing_446.htm#SEC486
3498	poly.lib sing_1070.htm#SEC1151
3499	poly2list sing_586.htm#SEC640
3500	poly2zdd sing_2360.htm#SEC2441 61839
3501	polyInterpolation sing_2549.htm#SEC2630
3502	polyVars sing_674.htm#SEC728
3503	poly_lib sing_1070.htm#SEC1151
3504	polybori sing_2344.htm#IDX957
3505	polybori.lib sing_2344.htm#IDX954
3506	polybori.lib sing_2344.htm#IDX958
3507	polybori_lib sing_2344.htm#IDX955
3508	polymake sing_2189.htm#IDX858
3509	polymake.lib sing_2189.htm#SEC2270
3510	polymakePolytope sing_2190.htm#SEC2271
3511	polymake_lib sing_2189.htm#SEC2270
3512	polynomial sing_2513.htm#IDX1081
3513	polynomial solutions sing_661.htm#IDX374
3514	polynomial, opposite sing_361.htm#IDX230
3515	polytope sing_191.htm#SEC231
3516	polytope sing_2189.htm#IDX854
3517	polytopeViaInequalities polytopeViaInequalities sing_2161.htm#SEC2242
3518	polytopeViaPoints sing_2162.htm#SEC2243
3519	pos_def sing_1201.htm#SEC1282
3520	poset sing_2329.htm#IDX943
3521	positiveOrthant sing_2132.htm#SEC2213
3522	posweight sing_1737.htm#SEC1818
3523	powSumSym sing_2391.htm#SEC2472
3524	power sing_1162.htm#SEC1243
3525	power set sing_2471.htm#IDX997
3526	powerN sing_2005.htm#SEC2086
3527	powerX sing_2014.htm#SEC2095
3528	power_products sing_1771.htm#SEC1852
3529	powerpolyX sing_1984.htm#SEC2065
3530	powersums sing_2107.htm#SEC2188
3531	preComp sing_1329.htm#SEC1410
3532	preimage sing_324.htm#SEC364
3533	preimage sing_715.htm#IDX379
3534	preimage (plural) sing_479.htm#SEC519
3535	preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1123.htm#IDX538
3536	preimageLattice sing_2747.htm#SEC2828
3537	preimageLoc sing_1123.htm#SEC1204
3538	preimageNC sing_717.htm#SEC771
3539	prepEmbDiv sing_1555.htm#SEC1636
3540	prepMat sing_1817.htm#SEC1898
3541	prepRealclassify sing_1613.htm#SEC1694
3542	prepSV sing_1919.htm#SEC2000
3543	prepareAss sing_1412.htm#SEC1493
3544	presentTree sing_1542.htm#SEC1623
3545	presentation sing_2705.htm#SEC2786
3546	presolve.lib sing_1827.htm#SEC1908
3547	presolve_lib sing_1827.htm#SEC1908
3548	primL sing_2009.htm#SEC2090
3549	primList sing_2008.htm#SEC2089
3550	primRoot sing_1452.htm#SEC1533
3551	primTest sing_1328.htm#SEC1409
3552	primary decomposition sing_1397.htm#IDX624
3553	primary decomposition sing_1420.htm#IDX625
3554	primary decomposition of modules sing_1318.htm#IDX601
3555	primary decomposition, numerical sing_1465.htm#IDX637
3556	primary_char0 sing_1761.htm#SEC1842
3557	primary_char0_no_molien primary_char0_no_molien sing_1763.htm#SEC1844
3558	primary_char0_no_molien_random primary_char0_no_molien_random sing_1768.htm#SEC1849
3559	primary_char0_random primary_char0_random sing_1766.htm#SEC1847
3560	primary_charp sing_1762.htm#SEC1843
3561	primary_charp_no_molien primary_charp_no_molien sing_1764.htm#SEC1845
3562	primary_charp_no_molien_random primary_charp_no_molien_random sing_1769.htm#SEC1850
3563	primary_charp_random primary_charp_random sing_1767.htm#SEC1848
3564	primary_charp_without primary_charp_without sing_1765.htm#SEC1846
3565	primary_charp_without_random primary_charp_without_random sing_1770.htm#SEC1851
3566	primary_invariants sing_1749.htm#SEC1830
3567	primary_invariants_random primary_invariants_random sing_1750.htm#SEC1831
3568	primdec.lib sing_1397.htm#SEC1478
3569	primdecGTZ sing_1399.htm#SEC1480
3570	primdecGTZE sing_1400.htm#SEC1481
3571	primdecMon sing_1317.htm#SEC1398
3572	primdecSY sing_1401.htm#SEC1482
3573	primdecSYE sing_1402.htm#SEC1483
3574	primdecZ sing_1421.htm#SEC1502
3575	primdecZM sing_1422.htm#SEC1503
3576	primdec_lib sing_1397.htm#SEC1478
3577	primdecint.lib sing_1420.htm#SEC1501
3578	primdecint_lib sing_1420.htm#SEC1501
3579	prime sing_325.htm#SEC365
3580	primeClosure sing_1356.htm#SEC1437
3581	primecoeffs sing_1022.htm#SEC1103
3582	primefactors sing_326.htm#SEC366
3583	primes sing_1017.htm#SEC1098
3584	primitiv.lib sing_1428.htm#SEC1509
3585	primitiv_lib sing_1428.htm#SEC1509
3586	primitive sing_1429.htm#SEC1510
3587	primitive element sing_1429.htm#IDX626
3588	primitiveSpan sing_2754.htm#SEC2835
3589	primitive_extra sing_1430.htm#SEC1511
3590	primparam sing_1624.htm#SEC1705
3591	principal intersection sing_502.htm#IDX316
3592	print sing_327.htm#SEC367
3593	print sing_2296.htm#IDX878
3594	print sing_2490.htm#IDX1031
3595	print sing_2492.htm#IDX1036
3596	print sing_2493.htm#IDX1037
3597	print sing_2515.htm#IDX1085
3598	print sing_2516.htm#IDX1086
3599	printBetti sing_2686.htm#SEC2767
3600	printFreeModule sing_2678.htm#SEC2759
3601	printGraph sing_1249.htm#SEC1330
3602	printGraphG sing_2860.htm#SEC2941
3603	printGroup sing_2735.htm#SEC2816
3604	printHom sing_2681.htm#SEC2762
3605	printMatrix sing_2677.htm#SEC2758
3606	printModule sing_2680.htm#SEC2761
3607	printMoebius sing_2335.htm#SEC2416
3608	printResolution sing_2679.htm#SEC2760
3609	printSheaf sing_2848.htm#SEC2929
3610	printStack sing_2862.htm#SEC2943
3611	printTask sing_1142.htm#SEC1223
3612	printVariety sing_2840.htm#SEC2921
3613	printf sing_328.htm#SEC368
3614	printlevel sing_404.htm#SEC444
3615	proc sing_157.htm#SEC197
3616	proc declaration sing_158.htm#SEC198
3617	proc expression sing_159.htm#SEC199
3618	procedure, ASCII help sing_56.htm#IDX125
3619	procedure, ASCII/Texinfo help sing_58.htm#IDX127
3620	procedure, texinfo help sing_57.htm#IDX126
3621	procedures, help string sing_45.htm#SEC82
3622	procedures, static Procedure definition sing_43.htm#SEC78
3623	procs with different argument types procs with different argument types sing_160.htm#SEC200
3624	prodcrit sing_2084.htm#SEC2165
3625	product sing_1018.htm#SEC1099
3626	product sing_2498.htm#IDX1047
3627	product sing_2520.htm#IDX1095
3628	product variety, abstract variety sing_2841.htm#IDX1203
3629	productVariety sing_2841.htm#SEC2922
3630	productgroup sing_2756.htm#SEC2837
3631	progress watch sing_318.htm#IDX163
3632	projectLattice sing_2748.htm#SEC2829
3633	projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2845.htm#IDX1207
3634	projective dimension purityfiltration_lib sing_771.htm#IDX388
3635	projective limes sing_32.htm#SEC46
3636	projective space, abstract variety sing_2844.htm#IDX1206
3637	projectiveBundle sing_2845.htm#SEC2926
3638	projectiveDimension sing_772.htm#SEC826
3639	projectiveSpace sing_2844.htm#SEC2925
3640	prompt sing_15.htm#SEC21
3641	prompt, option sing_318.htm#IDX182
3642	propagator sing_1247.htm#IDX563
3643	propagator sing_1250.htm#SEC1331
3644	prot, option sing_318.htm#IDX161
3645	protocol of computations sing_318.htm#IDX162
3646	proximitymatrix sing_1583.htm#SEC1664
3647	prune sing_329.htm#SEC369
3648	pruneModule sing_2712.htm#SEC2793
3649	prwalk sing_2835.htm#SEC2916
3650	psigncnd sing_1880.htm#SEC1961
3651	puiseux2generators sing_1682.htm#SEC1763
3652	puiseuxExpansion sing_2250.htm#SEC2331
3653	pure tensor sing_495.htm#IDX304
3654	purelist sing_782.htm#SEC836
3655	purity purityfiltration_lib sing_771.htm#IDX390
3656	purityFiltration sing_773.htm#SEC827
3657	purityTriang sing_774.htm#SEC828
3658	purityfiltration.lib purityfiltration_lib sing_771.htm#IDX383
3659	purityfiltration_lib purityfiltration_lib sing_771.htm#IDX384
3660	pushForward sing_2773.htm#SEC2854
3661	pwalk sing_1263.htm#SEC1344
3662	pyobject sing_192.htm#SEC232
3663	pyobject sing_2344.htm#IDX960
3664	pyobject declarations pyobject declarations sing_193.htm#SEC233
3665	pyobject expressions pyobject expressions sing_194.htm#SEC234
3666	pyobject operations sing_195.htm#SEC235
3667	pyobject related functions pyobject related functions sing_196.htm#SEC236
3668	pyramid sing_2567.htm#SEC2648
3669	python_eval sing_197.htm#SEC237
3670	python_import sing_198.htm#SEC238
3671	python_run sing_199.htm#SEC239
3672	qbase sing_2110.htm#SEC2191
3673	qepcad sing_2577.htm#SEC2658
3674	qepcadsystem sing_2578.htm#SEC2659
3675	qhmatrix sing_1735.htm#SEC1816
3676	qhmoduli.lib sing_1699.htm#SEC1780
3677	qhmoduli_lib sing_1699.htm#SEC1780
3678	qhspectrum sing_1722.htm#SEC1803
3679	qhweight sing_330.htm#SEC370
3680	qmatrix.lib sing_783.htm#SEC837
3681	qmatrix_lib sing_783.htm#SEC837
3682	qminor sing_785.htm#SEC839
3683	qrds sing_331.htm#SEC371
3684	qring Miscellaneous oddities sing_166.htm#SEC206
3685	qring sing_422.htm#IDX292
3686	qring (plural) sing_447.htm#SEC487
3687	qring declaration sing_170.htm#SEC210
3688	qring declaration (plural) qring declaration (plural) sing_448.htm#SEC488
3689	qring related functions (plural) qring related functions (plural) sing_449.htm#SEC489
3690	qring ring ideal 'factor ring' sing_1132.htm#IDX544
3691	qringNF, option sing_318.htm#IDX164
3692	qslimgb sing_997.htm#SEC1078
3693	quadraticSieve sing_2022.htm#SEC2103
3694	quantMat sing_784.htm#SEC838
3695	quickclass sing_1605.htm#SEC1686
3696	quit sing_394.htm#SEC434
3697	quotSheaf sing_2857.htm#SEC2938
3698	quote sing_332.htm#SEC372
3699	quotient sing_333.htm#SEC373
3700	quotient (plural) sing_480.htm#SEC520
3701	quotientLatticeBasis quotientLatticeBasis sing_2163.htm#SEC2244
3702	quotientMain sing_1872.htm#SEC1953
3703	quotientMon sing_1308.htm#SEC1389
3704	rHRR sing_2431.htm#SEC2512
3705	rJanet sing_2832.htm#SEC2913
3706	rMacaulay sing_1056.htm#SEC1137
3707	rad_con sing_1083.htm#SEC1164
3708	radical sing_1409.htm#SEC1490
3709	radicalEHV sing_1410.htm#SEC1491
3710	radicalMemberShip sing_2272.htm#SEC2353
3711	radicalMon sing_1309.htm#SEC1390
3712	radicalZ sing_1424.htm#SEC1505
3713	randcharpoly sing_2104.htm#SEC2185
3714	randlinpoly sing_2106.htm#SEC2187
3715	random sing_334.htm#SEC374
3716	random sing_361.htm#IDX242
3717	random sing_2317.htm#IDX917
3718	random sing_2318.htm#IDX919
3719	random number generator, seed sing_361.htm#IDX240
3720	random.lib sing_1091.htm#SEC1172
3721	randomBinomial sing_1103.htm#SEC1184
3722	randomCheck sing_1935.htm#SEC2016
3723	randomLast sing_1102.htm#SEC1183
3724	randomPoint sing_2164.htm#SEC2245
3725	randomPolyInT sing_2281.htm#SEC2362
3726	random_lib sing_1091.htm#SEC1172
3727	randomid sing_1093.htm#SEC1174
3728	randommat sing_1094.htm#SEC1175
3729	rank sing_210.htm#IDX137
3730	rank sing_335.htm#SEC375
3731	rankSheaf sing_2849.htm#SEC2930
3732	ratSol sing_669.htm#SEC723
3733	ratgb.lib sing_789.htm#IDX391
3734	ratgb_lib sing_789.htm#IDX392
3735	rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1487.htm#IDX664
3736	rational functions sing_873.htm#IDX423
3737	rational normal curve, projection. sing_1488.htm#IDX665
3738	rational normal curve, projection. sing_1491.htm#IDX666
3739	rational normal curve, projection. sing_1492.htm#IDX667
3740	rational solutions sing_661.htm#IDX375
3741	rational univariate projection sing_2104.htm#IDX851
3742	rationalCurve sing_2869.htm#SEC2950
3743	rationalPointConic sing_1489.htm#SEC1570
3744	ratstd sing_790.htm#SEC844
3745	rays sing_2165.htm#SEC2246
3746	rcolon sing_872.htm#SEC926
3747	re2squ sing_1466.htm#SEC1547
3748	read sing_336.htm#SEC376
3749	readNmzData sing_1384.htm#SEC1465 18957
3750	reading, option sing_318.htm#IDX183
3751	readline sing_1.htm#IDX5
3752	real sing_28.htm#IDX74
3753	real root isolation sing_2816.htm#IDX1182
3754	real roots, univariate polynomial sing_2111.htm#IDX853
3755	real roots, univariate projection sing_2095.htm#IDX849
3756	real roots,sign conditions sing_1878.htm#IDX829
3757	realclassify sing_2811.htm#SEC2892
3758	realclassify.lib sing_2810.htm#SEC2891
3759	realclassify_lib sing_2810.htm#SEC2891
3760	realizationDim sing_2244.htm#SEC2325
3761	realizationDimPoly sing_2246.htm#SEC2327
3762	realizationMatroids.lib realizationMatroids_lib sing_2243.htm#SEC2324
3763	realizationMatroids_lib realizationMatroids_lib sing_2243.htm#SEC2324
3764	realmorsesplit sing_2812.htm#SEC2893
3765	realpoly sing_1433.htm#SEC1514
3766	realrad sing_1435.htm#SEC1516
3767	realrad.lib sing_1432.htm#SEC1513
3768	realrad_lib sing_1432.htm#SEC1513
3769	realzero sing_1434.htm#SEC1515
3770	recursive_boolean_poly recursive_boolean_poly sing_2350.htm#SEC2431 17045
3771	recursive_from_boolean_poly recursive_from_boolean_poly sing_2356.htm#SEC2437 37794
3772	redSB, option sing_318.htm#IDX165
3773	redTail, option sing_318.htm#IDX167
3774	redThrough, option sing_318.htm#IDX168
3775	redefine, option sing_318.htm#IDX184
3776	reduce sing_337.htm#SEC377
3777	reduce sing_516.htm#IDX321
3778	reduce sing_1029.htm#IDX468
3779	reduce sing_1030.htm#IDX471
3780	reduce (letterplace) reduce (letterplace) sing_802.htm#SEC856
3781	reduce (plural) sing_481.htm#SEC521
3782	reduce (up to a bound) sing_361.htm#IDX243
3783	reduceIntChain sing_2717.htm#SEC2798
3784	reduced sing_1028.htm#IDX465
3785	reduced standard basis sing_318.htm#IDX166
3786	reduction sing_1787.htm#SEC1868
3787	reesclos.lib sing_1436.htm#SEC1517
3788	reesclos_lib sing_1436.htm#SEC1517
3789	reference sing_200.htm#SEC240
3790	reference declarations reference declarations sing_201.htm#SEC241
3791	reference expressions reference expressions sing_202.htm#SEC242
3792	reference operations reference and shared operations sing_205.htm#SEC245
3793	reference related functions reference and shared related functions sing_206.htm#SEC246
3794	regCM sing_1348.htm#SEC1429
3795	regIdeal sing_1334.htm#SEC1415
3796	regMonCurve sing_1337.htm#SEC1418
3797	regularity Syzygies and resolutions sing_338.htm#SEC378
3798	regularity sing_972.htm#SEC1034
3799	regularity sing_1348.htm#IDX606
3800	regularity sing_1349.htm#IDX607
3801	reiffen sing_555.htm#SEC609
3802	rel_orbit_variety sing_1780.htm#SEC1861
3803	relations sing_769.htm#IDX382
3804	relativeInteriorPoint relativeInteriorPoint sing_2166.htm#SEC2247
3805	relative_orbit_variety relative_orbit_variety sing_1781.htm#SEC1862
3806	relweight sing_1736.htm#SEC1817
3807	remainder sing_1865.htm#SEC1946
3808	remainderMain sing_1873.htm#SEC1954
3809	removeCone sing_2184.htm#SEC2265
3810	removepower sing_1593.htm#SEC1674
3811	repart sing_339.htm#SEC379
3812	replace sing_1974.htm#SEC2055
3813	representation, math objects Representation of mathematical objects sing_958.htm#SEC1015
3814	res sing_340.htm#SEC380
3815	resbinomial.lib sing_1496.htm#IDX670
3816	resbinomial_lib sing_1496.htm#IDX671
3817	reservedName sing_341.htm#SEC381
3818	resfunction sing_1510.htm#SEC1591
3819	resgraph.lib sing_1528.htm#SEC1609
3820	resgraph_lib sing_1528.htm#SEC1609
3821	resjung.lib sing_1532.htm#SEC1613
3822	resjung_lib sing_1532.htm#SEC1613
3823	reslist sing_1524.htm#SEC1605
3824	resolution purityfiltration_lib sing_161.htm#SEC201
3825	resolution sing_771.htm#IDX389
3826	resolution (plural) sing_450.htm#SEC490
3827	resolution declarations resolution declarations sing_162.htm#SEC202
3828	resolution declarations (plural) resolution declarations (plural) sing_451.htm#SEC491
3829	resolution expressions resolution expressions sing_163.htm#SEC203
3830	resolution expressions (plural) resolution expressions (plural) sing_452.htm#SEC492
3831	resolution graph sing_1578.htm#IDX684
3832	resolution related functions resolution related functions sing_164.htm#SEC204
3833	resolution related functions (plural) resolution related functions (plural) sing_453.htm#SEC493
3834	resolution, La Scala's method sing_291.htm#SEC331
3835	resolution, computation of sing_340.htm#IDX186
3836	resolution, hilbert-driven sing_266.htm#SEC306
3837	resolutionInLocalization resolutionInLocalization sing_2597.htm#SEC2678
3838	resolutiongraph sing_1579.htm#SEC1660
3839	resolve sing_1540.htm#SEC1621
3840	resolve.lib sing_1536.htm#SEC1617
3841	resolve_lib sing_1536.htm#SEC1617
3842	resources.lib sing_1104.htm#SEC1185
3843	resources_lib sing_1104.htm#SEC1185
3844	restriction sing_2310.htm#IDX905
3845	restriction sing_2326.htm#IDX938
3846	restriction sing_2327.htm#IDX940
3847	restriction of sing_560.htm#IDX344
3848	restrictionIdeal sing_570.htm#SEC624
3849	restrictionModule sing_571.htm#SEC625
3850	resultant sing_305.htm#SEC345
3851	resultant sing_342.htm#SEC382
3852	reszeta.lib sing_1549.htm#SEC1630
3853	reszeta_lib sing_1549.htm#SEC1630
3854	return sing_395.htm#SEC435
3855	return type of procedures Return type of procedures sing_420.htm#SEC460
3856	returnSB, option sing_318.htm#IDX152
3857	reverse sing_2125.htm#SEC2206
3858	reverse lexicographical ordering sing_962.htm#IDX429
3859	reynolds_molien sing_1756.htm#SEC1837
3860	rho sing_2016.htm#SEC2097
3861	rightInverse sing_1954.htm#SEC2035
3862	rightKernel sing_1952.htm#SEC2033
3863	rightModulo sing_735.htm#SEC789
3864	rightNF sing_734.htm#SEC788
3865	rightNFWeyl sing_686.htm#SEC740
3866	rightOre sing_755.htm#SEC809
3867	rightStd sing_733.htm#SEC787
3868	rightstd (letterplace) rightstd (letterplace) sing_803.htm#SEC857
3869	ring sing_165.htm#SEC205
3870	ring (plural) sing_454.htm#SEC494
3871	ring coefficients hasTransExtensionCoefficient sing_1130.htm#IDX542
3872	ring coefficients sing_1131.htm#IDX543
3873	ring declarations sing_167.htm#SEC207
3874	ring declarations (plural) ring declarations (plural) sing_455.htm#SEC495
3875	ring operations sing_169.htm#SEC209
3876	ring operations (plural) ring operations (plural) sing_456.htm#SEC496
3877	ring related functions ring related functions sing_168.htm#SEC208
3878	ring related functions (plural) ring related functions (plural) sing_457.htm#SEC497
3879	ring theory sing_849.htm#IDX404
3880	ring, opposite sing_361.htm#IDX227
3881	ring.lib sing_1109.htm#SEC1190
3882	ring_cf sing_210.htm#IDX138
3883	ring_lib sing_1109.htm#SEC1190
3884	ring_list sing_344.htm#SEC384
3885	ring_variable sing_2297.htm#IDX882
3886	ring_variable sing_2298.htm#IDX884
3887	ring_variable sing_2299.htm#IDX888
3888	ring_variable sing_2300.htm#IDX890
3889	ringlist sing_343.htm#SEC383
3890	ringlist (plural) sing_482.htm#SEC522
3891	ringtensor sing_1121.htm#SEC1202
3892	ringweights sing_1122.htm#SEC1203
3893	rinvar.lib sing_1792.htm#SEC1873
3894	rinvar_lib sing_1792.htm#SEC1873
3895	rmNmzFiles sing_1389.htm#SEC1470 32601
3896	rm_unitcol sing_1179.htm#SEC1260
3897	rm_unitrow sing_1178.htm#SEC1259
3898	rmx sing_1899.htm#SEC1980
3899	rncAntiCanonicalMap sing_1488.htm#SEC1569
3900	rncItProjEven sing_1492.htm#SEC1573
3901	rncItProjOdd sing_1491.htm#SEC1572
3902	root of Bernstein-Sato polynomial sing_537.htm#IDX333
3903	rootIsolation sing_2827.htm#SEC2908
3904	rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2826.htm#SEC2907
3905	rootIsolationPrimdec rootIsolationPrimdec sing_2828.htm#SEC2909
3906	rootisolation.lib sing_2816.htm#SEC2897
3907	rootisolation_lib sing_2816.htm#SEC2897
3908	rootofUnity sing_1124.htm#SEC1205
3909	roots sing_1866.htm#SEC1947
3910	rootsMain sing_1874.htm#SEC1955
3911	rootsModp sing_1998.htm#SEC2079
3912	rootsmr.lib sing_2095.htm#SEC2176
3913	rootsmr_lib sing_2095.htm#SEC2176
3914	rootsur.lib sing_2111.htm#SEC2192
3915	rootsur_lib sing_2111.htm#SEC2192
3916	round sing_1996.htm#SEC2077
3917	rowShift sing_210.htm#IDX141
3918	rowShift sing_212.htm#SEC252
3919	rowred sing_1175.htm#SEC1256
3920	rp, global ordering sing_962.htm#IDX428
3921	rstandard.lib sing_2829.htm#SEC2910
3922	rstandard_lib sing_2829.htm#SEC2910
3923	rswalk sing_2879.htm#SEC2960
3924	rtimer sing_408.htm#SEC448
3925	rvalue No rvalue of increments and assignments sing_414.htm#SEC454
3926	rvar sing_345.htm#SEC385
3927	rwalk sing_2836.htm#SEC2917
3928	rwalk.lib sing_2834.htm#SEC2915
3929	rwalk_lib sing_2834.htm#SEC2915
3930	sRes sing_2683.htm#SEC2764
3931	sa_poly_reduce sing_525.htm#SEC579
3932	sa_reduce sing_524.htm#SEC578
3933	sagbi sing_1442.htm#SEC1523
3934	sagbi basis sing_2459.htm#IDX994
3935	sagbi.lib sing_1439.htm#SEC1520
3936	sagbiAlg sing_2452.htm#SEC2533
3937	sagbiMod sing_2453.htm#SEC2534
3938	sagbiPart sing_1443.htm#SEC1524
3939	sagbiReduce sing_1441.htm#SEC1522
3940	sagbiSPoly sing_1440.htm#SEC1521
3941	sagbi_lib sing_1439.htm#SEC1520
3942	salida sing_1521.htm#SEC1602
3943	sameComponent sing_2078.htm#SEC2159
3944	sameQ sing_1877.htm#SEC1958
3945	sat sing_1244.htm#SEC1325
3946	satiety sing_1336.htm#SEC1417
3947	satstd sing_2338.htm#SEC2419
3948	saturation sing_1244.htm#IDX555
3949	saturation sing_1294.htm#IDX596
3950	saturation sing_1346.htm#IDX604
3951	saturation sing_1347.htm#IDX605
3952	sba sing_346.htm#SEC386
3953	scalarProd sing_514.htm#SEC568
3954	scheme sing_2558.htm#SEC2639
3955	schubert.lib sing_2838.htm#SEC2919
3956	schubert_lib sing_2838.htm#SEC2919
3957	sdb, source code debugger Source code debugger sing_66.htm#SEC103
3958	second degree sing_1043.htm#IDX511
3959	secondary fan sing_2189.htm#IDX856
3960	secondary polytope sing_2189.htm#IDX857
3961	secondaryPolytope sing_2194.htm#SEC2275
3962	secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1777.htm#SEC1858
3963	secondary_char0 sing_1772.htm#SEC1853
3964	secondary_charp sing_1774.htm#SEC1855
3965	secondary_no_molien sing_1775.htm#SEC1856
3966	secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1778.htm#SEC1859
3967	segre sing_2386.htm#SEC2467
3968	select sing_1245.htm#SEC1326
3969	select1 sing_1246.htm#SEC1327
3970	semaphore sing_361.htm#IDX247
3971	semaphore sing_1108.htm#SEC1189
3972	semaphores sing_1104.htm#IDX537
3973	semi-prime ideal sing_849.htm#IDX409
3974	semiCMcod2 sing_1733.htm#SEC1814
3975	semiGroup sing_2454.htm#SEC2535
3976	semiMod sing_2455.htm#SEC2536
3977	semidiv sing_2070.htm#SEC2151
3978	semigroup sing_1582.htm#SEC1663
3979	semigroup sing_1586.htm#IDX691
3980	semigroup of values sing_1672.htm#IDX806
3981	semigroupGenerator sing_2167.htm#SEC2248
3982	sep sing_1419.htm#SEC1500
3983	separateHNE sing_1683.htm#SEC1764
3984	separator sing_1319.htm#SEC1400
3985	serreRelations sing_822.htm#SEC876
3986	set sing_2292.htm#IDX868
3987	setBaseMultigrading sing_2728.htm#SEC2809
3988	setLetterplaceAttributes setLetterplaceAttributes sing_867.htm#SEC921
3989	setLinearForms sing_2168.htm#SEC2249
3990	setModuleGrading sing_2740.htm#SEC2821
3991	setMultiplicity sing_2169.htm#SEC2250
3992	setNmzDataPath sing_1386.htm#SEC1467 18123
3993	setNmzExecPath sing_1382.htm#SEC1463 38993
3994	setNmzFilename sing_1385.htm#SEC1466 20206
3995	setNmzOption sing_1379.htm#SEC1460 9012
3996	setUniformizingParameter setUniformizingParameter sing_2881.htm#SEC2962
3997	set_is_injective sing_2058.htm#SEC2139
3998	setcores sing_1106.htm#SEC1187
3999	setenv sing_361.htm#IDX250
4000	setinitials sing_2568.htm#SEC2649
4001	setring sing_347.htm#SEC387
4002	sh sing_361.htm#IDX252
4003	shared sing_200.htm#SEC240
4004	shared declarations sing_203.htm#SEC243
4005	shared expressions sing_204.htm#SEC244
4006	shared operations reference and shared operations sing_205.htm#SEC245
4007	shared related functions reference and shared related functions sing_206.htm#SEC246
4008	sheaf cohomology sing_1559.htm#IDX672
4009	sheafCoh sing_1565.htm#SEC1646 64501
4010	sheafCohBGG sing_1563.htm#SEC1644 13439
4011	sheafCohBGG2 sing_1564.htm#SEC1645 3338
4012	sheafcoh.lib sing_1559.htm#SEC1640
4013	sheafcoh_lib sing_1559.htm#SEC1640
4014	short sing_405.htm#SEC445
4015	show sing_1057.htm#SEC1138
4016	showBO sing_1541.htm#SEC1622
4017	showDataTypes sing_1543.htm#SEC1624
4018	showNmzOptions sing_1380.htm#SEC1461 64955
4019	showNuminvs sing_1377.htm#SEC1458 18934
4020	showgrades sing_776.htm#SEC830
4021	showrecursive sing_1058.htm#SEC1139
4022	signal handler sing_2908.htm#SEC3005
4023	signatureBrieskorn sing_1742.htm#SEC1823
4024	signatureL sing_2340.htm#SEC2421
4025	signatureLqf sing_2341.htm#SEC2422
4026	signatureNemethi sing_1744.htm#SEC1825
4027	signaturePuiseux sing_1743.htm#SEC1824
4028	signcnd sing_1879.htm#SEC1960
4029	signcond.lib sing_1878.htm#SEC1959
4030	signcond_lib sing_1878.htm#SEC1959
4031	simplePrune sing_2721.htm#SEC2802
4032	simplesolver sing_1823.htm#SEC1904
4033	simplex sing_348.htm#SEC388
4034	simplexOut sing_1850.htm#SEC1931
4035	simplify sing_349.htm#SEC389
4036	simplifyRat sing_681.htm#SEC735
4037	sing.lib sing_1709.htm#SEC1790
4038	sing4ti2.lib sing_1445.htm#SEC1526
4039	sing4ti2_lib sing_1445.htm#SEC1526
4040	sing_lib sing_1709.htm#SEC1790
4041	singular locus of D-module sing_661.htm#IDX369
4042	singularities sing_1641.htm#IDX708
4043	singularities sing_1642.htm#IDX719
4044	singularities sing_1643.htm#IDX722
4045	singularities sing_1644.htm#IDX725
4046	singularities sing_1645.htm#IDX728
4047	singularities sing_1646.htm#IDX732
4048	singularities sing_1647.htm#IDX736
4049	singularities sing_1648.htm#IDX742
4050	singularities sing_1649.htm#IDX750
4051	singularities sing_1650.htm#IDX756
4052	singularities sing_1651.htm#IDX764
4053	singularities sing_1652.htm#IDX774
4054	singularities sing_1740.htm#IDX821
4055	singularities sing_2364.htm#IDX980
4056	singularities sing_2448.htm#IDX989
4057	singularities, resolution of Resolution of singularities sing_945.htm#SEC1002
4058	singularity sing_1606.htm#SEC1687
4059	singularrc sing_20.htm#IDX73
4060	size Miscellaneous oddities sing_350.htm#SEC390
4061	size sing_422.htm#IDX291
4062	skewmat sing_1163.htm#SEC1244
4063	sleep sing_356.htm#SEC396
4064	slimgb sing_351.htm#SEC391
4065	slimgb sing_922.htm#SEC979
4066	slimgb (plural) sing_483.htm#SEC523
4067	slocus sing_1721.htm#SEC1802
4068	smaller sing_2503.htm#IDX1057
4069	smatrix sing_171.htm#SEC211
4070	smith sing_1963.htm#SEC2044
4071	smithNormalForm sing_2776.htm#SEC2857
4072	solutionsMod2 sing_2013.htm#SEC2094
4073	solve sing_1043.htm#IDX512
4074	solve sing_1844.htm#SEC1925
4075	solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_294.htm#SEC334
4076	solve.lib sing_1842.htm#SEC1923
4077	solveTInitialFormPar solveTInitialFormPar sing_2275.htm#SEC2356
4078	solve_IP sing_1289.htm#SEC1370
4079	solve_lib sing_1842.htm#SEC1923
4080	solvelinearpart sing_1837.htm#SEC1918
4081	sort sing_1019.htm#SEC1100
4082	sort sing_2508.htm#IDX1067
4083	sortIntvec sing_591.htm#SEC645
4084	sortandmap sing_1838.htm#SEC1919
4085	sortier sing_1791.htm#SEC1872
4086	sortvars sing_1839.htm#SEC1920
4087	sortvec sing_352.htm#SEC392
4088	source sing_2699.htm#SEC2780
4089	source code debugger, sdb Source code debugger sing_66.htm#SEC103
4090	spaceCur sing_2457.htm#SEC2538
4091	spadd sing_1655.htm#SEC1736
4092	span sing_2170.htm#SEC2251
4093	sparseHomogIdeal sing_1100.htm#SEC1181
4094	sparseInterpolation sing_2553.htm#SEC2634
4095	sparseid sing_1095.htm#SEC1176
4096	sparsemat sing_1097.htm#SEC1178
4097	sparsematrix sing_1096.htm#SEC1177
4098	sparsepoly sing_1098.htm#SEC1179
4099	sparsetriag sing_1099.htm#SEC1180
4100	spcurve.lib sing_1729.htm#SEC1810
4101	spcurve_lib sing_1729.htm#SEC1810
4102	special characters, non-english sing_411.htm#IDX284
4103	spectral pairs sing_1641.htm#IDX717
4104	spectral pairs sing_1648.htm#IDX749
4105	spectral pairs sing_1650.htm#IDX763
4106	spectral pairs sing_1651.htm#IDX772
4107	spectral pairs sing_1663.htm#IDX788
4108	spectral pairs sing_1665.htm#IDX799
4109	spectralNeg sing_1551.htm#SEC1632
4110	spectrum sing_1641.htm#IDX716
4111	spectrum sing_1647.htm#SEC1728
4112	spectrum sing_1647.htm#IDX741
4113	spectrum sing_1648.htm#IDX748
4114	spectrum sing_1649.htm#IDX755
4115	spectrum sing_1650.htm#IDX762
4116	spectrum sing_1651.htm#IDX771
4117	spectrum sing_1663.htm#IDX787
4118	spectrum sing_1665.htm#IDX798
4119	spectrum sing_1740.htm#IDX823
4120	spectrum.lib sing_1739.htm#SEC1820
4121	spectrum_lib sing_1739.htm#SEC1820
4122	spectrumnd sing_1740.htm#SEC1821
4123	spgamma sing_1662.htm#SEC1743
4124	spgeomgenus sing_1661.htm#SEC1742
4125	spissemicont sing_1658.htm#SEC1739
4126	split sing_1059.htm#SEC1140
4127	splitPolygon sing_2196.htm#SEC2277
4128	splitring sing_1431.htm#SEC1512
4129	splitting sing_1327.htm#SEC1408
4130	spmilnor sing_1660.htm#SEC1741
4131	spmul sing_1657.htm#SEC1738
4132	spnf sing_1205.htm#SEC1286
4133	spoly sing_2081.htm#SEC2162
4134	sppairs sing_1648.htm#SEC1729
4135	sppnf sing_1653.htm#SEC1734
4136	sppprint sing_1654.htm#SEC1735
4137	spprint sing_1206.htm#SEC1287
4138	sprintf sing_354.htm#SEC394
4139	spsemicont sing_1659.htm#SEC1740
4140	spsub sing_1656.htm#SEC1737
4141	sqfrNorm sing_1867.htm#SEC1948
4142	sqfrNormMain sing_1875.htm#SEC1956
4143	sqr sing_1993.htm#SEC2074
4144	sqrfree sing_353.htm#SEC393
4145	squareRoot sing_2012.htm#SEC2093
4146	squarefree sing_1684.htm#SEC1765
4147	sres sing_355.htm#SEC395
4148	ssi Parallelization with ssi links sing_917.htm#SEC974
4149	stabilizer sing_2377.htm#SEC2458
4150	stack, moduli space of stable maps sing_2862.htm#IDX1211
4151	stack, moduli space of stable maps, rational curves moduliSpace sing_2861.htm#IDX1210
4152	stackNets sing_2804.htm#SEC2885
4153	staircase sing_1884.htm#SEC1965
4154	standard sing_2088.htm#SEC2169
4155	standard bases, saturation sing_2338.htm#IDX951
4156	standard bases. sing_2337.htm#IDX950
4157	standard.lib sing_996.htm#IDX456
4158	standard_lib sing_996.htm#IDX457
4159	startNmz sing_1388.htm#SEC1469 21925
4160	startTasks sing_1143.htm#SEC1224
4161	static procedures Procedure definition sing_43.htm#SEC78
4162	status sing_356.htm#SEC396
4163	std sing_357.htm#SEC397
4164	std sing_920.htm#SEC977
4165	std (letterplace) sing_804.htm#SEC858
4166	std (plural) sing_484.htm#SEC524
4167	stdfglm sing_358.htm#SEC398
4168	stdhilb sing_359.htm#SEC399
4169	stdlocus sing_1040.htm#SEC1121
4170	stopTask sing_1144.htm#SEC1225
4171	storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2617.htm#SEC2698
4172	stratify sing_1818.htm#SEC1899
4173	stratify.lib sing_1816.htm#SEC1897
4174	stratify_lib sing_1816.htm#SEC1897
4175	string Miscellaneous oddities sing_172.htm#SEC212
4176	string sing_422.htm#IDX294
4177	string sing_2490.htm#IDX1030
4178	string sing_2492.htm#IDX1035
4179	string sing_2493.htm#IDX1038
4180	string sing_2515.htm#IDX1084
4181	string sing_2516.htm#IDX1087
4182	string declarations sing_173.htm#SEC213
4183	string expressions sing_174.htm#SEC214
4184	string operations sing_176.htm#SEC216
4185	string related functions string related functions sing_177.htm#SEC217
4186	string type cast sing_175.htm#SEC215
4187	stripHNE sing_1681.htm#SEC1762
4188	structure sing_2512.htm#IDX1078
4189	sturm sing_2121.htm#SEC2202
4190	sturmha sing_2123.htm#SEC2204
4191	sturmhaseq sing_2124.htm#SEC2205
4192	sturmquery sing_2099.htm#SEC2180
4193	sturmseq sing_2122.htm#SEC2203
4194	sublists sing_2471.htm#SEC2552
4195	submat sing_1164.htm#SEC1245
4196	subquotient sing_2691.htm#SEC2772
4197	subrInterred sing_1088.htm#SEC1169
4198	subset_sum01 sing_2042.htm#SEC2123
4199	subset_sum02 sing_2043.htm#SEC2124
4200	subst sing_360.htm#SEC400
4201	subst (plural) sing_485.htm#SEC525
4202	substitute sing_1087.htm#SEC1168
4203	sugarCrit, option sing_318.htm#IDX169
4204	sum sing_1020.htm#SEC1101
4205	sum sing_2495.htm#IDX1041
4206	sum sing_2517.htm#IDX1089
4207	sum_of_powers sing_2390.htm#SEC2471
4208	sumlist sing_1523.htm#SEC1604
4209	sumofquotients sing_2870.htm#SEC2951
4210	super-commutative algebras Graded commutative algebras (SCA) sing_791.htm#SEC845
4211	superCommutative sing_732.htm#SEC786
4212	super_increasing_knapsack super_increasing_knapsack sing_2054.htm#SEC2135
4213	surf.lib sing_1901.htm#SEC1982
4214	surf_lib sing_1901.htm#SEC1982
4215	surfacesignature.lib surfacesignature_lib sing_1741.htm#SEC1822
4216	surfacesignature_lib surfacesignature_lib sing_1741.htm#SEC1822
4217	surfer sing_1.htm#IDX8
4218	surfer sing_1903.htm#SEC1984
4219	surfex sing_1.htm#IDX7
4220	surfex.lib sing_1904.htm#SEC1985
4221	surfex_lib sing_1904.htm#SEC1985
4222	suspend sing_356.htm#SEC396
4223	swalk sing_2878.htm#SEC2959
4224	swalk.lib sing_2877.htm#SEC2958
4225	swalk_lib sing_2877.htm#SEC2958
4226	swap sing_1610.htm#SEC1691
4227	swap sing_2299.htm#IDX886
4228	switch No case or switch statement sing_416.htm#SEC456
4229	switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2886.htm#SEC2967
4230	syModStd sing_1455.htm#SEC1536
4231	symNsym sing_2384.htm#SEC2465
4232	sym_gauss sing_1189.htm#SEC1270
4233	symm sing_2383.htm#SEC2464
4234	symmStd sing_1454.htm#SEC1535
4235	symmat sing_1165.htm#SEC1246
4236	symmetric basis sing_1181.htm#IDX548
4237	symmetric power sing_1183.htm#IDX550
4238	symmetric product sing_2579.htm#IDX1137
4239	symmetricBasis sing_1181.htm#SEC1262
4240	symmetricPower sing_1183.htm#SEC1264
4241	symmetricPowerSheaf sing_2856.htm#SEC2937
4242	symmetries sing_2373.htm#IDX988
4243	symmfunc sing_2108.htm#SEC2189
4244	symodstd.lib sing_1449.htm#SEC1530
4245	symodstd_lib sing_1449.htm#SEC1530
4246	sympower sing_1812.htm#SEC1893
4247	symsignature sing_2098.htm#SEC2179
4248	syndrome sing_1931.htm#SEC2012
4249	sysBin sing_1929.htm#SEC2010
4250	sysCRHT sing_1926.htm#SEC2007
4251	sysCRHTMindist sing_1927.htm#SEC2008
4252	sysFL sing_1942.htm#SEC2023
4253	sysNewton sing_1928.htm#SEC2009
4254	sysQE sing_1932.htm#SEC2013
4255	sys_code sing_1923.htm#SEC2004
4256	system sing_361.htm#SEC401
4257	system, -- sing_361.htm#IDX274
4258	system, --long_option_name sing_361.htm#IDX277
4259	system, --long_option_name=value sing_361.htm#IDX279
4260	system, HC sing_361.htm#IDX213
4261	system, LLL sing_361.htm#IDX217
4262	system, Singular sing_361.htm#IDX256
4263	system, SingularLib sing_361.htm#IDX258
4264	system, absFact sing_361.htm#IDX190
4265	system, alarm sing_361.htm#IDX189
4266	system, blackbox sing_361.htm#IDX191
4267	system, bracket sing_361.htm#IDX196
4268	system, browsers sing_361.htm#IDX195
4269	system, complexNearZero sing_361.htm#IDX198
4270	system, contributors sing_361.htm#IDX200
4271	system, cpu sing_361.htm#IDX202
4272	system, cpu sing_361.htm#IDX273
4273	system, denom_list sing_361.htm#IDX204
4274	system, eigenvals sing_361.htm#IDX205
4275	system, env sing_361.htm#IDX206
4276	system, executable sing_361.htm#IDX208
4277	system, getPrecDigits sing_361.htm#IDX211
4278	system, getenv sing_361.htm#IDX210
4279	system, gmsnf sing_361.htm#IDX212
4280	system, hessenberg sing_361.htm#IDX214
4281	system, install sing_361.htm#IDX216
4282	system, nblocks sing_361.htm#IDX220
4283	system, nc_hilb sing_361.htm#IDX222
4284	system, neworder sing_361.htm#IDX223
4285	system, newstruct sing_361.htm#IDX224
4286	system, opp sing_361.htm#IDX225
4287	system, oppose sing_361.htm#IDX228
4288	system, pcvBasis sing_361.htm#IDX237
4289	system, pcvCV2P sing_361.htm#IDX235
4290	system, pcvDim sing_361.htm#IDX236
4291	system, pcvLAddL sing_361.htm#IDX231
4292	system, pcvMinDeg sing_361.htm#IDX233
4293	system, pcvP2CV sing_361.htm#IDX234
4294	system, pcvPMulL sing_361.htm#IDX232
4295	system, pid sing_361.htm#IDX239
4296	system, random sing_361.htm#IDX241
4297	system, reserve sing_361.htm#IDX245
4298	system, reservedLink sing_361.htm#IDX246
4299	system, semaphore sing_361.htm#IDX248
4300	system, semic sing_361.htm#IDX249
4301	system, setenv sing_361.htm#IDX251
4302	system, sh sing_361.htm#IDX253
4303	system, shrinktest sing_361.htm#IDX254
4304	system, spadd sing_361.htm#IDX259
4305	system, spectrum sing_361.htm#IDX260
4306	system, spmul sing_361.htm#IDX261
4307	system, std_syz sing_361.htm#IDX262
4308	system, tensorModuleMult sing_361.htm#IDX263
4309	system, twostd sing_361.htm#IDX264
4310	system, uname sing_361.htm#IDX267
4311	system, version sing_361.htm#IDX270
4312	system, with sing_361.htm#IDX271
4313	systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2594.htm#SEC2675
4314	syz sing_362.htm#SEC402
4315	syz (letterplace) sing_805.htm#SEC859
4316	syz (plural) sing_486.htm#SEC526
4317	tDetropicalise sing_2277.htm#SEC2358
4318	tInitialForm sing_2261.htm#SEC2342
4319	tInitialFormPar sing_2273.htm#SEC2354
4320	tInitialFormParMax sing_2274.htm#SEC2355
4321	tInitialIdeal sing_2262.htm#SEC2343
4322	tab sing_1060.htm#SEC1141
4323	tail sing_2077.htm#SEC2158
4324	tame polynomial sing_1663.htm#IDX780
4325	tame polynomial sing_1664.htm#IDX790
4326	tame polynomial sing_1665.htm#IDX791
4327	tangentGens sing_1479.htm#SEC1560
4328	tangentcone sing_1728.htm#SEC1809
4329	target sing_2698.htm#SEC2779
4330	task sing_1137.htm#IDX547
4331	tasks.lib sing_1137.htm#SEC1218
4332	tasks_lib sing_1137.htm#SEC1218
4333	tau_es sing_1636.htm#SEC1717
4334	tau_es2 sing_1590.htm#SEC1671
4335	tdCf sing_2419.htm#SEC2500
4336	tdFactor sing_2421.htm#SEC2502
4337	tdProj sing_2424.htm#SEC2505
4338	tdTerms sing_2420.htm#SEC2501
4339	teachstd.lib sing_2075.htm#SEC2156
4340	teachstd_lib sing_2075.htm#SEC2156
4341	template.lib sing_55.htm#IDX120
4342	template.lib sing_55.htm#IDX123
4343	template_lib sing_55.htm#SEC92
4344	template_lib sing_55.htm#IDX121
4345	tensor sing_363.htm#SEC403
4346	tensor sing_495.htm#IDX308
4347	tensor algebra sing_856.htm#IDX412
4348	tensorFreeModule sing_2710.htm#SEC2791
4349	tensorFreemodMod sing_2709.htm#SEC2790
4350	tensorMatrix sing_2706.htm#SEC2787
4351	tensorMod sing_1284.htm#SEC1365
4352	tensorModFreemod sing_2708.htm#SEC2789
4353	tensorModule sing_2707.htm#SEC2788
4354	tensorProduct sing_2711.htm#SEC2792
4355	tensorSheaf sing_2855.htm#SEC2936
4356	term orderings General definitions for orderings sing_961.htm#SEC1018
4357	term orderings introduction Introduction to orderings sing_960.htm#SEC1017
4358	testFraction sing_753.htm#SEC807
4359	testLift sing_868.htm#SEC922
4360	testLocData sing_750.htm#SEC804
4361	testNCfac sing_651.htm#SEC705
4362	testNcfrac sing_699.htm#SEC753
4363	testNcfracExamples sing_700.htm#SEC754
4364	testNcloc sing_711.htm#SEC765
4365	testNclocExamples sing_712.htm#SEC766
4366	testOlga sing_767.htm#SEC821
4367	testOlgaExamples sing_768.htm#SEC822
4368	testParametrization sing_1494.htm#SEC1575
4369	testPointConic sing_1495.htm#SEC1576
4370	testPrimary sing_1407.htm#SEC1488
4371	testPrimaryE sing_1408.htm#SEC1489
4372	testSyz sing_869.htm#SEC923
4373	tetrahedronGroup sing_847.htm#SEC901
4374	tex sing_1890.htm#SEC1971
4375	texDrawBasic sing_2268.htm#SEC2349
4376	texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2270.htm#SEC2351
4377	texDrawTriangulation texDrawTriangulation sing_2271.htm#SEC2352
4378	texDrawTropical sing_2269.htm#SEC2350
4379	texMatrix sing_2267.htm#SEC2348
4380	texNumber sing_2265.htm#SEC2346
4381	texPolynomial sing_2266.htm#SEC2347
4382	texcoef sing_1971.htm#SEC2052
4383	texdemo sing_1891.htm#SEC1972
4384	texfactorize sing_1892.htm#SEC1973
4385	texmap sing_1893.htm#SEC1974
4386	texname sing_1894.htm#SEC1975
4387	texobj sing_1895.htm#SEC1976
4388	texpoly sing_1896.htm#SEC1977
4389	texproc sing_1897.htm#SEC1978
4390	texring sing_1898.htm#SEC1979
4391	the first alternative algorithm sing_1261.htm#IDX584
4392	three_elements sing_2061.htm#SEC2142
4393	timeFactorize sing_1024.htm#SEC1105
4394	timeStd sing_1023.htm#SEC1104
4395	timer sing_406.htm#SEC446
4396	timer resolution, setting the sing_361.htm#IDX280
4397	timestep sing_2571.htm#SEC2652
4398	tjurina sing_1724.htm#SEC1805
4399	tmatrix sing_1651.htm#SEC1732
4400	todd sing_2416.htm#SEC2497
4401	toddE sing_2417.htm#SEC2498
4402	toddPoly sing_2430.htm#SEC2511
4403	tolessvars sing_1836.htm#SEC1917
4404	topChernClass sing_2852.htm#SEC2933
4405	topological invariants sing_1578.htm#IDX682
4406	topological invariants sing_1585.htm#IDX689
4407	topological invariants sing_1586.htm#IDX693
4408	topological invariants sing_1587.htm#IDX697
4409	topological invariants sing_1588.htm#IDX701
4410	toric ideals sing_976.htm#SEC1038
4411	toric ring sing_1366.htm#IDX623
4412	toric.lib sing_1456.htm#SEC1537
4413	toric_ideal sing_1457.htm#SEC1538
4414	toric_lib sing_1456.htm#SEC1537
4415	toric_std sing_1458.htm#SEC1539
4416	torus sing_1809.htm#SEC1890
4417	torusInvariants sing_1372.htm#SEC1453 911
4418	torusrep sing_1810.htm#SEC1891
4419	torusreynolds sing_1815.htm#SEC1896
4420	total divisors sing_495.htm#IDX305
4421	total multiplicities sing_1578.htm#IDX685
4422	totalChernClass sing_2850.htm#SEC2931
4423	totalSegreClass sing_2853.htm#SEC2934
4424	totalmultiplicities sing_1580.htm#SEC1661
4425	trace sing_364.htm#SEC404
4426	tracemult sing_2102.htm#SEC2183
4427	transpose sing_365.htm#SEC405
4428	trapezoid sing_2565.htm#SEC2646
4429	triMNewton sing_1862.htm#SEC1943
4430	triagmatrix sing_1101.htm#SEC1182
4431	triang.lib sing_1855.htm#SEC1936
4432	triangL sing_1856.htm#SEC1937
4433	triangL_solve sing_1853.htm#SEC1934
4434	triangLf_solve sing_1851.htm#SEC1932
4435	triangLfak sing_1857.htm#SEC1938
4436	triangM sing_1858.htm#SEC1939
4437	triangMH sing_1859.htm#SEC1940
4438	triangM_solve sing_1852.htm#SEC1933
4439	triang_lib sing_1855.htm#SEC1936
4440	triang_solve sing_1854.htm#SEC1935
4441	triangularGroup sing_848.htm#SEC902
4442	triangulations sing_2193.htm#SEC2274
4443	tropical curves sing_2247.htm#IDX863
4444	tropical geometry sing_1247.htm#IDX558
4445	tropical geometry sing_2880.htm#IDX1222
4446	tropical mirror symmetry sing_1247.htm#IDX560
4447	tropical polynomials sing_2247.htm#IDX864
4448	tropical varieties sing_2880.htm#IDX1223
4449	tropical.lib sing_2247.htm#IDX861
4450	tropicalCurve sing_2252.htm#SEC2333
4451	tropicalJInvariant sing_2255.htm#SEC2336
4452	tropicalLifting sing_2248.htm#SEC2329
4453	tropicalLinkNewton sing_2888.htm#SEC2969
4454	tropicalNewton.lib sing_2880.htm#SEC2961
4455	tropicalNewton_lib sing_2880.htm#SEC2961
4456	tropicalPointNewton sing_2885.htm#SEC2966
4457	tropicalSubst sing_2280.htm#SEC2361
4458	tropicalVariety sing_2287.htm#SEC2368
4459	tropicalVarietyNewton tropicalVarietyNewton sing_2887.htm#SEC2968
4460	tropical_lib sing_2247.htm#IDX862
4461	tropicalise sing_2259.htm#SEC2340
4462	tropicaliseSet sing_2260.htm#SEC2341
4463	truncate sing_1560.htm#SEC1641 13545
4464	truncateFast sing_1561.htm#SEC1642 22046
4465	truncated module sing_1560.htm#IDX673
4466	truncated module sing_1561.htm#IDX674
4467	tst_ncfactor sing_660.htm#SEC714
4468	twalk sing_1260.htm#SEC1341
4469	two-sided sing_495.htm#IDX306
4470	two-sided Groebner basis sing_495.htm#IDX307
4471	twostd sing_361.htm#IDX265
4472	twostd (letterplace) twostd (letterplace) sing_806.htm#SEC860
4473	twostd (plural) sing_487.htm#SEC527
4474	type sing_366.htm#SEC406
4475	type B sing_2315.htm#IDX913
4476	type D sing_2316.htm#IDX915
4477	type,custom Definition of a user defined type sing_184.htm#SEC224
4478	type2arr sing_2293.htm#SEC2374
4479	typecasting sing_2293.htm#IDX869
4480	typecasting sing_2294.htm#IDX871
4481	typecasting sing_2295.htm#IDX874
4482	typeof sing_367.htm#SEC407
4483	u sing_2557.htm#SEC2638
4484	uname sing_361.htm#IDX266
4485	unbounded_knapsack sing_2044.htm#SEC2125
4486	unipotent groups sing_1478.htm#IDX641
4487	uniquePoint sing_2171.htm#SEC2252
4488	unitMatrix sing_2822.htm#SEC2903
4489	unitmat sing_1166.htm#SEC1247
4490	univariate sing_368.htm#SEC408
4491	univarpoly sing_2109.htm#SEC2190
4492	universal sing_2509.htm#IDX1070
4493	universal sing_2510.htm#IDX1072
4494	universal derivation diffAlgebraUnivDerIdeal sing_2485.htm#IDX1021
4495	unknown syndrome Decoding method based on quadratic equations sing_992.htm#SEC1068
4496	unset sing_279.htm#SEC319
4497	untyped definitions sing_88.htm#SEC128
4498	untyped definitions sing_427.htm#SEC467
4499	updatePairs sing_2087.htm#SEC2168
4500	ures_solve sing_1845.htm#SEC1926
4501	uressolve sing_369.htm#SEC409
4502	usage, option sing_318.htm#IDX185
4503	used environment variables Used environment variables sing_2910.htm#SEC3007
4504	user interface, Emacs Emacs user interface sing_21.htm#SEC28
4505	vStd sing_2463.htm#SEC2544
4506	val sing_2882.htm#SEC2963
4507	valvars sing_1840.htm#SEC1921
4508	vandermonde sing_370.htm#SEC410
4509	vanishId sing_1941.htm#SEC2022
4510	var sing_371.htm#SEC411
4511	varMat sing_2297.htm#SEC2378
4512	varNum sing_2298.htm#SEC2379
4513	variables sing_372.htm#SEC412
4514	variables sing_2297.htm#IDX881
4515	variables sing_2298.htm#IDX883
4516	variables sing_2299.htm#IDX887
4517	variables sing_2300.htm#IDX889
4518	variablesSorted sing_533.htm#SEC587
4519	variablesStandard sing_532.htm#SEC586
4520	vars2pars sing_676.htm#SEC730
4521	varsigns sing_2114.htm#SEC2195
4522	varstr sing_373.htm#SEC413
4523	vdim sing_374.htm#SEC414
4524	vdim (plural) sing_488.htm#SEC528
4525	vec2poly sing_515.htm#SEC569
4526	vecFieldToMatrix sing_2896.htm#SEC2977
4527	vector sing_178.htm#SEC218
4528	vector declarations sing_179.htm#SEC219
4529	vector expressions sing_180.htm#SEC220
4530	vector operations sing_181.htm#SEC221
4531	vector related functions vector related functions sing_182.htm#SEC222
4532	verify sing_2105.htm#SEC2186
4533	versal sing_1631.htm#SEC1712
4534	version sing_361.htm#IDX269
4535	vertexAdjacencyGraph vertexAdjacencyGraph sing_2240.htm#SEC2321
4536	vertexEdgeGraph sing_2241.htm#SEC2322
4537	vertices sing_2187.htm#SEC2268
4538	vfilt sing_1649.htm#SEC1730
4539	view sing_1961.htm#SEC2042
4540	visual sing_2242.htm#SEC2323
4541	visualize sing_2556.htm#SEC2637
4542	voice sing_409.htm#SEC449
4543	vwfilt sing_1650.htm#SEC1731
4544	wUnit sing_1999.htm#SEC2080
4545	waitAllTasks sing_1146.htm#SEC1227
4546	waitTasks sing_1145.htm#SEC1226
4547	waitall sing_375.htm#SEC415
4548	waitfirst sing_376.htm#SEC416
4549	walk, groebner sing_1258.htm#IDX580
4550	walk, groebner sing_2722.htm#IDX1145
4551	walk, groebner sing_2834.htm#IDX1191
4552	walk, groebner sing_2877.htm#IDX1220
4553	warkedPreimageStd sing_2596.htm#SEC2677
4554	warn, option sing_70.htm#SEC110
4555	warn, option sing_318.htm#IDX151
4556	watchdog sing_1021.htm#SEC1102
4557	wedge sing_377.htm#SEC417
4558	weierstr.lib sing_2090.htm#SEC2171
4559	weierstrDiv sing_2091.htm#SEC2172
4560	weierstrPrep sing_2092.htm#SEC2173
4561	weierstr_lib sing_2090.htm#SEC2171
4562	weierstrassForm sing_2256.htm#SEC2337
4563	weight sing_378.htm#SEC418
4564	weight filtration sing_1641.htm#IDX713
4565	weight filtration sing_1648.htm#IDX747
4566	weight filtration sing_1650.htm#IDX761
4567	weight filtration sing_1651.htm#IDX769
4568	weight filtration sing_1663.htm#IDX785
4569	weight filtration sing_1665.htm#IDX796
4570	weightKB sing_379.htm#SEC419
4571	weightM, option sing_318.htm#IDX170
4572	weighted lexicographical ordering sing_962.htm#IDX436
4573	weighted reverse lexicographical ordering Global orderings sing_962.htm#IDX434
4574	weightedRing sing_725.htm#SEC779
4575	whichvariable sing_2113.htm#SEC2194
4576	while sing_396.htm#SEC436
4577	withDim sing_210.htm#IDX145
4578	withHilb sing_210.htm#IDX143
4579	withMult sing_210.htm#IDX146
4580	withRes sing_210.htm#IDX144
4581	withSB sing_210.htm#IDX142
4582	wp, global ordering sing_962.htm#IDX435
4583	write sing_380.htm#SEC420
4584	writeNmzData sing_1383.htm#SEC1464 38467
4585	writeNmzPaths sing_1387.htm#SEC1468 sprintf
4586	writing monomials sing_405.htm#SEC445
4587	ws, local ordering sing_963.htm#IDX446
4588	wurzel sing_1981.htm#SEC2062
4589	xchange sing_1975.htm#SEC2056
4590	xdvi sing_1900.htm#SEC1981
4591	zdd sing_2344.htm#IDX962
4592	zdd2poly sing_2361.htm#SEC2442 55047
4593	zero sing_2671.htm#SEC2752
4594	zero-dimensional sing_2110.htm#IDX852
4595	zeroMod sing_1323.htm#SEC1404
4596	zeroNcfrac sing_692.htm#SEC746
4597	zeroOpt sing_1332.htm#SEC1413
4598	zeroRadical sing_1229.htm#SEC1310
4599	zeroSet sing_1868.htm#SEC1949
4600	zerodec sing_1416.htm#SEC1497
4601	zeroset.lib sing_1863.htm#SEC1944
4602	zeroset_lib sing_1863.htm#SEC1944
4603	zetaDL sing_1553.htm#SEC1634
4604	{ sing_36.htm#IDX78
4605	\|\| sing_36.htm#IDX103
4606	\|\| sing_101.htm#SEC141
4607	} sing_36.htm#IDX79
4608	~ sing_36.htm#IDX117
4609	~ sing_397.htm#SEC437

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