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singular.idx @ 315439

spielwiese

Last change on this file since 315439 was 315439, checked in by Hans Schoenemann <hannes@…>, 6 years ago
doc: final version for 4-1-1
Property mode set to `100644`
File size: 174.2 KB

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1	! sing_36.htm#IDX101
2	!= sing_36.htm#IDX95
3	!= sing_100.htm#SEC140
4	" sing_36.htm#IDX104
5	# sing_36.htm#IDX118
6	$ sing_36.htm#IDX119
7	% sing_36.htm#IDX91
8	% sing_81.htm#SEC121
9	% sing_98.htm#SEC138
10	% sing_110.htm#SEC150
11	% sing_147.htm#SEC187
12	% sing_155.htm#SEC195
13	&& sing_36.htm#IDX102
14	&& sing_101.htm#SEC141
15	( sing_36.htm#IDX80
16	() sing_131.htm#IDX130
17	) sing_36.htm#IDX81
18	* bigintmat operations sing_36.htm#IDX89
19	* sing_81.htm#SEC121
20	* sing_87.htm#SEC127
21	* sing_93.htm#SEC133
22	* sing_98.htm#SEC138
23	* sing_106.htm#SEC146
24	* sing_110.htm#SEC150
25	* sing_137.htm#SEC177
26	* sing_142.htm#SEC182
27	* sing_147.htm#SEC187
28	* sing_155.htm#SEC195
29	** sing_36.htm#IDX93
30	+ bigintmat operations sing_36.htm#IDX85
31	+ sing_81.htm#SEC121
32	+ sing_87.htm#SEC127
33	+ sing_93.htm#SEC133
34	+ sing_98.htm#SEC138
35	+ sing_106.htm#SEC146
36	+ sing_110.htm#SEC150
37	+ sing_126.htm#SEC166
38	+ sing_137.htm#SEC177
39	+ sing_142.htm#SEC182
40	+ sing_147.htm#SEC187
41	+ sing_155.htm#SEC195
42	+ sing_169.htm#SEC209
43	+ sing_175.htm#SEC215
44	+ sing_180.htm#SEC220
45	++ sing_36.htm#IDX86
46	- bigintmat operations sing_36.htm#IDX87
47	- sing_81.htm#SEC121
48	- sing_87.htm#SEC127
49	- sing_98.htm#SEC138
50	- sing_106.htm#SEC146
51	- sing_110.htm#SEC150
52	- sing_137.htm#SEC177
53	- sing_147.htm#SEC187
54	- sing_155.htm#SEC195
55	- sing_180.htm#SEC220
56	-- sing_36.htm#IDX88
57	--MPhost sing_19.htm#IDX66
58	--MPport sing_19.htm#IDX65
59	--allow-net sing_19.htm#IDX39
60	--batch sing_19.htm#IDX64
61	--browser sing_19.htm#IDX43
62	--echo sing_19.htm#IDX35
63	--emacs sing_19.htm#IDX67
64	--emacs-dir sing_19.htm#IDX68
65	--emacs-load sing_19.htm#IDX69
66	--execute sing_19.htm#IDX56
67	--help sing_19.htm#IDX37
68	--min-time sing_19.htm#IDX61
69	--no-out sing_19.htm#IDX49
70	--no-rc sing_19.htm#IDX45
71	--no-shell sing_19.htm#IDX50
72	--no-stdlib sing_19.htm#IDX47
73	--no-tty sing_19.htm#IDX51
74	--no-warn sing_19.htm#IDX48
75	--quiet sing_19.htm#IDX53
76	--random sing_19.htm#IDX60
77	--sdb sing_19.htm#IDX32
78	--singular sing_19.htm#IDX70
79	--ticks-per-sec sing_19.htm#IDX62
80	--user-option sing_19.htm#IDX58
81	-> sing_159.htm#SEC199
82	-MPhost Command line options
83	-MPport Command line options
84	-allow-net Command line options
85	-b Command line options sing_19.htm#IDX63
86	-batch Command line options
87	-browser Command line options
88	-c Command line options sing_19.htm#IDX55
89	-d Command line options sing_19.htm#IDX31
90	-e Command line options sing_19.htm#IDX34
91	-echo Command line options
92	-emacs Command line options
93	-emacs-dir Command line options
94	-emacs-load Command line options
95	-execute Command line options
96	-h Command line options sing_19.htm#IDX36
97	-help Command line options
98	-min-time Command line options
99	-no-out Command line options
100	-no-rc Command line options
101	-no-shell Command line options
102	-no-stdlib Command line options
103	-no-tty Command line options
104	-no-warn Command line options
105	-q Command line options sing_19.htm#IDX52
106	-quiet Command line options
107	-r Command line options sing_19.htm#IDX59
108	-random Command line options
109	-sdb Command line options
110	-singular Command line options
111	-ticks-per-sec Command line options
112	-u Command line options sing_19.htm#IDX57
113	-user-option Command line options
114	-v Command line options sing_19.htm#IDX54
115	.. sing_36.htm#IDX113
116	.singularrc file sing_20.htm#IDX72
117	.singularrc file, no loading Command line options sing_19.htm#IDX46
118	/ sing_36.htm#IDX90
119	/ sing_76.htm#SEC116
120	/ sing_110.htm#SEC150
121	/ sing_137.htm#SEC177
122	/ sing_147.htm#SEC187
123	/ sing_155.htm#SEC195
124	/ sing_180.htm#SEC220
125	// sing_36.htm#IDX107
126	// sing_36.htm#IDX109
127	// sing_36.htm#IDX110
128	: sing_36.htm#IDX114
129	: sing_110.htm#SEC150
130	:: sing_36.htm#IDX115
131	:: sing_149.htm#SEC189
132	; sing_36.htm#IDX111
133	< sing_36.htm#IDX100
134	< sing_155.htm#SEC195
135	< sing_180.htm#SEC220
136	< sing_247.htm#SEC287
137	<= sing_36.htm#IDX99
138	<= sing_100.htm#SEC140
139	<= sing_147.htm#SEC187
140	<= sing_155.htm#SEC195
141	<= sing_175.htm#SEC215
142	<= sing_180.htm#SEC220
143	<> sing_36.htm#IDX96
144	<> sing_100.htm#SEC140
145	<> sing_137.htm#SEC177
146	<> sing_147.htm#SEC187
147	<> sing_155.htm#SEC195
148	<> sing_169.htm#SEC209
149	<> sing_175.htm#SEC215
150	<> sing_180.htm#SEC220
151	= sing_36.htm#IDX77
152	== sing_36.htm#IDX94
153	== sing_100.htm#SEC140
154	== sing_137.htm#SEC177
155	== sing_147.htm#SEC187
156	== sing_155.htm#SEC195
157	== sing_169.htm#SEC209
158	== sing_175.htm#SEC215
159	== sing_180.htm#SEC220
160	> sing_36.htm#IDX98
161	> sing_155.htm#SEC195
162	> sing_180.htm#SEC220
163	>= sing_36.htm#IDX97
164	>= sing_100.htm#SEC140
165	>= sing_147.htm#SEC187
166	>= sing_155.htm#SEC195
167	>= sing_175.htm#SEC215
168	>= sing_180.htm#SEC220
169	? sing_36.htm#IDX106
170	? sing_259.htm#IDX148
171	ADGT sing_945.htm#SEC1021 65350
172	AG codes sing_854.htm#SEC906
173	AGcode_L sing_1800.htm#SEC1876 60329
174	AGcode_Omega sing_1801.htm#SEC1877 56285
175	ASCII sing_904.htm#SEC980 26816
176	ASCII links sing_117.htm#SEC157
177	ASSUME sing_64.htm#SEC101
178	A_L sing_1499.htm#SEC1575 16721
179	A_Z sing_903.htm#SEC979 50866
180	Access to elements of a user defined type Access to elements of a user defined type sing_185.htm#SEC225
181	Adj_div sing_1795.htm#SEC1871 44919
182	Adjoint ideal sing_1376.htm#IDX611
183	Alexander polynomial sing_1470.htm#IDX635
184	Algebraic Geometry codes sing_1794.htm#IDX783
185	Algebraic dependence Algebraic dependence sing_833.htm#SEC885
186	Algebraic geometry sing_1351.htm#SEC1427
187	AltVarEnd sing_746.htm#SEC798 11020
188	AltVarStart sing_745.htm#SEC797 21592
189	Ann sing_1290.htm#SEC1366 61560
190	Appel function sing_563.htm#IDX351
191	Appel hypergeometric function sing_563.htm#IDX352
192	Applications sing_852.htm#SEC904
193	Arnold, classification. sing_2322.htm#IDX939
194	Arnold, classification. sing_2323.htm#IDX940
195	ArnoldAction sing_1592.htm#SEC1668 26958
196	Assignments for user defined types Assignments for user defined types sing_187.htm#SEC227
197	AssocTanToEnv sing_940.htm#SEC1016 46214
198	Atkin sing_1883.htm#SEC1959 sprintf
199	Authors sing_1.htm#IDX16
200	Automatic Deduction sing_945.htm#IDX482
201	Automatic Demonstration sing_945.htm#IDX483
202	BINresol sing_1389.htm#SEC1465 52996
203	Background sing_3.htm#SEC5
204	Basic programming sing_808.htm#SEC860
205	Basic programming sing_808.htm#SEC860
206	BelongSemig sing_2318.htm#SEC2394 22405
207	BerlekampMassey sing_2377.htm#SEC2453 2172
208	Bern sing_2291.htm#SEC2367 64051
209	Bernstein operator sing_540.htm#IDX333
210	Bernstein-Sato polynomial sing_505.htm#IDX314
211	Bernstein-Sato polynomial sing_540.htm#IDX330
212	Bernstein-Sato polynomial sing_1533.htm#IDX666
213	Bernstein-Sato polynomial sing_1537.htm#IDX683
214	Bernstein-Sato polynomial for variety sing_596.htm#IDX355
215	Betti sing_2507.htm#SEC2583 21134
216	Betti number Syzygies and resolutions sing_870.htm#SEC927
217	BettiNumsH sing_2407.htm#SEC2483 18661
218	BettiNumsN sing_2412.htm#SEC2488 44681
219	BettiNumsS sing_2410.htm#SEC2486 14964
220	Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_880.htm#SEC937
221	BlowingUp sing_1512.htm#SEC1588 43153
222	Blowupcenter sing_1392.htm#SEC1468 3423
223	BorelCheck sing_1467.htm#SEC1543 48787
224	Bott's formula sing_2702.htm#IDX1045
225	Branches of space curve singularities Branches of space curve singularities sing_841.htm#SEC893
226	Briancon-Maisonobe algorithm sing_540.htm#IDX339
227	Brieskorn lattice sing_1533.htm#IDX662
228	Brieskorn lattice sing_1534.htm#IDX673
229	Brieskorn lattice sing_1535.htm#IDX676
230	Brieskorn lattice sing_1536.htm#IDX679
231	Brieskorn lattice sing_1537.htm#IDX682
232	Brieskorn lattice sing_1538.htm#IDX686
233	Brieskorn lattice sing_1539.htm#IDX690
234	Brieskorn lattice sing_1540.htm#IDX696
235	Brieskorn lattice sing_1541.htm#IDX704
236	Brieskorn lattice sing_1542.htm#IDX710
237	Brieskorn lattice sing_1543.htm#IDX718
238	Brieskorn lattice sing_1544.htm#IDX728
239	Brieskorn lattice sing_1555.htm#IDX734
240	Brieskorn lattice sing_1557.htm#IDX745
241	Brieskorn lattice sing_1585.htm#IDX772
242	Brill-Noether algorithm sing_1794.htm#IDX784
243	BrillNoether sing_1797.htm#SEC1873 39919
244	Buchberger algorithm for toric ideals Buchberger algorithm sing_881.htm#SEC938
245	Budur-Mustata-Saito approach sing_596.htm#IDX359
246	Building Singular sing_2759.htm#SEC2848
247	C programming language Major differences to the C programming language sing_409.htm#SEC449
248	C, module ordering sing_862.htm#IDX413
249	CGS sing_925.htm#IDX426
250	CM_regularity sing_1454.htm#SEC1530 33865
251	CMtype sing_1623.htm#SEC1699 24849
252	CRHT-ideal sing_887.htm#SEC951
253	CSMA sing_2314.htm#SEC2390 49080
254	CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33
255	Castelnuovo-Mumford regularity sing_1454.htm#IDX627
256	Category string sing_51.htm#SEC88
257	CenCharDec sing_702.htm#SEC754 44505
258	Center sing_1431.htm#SEC1507 25541
259	CenterBO sing_1438.htm#SEC1514 34701
260	CentralQuot sing_700.htm#SEC752 56490
261	CentralSaturation sing_701.htm#SEC753 31585
262	Change of rings sing_9.htm#SEC15
263	Characteristic sets sing_871.htm#SEC928
264	CharacteristicExponents CharacteristicExponents sing_1518.htm#SEC1594 21795
265	ChernClass sing_2715.htm#SEC2791 32965
266	ChernRootsDual sing_2270.htm#SEC2346 40100
267	ChernRootsHom sing_2279.htm#SEC2355 48446
268	ChernRootsProd sing_2272.htm#SEC2348 13967
269	ChernRootsSum sing_2268.htm#SEC2344 57286
270	ChernRootsSymm sing_2281.htm#SEC2357 59304
271	ChernRootsWedge sing_2282.htm#SEC2358 7239
272	Chevalley-Rosenlicht theorem sing_1370.htm#IDX596
273	Chevalley-Rosenlicht theorem sing_1371.htm#IDX599
274	Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2706.htm#IDX1050
275	ChowRing sing_2706.htm#SEC2782 57977
276	Classification of hypersurface singularities Classification of hypersurface singularities sing_842.htm#SEC894
277	Classification of singularities sing_2675.htm#IDX1021
278	Code Codes and the decoding problem sing_886.htm#SEC944
279	Codes and the decoding problem Codes and the decoding problem sing_886.htm#SEC943
280	Coding theory sing_1793.htm#SEC1869
281	Coefficient rings Notes for Singular users sing_2757.htm#SEC2841
282	Command line options Command line options sing_19.htm#SEC26
283	Commands Functions and system variables sing_206.htm#SEC246
284	Commands for user defined types Commands for user defined types sing_186.htm#SEC226
285	Commutative Algebra sing_821.htm#SEC873
286	Commutative algebra sing_1106.htm#SEC1182
287	CompDecomp sing_502.htm#SEC554 9959
288	CompInt sing_2320.htm#SEC2396 7518
289	CompleteHomog sing_2258.htm#SEC2334 42123
290	ComplexValue sing_2399.htm#SEC2475 45546
291	Comprehensive Groebner System sing_925.htm#IDX429
292	Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_817.htm#SEC869
293	ConsLevels sing_933.htm#SEC1009 14282
294	ContactMatrix sing_1520.htm#SEC1596 40767
295	Conti-Traverso algorithm sing_876.htm#SEC933
296	Contributors sing_1.htm#IDX15
297	Control structures sing_377.htm#SEC417
298	Control theory System and Control theory sing_1827.htm#SEC1903
299	Cooper philosophy sing_887.htm#SEC949
300	Cornacchia sing_1873.htm#SEC1949 63434
301	CornacchiaModified sing_1874.htm#SEC1950 59790
302	Crep sing_928.htm#SEC1004 17485
303	Critical points sing_836.htm#SEC888
304	CurveParam sing_1514.htm#SEC1590 53605
305	CurveRes sing_1513.htm#SEC1589 48848
306	Curves sing_1376.htm#IDX608
307	Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36
308	Cyclic code sing_1808.htm#IDX791
309	Cyclic roots sing_814.htm#SEC866
310	D-integration sing_563.htm#IDX348
311	D-localization sing_563.htm#IDX344
312	D-localization sing_780.htm#IDX382
313	D-module purityfiltration_lib sing_505.htm#IDX312
314	D-module sing_540.htm#IDX327
315	D-module sing_563.htm#IDX341
316	D-module sing_596.htm#IDX353
317	D-module sing_758.htm#IDX367
318	D-module sing_780.htm#IDX379
319	D-module structure sing_540.htm#IDX328
320	D-module structure sing_596.htm#IDX354
321	D-restriction sing_563.htm#IDX346
322	DBM links sing_122.htm#SEC162
323	DISPLAY environment variable The online help system sing_16.htm#IDX28
324	DLoc sing_566.htm#SEC618 5981
325	DLoc0 sing_568.htm#SEC620 14327
326	Data types sing_72.htm#SEC112
327	Data types (plural) sing_422.htm#IDX298
328	Debugging tools sing_63.htm#SEC100
329	Decker, Wolfram sing_1.htm#IDX17
330	Declaration of objects of a user defined type Declaration of objects of a user defined type sing_184.htm#SEC224
331	Decoding sing_1808.htm#IDX793
332	Decoding codes with Groebner bases Decoding codes with Groebner bases sing_885.htm#SEC942
333	Decoding method based on quadratic equations Decoding method based on quadratic equations sing_890.htm#SEC960
334	Definition of a user defined type Definition of a user defined type sing_183.htm#SEC223
335	Deformations sing_839.htm#SEC891
336	Deformations, T1 and T2 sing_838.htm#SEC890
337	Deg sing_2510.htm#SEC2586 35419
338	Degree sing_2511.htm#SEC2587 48523
339	DegreePure sing_1355.htm#SEC1431 33003
340	Degrees sing_2512.htm#SEC2588 50349
341	Delta sing_1439.htm#SEC1515 33497
342	DeltaList sing_1440.htm#SEC1516 65148
343	Demo mode sing_24.htm#SEC35
344	Depth sing_828.htm#SEC880
345	Determinacy sing_2678.htm#IDX1025
346	Di Biase-Urbanke algorithm Di Biase and Urbanke sing_879.htm#SEC936
347	Distributed computing sing_956.htm#IDX489
348	Dlocalization sing_781.htm#SEC833 22140
349	Documentation Tool sing_60.htm#SEC97
350	Dp, global ordering sing_860.htm#IDX396
351	Ds, local ordering sing_861.htm#IDX406
352	DsingularLocus sing_785.htm#SEC837 46495
353	Dynamic loading sing_71.htm#SEC111
354	Dynamic modules sing_816.htm#SEC868
355	ECPP sing_1917.htm#SEC1993 55777
356	ECoef sing_1398.htm#SEC1474 14154
357	EOrdlist sing_1396.htm#SEC1472 36329
358	ERROR sing_236.htm#SEC276
359	ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33
360	Edatalist sing_1395.htm#SEC1471 61593
361	Edelman-Reiner sing_2201.htm#IDX874
362	Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
363	Editing input sing_18.htm#SEC25
364	Elimination sing_824.htm#SEC876
365	Emacs Emacs user interface sing_21.htm#SEC28
366	Emacs, Singular demo mode sing_24.htm#SEC35
367	Emacs, a quick guide A quick guide to Emacs sing_22.htm#SEC29
368	Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC36
369	Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC37
370	Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC38
371	Emacs, overview A quick guide to Emacs sing_22.htm#SEC29
372	Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30
373	Emacs, user interface Emacs user interface sing_21.htm#SEC28
374	Emaxcont sing_1400.htm#SEC1476 47312
375	Enumerative geometry sing_2702.htm#IDX1043
376	Equal sing_1354.htm#SEC1430 19984
377	Eresol sing_1390.htm#SEC1466 12842
378	EulerAff sing_2315.htm#SEC2391 54325
379	EulerProj sing_2316.htm#SEC2392 13537
380	Evaluation of logical expressions Evaluation of logical expressions sing_411.htm#SEC451
381	Examples sing_806.htm#SEC858
382	Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40
383	Exp for matrices sing_1372.htm#IDX600
384	Experimental libraries Experimental libraries sing_2245.htm#SEC2321
385	Ext sing_1166.htm#SEC1242 21909
386	Ext, computation of sing_827.htm#SEC879
387	Ext_R sing_1165.htm#SEC1241 53310
388	Exterior sing_732.htm#SEC784 23593
389	Extra weight vector sing_865.htm#SEC917
390	Factorization sing_829.htm#SEC881
391	FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_941.htm#SEC1017 18153
392	Feynman graph sing_1142.htm#IDX522
393	Finite fields sing_823.htm#SEC875
394	First steps sing_6.htm#SEC12
395	Fitzgerald-Lax method Fitzgerald-Lax method sing_889.htm#SEC957
396	Float sing_250.htm#SEC290
397	Flow control sing_40.htm#SEC70
398	Formal Checker sing_59.htm#SEC96
399	Formatting output sing_813.htm#SEC865
400	Free resolution sing_825.htm#SEC877
401	Free resolution, graded Handling graded modules sing_826.htm#SEC878
402	FultonA sing_2313.htm#SEC2389 33688
403	Functions sing_207.htm#SEC247
404	Future benefits of Singular 4 Notes for Singular users sing_2757.htm#SEC2846
405	G-algebra sing_486.htm#SEC526
406	G-algebra sing_486.htm#SEC528
407	G-algebra, setup sing_486.htm#SEC530
408	GBWeight sing_569.htm#SEC621 24641
409	GBsolve sing_1707.htm#SEC1783 16830
410	GIT-Fans sing_848.htm#SEC900
411	GITcone sing_2426.htm#SEC2502 64643
412	GITfan sing_2427.htm#SEC2503 32549
413	GITfanFromOrbitCones GITfanFromOrbitCones sing_2428.htm#SEC2504 63104
414	GITfanParallel sing_2429.htm#SEC2505 53071
415	GITfanParallelSymmetric GITfanParallelSymmetric sing_2444.htm#SEC2520 30232
416	GITfanSymmetric sing_2443.htm#SEC2519 25831
417	GKZfan sing_2430.htm#SEC2506 sprintf
418	GKZsystem sing_698.htm#SEC750 20528
419	GKdim sing_671.htm#SEC723 9814
420	GMP sing_1.htm#IDX3
421	GMP sing_2761.htm#SEC2850
422	GND.lib sing_2451.htm#SEC2527
423	GND_lib sing_2451.htm#SEC2527
424	GTZmod sing_1216.htm#SEC1292 30091
425	GTZopt sing_1223.htm#SEC1299 14642
426	G_a -Invariants sing_845.htm#SEC897
427	Gamma sing_1405.htm#SEC1481 3820
428	Gauss-Manin connection Gauss-Manin connection sing_872.htm#SEC929
429	Gauss-Manin connection sing_1585.htm#IDX771
430	Gauss-Manin connection sing_1632.htm#IDX774
431	Gauss-Manin system sing_1533.htm#IDX661
432	Gauss-Manin system sing_1534.htm#IDX672
433	Gauss-Manin system sing_1535.htm#IDX675
434	Gauss-Manin system sing_1536.htm#IDX678
435	Gauss-Manin system sing_1537.htm#IDX681
436	Gauss-Manin system sing_1538.htm#IDX685
437	Gauss-Manin system sing_1539.htm#IDX689
438	Gauss-Manin system sing_1540.htm#IDX695
439	Gauss-Manin system sing_1541.htm#IDX703
440	Gauss-Manin system sing_1542.htm#IDX709
441	Gauss-Manin system sing_1543.htm#IDX717
442	Gauss-Manin system sing_1544.htm#IDX727
443	Gauss-Manin system sing_1555.htm#IDX733
444	Gauss-Manin system sing_1557.htm#IDX744
445	General command syntax General command syntax sing_35.htm#SEC59
446	General concepts sing_12.htm#SEC18
447	General purpose sing_897.htm#SEC973
448	General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41
449	Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_488.htm#SEC538
450	Generalized Newton identities Generalized Newton identities sing_888.htm#SEC954
451	Geometric Invariant Theory Geometric Invariant Theory sing_847.htm#SEC899
452	Geometric Theorems sing_945.htm#IDX484
453	Geometric genus sing_1376.htm#IDX612
454	German Umlaute sing_407.htm#IDX285
455	Getting started sing_5.htm#SEC11
456	Global orderings sing_860.htm#SEC912
457	Goettsche's formula sing_2404.htm#IDX981
458	GoettscheF sing_2405.htm#SEC2481 27881
459	Graded commutative algebras Graded commutative algebras (SCA) sing_490.htm#SEC542
460	Grassmannian sing_2707.htm#SEC2783 43898
461	Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2707.htm#IDX1051
462	Greuel, Gert-Martin sing_1.htm#IDX18
463	Groebner Bases Computing Groebner and Standard Bases sing_817.htm#SEC869
464	Groebner bases in G-algebras Groebner bases in G-algebras sing_487.htm#SEC531
465	Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_493.htm#SEC545
466	Groebner bases, decodeGB sing_1808.htm#IDX795
467	Groebner bases, slim sing_820.htm#SEC872
468	Groebner basis conversion Groebner basis conversion sing_819.htm#SEC871
469	Groebner cover sing_924.htm#IDX422
470	Groebner cover sing_931.htm#IDX441
471	Groebner cover sing_932.htm#IDX448
472	Groebner fan sing_2071.htm#IDX812
473	Groebner walk sing_1157.htm#IDX543
474	Groebner walk sing_1159.htm#IDX545
475	Groebner walk sing_2699.htm#IDX1039
476	Groebner walk sing_2700.htm#IDX1040
477	Groebnerwalk sing_1153.htm#IDX539
478	Groebnerwalk sing_2544.htm#IDX992
479	Groebnerwalk sing_2698.htm#IDX1038
480	Groebnerwalk sing_2741.htm#IDX1067
481	Gromov-Witten invariants sing_1142.htm#IDX519
482	Gromov-Witten invariants sing_1148.htm#IDX528
483	Gromov-Witten invariants sing_1149.htm#IDX532
484	Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2732.htm#IDX1063
485	Gromov-Witten invariants, multiple covers sing_2731.htm#IDX1062
486	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2733.htm#IDX1064
487	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2734.htm#IDX1065
488	Gromov-Witten invariants. sing_2702.htm#IDX1046
489	Gweights sing_726.htm#SEC778 651
490	H2basis sing_1590.htm#SEC1666 3414
491	HHnormalForm sing_2331.htm#SEC2407 33972
492	Hamburger-Noether expansion sing_1470.htm#IDX631
493	Hamburger-Noether expansion sing_1558.htm#IDX753
494	Hamburger-Noether expansions sing_1795.htm#IDX785
495	Handling graded modules Handling graded modules sing_826.htm#SEC878
496	Hcode sing_1492.htm#SEC1568 26628
497	Help string sing_45.htm#SEC82
498	Hensel sing_241.htm#SEC281
499	Hilbert function sing_356.htm#IDX188
500	Hilbert function sing_869.htm#SEC923
501	Hilbert series sing_869.htm#SEC923
502	Hilbert-driven GB algorithm Groebner basis conversion sing_819.htm#SEC871
503	HilbertClassPoly sing_1880.htm#SEC1956 sprintf
504	HilbertSeries sing_1685.htm#SEC1761 21249
505	HilbertWeights sing_1686.htm#SEC1762 sprintf
506	Hom sing_1169.htm#SEC1245 61434
507	HomJJ sing_1246.htm#SEC1322 1525
508	Hosten-Sturmfels algorithm Hosten and Sturmfels sing_878.htm#SEC935
509	How to enter and exit How to enter and exit sing_14.htm#SEC20
510	How to use this manual How to use this manual sing_4.htm#SEC6
511	Hurwitz numbers sing_1148.htm#IDX531
512	Hurwitz numbers sing_1149.htm#IDX535
513	Hypersurface singularities, classification of Classification of hypersurface singularities sing_842.htm#SEC894
514	I-regular function sing_931.htm#IDX447
515	IN sing_280.htm#IDX149
516	Ideal membership sing_868.htm#IDX418
517	Identifiers, syntax of sing_37.htm#SEC65
518	ImageGroup sing_1688.htm#SEC1764 28808
519	ImageVariety sing_1687.htm#SEC1763 15252
520	Imap, option sing_315.htm#IDX175
521	Implemented algorithms Implemented algorithms sing_33.htm#SEC47
522	Incl sing_1353.htm#SEC1429 7621
523	Index sing_2766.htm#SEC2855
524	Info string sing_52.htm#SEC89
525	InterDiv sing_1421.htm#SEC1497 46142
526	Interactive use sing_13.htm#SEC19
527	Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24
528	IntersectWithSub sing_703.htm#SEC755 56289
529	Intersection theory sing_2702.htm#IDX1042
530	IntersectionMatrix sing_1519.htm#SEC1595 29351
531	Introduction sing_2.htm#SEC4
532	Invariant Theory sing_844.htm#SEC896
533	Invariant theory sing_1637.htm#SEC1713
534	InvariantQ sing_1690.htm#SEC1766 53256
535	InvariantRing sing_1689.htm#SEC1765 22928
536	Invariants of a finite group Invariants of a finite group sing_846.htm#SEC898
537	Invariants of plane curve singularities Invariants of plane curve singularities sing_840.htm#SEC892
538	IsSCA sing_747.htm#SEC799 58445
539	J-marked schemes sing_1461.htm#IDX629
540	J-marked schemes, Borel ideals sing_1466.htm#IDX630
541	JMBTest.lib sing_1461.htm#SEC1537
542	JMBTest_lib sing_1461.htm#SEC1537
543	JMSConst.lib sing_1466.htm#SEC1542
544	JMSConst_lib sing_1466.htm#SEC1542
545	JMarkedScheme sing_1468.htm#SEC1544 60696
546	Jacobi sing_1890.htm#SEC1966 29843
547	Jacobson form sing_1845.htm#IDX796
548	Jacobson normal form sing_1845.htm#IDX797
549	Janet basis sing_2697.htm#IDX1036
550	Janet division, Janet basis sing_2696.htm#IDX1035
551	JuReTopDim sing_1363.htm#SEC1439 sprintf
552	JuReZeroDim sing_1364.htm#SEC1440 sprintf
553	KScoef sing_1583.htm#SEC1659 sprintf
554	KSconvert sing_1581.htm#SEC1657 3585
555	KSker sing_1580.htm#SEC1656 40166
556	KSlinear sing_1582.htm#SEC1658 19896
557	KSpencerKernel sing_1630.htm#SEC1706 12490
558	KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2470.htm#SEC2546 20741
559	Ker sing_2516.htm#SEC2592 58279
560	Kernel of module homomorphisms Kernel of module homomorphisms sing_832.htm#SEC884
561	KoszulHomology sing_1178.htm#SEC1254 sprintf
562	Kronecker modules sing_2404.htm#IDX983
563	L, ordering sing_866.htm#SEC918
564	LETTERPLACE sing_491.htm#SEC543
565	LIB sing_284.htm#SEC324
566	LIB commands sing_53.htm#SEC90
567	LIBs sing_893.htm#SEC969
568	LLL sing_358.htm#IDX220
569	LOT algorithm sing_540.htm#IDX340
570	LU-decomposition of a matrix of numbers sing_289.htm#SEC329
571	Laurent series sing_1146.htm#IDX527
572	Left and two-sided Groebner bases Left and two-sided Groebner bases sing_850.htm#SEC902
573	Left ideal membership Groebner bases in G-algebras sing_487.htm#SEC534
574	Left normal form Groebner bases in G-algebras sing_487.htm#SEC533
575	LengthSym sing_757.htm#SEC809 16591
576	LengthSymElement sing_756.htm#SEC808 28292
577	Letterplace sing_491.htm#SEC543
578	Levels sing_934.htm#SEC1010 16031
579	Lexicographic Groebner bases, computation of Groebner basis conversion sing_819.htm#SEC871
580	Libraries Writing procedures and libraries sing_48.htm#SEC85
581	Libraries sing_809.htm#SEC861
582	Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86
583	Library versioning Notes for Singular users sing_2757.htm#SEC2844
584	Lie algebra sing_1371.htm#IDX597
585	Lie group sing_1374.htm#IDX602
586	Lie group sing_1375.htm#IDX605
587	Limitations sing_407.htm#SEC447
588	Linear algebra sing_1046.htm#SEC1122
589	Linear code sing_1808.htm#IDX792
590	LinearActionQ sing_1692.htm#SEC1768 62218
591	LinearCombinationQ sing_1693.htm#SEC1769 59373
592	LinearizeAction sing_1691.htm#SEC1767 60266
593	Loading a library sing_62.htm#SEC99
594	Local orderings sing_861.htm#SEC913
595	Log for matrices sing_1373.htm#IDX601
596	Long coefficients sing_811.htm#SEC863
597	M, ordering sing_863.htm#SEC915
598	MVComplex sing_2353.htm#SEC2429 62126
599	Macdonald's formula sing_2404.htm#IDX982
600	MacdonaldF sing_2408.htm#SEC2484 12751
601	Macintosh installation Macintosh installation instructions sing_2765.htm#SEC2854
602	Mathematical background Mathematical background sing_867.htm#SEC919
603	Mathematical background (plural) Mathematical background (plural) sing_485.htm#SEC525
604	Matrix orderings sing_863.htm#SEC915
605	Max sing_1599.htm#SEC1675 23
606	Maximus sing_1463.htm#SEC1539 10010
607	Maxord sing_1404.htm#SEC1480 14124
608	MillerRabin sing_1900.htm#SEC1976 15740
609	Milnor number Milnor and Tjurina number sing_835.htm#SEC887
610	Milnor number sing_2677.htm#IDX1024
611	Min sing_1600.htm#SEC1676 29622
612	MinMult sing_2319.htm#SEC2395 39835
613	MinimalDecomposition MinimalDecomposition sing_1694.htm#SEC1770 24161
614	Minimum distance sing_1808.htm#IDX794
615	Minimus sing_1462.htm#SEC1538 61721
616	Miscellaneous libraries Miscellaneous libraries sing_2172.htm#SEC2248
617	ModEqn sing_1593.htm#SEC1669 59394
618	Modular techniques sing_956.htm#IDX486
619	Module orderings sing_862.htm#SEC914
620	Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16
621	Monodromy sing_1585.htm#IDX769
622	Monomial orderings sing_857.htm#SEC909
623	Monomial orderings, Term orderings sing_31.htm#SEC44
624	Mori dream spaces sing_2246.htm#IDX934
625	Morse lemma addnondegeneratevariables sing_2676.htm#IDX1022
626	Morse lemma sing_2679.htm#IDX1026
627	MultiplicitySequence MultiplicitySequence sing_1517.htm#SEC1593 1309
628	NF sing_334.htm#SEC374
629	NF sing_477.htm#SEC517
630	NFMora sing_1966.htm#SEC2042 40670
631	NPos sing_1236.htm#SEC1312 15702
632	NPos_test sing_1234.htm#SEC1310 48172
633	NSplaces sing_1796.htm#SEC1872 48675
634	NTL sing_1.htm#IDX4
635	Names sing_37.htm#SEC65
636	Names in procedures sing_46.htm#SEC83
637	Names, indexed sing_37.htm#SEC65
638	New orderings for modules Notes for Singular users sing_2757.htm#SEC2845
639	Newton non-degenerate sing_1572.htm#IDX767
640	Newton polygon sing_1571.htm#IDX766
641	Newton polygon sing_1572.htm#IDX768
642	Newton polygons sing_2744.htm#IDX1070
643	Newton polytope sing_2071.htm#IDX811
644	Newton step sing_2680.htm#IDX1030
645	NoetherPosition sing_1230.htm#SEC1306 18735
646	Non-commutative LIBs Non-commutative libraries sing_497.htm#SEC549
647	Non-commutative algebra Non-commutative algebra sing_849.htm#SEC901
648	Non-commutative algebra sing_884.htm#SEC941
649	Non-commutative libraries Non-commutative libraries sing_497.htm#SEC549
650	Non-commutative subsystem Non-commutative subsystem sing_420.htm#SEC460
651	Nonhyp sing_1393.htm#SEC1469 sprintf
652	Normalization sing_831.htm#SEC883
653	Notes for Singular users Notes for Singular users sing_2757.htm#SEC2840
654	Notes for developers Notes for developers sing_2758.htm#SEC2847
655	NullCone sing_1695.htm#SEC1771 64635
656	NumIrrDecom sing_1367.htm#SEC1443 sprintf
657	NumLocalDim sing_1356.htm#SEC1432 1739
658	NumPrimDecom sing_1369.htm#SEC1445 34134
659	Oaku-Takayama algorithm sing_540.htm#IDX338
660	Objects sing_38.htm#SEC66
661	Orlik-Solomon sing_2202.htm#IDX875
662	Output sing_2526.htm#IDX990
663	Output sing_2623.htm#IDX997
664	Output sing_2625.htm#IDX998
665	Output sing_2626.htm#IDX999
666	Output sing_2627.htm#IDX1000
667	Output sing_2628.htm#IDX1001
668	Output sing_2629.htm#IDX1002
669	Output sing_2630.htm#IDX1003
670	Output sing_2631.htm#IDX1004
671	Output sing_2632.htm#IDX1005
672	Output sing_2633.htm#IDX1006
673	Output sing_2634.htm#IDX1007
674	Output sing_2635.htm#IDX1008
675	Output sing_2636.htm#IDX1009
676	Output sing_2637.htm#IDX1010
677	Output sing_2638.htm#IDX1011
678	Output sing_2639.htm#IDX1012
679	Output sing_2640.htm#IDX1013
680	Output sing_2641.htm#IDX1014
681	Output sing_2642.htm#IDX1015
682	Output sing_2643.htm#IDX1016
683	Output sing_2644.htm#IDX1017
684	Output sing_2645.htm#IDX1018
685	Output sing_2646.htm#IDX1019
686	Output sing_2647.htm#IDX1020
687	Output, formatting of sing_813.htm#SEC865
688	PBW sing_519.htm#IDX326
689	PBW basis sing_486.htm#SEC527
690	PBW_eqDeg sing_537.htm#SEC589 23181
691	PBW_maxDeg sing_538.htm#SEC590 59566
692	PBW_maxMonom sing_539.htm#SEC591 1155
693	PEsolve sing_1705.htm#SEC1781 9229
694	PH_ais sing_2224.htm#SEC2300 49473
695	PH_nais sing_2225.htm#SEC2301 46271
696	PLURAL sing_421.htm#SEC461
697	PLURAL LIBs Non-commutative libraries sing_497.htm#SEC549
698	PPolyH sing_2406.htm#SEC2482 25241
699	PPolyN sing_2411.htm#SEC2487 39067
700	PPolyS sing_2409.htm#SEC2485 13817
701	ParToVar sing_2401.htm#SEC2477 13991
702	Parallelization Parallelization with ssi links sing_815.htm#SEC867
703	Parallelization sing_956.htm#IDX487
704	Parameter list sing_44.htm#SEC81
705	Parameters sing_812.htm#SEC864
706	Parametrization sing_1376.htm#IDX609
707	Parametrization, image. sing_1386.htm#IDX621
708	PartC sing_2309.htm#SEC2385 54120
709	PartitionVar sing_2398.htm#SEC2474 41350
710	Path names Notes for Singular users sing_2757.htm#SEC2843
711	PerfectPowerTest sing_1863.htm#SEC1939 17450
712	Perturbation walk sing_1158.htm#IDX544
713	Pfister, Gerhard sing_1.htm#IDX19
714	Pipe links sing_121.htm#SEC161
715	PocklingtonLehmer sing_1902.htm#SEC1978 13634
716	Poincare polynomial sing_2214.htm#IDX899
717	Polar curves sing_837.htm#SEC889
718	PollardRho sing_1903.htm#SEC1979 49602
719	PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2227.htm#IDX915
720	PolyBoRi, Boolean Groebner Basis sing_2229.htm#IDX916
721	PolyBoRi, Boolean Groebner Basis sing_2230.htm#IDX917
722	PolyBoRi, Boolean Groebner Basis sing_2231.htm#IDX918
723	PolyBoRi, Boolean Groebner Basis sing_2232.htm#IDX919
724	PolyBoRi, Boolean Groebner Basis sing_2233.htm#IDX920
725	PolyBoRi, Boolean Groebner Basis sing_2234.htm#IDX921
726	PolyBoRi, Boolean Groebner Basis sing_2235.htm#IDX922
727	PolyBoRi, Boolean Groebner Basis sing_2236.htm#IDX923
728	PolyBoRi, Boolean Groebner Basis sing_2237.htm#IDX924
729	PolyBoRi, Boolean Groebner Basis sing_2238.htm#IDX925
730	PolyBoRi, Boolean Groebner Basis sing_2239.htm#IDX926
731	PolyBoRi, Boolean Groebner Basis sing_2240.htm#IDX927
732	PolyBoRi, Boolean Groebner Basis sing_2241.htm#IDX928
733	PolyBoRi, Boolean Groebner Basis sing_2243.htm#IDX930
734	PolyBoRi, zero-supressed decision diagram sing_2242.htm#IDX929
735	Polybori, Boolean Groebner Basis sing_2244.htm#IDX931
736	Polynomial data sing_855.htm#SEC907
737	Pottier algorithm sing_877.htm#SEC934
738	Preface sing_1.htm#SEC1
739	Prep sing_929.htm#SEC1005 55342
740	Primary decomposition Primary decomposition sing_830.htm#SEC882
741	PrimdecA sing_1212.htm#SEC1288 248
742	PrimdecB sing_1213.htm#SEC1289 9653
743	Procedure definition Procedure definition sing_43.htm#SEC78
744	Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84
745	Procedures sing_42.htm#SEC77
746	Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14
747	Procedures and libraries sing_809.htm#SEC861
748	Procedures in a library Procedures in a library sing_54.htm#SEC91
749	Product orderings sing_864.htm#SEC916
750	Programming sing_807.htm#SEC859
751	Pseudo ordering L sing_866.htm#SEC918
752	PtoCrep sing_930.htm#SEC1006 52961
753	Puiseux expansion sing_1470.htm#IDX632
754	Puiseux expansion sing_1558.htm#IDX754
755	Puiseux pairs Invariants of plane curve singularities sing_840.htm#SEC892
756	Puiseux pairs sing_1564.htm#IDX759
757	QQ sing_28.htm#SEC39
758	Qso3Casimir sing_697.htm#SEC749 40212
759	Quotient sing_1747.htm#SEC1823 24888
760	QuotientEquations sing_1594.htm#SEC1670 18230
761	Rational curves sing_1376.htm#IDX610
762	ReJunkUseHomo sing_1362.htm#SEC1438 10186
763	ReesAlgebra sing_1329.htm#SEC1405 59951
764	References sing_892.htm#SEC966
765	References (plural) sing_489.htm#SEC539
766	Release Notes sing_2753.htm#SEC2829
767	Res sing_2506.htm#SEC2582 92
768	ResTree sing_1422.htm#SEC1498 58727
769	Resolution sing_11.htm#SEC17
770	Resolution of singularities Resolution of singularities sing_843.htm#SEC895
771	Resolution, free sing_825.htm#SEC877
772	ReynoldsImage sing_1696.htm#SEC1772 35172
773	ReynoldsOperator sing_1697.htm#SEC1773 14986
774	RiemannRochBN sing_2254.htm#SEC2330 20085
775	RiemannRochHess sing_2489.htm#SEC2565 sprintf
776	Right Groebner bases and syzygies Right Groebner bases and syzygies sing_851.htm#SEC903
777	Ring-dependent options Notes for Singular users sing_2757.htm#SEC2842
778	Rings and orderings sing_28.htm#SEC39
779	Rings and standard bases Rings and standard bases sing_7.htm#SEC13
780	Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
781	SCA Graded commutative algebras (SCA) sing_490.htm#SEC542
782	SDB breakpoint Source code debugger sing_66.htm#SEC106
783	SDB debugger Source code debugger sing_66.htm#SEC106
784	SDLoc sing_567.htm#SEC619 9512
785	SINGULAR libraries sing_893.htm#SEC969
786	SINGULARHIST sing_18.htm#SEC25
787	SV-decoding algorithm sing_1803.htm#IDX788
788	SV-decoding algorithm, preprocessing sing_1802.htm#IDX787
789	Sannfs sing_543.htm#SEC595 42932
790	SannfsBFCT sing_552.htm#SEC604 59702
791	SannfsVar sing_599.htm#SEC651 37522
792	Sannfslog sing_544.htm#SEC596 49313
793	Saturation sing_822.htm#SEC874
794	Saturation sing_1139.htm#IDX513
795	Sch@"onemann, Hans sing_1.htm#IDX20
796	Schoof sing_1914.htm#SEC1990 49281
797	Schubert calculus sing_2702.htm#IDX1044
798	SchubertClass sing_2739.htm#SEC2815 62336
799	SchurCh sing_2306.htm#SEC2382 58575
800	SchurS sing_2305.htm#SEC2381 46004
801	SegreA sing_2312.htm#SEC2388 55776
802	Semigroup sing_1510.htm#SEC1586 22323
803	SetDeg sing_2509.htm#SEC2585 40547
804	Setting up a G-algebra sing_486.htm#SEC530
805	ShanksMestre sing_1913.htm#SEC1989 12973
806	SimplifyIdeal sing_1698.htm#SEC1774 sprintf
807	Singular sing_358.htm#IDX257
808	Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2755.htm#SEC2838
809	Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36
810	Singular, demo mode sing_24.htm#SEC35
811	Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
812	Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38
813	Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
814	Singular2bertini sing_1360.htm#SEC1436 7552
815	SingularLib sing_358.htm#IDX259
816	Singularities sing_1469.htm#SEC1545
817	Singularity Theory sing_834.htm#SEC886
818	Skeletons for parallelization sing_956.htm#IDX488
819	Smith form sing_1845.htm#IDX798
820	Smith normal form sing_1845.htm#IDX799
821	SolowayStrassen sing_1901.htm#SEC1977 22680
822	Solving systems of polynomial equations Solving systems of polynomial equations sing_853.htm#SEC905
823	Source sing_2498.htm#SEC2574 10351
824	Source code debugger, invocation Command line options sing_19.htm#IDX33
825	Space curve singularities, branches of Branches of space curve singularities sing_841.htm#SEC893
826	Special characters sing_36.htm#SEC64
827	Splitting lemma addnondegeneratevariables sing_2676.htm#IDX1023
828	Splitting lemma sing_2679.htm#IDX1027
829	Ssi file links sing_119.htm#SEC159
830	Ssi links sing_118.htm#SEC158
831	Ssi tcp links sing_120.htm#SEC160
832	StabEqn sing_1595.htm#SEC1671 28539
833	StabEqnId sing_1596.htm#SEC1672 27955
834	StabOrder sing_1597.htm#SEC1673 55603
835	Standard Bases Computing Groebner and Standard Bases sing_817.htm#SEC869
836	Standard bases sing_868.htm#SEC920
837	StartOrderingV sing_1464.htm#SEC1540 58927
838	Startup sequence sing_20.htm#SEC27
839	StringF sing_1584.htm#SEC1660 11590
840	SymGroup sing_755.htm#SEC807 56676
841	Symbolic-numerical solving Symbolic-numerical solving sing_853.htm#SEC905
842	Symbolic-numerical solving sing_1702.htm#SEC1778
843	System and Control theory System and Control theory sing_1827.htm#SEC1903
844	System dependent limitations System dependent limitations sing_408.htm#SEC448
845	System variables sing_394.htm#SEC434
846	Syzygies and resolutions Syzygies and resolutions sing_870.htm#SEC924
847	Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_488.htm#SEC535
848	T1 sing_838.htm#SEC890
849	T2 sing_838.htm#SEC890
850	TRACE Tracing of procedures sing_65.htm#SEC102
851	TRACE sing_403.htm#SEC443
852	T_1 sing_1617.htm#SEC1693 59277
853	T_12 sing_1619.htm#SEC1695 12923
854	T_2 sing_1618.htm#SEC1694 55781
855	Target sing_2497.htm#SEC2573 16006
856	Teaching sing_1859.htm#SEC1935
857	Template for writing a library sing_55.htm#SEC92
858	TestGRRes sing_2469.htm#SEC2545 8315
859	TestJMark sing_1465.htm#SEC1541 41314
860	The SINGULAR language The SINGULAR language sing_34.htm#SEC56
861	The Tran algorithm sing_1155.htm#IDX541
862	The fractal walk algorithm sing_1154.htm#IDX540
863	The fractal walk algorithm sing_2701.htm#IDX1041
864	The online help system The online help system sing_16.htm#SEC22
865	Tjurina sing_1615.htm#SEC1691 11249
866	Tjurina number Milnor and Tjurina number sing_835.htm#SEC887
867	Tjurina number sing_1251.htm#IDX570
868	Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38
869	Tor sing_1180.htm#SEC1256 sprintf
870	Toric ideals and integer programming Toric ideals and integer programming sing_873.htm#SEC930
871	Tricks and pitfalls sing_406.htm#SEC446
872	Tropical Geometry sing_2011.htm#SEC2087
873	Type casting Type conversion and casting sing_39.htm#SEC69
874	Type conversion Type conversion and casting sing_39.htm#SEC68
875	Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98
876	U_D_O sing_1095.htm#SEC1171 26192
877	Unix installation Unix installation instructions sing_2763.htm#SEC2852
878	UpOneMatrix sing_744.htm#SEC796 63020
879	UpperMonomials sing_1598.htm#SEC1674 20941
880	UseBertini sing_1359.htm#SEC1435 43362
881	User defined types sing_182.htm#SEC222
882	V-filtration sing_1533.htm#IDX664
883	V-filtration sing_1539.htm#IDX692
884	V-filtration sing_1540.htm#IDX698
885	V-filtration sing_1541.htm#IDX706
886	V-filtration sing_1542.htm#IDX712
887	V-filtration sing_1543.htm#IDX720
888	V-filtration sing_1544.htm#IDX730
889	V-filtration sing_1555.htm#IDX736
890	V-filtration sing_1557.htm#IDX747
891	VarToPar sing_2400.htm#SEC2476 10508
892	Variables, indexed sing_37.htm#SEC65
893	Version number Version schema for Singular sing_2756.htm#SEC2839
894	Version schema for Singular Version schema for Singular sing_2756.htm#SEC2839
895	Version string sing_50.htm#SEC87
896	Visualization sing_1765.htm#SEC1841
897	WLemma sing_943.htm#SEC1019 7302
898	WP, global ordering sing_860.htm#IDX400
899	WSemigroup sing_1515.htm#SEC1591 57449
900	Weierstrass sing_1798.htm#SEC1874 58220
901	Weierstrass semigroup sing_1794.htm#IDX782
902	Weyl sing_729.htm#SEC781 29212
903	Weyl algebra sing_540.htm#IDX332
904	Weyl algebra sing_596.htm#IDX357
905	Weyl closure sing_780.htm#IDX385
906	WeylClosure sing_782.htm#SEC834 23845
907	WeylClosure1 sing_783.htm#SEC835 15759
908	Wibmer's Lemma sing_943.htm#IDX481
909	Windows installation Windows installation instructions sing_2764.htm#SEC2853
910	WitSet sing_1366.htm#SEC1442 39803
911	WitSupSet sing_1365.htm#SEC1441 47758
912	Ws, local ordering sing_861.htm#IDX412
913	XLsolve sing_1708.htm#SEC1784 34970
914	ZZ sing_28.htm#SEC39
915	ZZ/m sing_28.htm#SEC39
916	ZZ/p sing_28.htm#SEC39
917	ZZsolve sing_1709.htm#SEC1785 18657
918	[ sing_36.htm#IDX83
919	[] sing_142.htm#SEC182
920	[] sing_155.htm#SEC195
921	[] sing_175.htm#SEC215
922	[] sing_180.htm#SEC220
923	\ sing_36.htm#IDX112
924	] sing_36.htm#IDX84
925	^ sing_36.htm#IDX92
926	^ sing_81.htm#SEC121
927	^ sing_93.htm#SEC133
928	^ sing_147.htm#SEC187
929	^ sing_155.htm#SEC195
930	_ sing_36.htm#IDX116
931	` sing_36.htm#IDX105
932	a, ordering sing_865.htm#SEC917
933	absFactorize sing_1108.htm#SEC1184 52546
934	absFactorizeBCG sing_1109.htm#SEC1185 55510
935	absPrimdecGTZ sing_1309.htm#SEC1385 46393
936	absPrimdecGTZE sing_1310.htm#SEC1386 48005
937	absValue sing_905.htm#SEC981 54595
938	absfact.lib sing_1107.htm#SEC1183
939	absfact_lib sing_1107.htm#SEC1183
940	absolute factorization. sing_1107.htm#IDX512
941	abstract variety, projective space, Grassmannian printVariety sing_2703.htm#IDX1047
942	abstract variety, projective space, Grassmannian sing_2704.htm#IDX1048
943	abstractR sing_1448.htm#SEC1524 22284
944	actionIsProper sing_1678.htm#SEC1754 52474
945	addLeftFractions sing_2663.htm#SEC2739 38826
946	addModules sing_2518.htm#SEC2594 51193
947	addNvarsTo sing_1030.htm#SEC1106 63123
948	addRat sing_801.htm#SEC853 4768
949	addSheaf sing_2722.htm#SEC2798 27062
950	addcol sing_1064.htm#SEC1140 52204
951	addcores sing_999.htm#SEC1075 41254
952	addnondegeneratevariables addnondegeneratevariables sing_2679.htm#SEC2755 40483
953	addrow sing_1065.htm#SEC1141 47055
954	addvarsTo sing_1029.htm#SEC1105 17717
955	ademRelations sing_661.htm#SEC713 30263
956	adjoint sing_1089.htm#SEC1165 56619
957	adjointIdeal sing_1377.htm#SEC1453 11455
958	adjunction divisor sing_1795.htm#IDX786
959	admissibleSub sing_720.htm#SEC772 6583
960	afaces sing_2422.htm#SEC2498 28045
961	affine code Fitzgerald-Lax method sing_889.htm#SEC958
962	ainvar.lib sing_1675.htm#SEC1751
963	ainvar_lib sing_1675.htm#SEC1751
964	aksaka.lib sing_1860.htm#SEC1936
965	aksaka_lib sing_1860.htm#SEC1936
966	alexanderpolynomial sing_1473.htm#SEC1549 36814
967	alexpoly.lib sing_1470.htm#SEC1546
968	alexpoly_lib sing_1470.htm#SEC1546
969	algDependent sing_1114.htm#SEC1190 20789
970	alg_kernel sing_1115.htm#SEC1191 307
971	algebra.lib sing_1110.htm#SEC1186
972	algebra_containment sing_1111.htm#SEC1187 47912
973	algebra_lib sing_1110.htm#SEC1186
974	algebraic dependence sing_750.htm#IDX363
975	algebraic field extension sing_1323.htm#IDX579
976	algebraicDependence sing_1336.htm#SEC1412 38500
977	algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_880.htm#SEC937
978	algorithm of Conti and Traverso sing_876.htm#SEC933
979	algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_879.htm#SEC936
980	algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_878.htm#SEC935
981	algorithm of Pottier sing_877.htm#SEC934
982	alias General command syntax sing_35.htm#SEC59
983	align sing_208.htm#SEC248
984	all.lib sing_898.htm#SEC974
985	allDoubleExt sing_767.htm#SEC819 43457
986	allExtOfLeft sing_764.htm#SEC816 6405
987	allExtOfRight sing_765.htm#SEC817 56781
988	allPositive sing_516.htm#SEC568 1409
989	all_lib sing_898.htm#SEC974
990	allowing net access Command line options sing_19.htm#IDX41
991	allprint sing_947.htm#SEC1023 5195
992	allreal sing_2003.htm#SEC2079 57232
993	allrealst sing_2001.htm#SEC2077 40962
994	allsquarefree sing_1577.htm#SEC1653 45545
995	ambientDimension sing_2016.htm#SEC2092 18907
996	and Evaluation of logical expressions sing_101.htm#SEC141
997	and sing_411.htm#SEC451
998	annPoly sing_564.htm#SEC616 18228
999	annRat sing_565.htm#SEC617 62662
1000	annRatSyz sing_790.htm#SEC842 15672
1001	annfs sing_541.htm#SEC593 38155
1002	annfs0 sing_553.htm#SEC605 26476
1003	annfs2 sing_554.htm#SEC606 47962
1004	annfsBMI sing_550.htm#SEC602 2532
1005	annfsParamBM sing_549.htm#SEC601 43587
1006	annfsRB sing_555.htm#SEC607 31892
1007	annfspecial sing_542.htm#SEC594 27566
1008	annihilator of polynomial sing_563.htm#IDX342
1009	annihilator of rational function sing_563.htm#IDX343
1010	annihilator of rational function sing_780.htm#IDX388
1011	annil sing_1218.htm#SEC1294 48744
1012	appelF1 sing_582.htm#SEC634 63146
1013	appelF2 sing_583.htm#SEC635 22460
1014	appelF4 sing_584.htm#SEC636 6847
1015	appendWeight2Ord sing_722.htm#SEC774 21488
1016	apply sing_378.htm#SEC418
1017	applyAdF sing_532.htm#SEC584 40329
1018	applyPermutationToIntvec applyPermutationToIntvec sing_2447.htm#SEC2523 28900
1019	arcpoint.lib sing_1483.htm#SEC1559
1020	arcpoint_lib sing_1483.htm#SEC1559
1021	areEqualLeftFractions areEqualLeftFractions sing_2665.htm#SEC2741 29498
1022	areZeroElements sing_2585.htm#SEC2661 14728
1023	argument, default sing_44.htm#SEC81
1024	argument, optional sing_44.htm#SEC81
1025	arr.lib sing_2173.htm#SEC2249
1026	arr2multarr sing_2206.htm#SEC2282 15063
1027	arrBoolean sing_2195.htm#SEC2271 63256
1028	arrBoundedChambers sing_2216.htm#SEC2292 18347
1029	arrBraid sing_2196.htm#SEC2272 34093
1030	arrCenter sing_2183.htm#SEC2259 24565
1031	arrCentered sing_2185.htm#SEC2261 15904
1032	arrCentral sing_2184.htm#SEC2260 14086
1033	arrCentralize sing_2186.htm#SEC2262 53235
1034	arrChambers sing_2215.htm#SEC2291 44578
1035	arrCharPoly sing_2213.htm#SEC2289 44129
1036	arrCone sing_2189.htm#SEC2265 38068
1037	arrCoordChange sing_2187.htm#SEC2263 61430
1038	arrCoordNormalize sing_2188.htm#SEC2264 46273
1039	arrDecone sing_2190.htm#SEC2266 54637
1040	arrDer sing_2203.htm#SEC2279 48815
1041	arrEdelmanReiner sing_2201.htm#SEC2277 59091
1042	arrEssentialize sing_2194.htm#SEC2270 6667
1043	arrExponents sing_2205.htm#SEC2281 1948
1044	arrFlats sing_2210.htm#SEC2286 64792
1045	arrIsEssential sing_2193.htm#SEC2269 34363
1046	arrIsFree sing_2204.htm#SEC2280 3860
1047	arrLastVar sing_2182.htm#SEC2258 25835
1048	arrLattice sing_2211.htm#SEC2287 58951
1049	arrLocalize sing_2191.htm#SEC2267 56070
1050	arrOrlikSolomon sing_2202.htm#SEC2278 31686
1051	arrPoincare sing_2214.htm#SEC2290 412
1052	arrPrintMatrix sing_2178.htm#SEC2254 21204
1053	arrRandom sing_2199.htm#SEC2275 59986
1054	arrRandomCentral sing_2200.htm#SEC2276 43698
1055	arrRestrict sing_2192.htm#SEC2268 sprintf
1056	arrSet sing_2174.htm#SEC2250 53769
1057	arrSwapVar sing_2181.htm#SEC2257 44919
1058	arrTypeB sing_2197.htm#SEC2273 22358
1059	arrTypeD sing_2198.htm#SEC2274 26495
1060	arr_lib sing_2173.htm#SEC2249
1061	arrange sing_557.htm#SEC609 50350
1062	arrangement sing_2174.htm#IDX817
1063	arrangement sing_2175.htm#IDX822
1064	arrangement sing_2206.htm#IDX884
1065	arrangement sing_2207.htm#IDX887
1066	ask sing_1868.htm#SEC1944 3862
1067	assPrimes sing_1125.htm#SEC1201 sprintf
1068	assign sing_2174.htm#IDX819
1069	assignment,custom Assignments for user defined types sing_187.htm#SEC227
1070	associated tangent FamElemsAtEnvCompPoints sing_940.htm#IDX474
1071	associated tangent sing_941.htm#IDX478
1072	assprimeszerodim.lib assprimeszerodim_lib sing_1123.htm#SEC1199
1073	assprimeszerodim_lib assprimeszerodim_lib sing_1123.htm#SEC1199
1074	atkins.lib sing_1869.htm#SEC1945
1075	atkins_lib sing_1869.htm#SEC1945
1076	attrib sing_209.htm#SEC249
1077	autGenWeights sing_2249.htm#SEC2325 32642
1078	autGradAlg sing_2248.htm#SEC2324 21136
1079	autKS sing_2247.htm#SEC2323 51607
1080	autX sing_2252.htm#SEC2328 43261
1081	autXhat sing_2251.htm#SEC2327 35932
1082	autgradalg.lib sing_2246.htm#SEC2322
1083	autgradalg_lib sing_2246.htm#SEC2322
1084	automorphism group sing_2246.htm#IDX935
1085	automorphisms sing_2246.htm#IDX932
1086	autonom sing_1832.htm#SEC1908 57044
1087	autonomDim sing_1833.htm#SEC1909 30055
1088	awalk1 sing_1156.htm#SEC1232 11044
1089	awalk2 sing_1157.htm#SEC1233 8955
1090	b-function sing_505.htm#IDX315
1091	bFactor sing_587.htm#SEC639 15179
1092	babyGiant sing_1898.htm#SEC1974 41113
1093	backward sing_2387.htm#SEC2463 11225
1094	bareiss sing_210.htm#SEC250
1095	base2str sing_901.htm#SEC977 sprintf
1096	basering sing_28.htm#IDX76
1097	basering sing_88.htm#SEC128
1098	basicinvariants sing_1489.htm#SEC1565 32136
1099	belongSemigroup sing_1128.htm#SEC1204 19983
1100	bernstein sing_1537.htm#SEC1613 5605
1101	bernsteinBM sing_545.htm#SEC597 57689
1102	bernsteinLift sing_546.htm#SEC598 22885
1103	bertini sing_1352.htm#IDX583
1104	bertini sing_1357.htm#IDX590
1105	bertini2Singular sing_1361.htm#SEC1437 58501
1106	betti sing_211.htm#SEC251
1107	betti (plural) sing_455.htm#SEC495
1108	betti number sing_2404.htm#IDX980
1109	bfct sing_506.htm#SEC558 29858
1110	bfctAnn sing_508.htm#SEC560 36658
1111	bfctBound sing_789.htm#SEC841 5630
1112	bfctIdeal sing_510.htm#SEC562 41018
1113	bfctOneGB sing_509.htm#SEC561 9696
1114	bfctSyz sing_507.htm#SEC559 26796
1115	bfctVarAnn sing_598.htm#SEC650 51667
1116	bfctVarIn sing_597.htm#SEC649 9274
1117	bfun.lib sing_505.htm#SEC557
1118	bfun_lib sing_505.htm#SEC557
1119	bigint sing_78.htm#SEC118
1120	bigint declarations sing_79.htm#SEC119
1121	bigint expressions sing_80.htm#SEC120
1122	bigint operations sing_81.htm#SEC121
1123	bigint related functions bigint related functions sing_82.htm#SEC122
1124	bigintToBinary sing_2445.htm#SEC2521 59742
1125	bigintmat sing_83.htm#SEC123
1126	bigintmat declarations bigintmat declarations sing_84.htm#SEC124
1127	bigintmat expressions bigintmat expressions sing_85.htm#SEC125
1128	bigintmat operations bigintmat operations sing_87.htm#SEC127
1129	bigintmat type cast sing_86.htm#SEC126
1130	bimodules sing_498.htm#IDX303
1131	bimodules.lib sing_498.htm#SEC550
1132	bimodules_lib sing_498.htm#SEC550
1133	binaryToBigint sing_2446.htm#SEC2522 sprintf
1134	binary_add sing_1921.htm#SEC1997 42817
1135	binomial sing_906.htm#SEC982 23208
1136	binomials2intmat sing_1284.htm#SEC1360 58804
1137	birational map, image, inverse. sing_1378.htm#IDX615
1138	bistd sing_499.htm#SEC551 45237
1139	bisyzygies sing_498.htm#IDX304
1140	bitrinity sing_500.htm#SEC552 3516
1141	blackbox sing_191.htm#SEC231
1142	blackbox sing_199.htm#SEC239
1143	block sing_40.htm#SEC70
1144	block sing_377.htm#SEC417
1145	blowUp sing_1429.htm#SEC1505 34819
1146	blowUp2 sing_1430.htm#SEC1506 65264
1147	blowUpBO sing_1436.htm#SEC1512 58146
1148	blowup0 sing_1133.htm#SEC1209 44451
1149	boolean sing_2195.htm#IDX861
1150	boolean expressions sing_100.htm#SEC140
1151	boolean operations sing_101.htm#SEC141
1152	boolean_constant sing_2229.htm#SEC2305 52873
1153	boolean_ideal sing_2233.htm#SEC2309 53515
1154	boolean_poly sing_2230.htm#SEC2306 41652
1155	boolean_poly_ring sing_2228.htm#SEC2304 sprintf
1156	boolean_set sing_2234.htm#SEC2310 58235
1157	boolean_std sing_2227.htm#SEC2303 5921
1158	border basis sing_2693.htm#IDX1031
1159	borderBasis sing_2694.htm#SEC2770 33172
1160	boundBuFou sing_1998.htm#SEC2074 26589
1161	boundDes sing_2000.htm#SEC2076 35149
1162	boundaryLatticePoints boundaryLatticePoints sing_2086.htm#SEC2162 6238
1163	boundposDes sing_1999.htm#SEC2075 58854
1164	bounds sing_2681.htm#SEC2757 50218
1165	boxSet sing_2683.htm#SEC2759 8552
1166	bracket sing_358.htm#IDX197
1167	bracket sing_414.htm#SEC454
1168	bracket sing_456.htm#SEC496
1169	braid sing_2196.htm#IDX863
1170	branchTo procs with different argument types sing_160.htm#SEC200
1171	break sing_379.htm#SEC419
1172	break point sing_393.htm#SEC433
1173	breakpoint sing_380.htm#SEC420
1174	brillnoether.lib sing_2253.htm#SEC2329
1175	brillnoether_lib sing_2253.htm#SEC2329
1176	brnoeth.lib sing_1794.htm#SEC1870
1177	brnoeth_lib sing_1794.htm#SEC1870
1178	browser, command line option Command line options sing_19.htm#IDX44
1179	browser, setting the sing_358.htm#IDX193
1180	browsers The online help system sing_16.htm#IDX21
1181	browsers, setting the sing_358.htm#IDX192
1182	bubblesort sing_1871.htm#SEC1947 63278
1183	busadj sing_1087.htm#SEC1163 36301
1184	bvar sing_2241.htm#SEC2317 52773
1185	c, module ordering sing_862.htm#IDX415
1186	cProj sing_2295.htm#SEC2371 24037
1187	calculateI sing_1403.htm#SEC1479 31107
1188	calculate_max_sum sing_1940.htm#SEC2016 4706
1189	calculate_ordering sing_1918.htm#SEC1994 42616
1190	cancelunit, option sing_315.htm#IDX171
1191	canonMap sing_1161.htm#SEC1237 47599
1192	canoncial form sing_928.htm#IDX436
1193	canoncial form sing_929.htm#IDX438
1194	canoncial form sing_930.htm#IDX440
1195	canonical sing_924.htm#IDX424
1196	canonical form sing_933.htm#IDX454
1197	canonical form sing_934.htm#IDX456
1198	canonical, sing_932.htm#IDX450
1199	canonicalizeCone sing_2017.htm#SEC2093 6251
1200	canonize sing_1840.htm#SEC1916 54090
1201	cantoradd sing_1954.htm#SEC2030 55304
1202	cantormult sing_1957.htm#SEC2033 57569
1203	cantorred sing_1955.htm#SEC2031 46502
1204	cardGroup sing_1130.htm#SEC1206 5553
1205	case No case or switch statement sing_412.htm#SEC452
1206	catNets sing_2623.htm#SEC2699 24760
1207	cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2748.htm#SEC2824 55393
1208	cdd sing_1.htm#IDX10
1209	cddlib sing_1.htm#IDX11
1210	center sing_519.htm#IDX322 65108
1211	center sing_525.htm#SEC577
1212	center sing_2183.htm#IDX843
1213	center sing_2184.htm#IDX844
1214	center sing_2185.htm#IDX846
1215	center sing_2186.htm#IDX848
1216	centerRed sing_524.htm#SEC576 59910
1217	centerVS sing_523.htm#SEC575 27548
1218	central sing_2177.htm#IDX829
1219	central sing_2184.htm#IDX845
1220	central sing_2186.htm#IDX847
1221	central sing_2200.htm#IDX872
1222	central.lib sing_519.htm#SEC571
1223	central1st sing_2388.htm#SEC2464 29090
1224	central2nd sing_2389.htm#SEC2465 37545
1225	central_lib sing_519.htm#SEC571
1226	centralize sing_519.htm#IDX325
1227	centralizeSet sing_520.htm#SEC572 55737
1228	centralizer sing_519.htm#IDX323 65261
1229	centralizer sing_526.htm#SEC578
1230	centralizerRed sing_522.htm#SEC574 8209
1231	centralizerVS sing_521.htm#SEC573 22925
1232	cf_class sing_209.htm#IDX132
1233	cgs sing_900.htm#SEC976 57776
1234	cgsdr sing_925.htm#SEC1001 44460
1235	chAll sing_2265.htm#SEC2341 2690
1236	chAllInv sing_2266.htm#SEC2342 57760
1237	chDual sing_2271.htm#SEC2347 17745
1238	chHE sing_2267.htm#SEC2343 63916
1239	chHom sing_2280.htm#SEC2356 54776
1240	chNum sing_2261.htm#SEC2337 54415
1241	chNumbers sing_2262.htm#SEC2338 42134
1242	chNumbersProj sing_2299.htm#SEC2375 28837
1243	chProd sing_2273.htm#SEC2349 40209
1244	chProdE sing_2274.htm#SEC2350 33460
1245	chProdL sing_2275.htm#SEC2351 44795
1246	chProdLP sing_2276.htm#SEC2352 8881
1247	chProdM sing_2277.htm#SEC2353 64514
1248	chProdMP sing_2278.htm#SEC2354 17103
1249	chProj sing_2296.htm#SEC2372 32311
1250	chSum sing_2269.htm#SEC2345 21088
1251	chSymm sing_2283.htm#SEC2359 24066
1252	chSymm2L sing_2284.htm#SEC2360 51625
1253	chSymm2LP sing_2285.htm#SEC2361 26099
1254	chWedge sing_2286.htm#SEC2362 57678
1255	chWedge2L sing_2287.htm#SEC2363 46597
1256	chWedge2LP sing_2288.htm#SEC2364 8876
1257	chaincrit sing_1968.htm#SEC2044 9502
1258	chambers sing_2215.htm#IDX900
1259	chambers sing_2216.htm#IDX901
1260	changeDenominator sing_1256.htm#SEC1332 21094
1261	changechar sing_1004.htm#SEC1080 65454
1262	changeord sing_1005.htm#SEC1081 55156
1263	changeordTo sing_1028.htm#SEC1104 41903
1264	changes sing_2754.htm#SEC2830
1265	changevar sing_1006.htm#SEC1082 32829
1266	char sing_212.htm#SEC252
1267	charInfo sing_580.htm#SEC632 11034
1268	charVariety sing_579.htm#SEC631 18306
1269	char_series sing_213.htm#SEC253
1270	characteristic exponents sing_1477.htm#IDX639
1271	characteristic exponents sing_1478.htm#IDX644
1272	characteristic exponents sing_1479.htm#IDX647
1273	characteristic exponents sing_1480.htm#IDX651
1274	characteristic exponents sing_1564.htm#IDX757
1275	characteristic polynomial sing_2213.htm#IDX898
1276	characteristic variety sing_563.htm#IDX350
1277	characteristic variety sing_780.htm#IDX384
1278	charexp2conductor sing_1480.htm#SEC1556 sprintf
1279	charexp2generators sing_1478.htm#SEC1554 16838
1280	charexp2inter sing_1479.htm#SEC1555 39881
1281	charexp2multseq sing_1477.htm#SEC1553 334
1282	charexp2poly sing_1481.htm#SEC1557 sprintf
1283	charpoly sing_1088.htm#SEC1164 29561
1284	charstr sing_214.htm#SEC254
1285	checkFactor sing_556.htm#SEC608 55900
1286	checkRoot sing_551.htm#SEC603 37045
1287	chern sing_2260.htm#SEC2336 4916
1288	chern.lib sing_2255.htm#SEC2331
1289	chernCharPoly sing_2302.htm#SEC2378 31610
1290	chernPoly sing_2301.htm#SEC2377 31316
1291	chern_lib sing_2255.htm#SEC2331
1292	chineseRem sing_1889.htm#SEC1965 38560
1293	chinrem sing_215.htm#SEC255
1294	chinrempoly sing_2649.htm#SEC2725 42312
1295	chinrestp sing_1948.htm#SEC2024 24779
1296	cimonom.lib sing_2317.htm#SEC2393
1297	cimonom_lib sing_2317.htm#SEC2393
1298	cisimplicial.lib sing_1126.htm#SEC1202
1299	cisimplicial_lib sing_1126.htm#SEC1202
1300	classification sing_2321.htm#IDX938
1301	classify sing_1490.htm#SEC1566 4953
1302	classify.lib sing_1488.htm#SEC1564
1303	classify2.lib sing_2321.htm#SEC2397
1304	classify2_lib sing_2321.htm#SEC2397
1305	classifyCeq sing_1507.htm#SEC1583 42719
1306	classifyMapGerms.lib classifyMapGerms_lib sing_2333.htm#SEC2409
1307	classifyMapGerms_lib classifyMapGerms_lib sing_2333.htm#SEC2409
1308	classifySimpleMaps sing_2339.htm#SEC2415 62176
1309	classifySimpleMaps1 sing_2340.htm#SEC2416 24789
1310	classifyUnimodalMaps classifyUnimodalMaps sing_2341.htm#SEC2417 63464
1311	classify_aeq.lib sing_2324.htm#SEC2400
1312	classify_aeq_lib sing_2324.htm#SEC2400
1313	classify_lib sing_1488.htm#SEC1564
1314	classifyceq.lib sing_1506.htm#IDX654
1315	classifyceq_lib sing_1506.htm#IDX655
1316	classifyci.lib sing_1508.htm#IDX656
1317	classifyci_lib sing_1508.htm#IDX657
1318	classifyicis sing_1509.htm#SEC1585 37651
1319	classpoly sing_2300.htm#SEC2376 45724
1320	cleanTmp sing_2164.htm#SEC2240 14108
1321	cleanunit sing_1401.htm#SEC1477 sprintf
1322	cleardenom sing_216.htm#SEC256
1323	close sing_217.htm#SEC257
1324	closed_points sing_1804.htm#SEC1880 47269
1325	closetex sing_1771.htm#SEC1847 42334
1326	closureFrac sing_1249.htm#SEC1325 9252
1327	coDim sing_2335.htm#SEC2411 60680
1328	coDimMap sing_2334.htm#SEC2410 2002
1329	coHom sing_773.htm#SEC825 51043
1330	codim sing_1602.htm#SEC1678 14253
1331	codimension sing_2018.htm#SEC2094 32207
1332	coding theory sing_854.htm#SEC906
1333	coef sing_218.htm#SEC258
1334	coefficient sing_2176.htm#IDX825
1335	coefficient sing_2177.htm#IDX828
1336	coefficient sing_2178.htm#IDX832
1337	coefficient field sing_144.htm#SEC184
1338	coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45
1339	coefficients, long sing_811.htm#SEC863
1340	coeffmod sing_1866.htm#SEC1942 23531
1341	coeffs sing_219.htm#SEC259
1342	coker sing_2514.htm#SEC2590 35639
1343	colength of derivations curveColengthDerivations sing_2350.htm#IDX958
1344	collectDiv sing_1446.htm#SEC1522 50348
1345	colrank sing_1838.htm#SEC1914 52290
1346	colred sing_1071.htm#SEC1147 1693
1347	combinat.lib sing_2342.htm#SEC2418
1348	combinat_lib sing_2342.htm#SEC2418
1349	commRing sing_804.htm#SEC856 30892
1350	comma sing_413.htm#SEC453
1351	command,custom Commands for user defined types sing_186.htm#SEC226
1352	command-line option, setting value of sing_358.htm#IDX281
1353	command-line option, value of sing_358.htm#IDX279
1354	command-line options, print all values of sing_358.htm#IDX278
1355	command-line options, short help Command line options sing_19.htm#IDX38
1356	commands (plural) sing_454.htm#IDX302
1357	comment sing_36.htm#IDX108
1358	compareMatrix sing_2522.htm#SEC2598 49930
1359	compareModules sing_2517.htm#SEC2593 3692
1360	compareTasks sing_1035.htm#SEC1111 45157
1361	compareVectors sing_2542.htm#SEC2618 12881
1362	completeReduction sing_1680.htm#SEC1756 57157
1363	complex sing_28.htm#IDX75
1364	complexClassify sing_2322.htm#SEC2398 22796
1365	complexSingType sing_1504.htm#SEC1580 34483
1366	complexType sing_2323.htm#SEC2399 55772
1367	compregb.lib sing_899.htm#SEC975
1368	compregb_lib sing_899.htm#SEC975
1369	comprehensive Groebner system sing_899.htm#IDX421
1370	compress sing_1048.htm#SEC1124 61998
1371	computeAfaceOrbits sing_2432.htm#SEC2508 28683
1372	computeConstant sing_1146.htm#SEC1222 55024
1373	computeGromovWitten sing_1149.htm#SEC1225 18834
1374	computeN sing_1450.htm#SEC1526 61628
1375	computeV sing_1449.htm#SEC1525 40316
1376	computemcm sing_1408.htm#SEC1484 36956
1377	concat sing_1049.htm#SEC1125 16653
1378	conductor sing_1257.htm#IDX571
1379	conductor sing_1480.htm#IDX650
1380	conductor sing_2348.htm#IDX952
1381	conductor, degree sing_1564.htm#IDX760
1382	cone sing_188.htm#SEC228
1383	cone sing_2189.htm#IDX852
1384	cone sing_2190.htm#IDX854
1385	coneLink sing_2021.htm#SEC2097 13635
1386	coneViaInequalities sing_2020.htm#SEC2096 25661
1387	coneViaPoints sing_2019.htm#SEC2095 3386
1388	conic, parametrization, rational point. sing_1385.htm#IDX620
1389	conicWithTangents sing_2140.htm#SEC2216 60752
1390	constructH sing_1409.htm#SEC1485 59577
1391	constructblwup sing_1410.htm#SEC1486 19326
1392	constructible set sing_933.htm#IDX452
1393	constructible sets sing_934.htm#IDX455
1394	constructlastblwup sing_1411.htm#SEC1487 7639
1395	constructor sing_2206.htm#IDX885
1396	constructor sing_2207.htm#IDX888
1397	contact matrix sing_1479.htm#IDX646
1398	containedQ sing_1759.htm#SEC1835 46718
1399	containsAsFace sing_2022.htm#SEC2098 25159
1400	containsInCollection containsInCollection sing_2055.htm#SEC2131 14368
1401	containsInSupport sing_2023.htm#SEC2099 32493
1402	containsPositiveVector containsPositiveVector sing_2024.htm#SEC2100 27042
1403	containsRelatively sing_2025.htm#SEC2101 17126
1404	content sing_978.htm#SEC1054 9095
1405	contentSB, option sing_315.htm#IDX172
1406	continue Behavior of continue sing_381.htm#SEC421
1407	continue sing_415.htm#SEC455
1408	contraHom sing_774.htm#SEC826 54270
1409	contract sing_220.htm#SEC260
1410	contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2729.htm#IDX1060
1411	contributionBundle sing_2729.htm#SEC2805 32874
1412	contributors sing_358.htm#IDX200
1413	control sing_1830.htm#SEC1906 44498
1414	control.lib sing_1829.htm#SEC1905
1415	controlDim sing_1831.htm#SEC1907 2417
1416	controlExample sing_1843.htm#SEC1919 2678
1417	control_Matrix sing_1532.htm#SEC1608 sprintf
1418	control_lib sing_1829.htm#SEC1905
1419	convertLeftToRightFraction convertLeftToRightFraction sing_2662.htm#SEC2738 4318
1420	convertRightToLeftFraction convertRightToLeftFraction sing_2661.htm#SEC2737 19389
1421	convertdata sing_1406.htm#SEC1482 54629
1422	convexHull sing_2026.htm#SEC2102 56690
1423	convexIntersection sing_2027.htm#SEC2103 63587
1424	convloc sing_560.htm#SEC612 19122
1425	coordinate change sing_2186.htm#IDX849
1426	coordinate change sing_2187.htm#IDX850
1427	coordinate change sing_2188.htm#IDX851
1428	coordinates sing_1986.htm#IDX802
1429	coords sing_1986.htm#SEC2062 29362
1430	copyTask sing_1034.htm#SEC1110 65331
1431	copyright sing_1.htm#IDX1
1432	corank sing_1491.htm#SEC1567 33709
1433	cornerMonomials sing_1287.htm#SEC1363 33995
1434	countPoints sing_1911.htm#SEC1987 58566
1435	coverings sing_1148.htm#IDX530
1436	coverings sing_1149.htm#IDX534
1437	cpu sing_358.htm#IDX202
1438	cpu sing_358.htm#IDX275
1439	createBO sing_1437.htm#SEC1513 32669
1440	createGradedRingHomomorphism createGradedRingHomomorphism sing_2561.htm#SEC2637 62177
1441	createGroup sing_2554.htm#SEC2630 28500
1442	createQuotientGroup sing_2555.htm#SEC2631 26374
1443	createTask sing_1032.htm#SEC1108 48404
1444	createTorsionFreeGroup createTorsionFreeGroup sing_2556.htm#SEC2632 51944
1445	createlist sing_1419.htm#SEC1495 61781
1446	cring sing_73.htm#SEC113
1447	cring declarations sing_74.htm#SEC114
1448	cring expressions sing_75.htm#SEC115
1449	cring operations sing_76.htm#SEC116
1450	cring related functions cring related functions sing_77.htm#SEC117
1451	crossprod sing_221.htm#SEC261
1452	crypto.lib sing_1884.htm#SEC1960
1453	crypto_lib sing_1884.htm#SEC1960
1454	cup sing_1162.htm#SEC1238 57972
1455	cupproduct sing_1163.htm#SEC1239 43349
1456	curve singularities sing_1470.htm#IDX633
1457	curve singularities sing_1558.htm#IDX755
1458	curve singularity sing_2346.htm#IDX947
1459	curveColengthDerivations curveColengthDerivations sing_2350.htm#SEC2426 2078
1460	curveConductorMult sing_2348.htm#SEC2424 15897
1461	curveDeligneNumber sing_2349.htm#SEC2425 12294
1462	curveDeltaInv sing_2347.htm#SEC2423 16375
1463	curveInv.lib sing_2346.htm#SEC2422
1464	curveInv_lib sing_2346.htm#SEC2422
1465	curvepar.lib sing_1511.htm#SEC1587
1466	curvepar_lib sing_1511.htm#SEC1587
1467	custom assignment Assignments for user defined types sing_187.htm#SEC227
1468	custom command Commands for user defined types sing_186.htm#SEC226
1469	custom type Definition of a user defined type sing_183.htm#SEC223
1470	customstd.lib sing_2218.htm#SEC2294
1471	customstd_lib sing_2218.htm#SEC2294
1472	cycleLength sing_2077.htm#SEC2153 16898
1473	cyclePoints sing_2081.htm#SEC2157 54460
1474	cyclic sing_965.htm#SEC1041 21375
1475	cyclic code Codes and the decoding problem sing_886.htm#SEC945
1476	cyclotomic sing_1645.htm#SEC1721 33749
1477	datetime sing_222.htm#SEC262 50127
1478	dbprint sing_223.htm#SEC263
1479	deRham.lib sing_2351.htm#SEC2427
1480	deRhamCohom sing_577.htm#SEC629 58222
1481	deRhamCohomIdeal sing_578.htm#SEC630 42169
1482	deRhamCohomology sing_2352.htm#SEC2428 41947
1483	deRham_lib sing_2351.htm#SEC2427
1484	debugLib, option sing_315.htm#IDX176
1485	debug_log sing_1501.htm#SEC1577 62043
1486	debugger Source code debugger sing_66.htm#SEC103
1487	debugging library code Source code debugger sing_66.htm#SEC103
1488	dec1var sing_1217.htm#SEC1293 36098
1489	decimal sing_1885.htm#SEC1961 56066
1490	decode sing_1821.htm#SEC1897 64330
1491	decodeCode sing_1823.htm#SEC1899 28262
1492	decodeRandom sing_1822.htm#SEC1898 40118
1493	decodeRandomFL sing_1826.htm#SEC1902 35423
1494	decodeSV sing_1803.htm#SEC1879 37975
1495	decodegb.lib sing_1808.htm#SEC1884
1496	decodegb_lib sing_1808.htm#SEC1884
1497	decoding, decoding problem Codes and the decoding problem sing_886.htm#SEC946
1498	decoef sing_1851.htm#SEC1927 60284
1499	decomposition of modules sing_1210.htm#IDX559
1500	decomposition, numerical sing_1357.htm#IDX588
1501	decone sing_2189.htm#IDX853
1502	decone sing_2190.htm#IDX855
1503	def sing_88.htm#SEC128
1504	def declarations sing_89.htm#SEC129
1505	defRes, option sing_315.htm#IDX177
1506	default argument sing_44.htm#SEC81
1507	defineHomogeneous sing_2594.htm#SEC2670 55072
1508	defined sing_224.htm#SEC264
1509	defl sing_1368.htm#SEC1444 11825
1510	deform sing_1603.htm#SEC1679 5250
1511	deform.lib sing_1522.htm#SEC1598
1512	deform_lib sing_1522.htm#SEC1598
1513	defring sing_1007.htm#SEC1083 1814
1514	defringp sing_1009.htm#SEC1085 42905
1515	defrings sing_1008.htm#SEC1084 1034
1516	deg sing_225.htm#SEC265
1517	degBound sing_395.htm#SEC435
1518	degree Miscellaneous oddities sing_226.htm#SEC266
1519	degree sing_418.htm#IDX292
1520	degree lexicographical ordering sing_860.htm#IDX395
1521	degree of a polynomial Miscellaneous oddities sing_418.htm#IDX296
1522	degree reverse lexicographical ordering sing_860.htm#IDX393
1523	degreeDivisor sing_2362.htm#SEC2438 31751
1524	degreeFormalDivisor sing_2370.htm#SEC2446 42503
1525	degreepart sing_1711.htm#SEC1787 53036
1526	delete sing_126.htm#SEC166
1527	delete sing_227.htm#SEC267
1528	delete sing_276.htm#SEC316
1529	deleteGenerator sing_592.htm#SEC644 24917
1530	deleteSublist sing_907.htm#SEC983 20406
1531	deligne number curveColengthDerivations sing_2346.htm#IDX949
1532	deligne number sing_2349.htm#IDX954
1533	deligne number sing_2350.htm#IDX956
1534	delta sing_1570.htm#SEC1646 56952
1535	delta invariant sing_1251.htm#IDX569
1536	delta invariant sing_1570.htm#IDX765
1537	delta invariant sing_2347.htm#IDX950
1538	delta invariant. sing_1243.htm#IDX562
1539	delta invariant. sing_1244.htm#IDX565
1540	delta invariant. sing_1245.htm#IDX568
1541	deltaLoc sing_1251.htm#SEC1327 35192
1542	denom_list sing_358.htm#IDX204
1543	denominator sing_228.htm#SEC268
1544	depth sing_1164.htm#SEC1240 17777
1545	depthIdeal sing_1227.htm#SEC1303 54782
1546	derivate sing_1677.htm#SEC1753 15409
1547	derivation sing_2203.htm#IDX876
1548	desingularization sing_2451.htm#IDX985 59041
1549	desingularization sing_2452.htm#SEC2528
1550	det sing_229.htm#SEC269
1551	det_B sing_1090.htm#SEC1166 60143
1552	detadj sing_1586.htm#SEC1662 5914
1553	determinacy sing_2678.htm#SEC2754 44818
1554	determinecenter sing_1391.htm#SEC1467 44496
1555	detropicalise sing_2158.htm#SEC2234 38025
1556	develop sing_1560.htm#SEC1636 48457
1557	diag sing_1050.htm#SEC1126 56759
1558	diagInvariants sing_1266.htm#SEC1342 62096
1559	diag_test sing_1086.htm#SEC1162 31469
1560	diff sing_230.htm#SEC270
1561	diffRat sing_803.htm#SEC855 36134
1562	difpoly2tex sing_1852.htm#SEC1928 6451
1563	dim sing_231.htm#SEC271
1564	dim (plural) sing_457.htm#SEC497
1565	dimGradedPart sing_1459.htm#SEC1535 11262
1566	dimH sing_1458.htm#SEC1534 38534
1567	dimMon sing_1207.htm#SEC1283 39971
1568	dimStack sing_2727.htm#SEC2803 47772
1569	dim_slocus sing_1604.htm#SEC1680 47218
1570	dimension sing_2028.htm#SEC2104 35262
1571	dimension, moduli space of stable maps, rational curves dimStack sing_2727.htm#IDX1058
1572	dimensionOfLocalization dimensionOfLocalization sing_2415.htm#SEC2491 25632
1573	direct_boolean_poly sing_2231.htm#SEC2307 49893
1574	direct_from_boolean_poly direct_from_boolean_poly sing_2237.htm#SEC2313 36941
1575	disc sing_1872.htm#SEC1948 45279
1576	discr sing_1626.htm#SEC1702 9642
1577	discrepancy sing_1444.htm#SEC1520 5597
1578	discrim sing_942.htm#SEC1018 44091
1579	discussion of parametric ideal sing_924.htm#IDX425
1580	disjoint sing_925.htm#IDX427
1581	disp_zdd sing_2244.htm#SEC2320 41439
1582	displayCohom sing_1460.htm#SEC1536 22633
1583	displayHNE sing_1563.htm#SEC1639 29845
1584	displayInvariants sing_1565.htm#SEC1641 13678
1585	displayMultsequence sing_1567.htm#SEC1643 16668
1586	displayPuiseuxExpansion displayPuiseuxExpansion sing_2133.htm#SEC2209 560
1587	displayTropicalLifting displayTropicalLifting sing_2131.htm#SEC2207 28144
1588	distributed computing sing_958.htm#IDX492
1589	distributed computing sing_998.htm#IDX494
1590	distributed computing sing_1031.htm#IDX504
1591	div Miscellaneous oddities sing_81.htm#SEC121
1592	div sing_98.htm#SEC138
1593	div sing_155.htm#SEC195
1594	div sing_418.htm#IDX289
1595	divideUnits sing_1848.htm#SEC1924 26711
1596	dividelist sing_1418.htm#SEC1494 34210
1597	division sing_232.htm#SEC272
1598	division sing_926.htm#IDX430
1599	division sing_927.htm#IDX432
1600	division (plural) sing_458.htm#SEC498
1601	divisor sing_1951.htm#SEC2027 47231
1602	divisorplus sing_2356.htm#SEC2432 34248
1603	divisors negativeformaldivisor sing_2355.htm#IDX959
1604	divisors sing_2356.htm#IDX960
1605	divisors sing_2357.htm#IDX961
1606	divisors sing_2358.htm#IDX962
1607	divisors sing_2359.htm#IDX963
1608	divisors sing_2360.htm#IDX964
1609	divisors sing_2361.htm#IDX965
1610	divisors sing_2362.htm#IDX966
1611	divisors sing_2363.htm#IDX967
1612	divisors sing_2364.htm#IDX968
1613	divisors sing_2365.htm#IDX969
1614	divisors sing_2366.htm#IDX970
1615	divisors sing_2367.htm#IDX971
1616	divisors sing_2368.htm#IDX972
1617	divisors sing_2369.htm#IDX973
1618	divisors sing_2370.htm#IDX974
1619	divisors, polyhedra sing_2371.htm#IDX975
1620	divisors, polyhedra sing_2372.htm#IDX976
1621	divisors, polyhedra sing_2373.htm#IDX977
1622	divisors.lib sing_2354.htm#SEC2430
1623	divisors_lib sing_2354.htm#SEC2430
1624	dmod.lib sing_540.htm#SEC592
1625	dmodAction sing_798.htm#SEC850 9763
1626	dmodActionRat sing_799.htm#SEC851 6277
1627	dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_791.htm#SEC843 44337
1628	dmod_lib sing_540.htm#SEC592
1629	dmodapp.lib sing_563.htm#SEC615
1630	dmodapp_lib sing_563.htm#SEC615
1631	dmodloc.lib sing_780.htm#IDX377
1632	dmodloc_lib sing_780.htm#IDX378
1633	dmodoublext sing_775.htm#SEC827 60637
1634	dmodvar.lib sing_596.htm#SEC648
1635	dmodvar_lib sing_596.htm#SEC648
1636	double sing_1956.htm#SEC2032 34697
1637	doubleExt sing_766.htm#SEC818 56896
1638	downloading Download instructions sing_2762.htm#SEC2851
1639	dp, global ordering sing_860.htm#IDX394
1640	drawNewtonSubdivision drawNewtonSubdivision sing_2136.htm#SEC2212 50904
1641	drawTropicalCurve sing_2135.htm#SEC2211 10441
1642	ds, local ordering sing_861.htm#IDX404
1643	dsum sing_1051.htm#SEC1127 1303
1644	dualCone sing_2029.htm#SEC2105 61460
1645	dualConic sing_2160.htm#SEC2236 31080
1646	dualPart sing_2308.htm#SEC2384 13279
1647	dualPartition sing_2740.htm#SEC2816 24739
1648	dualPolytope sing_2068.htm#SEC2144 32081
1649	dualSheaf sing_2718.htm#SEC2794 633
1650	dual_code sing_1805.htm#SEC1881 57229
1651	dump sing_233.htm#SEC273
1652	dynamic geometry sing_935.htm#IDX459
1653	dynamic geometry sing_936.htm#IDX462
1654	ecart sing_1959.htm#SEC2035 32475
1655	echo sing_396.htm#SEC436
1656	eexgcdN sing_1886.htm#SEC1962 53237
1657	effective sing_2364.htm#SEC2440 53028
1658	egcdMain sing_1752.htm#SEC1828 25359
1659	ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2087.htm#SEC2163 38271
1660	ehrhartRing sing_1262.htm#SEC1338 16966
1661	eigenvals sing_1098.htm#SEC1174 11228
1662	eigenvalue sing_328.htm#SEC368
1663	eigenvalue sing_1098.htm#IDX510
1664	eigenvalues sing_1345.htm#SEC1421 2182
1665	elemSymmId sing_966.htm#SEC1042 sprintf
1666	elim sing_1135.htm#SEC1211 62585
1667	elim.lib sing_1132.htm#SEC1208
1668	elim1 sing_1136.htm#SEC1212 15653
1669	elim2 sing_1137.htm#SEC1213 44749
1670	elimRing sing_1134.htm#SEC1210 12194
1671	elimWeight sing_723.htm#SEC775 54297
1672	elim_lib sing_1132.htm#SEC1208
1673	eliminate sing_234.htm#SEC274
1674	eliminate (plural) sing_459.htm#SEC499
1675	eliminateNC sing_718.htm#SEC770 3777
1676	elimination sing_717.htm#IDX362
1677	elimlinearpart sing_1712.htm#SEC1788 14251
1678	elimpart sing_1713.htm#SEC1789 10258
1679	elimpartanyr sing_1714.htm#SEC1790 39751
1680	elimrep sing_1399.htm#SEC1475 23641
1681	elliptic curve sing_1145.htm#IDX526
1682	elliptic curves sing_1142.htm#IDX520
1683	elliptic curves sing_1148.htm#IDX529
1684	elliptic curves sing_1149.htm#IDX533
1685	ellipticAdd sing_1907.htm#SEC1983 13279
1686	ellipticAllPoints sing_1912.htm#SEC1988 60770
1687	ellipticMult sing_1908.htm#SEC1984 1558
1688	ellipticNF sing_2084.htm#SEC2160 5045
1689	ellipticNFDB sing_2085.htm#SEC2161 27917
1690	ellipticRandomCurve sing_1909.htm#SEC1985 36980
1691	ellipticRandomPoint sing_1910.htm#SEC1986 6866
1692	ellipticcovers.lib sing_1142.htm#IDX514
1693	ellipticcovers_lib sing_1142.htm#IDX515
1694	else sing_386.htm#SEC426
1695	embedMat sing_749.htm#SEC801 17119
1696	emptyFan sing_2056.htm#SEC2132 7396
1697	encode sing_1813.htm#SEC1889 56687
1698	endomorphism filtration sing_1544.htm#IDX731
1699	endvfilt sing_1544.htm#SEC1620 26670
1700	engine sing_593.htm#SEC645 30876
1701	ensureLeftNcfrac sing_2611.htm#SEC2687 64571
1702	ensureRightNcfrac sing_2612.htm#SEC2688 14107
1703	envelop FamElemsAtEnvCompPoints sing_937.htm#SEC1013 27362
1704	envelop sing_937.htm#IDX465
1705	envelop sing_938.htm#IDX468
1706	envelop sing_940.htm#IDX473
1707	envelop sing_941.htm#IDX477
1708	envelope sing_460.htm#SEC500
1709	enveloping algebra sing_358.htm#IDX208
1710	enveloping algebra sing_498.htm#IDX306
1711	environment variable, DISPLAY The online help system sing_16.htm#IDX29
1712	equalJinI sing_1487.htm#SEC1563 18502
1713	equalMultiDeg sing_2587.htm#SEC2663 37090
1714	equations sing_2030.htm#SEC2106 7896
1715	equiRadical sing_1303.htm#SEC1379 8884
1716	equidim sing_1305.htm#SEC1381 38541
1717	equidimMax sing_1306.htm#SEC1382 49289
1718	equidimMaxEHV sing_1307.htm#SEC1383 42650
1719	equidimZ sing_1318.htm#SEC1394 49610
1720	equising.lib sing_1527.htm#SEC1603
1721	equising_lib sing_1527.htm#SEC1603
1722	equisingular Tjurina number sing_1470.htm#IDX638
1723	equisingularity ideal sing_1529.htm#IDX658
1724	equisingularity stratum sing_1530.htm#IDX659
1725	error recovery sing_15.htm#SEC21
1726	errorInsert sing_1816.htm#SEC1892 59470
1727	errorRand sing_1817.htm#SEC1893 5727
1728	errormap sing_2394.htm#SEC2470 7782
1729	esIdeal sing_1529.htm#SEC1605 60477
1730	esStratum sing_1530.htm#SEC1606 50094
1731	essential sing_2193.htm#IDX858
1732	essential sing_2194.htm#IDX859
1733	eta sing_2079.htm#SEC2155 60729
1734	euler sing_1865.htm#SEC1941 10519
1735	eulerChProj sing_2298.htm#SEC2374 28549
1736	eval sing_235.htm#SEC275
1737	evalJacobianAtBox sing_2689.htm#SEC2765 42716
1738	evalPolyAtBox sing_2688.htm#SEC2764 43040
1739	evaluateFormalDivisor evaluateFormalDivisor sing_2366.htm#SEC2442 3535
1740	evaluatePDivisor sing_2372.htm#SEC2448 18855
1741	evaluateProduct sing_2442.htm#SEC2518 54515
1742	evaluate_reynolds sing_1650.htm#SEC1726 46353
1743	evalutateIntegral sing_1147.htm#SEC1223 sprintf
1744	example sing_237.htm#SEC277
1745	example sing_2195.htm#IDX860
1746	example sing_2196.htm#IDX862
1747	example sing_2197.htm#IDX864
1748	example sing_2198.htm#IDX866
1749	example sing_2199.htm#IDX868
1750	example sing_2200.htm#IDX870
1751	example sing_2201.htm#IDX873
1752	execute sing_238.htm#SEC278
1753	exit sing_390.htm#SEC430
1754	exp2pt sing_1853.htm#SEC1929 19621
1755	expo sing_1877.htm#SEC1953 8833
1756	exponents sing_2205.htm#IDX881
1757	export sing_383.htm#SEC423
1758	exportNuminvs sing_1270.htm#SEC1346 10423
1759	exportto sing_384.htm#SEC424
1760	expp sing_2738.htm#SEC2814 15751
1761	expression list sing_72.htm#IDX128
1762	expression list sing_422.htm#IDX299
1763	ext-module purityfiltration_lib sing_758.htm#IDX368
1764	extcurve sing_1799.htm#SEC1875 6730
1765	extdevelop sing_1561.htm#SEC1637 51044
1766	extendGC sing_932.htm#SEC1008 40951
1767	extendWeyl sing_792.htm#SEC844 49954
1768	extendedTensor sing_724.htm#SEC776 4975
1769	extendpoly sing_931.htm#SEC1007 29201
1770	extendring sing_1010.htm#SEC1086 64781
1771	extension of rings sing_1323.htm#IDX580
1772	exterior basis sing_1077.htm#IDX507
1773	exterior power sing_1079.htm#IDX509
1774	exteriorBasis sing_1077.htm#SEC1153 sprintf
1775	exteriorPower sing_1079.htm#SEC1155 20173
1776	extgcd sing_239.htm#SEC279
1777	fVector sing_2059.htm#SEC2135 3715
1778	fVectorP sing_2088.htm#SEC2164 31843
1779	facFirstShift sing_711.htm#SEC763 6469
1780	facFirstWeyl sing_707.htm#SEC759 42412
1781	facGBIdeal sing_1288.htm#SEC1364 9924
1782	facShift sing_710.htm#SEC762 48551
1783	facSubWeyl sing_709.htm#SEC761 9630
1784	facWeyl sing_706.htm#SEC758 32331
1785	faceContaining sing_2031.htm#SEC2107 64804
1786	facetVertexLatticeDistances facetVertexLatticeDistances sing_2089.htm#SEC2165 60714
1787	facetWidth sing_2090.htm#SEC2166 62810
1788	facetWidths sing_2091.htm#SEC2167 5503
1789	facets sing_2032.htm#SEC2108 8112
1790	facstd sing_240.htm#SEC280
1791	factmodd sing_241.htm#SEC281
1792	factor sing_322.htm#SEC362
1793	factorH sing_922.htm#SEC998 24814
1794	factorLenstraECM sing_1916.htm#SEC1992 54951
1795	factorMain sing_1753.htm#SEC1829 65152
1796	factorgroup sing_2577.htm#SEC2653 59914
1797	factorial sing_908.htm#SEC984 32871
1798	factorization sing_323.htm#SEC363
1799	factorization sing_1107.htm#IDX511
1800	factorize sing_242.htm#SEC282
1801	factorize sing_322.htm#SEC362
1802	factory sing_1.htm#IDX2
1803	fan sing_189.htm#SEC229
1804	fan sing_2071.htm#IDX807
1805	fanViaCones sing_2057.htm#SEC2133 16418
1806	farey sing_243.htm#SEC283
1807	fareypoly sing_2375.htm#SEC2451 12389
1808	fastExpt sing_1861.htm#SEC1937 43912
1809	fastHC, option sing_315.htm#IDX153
1810	fastelim sing_1715.htm#SEC1791 7409
1811	fetch sing_244.htm#SEC284
1812	fetch (plural) sing_461.htm#SEC501
1813	fetchall sing_1011.htm#SEC1087 7537
1814	ffmodStd sing_2379.htm#SEC2455 50680
1815	ffmodstd.lib sing_2374.htm#SEC2450
1816	ffmodstd_lib sing_2374.htm#SEC2450
1817	ffsolve sing_1704.htm#SEC1780 20432
1818	ffsolve.lib sing_1703.htm#SEC1779
1819	ffsolve_lib sing_1703.htm#SEC1779
1820	fglm sing_245.htm#SEC285
1821	fglm sing_355.htm#IDX187
1822	fglm_solve sing_1731.htm#SEC1807 51398
1823	fglmquot sing_246.htm#SEC286
1824	fibonacci sing_909.htm#SEC985 24750
1825	field sing_144.htm#SEC184
1826	file, .singularrc sing_20.htm#IDX71
1827	filecmd sing_247.htm#SEC287
1828	filtration purityfiltration_lib sing_758.htm#IDX369
1829	finalCharts sing_1423.htm#SEC1499 37296
1830	find sing_248.htm#SEC288
1831	findAuto sing_665.htm#SEC717 51205
1832	findInvo sing_663.htm#SEC715 18177
1833	findInvoDiag sing_664.htm#SEC716 7365
1834	findOrientedBoundary findOrientedBoundary sing_2080.htm#SEC2156 24110
1835	findTorsion sing_1842.htm#SEC1918 29572
1836	find_first_primitive_root find_first_primitive_root sing_1920.htm#SEC1996 33327
1837	find_index sing_1924.htm#SEC2000 62564
1838	findifs.lib sing_1849.htm#SEC1925
1839	findifs_example sing_1850.htm#SEC1926 33849
1840	findifs_lib sing_1849.htm#SEC1925
1841	findimAlgebra sing_733.htm#SEC785 64612
1842	finduni sing_249.htm#SEC289
1843	findvars sing_1716.htm#SEC1792 54503
1844	finite field sing_144.htm#SEC184
1845	finite field sing_1703.htm#IDX780
1846	finiteDiagInvariants finiteDiagInvariants sing_1265.htm#SEC1341 3508
1847	finitediff.lib sing_2380.htm#IDX978
1848	finitediff_lib sing_2380.htm#IDX979
1849	finitenessTest sing_1121.htm#SEC1197 40633
1850	finvar.lib sing_1638.htm#SEC1714
1851	finvar_lib sing_1638.htm#SEC1714
1852	first index is 1 sing_417.htm#SEC457
1853	firstoct sing_1764.htm#SEC1840 11498
1854	fitting sing_1167.htm#SEC1243 20661
1855	fixed points, moduli space of stable maps, graph fixedPoints sing_2728.htm#IDX1059
1856	fixedPoints sing_2728.htm#SEC2804 25366
1857	fl2poly sing_590.htm#SEC642 51682
1858	flatten sing_1052.htm#SEC1128 55617
1859	flatteningStrat sing_1168.htm#SEC1244 15622
1860	floating point sing_1020.htm#IDX497
1861	for sing_385.htm#SEC425
1862	formaldivisorplus sing_2367.htm#SEC2443 31959
1863	forward sing_2386.htm#SEC2462 15383
1864	fourier sing_585.htm#SEC637 5326
1865	fouriersystem sing_2397.htm#SEC2473 43681
1866	fpadim.lib sing_601.htm#SEC653
1867	fpadim_lib sing_601.htm#SEC653
1868	fpaprops.lib sing_635.htm#SEC687
1869	fpaprops_lib sing_635.htm#SEC687
1870	fprintf sing_251.htm#SEC291 13662
1871	fracStatus sing_2657.htm#SEC2733 14582
1872	frandwalk sing_2701.htm#SEC2777 25555
1873	free sing_2204.htm#IDX878
1874	free sing_2205.htm#IDX880
1875	free associative algebra, tensor algebra Free associative algebras sing_492.htm#SEC544
1876	freeGBasis sing_649.htm#SEC701 43055
1877	freeModule sing_2494.htm#SEC2570 34173
1878	freeModule2Module sing_2523.htm#SEC2599 15296
1879	freegb.lib sing_644.htm#SEC696
1880	freegb_lib sing_644.htm#SEC696
1881	freemodule sing_252.htm#SEC292
1882	freerank sing_968.htm#SEC1044 52218
1883	fres sing_253.htm#SEC293
1884	from_boolean_constant from_boolean_constant sing_2235.htm#SEC2311 44881
1885	from_boolean_ideal sing_2239.htm#SEC2315 62698
1886	from_boolean_poly sing_2236.htm#SEC2312 27864
1887	from_boolean_set sing_2240.htm#SEC2316 60615
1888	frwalk sing_254.htm#SEC294
1889	full representation sing_931.htm#IDX446
1890	full representation sing_932.htm#IDX451
1891	fullDimImages sing_2423.htm#SEC2499 20094
1892	fullFan sing_2058.htm#SEC2134 7534
1893	fullSerreRelations sing_659.htm#SEC711 27691
1894	fullSpace sing_2013.htm#SEC2089 19485
1895	furtherInvar sing_1682.htm#SEC1758 19209
1896	further_hn_proc sing_1578.htm#SEC1654 63500
1897	fwalk sing_1154.htm#SEC1230 15070
1898	galois field sing_144.htm#SEC184
1899	gauss_col sing_1062.htm#SEC1138 36252
1900	gauss_nf sing_1093.htm#SEC1169 51060
1901	gauss_row sing_1063.htm#SEC1139 58877
1902	gaussred sing_1091.htm#SEC1167 29001
1903	gaussred_pivot sing_1092.htm#SEC1168 25477
1904	gcd sing_255.htm#SEC295
1905	gcdMon sing_1196.htm#SEC1272 42448
1906	gcddivisor sing_1952.htm#SEC2028 1276
1907	gen sing_256.htm#SEC296
1908	genMDSMat sing_1819.htm#SEC1895 3347
1909	genSymId sing_1342.htm#SEC1418 17521
1910	general error-locator polynomial sing_887.htm#SEC952
1911	general neron. sing_2451.htm#IDX986
1912	general weighted lexicographical ordering sing_861.htm#IDX410
1913	general weighted reverse lexicographical ordering Local orderings sing_861.htm#IDX407
1914	general.lib sing_902.htm#SEC978
1915	generalOrder sing_1977.htm#SEC2053 42536
1916	general_lib sing_902.htm#SEC978
1917	generateG sing_1915.htm#SEC1991 51697
1918	generators sing_1478.htm#IDX642
1919	generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2033.htm#SEC2109 4454
1920	generatorsOfSpan sing_2034.htm#SEC2110 40297
1921	generic representation sing_931.htm#IDX445
1922	genericid sing_986.htm#SEC1062 29731
1923	genericity sing_1839.htm#SEC1915 16822
1924	genericmat sing_1053.htm#SEC1129 35016
1925	genoutput sing_1412.htm#SEC1488 18973
1926	genus sing_1247.htm#SEC1323 sprintf
1927	geometrical locus FamElemsAtEnvCompPoints sing_935.htm#IDX457
1928	geometrical locus sing_936.htm#IDX460
1929	geometrical locus sing_937.htm#IDX463
1930	geometrical locus sing_938.htm#IDX466
1931	geometrical locus sing_939.htm#IDX469
1932	geometrical locus sing_940.htm#IDX471
1933	geometrical locus sing_941.htm#IDX475
1934	getArguments sing_1043.htm#SEC1119 14254
1935	getCommand sing_1042.htm#SEC1118 32181
1936	getCone sing_2060.htm#SEC2136 41394
1937	getGradingGroup sing_2552.htm#SEC2628 18137
1938	getLattice sing_2553.htm#SEC2629 7775
1939	getLinearForms sing_2035.htm#SEC2111 47590
1940	getModuleGrading sing_2563.htm#SEC2639 43451
1941	getMultiplicity sing_2036.htm#SEC2112 639
1942	getOneVar sing_1255.htm#SEC1331 55402
1943	getResult sing_1044.htm#SEC1120 51722
1944	getSmallest sing_1254.htm#SEC1330 1623
1945	getState sing_1045.htm#SEC1121 36453
1946	getVariableWeights sing_2551.htm#SEC2627 9591
1947	getcores sing_1001.htm#SEC1077 30785
1948	getdump sing_257.htm#SEC297
1949	getenv sing_358.htm#IDX211
1950	gfan.lib sing_2012.htm#SEC2088
1951	gfan_lib sing_2012.htm#SEC2088
1952	gfanlib sing_1.htm#IDX9
1953	gitCone sing_2450.htm#SEC2526 23853
1954	gitfan.lib sing_2420.htm#SEC2496
1955	gitfan_lib sing_2420.htm#SEC2496
1956	gkdim.lib sing_670.htm#SEC722
1957	gkdim_lib sing_670.htm#SEC722
1958	global sing_209.htm#IDX133
1959	global Bernstein-Sato polynomial sing_505.htm#IDX313
1960	global Bernstein-Sato polynomial sing_540.htm#IDX331
1961	global Bernstein-Sato polynomial for variety sing_596.htm#IDX356
1962	globalSections sing_2361.htm#SEC2437 55191
1963	gmscoeffs sing_1536.htm#SEC1612 13182
1964	gmsnf sing_1535.htm#SEC1611 44676
1965	gmspoly.lib sing_1555.htm#SEC1631
1966	gmspoly_lib sing_1555.htm#SEC1631
1967	gmsring sing_1534.htm#SEC1610 59438
1968	gmssing.lib sing_1533.htm#SEC1609
1969	gmssing_lib sing_1533.htm#SEC1609
1970	goettsche.lib sing_2404.htm#SEC2480
1971	goettsche_lib sing_2404.htm#SEC2480
1972	good basis sing_1533.htm#IDX670
1973	good basis sing_1543.htm#IDX725
1974	good basis sing_1555.htm#IDX741
1975	good basis sing_1557.htm#IDX752
1976	goodBasis sing_1557.htm#SEC1633 41606
1977	gorensteinIndex sing_2092.htm#SEC2168 52919
1978	gorensteinVector sing_2093.htm#SEC2169 50407
1979	graal.lib sing_2413.htm#SEC2489
1980	graalMixed sing_2414.htm#SEC2490 6401
1981	graal_lib sing_2413.htm#SEC2489
1982	gradeNumber sing_762.htm#SEC814 29956
1983	graded Weyl algebra sing_505.htm#IDX316
1984	graded algebra sing_2246.htm#IDX933
1985	graded module, graded piece sing_1459.htm#IDX628
1986	graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2453.htm#IDX987
1987	graded modules, handling of Handling graded modules sing_826.htm#SEC878
1988	graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2491.htm#IDX989
1989	gradedModules.lib sing_2453.htm#SEC2529
1990	gradedModules_lib sing_2453.htm#SEC2529
1991	gradiator sing_2596.htm#SEC2672 53802
1992	graph sing_1143.htm#IDX524
1993	graph sing_1144.htm#IDX525
1994	graph sing_2723.htm#IDX1054
1995	graph sing_2724.htm#IDX1055
1996	graphics.lib sing_1766.htm#SEC1842
1997	graphics_lib sing_1766.htm#SEC1842
1998	graphviz sing_1.htm#IDX13
1999	graver4ti2 sing_1340.htm#SEC1416 39635
2000	grconcat sing_2476.htm#SEC2552 16754
2001	grdeg sing_2456.htm#SEC2532 22879
2002	grgens sing_2465.htm#SEC2541 12823
2003	grgroebner sing_2475.htm#SEC2551 29288
2004	grlift sing_2473.htm#SEC2549 21656
2005	grlifting sing_2480.htm#SEC2556 51177
2006	grlifting2 sing_2481.htm#SEC2557 59011
2007	grlifting3 sing_2483.htm#SEC2559 6369
2008	grneg sing_2486.htm#SEC2562 64584
2009	grobcov sing_924.htm#SEC1000 44826
2010	grobcov.lib sing_923.htm#SEC999
2011	grobcov_lib sing_923.htm#SEC999
2012	grobj sing_2454.htm#SEC2530 18115
2013	groebner sing_258.htm#SEC298 53038
2014	groebner sing_818.htm#SEC870
2015	groebner basis computations sing_258.htm#IDX147
2016	groebnerComplex sing_2171.htm#SEC2247 2421
2017	groebnerCone sing_2165.htm#SEC2241 58776
2018	groebnerFan sing_2170.htm#SEC2246 48157
2019	gromovWitten sing_1148.htm#SEC1224 28559
2020	grorder sing_2467.htm#SEC2543 20857
2021	ground field sing_144.htm#SEC184
2022	groupActionOnHashes sing_2438.htm#SEC2514 406
2023	groupActionOnQImage sing_2437.htm#SEC2513 53270
2024	group_reynolds sing_1646.htm#SEC1722 35079
2025	grpower sing_2463.htm#SEC2539 3960
2026	grpres sing_2466.htm#SEC2542 18145
2027	grprod sing_2474.htm#SEC2550 41525
2028	grrange sing_2485.htm#SEC2561 41835
2029	grres sing_2472.htm#SEC2548 35795
2030	grrndmap sing_2478.htm#SEC2554 4054
2031	grrndmap2 sing_2479.htm#SEC2555 50536
2032	grrndmat sing_2477.htm#SEC2553 42634
2033	grshift sing_2458.htm#SEC2534 1415
2034	grsum sing_2462.htm#SEC2538 60602
2035	grsyz sing_2471.htm#SEC2547 61843
2036	grtest sing_2455.htm#SEC2531 62577
2037	grtranspose sing_2464.htm#SEC2540 13865
2038	grtranspose1 sing_2468.htm#SEC2544 3637
2039	grtwist sing_2460.htm#SEC2536 10498
2040	grtwists sing_2461.htm#SEC2537 56638
2041	grview sing_2457.htm#SEC2533 6878
2042	grwalk.lib sing_1153.htm#SEC1229
2043	grwalk_lib sing_1153.htm#SEC1229
2044	grzero sing_2459.htm#SEC2535 4212
2045	gwalk sing_1159.htm#SEC1235 38238
2046	hStarVector sing_2094.htm#SEC2170 60821
2047	hVector sing_2095.htm#SEC2171 46486
2048	h_increasing_knapsack h_increasing_knapsack sing_1938.htm#SEC2014 62968
2049	hardware platform sing_358.htm#IDX271
2050	hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1024.htm#SEC1100 54609
2051	hasCommutativeVars sing_1021.htm#SEC1097 3152
2052	hasGlobalOrdering sing_1022.htm#SEC1098 34053
2053	hasLeftDenom sing_2605.htm#SEC2681 47260
2054	hasMixedOrdering sing_1023.htm#SEC1099 29738
2055	hasNumericCoeffs sing_1020.htm#SEC1096 14522
2056	hasRightDenom sing_2606.htm#SEC2682 34279
2057	hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1025.htm#SEC1101 56211
2058	hashToCone sing_2448.htm#SEC2524 6929
2059	hashesToFan sing_2449.htm#SEC2525 26774
2060	headStand sing_1075.htm#SEC1151 14413
2061	heightZ sing_1317.htm#SEC1393 16800
2062	help sing_259.htm#SEC299
2063	help browsers The online help system sing_16.htm#IDX22
2064	help browsers, dummy The online help system sing_16.htm#IDX25
2065	help browsers, dummy sing_16.htm#IDX27
2066	help browsers, emacs The online help system sing_16.htm#IDX26
2067	help browsers, html The online help system sing_16.htm#IDX23
2068	help browsers, setting command to use The online help system sing_16.htm#IDX30
2069	help browsers, setting the sing_358.htm#IDX194
2070	help, accessing over the net Command line options sing_19.htm#IDX42
2071	help, online help system The online help system sing_16.htm#SEC22
2072	hermiteNormalForm sing_2597.htm#SEC2673 37225
2073	hess.lib sing_2488.htm#SEC2564
2074	hess_lib sing_2488.htm#SEC2564
2075	hessenberg sing_358.htm#IDX217 24168
2076	hessenberg sing_1097.htm#SEC1173
2077	highcorner sing_260.htm#SEC300
2078	hilb sing_261.htm#SEC301
2079	hilbPoly sing_984.htm#SEC1060 36118
2080	hilbert4ti2 sing_1339.htm#SEC1415 13993
2081	hilbertBasis sing_2096.htm#SEC2172 35423
2082	hilbertSeries sing_2599.htm#SEC2675 60148
2083	hilbvec sing_1717.htm#SEC1793 9204
2084	hnexpansion sing_1559.htm#SEC1635 46990
2085	hnoether.lib sing_1558.htm#SEC1634
2086	hnoether_lib sing_1558.htm#SEC1634
2087	holonomic rank sing_780.htm#IDX380
2088	holonomicRank sing_784.htm#SEC836 41306
2089	hom sing_2535.htm#SEC2611 40032
2090	hom_kernel sing_1175.htm#SEC1251 32604
2091	homog sing_262.htm#SEC302
2092	homog_part sing_2735.htm#SEC2811 20875
2093	homog_parts sing_2736.htm#SEC2812 12854
2094	homogeneitySpace sing_2167.htm#SEC2243 48243
2095	homogfacFirstQWeyl sing_713.htm#SEC765 32751
2096	homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_715.htm#SEC767 9014
2097	homogfacNthQWeyl sing_712.htm#SEC764 19238
2098	homogfacNthQWeyl_all homogfacNthQWeyl_all sing_714.htm#SEC766 56179
2099	homolog.lib sing_1160.htm#SEC1236
2100	homolog_lib sing_1160.htm#SEC1236
2101	homology sing_1170.htm#SEC1246 15040
2102	homomorphism sing_2519.htm#SEC2595 27115
2103	howto, download Download instructions sing_2762.htm#SEC2851
2104	howto, install on Macintosh Macintosh installation instructions sing_2765.htm#SEC2854
2105	howto, install on Unix Unix installation instructions sing_2763.htm#SEC2852
2106	howto, install on Windows Windows installation instructions sing_2764.htm#SEC2853
2107	hres sing_263.htm#SEC303
2108	html, default help The online help system sing_16.htm#IDX24
2109	hyperel.lib sing_1945.htm#SEC2021
2110	hyperel_lib sing_1945.htm#SEC2021
2111	hyperplane sing_2174.htm#IDX818
2112	hyperplane arrangement sing_540.htm#IDX337
2113	hypersurface singularity sing_1585.htm#IDX770
2114	iMult sing_1250.htm#SEC1326 22059
2115	id sing_2492.htm#SEC2568 47592
2116	id2mod sing_980.htm#SEC1056 32918
2117	ideal sing_90.htm#SEC130
2118	ideal declarations sing_91.htm#SEC131
2119	ideal declarations (plural) ideal declarations (plural) sing_424.htm#SEC464
2120	ideal expressions sing_92.htm#SEC132
2121	ideal expressions (plural) ideal expressions (plural) sing_425.htm#SEC465
2122	ideal operations sing_93.htm#SEC133
2123	ideal operations (plural) ideal operations (plural) sing_426.htm#SEC466
2124	ideal related functions ideal related functions sing_94.htm#SEC134
2125	ideal related functions (plural) ideal related functions (plural) sing_427.htm#SEC467
2126	ideal, toric sing_874.htm#SEC931
2127	idealSplit sing_1724.htm#SEC1800 4673
2128	ideals Miscellaneous oddities sing_418.htm#IDX293
2129	idealsimplify sing_1486.htm#SEC1562 38569
2130	identifier Identifier resolution sing_419.htm#SEC459
2131	identifyvar sing_1394.htm#SEC1470 59662
2132	if sing_386.htm#SEC426
2133	image sing_2515.htm#SEC2591 43481
2134	imageLattice sing_2565.htm#SEC2641 15740
2135	image_of_variety sing_1674.htm#SEC1750 43711
2136	imap sing_264.htm#SEC304
2137	imap (plural) sing_462.htm#SEC502
2138	imapall sing_1012.htm#SEC1088 16023
2139	impart sing_265.htm#SEC305
2140	importfrom sing_387.htm#SEC427
2141	inCenter sing_529.htm#SEC581 22152
2142	inCentralizer sing_530.htm#SEC582 49000
2143	inForm sing_572.htm#SEC624 5283
2144	inSubring sing_1113.htm#SEC1189 24817
2145	indSet sing_1222.htm#SEC1298 32828
2146	indepSet sing_266.htm#SEC306
2147	indexed names sing_36.htm#IDX82
2148	indexed names sing_37.htm#SEC65
2149	indices, multi sing_37.htm#SEC65
2150	inequalities sing_2037.htm#SEC2113 10122
2151	infRedTail, option sing_315.htm#IDX154
2152	info The online help system sing_16.htm#SEC23
2153	iniD sing_1414.htm#SEC1490 35084
2154	init_debug sing_1493.htm#SEC1569 29863
2155	initial sing_2168.htm#SEC2244 8678
2156	initial form sing_505.htm#IDX318
2157	initial ideal sing_505.htm#IDX317
2158	initial ideal approach sing_505.htm#IDX321
2159	initial ideal approach sing_596.htm#IDX360
2160	initialForm sing_2145.htm#SEC2221 57793
2161	initialIdeal sing_2146.htm#SEC2222 22205
2162	initialIdealW sing_571.htm#SEC623 36086
2163	initialMalgrange sing_570.htm#SEC622 26846
2164	injective_knapsack sing_1939.htm#SEC2015 7619
2165	inout.lib sing_946.htm#SEC1022
2166	inout_lib sing_946.htm#SEC1022
2167	input sing_41.htm#SEC71
2168	insert sing_126.htm#SEC166
2169	insert sing_267.htm#SEC307
2170	insertCone sing_2061.htm#SEC2137 13858
2171	insertGenerator sing_591.htm#SEC643 13951
2172	instructions, Macintosh installation Macintosh installation instructions sing_2765.htm#SEC2854
2173	instructions, Unix installation Unix installation instructions sing_2763.htm#SEC2852
2174	instructions, Windows installation Windows installation instructions sing_2764.htm#SEC2853
2175	instructions, downloading Download instructions sing_2762.htm#SEC2851
2176	int sing_95.htm#SEC135
2177	int declarations sing_96.htm#SEC136
2178	int expressions sing_97.htm#SEC137
2179	int operations sing_98.htm#SEC138
2180	int related functions int related functions sing_99.htm#SEC139
2181	intInverse sing_2574.htm#SEC2650 sprintf
2182	intPart sing_1893.htm#SEC1969 48360
2183	intRank sing_2566.htm#SEC2642 1830
2184	intRoot sing_1894.htm#SEC1970 54582
2185	intRoots sing_588.htm#SEC640 24538
2186	intStrategy, option sing_315.htm#IDX155
2187	intclMonIdeal sing_1263.htm#SEC1339 22338
2188	intclToricRing sing_1259.htm#SEC1335 62143
2189	integer division Miscellaneous oddities sing_418.htm#IDX288
2190	integer programming sing_882.htm#SEC939
2191	integral sing_2710.htm#SEC2786 62683
2192	integral basis sing_1182.htm#IDX546
2193	integral basis sing_1377.htm#IDX613
2194	integral closure sing_1243.htm#IDX561
2195	integral closure sing_1244.htm#IDX564
2196	integral closure sing_1245.htm#IDX567
2197	integral closure sing_1258.htm#IDX573
2198	integralBasis sing_1182.htm#SEC1258 38114
2199	integralIdeal sing_575.htm#SEC627 29194
2200	integralModule sing_576.htm#SEC628 58078
2201	integralSection sing_2575.htm#SEC2651 sprintf
2202	integralbasis.lib sing_1181.htm#SEC1257
2203	integralbasis_lib sing_1181.htm#SEC1257
2204	integration of D-module sing_563.htm#IDX349
2205	interface, Emacs Emacs user interface sing_21.htm#SEC28
2206	interiorLatticePoints interiorLatticePoints sing_2097.htm#SEC2173 49868
2207	internalfunctions sing_1494.htm#SEC1570 61230
2208	interpolate sing_1730.htm#SEC1806 51502
2209	interpolation sing_268.htm#SEC308
2210	interpret sing_2537.htm#SEC2613 48499
2211	interpretElem sing_2540.htm#SEC2616 51740
2212	interpretInv sing_2538.htm#SEC2614 6149
2213	interpretList sing_2541.htm#SEC2617 64061
2214	interred sing_269.htm#SEC309
2215	intersect sing_270.htm#SEC310
2216	intersect (plural) sing_463.htm#SEC503
2217	intersectElim, option sing_315.htm#IDX173
2218	intersectLattices sing_2571.htm#SEC2647 41354
2219	intersectLists sing_2343.htm#SEC2419 4153
2220	intersectMon sing_1199.htm#SEC1275 44572
2221	intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2436.htm#SEC2512 19444
2222	intersectSyz, option sing_315.htm#IDX174
2223	intersectZ sing_1319.htm#SEC1395 sprintf
2224	intersection sing_1568.htm#SEC1644 46938
2225	intersection lattice sing_2210.htm#IDX893
2226	intersection lattice sing_2211.htm#IDX894
2227	intersection multiplicity sing_1479.htm#IDX648
2228	intersection multiplicity sing_1568.htm#IDX763
2229	intersectionDiv sing_1442.htm#SEC1518 29017
2230	intersectionValRingIdeals intersectionValRingIdeals sing_1268.htm#SEC1344 38773
2231	intersectionValRings intersectionValRings sing_1267.htm#SEC1343 35761
2232	intersectpar sing_944.htm#SEC1020 2975
2233	interval arithmetic sing_2680.htm#IDX1029
2234	intmat sing_102.htm#SEC142
2235	intmat declarations sing_103.htm#SEC143
2236	intmat expressions sing_104.htm#SEC144
2237	intmat operations sing_106.htm#SEC146
2238	intmat related functions intmat related functions sing_107.htm#SEC147
2239	intmat type cast sing_105.htm#SEC145
2240	intmat2mons sing_1283.htm#SEC1359 21150
2241	intprog.lib sing_1183.htm#SEC1259
2242	intprog_lib sing_1183.htm#SEC1259
2243	intvec sing_108.htm#SEC148
2244	intvec declarations sing_109.htm#SEC149
2245	intvec expressions sing_110.htm#SEC150
2246	intvec operations sing_111.htm#SEC151
2247	intvec related functions intvec related functions sing_112.htm#SEC152
2248	invariant sing_2349.htm#IDX955
2249	invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1643.htm#IDX776
2250	invariant ring minimal generating set permutation group invariant_algebra_perm sing_1644.htm#IDX777
2251	invariantRing sing_1676.htm#SEC1752 18582
2252	invariant_algebra_perm invariant_algebra_perm sing_1644.htm#SEC1720 63525
2253	invariant_algebra_reynolds invariant_algebra_reynolds sing_1643.htm#SEC1719 35705
2254	invariant_basis sing_1651.htm#SEC1727 18343
2255	invariant_basis_reynolds invariant_basis_reynolds sing_1652.htm#SEC1728 54788
2256	invariant_ring sing_1639.htm#SEC1715 8059
2257	invariant_ring_random invariant_ring_random sing_1640.htm#SEC1716 6986
2258	invariants curveColengthDerivations sing_1564.htm#SEC1640 57499
2259	invariants sing_2346.htm#IDX948
2260	invariants sing_2350.htm#IDX957
2261	inverse sing_1081.htm#SEC1157 27411
2262	inverse of a matrix via its LU-decomposition sing_290.htm#SEC330
2263	inverseFourier sing_586.htm#SEC638 65140
2264	inverse_B sing_1082.htm#SEC1158 17616
2265	inverse_L sing_1083.htm#SEC1159 49271
2266	inverse_modulus sing_1922.htm#SEC1998 60822
2267	invertBirMap sing_1378.htm#SEC1454 16086
2268	invertLeftFraction sing_2667.htm#SEC2743 51903
2269	invertNcfrac sing_2615.htm#SEC2691 50842
2270	invertNumberMain sing_1754.htm#SEC1830 62615
2271	involut.lib sing_662.htm#SEC714
2272	involut_lib sing_662.htm#SEC714
2273	involution sing_667.htm#SEC719 34280
2274	invunit sing_1587.htm#SEC1663 62398
2275	iostruct sing_1841.htm#SEC1917 60444
2276	irrRealizationDim sing_2127.htm#SEC2203 7814
2277	irred_secondary_char0 irred_secondary_char0 sing_1665.htm#SEC1741 2943
2278	irred_secondary_no_molien irred_secondary_no_molien sing_1668.htm#SEC1744 55905
2279	irreddecMon sing_1208.htm#SEC1284 20160
2280	irreducible power series sing_1569.htm#IDX764
2281	irreducible secondary invariant irred_secondary_char0 sing_1665.htm#IDX778
2282	isAface sing_2421.htm#SEC2497 25344
2283	isAntiEndo sing_669.htm#SEC721 19156
2284	isBounded sing_2098.htm#SEC2174 28183
2285	isCI sing_209.htm#IDX139 58425
2286	isCI sing_1131.htm#SEC1207
2287	isCM sing_209.htm#IDX140 50469
2288	isCM sing_1171.htm#SEC1247
2289	isCMcod2 sing_1622.htm#SEC1698 2563
2290	isCanonical sing_2099.htm#SEC2175 51109
2291	isCartan sing_531.htm#SEC583 39541
2292	isCentral sing_740.htm#SEC792 54650
2293	isCommutative sing_742.htm#SEC794 60728
2294	isCompatible sing_2062.htm#SEC2138 57323
2295	isCompressed sing_2100.htm#SEC2176 2849
2296	isDenom sing_2619.htm#SEC2695 55537
2297	isEqualDivisor sing_2360.htm#SEC2436 17569
2298	isEquising sing_1531.htm#SEC1607 1424
2299	isFlat sing_1172.htm#SEC1248 14706
2300	isFsat sing_581.htm#SEC633 28225
2301	isFullSpace sing_2038.htm#SEC2114 27433
2302	isGorenstein sing_2101.htm#SEC2177 24010
2303	isGradedRingHomomorphism isGradedRingHomomorphism sing_2560.htm#SEC2636 39551
2304	isGroup sing_2558.htm#SEC2634 55744
2305	isGroupHomomorphism sing_2559.htm#SEC2635 65475
2306	isHolonomic sing_559.htm#SEC611 30274
2307	isHomg sing_209.htm#IDX135
2308	isHomogeneous sing_2586.htm#SEC2662 3034
2309	isInS sing_2656.htm#SEC2732 30907
2310	isInt sing_594.htm#SEC646 9879
2311	isIntegralSurjective isIntegralSurjective sing_2572.htm#SEC2648 sprintf
2312	isInvertibleLeftFraction isInvertibleLeftFraction sing_2666.htm#SEC2742 623
2313	isInvertibleNcfrac sing_2614.htm#SEC2690 48367
2314	isInvolution sing_668.htm#SEC720 13601
2315	isLatticeEmpty sing_2102.htm#SEC2178 48517
2316	isLocalizationRegular isLocalizationRegular sing_2417.htm#SEC2493 11221
2317	isLocallyFree sing_1173.htm#SEC1249 46389
2318	isMonomial sing_1194.htm#SEC1270 57615
2319	isNC sing_741.htm#SEC793 57151
2320	isNormal sing_2103.htm#SEC2179 64236
2321	isOnCurve sing_1906.htm#SEC1982 36324
2322	isOneFraction sing_2669.htm#SEC2745 55015
2323	isOneNcfrac sing_2608.htm#SEC2684 12754
2324	isOrigin sing_2039.htm#SEC2115 13977
2325	isPositive sing_2583.htm#SEC2659 50852
2326	isPrimitiveSublattice isPrimitiveSublattice sing_2573.htm#SEC2649 sprintf
2327	isPure sing_2063.htm#SEC2139 44002
2328	isPureTensor sing_503.htm#SEC555 21323
2329	isQuotientRing sing_1026.htm#SEC1102 sprintf
2330	isRational sing_562.htm#SEC614 57398
2331	isReflexive sing_2104.htm#SEC2180 3991
2332	isReg sing_1174.htm#SEC1250 40920
2333	isSB sing_209.htm#IDX134
2334	isSimplicial sing_2040.htm#SEC2116 57789
2335	isSmooth sing_2105.htm#SEC2181 37647
2336	isSubModule sing_1027.htm#SEC1103 sprintf
2337	isSublattice sing_2564.htm#SEC2640 10501
2338	isSymmetric sing_1343.htm#SEC1419 61363
2339	isTame sing_1556.htm#SEC1632 31925
2340	isTerminal sing_2106.htm#SEC2182 29416
2341	isTorsionFree sing_2582.htm#SEC2658 52228
2342	isTwoSidedGB sing_504.htm#SEC556 36558
2343	isUpperTriangular sing_721.htm#SEC773 40655
2344	isVar sing_660.htm#SEC712 43851
2345	isVeryAmple sing_2107.htm#SEC2183 64652
2346	isWeyl sing_743.htm#SEC795 28994
2347	isZeroElement sing_2584.htm#SEC2660 514
2348	isZeroFraction sing_2668.htm#SEC2744 1926
2349	isZeroNcfrac sing_2607.htm#SEC2683 6841
2350	is_NND sing_1572.htm#SEC1648 26564
2351	is_NP sing_1231.htm#SEC1307 43891
2352	is_active sing_1605.htm#SEC1681 6867
2353	is_bijective sing_1118.htm#SEC1194 49512
2354	is_cenBimodule sing_776.htm#SEC828 35450
2355	is_cenSubbimodule sing_777.htm#SEC829 26181
2356	is_ci sing_1606.htm#SEC1682 35370
2357	is_complex sing_1054.htm#SEC1130 1234
2358	is_fix_injective sing_1943.htm#SEC2019 11663
2359	is_h_injective sing_1942.htm#SEC2018 36696
2360	is_injective sing_1116.htm#SEC1192 15776
2361	is_irred sing_1569.htm#SEC1645 51150
2362	is_is sing_1607.htm#SEC1683 64105
2363	is_nested sing_1232.htm#SEC1308 9200
2364	is_prime sing_1923.htm#SEC1999 29018
2365	is_primitive_root sing_1919.htm#SEC1995 42838
2366	is_pure sing_768.htm#SEC820 59105
2367	is_reg sing_1608.htm#SEC1684 18146
2368	is_regs sing_1609.htm#SEC1685 50242
2369	is_surjective sing_1117.htm#SEC1193 57044
2370	is_zero sing_969.htm#SEC1045 24341
2371	isartinianMon sing_1205.htm#SEC1281 1103
2372	isgenericMon sing_1206.htm#SEC1282 14444
2373	ishyper sing_1946.htm#SEC2022 65518
2374	isirreducibleMon sing_1204.htm#SEC1280 22428
2375	isoncurve sing_1947.htm#SEC2023 16384
2376	isparam sing_2010.htm#SEC2086 56395
2377	isprimaryMon sing_1203.htm#SEC1279 57367
2378	isprimeMon sing_1202.htm#SEC1278 9124
2379	isuni sing_1995.htm#SEC2071 39427
2380	iv2lp sing_629.htm#SEC681 59849
2381	iv2lpList sing_630.htm#SEC682 18518
2382	iv2lpMat sing_631.htm#SEC683 21612
2383	ivDHilbert sing_609.htm#SEC661 56709
2384	ivDHilbertSickle sing_610.htm#SEC662 43194
2385	ivDimCheck sing_611.htm#SEC663 258
2386	ivHilbert sing_612.htm#SEC664 37184
2387	ivKDim sing_613.htm#SEC665 26109
2388	ivL2lpI sing_628.htm#SEC680 2454
2389	ivMaxIdeal sing_625.htm#SEC677 48114
2390	ivMis2Base sing_614.htm#SEC666 57812
2391	ivMis2Dim sing_615.htm#SEC667 42072
2392	ivOrdMisLex sing_616.htm#SEC668 27789
2393	ivSickle sing_617.htm#SEC669 42888
2394	ivSickleDim sing_619.htm#SEC671 64347
2395	ivSickleHil sing_618.htm#SEC670 41396
2396	ivmatGaussian sing_2687.htm#SEC2763 37718
2397	ivmatInit sing_2684.htm#SEC2760 22774
2398	ivmatSet sing_2685.htm#SEC2761 53480
2399	jInvariant sing_2139.htm#SEC2215 2369
2400	jOft sing_1878.htm#SEC1954 25716
2401	jacob sing_271.htm#SEC311
2402	jacoblift sing_1588.htm#SEC1664 40125
2403	jacobson sing_1847.htm#SEC1923 59267
2404	jacobson.lib sing_1845.htm#SEC1921
2405	jacobson_lib sing_1845.htm#SEC1921
2406	janet sing_272.htm#SEC312
2407	janet basis sing_2693.htm#IDX1032
2408	jet sing_273.htm#SEC313
2409	jordan sing_1102.htm#SEC1178 16602
2410	jordanbasis sing_1103.htm#SEC1179 12736
2411	jordanmatrix sing_1104.htm#SEC1180 2886
2412	jordannf sing_1105.htm#SEC1181 20535
2413	jungfib sing_1427.htm#SEC1503 5432
2414	jungnormal sing_1426.htm#SEC1502 43561
2415	jungresolve sing_1425.htm#SEC1501 45004
2416	katsura sing_967.htm#SEC1043 45913
2417	kbase sing_274.htm#SEC314
2418	kbase (plural) sing_464.htm#SEC504
2419	keepring sing_388.htm#SEC428
2420	kerHom sing_2536.htm#SEC2612 53906
2421	kernel sing_275.htm#SEC315
2422	kernelLattice sing_2567.htm#SEC2643 36320
2423	kill sing_276.htm#SEC316
2424	killTask sing_1033.htm#SEC1109 39317
2425	killall sing_911.htm#SEC987 34661
2426	killattrib sing_277.htm#SEC317
2427	kmemory sing_910.htm#SEC986 52193
2428	kohom sing_1176.htm#SEC1252 50086
2429	kontrahom sing_1177.htm#SEC1253 58549
2430	koszul sing_278.htm#SEC318
2431	kskernel.lib sing_1579.htm#SEC1655
2432	kskernel_lib sing_1579.htm#SEC1655
2433	l-adic numbers sing_32.htm#SEC46
2434	laguerre sing_279.htm#SEC319
2435	laguerre_solve sing_1726.htm#SEC1802 10155
2436	lastvarGeneral sing_1976.htm#SEC2052 28645
2437	latex.lib sing_1770.htm#SEC1846
2438	latex_lib sing_1770.htm#SEC1846
2439	lattice sing_2211.htm#IDX896
2440	latticeArea sing_2082.htm#SEC2158 53771
2441	latticeBasis sing_2568.htm#SEC2644 43162
2442	latticeCodegree sing_2108.htm#SEC2184 25482
2443	latticeDegree sing_2109.htm#SEC2185 52881
2444	latticePoints sing_2110.htm#SEC2186 41965
2445	latticeVolume sing_2111.htm#SEC2187 42234
2446	laxfrT sing_2384.htm#SEC2460 60899
2447	laxfrX sing_2385.htm#SEC2461 57254
2448	lazy, option sing_315.htm#IDX156
2449	lcm sing_970.htm#SEC1046 44755
2450	lcmMon sing_1197.htm#SEC1273 52749
2451	lcmN sing_1887.htm#SEC1963 52355
2452	lcmofall sing_1407.htm#SEC1483 56889
2453	lead sing_280.htm#SEC320
2454	leadcoef sing_281.htm#SEC321
2455	leadexp sing_282.htm#SEC322
2456	leadmonom sing_283.htm#SEC323
2457	leadmonomial sing_1962.htm#SEC2038 8195
2458	left annihilator ideal sing_540.htm#IDX329
2459	leftInverse sing_1836.htm#SEC1912 41469
2460	leftKernel sing_1834.htm#SEC1910 9292
2461	leftOre sing_2659.htm#SEC2735 44669
2462	length sing_2682.htm#SEC2758 9547
2463	length, option sing_315.htm#IDX157
2464	letplaceGBasis sing_646.htm#SEC698 33757
2465	letterplace correspondence Letterplace correspondence sing_494.htm#SEC546
2466	lex_solve sing_1732.htm#SEC1808 48692
2467	lexicographical ordering sing_860.htm#IDX390
2468	lib2doc sing_60.htm#SEC97
2469	libSingular sing_2761.htm#SEC2850
2470	libcdd sing_1.htm#IDX12
2471	libfac sing_1.htm#IDX6
2472	libparse sing_69.htm#SEC109
2473	library sing_2226.htm#IDX911
2474	library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2420.htm#IDX984
2475	library, info string sing_55.htm#IDX124
2476	library, polybori.lib sing_2226.htm#IDX908
2477	library, template sing_55.htm#SEC92
2478	library, template.lib sing_55.htm#IDX122
2479	lieBracket sing_653.htm#SEC705 50745
2480	lift sing_285.htm#SEC325
2481	lift sing_498.htm#IDX305
2482	lift (plural) sing_465.htm#SEC505
2483	lift_kbase sing_1525.htm#SEC1601 10906
2484	lift_rel_kb sing_1526.htm#SEC1602 13673
2485	liftenvelope sing_501.htm#SEC553 58802
2486	liftstd sing_286.htm#SEC326
2487	liftstd (plural) sing_466.htm#SEC506
2488	linReduce sing_513.htm#SEC565 57527
2489	linReduceIdeal sing_514.htm#SEC566 19076
2490	linSyzSolve sing_515.htm#SEC567 26185
2491	linalg.lib sing_1080.htm#SEC1156
2492	linalg_lib sing_1080.htm#SEC1156
2493	linealityDimension sing_2041.htm#SEC2117 30751
2494	linealitySpace sing_2042.htm#SEC2118 14489
2495	linear algebra sing_210.htm#SEC250
2496	linear algebra sing_289.htm#SEC329
2497	linear algebra sing_290.htm#SEC330
2498	linear algebra sing_291.htm#SEC331
2499	linear code, dual sing_1805.htm#IDX789
2500	linear code, systematic sing_1806.htm#IDX790
2501	linear interreduction sing_505.htm#IDX320
2502	linearCombinations sing_534.htm#SEC586 20514
2503	linearMapKernel sing_533.htm#SEC585 43761
2504	linear_relations sing_1072.htm#SEC1148 45983
2505	linearlyEquivalent sing_2363.htm#SEC2439 28351
2506	linearpart sing_1718.htm#SEC1794 2162
2507	linesHypersurface sing_2732.htm#SEC2808 9129
2508	link Parallelization with ssi links sing_113.htm#SEC153
2509	link sing_815.htm#SEC867
2510	link declarations sing_114.htm#SEC154
2511	link expressions sing_115.htm#SEC155
2512	link related functions link related functions sing_116.htm#SEC156
2513	list sing_123.htm#SEC163
2514	list declarations sing_124.htm#SEC164
2515	list expressions sing_125.htm#SEC165
2516	list operations sing_126.htm#SEC166
2517	list related functions list related functions sing_127.htm#SEC167
2518	lists sing_2343.htm#IDX944
2519	lists, elements sing_2345.htm#IDX946
2520	listvar sing_287.htm#SEC327
2521	lll sing_2600.htm#SEC2676 35827
2522	load sing_389.htm#SEC429
2523	loadLib, option sing_315.htm#IDX178
2524	loadProc, option sing_315.htm#IDX179
2525	locAtZero sing_1252.htm#SEC1328 5687
2526	locNormal sing_1186.htm#SEC1262 52237
2527	locStatus sing_2654.htm#SEC2730 54575
2528	local methods sing_1185.htm#IDX549
2529	local methods sing_1186.htm#IDX552
2530	local names sing_46.htm#SEC83
2531	local rings, computing in Rings associated to monomial orderings sing_810.htm#SEC862
2532	local weighted lexicographical ordering sing_861.htm#IDX411
2533	local weighted reverse lexicographical ordering Local orderings sing_861.htm#IDX408
2534	localInvar sing_1681.htm#SEC1757 38478
2535	localization Rings associated to monomial orderings sing_810.htm#SEC862
2536	localization sing_2191.htm#IDX856
2537	localization of D-module sing_563.htm#IDX345
2538	localization of D-module sing_780.htm#IDX383
2539	locally closed set sing_928.htm#IDX435
2540	locally closed set sing_929.htm#IDX437
2541	locally closed set sing_930.htm#IDX439
2542	locally closed set sing_931.htm#IDX443
2543	locally closed set sing_933.htm#IDX453
2544	localstd sing_1972.htm#SEC2048 25562
2545	locnormal.lib sing_1185.htm#SEC1261
2546	locnormal_lib sing_1185.htm#SEC1261
2547	locstd sing_1610.htm#SEC1686 25864
2548	locus FamElemsAtEnvCompPoints sing_935.htm#SEC1011 22530
2549	locus sing_935.htm#IDX458
2550	locus sing_936.htm#IDX461
2551	locus sing_937.htm#IDX464
2552	locus sing_938.htm#IDX467
2553	locus sing_939.htm#IDX470
2554	locus sing_940.htm#IDX472
2555	locus sing_941.htm#IDX476
2556	locusdg sing_936.htm#SEC1012 6077
2557	locusto sing_938.htm#SEC1014 730
2558	log2 sing_1862.htm#SEC1938 40703
2559	logarithmic annihilator ideal sing_540.htm#IDX334
2560	logg sing_2737.htm#SEC2813 38736
2561	lp, global ordering sing_860.htm#IDX389
2562	lp2iv sing_632.htm#SEC684 17398
2563	lp2ivId sing_633.htm#SEC685 16290
2564	lp2lstr sing_654.htm#SEC706 24713
2565	lpCalcSubstDegBound sing_642.htm#SEC694 46179
2566	lpCalcSubstDegBounds lpCalcSubstDegBounds sing_643.htm#SEC695 56500
2567	lpDHilbert sing_607.htm#SEC659 10461
2568	lpDHilbertSickle sing_608.htm#SEC660 41445
2569	lpDimCheck sing_604.htm#SEC656 9807
2570	lpGkDim sing_639.htm#SEC691 10351
2571	lpGlDimBound sing_640.htm#SEC692 53074
2572	lpHilbert sing_606.htm#SEC658 44093
2573	lpId2ivLi sing_634.htm#SEC686 13273
2574	lpIsPrime sing_638.htm#SEC690 27562
2575	lpIsSemiPrime sing_637.htm#SEC689 27642
2576	lpKDim sing_603.htm#SEC655 18278
2577	lpMaxIdeal sing_626.htm#SEC678 37571
2578	lpMis2Base sing_605.htm#SEC657 10826
2579	lpMis2Dim sing_602.htm#SEC654 39947
2580	lpMult sing_650.htm#SEC702 58898
2581	lpNF sing_647.htm#SEC699 2851
2582	lpNoetherian sing_636.htm#SEC688 43125
2583	lpOrdMisLex sing_620.htm#SEC672 30943
2584	lpPower sing_652.htm#SEC704 7325
2585	lpSickle sing_621.htm#SEC673 288
2586	lpSickleDim sing_623.htm#SEC675 61018
2587	lpSickleHil sing_622.htm#SEC674 55268
2588	lpSubstitute sing_641.htm#SEC693 54386
2589	lprint sing_948.htm#SEC1024 5285
2590	lres sing_288.htm#SEC328
2591	ls, local ordering sing_861.htm#IDX402
2592	lst2str sing_655.htm#SEC707 10088
2593	lsum sing_1152.htm#SEC1228 50315
2594	ludecomp sing_289.htm#SEC329
2595	luinverse sing_290.htm#SEC330
2596	lusolve sing_291.htm#SEC331
2597	mRes sing_2504.htm#SEC2580 58702
2598	m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1934.htm#SEC2010 57945
2599	m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1933.htm#SEC2009 33857
2600	m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1932.htm#SEC2008 7880
2601	magnitude sing_1856.htm#SEC1932 37967
2602	makeDivisor sing_2355.htm#SEC2431 3414
2603	makeFormalDivisor sing_2365.htm#SEC2441 54579
2604	makeGraph sing_1143.htm#SEC1219 21758
2605	makeGraphVE sing_2723.htm#SEC2799 sprintf
2606	makeHeisenberg sing_731.htm#SEC783 2050
2607	makeIdeal sing_2496.htm#SEC2572 57829
2608	makeLetterplaceRing sing_645.htm#SEC697 1592
2609	makeMalgrange sing_600.htm#SEC652 41377
2610	makeMatrix sing_2495.htm#SEC2571 64348
2611	makeModElimRing sing_748.htm#SEC800 56092
2612	makePDivisor sing_2371.htm#SEC2447 45273
2613	makeQsl2 sing_695.htm#SEC747 3997
2614	makeQsl3 sing_696.htm#SEC748 41249
2615	makeQso3 sing_694.htm#SEC746 58910
2616	makeSheaf sing_2711.htm#SEC2787 10497
2617	makeUe6 sing_691.htm#SEC743 58585
2618	makeUe7 sing_692.htm#SEC744 61849
2619	makeUe8 sing_693.htm#SEC745 64987
2620	makeUf4 sing_690.htm#SEC742 8408
2621	makeUg2 sing_689.htm#SEC741 34512
2622	makeUgl sing_675.htm#SEC727 3543
2623	makeUsl sing_674.htm#SEC726 24536
2624	makeUsl2 sing_673.htm#SEC725 42637
2625	makeUso10 sing_681.htm#SEC733 6936
2626	makeUso11 sing_682.htm#SEC734 35873
2627	makeUso12 sing_683.htm#SEC735 19319
2628	makeUso5 sing_676.htm#SEC728 34378
2629	makeUso6 sing_677.htm#SEC729 65009
2630	makeUso7 sing_678.htm#SEC730 49142
2631	makeUso8 sing_679.htm#SEC731 33275
2632	makeUso9 sing_680.htm#SEC732 16896
2633	makeUsp1 sing_684.htm#SEC736 44522
2634	makeUsp2 sing_685.htm#SEC737 18017
2635	makeUsp3 sing_686.htm#SEC738 57445
2636	makeUsp4 sing_687.htm#SEC739 51690
2637	makeUsp5 sing_688.htm#SEC740 35951
2638	makeVariety sing_2703.htm#SEC2779 23915
2639	makeVector sing_2524.htm#SEC2600 9049
2640	makeWeyl sing_730.htm#SEC782 8554
2641	map sing_128.htm#SEC168
2642	map (plural) sing_428.htm#SEC468
2643	map declarations sing_129.htm#SEC169
2644	map declarations (plural) map declarations (plural) sing_429.htm#SEC469
2645	map expressions sing_130.htm#SEC170
2646	map expressions (plural) map expressions (plural) sing_430.htm#SEC470
2647	map operations sing_131.htm#IDX129
2648	map operations (plural) map operations (plural) sing_431.htm#IDX300
2649	map related functions map related functions sing_132.htm#IDX131
2650	map related functions (plural) map related functions (plural) sing_432.htm#IDX301
2651	mapIsFinite sing_1120.htm#SEC1196 60897
2652	mapToRatNormCurve sing_1382.htm#SEC1458 8877
2653	mapall sing_1013.htm#SEC1089 14907
2654	mappingcone sing_2482.htm#SEC2558 48219
2655	mappingcone3 sing_2484.htm#SEC2560 58973
2656	markov4ti2 sing_1338.htm#SEC1414 9163
2657	mat2arr sing_2176.htm#SEC2252 20840
2658	mat2carr sing_2177.htm#SEC2253 13777
2659	mat_rk sing_1094.htm#SEC1170 32196
2660	matbil sing_1983.htm#SEC2059 1611
2661	mathematical objects Representation of mathematical objects sing_856.htm#SEC908
2662	mathinit sing_1768.htm#SEC1844 16793
2663	matmult sing_1984.htm#SEC2060 60088
2664	matrix sing_133.htm#SEC173
2665	matrix sing_2176.htm#IDX824
2666	matrix sing_2177.htm#IDX827
2667	matrix sing_2178.htm#IDX831
2668	matrix declarations sing_134.htm#SEC174
2669	matrix diagonalization sing_1845.htm#IDX800
2670	matrix expressions sing_135.htm#SEC175
2671	matrix operations sing_137.htm#SEC177
2672	matrix related functions matrix related functions sing_138.htm#SEC178
2673	matrix type cast sing_136.htm#SEC176
2674	matrix.lib sing_1047.htm#SEC1123
2675	matrixExp sing_1372.htm#SEC1448 53063
2676	matrixLog sing_1373.htm#SEC1449 26235
2677	matrixT1 sing_1624.htm#SEC1700 15051
2678	matrix_lib sing_1047.htm#SEC1123
2679	matrixpres sing_2487.htm#SEC2563 60645
2680	matrixsystem sing_2395.htm#SEC2471 62950
2681	max sing_292.htm#SEC332 23624
2682	maxEord sing_1397.htm#SEC1473 64032
2683	maxExp sing_209.htm#IDX136
2684	maxIntRoot sing_797.htm#SEC849 37127
2685	maxZeros sing_1375.htm#SEC1451 35964
2686	maxabs sing_2002.htm#SEC2078 64510
2687	maxcoef sing_971.htm#SEC1047 50577
2688	maxdeg sing_972.htm#SEC1048 39794
2689	maxdeg1 sing_973.htm#SEC1049 21545
2690	maxideal sing_293.htm#SEC333
2691	maximalFace sing_2112.htm#SEC2188 35224
2692	maximalGroebnerCone sing_2166.htm#SEC2242 62935
2693	maximalValue sing_2113.htm#SEC2189 32783
2694	maximum sing_1875.htm#SEC1951 2355
2695	maximum number of zeroes sing_1375.htm#IDX607
2696	mdouble sing_56.htm#SEC93 56685
2697	mem, option sing_315.htm#IDX180
2698	member sing_2345.htm#SEC2421 1765
2699	membershipMon sing_1198.htm#SEC1274 40876
2700	memory sing_294.htm#SEC334
2701	memory managment sing_294.htm#SEC334
2702	merkle_hellman_decryption merkle_hellman_decryption sing_1936.htm#SEC2012 49106
2703	merkle_hellman_encryption merkle_hellman_encryption sing_1935.htm#SEC2011 13645
2704	methods, hashtables sing_2490.htm#IDX988
2705	methods.lib sing_2490.htm#SEC2566
2706	methods_lib sing_2490.htm#SEC2566
2707	midpoint sing_2391.htm#SEC2467 29391
2708	milnor sing_1611.htm#SEC1687 23173
2709	milnorcode sing_1495.htm#SEC1571 13849
2710	milnornumber sing_2677.htm#SEC2753 21855
2711	min sing_295.htm#SEC335 56342
2712	minAssChar sing_1297.htm#SEC1373 18758
2713	minAssCharE sing_1298.htm#SEC1374 31570
2714	minAssGTZ sing_1295.htm#SEC1371 41315
2715	minAssGTZE sing_1296.htm#SEC1372 50867
2716	minAssZ sing_1315.htm#SEC1391 54152
2717	minEcart sing_1965.htm#SEC2041 34890
2718	minIntRoot sing_561.htm#SEC613 3288
2719	minIntRoot2 sing_796.htm#SEC848 46494
2720	minMult sing_1127.htm#SEC1203 31978
2721	minbase sing_296.htm#SEC336
2722	minbaseMon sing_1195.htm#SEC1271 1501
2723	mindeg sing_974.htm#SEC1050 16307
2724	mindeg1 sing_975.htm#SEC1051 39698
2725	mindist sing_1820.htm#SEC1896 55281
2726	minimal display time, setting the sing_358.htm#IDX284
2727	minimalAfaceOrbits sing_2433.htm#SEC2509 2467
2728	minimalAfaces sing_2424.htm#SEC2500 47736
2729	minimalFace sing_2114.htm#SEC2190 40971
2730	minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2435.htm#SEC2511 11756
2731	minimalValue sing_2115.htm#SEC2191 31262
2732	minipoly sing_1099.htm#SEC1175 4927
2733	minkowskiSum sing_2116.htm#SEC2192 3969
2734	minor sing_297.htm#SEC337
2735	minpoly sing_397.htm#SEC437
2736	minres sing_298.htm#SEC338
2737	minres (plural) sing_467.htm#SEC507
2738	mirror symmetry sing_1142.htm#IDX517
2739	mixed Hodge structure sing_1533.htm#IDX663
2740	mixed Hodge structure sing_1539.htm#IDX691
2741	mixed Hodge structure sing_1540.htm#IDX697
2742	mixed Hodge structure sing_1541.htm#IDX705
2743	mixed Hodge structure sing_1542.htm#IDX711
2744	mixed Hodge structure sing_1543.htm#IDX719
2745	mixed Hodge structure sing_1544.htm#IDX729
2746	mixed Hodge structure sing_1555.htm#IDX735
2747	mixed Hodge structure sing_1557.htm#IDX746
2748	mod sing_81.htm#SEC121
2749	mod sing_98.htm#SEC138
2750	mod sing_147.htm#SEC187
2751	mod sing_155.htm#SEC195
2752	mod2id sing_979.htm#SEC1055 27927
2753	mod2str sing_656.htm#SEC708 35236
2754	modBorder sing_2695.htm#SEC2771 19224
2755	modDec sing_1214.htm#SEC1290 48578
2756	modIntersect sing_1192.htm#SEC1268 43699
2757	modJanet sing_2697.htm#SEC2773 8550
2758	modNPos sing_1237.htm#SEC1313 17130
2759	modNormal sing_1188.htm#SEC1264 39654
2760	modNpos_test sing_1235.htm#SEC1311 34326
2761	modSagbiAlg sing_2332.htm#SEC2408 25025
2762	modStd sing_1190.htm#SEC1266 7824
2763	modSyz sing_1191.htm#SEC1267 37065
2764	modVStd sing_2337.htm#SEC2413 38529
2765	modVStd0 sing_2338.htm#SEC2414 46080
2766	modWalk sing_2545.htm#SEC2621 sprintf
2767	mod_versal sing_1524.htm#SEC1600 63927
2768	modality sing_1503.htm#SEC1579 49951
2769	modfWalk sing_2547.htm#SEC2623 sprintf
2770	modfrWalk sing_2548.htm#SEC2624 sprintf
2771	modnormal.lib sing_1187.htm#SEC1263
2772	modnormal_lib sing_1187.htm#SEC1263
2773	modrWalk sing_2546.htm#SEC2622 sprintf
2774	modregCM sing_1241.htm#SEC1317 5049
2775	modsatiety sing_1239.htm#SEC1315 44506
2776	modstd.lib sing_1189.htm#SEC1265
2777	modstd_lib sing_1189.htm#SEC1265
2778	modular sing_957.htm#SEC1033 16950
2779	modular methods sing_1185.htm#IDX550
2780	modular methods sing_1187.htm#IDX555
2781	modular methods. sing_1186.htm#IDX553
2782	modular techniques. sing_1188.htm#IDX557
2783	modular.lib sing_956.htm#SEC1032
2784	modular_lib sing_956.htm#SEC1032
2785	modular_lib sing_956.htm#IDX485
2786	module sing_139.htm#SEC179
2787	module (plural) sing_433.htm#SEC473
2788	module declarations sing_140.htm#SEC180
2789	module declarations (plural) module declarations (plural) sing_434.htm#SEC474
2790	module expressions sing_141.htm#SEC181
2791	module expressions (plural) module expressions (plural) sing_435.htm#SEC475
2792	module operations sing_142.htm#SEC182
2793	module operations (plural) module operations (plural) sing_436.htm#SEC476
2794	module ordering C sing_862.htm#IDX414
2795	module ordering c sing_862.htm#IDX416
2796	module related functions module related functions sing_143.htm#SEC183
2797	module related functions (plural) module related functions (plural) sing_437.htm#SEC477
2798	module_containment sing_1112.htm#SEC1188 31620
2799	modules.lib sing_2491.htm#SEC2567
2800	modules_lib sing_2491.htm#SEC2567
2801	moduliSpace sing_2725.htm#SEC2801 37013
2802	modulo sing_299.htm#SEC339
2803	modulo (plural) sing_468.htm#SEC508
2804	moduloSlim sing_738.htm#SEC790 52636
2805	modwalk.lib sing_2544.htm#SEC2620
2806	modwalk_lib sing_2544.htm#SEC2620
2807	moebius sing_2212.htm#SEC2288 61319
2808	moebius function sing_2212.htm#IDX897
2809	molien sing_1647.htm#SEC1723 63561
2810	mondromy.lib sing_1585.htm#SEC1661
2811	mondromy_lib sing_1585.htm#SEC1661
2812	monitor sing_300.htm#SEC340
2813	monodromy sing_1533.htm#IDX667 40112
2814	monodromy sing_1538.htm#SEC1614
2815	monodromy sing_1538.htm#IDX687
2816	monodromy sing_1543.htm#IDX722
2817	monodromy sing_1555.htm#IDX738
2818	monodromy sing_1557.htm#IDX749
2819	monodromyB sing_1589.htm#SEC1665 46517
2820	monomial sing_301.htm#SEC341
2821	monomial ordering sing_1022.htm#IDX499
2822	monomial orderings General definitions for orderings sing_810.htm#SEC862
2823	monomial orderings sing_859.htm#SEC911
2824	monomial orderings introduction Introduction to orderings sing_858.htm#SEC910
2825	monomialBasis sing_627.htm#SEC679 14185
2826	monomialInIdeal sing_794.htm#SEC846 4687
2827	monomialLcm sing_1963.htm#SEC2039 36233
2828	monomialabortstd sing_2219.htm#SEC2295 14901
2829	monomialideal.lib sing_1193.htm#SEC1269
2830	monomialideal_lib sing_1193.htm#SEC1269
2831	monomials and precedence Miscellaneous oddities sing_418.htm#IDX290
2832	mons2intmat sing_1282.htm#SEC1358 15555
2833	morsesplit sing_1496.htm#SEC1572 3417
2834	movingCone sing_2431.htm#SEC2507 39892
2835	mp_res_mat sing_1729.htm#SEC1805 44453
2836	mplot sing_1769.htm#SEC1845 21740
2837	mpresmat sing_302.htm#SEC342
2838	mprimdec.lib sing_1210.htm#SEC1286
2839	mprimdec_lib sing_1210.htm#SEC1286
2840	mregular.lib sing_1225.htm#SEC1301
2841	mregular_lib sing_1225.htm#SEC1301
2842	mres sing_303.htm#SEC343
2843	mres (plural) sing_469.htm#SEC509
2844	mstd sing_304.htm#SEC344
2845	msum sing_58.htm#SEC95 53344
2846	mtriple sing_57.htm#SEC94 55390
2847	mult Miscellaneous oddities sing_305.htm#SEC345
2848	mult sing_418.htm#IDX291
2849	multBound sing_398.htm#SEC438
2850	multRat sing_802.htm#SEC854 44047
2851	multarr2arr sing_2207.htm#SEC2283 44731
2852	multarrMultRestrict sing_2209.htm#SEC2285 41742
2853	multarrRestrict sing_2208.htm#SEC2284 sprintf
2854	multcol sing_1066.htm#SEC1142 21899
2855	multdivisor sing_2357.htm#SEC2433 65139
2856	multformaldivisor sing_2369.htm#SEC2445 32238
2857	multi sing_1950.htm#SEC2026 18473
2858	multi indices sing_37.htm#SEC65
2859	multiDeg sing_2579.htm#SEC2655 7049
2860	multiDegBasis sing_2580.htm#SEC2656 3320
2861	multiDegGroebner sing_2588.htm#SEC2664 1040
2862	multiDegModulo sing_2590.htm#SEC2666 27244
2863	multiDegPartition sing_2581.htm#SEC2657 9577
2864	multiDegResolution sing_2591.htm#SEC2667 38535
2865	multiDegSyzygy sing_2589.htm#SEC2665 54075
2866	multiDegTensor sing_2592.htm#SEC2668 45108
2867	multiDegTor sing_2593.htm#SEC2669 sprintf
2868	multiarrangement sing_2203.htm#IDX877
2869	multiarrangement sing_2204.htm#IDX879
2870	multiarrangement sing_2205.htm#IDX882
2871	multiarrangement sing_2206.htm#IDX883
2872	multiarrangement sing_2207.htm#IDX886
2873	multiarrangement sing_2208.htm#IDX889
2874	multiarrangement sing_2209.htm#IDX891
2875	multidimensional_knapsack multidimensional_knapsack sing_1928.htm#SEC2004 15647
2876	multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2549.htm#IDX995
2877	multigrading.lib sing_2549.htm#IDX993
2878	multigrading_lib sing_2549.htm#IDX994
2879	multipleCover sing_2731.htm#SEC2807 55988
2880	multiplicities, sequence of sing_1564.htm#IDX761
2881	multiplicity sing_2348.htm#IDX953
2882	multiplicity sequence sing_1477.htm#IDX640
2883	multiplicity sequence sing_1480.htm#IDX652
2884	multiplicity sequence sing_1566.htm#IDX762
2885	multiplyLeftFractions multiplyLeftFractions sing_2664.htm#SEC2740 57489
2886	multiplylist sing_1417.htm#SEC1493 34999
2887	multivariate equations sing_1703.htm#IDX779
2888	multrow sing_1067.htm#SEC1143 871
2889	multseq2charexp sing_1476.htm#SEC1552 sprintf
2890	multsequence sing_1566.htm#SEC1642 35117
2891	nBoundaryLatticePoints nBoundaryLatticePoints sing_2117.htm#SEC2193 49670
2892	nHilbertBasis sing_2118.htm#SEC2194 173
2893	nInteriorLatticePoints nInteriorLatticePoints sing_2119.htm#SEC2195 42152
2894	nLatticePoints sing_2120.htm#SEC2196 5977
2895	naccache_stern_decryption naccache_stern_decryption sing_1931.htm#SEC2007 31429
2896	naccache_stern_encryption naccache_stern_encryption sing_1930.htm#SEC2006 60034
2897	naccache_stern_generation naccache_stern_generation sing_1929.htm#SEC2005 2559
2898	nameof sing_306.htm#SEC346
2899	names sing_307.htm#SEC347
2900	nashmult sing_1484.htm#SEC1560 8491
2901	nblocks sing_358.htm#IDX221
2902	ncExt_R sing_771.htm#SEC823 14357
2903	ncHilb.lib sing_2601.htm#SEC2677
2904	ncHilb_lib sing_2601.htm#SEC2677
2905	ncHom sing_772.htm#SEC824 45033
2906	ncRelations sing_739.htm#SEC791 7225
2907	nc_algebra sing_470.htm#SEC510
2908	nc_hilb sing_358.htm#IDX223
2909	ncalg.lib sing_672.htm#SEC724
2910	ncalg_lib sing_672.htm#SEC724
2911	ncalgebra sing_471.htm#SEC511
2912	ncdecomp.lib sing_699.htm#SEC751
2913	ncdecomp_lib sing_699.htm#SEC751
2914	ncdetection sing_666.htm#SEC718 24994
2915	ncfactor sing_705.htm#SEC757 53809
2916	ncfactor.lib sing_704.htm#SEC756
2917	ncfactor_lib sing_704.htm#SEC756
2918	ncfrac.lib sing_2604.htm#SEC2680
2919	ncfrac_lib sing_2604.htm#SEC2680
2920	nchilb sing_2602.htm#SEC2678 40517
2921	nchomolog.lib sing_770.htm#IDX373
2922	nchomolog_lib sing_770.htm#IDX374
2923	ncloc.lib sing_2618.htm#SEC2694
2924	ncloc_lib sing_2618.htm#SEC2694
2925	ncols sing_308.htm#SEC348
2926	ncones sing_2065.htm#SEC2141 48316
2927	ncpreim.lib sing_717.htm#SEC769
2928	ncpreim_lib sing_717.htm#SEC769
2929	nctools.lib sing_725.htm#SEC777
2930	nctools_lib sing_725.htm#SEC777
2931	ndcond sing_728.htm#SEC780 1006
2932	negateNcfrac sing_2613.htm#SEC2689 23626
2933	negatedCone sing_2043.htm#SEC2119 38527
2934	negative degree lexicographical ordering sing_861.htm#IDX405
2935	negative degree reverse lexicographical ordering Local orderings sing_861.htm#IDX403
2936	negative lexicographical ordering sing_861.htm#IDX401
2937	negativedivisor sing_2358.htm#SEC2434 8274
2938	negativeformaldivisor negativeformaldivisor sing_2368.htm#SEC2444 55026
2939	net sing_2622.htm#IDX996 sprintf
2940	net sing_2624.htm#SEC2700
2941	net access Command line options sing_19.htm#IDX40
2942	netBigInt sing_2630.htm#SEC2706 63523
2943	netBigIntMat sing_2625.htm#SEC2701 36296
2944	netBigIntMatShort sing_2626.htm#SEC2702 30702
2945	netCoefficientRing sing_2627.htm#SEC2703 6081
2946	netIdeal sing_2628.htm#SEC2704 64434
2947	netInt sing_2629.htm#SEC2705 19545
2948	netIntMat sing_2631.htm#SEC2707 34242
2949	netIntMatShort sing_2632.htm#SEC2708 21160
2950	netIntVector sing_2633.htm#SEC2709 17568
2951	netIntVectorShort sing_2634.htm#SEC2710 16105
2952	netList sing_2636.htm#SEC2712 29178
2953	netMap sing_2637.htm#SEC2713 19115
2954	netMap2 sing_2638.htm#SEC2714 44053
2955	netMatrix sing_2526.htm#SEC2602 29311
2956	netNumber sing_2635.htm#SEC2711 24930
2957	netPoly sing_2641.htm#SEC2717 7938
2958	netPrimePower sing_2642.htm#SEC2718 54219
2959	netRing sing_2643.htm#SEC2719 42246
2960	netString sing_2644.htm#SEC2720 43247
2961	netVector sing_2525.htm#SEC2601 32453
2962	netmatrix sing_2639.htm#SEC2715 4023
2963	netmatrixShort sing_2640.htm#SEC2716 24709
2964	nets.lib sing_2622.htm#SEC2698
2965	nets_lib sing_2622.htm#SEC2698
2966	netvector sing_2645.htm#SEC2721 39957
2967	netvectorShort sing_2646.htm#SEC2722 22053
2968	newTest sing_1870.htm#SEC1946 36655
2969	newline sing_171.htm#SEC211
2970	news sing_2754.htm#SEC2830
2971	newstruct sing_182.htm#SEC222
2972	newstruct sing_2226.htm#IDX913
2973	newtonDiag sing_983.htm#SEC1059 56652
2974	newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2747.htm#SEC2823 22052
2975	newtonPolytope sing_2069.htm#SEC2145 56291
2976	newtonPolytopeLP sing_2074.htm#SEC2150 36186
2977	newtonPolytopeP sing_2073.htm#SEC2149 29927
2978	newtonpoly sing_1571.htm#SEC1647 31930
2979	nf_icis sing_1612.htm#SEC1688 49093
2980	nfmodStd sing_2650.htm#SEC2726 46077
2981	nfmodSyz sing_2652.htm#SEC2728 55942
2982	nfmodstd.lib sing_2648.htm#SEC2724
2983	nfmodstd_lib sing_2648.htm#SEC2724
2984	nfmodsyz.lib sing_2651.htm#SEC2727
2985	nfmodsyz_lib sing_2651.htm#SEC2727
2986	nilpotent Lie algebras sing_1370.htm#IDX592
2987	nmaxcones sing_2064.htm#SEC2140 660
2988	noether sing_399.htm#SEC439
2989	noether.lib sing_1233.htm#SEC1309
2990	noetherNormal sing_1119.htm#SEC1195 44522
2991	noether_lib sing_1233.htm#SEC1309
2992	non-english special characters sing_407.htm#IDX286
2993	nonMonomials sing_1286.htm#SEC1362 16309
2994	nonZeroEntry sing_1122.htm#SEC1198 933
2995	none, option sing_315.htm#IDX150
2996	norTest sing_1253.htm#SEC1329 sprintf
2997	norm sing_1949.htm#SEC2025 31143
2998	normaform (up to a bound) sing_358.htm#IDX246
2999	normal sing_1243.htm#SEC1319 61073
3000	normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2730.htm#IDX1061
3001	normal form sing_868.htm#IDX417
3002	normal.lib sing_1242.htm#SEC1318
3003	normalBundle sing_2730.htm#SEC2806 sprintf
3004	normalC sing_1245.htm#SEC1321 34842
3005	normalConductor sing_1257.htm#SEC1333 26085
3006	normalFan sing_2121.htm#SEC2197 39216
3007	normalForm sing_2359.htm#SEC2435 34962
3008	normalI sing_1330.htm#SEC1406 7516
3009	normalP sing_1244.htm#SEC1320 36584
3010	normalToricRing sing_1260.htm#SEC1336 29638
3011	normalToricRingFromBinomials normalToricRingFromBinomials sing_1261.htm#SEC1337 2301
3012	normal_lib sing_1242.htm#SEC1318
3013	normalform sing_1500.htm#SEC1576 5550
3014	normalform sing_2331.htm#IDX941
3015	normaliz sing_1.htm#IDX14 18426
3016	normaliz sing_1273.htm#SEC1349
3017	normaliz.lib sing_1258.htm#SEC1334
3018	normaliz_lib sing_1258.htm#SEC1334
3019	normalization sing_1185.htm#IDX548
3020	normalization sing_1186.htm#IDX551
3021	normalization sing_1187.htm#IDX554
3022	normalization sing_1188.htm#IDX556
3023	normalization sing_1243.htm#IDX560
3024	normalization sing_1244.htm#IDX563
3025	normalization sing_1245.htm#IDX566
3026	normalization sing_1257.htm#IDX572
3027	normalization sing_1258.htm#IDX574
3028	normalization sing_2347.htm#IDX951
3029	normalization. sing_1182.htm#IDX547
3030	normalization. sing_1377.htm#IDX614
3031	normalize sing_976.htm#SEC1052 44788
3032	normalizeMonoidal sing_2670.htm#SEC2746 33071
3033	normalizeRational sing_2671.htm#SEC2747 55177
3034	not sing_101.htm#SEC141
3035	notBuckets, option sing_315.htm#IDX160
3036	notRegularity, option sing_315.htm#IDX158
3037	notSugar, option sing_315.htm#IDX159
3038	notWarnSB, option sing_315.htm#IDX181
3039	npar sing_1855.htm#SEC1931 5753
3040	npars sing_309.htm#SEC349
3041	nrRootsDeterm sing_1980.htm#SEC2056 sprintf
3042	nrRootsProbab sing_1979.htm#SEC2055 sprintf
3043	nres sing_310.htm#SEC350
3044	nres (plural) sing_472.htm#SEC512
3045	nrows sing_311.htm#SEC351
3046	nrroots sing_2009.htm#SEC2085 54867
3047	nsatiety sing_1238.htm#SEC1314 53333
3048	nselect sing_1138.htm#SEC1214 34057
3049	nt_solve sing_1744.htm#SEC1820 33061
3050	ntsolve.lib sing_1743.htm#SEC1819
3051	ntsolve_lib sing_1743.htm#SEC1819
3052	number sing_144.htm#SEC184
3053	number sing_2180.htm#IDX837
3054	number declarations sing_145.htm#SEC185
3055	number expressions sing_146.htm#SEC186
3056	number operations sing_147.htm#SEC187
3057	number related functions number related functions sing_148.htm#SEC188
3058	numberOfConesOfDimension numberOfConesOfDimension sing_2066.htm#SEC2142 5905
3059	number_e sing_912.htm#SEC988 59152
3060	number_pi sing_913.htm#SEC989 15492
3061	numerAlg.lib sing_1352.htm#IDX581
3062	numerAlg_lib sing_1352.htm#IDX582
3063	numerAlg_lib sing_1357.htm#IDX591
3064	numerDecom.lib sing_1357.htm#IDX585
3065	numerDecom_lib sing_1352.htm#IDX584
3066	numerDecom_lib sing_1357.htm#IDX586
3067	numerator sing_312.htm#SEC352
3068	numerical irreducible decomposition sing_1357.htm#IDX587
3069	nvars sing_313.htm#SEC353
3070	olga.lib sing_2653.htm#SEC2729
3071	olga_lib sing_2653.htm#SEC2729
3072	oneDimBelongSemigroup oneDimBelongSemigroup sing_1129.htm#SEC1205 34399
3073	oneNcfrac sing_2610.htm#SEC2686 35654
3074	online help The online help system sing_16.htm#SEC22
3075	open sing_314.htm#SEC354
3076	opentex sing_1772.htm#SEC1848 54236
3077	operatorBM sing_547.htm#SEC599 54875
3078	operatorModulo sing_548.htm#SEC600 26064
3079	oppose sing_473.htm#SEC513
3080	opposite sing_474.htm#SEC514
3081	opposite polynomial sing_358.htm#IDX231
3082	opposite ring sing_358.htm#IDX228
3083	option sing_315.htm#SEC355
3084	option(warn) sing_70.htm#SEC110
3085	optionIsSet sing_1019.htm#SEC1095 57325
3086	or Evaluation of logical expressions sing_101.htm#SEC141
3087	or sing_411.htm#SEC451
3088	orbit sing_1370.htm#IDX594
3089	orbit sing_1371.htm#IDX598
3090	orbit sing_1374.htm#IDX603
3091	orbit sing_1375.htm#IDX606
3092	orbitConeOrbits sing_2434.htm#SEC2510 60979
3093	orbitCones sing_2425.htm#SEC2501 60528
3094	orbit_variety sing_1671.htm#SEC1747 22665
3095	orbitparam.lib sing_1370.htm#SEC1446
3096	orbitparam_lib sing_1370.htm#SEC1446
3097	ord sing_316.htm#SEC356
3098	ord_test sing_1014.htm#SEC1090 36532
3099	order ideal, border basis sing_2694.htm#IDX1033
3100	order ideal, border basis sing_2695.htm#IDX1034
3101	orderings General definitions for orderings sing_859.htm#SEC911
3102	orderings introduction Introduction to orderings sing_858.htm#SEC910
3103	orderings, L sing_866.htm#SEC918
3104	orderings, M sing_863.htm#SEC915
3105	orderings, a sing_865.htm#SEC917
3106	orderings, global sing_860.htm#SEC912
3107	orderings, local sing_861.htm#SEC913
3108	orderings, product sing_864.htm#SEC916
3109	ordstr sing_317.htm#SEC357
3110	origin sing_2014.htm#SEC2090 31408
3111	orthogonalize sing_1085.htm#SEC1161 63711
3112	outer sing_1055.htm#SEC1131 64048
3113	output sing_41.htm#SEC71
3114	p-adic numbers sing_32.htm#SEC46
3115	pFactor sing_1904.htm#SEC1980 31504
3116	pIntersect sing_511.htm#SEC563 44055
3117	pIntersectSyz sing_512.htm#SEC564 45608
3118	package sing_149.htm#SEC189
3119	package declarations package declarations sing_150.htm#SEC190
3120	package related functions package related functions sing_151.htm#SEC191
3121	pairset sing_1969.htm#SEC2045 38258
3122	par sing_318.htm#SEC358
3123	par2varRing sing_896.htm#SEC972 44769
3124	paraConic sing_1385.htm#SEC1461 9828
3125	paraPlaneCurve sing_1379.htm#SEC1455 34094
3126	parallel skeletons sing_958.htm#IDX491
3127	parallel.lib sing_958.htm#SEC1034
3128	parallelTestAND sing_962.htm#SEC1038 1415
3129	parallelTestOR sing_963.htm#SEC1039 14920
3130	parallelWaitAll sing_961.htm#SEC1037 2017
3131	parallelWaitFirst sing_960.htm#SEC1036 32
3132	parallelWaitN sing_959.htm#SEC1035 38878
3133	parallel_lib sing_958.htm#SEC1034
3134	parallelization sing_958.htm#IDX490
3135	parallelization sing_998.htm#IDX493
3136	parallelization sing_1031.htm#IDX503
3137	param sing_1562.htm#SEC1638 57220
3138	parameter, as numbers sing_144.htm#SEC184
3139	parameterSubstitute sing_2161.htm#SEC2237 63147
3140	parametric annihilator sing_540.htm#IDX335
3141	parametric annihilator for variety sing_596.htm#IDX358
3142	parametric ideal sing_924.htm#IDX423
3143	parametric ideal sing_931.htm#IDX442
3144	parametric ideal sing_931.htm#IDX444
3145	parametric ideal sing_932.htm#IDX449
3146	parametrization sing_1370.htm#IDX595
3147	parametrization sing_1374.htm#IDX604
3148	parametrization sing_1562.htm#IDX756
3149	parametrizeOrbit sing_1374.htm#SEC1450 26969
3150	paraplanecurves.lib sing_1376.htm#SEC1452
3151	paraplanecurves_lib sing_1376.htm#SEC1452
3152	pardeg sing_319.htm#SEC359
3153	parstr sing_320.htm#SEC360
3154	part sing_2307.htm#SEC2383 31485
3155	partOver sing_2310.htm#SEC2386 25555
3156	partUnder sing_2311.htm#SEC2387 13123
3157	partial_molien sing_1649.htm#SEC1725 21772
3158	partitions sing_1150.htm#SEC1226 48089
3159	partitions sing_1150.htm#IDX536
3160	path integral sing_1142.htm#IDX523
3161	pause sing_955.htm#SEC1031 2273
3162	pdivi sing_926.htm#SEC1002 21786
3163	pdivi sing_927.htm#IDX433
3164	pdivisorplus sing_2373.htm#SEC2449 47486
3165	permcol sing_1068.htm#SEC1144 12886
3166	permrow sing_1069.htm#SEC1145 26561
3167	permutationFromIntvec permutationFromIntvec sing_2440.htm#SEC2516 6533
3168	permutationToIntvec sing_2441.htm#SEC2517 1989
3169	permutations sing_1151.htm#IDX537
3170	permutations, sum, max, min sing_2342.htm#IDX943
3171	permute sing_1151.htm#SEC1227 40893
3172	permute_L sing_1807.htm#SEC1883 10716
3173	perron sing_751.htm#SEC803 3782
3174	perron.lib sing_750.htm#SEC802
3175	perron_lib sing_750.htm#SEC802
3176	phindex.lib sing_2221.htm#IDX904
3177	phindex_lib sing_2221.htm#IDX905
3178	picksFormula sing_2083.htm#SEC2159 14656
3179	pid sing_358.htm#IDX240
3180	plainInvariants sing_1521.htm#SEC1597 40916
3181	planeCur sing_2329.htm#SEC2405 sprintf
3182	plot sing_1785.htm#SEC1861 46610
3183	plotRot sing_1789.htm#SEC1865 57150
3184	plotRotated sing_1788.htm#SEC1864 33009
3185	plotRotatedDirect sing_1791.htm#SEC1867 18202
3186	plotRotatedList sing_1790.htm#SEC1866 41668
3187	plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1792.htm#SEC1868 38856
3188	plural sing_1021.htm#IDX498
3189	pmat sing_949.htm#SEC1025 3857
3190	pnormalf sing_927.htm#SEC1003 26174
3191	pointid.lib sing_1285.htm#SEC1361
3192	pointid_lib sing_1285.htm#SEC1361
3193	polSol sing_786.htm#SEC838 323
3194	polSolFiniteRank sing_787.htm#SEC839 30875
3195	pollTask sing_1041.htm#SEC1117 53950
3196	poly sing_152.htm#SEC192
3197	poly (plural) sing_438.htm#SEC478
3198	poly declarations sing_153.htm#SEC193
3199	poly declarations (plural) poly declarations (plural) sing_439.htm#SEC479
3200	poly expressions sing_154.htm#SEC194
3201	poly expressions (plural) poly expressions (plural) sing_440.htm#SEC480
3202	poly operations sing_155.htm#SEC195
3203	poly operations (plural) poly operations (plural) sing_441.htm#SEC481
3204	poly related functions poly related functions sing_156.htm#SEC196
3205	poly related functions (plural) poly related functions (plural) sing_442.htm#SEC482
3206	poly.lib sing_964.htm#SEC1040
3207	poly2list sing_589.htm#SEC641 4960
3208	poly2zdd sing_2242.htm#SEC2318 61839
3209	polyInterpolation sing_2376.htm#SEC2452 45866
3210	polyVars sing_793.htm#SEC845 43882
3211	poly_lib sing_964.htm#SEC1040
3212	polybori sing_2226.htm#IDX909
3213	polybori.lib sing_2226.htm#IDX906
3214	polybori.lib sing_2226.htm#IDX910
3215	polybori_lib sing_2226.htm#IDX907
3216	polymake sing_2071.htm#IDX810
3217	polymake.lib sing_2071.htm#SEC2147
3218	polymakePolytope sing_2072.htm#SEC2148 47302
3219	polymake_lib sing_2071.htm#SEC2147
3220	polynomial solutions sing_780.htm#IDX386
3221	polynomial, opposite sing_358.htm#IDX232
3222	polytope sing_190.htm#SEC230
3223	polytope sing_2071.htm#IDX806
3224	polytopeViaInequalities polytopeViaInequalities sing_2044.htm#SEC2120 52084
3225	polytopeViaPoints sing_2045.htm#SEC2121 281
3226	pos_def sing_1096.htm#SEC1172 4994
3227	poset sing_2211.htm#IDX895
3228	positiveOrthant sing_2015.htm#SEC2091 42102
3229	posweight sing_1629.htm#SEC1705 3364
3230	powSumSym sing_2264.htm#SEC2340 2339
3231	power sing_1056.htm#SEC1132 23365
3232	power set sing_2344.htm#IDX945
3233	powerN sing_1888.htm#SEC1964 20170
3234	powerX sing_1897.htm#SEC1973 47971
3235	power_products sing_1663.htm#SEC1739 54629
3236	powerpolyX sing_1867.htm#SEC1943 37247
3237	powersums sing_1990.htm#SEC2066 59049
3238	preComp sing_1221.htm#SEC1297 16160
3239	preimage sing_321.htm#SEC361
3240	preimage sing_717.htm#IDX361
3241	preimage (plural) sing_475.htm#SEC515
3242	preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1017.htm#IDX496
3243	preimageLattice sing_2569.htm#SEC2645 37348
3244	preimageLoc sing_1017.htm#SEC1093 33315
3245	preimageNC sing_719.htm#SEC771 16037
3246	prepEmbDiv sing_1447.htm#SEC1523 36708
3247	prepMat sing_1700.htm#SEC1776 39868
3248	prepRealclassify sing_1505.htm#SEC1581 10994
3249	prepSV sing_1802.htm#SEC1878 50095
3250	prepareAss sing_1304.htm#SEC1380 21802
3251	presentTree sing_1434.htm#SEC1510 10731
3252	presentation sing_2527.htm#SEC2603 40323
3253	presolve.lib sing_1710.htm#SEC1786
3254	presolve_lib sing_1710.htm#SEC1786
3255	primL sing_1892.htm#SEC1968 14513
3256	primList sing_1891.htm#SEC1967 6802
3257	primRoot sing_1344.htm#SEC1420 14210
3258	primTest sing_1220.htm#SEC1296 8105
3259	primary decomposition sing_1289.htm#IDX576
3260	primary decomposition sing_1312.htm#IDX577
3261	primary decomposition of modules sing_1210.htm#IDX558
3262	primary decomposition, numerical sing_1357.htm#IDX589
3263	primary_char0 sing_1653.htm#SEC1729 61413
3264	primary_char0_no_molien primary_char0_no_molien sing_1655.htm#SEC1731 50477
3265	primary_char0_no_molien_random primary_char0_no_molien_random sing_1660.htm#SEC1736 8422
3266	primary_char0_random primary_char0_random sing_1658.htm#SEC1734 5996
3267	primary_charp sing_1654.htm#SEC1730 37863
3268	primary_charp_no_molien primary_charp_no_molien sing_1656.htm#SEC1732 32282
3269	primary_charp_no_molien_random primary_charp_no_molien_random sing_1661.htm#SEC1737 11498
3270	primary_charp_random primary_charp_random sing_1659.htm#SEC1735 24739
3271	primary_charp_without primary_charp_without sing_1657.htm#SEC1733 49585
3272	primary_charp_without_random primary_charp_without_random sing_1662.htm#SEC1738 36998
3273	primary_invariants sing_1641.htm#SEC1717 5500
3274	primary_invariants_random primary_invariants_random sing_1642.htm#SEC1718 28958
3275	primdec.lib sing_1289.htm#SEC1365
3276	primdecGTZ sing_1291.htm#SEC1367 6091
3277	primdecGTZE sing_1292.htm#SEC1368 64882
3278	primdecMon sing_1209.htm#SEC1285 3856
3279	primdecSY sing_1293.htm#SEC1369 6547
3280	primdecSYE sing_1294.htm#SEC1370 52788
3281	primdecZ sing_1313.htm#SEC1389 48194
3282	primdecZM sing_1314.htm#SEC1390 17214
3283	primdec_lib sing_1289.htm#SEC1365
3284	primdecint.lib sing_1312.htm#SEC1388
3285	primdecint_lib sing_1312.htm#SEC1388
3286	prime sing_322.htm#SEC362
3287	primeClosure sing_1248.htm#SEC1324 43589
3288	primecoeffs sing_919.htm#SEC995 46153
3289	primefactors sing_323.htm#SEC363
3290	primes sing_914.htm#SEC990 24408
3291	primitiv.lib sing_1320.htm#SEC1396
3292	primitiv_lib sing_1320.htm#SEC1396
3293	primitive sing_1321.htm#SEC1397 36163
3294	primitive element sing_1321.htm#IDX578
3295	primitiveSpan sing_2576.htm#SEC2652 sprintf
3296	primitive_extra sing_1322.htm#SEC1398 49025
3297	primparam sing_1516.htm#SEC1592 35357
3298	principal intersection sing_505.htm#IDX319
3299	print sing_324.htm#SEC364
3300	print sing_2178.htm#IDX830
3301	printBetti sing_2508.htm#SEC2584 28941
3302	printFreeModule sing_2500.htm#SEC2576 13316
3303	printGraph sing_1144.htm#SEC1220 45041
3304	printGraphG sing_2724.htm#SEC2800 48742
3305	printGroup sing_2557.htm#SEC2633 6791
3306	printHom sing_2503.htm#SEC2579 7070
3307	printMatrix sing_2499.htm#SEC2575 15522
3308	printModule sing_2502.htm#SEC2578 sprintf
3309	printMoebius sing_2217.htm#SEC2293 45828
3310	printResolution sing_2501.htm#SEC2577 29278
3311	printSheaf sing_2712.htm#SEC2788 31762
3312	printStack sing_2726.htm#SEC2802 3692
3313	printTask sing_1036.htm#SEC1112 54549
3314	printVariety sing_2704.htm#SEC2780 2846
3315	printf sing_325.htm#SEC365 2294
3316	printlevel sing_400.htm#SEC440
3317	proc sing_157.htm#SEC197
3318	proc declaration sing_158.htm#SEC198
3319	proc expression sing_159.htm#SEC199
3320	procedure, ASCII help sing_56.htm#IDX125
3321	procedure, ASCII/Texinfo help sing_58.htm#IDX127
3322	procedure, texinfo help sing_57.htm#IDX126
3323	procedures, help string sing_45.htm#SEC82
3324	procedures, static Procedure definition sing_43.htm#SEC78
3325	procs with different argument types procs with different argument types sing_160.htm#SEC200
3326	prodcrit sing_1967.htm#SEC2043 56231
3327	product sing_915.htm#SEC991 54431
3328	product variety, abstract variety sing_2705.htm#IDX1049
3329	productVariety sing_2705.htm#SEC2781 54191
3330	productgroup sing_2578.htm#SEC2654 55937
3331	progress watch sing_315.htm#IDX163
3332	projectLattice sing_2570.htm#SEC2646 28463
3333	projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2709.htm#IDX1053
3334	projective dimension purityfiltration_lib sing_758.htm#IDX370
3335	projective limes sing_32.htm#SEC46
3336	projective space, abstract variety sing_2708.htm#IDX1052
3337	projectiveBundle sing_2709.htm#SEC2785 13791
3338	projectiveDimension sing_759.htm#SEC811 8165
3339	projectiveSpace sing_2708.htm#SEC2784 21729
3340	prompt sing_15.htm#SEC21
3341	prompt, option sing_315.htm#IDX182
3342	propagator sing_1142.htm#IDX521 42460
3343	propagator sing_1145.htm#SEC1221
3344	prot, option sing_315.htm#IDX161
3345	protocol of computations sing_315.htm#IDX162
3346	proximitymatrix sing_1475.htm#SEC1551 58403
3347	prune sing_326.htm#SEC366
3348	pruneModule sing_2534.htm#SEC2610 51453
3349	prwalk sing_2699.htm#SEC2775 46963
3350	psigncnd sing_1763.htm#SEC1839 57734
3351	puiseux2generators sing_1574.htm#SEC1650 64508
3352	puiseuxExpansion sing_2132.htm#SEC2208 46277
3353	pure tensor sing_498.htm#IDX307
3354	purelist sing_769.htm#SEC821 15517
3355	purity purityfiltration_lib sing_758.htm#IDX372
3356	purityFiltration sing_760.htm#SEC812 5742
3357	purityTriang sing_761.htm#SEC813 3665
3358	purityfiltration.lib purityfiltration_lib sing_758.htm#IDX365
3359	purityfiltration_lib purityfiltration_lib sing_758.htm#IDX366
3360	pushForward sing_2595.htm#SEC2671 26697
3361	pwalk sing_1158.htm#SEC1234 61187
3362	pyobject sing_191.htm#SEC231
3363	pyobject sing_2226.htm#IDX912
3364	pyobject declarations pyobject declarations sing_192.htm#SEC232
3365	pyobject expressions pyobject expressions sing_193.htm#SEC233
3366	pyobject operations sing_194.htm#SEC234
3367	pyobject related functions pyobject related functions sing_195.htm#SEC235
3368	pyramid sing_2392.htm#SEC2468 7421
3369	python_eval sing_196.htm#SEC236
3370	python_import sing_197.htm#SEC237
3371	python_run sing_198.htm#SEC238
3372	qbase sing_1993.htm#SEC2069 8633
3373	qepcad sing_2402.htm#SEC2478 39171
3374	qepcadsystem sing_2403.htm#SEC2479 31977
3375	qhmatrix sing_1627.htm#SEC1703 61813
3376	qhmoduli.lib sing_1591.htm#SEC1667
3377	qhmoduli_lib sing_1591.htm#SEC1667
3378	qhspectrum sing_1614.htm#SEC1690 13732
3379	qhweight sing_327.htm#SEC367
3380	qmatrix.lib sing_752.htm#SEC804
3381	qmatrix_lib sing_752.htm#SEC804
3382	qminor sing_754.htm#SEC806 52670
3383	qrds sing_328.htm#SEC368
3384	qring Miscellaneous oddities sing_166.htm#SEC206
3385	qring sing_418.htm#IDX295
3386	qring (plural) sing_443.htm#SEC483
3387	qring declaration sing_170.htm#SEC210
3388	qring declaration (plural) qring declaration (plural) sing_444.htm#SEC484
3389	qring related functions (plural) qring related functions (plural) sing_445.htm#SEC485
3390	qring ring ideal 'factor ring' sing_1026.htm#IDX502
3391	qringNF, option sing_315.htm#IDX164
3392	qslimgb sing_895.htm#SEC971 51999
3393	quadraticSieve sing_1905.htm#SEC1981 58557
3394	quantMat sing_753.htm#SEC805 56227
3395	quickclass sing_1497.htm#SEC1573 14018
3396	quit sing_390.htm#SEC430
3397	quotSheaf sing_2721.htm#SEC2797 49619
3398	quote sing_329.htm#SEC369
3399	quotient sing_330.htm#SEC370
3400	quotient (plural) sing_476.htm#SEC516
3401	quotientLatticeBasis quotientLatticeBasis sing_2046.htm#SEC2122 15613
3402	quotientMain sing_1755.htm#SEC1831 39870
3403	quotientMon sing_1200.htm#SEC1276 57149
3404	rHRR sing_2304.htm#SEC2380 20131
3405	rJanet sing_2696.htm#SEC2772 30716
3406	rMacaulay sing_950.htm#SEC1026 45499
3407	rad_con sing_977.htm#SEC1053 21777
3408	radical sing_1301.htm#SEC1377 1407
3409	radicalEHV sing_1302.htm#SEC1378 33703
3410	radicalMemberShip sing_2154.htm#SEC2230 28527
3411	radicalMon sing_1201.htm#SEC1277 64912
3412	radicalZ sing_1316.htm#SEC1392 5783
3413	randcharpoly sing_1987.htm#SEC2063 37737
3414	randlinpoly sing_1989.htm#SEC2065 22330
3415	random sing_331.htm#SEC371
3416	random sing_358.htm#IDX244
3417	random sing_2199.htm#IDX869
3418	random sing_2200.htm#IDX871
3419	random number generator, seed sing_358.htm#IDX242
3420	random.lib sing_985.htm#SEC1061
3421	randomBinomial sing_997.htm#SEC1073 17913
3422	randomCheck sing_1818.htm#SEC1894 20973
3423	randomLast sing_996.htm#SEC1072 2046
3424	randomPoint sing_2047.htm#SEC2123 22561
3425	randomPolyInT sing_2163.htm#SEC2239 2264
3426	random_lib sing_985.htm#SEC1061
3427	randomid sing_987.htm#SEC1063 7815
3428	randommat sing_988.htm#SEC1064 33569
3429	rank sing_209.htm#IDX137
3430	rank sing_332.htm#SEC372
3431	rankSheaf sing_2713.htm#SEC2789 11850
3432	ratSol sing_788.htm#SEC840 62488
3433	ratgb.lib sing_778.htm#IDX375
3434	ratgb_lib sing_778.htm#IDX376
3435	rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1379.htm#IDX616
3436	rational normal curve, projection. sing_1380.htm#IDX617
3437	rational normal curve, projection. sing_1383.htm#IDX618
3438	rational normal curve, projection. sing_1384.htm#IDX619
3439	rational solutions sing_780.htm#IDX387
3440	rational univariate projection sing_1987.htm#IDX803
3441	rationalCurve sing_2733.htm#SEC2809 61201
3442	rationalPointConic sing_1381.htm#SEC1457 9761
3443	ratstd sing_779.htm#SEC831 61346
3444	rays sing_2048.htm#SEC2124 44445
3445	rcolon sing_2603.htm#SEC2679 1208
3446	re2squ sing_1358.htm#SEC1434 24350
3447	read sing_333.htm#SEC373
3448	readNmzData sing_1276.htm#SEC1352 18957
3449	reading, option sing_315.htm#IDX183
3450	readline sing_1.htm#IDX5
3451	real sing_28.htm#IDX74
3452	real root isolation sing_2680.htm#IDX1028
3453	real roots, univariate polynomial sing_1994.htm#IDX805
3454	real roots, univariate projection sing_1978.htm#IDX801
3455	real roots,sign conditions sing_1761.htm#IDX781
3456	realclassify sing_2675.htm#SEC2751 51416
3457	realclassify.lib sing_2674.htm#SEC2750
3458	realclassify_lib sing_2674.htm#SEC2750
3459	realizationDim sing_2126.htm#SEC2202 37756
3460	realizationDimPoly sing_2128.htm#SEC2204 3611
3461	realizationMatroids.lib realizationMatroids_lib sing_2125.htm#SEC2201
3462	realizationMatroids_lib realizationMatroids_lib sing_2125.htm#SEC2201
3463	realmorsesplit sing_2676.htm#SEC2752 16318
3464	realpoly sing_1325.htm#SEC1401 9453
3465	realrad sing_1327.htm#SEC1403 43381
3466	realrad.lib sing_1324.htm#SEC1400
3467	realrad_lib sing_1324.htm#SEC1400
3468	realzero sing_1326.htm#SEC1402 12712
3469	recursive_boolean_poly recursive_boolean_poly sing_2232.htm#SEC2308 17045
3470	recursive_from_boolean_poly recursive_from_boolean_poly sing_2238.htm#SEC2314 37794
3471	redSB, option sing_315.htm#IDX165
3472	redTail, option sing_315.htm#IDX167
3473	redThrough, option sing_315.htm#IDX168
3474	redefine, option sing_315.htm#IDX184
3475	reduce sing_334.htm#SEC374
3476	reduce sing_519.htm#IDX324
3477	reduce sing_926.htm#IDX431
3478	reduce sing_927.htm#IDX434
3479	reduce (plural) sing_477.htm#SEC517
3480	reduce (up to a bound) sing_358.htm#IDX245
3481	reduceIntChain sing_2539.htm#SEC2615 17776
3482	reduced sing_925.htm#IDX428
3483	reduced standard basis sing_315.htm#IDX166
3484	reduction sing_1679.htm#SEC1755 31048
3485	reesclos.lib sing_1328.htm#SEC1404
3486	reesclos_lib sing_1328.htm#SEC1404
3487	reference sing_199.htm#SEC239
3488	reference declarations reference declarations sing_200.htm#SEC240
3489	reference expressions reference expressions sing_201.htm#SEC241
3490	reference operations reference and shared operations sing_204.htm#SEC244
3491	reference related functions reference and shared related functions sing_205.htm#SEC245
3492	regCM sing_1240.htm#SEC1316 25488
3493	regIdeal sing_1226.htm#SEC1302 3827
3494	regMonCurve sing_1229.htm#SEC1305 41311
3495	regularity Syzygies and resolutions sing_335.htm#SEC375
3496	regularity sing_870.htm#SEC927
3497	reiffen sing_558.htm#SEC610 32856
3498	rel_orbit_variety sing_1672.htm#SEC1748 34278
3499	relations sing_750.htm#IDX364
3500	relativeInteriorPoint relativeInteriorPoint sing_2049.htm#SEC2125 30097
3501	relative_orbit_variety relative_orbit_variety sing_1673.htm#SEC1749 32995
3502	relweight sing_1628.htm#SEC1704 10658
3503	remainder sing_1748.htm#SEC1824 1191
3504	remainderMain sing_1756.htm#SEC1832 3532
3505	removeCone sing_2067.htm#SEC2143 33877
3506	removepower sing_1485.htm#SEC1561 47644
3507	repart sing_336.htm#SEC376
3508	replace sing_1857.htm#SEC1933 50075
3509	representation, math objects Representation of mathematical objects sing_856.htm#SEC908
3510	res sing_337.htm#SEC377 10393
3511	resbinomial.lib sing_1388.htm#IDX622
3512	resbinomial_lib sing_1388.htm#IDX623
3513	reservedName sing_338.htm#SEC378
3514	resfunction sing_1402.htm#SEC1478 59312
3515	resgraph.lib sing_1420.htm#SEC1496
3516	resgraph_lib sing_1420.htm#SEC1496
3517	resjung.lib sing_1424.htm#SEC1500
3518	resjung_lib sing_1424.htm#SEC1500
3519	reslist sing_1416.htm#SEC1492 64950
3520	resolution purityfiltration_lib sing_161.htm#SEC201
3521	resolution sing_758.htm#IDX371
3522	resolution (plural) sing_446.htm#SEC486
3523	resolution declarations resolution declarations sing_162.htm#SEC202
3524	resolution declarations (plural) resolution declarations (plural) sing_447.htm#SEC487
3525	resolution expressions resolution expressions sing_163.htm#SEC203
3526	resolution expressions (plural) resolution expressions (plural) sing_448.htm#SEC488
3527	resolution graph sing_1470.htm#IDX636
3528	resolution related functions resolution related functions sing_164.htm#SEC204
3529	resolution related functions (plural) resolution related functions (plural) sing_449.htm#SEC489
3530	resolution, La Scala's method sing_288.htm#SEC328
3531	resolution, computation of sing_337.htm#IDX186
3532	resolution, hilbert-driven sing_263.htm#SEC303
3533	resolutionInLocalization resolutionInLocalization sing_2419.htm#SEC2495 31106
3534	resolutiongraph sing_1471.htm#SEC1547 32697
3535	resolve sing_1432.htm#SEC1508 27374
3536	resolve.lib sing_1428.htm#SEC1504
3537	resolve_lib sing_1428.htm#SEC1504
3538	resources.lib sing_998.htm#SEC1074
3539	resources_lib sing_998.htm#SEC1074
3540	restriction sing_2192.htm#IDX857
3541	restriction sing_2208.htm#IDX890
3542	restriction sing_2209.htm#IDX892
3543	restriction of sing_563.htm#IDX347
3544	restrictionIdeal sing_573.htm#SEC625 49796
3545	restrictionModule sing_574.htm#SEC626 62461
3546	resultant sing_302.htm#SEC342
3547	resultant sing_339.htm#SEC379
3548	reszeta.lib sing_1441.htm#SEC1517
3549	reszeta_lib sing_1441.htm#SEC1517
3550	return sing_391.htm#SEC431
3551	return type of procedures Return type of procedures sing_416.htm#SEC456
3552	returnSB, option sing_315.htm#IDX152
3553	reverse sing_2008.htm#SEC2084 35880
3554	reverse lexicographical ordering sing_860.htm#IDX392
3555	reynolds_molien sing_1648.htm#SEC1724 45316
3556	rho sing_1899.htm#SEC1975 51414
3557	rightInverse sing_1837.htm#SEC1913 6558
3558	rightKernel sing_1835.htm#SEC1911 46603
3559	rightModulo sing_737.htm#SEC789 12618
3560	rightNF sing_736.htm#SEC788 42610
3561	rightNFWeyl sing_805.htm#SEC857 35828
3562	rightOre sing_2660.htm#SEC2736 56918
3563	rightStd sing_735.htm#SEC787 5740
3564	ring sing_165.htm#SEC205
3565	ring (plural) sing_450.htm#SEC490
3566	ring coefficients hasTransExtensionCoefficient sing_1024.htm#IDX500
3567	ring coefficients sing_1025.htm#IDX501
3568	ring declarations sing_167.htm#SEC207
3569	ring declarations (plural) ring declarations (plural) sing_451.htm#SEC491
3570	ring operations sing_169.htm#SEC209
3571	ring operations (plural) ring operations (plural) sing_452.htm#SEC492
3572	ring related functions ring related functions sing_168.htm#SEC208
3573	ring related functions (plural) ring related functions (plural) sing_453.htm#SEC493
3574	ring, opposite sing_358.htm#IDX229
3575	ring.lib sing_1003.htm#SEC1079
3576	ring_cf sing_209.htm#IDX138
3577	ring_lib sing_1003.htm#SEC1079
3578	ring_list sing_341.htm#SEC381
3579	ring_variable sing_2179.htm#IDX834
3580	ring_variable sing_2180.htm#IDX836
3581	ring_variable sing_2181.htm#IDX840
3582	ring_variable sing_2182.htm#IDX842
3583	ringlist sing_340.htm#SEC380
3584	ringlist (plural) sing_478.htm#SEC518
3585	ringtensor sing_1015.htm#SEC1091 56648
3586	ringweights sing_1016.htm#SEC1092 33307
3587	rinvar.lib sing_1684.htm#SEC1760
3588	rinvar_lib sing_1684.htm#SEC1760
3589	rmNmzFiles sing_1281.htm#SEC1357 32601
3590	rm_unitcol sing_1074.htm#SEC1150 5591
3591	rm_unitrow sing_1073.htm#SEC1149 35694
3592	rmx sing_1782.htm#SEC1858 17675
3593	rncAntiCanonicalMap sing_1380.htm#SEC1456 41965
3594	rncItProjEven sing_1384.htm#SEC1460 18200
3595	rncItProjOdd sing_1383.htm#SEC1459 61976
3596	root of Bernstein-Sato polynomial sing_540.htm#IDX336
3597	rootIsolation sing_2691.htm#SEC2767 34513
3598	rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2690.htm#SEC2766 42387
3599	rootIsolationPrimdec rootIsolationPrimdec sing_2692.htm#SEC2768 35485
3600	rootisolation.lib sing_2680.htm#SEC2756
3601	rootisolation_lib sing_2680.htm#SEC2756
3602	rootofUnity sing_1018.htm#SEC1094 21365
3603	roots sing_1749.htm#SEC1825 18436
3604	rootsMain sing_1757.htm#SEC1833 54934
3605	rootsModp sing_1881.htm#SEC1957 47315
3606	rootsmr.lib sing_1978.htm#SEC2054
3607	rootsmr_lib sing_1978.htm#SEC2054
3608	rootsur.lib sing_1994.htm#SEC2070
3609	rootsur_lib sing_1994.htm#SEC2070
3610	round sing_1879.htm#SEC1955 9248
3611	rowShift sing_209.htm#IDX141
3612	rowShift sing_211.htm#SEC251
3613	rowred sing_1070.htm#SEC1146 63416
3614	rp, global ordering sing_860.htm#IDX391
3615	rstandard.lib sing_2693.htm#SEC2769
3616	rstandard_lib sing_2693.htm#SEC2769
3617	rswalk sing_2743.htm#SEC2819 50903
3618	rtimer sing_404.htm#SEC444
3619	rvalue No rvalue of increments and assignments sing_410.htm#SEC450
3620	rvar sing_342.htm#SEC382
3621	rwalk sing_2700.htm#SEC2776 42525
3622	rwalk.lib sing_2698.htm#SEC2774
3623	rwalk_lib sing_2698.htm#SEC2774
3624	sRes sing_2505.htm#SEC2581 23381
3625	sa_poly_reduce sing_528.htm#SEC580 60856
3626	sa_reduce sing_527.htm#SEC579 55799
3627	sagbi sing_1334.htm#SEC1410 46653
3628	sagbi basis sing_2332.htm#IDX942
3629	sagbi.lib sing_1331.htm#SEC1407
3630	sagbiAlg sing_2325.htm#SEC2401 sprintf
3631	sagbiMod sing_2326.htm#SEC2402 sprintf
3632	sagbiPart sing_1335.htm#SEC1411 56066
3633	sagbiReduce sing_1333.htm#SEC1409 19036
3634	sagbiSPoly sing_1332.htm#SEC1408 17365
3635	sagbi_lib sing_1331.htm#SEC1407
3636	salida sing_1413.htm#SEC1489 9839
3637	sameComponent sing_1961.htm#SEC2037 13540
3638	sameQ sing_1760.htm#SEC1836 45579
3639	sat sing_1139.htm#SEC1215 6266
3640	satiety sing_1228.htm#SEC1304 34323
3641	satstd sing_2220.htm#SEC2296 16128
3642	sba sing_343.htm#SEC383
3643	scalarProd sing_517.htm#SEC569 54488
3644	scheme sing_2383.htm#SEC2459 15722
3645	schubert.lib sing_2702.htm#SEC2778
3646	schubert_lib sing_2702.htm#SEC2778
3647	sdb, source code debugger Source code debugger sing_66.htm#SEC103
3648	second degree sing_942.htm#IDX479
3649	secondary fan sing_2071.htm#IDX808
3650	secondary polytope sing_2071.htm#IDX809
3651	secondaryPolytope sing_2076.htm#SEC2152 48451
3652	secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1669.htm#SEC1745 37058
3653	secondary_char0 sing_1664.htm#SEC1740 31029
3654	secondary_charp sing_1666.htm#SEC1742 16364
3655	secondary_no_molien sing_1667.htm#SEC1743 3616
3656	secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1670.htm#SEC1746 31675
3657	segre sing_2259.htm#SEC2335 44035
3658	select sing_1140.htm#SEC1216 17096
3659	select1 sing_1141.htm#SEC1217 32617
3660	semaphore sing_358.htm#IDX249 44342
3661	semaphore sing_1002.htm#SEC1078
3662	semaphores sing_998.htm#IDX495
3663	semiCMcod2 sing_1625.htm#SEC1701 15905
3664	semiGroup sing_2327.htm#SEC2403 sprintf
3665	semiMod sing_2328.htm#SEC2404 sprintf
3666	semidiv sing_1953.htm#SEC2029 58107
3667	semigroup sing_1474.htm#SEC1550 29045
3668	semigroup sing_1478.htm#IDX643
3669	semigroup of values sing_1564.htm#IDX758
3670	semigroupGenerator sing_2050.htm#SEC2126 59446
3671	sep sing_1311.htm#SEC1387 sprintf
3672	separateHNE sing_1575.htm#SEC1651 12052
3673	separator sing_1211.htm#SEC1287 33000
3674	serreRelations sing_658.htm#SEC710 33994
3675	set sing_2174.htm#IDX820
3676	setBaseMultigrading sing_2550.htm#SEC2626 6575
3677	setLetterplaceAttributes setLetterplaceAttributes sing_648.htm#SEC700 5759
3678	setLinearForms sing_2051.htm#SEC2127 62731
3679	setModuleGrading sing_2562.htm#SEC2638 59018
3680	setMultiplicity sing_2052.htm#SEC2128 27537
3681	setNmzDataPath sing_1278.htm#SEC1354 18123
3682	setNmzExecPath sing_1274.htm#SEC1350 38993
3683	setNmzFilename sing_1277.htm#SEC1353 20206
3684	setNmzOption sing_1271.htm#SEC1347 9012
3685	setUniformizingParameter setUniformizingParameter sing_2745.htm#SEC2821 63635
3686	set_is_injective sing_1941.htm#SEC2017 8429
3687	setcores sing_1000.htm#SEC1076 49704
3688	setenv sing_358.htm#IDX252
3689	setinitials sing_2393.htm#SEC2469 24792
3690	setring sing_344.htm#SEC384
3691	sh sing_358.htm#IDX254
3692	shared sing_199.htm#SEC239
3693	shared declarations sing_202.htm#SEC242
3694	shared expressions sing_203.htm#SEC243
3695	shared operations reference and shared operations sing_204.htm#SEC244
3696	shared related functions reference and shared related functions sing_205.htm#SEC245
3697	sheaf cohomology sing_1451.htm#IDX624
3698	sheafCoh sing_1457.htm#SEC1533 64501
3699	sheafCohBGG sing_1455.htm#SEC1531 13439
3700	sheafCohBGG2 sing_1456.htm#SEC1532 3338
3701	sheafcoh.lib sing_1451.htm#SEC1527
3702	sheafcoh_lib sing_1451.htm#SEC1527
3703	shiftPoly sing_651.htm#SEC703 65223
3704	short sing_401.htm#SEC441
3705	show sing_951.htm#SEC1027 15599
3706	showBO sing_1433.htm#SEC1509 20089
3707	showDataTypes sing_1435.htm#SEC1511 4270
3708	showNmzOptions sing_1272.htm#SEC1348 64955
3709	showNuminvs sing_1269.htm#SEC1345 18934
3710	showgrades sing_763.htm#SEC815 48081
3711	showrecursive sing_952.htm#SEC1028 6127
3712	sickle sing_624.htm#SEC676 54811
3713	signal handler sing_2761.htm#SEC2850
3714	signatureBrieskorn sing_1634.htm#SEC1710 26283
3715	signatureL sing_2222.htm#SEC2298 65493
3716	signatureLqf sing_2223.htm#SEC2299 18811
3717	signatureNemethi sing_1636.htm#SEC1712 21981
3718	signaturePuiseux sing_1635.htm#SEC1711 23398
3719	signcnd sing_1762.htm#SEC1838 40147
3720	signcond.lib sing_1761.htm#SEC1837
3721	signcond_lib sing_1761.htm#SEC1837
3722	simplePrune sing_2543.htm#SEC2619 sprintf
3723	simplesolver sing_1706.htm#SEC1782 13418
3724	simplex sing_345.htm#SEC385
3725	simplexOut sing_1733.htm#SEC1809 56099
3726	simplify sing_346.htm#SEC386
3727	simplifyRat sing_800.htm#SEC852 52658
3728	sing.lib sing_1601.htm#SEC1677
3729	sing4ti2.lib sing_1337.htm#SEC1413
3730	sing4ti2_lib sing_1337.htm#SEC1413
3731	sing_lib sing_1601.htm#SEC1677
3732	singular locus of D-module sing_780.htm#IDX381
3733	singularities sing_1533.htm#IDX660
3734	singularities sing_1534.htm#IDX671
3735	singularities sing_1535.htm#IDX674
3736	singularities sing_1536.htm#IDX677
3737	singularities sing_1537.htm#IDX680
3738	singularities sing_1538.htm#IDX684
3739	singularities sing_1539.htm#IDX688
3740	singularities sing_1540.htm#IDX694
3741	singularities sing_1541.htm#IDX702
3742	singularities sing_1542.htm#IDX708
3743	singularities sing_1543.htm#IDX716
3744	singularities sing_1544.htm#IDX726
3745	singularities sing_1632.htm#IDX773
3746	singularities sing_2321.htm#IDX937
3747	singularities, resolution of Resolution of singularities sing_843.htm#SEC895
3748	singularity sing_1498.htm#SEC1574 23002
3749	singularrc sing_20.htm#IDX73
3750	size Miscellaneous oddities sing_347.htm#SEC387
3751	size sing_418.htm#IDX294
3752	skewmat sing_1057.htm#SEC1133 2167
3753	sleep sing_353.htm#SEC393
3754	slimgb sing_348.htm#SEC388
3755	slimgb sing_820.htm#SEC872
3756	slimgb (plural) sing_479.htm#SEC519
3757	slocus sing_1613.htm#SEC1689 27853
3758	smith sing_1846.htm#SEC1922 61915
3759	smithNormalForm sing_2598.htm#SEC2674 7174
3760	solutionsMod2 sing_1896.htm#SEC1972 53360
3761	solve sing_942.htm#IDX480 3078
3762	solve sing_1727.htm#SEC1803
3763	solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_291.htm#SEC331
3764	solve.lib sing_1725.htm#SEC1801
3765	solveTInitialFormPar solveTInitialFormPar sing_2157.htm#SEC2233 36670
3766	solve_IP sing_1184.htm#SEC1260 59518
3767	solve_lib sing_1725.htm#SEC1801
3768	solvelinearpart sing_1720.htm#SEC1796 42872
3769	sort sing_916.htm#SEC992 58207
3770	sortIntvec sing_595.htm#SEC647 60798
3771	sortandmap sing_1721.htm#SEC1797 10314
3772	sortier sing_1683.htm#SEC1759 3555
3773	sortvars sing_1722.htm#SEC1798 61778
3774	sortvec sing_349.htm#SEC389
3775	source sing_2521.htm#SEC2597 63163
3776	source code debugger, sdb Source code debugger sing_66.htm#SEC103
3777	spaceCur sing_2330.htm#SEC2406 sprintf
3778	spadd sing_1547.htm#SEC1623 48739
3779	span sing_2053.htm#SEC2129 64343
3780	sparseHomogIdeal sing_994.htm#SEC1070 22631
3781	sparseInterpolation sing_2378.htm#SEC2454 28771
3782	sparseid sing_989.htm#SEC1065 20824
3783	sparsemat sing_991.htm#SEC1067 17653
3784	sparsematrix sing_990.htm#SEC1066 41031
3785	sparsepoly sing_992.htm#SEC1068 21649
3786	sparsetriag sing_993.htm#SEC1069 50657
3787	spcurve.lib sing_1621.htm#SEC1697
3788	spcurve_lib sing_1621.htm#SEC1697
3789	special characters, non-english sing_407.htm#IDX287
3790	spectral pairs sing_1533.htm#IDX669
3791	spectral pairs sing_1540.htm#IDX701
3792	spectral pairs sing_1542.htm#IDX715
3793	spectral pairs sing_1543.htm#IDX724
3794	spectral pairs sing_1555.htm#IDX740
3795	spectral pairs sing_1557.htm#IDX751
3796	spectralNeg sing_1443.htm#SEC1519 36691
3797	spectrum sing_1533.htm#IDX668 47545
3798	spectrum sing_1539.htm#SEC1615
3799	spectrum sing_1539.htm#IDX693
3800	spectrum sing_1540.htm#IDX700
3801	spectrum sing_1541.htm#IDX707
3802	spectrum sing_1542.htm#IDX714
3803	spectrum sing_1543.htm#IDX723
3804	spectrum sing_1555.htm#IDX739
3805	spectrum sing_1557.htm#IDX750
3806	spectrum sing_1632.htm#IDX775
3807	spectrum.lib sing_1631.htm#SEC1707
3808	spectrum_lib sing_1631.htm#SEC1707
3809	spectrumnd sing_1632.htm#SEC1708 29943
3810	spgamma sing_1554.htm#SEC1630 59653
3811	spgeomgenus sing_1553.htm#SEC1629 57796
3812	spissemicont sing_1550.htm#SEC1626 23679
3813	split sing_953.htm#SEC1029 29794
3814	splitPolygon sing_2078.htm#SEC2154 706
3815	splitring sing_1323.htm#SEC1399 56404
3816	splitting sing_1219.htm#SEC1295 34734
3817	spmilnor sing_1552.htm#SEC1628 32933
3818	spmul sing_1549.htm#SEC1625 43607
3819	spnf sing_1100.htm#SEC1176 57309
3820	spoly sing_1964.htm#SEC2040 35454
3821	sppairs sing_1540.htm#SEC1616 49513
3822	sppnf sing_1545.htm#SEC1621 16650
3823	sppprint sing_1546.htm#SEC1622 43682
3824	spprint sing_1101.htm#SEC1177 18671
3825	sprintf sing_351.htm#SEC391 55889
3826	spsemicont sing_1551.htm#SEC1627 61169
3827	spsub sing_1548.htm#SEC1624 54296
3828	sqfrNorm sing_1750.htm#SEC1826 20546
3829	sqfrNormMain sing_1758.htm#SEC1834 9890
3830	sqr sing_1876.htm#SEC1952 sprintf
3831	sqrfree sing_350.htm#SEC390
3832	squareRoot sing_1895.htm#SEC1971 17446
3833	squarefree sing_1576.htm#SEC1652 48485
3834	sres sing_352.htm#SEC392
3835	ssi Parallelization with ssi links sing_815.htm#SEC867
3836	stabilizer sing_2250.htm#SEC2326 36692
3837	stack, moduli space of stable maps sing_2726.htm#IDX1057
3838	stack, moduli space of stable maps, rational curves moduliSpace sing_2725.htm#IDX1056
3839	stackNets sing_2647.htm#SEC2723 30974
3840	staircase sing_1767.htm#SEC1843 49781
3841	standard sing_1971.htm#SEC2047 14067
3842	standard bases, saturation sing_2220.htm#IDX903
3843	standard bases. sing_2219.htm#IDX902
3844	standard.lib sing_894.htm#IDX419
3845	standard_lib sing_894.htm#IDX420
3846	startNmz sing_1280.htm#SEC1356 21925
3847	startTasks sing_1037.htm#SEC1113 16715
3848	static procedures Procedure definition sing_43.htm#SEC78
3849	status sing_353.htm#SEC393
3850	std sing_354.htm#SEC394
3851	std sing_818.htm#SEC870
3852	std (plural) sing_480.htm#SEC520
3853	stdfglm sing_355.htm#SEC395 256
3854	stdhilb sing_356.htm#SEC396 63138
3855	stdlocus sing_939.htm#SEC1015 25619
3856	stopTask sing_1038.htm#SEC1114 6801
3857	storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2439.htm#SEC2515 64428
3858	stratify sing_1701.htm#SEC1777 56744
3859	stratify.lib sing_1699.htm#SEC1775
3860	stratify_lib sing_1699.htm#SEC1775
3861	string Miscellaneous oddities sing_171.htm#SEC211
3862	string sing_418.htm#IDX297
3863	string declarations sing_172.htm#SEC212
3864	string expressions sing_173.htm#SEC213
3865	string operations sing_175.htm#SEC215
3866	string related functions string related functions sing_176.htm#SEC216
3867	string type cast sing_174.htm#SEC214
3868	stripHNE sing_1573.htm#SEC1649 19265
3869	sturm sing_2004.htm#SEC2080 54353
3870	sturmha sing_2006.htm#SEC2082 12467
3871	sturmhaseq sing_2007.htm#SEC2083 59133
3872	sturmquery sing_1982.htm#SEC2058 10805
3873	sturmseq sing_2005.htm#SEC2081 23005
3874	sublists sing_2344.htm#SEC2420 2979
3875	submat sing_1058.htm#SEC1134 37665
3876	subquotient sing_2513.htm#SEC2589 40364
3877	subrInterred sing_982.htm#SEC1058 10165
3878	subset_sum01 sing_1925.htm#SEC2001 60620
3879	subset_sum02 sing_1926.htm#SEC2002 37340
3880	subst sing_357.htm#SEC397
3881	subst (plural) sing_481.htm#SEC521
3882	substitute sing_981.htm#SEC1057 28919
3883	sugarCrit, option sing_315.htm#IDX169
3884	sum sing_917.htm#SEC993 555
3885	sum_of_powers sing_2263.htm#SEC2339 12170
3886	sumlist sing_1415.htm#SEC1491 59918
3887	sumofquotients sing_2734.htm#SEC2810 4569
3888	super-commutative algebras Graded commutative algebras (SCA) sing_490.htm#SEC542
3889	superCommutative sing_734.htm#SEC786 45528
3890	super_increasing_knapsack super_increasing_knapsack sing_1937.htm#SEC2013 9177
3891	surf.lib sing_1784.htm#SEC1860
3892	surf_lib sing_1784.htm#SEC1860
3893	surfacesignature.lib surfacesignature_lib sing_1633.htm#SEC1709
3894	surfacesignature_lib surfacesignature_lib sing_1633.htm#SEC1709
3895	surfer sing_1.htm#IDX8 14287
3896	surfer sing_1786.htm#SEC1862
3897	surfex sing_1.htm#IDX7
3898	surfex.lib sing_1787.htm#SEC1863
3899	surfex_lib sing_1787.htm#SEC1863
3900	suspend sing_353.htm#SEC393
3901	swalk sing_2742.htm#SEC2818 16794
3902	swalk.lib sing_2741.htm#SEC2817
3903	swalk_lib sing_2741.htm#SEC2817
3904	swap sing_1502.htm#SEC1578 15408
3905	swap sing_2181.htm#IDX838
3906	switch No case or switch statement sing_412.htm#SEC452
3907	switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2750.htm#SEC2826 1827
3908	syModStd sing_1347.htm#SEC1423 50246
3909	symNsym sing_2257.htm#SEC2333 55230
3910	sym_gauss sing_1084.htm#SEC1160 5121
3911	symm sing_2256.htm#SEC2332 64628
3912	symmStd sing_1346.htm#SEC1422 39353
3913	symmat sing_1059.htm#SEC1135 61294
3914	symmetric basis sing_1076.htm#IDX506
3915	symmetric power sing_1078.htm#IDX508
3916	symmetricBasis sing_1076.htm#SEC1152 sprintf
3917	symmetricPower sing_1078.htm#SEC1154 6542
3918	symmetricPowerSheaf sing_2720.htm#SEC2796 56922
3919	symmetries sing_2246.htm#IDX936
3920	symmfunc sing_1991.htm#SEC2067 45575
3921	symodstd.lib sing_1341.htm#SEC1417
3922	symodstd_lib sing_1341.htm#SEC1417
3923	symsignature sing_1981.htm#SEC2057 10520
3924	syndrome sing_1814.htm#SEC1890 14057
3925	sysBin sing_1812.htm#SEC1888 41948
3926	sysCRHT sing_1809.htm#SEC1885 58930
3927	sysCRHTMindist sing_1810.htm#SEC1886 13692
3928	sysFL sing_1825.htm#SEC1901 53040
3929	sysNewton sing_1811.htm#SEC1887 19704
3930	sysQE sing_1815.htm#SEC1891 61026
3931	sys_code sing_1806.htm#SEC1882 20220
3932	system sing_358.htm#SEC398
3933	system, -- sing_358.htm#IDX277
3934	system, --long_option_name sing_358.htm#IDX280
3935	system, --long_option_name=value sing_358.htm#IDX282
3936	system, HC sing_358.htm#IDX215
3937	system, LLL sing_358.htm#IDX219
3938	system, Singular sing_358.htm#IDX258
3939	system, SingularLib sing_358.htm#IDX260
3940	system, absFact sing_358.htm#IDX190
3941	system, alarm sing_358.htm#IDX189
3942	system, blackbox sing_358.htm#IDX191
3943	system, bracket sing_358.htm#IDX196
3944	system, browsers sing_358.htm#IDX195
3945	system, btest sing_358.htm#IDX198
3946	system, complexNearZero sing_358.htm#IDX199
3947	system, contributors sing_358.htm#IDX201
3948	system, cpu sing_358.htm#IDX203
3949	system, cpu sing_358.htm#IDX276
3950	system, denom_list sing_358.htm#IDX205
3951	system, eigenvals sing_358.htm#IDX206
3952	system, env sing_358.htm#IDX207
3953	system, executable sing_358.htm#IDX209
3954	system, freegb sing_358.htm#IDX210
3955	system, getPrecDigits sing_358.htm#IDX213
3956	system, getenv sing_358.htm#IDX212
3957	system, gmsnf sing_358.htm#IDX214
3958	system, hessenberg sing_358.htm#IDX216
3959	system, install sing_358.htm#IDX218
3960	system, nblocks sing_358.htm#IDX222
3961	system, nc_hilb sing_358.htm#IDX224
3962	system, neworder sing_358.htm#IDX225
3963	system, newstruct sing_358.htm#IDX226
3964	system, opp sing_358.htm#IDX227
3965	system, oppose sing_358.htm#IDX230
3966	system, pcvBasis sing_358.htm#IDX239
3967	system, pcvCV2P sing_358.htm#IDX237
3968	system, pcvDim sing_358.htm#IDX238
3969	system, pcvLAddL sing_358.htm#IDX233
3970	system, pcvMinDeg sing_358.htm#IDX235
3971	system, pcvP2CV sing_358.htm#IDX236
3972	system, pcvPMulL sing_358.htm#IDX234
3973	system, pid sing_358.htm#IDX241
3974	system, random sing_358.htm#IDX243
3975	system, reserve sing_358.htm#IDX247
3976	system, reservedLink sing_358.htm#IDX248
3977	system, semaphore sing_358.htm#IDX250
3978	system, semic sing_358.htm#IDX251
3979	system, setenv sing_358.htm#IDX253
3980	system, sh sing_358.htm#IDX255
3981	system, shrinktest sing_358.htm#IDX256
3982	system, spadd sing_358.htm#IDX261
3983	system, spectrum sing_358.htm#IDX262
3984	system, spmul sing_358.htm#IDX263
3985	system, std_syz sing_358.htm#IDX264
3986	system, stest sing_358.htm#IDX265
3987	system, tensorModuleMult sing_358.htm#IDX266
3988	system, twostd sing_358.htm#IDX267
3989	system, uname sing_358.htm#IDX270
3990	system, version sing_358.htm#IDX273
3991	system, with sing_358.htm#IDX274
3992	systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2416.htm#SEC2492 63094
3993	syz sing_359.htm#SEC399
3994	syz (plural) sing_482.htm#SEC522
3995	tDetropicalise sing_2159.htm#SEC2235 23532
3996	tInitialForm sing_2143.htm#SEC2219 24484
3997	tInitialFormPar sing_2155.htm#SEC2231 9584
3998	tInitialFormParMax sing_2156.htm#SEC2232 7829
3999	tInitialIdeal sing_2144.htm#SEC2220 17937
4000	tab sing_954.htm#SEC1030 60407
4001	tail sing_1960.htm#SEC2036 13066
4002	tame polynomial sing_1555.htm#IDX732
4003	tame polynomial sing_1556.htm#IDX742
4004	tame polynomial sing_1557.htm#IDX743
4005	tangentGens sing_1371.htm#SEC1447 37797
4006	tangentcone sing_1620.htm#SEC1696 20056
4007	target sing_2520.htm#SEC2596 18743
4008	task sing_1031.htm#IDX505
4009	tasks.lib sing_1031.htm#SEC1107
4010	tasks_lib sing_1031.htm#SEC1107
4011	tau_es sing_1528.htm#SEC1604 17043
4012	tau_es2 sing_1482.htm#SEC1558 38083
4013	tdCf sing_2292.htm#SEC2368 21522
4014	tdFactor sing_2294.htm#SEC2370 37910
4015	tdProj sing_2297.htm#SEC2373 38406
4016	tdTerms sing_2293.htm#SEC2369 30166
4017	teachstd.lib sing_1958.htm#SEC2034
4018	teachstd_lib sing_1958.htm#SEC2034
4019	template.lib sing_55.htm#IDX120
4020	template.lib sing_55.htm#IDX123
4021	template_lib sing_55.htm#SEC92
4022	template_lib sing_55.htm#IDX121
4023	tensor sing_498.htm#IDX311 65451
4024	tensor sing_1060.htm#SEC1136
4025	tensorFreeModule sing_2532.htm#SEC2608 59314
4026	tensorFreemodMod sing_2531.htm#SEC2607 sprintf
4027	tensorMatrix sing_2528.htm#SEC2604 31437
4028	tensorMod sing_1179.htm#SEC1255 21961
4029	tensorModFreemod sing_2530.htm#SEC2606 11852
4030	tensorModule sing_2529.htm#SEC2605 58772
4031	tensorProduct sing_2533.htm#SEC2609 sprintf
4032	tensorSheaf sing_2719.htm#SEC2795 24072
4033	term orderings General definitions for orderings sing_859.htm#SEC911
4034	term orderings introduction Introduction to orderings sing_858.htm#SEC910
4035	testFraction sing_2658.htm#SEC2734 28466
4036	testLocData sing_2655.htm#SEC2731 50986
4037	testNCfac sing_708.htm#SEC760 60394
4038	testNcfrac sing_2616.htm#SEC2692 34186
4039	testNcfracExamples sing_2617.htm#SEC2693 15399
4040	testNcloc sing_2620.htm#SEC2696 62706
4041	testNclocExamples sing_2621.htm#SEC2697 14584
4042	testOlga sing_2672.htm#SEC2748 53953
4043	testOlgaExamples sing_2673.htm#SEC2749 62869
4044	testParametrization sing_1386.htm#SEC1462 18686
4045	testPointConic sing_1387.htm#SEC1463 25315
4046	testPrimary sing_1299.htm#SEC1375 34254
4047	testPrimaryE sing_1300.htm#SEC1376 20693
4048	tex sing_1773.htm#SEC1849 12226
4049	texDrawBasic sing_2150.htm#SEC2226 3635
4050	texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2152.htm#SEC2228 42021
4051	texDrawTriangulation texDrawTriangulation sing_2153.htm#SEC2229 18865
4052	texDrawTropical sing_2151.htm#SEC2227 58447
4053	texMatrix sing_2149.htm#SEC2225 1334
4054	texNumber sing_2147.htm#SEC2223 12628
4055	texPolynomial sing_2148.htm#SEC2224 41136
4056	texcoef sing_1854.htm#SEC1930 28189
4057	texdemo sing_1774.htm#SEC1850 13008
4058	texfactorize sing_1775.htm#SEC1851 6682
4059	texmap sing_1776.htm#SEC1852 35265
4060	texname sing_1777.htm#SEC1853 1008
4061	texobj sing_1778.htm#SEC1854 2107
4062	texpoly sing_1779.htm#SEC1855 64109
4063	texproc sing_1780.htm#SEC1856 23626
4064	texring sing_1781.htm#SEC1857 38275
4065	the first alternative algorithm sing_1156.htm#IDX542
4066	three_elements sing_1944.htm#SEC2020 513
4067	timeFactorize sing_921.htm#SEC997 49531
4068	timeStd sing_920.htm#SEC996 31506
4069	timer sing_402.htm#SEC442
4070	timer resolution, setting the sing_358.htm#IDX283
4071	timestep sing_2396.htm#SEC2472 38225
4072	tjurina sing_1616.htm#SEC1692 9100
4073	tmatrix sing_1543.htm#SEC1619 57332
4074	todd sing_2289.htm#SEC2365 25618
4075	toddE sing_2290.htm#SEC2366 17823
4076	toddPoly sing_2303.htm#SEC2379 65066
4077	tolessvars sing_1719.htm#SEC1795 56590
4078	topChernClass sing_2716.htm#SEC2792 17374
4079	topological invariants sing_1470.htm#IDX634
4080	topological invariants sing_1477.htm#IDX641
4081	topological invariants sing_1478.htm#IDX645
4082	topological invariants sing_1479.htm#IDX649
4083	topological invariants sing_1480.htm#IDX653
4084	toric ideals sing_874.htm#SEC931
4085	toric ring sing_1258.htm#IDX575
4086	toric.lib sing_1348.htm#SEC1424
4087	toric_ideal sing_1349.htm#SEC1425 5760
4088	toric_lib sing_1348.htm#SEC1424
4089	toric_std sing_1350.htm#SEC1426 26141
4090	torusInvariants sing_1264.htm#SEC1340 911
4091	total divisors sing_498.htm#IDX308
4092	total multiplicities sing_1470.htm#IDX637
4093	totalChernClass sing_2714.htm#SEC2790 6153
4094	totalSegreClass sing_2717.htm#SEC2793 3291
4095	totalmultiplicities sing_1472.htm#SEC1548 58264
4096	trace sing_360.htm#SEC400
4097	tracemult sing_1985.htm#SEC2061 58303
4098	transpose sing_361.htm#SEC401
4099	trapezoid sing_2390.htm#SEC2466 61525
4100	triMNewton sing_1745.htm#SEC1821 62822
4101	triagmatrix sing_995.htm#SEC1071 17944
4102	triang.lib sing_1738.htm#SEC1814
4103	triangL sing_1739.htm#SEC1815 51847
4104	triangL_solve sing_1736.htm#SEC1812 10101
4105	triangLf_solve sing_1734.htm#SEC1810 49796
4106	triangLfak sing_1740.htm#SEC1816 50093
4107	triangM sing_1741.htm#SEC1817 59334
4108	triangMH sing_1742.htm#SEC1818 34277
4109	triangM_solve sing_1735.htm#SEC1811 63652
4110	triang_lib sing_1738.htm#SEC1814
4111	triang_solve sing_1737.htm#SEC1813 64404
4112	triangulations sing_2075.htm#SEC2151 61888
4113	tropical curves sing_2129.htm#IDX815
4114	tropical geometry sing_1142.htm#IDX516
4115	tropical geometry sing_2744.htm#IDX1068
4116	tropical mirror symmetry sing_1142.htm#IDX518
4117	tropical polynomials sing_2129.htm#IDX816
4118	tropical varieties sing_2744.htm#IDX1069
4119	tropical.lib sing_2129.htm#IDX813
4120	tropicalCurve sing_2134.htm#SEC2210 16865
4121	tropicalJInvariant sing_2137.htm#SEC2213 40395
4122	tropicalLifting sing_2130.htm#SEC2206 7052
4123	tropicalLinkNewton sing_2752.htm#SEC2828 63886
4124	tropicalNewton.lib sing_2744.htm#SEC2820
4125	tropicalNewton_lib sing_2744.htm#SEC2820
4126	tropicalPointNewton sing_2749.htm#SEC2825 18572
4127	tropicalSubst sing_2162.htm#SEC2238 49846
4128	tropicalVariety sing_2169.htm#SEC2245 39087
4129	tropicalVarietyNewton tropicalVarietyNewton sing_2751.htm#SEC2827 28532
4130	tropical_lib sing_2129.htm#IDX814
4131	tropicalise sing_2141.htm#SEC2217 49739
4132	tropicaliseSet sing_2142.htm#SEC2218 35136
4133	truncate sing_1452.htm#SEC1528 13545
4134	truncateFast sing_1453.htm#SEC1529 5124
4135	truncated module sing_1452.htm#IDX625
4136	truncated module sing_1453.htm#IDX626
4137	tst_ncfactor sing_716.htm#SEC768 3339
4138	twalk sing_1155.htm#SEC1231 35753
4139	two-sided sing_498.htm#IDX309
4140	two-sided Groebner basis sing_498.htm#IDX310
4141	twostd sing_358.htm#IDX268
4142	twostd sing_483.htm#SEC523
4143	type sing_362.htm#SEC402
4144	type B sing_2197.htm#IDX865
4145	type D sing_2198.htm#IDX867
4146	type,custom Definition of a user defined type sing_183.htm#SEC223
4147	type2arr sing_2175.htm#SEC2251 62624
4148	typecasting sing_2175.htm#IDX821
4149	typecasting sing_2176.htm#IDX823
4150	typecasting sing_2177.htm#IDX826
4151	typeof sing_363.htm#SEC403
4152	u sing_2382.htm#SEC2458 12154
4153	uname sing_358.htm#IDX269
4154	unbounded_knapsack sing_1927.htm#SEC2003 17226
4155	unipotent groups sing_1370.htm#IDX593
4156	uniquePoint sing_2054.htm#SEC2130 893
4157	unitMatrix sing_2686.htm#SEC2762 33014
4158	unitmat sing_1061.htm#SEC1137 12862
4159	univariate sing_364.htm#SEC404
4160	univarpoly sing_1992.htm#SEC2068 46288
4161	unknown syndrome Decoding method based on quadratic equations sing_890.htm#SEC961
4162	unset sing_276.htm#SEC316
4163	untyped definitions sing_88.htm#SEC128
4164	untyped definitions sing_423.htm#SEC463
4165	updatePairs sing_1970.htm#SEC2046 51144
4166	ures_solve sing_1728.htm#SEC1804 32449
4167	uressolve sing_365.htm#SEC405
4168	usage, option sing_315.htm#IDX185
4169	user interface, Emacs Emacs user interface sing_21.htm#SEC28
4170	vStd sing_2336.htm#SEC2412 12321
4171	val sing_2746.htm#SEC2822 62171
4172	valvars sing_1723.htm#SEC1799 15723
4173	vandermonde sing_366.htm#SEC406
4174	vanishId sing_1824.htm#SEC1900 49148
4175	var sing_367.htm#SEC407
4176	varMat sing_2179.htm#SEC2255 51772
4177	varNum sing_2180.htm#SEC2256 18485
4178	variables sing_368.htm#SEC408
4179	variables sing_2179.htm#IDX833
4180	variables sing_2180.htm#IDX835
4181	variables sing_2181.htm#IDX839
4182	variables sing_2182.htm#IDX841
4183	variablesSorted sing_536.htm#SEC588 13533
4184	variablesStandard sing_535.htm#SEC587 56500
4185	vars2pars sing_795.htm#SEC847 47343
4186	varsigns sing_1997.htm#SEC2073 3471
4187	varstr sing_369.htm#SEC409
4188	vct2str sing_657.htm#SEC709 51983
4189	vdim sing_370.htm#SEC410
4190	vdim (plural) sing_484.htm#SEC524
4191	vec2poly sing_518.htm#SEC570 27377
4192	vector sing_177.htm#SEC217
4193	vector declarations sing_178.htm#SEC218
4194	vector expressions sing_179.htm#SEC219
4195	vector operations sing_180.htm#SEC220
4196	vector related functions vector related functions sing_181.htm#SEC221
4197	verify sing_1988.htm#SEC2064 32271
4198	versal sing_1523.htm#SEC1599 46247
4199	version sing_358.htm#IDX272
4200	vertexAdjacencyGraph vertexAdjacencyGraph sing_2122.htm#SEC2198 60102
4201	vertexEdgeGraph sing_2123.htm#SEC2199 32816
4202	vertices sing_2070.htm#SEC2146 11398
4203	vfilt sing_1541.htm#SEC1617 9283
4204	view sing_1844.htm#SEC1920 29284
4205	visual sing_2124.htm#SEC2200 51434
4206	visualize sing_2381.htm#SEC2457 6750
4207	voice sing_405.htm#SEC445
4208	vwfilt sing_1542.htm#SEC1618 8281
4209	wUnit sing_1882.htm#SEC1958 27198
4210	waitAllTasks sing_1040.htm#SEC1116 7087
4211	waitTasks sing_1039.htm#SEC1115 52857
4212	waitall sing_371.htm#SEC411
4213	waitfirst sing_372.htm#SEC412
4214	walk, groebner sing_1153.htm#IDX538
4215	walk, groebner sing_2544.htm#IDX991
4216	walk, groebner sing_2698.htm#IDX1037
4217	walk, groebner sing_2741.htm#IDX1066
4218	warkedPreimageStd sing_2418.htm#SEC2494 14759
4219	warn, option sing_70.htm#SEC110
4220	warn, option sing_315.htm#IDX151
4221	watchdog sing_918.htm#SEC994 sprintf
4222	wedge sing_373.htm#SEC413
4223	weierstr.lib sing_1973.htm#SEC2049
4224	weierstrDiv sing_1974.htm#SEC2050 260
4225	weierstrPrep sing_1975.htm#SEC2051 5752
4226	weierstr_lib sing_1973.htm#SEC2049
4227	weierstrassForm sing_2138.htm#SEC2214 60874
4228	weight sing_374.htm#SEC414
4229	weight filtration sing_1533.htm#IDX665
4230	weight filtration sing_1540.htm#IDX699
4231	weight filtration sing_1542.htm#IDX713
4232	weight filtration sing_1543.htm#IDX721
4233	weight filtration sing_1555.htm#IDX737
4234	weight filtration sing_1557.htm#IDX748
4235	weightKB sing_375.htm#SEC415 21753
4236	weightM, option sing_315.htm#IDX170
4237	weighted lexicographical ordering sing_860.htm#IDX399
4238	weighted reverse lexicographical ordering Global orderings sing_860.htm#IDX397
4239	weightedRing sing_727.htm#SEC779 33786
4240	whichvariable sing_1996.htm#SEC2072 27122
4241	while sing_392.htm#SEC432
4242	withDim sing_209.htm#IDX145
4243	withHilb sing_209.htm#IDX143
4244	withMult sing_209.htm#IDX146
4245	withRes sing_209.htm#IDX144
4246	withSB sing_209.htm#IDX142
4247	wp, global ordering sing_860.htm#IDX398
4248	write sing_376.htm#SEC416
4249	writeNmzData sing_1275.htm#SEC1351 38467
4250	writeNmzPaths sing_1279.htm#SEC1355 sprintf
4251	ws, local ordering sing_861.htm#IDX409
4252	wurzel sing_1864.htm#SEC1940 12755
4253	xchange sing_1858.htm#SEC1934 40741
4254	xdvi sing_1783.htm#SEC1859 16898
4255	zdd sing_2226.htm#IDX914
4256	zdd2poly sing_2243.htm#SEC2319 55047
4257	zero sing_2493.htm#SEC2569 12060
4258	zero-dimensional sing_1993.htm#IDX804
4259	zeroMod sing_1215.htm#SEC1291 60609
4260	zeroNcfrac sing_2609.htm#SEC2685 50840
4261	zeroOpt sing_1224.htm#SEC1300 19260
4262	zeroRadical sing_1124.htm#SEC1200 35598
4263	zeroSet sing_1751.htm#SEC1827 60030
4264	zerodec sing_1308.htm#SEC1384 30765
4265	zeroset.lib sing_1746.htm#SEC1822
4266	zeroset_lib sing_1746.htm#SEC1822
4267	zetaDL sing_1445.htm#SEC1521 sprintf
4268	{ sing_36.htm#IDX78
4269	\|\| sing_36.htm#IDX103
4270	\|\| sing_101.htm#SEC141
4271	} sing_36.htm#IDX79
4272	~ sing_36.htm#IDX117
4273	~ sing_393.htm#SEC433

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