Context Navigation

singular.idx @ 54fdec1

spielwiese

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

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

Note: See TracBrowser for help on using the repository browser.

Download in other formats:

Original Format