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singular.idx @ b6ef022

fieker-DuValspielwiese

Last change on this file since b6ef022 was 2542b2, checked in by Hans Schoenemann <hannes@…>, 6 years ago
doc: 4.1.1p3
Property mode set to `100644`
File size: 178.0 KB

Line
1	! sing_36.htm#IDX101
2	!= sing_36.htm#IDX95
3	!= sing_100.htm#SEC140
4	" sing_36.htm#IDX104
5	# sing_36.htm#IDX118
6	$ sing_36.htm#IDX119
7	% sing_36.htm#IDX91
8	% sing_81.htm#SEC121
9	% sing_98.htm#SEC138
10	% sing_110.htm#SEC150
11	% sing_147.htm#SEC187
12	% sing_155.htm#SEC195
13	&& sing_36.htm#IDX102
14	&& sing_101.htm#SEC141
15	( sing_36.htm#IDX80
16	() sing_131.htm#IDX130
17	) sing_36.htm#IDX81
18	* bigintmat operations sing_36.htm#IDX89
19	* sing_81.htm#SEC121
20	* sing_87.htm#SEC127
21	* sing_93.htm#SEC133
22	* sing_98.htm#SEC138
23	* sing_106.htm#SEC146
24	* sing_110.htm#SEC150
25	* sing_137.htm#SEC177
26	* sing_142.htm#SEC182
27	* sing_147.htm#SEC187
28	* sing_155.htm#SEC195
29	** sing_36.htm#IDX93
30	+ bigintmat operations sing_36.htm#IDX85
31	+ sing_81.htm#SEC121
32	+ sing_87.htm#SEC127
33	+ sing_93.htm#SEC133
34	+ sing_98.htm#SEC138
35	+ sing_106.htm#SEC146
36	+ sing_110.htm#SEC150
37	+ sing_126.htm#SEC166
38	+ sing_137.htm#SEC177
39	+ sing_142.htm#SEC182
40	+ sing_147.htm#SEC187
41	+ sing_155.htm#SEC195
42	+ sing_169.htm#SEC209
43	+ sing_176.htm#SEC216
44	+ sing_181.htm#SEC221
45	++ sing_36.htm#IDX86
46	- bigintmat operations sing_36.htm#IDX87
47	- sing_81.htm#SEC121
48	- sing_87.htm#SEC127
49	- sing_98.htm#SEC138
50	- sing_106.htm#SEC146
51	- sing_110.htm#SEC150
52	- sing_137.htm#SEC177
53	- sing_147.htm#SEC187
54	- sing_155.htm#SEC195
55	- sing_181.htm#SEC221
56	-- sing_36.htm#IDX88
57	--MPhost sing_19.htm#IDX66
58	--MPport sing_19.htm#IDX65
59	--allow-net sing_19.htm#IDX39
60	--batch sing_19.htm#IDX64
61	--browser sing_19.htm#IDX43
62	--echo sing_19.htm#IDX35
63	--emacs sing_19.htm#IDX67
64	--emacs-dir sing_19.htm#IDX68
65	--emacs-load sing_19.htm#IDX69
66	--execute sing_19.htm#IDX56
67	--help sing_19.htm#IDX37
68	--min-time sing_19.htm#IDX61
69	--no-out sing_19.htm#IDX49
70	--no-rc sing_19.htm#IDX45
71	--no-shell sing_19.htm#IDX50
72	--no-stdlib sing_19.htm#IDX47
73	--no-tty sing_19.htm#IDX51
74	--no-warn sing_19.htm#IDX48
75	--quiet sing_19.htm#IDX53
76	--random sing_19.htm#IDX60
77	--sdb sing_19.htm#IDX32
78	--singular sing_19.htm#IDX70
79	--ticks-per-sec sing_19.htm#IDX62
80	--user-option sing_19.htm#IDX58
81	-> sing_159.htm#SEC199
82	-MPhost Command line options
83	-MPport Command line options
84	-allow-net Command line options
85	-b Command line options sing_19.htm#IDX63
86	-batch Command line options
87	-browser Command line options
88	-c Command line options sing_19.htm#IDX55
89	-d Command line options sing_19.htm#IDX31
90	-e Command line options sing_19.htm#IDX34
91	-echo Command line options
92	-emacs Command line options
93	-emacs-dir Command line options
94	-emacs-load Command line options
95	-execute Command line options
96	-h Command line options sing_19.htm#IDX36
97	-help Command line options
98	-min-time Command line options
99	-no-out Command line options
100	-no-rc Command line options
101	-no-shell Command line options
102	-no-stdlib Command line options
103	-no-tty Command line options
104	-no-warn Command line options
105	-q Command line options sing_19.htm#IDX52
106	-quiet Command line options
107	-r Command line options sing_19.htm#IDX59
108	-random Command line options
109	-sdb Command line options
110	-singular Command line options
111	-ticks-per-sec Command line options
112	-u Command line options sing_19.htm#IDX57
113	-user-option Command line options
114	-v Command line options sing_19.htm#IDX54
115	.. sing_36.htm#IDX113
116	.singularrc file sing_20.htm#IDX72
117	.singularrc file, no loading Command line options sing_19.htm#IDX46
118	/ sing_36.htm#IDX90
119	/ sing_76.htm#SEC116
120	/ sing_110.htm#SEC150
121	/ sing_137.htm#SEC177
122	/ sing_147.htm#SEC187
123	/ sing_155.htm#SEC195
124	/ sing_181.htm#SEC221
125	// sing_36.htm#IDX107
126	// sing_36.htm#IDX109
127	// sing_36.htm#IDX110
128	: sing_36.htm#IDX114
129	: sing_110.htm#SEC150
130	:: sing_36.htm#IDX115
131	:: sing_149.htm#SEC189
132	; sing_36.htm#IDX111
133	< sing_36.htm#IDX100
134	< sing_155.htm#SEC195
135	< sing_181.htm#SEC221
136	< sing_248.htm#SEC288
137	<= sing_36.htm#IDX99
138	<= sing_100.htm#SEC140
139	<= sing_147.htm#SEC187
140	<= sing_155.htm#SEC195
141	<= sing_176.htm#SEC216
142	<= sing_181.htm#SEC221
143	<> sing_36.htm#IDX96
144	<> sing_100.htm#SEC140
145	<> sing_137.htm#SEC177
146	<> sing_147.htm#SEC187
147	<> sing_155.htm#SEC195
148	<> sing_169.htm#SEC209
149	<> sing_176.htm#SEC216
150	<> sing_181.htm#SEC221
151	= sing_36.htm#IDX77
152	== sing_36.htm#IDX94
153	== sing_100.htm#SEC140
154	== sing_137.htm#SEC177
155	== sing_147.htm#SEC187
156	== sing_155.htm#SEC195
157	== sing_169.htm#SEC209
158	== sing_176.htm#SEC216
159	== sing_181.htm#SEC221
160	> sing_36.htm#IDX98
161	> sing_155.htm#SEC195
162	> sing_181.htm#SEC221
163	>= sing_36.htm#IDX97
164	>= sing_100.htm#SEC140
165	>= sing_147.htm#SEC187
166	>= sing_155.htm#SEC195
167	>= sing_176.htm#SEC216
168	>= sing_181.htm#SEC221
169	? sing_36.htm#IDX106
170	? sing_260.htm#IDX148
171	ADGT sing_1008.htm#SEC1084 1598
172	AG codes sing_917.htm#SEC969
173	AGcode_L sing_1862.htm#SEC1938 60329
174	AGcode_Omega sing_1863.htm#SEC1939 56285
175	ASCII sing_967.htm#SEC1043 26816
176	ASCII links sing_117.htm#SEC157
177	ASSUME sing_64.htm#SEC101
178	A_L sing_1561.htm#SEC1637 16721
179	A_Z sing_966.htm#SEC1042 50866
180	Access to elements of a user defined type Access to elements of a user defined type sing_186.htm#SEC226
181	Adj_div sing_1857.htm#SEC1933 44919
182	Adjoint ideal sing_1438.htm#IDX617
183	Alexander polynomial sing_1532.htm#IDX641
184	Algebraic Geometry codes sing_1856.htm#IDX789
185	Algebraic dependence Algebraic dependence sing_896.htm#SEC948
186	Algebraic geometry sing_1413.htm#SEC1489
187	AltVarEnd sing_775.htm#SEC827 11020
188	AltVarStart sing_774.htm#SEC826 21592
189	Ann sing_1352.htm#SEC1428 61560
190	Appel function sing_565.htm#IDX351
191	Appel hypergeometric function sing_565.htm#IDX352
192	Applications sing_915.htm#SEC967
193	Arnold, classification. sing_2384.htm#IDX945
194	Arnold, classification. sing_2385.htm#IDX946
195	ArnoldAction sing_1654.htm#SEC1730 26958
196	Assignments for user defined types Assignments for user defined types sing_188.htm#SEC228
197	AssocTanToEnv sing_1003.htm#SEC1079 46214
198	Atkin sing_1945.htm#SEC2021 sprintf
199	Authors sing_1.htm#IDX16
200	Automatic Deduction sing_1008.htm#IDX488
201	Automatic Demonstration sing_1008.htm#IDX489
202	BINresol sing_1451.htm#SEC1527 52996
203	Background sing_3.htm#SEC5
204	Basic programming sing_871.htm#SEC923
205	Basic programming sing_871.htm#SEC923
206	BelongSemig sing_2380.htm#SEC2456 22405
207	BerlekampMassey sing_2439.htm#SEC2515 2172
208	Bern sing_2353.htm#SEC2429 64051
209	Bernstein operator sing_542.htm#IDX333
210	Bernstein-Sato polynomial sing_507.htm#IDX314
211	Bernstein-Sato polynomial sing_542.htm#IDX330
212	Bernstein-Sato polynomial sing_1595.htm#IDX672
213	Bernstein-Sato polynomial sing_1599.htm#IDX689
214	Bernstein-Sato polynomial for variety sing_598.htm#IDX355
215	Betti sing_2572.htm#SEC2648 21134
216	Betti number Syzygies and resolutions sing_933.htm#SEC990
217	BettiNumsH sing_2469.htm#SEC2545 18661
218	BettiNumsN sing_2477.htm#SEC2553 44681
219	BettiNumsQp sing_2472.htm#SEC2548 16693
220	BettiNumsS sing_2475.htm#SEC2551 14964
221	Betty number sing_2466.htm#IDX986
222	Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_943.htm#SEC1000
223	BlowingUp sing_1574.htm#SEC1650 43153
224	Blowupcenter sing_1454.htm#SEC1530 3423
225	BorelCheck sing_1529.htm#SEC1605 48787
226	Bott's formula sing_2767.htm#IDX1055
227	Branches of space curve singularities Branches of space curve singularities sing_904.htm#SEC956
228	Briancon-Maisonobe algorithm sing_542.htm#IDX339
229	Brieskorn lattice sing_1595.htm#IDX668
230	Brieskorn lattice sing_1596.htm#IDX679
231	Brieskorn lattice sing_1597.htm#IDX682
232	Brieskorn lattice sing_1598.htm#IDX685
233	Brieskorn lattice sing_1599.htm#IDX688
234	Brieskorn lattice sing_1600.htm#IDX692
235	Brieskorn lattice sing_1601.htm#IDX696
236	Brieskorn lattice sing_1602.htm#IDX702
237	Brieskorn lattice sing_1603.htm#IDX710
238	Brieskorn lattice sing_1604.htm#IDX716
239	Brieskorn lattice sing_1605.htm#IDX724
240	Brieskorn lattice sing_1606.htm#IDX734
241	Brieskorn lattice sing_1617.htm#IDX740
242	Brieskorn lattice sing_1619.htm#IDX751
243	Brieskorn lattice sing_1647.htm#IDX778
244	Brill-Noether algorithm sing_1856.htm#IDX790
245	BrillNoether sing_1859.htm#SEC1935 39919
246	Buchberger algorithm for toric ideals Buchberger algorithm sing_944.htm#SEC1001
247	Budur-Mustata-Saito approach sing_598.htm#IDX359
248	Building Singular sing_2824.htm#SEC2914
249	C programming language Major differences to the C programming language sing_411.htm#SEC451
250	C, module ordering sing_925.htm#IDX419
251	CGS sing_988.htm#IDX432
252	CM_regularity sing_1516.htm#SEC1592 33865
253	CMtype sing_1685.htm#SEC1761 24849
254	CRHT-ideal sing_950.htm#SEC1014
255	CSMA sing_2376.htm#SEC2452 49080
256	CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33
257	Castelnuovo-Mumford regularity sing_1516.htm#IDX633
258	Category string sing_51.htm#SEC88
259	CenCharDec sing_731.htm#SEC783 44505
260	Center sing_1493.htm#SEC1569 25541
261	CenterBO sing_1500.htm#SEC1576 34701
262	CentralQuot sing_729.htm#SEC781 56490
263	CentralSaturation sing_730.htm#SEC782 31585
264	Change of rings sing_9.htm#SEC15
265	Characteristic sets sing_934.htm#SEC991
266	CharacteristicExponents CharacteristicExponents sing_1580.htm#SEC1656 21795
267	ChernClass sing_2780.htm#SEC2856 32965
268	ChernRootsDual sing_2332.htm#SEC2408 40100
269	ChernRootsHom sing_2341.htm#SEC2417 48446
270	ChernRootsProd sing_2334.htm#SEC2410 13967
271	ChernRootsSum sing_2330.htm#SEC2406 57286
272	ChernRootsSymm sing_2343.htm#SEC2419 59304
273	ChernRootsWedge sing_2344.htm#SEC2420 7239
274	Chevalley-Rosenlicht theorem sing_1432.htm#IDX602
275	Chevalley-Rosenlicht theorem sing_1433.htm#IDX605
276	Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_2771.htm#IDX1060
277	ChowRing sing_2771.htm#SEC2847 57977
278	Classification of hypersurface singularities Classification of hypersurface singularities sing_905.htm#SEC957
279	Classification of singularities sing_2740.htm#IDX1031
280	Code Codes and the decoding problem sing_949.htm#SEC1007
281	Codes and the decoding problem Codes and the decoding problem sing_949.htm#SEC1006
282	Coding theory sing_1855.htm#SEC1931
283	Coefficient rings Notes for Singular users sing_2822.htm#SEC2907
284	Command line options Command line options sing_19.htm#SEC26
285	Commands Functions and system variables sing_207.htm#SEC247
286	Commands for user defined types Commands for user defined types sing_187.htm#SEC227
287	Commutative Algebra sing_884.htm#SEC936
288	Commutative algebra sing_1168.htm#SEC1244
289	CompDecomp sing_504.htm#SEC556 9959
290	CompInt sing_2382.htm#SEC2458 7518
291	CompleteHomog sing_2320.htm#SEC2396 42123
292	ComplexValue sing_2461.htm#SEC2537 45546
293	Comprehensive Groebner System sing_988.htm#IDX435
294	Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_880.htm#SEC932
295	ConsLevels sing_996.htm#SEC1072 14282
296	ContactMatrix sing_1582.htm#SEC1658 40767
297	Conti-Traverso algorithm sing_939.htm#SEC996
298	Contributors sing_1.htm#IDX15
299	Control structures sing_379.htm#SEC419
300	Control theory System and Control theory sing_1889.htm#SEC1965
301	Cooper philosophy sing_950.htm#SEC1012
302	Cornacchia sing_1935.htm#SEC2011 63434
303	CornacchiaModified sing_1936.htm#SEC2012 59790
304	Crep sing_991.htm#SEC1067 17485
305	Critical points sing_899.htm#SEC951
306	CurveParam sing_1576.htm#SEC1652 53605
307	CurveRes sing_1575.htm#SEC1651 48848
308	Curves sing_1438.htm#IDX614
309	Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36
310	Cyclic code sing_1870.htm#IDX797
311	Cyclic roots sing_877.htm#SEC929
312	D-integration sing_565.htm#IDX348
313	D-localization sing_565.htm#IDX344
314	D-localization sing_843.htm#IDX388
315	D-module purityfiltration_lib sing_507.htm#IDX312
316	D-module sing_542.htm#IDX327
317	D-module sing_565.htm#IDX341
318	D-module sing_598.htm#IDX353
319	D-module sing_787.htm#IDX367
320	D-module sing_843.htm#IDX385
321	D-module structure sing_542.htm#IDX328
322	D-module structure sing_598.htm#IDX354
323	D-restriction sing_565.htm#IDX346
324	DBM links sing_122.htm#SEC162
325	DISPLAY environment variable The online help system sing_16.htm#IDX28
326	DLoc sing_568.htm#SEC620 5981
327	DLoc0 sing_570.htm#SEC622 14327
328	Data types sing_72.htm#SEC112
329	Data types (plural) sing_424.htm#IDX298
330	Debugging tools sing_63.htm#SEC100
331	Decker, Wolfram sing_1.htm#IDX17
332	Declaration of objects of a user defined type Declaration of objects of a user defined type sing_185.htm#SEC225
333	Decoding sing_1870.htm#IDX799
334	Decoding codes with Groebner bases Decoding codes with Groebner bases sing_948.htm#SEC1005
335	Decoding method based on quadratic equations Decoding method based on quadratic equations sing_953.htm#SEC1023
336	Definition of a user defined type Definition of a user defined type sing_184.htm#SEC224
337	Deformations sing_902.htm#SEC954
338	Deformations, T1 and T2 sing_901.htm#SEC953
339	Deg sing_2575.htm#SEC2651 35419
340	Degree sing_2576.htm#SEC2652 48523
341	DegreePure sing_1417.htm#SEC1493 33003
342	Degrees sing_2577.htm#SEC2653 50349
343	Delta sing_1501.htm#SEC1577 33497
344	DeltaList sing_1502.htm#SEC1578 65148
345	Demo mode sing_24.htm#SEC35
346	Depth sing_891.htm#SEC943
347	Determinacy sing_2743.htm#IDX1035
348	Di Biase-Urbanke algorithm Di Biase and Urbanke sing_942.htm#SEC999
349	Distributed computing sing_1019.htm#IDX495
350	Dlocalization sing_844.htm#SEC896 22140
351	Documentation Tool sing_60.htm#SEC97
352	Dp, global ordering sing_923.htm#IDX402
353	Ds, local ordering sing_924.htm#IDX412
354	DsingularLocus sing_848.htm#SEC900 46495
355	Dynamic loading sing_71.htm#SEC111
356	Dynamic modules sing_879.htm#SEC931
357	ECPP sing_1979.htm#SEC2055 55777
358	ECoef sing_1460.htm#SEC1536 14154
359	EOrdlist sing_1458.htm#SEC1534 36329
360	ERROR sing_237.htm#SEC277
361	ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33
362	Edatalist sing_1457.htm#SEC1533 61593
363	Edelman-Reiner sing_2263.htm#IDX880
364	Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
365	Editing input sing_18.htm#SEC25
366	Elimination sing_887.htm#SEC939
367	Emacs Emacs user interface sing_21.htm#SEC28
368	Emacs, Singular demo mode sing_24.htm#SEC35
369	Emacs, a quick guide A quick guide to Emacs sing_22.htm#SEC29
370	Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC36
371	Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC37
372	Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC38
373	Emacs, overview A quick guide to Emacs sing_22.htm#SEC29
374	Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30
375	Emacs, user interface Emacs user interface sing_21.htm#SEC28
376	Emaxcont sing_1462.htm#SEC1538 47312
377	Enumerative geometry sing_2767.htm#IDX1053
378	Equal sing_1416.htm#SEC1492 19984
379	Eresol sing_1452.htm#SEC1528 12842
380	EulerAff sing_2377.htm#SEC2453 54325
381	EulerProj sing_2378.htm#SEC2454 13537
382	Evaluation of logical expressions Evaluation of logical expressions sing_413.htm#SEC453
383	Examples sing_869.htm#SEC921
384	Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40
385	Exp for matrices sing_1434.htm#IDX606
386	Experimental libraries Experimental libraries sing_2307.htm#SEC2383
387	Ext sing_1228.htm#SEC1304 21909
388	Ext, computation of sing_890.htm#SEC942
389	Ext_R sing_1227.htm#SEC1303 53310
390	Exterior sing_761.htm#SEC813 23593
391	Extra weight vector sing_928.htm#SEC980
392	Factorization sing_892.htm#SEC944
393	FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_1004.htm#SEC1080 18153
394	Feynman graph sing_1204.htm#IDX528
395	Finite fields sing_886.htm#SEC938
396	First steps sing_6.htm#SEC12
397	Fitzgerald-Lax method Fitzgerald-Lax method sing_952.htm#SEC1020
398	Float sing_251.htm#SEC291
399	Flow control sing_40.htm#SEC70
400	Formal Checker sing_59.htm#SEC96
401	Formatting output sing_876.htm#SEC928
402	Free resolution sing_888.htm#SEC940
403	Free resolution, graded Handling graded modules sing_889.htm#SEC941
404	FultonA sing_2375.htm#SEC2451 33688
405	Functions sing_208.htm#SEC248
406	Future benefits of Singular 4 Notes for Singular users sing_2822.htm#SEC2912
407	G-algebra sing_488.htm#SEC528
408	G-algebra sing_488.htm#SEC530
409	G-algebra, setup sing_488.htm#SEC532
410	GBWeight sing_571.htm#SEC623 24641
411	GBsolve sing_1769.htm#SEC1845 16830
412	GIT-Fans sing_911.htm#SEC963
413	GITcone sing_2491.htm#SEC2567 64643
414	GITfan sing_2492.htm#SEC2568 32549
415	GITfanFromOrbitCones GITfanFromOrbitCones sing_2493.htm#SEC2569 63104
416	GITfanParallel sing_2494.htm#SEC2570 53071
417	GITfanParallelSymmetric GITfanParallelSymmetric sing_2509.htm#SEC2585 30232
418	GITfanSymmetric sing_2508.htm#SEC2584 25831
419	GKZfan sing_2495.htm#SEC2571 sprintf
420	GKZsystem sing_727.htm#SEC779 20528
421	GKdim sing_700.htm#SEC752 9814
422	GMP sing_1.htm#IDX3
423	GMP sing_2826.htm#SEC2916
424	GND.lib sing_2516.htm#SEC2592
425	GND_lib sing_2516.htm#SEC2592
426	GTZmod sing_1278.htm#SEC1354 30091
427	GTZopt sing_1285.htm#SEC1361 14642
428	G_a -Invariants sing_908.htm#SEC960
429	Gamma sing_1467.htm#SEC1543 3820
430	Gauss-Manin connection Gauss-Manin connection sing_935.htm#SEC992
431	Gauss-Manin connection sing_1647.htm#IDX777
432	Gauss-Manin connection sing_1694.htm#IDX780
433	Gauss-Manin system sing_1595.htm#IDX667
434	Gauss-Manin system sing_1596.htm#IDX678
435	Gauss-Manin system sing_1597.htm#IDX681
436	Gauss-Manin system sing_1598.htm#IDX684
437	Gauss-Manin system sing_1599.htm#IDX687
438	Gauss-Manin system sing_1600.htm#IDX691
439	Gauss-Manin system sing_1601.htm#IDX695
440	Gauss-Manin system sing_1602.htm#IDX701
441	Gauss-Manin system sing_1603.htm#IDX709
442	Gauss-Manin system sing_1604.htm#IDX715
443	Gauss-Manin system sing_1605.htm#IDX723
444	Gauss-Manin system sing_1606.htm#IDX733
445	Gauss-Manin system sing_1617.htm#IDX739
446	Gauss-Manin system sing_1619.htm#IDX750
447	General command syntax General command syntax sing_35.htm#SEC59
448	General concepts sing_12.htm#SEC18
449	General purpose sing_960.htm#SEC1036
450	General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41
451	Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_490.htm#SEC540
452	Generalized Newton identities Generalized Newton identities sing_951.htm#SEC1017
453	Geometric Invariant Theory Geometric Invariant Theory sing_910.htm#SEC962
454	Geometric Theorems sing_1008.htm#IDX490
455	Geometric genus sing_1438.htm#IDX618
456	German Umlaute sing_409.htm#IDX285
457	Getting started sing_5.htm#SEC11
458	Global orderings sing_923.htm#SEC975
459	Goettsche's formula sing_2466.htm#IDX987
460	GoettscheF sing_2467.htm#SEC2543 27881
461	Graded commutative algebras Graded commutative algebras (SCA) sing_492.htm#SEC544
462	Grassmannian sing_2772.htm#SEC2848 43898
463	Grassmannian, abstract variety, Schubert calculus Grassmannian sing_2772.htm#IDX1061
464	Greuel, Gert-Martin sing_1.htm#IDX18
465	Groebner Bases Computing Groebner and Standard Bases sing_880.htm#SEC932
466	Groebner bases in G-algebras Groebner bases in G-algebras sing_489.htm#SEC533
467	Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_495.htm#SEC547
468	Groebner bases, decodeGB sing_1870.htm#IDX801
469	Groebner bases, slim sing_883.htm#SEC935
470	Groebner basis conversion Groebner basis conversion sing_882.htm#SEC934
471	Groebner cover sing_987.htm#IDX428
472	Groebner cover sing_994.htm#IDX447
473	Groebner cover sing_995.htm#IDX454
474	Groebner fan sing_2133.htm#IDX818
475	Groebner walk sing_1219.htm#IDX549
476	Groebner walk sing_1221.htm#IDX551
477	Groebner walk sing_2764.htm#IDX1049
478	Groebner walk sing_2765.htm#IDX1050
479	Groebnerwalk sing_1215.htm#IDX545
480	Groebnerwalk sing_2609.htm#IDX1002
481	Groebnerwalk sing_2763.htm#IDX1048
482	Groebnerwalk sing_2806.htm#IDX1077
483	Gromov-Witten invariants sing_1204.htm#IDX525
484	Gromov-Witten invariants sing_1210.htm#IDX534
485	Gromov-Witten invariants sing_1211.htm#IDX538
486	Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_2797.htm#IDX1073
487	Gromov-Witten invariants, multiple covers sing_2796.htm#IDX1072
488	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_2798.htm#IDX1074
489	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_2799.htm#IDX1075
490	Gromov-Witten invariants. sing_2767.htm#IDX1056
491	Gweights sing_755.htm#SEC807 651
492	H2basis sing_1652.htm#SEC1728 3414
493	HHnormalForm sing_2393.htm#SEC2469 33972
494	Hamburger-Noether expansion sing_1532.htm#IDX637
495	Hamburger-Noether expansion sing_1620.htm#IDX759
496	Hamburger-Noether expansions sing_1857.htm#IDX791
497	Handling graded modules Handling graded modules sing_889.htm#SEC941
498	Hcode sing_1554.htm#SEC1630 26628
499	Help string sing_45.htm#SEC82
500	Hensel sing_242.htm#SEC282
501	Hilbert function sing_357.htm#IDX188
502	Hilbert function sing_932.htm#SEC986
503	Hilbert scheme sing_2466.htm#IDX990
504	Hilbert series sing_932.htm#SEC986
505	Hilbert-driven GB algorithm Groebner basis conversion sing_882.htm#SEC934
506	HilbertClassPoly sing_1942.htm#SEC2018 sprintf
507	HilbertSeries sing_1747.htm#SEC1823 21249
508	HilbertWeights sing_1748.htm#SEC1824 sprintf
509	Hom sing_1231.htm#SEC1307 61434
510	HomJJ sing_1308.htm#SEC1384 1525
511	Hosten-Sturmfels algorithm Hosten and Sturmfels sing_941.htm#SEC998
512	How to enter and exit How to enter and exit sing_14.htm#SEC20
513	How to use this manual How to use this manual sing_4.htm#SEC6
514	Hurwitz numbers sing_1210.htm#IDX537
515	Hurwitz numbers sing_1211.htm#IDX541
516	Hypersurface singularities, classification of Classification of hypersurface singularities sing_905.htm#SEC957
517	I-regular function sing_994.htm#IDX453
518	IN sing_281.htm#IDX149
519	Ideal membership sing_931.htm#IDX424
520	Identifiers, syntax of sing_37.htm#SEC65
521	ImageGroup sing_1750.htm#SEC1826 28808
522	ImageVariety sing_1749.htm#SEC1825 15252
523	Imap, option sing_316.htm#IDX175
524	Implemented algorithms Implemented algorithms sing_33.htm#SEC47
525	Incl sing_1415.htm#SEC1491 7621
526	Index sing_2831.htm#SEC2921
527	Info string sing_52.htm#SEC89
528	InterDiv sing_1483.htm#SEC1559 46142
529	Interactive use sing_13.htm#SEC19
530	Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24
531	IntersectWithSub sing_732.htm#SEC784 56289
532	Intersection theory sing_2767.htm#IDX1052
533	IntersectionMatrix sing_1581.htm#SEC1657 29351
534	Introduction sing_2.htm#SEC4
535	Invariant Theory sing_907.htm#SEC959
536	Invariant theory sing_1699.htm#SEC1775
537	InvariantQ sing_1752.htm#SEC1828 53256
538	InvariantRing sing_1751.htm#SEC1827 22928
539	Invariants of a finite group Invariants of a finite group sing_909.htm#SEC961
540	Invariants of plane curve singularities Invariants of plane curve singularities sing_903.htm#SEC955
541	IsSCA sing_776.htm#SEC828 58445
542	J-marked schemes sing_1523.htm#IDX635
543	J-marked schemes, Borel ideals sing_1528.htm#IDX636
544	JMBTest.lib sing_1523.htm#SEC1599
545	JMBTest_lib sing_1523.htm#SEC1599
546	JMSConst.lib sing_1528.htm#SEC1604
547	JMSConst_lib sing_1528.htm#SEC1604
548	JMarkedScheme sing_1530.htm#SEC1606 60696
549	Jacobi sing_1952.htm#SEC2028 29843
550	Jacobson form sing_1907.htm#IDX802
551	Jacobson normal form sing_1907.htm#IDX803
552	Janet basis sing_2762.htm#IDX1046
553	Janet division, Janet basis sing_2761.htm#IDX1045
554	JuReTopDim sing_1425.htm#SEC1501 sprintf
555	JuReZeroDim sing_1426.htm#SEC1502 sprintf
556	KScoef sing_1645.htm#SEC1721 sprintf
557	KSconvert sing_1643.htm#SEC1719 3585
558	KSker sing_1642.htm#SEC1718 40166
559	KSlinear sing_1644.htm#SEC1720 19896
560	KSpencerKernel sing_1692.htm#SEC1768 12490
561	KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2535.htm#SEC2611 20741
562	Ker sing_2581.htm#SEC2657 58279
563	Kernel of module homomorphisms Kernel of module homomorphisms sing_895.htm#SEC947
564	KoszulHomology sing_1240.htm#SEC1316 sprintf
565	Kronecker module sing_2466.htm#IDX989
566	Kronecker product sing_361.htm#SEC401
567	L, ordering sing_929.htm#SEC981
568	LETTERPLACE sing_493.htm#SEC545
569	LIB sing_285.htm#SEC325
570	LIB commands sing_53.htm#SEC90
571	LIBs sing_956.htm#SEC1032
572	LLL sing_359.htm#IDX220
573	LOT algorithm sing_542.htm#IDX340
574	LU-decomposition of a matrix of numbers sing_290.htm#SEC330
575	Laurent series sing_1208.htm#IDX533
576	Left and two-sided Groebner bases Left and two-sided Groebner bases sing_913.htm#SEC965
577	Left ideal membership Groebner bases in G-algebras sing_489.htm#SEC536
578	Left normal form Groebner bases in G-algebras sing_489.htm#SEC535
579	LengthSym sing_786.htm#SEC838 16591
580	LengthSymElement sing_785.htm#SEC837 28292
581	Letterplace sing_493.htm#SEC545
582	Levels sing_997.htm#SEC1073 16031
583	Lexicographic Groebner bases, computation of Groebner basis conversion sing_882.htm#SEC934
584	Libraries Writing procedures and libraries sing_48.htm#SEC85
585	Libraries sing_872.htm#SEC924
586	Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86
587	Library versioning Notes for Singular users sing_2822.htm#SEC2910
588	Lie algebra sing_1433.htm#IDX603
589	Lie group sing_1436.htm#IDX608
590	Lie group sing_1437.htm#IDX611
591	Limitations sing_409.htm#SEC449
592	Linear algebra sing_1109.htm#SEC1185
593	Linear code sing_1870.htm#IDX798
594	LinearActionQ sing_1754.htm#SEC1830 62218
595	LinearCombinationQ sing_1755.htm#SEC1831 59373
596	LinearizeAction sing_1753.htm#SEC1829 60266
597	Loading a library sing_62.htm#SEC99
598	Local orderings sing_924.htm#SEC976
599	Log for matrices sing_1435.htm#IDX607
600	Long coefficients sing_874.htm#SEC926
601	M, ordering sing_926.htm#SEC978
602	MVComplex sing_2415.htm#SEC2491 62126
603	Macdonald's formula sing_2466.htm#IDX988
604	MacdonaldF sing_2473.htm#SEC2549 12751
605	Macintosh installation Macintosh installation instructions sing_2830.htm#SEC2920
606	Mathematical background Mathematical background sing_930.htm#SEC982
607	Mathematical background (plural) Mathematical background (plural) sing_487.htm#SEC527
608	Matrix orderings sing_926.htm#SEC978
609	Max sing_1661.htm#SEC1737 23
610	Maximus sing_1525.htm#SEC1601 10010
611	Maxord sing_1466.htm#SEC1542 14124
612	MillerRabin sing_1962.htm#SEC2038 15740
613	Milnor number Milnor and Tjurina number sing_898.htm#SEC950
614	Milnor number sing_2742.htm#IDX1034
615	Min sing_1662.htm#SEC1738 29622
616	MinMult sing_2381.htm#SEC2457 39835
617	MinimalDecomposition MinimalDecomposition sing_1756.htm#SEC1832 24161
618	Minimum distance sing_1870.htm#IDX800
619	Minimus sing_1524.htm#SEC1600 61721
620	Miscellaneous libraries Miscellaneous libraries sing_2234.htm#SEC2310
621	ModEqn sing_1655.htm#SEC1731 59394
622	Modular techniques sing_1019.htm#IDX492
623	Module orderings sing_925.htm#SEC977
624	Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16
625	Monodromy sing_1647.htm#IDX775
626	Monomial orderings sing_920.htm#SEC972
627	Monomial orderings, Term orderings sing_31.htm#SEC44
628	Mori dream spaces sing_2308.htm#IDX940
629	Morse lemma addnondegeneratevariables sing_2741.htm#IDX1032
630	Morse lemma sing_2744.htm#IDX1036
631	MultiplicitySequence MultiplicitySequence sing_1579.htm#SEC1655 1309
632	NF sing_335.htm#SEC375
633	NF sing_479.htm#SEC519
634	NFMora sing_2028.htm#SEC2104 40670
635	NPos sing_1298.htm#SEC1374 15702
636	NPos_test sing_1296.htm#SEC1372 48172
637	NSplaces sing_1858.htm#SEC1934 48675
638	NTL sing_1.htm#IDX4
639	NakYoshF sing_2470.htm#SEC2546 58602
640	Names sing_37.htm#SEC65
641	Names in procedures sing_46.htm#SEC83
642	Names, indexed sing_37.htm#SEC65
643	New orderings for modules Notes for Singular users sing_2822.htm#SEC2911
644	Newton non-degenerate sing_1634.htm#IDX773
645	Newton polygon sing_1633.htm#IDX772
646	Newton polygon sing_1634.htm#IDX774
647	Newton polygons sing_2809.htm#IDX1080
648	Newton polytope sing_2133.htm#IDX817
649	Newton step sing_2745.htm#IDX1040
650	NoetherPosition sing_1292.htm#SEC1368 18735
651	Non-commutative LIBs Non-commutative libraries sing_499.htm#SEC551
652	Non-commutative algebra Non-commutative algebra sing_912.htm#SEC964
653	Non-commutative algebra sing_947.htm#SEC1004
654	Non-commutative libraries Non-commutative libraries sing_499.htm#SEC551
655	Non-commutative subsystem Non-commutative subsystem sing_422.htm#SEC462
656	Nonhyp sing_1455.htm#SEC1531 sprintf
657	Normalization sing_894.htm#SEC946
658	Notes for Singular users Notes for Singular users sing_2822.htm#SEC2906
659	Notes for developers Notes for developers sing_2823.htm#SEC2913
660	NullCone sing_1757.htm#SEC1833 64635
661	NumIrrDecom sing_1429.htm#SEC1505 sprintf
662	NumLocalDim sing_1418.htm#SEC1494 1739
663	NumPrimDecom sing_1431.htm#SEC1507 34134
664	Oaku-Takayama algorithm sing_542.htm#IDX338
665	Objects sing_38.htm#SEC66
666	Orlik-Solomon sing_2264.htm#IDX881
667	Output sing_2591.htm#IDX1000
668	Output sing_2688.htm#IDX1007
669	Output sing_2690.htm#IDX1008
670	Output sing_2691.htm#IDX1009
671	Output sing_2692.htm#IDX1010
672	Output sing_2693.htm#IDX1011
673	Output sing_2694.htm#IDX1012
674	Output sing_2695.htm#IDX1013
675	Output sing_2696.htm#IDX1014
676	Output sing_2697.htm#IDX1015
677	Output sing_2698.htm#IDX1016
678	Output sing_2699.htm#IDX1017
679	Output sing_2700.htm#IDX1018
680	Output sing_2701.htm#IDX1019
681	Output sing_2702.htm#IDX1020
682	Output sing_2703.htm#IDX1021
683	Output sing_2704.htm#IDX1022
684	Output sing_2705.htm#IDX1023
685	Output sing_2706.htm#IDX1024
686	Output sing_2707.htm#IDX1025
687	Output sing_2708.htm#IDX1026
688	Output sing_2709.htm#IDX1027
689	Output sing_2710.htm#IDX1028
690	Output sing_2711.htm#IDX1029
691	Output sing_2712.htm#IDX1030
692	Output, formatting of sing_876.htm#SEC928
693	PBW sing_521.htm#IDX326
694	PBW basis sing_488.htm#SEC529
695	PBW_eqDeg sing_539.htm#SEC591 23181
696	PBW_maxDeg sing_540.htm#SEC592 59566
697	PBW_maxMonom sing_541.htm#SEC593 1155
698	PEsolve sing_1767.htm#SEC1843 9229
699	PH_ais sing_2286.htm#SEC2362 49473
700	PH_nais sing_2287.htm#SEC2363 46271
701	PLURAL sing_423.htm#SEC463
702	PLURAL LIBs Non-commutative libraries sing_499.htm#SEC551
703	PPolyH sing_2468.htm#SEC2544 25241
704	PPolyN sing_2476.htm#SEC2552 39067
705	PPolyQp sing_2471.htm#SEC2547 35707
706	PPolyS sing_2474.htm#SEC2550 13817
707	ParToVar sing_2463.htm#SEC2539 13991
708	Parallelization Parallelization with ssi links sing_878.htm#SEC930
709	Parallelization sing_1019.htm#IDX493
710	Parameter list sing_44.htm#SEC81
711	Parameters sing_875.htm#SEC927
712	Parametrization sing_1438.htm#IDX615
713	Parametrization, image. sing_1448.htm#IDX627
714	PartC sing_2371.htm#SEC2447 54120
715	PartitionVar sing_2460.htm#SEC2536 41350
716	Path names Notes for Singular users sing_2822.htm#SEC2909
717	PerfectPowerTest sing_1925.htm#SEC2001 17450
718	Perturbation walk sing_1220.htm#IDX550
719	Pfister, Gerhard sing_1.htm#IDX19
720	Pipe links sing_121.htm#SEC161
721	PocklingtonLehmer sing_1964.htm#SEC2040 13634
722	Poincare polynomial sing_2276.htm#IDX905
723	Polar curves sing_900.htm#SEC952
724	PollardRho sing_1965.htm#SEC2041 49602
725	PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2289.htm#IDX921
726	PolyBoRi, Boolean Groebner Basis sing_2291.htm#IDX922
727	PolyBoRi, Boolean Groebner Basis sing_2292.htm#IDX923
728	PolyBoRi, Boolean Groebner Basis sing_2293.htm#IDX924
729	PolyBoRi, Boolean Groebner Basis sing_2294.htm#IDX925
730	PolyBoRi, Boolean Groebner Basis sing_2295.htm#IDX926
731	PolyBoRi, Boolean Groebner Basis sing_2296.htm#IDX927
732	PolyBoRi, Boolean Groebner Basis sing_2297.htm#IDX928
733	PolyBoRi, Boolean Groebner Basis sing_2298.htm#IDX929
734	PolyBoRi, Boolean Groebner Basis sing_2299.htm#IDX930
735	PolyBoRi, Boolean Groebner Basis sing_2300.htm#IDX931
736	PolyBoRi, Boolean Groebner Basis sing_2301.htm#IDX932
737	PolyBoRi, Boolean Groebner Basis sing_2302.htm#IDX933
738	PolyBoRi, Boolean Groebner Basis sing_2303.htm#IDX934
739	PolyBoRi, Boolean Groebner Basis sing_2305.htm#IDX936
740	PolyBoRi, zero-supressed decision diagram sing_2304.htm#IDX935
741	Polybori, Boolean Groebner Basis sing_2306.htm#IDX937
742	Polynomial data sing_918.htm#SEC970
743	Pottier algorithm sing_940.htm#SEC997
744	Preface sing_1.htm#SEC1
745	Prep sing_992.htm#SEC1068 55342
746	Primary decomposition Primary decomposition sing_893.htm#SEC945
747	PrimdecA sing_1274.htm#SEC1350 248
748	PrimdecB sing_1275.htm#SEC1351 9653
749	Procedure definition Procedure definition sing_43.htm#SEC78
750	Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84
751	Procedures sing_42.htm#SEC77
752	Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14
753	Procedures and libraries sing_872.htm#SEC924
754	Procedures in a library Procedures in a library sing_54.htm#SEC91
755	Product orderings sing_927.htm#SEC979
756	Programming sing_870.htm#SEC922
757	Pseudo ordering L sing_929.htm#SEC981
758	PtoCrep sing_993.htm#SEC1069 52961
759	Puiseux expansion sing_1532.htm#IDX638
760	Puiseux expansion sing_1620.htm#IDX760
761	Puiseux pairs Invariants of plane curve singularities sing_903.htm#SEC955
762	Puiseux pairs sing_1626.htm#IDX765
763	QQ sing_28.htm#SEC39
764	Qso3Casimir sing_726.htm#SEC778 40212
765	Quot-scheme sing_2466.htm#IDX991
766	Quotient sing_1809.htm#SEC1885 24888
767	QuotientEquations sing_1656.htm#SEC1732 18230
768	Rational curves sing_1438.htm#IDX616
769	ReJunkUseHomo sing_1424.htm#SEC1500 10186
770	ReesAlgebra sing_1391.htm#SEC1467 59951
771	References sing_955.htm#SEC1029
772	References (plural) sing_491.htm#SEC541
773	Release Notes sing_2818.htm#SEC2894
774	Res sing_2571.htm#SEC2647 92
775	ResTree sing_1484.htm#SEC1560 58727
776	Resolution sing_11.htm#SEC17
777	Resolution of singularities Resolution of singularities sing_906.htm#SEC958
778	Resolution, free sing_888.htm#SEC940
779	ReynoldsImage sing_1758.htm#SEC1834 35172
780	ReynoldsOperator sing_1759.htm#SEC1835 14986
781	RiemannRochBN sing_2316.htm#SEC2392 20085
782	RiemannRochHess sing_2554.htm#SEC2630 sprintf
783	Right Groebner bases and syzygies Right Groebner bases and syzygies sing_914.htm#SEC966
784	Ring-dependent options Notes for Singular users sing_2822.htm#SEC2908
785	Rings and orderings sing_28.htm#SEC39
786	Rings and standard bases Rings and standard bases sing_7.htm#SEC13
787	Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
788	SCA Graded commutative algebras (SCA) sing_492.htm#SEC544
789	SDB breakpoint Source code debugger sing_66.htm#SEC106
790	SDB debugger Source code debugger sing_66.htm#SEC106
791	SDLoc sing_569.htm#SEC621 9512
792	SINGULAR libraries sing_956.htm#SEC1032
793	SINGULARHIST sing_18.htm#SEC25
794	SV-decoding algorithm sing_1865.htm#IDX794
795	SV-decoding algorithm, preprocessing sing_1864.htm#IDX793
796	Sannfs sing_545.htm#SEC597 42932
797	SannfsBFCT sing_554.htm#SEC606 59702
798	SannfsVar sing_601.htm#SEC653 37522
799	Sannfslog sing_546.htm#SEC598 49313
800	Saturation sing_885.htm#SEC937
801	Saturation sing_1201.htm#IDX519
802	Sch@"onemann, Hans sing_1.htm#IDX20
803	Schoof sing_1976.htm#SEC2052 49281
804	Schubert calculus sing_2767.htm#IDX1054
805	SchubertClass sing_2804.htm#SEC2880 62336
806	SchurCh sing_2368.htm#SEC2444 58575
807	SchurS sing_2367.htm#SEC2443 46004
808	SegreA sing_2374.htm#SEC2450 55776
809	Semigroup sing_1572.htm#SEC1648 22323
810	SetDeg sing_2574.htm#SEC2650 40547
811	Setting up a G-algebra sing_488.htm#SEC532
812	ShanksMestre sing_1975.htm#SEC2051 12973
813	SimplifyIdeal sing_1760.htm#SEC1836 sprintf
814	Singular sing_359.htm#IDX257
815	Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2820.htm#SEC2904
816	Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36
817	Singular, demo mode sing_24.htm#SEC35
818	Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
819	Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38
820	Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
821	Singular2bertini sing_1422.htm#SEC1498 7552
822	SingularLib sing_359.htm#IDX259
823	Singularities sing_1531.htm#SEC1607
824	Singularity Theory sing_897.htm#SEC949
825	Skeletons for parallelization sing_1019.htm#IDX494
826	Smith form sing_1907.htm#IDX804
827	Smith normal form sing_1907.htm#IDX805
828	SolowayStrassen sing_1963.htm#SEC2039 22680
829	Solving systems of polynomial equations Solving systems of polynomial equations sing_916.htm#SEC968
830	Source sing_2563.htm#SEC2639 10351
831	Source code debugger, invocation Command line options sing_19.htm#IDX33
832	Space curve singularities, branches of Branches of space curve singularities sing_904.htm#SEC956
833	Special characters sing_36.htm#SEC64
834	Splitting lemma addnondegeneratevariables sing_2741.htm#IDX1033
835	Splitting lemma sing_2744.htm#IDX1037
836	Ssi file links sing_119.htm#SEC159
837	Ssi links sing_118.htm#SEC158
838	Ssi tcp links sing_120.htm#SEC160
839	StabEqn sing_1657.htm#SEC1733 28539
840	StabEqnId sing_1658.htm#SEC1734 27955
841	StabOrder sing_1659.htm#SEC1735 55603
842	Standard Bases Computing Groebner and Standard Bases sing_880.htm#SEC932
843	Standard bases sing_931.htm#SEC983
844	StartOrderingV sing_1526.htm#SEC1602 58927
845	Startup sequence sing_20.htm#SEC27
846	StringF sing_1646.htm#SEC1722 11590
847	SymGroup sing_784.htm#SEC836 56676
848	Symbolic-numerical solving Symbolic-numerical solving sing_916.htm#SEC968
849	Symbolic-numerical solving sing_1764.htm#SEC1840
850	System and Control theory System and Control theory sing_1889.htm#SEC1965
851	System dependent limitations System dependent limitations sing_410.htm#SEC450
852	System variables sing_396.htm#SEC436
853	Syzygies and resolutions Syzygies and resolutions sing_933.htm#SEC987
854	Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_490.htm#SEC537
855	T1 sing_901.htm#SEC953
856	T2 sing_901.htm#SEC953
857	TRACE Tracing of procedures sing_65.htm#SEC102
858	TRACE sing_405.htm#SEC445
859	T_1 sing_1679.htm#SEC1755 59277
860	T_12 sing_1681.htm#SEC1757 12923
861	T_2 sing_1680.htm#SEC1756 55781
862	Target sing_2562.htm#SEC2638 16006
863	Teaching sing_1921.htm#SEC1997
864	Template for writing a library sing_55.htm#SEC92
865	TestGRRes sing_2534.htm#SEC2610 8315
866	TestJMark sing_1527.htm#SEC1603 41314
867	The SINGULAR language The SINGULAR language sing_34.htm#SEC56
868	The Tran algorithm sing_1217.htm#IDX547
869	The fractal walk algorithm sing_1216.htm#IDX546
870	The fractal walk algorithm sing_2766.htm#IDX1051
871	The online help system The online help system sing_16.htm#SEC22
872	Tjurina sing_1677.htm#SEC1753 11249
873	Tjurina number Milnor and Tjurina number sing_898.htm#SEC950
874	Tjurina number sing_1313.htm#IDX576
875	Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38
876	Tor sing_1242.htm#SEC1318 sprintf
877	Toric ideals and integer programming Toric ideals and integer programming sing_936.htm#SEC993
878	Tricks and pitfalls sing_408.htm#SEC448
879	Tropical Geometry sing_2073.htm#SEC2149
880	Type casting Type conversion and casting sing_39.htm#SEC69
881	Type conversion Type conversion and casting sing_39.htm#SEC68
882	Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98
883	U_D_O sing_1157.htm#SEC1233 26192
884	Unix installation Unix installation instructions sing_2828.htm#SEC2918
885	UpOneMatrix sing_773.htm#SEC825 63020
886	UpperMonomials sing_1660.htm#SEC1736 20941
887	UseBertini sing_1421.htm#SEC1497 43362
888	User defined types sing_183.htm#SEC223
889	V-filtration sing_1595.htm#IDX670
890	V-filtration sing_1601.htm#IDX698
891	V-filtration sing_1602.htm#IDX704
892	V-filtration sing_1603.htm#IDX712
893	V-filtration sing_1604.htm#IDX718
894	V-filtration sing_1605.htm#IDX726
895	V-filtration sing_1606.htm#IDX736
896	V-filtration sing_1617.htm#IDX742
897	V-filtration sing_1619.htm#IDX753
898	VarToPar sing_2462.htm#SEC2538 10508
899	Variables, indexed sing_37.htm#SEC65
900	Version number Version schema for Singular sing_2821.htm#SEC2905
901	Version schema for Singular Version schema for Singular sing_2821.htm#SEC2905
902	Version string sing_50.htm#SEC87
903	Visualization sing_1827.htm#SEC1903
904	WLemma sing_1006.htm#SEC1082 7302
905	WP, global ordering sing_923.htm#IDX406
906	WSemigroup sing_1577.htm#SEC1653 57449
907	Weierstrass sing_1860.htm#SEC1936 58220
908	Weierstrass semigroup sing_1856.htm#IDX788
909	Weyl sing_758.htm#SEC810 29212
910	Weyl algebra sing_542.htm#IDX332
911	Weyl algebra sing_598.htm#IDX357
912	Weyl closure sing_843.htm#IDX391
913	WeylClosure sing_845.htm#SEC897 23845
914	WeylClosure1 sing_846.htm#SEC898 15759
915	Wibmer's Lemma sing_1006.htm#IDX487
916	Windows installation Windows installation instructions sing_2829.htm#SEC2919
917	WitSet sing_1428.htm#SEC1504 39803
918	WitSupSet sing_1427.htm#SEC1503 47758
919	Ws, local ordering sing_924.htm#IDX418
920	XLsolve sing_1770.htm#SEC1846 34970
921	ZZ sing_28.htm#SEC39
922	ZZ/m sing_28.htm#SEC39
923	ZZ/p sing_28.htm#SEC39
924	ZZsolve sing_1771.htm#SEC1847 18657
925	[ sing_36.htm#IDX83
926	[] sing_142.htm#SEC182
927	[] sing_155.htm#SEC195
928	[] sing_176.htm#SEC216
929	[] sing_181.htm#SEC221
930	\ sing_36.htm#IDX112
931	] sing_36.htm#IDX84
932	^ sing_36.htm#IDX92
933	^ sing_81.htm#SEC121
934	^ sing_93.htm#SEC133
935	^ sing_147.htm#SEC187
936	^ sing_155.htm#SEC195
937	_ sing_36.htm#IDX116
938	` sing_36.htm#IDX105
939	a, ordering sing_928.htm#SEC980
940	absFactorize sing_1170.htm#SEC1246 52546
941	absFactorizeBCG sing_1171.htm#SEC1247 55510
942	absPrimdecGTZ sing_1371.htm#SEC1447 46393
943	absPrimdecGTZE sing_1372.htm#SEC1448 48005
944	absValue sing_968.htm#SEC1044 54595
945	absfact.lib sing_1169.htm#SEC1245
946	absfact_lib sing_1169.htm#SEC1245
947	absolute factorization. sing_1169.htm#IDX518
948	abstract variety, projective space, Grassmannian printVariety sing_2768.htm#IDX1057
949	abstract variety, projective space, Grassmannian sing_2769.htm#IDX1058
950	abstractR sing_1510.htm#SEC1586 22284
951	actionIsProper sing_1740.htm#SEC1816 52474
952	addLeftFractions sing_2728.htm#SEC2804 38826
953	addModules sing_2583.htm#SEC2659 51193
954	addNvarsTo sing_1093.htm#SEC1169 63123
955	addRat sing_864.htm#SEC916 4768
956	addSheaf sing_2787.htm#SEC2863 27062
957	addcol sing_1126.htm#SEC1202 52204
958	addcores sing_1062.htm#SEC1138 41254
959	addnondegeneratevariables addnondegeneratevariables sing_2744.htm#SEC2820 40483
960	addrow sing_1127.htm#SEC1203 47055
961	addvarsTo sing_1092.htm#SEC1168 17717
962	ademRelations sing_689.htm#SEC741 30263
963	adjoint sing_1151.htm#SEC1227 56619
964	adjointIdeal sing_1439.htm#SEC1515 11455
965	adjunction divisor sing_1857.htm#IDX792
966	admissibleSub sing_749.htm#SEC801 6583
967	afaces sing_2487.htm#SEC2563 28045
968	affine code Fitzgerald-Lax method sing_952.htm#SEC1021
969	ainvar.lib sing_1737.htm#SEC1813
970	ainvar_lib sing_1737.htm#SEC1813
971	aksaka.lib sing_1922.htm#SEC1998
972	aksaka_lib sing_1922.htm#SEC1998
973	alexanderpolynomial sing_1535.htm#SEC1611 36814
974	alexpoly.lib sing_1532.htm#SEC1608
975	alexpoly_lib sing_1532.htm#SEC1608
976	algDependent sing_1176.htm#SEC1252 20789
977	alg_kernel sing_1177.htm#SEC1253 307
978	algebra.lib sing_1172.htm#SEC1248
979	algebra_containment sing_1173.htm#SEC1249 47912
980	algebra_lib sing_1172.htm#SEC1248
981	algebraic dependence sing_779.htm#IDX363
982	algebraic field extension sing_1385.htm#IDX585
983	algebraicDependence sing_1398.htm#SEC1474 38500
984	algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_943.htm#SEC1000
985	algorithm of Conti and Traverso sing_939.htm#SEC996
986	algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_942.htm#SEC999
987	algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_941.htm#SEC998
988	algorithm of Pottier sing_940.htm#SEC997
989	alias General command syntax sing_35.htm#SEC59
990	align sing_209.htm#SEC249
991	all.lib sing_961.htm#SEC1037
992	allDoubleExt sing_796.htm#SEC848 43457
993	allExtOfLeft sing_793.htm#SEC845 6405
994	allExtOfRight sing_794.htm#SEC846 56781
995	allPositive sing_518.htm#SEC570 1409
996	all_lib sing_961.htm#SEC1037
997	allowing net access Command line options sing_19.htm#IDX41
998	allprint sing_1010.htm#SEC1086 5195
999	allreal sing_2065.htm#SEC2141 57232
1000	allrealst sing_2063.htm#SEC2139 40962
1001	allsquarefree sing_1639.htm#SEC1715 45545
1002	ambientDimension sing_2078.htm#SEC2154 18907
1003	and Evaluation of logical expressions sing_101.htm#SEC141
1004	and sing_413.htm#SEC453
1005	annPoly sing_566.htm#SEC618 18228
1006	annRat sing_567.htm#SEC619 62662
1007	annRatSyz sing_853.htm#SEC905 15672
1008	annfs sing_543.htm#SEC595 38155
1009	annfs0 sing_555.htm#SEC607 26476
1010	annfs2 sing_556.htm#SEC608 47962
1011	annfsBMI sing_552.htm#SEC604 2532
1012	annfsParamBM sing_551.htm#SEC603 43587
1013	annfsRB sing_557.htm#SEC609 31892
1014	annfspecial sing_544.htm#SEC596 27566
1015	annihilator of polynomial sing_565.htm#IDX342
1016	annihilator of rational function sing_565.htm#IDX343
1017	annihilator of rational function sing_843.htm#IDX394
1018	annil sing_1280.htm#SEC1356 48744
1019	appelF1 sing_584.htm#SEC636 63146
1020	appelF2 sing_585.htm#SEC637 22460
1021	appelF4 sing_586.htm#SEC638 6847
1022	appendWeight2Ord sing_751.htm#SEC803 21488
1023	apply sing_380.htm#SEC420
1024	applyAdF sing_534.htm#SEC586 40329
1025	applyPermutationToIntvec applyPermutationToIntvec sing_2512.htm#SEC2588 28900
1026	arcpoint.lib sing_1545.htm#SEC1621
1027	arcpoint_lib sing_1545.htm#SEC1621
1028	areEqualLeftFractions areEqualLeftFractions sing_2730.htm#SEC2806 29498
1029	areZeroElements sing_2650.htm#SEC2726 14728
1030	argument, default sing_44.htm#SEC81
1031	argument, optional sing_44.htm#SEC81
1032	arr.lib sing_2235.htm#SEC2311
1033	arr2multarr sing_2268.htm#SEC2344 15063
1034	arrBoolean sing_2257.htm#SEC2333 63256
1035	arrBoundedChambers sing_2278.htm#SEC2354 18347
1036	arrBraid sing_2258.htm#SEC2334 34093
1037	arrCenter sing_2245.htm#SEC2321 24565
1038	arrCentered sing_2247.htm#SEC2323 15904
1039	arrCentral sing_2246.htm#SEC2322 14086
1040	arrCentralize sing_2248.htm#SEC2324 53235
1041	arrChambers sing_2277.htm#SEC2353 44578
1042	arrCharPoly sing_2275.htm#SEC2351 44129
1043	arrCone sing_2251.htm#SEC2327 38068
1044	arrCoordChange sing_2249.htm#SEC2325 61430
1045	arrCoordNormalize sing_2250.htm#SEC2326 45861
1046	arrDecone sing_2252.htm#SEC2328 54637
1047	arrDer sing_2265.htm#SEC2341 48815
1048	arrEdelmanReiner sing_2263.htm#SEC2339 59091
1049	arrEssentialize sing_2256.htm#SEC2332 6667
1050	arrExponents sing_2267.htm#SEC2343 1948
1051	arrFlats sing_2272.htm#SEC2348 64792
1052	arrIsEssential sing_2255.htm#SEC2331 34363
1053	arrIsFree sing_2266.htm#SEC2342 3860
1054	arrLastVar sing_2244.htm#SEC2320 25835
1055	arrLattice sing_2273.htm#SEC2349 58951
1056	arrLocalize sing_2253.htm#SEC2329 56070
1057	arrOrlikSolomon sing_2264.htm#SEC2340 31686
1058	arrPoincare sing_2276.htm#SEC2352 412
1059	arrPrintMatrix sing_2240.htm#SEC2316 21204
1060	arrRandom sing_2261.htm#SEC2337 59986
1061	arrRandomCentral sing_2262.htm#SEC2338 43698
1062	arrRestrict sing_2254.htm#SEC2330 sprintf
1063	arrSet sing_2236.htm#SEC2312 53769
1064	arrSwapVar sing_2243.htm#SEC2319 44919
1065	arrTypeB sing_2259.htm#SEC2335 22358
1066	arrTypeD sing_2260.htm#SEC2336 26495
1067	arr_lib sing_2235.htm#SEC2311
1068	arrange sing_559.htm#SEC611 50350
1069	arrangement sing_2236.htm#IDX823
1070	arrangement sing_2237.htm#IDX828
1071	arrangement sing_2268.htm#IDX890
1072	arrangement sing_2269.htm#IDX893
1073	ask sing_1930.htm#SEC2006 3862
1074	assPrimes sing_1187.htm#SEC1263 sprintf
1075	assign sing_2236.htm#IDX825
1076	assignment,custom Assignments for user defined types sing_188.htm#SEC228
1077	associated tangent FamElemsAtEnvCompPoints sing_1003.htm#IDX480
1078	associated tangent sing_1004.htm#IDX484
1079	assprimeszerodim.lib assprimeszerodim_lib sing_1185.htm#SEC1261
1080	assprimeszerodim_lib assprimeszerodim_lib sing_1185.htm#SEC1261
1081	atkins.lib sing_1931.htm#SEC2007
1082	atkins_lib sing_1931.htm#SEC2007
1083	attrib sing_210.htm#SEC250
1084	autGenWeights sing_2311.htm#SEC2387 32642
1085	autGradAlg sing_2310.htm#SEC2386 21136
1086	autKS sing_2309.htm#SEC2385 51607
1087	autX sing_2314.htm#SEC2390 43261
1088	autXhat sing_2313.htm#SEC2389 35932
1089	autgradalg.lib sing_2308.htm#SEC2384
1090	autgradalg_lib sing_2308.htm#SEC2384
1091	automorphism group sing_2308.htm#IDX941
1092	automorphisms sing_2308.htm#IDX938
1093	autonom sing_1894.htm#SEC1970 57044
1094	autonomDim sing_1895.htm#SEC1971 30055
1095	awalk1 sing_1218.htm#SEC1294 11044
1096	awalk2 sing_1219.htm#SEC1295 8955
1097	b-function sing_507.htm#IDX315
1098	bFactor sing_589.htm#SEC641 15179
1099	babyGiant sing_1960.htm#SEC2036 41113
1100	backward sing_2449.htm#SEC2525 11225
1101	bareiss sing_211.htm#SEC251
1102	base2str sing_964.htm#SEC1040 sprintf
1103	basering sing_28.htm#IDX76
1104	basering sing_88.htm#SEC128
1105	basicinvariants sing_1551.htm#SEC1627 32136
1106	baumslagGroup sing_640.htm#SEC692 64086
1107	baumslagSolitar sing_639.htm#SEC691 53837
1108	belongSemigroup sing_1190.htm#SEC1266 19983
1109	bernstein sing_1599.htm#SEC1675 5605
1110	bernsteinBM sing_547.htm#SEC599 57689
1111	bernsteinLift sing_548.htm#SEC600 22885
1112	bertini sing_1414.htm#IDX589
1113	bertini sing_1419.htm#IDX596
1114	bertini2Singular sing_1423.htm#SEC1499 58501
1115	betti sing_212.htm#SEC252
1116	betti (plural) sing_457.htm#SEC497
1117	bfct sing_508.htm#SEC560 29858
1118	bfctAnn sing_510.htm#SEC562 36658
1119	bfctBound sing_852.htm#SEC904 5630
1120	bfctIdeal sing_512.htm#SEC564 41018
1121	bfctOneGB sing_511.htm#SEC563 9696
1122	bfctSyz sing_509.htm#SEC561 26796
1123	bfctVarAnn sing_600.htm#SEC652 51667
1124	bfctVarIn sing_599.htm#SEC651 9274
1125	bfun.lib sing_507.htm#SEC559
1126	bfun_lib sing_507.htm#SEC559
1127	bigint sing_78.htm#SEC118
1128	bigint declarations sing_79.htm#SEC119
1129	bigint expressions sing_80.htm#SEC120
1130	bigint operations sing_81.htm#SEC121
1131	bigint related functions bigint related functions sing_82.htm#SEC122
1132	bigintToBinary sing_2510.htm#SEC2586 59742
1133	bigintmat sing_83.htm#SEC123
1134	bigintmat declarations bigintmat declarations sing_84.htm#SEC124
1135	bigintmat expressions bigintmat expressions sing_85.htm#SEC125
1136	bigintmat operations bigintmat operations sing_87.htm#SEC127
1137	bigintmat type cast sing_86.htm#SEC126
1138	bimodules sing_500.htm#IDX303
1139	bimodules.lib sing_500.htm#SEC552
1140	bimodules_lib sing_500.htm#SEC552
1141	binaryToBigint sing_2511.htm#SEC2587 sprintf
1142	binary_add sing_1983.htm#SEC2059 42817
1143	binomial sing_969.htm#SEC1045 23208
1144	binomials2intmat sing_1346.htm#SEC1422 58804
1145	birational map, image, inverse. sing_1440.htm#IDX621
1146	bistd sing_501.htm#SEC553 45237
1147	bisyzygies sing_500.htm#IDX304
1148	bitrinity sing_502.htm#SEC554 3516
1149	blackbox sing_192.htm#SEC232
1150	blackbox sing_200.htm#SEC240
1151	block sing_40.htm#SEC70
1152	block sing_379.htm#SEC419
1153	blowUp sing_1491.htm#SEC1567 34819
1154	blowUp2 sing_1492.htm#SEC1568 65264
1155	blowUpBO sing_1498.htm#SEC1574 58146
1156	blowup0 sing_1195.htm#SEC1271 44451
1157	boolean sing_2257.htm#IDX867
1158	boolean expressions sing_100.htm#SEC140
1159	boolean operations sing_101.htm#SEC141
1160	boolean_constant sing_2291.htm#SEC2367 52873
1161	boolean_ideal sing_2295.htm#SEC2371 53515
1162	boolean_poly sing_2292.htm#SEC2368 41652
1163	boolean_poly_ring sing_2290.htm#SEC2366 sprintf
1164	boolean_set sing_2296.htm#SEC2372 58235
1165	boolean_std sing_2289.htm#SEC2365 5921
1166	border basis sing_2758.htm#IDX1041
1167	borderBasis sing_2759.htm#SEC2835 33172
1168	boundBuFou sing_2060.htm#SEC2136 26589
1169	boundDes sing_2062.htm#SEC2138 35149
1170	boundaryLatticePoints boundaryLatticePoints sing_2148.htm#SEC2224 6238
1171	boundposDes sing_2061.htm#SEC2137 58854
1172	bounds sing_2746.htm#SEC2822 50218
1173	boxSet sing_2748.htm#SEC2824 8552
1174	bracket sing_359.htm#IDX197
1175	bracket sing_416.htm#SEC456
1176	bracket sing_458.htm#SEC498
1177	braid sing_2258.htm#IDX869
1178	branchTo procs with different argument types sing_160.htm#SEC200
1179	break sing_381.htm#SEC421
1180	break point sing_395.htm#SEC435
1181	breakpoint sing_382.htm#SEC422
1182	brillnoether.lib sing_2315.htm#SEC2391
1183	brillnoether_lib sing_2315.htm#SEC2391
1184	brnoeth.lib sing_1856.htm#SEC1932
1185	brnoeth_lib sing_1856.htm#SEC1932
1186	browser, command line option Command line options sing_19.htm#IDX44
1187	browser, setting the sing_359.htm#IDX193
1188	browsers The online help system sing_16.htm#IDX21
1189	browsers, setting the sing_359.htm#IDX192
1190	bubblesort sing_1933.htm#SEC2009 63278
1191	busadj sing_1149.htm#SEC1225 36301
1192	bvar sing_2303.htm#SEC2379 52773
1193	c, module ordering sing_925.htm#IDX421
1194	cProj sing_2357.htm#SEC2433 24037
1195	calculateI sing_1465.htm#SEC1541 31107
1196	calculate_max_sum sing_2002.htm#SEC2078 4706
1197	calculate_ordering sing_1980.htm#SEC2056 42616
1198	cancelunit, option sing_316.htm#IDX171
1199	canonMap sing_1223.htm#SEC1299 47599
1200	canoncial form sing_991.htm#IDX442
1201	canoncial form sing_992.htm#IDX444
1202	canoncial form sing_993.htm#IDX446
1203	canonical sing_987.htm#IDX430
1204	canonical form sing_996.htm#IDX460
1205	canonical form sing_997.htm#IDX462
1206	canonical, sing_995.htm#IDX456
1207	canonicalizeCone sing_2079.htm#SEC2155 6251
1208	canonize sing_1902.htm#SEC1978 54090
1209	cantoradd sing_2016.htm#SEC2092 55304
1210	cantormult sing_2019.htm#SEC2095 57569
1211	cantorred sing_2017.htm#SEC2093 46502
1212	cardGroup sing_1192.htm#SEC1268 5553
1213	case No case or switch statement sing_414.htm#SEC454
1214	catNets sing_2688.htm#SEC2764 24760
1215	cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2813.htm#SEC2889 55393
1216	cdd sing_1.htm#IDX10
1217	cddlib sing_1.htm#IDX11
1218	center sing_521.htm#IDX322 65108
1219	center sing_527.htm#SEC579
1220	center sing_2245.htm#IDX849
1221	center sing_2246.htm#IDX850
1222	center sing_2247.htm#IDX852
1223	center sing_2248.htm#IDX854
1224	centerRed sing_526.htm#SEC578 59910
1225	centerVS sing_525.htm#SEC577 27548
1226	central sing_2239.htm#IDX835
1227	central sing_2246.htm#IDX851
1228	central sing_2248.htm#IDX853
1229	central sing_2262.htm#IDX878
1230	central.lib sing_521.htm#SEC573
1231	central1st sing_2450.htm#SEC2526 29090
1232	central2nd sing_2451.htm#SEC2527 37545
1233	central_lib sing_521.htm#SEC573
1234	centralize sing_521.htm#IDX325
1235	centralizeSet sing_522.htm#SEC574 55737
1236	centralizer sing_521.htm#IDX323 65261
1237	centralizer sing_528.htm#SEC580
1238	centralizerRed sing_524.htm#SEC576 8209
1239	centralizerVS sing_523.htm#SEC575 22925
1240	cf_class sing_210.htm#IDX132
1241	cgs sing_963.htm#SEC1039 57776
1242	cgsdr sing_988.htm#SEC1064 44460
1243	chAll sing_2327.htm#SEC2403 2690
1244	chAllInv sing_2328.htm#SEC2404 57760
1245	chDual sing_2333.htm#SEC2409 17745
1246	chHE sing_2329.htm#SEC2405 63916
1247	chHom sing_2342.htm#SEC2418 54776
1248	chNum sing_2323.htm#SEC2399 54415
1249	chNumbers sing_2324.htm#SEC2400 42134
1250	chNumbersProj sing_2361.htm#SEC2437 28837
1251	chProd sing_2335.htm#SEC2411 40209
1252	chProdE sing_2336.htm#SEC2412 33460
1253	chProdL sing_2337.htm#SEC2413 44795
1254	chProdLP sing_2338.htm#SEC2414 8881
1255	chProdM sing_2339.htm#SEC2415 64514
1256	chProdMP sing_2340.htm#SEC2416 17103
1257	chProj sing_2358.htm#SEC2434 32311
1258	chSum sing_2331.htm#SEC2407 21088
1259	chSymm sing_2345.htm#SEC2421 24066
1260	chSymm2L sing_2346.htm#SEC2422 51625
1261	chSymm2LP sing_2347.htm#SEC2423 26099
1262	chWedge sing_2348.htm#SEC2424 57678
1263	chWedge2L sing_2349.htm#SEC2425 46597
1264	chWedge2LP sing_2350.htm#SEC2426 8876
1265	chaincrit sing_2030.htm#SEC2106 9502
1266	chambers sing_2277.htm#IDX906
1267	chambers sing_2278.htm#IDX907
1268	changeDenominator sing_1318.htm#SEC1394 21094
1269	changechar sing_1067.htm#SEC1143 65454
1270	changeord sing_1068.htm#SEC1144 55156
1271	changeordTo sing_1091.htm#SEC1167 41903
1272	changes sing_2819.htm#SEC2895
1273	changevar sing_1069.htm#SEC1145 32829
1274	char sing_213.htm#SEC253
1275	charInfo sing_582.htm#SEC634 11034
1276	charVariety sing_581.htm#SEC633 18306
1277	char_series sing_214.htm#SEC254
1278	characteristic exponents sing_1539.htm#IDX645
1279	characteristic exponents sing_1540.htm#IDX650
1280	characteristic exponents sing_1541.htm#IDX653
1281	characteristic exponents sing_1542.htm#IDX657
1282	characteristic exponents sing_1626.htm#IDX763
1283	characteristic polynomial sing_2275.htm#IDX904
1284	characteristic variety sing_565.htm#IDX350
1285	characteristic variety sing_843.htm#IDX390
1286	charexp2conductor sing_1542.htm#SEC1618 sprintf
1287	charexp2generators sing_1540.htm#SEC1616 16838
1288	charexp2inter sing_1541.htm#SEC1617 39881
1289	charexp2multseq sing_1539.htm#SEC1615 334
1290	charexp2poly sing_1543.htm#SEC1619 sprintf
1291	charpoly sing_1150.htm#SEC1226 29561
1292	charstr sing_215.htm#SEC255
1293	checkFactor sing_558.htm#SEC610 55900
1294	checkRoot sing_553.htm#SEC605 37045
1295	chern sing_2322.htm#SEC2398 4916
1296	chern.lib sing_2317.htm#SEC2393
1297	chernCharPoly sing_2364.htm#SEC2440 31610
1298	chernPoly sing_2363.htm#SEC2439 31316
1299	chern_lib sing_2317.htm#SEC2393
1300	chineseRem sing_1951.htm#SEC2027 38560
1301	chinrem sing_216.htm#SEC256
1302	chinrempoly sing_2714.htm#SEC2790 42312
1303	chinrestp sing_2010.htm#SEC2086 24779
1304	cimonom.lib sing_2379.htm#SEC2455
1305	cimonom_lib sing_2379.htm#SEC2455
1306	cisimplicial.lib sing_1188.htm#SEC1264
1307	cisimplicial_lib sing_1188.htm#SEC1264
1308	classification sing_2383.htm#IDX944
1309	classify sing_1552.htm#SEC1628 4953
1310	classify.lib sing_1550.htm#SEC1626
1311	classify2.lib sing_2383.htm#SEC2459
1312	classify2_lib sing_2383.htm#SEC2459
1313	classifyCeq sing_1569.htm#SEC1645 42719
1314	classifyMapGerms.lib classifyMapGerms_lib sing_2395.htm#SEC2471
1315	classifyMapGerms_lib classifyMapGerms_lib sing_2395.htm#SEC2471
1316	classifySimpleMaps sing_2401.htm#SEC2477 62176
1317	classifySimpleMaps1 sing_2402.htm#SEC2478 24789
1318	classifyUnimodalMaps classifyUnimodalMaps sing_2403.htm#SEC2479 63464
1319	classify_aeq.lib sing_2386.htm#SEC2462
1320	classify_aeq_lib sing_2386.htm#SEC2462
1321	classify_lib sing_1550.htm#SEC1626
1322	classifyceq.lib sing_1568.htm#IDX660
1323	classifyceq_lib sing_1568.htm#IDX661
1324	classifyci.lib sing_1570.htm#IDX662
1325	classifyci_lib sing_1570.htm#IDX663
1326	classifyicis sing_1571.htm#SEC1647 37651
1327	classpoly sing_2362.htm#SEC2438 45724
1328	cleanTmp sing_2226.htm#SEC2302 14108
1329	cleanunit sing_1463.htm#SEC1539 sprintf
1330	cleardenom sing_217.htm#SEC257
1331	close sing_218.htm#SEC258
1332	closed_points sing_1866.htm#SEC1942 47269
1333	closetex sing_1833.htm#SEC1909 42334
1334	closureFrac sing_1311.htm#SEC1387 9252
1335	coDim sing_2397.htm#SEC2473 60680
1336	coDimMap sing_2396.htm#SEC2472 2002
1337	coHom sing_802.htm#SEC854 51043
1338	codim sing_1664.htm#SEC1740 14253
1339	codimension sing_2080.htm#SEC2156 32207
1340	coding theory sing_917.htm#SEC969
1341	coef sing_219.htm#SEC259
1342	coefficient sing_2238.htm#IDX831
1343	coefficient sing_2239.htm#IDX834
1344	coefficient sing_2240.htm#IDX838
1345	coefficient field sing_144.htm#SEC184
1346	coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45
1347	coefficients, long sing_874.htm#SEC926
1348	coeffmod sing_1928.htm#SEC2004 23531
1349	coeffs sing_220.htm#SEC260
1350	coker sing_2579.htm#SEC2655 35639
1351	colength of derivations curveColengthDerivations sing_2412.htm#IDX964
1352	collectDiv sing_1508.htm#SEC1584 50348
1353	colrank sing_1900.htm#SEC1976 52290
1354	colred sing_1133.htm#SEC1209 1693
1355	combinat.lib sing_2404.htm#SEC2480
1356	combinat_lib sing_2404.htm#SEC2480
1357	commRing sing_867.htm#SEC919 30892
1358	comma sing_415.htm#SEC455
1359	command,custom Commands for user defined types sing_187.htm#SEC227
1360	command-line option, setting value of sing_359.htm#IDX281
1361	command-line option, value of sing_359.htm#IDX279
1362	command-line options, print all values of sing_359.htm#IDX278
1363	command-line options, short help Command line options sing_19.htm#IDX38
1364	commands (plural) sing_456.htm#IDX302
1365	comment sing_36.htm#IDX108
1366	compareMatrix sing_2587.htm#SEC2663 49930
1367	compareModules sing_2582.htm#SEC2658 3692
1368	compareTasks sing_1098.htm#SEC1174 45157
1369	compareVectors sing_2607.htm#SEC2683 12881
1370	completeReduction sing_1742.htm#SEC1818 57157
1371	complex sing_28.htm#IDX75
1372	complexClassify sing_2384.htm#SEC2460 22796
1373	complexSingType sing_1566.htm#SEC1642 34483
1374	complexType sing_2385.htm#SEC2461 55772
1375	compregb.lib sing_962.htm#SEC1038
1376	compregb_lib sing_962.htm#SEC1038
1377	comprehensive Groebner system sing_962.htm#IDX427
1378	compress sing_1111.htm#SEC1187 61998
1379	computeAfaceOrbits sing_2497.htm#SEC2573 28683
1380	computeConstant sing_1208.htm#SEC1284 55024
1381	computeGromovWitten sing_1211.htm#SEC1287 18834
1382	computeN sing_1512.htm#SEC1588 61628
1383	computeV sing_1511.htm#SEC1587 40316
1384	computemcm sing_1470.htm#SEC1546 36956
1385	concat sing_1112.htm#SEC1188 16653
1386	conductor sing_1319.htm#IDX577
1387	conductor sing_1542.htm#IDX656
1388	conductor sing_2410.htm#IDX958
1389	conductor, degree sing_1626.htm#IDX766
1390	cone sing_189.htm#SEC229
1391	cone sing_2251.htm#IDX858
1392	cone sing_2252.htm#IDX860
1393	coneLink sing_2083.htm#SEC2159 13635
1394	coneViaInequalities sing_2082.htm#SEC2158 25661
1395	coneViaPoints sing_2081.htm#SEC2157 3386
1396	conic, parametrization, rational point. sing_1447.htm#IDX626
1397	conicWithTangents sing_2202.htm#SEC2278 60752
1398	constructH sing_1471.htm#SEC1547 59577
1399	constructblwup sing_1472.htm#SEC1548 19326
1400	constructible set sing_996.htm#IDX458
1401	constructible sets sing_997.htm#IDX461
1402	constructlastblwup sing_1473.htm#SEC1549 7639
1403	constructor sing_2268.htm#IDX891
1404	constructor sing_2269.htm#IDX894
1405	contact matrix sing_1541.htm#IDX652
1406	containedQ sing_1821.htm#SEC1897 46718
1407	containsAsFace sing_2084.htm#SEC2160 25159
1408	containsInCollection containsInCollection sing_2117.htm#SEC2193 14368
1409	containsInSupport sing_2085.htm#SEC2161 32493
1410	containsPositiveVector containsPositiveVector sing_2086.htm#SEC2162 27042
1411	containsRelatively sing_2087.htm#SEC2163 17126
1412	content sing_1041.htm#SEC1117 9095
1413	contentSB, option sing_316.htm#IDX172
1414	continue Behavior of continue sing_383.htm#SEC423
1415	continue sing_417.htm#SEC457
1416	contraHom sing_803.htm#SEC855 54270
1417	contract sing_221.htm#SEC261
1418	contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_2794.htm#IDX1070
1419	contributionBundle sing_2794.htm#SEC2870 32874
1420	contributors sing_359.htm#IDX200
1421	control sing_1892.htm#SEC1968 44498
1422	control.lib sing_1891.htm#SEC1967
1423	controlDim sing_1893.htm#SEC1969 2417
1424	controlExample sing_1905.htm#SEC1981 2678
1425	control_Matrix sing_1594.htm#SEC1670 sprintf
1426	control_lib sing_1891.htm#SEC1967
1427	convertLeftToRightFraction convertLeftToRightFraction sing_2727.htm#SEC2803 4318
1428	convertRightToLeftFraction convertRightToLeftFraction sing_2726.htm#SEC2802 19389
1429	convertdata sing_1468.htm#SEC1544 54629
1430	convexHull sing_2088.htm#SEC2164 56690
1431	convexIntersection sing_2089.htm#SEC2165 63587
1432	convloc sing_562.htm#SEC614 19122
1433	coordinate change sing_2248.htm#IDX855
1434	coordinate change sing_2249.htm#IDX856
1435	coordinate change sing_2250.htm#IDX857
1436	coordinates sing_2048.htm#IDX808
1437	coords sing_2048.htm#SEC2124 29362
1438	copyTask sing_1097.htm#SEC1173 65331
1439	copyright sing_1.htm#IDX1
1440	corank sing_1553.htm#SEC1629 33709
1441	cornerMonomials sing_1349.htm#SEC1425 33995
1442	countPoints sing_1973.htm#SEC2049 58566
1443	coverings sing_1210.htm#IDX536
1444	coverings sing_1211.htm#IDX540
1445	cpu sing_359.htm#IDX202
1446	cpu sing_359.htm#IDX275
1447	createBO sing_1499.htm#SEC1575 32669
1448	createGradedRingHomomorphism createGradedRingHomomorphism sing_2626.htm#SEC2702 62177
1449	createGroup sing_2619.htm#SEC2695 28500
1450	createQuotientGroup sing_2620.htm#SEC2696 26374
1451	createTask sing_1095.htm#SEC1171 48404
1452	createTorsionFreeGroup createTorsionFreeGroup sing_2621.htm#SEC2697 51944
1453	createlist sing_1481.htm#SEC1557 61781
1454	cring sing_73.htm#SEC113
1455	cring declarations sing_74.htm#SEC114
1456	cring expressions sing_75.htm#SEC115
1457	cring operations sing_76.htm#SEC116
1458	cring related functions cring related functions sing_77.htm#SEC117
1459	crossprod sing_222.htm#SEC262
1460	crypto.lib sing_1946.htm#SEC2022
1461	crypto_lib sing_1946.htm#SEC2022
1462	crystallographicGroupC2MM crystallographicGroupC2MM sing_648.htm#SEC700 41262
1463	crystallographicGroupCM crystallographicGroupCM sing_647.htm#SEC699 24754
1464	crystallographicGroupP1 crystallographicGroupP1 sing_641.htm#SEC693 48853
1465	crystallographicGroupP2 crystallographicGroupP2 sing_645.htm#SEC697 35903
1466	crystallographicGroupP2GG crystallographicGroupP2GG sing_646.htm#SEC698 27952
1467	crystallographicGroupP2MM crystallographicGroupP2MM sing_644.htm#SEC696 13909
1468	crystallographicGroupP3 crystallographicGroupP3 sing_652.htm#SEC704 10088
1469	crystallographicGroupP31M crystallographicGroupP31M sing_653.htm#SEC705 31189
1470	crystallographicGroupP3M1 crystallographicGroupP3M1 sing_654.htm#SEC706 1687
1471	crystallographicGroupP4 crystallographicGroupP4 sing_649.htm#SEC701 39932
1472	crystallographicGroupP4GM crystallographicGroupP4GM sing_651.htm#SEC703 52244
1473	crystallographicGroupP4MM crystallographicGroupP4MM sing_650.htm#SEC702 3914
1474	crystallographicGroupP6 crystallographicGroupP6 sing_655.htm#SEC707 38438
1475	crystallographicGroupP6MM crystallographicGroupP6MM sing_656.htm#SEC708 30180
1476	crystallographicGroupPG crystallographicGroupPG sing_643.htm#SEC695 39728
1477	crystallographicGroupPM crystallographicGroupPM sing_642.htm#SEC694 10105
1478	cup sing_1224.htm#SEC1300 57972
1479	cupproduct sing_1225.htm#SEC1301 43349
1480	curve singularities sing_1532.htm#IDX639
1481	curve singularities sing_1620.htm#IDX761
1482	curve singularity sing_2408.htm#IDX953
1483	curveColengthDerivations curveColengthDerivations sing_2412.htm#SEC2488 2078
1484	curveConductorMult sing_2410.htm#SEC2486 15897
1485	curveDeligneNumber sing_2411.htm#SEC2487 12294
1486	curveDeltaInv sing_2409.htm#SEC2485 16375
1487	curveInv.lib sing_2408.htm#SEC2484
1488	curveInv_lib sing_2408.htm#SEC2484
1489	curvepar.lib sing_1573.htm#SEC1649
1490	curvepar_lib sing_1573.htm#SEC1649
1491	custom assignment Assignments for user defined types sing_188.htm#SEC228
1492	custom command Commands for user defined types sing_187.htm#SEC227
1493	custom type Definition of a user defined type sing_184.htm#SEC224
1494	customstd.lib sing_2280.htm#SEC2356
1495	customstd_lib sing_2280.htm#SEC2356
1496	cycleLength sing_2139.htm#SEC2215 16898
1497	cyclePoints sing_2143.htm#SEC2219 54460
1498	cyclic sing_1028.htm#SEC1104 21375
1499	cyclic code Codes and the decoding problem sing_949.htm#SEC1008
1500	cyclotomic sing_1707.htm#SEC1783 33749
1501	datetime sing_223.htm#SEC263 50127
1502	dbprint sing_224.htm#SEC264
1503	deRham.lib sing_2413.htm#SEC2489
1504	deRhamCohom sing_579.htm#SEC631 58222
1505	deRhamCohomIdeal sing_580.htm#SEC632 42169
1506	deRhamCohomology sing_2414.htm#SEC2490 41947
1507	deRham_lib sing_2413.htm#SEC2489
1508	debugLib, option sing_316.htm#IDX176
1509	debug_log sing_1563.htm#SEC1639 62043
1510	debugger Source code debugger sing_66.htm#SEC103
1511	debugging library code Source code debugger sing_66.htm#SEC103
1512	dec1var sing_1279.htm#SEC1355 36098
1513	decimal sing_1947.htm#SEC2023 56066
1514	decode sing_1883.htm#SEC1959 64330
1515	decodeCode sing_1885.htm#SEC1961 28262
1516	decodeRandom sing_1884.htm#SEC1960 40118
1517	decodeRandomFL sing_1888.htm#SEC1964 35423
1518	decodeSV sing_1865.htm#SEC1941 37975
1519	decodegb.lib sing_1870.htm#SEC1946
1520	decodegb_lib sing_1870.htm#SEC1946
1521	decoding, decoding problem Codes and the decoding problem sing_949.htm#SEC1009
1522	decoef sing_1913.htm#SEC1989 60284
1523	decomposition of modules sing_1272.htm#IDX565
1524	decomposition, numerical sing_1419.htm#IDX594
1525	decone sing_2251.htm#IDX859
1526	decone sing_2252.htm#IDX861
1527	def sing_88.htm#SEC128
1528	def declarations sing_89.htm#SEC129
1529	defRes, option sing_316.htm#IDX177
1530	default argument sing_44.htm#SEC81
1531	defineHomogeneous sing_2659.htm#SEC2735 55072
1532	defined sing_225.htm#SEC265
1533	defl sing_1430.htm#SEC1506 11825
1534	deform sing_1665.htm#SEC1741 5250
1535	deform.lib sing_1584.htm#SEC1660
1536	deform_lib sing_1584.htm#SEC1660
1537	defring sing_1070.htm#SEC1146 1814
1538	defringp sing_1072.htm#SEC1148 42905
1539	defrings sing_1071.htm#SEC1147 1034
1540	deg sing_226.htm#SEC266
1541	degBound sing_397.htm#SEC437
1542	degree Miscellaneous oddities sing_227.htm#SEC267
1543	degree sing_420.htm#IDX292
1544	degree lexicographical ordering sing_923.htm#IDX401
1545	degree of a polynomial Miscellaneous oddities sing_420.htm#IDX296
1546	degree reverse lexicographical ordering sing_923.htm#IDX399
1547	degreeDivisor sing_2424.htm#SEC2500 31751
1548	degreeFormalDivisor sing_2432.htm#SEC2508 42503
1549	degreepart sing_1773.htm#SEC1849 53036
1550	delete sing_126.htm#SEC166
1551	delete sing_228.htm#SEC268
1552	delete sing_277.htm#SEC317
1553	deleteGenerator sing_594.htm#SEC646 24917
1554	deleteSublist sing_970.htm#SEC1046 20406
1555	deligne number curveColengthDerivations sing_2408.htm#IDX955
1556	deligne number sing_2411.htm#IDX960
1557	deligne number sing_2412.htm#IDX962
1558	delta sing_1632.htm#SEC1708 56952
1559	delta invariant sing_1313.htm#IDX575
1560	delta invariant sing_1632.htm#IDX771
1561	delta invariant sing_2409.htm#IDX956
1562	delta invariant. sing_1305.htm#IDX568
1563	delta invariant. sing_1306.htm#IDX571
1564	delta invariant. sing_1307.htm#IDX574
1565	deltaLoc sing_1313.htm#SEC1389 35192
1566	denom_list sing_359.htm#IDX204
1567	denominator sing_229.htm#SEC269
1568	depth sing_1226.htm#SEC1302 17777
1569	depthIdeal sing_1289.htm#SEC1365 54782
1570	derivate sing_1739.htm#SEC1815 15409
1571	derivation sing_2265.htm#IDX882
1572	desingularization sing_2516.htm#IDX995 59041
1573	desingularization sing_2517.htm#SEC2593
1574	det sing_230.htm#SEC270
1575	det_B sing_1152.htm#SEC1228 60143
1576	detadj sing_1648.htm#SEC1724 5914
1577	determinacy sing_2743.htm#SEC2819 44818
1578	determinecenter sing_1453.htm#SEC1529 44496
1579	detropicalise sing_2220.htm#SEC2296 38025
1580	develop sing_1622.htm#SEC1698 48457
1581	diag sing_1113.htm#SEC1189 56759
1582	diagInvariants sing_1328.htm#SEC1404 62096
1583	diag_test sing_1148.htm#SEC1224 31469
1584	diff sing_231.htm#SEC271
1585	diffRat sing_866.htm#SEC918 36134
1586	difpoly2tex sing_1914.htm#SEC1990 6451
1587	dim sing_232.htm#SEC272
1588	dim (plural) sing_459.htm#SEC499
1589	dimGradedPart sing_1521.htm#SEC1597 11262
1590	dimH sing_1520.htm#SEC1596 38534
1591	dimMon sing_1269.htm#SEC1345 39971
1592	dimStack sing_2792.htm#SEC2868 47772
1593	dim_slocus sing_1666.htm#SEC1742 47218
1594	dimension sing_2090.htm#SEC2166 35262
1595	dimension, moduli space of stable maps, rational curves dimStack sing_2792.htm#IDX1068
1596	dimensionOfLocalization dimensionOfLocalization sing_2480.htm#SEC2556 25632
1597	direct_boolean_poly sing_2293.htm#SEC2369 49893
1598	direct_from_boolean_poly direct_from_boolean_poly sing_2299.htm#SEC2375 36941
1599	disc sing_1934.htm#SEC2010 45279
1600	discr sing_1688.htm#SEC1764 9642
1601	discrepancy sing_1506.htm#SEC1582 5597
1602	discrim sing_1005.htm#SEC1081 44091
1603	discussion of parametric ideal sing_987.htm#IDX431
1604	disjoint sing_988.htm#IDX433
1605	disp_zdd sing_2306.htm#SEC2382 41439
1606	displayCohom sing_1522.htm#SEC1598 22633
1607	displayHNE sing_1625.htm#SEC1701 29845
1608	displayInvariants sing_1627.htm#SEC1703 13678
1609	displayMultsequence sing_1629.htm#SEC1705 16668
1610	displayPuiseuxExpansion displayPuiseuxExpansion sing_2195.htm#SEC2271 560
1611	displayTropicalLifting displayTropicalLifting sing_2193.htm#SEC2269 28144
1612	distributed computing sing_1021.htm#IDX498
1613	distributed computing sing_1061.htm#IDX500
1614	distributed computing sing_1094.htm#IDX510
1615	div Miscellaneous oddities sing_81.htm#SEC121
1616	div sing_98.htm#SEC138
1617	div sing_155.htm#SEC195
1618	div sing_420.htm#IDX289
1619	divideUnits sing_1910.htm#SEC1986 26711
1620	dividelist sing_1480.htm#SEC1556 34210
1621	division sing_233.htm#SEC273
1622	division sing_989.htm#IDX436
1623	division sing_990.htm#IDX438
1624	division (plural) sing_460.htm#SEC500
1625	divisor sing_2013.htm#SEC2089 47231
1626	divisorplus sing_2418.htm#SEC2494 34248
1627	divisors negativeformaldivisor sing_2417.htm#IDX965
1628	divisors sing_2418.htm#IDX966
1629	divisors sing_2419.htm#IDX967
1630	divisors sing_2420.htm#IDX968
1631	divisors sing_2421.htm#IDX969
1632	divisors sing_2422.htm#IDX970
1633	divisors sing_2423.htm#IDX971
1634	divisors sing_2424.htm#IDX972
1635	divisors sing_2425.htm#IDX973
1636	divisors sing_2426.htm#IDX974
1637	divisors sing_2427.htm#IDX975
1638	divisors sing_2428.htm#IDX976
1639	divisors sing_2429.htm#IDX977
1640	divisors sing_2430.htm#IDX978
1641	divisors sing_2431.htm#IDX979
1642	divisors sing_2432.htm#IDX980
1643	divisors, polyhedra sing_2433.htm#IDX981
1644	divisors, polyhedra sing_2434.htm#IDX982
1645	divisors, polyhedra sing_2435.htm#IDX983
1646	divisors.lib sing_2416.htm#SEC2492
1647	divisors_lib sing_2416.htm#SEC2492
1648	dmod.lib sing_542.htm#SEC594
1649	dmodAction sing_861.htm#SEC913 9763
1650	dmodActionRat sing_862.htm#SEC914 6277
1651	dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_854.htm#SEC906 44337
1652	dmod_lib sing_542.htm#SEC594
1653	dmodapp.lib sing_565.htm#SEC617
1654	dmodapp_lib sing_565.htm#SEC617
1655	dmodloc.lib sing_843.htm#IDX383
1656	dmodloc_lib sing_843.htm#IDX384
1657	dmodoublext sing_804.htm#SEC856 60637
1658	dmodvar.lib sing_598.htm#SEC650
1659	dmodvar_lib sing_598.htm#SEC650
1660	double sing_2018.htm#SEC2094 34697
1661	doubleExt sing_795.htm#SEC847 56896
1662	downloading Download instructions sing_2827.htm#SEC2917
1663	dp, global ordering sing_923.htm#IDX400
1664	drawNewtonSubdivision drawNewtonSubdivision sing_2198.htm#SEC2274 50904
1665	drawTropicalCurve sing_2197.htm#SEC2273 10441
1666	ds, local ordering sing_924.htm#IDX410
1667	dsum sing_1114.htm#SEC1190 1303
1668	dualCone sing_2091.htm#SEC2167 61460
1669	dualConic sing_2222.htm#SEC2298 31080
1670	dualPart sing_2370.htm#SEC2446 13279
1671	dualPartition sing_2805.htm#SEC2881 24739
1672	dualPolytope sing_2130.htm#SEC2206 32081
1673	dualSheaf sing_2783.htm#SEC2859 633
1674	dual_code sing_1867.htm#SEC1943 57229
1675	dump sing_234.htm#SEC274
1676	dyckGroup1 sing_657.htm#SEC709 62819
1677	dyckGroup2 sing_658.htm#SEC710 13793
1678	dyckGroup3 sing_659.htm#SEC711 42596
1679	dynamic geometry sing_998.htm#IDX465
1680	dynamic geometry sing_999.htm#IDX468
1681	ecart sing_2021.htm#SEC2097 32475
1682	echo sing_398.htm#SEC438
1683	eexgcdN sing_1948.htm#SEC2024 53237
1684	effective sing_2426.htm#SEC2502 53028
1685	egcdMain sing_1814.htm#SEC1890 25359
1686	ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2149.htm#SEC2225 38271
1687	ehrhartRing sing_1324.htm#SEC1400 16966
1688	eigenvals sing_1160.htm#SEC1236 11228
1689	eigenvalue sing_329.htm#SEC369
1690	eigenvalue sing_1160.htm#IDX516
1691	eigenvalues sing_1407.htm#SEC1483 2182
1692	elemSymmId sing_1029.htm#SEC1105 sprintf
1693	elim sing_1197.htm#SEC1273 62585
1694	elim.lib sing_1194.htm#SEC1270
1695	elim1 sing_1198.htm#SEC1274 15653
1696	elim2 sing_1199.htm#SEC1275 44749
1697	elimRing sing_1196.htm#SEC1272 12194
1698	elimWeight sing_752.htm#SEC804 54297
1699	elim_lib sing_1194.htm#SEC1270
1700	eliminate sing_235.htm#SEC275
1701	eliminate (plural) sing_461.htm#SEC501
1702	eliminateNC sing_747.htm#SEC799 3777
1703	elimination sing_746.htm#IDX362
1704	elimlinearpart sing_1774.htm#SEC1850 14251
1705	elimpart sing_1775.htm#SEC1851 10258
1706	elimpartanyr sing_1776.htm#SEC1852 39751
1707	elimrep sing_1461.htm#SEC1537 23641
1708	elliptic curve sing_1207.htm#IDX532
1709	elliptic curves sing_1204.htm#IDX526
1710	elliptic curves sing_1210.htm#IDX535
1711	elliptic curves sing_1211.htm#IDX539
1712	ellipticAdd sing_1969.htm#SEC2045 13279
1713	ellipticAllPoints sing_1974.htm#SEC2050 60770
1714	ellipticMult sing_1970.htm#SEC2046 1558
1715	ellipticNF sing_2146.htm#SEC2222 5045
1716	ellipticNFDB sing_2147.htm#SEC2223 27917
1717	ellipticRandomCurve sing_1971.htm#SEC2047 36980
1718	ellipticRandomPoint sing_1972.htm#SEC2048 6866
1719	ellipticcovers.lib sing_1204.htm#IDX520
1720	ellipticcovers_lib sing_1204.htm#IDX521
1721	else sing_388.htm#SEC428
1722	embedMat sing_778.htm#SEC830 17119
1723	emptyFan sing_2118.htm#SEC2194 7396
1724	encode sing_1875.htm#SEC1951 56687
1725	endomorphism filtration sing_1606.htm#IDX737
1726	endvfilt sing_1606.htm#SEC1682 26670
1727	engine sing_595.htm#SEC647 30876
1728	ensureLeftNcfrac sing_2676.htm#SEC2752 64571
1729	ensureRightNcfrac sing_2677.htm#SEC2753 14107
1730	envelop FamElemsAtEnvCompPoints sing_1000.htm#SEC1076 27362
1731	envelop sing_1000.htm#IDX471
1732	envelop sing_1001.htm#IDX474
1733	envelop sing_1003.htm#IDX479
1734	envelop sing_1004.htm#IDX483
1735	envelope sing_462.htm#SEC502
1736	enveloping algebra sing_359.htm#IDX208
1737	enveloping algebra sing_500.htm#IDX306
1738	environment variable, DISPLAY The online help system sing_16.htm#IDX29
1739	equalJinI sing_1549.htm#SEC1625 18502
1740	equalMultiDeg sing_2652.htm#SEC2728 37090
1741	equations sing_2092.htm#SEC2168 7896
1742	equiRadical sing_1365.htm#SEC1441 8884
1743	equidim sing_1367.htm#SEC1443 38541
1744	equidimMax sing_1368.htm#SEC1444 49289
1745	equidimMaxEHV sing_1369.htm#SEC1445 42650
1746	equidimZ sing_1380.htm#SEC1456 49610
1747	equising.lib sing_1589.htm#SEC1665
1748	equising_lib sing_1589.htm#SEC1665
1749	equisingular Tjurina number sing_1532.htm#IDX644
1750	equisingularity ideal sing_1591.htm#IDX664
1751	equisingularity stratum sing_1592.htm#IDX665
1752	error recovery sing_15.htm#SEC21
1753	errorInsert sing_1878.htm#SEC1954 59470
1754	errorRand sing_1879.htm#SEC1955 5727
1755	errormap sing_2456.htm#SEC2532 7782
1756	esIdeal sing_1591.htm#SEC1667 60477
1757	esStratum sing_1592.htm#SEC1668 50094
1758	essential sing_2255.htm#IDX864
1759	essential sing_2256.htm#IDX865
1760	eta sing_2141.htm#SEC2217 60729
1761	euler sing_1927.htm#SEC2003 10519
1762	eulerChProj sing_2360.htm#SEC2436 28549
1763	eval sing_236.htm#SEC276
1764	evalJacobianAtBox sing_2754.htm#SEC2830 42716
1765	evalPolyAtBox sing_2753.htm#SEC2829 43040
1766	evaluateFormalDivisor evaluateFormalDivisor sing_2428.htm#SEC2504 3535
1767	evaluatePDivisor sing_2434.htm#SEC2510 18855
1768	evaluateProduct sing_2507.htm#SEC2583 54515
1769	evaluate_reynolds sing_1712.htm#SEC1788 46353
1770	evalutateIntegral sing_1209.htm#SEC1285 sprintf
1771	example sing_238.htm#SEC278
1772	example sing_2257.htm#IDX866
1773	example sing_2258.htm#IDX868
1774	example sing_2259.htm#IDX870
1775	example sing_2260.htm#IDX872
1776	example sing_2261.htm#IDX874
1777	example sing_2262.htm#IDX876
1778	example sing_2263.htm#IDX879
1779	execute sing_239.htm#SEC279
1780	exit sing_392.htm#SEC432
1781	exp2pt sing_1915.htm#SEC1991 19621
1782	expo sing_1939.htm#SEC2015 8833
1783	exponents sing_2267.htm#IDX887
1784	export sing_385.htm#SEC425
1785	exportNuminvs sing_1332.htm#SEC1408 10423
1786	exportto sing_386.htm#SEC426
1787	expp sing_2803.htm#SEC2879 15751
1788	expression list sing_72.htm#IDX128
1789	expression list sing_424.htm#IDX299
1790	ext-module purityfiltration_lib sing_787.htm#IDX368
1791	extcurve sing_1861.htm#SEC1937 6730
1792	extdevelop sing_1623.htm#SEC1699 51044
1793	extendGC sing_995.htm#SEC1071 40951
1794	extendWeyl sing_855.htm#SEC907 49954
1795	extendedTensor sing_753.htm#SEC805 4975
1796	extendpoly sing_994.htm#SEC1070 29201
1797	extendring sing_1073.htm#SEC1149 64781
1798	extension of rings sing_1385.htm#IDX586
1799	exterior basis sing_1139.htm#IDX513
1800	exterior power sing_1141.htm#IDX515
1801	exteriorBasis sing_1139.htm#SEC1215 sprintf
1802	exteriorPower sing_1141.htm#SEC1217 20173
1803	extgcd sing_240.htm#SEC280
1804	fVector sing_2121.htm#SEC2197 3715
1805	fVectorP sing_2150.htm#SEC2226 31843
1806	facFirstShift sing_740.htm#SEC792 6469
1807	facFirstWeyl sing_736.htm#SEC788 42412
1808	facGBIdeal sing_1350.htm#SEC1426 9924
1809	facShift sing_739.htm#SEC791 48551
1810	facSubWeyl sing_738.htm#SEC790 9630
1811	facWeyl sing_735.htm#SEC787 32331
1812	faceContaining sing_2093.htm#SEC2169 64804
1813	facetVertexLatticeDistances facetVertexLatticeDistances sing_2151.htm#SEC2227 60714
1814	facetWidth sing_2152.htm#SEC2228 62810
1815	facetWidths sing_2153.htm#SEC2229 5503
1816	facets sing_2094.htm#SEC2170 8112
1817	facstd sing_241.htm#SEC281
1818	factmodd sing_242.htm#SEC282
1819	factor sing_323.htm#SEC363
1820	factorH sing_985.htm#SEC1061 24814
1821	factorLenstraECM sing_1978.htm#SEC2054 54951
1822	factorMain sing_1815.htm#SEC1891 65152
1823	factorgroup sing_2642.htm#SEC2718 59914
1824	factorial sing_971.htm#SEC1047 32871
1825	factorization sing_324.htm#SEC364
1826	factorization sing_1169.htm#IDX517
1827	factorize sing_243.htm#SEC283
1828	factorize sing_323.htm#SEC363
1829	factory sing_1.htm#IDX2
1830	fan sing_190.htm#SEC230
1831	fan sing_2133.htm#IDX813
1832	fanViaCones sing_2119.htm#SEC2195 16418
1833	farey sing_244.htm#SEC284
1834	fareypoly sing_2437.htm#SEC2513 12389
1835	fastExpt sing_1923.htm#SEC1999 43912
1836	fastHC, option sing_316.htm#IDX153
1837	fastelim sing_1777.htm#SEC1853 7409
1838	fetch sing_245.htm#SEC285
1839	fetch (plural) sing_463.htm#SEC503
1840	fetchall sing_1074.htm#SEC1150 7537
1841	ffmodStd sing_2441.htm#SEC2517 50680
1842	ffmodstd.lib sing_2436.htm#SEC2512
1843	ffmodstd_lib sing_2436.htm#SEC2512
1844	ffsolve sing_1766.htm#SEC1842 20432
1845	ffsolve.lib sing_1765.htm#SEC1841
1846	ffsolve_lib sing_1765.htm#SEC1841
1847	fglm sing_246.htm#SEC286
1848	fglm sing_356.htm#IDX187
1849	fglm_solve sing_1793.htm#SEC1869 51398
1850	fglmquot sing_247.htm#SEC287
1851	fibonacci sing_972.htm#SEC1048 24750
1852	fibonacciGroup sing_660.htm#SEC712 25145
1853	field sing_144.htm#SEC184
1854	file, .singularrc sing_20.htm#IDX71
1855	filecmd sing_248.htm#SEC288
1856	filtration purityfiltration_lib sing_787.htm#IDX369
1857	finalCharts sing_1485.htm#SEC1561 37296
1858	find sing_249.htm#SEC289
1859	findAuto sing_694.htm#SEC746 51205
1860	findInvo sing_692.htm#SEC744 18177
1861	findInvoDiag sing_693.htm#SEC745 7365
1862	findOrientedBoundary findOrientedBoundary sing_2142.htm#SEC2218 24110
1863	findTorsion sing_1904.htm#SEC1980 29572
1864	find_first_primitive_root find_first_primitive_root sing_1982.htm#SEC2058 33327
1865	find_index sing_1986.htm#SEC2062 62564
1866	findifs.lib sing_1911.htm#SEC1987
1867	findifs_example sing_1912.htm#SEC1988 33849
1868	findifs_lib sing_1911.htm#SEC1987
1869	findimAlgebra sing_762.htm#SEC814 64612
1870	finduni sing_250.htm#SEC290
1871	findvars sing_1778.htm#SEC1854 54503
1872	finite field sing_144.htm#SEC184
1873	finite field sing_1765.htm#IDX786
1874	finiteDiagInvariants finiteDiagInvariants sing_1327.htm#SEC1403 3508
1875	finitediff.lib sing_2442.htm#IDX984
1876	finitediff_lib sing_2442.htm#IDX985
1877	finitenessTest sing_1183.htm#SEC1259 40633
1878	finvar.lib sing_1700.htm#SEC1776
1879	finvar_lib sing_1700.htm#SEC1776
1880	first index is 1 sing_419.htm#SEC459
1881	firstoct sing_1826.htm#SEC1902 11498
1882	fitting sing_1229.htm#SEC1305 20661
1883	fixed points, moduli space of stable maps, graph fixedPoints sing_2793.htm#IDX1069
1884	fixedPoints sing_2793.htm#SEC2869 25366
1885	fl2poly sing_592.htm#SEC644 51682
1886	flatten sing_1115.htm#SEC1191 58972
1887	flatteningStrat sing_1230.htm#SEC1306 15622
1888	floating point sing_1083.htm#IDX503
1889	for sing_387.htm#SEC427
1890	formal linear representations sing_807.htm#IDX379
1891	formaldivisorplus sing_2429.htm#SEC2505 31959
1892	forward sing_2448.htm#SEC2524 15383
1893	fourier sing_587.htm#SEC639 5326
1894	fouriersystem sing_2459.htm#SEC2535 43681
1895	fpadim.lib sing_603.htm#SEC655
1896	fpadim_lib sing_603.htm#SEC655
1897	fpalgebras.lib sing_637.htm#SEC689
1898	fpalgebras_lib sing_637.htm#SEC689
1899	fpaprops.lib sing_663.htm#SEC715
1900	fpaprops_lib sing_663.htm#SEC715
1901	fprintf sing_252.htm#SEC292 13662
1902	fracStatus sing_2722.htm#SEC2798 14582
1903	framed sheaves sing_2466.htm#IDX992
1904	frandwalk sing_2766.htm#SEC2842 25555
1905	free sing_2266.htm#IDX884
1906	free sing_2267.htm#IDX886
1907	free associative algebra, tensor algebra Free associative algebras sing_494.htm#SEC546
1908	freeGBasis sing_677.htm#SEC729 43055
1909	freeModule sing_2559.htm#SEC2635 34173
1910	freeModule2Module sing_2588.htm#SEC2664 15296
1911	freegb.lib sing_672.htm#SEC724
1912	freegb_lib sing_672.htm#SEC724
1913	freemodule sing_253.htm#SEC293
1914	freerank sing_1031.htm#SEC1107 52218
1915	fres sing_254.htm#SEC294
1916	from_boolean_constant from_boolean_constant sing_2297.htm#SEC2373 44881
1917	from_boolean_ideal sing_2301.htm#SEC2377 62698
1918	from_boolean_poly sing_2298.htm#SEC2374 27864
1919	from_boolean_set sing_2302.htm#SEC2378 60615
1920	frwalk sing_255.htm#SEC295
1921	full representation sing_994.htm#IDX452
1922	full representation sing_995.htm#IDX457
1923	fullDimImages sing_2488.htm#SEC2564 20094
1924	fullFan sing_2120.htm#SEC2196 7534
1925	fullSerreRelations sing_687.htm#SEC739 27691
1926	fullSpace sing_2075.htm#SEC2151 19485
1927	furtherInvar sing_1744.htm#SEC1820 19209
1928	further_hn_proc sing_1640.htm#SEC1716 63500
1929	fwalk sing_1216.htm#SEC1292 15070
1930	galois field sing_144.htm#SEC184
1931	gauss_col sing_1124.htm#SEC1200 36252
1932	gauss_nf sing_1155.htm#SEC1231 51060
1933	gauss_row sing_1125.htm#SEC1201 58877
1934	gaussred sing_1153.htm#SEC1229 29001
1935	gaussred_pivot sing_1154.htm#SEC1230 25477
1936	gcd sing_256.htm#SEC296
1937	gcdMon sing_1258.htm#SEC1334 42448
1938	gcddivisor sing_2014.htm#SEC2090 1276
1939	gen sing_257.htm#SEC297
1940	genMDSMat sing_1881.htm#SEC1957 3347
1941	genSymId sing_1404.htm#SEC1480 17521
1942	general error-locator polynomial sing_950.htm#SEC1015
1943	general neron. sing_2516.htm#IDX996
1944	general weighted lexicographical ordering sing_924.htm#IDX416
1945	general weighted reverse lexicographical ordering Local orderings sing_924.htm#IDX413
1946	general.lib sing_965.htm#SEC1041
1947	generalOrder sing_2039.htm#SEC2115 42536
1948	general_lib sing_965.htm#SEC1041
1949	generateG sing_1977.htm#SEC2053 51697
1950	generators sing_1540.htm#IDX648
1951	generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2095.htm#SEC2171 4454
1952	generatorsOfSpan sing_2096.htm#SEC2172 40297
1953	generic representation sing_994.htm#IDX451
1954	genericid sing_1049.htm#SEC1125 29731
1955	genericity sing_1901.htm#SEC1977 16822
1956	genericmat sing_1116.htm#SEC1192 35016
1957	genoutput sing_1474.htm#SEC1550 18973
1958	genus sing_1309.htm#SEC1385 sprintf
1959	geometrical locus FamElemsAtEnvCompPoints sing_998.htm#IDX463
1960	geometrical locus sing_999.htm#IDX466
1961	geometrical locus sing_1000.htm#IDX469
1962	geometrical locus sing_1001.htm#IDX472
1963	geometrical locus sing_1002.htm#IDX475
1964	geometrical locus sing_1003.htm#IDX477
1965	geometrical locus sing_1004.htm#IDX481
1966	getArguments sing_1106.htm#SEC1182 14254
1967	getCommand sing_1105.htm#SEC1181 32181
1968	getCone sing_2122.htm#SEC2198 41394
1969	getGradingGroup sing_2617.htm#SEC2693 18137
1970	getLattice sing_2618.htm#SEC2694 7775
1971	getLinearForms sing_2097.htm#SEC2173 47590
1972	getModuleGrading sing_2628.htm#SEC2704 43451
1973	getMultiplicity sing_2098.htm#SEC2174 639
1974	getOneVar sing_1317.htm#SEC1393 55402
1975	getResult sing_1107.htm#SEC1183 51722
1976	getSmallest sing_1316.htm#SEC1392 1623
1977	getState sing_1108.htm#SEC1184 36453
1978	getVariableWeights sing_2616.htm#SEC2692 9591
1979	getcores sing_1064.htm#SEC1140 30785
1980	getdump sing_258.htm#SEC298
1981	getenv sing_359.htm#IDX211
1982	gfan.lib sing_2074.htm#SEC2150
1983	gfan_lib sing_2074.htm#SEC2150
1984	gfanlib sing_1.htm#IDX9
1985	gitCone sing_2515.htm#SEC2591 23853
1986	gitfan.lib sing_2485.htm#SEC2561
1987	gitfan_lib sing_2485.htm#SEC2561
1988	gkdim.lib sing_699.htm#SEC751
1989	gkdim_lib sing_699.htm#SEC751
1990	global sing_210.htm#IDX133
1991	global Bernstein-Sato polynomial sing_507.htm#IDX313
1992	global Bernstein-Sato polynomial sing_542.htm#IDX331
1993	global Bernstein-Sato polynomial for variety sing_598.htm#IDX356
1994	globalSections sing_2423.htm#SEC2499 55191
1995	gmscoeffs sing_1598.htm#SEC1674 13182
1996	gmsnf sing_1597.htm#SEC1673 44676
1997	gmspoly.lib sing_1617.htm#SEC1693
1998	gmspoly_lib sing_1617.htm#SEC1693
1999	gmsring sing_1596.htm#SEC1672 59438
2000	gmssing.lib sing_1595.htm#SEC1671
2001	gmssing_lib sing_1595.htm#SEC1671
2002	goettsche.lib sing_2466.htm#SEC2542
2003	goettsche_lib sing_2466.htm#SEC2542
2004	good basis sing_1595.htm#IDX676
2005	good basis sing_1605.htm#IDX731
2006	good basis sing_1617.htm#IDX747
2007	good basis sing_1619.htm#IDX758
2008	goodBasis sing_1619.htm#SEC1695 41606
2009	gorensteinIndex sing_2154.htm#SEC2230 52919
2010	gorensteinVector sing_2155.htm#SEC2231 50407
2011	graal.lib sing_2478.htm#SEC2554
2012	graalMixed sing_2479.htm#SEC2555 6401
2013	graal_lib sing_2478.htm#SEC2554
2014	gradeNumber sing_791.htm#SEC843 29956
2015	graded Weyl algebra sing_507.htm#IDX316
2016	graded algebra sing_2308.htm#IDX939
2017	graded module, graded piece sing_1521.htm#IDX634
2018	graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2518.htm#IDX997
2019	graded modules, handling of Handling graded modules sing_889.htm#SEC941
2020	graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2556.htm#IDX999
2021	gradedModules.lib sing_2518.htm#SEC2594
2022	gradedModules_lib sing_2518.htm#SEC2594
2023	gradiator sing_2661.htm#SEC2737 53802
2024	graph sing_1205.htm#IDX530
2025	graph sing_1206.htm#IDX531
2026	graph sing_2788.htm#IDX1064
2027	graph sing_2789.htm#IDX1065
2028	graphics.lib sing_1828.htm#SEC1904
2029	graphics_lib sing_1828.htm#SEC1904
2030	graphviz sing_1.htm#IDX13
2031	graver4ti2 sing_1402.htm#SEC1478 39635
2032	grconcat sing_2541.htm#SEC2617 16754
2033	grdeg sing_2521.htm#SEC2597 22879
2034	grgens sing_2530.htm#SEC2606 12823
2035	grgroebner sing_2540.htm#SEC2616 29288
2036	grlift sing_2538.htm#SEC2614 21656
2037	grlifting sing_2545.htm#SEC2621 51177
2038	grlifting2 sing_2546.htm#SEC2622 59011
2039	grlifting3 sing_2548.htm#SEC2624 6369
2040	grneg sing_2551.htm#SEC2627 64584
2041	grobcov sing_987.htm#SEC1063 40493
2042	grobcov.lib sing_986.htm#SEC1062
2043	grobcov_lib sing_986.htm#SEC1062
2044	grobj sing_2519.htm#SEC2595 18115
2045	groebner sing_259.htm#SEC299 53038
2046	groebner sing_881.htm#SEC933
2047	groebner basis computations sing_259.htm#IDX147
2048	groebnerComplex sing_2233.htm#SEC2309 2421
2049	groebnerCone sing_2227.htm#SEC2303 58776
2050	groebnerFan sing_2232.htm#SEC2308 48157
2051	gromovWitten sing_1210.htm#SEC1286 28559
2052	grorder sing_2532.htm#SEC2608 20857
2053	ground field sing_144.htm#SEC184
2054	groupActionOnHashes sing_2503.htm#SEC2579 406
2055	groupActionOnQImage sing_2502.htm#SEC2578 53270
2056	group_reynolds sing_1708.htm#SEC1784 35079
2057	grpower sing_2528.htm#SEC2604 3960
2058	grpres sing_2531.htm#SEC2607 18145
2059	grprod sing_2539.htm#SEC2615 41525
2060	grrange sing_2550.htm#SEC2626 41835
2061	grres sing_2537.htm#SEC2613 35795
2062	grrndmap sing_2543.htm#SEC2619 4054
2063	grrndmap2 sing_2544.htm#SEC2620 50536
2064	grrndmat sing_2542.htm#SEC2618 42634
2065	grshift sing_2523.htm#SEC2599 1415
2066	grsum sing_2527.htm#SEC2603 60602
2067	grsyz sing_2536.htm#SEC2612 61843
2068	grtest sing_2520.htm#SEC2596 62577
2069	grtranspose sing_2529.htm#SEC2605 13865
2070	grtranspose1 sing_2533.htm#SEC2609 3637
2071	grtwist sing_2525.htm#SEC2601 10498
2072	grtwists sing_2526.htm#SEC2602 56638
2073	grview sing_2522.htm#SEC2598 6878
2074	grwalk.lib sing_1215.htm#SEC1291
2075	grwalk_lib sing_1215.htm#SEC1291
2076	grzero sing_2524.htm#SEC2600 4212
2077	gwalk sing_1221.htm#SEC1297 38238
2078	hStarVector sing_2156.htm#SEC2232 60821
2079	hVector sing_2157.htm#SEC2233 46486
2080	h_increasing_knapsack h_increasing_knapsack sing_2000.htm#SEC2076 62968
2081	hardware platform sing_359.htm#IDX271
2082	hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1087.htm#SEC1163 54609
2083	hasCommutativeVars sing_1084.htm#SEC1160 3152
2084	hasGlobalOrdering sing_1085.htm#SEC1161 34053
2085	hasLeftDenom sing_2670.htm#SEC2746 47260
2086	hasMixedOrdering sing_1086.htm#SEC1162 29738
2087	hasNumericCoeffs sing_1083.htm#SEC1159 14522
2088	hasRightDenom sing_2671.htm#SEC2747 34279
2089	hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1088.htm#SEC1164 56211
2090	hashToCone sing_2513.htm#SEC2589 6929
2091	hashesToFan sing_2514.htm#SEC2590 26774
2092	headStand sing_1137.htm#SEC1213 14413
2093	heightZ sing_1379.htm#SEC1455 16800
2094	help sing_260.htm#SEC300
2095	help browsers The online help system sing_16.htm#IDX22
2096	help browsers, dummy The online help system sing_16.htm#IDX25
2097	help browsers, dummy sing_16.htm#IDX27
2098	help browsers, emacs The online help system sing_16.htm#IDX26
2099	help browsers, html The online help system sing_16.htm#IDX23
2100	help browsers, setting command to use The online help system sing_16.htm#IDX30
2101	help browsers, setting the sing_359.htm#IDX194
2102	help, accessing over the net Command line options sing_19.htm#IDX42
2103	help, online help system The online help system sing_16.htm#SEC22
2104	hermiteNormalForm sing_2662.htm#SEC2738 37225
2105	hess.lib sing_2553.htm#SEC2629
2106	hess_lib sing_2553.htm#SEC2629
2107	hessenberg sing_359.htm#IDX217 24168
2108	hessenberg sing_1159.htm#SEC1235
2109	highcorner sing_261.htm#SEC301
2110	hilb sing_262.htm#SEC302
2111	hilbPoly sing_1047.htm#SEC1123 36118
2112	hilbert4ti2 sing_1401.htm#SEC1477 13993
2113	hilbertBasis sing_2158.htm#SEC2234 35423
2114	hilbertSeries sing_2664.htm#SEC2740 60148
2115	hilbvec sing_1779.htm#SEC1855 9204
2116	hnexpansion sing_1621.htm#SEC1697 46990
2117	hnoether.lib sing_1620.htm#SEC1696
2118	hnoether_lib sing_1620.htm#SEC1696
2119	holonomic rank sing_843.htm#IDX386
2120	holonomicRank sing_847.htm#SEC899 41306
2121	hom sing_2600.htm#SEC2676 40032
2122	hom_kernel sing_1237.htm#SEC1313 32604
2123	homog sing_263.htm#SEC303
2124	homog_part sing_2800.htm#SEC2876 20875
2125	homog_parts sing_2801.htm#SEC2877 12854
2126	homogeneitySpace sing_2229.htm#SEC2305 48243
2127	homogfacFirstQWeyl sing_742.htm#SEC794 32751
2128	homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_744.htm#SEC796 9014
2129	homogfacNthQWeyl sing_741.htm#SEC793 19238
2130	homogfacNthQWeyl_all homogfacNthQWeyl_all sing_743.htm#SEC795 56179
2131	homolog.lib sing_1222.htm#SEC1298
2132	homolog_lib sing_1222.htm#SEC1298
2133	homology sing_1232.htm#SEC1308 15040
2134	homomorphism sing_2584.htm#SEC2660 27115
2135	howto, download Download instructions sing_2827.htm#SEC2917
2136	howto, install on Macintosh Macintosh installation instructions sing_2830.htm#SEC2920
2137	howto, install on Unix Unix installation instructions sing_2828.htm#SEC2918
2138	howto, install on Windows Windows installation instructions sing_2829.htm#SEC2919
2139	hres sing_264.htm#SEC304
2140	html, default help The online help system sing_16.htm#IDX24
2141	hyperel.lib sing_2007.htm#SEC2083
2142	hyperel_lib sing_2007.htm#SEC2083
2143	hyperplane sing_2236.htm#IDX824
2144	hyperplane arrangement sing_542.htm#IDX337
2145	hypersurface singularity sing_1647.htm#IDX776
2146	iMult sing_1312.htm#SEC1388 22059
2147	id sing_2557.htm#SEC2633 47592
2148	id2mod sing_1043.htm#SEC1119 32918
2149	ideal sing_90.htm#SEC130
2150	ideal declarations sing_91.htm#SEC131
2151	ideal declarations (plural) ideal declarations (plural) sing_426.htm#SEC466
2152	ideal expressions sing_92.htm#SEC132
2153	ideal expressions (plural) ideal expressions (plural) sing_427.htm#SEC467
2154	ideal operations sing_93.htm#SEC133
2155	ideal operations (plural) ideal operations (plural) sing_428.htm#SEC468
2156	ideal related functions ideal related functions sing_94.htm#SEC134
2157	ideal related functions (plural) ideal related functions (plural) sing_429.htm#SEC469
2158	ideal, toric sing_937.htm#SEC994
2159	idealSplit sing_1786.htm#SEC1862 4673
2160	ideals Miscellaneous oddities sing_420.htm#IDX293
2161	idealsimplify sing_1548.htm#SEC1624 38569
2162	identifier Identifier resolution sing_421.htm#SEC461
2163	identifyvar sing_1456.htm#SEC1532 59662
2164	if sing_388.htm#SEC428
2165	image sing_2580.htm#SEC2656 43481
2166	imageLattice sing_2630.htm#SEC2706 15740
2167	image_of_variety sing_1736.htm#SEC1812 43711
2168	imap sing_265.htm#SEC305
2169	imap (plural) sing_464.htm#SEC504
2170	imapall sing_1075.htm#SEC1151 16023
2171	impart sing_266.htm#SEC306
2172	importfrom sing_389.htm#SEC429
2173	inCenter sing_531.htm#SEC583 22152
2174	inCentralizer sing_532.htm#SEC584 49000
2175	inForm sing_574.htm#SEC626 5283
2176	inSubring sing_1175.htm#SEC1251 24817
2177	indSet sing_1284.htm#SEC1360 32828
2178	indepSet sing_267.htm#SEC307
2179	indexed names sing_36.htm#IDX82
2180	indexed names sing_37.htm#SEC65
2181	indices, multi sing_37.htm#SEC65
2182	inequalities sing_2099.htm#SEC2175 10122
2183	infRedTail, option sing_316.htm#IDX154
2184	info The online help system sing_16.htm#SEC23
2185	iniD sing_1476.htm#SEC1552 35084
2186	init_debug sing_1555.htm#SEC1631 29863
2187	initial sing_2230.htm#SEC2306 8678
2188	initial form sing_507.htm#IDX318
2189	initial ideal sing_507.htm#IDX317
2190	initial ideal approach sing_507.htm#IDX321
2191	initial ideal approach sing_598.htm#IDX360
2192	initialForm sing_2207.htm#SEC2283 57793
2193	initialIdeal sing_2208.htm#SEC2284 22205
2194	initialIdealW sing_573.htm#SEC625 36086
2195	initialMalgrange sing_572.htm#SEC624 26846
2196	injective_knapsack sing_2001.htm#SEC2077 7619
2197	inout.lib sing_1009.htm#SEC1085
2198	inout_lib sing_1009.htm#SEC1085
2199	input sing_41.htm#SEC71
2200	insert sing_126.htm#SEC166
2201	insert sing_268.htm#SEC308
2202	insertCone sing_2123.htm#SEC2199 13858
2203	insertGenerator sing_593.htm#SEC645 13951
2204	instructions, Macintosh installation Macintosh installation instructions sing_2830.htm#SEC2920
2205	instructions, Unix installation Unix installation instructions sing_2828.htm#SEC2918
2206	instructions, Windows installation Windows installation instructions sing_2829.htm#SEC2919
2207	instructions, downloading Download instructions sing_2827.htm#SEC2917
2208	int sing_95.htm#SEC135
2209	int declarations sing_96.htm#SEC136
2210	int expressions sing_97.htm#SEC137
2211	int operations sing_98.htm#SEC138
2212	int related functions int related functions sing_99.htm#SEC139
2213	intInverse sing_2639.htm#SEC2715 sprintf
2214	intPart sing_1955.htm#SEC2031 48360
2215	intRank sing_2631.htm#SEC2707 1830
2216	intRoot sing_1956.htm#SEC2032 54582
2217	intRoots sing_590.htm#SEC642 24538
2218	intStrategy, option sing_316.htm#IDX155
2219	intclMonIdeal sing_1325.htm#SEC1401 22338
2220	intclToricRing sing_1321.htm#SEC1397 62143
2221	integer division Miscellaneous oddities sing_420.htm#IDX288
2222	integer programming sing_945.htm#SEC1002
2223	integral sing_2775.htm#SEC2851 62683
2224	integral basis sing_1244.htm#IDX552
2225	integral basis sing_1439.htm#IDX619
2226	integral closure sing_1305.htm#IDX567
2227	integral closure sing_1306.htm#IDX570
2228	integral closure sing_1307.htm#IDX573
2229	integral closure sing_1320.htm#IDX579
2230	integralBasis sing_1244.htm#SEC1320 38114
2231	integralIdeal sing_577.htm#SEC629 29194
2232	integralModule sing_578.htm#SEC630 58078
2233	integralSection sing_2640.htm#SEC2716 sprintf
2234	integralbasis.lib sing_1243.htm#SEC1319
2235	integralbasis_lib sing_1243.htm#SEC1319
2236	integration of D-module sing_565.htm#IDX349
2237	interface, Emacs Emacs user interface sing_21.htm#SEC28
2238	interiorLatticePoints interiorLatticePoints sing_2159.htm#SEC2235 49868
2239	internalfunctions sing_1556.htm#SEC1632 61230
2240	interpolate sing_1792.htm#SEC1868 51502
2241	interpolation sing_269.htm#SEC309
2242	interpret sing_2602.htm#SEC2678 48499
2243	interpretElem sing_2605.htm#SEC2681 51740
2244	interpretInv sing_2603.htm#SEC2679 6149
2245	interpretList sing_2606.htm#SEC2682 64061
2246	interred sing_270.htm#SEC310
2247	intersect sing_271.htm#SEC311
2248	intersect (plural) sing_465.htm#SEC505
2249	intersectElim, option sing_316.htm#IDX173
2250	intersectLattices sing_2636.htm#SEC2712 41354
2251	intersectLists sing_2405.htm#SEC2481 4153
2252	intersectMon sing_1261.htm#SEC1337 44572
2253	intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2501.htm#SEC2577 19444
2254	intersectSyz, option sing_316.htm#IDX174
2255	intersectZ sing_1381.htm#SEC1457 sprintf
2256	intersection sing_1630.htm#SEC1706 46938
2257	intersection lattice sing_2272.htm#IDX899
2258	intersection lattice sing_2273.htm#IDX900
2259	intersection multiplicity sing_1541.htm#IDX654
2260	intersection multiplicity sing_1630.htm#IDX769
2261	intersectionDiv sing_1504.htm#SEC1580 29017
2262	intersectionValRingIdeals intersectionValRingIdeals sing_1330.htm#SEC1406 38773
2263	intersectionValRings intersectionValRings sing_1329.htm#SEC1405 35761
2264	intersectpar sing_1007.htm#SEC1083 2975
2265	interval arithmetic sing_2745.htm#IDX1039
2266	intmat sing_102.htm#SEC142
2267	intmat declarations sing_103.htm#SEC143
2268	intmat expressions sing_104.htm#SEC144
2269	intmat operations sing_106.htm#SEC146
2270	intmat related functions intmat related functions sing_107.htm#SEC147
2271	intmat type cast sing_105.htm#SEC145
2272	intmat2mons sing_1345.htm#SEC1421 21150
2273	intprog.lib sing_1245.htm#SEC1321
2274	intprog_lib sing_1245.htm#SEC1321
2275	intvec sing_108.htm#SEC148
2276	intvec declarations sing_109.htm#SEC149
2277	intvec expressions sing_110.htm#SEC150
2278	intvec operations sing_111.htm#SEC151
2279	intvec related functions intvec related functions sing_112.htm#SEC152
2280	invariant sing_2411.htm#IDX961
2281	invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1705.htm#IDX782
2282	invariant ring minimal generating set permutation group invariant_algebra_perm sing_1706.htm#IDX783
2283	invariantRing sing_1738.htm#SEC1814 18582
2284	invariant_algebra_perm invariant_algebra_perm sing_1706.htm#SEC1782 63525
2285	invariant_algebra_reynolds invariant_algebra_reynolds sing_1705.htm#SEC1781 35705
2286	invariant_basis sing_1713.htm#SEC1789 18343
2287	invariant_basis_reynolds invariant_basis_reynolds sing_1714.htm#SEC1790 54788
2288	invariant_ring sing_1701.htm#SEC1777 8059
2289	invariant_ring_random invariant_ring_random sing_1702.htm#SEC1778 6986
2290	invariants curveColengthDerivations sing_1626.htm#SEC1702 57499
2291	invariants sing_2408.htm#IDX954
2292	invariants sing_2412.htm#IDX963
2293	inverse sing_1143.htm#SEC1219 27411
2294	inverse of a matrix via its LU-decomposition sing_291.htm#SEC331
2295	inverseFourier sing_588.htm#SEC640 65140
2296	inverse_B sing_1144.htm#SEC1220 17616
2297	inverse_L sing_1145.htm#SEC1221 49271
2298	inverse_modulus sing_1984.htm#SEC2060 60822
2299	invertBirMap sing_1440.htm#SEC1516 16086
2300	invertLeftFraction sing_2732.htm#SEC2808 51903
2301	invertNcfrac sing_2680.htm#SEC2756 50842
2302	invertNumberMain sing_1816.htm#SEC1892 62615
2303	involut.lib sing_691.htm#SEC743
2304	involut_lib sing_691.htm#SEC743
2305	involution sing_696.htm#SEC748 34280
2306	invunit sing_1649.htm#SEC1725 62398
2307	iostruct sing_1903.htm#SEC1979 60444
2308	irrRealizationDim sing_2189.htm#SEC2265 7814
2309	irred_secondary_char0 irred_secondary_char0 sing_1727.htm#SEC1803 2943
2310	irred_secondary_no_molien irred_secondary_no_molien sing_1730.htm#SEC1806 55905
2311	irreddecMon sing_1270.htm#SEC1346 20160
2312	irreducible power series sing_1631.htm#IDX770
2313	irreducible secondary invariant irred_secondary_char0 sing_1727.htm#IDX784
2314	isAface sing_2486.htm#SEC2562 25344
2315	isAntiEndo sing_698.htm#SEC750 19156
2316	isBounded sing_2160.htm#SEC2236 28183
2317	isCI sing_210.htm#IDX139 58425
2318	isCI sing_1193.htm#SEC1269
2319	isCM sing_210.htm#IDX140 50469
2320	isCM sing_1233.htm#SEC1309
2321	isCMcod2 sing_1684.htm#SEC1760 2563
2322	isCanonical sing_2161.htm#SEC2237 51109
2323	isCartan sing_533.htm#SEC585 39541
2324	isCentral sing_769.htm#SEC821 54650
2325	isCommutative sing_771.htm#SEC823 60728
2326	isCompatible sing_2124.htm#SEC2200 57323
2327	isCompressed sing_2162.htm#SEC2238 2849
2328	isDenom sing_2684.htm#SEC2760 55537
2329	isEqualDivisor sing_2422.htm#SEC2498 17569
2330	isEquising sing_1593.htm#SEC1669 1424
2331	isFlat sing_1234.htm#SEC1310 14706
2332	isFsat sing_583.htm#SEC635 28225
2333	isFullSpace sing_2100.htm#SEC2176 27433
2334	isGorenstein sing_2163.htm#SEC2239 24010
2335	isGradedRingHomomorphism isGradedRingHomomorphism sing_2625.htm#SEC2701 39551
2336	isGroup sing_2623.htm#SEC2699 55744
2337	isGroupHomomorphism sing_2624.htm#SEC2700 65475
2338	isHolonomic sing_561.htm#SEC613 30274
2339	isHomg sing_210.htm#IDX135
2340	isHomogeneous sing_2651.htm#SEC2727 3034
2341	isInS sing_2721.htm#SEC2797 30907
2342	isInt sing_596.htm#SEC648 9879
2343	isIntegralSurjective isIntegralSurjective sing_2637.htm#SEC2713 sprintf
2344	isInvertibleLeftFraction isInvertibleLeftFraction sing_2731.htm#SEC2807 623
2345	isInvertibleNcfrac sing_2679.htm#SEC2755 48367
2346	isInvolution sing_697.htm#SEC749 13601
2347	isLatticeEmpty sing_2164.htm#SEC2240 48517
2348	isLocalizationRegular isLocalizationRegular sing_2482.htm#SEC2558 11221
2349	isLocallyFree sing_1235.htm#SEC1311 46389
2350	isMonomial sing_1256.htm#SEC1332 57615
2351	isNC sing_770.htm#SEC822 57151
2352	isNormal sing_2165.htm#SEC2241 64236
2353	isOnCurve sing_1968.htm#SEC2044 36324
2354	isOneFraction sing_2734.htm#SEC2810 55015
2355	isOneNcfrac sing_2673.htm#SEC2749 12754
2356	isOrigin sing_2101.htm#SEC2177 13977
2357	isPositive sing_2648.htm#SEC2724 50852
2358	isPrimitiveSublattice isPrimitiveSublattice sing_2638.htm#SEC2714 sprintf
2359	isPure sing_2125.htm#SEC2201 44002
2360	isPureTensor sing_505.htm#SEC557 21323
2361	isQuotientRing sing_1089.htm#SEC1165 sprintf
2362	isRational sing_564.htm#SEC616 57398
2363	isReflexive sing_2166.htm#SEC2242 3991
2364	isReg sing_1236.htm#SEC1312 40920
2365	isSB sing_210.htm#IDX134
2366	isSimplicial sing_2102.htm#SEC2178 57789
2367	isSmooth sing_2167.htm#SEC2243 37647
2368	isSubModule sing_1090.htm#SEC1166 sprintf
2369	isSublattice sing_2629.htm#SEC2705 10501
2370	isSymmetric sing_1405.htm#SEC1481 61363
2371	isTame sing_1618.htm#SEC1694 31925
2372	isTerminal sing_2168.htm#SEC2244 29416
2373	isTorsionFree sing_2647.htm#SEC2723 52228
2374	isTwoSidedGB sing_506.htm#SEC558 36558
2375	isUpperTriangular sing_750.htm#SEC802 40655
2376	isVar sing_688.htm#SEC740 43851
2377	isVeryAmple sing_2169.htm#SEC2245 64652
2378	isWeyl sing_772.htm#SEC824 28994
2379	isZeroElement sing_2649.htm#SEC2725 514
2380	isZeroFraction sing_2733.htm#SEC2809 1926
2381	isZeroNcfrac sing_2672.htm#SEC2748 6841
2382	is_NND sing_1634.htm#SEC1710 26564
2383	is_NP sing_1293.htm#SEC1369 43891
2384	is_active sing_1667.htm#SEC1743 6867
2385	is_bijective sing_1180.htm#SEC1256 49512
2386	is_cenBimodule sing_805.htm#SEC857 35450
2387	is_cenSubbimodule sing_806.htm#SEC858 26181
2388	is_ci sing_1668.htm#SEC1744 35370
2389	is_complex sing_1117.htm#SEC1193 1234
2390	is_fix_injective sing_2005.htm#SEC2081 11663
2391	is_h_injective sing_2004.htm#SEC2080 36696
2392	is_injective sing_1178.htm#SEC1254 15776
2393	is_irred sing_1631.htm#SEC1707 51150
2394	is_is sing_1669.htm#SEC1745 64105
2395	is_nested sing_1294.htm#SEC1370 9200
2396	is_prime sing_1985.htm#SEC2061 29018
2397	is_primitive_root sing_1981.htm#SEC2057 42838
2398	is_pure sing_797.htm#SEC849 59105
2399	is_reg sing_1670.htm#SEC1746 18146
2400	is_regs sing_1671.htm#SEC1747 50242
2401	is_surjective sing_1179.htm#SEC1255 57044
2402	is_zero sing_1032.htm#SEC1108 24341
2403	isartinianMon sing_1267.htm#SEC1343 1103
2404	isgenericMon sing_1268.htm#SEC1344 14444
2405	ishyper sing_2008.htm#SEC2084 65518
2406	isirreducibleMon sing_1266.htm#SEC1342 22428
2407	isoncurve sing_2009.htm#SEC2085 16384
2408	isparam sing_2072.htm#SEC2148 56395
2409	isprimaryMon sing_1265.htm#SEC1341 57367
2410	isprimeMon sing_1264.htm#SEC1340 9124
2411	isuni sing_2057.htm#SEC2133 39427
2412	iv2lp sing_631.htm#SEC683 59849
2413	iv2lpList sing_632.htm#SEC684 18518
2414	iv2lpMat sing_633.htm#SEC685 21612
2415	ivDHilbert sing_611.htm#SEC663 56709
2416	ivDHilbertSickle sing_612.htm#SEC664 43194
2417	ivDimCheck sing_613.htm#SEC665 258
2418	ivHilbert sing_614.htm#SEC666 37184
2419	ivKDim sing_615.htm#SEC667 26109
2420	ivL2lpI sing_630.htm#SEC682 2454
2421	ivMaxIdeal sing_627.htm#SEC679 48114
2422	ivMis2Base sing_616.htm#SEC668 57812
2423	ivMis2Dim sing_617.htm#SEC669 42072
2424	ivOrdMisLex sing_618.htm#SEC670 27789
2425	ivSickle sing_619.htm#SEC671 42888
2426	ivSickleDim sing_621.htm#SEC673 64347
2427	ivSickleHil sing_620.htm#SEC672 41396
2428	ivmatGaussian sing_2752.htm#SEC2828 37718
2429	ivmatInit sing_2749.htm#SEC2825 22774
2430	ivmatSet sing_2750.htm#SEC2826 53480
2431	jInvariant sing_2201.htm#SEC2277 2369
2432	jOft sing_1940.htm#SEC2016 25716
2433	jacob sing_272.htm#SEC312
2434	jacoblift sing_1650.htm#SEC1726 40125
2435	jacobson sing_1909.htm#SEC1985 59267
2436	jacobson.lib sing_1907.htm#SEC1983
2437	jacobson_lib sing_1907.htm#SEC1983
2438	janet sing_273.htm#SEC313
2439	janet basis sing_2758.htm#IDX1042
2440	jet sing_274.htm#SEC314
2441	jordan sing_1164.htm#SEC1240 16602
2442	jordanbasis sing_1165.htm#SEC1241 12736
2443	jordanmatrix sing_1166.htm#SEC1242 2886
2444	jordannf sing_1167.htm#SEC1243 20535
2445	jungfib sing_1489.htm#SEC1565 5432
2446	jungnormal sing_1488.htm#SEC1564 43561
2447	jungresolve sing_1487.htm#SEC1563 45004
2448	katsura sing_1030.htm#SEC1106 45913
2449	kbase sing_275.htm#SEC315
2450	kbase (plural) sing_466.htm#SEC506
2451	keepring sing_390.htm#SEC430
2452	kerHom sing_2601.htm#SEC2677 53906
2453	kernel sing_276.htm#SEC316
2454	kernelLattice sing_2632.htm#SEC2708 36320
2455	kill sing_277.htm#SEC317
2456	killTask sing_1096.htm#SEC1172 39317
2457	killall sing_974.htm#SEC1050 34661
2458	killattrib sing_278.htm#SEC318
2459	kmemory sing_973.htm#SEC1049 52193
2460	kohom sing_1238.htm#SEC1314 50086
2461	kontrahom sing_1239.htm#SEC1315 58549
2462	koszul sing_279.htm#SEC319
2463	kskernel.lib sing_1641.htm#SEC1717
2464	kskernel_lib sing_1641.htm#SEC1717
2465	l-adic numbers sing_32.htm#SEC46
2466	laguerre sing_280.htm#SEC320
2467	laguerre_solve sing_1788.htm#SEC1864 10155
2468	lastvarGeneral sing_2038.htm#SEC2114 28645
2469	latex.lib sing_1832.htm#SEC1908
2470	latex_lib sing_1832.htm#SEC1908
2471	lattice sing_2273.htm#IDX902
2472	latticeArea sing_2144.htm#SEC2220 53771
2473	latticeBasis sing_2633.htm#SEC2709 43162
2474	latticeCodegree sing_2170.htm#SEC2246 25482
2475	latticeDegree sing_2171.htm#SEC2247 52881
2476	latticePoints sing_2172.htm#SEC2248 41965
2477	latticeVolume sing_2173.htm#SEC2249 42234
2478	laxfrT sing_2446.htm#SEC2522 60899
2479	laxfrX sing_2447.htm#SEC2523 57254
2480	lazy, option sing_316.htm#IDX156
2481	lcm sing_1033.htm#SEC1109 44755
2482	lcmMon sing_1259.htm#SEC1335 52749
2483	lcmN sing_1949.htm#SEC2025 52355
2484	lcmofall sing_1469.htm#SEC1545 56889
2485	lead sing_281.htm#SEC321
2486	leadcoef sing_282.htm#SEC322
2487	leadexp sing_283.htm#SEC323
2488	leadmonom sing_284.htm#SEC324
2489	leadmonomial sing_2024.htm#SEC2100 8195
2490	left annihilator ideal sing_542.htm#IDX329
2491	leftInverse sing_1898.htm#SEC1974 41469
2492	leftKernel sing_1896.htm#SEC1972 9292
2493	leftOre sing_2724.htm#SEC2800 44669
2494	length sing_2747.htm#SEC2823 9547
2495	length, option sing_316.htm#IDX157
2496	letplaceGBasis sing_674.htm#SEC726 64298
2497	letterplace correspondence Letterplace correspondence sing_496.htm#SEC548
2498	lex_solve sing_1794.htm#SEC1870 48692
2499	lexicographical ordering sing_923.htm#IDX396
2500	lib2doc sing_60.htm#SEC97
2501	libSingular sing_2826.htm#SEC2916
2502	libcdd sing_1.htm#IDX12
2503	libfac sing_1.htm#IDX6
2504	libparse sing_69.htm#SEC109
2505	library sing_2288.htm#IDX917
2506	library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2485.htm#IDX994
2507	library, info string sing_55.htm#IDX124
2508	library, polybori.lib sing_2288.htm#IDX914
2509	library, template sing_55.htm#SEC92
2510	library, template.lib sing_55.htm#IDX122
2511	lieBracket sing_681.htm#SEC733 50745
2512	lift sing_286.htm#SEC326
2513	lift sing_500.htm#IDX305
2514	lift (plural) sing_467.htm#SEC507
2515	lift_kbase sing_1587.htm#SEC1663 10906
2516	lift_rel_kb sing_1588.htm#SEC1664 13673
2517	liftenvelope sing_503.htm#SEC555 58802
2518	liftstd sing_287.htm#SEC327
2519	liftstd (plural) sing_468.htm#SEC508
2520	linReduce sing_515.htm#SEC567 57527
2521	linReduceIdeal sing_516.htm#SEC568 19076
2522	linSyzSolve sing_517.htm#SEC569 26185
2523	linalg.lib sing_1142.htm#SEC1218
2524	linalg_lib sing_1142.htm#SEC1218
2525	linealityDimension sing_2103.htm#SEC2179 30751
2526	linealitySpace sing_2104.htm#SEC2180 14489
2527	linear algebra sing_211.htm#SEC251
2528	linear algebra sing_290.htm#SEC330
2529	linear algebra sing_291.htm#SEC331
2530	linear algebra sing_292.htm#SEC332
2531	linear code, dual sing_1867.htm#IDX795
2532	linear code, systematic sing_1868.htm#IDX796
2533	linear interreduction sing_507.htm#IDX320
2534	linearCombinations sing_536.htm#SEC588 20514
2535	linearMapKernel sing_535.htm#SEC587 43761
2536	linear_relations sing_1134.htm#SEC1210 45983
2537	linearlyEquivalent sing_2425.htm#SEC2501 28351
2538	linearpart sing_1780.htm#SEC1856 2162
2539	linesHypersurface sing_2797.htm#SEC2873 9129
2540	link Parallelization with ssi links sing_113.htm#SEC153
2541	link sing_878.htm#SEC930
2542	link declarations sing_114.htm#SEC154
2543	link expressions sing_115.htm#SEC155
2544	link related functions link related functions sing_116.htm#SEC156
2545	list sing_123.htm#SEC163
2546	list declarations sing_124.htm#SEC164
2547	list expressions sing_125.htm#SEC165
2548	list operations sing_126.htm#SEC166
2549	list related functions list related functions sing_127.htm#SEC167
2550	lists sing_2405.htm#IDX950
2551	lists, elements sing_2407.htm#IDX952
2552	listvar sing_288.htm#SEC328
2553	lll sing_2665.htm#SEC2741 35827
2554	load sing_391.htm#SEC431
2555	loadLib, option sing_316.htm#IDX178
2556	loadProc, option sing_316.htm#IDX179
2557	locAtZero sing_1314.htm#SEC1390 5687
2558	locNormal sing_1248.htm#SEC1324 52237
2559	locStatus sing_2719.htm#SEC2795 54575
2560	local methods sing_1247.htm#IDX555
2561	local methods sing_1248.htm#IDX558
2562	local names sing_46.htm#SEC83
2563	local rings, computing in Rings associated to monomial orderings sing_873.htm#SEC925
2564	local weighted lexicographical ordering sing_924.htm#IDX417
2565	local weighted reverse lexicographical ordering Local orderings sing_924.htm#IDX414
2566	localInvar sing_1743.htm#SEC1819 38478
2567	localization Rings associated to monomial orderings sing_873.htm#SEC925
2568	localization sing_2253.htm#IDX862
2569	localization of D-module sing_565.htm#IDX345
2570	localization of D-module sing_843.htm#IDX389
2571	locally closed set sing_991.htm#IDX441
2572	locally closed set sing_992.htm#IDX443
2573	locally closed set sing_993.htm#IDX445
2574	locally closed set sing_994.htm#IDX449
2575	locally closed set sing_996.htm#IDX459
2576	localstd sing_2034.htm#SEC2110 25562
2577	locnormal.lib sing_1247.htm#SEC1323
2578	locnormal_lib sing_1247.htm#SEC1323
2579	locstd sing_1672.htm#SEC1748 25864
2580	locus FamElemsAtEnvCompPoints sing_998.htm#SEC1074 22530
2581	locus sing_998.htm#IDX464
2582	locus sing_999.htm#IDX467
2583	locus sing_1000.htm#IDX470
2584	locus sing_1001.htm#IDX473
2585	locus sing_1002.htm#IDX476
2586	locus sing_1003.htm#IDX478
2587	locus sing_1004.htm#IDX482
2588	locusdg sing_999.htm#SEC1075 6077
2589	locusto sing_1001.htm#SEC1077 730
2590	log2 sing_1924.htm#SEC2000 40703
2591	logarithmic annihilator ideal sing_542.htm#IDX334
2592	logg sing_2802.htm#SEC2878 38736
2593	lp, global ordering sing_923.htm#IDX395
2594	lp2iv sing_634.htm#SEC686 17398
2595	lp2ivId sing_635.htm#SEC687 16290
2596	lp2lstr sing_682.htm#SEC734 24713
2597	lpCalcSubstDegBound sing_670.htm#SEC722 46179
2598	lpCalcSubstDegBounds lpCalcSubstDegBounds sing_671.htm#SEC723 56500
2599	lpDHilbert sing_609.htm#SEC661 10461
2600	lpDHilbertSickle sing_610.htm#SEC662 41445
2601	lpDimCheck sing_606.htm#SEC658 9807
2602	lpGkDim sing_667.htm#SEC719 10351
2603	lpGlDimBound sing_668.htm#SEC720 53074
2604	lpHilbert sing_608.htm#SEC660 44093
2605	lpId2ivLi sing_636.htm#SEC688 13273
2606	lpIsPrime sing_666.htm#SEC718 40779
2607	lpIsSemiPrime sing_665.htm#SEC717 41065
2608	lpKDim sing_605.htm#SEC657 18278
2609	lpMaxIdeal sing_628.htm#SEC680 37571
2610	lpMis2Base sing_607.htm#SEC659 10826
2611	lpMis2Dim sing_604.htm#SEC656 39947
2612	lpMult sing_678.htm#SEC730 58898
2613	lpNF sing_675.htm#SEC727 2851
2614	lpNoetherian sing_664.htm#SEC716 44964
2615	lpOrdMisLex sing_622.htm#SEC674 30943
2616	lpPower sing_680.htm#SEC732 7325
2617	lpPrint sing_690.htm#SEC742 35540
2618	lpSickle sing_623.htm#SEC675 288
2619	lpSickleDim sing_625.htm#SEC677 61018
2620	lpSickleHil sing_624.htm#SEC676 55268
2621	lpSubstitute sing_669.htm#SEC721 54386
2622	lprint sing_1011.htm#SEC1087 5285
2623	lres sing_289.htm#SEC329
2624	ls, local ordering sing_924.htm#IDX408
2625	lst2str sing_683.htm#SEC735 10088
2626	lsum sing_1214.htm#SEC1290 50315
2627	ludecomp sing_290.htm#SEC330
2628	luinverse sing_291.htm#SEC331
2629	lusolve sing_292.htm#SEC332
2630	mRes sing_2569.htm#SEC2645 58702
2631	m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1996.htm#SEC2072 57945
2632	m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1995.htm#SEC2071 33857
2633	m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1994.htm#SEC2070 7880
2634	magnitude sing_1918.htm#SEC1994 37967
2635	makeDivisor sing_2417.htm#SEC2493 3414
2636	makeFormalDivisor sing_2427.htm#SEC2503 54579
2637	makeGraph sing_1205.htm#SEC1281 21758
2638	makeGraphVE sing_2788.htm#SEC2864 sprintf
2639	makeHeisenberg sing_760.htm#SEC812 2050
2640	makeIdeal sing_2561.htm#SEC2637 57829
2641	makeLetterplaceRing sing_673.htm#SEC725 1592
2642	makeMalgrange sing_602.htm#SEC654 41377
2643	makeMatrix sing_2560.htm#SEC2636 64348
2644	makeModElimRing sing_777.htm#SEC829 56092
2645	makePDivisor sing_2433.htm#SEC2509 45273
2646	makeQsl2 sing_724.htm#SEC776 3997
2647	makeQsl3 sing_725.htm#SEC777 41249
2648	makeQso3 sing_723.htm#SEC775 58910
2649	makeSheaf sing_2776.htm#SEC2852 10497
2650	makeUe6 sing_720.htm#SEC772 58585
2651	makeUe7 sing_721.htm#SEC773 61849
2652	makeUe8 sing_722.htm#SEC774 64987
2653	makeUf4 sing_719.htm#SEC771 8408
2654	makeUg2 sing_718.htm#SEC770 34512
2655	makeUgl sing_704.htm#SEC756 3543
2656	makeUsl sing_703.htm#SEC755 24536
2657	makeUsl2 sing_702.htm#SEC754 42637
2658	makeUso10 sing_710.htm#SEC762 6936
2659	makeUso11 sing_711.htm#SEC763 35873
2660	makeUso12 sing_712.htm#SEC764 19319
2661	makeUso5 sing_705.htm#SEC757 34378
2662	makeUso6 sing_706.htm#SEC758 65009
2663	makeUso7 sing_707.htm#SEC759 49142
2664	makeUso8 sing_708.htm#SEC760 33275
2665	makeUso9 sing_709.htm#SEC761 16896
2666	makeUsp1 sing_713.htm#SEC765 44522
2667	makeUsp2 sing_714.htm#SEC766 18017
2668	makeUsp3 sing_715.htm#SEC767 57445
2669	makeUsp4 sing_716.htm#SEC768 51690
2670	makeUsp5 sing_717.htm#SEC769 35951
2671	makeVariety sing_2768.htm#SEC2844 23915
2672	makeVector sing_2589.htm#SEC2665 9049
2673	makeWeyl sing_759.htm#SEC811 8554
2674	map sing_128.htm#SEC168
2675	map (plural) sing_430.htm#SEC470
2676	map declarations sing_129.htm#SEC169
2677	map declarations (plural) map declarations (plural) sing_431.htm#SEC471
2678	map expressions sing_130.htm#SEC170
2679	map expressions (plural) map expressions (plural) sing_432.htm#SEC472
2680	map operations sing_131.htm#IDX129
2681	map operations (plural) map operations (plural) sing_433.htm#IDX300
2682	map related functions map related functions sing_132.htm#IDX131
2683	map related functions (plural) map related functions (plural) sing_434.htm#IDX301
2684	mapIsFinite sing_1182.htm#SEC1258 60897
2685	mapToRatNormCurve sing_1444.htm#SEC1520 8877
2686	mapall sing_1076.htm#SEC1152 14907
2687	mappingcone sing_2547.htm#SEC2623 48219
2688	mappingcone3 sing_2549.htm#SEC2625 58973
2689	markov4ti2 sing_1400.htm#SEC1476 9163
2690	mat2arr sing_2238.htm#SEC2314 20840
2691	mat2carr sing_2239.htm#SEC2315 13777
2692	mat_rk sing_1156.htm#SEC1232 32196
2693	matbil sing_2045.htm#SEC2121 1611
2694	mathematical objects Representation of mathematical objects sing_919.htm#SEC971
2695	mathinit sing_1830.htm#SEC1906 16793
2696	matmult sing_2046.htm#SEC2122 60088
2697	matrix sing_133.htm#SEC173
2698	matrix sing_2238.htm#IDX830
2699	matrix sing_2239.htm#IDX833
2700	matrix sing_2240.htm#IDX837
2701	matrix declarations sing_134.htm#SEC174
2702	matrix diagonalization sing_1907.htm#IDX806
2703	matrix expressions sing_135.htm#SEC175
2704	matrix operations sing_137.htm#SEC177
2705	matrix related functions matrix related functions sing_138.htm#SEC178
2706	matrix type cast sing_136.htm#SEC176
2707	matrix.lib sing_1110.htm#SEC1186
2708	matrixExp sing_1434.htm#SEC1510 53063
2709	matrixLog sing_1435.htm#SEC1511 26235
2710	matrixT1 sing_1686.htm#SEC1762 15051
2711	matrix_lib sing_1110.htm#SEC1186
2712	matrixpres sing_2552.htm#SEC2628 60645
2713	matrixsystem sing_2457.htm#SEC2533 62950
2714	max sing_293.htm#SEC333 23624
2715	maxEord sing_1459.htm#SEC1535 64032
2716	maxExp sing_210.htm#IDX136
2717	maxIntRoot sing_860.htm#SEC912 37127
2718	maxZeros sing_1437.htm#SEC1513 35964
2719	maxabs sing_2064.htm#SEC2140 64510
2720	maxcoef sing_1034.htm#SEC1110 50577
2721	maxdeg sing_1035.htm#SEC1111 39794
2722	maxdeg1 sing_1036.htm#SEC1112 21545
2723	maxideal sing_294.htm#SEC334
2724	maximalFace sing_2174.htm#SEC2250 35224
2725	maximalGroebnerCone sing_2228.htm#SEC2304 62935
2726	maximalValue sing_2175.htm#SEC2251 32783
2727	maximum sing_1937.htm#SEC2013 2355
2728	maximum number of zeroes sing_1437.htm#IDX613
2729	mdouble sing_56.htm#SEC93 56685
2730	mem, option sing_316.htm#IDX180
2731	member sing_2407.htm#SEC2483 1765
2732	membershipMon sing_1260.htm#SEC1336 40876
2733	memory sing_295.htm#SEC335
2734	memory managment sing_295.htm#SEC335
2735	merkle_hellman_decryption merkle_hellman_decryption sing_1998.htm#SEC2074 49106
2736	merkle_hellman_encryption merkle_hellman_encryption sing_1997.htm#SEC2073 13645
2737	methods, hashtables sing_2555.htm#IDX998
2738	methods.lib sing_2555.htm#SEC2631
2739	methods_lib sing_2555.htm#SEC2631
2740	midpoint sing_2453.htm#SEC2529 29391
2741	milnor sing_1673.htm#SEC1749 23173
2742	milnorcode sing_1557.htm#SEC1633 13849
2743	milnornumber sing_2742.htm#SEC2818 21855
2744	min sing_296.htm#SEC336 56342
2745	minAssChar sing_1359.htm#SEC1435 18758
2746	minAssCharE sing_1360.htm#SEC1436 31570
2747	minAssGTZ sing_1357.htm#SEC1433 41315
2748	minAssGTZE sing_1358.htm#SEC1434 50867
2749	minAssZ sing_1377.htm#SEC1453 54152
2750	minEcart sing_2027.htm#SEC2103 34890
2751	minIntRoot sing_563.htm#SEC615 3288
2752	minIntRoot2 sing_859.htm#SEC911 46494
2753	minMult sing_1189.htm#SEC1265 31978
2754	minbase sing_297.htm#SEC337
2755	minbaseMon sing_1257.htm#SEC1333 1501
2756	mindeg sing_1037.htm#SEC1113 16307
2757	mindeg1 sing_1038.htm#SEC1114 39698
2758	mindist sing_1882.htm#SEC1958 55281
2759	minimal display time, setting the sing_359.htm#IDX284
2760	minimal representations sing_807.htm#IDX380
2761	minimalAfaceOrbits sing_2498.htm#SEC2574 2467
2762	minimalAfaces sing_2489.htm#SEC2565 47736
2763	minimalFace sing_2176.htm#SEC2252 40971
2764	minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2500.htm#SEC2576 11756
2765	minimalValue sing_2177.htm#SEC2253 31262
2766	minipoly sing_1161.htm#SEC1237 4927
2767	minkowskiSum sing_2178.htm#SEC2254 3969
2768	minor sing_298.htm#SEC338
2769	minpoly sing_399.htm#SEC439
2770	minres sing_299.htm#SEC339
2771	minres (plural) sing_469.htm#SEC509
2772	mirror symmetry sing_1204.htm#IDX523
2773	mixed Hodge structure sing_1595.htm#IDX669
2774	mixed Hodge structure sing_1601.htm#IDX697
2775	mixed Hodge structure sing_1602.htm#IDX703
2776	mixed Hodge structure sing_1603.htm#IDX711
2777	mixed Hodge structure sing_1604.htm#IDX717
2778	mixed Hodge structure sing_1605.htm#IDX725
2779	mixed Hodge structure sing_1606.htm#IDX735
2780	mixed Hodge structure sing_1617.htm#IDX741
2781	mixed Hodge structure sing_1619.htm#IDX752
2782	mod sing_81.htm#SEC121
2783	mod sing_98.htm#SEC138
2784	mod sing_147.htm#SEC187
2785	mod sing_155.htm#SEC195
2786	mod2id sing_1042.htm#SEC1118 27927
2787	mod2str sing_684.htm#SEC736 35236
2788	modBorder sing_2760.htm#SEC2836 19224
2789	modDec sing_1276.htm#SEC1352 48578
2790	modIntersect sing_1254.htm#SEC1330 43699
2791	modJanet sing_2762.htm#SEC2838 8550
2792	modNPos sing_1299.htm#SEC1375 17130
2793	modNormal sing_1250.htm#SEC1326 39654
2794	modNpos_test sing_1297.htm#SEC1373 34326
2795	modSagbiAlg sing_2394.htm#SEC2470 25025
2796	modStd sing_1252.htm#SEC1328 7824
2797	modSyz sing_1253.htm#SEC1329 37065
2798	modVStd sing_2399.htm#SEC2475 38529
2799	modVStd0 sing_2400.htm#SEC2476 46080
2800	modWalk sing_2610.htm#SEC2686 sprintf
2801	mod_versal sing_1586.htm#SEC1662 63927
2802	modality sing_1565.htm#SEC1641 49951
2803	modfWalk sing_2612.htm#SEC2688 sprintf
2804	modfrWalk sing_2613.htm#SEC2689 sprintf
2805	modnormal.lib sing_1249.htm#SEC1325
2806	modnormal_lib sing_1249.htm#SEC1325
2807	modrWalk sing_2611.htm#SEC2687 sprintf
2808	modregCM sing_1303.htm#SEC1379 5049
2809	modsatiety sing_1301.htm#SEC1377 44506
2810	modstd.lib sing_1251.htm#SEC1327
2811	modstd_lib sing_1251.htm#SEC1327
2812	modular sing_1020.htm#SEC1096 16950
2813	modular methods sing_1247.htm#IDX556
2814	modular methods sing_1249.htm#IDX561
2815	modular methods. sing_1248.htm#IDX559
2816	modular techniques. sing_1250.htm#IDX563
2817	modular.lib sing_1019.htm#SEC1095
2818	modular_lib sing_1019.htm#SEC1095
2819	modular_lib sing_1019.htm#IDX491
2820	module sing_139.htm#SEC179
2821	module (plural) sing_435.htm#SEC475
2822	module declarations sing_140.htm#SEC180
2823	module declarations (plural) module declarations (plural) sing_436.htm#SEC476
2824	module expressions sing_141.htm#SEC181
2825	module expressions (plural) module expressions (plural) sing_437.htm#SEC477
2826	module operations sing_142.htm#SEC182
2827	module operations (plural) module operations (plural) sing_438.htm#SEC478
2828	module ordering C sing_925.htm#IDX420
2829	module ordering c sing_925.htm#IDX422
2830	module related functions module related functions sing_143.htm#SEC183
2831	module related functions (plural) module related functions (plural) sing_439.htm#SEC479
2832	module_containment sing_1174.htm#SEC1250 31620
2833	modules.lib sing_2556.htm#SEC2632
2834	modules_lib sing_2556.htm#SEC2632
2835	moduliSpace sing_2790.htm#SEC2866 37013
2836	modulo sing_300.htm#SEC340
2837	modulo (plural) sing_470.htm#SEC510
2838	moduloSlim sing_767.htm#SEC819 52636
2839	modwalk.lib sing_2609.htm#SEC2685
2840	modwalk_lib sing_2609.htm#SEC2685
2841	moebius sing_2274.htm#SEC2350 61319
2842	moebius function sing_2274.htm#IDX903
2843	molien sing_1709.htm#SEC1785 63561
2844	mondromy.lib sing_1647.htm#SEC1723
2845	mondromy_lib sing_1647.htm#SEC1723
2846	monitor sing_301.htm#SEC341
2847	monodromy sing_1595.htm#IDX673 40112
2848	monodromy sing_1600.htm#SEC1676
2849	monodromy sing_1600.htm#IDX693
2850	monodromy sing_1605.htm#IDX728
2851	monodromy sing_1617.htm#IDX744
2852	monodromy sing_1619.htm#IDX755
2853	monodromyB sing_1651.htm#SEC1727 46517
2854	monomial sing_302.htm#SEC342
2855	monomial ordering sing_1085.htm#IDX505
2856	monomial orderings General definitions for orderings sing_873.htm#SEC925
2857	monomial orderings sing_922.htm#SEC974
2858	monomial orderings introduction Introduction to orderings sing_921.htm#SEC973
2859	monomialBasis sing_629.htm#SEC681 14185
2860	monomialInIdeal sing_857.htm#SEC909 4687
2861	monomialLcm sing_2025.htm#SEC2101 36233
2862	monomialabortstd sing_2281.htm#SEC2357 14901
2863	monomialideal.lib sing_1255.htm#SEC1331
2864	monomialideal_lib sing_1255.htm#SEC1331
2865	monomials and precedence Miscellaneous oddities sing_420.htm#IDX290
2866	mons2intmat sing_1344.htm#SEC1420 15555
2867	morsesplit sing_1558.htm#SEC1634 3417
2868	movingCone sing_2496.htm#SEC2572 39892
2869	mp_res_mat sing_1791.htm#SEC1867 44453
2870	mplot sing_1831.htm#SEC1907 21740
2871	mpresmat sing_303.htm#SEC343
2872	mprimdec.lib sing_1272.htm#SEC1348
2873	mprimdec_lib sing_1272.htm#SEC1348
2874	mregular.lib sing_1287.htm#SEC1363
2875	mregular_lib sing_1287.htm#SEC1363
2876	mres sing_304.htm#SEC344
2877	mres (plural) sing_471.htm#SEC511
2878	mstd sing_305.htm#SEC345
2879	msum sing_58.htm#SEC95 53344
2880	mtriple sing_57.htm#SEC94 55390
2881	mult Miscellaneous oddities sing_306.htm#SEC346
2882	mult sing_420.htm#IDX291
2883	multBound sing_400.htm#SEC440
2884	multRat sing_865.htm#SEC917 44047
2885	multarr2arr sing_2269.htm#SEC2345 44731
2886	multarrMultRestrict sing_2271.htm#SEC2347 41742
2887	multarrRestrict sing_2270.htm#SEC2346 sprintf
2888	multcol sing_1128.htm#SEC1204 21899
2889	multdivisor sing_2419.htm#SEC2495 65139
2890	multformaldivisor sing_2431.htm#SEC2507 32238
2891	multi sing_2012.htm#SEC2088 18473
2892	multi indices sing_37.htm#SEC65
2893	multiDeg sing_2644.htm#SEC2720 7049
2894	multiDegBasis sing_2645.htm#SEC2721 3320
2895	multiDegGroebner sing_2653.htm#SEC2729 1040
2896	multiDegModulo sing_2655.htm#SEC2731 27244
2897	multiDegPartition sing_2646.htm#SEC2722 9577
2898	multiDegResolution sing_2656.htm#SEC2732 38535
2899	multiDegSyzygy sing_2654.htm#SEC2730 54075
2900	multiDegTensor sing_2657.htm#SEC2733 45108
2901	multiDegTor sing_2658.htm#SEC2734 sprintf
2902	multiarrangement sing_2265.htm#IDX883
2903	multiarrangement sing_2266.htm#IDX885
2904	multiarrangement sing_2267.htm#IDX888
2905	multiarrangement sing_2268.htm#IDX889
2906	multiarrangement sing_2269.htm#IDX892
2907	multiarrangement sing_2270.htm#IDX895
2908	multiarrangement sing_2271.htm#IDX897
2909	multidimensional_knapsack multidimensional_knapsack sing_1990.htm#SEC2066 15647
2910	multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2614.htm#IDX1005
2911	multigrading.lib sing_2614.htm#IDX1003
2912	multigrading_lib sing_2614.htm#IDX1004
2913	multipleCover sing_2796.htm#SEC2872 55988
2914	multiplicities, sequence of sing_1626.htm#IDX767
2915	multiplicity sing_2410.htm#IDX959
2916	multiplicity sequence sing_1539.htm#IDX646
2917	multiplicity sequence sing_1542.htm#IDX658
2918	multiplicity sequence sing_1628.htm#IDX768
2919	multiplyLeftFractions multiplyLeftFractions sing_2729.htm#SEC2805 57489
2920	multiplylist sing_1479.htm#SEC1555 34999
2921	multivariate equations sing_1765.htm#IDX785
2922	multrow sing_1129.htm#SEC1205 871
2923	multseq2charexp sing_1538.htm#SEC1614 sprintf
2924	multsequence sing_1628.htm#SEC1704 35117
2925	nBoundaryLatticePoints nBoundaryLatticePoints sing_2179.htm#SEC2255 49670
2926	nHilbertBasis sing_2180.htm#SEC2256 173
2927	nInteriorLatticePoints nInteriorLatticePoints sing_2181.htm#SEC2257 42152
2928	nLatticePoints sing_2182.htm#SEC2258 5977
2929	naccache_stern_decryption naccache_stern_decryption sing_1993.htm#SEC2069 31429
2930	naccache_stern_encryption naccache_stern_encryption sing_1992.htm#SEC2068 60034
2931	naccache_stern_generation naccache_stern_generation sing_1991.htm#SEC2067 2559
2932	nameof sing_307.htm#SEC347
2933	names sing_308.htm#SEC348
2934	nashmult sing_1546.htm#SEC1622 8491
2935	nblocks sing_359.htm#IDX221
2936	ncExt_R sing_800.htm#SEC852 14357
2937	ncHilb.lib sing_2666.htm#SEC2742
2938	ncHilb_lib sing_2666.htm#SEC2742
2939	ncHom sing_801.htm#SEC853 45033
2940	ncInit sing_808.htm#SEC860 55321
2941	ncRelations sing_768.htm#SEC820 7225
2942	ncVarsAdd sing_810.htm#SEC862 55173
2943	ncVarsGet sing_809.htm#SEC861 41459
2944	nc_algebra sing_472.htm#SEC512
2945	nc_hilb sing_359.htm#IDX223
2946	ncalg.lib sing_701.htm#SEC753
2947	ncalg_lib sing_701.htm#SEC753
2948	ncalgebra sing_473.htm#SEC513
2949	ncdecomp.lib sing_728.htm#SEC780
2950	ncdecomp_lib sing_728.htm#SEC780
2951	ncdetection sing_695.htm#SEC747 24994
2952	ncfactor sing_734.htm#SEC786 53809
2953	ncfactor.lib sing_733.htm#SEC785
2954	ncfactor_lib sing_733.htm#SEC785
2955	ncfrac.lib sing_2669.htm#SEC2745
2956	ncfrac_lib sing_2669.htm#SEC2745
2957	nchilb sing_2667.htm#SEC2743 40517
2958	nchomolog.lib sing_799.htm#IDX373
2959	nchomolog_lib sing_799.htm#IDX374
2960	ncloc.lib sing_2683.htm#SEC2759
2961	ncloc_lib sing_2683.htm#SEC2759
2962	ncols sing_309.htm#SEC349
2963	ncones sing_2127.htm#SEC2203 48316
2964	ncpreim.lib sing_746.htm#SEC798
2965	ncpreim_lib sing_746.htm#SEC798
2966	ncrat.lib sing_807.htm#IDX375
2967	ncratAdd sing_812.htm#SEC864 34791
2968	ncratDefine sing_811.htm#SEC863 53337
2969	ncratEvaluateAt sing_821.htm#SEC873 38737
2970	ncratFromPoly sing_819.htm#SEC871 13980
2971	ncratFromString sing_818.htm#SEC870 27148
2972	ncratInvert sing_815.htm#SEC867 41502
2973	ncratMultiply sing_814.htm#SEC866 36291
2974	ncratPower sing_820.htm#SEC872 1973
2975	ncratPrint sing_817.htm#SEC869 13600
2976	ncratSPrint sing_816.htm#SEC868 65300
2977	ncratSubstract sing_813.htm#SEC865 37583
2978	ncrat_lib sing_807.htm#IDX376
2979	ncrepAdd sing_823.htm#SEC875 16569
2980	ncrepDim sing_828.htm#SEC880 48352
2981	ncrepEvaluate sing_830.htm#SEC882 53482
2982	ncrepEvaluateAt sing_831.htm#SEC883 21150
2983	ncrepGet sing_822.htm#SEC874 25651
2984	ncrepGetRegularMinimal ncrepGetRegularMinimal sing_838.htm#SEC890 43477
2985	ncrepGetRegularZeroMinimal ncrepGetRegularZeroMinimal sing_837.htm#SEC889 17269
2986	ncrepInvert sing_826.htm#SEC878 54448
2987	ncrepIsDefined sing_833.htm#SEC885 60090
2988	ncrepIsDefinedDim sing_832.htm#SEC884 6513
2989	ncrepIsRegular sing_834.htm#SEC886 60397
2990	ncrepMultiply sing_825.htm#SEC877 13469
2991	ncrepPencilCombine sing_840.htm#SEC892 20857
2992	ncrepPencilGet sing_839.htm#SEC891 64708
2993	ncrepPrint sing_827.htm#SEC879 65099
2994	ncrepRegularMinimize ncrepRegularMinimize sing_836.htm#SEC888 36893
2995	ncrepRegularZeroMinimize ncrepRegularZeroMinimize sing_835.htm#SEC887 17270
2996	ncrepSubstitute sing_829.htm#SEC881 977
2997	ncrepSubstract sing_824.htm#SEC876 46335
2998	nctools.lib sing_754.htm#SEC806
2999	nctools_lib sing_754.htm#SEC806
3000	ndcond sing_757.htm#SEC809 1006
3001	negateNcfrac sing_2678.htm#SEC2754 23626
3002	negatedCone sing_2105.htm#SEC2181 38527
3003	negative degree lexicographical ordering sing_924.htm#IDX411
3004	negative degree reverse lexicographical ordering Local orderings sing_924.htm#IDX409
3005	negative lexicographical ordering sing_924.htm#IDX407
3006	negativedivisor sing_2420.htm#SEC2496 8274
3007	negativeformaldivisor negativeformaldivisor sing_2430.htm#SEC2506 55026
3008	net sing_2687.htm#IDX1006 sprintf
3009	net sing_2689.htm#SEC2765
3010	net access Command line options sing_19.htm#IDX40
3011	netBigInt sing_2695.htm#SEC2771 63523
3012	netBigIntMat sing_2690.htm#SEC2766 36296
3013	netBigIntMatShort sing_2691.htm#SEC2767 30702
3014	netCoefficientRing sing_2692.htm#SEC2768 6081
3015	netIdeal sing_2693.htm#SEC2769 64434
3016	netInt sing_2694.htm#SEC2770 19545
3017	netIntMat sing_2696.htm#SEC2772 34242
3018	netIntMatShort sing_2697.htm#SEC2773 21160
3019	netIntVector sing_2698.htm#SEC2774 17568
3020	netIntVectorShort sing_2699.htm#SEC2775 16105
3021	netList sing_2701.htm#SEC2777 29178
3022	netMap sing_2702.htm#SEC2778 19115
3023	netMap2 sing_2703.htm#SEC2779 44053
3024	netMatrix sing_2591.htm#SEC2667 29311
3025	netNumber sing_2700.htm#SEC2776 24930
3026	netPoly sing_2706.htm#SEC2782 7938
3027	netPrimePower sing_2707.htm#SEC2783 54219
3028	netRing sing_2708.htm#SEC2784 42246
3029	netString sing_2709.htm#SEC2785 43247
3030	netVector sing_2590.htm#SEC2666 32453
3031	netmatrix sing_2704.htm#SEC2780 4023
3032	netmatrixShort sing_2705.htm#SEC2781 24709
3033	nets.lib sing_2687.htm#SEC2763
3034	nets_lib sing_2687.htm#SEC2763
3035	netvector sing_2710.htm#SEC2786 39957
3036	netvectorShort sing_2711.htm#SEC2787 22053
3037	newTest sing_1932.htm#SEC2008 36655
3038	newline sing_172.htm#SEC212
3039	news sing_2819.htm#SEC2895
3040	newstruct sing_183.htm#SEC223
3041	newstruct sing_2288.htm#IDX919
3042	newtonDiag sing_1046.htm#SEC1122 56652
3043	newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2812.htm#SEC2888 22052
3044	newtonPolytope sing_2131.htm#SEC2207 56291
3045	newtonPolytopeLP sing_2136.htm#SEC2212 36186
3046	newtonPolytopeP sing_2135.htm#SEC2211 29927
3047	newtonpoly sing_1633.htm#SEC1709 31930
3048	nf_icis sing_1674.htm#SEC1750 49093
3049	nfmodStd sing_2715.htm#SEC2791 46077
3050	nfmodSyz sing_2717.htm#SEC2793 55942
3051	nfmodstd.lib sing_2713.htm#SEC2789
3052	nfmodstd_lib sing_2713.htm#SEC2789
3053	nfmodsyz.lib sing_2716.htm#SEC2792
3054	nfmodsyz_lib sing_2716.htm#SEC2792
3055	nilpotent Lie algebras sing_1432.htm#IDX598
3056	nmaxcones sing_2126.htm#SEC2202 660
3057	noether sing_401.htm#SEC441
3058	noether.lib sing_1295.htm#SEC1371
3059	noetherNormal sing_1181.htm#SEC1257 44522
3060	noether_lib sing_1295.htm#SEC1371
3061	non-english special characters sing_409.htm#IDX286
3062	nonMonomials sing_1348.htm#SEC1424 16309
3063	nonZeroEntry sing_1184.htm#SEC1260 933
3064	noncommutative, rational expressions sing_807.htm#IDX377
3065	none, option sing_316.htm#IDX150
3066	norTest sing_1315.htm#SEC1391 sprintf
3067	norm sing_2011.htm#SEC2087 31143
3068	normaform (up to a bound) sing_359.htm#IDX246
3069	normal sing_1305.htm#SEC1381 61073
3070	normal bundle, graph, rational curves, mutiple covers, lines on normalBundle sing_2795.htm#IDX1071
3071	normal form sing_931.htm#IDX423
3072	normal.lib sing_1304.htm#SEC1380
3073	normalBundle sing_2795.htm#SEC2871 sprintf
3074	normalC sing_1307.htm#SEC1383 34842
3075	normalConductor sing_1319.htm#SEC1395 26085
3076	normalFan sing_2183.htm#SEC2259 39216
3077	normalForm sing_2421.htm#SEC2497 34962
3078	normalI sing_1392.htm#SEC1468 7516
3079	normalP sing_1306.htm#SEC1382 36584
3080	normalToricRing sing_1322.htm#SEC1398 29638
3081	normalToricRingFromBinomials normalToricRingFromBinomials sing_1323.htm#SEC1399 2301
3082	normal_lib sing_1304.htm#SEC1380
3083	normalform sing_1562.htm#SEC1638 5550
3084	normalform sing_2393.htm#IDX947
3085	normaliz sing_1.htm#IDX14 18426
3086	normaliz sing_1335.htm#SEC1411
3087	normaliz.lib sing_1320.htm#SEC1396
3088	normaliz_lib sing_1320.htm#SEC1396
3089	normalization sing_1247.htm#IDX554
3090	normalization sing_1248.htm#IDX557
3091	normalization sing_1249.htm#IDX560
3092	normalization sing_1250.htm#IDX562
3093	normalization sing_1305.htm#IDX566
3094	normalization sing_1306.htm#IDX569
3095	normalization sing_1307.htm#IDX572
3096	normalization sing_1319.htm#IDX578
3097	normalization sing_1320.htm#IDX580
3098	normalization sing_2409.htm#IDX957
3099	normalization. sing_1244.htm#IDX553
3100	normalization. sing_1439.htm#IDX620
3101	normalize sing_1039.htm#SEC1115 44788
3102	normalizeMonoidal sing_2735.htm#SEC2811 33071
3103	normalizeRational sing_2736.htm#SEC2812 55177
3104	not sing_101.htm#SEC141
3105	notBuckets, option sing_316.htm#IDX160
3106	notRegularity, option sing_316.htm#IDX158
3107	notSugar, option sing_316.htm#IDX159
3108	notWarnSB, option sing_316.htm#IDX181
3109	npar sing_1917.htm#SEC1993 5753
3110	npars sing_310.htm#SEC350
3111	nrRootsDeterm sing_2042.htm#SEC2118 sprintf
3112	nrRootsProbab sing_2041.htm#SEC2117 sprintf
3113	nres sing_311.htm#SEC351
3114	nres (plural) sing_474.htm#SEC514
3115	nrows sing_312.htm#SEC352
3116	nrroots sing_2071.htm#SEC2147 54867
3117	nsatiety sing_1300.htm#SEC1376 53333
3118	nselect sing_1200.htm#SEC1276 34057
3119	nt_solve sing_1806.htm#SEC1882 33061
3120	ntsolve.lib sing_1805.htm#SEC1881
3121	ntsolve_lib sing_1805.htm#SEC1881
3122	number sing_144.htm#SEC184
3123	number sing_2242.htm#IDX843
3124	number declarations sing_145.htm#SEC185
3125	number expressions sing_146.htm#SEC186
3126	number operations sing_147.htm#SEC187
3127	number related functions number related functions sing_148.htm#SEC188
3128	numberOfConesOfDimension numberOfConesOfDimension sing_2128.htm#SEC2204 5905
3129	number_e sing_975.htm#SEC1051 59152
3130	number_pi sing_976.htm#SEC1052 15492
3131	numerAlg.lib sing_1414.htm#IDX587
3132	numerAlg_lib sing_1414.htm#IDX588
3133	numerAlg_lib sing_1419.htm#IDX597
3134	numerDecom.lib sing_1419.htm#IDX591
3135	numerDecom_lib sing_1414.htm#IDX590
3136	numerDecom_lib sing_1419.htm#IDX592
3137	numerator sing_313.htm#SEC353
3138	numerical irreducible decomposition sing_1419.htm#IDX593
3139	nvars sing_314.htm#SEC354
3140	olga.lib sing_2718.htm#SEC2794
3141	olga_lib sing_2718.htm#SEC2794
3142	oneDimBelongSemigroup oneDimBelongSemigroup sing_1191.htm#SEC1267 34399
3143	oneNcfrac sing_2675.htm#SEC2751 35654
3144	online help The online help system sing_16.htm#SEC22
3145	open sing_315.htm#SEC355
3146	opentex sing_1834.htm#SEC1910 54236
3147	operatorAlgebra sing_638.htm#SEC690 36252
3148	operatorBM sing_549.htm#SEC601 54875
3149	operatorModulo sing_550.htm#SEC602 26064
3150	oppose sing_475.htm#SEC515
3151	opposite sing_476.htm#SEC516
3152	opposite polynomial sing_359.htm#IDX231
3153	opposite ring sing_359.htm#IDX228
3154	option sing_316.htm#SEC356
3155	option(warn) sing_70.htm#SEC110
3156	optionIsSet sing_1082.htm#SEC1158 57325
3157	or Evaluation of logical expressions sing_101.htm#SEC141
3158	or sing_413.htm#SEC453
3159	orbit sing_1432.htm#IDX600
3160	orbit sing_1433.htm#IDX604
3161	orbit sing_1436.htm#IDX609
3162	orbit sing_1437.htm#IDX612
3163	orbitConeOrbits sing_2499.htm#SEC2575 60979
3164	orbitCones sing_2490.htm#SEC2566 60528
3165	orbit_variety sing_1733.htm#SEC1809 22665
3166	orbitparam.lib sing_1432.htm#SEC1508
3167	orbitparam_lib sing_1432.htm#SEC1508
3168	ord sing_317.htm#SEC357
3169	ord_test sing_1077.htm#SEC1153 36532
3170	order ideal, border basis sing_2759.htm#IDX1043
3171	order ideal, border basis sing_2760.htm#IDX1044
3172	orderings General definitions for orderings sing_922.htm#SEC974
3173	orderings introduction Introduction to orderings sing_921.htm#SEC973
3174	orderings, L sing_929.htm#SEC981
3175	orderings, M sing_926.htm#SEC978
3176	orderings, a sing_928.htm#SEC980
3177	orderings, global sing_923.htm#SEC975
3178	orderings, local sing_924.htm#SEC976
3179	orderings, product sing_927.htm#SEC979
3180	ordstr sing_318.htm#SEC358
3181	origin sing_2076.htm#SEC2152 31408
3182	orthogonalize sing_1147.htm#SEC1223 63711
3183	outer sing_1118.htm#SEC1194 64048
3184	output sing_41.htm#SEC71
3185	p-adic numbers sing_32.htm#SEC46
3186	pFactor sing_1966.htm#SEC2042 31504
3187	pIntersect sing_513.htm#SEC565 44055
3188	pIntersectSyz sing_514.htm#SEC566 45608
3189	package sing_149.htm#SEC189
3190	package declarations package declarations sing_150.htm#SEC190
3191	package related functions package related functions sing_151.htm#SEC191
3192	pairset sing_2031.htm#SEC2107 38258
3193	par sing_319.htm#SEC359
3194	par2varRing sing_959.htm#SEC1035 44769
3195	paraConic sing_1447.htm#SEC1523 9828
3196	paraPlaneCurve sing_1441.htm#SEC1517 34094
3197	parallel skeletons sing_1021.htm#IDX497
3198	parallel.lib sing_1021.htm#SEC1097
3199	parallelTestAND sing_1025.htm#SEC1101 1415
3200	parallelTestOR sing_1026.htm#SEC1102 14920
3201	parallelWaitAll sing_1024.htm#SEC1100 2017
3202	parallelWaitFirst sing_1023.htm#SEC1099 32
3203	parallelWaitN sing_1022.htm#SEC1098 38878
3204	parallel_lib sing_1021.htm#SEC1097
3205	parallelization sing_1021.htm#IDX496
3206	parallelization sing_1061.htm#IDX499
3207	parallelization sing_1094.htm#IDX509
3208	param sing_1624.htm#SEC1700 57220
3209	parameter, as numbers sing_144.htm#SEC184
3210	parameterSubstitute sing_2223.htm#SEC2299 63147
3211	parametric annihilator sing_542.htm#IDX335
3212	parametric annihilator for variety sing_598.htm#IDX358
3213	parametric ideal sing_987.htm#IDX429
3214	parametric ideal sing_994.htm#IDX448
3215	parametric ideal sing_994.htm#IDX450
3216	parametric ideal sing_995.htm#IDX455
3217	parametrization sing_1432.htm#IDX601
3218	parametrization sing_1436.htm#IDX610
3219	parametrization sing_1624.htm#IDX762
3220	parametrizeOrbit sing_1436.htm#SEC1512 26969
3221	paraplanecurves.lib sing_1438.htm#SEC1514
3222	paraplanecurves_lib sing_1438.htm#SEC1514
3223	pardeg sing_320.htm#SEC360
3224	parstr sing_321.htm#SEC361
3225	part sing_2369.htm#SEC2445 31485
3226	partOver sing_2372.htm#SEC2448 25555
3227	partUnder sing_2373.htm#SEC2449 13123
3228	partial_molien sing_1711.htm#SEC1787 21772
3229	partitions sing_1212.htm#SEC1288 48089
3230	partitions sing_1212.htm#IDX542
3231	path integral sing_1204.htm#IDX529
3232	pause sing_1018.htm#SEC1094 2273
3233	pdivi sing_989.htm#SEC1065 21786
3234	pdivi sing_990.htm#IDX439
3235	pdivisorplus sing_2435.htm#SEC2511 47486
3236	permcol sing_1130.htm#SEC1206 12886
3237	permrow sing_1131.htm#SEC1207 26561
3238	permutationFromIntvec permutationFromIntvec sing_2505.htm#SEC2581 6533
3239	permutationToIntvec sing_2506.htm#SEC2582 1989
3240	permutations sing_1213.htm#IDX543
3241	permutations, sum, max, min sing_2404.htm#IDX949
3242	permute sing_1213.htm#SEC1289 40893
3243	permute_L sing_1869.htm#SEC1945 10716
3244	perron sing_780.htm#SEC832 3782
3245	perron.lib sing_779.htm#SEC831
3246	perron_lib sing_779.htm#SEC831
3247	phindex.lib sing_2283.htm#IDX910
3248	phindex_lib sing_2283.htm#IDX911
3249	picksFormula sing_2145.htm#SEC2221 14656
3250	pid sing_359.htm#IDX240
3251	plainInvariants sing_1583.htm#SEC1659 40916
3252	planeCur sing_2391.htm#SEC2467 sprintf
3253	plot sing_1847.htm#SEC1923 46610
3254	plotRot sing_1851.htm#SEC1927 57150
3255	plotRotated sing_1850.htm#SEC1926 33009
3256	plotRotatedDirect sing_1853.htm#SEC1929 18202
3257	plotRotatedList sing_1852.htm#SEC1928 41668
3258	plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1854.htm#SEC1930 38856
3259	plural sing_1084.htm#IDX504
3260	pmat sing_1012.htm#SEC1088 3857
3261	pnormalf sing_990.htm#SEC1066 26174
3262	pointid.lib sing_1347.htm#SEC1423
3263	pointid_lib sing_1347.htm#SEC1423
3264	polSol sing_849.htm#SEC901 323
3265	polSolFiniteRank sing_850.htm#SEC902 30875
3266	pollTask sing_1104.htm#SEC1180 53950
3267	poly sing_152.htm#SEC192
3268	poly (plural) sing_440.htm#SEC480
3269	poly declarations sing_153.htm#SEC193
3270	poly declarations (plural) poly declarations (plural) sing_441.htm#SEC481
3271	poly expressions sing_154.htm#SEC194
3272	poly expressions (plural) poly expressions (plural) sing_442.htm#SEC482
3273	poly operations sing_155.htm#SEC195
3274	poly operations (plural) poly operations (plural) sing_443.htm#SEC483
3275	poly related functions poly related functions sing_156.htm#SEC196
3276	poly related functions (plural) poly related functions (plural) sing_444.htm#SEC484
3277	poly.lib sing_1027.htm#SEC1103
3278	poly2list sing_591.htm#SEC643 4960
3279	poly2zdd sing_2304.htm#SEC2380 61839
3280	polyInterpolation sing_2438.htm#SEC2514 45866
3281	polyVars sing_856.htm#SEC908 43882
3282	poly_lib sing_1027.htm#SEC1103
3283	polybori sing_2288.htm#IDX915
3284	polybori.lib sing_2288.htm#IDX912
3285	polybori.lib sing_2288.htm#IDX916
3286	polybori_lib sing_2288.htm#IDX913
3287	polymake sing_2133.htm#IDX816
3288	polymake.lib sing_2133.htm#SEC2209
3289	polymakePolytope sing_2134.htm#SEC2210 47302
3290	polymake_lib sing_2133.htm#SEC2209
3291	polynomial solutions sing_843.htm#IDX392
3292	polynomial, opposite sing_359.htm#IDX232
3293	polytope sing_191.htm#SEC231
3294	polytope sing_2133.htm#IDX812
3295	polytopeViaInequalities polytopeViaInequalities sing_2106.htm#SEC2182 52084
3296	polytopeViaPoints sing_2107.htm#SEC2183 281
3297	pos_def sing_1158.htm#SEC1234 4994
3298	poset sing_2273.htm#IDX901
3299	positiveOrthant sing_2077.htm#SEC2153 42102
3300	posweight sing_1691.htm#SEC1767 3364
3301	powSumSym sing_2326.htm#SEC2402 2339
3302	power sing_1119.htm#SEC1195 23365
3303	power set sing_2406.htm#IDX951
3304	powerN sing_1950.htm#SEC2026 20170
3305	powerX sing_1959.htm#SEC2035 47971
3306	power_products sing_1725.htm#SEC1801 54629
3307	powerpolyX sing_1929.htm#SEC2005 37247
3308	powersums sing_2052.htm#SEC2128 59049
3309	preComp sing_1283.htm#SEC1359 16160
3310	preimage sing_322.htm#SEC362
3311	preimage sing_746.htm#IDX361
3312	preimage (plural) sing_477.htm#SEC517
3313	preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1080.htm#IDX502
3314	preimageLattice sing_2634.htm#SEC2710 37348
3315	preimageLoc sing_1080.htm#SEC1156 33315
3316	preimageNC sing_748.htm#SEC800 16037
3317	prepEmbDiv sing_1509.htm#SEC1585 36708
3318	prepMat sing_1762.htm#SEC1838 39868
3319	prepRealclassify sing_1567.htm#SEC1643 10994
3320	prepSV sing_1864.htm#SEC1940 50095
3321	prepareAss sing_1366.htm#SEC1442 21802
3322	presentTree sing_1496.htm#SEC1572 10731
3323	presentation sing_2592.htm#SEC2668 40323
3324	presolve.lib sing_1772.htm#SEC1848
3325	presolve_lib sing_1772.htm#SEC1848
3326	primL sing_1954.htm#SEC2030 14513
3327	primList sing_1953.htm#SEC2029 6802
3328	primRoot sing_1406.htm#SEC1482 14210
3329	primTest sing_1282.htm#SEC1358 8105
3330	primary decomposition sing_1351.htm#IDX582
3331	primary decomposition sing_1374.htm#IDX583
3332	primary decomposition of modules sing_1272.htm#IDX564
3333	primary decomposition, numerical sing_1419.htm#IDX595
3334	primary_char0 sing_1715.htm#SEC1791 61413
3335	primary_char0_no_molien primary_char0_no_molien sing_1717.htm#SEC1793 50477
3336	primary_char0_no_molien_random primary_char0_no_molien_random sing_1722.htm#SEC1798 8422
3337	primary_char0_random primary_char0_random sing_1720.htm#SEC1796 5996
3338	primary_charp sing_1716.htm#SEC1792 37863
3339	primary_charp_no_molien primary_charp_no_molien sing_1718.htm#SEC1794 32282
3340	primary_charp_no_molien_random primary_charp_no_molien_random sing_1723.htm#SEC1799 11498
3341	primary_charp_random primary_charp_random sing_1721.htm#SEC1797 24739
3342	primary_charp_without primary_charp_without sing_1719.htm#SEC1795 49585
3343	primary_charp_without_random primary_charp_without_random sing_1724.htm#SEC1800 36998
3344	primary_invariants sing_1703.htm#SEC1779 5500
3345	primary_invariants_random primary_invariants_random sing_1704.htm#SEC1780 28958
3346	primdec.lib sing_1351.htm#SEC1427
3347	primdecGTZ sing_1353.htm#SEC1429 6091
3348	primdecGTZE sing_1354.htm#SEC1430 64882
3349	primdecMon sing_1271.htm#SEC1347 3856
3350	primdecSY sing_1355.htm#SEC1431 6547
3351	primdecSYE sing_1356.htm#SEC1432 52788
3352	primdecZ sing_1375.htm#SEC1451 48194
3353	primdecZM sing_1376.htm#SEC1452 17214
3354	primdec_lib sing_1351.htm#SEC1427
3355	primdecint.lib sing_1374.htm#SEC1450
3356	primdecint_lib sing_1374.htm#SEC1450
3357	prime sing_323.htm#SEC363
3358	primeClosure sing_1310.htm#SEC1386 43589
3359	primecoeffs sing_982.htm#SEC1058 46153
3360	primefactors sing_324.htm#SEC364
3361	primes sing_977.htm#SEC1053 24408
3362	primitiv.lib sing_1382.htm#SEC1458
3363	primitiv_lib sing_1382.htm#SEC1458
3364	primitive sing_1383.htm#SEC1459 36163
3365	primitive element sing_1383.htm#IDX584
3366	primitiveSpan sing_2641.htm#SEC2717 sprintf
3367	primitive_extra sing_1384.htm#SEC1460 49025
3368	primparam sing_1578.htm#SEC1654 35357
3369	principal intersection sing_507.htm#IDX319
3370	print sing_325.htm#SEC365
3371	print sing_2240.htm#IDX836
3372	printBetti sing_2573.htm#SEC2649 28941
3373	printFreeModule sing_2565.htm#SEC2641 13316
3374	printGraph sing_1206.htm#SEC1282 45041
3375	printGraphG sing_2789.htm#SEC2865 48742
3376	printGroup sing_2622.htm#SEC2698 6791
3377	printHom sing_2568.htm#SEC2644 7070
3378	printMatrix sing_2564.htm#SEC2640 15522
3379	printModule sing_2567.htm#SEC2643 sprintf
3380	printMoebius sing_2279.htm#SEC2355 45828
3381	printResolution sing_2566.htm#SEC2642 29278
3382	printSheaf sing_2777.htm#SEC2853 31762
3383	printStack sing_2791.htm#SEC2867 3692
3384	printTask sing_1099.htm#SEC1175 54549
3385	printVariety sing_2769.htm#SEC2845 2846
3386	printf sing_326.htm#SEC366 2294
3387	printlevel sing_402.htm#SEC442
3388	proc sing_157.htm#SEC197
3389	proc declaration sing_158.htm#SEC198
3390	proc expression sing_159.htm#SEC199
3391	procedure, ASCII help sing_56.htm#IDX125
3392	procedure, ASCII/Texinfo help sing_58.htm#IDX127
3393	procedure, texinfo help sing_57.htm#IDX126
3394	procedures, help string sing_45.htm#SEC82
3395	procedures, static Procedure definition sing_43.htm#SEC78
3396	procs with different argument types procs with different argument types sing_160.htm#SEC200
3397	prodcrit sing_2029.htm#SEC2105 56231
3398	product sing_978.htm#SEC1054 54431
3399	product variety, abstract variety sing_2770.htm#IDX1059
3400	productVariety sing_2770.htm#SEC2846 54191
3401	productgroup sing_2643.htm#SEC2719 55937
3402	progress watch sing_316.htm#IDX163
3403	projectLattice sing_2635.htm#SEC2711 28463
3404	projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_2774.htm#IDX1063
3405	projective dimension purityfiltration_lib sing_787.htm#IDX370
3406	projective limes sing_32.htm#SEC46
3407	projective space, abstract variety sing_2773.htm#IDX1062
3408	projectiveBundle sing_2774.htm#SEC2850 13791
3409	projectiveDimension sing_788.htm#SEC840 8165
3410	projectiveSpace sing_2773.htm#SEC2849 21729
3411	prompt sing_15.htm#SEC21
3412	prompt, option sing_316.htm#IDX182
3413	propagator sing_1204.htm#IDX527 42460
3414	propagator sing_1207.htm#SEC1283
3415	prot, option sing_316.htm#IDX161
3416	protocol of computations sing_316.htm#IDX162
3417	proximitymatrix sing_1537.htm#SEC1613 58403
3418	prune sing_327.htm#SEC367
3419	pruneModule sing_2599.htm#SEC2675 51453
3420	prwalk sing_2764.htm#SEC2840 46963
3421	psigncnd sing_1825.htm#SEC1901 57734
3422	puiseux2generators sing_1636.htm#SEC1712 64508
3423	puiseuxExpansion sing_2194.htm#SEC2270 46277
3424	pure tensor sing_500.htm#IDX307
3425	purelist sing_798.htm#SEC850 15517
3426	purity purityfiltration_lib sing_787.htm#IDX372
3427	purityFiltration sing_789.htm#SEC841 5742
3428	purityTriang sing_790.htm#SEC842 3665
3429	purityfiltration.lib purityfiltration_lib sing_787.htm#IDX365
3430	purityfiltration_lib purityfiltration_lib sing_787.htm#IDX366
3431	pushForward sing_2660.htm#SEC2736 26697
3432	pwalk sing_1220.htm#SEC1296 61187
3433	pyobject sing_192.htm#SEC232
3434	pyobject sing_2288.htm#IDX918
3435	pyobject declarations pyobject declarations sing_193.htm#SEC233
3436	pyobject expressions pyobject expressions sing_194.htm#SEC234
3437	pyobject operations sing_195.htm#SEC235
3438	pyobject related functions pyobject related functions sing_196.htm#SEC236
3439	pyramid sing_2454.htm#SEC2530 7421
3440	python_eval sing_197.htm#SEC237
3441	python_import sing_198.htm#SEC238
3442	python_run sing_199.htm#SEC239
3443	qbase sing_2055.htm#SEC2131 8633
3444	qepcad sing_2464.htm#SEC2540 39171
3445	qepcadsystem sing_2465.htm#SEC2541 31977
3446	qhmatrix sing_1689.htm#SEC1765 61813
3447	qhmoduli.lib sing_1653.htm#SEC1729
3448	qhmoduli_lib sing_1653.htm#SEC1729
3449	qhspectrum sing_1676.htm#SEC1752 13732
3450	qhweight sing_328.htm#SEC368
3451	qmatrix.lib sing_781.htm#SEC833
3452	qmatrix_lib sing_781.htm#SEC833
3453	qminor sing_783.htm#SEC835 52670
3454	qrds sing_329.htm#SEC369
3455	qring Miscellaneous oddities sing_166.htm#SEC206
3456	qring sing_420.htm#IDX295
3457	qring (plural) sing_445.htm#SEC485
3458	qring declaration sing_170.htm#SEC210
3459	qring declaration (plural) qring declaration (plural) sing_446.htm#SEC486
3460	qring related functions (plural) qring related functions (plural) sing_447.htm#SEC487
3461	qring ring ideal 'factor ring' sing_1089.htm#IDX508
3462	qringNF, option sing_316.htm#IDX164
3463	qslimgb sing_958.htm#SEC1034 51999
3464	quadraticSieve sing_1967.htm#SEC2043 58557
3465	quantMat sing_782.htm#SEC834 56227
3466	quickclass sing_1559.htm#SEC1635 14018
3467	quit sing_392.htm#SEC432
3468	quotSheaf sing_2786.htm#SEC2862 49619
3469	quote sing_330.htm#SEC370
3470	quotient sing_331.htm#SEC371
3471	quotient (plural) sing_478.htm#SEC518
3472	quotientLatticeBasis quotientLatticeBasis sing_2108.htm#SEC2184 15613
3473	quotientMain sing_1817.htm#SEC1893 39870
3474	quotientMon sing_1262.htm#SEC1338 57149
3475	rHRR sing_2366.htm#SEC2442 20131
3476	rJanet sing_2761.htm#SEC2837 30716
3477	rMacaulay sing_1013.htm#SEC1089 45499
3478	rad_con sing_1040.htm#SEC1116 21777
3479	radical sing_1363.htm#SEC1439 1407
3480	radicalEHV sing_1364.htm#SEC1440 33703
3481	radicalMemberShip sing_2216.htm#SEC2292 28527
3482	radicalMon sing_1263.htm#SEC1339 64912
3483	radicalZ sing_1378.htm#SEC1454 5783
3484	randcharpoly sing_2049.htm#SEC2125 37737
3485	randlinpoly sing_2051.htm#SEC2127 22330
3486	random sing_332.htm#SEC372
3487	random sing_359.htm#IDX244
3488	random sing_2261.htm#IDX875
3489	random sing_2262.htm#IDX877
3490	random number generator, seed sing_359.htm#IDX242
3491	random.lib sing_1048.htm#SEC1124
3492	randomBinomial sing_1060.htm#SEC1136 17913
3493	randomCheck sing_1880.htm#SEC1956 20973
3494	randomLast sing_1059.htm#SEC1135 2046
3495	randomPoint sing_2109.htm#SEC2185 22561
3496	randomPolyInT sing_2225.htm#SEC2301 2264
3497	random_lib sing_1048.htm#SEC1124
3498	randomid sing_1050.htm#SEC1126 7815
3499	randommat sing_1051.htm#SEC1127 33569
3500	rank sing_210.htm#IDX137
3501	rank sing_333.htm#SEC373
3502	rankSheaf sing_2778.htm#SEC2854 11850
3503	ratSol sing_851.htm#SEC903 62488
3504	ratgb.lib sing_841.htm#IDX381
3505	ratgb_lib sing_841.htm#IDX382
3506	rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1441.htm#IDX622
3507	rational functions sing_807.htm#IDX378
3508	rational normal curve, projection. sing_1442.htm#IDX623
3509	rational normal curve, projection. sing_1445.htm#IDX624
3510	rational normal curve, projection. sing_1446.htm#IDX625
3511	rational solutions sing_843.htm#IDX393
3512	rational univariate projection sing_2049.htm#IDX809
3513	rationalCurve sing_2798.htm#SEC2874 61201
3514	rationalPointConic sing_1443.htm#SEC1519 9761
3515	ratstd sing_842.htm#SEC894 61346
3516	rays sing_2110.htm#SEC2186 44445
3517	rcolon sing_2668.htm#SEC2744 1208
3518	re2squ sing_1420.htm#SEC1496 24350
3519	read sing_334.htm#SEC374
3520	readNmzData sing_1338.htm#SEC1414 18957
3521	reading, option sing_316.htm#IDX183
3522	readline sing_1.htm#IDX5
3523	real sing_28.htm#IDX74
3524	real root isolation sing_2745.htm#IDX1038
3525	real roots, univariate polynomial sing_2056.htm#IDX811
3526	real roots, univariate projection sing_2040.htm#IDX807
3527	real roots,sign conditions sing_1823.htm#IDX787
3528	realclassify sing_2740.htm#SEC2816 51416
3529	realclassify.lib sing_2739.htm#SEC2815
3530	realclassify_lib sing_2739.htm#SEC2815
3531	realizationDim sing_2188.htm#SEC2264 37756
3532	realizationDimPoly sing_2190.htm#SEC2266 3611
3533	realizationMatroids.lib realizationMatroids_lib sing_2187.htm#SEC2263
3534	realizationMatroids_lib realizationMatroids_lib sing_2187.htm#SEC2263
3535	realmorsesplit sing_2741.htm#SEC2817 16318
3536	realpoly sing_1387.htm#SEC1463 9453
3537	realrad sing_1389.htm#SEC1465 43381
3538	realrad.lib sing_1386.htm#SEC1462
3539	realrad_lib sing_1386.htm#SEC1462
3540	realzero sing_1388.htm#SEC1464 12712
3541	recursive_boolean_poly recursive_boolean_poly sing_2294.htm#SEC2370 17045
3542	recursive_from_boolean_poly recursive_from_boolean_poly sing_2300.htm#SEC2376 37794
3543	redSB, option sing_316.htm#IDX165
3544	redTail, option sing_316.htm#IDX167
3545	redThrough, option sing_316.htm#IDX168
3546	redefine, option sing_316.htm#IDX184
3547	reduce sing_335.htm#SEC375
3548	reduce sing_521.htm#IDX324
3549	reduce sing_989.htm#IDX437
3550	reduce sing_990.htm#IDX440
3551	reduce (plural) sing_479.htm#SEC519
3552	reduce (up to a bound) sing_359.htm#IDX245
3553	reduceIntChain sing_2604.htm#SEC2680 17776
3554	reduced sing_988.htm#IDX434
3555	reduced standard basis sing_316.htm#IDX166
3556	reduction sing_1741.htm#SEC1817 31048
3557	reesclos.lib sing_1390.htm#SEC1466
3558	reesclos_lib sing_1390.htm#SEC1466
3559	reference sing_200.htm#SEC240
3560	reference declarations reference declarations sing_201.htm#SEC241
3561	reference expressions reference expressions sing_202.htm#SEC242
3562	reference operations reference and shared operations sing_205.htm#SEC245
3563	reference related functions reference and shared related functions sing_206.htm#SEC246
3564	regCM sing_1302.htm#SEC1378 25488
3565	regIdeal sing_1288.htm#SEC1364 3827
3566	regMonCurve sing_1291.htm#SEC1367 41311
3567	regularity Syzygies and resolutions sing_336.htm#SEC376
3568	regularity sing_933.htm#SEC990
3569	reiffen sing_560.htm#SEC612 32856
3570	rel_orbit_variety sing_1734.htm#SEC1810 34278
3571	relations sing_779.htm#IDX364
3572	relativeInteriorPoint relativeInteriorPoint sing_2111.htm#SEC2187 30097
3573	relative_orbit_variety relative_orbit_variety sing_1735.htm#SEC1811 32995
3574	relweight sing_1690.htm#SEC1766 10658
3575	remainder sing_1810.htm#SEC1886 1191
3576	remainderMain sing_1818.htm#SEC1894 3532
3577	removeCone sing_2129.htm#SEC2205 33877
3578	removepower sing_1547.htm#SEC1623 47644
3579	repart sing_337.htm#SEC377
3580	replace sing_1919.htm#SEC1995 50075
3581	representation, math objects Representation of mathematical objects sing_919.htm#SEC971
3582	res sing_338.htm#SEC378 10393
3583	resbinomial.lib sing_1450.htm#IDX628
3584	resbinomial_lib sing_1450.htm#IDX629
3585	reservedName sing_339.htm#SEC379
3586	resfunction sing_1464.htm#SEC1540 59312
3587	resgraph.lib sing_1482.htm#SEC1558
3588	resgraph_lib sing_1482.htm#SEC1558
3589	resjung.lib sing_1486.htm#SEC1562
3590	resjung_lib sing_1486.htm#SEC1562
3591	reslist sing_1478.htm#SEC1554 64950
3592	resolution purityfiltration_lib sing_161.htm#SEC201
3593	resolution sing_787.htm#IDX371
3594	resolution (plural) sing_448.htm#SEC488
3595	resolution declarations resolution declarations sing_162.htm#SEC202
3596	resolution declarations (plural) resolution declarations (plural) sing_449.htm#SEC489
3597	resolution expressions resolution expressions sing_163.htm#SEC203
3598	resolution expressions (plural) resolution expressions (plural) sing_450.htm#SEC490
3599	resolution graph sing_1532.htm#IDX642
3600	resolution related functions resolution related functions sing_164.htm#SEC204
3601	resolution related functions (plural) resolution related functions (plural) sing_451.htm#SEC491
3602	resolution, La Scala's method sing_289.htm#SEC329
3603	resolution, computation of sing_338.htm#IDX186
3604	resolution, hilbert-driven sing_264.htm#SEC304
3605	resolutionInLocalization resolutionInLocalization sing_2484.htm#SEC2560 31106
3606	resolutiongraph sing_1533.htm#SEC1609 32697
3607	resolve sing_1494.htm#SEC1570 27374
3608	resolve.lib sing_1490.htm#SEC1566
3609	resolve_lib sing_1490.htm#SEC1566
3610	resources.lib sing_1061.htm#SEC1137
3611	resources_lib sing_1061.htm#SEC1137
3612	restriction sing_2254.htm#IDX863
3613	restriction sing_2270.htm#IDX896
3614	restriction sing_2271.htm#IDX898
3615	restriction of sing_565.htm#IDX347
3616	restrictionIdeal sing_575.htm#SEC627 49796
3617	restrictionModule sing_576.htm#SEC628 62461
3618	resultant sing_303.htm#SEC343
3619	resultant sing_340.htm#SEC380
3620	reszeta.lib sing_1503.htm#SEC1579
3621	reszeta_lib sing_1503.htm#SEC1579
3622	return sing_393.htm#SEC433
3623	return type of procedures Return type of procedures sing_418.htm#SEC458
3624	returnSB, option sing_316.htm#IDX152
3625	reverse sing_2070.htm#SEC2146 35880
3626	reverse lexicographical ordering sing_923.htm#IDX398
3627	reynolds_molien sing_1710.htm#SEC1786 45316
3628	rho sing_1961.htm#SEC2037 51414
3629	rightInverse sing_1899.htm#SEC1975 6558
3630	rightKernel sing_1897.htm#SEC1973 46603
3631	rightModulo sing_766.htm#SEC818 12618
3632	rightNF sing_765.htm#SEC817 42610
3633	rightNFWeyl sing_868.htm#SEC920 35828
3634	rightOre sing_2725.htm#SEC2801 56918
3635	rightStd sing_764.htm#SEC816 5740
3636	ring sing_165.htm#SEC205
3637	ring (plural) sing_452.htm#SEC492
3638	ring coefficients hasTransExtensionCoefficient sing_1087.htm#IDX506
3639	ring coefficients sing_1088.htm#IDX507
3640	ring declarations sing_167.htm#SEC207
3641	ring declarations (plural) ring declarations (plural) sing_453.htm#SEC493
3642	ring operations sing_169.htm#SEC209
3643	ring operations (plural) ring operations (plural) sing_454.htm#SEC494
3644	ring related functions ring related functions sing_168.htm#SEC208
3645	ring related functions (plural) ring related functions (plural) sing_455.htm#SEC495
3646	ring, opposite sing_359.htm#IDX229
3647	ring.lib sing_1066.htm#SEC1142
3648	ring_cf sing_210.htm#IDX138
3649	ring_lib sing_1066.htm#SEC1142
3650	ring_list sing_342.htm#SEC382
3651	ring_variable sing_2241.htm#IDX840
3652	ring_variable sing_2242.htm#IDX842
3653	ring_variable sing_2243.htm#IDX846
3654	ring_variable sing_2244.htm#IDX848
3655	ringlist sing_341.htm#SEC381
3656	ringlist (plural) sing_480.htm#SEC520
3657	ringtensor sing_1078.htm#SEC1154 56648
3658	ringweights sing_1079.htm#SEC1155 33307
3659	rinvar.lib sing_1746.htm#SEC1822
3660	rinvar_lib sing_1746.htm#SEC1822
3661	rmNmzFiles sing_1343.htm#SEC1419 32601
3662	rm_unitcol sing_1136.htm#SEC1212 5591
3663	rm_unitrow sing_1135.htm#SEC1211 35694
3664	rmx sing_1844.htm#SEC1920 17675
3665	rncAntiCanonicalMap sing_1442.htm#SEC1518 41965
3666	rncItProjEven sing_1446.htm#SEC1522 18200
3667	rncItProjOdd sing_1445.htm#SEC1521 61976
3668	root of Bernstein-Sato polynomial sing_542.htm#IDX336
3669	rootIsolation sing_2756.htm#SEC2832 34513
3670	rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2755.htm#SEC2831 42387
3671	rootIsolationPrimdec rootIsolationPrimdec sing_2757.htm#SEC2833 35485
3672	rootisolation.lib sing_2745.htm#SEC2821
3673	rootisolation_lib sing_2745.htm#SEC2821
3674	rootofUnity sing_1081.htm#SEC1157 21365
3675	roots sing_1811.htm#SEC1887 18436
3676	rootsMain sing_1819.htm#SEC1895 54934
3677	rootsModp sing_1943.htm#SEC2019 47315
3678	rootsmr.lib sing_2040.htm#SEC2116
3679	rootsmr_lib sing_2040.htm#SEC2116
3680	rootsur.lib sing_2056.htm#SEC2132
3681	rootsur_lib sing_2056.htm#SEC2132
3682	round sing_1941.htm#SEC2017 9248
3683	rowShift sing_210.htm#IDX141
3684	rowShift sing_212.htm#SEC252
3685	rowred sing_1132.htm#SEC1208 63416
3686	rp, global ordering sing_923.htm#IDX397
3687	rstandard.lib sing_2758.htm#SEC2834
3688	rstandard_lib sing_2758.htm#SEC2834
3689	rswalk sing_2808.htm#SEC2884 50903
3690	rtimer sing_406.htm#SEC446
3691	rvalue No rvalue of increments and assignments sing_412.htm#SEC452
3692	rvar sing_343.htm#SEC383
3693	rwalk sing_2765.htm#SEC2841 42525
3694	rwalk.lib sing_2763.htm#SEC2839
3695	rwalk_lib sing_2763.htm#SEC2839
3696	sRes sing_2570.htm#SEC2646 23381
3697	sa_poly_reduce sing_530.htm#SEC582 60856
3698	sa_reduce sing_529.htm#SEC581 55799
3699	sagbi sing_1396.htm#SEC1472 46653
3700	sagbi basis sing_2394.htm#IDX948
3701	sagbi.lib sing_1393.htm#SEC1469
3702	sagbiAlg sing_2387.htm#SEC2463 sprintf
3703	sagbiMod sing_2388.htm#SEC2464 sprintf
3704	sagbiPart sing_1397.htm#SEC1473 56066
3705	sagbiReduce sing_1395.htm#SEC1471 19036
3706	sagbiSPoly sing_1394.htm#SEC1470 17365
3707	sagbi_lib sing_1393.htm#SEC1469
3708	salida sing_1475.htm#SEC1551 9839
3709	sameComponent sing_2023.htm#SEC2099 13540
3710	sameQ sing_1822.htm#SEC1898 45579
3711	sat sing_1201.htm#SEC1277 6266
3712	satiety sing_1290.htm#SEC1366 34323
3713	satstd sing_2282.htm#SEC2358 16128
3714	sba sing_344.htm#SEC384
3715	scalarProd sing_519.htm#SEC571 54488
3716	scheme sing_2445.htm#SEC2521 15722
3717	schubert.lib sing_2767.htm#SEC2843
3718	schubert_lib sing_2767.htm#SEC2843
3719	sdb, source code debugger Source code debugger sing_66.htm#SEC103
3720	second degree sing_1005.htm#IDX485
3721	secondary fan sing_2133.htm#IDX814
3722	secondary polytope sing_2133.htm#IDX815
3723	secondaryPolytope sing_2138.htm#SEC2214 48451
3724	secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1731.htm#SEC1807 37058
3725	secondary_char0 sing_1726.htm#SEC1802 31029
3726	secondary_charp sing_1728.htm#SEC1804 16364
3727	secondary_no_molien sing_1729.htm#SEC1805 3616
3728	secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1732.htm#SEC1808 31675
3729	segre sing_2321.htm#SEC2397 44035
3730	select sing_1202.htm#SEC1278 17096
3731	select1 sing_1203.htm#SEC1279 32617
3732	semaphore sing_359.htm#IDX249 44342
3733	semaphore sing_1065.htm#SEC1141
3734	semaphores sing_1061.htm#IDX501
3735	semiCMcod2 sing_1687.htm#SEC1763 15905
3736	semiGroup sing_2389.htm#SEC2465 sprintf
3737	semiMod sing_2390.htm#SEC2466 sprintf
3738	semidiv sing_2015.htm#SEC2091 58107
3739	semigroup sing_1536.htm#SEC1612 29045
3740	semigroup sing_1540.htm#IDX649
3741	semigroup of values sing_1626.htm#IDX764
3742	semigroupGenerator sing_2112.htm#SEC2188 59446
3743	sep sing_1373.htm#SEC1449 sprintf
3744	separateHNE sing_1637.htm#SEC1713 12052
3745	separator sing_1273.htm#SEC1349 33000
3746	serreRelations sing_686.htm#SEC738 33994
3747	set sing_2236.htm#IDX826
3748	setBaseMultigrading sing_2615.htm#SEC2691 6575
3749	setLetterplaceAttributes setLetterplaceAttributes sing_676.htm#SEC728 5759
3750	setLinearForms sing_2113.htm#SEC2189 62731
3751	setModuleGrading sing_2627.htm#SEC2703 59018
3752	setMultiplicity sing_2114.htm#SEC2190 27537
3753	setNmzDataPath sing_1340.htm#SEC1416 18123
3754	setNmzExecPath sing_1336.htm#SEC1412 38993
3755	setNmzFilename sing_1339.htm#SEC1415 20206
3756	setNmzOption sing_1333.htm#SEC1409 9012
3757	setUniformizingParameter setUniformizingParameter sing_2810.htm#SEC2886 63635
3758	set_is_injective sing_2003.htm#SEC2079 8429
3759	setcores sing_1063.htm#SEC1139 49704
3760	setenv sing_359.htm#IDX252
3761	setinitials sing_2455.htm#SEC2531 24792
3762	setring sing_345.htm#SEC385
3763	sh sing_359.htm#IDX254
3764	shared sing_200.htm#SEC240
3765	shared declarations sing_203.htm#SEC243
3766	shared expressions sing_204.htm#SEC244
3767	shared operations reference and shared operations sing_205.htm#SEC245
3768	shared related functions reference and shared related functions sing_206.htm#SEC246
3769	sheaf cohomology sing_1513.htm#IDX630
3770	sheafCoh sing_1519.htm#SEC1595 64501
3771	sheafCohBGG sing_1517.htm#SEC1593 13439
3772	sheafCohBGG2 sing_1518.htm#SEC1594 3338
3773	sheafcoh.lib sing_1513.htm#SEC1589
3774	sheafcoh_lib sing_1513.htm#SEC1589
3775	shiftPoly sing_679.htm#SEC731 65223
3776	short sing_403.htm#SEC443
3777	show sing_1014.htm#SEC1090 15599
3778	showBO sing_1495.htm#SEC1571 20089
3779	showDataTypes sing_1497.htm#SEC1573 4270
3780	showNmzOptions sing_1334.htm#SEC1410 64955
3781	showNuminvs sing_1331.htm#SEC1407 18934
3782	showgrades sing_792.htm#SEC844 48081
3783	showrecursive sing_1015.htm#SEC1091 6127
3784	sickle sing_626.htm#SEC678 54811
3785	signal handler sing_2826.htm#SEC2916
3786	signatureBrieskorn sing_1696.htm#SEC1772 26283
3787	signatureL sing_2284.htm#SEC2360 65493
3788	signatureLqf sing_2285.htm#SEC2361 18811
3789	signatureNemethi sing_1698.htm#SEC1774 21981
3790	signaturePuiseux sing_1697.htm#SEC1773 23398
3791	signcnd sing_1824.htm#SEC1900 40147
3792	signcond.lib sing_1823.htm#SEC1899
3793	signcond_lib sing_1823.htm#SEC1899
3794	simplePrune sing_2608.htm#SEC2684 sprintf
3795	simplesolver sing_1768.htm#SEC1844 13418
3796	simplex sing_346.htm#SEC386
3797	simplexOut sing_1795.htm#SEC1871 56099
3798	simplify sing_347.htm#SEC387
3799	simplifyRat sing_863.htm#SEC915 52658
3800	sing.lib sing_1663.htm#SEC1739
3801	sing4ti2.lib sing_1399.htm#SEC1475
3802	sing4ti2_lib sing_1399.htm#SEC1475
3803	sing_lib sing_1663.htm#SEC1739
3804	singular locus of D-module sing_843.htm#IDX387
3805	singularities sing_1595.htm#IDX666
3806	singularities sing_1596.htm#IDX677
3807	singularities sing_1597.htm#IDX680
3808	singularities sing_1598.htm#IDX683
3809	singularities sing_1599.htm#IDX686
3810	singularities sing_1600.htm#IDX690
3811	singularities sing_1601.htm#IDX694
3812	singularities sing_1602.htm#IDX700
3813	singularities sing_1603.htm#IDX708
3814	singularities sing_1604.htm#IDX714
3815	singularities sing_1605.htm#IDX722
3816	singularities sing_1606.htm#IDX732
3817	singularities sing_1694.htm#IDX779
3818	singularities sing_2383.htm#IDX943
3819	singularities, resolution of Resolution of singularities sing_906.htm#SEC958
3820	singularity sing_1560.htm#SEC1636 23002
3821	singularrc sing_20.htm#IDX73
3822	size Miscellaneous oddities sing_348.htm#SEC388
3823	size sing_420.htm#IDX294
3824	skewmat sing_1120.htm#SEC1196 2167
3825	sleep sing_354.htm#SEC394
3826	slimgb sing_349.htm#SEC389
3827	slimgb sing_883.htm#SEC935
3828	slimgb (plural) sing_481.htm#SEC521
3829	slocus sing_1675.htm#SEC1751 27853
3830	smatrix sing_171.htm#SEC211
3831	smith sing_1908.htm#SEC1984 61915
3832	smithNormalForm sing_2663.htm#SEC2739 7174
3833	solutionsMod2 sing_1958.htm#SEC2034 53360
3834	solve sing_1005.htm#IDX486 3078
3835	solve sing_1789.htm#SEC1865
3836	solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_292.htm#SEC332
3837	solve.lib sing_1787.htm#SEC1863
3838	solveTInitialFormPar solveTInitialFormPar sing_2219.htm#SEC2295 36670
3839	solve_IP sing_1246.htm#SEC1322 59518
3840	solve_lib sing_1787.htm#SEC1863
3841	solvelinearpart sing_1782.htm#SEC1858 42872
3842	sort sing_979.htm#SEC1055 58207
3843	sortIntvec sing_597.htm#SEC649 60798
3844	sortandmap sing_1783.htm#SEC1859 10314
3845	sortier sing_1745.htm#SEC1821 3555
3846	sortvars sing_1784.htm#SEC1860 61778
3847	sortvec sing_350.htm#SEC390
3848	source sing_2586.htm#SEC2662 63163
3849	source code debugger, sdb Source code debugger sing_66.htm#SEC103
3850	spaceCur sing_2392.htm#SEC2468 sprintf
3851	spadd sing_1609.htm#SEC1685 48739
3852	span sing_2115.htm#SEC2191 64343
3853	sparseHomogIdeal sing_1057.htm#SEC1133 22631
3854	sparseInterpolation sing_2440.htm#SEC2516 28771
3855	sparseid sing_1052.htm#SEC1128 20824
3856	sparsemat sing_1054.htm#SEC1130 17653
3857	sparsematrix sing_1053.htm#SEC1129 41031
3858	sparsepoly sing_1055.htm#SEC1131 21649
3859	sparsetriag sing_1056.htm#SEC1132 50657
3860	spcurve.lib sing_1683.htm#SEC1759
3861	spcurve_lib sing_1683.htm#SEC1759
3862	special characters, non-english sing_409.htm#IDX287
3863	spectral pairs sing_1595.htm#IDX675
3864	spectral pairs sing_1602.htm#IDX707
3865	spectral pairs sing_1604.htm#IDX721
3866	spectral pairs sing_1605.htm#IDX730
3867	spectral pairs sing_1617.htm#IDX746
3868	spectral pairs sing_1619.htm#IDX757
3869	spectralNeg sing_1505.htm#SEC1581 36691
3870	spectrum sing_1595.htm#IDX674 47545
3871	spectrum sing_1601.htm#SEC1677
3872	spectrum sing_1601.htm#IDX699
3873	spectrum sing_1602.htm#IDX706
3874	spectrum sing_1603.htm#IDX713
3875	spectrum sing_1604.htm#IDX720
3876	spectrum sing_1605.htm#IDX729
3877	spectrum sing_1617.htm#IDX745
3878	spectrum sing_1619.htm#IDX756
3879	spectrum sing_1694.htm#IDX781
3880	spectrum.lib sing_1693.htm#SEC1769
3881	spectrum_lib sing_1693.htm#SEC1769
3882	spectrumnd sing_1694.htm#SEC1770 29943
3883	spgamma sing_1616.htm#SEC1692 59653
3884	spgeomgenus sing_1615.htm#SEC1691 57796
3885	spissemicont sing_1612.htm#SEC1688 23679
3886	split sing_1016.htm#SEC1092 29794
3887	splitPolygon sing_2140.htm#SEC2216 706
3888	splitring sing_1385.htm#SEC1461 56404
3889	splitting sing_1281.htm#SEC1357 34734
3890	spmilnor sing_1614.htm#SEC1690 32933
3891	spmul sing_1611.htm#SEC1687 43607
3892	spnf sing_1162.htm#SEC1238 57309
3893	spoly sing_2026.htm#SEC2102 35454
3894	sppairs sing_1602.htm#SEC1678 49513
3895	sppnf sing_1607.htm#SEC1683 16650
3896	sppprint sing_1608.htm#SEC1684 43682
3897	spprint sing_1163.htm#SEC1239 18671
3898	sprintf sing_352.htm#SEC392 55889
3899	spsemicont sing_1613.htm#SEC1689 61169
3900	spsub sing_1610.htm#SEC1686 54296
3901	sqfrNorm sing_1812.htm#SEC1888 20546
3902	sqfrNormMain sing_1820.htm#SEC1896 9890
3903	sqr sing_1938.htm#SEC2014 sprintf
3904	sqrfree sing_351.htm#SEC391
3905	squareRoot sing_1957.htm#SEC2033 17446
3906	squarefree sing_1638.htm#SEC1714 48485
3907	sres sing_353.htm#SEC393
3908	ssi Parallelization with ssi links sing_878.htm#SEC930
3909	stabilizer sing_2312.htm#SEC2388 36692
3910	stack, moduli space of stable maps sing_2791.htm#IDX1067
3911	stack, moduli space of stable maps, rational curves moduliSpace sing_2790.htm#IDX1066
3912	stackNets sing_2712.htm#SEC2788 30974
3913	staircase sing_1829.htm#SEC1905 49781
3914	standard sing_2033.htm#SEC2109 14067
3915	standard bases, saturation sing_2282.htm#IDX909
3916	standard bases. sing_2281.htm#IDX908
3917	standard.lib sing_957.htm#IDX425
3918	standard_lib sing_957.htm#IDX426
3919	startNmz sing_1342.htm#SEC1418 21925
3920	startTasks sing_1100.htm#SEC1176 16715
3921	static procedures Procedure definition sing_43.htm#SEC78
3922	status sing_354.htm#SEC394
3923	std sing_355.htm#SEC395
3924	std sing_881.htm#SEC933
3925	std (plural) sing_482.htm#SEC522
3926	stdfglm sing_356.htm#SEC396 256
3927	stdhilb sing_357.htm#SEC397 63138
3928	stdlocus sing_1002.htm#SEC1078 25619
3929	stopTask sing_1101.htm#SEC1177 6801
3930	storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2504.htm#SEC2580 64428
3931	stratify sing_1763.htm#SEC1839 56744
3932	stratify.lib sing_1761.htm#SEC1837
3933	stratify_lib sing_1761.htm#SEC1837
3934	string Miscellaneous oddities sing_172.htm#SEC212
3935	string sing_420.htm#IDX297
3936	string declarations sing_173.htm#SEC213
3937	string expressions sing_174.htm#SEC214
3938	string operations sing_176.htm#SEC216
3939	string related functions string related functions sing_177.htm#SEC217
3940	string type cast sing_175.htm#SEC215
3941	stripHNE sing_1635.htm#SEC1711 19265
3942	sturm sing_2066.htm#SEC2142 54353
3943	sturmha sing_2068.htm#SEC2144 12467
3944	sturmhaseq sing_2069.htm#SEC2145 59133
3945	sturmquery sing_2044.htm#SEC2120 10805
3946	sturmseq sing_2067.htm#SEC2143 23005
3947	sublists sing_2406.htm#SEC2482 2979
3948	submat sing_1121.htm#SEC1197 37665
3949	subquotient sing_2578.htm#SEC2654 40364
3950	subrInterred sing_1045.htm#SEC1121 10165
3951	subset_sum01 sing_1987.htm#SEC2063 60620
3952	subset_sum02 sing_1988.htm#SEC2064 37340
3953	subst sing_358.htm#SEC398
3954	subst (plural) sing_483.htm#SEC523
3955	substitute sing_1044.htm#SEC1120 28919
3956	sugarCrit, option sing_316.htm#IDX169
3957	sum sing_980.htm#SEC1056 555
3958	sum_of_powers sing_2325.htm#SEC2401 12170
3959	sumlist sing_1477.htm#SEC1553 59918
3960	sumofquotients sing_2799.htm#SEC2875 4569
3961	super-commutative algebras Graded commutative algebras (SCA) sing_492.htm#SEC544
3962	superCommutative sing_763.htm#SEC815 45528
3963	super_increasing_knapsack super_increasing_knapsack sing_1999.htm#SEC2075 9177
3964	surf.lib sing_1846.htm#SEC1922
3965	surf_lib sing_1846.htm#SEC1922
3966	surfacesignature.lib surfacesignature_lib sing_1695.htm#SEC1771
3967	surfacesignature_lib surfacesignature_lib sing_1695.htm#SEC1771
3968	surfer sing_1.htm#IDX8 14287
3969	surfer sing_1848.htm#SEC1924
3970	surfex sing_1.htm#IDX7
3971	surfex.lib sing_1849.htm#SEC1925
3972	surfex_lib sing_1849.htm#SEC1925
3973	suspend sing_354.htm#SEC394
3974	swalk sing_2807.htm#SEC2883 16794
3975	swalk.lib sing_2806.htm#SEC2882
3976	swalk_lib sing_2806.htm#SEC2882
3977	swap sing_1564.htm#SEC1640 15408
3978	swap sing_2243.htm#IDX844
3979	switch No case or switch statement sing_414.htm#SEC454
3980	switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2815.htm#SEC2891 1827
3981	syModStd sing_1409.htm#SEC1485 50246
3982	symNsym sing_2319.htm#SEC2395 55230
3983	sym_gauss sing_1146.htm#SEC1222 5121
3984	symm sing_2318.htm#SEC2394 64628
3985	symmStd sing_1408.htm#SEC1484 39353
3986	symmat sing_1122.htm#SEC1198 61294
3987	symmetric basis sing_1138.htm#IDX512
3988	symmetric power sing_1140.htm#IDX514
3989	symmetric product sing_2466.htm#IDX993
3990	symmetricBasis sing_1138.htm#SEC1214 sprintf
3991	symmetricPower sing_1140.htm#SEC1216 6542
3992	symmetricPowerSheaf sing_2785.htm#SEC2861 56922
3993	symmetries sing_2308.htm#IDX942
3994	symmfunc sing_2053.htm#SEC2129 45575
3995	symodstd.lib sing_1403.htm#SEC1479
3996	symodstd_lib sing_1403.htm#SEC1479
3997	symsignature sing_2043.htm#SEC2119 10520
3998	syndrome sing_1876.htm#SEC1952 14057
3999	sysBin sing_1874.htm#SEC1950 41948
4000	sysCRHT sing_1871.htm#SEC1947 58930
4001	sysCRHTMindist sing_1872.htm#SEC1948 13692
4002	sysFL sing_1887.htm#SEC1963 53040
4003	sysNewton sing_1873.htm#SEC1949 19704
4004	sysQE sing_1877.htm#SEC1953 61026
4005	sys_code sing_1868.htm#SEC1944 20220
4006	system sing_359.htm#SEC399
4007	system, -- sing_359.htm#IDX277
4008	system, --long_option_name sing_359.htm#IDX280
4009	system, --long_option_name=value sing_359.htm#IDX282
4010	system, HC sing_359.htm#IDX215
4011	system, LLL sing_359.htm#IDX219
4012	system, Singular sing_359.htm#IDX258
4013	system, SingularLib sing_359.htm#IDX260
4014	system, absFact sing_359.htm#IDX190
4015	system, alarm sing_359.htm#IDX189
4016	system, blackbox sing_359.htm#IDX191
4017	system, bracket sing_359.htm#IDX196
4018	system, browsers sing_359.htm#IDX195
4019	system, btest sing_359.htm#IDX198
4020	system, complexNearZero sing_359.htm#IDX199
4021	system, contributors sing_359.htm#IDX201
4022	system, cpu sing_359.htm#IDX203
4023	system, cpu sing_359.htm#IDX276
4024	system, denom_list sing_359.htm#IDX205
4025	system, eigenvals sing_359.htm#IDX206
4026	system, env sing_359.htm#IDX207
4027	system, executable sing_359.htm#IDX209
4028	system, freegb sing_359.htm#IDX210
4029	system, getPrecDigits sing_359.htm#IDX213
4030	system, getenv sing_359.htm#IDX212
4031	system, gmsnf sing_359.htm#IDX214
4032	system, hessenberg sing_359.htm#IDX216
4033	system, install sing_359.htm#IDX218
4034	system, nblocks sing_359.htm#IDX222
4035	system, nc_hilb sing_359.htm#IDX224
4036	system, neworder sing_359.htm#IDX225
4037	system, newstruct sing_359.htm#IDX226
4038	system, opp sing_359.htm#IDX227
4039	system, oppose sing_359.htm#IDX230
4040	system, pcvBasis sing_359.htm#IDX239
4041	system, pcvCV2P sing_359.htm#IDX237
4042	system, pcvDim sing_359.htm#IDX238
4043	system, pcvLAddL sing_359.htm#IDX233
4044	system, pcvMinDeg sing_359.htm#IDX235
4045	system, pcvP2CV sing_359.htm#IDX236
4046	system, pcvPMulL sing_359.htm#IDX234
4047	system, pid sing_359.htm#IDX241
4048	system, random sing_359.htm#IDX243
4049	system, reserve sing_359.htm#IDX247
4050	system, reservedLink sing_359.htm#IDX248
4051	system, semaphore sing_359.htm#IDX250
4052	system, semic sing_359.htm#IDX251
4053	system, setenv sing_359.htm#IDX253
4054	system, sh sing_359.htm#IDX255
4055	system, shrinktest sing_359.htm#IDX256
4056	system, spadd sing_359.htm#IDX261
4057	system, spectrum sing_359.htm#IDX262
4058	system, spmul sing_359.htm#IDX263
4059	system, std_syz sing_359.htm#IDX264
4060	system, stest sing_359.htm#IDX265
4061	system, tensorModuleMult sing_359.htm#IDX266
4062	system, twostd sing_359.htm#IDX267
4063	system, uname sing_359.htm#IDX270
4064	system, version sing_359.htm#IDX273
4065	system, with sing_359.htm#IDX274
4066	systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2481.htm#SEC2557 63094
4067	syz sing_360.htm#SEC400
4068	syz (plural) sing_484.htm#SEC524
4069	tDetropicalise sing_2221.htm#SEC2297 23532
4070	tInitialForm sing_2205.htm#SEC2281 24484
4071	tInitialFormPar sing_2217.htm#SEC2293 9584
4072	tInitialFormParMax sing_2218.htm#SEC2294 7829
4073	tInitialIdeal sing_2206.htm#SEC2282 17937
4074	tab sing_1017.htm#SEC1093 60407
4075	tail sing_2022.htm#SEC2098 13066
4076	tame polynomial sing_1617.htm#IDX738
4077	tame polynomial sing_1618.htm#IDX748
4078	tame polynomial sing_1619.htm#IDX749
4079	tangentGens sing_1433.htm#SEC1509 37797
4080	tangentcone sing_1682.htm#SEC1758 20056
4081	target sing_2585.htm#SEC2661 18743
4082	task sing_1094.htm#IDX511
4083	tasks.lib sing_1094.htm#SEC1170
4084	tasks_lib sing_1094.htm#SEC1170
4085	tau_es sing_1590.htm#SEC1666 17043
4086	tau_es2 sing_1544.htm#SEC1620 38083
4087	tdCf sing_2354.htm#SEC2430 21522
4088	tdFactor sing_2356.htm#SEC2432 37910
4089	tdProj sing_2359.htm#SEC2435 38406
4090	tdTerms sing_2355.htm#SEC2431 30166
4091	teachstd.lib sing_2020.htm#SEC2096
4092	teachstd_lib sing_2020.htm#SEC2096
4093	template.lib sing_55.htm#IDX120
4094	template.lib sing_55.htm#IDX123
4095	template_lib sing_55.htm#SEC92
4096	template_lib sing_55.htm#IDX121
4097	tensor sing_361.htm#SEC401
4098	tensor sing_500.htm#IDX311
4099	tensorFreeModule sing_2597.htm#SEC2673 59314
4100	tensorFreemodMod sing_2596.htm#SEC2672 sprintf
4101	tensorMatrix sing_2593.htm#SEC2669 31437
4102	tensorMod sing_1241.htm#SEC1317 21961
4103	tensorModFreemod sing_2595.htm#SEC2671 11852
4104	tensorModule sing_2594.htm#SEC2670 58772
4105	tensorProduct sing_2598.htm#SEC2674 sprintf
4106	tensorSheaf sing_2784.htm#SEC2860 24072
4107	term orderings General definitions for orderings sing_922.htm#SEC974
4108	term orderings introduction Introduction to orderings sing_921.htm#SEC973
4109	testFraction sing_2723.htm#SEC2799 28466
4110	testLocData sing_2720.htm#SEC2796 50986
4111	testNCfac sing_737.htm#SEC789 60394
4112	testNcfrac sing_2681.htm#SEC2757 34186
4113	testNcfracExamples sing_2682.htm#SEC2758 15399
4114	testNcloc sing_2685.htm#SEC2761 62706
4115	testNclocExamples sing_2686.htm#SEC2762 14584
4116	testOlga sing_2737.htm#SEC2813 53953
4117	testOlgaExamples sing_2738.htm#SEC2814 62869
4118	testParametrization sing_1448.htm#SEC1524 18686
4119	testPointConic sing_1449.htm#SEC1525 25315
4120	testPrimary sing_1361.htm#SEC1437 34254
4121	testPrimaryE sing_1362.htm#SEC1438 20693
4122	tetrahedronGroup sing_661.htm#SEC713 16398
4123	tex sing_1835.htm#SEC1911 12226
4124	texDrawBasic sing_2212.htm#SEC2288 3635
4125	texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2214.htm#SEC2290 42021
4126	texDrawTriangulation texDrawTriangulation sing_2215.htm#SEC2291 18865
4127	texDrawTropical sing_2213.htm#SEC2289 58447
4128	texMatrix sing_2211.htm#SEC2287 1334
4129	texNumber sing_2209.htm#SEC2285 12628
4130	texPolynomial sing_2210.htm#SEC2286 41136
4131	texcoef sing_1916.htm#SEC1992 28189
4132	texdemo sing_1836.htm#SEC1912 13008
4133	texfactorize sing_1837.htm#SEC1913 6682
4134	texmap sing_1838.htm#SEC1914 35265
4135	texname sing_1839.htm#SEC1915 1008
4136	texobj sing_1840.htm#SEC1916 2107
4137	texpoly sing_1841.htm#SEC1917 64109
4138	texproc sing_1842.htm#SEC1918 23626
4139	texring sing_1843.htm#SEC1919 38275
4140	the first alternative algorithm sing_1218.htm#IDX548
4141	three_elements sing_2006.htm#SEC2082 513
4142	timeFactorize sing_984.htm#SEC1060 49531
4143	timeStd sing_983.htm#SEC1059 31506
4144	timer sing_404.htm#SEC444
4145	timer resolution, setting the sing_359.htm#IDX283
4146	timestep sing_2458.htm#SEC2534 38225
4147	tjurina sing_1678.htm#SEC1754 9100
4148	tmatrix sing_1605.htm#SEC1681 57332
4149	todd sing_2351.htm#SEC2427 25618
4150	toddE sing_2352.htm#SEC2428 17823
4151	toddPoly sing_2365.htm#SEC2441 65066
4152	tolessvars sing_1781.htm#SEC1857 56590
4153	topChernClass sing_2781.htm#SEC2857 17374
4154	topological invariants sing_1532.htm#IDX640
4155	topological invariants sing_1539.htm#IDX647
4156	topological invariants sing_1540.htm#IDX651
4157	topological invariants sing_1541.htm#IDX655
4158	topological invariants sing_1542.htm#IDX659
4159	toric ideals sing_937.htm#SEC994
4160	toric ring sing_1320.htm#IDX581
4161	toric.lib sing_1410.htm#SEC1486
4162	toric_ideal sing_1411.htm#SEC1487 5760
4163	toric_lib sing_1410.htm#SEC1486
4164	toric_std sing_1412.htm#SEC1488 26141
4165	torusInvariants sing_1326.htm#SEC1402 911
4166	total divisors sing_500.htm#IDX308
4167	total multiplicities sing_1532.htm#IDX643
4168	totalChernClass sing_2779.htm#SEC2855 6153
4169	totalSegreClass sing_2782.htm#SEC2858 3291
4170	totalmultiplicities sing_1534.htm#SEC1610 58264
4171	trace sing_362.htm#SEC402
4172	tracemult sing_2047.htm#SEC2123 58303
4173	transpose sing_363.htm#SEC403
4174	trapezoid sing_2452.htm#SEC2528 61525
4175	triMNewton sing_1807.htm#SEC1883 62822
4176	triagmatrix sing_1058.htm#SEC1134 17944
4177	triang.lib sing_1800.htm#SEC1876
4178	triangL sing_1801.htm#SEC1877 51847
4179	triangL_solve sing_1798.htm#SEC1874 10101
4180	triangLf_solve sing_1796.htm#SEC1872 49796
4181	triangLfak sing_1802.htm#SEC1878 50093
4182	triangM sing_1803.htm#SEC1879 59334
4183	triangMH sing_1804.htm#SEC1880 34277
4184	triangM_solve sing_1797.htm#SEC1873 63652
4185	triang_lib sing_1800.htm#SEC1876
4186	triang_solve sing_1799.htm#SEC1875 64404
4187	triangularGroup sing_662.htm#SEC714 23560
4188	triangulations sing_2137.htm#SEC2213 61888
4189	tropical curves sing_2191.htm#IDX821
4190	tropical geometry sing_1204.htm#IDX522
4191	tropical geometry sing_2809.htm#IDX1078
4192	tropical mirror symmetry sing_1204.htm#IDX524
4193	tropical polynomials sing_2191.htm#IDX822
4194	tropical varieties sing_2809.htm#IDX1079
4195	tropical.lib sing_2191.htm#IDX819
4196	tropicalCurve sing_2196.htm#SEC2272 16865
4197	tropicalJInvariant sing_2199.htm#SEC2275 40395
4198	tropicalLifting sing_2192.htm#SEC2268 7052
4199	tropicalLinkNewton sing_2817.htm#SEC2893 63886
4200	tropicalNewton.lib sing_2809.htm#SEC2885
4201	tropicalNewton_lib sing_2809.htm#SEC2885
4202	tropicalPointNewton sing_2814.htm#SEC2890 18572
4203	tropicalSubst sing_2224.htm#SEC2300 49846
4204	tropicalVariety sing_2231.htm#SEC2307 39087
4205	tropicalVarietyNewton tropicalVarietyNewton sing_2816.htm#SEC2892 28532
4206	tropical_lib sing_2191.htm#IDX820
4207	tropicalise sing_2203.htm#SEC2279 49739
4208	tropicaliseSet sing_2204.htm#SEC2280 35136
4209	truncate sing_1514.htm#SEC1590 13545
4210	truncateFast sing_1515.htm#SEC1591 5124
4211	truncated module sing_1514.htm#IDX631
4212	truncated module sing_1515.htm#IDX632
4213	tst_ncfactor sing_745.htm#SEC797 3339
4214	twalk sing_1217.htm#SEC1293 35753
4215	two-sided sing_500.htm#IDX309
4216	two-sided Groebner basis sing_500.htm#IDX310
4217	twostd sing_359.htm#IDX268
4218	twostd sing_485.htm#SEC525
4219	type sing_364.htm#SEC404
4220	type B sing_2259.htm#IDX871
4221	type D sing_2260.htm#IDX873
4222	type,custom Definition of a user defined type sing_184.htm#SEC224
4223	type2arr sing_2237.htm#SEC2313 62624
4224	typecasting sing_2237.htm#IDX827
4225	typecasting sing_2238.htm#IDX829
4226	typecasting sing_2239.htm#IDX832
4227	typeof sing_365.htm#SEC405
4228	u sing_2444.htm#SEC2520 12154
4229	uname sing_359.htm#IDX269
4230	unbounded_knapsack sing_1989.htm#SEC2065 17226
4231	unipotent groups sing_1432.htm#IDX599
4232	uniquePoint sing_2116.htm#SEC2192 893
4233	unitMatrix sing_2751.htm#SEC2827 33014
4234	unitmat sing_1123.htm#SEC1199 12862
4235	univariate sing_366.htm#SEC406
4236	univarpoly sing_2054.htm#SEC2130 46288
4237	unknown syndrome Decoding method based on quadratic equations sing_953.htm#SEC1024
4238	unset sing_277.htm#SEC317
4239	untyped definitions sing_88.htm#SEC128
4240	untyped definitions sing_425.htm#SEC465
4241	updatePairs sing_2032.htm#SEC2108 51144
4242	ures_solve sing_1790.htm#SEC1866 32449
4243	uressolve sing_367.htm#SEC407
4244	usage, option sing_316.htm#IDX185
4245	user interface, Emacs Emacs user interface sing_21.htm#SEC28
4246	vStd sing_2398.htm#SEC2474 12321
4247	val sing_2811.htm#SEC2887 62171
4248	valvars sing_1785.htm#SEC1861 15723
4249	vandermonde sing_368.htm#SEC408
4250	vanishId sing_1886.htm#SEC1962 49148
4251	var sing_369.htm#SEC409
4252	varMat sing_2241.htm#SEC2317 51772
4253	varNum sing_2242.htm#SEC2318 18485
4254	variables sing_370.htm#SEC410
4255	variables sing_2241.htm#IDX839
4256	variables sing_2242.htm#IDX841
4257	variables sing_2243.htm#IDX845
4258	variables sing_2244.htm#IDX847
4259	variablesSorted sing_538.htm#SEC590 13533
4260	variablesStandard sing_537.htm#SEC589 56500
4261	vars2pars sing_858.htm#SEC910 47343
4262	varsigns sing_2059.htm#SEC2135 3471
4263	varstr sing_371.htm#SEC411
4264	vct2str sing_685.htm#SEC737 51983
4265	vdim sing_372.htm#SEC412
4266	vdim (plural) sing_486.htm#SEC526
4267	vec2poly sing_520.htm#SEC572 27377
4268	vector sing_178.htm#SEC218
4269	vector declarations sing_179.htm#SEC219
4270	vector expressions sing_180.htm#SEC220
4271	vector operations sing_181.htm#SEC221
4272	vector related functions vector related functions sing_182.htm#SEC222
4273	verify sing_2050.htm#SEC2126 32271
4274	versal sing_1585.htm#SEC1661 46247
4275	version sing_359.htm#IDX272
4276	vertexAdjacencyGraph vertexAdjacencyGraph sing_2184.htm#SEC2260 60102
4277	vertexEdgeGraph sing_2185.htm#SEC2261 32816
4278	vertices sing_2132.htm#SEC2208 11398
4279	vfilt sing_1603.htm#SEC1679 9283
4280	view sing_1906.htm#SEC1982 29284
4281	visual sing_2186.htm#SEC2262 51434
4282	visualize sing_2443.htm#SEC2519 6750
4283	voice sing_407.htm#SEC447
4284	vwfilt sing_1604.htm#SEC1680 8281
4285	wUnit sing_1944.htm#SEC2020 27198
4286	waitAllTasks sing_1103.htm#SEC1179 7087
4287	waitTasks sing_1102.htm#SEC1178 52857
4288	waitall sing_373.htm#SEC413
4289	waitfirst sing_374.htm#SEC414
4290	walk, groebner sing_1215.htm#IDX544
4291	walk, groebner sing_2609.htm#IDX1001
4292	walk, groebner sing_2763.htm#IDX1047
4293	walk, groebner sing_2806.htm#IDX1076
4294	warkedPreimageStd sing_2483.htm#SEC2559 14759
4295	warn, option sing_70.htm#SEC110
4296	warn, option sing_316.htm#IDX151
4297	watchdog sing_981.htm#SEC1057 sprintf
4298	wedge sing_375.htm#SEC415
4299	weierstr.lib sing_2035.htm#SEC2111
4300	weierstrDiv sing_2036.htm#SEC2112 260
4301	weierstrPrep sing_2037.htm#SEC2113 5752
4302	weierstr_lib sing_2035.htm#SEC2111
4303	weierstrassForm sing_2200.htm#SEC2276 60874
4304	weight sing_376.htm#SEC416
4305	weight filtration sing_1595.htm#IDX671
4306	weight filtration sing_1602.htm#IDX705
4307	weight filtration sing_1604.htm#IDX719
4308	weight filtration sing_1605.htm#IDX727
4309	weight filtration sing_1617.htm#IDX743
4310	weight filtration sing_1619.htm#IDX754
4311	weightKB sing_377.htm#SEC417 21753
4312	weightM, option sing_316.htm#IDX170
4313	weighted lexicographical ordering sing_923.htm#IDX405
4314	weighted reverse lexicographical ordering Global orderings sing_923.htm#IDX403
4315	weightedRing sing_756.htm#SEC808 33786
4316	whichvariable sing_2058.htm#SEC2134 27122
4317	while sing_394.htm#SEC434
4318	withDim sing_210.htm#IDX145
4319	withHilb sing_210.htm#IDX143
4320	withMult sing_210.htm#IDX146
4321	withRes sing_210.htm#IDX144
4322	withSB sing_210.htm#IDX142
4323	wp, global ordering sing_923.htm#IDX404
4324	write sing_378.htm#SEC418
4325	writeNmzData sing_1337.htm#SEC1413 38467
4326	writeNmzPaths sing_1341.htm#SEC1417 sprintf
4327	ws, local ordering sing_924.htm#IDX415
4328	wurzel sing_1926.htm#SEC2002 12755
4329	xchange sing_1920.htm#SEC1996 40741
4330	xdvi sing_1845.htm#SEC1921 16898
4331	zdd sing_2288.htm#IDX920
4332	zdd2poly sing_2305.htm#SEC2381 55047
4333	zero sing_2558.htm#SEC2634 12060
4334	zero-dimensional sing_2055.htm#IDX810
4335	zeroMod sing_1277.htm#SEC1353 60609
4336	zeroNcfrac sing_2674.htm#SEC2750 50840
4337	zeroOpt sing_1286.htm#SEC1362 19260
4338	zeroRadical sing_1186.htm#SEC1262 35598
4339	zeroSet sing_1813.htm#SEC1889 60030
4340	zerodec sing_1370.htm#SEC1446 30765
4341	zeroset.lib sing_1808.htm#SEC1884
4342	zeroset_lib sing_1808.htm#SEC1884
4343	zetaDL sing_1507.htm#SEC1583 sprintf
4344	{ sing_36.htm#IDX78
4345	\|\| sing_36.htm#IDX103
4346	\|\| sing_101.htm#SEC141
4347	} sing_36.htm#IDX79
4348	~ sing_36.htm#IDX117
4349	~ sing_395.htm#SEC435

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