Context Navigation

singular.idx @ 39d022e

spielwiese

Last change on this file since 39d022e was fc474ad, checked in by Hans Schoenemann <hannes@…>, 3 years ago
4.2.0 for singular.idx, hlp-cmpl.el
Property mode set to `100644`
File size: 186.6 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_249.htm#SEC289
137	<= sing_36.htm#IDX99
138	<= sing_100.htm#SEC140
139	<= sing_147.htm#SEC187
140	<= sing_155.htm#SEC195
141	<= sing_176.htm#SEC216
142	<= sing_181.htm#SEC221
143	<> sing_36.htm#IDX96
144	<> sing_100.htm#SEC140
145	<> sing_137.htm#SEC177
146	<> sing_147.htm#SEC187
147	<> sing_155.htm#SEC195
148	<> sing_169.htm#SEC209
149	<> sing_176.htm#SEC216
150	<> sing_181.htm#SEC221
151	= sing_36.htm#IDX77
152	== sing_36.htm#IDX94
153	== sing_100.htm#SEC140
154	== sing_137.htm#SEC177
155	== sing_147.htm#SEC187
156	== sing_155.htm#SEC195
157	== sing_169.htm#SEC209
158	== sing_176.htm#SEC216
159	== sing_181.htm#SEC221
160	> sing_36.htm#IDX98
161	> sing_155.htm#SEC195
162	> sing_181.htm#SEC221
163	>= sing_36.htm#IDX97
164	>= sing_100.htm#SEC140
165	>= sing_147.htm#SEC187
166	>= sing_155.htm#SEC195
167	>= sing_176.htm#SEC216
168	>= sing_181.htm#SEC221
169	? sing_36.htm#IDX106
170	? sing_262.htm#IDX148
171	ADGT sing_1054.htm#SEC1135
172	AG codes sing_963.htm#SEC1020
173	AGcode_L sing_2167.htm#SEC2248
174	AGcode_Omega sing_2168.htm#SEC2249
175	ASCII sing_1014.htm#SEC1095
176	ASCII links sing_117.htm#SEC157
177	ASSUME sing_64.htm#SEC101
178	A_L sing_1789.htm#SEC1870
179	A_Z sing_1012.htm#SEC1093
180	A_Z_L sing_1013.htm#SEC1094
181	Access to elements of a user defined type Access to elements of a user defined type sing_186.htm#SEC226
182	Adj_div sing_2162.htm#SEC2243
183	Adjoint ideal sing_1618.htm#IDX719
184	Alexander polynomial sing_1751.htm#IDX767
185	Algebraic Geometry codes sing_2161.htm#IDX936
186	Algebraic dependence Algebraic dependence sing_942.htm#SEC999
187	Algebraic geometry sing_1504.htm#SEC1585
188	AltVarEnd sing_751.htm#SEC805
189	AltVarStart sing_750.htm#SEC804
190	Ann sing_1438.htm#SEC1519
191	Appel function sing_560.htm#IDX351
192	Appel hypergeometric function sing_560.htm#IDX352
193	Applications sing_961.htm#SEC1018
194	Arnol'd sing_1769.htm#IDX787
195	Arnold, classification. sing_1797.htm#IDX792
196	Arnold, classification. sing_1798.htm#IDX793
197	ArnoldAction sing_1904.htm#SEC1985
198	Assignments for user defined types Assignments for user defined types sing_188.htm#SEC228
199	AssocTanToEnv sing_1048.htm#SEC1129
200	Atkin sing_2250.htm#SEC2331
201	Authors sing_1.htm#IDX16
202	Automatic Deduction sing_1054.htm#IDX527
203	Automatic Demonstration sing_1054.htm#IDX528
204	BFBoundsBudur sing_597.htm#SEC651
205	BINresol sing_1631.htm#SEC1712
206	BSidealFromAnn sing_595.htm#SEC649
207	Background sing_3.htm#SEC5
208	Basic programming sing_917.htm#SEC974
209	Basic programming sing_917.htm#SEC974
210	BelongSemig sing_2380.htm#SEC2461
211	BerlekampMassey sing_1289.htm#SEC1370
212	Bern sing_1543.htm#SEC1624
213	Bernstein operator sing_537.htm#IDX333
214	Bernstein-Sato ideal sing_592.htm#IDX354
215	Bernstein-Sato polynomial sing_502.htm#IDX314
216	Bernstein-Sato polynomial sing_537.htm#IDX330
217	Bernstein-Sato polynomial sing_1845.htm#IDX804
218	Bernstein-Sato polynomial sing_1849.htm#IDX821
219	Bernstein-Sato polynomial for variety sing_600.htm#IDX362
220	BernsteinSatoIdeal sing_596.htm#SEC650
221	Betti sing_2818.htm#SEC2899
222	Betti number Syzygies and resolutions sing_979.htm#SEC1041
223	BettiNumsH sing_2742.htm#SEC2823
224	BettiNumsN sing_2750.htm#SEC2831
225	BettiNumsQp sing_2745.htm#SEC2826
226	BettiNumsS sing_2748.htm#SEC2829
227	Betty number sing_2739.htm#IDX1196
228	Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_989.htm#SEC1051
229	Bimodules Bimodules and syzygies and lifts sing_818.htm#SEC872
230	Bisyzygy Bimodules and syzygies and lifts sing_818.htm#SEC872
231	BlowingUp sing_1824.htm#SEC1905
232	Blowupcenter sing_1634.htm#SEC1715
233	BorelCheck sing_1748.htm#SEC1829
234	Bott's formula sing_1693.htm#IDX735
235	Branches of space curve singularities Branches of space curve singularities sing_950.htm#SEC1007
236	Briancon-Maisonobe algorithm sing_537.htm#IDX339
237	Brieskorn lattice sing_1845.htm#IDX800
238	Brieskorn lattice sing_1846.htm#IDX811
239	Brieskorn lattice sing_1847.htm#IDX814
240	Brieskorn lattice sing_1848.htm#IDX817
241	Brieskorn lattice sing_1849.htm#IDX820
242	Brieskorn lattice sing_1850.htm#IDX824
243	Brieskorn lattice sing_1851.htm#IDX828
244	Brieskorn lattice sing_1852.htm#IDX834
245	Brieskorn lattice sing_1853.htm#IDX842
246	Brieskorn lattice sing_1854.htm#IDX848
247	Brieskorn lattice sing_1855.htm#IDX856
248	Brieskorn lattice sing_1856.htm#IDX866
249	Brieskorn lattice sing_1867.htm#IDX872
250	Brieskorn lattice sing_1869.htm#IDX883
251	Brieskorn lattice sing_1897.htm#IDX910
252	Brill-Noether algorithm sing_2161.htm#IDX937
253	BrillNoether sing_2164.htm#SEC2245
254	Buchberger algorithm for toric ideals Buchberger algorithm sing_990.htm#SEC1052
255	Budur-Mustata-Saito approach sing_600.htm#IDX366
256	Building Singular sing_2999.htm#SEC3096
257	C programming language Major differences to the C programming language sing_413.htm#SEC453
258	C, module ordering sing_971.htm#IDX463
259	CGS sing_1035.htm#IDX476
260	CGS, disjoint, reduced, comprehensive Groebner system buildtree sing_1106.htm#IDX553
261	CM_regularity sing_1735.htm#SEC1816 33865
262	CMtype sing_1941.htm#SEC2022
263	CRHT-ideal sing_996.htm#SEC1065
264	CSMA sing_1566.htm#SEC1647
265	CYGWIN and ESingular Running SINGULAR under Emacs sing_23.htm#SEC33
266	Castelnuovo-Mumford regularity sing_1735.htm#IDX759
267	Category string sing_51.htm#SEC88
268	CenCharDec sing_645.htm#SEC699
269	Center sing_1673.htm#SEC1754
270	CenterBO sing_1680.htm#SEC1761
271	CentralQuot sing_643.htm#SEC697
272	CentralSaturation sing_644.htm#SEC698
273	Change of rings sing_9.htm#SEC15
274	Characteristic sets sing_980.htm#SEC1042
275	CharacteristicExponents CharacteristicExponents sing_1830.htm#SEC1911
276	ChernClass sing_1706.htm#SEC1787
277	ChernRootsDual sing_1522.htm#SEC1603
278	ChernRootsHom sing_1531.htm#SEC1612
279	ChernRootsProd sing_1524.htm#SEC1605
280	ChernRootsSum sing_1520.htm#SEC1601
281	ChernRootsSymm sing_1533.htm#SEC1614
282	ChernRootsWedge sing_1534.htm#SEC1615
283	Chevalley-Rosenlicht theorem sing_1612.htm#IDX704
284	Chevalley-Rosenlicht theorem sing_1613.htm#IDX707
285	Chow ring, abstract variety, projective space, Grassmannian ChowRing sing_1697.htm#IDX740
286	ChowRing sing_1697.htm#SEC1778
287	Classification of hypersurface singularities Classification of hypersurface singularities sing_951.htm#SEC1008
288	Classification of singularities sing_1914.htm#IDX911
289	Code Codes and the decoding problem sing_995.htm#SEC1058
290	Codes and the decoding problem Codes and the decoding problem sing_995.htm#SEC1057
291	Coding theory sing_2160.htm#SEC2241
292	Coefficient rings Notes for Singular users sing_2997.htm#SEC3089
293	Command line options Command line options sing_19.htm#SEC26
294	Commands Functions and system variables sing_207.htm#SEC247
295	Commands for user defined types Commands for user defined types sing_187.htm#SEC227
296	Commutative Algebra sing_930.htm#SEC987
297	Commutative algebra sing_1233.htm#SEC1314
298	CompDecomp sing_499.htm#SEC553
299	CompInt sing_2382.htm#SEC2463
300	CompleteHomog sing_1510.htm#SEC1591
301	ComplexValue sing_2734.htm#SEC2815
302	Comprehensive Groebner System sing_1035.htm#IDX479
303	Comprehensive Groebner Systems sing_1033.htm#SEC1114
304	Comprehensive Groebner Systems sing_1098.htm#SEC1179
305	Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_926.htm#SEC983
306	ConsLevels sing_1055.htm#SEC1136
307	ContactMatrix sing_1832.htm#SEC1913
308	Conti-Traverso algorithm sing_985.htm#SEC1047
309	Contributors sing_1.htm#IDX15
310	Control structures sing_381.htm#SEC421
311	Control theory System and Control theory sing_2194.htm#SEC2275
312	Cooper philosophy sing_996.htm#SEC1063
313	Cornacchia sing_2240.htm#SEC2321
314	CornacchiaModified sing_2241.htm#SEC2322
315	Crep sing_1038.htm#SEC1119
316	Critical points sing_945.htm#SEC1002
317	CurveParam sing_1826.htm#SEC1907
318	CurveRes sing_1825.htm#SEC1906
319	Curves sing_1618.htm#IDX716
320	Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC36
321	Cyclic code sing_2175.htm#IDX944
322	Cyclic roots sing_923.htm#SEC980
323	D-integration sing_560.htm#IDX348
324	D-localization sing_560.htm#IDX344
325	D-localization sing_668.htm#IDX383
326	D-module purityfiltration_lib sing_502.htm#IDX312
327	D-module sing_537.htm#IDX327
328	D-module sing_560.htm#IDX341
329	D-module sing_592.htm#IDX353
330	D-module sing_600.htm#IDX360
331	D-module sing_668.htm#IDX380
332	D-module sing_778.htm#IDX398
333	D-module structure sing_537.htm#IDX328
334	D-module structure sing_592.htm#IDX356
335	D-module structure sing_600.htm#IDX361
336	D-restriction sing_560.htm#IDX346
337	DBM links sing_122.htm#SEC162
338	DISPLAY environment variable The online help system sing_16.htm#IDX28
339	DLoc sing_563.htm#SEC617
340	DLoc0 sing_565.htm#SEC619
341	Data types sing_72.htm#SEC112
342	Data types (plural) sing_426.htm#IDX298
343	Debugging tools sing_63.htm#SEC100
344	Decker, Wolfram sing_1.htm#IDX17
345	Declaration of objects of a user defined type Declaration of objects of a user defined type sing_185.htm#SEC225
346	Decoding sing_2175.htm#IDX946
347	Decoding codes with Groebner bases Decoding codes with Groebner bases sing_994.htm#SEC1056
348	Decoding method based on quadratic equations Decoding method based on quadratic equations sing_999.htm#SEC1074
349	Definition of a user defined type Definition of a user defined type sing_184.htm#SEC224
350	Deformations sing_948.htm#SEC1005
351	Deformations, T1 and T2 sing_947.htm#SEC1004
352	Deg sing_2821.htm#SEC2902
353	Degree sing_2822.htm#SEC2903
354	DegreePure sing_1597.htm#SEC1678
355	Degrees sing_2823.htm#SEC2904
356	Delta sing_1681.htm#SEC1762
357	DeltaList sing_1682.htm#SEC1763
358	Demo mode sing_24.htm#SEC35
359	Depth sing_937.htm#SEC994
360	Determinacy sing_1917.htm#IDX915
361	Di Biase-Urbanke algorithm Di Biase and Urbanke sing_988.htm#SEC1050
362	DifConsLCSets sing_1058.htm#SEC1139
363	Distributed computing sing_1069.htm#IDX544
364	Dlocalization sing_669.htm#SEC723
365	Documentation Tool sing_60.htm#SEC97
366	Dp, global ordering sing_969.htm#IDX446
367	Ds, local ordering sing_970.htm#IDX456
368	DsingularLocus sing_673.htm#SEC727
369	Dynamic loading sing_71.htm#SEC111
370	Dynamic modules sing_925.htm#SEC982
371	ECPP sing_2284.htm#SEC2365
372	ECoef sing_1640.htm#SEC1721
373	EOrdlist sing_1638.htm#SEC1719
374	ERROR sing_238.htm#SEC278
375	ESingular, CYGWIN Running SINGULAR under Emacs sing_23.htm#SEC33
376	Edatalist sing_1637.htm#SEC1718
377	Edelman-Reiner sing_2613.htm#IDX1029
378	Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
379	Editing input sing_18.htm#SEC25
380	Elimination sing_933.htm#SEC990
381	Emacs Emacs user interface sing_21.htm#SEC28
382	Emacs, Singular demo mode sing_24.htm#SEC35
383	Emacs, a quick guide A quick guide to Emacs sing_22.htm#SEC29
384	Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC36
385	Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC37
386	Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC38
387	Emacs, overview A quick guide to Emacs sing_22.htm#SEC29
388	Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30
389	Emacs, user interface Emacs user interface sing_21.htm#SEC28
390	Emaxcont sing_1642.htm#SEC1723
391	Enumerative geometry sing_1693.htm#IDX733
392	Equal sing_1596.htm#SEC1677
393	Eresol sing_1632.htm#SEC1713
394	EulerAff sing_1567.htm#SEC1648
395	EulerProj sing_1568.htm#SEC1649
396	Evaluation of logical expressions Evaluation of logical expressions sing_415.htm#SEC455
397	Examples sing_915.htm#SEC972
398	Examples of ring declarations Examples of ring declarations sing_29.htm#SEC40
399	Examples of use of Letterplace Examples of use of Letterplace sing_800.htm#SEC854
400	Examples of use of Letterplace over Z Examples of use of Letterplace over Z sing_801.htm#SEC855
401	Exp for matrices sing_1614.htm#IDX708
402	Experimental libraries Experimental libraries sing_2657.htm#SEC2738
403	Ext sing_1306.htm#SEC1387
404	Ext, computation of sing_936.htm#SEC993
405	Ext_R sing_1305.htm#SEC1386
406	Exterior sing_737.htm#SEC791
407	Extra weight vector sing_974.htm#SEC1031
408	Factorization sing_938.htm#SEC995
409	FamElemsAtEnvCompPoints FamElemsAtEnvCompPoints sing_1049.htm#SEC1130
410	Feynman graph sing_1274.htm#IDX599
411	Finite fields sing_932.htm#SEC989
412	First steps sing_6.htm#SEC12
413	Fitzgerald-Lax method Fitzgerald-Lax method sing_998.htm#SEC1071
414	Float sing_253.htm#SEC293
415	Flow control sing_40.htm#SEC70
416	Formal Checker sing_59.htm#SEC96
417	Formatting output sing_922.htm#SEC979
418	Free associative algebras Free associative algebras sing_815.htm#SEC869
419	Free resolution sing_934.htm#SEC991
420	Free resolution, graded Handling graded modules sing_935.htm#SEC992
421	FultonA sing_1565.htm#SEC1646
422	Functionality and release notes of Letterplace Functionality and release notes of Letterplace sing_802.htm#SEC856
423	Functions sing_208.htm#SEC248
424	Functions (letterplace) Functions (letterplace) sing_804.htm#SEC858
425	Future benefits of Singular 4 Notes for Singular users sing_2997.htm#SEC3094
426	G-algebra sing_490.htm#SEC530
427	G-algebra sing_490.htm#SEC532
428	G-algebra sing_661.htm#IDX368
429	G-algebra sing_662.htm#IDX375
430	G-algebra, setup sing_490.htm#SEC534
431	GBWeight sing_566.htm#SEC620
432	GBsolve sing_2034.htm#SEC2115
433	GIT-Fans sing_957.htm#SEC1014
434	GITcone sing_2449.htm#SEC2530
435	GITfan sing_2450.htm#SEC2531
436	GITfanFromOrbitCones GITfanFromOrbitCones sing_2451.htm#SEC2532
437	GITfanParallel sing_2452.htm#SEC2533
438	GITfanParallelSymmetric GITfanParallelSymmetric sing_2467.htm#SEC2548
439	GITfanSymmetric sing_2466.htm#SEC2547
440	GKExp sing_666.htm#SEC720
441	GKZfan sing_2453.htm#SEC2534
442	GKZsystem sing_641.htm#SEC695
443	GKdim sing_614.htm#SEC668
444	GMP sing_1.htm#IDX3
445	GMP sing_3001.htm#SEC3098
446	GND.lib sing_2758.htm#SEC2839
447	GND_lib sing_2758.htm#SEC2839
448	GTZmod sing_1359.htm#SEC1440
449	GTZopt sing_1366.htm#SEC1447
450	G_a -Invariants sing_954.htm#SEC1011
451	Gamma sing_1647.htm#SEC1728
452	Gauss-Manin connection Gauss-Manin connection sing_981.htm#SEC1043
453	Gauss-Manin connection sing_1897.htm#IDX909
454	Gauss-Manin connection sing_1950.htm#IDX919
455	Gauss-Manin system sing_1845.htm#IDX799
456	Gauss-Manin system sing_1846.htm#IDX810
457	Gauss-Manin system sing_1847.htm#IDX813
458	Gauss-Manin system sing_1848.htm#IDX816
459	Gauss-Manin system sing_1849.htm#IDX819
460	Gauss-Manin system sing_1850.htm#IDX823
461	Gauss-Manin system sing_1851.htm#IDX827
462	Gauss-Manin system sing_1852.htm#IDX833
463	Gauss-Manin system sing_1853.htm#IDX841
464	Gauss-Manin system sing_1854.htm#IDX847
465	Gauss-Manin system sing_1855.htm#IDX855
466	Gauss-Manin system sing_1856.htm#IDX865
467	Gauss-Manin system sing_1867.htm#IDX871
468	Gauss-Manin system sing_1869.htm#IDX882
469	Gelfand-Kirillov dimension sing_856.htm#IDX420
470	Gelfand-Kirillov dimension, G-Algebra sing_666.htm#IDX376
471	General command syntax General command syntax sing_35.htm#SEC59
472	General concepts sing_12.htm#SEC18
473	General purpose sing_1006.htm#SEC1087
474	General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC41
475	Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_492.htm#SEC544
476	Generalized Newton identities Generalized Newton identities sing_997.htm#SEC1068
477	Geometric Invariant Theory Geometric Invariant Theory sing_956.htm#SEC1013
478	Geometric Theorems sing_1054.htm#IDX529
479	Geometric genus sing_1618.htm#IDX720
480	German Umlaute sing_411.htm#IDX285
481	Getting started sing_5.htm#SEC11
482	Global orderings sing_969.htm#SEC1026
483	Goettsche's formula sing_2739.htm#IDX1197
484	GoettscheF sing_2740.htm#SEC2821
485	Graded commutative algebras Graded commutative algebras (SCA) sing_798.htm#SEC852
486	Grassmannian sing_1698.htm#SEC1779
487	Grassmannian, abstract variety, Schubert calculus Grassmannian sing_1698.htm#IDX741
488	Greuel, Gert-Martin sing_1.htm#IDX18
489	Grob1Levels sing_1057.htm#SEC1138
490	Groebner Bases Computing Groebner and Standard Bases sing_926.htm#SEC983
491	Groebner bases for two-sided ideals in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_817.htm#SEC871
492	Groebner bases in G-algebras Groebner bases in G-algebras sing_491.htm#SEC535
493	Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_817.htm#SEC871
494	Groebner bases, decodeGB sing_2175.htm#IDX948
495	Groebner bases, slim sing_929.htm#SEC986
496	Groebner basis conversion Groebner basis conversion sing_928.htm#SEC985
497	Groebner cover sing_1034.htm#IDX472
498	Groebner cover sing_1041.htm#IDX491
499	Groebner cover sing_1042.htm#IDX498
500	Groebner fan sing_2474.htm#IDX966
501	Groebner walk sing_1297.htm#IDX620
502	Groebner walk sing_1299.htm#IDX622
503	Groebner walk sing_2959.htm#IDX1254
504	Groebner walk sing_2960.htm#IDX1255
505	Groebner-Shirshov bases Groebner bases for two-sided ideals in free associative algebras sing_817.htm#SEC871
506	Groebner-Shirshov bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_817.htm#SEC871
507	Groebnerwalk sing_1293.htm#IDX616
508	Groebnerwalk sing_2855.htm#IDX1214
509	Groebnerwalk sing_2958.htm#IDX1253
510	Groebnerwalk sing_2978.htm#IDX1267
511	Gromov-Witten invariants sing_1274.htm#IDX596
512	Gromov-Witten invariants sing_1280.htm#IDX605
513	Gromov-Witten invariants sing_1281.htm#IDX609
514	Gromov-Witten invariants, lines on hypersurfaces linesHypersurface sing_1723.htm#IDX753
515	Gromov-Witten invariants, multiple covers sing_1722.htm#IDX752
516	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sumofquotients sing_1724.htm#IDX754
517	Gromov-Witten invariants, rational curves on Calabi-Yau threefolds sing_1725.htm#IDX755
518	Gromov-Witten invariants. sing_1693.htm#IDX736
519	Gweights sing_731.htm#SEC785
520	H2basis sing_1902.htm#SEC1983
521	HHnormalForm sing_1806.htm#SEC1887
522	Hamburger-Noether expansion sing_1751.htm#IDX763
523	Hamburger-Noether expansion sing_1870.htm#IDX891
524	Hamburger-Noether expansions sing_2162.htm#IDX938
525	Handling graded modules Handling graded modules sing_935.htm#SEC992
526	Hcode sing_1782.htm#SEC1863
527	Help string sing_45.htm#SEC82
528	Hensel sing_243.htm#SEC283
529	Hilbert function sing_359.htm#IDX188
530	Hilbert function sing_661.htm#IDX369
531	Hilbert function sing_662.htm#IDX373
532	Hilbert function sing_978.htm#SEC1037
533	Hilbert polynomial sing_661.htm#IDX371
534	Hilbert scheme sing_2739.htm#IDX1200
535	Hilbert series sing_661.htm#IDX370
536	Hilbert series sing_662.htm#IDX374
537	Hilbert series sing_821.htm#IDX411
538	Hilbert series sing_978.htm#SEC1037
539	Hilbert-driven GB algorithm Groebner basis conversion sing_928.htm#SEC985
540	HilbertClassPoly sing_2247.htm#SEC2328
541	HilbertSeries sing_2003.htm#SEC2084
542	HilbertWeights sing_2004.htm#SEC2085
543	Hom sing_1309.htm#SEC1390
544	HomJJ sing_1394.htm#SEC1475
545	Hosten-Sturmfels algorithm Hosten and Sturmfels sing_987.htm#SEC1049
546	How to enter and exit How to enter and exit sing_14.htm#SEC20
547	How to use this manual How to use this manual sing_4.htm#SEC6
548	Hurwitz numbers sing_1280.htm#IDX608
549	Hurwitz numbers sing_1281.htm#IDX612
550	Hypersurface singularities, classification of Classification of hypersurface singularities sing_951.htm#SEC1008
551	I-regular function sing_1041.htm#IDX497
552	IN sing_283.htm#IDX149
553	Ideal membership sing_977.htm#IDX468
554	Identifiers, syntax of sing_37.htm#SEC65
555	ImageGroup sing_2006.htm#SEC2087
556	ImageVariety sing_2005.htm#SEC2086
557	Imap, option sing_318.htm#IDX175
558	Implemented algorithms Implemented algorithms sing_33.htm#SEC47
559	Incl sing_1595.htm#SEC1676
560	Index sing_3007.htm#SEC3104
561	Info string sing_52.htm#SEC89
562	InterDiv sing_1663.htm#SEC1744
563	Interactive use sing_13.htm#SEC19
564	Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24
565	IntersectWithSub sing_646.htm#SEC700
566	Intersection theory sing_1693.htm#IDX732
567	IntersectionMatrix sing_1831.htm#SEC1912
568	Introduction sing_2.htm#SEC4
569	Invariant Theory sing_953.htm#SEC1010
570	Invariant theory sing_1955.htm#SEC2036
571	InvariantQ sing_2008.htm#SEC2089
572	InvariantRing sing_2007.htm#SEC2088
573	Invariants of a finite group Invariants of a finite group sing_955.htm#SEC1012
574	Invariants of plane curve singularities Invariants of plane curve singularities sing_949.htm#SEC1006
575	IsSCA sing_752.htm#SEC806
576	J-marked schemes sing_1742.htm#IDX761
577	J-marked schemes, Borel ideals sing_1747.htm#IDX762
578	JMBTest.lib sing_1742.htm#SEC1823
579	JMBTest_lib sing_1742.htm#SEC1823
580	JMSConst.lib sing_1747.htm#SEC1828
581	JMSConst_lib sing_1747.htm#SEC1828
582	JMarkedScheme sing_1749.htm#SEC1830
583	Jacobi sing_2257.htm#SEC2338
584	Jacobson form sing_2212.htm#IDX949
585	Jacobson normal form sing_2212.htm#IDX950
586	Janet basis sing_1483.htm#IDX669
587	Janet division, Janet basis sing_1482.htm#IDX668
588	JuReTopDim sing_1605.htm#SEC1686
589	JuReZeroDim sing_1606.htm#SEC1687
590	K-basis sing_821.htm#IDX409
591	K-dimension sing_821.htm#IDX410
592	KScoef sing_1895.htm#SEC1976
593	KSconvert sing_1893.htm#SEC1974
594	KSker sing_1892.htm#SEC1973
595	KSlinear sing_1894.htm#SEC1975
596	KSpencerKernel sing_1948.htm#SEC2029
597	KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2777.htm#SEC2858
598	Ker sing_2827.htm#SEC2908
599	Kernel of module homomorphisms Kernel of module homomorphisms sing_941.htm#SEC998
600	KoszulHomology sing_1318.htm#SEC1399
601	Kronecker module sing_2739.htm#IDX1199
602	Kronecker product sing_363.htm#SEC403
603	L, ordering sing_975.htm#SEC1032
604	LETTERPLACE sing_799.htm#SEC853
605	LETTERPLACE libraries LETTERPLACE libraries sing_820.htm#SEC874
606	LIB sing_287.htm#SEC327
607	LIB commands sing_53.htm#SEC90
608	LIBs sing_1002.htm#SEC1083
609	LLL sing_361.htm#IDX218
610	LOT algorithm sing_537.htm#IDX340
611	LU-decomposition of a matrix of numbers sing_292.htm#SEC332
612	Laurent series sing_1278.htm#IDX604
613	Left and two-sided Groebner bases Left and two-sided Groebner bases sing_959.htm#SEC1016
614	Left ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC538
615	Left normal form Groebner bases in G-algebras sing_491.htm#SEC537
616	Leinartas sing_2938.htm#IDX1245
617	LengthSym sing_795.htm#SEC849
618	LengthSymElement sing_794.htm#SEC848
619	Letterplace sing_799.htm#SEC853
620	Letterplace Groebner basis sing_821.htm#IDX408
621	Letterplace Groebner basis sing_856.htm#IDX418
622	Letterplace Groebner basis sing_863.htm#IDX427
623	Letterplace correspondence Letterplace correspondence sing_819.htm#SEC873
624	Letterplace libraries LETTERPLACE libraries sing_820.htm#SEC874
625	Letterplace ring sing_357.htm#SEC397
626	Levels sing_1056.htm#SEC1137
627	Lexicographic Groebner bases, computation of Groebner basis conversion sing_928.htm#SEC985
628	Libraries Writing procedures and libraries sing_48.htm#SEC85
629	Libraries sing_918.htm#SEC975
630	Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC86
631	Library versioning Notes for Singular users sing_2997.htm#SEC3092
632	Lie sing_2714.htm#IDX1192
633	Lie algebra sing_1613.htm#IDX705
634	Lie bracket sing_460.htm#SEC500
635	Lie group sing_1616.htm#IDX710
636	Lie group sing_1617.htm#IDX713
637	Limitations sing_411.htm#SEC451
638	Linear algebra sing_1174.htm#SEC1255
639	Linear code sing_2175.htm#IDX945
640	LinearActionQ sing_2010.htm#SEC2091
641	LinearCombinationQ sing_2011.htm#SEC2092
642	LinearizeAction sing_2009.htm#SEC2090
643	Loading a library sing_62.htm#SEC99
644	Local orderings sing_970.htm#SEC1027
645	Log for matrices sing_1615.htm#IDX709
646	Long coefficients sing_920.htm#SEC977
647	M, ordering sing_972.htm#SEC1029
648	MVComplex sing_1571.htm#SEC1652
649	Macdonald's formula sing_2739.htm#IDX1198
650	MacdonaldF sing_2746.htm#SEC2827
651	Macintosh installation Macintosh installation instructions sing_3006.htm#SEC3103
652	Mathematical background Mathematical background sing_976.htm#SEC1033
653	Mathematical background (letterplace) Mathematical background (letterplace) sing_814.htm#SEC868
654	Mathematical background (plural) Mathematical background (plural) sing_489.htm#SEC529
655	Matrix orderings sing_972.htm#SEC1029
656	Max sing_1911.htm#SEC1992
657	Maximus sing_1744.htm#SEC1825
658	Maxord sing_1646.htm#SEC1727
659	MillerRabin sing_2267.htm#SEC2348
660	Milnor code sing_1769.htm#IDX789
661	Milnor number Milnor and Tjurina number sing_944.htm#SEC1001
662	Milnor number sing_1916.htm#IDX914
663	Min sing_1912.htm#SEC1993
664	MinMult sing_2381.htm#SEC2462
665	MinimalDecomposition MinimalDecomposition sing_2012.htm#SEC2093
666	Minimum distance sing_2175.htm#IDX947
667	Minimus sing_1743.htm#SEC1824
668	Miscellaneous libraries Miscellaneous libraries sing_2584.htm#SEC2665
669	ModEqn sing_1905.htm#SEC1986
670	Modular techniques sing_1069.htm#IDX541
671	Module orderings sing_971.htm#SEC1028
672	Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16
673	Monodromy sing_1897.htm#IDX907
674	Monomial orderings sing_966.htm#SEC1023
675	Monomial orderings on free algebras Monomial orderings on free algebras sing_816.htm#SEC870
676	Monomial orderings, Term orderings sing_31.htm#SEC44
677	Mori dream spaces sing_2658.htm#IDX1089
678	Morse lemma addnondegeneratevariables sing_1915.htm#IDX912
679	Morse lemma sing_1918.htm#IDX916
680	MultiplicitySequence MultiplicitySequence sing_1829.htm#SEC1910
681	NF sing_337.htm#SEC377
682	NF (letterplace) reduce (letterplace) sing_809.htm#SEC863
683	NF (plural) sing_481.htm#SEC521
684	NFMora sing_2333.htm#SEC2414
685	NPos sing_1384.htm#SEC1465
686	NPos_test sing_1382.htm#SEC1463
687	NSplaces sing_2163.htm#SEC2244
688	NTL sing_1.htm#IDX4
689	NakYoshF sing_2743.htm#SEC2824
690	Names sing_37.htm#SEC65
691	Names in procedures sing_46.htm#SEC83
692	Names, indexed sing_37.htm#SEC65
693	New orderings for modules Notes for Singular users sing_2997.htm#SEC3093
694	Newton non-degenerate sing_1884.htm#IDX905
695	Newton polygon sing_1883.htm#IDX904
696	Newton polygon sing_1884.htm#IDX906
697	Newton polygons sing_2575.htm#IDX971
698	Newton polytope sing_2474.htm#IDX965
699	Newton step sing_2100.htm#IDX933
700	Noether position sing_1384.htm#IDX638
701	NoetherPosition sing_1373.htm#SEC1454
702	Non-commutative algebra Non-commutative algebra sing_958.htm#SEC1015
703	Non-commutative algebra sing_993.htm#SEC1055
704	Non-commutative subsystem Non-commutative subsystem sing_424.htm#SEC464
705	Nonhyp sing_1635.htm#SEC1716
706	Normalization sing_940.htm#SEC997
707	Notes for Singular users Notes for Singular users sing_2997.htm#SEC3088
708	Notes for developers Notes for developers sing_2998.htm#SEC3095
709	NullCone sing_2013.htm#SEC2094
710	NumIrrDecom sing_1609.htm#SEC1690
711	NumLocalDim sing_1598.htm#SEC1679
712	NumPrimDecom sing_1611.htm#SEC1692
713	Oaku-Takayama algorithm sing_537.htm#IDX338
714	Objects sing_38.htm#SEC66
715	Orlik-Solomon sing_2614.htm#IDX1030
716	Output sing_2837.htm#IDX1212
717	Output sing_2913.htm#IDX1219
718	Output sing_2915.htm#IDX1220
719	Output sing_2916.htm#IDX1221
720	Output sing_2917.htm#IDX1222
721	Output sing_2918.htm#IDX1223
722	Output sing_2919.htm#IDX1224
723	Output sing_2920.htm#IDX1225
724	Output sing_2921.htm#IDX1226
725	Output sing_2922.htm#IDX1227
726	Output sing_2923.htm#IDX1228
727	Output sing_2924.htm#IDX1229
728	Output sing_2925.htm#IDX1230
729	Output sing_2926.htm#IDX1231
730	Output sing_2927.htm#IDX1232
731	Output sing_2928.htm#IDX1233
732	Output sing_2929.htm#IDX1234
733	Output sing_2930.htm#IDX1235
734	Output sing_2931.htm#IDX1236
735	Output sing_2932.htm#IDX1237
736	Output sing_2933.htm#IDX1238
737	Output sing_2934.htm#IDX1239
738	Output sing_2935.htm#IDX1240
739	Output sing_2936.htm#IDX1241
740	Output sing_2937.htm#IDX1242
741	Output, formatting of sing_922.htm#SEC979
742	PBW sing_516.htm#IDX326
743	PBW basis sing_490.htm#SEC531
744	PBW_eqDeg sing_534.htm#SEC588
745	PBW_maxDeg sing_535.htm#SEC589
746	PBW_maxMonom sing_536.htm#SEC590
747	PEsolve sing_2032.htm#SEC2113
748	PH_ais sing_2636.htm#SEC2717
749	PH_nais sing_2637.htm#SEC2718
750	PLURAL sing_425.htm#SEC465
751	PLURAL LIBs sing_494.htm#SEC548
752	PLURAL libraries sing_494.htm#SEC548
753	PPolyH sing_2741.htm#SEC2822
754	PPolyN sing_2749.htm#SEC2830
755	PPolyQp sing_2744.htm#SEC2825
756	PPolyS sing_2747.htm#SEC2828
757	ParToVar sing_2736.htm#SEC2817
758	Parallelization Parallelization with ssi links sing_924.htm#SEC981
759	Parallelization sing_1069.htm#IDX542
760	Parameter list sing_44.htm#SEC81
761	Parameters sing_921.htm#SEC978
762	Parametrization sing_1618.htm#IDX717
763	Parametrization, image. sing_1628.htm#IDX729
764	PartC sing_1561.htm#SEC1642
765	PartitionVar sing_2733.htm#SEC2814
766	Path names Notes for Singular users sing_2997.htm#SEC3091
767	PerfectPowerTest sing_2230.htm#SEC2311
768	Perturbation walk sing_1298.htm#IDX621
769	Pfister, Gerhard sing_1.htm#IDX19
770	Pipe links sing_121.htm#SEC161
771	PocklingtonLehmer sing_2269.htm#SEC2350
772	Poincare polynomial sing_2626.htm#IDX1054
773	Polar curves sing_946.htm#SEC1003
774	PollardRho sing_2270.htm#SEC2351
775	PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2639.htm#IDX1070
776	PolyBoRi, Boolean Groebner Basis sing_2641.htm#IDX1071
777	PolyBoRi, Boolean Groebner Basis sing_2642.htm#IDX1072
778	PolyBoRi, Boolean Groebner Basis sing_2643.htm#IDX1073
779	PolyBoRi, Boolean Groebner Basis sing_2644.htm#IDX1074
780	PolyBoRi, Boolean Groebner Basis sing_2645.htm#IDX1075
781	PolyBoRi, Boolean Groebner Basis sing_2646.htm#IDX1076
782	PolyBoRi, Boolean Groebner Basis sing_2647.htm#IDX1077
783	PolyBoRi, Boolean Groebner Basis sing_2648.htm#IDX1078
784	PolyBoRi, Boolean Groebner Basis sing_2649.htm#IDX1079
785	PolyBoRi, Boolean Groebner Basis sing_2650.htm#IDX1080
786	PolyBoRi, Boolean Groebner Basis sing_2651.htm#IDX1081
787	PolyBoRi, Boolean Groebner Basis sing_2652.htm#IDX1082
788	PolyBoRi, Boolean Groebner Basis sing_2653.htm#IDX1083
789	PolyBoRi, Boolean Groebner Basis sing_2655.htm#IDX1085
790	PolyBoRi, zero-supressed decision diagram sing_2654.htm#IDX1084
791	Polybori, Boolean Groebner Basis sing_2656.htm#IDX1086
792	Polynomial data sing_964.htm#SEC1021
793	Pottier algorithm sing_986.htm#SEC1048
794	Preface sing_1.htm#SEC1
795	Prep sing_1039.htm#SEC1120
796	Primary decomposition Primary decomposition sing_939.htm#SEC996
797	PrimdecA sing_1355.htm#SEC1436
798	PrimdecB sing_1356.htm#SEC1437
799	Procedure definition Procedure definition sing_43.htm#SEC78
800	Procedure-specific commands Procedure-specific commands sing_47.htm#SEC84
801	Procedures sing_42.htm#SEC77
802	Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14
803	Procedures and libraries sing_918.htm#SEC975
804	Procedures in a library Procedures in a library sing_54.htm#SEC91
805	Product orderings sing_973.htm#SEC1030
806	Programming sing_916.htm#SEC973
807	Pseudo ordering L sing_975.htm#SEC1032
808	PtoCrep sing_1040.htm#SEC1121
809	Puiseux expansion sing_1751.htm#IDX764
810	Puiseux expansion sing_1870.htm#IDX892
811	Puiseux pairs Invariants of plane curve singularities sing_949.htm#SEC1006
812	Puiseux pairs sing_1876.htm#IDX897
813	QPoly, quotient ring. sing_2974.htm#IDX1262
814	QQ sing_28.htm#SEC39
815	QQ sing_75.htm#SEC115
816	Qso3Casimir sing_640.htm#SEC694
817	Quot-scheme sing_2739.htm#IDX1201
818	Quotient sing_2118.htm#SEC2199
819	QuotientEquations sing_1906.htm#SEC1987
820	Rational curves sing_1618.htm#IDX718
821	ReJunkUseHomo sing_1604.htm#SEC1685
822	Reduced Comprehensive Groebner Systems sing_1098.htm#SEC1179
823	ReesAlgebra sing_1477.htm#SEC1558
824	References sing_1001.htm#SEC1080
825	References (plural) sing_493.htm#SEC545
826	References and history of Letterplace References and history of Letterplace sing_803.htm#SEC857
827	Release Notes sing_2993.htm#SEC3074
828	Release Notes (letterplace) Release Notes (letterplace) sing_914.htm#SEC968
829	Res sing_2817.htm#SEC2898
830	ResTree sing_1664.htm#SEC1745
831	Resolution sing_11.htm#SEC17
832	Resolution of singularities Resolution of singularities sing_952.htm#SEC1009
833	Resolution, free sing_934.htm#SEC991
834	ReynoldsImage sing_2014.htm#SEC2095
835	ReynoldsOperator sing_2015.htm#SEC2096
836	RiemannRochBN sing_1506.htm#SEC1587
837	RiemannRochHess sing_1593.htm#SEC1674
838	Right Groebner bases and syzygies Right Groebner bases and syzygies sing_960.htm#SEC1017
839	Right ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC539
840	Ring-dependent options Notes for Singular users sing_2997.htm#SEC3090
841	Rings and orderings sing_28.htm#SEC39
842	Rings and standard bases Rings and standard bases sing_7.htm#SEC13
843	Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
844	SCA Graded commutative algebras (SCA) sing_798.htm#SEC852
845	SDB breakpoint Source code debugger sing_66.htm#SEC106
846	SDB debugger Source code debugger sing_66.htm#SEC106
847	SDLoc sing_564.htm#SEC618
848	SINGULAR libraries sing_1002.htm#SEC1083
849	SINGULARHIST sing_18.htm#SEC25
850	SL sing_2018.htm#SEC2099
851	SLreynolds sing_2024.htm#SEC2105
852	SV-decoding algorithm sing_2170.htm#IDX941
853	SV-decoding algorithm, preprocessing sing_2169.htm#IDX940
854	SaitoBase sing_2987.htm#SEC3068
855	Sannfs sing_540.htm#SEC594
856	SannfsBFCT sing_549.htm#SEC603
857	SannfsVar sing_603.htm#SEC657
858	Sannfslog sing_541.htm#SEC595
859	Saturation sing_931.htm#SEC988
860	Sch@"onemann, Hans sing_1.htm#IDX20
861	Schoof sing_2281.htm#SEC2362
862	Schubert calculus sing_1693.htm#IDX734
863	SchubertClass sing_1730.htm#SEC1811
864	SchurCh sing_1558.htm#SEC1639
865	SchurS sing_1557.htm#SEC1638
866	SegreA sing_1564.htm#SEC1645
867	Semigroup sing_1813.htm#SEC1894
868	Serre relations sing_827.htm#IDX415
869	SetDeg sing_2820.htm#SEC2901
870	Setting up a G-algebra sing_490.htm#SEC534
871	ShanksMestre sing_2280.htm#SEC2361
872	SimplifyIdeal sing_2016.htm#SEC2097
873	Singular sing_361.htm#IDX255
874	Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2995.htm#SEC3086
875	Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC36
876	Singular, demo mode sing_24.htm#SEC35
877	Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC37
878	Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC38
879	Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
880	Singular2bertini sing_1602.htm#SEC1683
881	SingularLib sing_361.htm#IDX257
882	Singularities sing_1750.htm#SEC1831
883	Singularity Theory sing_943.htm#SEC1000
884	SingularityDBM.lib sing_1769.htm#SEC1850
885	SingularityDBM_lib sing_1769.htm#SEC1850
886	Skeletons for parallelization sing_1069.htm#IDX543
887	Smith form sing_2212.htm#IDX951
888	Smith normal form sing_2212.htm#IDX952
889	SolowayStrassen sing_2268.htm#SEC2349
890	Solving systems of polynomial equations Solving systems of polynomial equations sing_962.htm#SEC1019
891	Source sing_2809.htm#SEC2890
892	Source code debugger, invocation Command line options sing_19.htm#IDX33
893	Space curve singularities, branches of Branches of space curve singularities sing_950.htm#SEC1007
894	Special characters sing_36.htm#SEC64
895	Splitting lemma addnondegeneratevariables sing_1915.htm#IDX913
896	Splitting lemma sing_1918.htm#IDX917
897	Ssi file links sing_119.htm#SEC159
898	Ssi links sing_118.htm#SEC158
899	Ssi tcp links sing_120.htm#SEC160
900	StabEqn sing_1907.htm#SEC1988
901	StabEqnId sing_1908.htm#SEC1989
902	StabOrder sing_1909.htm#SEC1990
903	Standard Bases Computing Groebner and Standard Bases sing_926.htm#SEC983
904	Standard bases sing_977.htm#SEC1034
905	Stanely-Reisner ideals, Stanley-Reisner rings, deformations stanleyreisner_lib sing_2971.htm#IDX1259
906	StartOrderingV sing_1745.htm#SEC1826
907	Startup sequence sing_20.htm#SEC27
908	StringF sing_1896.htm#SEC1977
909	SymGroup sing_793.htm#SEC847
910	Symbolic-numerical solving Symbolic-numerical solving sing_962.htm#SEC1019
911	Symbolic-numerical solving sing_2029.htm#SEC2110
912	System and Control theory System and Control theory sing_2194.htm#SEC2275
913	System dependent limitations System dependent limitations sing_412.htm#SEC452
914	System variables sing_398.htm#SEC438
915	Syzygies and resolutions Syzygies and resolutions sing_979.htm#SEC1038
916	Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_492.htm#SEC541
917	Syzygy bimodule Bimodules and syzygies and lifts sing_818.htm#SEC872
918	T1 sing_947.htm#SEC1004
919	T1 sing_2972.htm#SEC3053
920	T2 sing_947.htm#SEC1004
921	T2 sing_2973.htm#SEC3054
922	TRACE Tracing of procedures sing_65.htm#SEC102
923	TRACE sing_407.htm#SEC447
924	T_1 sing_1935.htm#SEC2016
925	T_12 sing_1937.htm#SEC2018
926	T_2 sing_1936.htm#SEC2017
927	Target sing_2808.htm#SEC2889
928	Teaching sing_2226.htm#SEC2307
929	Template for writing a library sing_55.htm#SEC92
930	TestGRRes sing_2776.htm#SEC2857
931	TestJMark sing_1746.htm#SEC1827
932	The SINGULAR language The SINGULAR language sing_34.htm#SEC56
933	The Tran algorithm sing_1295.htm#IDX618
934	The fractal walk algorithm sing_1294.htm#IDX617
935	The fractal walk algorithm sing_2961.htm#IDX1256
936	The online help system The online help system sing_16.htm#SEC22
937	Tjurina sing_1933.htm#SEC2014
938	Tjurina number Milnor and Tjurina number sing_944.htm#SEC1001
939	Tjurina number sing_1399.htm#IDX653
940	Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC38
941	Tor sing_1320.htm#SEC1401
942	Toric ideals and integer programming Toric ideals and integer programming sing_982.htm#SEC1044
943	Tricks and pitfalls sing_410.htm#SEC450
944	Tropical Geometry sing_2378.htm#SEC2459
945	Two-sided ideal membership (plural) Groebner bases in G-algebras sing_491.htm#SEC540
946	Type casting Type conversion and casting sing_39.htm#SEC69
947	Type conversion Type conversion and casting sing_39.htm#SEC68
948	Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC98
949	U_D_O sing_1222.htm#SEC1303
950	Ufnarovski graph sing_856.htm#IDX423
951	Unix installation Unix installation instructions sing_3004.htm#SEC3101
952	UpOneMatrix sing_749.htm#SEC803
953	UpperMonomials sing_1910.htm#SEC1991
954	UseBertini sing_1601.htm#SEC1682
955	User defined types sing_183.htm#SEC223
956	V-filtration sing_1845.htm#IDX802
957	V-filtration sing_1851.htm#IDX830
958	V-filtration sing_1852.htm#IDX836
959	V-filtration sing_1853.htm#IDX844
960	V-filtration sing_1854.htm#IDX850
961	V-filtration sing_1855.htm#IDX858
962	V-filtration sing_1856.htm#IDX868
963	V-filtration sing_1867.htm#IDX874
964	V-filtration sing_1869.htm#IDX885
965	VarToPar sing_2735.htm#SEC2816
966	Variables, indexed sing_37.htm#SEC65
967	VecField.lib sing_2982.htm#SEC3063
968	VecField_lib sing_2982.htm#SEC3063
969	Version number Version schema for Singular sing_2996.htm#SEC3087
970	Version schema for Singular Version schema for Singular sing_2996.htm#SEC3087
971	Version string sing_50.htm#SEC87
972	Visualization sing_2132.htm#SEC2213
973	WLCGS sing_1052.htm#SEC1133
974	WLemma sing_1051.htm#SEC1132
975	WP, global ordering sing_969.htm#IDX450
976	WSemigroup sing_1827.htm#SEC1908
977	Weierstrass sing_2165.htm#SEC2246
978	Weierstrass semigroup sing_2161.htm#IDX935
979	Weyl sing_734.htm#SEC788
980	Weyl algebra sing_537.htm#IDX332
981	Weyl algebra sing_592.htm#IDX358
982	Weyl algebra sing_600.htm#IDX364
983	Weyl closure sing_668.htm#IDX386
984	WeylClosure sing_670.htm#SEC724
985	WeylClosure1 sing_671.htm#SEC725
986	Wibmer's Lemma sing_1051.htm#IDX526
987	Windows installation Windows installation instructions sing_3005.htm#SEC3102
988	WitSet sing_1608.htm#SEC1689
989	WitSupSet sing_1607.htm#SEC1688
990	Ws, local ordering sing_970.htm#IDX462
991	XLsolve sing_2035.htm#SEC2116
992	ZZ sing_28.htm#SEC39
993	ZZ sing_75.htm#SEC115
994	ZZ/m sing_28.htm#SEC39
995	ZZ/p sing_28.htm#SEC39
996	ZZsolve sing_2036.htm#SEC2117
997	[ sing_36.htm#IDX83
998	[] sing_142.htm#SEC182
999	[] sing_155.htm#SEC195
1000	[] sing_176.htm#SEC216
1001	[] sing_181.htm#SEC221
1002	\ sing_36.htm#IDX112
1003	] sing_36.htm#IDX84
1004	^ sing_36.htm#IDX92
1005	^ sing_81.htm#SEC121
1006	^ sing_93.htm#SEC133
1007	^ sing_147.htm#SEC187
1008	^ sing_155.htm#SEC195
1009	_ sing_36.htm#IDX116
1010	` sing_36.htm#IDX105
1011	a, ordering sing_974.htm#SEC1031
1012	absFactorize sing_1235.htm#SEC1316
1013	absFactorizeBCG sing_1236.htm#SEC1317
1014	absPrimdecGTZ sing_1457.htm#SEC1538
1015	absPrimdecGTZE sing_1458.htm#SEC1539
1016	absValue sing_1015.htm#SEC1096
1017	absfact.lib sing_1234.htm#SEC1315
1018	absfact_lib sing_1234.htm#SEC1315
1019	absolute factorization. sing_1234.htm#IDX579
1020	abstract variety, projective space, Grassmannian printVariety sing_1694.htm#IDX737
1021	abstract variety, projective space, Grassmannian sing_1695.htm#IDX738
1022	abstractR sing_1690.htm#SEC1771
1023	actionIsProper sing_1996.htm#SEC2077
1024	add sing_2683.htm#IDX1125
1025	add sing_2705.htm#IDX1173
1026	addElement sing_2970.htm#SEC3051
1027	addLeftFractions sing_765.htm#SEC819
1028	addModules sing_2829.htm#SEC2910
1029	addNvarsTo sing_1158.htm#SEC1239
1030	addRat sing_689.htm#SEC743
1031	addSheaf sing_1713.htm#SEC1794
1032	addcol sing_1191.htm#SEC1272
1033	addcores sing_1127.htm#SEC1208
1034	addnondegeneratevariables addnondegeneratevariables sing_1918.htm#SEC1999
1035	addrow sing_1192.htm#SEC1273
1036	addvarsTo sing_1157.htm#SEC1238
1037	ademRelations sing_831.htm#SEC885
1038	adjoint sing_1216.htm#SEC1297
1039	adjointIdeal sing_1619.htm#SEC1700
1040	adjunction divisor sing_2162.htm#IDX939
1041	admissibleSub sing_725.htm#SEC779
1042	afaces sing_2445.htm#SEC2526
1043	affine code Fitzgerald-Lax method sing_998.htm#SEC1072
1044	ainvar.lib sing_1993.htm#SEC2074
1045	ainvar_lib sing_1993.htm#SEC2074
1046	aksaka.lib sing_2227.htm#SEC2308
1047	aksaka_lib sing_2227.htm#SEC2308
1048	alexanderpolynomial sing_1754.htm#SEC1835
1049	alexpoly.lib sing_1751.htm#SEC1832
1050	alexpoly_lib sing_1751.htm#SEC1832
1051	algDependent sing_1241.htm#SEC1322
1052	alg_kernel sing_1242.htm#SEC1323
1053	algebra.lib sing_1237.htm#SEC1318
1054	algebra_containment sing_1238.htm#SEC1319
1055	algebra_lib sing_1237.htm#SEC1318
1056	algebraic dependence sing_776.htm#IDX394
1057	algebraic field extension sing_1471.htm#IDX662
1058	algebraic statistics sing_2795.htm#IDX1207
1059	algebraicDependence sing_1489.htm#SEC1570
1060	algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_989.htm#SEC1051
1061	algorithm of Conti and Traverso sing_985.htm#SEC1047
1062	algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_988.htm#SEC1050
1063	algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_987.htm#SEC1049
1064	algorithm of Pottier sing_986.htm#SEC1048
1065	alias General command syntax sing_35.htm#SEC59
1066	align sing_209.htm#SEC249
1067	all.lib sing_1007.htm#SEC1088
1068	allDoubleExt sing_787.htm#SEC841
1069	allExtOfLeft sing_784.htm#SEC838
1070	allExtOfRight sing_785.htm#SEC839
1071	allPositive sing_513.htm#SEC567
1072	all_lib sing_1007.htm#SEC1088
1073	allowing net access Command line options sing_19.htm#IDX41
1074	allprint sing_1060.htm#SEC1141
1075	allreal sing_2370.htm#SEC2451
1076	allrealst sing_2368.htm#SEC2449
1077	allsquarefree sing_1889.htm#SEC1970
1078	ambientDimension sing_2387.htm#SEC2468
1079	and Evaluation of logical expressions sing_101.htm#SEC141
1080	and sing_415.htm#SEC455
1081	annPoly sing_561.htm#SEC615
1082	annRat sing_562.htm#SEC616
1083	annRatSyz sing_678.htm#SEC732
1084	annfalphaI sing_598.htm#SEC652
1085	annfs sing_538.htm#SEC592
1086	annfs0 sing_550.htm#SEC604
1087	annfs2 sing_551.htm#SEC605
1088	annfsBMI sing_547.htm#SEC601
1089	annfsLogIdeal sing_593.htm#SEC647
1090	annfsParamBM sing_546.htm#SEC600
1091	annfsRB sing_552.htm#SEC606
1092	annfspecial sing_539.htm#SEC593
1093	annihilator of polynomial sing_560.htm#IDX342
1094	annihilator of rational function sing_560.htm#IDX343
1095	annihilator of rational function sing_668.htm#IDX389
1096	annihilatorMultiFs sing_594.htm#SEC648
1097	annil sing_1361.htm#SEC1442
1098	appelF1 sing_579.htm#SEC633
1099	appelF2 sing_580.htm#SEC634
1100	appelF4 sing_581.htm#SEC635
1101	appendWeight2Ord sing_727.htm#SEC781
1102	application sing_2711.htm#IDX1188
1103	apply sing_382.htm#SEC422
1104	applyAdF sing_529.htm#SEC583
1105	applyMatrix sing_2042.htm#SEC2123
1106	applyPermutationToIntvec applyPermutationToIntvec sing_2470.htm#SEC2551
1107	applyVecField sing_2983.htm#SEC3064
1108	arcpoint.lib sing_1764.htm#SEC1845
1109	arcpoint_lib sing_1764.htm#SEC1845
1110	areEqualLeftFractions areEqualLeftFractions sing_767.htm#SEC821
1111	areZeroElements sing_2896.htm#SEC2977
1112	argument, default sing_44.htm#SEC81
1113	argument, optional sing_44.htm#SEC81
1114	arnoldClassify sing_1773.htm#SEC1854
1115	arnoldCorank sing_1774.htm#SEC1855
1116	arnoldDeterminacy sing_1775.htm#SEC1856
1117	arnoldListAllSeries sing_1770.htm#SEC1851
1118	arnoldMilnorCode sing_1776.htm#SEC1857
1119	arnoldMorseSplit sing_1777.htm#SEC1858
1120	arnoldNormalForm sing_1772.htm#SEC1853
1121	arnoldShowSeries sing_1771.htm#SEC1852
1122	arnoldclassify.lib sing_1769.htm#SEC1850
1123	arnoldclassify_lib sing_1769.htm#SEC1850
1124	arr.lib sing_2585.htm#SEC2666
1125	arr2multarr sing_2618.htm#SEC2699
1126	arrBoolean sing_2607.htm#SEC2688
1127	arrBoundedChambers sing_2628.htm#SEC2709
1128	arrBraid sing_2608.htm#SEC2689
1129	arrCenter sing_2595.htm#SEC2676
1130	arrCentered sing_2597.htm#SEC2678
1131	arrCentral sing_2596.htm#SEC2677
1132	arrCentralize sing_2598.htm#SEC2679
1133	arrChambers sing_2627.htm#SEC2708
1134	arrCharPoly sing_2625.htm#SEC2706
1135	arrCone sing_2601.htm#SEC2682
1136	arrCoordChange sing_2599.htm#SEC2680
1137	arrCoordNormalize sing_2600.htm#SEC2681
1138	arrDecone sing_2602.htm#SEC2683
1139	arrDer sing_2615.htm#SEC2696
1140	arrEdelmanReiner sing_2613.htm#SEC2694
1141	arrEssentialize sing_2606.htm#SEC2687
1142	arrExponents sing_2617.htm#SEC2698
1143	arrFlats sing_2622.htm#SEC2703
1144	arrIsEssential sing_2605.htm#SEC2686
1145	arrIsFree sing_2616.htm#SEC2697
1146	arrLastVar sing_2594.htm#SEC2675
1147	arrLattice sing_2623.htm#SEC2704
1148	arrLocalize sing_2603.htm#SEC2684
1149	arrOrlikSolomon sing_2614.htm#SEC2695
1150	arrPoincare sing_2626.htm#SEC2707
1151	arrPrintMatrix sing_2590.htm#SEC2671
1152	arrRandom sing_2611.htm#SEC2692
1153	arrRandomCentral sing_2612.htm#SEC2693
1154	arrRestrict sing_2604.htm#SEC2685
1155	arrSet sing_2586.htm#SEC2667
1156	arrSwapVar sing_2593.htm#SEC2674
1157	arrTypeB sing_2609.htm#SEC2690
1158	arrTypeD sing_2610.htm#SEC2691
1159	arr_lib sing_2585.htm#SEC2666
1160	arrange sing_554.htm#SEC608
1161	arrangement sing_2586.htm#IDX972
1162	arrangement sing_2587.htm#IDX977
1163	arrangement sing_2618.htm#IDX1039
1164	arrangement sing_2619.htm#IDX1042
1165	ask sing_2235.htm#SEC2316
1166	assPrimes sing_1252.htm#SEC1333
1167	assign sing_2586.htm#IDX974
1168	assignment,custom Assignments for user defined types sing_188.htm#SEC228
1169	associated tangent FamElemsAtEnvCompPoints sing_1048.htm#IDX519
1170	associated tangent sing_1049.htm#IDX523
1171	assprimeszerodim.lib assprimeszerodim_lib sing_1250.htm#SEC1331
1172	assprimeszerodim_lib assprimeszerodim_lib sing_1250.htm#SEC1331
1173	atkins.lib sing_2236.htm#SEC2317
1174	atkins_lib sing_2236.htm#SEC2317
1175	attrib sing_210.htm#SEC250
1176	autGenWeights sing_2661.htm#SEC2742
1177	autGradAlg sing_2660.htm#SEC2741
1178	autKS sing_2659.htm#SEC2740
1179	autX sing_2664.htm#SEC2745
1180	autXhat sing_2663.htm#SEC2744
1181	autgradalg.lib sing_2658.htm#SEC2739
1182	autgradalg_lib sing_2658.htm#SEC2739
1183	automorphism group sing_2658.htm#IDX1090
1184	automorphisms sing_2658.htm#IDX1087
1185	autonom sing_2199.htm#SEC2280
1186	autonomDim sing_2200.htm#SEC2281
1187	awalk1 sing_1296.htm#SEC1377
1188	awalk2 sing_1297.htm#SEC1378
1189	b-function sing_502.htm#IDX315
1190	bFactor sing_584.htm#SEC638
1191	babyGiant sing_2265.htm#SEC2346
1192	backward sing_2722.htm#SEC2803
1193	bareiss sing_211.htm#SEC251
1194	base2str sing_1010.htm#SEC1091
1195	basering sing_28.htm#IDX76
1196	basering sing_88.htm#SEC128
1197	basicinvariants sing_1779.htm#SEC1860
1198	baumslagGroup sing_833.htm#SEC887
1199	baumslagSolitar sing_832.htm#SEC886
1200	belongSemigroup sing_1255.htm#SEC1336
1201	bernstein sing_1849.htm#SEC1930
1202	bernsteinBM sing_542.htm#SEC596
1203	bernsteinLift sing_543.htm#SEC597
1204	bertini sing_1594.htm#IDX691
1205	bertini sing_1599.htm#IDX698
1206	bertini sing_2082.htm#IDX930
1207	bertini2Singular sing_1603.htm#SEC1684
1208	betti sing_212.htm#SEC252
1209	betti (plural) sing_459.htm#SEC499
1210	bfct sing_503.htm#SEC557
1211	bfctAnn sing_505.htm#SEC559
1212	bfctBound sing_677.htm#SEC731
1213	bfctIdeal sing_507.htm#SEC561
1214	bfctOneGB sing_506.htm#SEC560
1215	bfctSyz sing_504.htm#SEC558
1216	bfctVarAnn sing_602.htm#SEC656
1217	bfctVarIn sing_601.htm#SEC655
1218	bfun.lib sing_502.htm#SEC556
1219	bfun_lib sing_502.htm#SEC556
1220	bigger sing_2690.htm#IDX1139
1221	bigint sing_78.htm#SEC118
1222	bigint declarations sing_79.htm#SEC119
1223	bigint expressions sing_80.htm#SEC120
1224	bigint operations sing_81.htm#SEC121
1225	bigint related functions bigint related functions sing_82.htm#SEC122
1226	bigintToBinary sing_2468.htm#SEC2549
1227	bigintmat sing_83.htm#SEC123
1228	bigintmat declarations bigintmat declarations sing_84.htm#SEC124
1229	bigintmat expressions bigintmat expressions sing_85.htm#SEC125
1230	bigintmat operations bigintmat operations sing_87.htm#SEC127
1231	bigintmat type cast sing_86.htm#SEC126
1232	bimodules sing_495.htm#IDX303
1233	bimodules.lib sing_495.htm#SEC549
1234	bimodules_lib sing_495.htm#SEC549
1235	binaryToBigint sing_2469.htm#SEC2550
1236	binary_add sing_2288.htm#SEC2369
1237	binomial sing_1016.htm#SEC1097
1238	binomials2intmat sing_1432.htm#SEC1513 58804
1239	birational map, image, inverse. sing_1620.htm#IDX723
1240	bistd sing_496.htm#SEC550
1241	bisyzygies sing_495.htm#IDX304
1242	bitrinity sing_497.htm#SEC551
1243	blackbox sing_192.htm#SEC232
1244	blackbox sing_200.htm#SEC240
1245	block sing_40.htm#SEC70
1246	block sing_381.htm#SEC421
1247	blowUp sing_1671.htm#SEC1752
1248	blowUp2 sing_1672.htm#SEC1753
1249	blowUpBO sing_1678.htm#SEC1759
1250	blowup0 sing_1265.htm#SEC1346
1251	boolean sing_2607.htm#IDX1016
1252	boolean expressions sing_100.htm#SEC140
1253	boolean operations sing_101.htm#SEC141
1254	boolean_constant sing_2641.htm#SEC2722 52873
1255	boolean_ideal sing_2645.htm#SEC2726 53515
1256	boolean_poly sing_2642.htm#SEC2723 41652
1257	boolean_poly_ring sing_2640.htm#SEC2721 sprintf
1258	boolean_set sing_2646.htm#SEC2727 58235
1259	boolean_std sing_2639.htm#SEC2720 5921
1260	border basis sing_1479.htm#IDX664
1261	borderBasis sing_1480.htm#SEC1561
1262	boundBuFou sing_2365.htm#SEC2446
1263	boundDes sing_2367.htm#SEC2448
1264	boundaryLatticePoints boundaryLatticePoints sing_2489.htm#SEC2570
1265	boundposDes sing_2366.htm#SEC2447
1266	bounds sing_2101.htm#SEC2182
1267	bounds2 sing_2039.htm#SEC2120
1268	boxSet sing_2103.htm#SEC2184
1269	bracket sing_361.htm#IDX197
1270	bracket sing_418.htm#SEC458
1271	bracket sing_460.htm#SEC500
1272	braid sing_2608.htm#IDX1018
1273	branchTo procs with different argument types sing_160.htm#SEC200
1274	break sing_383.htm#SEC423
1275	break point sing_397.htm#SEC437
1276	breakpoint sing_384.htm#SEC424
1277	brillnoether.lib sing_1505.htm#SEC1586
1278	brillnoether_lib sing_1505.htm#SEC1586
1279	brnoeth.lib sing_2161.htm#SEC2242
1280	brnoeth_lib sing_2161.htm#SEC2242
1281	browser, command line option Command line options sing_19.htm#IDX44
1282	browser, setting the sing_361.htm#IDX193
1283	browsers The online help system sing_16.htm#IDX21
1284	browsers, setting the sing_361.htm#IDX192
1285	bubblesort sing_2238.htm#SEC2319
1286	buildtree sing_1106.htm#SEC1187
1287	buildtree, Maple sing_1107.htm#IDX554
1288	buildtree, buildtreetoMaple, CGS sing_1108.htm#IDX555
1289	buildtreetoMaple sing_1107.htm#SEC1188
1290	busadj sing_1214.htm#SEC1295
1291	bvar sing_2653.htm#SEC2734 52773
1292	c, module ordering sing_971.htm#IDX465
1293	cProj sing_1547.htm#SEC1628
1294	calculateI sing_1645.htm#SEC1726
1295	calculate_max_sum sing_2307.htm#SEC2388
1296	calculate_ordering sing_2285.htm#SEC2366
1297	cancelunit, option sing_318.htm#IDX171
1298	canonMap sing_1301.htm#SEC1382
1299	canonical sing_1034.htm#IDX474
1300	canonical form sing_1038.htm#IDX486
1301	canonical form sing_1039.htm#IDX488
1302	canonical form sing_1040.htm#IDX490
1303	canonical form sing_1055.htm#IDX532
1304	canonical form sing_1056.htm#IDX534
1305	canonical form sing_1057.htm#IDX537
1306	canonical form sing_1058.htm#IDX539
1307	canonical, sing_1042.htm#IDX500
1308	canonicalizeCone sing_2388.htm#SEC2469
1309	canonize sing_2207.htm#SEC2288
1310	cantodiffcgs sing_1112.htm#SEC1193
1311	cantoradd sing_2321.htm#SEC2402
1312	cantormult sing_2324.htm#SEC2405
1313	cantorred sing_2322.htm#SEC2403
1314	cardGroup sing_1257.htm#SEC1338
1315	case No case or switch statement sing_416.htm#SEC456
1316	catNets sing_2913.htm#SEC2994
1317	cccMatrixToPositiveIntvec cccMatrixToPositiveIntvec sing_2579.htm#SEC2660
1318	cdd sing_1.htm#IDX10
1319	cddlib sing_1.htm#IDX11
1320	center sing_516.htm#IDX322
1321	center sing_522.htm#SEC576
1322	center sing_2595.htm#IDX998
1323	center sing_2596.htm#IDX999
1324	center sing_2597.htm#IDX1001
1325	center sing_2598.htm#IDX1003
1326	centerRed sing_521.htm#SEC575
1327	centerVS sing_520.htm#SEC574
1328	central sing_2589.htm#IDX984
1329	central sing_2596.htm#IDX1000
1330	central sing_2598.htm#IDX1002
1331	central sing_2612.htm#IDX1027
1332	central.lib sing_516.htm#SEC570
1333	central1st sing_2723.htm#SEC2804
1334	central2nd sing_2724.htm#SEC2805
1335	central_lib sing_516.htm#SEC570
1336	centralize sing_516.htm#IDX325
1337	centralizeSet sing_517.htm#SEC571
1338	centralizer sing_516.htm#IDX323
1339	centralizer sing_523.htm#SEC577
1340	centralizerRed sing_519.htm#SEC573
1341	centralizerVS sing_518.htm#SEC572
1342	cf_class sing_210.htm#IDX132
1343	cgs sing_1009.htm#SEC1090
1344	cgsdr sing_1035.htm#SEC1116
1345	chAll sing_1517.htm#SEC1598
1346	chAllInv sing_1518.htm#SEC1599
1347	chDual sing_1523.htm#SEC1604
1348	chHE sing_1519.htm#SEC1600
1349	chHom sing_1532.htm#SEC1613
1350	chNum sing_1513.htm#SEC1594
1351	chNumbers sing_1514.htm#SEC1595
1352	chNumbersProj sing_1551.htm#SEC1632
1353	chProd sing_1525.htm#SEC1606
1354	chProdE sing_1526.htm#SEC1607
1355	chProdL sing_1527.htm#SEC1608
1356	chProdLP sing_1528.htm#SEC1609
1357	chProdM sing_1529.htm#SEC1610
1358	chProdMP sing_1530.htm#SEC1611
1359	chProj sing_1548.htm#SEC1629
1360	chSum sing_1521.htm#SEC1602
1361	chSymm sing_1535.htm#SEC1616
1362	chSymm2L sing_1536.htm#SEC1617
1363	chSymm2LP sing_1537.htm#SEC1618
1364	chWedge sing_1538.htm#SEC1619
1365	chWedge2L sing_1539.htm#SEC1620
1366	chWedge2LP sing_1540.htm#SEC1621
1367	chaincrit sing_2335.htm#SEC2416
1368	chambers sing_2627.htm#IDX1055
1369	chambers sing_2628.htm#IDX1056
1370	changeCoordinates sing_2984.htm#SEC3065
1371	changeDenominator sing_1404.htm#SEC1485
1372	changechar sing_1132.htm#SEC1213
1373	changeord sing_1133.htm#SEC1214
1374	changeordTo sing_1156.htm#SEC1237
1375	changes sing_2994.htm#SEC3075
1376	changevar sing_1134.htm#SEC1215
1377	char sing_213.htm#SEC253
1378	charInfo sing_577.htm#SEC631
1379	charVariety sing_576.htm#SEC630
1380	char_series sing_214.htm#SEC254
1381	characteristic exponents sing_1758.htm#IDX771
1382	characteristic exponents sing_1759.htm#IDX776
1383	characteristic exponents sing_1760.htm#IDX779
1384	characteristic exponents sing_1761.htm#IDX783
1385	characteristic exponents sing_1876.htm#IDX895
1386	characteristic polynomial sing_2625.htm#IDX1053
1387	characteristic variety sing_560.htm#IDX350
1388	characteristic variety sing_668.htm#IDX385
1389	charexp2conductor sing_1761.htm#SEC1842
1390	charexp2generators sing_1759.htm#SEC1840
1391	charexp2inter sing_1760.htm#SEC1841
1392	charexp2multseq sing_1758.htm#SEC1839
1393	charexp2poly sing_1762.htm#SEC1843
1394	charpoly sing_1215.htm#SEC1296
1395	charstr sing_215.htm#SEC255
1396	checkFactor sing_553.htm#SEC607
1397	checkRoot sing_548.htm#SEC602
1398	checkpfd sing_2940.htm#SEC3021
1399	checkpfdMat sing_2948.htm#SEC3029
1400	chern sing_1512.htm#SEC1593
1401	chern.lib sing_1507.htm#SEC1588
1402	chernCharPoly sing_1554.htm#SEC1635
1403	chernPoly sing_1553.htm#SEC1634
1404	chern_lib sing_1507.htm#SEC1588
1405	chineseRem sing_2256.htm#SEC2337
1406	chinrem sing_216.htm#SEC256
1407	chinrempoly sing_1377.htm#SEC1458
1408	chinrestp sing_2315.htm#SEC2396
1409	cimonom.lib sing_2379.htm#SEC2460
1410	cimonom_lib sing_2379.htm#SEC2460
1411	cisimplicial.lib sing_1253.htm#SEC1334
1412	cisimplicial_lib sing_1253.htm#SEC1334
1413	classSpaceCurve sing_1808.htm#SEC1889
1414	classification sing_1769.htm#IDX788
1415	classification sing_1796.htm#IDX791
1416	classify sing_1780.htm#SEC1861
1417	classify.lib sing_1778.htm#SEC1859
1418	classify2.lib sing_1796.htm#SEC1877
1419	classify2_lib sing_1796.htm#SEC1877
1420	classifyCeq sing_1810.htm#SEC1891
1421	classifyMapGerms.lib classifyMapGerms_lib sing_1814.htm#SEC1895
1422	classifyMapGerms_lib classifyMapGerms_lib sing_1814.htm#SEC1895
1423	classifySimpleMaps sing_1820.htm#SEC1901
1424	classifySimpleMaps1 sing_1821.htm#SEC1902
1425	classifyUnimodalMaps classifyUnimodalMaps sing_1822.htm#SEC1903
1426	classify_aeq.lib sing_1799.htm#SEC1880
1427	classify_aeq_lib sing_1799.htm#SEC1880
1428	classify_lib sing_1778.htm#SEC1859
1429	classifyceq.lib sing_1809.htm#SEC1890
1430	classifyceq_lib sing_1809.htm#SEC1890
1431	classifyci.lib sing_1811.htm#SEC1892
1432	classifyci_lib sing_1811.htm#SEC1892
1433	classifyicis sing_1812.htm#SEC1893
1434	classpoly sing_1552.htm#SEC1633
1435	cleanTmp sing_2567.htm#SEC2648
1436	cleanunit sing_1643.htm#SEC1724
1437	cleardenom sing_217.htm#SEC257
1438	close sing_218.htm#SEC258
1439	closed_points sing_2171.htm#SEC2252
1440	closetex sing_2138.htm#SEC2219
1441	closureFrac sing_1397.htm#SEC1478
1442	coDim sing_1816.htm#SEC1897
1443	coDimMap sing_1815.htm#SEC1896
1444	coHom sing_711.htm#SEC765
1445	codim sing_1920.htm#SEC2001
1446	codimension sing_2389.htm#SEC2470
1447	coding theory sing_963.htm#SEC1020
1448	coef sing_219.htm#SEC259
1449	coefficient sing_2588.htm#IDX980
1450	coefficient sing_2589.htm#IDX983
1451	coefficient sing_2590.htm#IDX987
1452	coefficient field sing_144.htm#SEC184
1453	coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC45
1454	coefficients sing_2677.htm#IDX1114
1455	coefficients, long sing_920.htm#SEC977
1456	coeffmod sing_2233.htm#SEC2314
1457	coeffs sing_220.htm#SEC260
1458	coker sing_2825.htm#SEC2906
1459	colength of derivations curveColengthDerivations sing_1263.htm#IDX591
1460	collectDiv sing_1688.htm#SEC1769
1461	colrank sing_2205.htm#SEC2286
1462	colred sing_1198.htm#SEC1279
1463	combinat.lib sing_2665.htm#SEC2746
1464	combinat_lib sing_2665.htm#SEC2746
1465	commRing sing_692.htm#SEC746
1466	comma sing_417.htm#SEC457
1467	command,custom Commands for user defined types sing_187.htm#SEC227
1468	command-line option, setting value of sing_361.htm#IDX281
1469	command-line option, value of sing_361.htm#IDX279
1470	command-line options, print all values of sing_361.htm#IDX278
1471	command-line options, short help Command line options sing_19.htm#IDX38
1472	commands (letterplace) Functions (letterplace) sing_804.htm#SEC858
1473	commands (plural) sing_458.htm#IDX302
1474	comment sing_36.htm#IDX108
1475	compare sing_2688.htm#IDX1134
1476	compare sing_2689.htm#IDX1136
1477	compare sing_2690.htm#IDX1140
1478	compare sing_2691.htm#IDX1143
1479	compare sing_2709.htm#IDX1181
1480	compare sing_2710.htm#IDX1183
1481	compareMatrix sing_2833.htm#SEC2914
1482	compareModules sing_2828.htm#SEC2909
1483	compareTasks sing_1163.htm#SEC1244
1484	compareVectors sing_2853.htm#SEC2934
1485	complement sing_2966.htm#SEC3047
1486	completeReduction sing_1998.htm#SEC2079
1487	complex sing_28.htm#IDX75
1488	complexClassify sing_1797.htm#SEC1878
1489	complexSingType sing_1794.htm#SEC1875
1490	complexType sing_1798.htm#SEC1879
1491	compregb.lib sing_1008.htm#SEC1089
1492	compregb_lib sing_1008.htm#SEC1089
1493	comprehensive Groebner system sing_1008.htm#IDX471
1494	compress sing_1176.htm#SEC1257
1495	computeAfaceOrbits sing_2455.htm#SEC2536
1496	computeConstant sing_1278.htm#SEC1359
1497	computeGromovWitten sing_1281.htm#SEC1362
1498	computeN sing_1692.htm#SEC1773
1499	computeV sing_1691.htm#SEC1772
1500	computemcm sing_1650.htm#SEC1731
1501	concat sing_1177.htm#SEC1258
1502	conductor sing_1261.htm#IDX585
1503	conductor sing_1405.htm#IDX654
1504	conductor sing_1761.htm#IDX782
1505	conductor, degree sing_1876.htm#IDX898
1506	cone sing_189.htm#SEC229
1507	cone sing_2601.htm#IDX1007
1508	cone sing_2602.htm#IDX1009
1509	coneLink sing_2392.htm#SEC2473
1510	coneViaInequalities sing_2391.htm#SEC2472
1511	coneViaPoints sing_2390.htm#SEC2471
1512	conic, parametrization, rational point. sing_1627.htm#IDX728
1513	conicWithTangents sing_2543.htm#SEC2624
1514	constructH sing_1651.htm#SEC1732
1515	constructblwup sing_1652.htm#SEC1733
1516	constructible set sing_1055.htm#IDX530
1517	constructible set sing_1057.htm#IDX535
1518	constructible sets sing_1056.htm#IDX533
1519	constructible sets sing_1058.htm#IDX538
1520	constructlastblwup sing_1653.htm#SEC1734
1521	constructor derivationConstructor sing_2618.htm#IDX1040
1522	constructor sing_2619.htm#IDX1043
1523	constructor sing_2676.htm#IDX1110
1524	constructor sing_2699.htm#IDX1159
1525	constructor sing_2700.htm#IDX1161
1526	constructor sing_2701.htm#IDX1164
1527	constructor sing_2702.htm#IDX1167
1528	contact matrix sing_1760.htm#IDX778
1529	containedQ sing_2130.htm#SEC2211
1530	containment sing_2695.htm#IDX1150
1531	containsAsFace sing_2393.htm#SEC2474
1532	containsInCollection containsInCollection sing_2426.htm#SEC2507
1533	containsInSupport sing_2394.htm#SEC2475
1534	containsPositiveVector containsPositiveVector sing_2395.htm#SEC2476
1535	containsRelatively sing_2396.htm#SEC2477
1536	content sing_1091.htm#SEC1172
1537	contentSB, option sing_318.htm#IDX172
1538	continue Behavior of continue sing_385.htm#SEC425
1539	continue sing_419.htm#SEC459
1540	contraHom sing_712.htm#SEC766
1541	contract sing_221.htm#SEC261
1542	contraction derivationContraction sing_2712.htm#IDX1189
1543	contraction sing_2713.htm#IDX1191
1544	contraction sing_2714.htm#IDX1193
1545	contribution bundle, graph, multiple cover, rational curve, contributionBundle sing_1720.htm#IDX750
1546	contributionBundle sing_1720.htm#SEC1801
1547	contributors sing_361.htm#IDX199
1548	control sing_2197.htm#SEC2278
1549	control.lib sing_2196.htm#SEC2277
1550	controlDim sing_2198.htm#SEC2279
1551	controlExample sing_2210.htm#SEC2291
1552	control_Matrix sing_1844.htm#SEC1925
1553	control_lib sing_2196.htm#SEC2277
1554	convertLeftToRightFraction convertLeftToRightFraction sing_764.htm#SEC818
1555	convertRightToLeftFraction convertRightToLeftFraction sing_763.htm#SEC817
1556	convertdata sing_1648.htm#SEC1729
1557	convexHull sing_2397.htm#SEC2478
1558	convexIntersection sing_2398.htm#SEC2479
1559	convloc sing_557.htm#SEC611
1560	coordinate change sing_2598.htm#IDX1004
1561	coordinate change sing_2599.htm#IDX1005
1562	coordinate change sing_2600.htm#IDX1006
1563	coordinates sing_2353.htm#IDX955
1564	coords sing_2353.htm#SEC2434
1565	copyTask sing_1162.htm#SEC1243
1566	copyright sing_1.htm#IDX1
1567	corank sing_1781.htm#SEC1862
1568	cornerMonomials sing_1435.htm#SEC1516
1569	countPoints sing_2278.htm#SEC2359
1570	coverings sing_1280.htm#IDX607
1571	coverings sing_1281.htm#IDX611
1572	cpu sing_361.htm#IDX201
1573	cpu sing_361.htm#IDX275
1574	crcgs sing_1111.htm#SEC1192
1575	createBO sing_1679.htm#SEC1760
1576	createGradedRingHomomorphism createGradedRingHomomorphism sing_2872.htm#SEC2953
1577	createGroup sing_2865.htm#SEC2946
1578	createQuotientGroup sing_2866.htm#SEC2947
1579	createTask sing_1160.htm#SEC1241
1580	createTorsionFreeGroup createTorsionFreeGroup sing_2867.htm#SEC2948
1581	create_ring sing_222.htm#SEC262
1582	createlist sing_1661.htm#SEC1742
1583	cring sing_73.htm#SEC113
1584	cring declarations sing_74.htm#SEC114
1585	cring expressions sing_75.htm#SEC115
1586	cring operations sing_76.htm#SEC116
1587	cring related functions cring related functions sing_77.htm#SEC117
1588	crossprod sing_223.htm#SEC263
1589	crypto.lib sing_2251.htm#SEC2332
1590	crypto_lib sing_2251.htm#SEC2332
1591	crystallographicGroupC2MM crystallographicGroupC2MM sing_841.htm#SEC895
1592	crystallographicGroupCM crystallographicGroupCM sing_840.htm#SEC894
1593	crystallographicGroupP1 crystallographicGroupP1 sing_834.htm#SEC888
1594	crystallographicGroupP2 crystallographicGroupP2 sing_838.htm#SEC892
1595	crystallographicGroupP2GG crystallographicGroupP2GG sing_839.htm#SEC893
1596	crystallographicGroupP2MM crystallographicGroupP2MM sing_837.htm#SEC891
1597	crystallographicGroupP3 crystallographicGroupP3 sing_845.htm#SEC899
1598	crystallographicGroupP31M crystallographicGroupP31M sing_846.htm#SEC900
1599	crystallographicGroupP3M1 crystallographicGroupP3M1 sing_847.htm#SEC901
1600	crystallographicGroupP4 crystallographicGroupP4 sing_842.htm#SEC896
1601	crystallographicGroupP4GM crystallographicGroupP4GM sing_844.htm#SEC898
1602	crystallographicGroupP4MM crystallographicGroupP4MM sing_843.htm#SEC897
1603	crystallographicGroupP6 crystallographicGroupP6 sing_848.htm#SEC902
1604	crystallographicGroupP6MM crystallographicGroupP6MM sing_849.htm#SEC903
1605	crystallographicGroupPG crystallographicGroupPG sing_836.htm#SEC890
1606	crystallographicGroupPM crystallographicGroupPM sing_835.htm#SEC889
1607	cup sing_1302.htm#SEC1383
1608	cupproduct sing_1303.htm#SEC1384
1609	curve singularities sing_1751.htm#IDX765
1610	curve singularities sing_1870.htm#IDX893
1611	curve singularity sing_1259.htm#IDX580
1612	curveColengthDerivations curveColengthDerivations sing_1263.htm#SEC1344
1613	curveConductorMult sing_1261.htm#SEC1342
1614	curveDeligneNumber sing_1262.htm#SEC1343
1615	curveDeltaInv sing_1260.htm#SEC1341
1616	curveInv.lib sing_1259.htm#SEC1340
1617	curveInv_lib sing_1259.htm#SEC1340
1618	curvepar.lib sing_1823.htm#SEC1904
1619	curvepar_lib sing_1823.htm#SEC1904
1620	custom assignment Assignments for user defined types sing_188.htm#SEC228
1621	custom command Commands for user defined types sing_187.htm#SEC227
1622	custom type Definition of a user defined type sing_184.htm#SEC224
1623	customstd.lib sing_2630.htm#SEC2711
1624	customstd_lib sing_2630.htm#SEC2711
1625	cycleLength sing_2480.htm#SEC2561
1626	cyclePoints sing_2484.htm#SEC2565
1627	cyclic sing_1078.htm#SEC1159
1628	cyclic code Codes and the decoding problem sing_995.htm#SEC1059
1629	cyclotomic sing_1963.htm#SEC2044
1630	datetime sing_224.htm#SEC264
1631	dbprint sing_225.htm#SEC265
1632	deRham.lib sing_1569.htm#SEC1650
1633	deRhamCohom sing_574.htm#SEC628
1634	deRhamCohomIdeal sing_575.htm#SEC629
1635	deRhamCohomology sing_1570.htm#SEC1651
1636	deRham_lib sing_1569.htm#SEC1650
1637	debugLib, option sing_318.htm#IDX176
1638	debug_log sing_1791.htm#SEC1872
1639	debugger Source code debugger sing_66.htm#SEC103
1640	debugging library code Source code debugger sing_66.htm#SEC103
1641	dec1var sing_1360.htm#SEC1441
1642	decimal sing_2252.htm#SEC2333
1643	decode sing_2188.htm#SEC2269
1644	decodeCode sing_2190.htm#SEC2271
1645	decodeRandom sing_2189.htm#SEC2270
1646	decodeRandomFL sing_2193.htm#SEC2274
1647	decodeSV sing_2170.htm#SEC2251
1648	decodegb.lib sing_2175.htm#SEC2256
1649	decodegb_lib sing_2175.htm#SEC2256
1650	decoding, decoding problem Codes and the decoding problem sing_995.htm#SEC1060
1651	decoef sing_2218.htm#SEC2299
1652	decomposeVecField sing_2990.htm#SEC3071
1653	decomposition sing_2677.htm#IDX1112
1654	decomposition sing_2938.htm#IDX1244
1655	decomposition of modules sing_1353.htm#IDX637
1656	decomposition, numerical sing_1599.htm#IDX696
1657	decone sing_2601.htm#IDX1008
1658	decone sing_2602.htm#IDX1010
1659	def sing_88.htm#SEC128
1660	def declarations sing_89.htm#SEC129
1661	defRes, option sing_318.htm#IDX177
1662	default argument sing_44.htm#SEC81
1663	defineHomogeneous sing_2905.htm#SEC2986
1664	defined sing_226.htm#SEC266
1665	defl sing_1610.htm#SEC1691
1666	deform sing_1921.htm#SEC2002
1667	deform.lib sing_1834.htm#SEC1915
1668	deform_lib sing_1834.htm#SEC1915
1669	defring sing_1135.htm#SEC1216
1670	defringp sing_1137.htm#SEC1218
1671	defrings sing_1136.htm#SEC1217
1672	deg sing_227.htm#SEC267
1673	degBound sing_399.htm#SEC439
1674	degree Miscellaneous oddities sing_228.htm#SEC268
1675	degree sing_422.htm#IDX292
1676	degree sing_2692.htm#IDX1145
1677	degree sing_2694.htm#IDX1149
1678	degree lexicographical ordering sing_969.htm#IDX445
1679	degree of a polynomial Miscellaneous oddities sing_422.htm#IDX296
1680	degree reverse lexicographical ordering sing_969.htm#IDX443
1681	degreeDivisor sing_1580.htm#SEC1661
1682	degreeFormalDivisor sing_1588.htm#SEC1669
1683	degreepart sing_2047.htm#SEC2128
1684	delete sing_126.htm#SEC166
1685	delete sing_229.htm#SEC269
1686	delete sing_279.htm#SEC319
1687	deleteGenerator sing_589.htm#SEC643
1688	deleteSublist sing_1017.htm#SEC1098
1689	deligne number curveColengthDerivations sing_1259.htm#IDX582
1690	deligne number sing_1262.htm#IDX587
1691	deligne number sing_1263.htm#IDX589
1692	delta sing_1882.htm#SEC1963
1693	delta invariant sing_1260.htm#IDX583
1694	delta invariant sing_1399.htm#IDX652
1695	delta invariant sing_1882.htm#IDX903
1696	delta invariant. sing_1391.htm#IDX645
1697	delta invariant. sing_1392.htm#IDX648
1698	delta invariant. sing_1393.htm#IDX651
1699	deltaLoc sing_1399.htm#SEC1480
1700	denom_list sing_361.htm#IDX203
1701	denominator sing_230.htm#SEC270
1702	depth sing_1304.htm#SEC1385
1703	depthIdeal sing_1370.htm#SEC1451
1704	derivate sing_1995.htm#SEC2076
1705	derivation derivationConstructor sing_2615.htm#IDX1031
1706	derivation sing_2697.htm#IDX1154
1707	derivation sing_2698.htm#IDX1158
1708	derivation sing_2699.htm#IDX1160
1709	derivation sing_2700.htm#IDX1162
1710	derivation sing_2701.htm#IDX1165
1711	derivation sing_2702.htm#IDX1168
1712	derivation sing_2711.htm#IDX1187
1713	derivationAdd sing_2705.htm#SEC2786
1714	derivationCheckList sing_2700.htm#SEC2781
1715	derivationConstructor derivationConstructor sing_2702.htm#SEC2783
1716	derivationContraction derivationContraction sing_2713.htm#SEC2794
1717	derivationContractionGen derivationContractionGen sing_2712.htm#SEC2793
1718	derivationEqu sing_2709.htm#SEC2790
1719	derivationEval sing_2711.htm#SEC2792
1720	derivationFromList sing_2699.htm#SEC2780
1721	derivationFromPoly sing_2701.htm#SEC2782
1722	derivationLie sing_2714.htm#SEC2795
1723	derivationMul sing_2708.htm#SEC2789
1724	derivationNeg sing_2707.htm#SEC2788
1725	derivationNeq sing_2710.htm#SEC2791
1726	derivationPrint sing_2704.htm#SEC2785
1727	derivationSub sing_2706.htm#SEC2787
1728	derivationToString sing_2703.htm#SEC2784
1729	desingularization sing_2758.htm#IDX1204
1730	desingularization sing_2759.htm#SEC2840
1731	det sing_231.htm#SEC271
1732	det_B sing_1217.htm#SEC1298
1733	detadj sing_1898.htm#SEC1979
1734	determinacy sing_1917.htm#SEC1998
1735	determinecenter sing_1633.htm#SEC1714
1736	detropicalise sing_2561.htm#SEC2642
1737	develop sing_1872.htm#SEC1953
1738	diag sing_1178.htm#SEC1259
1739	diagInvariants sing_1414.htm#SEC1495 62096
1740	diag_test sing_1213.htm#SEC1294
1741	diagonalizeMatrixSimul diagonalizeMatrixSimul sing_2991.htm#SEC3072
1742	diagonalizeVecField sing_2988.htm#SEC3069
1743	diagonalizeVecFieldLin diagonalizeVecFieldLin sing_2986.htm#SEC3067
1744	diff sing_232.htm#SEC272
1745	diffAlgebra sing_2670.htm#SEC2751
1746	diffAlgebraChangeOrd diffAlgebraChangeOrd sing_2674.htm#SEC2755
1747	diffAlgebraGens sing_2672.htm#SEC2753
1748	diffAlgebraListGen sing_2675.htm#SEC2756
1749	diffAlgebraStructure diffAlgebraStructure sing_2671.htm#SEC2752
1750	diffAlgebraUnivDerIdeal diffAlgebraUnivDerIdeal sing_2673.htm#SEC2754
1751	diffRat sing_691.htm#SEC745
1752	difference sing_2684.htm#IDX1128
1753	difference sing_2706.htm#IDX1176
1754	difference sing_2707.htm#IDX1178
1755	differential sing_2676.htm#IDX1111
1756	differential sing_2698.htm#IDX1156
1757	differential algebra diffAlgebraUnivDerIdeal sing_2669.htm#IDX1098
1758	differential algebra sing_2670.htm#IDX1099
1759	differential algebra sing_2671.htm#IDX1102
1760	differential algebra sing_2672.htm#IDX1103
1761	differential algebra sing_2673.htm#IDX1105
1762	differential forms sing_2669.htm#IDX1096
1763	differential forms sing_2670.htm#IDX1100
1764	differentials sing_2669.htm#IDX1097
1765	differentials sing_2670.htm#IDX1101
1766	difform.lib sing_2669.htm#SEC2750
1767	difformAdd sing_2683.htm#SEC2764
1768	difformCoef sing_2677.htm#SEC2758
1769	difformDeg sing_2692.htm#SEC2773
1770	difformDiff sing_2698.htm#SEC2779
1771	difformDiv sing_2687.htm#SEC2768
1772	difformEqu sing_2688.htm#SEC2769
1773	difformFromPoly sing_2676.htm#SEC2757
1774	difformGenToString sing_2678.htm#SEC2759
1775	difformHomogDecomp sing_2679.htm#SEC2760
1776	difformIsBigger sing_2690.htm#SEC2771
1777	difformIsGen sing_2682.htm#SEC2763
1778	difformIsHomog sing_2693.htm#SEC2774
1779	difformIsHomogDeg sing_2694.htm#SEC2775
1780	difformIsSmaller sing_2691.htm#SEC2772
1781	difformListCont sing_2695.htm#SEC2776
1782	difformListSort sing_2696.htm#SEC2777
1783	difformMul sing_2686.htm#SEC2767
1784	difformNeg sing_2685.htm#SEC2766
1785	difformNeq sing_2689.htm#SEC2770
1786	difformPrint sing_2681.htm#SEC2762
1787	difformSub sing_2684.htm#SEC2765
1788	difformToString sing_2680.htm#SEC2761
1789	difformUnivDer sing_2697.htm#SEC2778
1790	difform_lib sing_2669.htm#SEC2750
1791	difpoly2tex sing_2219.htm#SEC2300
1792	dim sing_233.htm#SEC273
1793	dim (plural) sing_461.htm#SEC501
1794	dimGradedPart sing_1740.htm#SEC1821 11262
1795	dimH sing_1739.htm#SEC1820 38534
1796	dimMon sing_1350.htm#SEC1431
1797	dimStack sing_1718.htm#SEC1799
1798	dim_slocus sing_1922.htm#SEC2003
1799	dimension sing_2399.htm#SEC2480
1800	dimension, moduli space of stable maps, rational curves dimStack sing_1718.htm#IDX748
1801	dimensionOfLocalization dimensionOfLocalization sing_2753.htm#SEC2834
1802	direct_boolean_poly sing_2643.htm#SEC2724 49893
1803	direct_from_boolean_poly direct_from_boolean_poly sing_2649.htm#SEC2730 36941
1804	disc sing_2239.htm#SEC2320
1805	discr sing_1944.htm#SEC2025
1806	discrepancy sing_1686.htm#SEC1767
1807	discrim sing_1050.htm#SEC1131
1808	discussion of parametric ideal sing_1034.htm#IDX475
1809	disjoint sing_1035.htm#IDX477
1810	disp_zdd sing_2656.htm#SEC2737 41439
1811	displayCohom sing_1741.htm#SEC1822 22633
1812	displayHNE sing_1875.htm#SEC1956
1813	displayInvariants sing_1877.htm#SEC1958
1814	displayMultsequence sing_1879.htm#SEC1960
1815	displayPuiseuxExpansion displayPuiseuxExpansion sing_2536.htm#SEC2617
1816	displayTropicalLifting displayTropicalLifting sing_2534.htm#SEC2615
1817	displaypfd sing_2942.htm#SEC3023
1818	displaypfd_long sing_2943.htm#SEC3024
1819	distributed computing sing_1071.htm#IDX547
1820	distributed computing sing_1126.htm#IDX561
1821	distributed computing sing_1159.htm#IDX571
1822	div Miscellaneous oddities sing_81.htm#SEC121
1823	div sing_98.htm#SEC138
1824	div sing_155.htm#SEC195
1825	div sing_422.htm#IDX289
1826	divideUnits sing_2215.htm#SEC2296
1827	dividelist sing_1660.htm#SEC1741
1828	division sing_234.htm#SEC274
1829	division sing_1036.htm#IDX480
1830	division sing_1037.htm#IDX482
1831	division sing_2687.htm#IDX1133
1832	division (plural) sing_462.htm#SEC502
1833	division, pdivi2, reduce sing_1105.htm#IDX552
1834	division, reduce sing_1102.htm#IDX549
1835	divisor sing_2318.htm#SEC2399
1836	divisorplus sing_1574.htm#SEC1655
1837	divisors negativeformaldivisor sing_1573.htm#IDX670
1838	divisors sing_1574.htm#IDX671
1839	divisors sing_1575.htm#IDX672
1840	divisors sing_1576.htm#IDX673
1841	divisors sing_1577.htm#IDX674
1842	divisors sing_1578.htm#IDX675
1843	divisors sing_1579.htm#IDX676
1844	divisors sing_1580.htm#IDX677
1845	divisors sing_1581.htm#IDX678
1846	divisors sing_1582.htm#IDX679
1847	divisors sing_1583.htm#IDX680
1848	divisors sing_1584.htm#IDX681
1849	divisors sing_1585.htm#IDX682
1850	divisors sing_1586.htm#IDX683
1851	divisors sing_1587.htm#IDX684
1852	divisors sing_1588.htm#IDX685
1853	divisors, polyhedra sing_1589.htm#IDX686
1854	divisors, polyhedra sing_1590.htm#IDX687
1855	divisors, polyhedra sing_1591.htm#IDX688
1856	divisors.lib sing_1572.htm#SEC1653
1857	divisors_lib sing_1572.htm#SEC1653
1858	dmod.lib sing_537.htm#SEC591
1859	dmodAction sing_686.htm#SEC740
1860	dmodActionRat sing_687.htm#SEC741
1861	dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_679.htm#SEC733
1862	dmod_lib sing_537.htm#SEC591
1863	dmodapp.lib sing_560.htm#SEC614
1864	dmodapp_lib sing_560.htm#SEC614
1865	dmodideal.lib sing_592.htm#SEC646
1866	dmodideal_lib sing_592.htm#SEC646
1867	dmodloc.lib sing_668.htm#IDX378
1868	dmodloc_lib sing_668.htm#IDX379
1869	dmodoublext sing_713.htm#SEC767
1870	dmodvar.lib sing_600.htm#SEC654
1871	dmodvar_lib sing_600.htm#SEC654
1872	double sing_2323.htm#SEC2404
1873	doubleExt sing_786.htm#SEC840
1874	downloading Download instructions sing_3002.htm#SEC3099
1875	dp, global ordering sing_969.htm#IDX444
1876	drawNewtonSubdivision drawNewtonSubdivision sing_2539.htm#SEC2620
1877	drawTropicalCurve sing_2538.htm#SEC2619
1878	ds, local ordering sing_970.htm#IDX454
1879	dsum sing_1179.htm#SEC1260
1880	dualCone sing_2400.htm#SEC2481
1881	dualConic sing_2563.htm#SEC2644
1882	dualPart sing_1560.htm#SEC1641
1883	dualPartition sing_1731.htm#SEC1812
1884	dualPolytope sing_2439.htm#SEC2520
1885	dualSheaf sing_1709.htm#SEC1790
1886	dual_code sing_2172.htm#SEC2253
1887	dump sing_235.htm#SEC275
1888	dyckGroup1 sing_850.htm#SEC904
1889	dyckGroup2 sing_851.htm#SEC905
1890	dyckGroup3 sing_852.htm#SEC906
1891	dynamic geometry sing_1043.htm#IDX504
1892	dynamic geometry sing_1044.htm#IDX507
1893	ecart sing_2326.htm#SEC2407
1894	echo sing_400.htm#SEC440
1895	eexgcdN sing_2253.htm#SEC2334
1896	effective sing_1582.htm#SEC1663
1897	egcdMain sing_2123.htm#SEC2204
1898	ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2490.htm#SEC2571
1899	ehrhartRing sing_1410.htm#SEC1491 16966
1900	eigenvals sing_1225.htm#SEC1306
1901	eigenvalue sing_331.htm#SEC371
1902	eigenvalue sing_1225.htm#IDX577
1903	eigenvalues sing_1498.htm#SEC1579
1904	elemSymmId sing_1079.htm#SEC1160
1905	elim sing_1267.htm#SEC1348
1906	elim.lib sing_1264.htm#SEC1345
1907	elim1 sing_1268.htm#SEC1349
1908	elim2 sing_1269.htm#SEC1350
1909	elimRing sing_1266.htm#SEC1347
1910	elimWeight sing_728.htm#SEC782
1911	elim_lib sing_1264.htm#SEC1345
1912	eliminate sing_236.htm#SEC276
1913	eliminate (plural) sing_463.htm#SEC503
1914	eliminateNC sing_723.htm#SEC777
1915	elimination sing_722.htm#IDX393
1916	elimlinearpart sing_2048.htm#SEC2129
1917	elimpart sing_2049.htm#SEC2130
1918	elimpartanyr sing_2050.htm#SEC2131
1919	elimrep sing_1641.htm#SEC1722
1920	elliptic curve sing_1277.htm#IDX603
1921	elliptic curves sing_1274.htm#IDX597
1922	elliptic curves sing_1280.htm#IDX606
1923	elliptic curves sing_1281.htm#IDX610
1924	ellipticAdd sing_2274.htm#SEC2355
1925	ellipticAllPoints sing_2279.htm#SEC2360
1926	ellipticMult sing_2275.htm#SEC2356
1927	ellipticNF sing_2487.htm#SEC2568
1928	ellipticNFDB sing_2488.htm#SEC2569
1929	ellipticRandomCurve sing_2276.htm#SEC2357
1930	ellipticRandomPoint sing_2277.htm#SEC2358
1931	ellipticcovers.lib sing_1274.htm#SEC1355
1932	ellipticcovers_lib sing_1274.htm#SEC1355
1933	else sing_390.htm#SEC430
1934	embedMat sing_754.htm#SEC808
1935	emptyFan sing_2427.htm#SEC2508
1936	encode sing_2180.htm#SEC2261
1937	endomorphism filtration sing_1856.htm#IDX869
1938	endvfilt sing_1856.htm#SEC1937
1939	ensureLeftNcfrac sing_701.htm#SEC755
1940	ensureRightNcfrac sing_702.htm#SEC756
1941	envelop FamElemsAtEnvCompPoints sing_1045.htm#SEC1126
1942	envelop sing_1045.htm#IDX510
1943	envelop sing_1046.htm#IDX513
1944	envelop sing_1048.htm#IDX518
1945	envelop sing_1049.htm#IDX522
1946	envelope sing_464.htm#SEC504
1947	enveloping algebra sing_361.htm#IDX207
1948	enveloping algebra sing_495.htm#IDX306
1949	environment variable, DISPLAY The online help system sing_16.htm#IDX29
1950	environment variables Used environment variables sing_3003.htm#SEC3100
1951	equal sing_2688.htm#IDX1135
1952	equal sing_2689.htm#IDX1137
1953	equal sing_2709.htm#IDX1182
1954	equal sing_2710.htm#IDX1184
1955	equalJinI sing_1768.htm#SEC1849
1956	equalMultiDeg sing_2898.htm#SEC2979
1957	equations sing_2401.htm#SEC2482
1958	equiRadical sing_1451.htm#SEC1532
1959	equidim sing_1453.htm#SEC1534
1960	equidimMax sing_1454.htm#SEC1535
1961	equidimMaxEHV sing_1455.htm#SEC1536
1962	equidimZ sing_1466.htm#SEC1547
1963	equising.lib sing_1839.htm#SEC1920
1964	equising_lib sing_1839.htm#SEC1920
1965	equisingular Tjurina number sing_1751.htm#IDX770
1966	equisingularity ideal sing_1841.htm#IDX796
1967	equisingularity stratum sing_1842.htm#IDX797
1968	error recovery sing_15.htm#SEC21
1969	errorInsert sing_2183.htm#SEC2264
1970	errorRand sing_2184.htm#SEC2265
1971	errormap sing_2729.htm#SEC2810
1972	esIdeal sing_1841.htm#SEC1922
1973	esStratum sing_1842.htm#SEC1923
1974	essential sing_2605.htm#IDX1013
1975	essential sing_2606.htm#IDX1014
1976	eta sing_2482.htm#SEC2563
1977	euler sing_2232.htm#SEC2313
1978	eulerChProj sing_1550.htm#SEC1631
1979	eval sing_237.htm#SEC277
1980	evalJacobianAtBox sing_2109.htm#SEC2190
1981	evalPolyAtBox sing_2108.htm#SEC2189
1982	evalPolyAtBox2 sing_2044.htm#SEC2125
1983	evaluateFormalDivisor evaluateFormalDivisor sing_1584.htm#SEC1665
1984	evaluatePDivisor sing_1590.htm#SEC1671
1985	evaluateProduct sing_2465.htm#SEC2546
1986	evaluate_reynolds sing_1968.htm#SEC2049
1987	evaluatepfd sing_2941.htm#SEC3022
1988	evaluation sing_2711.htm#IDX1186
1989	evalutateIntegral sing_1279.htm#SEC1360
1990	exactness recovery sing_2082.htm#IDX928
1991	example sing_239.htm#SEC279
1992	example sing_2607.htm#IDX1015
1993	example sing_2608.htm#IDX1017
1994	example sing_2609.htm#IDX1019
1995	example sing_2610.htm#IDX1021
1996	example sing_2611.htm#IDX1023
1997	example sing_2612.htm#IDX1025
1998	example sing_2613.htm#IDX1028
1999	exclusionTest sing_2045.htm#SEC2126
2000	execute sing_240.htm#SEC280
2001	exit sing_394.htm#SEC434
2002	exp2pt sing_2220.htm#SEC2301
2003	expo sing_2244.htm#SEC2325
2004	exponents sing_2617.htm#IDX1036
2005	export sing_387.htm#SEC427
2006	exportNuminvs sing_1418.htm#SEC1499 10423
2007	exportto sing_388.htm#SEC428
2008	expp sing_1729.htm#SEC1810
2009	expression list sing_72.htm#IDX128
2010	expression list sing_426.htm#IDX299
2011	ext-module purityfiltration_lib sing_778.htm#IDX399
2012	extcurve sing_2166.htm#SEC2247
2013	extdevelop sing_1873.htm#SEC1954
2014	extendGC sing_1042.htm#SEC1123
2015	extendWeyl sing_680.htm#SEC734
2016	extendedTensor sing_729.htm#SEC783
2017	extendpoly sing_1041.htm#SEC1122
2018	extendring sing_1138.htm#SEC1219
2019	extension of rings sing_1471.htm#IDX663
2020	exterior basis sing_1204.htm#IDX574
2021	exterior power sing_1206.htm#IDX576
2022	exteriorBasis sing_1204.htm#SEC1285
2023	exteriorPower sing_1206.htm#SEC1287
2024	extgcd sing_241.htm#SEC281
2025	extractS sing_599.htm#SEC653
2026	fPiece sing_2975.htm#SEC3056
2027	fVector sing_2430.htm#SEC2511
2028	fVectorP sing_2491.htm#SEC2572
2029	facFirstShift sing_654.htm#SEC708
2030	facFirstWeyl sing_650.htm#SEC704
2031	facGBIdeal sing_1436.htm#SEC1517
2032	facShift sing_653.htm#SEC707
2033	facSubWeyl sing_652.htm#SEC706
2034	facWeyl sing_649.htm#SEC703
2035	faceContaining sing_2402.htm#SEC2483
2036	facetVertexLatticeDistances facetVertexLatticeDistances sing_2492.htm#SEC2573
2037	facetWidth sing_2493.htm#SEC2574
2038	facetWidths sing_2494.htm#SEC2575
2039	facets sing_2403.htm#SEC2484
2040	facstd sing_242.htm#SEC282
2041	factmodd sing_243.htm#SEC283
2042	factor sing_325.htm#SEC365
2043	factor sing_1103.htm#IDX550
2044	factorH sing_1032.htm#SEC1113
2045	factorLenstraECM sing_2283.htm#SEC2364
2046	factorMain sing_2124.htm#SEC2205
2047	factorgroup sing_2888.htm#SEC2969
2048	factorial sing_1018.htm#SEC1099
2049	factorization sing_326.htm#SEC366
2050	factorization sing_1234.htm#IDX578
2051	factorize sing_244.htm#SEC284
2052	factorize sing_325.htm#SEC365
2053	factory sing_1.htm#IDX2
2054	facvar sing_1103.htm#SEC1184
2055	fan sing_190.htm#SEC230
2056	fan sing_2474.htm#IDX961
2057	fanViaCones sing_2428.htm#SEC2509
2058	farey sing_245.htm#SEC285
2059	fareypoly sing_1286.htm#SEC1367
2060	fastExpt sing_2228.htm#SEC2309
2061	fastHC, option sing_318.htm#IDX153
2062	fastelim sing_2051.htm#SEC2132
2063	fetch sing_246.htm#SEC286
2064	fetch (plural) sing_465.htm#SEC505
2065	fetchall sing_1139.htm#SEC1220
2066	ffmodStd sing_1292.htm#SEC1373
2067	ffmodstd.lib sing_1285.htm#SEC1366
2068	ffmodstd_lib sing_1285.htm#SEC1366
2069	ffsolve sing_2031.htm#SEC2112
2070	ffsolve.lib sing_2030.htm#SEC2111
2071	ffsolve_lib sing_2030.htm#SEC2111
2072	fglm sing_247.htm#SEC287
2073	fglm sing_358.htm#IDX187
2074	fglm_solve sing_2067.htm#SEC2148
2075	fglmquot sing_248.htm#SEC288
2076	fibonacci sing_1019.htm#SEC1100
2077	fibonacciGroup sing_853.htm#SEC907
2078	field sing_144.htm#SEC184
2079	file, .singularrc sing_20.htm#IDX71
2080	filecmd sing_249.htm#SEC289
2081	filtration purityfiltration_lib sing_778.htm#IDX400
2082	finalCharts sing_1665.htm#SEC1746
2083	finalcases sing_1108.htm#SEC1189
2084	find sing_250.htm#SEC290
2085	findAuto sing_608.htm#SEC662
2086	findInvo sing_606.htm#SEC660
2087	findInvoDiag sing_607.htm#SEC661
2088	findOrientedBoundary findOrientedBoundary sing_2483.htm#SEC2564
2089	findTorsion sing_2209.htm#SEC2290
2090	findZeroPoly sing_2954.htm#SEC3035
2091	find_first_primitive_root find_first_primitive_root sing_2287.htm#SEC2368
2092	find_index sing_2291.htm#SEC2372
2093	findifs.lib sing_2216.htm#SEC2297
2094	findifs_example sing_2217.htm#SEC2298
2095	findifs_lib sing_2216.htm#SEC2297
2096	findimAlgebra sing_738.htm#SEC792
2097	finduni sing_251.htm#SEC291
2098	findvars sing_2052.htm#SEC2133
2099	finite field sing_144.htm#SEC184
2100	finite field sing_2030.htm#IDX925
2101	finiteDiagInvariants finiteDiagInvariants sing_1413.htm#SEC1494 3508
2102	finitediff.lib sing_2715.htm#IDX1194
2103	finitediff_lib sing_2715.htm#IDX1195
2104	finitely presented algebra sing_821.htm#IDX407
2105	finitely presented algebra sing_827.htm#IDX413
2106	finitely presented algebra sing_856.htm#IDX416
2107	finitely presented algebra sing_863.htm#IDX428
2108	finitely presented algebra sing_877.htm#IDX429
2109	finitely presented algebra, standard finitely presented algebra Free associative algebras sing_815.htm#IDX406
2110	finitely presented group sing_827.htm#IDX414
2111	finitenessTest sing_1248.htm#SEC1329
2112	finiterep sing_2021.htm#SEC2102
2113	finvar.lib sing_1956.htm#SEC2037
2114	finvar_lib sing_1956.htm#SEC2037
2115	first index is 1 sing_421.htm#SEC461
2116	first order deformation sing_2972.htm#IDX1260
2117	first order deformation sing_2975.htm#IDX1263
2118	firstoct sing_2116.htm#SEC2197
2119	fitting sing_1307.htm#SEC1388
2120	fixed points, moduli space of stable maps, graph fixedPoints sing_1719.htm#IDX749
2121	fixedPoints sing_1719.htm#SEC1800
2122	fl2poly sing_587.htm#SEC641
2123	flatten sing_1180.htm#SEC1261
2124	flatteningStrat sing_1308.htm#SEC1389
2125	flintQ sing_252.htm#SEC292
2126	floating point sing_1148.htm#IDX564
2127	for sing_389.htm#SEC429
2128	formal linear representations sing_880.htm#IDX437
2129	formaldivisorplus sing_1585.htm#SEC1666
2130	forward sing_2721.htm#SEC2802
2131	fourier sing_582.htm#SEC636
2132	fouriersystem sing_2732.htm#SEC2813
2133	fpadim.lib sing_821.htm#SEC875
2134	fpadim_lib sing_821.htm#SEC875
2135	fpalgebras.lib sing_827.htm#SEC881
2136	fpalgebras_lib sing_827.htm#SEC881
2137	fpaprops.lib sing_856.htm#SEC910
2138	fpaprops_lib sing_856.htm#SEC910
2139	fprintf sing_254.htm#SEC294
2140	fracStatus sing_759.htm#SEC813
2141	framed sheaves sing_2739.htm#IDX1202
2142	frandwalk sing_2961.htm#SEC3042
2143	free sing_2616.htm#IDX1033
2144	free sing_2617.htm#IDX1035
2145	free associative algebra sing_827.htm#IDX412
2146	free associative algebra sing_863.htm#IDX424
2147	free associative algebra, tensor algebra Free associative algebras sing_815.htm#SEC869
2148	free noncommutative Groebner basis sing_863.htm#IDX426
2149	freeAlgebra (letterplace) freeAlgebra (letterplace) sing_805.htm#SEC859
2150	freeModule sing_2805.htm#SEC2886
2151	freeModule2Module sing_2834.htm#SEC2915
2152	freegb.lib sing_863.htm#SEC917
2153	freegb_lib sing_863.htm#SEC917
2154	freemodule sing_255.htm#SEC295
2155	freerank sing_1081.htm#SEC1162
2156	fres sing_256.htm#SEC296
2157	from_boolean_constant from_boolean_constant sing_2647.htm#SEC2728 44881
2158	from_boolean_ideal sing_2651.htm#SEC2732 62698
2159	from_boolean_poly sing_2648.htm#SEC2729 27864
2160	from_boolean_set sing_2652.htm#SEC2733 60615
2161	frwalk sing_257.htm#SEC297
2162	full representation sing_1041.htm#IDX496
2163	full representation sing_1042.htm#IDX501
2164	fullDimImages sing_2446.htm#SEC2527
2165	fullFan sing_2429.htm#SEC2510
2166	fullSerreRelations sing_830.htm#SEC884
2167	fullSpace sing_2384.htm#SEC2465
2168	furtherInvar sing_2000.htm#SEC2081
2169	further_hn_proc sing_1890.htm#SEC1971
2170	fwalk sing_1294.htm#SEC1375
2171	galois field sing_144.htm#SEC184
2172	gaussColWithoutPerm sing_2088.htm#SEC2169
2173	gaussRowWithoutPerm sing_2087.htm#SEC2168
2174	gauss_col sing_1189.htm#SEC1270
2175	gauss_nf sing_1220.htm#SEC1301
2176	gauss_row sing_1190.htm#SEC1271
2177	gaussred sing_1218.htm#SEC1299
2178	gaussred_pivot sing_1219.htm#SEC1300
2179	gcd sing_258.htm#SEC298
2180	gcdMon sing_1339.htm#SEC1420
2181	gcddivisor sing_2319.htm#SEC2400
2182	gen sing_259.htm#SEC299
2183	genMDSMat sing_2186.htm#SEC2267
2184	genSymId sing_1495.htm#SEC1576
2185	general error-locator polynomial sing_996.htm#SEC1066
2186	general neron. sing_2758.htm#IDX1205
2187	general weighted lexicographical ordering sing_970.htm#IDX460
2188	general weighted reverse lexicographical ordering Local orderings sing_970.htm#IDX457
2189	general.lib sing_1011.htm#SEC1092
2190	generalOrder sing_2344.htm#SEC2425
2191	general_lib sing_1011.htm#SEC1092
2192	generateG sing_2282.htm#SEC2363
2193	generator derivationContractionGen sing_2672.htm#IDX1104
2194	generator sing_2682.htm#IDX1124
2195	generator sing_2712.htm#IDX1190
2196	generators sing_1759.htm#IDX774
2197	generators sing_2675.htm#IDX1108
2198	generators sing_2677.htm#IDX1113
2199	generators sing_2678.htm#IDX1117
2200	generatorsOfLinealitySpace generatorsOfLinealitySpace sing_2404.htm#SEC2485
2201	generatorsOfSpan sing_2405.htm#SEC2486
2202	generic representation sing_1041.htm#IDX495
2203	genericid sing_1114.htm#SEC1195
2204	genericity sing_2206.htm#SEC2287
2205	genericmat sing_1181.htm#SEC1262
2206	genoutput sing_1654.htm#SEC1735
2207	genus sing_1395.htm#SEC1476
2208	geometrical locus FamElemsAtEnvCompPoints sing_1043.htm#IDX502
2209	geometrical locus sing_1044.htm#IDX505
2210	geometrical locus sing_1045.htm#IDX508
2211	geometrical locus sing_1046.htm#IDX511
2212	geometrical locus sing_1047.htm#IDX514
2213	geometrical locus sing_1048.htm#IDX516
2214	geometrical locus sing_1049.htm#IDX520
2215	getArguments sing_1171.htm#SEC1252
2216	getCommand sing_1170.htm#SEC1251
2217	getCone sing_2431.htm#SEC2512
2218	getGradingGroup sing_2863.htm#SEC2944
2219	getLattice sing_2864.htm#SEC2945
2220	getLinearForms sing_2406.htm#SEC2487
2221	getMaxPoints sing_2798.htm#SEC2879
2222	getModuleGrading sing_2874.htm#SEC2955
2223	getMultiplicity sing_2407.htm#SEC2488
2224	getOneVar sing_1403.htm#SEC1484
2225	getRelations sing_2085.htm#SEC2166
2226	getRelationsRadical sing_2086.htm#SEC2167
2227	getResult sing_1172.htm#SEC1253
2228	getSmallest sing_1402.htm#SEC1483
2229	getState sing_1173.htm#SEC1254
2230	getStringpfd sing_2944.htm#SEC3025
2231	getStringpfd_indexed getStringpfd_indexed sing_2945.htm#SEC3026
2232	getVariableWeights sing_2862.htm#SEC2943
2233	getWitnessSet sing_2089.htm#SEC2170
2234	getcores sing_1129.htm#SEC1210
2235	getdump sing_260.htm#SEC300
2236	getenv sing_361.htm#IDX209
2237	gfan.lib sing_2383.htm#SEC2464
2238	gfan_lib sing_2383.htm#SEC2464
2239	gfanlib sing_1.htm#IDX9
2240	gitCone sing_2473.htm#SEC2554
2241	gitfan.lib sing_2443.htm#SEC2524
2242	gitfan_lib sing_2443.htm#SEC2524
2243	gkdim.lib sing_613.htm#SEC667
2244	gkdim_lib sing_613.htm#SEC667
2245	global sing_210.htm#IDX133
2246	global Bernstein-Sato ideal sing_592.htm#IDX355
2247	global Bernstein-Sato polynomial sing_502.htm#IDX313
2248	global Bernstein-Sato polynomial sing_537.htm#IDX331
2249	global Bernstein-Sato polynomial for variety sing_600.htm#IDX363
2250	global homological dimension sing_856.htm#IDX421
2251	globalSections sing_1579.htm#SEC1660
2252	gmscoeffs sing_1848.htm#SEC1929
2253	gmsnf sing_1847.htm#SEC1928
2254	gmspoly.lib sing_1867.htm#SEC1948
2255	gmspoly_lib sing_1867.htm#SEC1948
2256	gmsring sing_1846.htm#SEC1927
2257	gmssing.lib sing_1845.htm#SEC1926
2258	gmssing_lib sing_1845.htm#SEC1926
2259	goettsche.lib sing_2739.htm#SEC2820
2260	goettsche_lib sing_2739.htm#SEC2820
2261	good basis sing_1845.htm#IDX808
2262	good basis sing_1855.htm#IDX863
2263	good basis sing_1867.htm#IDX879
2264	good basis sing_1869.htm#IDX890
2265	goodBasis sing_1869.htm#SEC1950
2266	gorensteinIndex sing_2495.htm#SEC2576
2267	gorensteinVector sing_2496.htm#SEC2577
2268	graal.lib sing_2751.htm#SEC2832
2269	graalMixed sing_2752.htm#SEC2833
2270	graal_lib sing_2751.htm#SEC2832
2271	gradeNumber sing_782.htm#SEC836
2272	graded sing_2675.htm#IDX1109
2273	graded Hilbert series sing_877.htm#IDX431
2274	graded Weyl algebra sing_502.htm#IDX316
2275	graded algebra sing_2658.htm#IDX1088
2276	graded module, graded piece sing_1740.htm#IDX760
2277	graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2760.htm#IDX1206
2278	graded modules, handling of Handling graded modules sing_935.htm#SEC992
2279	graded piece, second order piece sing_2976.htm#IDX1264
2280	graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism modules_lib sing_2802.htm#IDX1211
2281	gradedModules.lib sing_2760.htm#SEC2841
2282	gradedModules_lib sing_2760.htm#SEC2841
2283	gradiator sing_2907.htm#SEC2988
2284	graph sing_1275.htm#IDX601
2285	graph sing_1276.htm#IDX602
2286	graph sing_1714.htm#IDX744
2287	graph sing_1715.htm#IDX745
2288	graphics.lib sing_2133.htm#SEC2214
2289	graphics_lib sing_2133.htm#SEC2214
2290	graphviz sing_1.htm#IDX13
2291	graver4ti2 sing_1493.htm#SEC1574 39635
2292	grconcat sing_2783.htm#SEC2864
2293	grdeg sing_2763.htm#SEC2844
2294	grgens sing_2772.htm#SEC2853
2295	grgroebner sing_2782.htm#SEC2863
2296	grlift sing_2780.htm#SEC2861
2297	grlifting sing_2787.htm#SEC2868
2298	grlifting2 sing_2788.htm#SEC2869
2299	grlifting3 sing_2790.htm#SEC2871
2300	grneg sing_2793.htm#SEC2874
2301	grobcov sing_1034.htm#SEC1115
2302	grobcov.lib sing_1033.htm#SEC1114
2303	grobcov_lib sing_1033.htm#SEC1114
2304	grobj sing_2761.htm#SEC2842
2305	groebner sing_261.htm#SEC301
2306	groebner sing_927.htm#SEC984
2307	groebner basis computations sing_261.htm#IDX147
2308	groebnerComplex sing_2574.htm#SEC2655
2309	groebnerCone sing_2568.htm#SEC2649
2310	groebnerFan sing_2573.htm#SEC2654
2311	gromovWitten sing_1280.htm#SEC1361
2312	grorder sing_2774.htm#SEC2855
2313	ground field sing_144.htm#SEC184
2314	groupActionOnHashes sing_2461.htm#SEC2542
2315	groupActionOnQImage sing_2460.htm#SEC2541
2316	group_reynolds sing_1964.htm#SEC2045
2317	growth of algebra sing_856.htm#IDX419
2318	grpower sing_2770.htm#SEC2851
2319	grpres sing_2773.htm#SEC2854
2320	grprod sing_2781.htm#SEC2862
2321	grrange sing_2792.htm#SEC2873
2322	grres sing_2779.htm#SEC2860
2323	grrndmap sing_2785.htm#SEC2866
2324	grrndmap2 sing_2786.htm#SEC2867
2325	grrndmat sing_2784.htm#SEC2865
2326	grshift sing_2765.htm#SEC2846
2327	grsum sing_2769.htm#SEC2850
2328	grsyz sing_2778.htm#SEC2859
2329	grtest sing_2762.htm#SEC2843
2330	grtranspose sing_2771.htm#SEC2852
2331	grtranspose1 sing_2775.htm#SEC2856
2332	grtwist sing_2767.htm#SEC2848
2333	grtwists sing_2768.htm#SEC2849
2334	grview sing_2764.htm#SEC2845
2335	grwalk.lib sing_1293.htm#SEC1374
2336	grwalk_lib sing_1293.htm#SEC1374
2337	grzero sing_2766.htm#SEC2847
2338	gwalk sing_1299.htm#SEC1380
2339	hStarVector sing_2497.htm#SEC2578
2340	hVector sing_2498.htm#SEC2579
2341	h_increasing_knapsack h_increasing_knapsack sing_2305.htm#SEC2386
2342	hardware platform sing_361.htm#IDX268
2343	hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1152.htm#SEC1233
2344	hasCommutativeVars sing_1149.htm#SEC1230
2345	hasGlobalOrdering sing_1150.htm#SEC1231
2346	hasLeftDenom sing_695.htm#SEC749
2347	hasMixedOrdering sing_1151.htm#SEC1232
2348	hasNumericCoeffs sing_1148.htm#SEC1229
2349	hasRightDenom sing_696.htm#SEC750
2350	hasTransExtensionCoefficient hasTransExtensionCoefficient sing_1153.htm#SEC1234
2351	hashToCone sing_2471.htm#SEC2552
2352	hashesToFan sing_2472.htm#SEC2553
2353	headStand sing_1202.htm#SEC1283
2354	heightZ sing_1465.htm#SEC1546
2355	help sing_262.htm#SEC302
2356	help browsers The online help system sing_16.htm#IDX22
2357	help browsers, dummy The online help system sing_16.htm#IDX25
2358	help browsers, dummy sing_16.htm#IDX27
2359	help browsers, emacs The online help system sing_16.htm#IDX26
2360	help browsers, html The online help system sing_16.htm#IDX23
2361	help browsers, setting command to use The online help system sing_16.htm#IDX30
2362	help browsers, setting the sing_361.htm#IDX194
2363	help, accessing over the net Command line options sing_19.htm#IDX42
2364	help, online help system The online help system sing_16.htm#SEC22
2365	hermiteNormalForm sing_2908.htm#SEC2989
2366	hess.lib sing_1592.htm#SEC1673
2367	hess_lib sing_1592.htm#SEC1673
2368	hessenberg sing_361.htm#IDX215
2369	hessenberg sing_1224.htm#SEC1305
2370	highcorner sing_263.htm#SEC303
2371	hilb sing_264.htm#SEC304
2372	hilbPoly sing_1097.htm#SEC1178
2373	hilbert4ti2 sing_1492.htm#SEC1573 13993
2374	hilbertBasis sing_2499.htm#SEC2580
2375	hilbertSeries sing_2910.htm#SEC2991
2376	hilbvec sing_2053.htm#SEC2134
2377	hnexpansion sing_1871.htm#SEC1952
2378	hnoether.lib sing_1870.htm#SEC1951
2379	hnoether_lib sing_1870.htm#SEC1951
2380	holonomic rank sing_668.htm#IDX381
2381	holonomicRank sing_672.htm#SEC726
2382	hom sing_2846.htm#SEC2927
2383	hom_kernel sing_1315.htm#SEC1396
2384	homog sing_265.htm#SEC305
2385	homog sing_2693.htm#IDX1147
2386	homog_part sing_1726.htm#SEC1807
2387	homog_parts sing_1727.htm#SEC1808
2388	homogeneitySpace sing_2570.htm#SEC2651
2389	homogeneous sing_2679.htm#IDX1118
2390	homogeneous sing_2693.htm#IDX1146
2391	homogeneous sing_2694.htm#IDX1148
2392	homogeneous decomposition sing_2679.htm#IDX1119
2393	homogfacFirstQWeyl sing_657.htm#SEC711
2394	homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_659.htm#SEC713
2395	homogfacNthQWeyl sing_656.htm#SEC710
2396	homogfacNthQWeyl_all homogfacNthQWeyl_all sing_658.htm#SEC712
2397	homogfacNthWeyl sing_655.htm#SEC709
2398	homolog.lib sing_1300.htm#SEC1381
2399	homolog_lib sing_1300.htm#SEC1381
2400	homology sing_1310.htm#SEC1391
2401	homomorphism sing_2830.htm#SEC2911
2402	howto, download Download instructions sing_3002.htm#SEC3099
2403	howto, install on Macintosh Macintosh installation instructions sing_3006.htm#SEC3103
2404	howto, install on Unix Unix installation instructions sing_3004.htm#SEC3101
2405	howto, install on Windows Windows installation instructions sing_3005.htm#SEC3102
2406	hres sing_266.htm#SEC306
2407	html, default help The online help system sing_16.htm#IDX24
2408	hybrid algorithms sing_2082.htm#IDX927
2409	hyperel.lib sing_2312.htm#SEC2393
2410	hyperel_lib sing_2312.htm#SEC2393
2411	hyperplane sing_2586.htm#IDX973
2412	hyperplane arrangement sing_537.htm#IDX337
2413	hypersurface singularity sing_1897.htm#IDX908
2414	iMult sing_1398.htm#SEC1479
2415	id sing_2803.htm#SEC2884
2416	id2mod sing_1093.htm#SEC1174
2417	ideal sing_90.htm#SEC130
2418	ideal (plural) sing_427.htm#SEC467
2419	ideal declarations sing_91.htm#SEC131
2420	ideal declarations (plural) ideal declarations (plural) sing_428.htm#SEC468
2421	ideal expressions sing_92.htm#SEC132
2422	ideal expressions (plural) ideal expressions (plural) sing_429.htm#SEC469
2423	ideal operations sing_93.htm#SEC133
2424	ideal operations (plural) ideal operations (plural) sing_430.htm#SEC470
2425	ideal related functions ideal related functions sing_94.htm#SEC134
2426	ideal related functions (plural) ideal related functions (plural) sing_431.htm#SEC471
2427	ideal, toric sing_983.htm#SEC1045
2428	idealSplit sing_2060.htm#SEC2141
2429	ideals Miscellaneous oddities sing_422.htm#IDX293
2430	idealsimplify sing_1767.htm#SEC1848
2431	identifier Identifier resolution sing_423.htm#SEC463
2432	identifyvar sing_1636.htm#SEC1717
2433	if sing_390.htm#SEC430
2434	image sing_2826.htm#SEC2907
2435	imageLattice sing_2876.htm#SEC2957
2436	image_of_variety sing_1992.htm#SEC2073
2437	imap sing_267.htm#SEC307
2438	imap (plural) sing_466.htm#SEC506
2439	imapall sing_1140.htm#SEC1221
2440	impart sing_268.htm#SEC308
2441	importfrom sing_391.htm#SEC431
2442	inCenter sing_526.htm#SEC580
2443	inCentralizer sing_527.htm#SEC581
2444	inForm sing_569.htm#SEC623
2445	inSubring sing_1240.htm#SEC1321
2446	indSet sing_1365.htm#SEC1446
2447	indepSet sing_269.htm#SEC309
2448	indexed names sing_36.htm#IDX82
2449	indexed names sing_37.htm#SEC65
2450	indices, multi sing_37.htm#SEC65
2451	inequalities sing_2408.htm#SEC2489
2452	infRedTail, option sing_318.htm#IDX154
2453	infinitely presented algebra sing_877.htm#IDX430
2454	info The online help system sing_16.htm#SEC23
2455	iniD sing_1656.htm#SEC1737
2456	init_debug sing_1783.htm#SEC1864
2457	initial sing_2571.htm#SEC2652
2458	initial form sing_502.htm#IDX318
2459	initial ideal sing_502.htm#IDX317
2460	initial ideal approach sing_502.htm#IDX321
2461	initial ideal approach sing_600.htm#IDX367
2462	initialForm sing_2548.htm#SEC2629
2463	initialIdeal sing_2549.htm#SEC2630
2464	initialIdealW sing_568.htm#SEC622
2465	initialMalgrange sing_567.htm#SEC621
2466	injective_knapsack sing_2306.htm#SEC2387
2467	inout.lib sing_1059.htm#SEC1140
2468	inout_lib sing_1059.htm#SEC1140
2469	input sing_41.htm#SEC71
2470	insert sing_126.htm#SEC166
2471	insert sing_270.htm#SEC310
2472	insertCone sing_2432.htm#SEC2513
2473	insertGenerator sing_588.htm#SEC642
2474	instructions, Macintosh installation Macintosh installation instructions sing_3006.htm#SEC3103
2475	instructions, Unix installation Unix installation instructions sing_3004.htm#SEC3101
2476	instructions, Windows installation Windows installation instructions sing_3005.htm#SEC3102
2477	instructions, downloading Download instructions sing_3002.htm#SEC3099
2478	int sing_95.htm#SEC135
2479	int declarations sing_96.htm#SEC136
2480	int expressions sing_97.htm#SEC137
2481	int operations sing_98.htm#SEC138
2482	int related functions int related functions sing_99.htm#SEC139
2483	intInverse sing_2885.htm#SEC2966
2484	intPart sing_2260.htm#SEC2341
2485	intRank sing_2877.htm#SEC2958
2486	intRoot sing_2261.htm#SEC2342
2487	intRoots sing_585.htm#SEC639
2488	intStrategy, option sing_318.htm#IDX155
2489	intclMonIdeal sing_1411.htm#SEC1492 62182
2490	intclToricRing sing_1407.htm#SEC1488 62143
2491	integer division Miscellaneous oddities sing_422.htm#IDX288
2492	integer programming sing_991.htm#SEC1053
2493	integral sing_1701.htm#SEC1782
2494	integral basis sing_1322.htm#IDX623
2495	integral basis sing_1619.htm#IDX721
2496	integral closure sing_1391.htm#IDX644
2497	integral closure sing_1392.htm#IDX647
2498	integral closure sing_1393.htm#IDX650
2499	integral closure sing_1406.htm#IDX656
2500	integralBasis sing_1322.htm#SEC1403
2501	integralIdeal sing_572.htm#SEC626
2502	integralModule sing_573.htm#SEC627
2503	integralSection sing_2886.htm#SEC2967
2504	integralbasis.lib sing_1321.htm#SEC1402
2505	integralbasis_lib sing_1321.htm#SEC1402
2506	integration of D-module sing_560.htm#IDX349
2507	interface, Emacs Emacs user interface sing_21.htm#SEC28
2508	interiorLatticePoints interiorLatticePoints sing_2500.htm#SEC2581
2509	internalfunctions sing_1784.htm#SEC1865
2510	interpolate sing_2066.htm#SEC2147
2511	interpolation sing_271.htm#SEC311
2512	interpret sing_2848.htm#SEC2929
2513	interpretElem sing_2851.htm#SEC2932
2514	interpretInv sing_2849.htm#SEC2930
2515	interpretList sing_2852.htm#SEC2933
2516	interred sing_272.htm#SEC312
2517	intersect sing_273.htm#SEC313
2518	intersect (plural) sing_467.htm#SEC507
2519	intersectElim, option sing_318.htm#IDX173
2520	intersectLattices sing_2882.htm#SEC2963
2521	intersectLists sing_2666.htm#SEC2747
2522	intersectMon sing_1342.htm#SEC1423
2523	intersectOrbitsWithMovingCone intersectOrbitsWithMovingCone sing_2459.htm#SEC2540
2524	intersectSyz, option sing_318.htm#IDX174
2525	intersectZ sing_1467.htm#SEC1548
2526	intersection sing_1880.htm#SEC1961
2527	intersection sing_2965.htm#IDX1258
2528	intersection lattice sing_2622.htm#IDX1048
2529	intersection lattice sing_2623.htm#IDX1049
2530	intersection multiplicity sing_1760.htm#IDX780
2531	intersection multiplicity sing_1880.htm#IDX901
2532	intersectionDiv sing_1684.htm#SEC1765
2533	intersectionSet sing_2965.htm#SEC3046
2534	intersectionValRingIdeals intersectionValRingIdeals sing_1416.htm#SEC1497 38773
2535	intersectionValRings intersectionValRings sing_1415.htm#SEC1496 35761
2536	intersectpar sing_1053.htm#SEC1134
2537	interval arithmetic sing_2100.htm#IDX932
2538	interval.lib sing_2037.htm#SEC2118
2539	interval_lib sing_2037.htm#SEC2118
2540	intervalmatrixInit sing_2040.htm#SEC2121
2541	intmat sing_102.htm#SEC142
2542	intmat declarations sing_103.htm#SEC143
2543	intmat expressions sing_104.htm#SEC144
2544	intmat operations sing_106.htm#SEC146
2545	intmat related functions intmat related functions sing_107.htm#SEC147
2546	intmat type cast sing_105.htm#SEC145
2547	intmat2mons sing_1431.htm#SEC1512 21150
2548	intprog.lib sing_1323.htm#SEC1404
2549	intprog_lib sing_1323.htm#SEC1404
2550	intvec sing_108.htm#SEC148
2551	intvec declarations sing_109.htm#SEC149
2552	intvec expressions sing_110.htm#SEC150
2553	intvec operations sing_111.htm#SEC151
2554	intvec related functions intvec related functions sing_112.htm#SEC152
2555	invar sing_2023.htm#SEC2104
2556	invar.lib sing_2017.htm#SEC2098
2557	invar_lib sing_2017.htm#SEC2098
2558	invariant sing_1262.htm#IDX588
2559	invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1961.htm#IDX921
2560	invariant ring minimal generating set permutation group invariant_algebra_perm sing_1962.htm#IDX922
2561	invariantRing sing_1994.htm#SEC2075
2562	invariant_algebra_perm invariant_algebra_perm sing_1962.htm#SEC2043
2563	invariant_algebra_reynolds invariant_algebra_reynolds sing_1961.htm#SEC2042
2564	invariant_basis sing_1969.htm#SEC2050
2565	invariant_basis_reynolds invariant_basis_reynolds sing_1970.htm#SEC2051
2566	invariant_ring sing_1957.htm#SEC2038
2567	invariant_ring_random invariant_ring_random sing_1958.htm#SEC2039
2568	invariants curveColengthDerivations sing_1259.htm#IDX581
2569	invariants sing_1263.htm#IDX590
2570	invariants sing_1876.htm#SEC1957
2571	inverse sing_1208.htm#SEC1289
2572	inverse of a matrix via its LU-decomposition sing_293.htm#SEC333
2573	inverseFourier sing_583.htm#SEC637
2574	inverse_B sing_1209.htm#SEC1290
2575	inverse_L sing_1210.htm#SEC1291
2576	inverse_modulus sing_2289.htm#SEC2370
2577	invertAlgebraMorphism invertAlgebraMorphism sing_2992.htm#SEC3073
2578	invertBirMap sing_1620.htm#SEC1701
2579	invertLeftFraction sing_769.htm#SEC823
2580	invertNcfrac sing_705.htm#SEC759
2581	invertNumberMain sing_2125.htm#SEC2206
2582	involut.lib sing_605.htm#SEC659
2583	involut_lib sing_605.htm#SEC659
2584	involution sing_610.htm#SEC664
2585	invunit sing_1899.htm#SEC1980
2586	iostruct sing_2208.htm#SEC2289
2587	irrRealizationDim sing_2530.htm#SEC2611
2588	irred_secondary_char0 irred_secondary_char0 sing_1983.htm#SEC2064
2589	irred_secondary_no_molien irred_secondary_no_molien sing_1986.htm#SEC2067
2590	irreddecMon sing_1351.htm#SEC1432
2591	irreducible power series sing_1881.htm#IDX902
2592	irreducible secondary invariant irred_secondary_char0 sing_1983.htm#IDX923
2593	isAface sing_2444.htm#SEC2525
2594	isAntiEndo sing_612.htm#SEC666
2595	isBounded sing_2501.htm#SEC2582
2596	isCI sing_210.htm#IDX139
2597	isCI sing_1258.htm#SEC1339
2598	isCM sing_210.htm#IDX140
2599	isCM sing_1311.htm#SEC1392
2600	isCMcod2 sing_1940.htm#SEC2021
2601	isCanonical sing_2502.htm#SEC2583
2602	isCartan sing_528.htm#SEC582
2603	isCentral sing_745.htm#SEC799
2604	isCommutative sing_747.htm#SEC801
2605	isCompatible sing_2433.htm#SEC2514
2606	isCompressed sing_2503.htm#SEC2584
2607	isDenom sing_717.htm#SEC771
2608	isElement sing_2967.htm#SEC3048
2609	isEqualDivisor sing_1578.htm#SEC1659
2610	isEquising sing_1843.htm#SEC1924
2611	isFlat sing_1312.htm#SEC1393
2612	isFreeAlgebra sing_864.htm#SEC918
2613	isFsat sing_578.htm#SEC632
2614	isFullSpace sing_2409.htm#SEC2490
2615	isGorenstein sing_2504.htm#SEC2585
2616	isGradedRingHomomorphism isGradedRingHomomorphism sing_2871.htm#SEC2952
2617	isGroup sing_2869.htm#SEC2950
2618	isGroupHomomorphism sing_2870.htm#SEC2951
2619	isHolonomic sing_556.htm#SEC610
2620	isHomog sing_210.htm#IDX135
2621	isHomogeneous sing_2897.htm#SEC2978
2622	isInS sing_758.htm#SEC812
2623	isInt sing_590.htm#SEC644
2624	isIntegralSurjective isIntegralSurjective sing_2883.htm#SEC2964
2625	isInvertibleLeftFraction isInvertibleLeftFraction sing_768.htm#SEC822
2626	isInvertibleNcfrac sing_704.htm#SEC758
2627	isInvolution sing_611.htm#SEC665
2628	isLatticeEmpty sing_2505.htm#SEC2586
2629	isLocalizationRegular isLocalizationRegular sing_2755.htm#SEC2836
2630	isLocallyFree sing_1313.htm#SEC1394
2631	isMonomial sing_1337.htm#SEC1418
2632	isNC sing_746.htm#SEC800
2633	isNormal sing_2506.htm#SEC2587
2634	isOnCurve sing_2273.htm#SEC2354
2635	isOneFraction sing_771.htm#SEC825
2636	isOneNcfrac sing_698.htm#SEC752
2637	isOrderingShiftInvariant isOrderingShiftInvariant sing_870.htm#SEC924
2638	isOrigin sing_2410.htm#SEC2491
2639	isPositive sing_2894.htm#SEC2975
2640	isPrimitiveSublattice isPrimitiveSublattice sing_2884.htm#SEC2965
2641	isPure sing_2434.htm#SEC2515
2642	isPureTensor sing_500.htm#SEC554
2643	isQuotientRing sing_1154.htm#SEC1235
2644	isRational sing_559.htm#SEC613
2645	isReflexive sing_2507.htm#SEC2588
2646	isReg sing_1314.htm#SEC1395
2647	isSB sing_210.htm#IDX134
2648	isSimplicial sing_2411.htm#SEC2492
2649	isSmooth sing_2508.htm#SEC2589
2650	isSubModule sing_1155.htm#SEC1236
2651	isSublattice sing_2875.htm#SEC2956
2652	isSubset sing_2968.htm#SEC3049
2653	isSuperset sing_2969.htm#SEC3050
2654	isSymmetric sing_1496.htm#SEC1577
2655	isTame sing_1868.htm#SEC1949
2656	isTerminal sing_2509.htm#SEC2590
2657	isTorsionFree sing_2893.htm#SEC2974
2658	isTwoSidedGB sing_501.htm#SEC555
2659	isUpperTriangular sing_726.htm#SEC780
2660	isVeryAmple sing_2510.htm#SEC2591
2661	isWeyl sing_748.htm#SEC802
2662	isZeroElement sing_2895.htm#SEC2976
2663	isZeroFraction sing_770.htm#SEC824
2664	isZeroNcfrac sing_697.htm#SEC751
2665	is_NND sing_1884.htm#SEC1965
2666	is_NP sing_1374.htm#SEC1455
2667	is_active sing_1923.htm#SEC2004
2668	is_bijective sing_1245.htm#SEC1326
2669	is_cenBimodule sing_714.htm#SEC768
2670	is_cenSubbimodule sing_715.htm#SEC769
2671	is_ci sing_1924.htm#SEC2005
2672	is_complex sing_1182.htm#SEC1263
2673	is_fix_injective sing_2310.htm#SEC2391
2674	is_h_injective sing_2309.htm#SEC2390
2675	is_injective sing_1243.htm#SEC1324
2676	is_irred sing_1881.htm#SEC1962
2677	is_is sing_1925.htm#SEC2006
2678	is_nested sing_1375.htm#SEC1456
2679	is_prime sing_2290.htm#SEC2371
2680	is_primitive_root sing_2286.htm#SEC2367
2681	is_pure sing_788.htm#SEC842
2682	is_reg sing_1926.htm#SEC2007
2683	is_regs sing_1927.htm#SEC2008
2684	is_surjective sing_1244.htm#SEC1325
2685	is_zero sing_1082.htm#SEC1163
2686	isartinianMon sing_1348.htm#SEC1429
2687	isgenericMon sing_1349.htm#SEC1430
2688	ishyper sing_2313.htm#SEC2394
2689	isirreducibleMon sing_1347.htm#SEC1428
2690	isoncurve sing_2314.htm#SEC2395
2691	isparam sing_2377.htm#SEC2458
2692	isprimaryMon sing_1346.htm#SEC1427
2693	isprimeMon sing_1345.htm#SEC1426
2694	isuni sing_2362.htm#SEC2443
2695	ivmatGaussian sing_2107.htm#SEC2188
2696	ivmatGaussian2 sing_2043.htm#SEC2124
2697	ivmatInit sing_2104.htm#SEC2185
2698	ivmatSet sing_2105.htm#SEC2186
2699	jInvariant sing_2542.htm#SEC2623
2700	jOft sing_2245.htm#SEC2326
2701	jacob sing_274.htm#SEC314
2702	jacoblift sing_1900.htm#SEC1981
2703	jacobson sing_2214.htm#SEC2295
2704	jacobson.lib sing_2212.htm#SEC2293
2705	jacobson_lib sing_2212.htm#SEC2293
2706	janet sing_275.htm#SEC315
2707	janet basis sing_1479.htm#IDX665
2708	jet sing_276.htm#SEC316
2709	jordan sing_1229.htm#SEC1310
2710	jordanVecField sing_2985.htm#SEC3066
2711	jordanbasis sing_1230.htm#SEC1311
2712	jordanmatrix sing_1231.htm#SEC1312
2713	jordannf sing_1232.htm#SEC1313
2714	jungfib sing_1669.htm#SEC1750
2715	jungnormal sing_1668.htm#SEC1749
2716	jungresolve sing_1667.htm#SEC1748
2717	katsura sing_1080.htm#SEC1161
2718	kbase sing_277.htm#SEC317
2719	kbase (plural) sing_468.htm#SEC508
2720	keepring sing_392.htm#SEC432
2721	kerHom sing_2847.htm#SEC2928
2722	kernel sing_278.htm#SEC318
2723	kernelLattice sing_2878.htm#SEC2959
2724	kill sing_279.htm#SEC319
2725	killTask sing_1161.htm#SEC1242
2726	killall sing_1021.htm#SEC1102
2727	killattrib sing_280.htm#SEC320
2728	kmemory sing_1020.htm#SEC1101
2729	kohom sing_1316.htm#SEC1397
2730	kontrahom sing_1317.htm#SEC1398
2731	koszul sing_281.htm#SEC321
2732	kskernel.lib sing_1891.htm#SEC1972
2733	kskernel_lib sing_1891.htm#SEC1972
2734	l-adic numbers sing_32.htm#SEC46
2735	laguerre sing_282.htm#SEC322
2736	laguerre_solve sing_2062.htm#SEC2143
2737	lastvarGeneral sing_2343.htm#SEC2424
2738	latex.lib sing_2137.htm#SEC2218
2739	latex_lib sing_2137.htm#SEC2218
2740	lattice sing_2623.htm#IDX1051
2741	latticeArea sing_2485.htm#SEC2566
2742	latticeBasis sing_2879.htm#SEC2960
2743	latticeCodegree sing_2511.htm#SEC2592
2744	latticeDegree sing_2512.htm#SEC2593
2745	latticePoints sing_2513.htm#SEC2594
2746	latticeVolume sing_2514.htm#SEC2595
2747	laxfrT sing_2719.htm#SEC2800
2748	laxfrX sing_2720.htm#SEC2801
2749	lazy, option sing_318.htm#IDX156
2750	lcm sing_1083.htm#SEC1164
2751	lcmMon sing_1340.htm#SEC1421
2752	lcmN sing_2254.htm#SEC2335
2753	lcmofall sing_1649.htm#SEC1730
2754	lead sing_283.htm#SEC323
2755	leadcoef sing_284.htm#SEC324
2756	leadexp sing_285.htm#SEC325
2757	leadmonom sing_286.htm#SEC326
2758	leadmonomial sing_2329.htm#SEC2410
2759	left annihilator ideal sing_537.htm#IDX329
2760	left annihilator ideal sing_592.htm#IDX357
2761	leftInverse sing_2203.htm#SEC2284
2762	leftKernel sing_2201.htm#SEC2282
2763	leftOre sing_761.htm#SEC815
2764	length sing_2102.htm#SEC2183
2765	length, option sing_318.htm#IDX157
2766	length2 sing_2038.htm#SEC2119
2767	letplaceGBasis sing_872.htm#SEC926
2768	letterplace sing_296.htm#SEC336
2769	letterplace sing_337.htm#SEC377
2770	lex_solve sing_2068.htm#SEC2149
2771	lexicographical ordering sing_969.htm#IDX440
2772	lib2doc sing_60.htm#SEC97
2773	libSingular sing_3001.htm#SEC3098
2774	libcdd sing_1.htm#IDX12
2775	libfac sing_1.htm#IDX6
2776	libparse sing_69.htm#SEC109
2777	library sing_2638.htm#IDX1066
2778	library, gitfan, GIT, geometric invariant theory, quotients gitfan_lib sing_2443.htm#IDX959
2779	library, info string sing_55.htm#IDX124
2780	library, polybori.lib sing_2638.htm#IDX1063
2781	library, ringgb.lib sing_2953.htm#IDX1250
2782	library, template sing_55.htm#SEC92
2783	library, template.lib sing_55.htm#IDX122
2784	lieBracket sing_873.htm#SEC927
2785	lift sing_288.htm#SEC328
2786	lift sing_495.htm#IDX305
2787	lift (letterplace) sing_806.htm#SEC860
2788	lift (plural) sing_469.htm#SEC509
2789	lift_kbase sing_1837.htm#SEC1918
2790	lift_rel_kb sing_1838.htm#SEC1919
2791	liftenvelope sing_498.htm#SEC552
2792	liftstd sing_289.htm#SEC329
2793	liftstd (letterplace) liftstd (letterplace) sing_807.htm#SEC861
2794	liftstd (plural) sing_470.htm#SEC510
2795	likeIdeal sing_2796.htm#SEC2877
2796	likelihood ideal sing_2795.htm#IDX1208
2797	linReduce sing_510.htm#SEC564
2798	linReduceIdeal sing_511.htm#SEC565
2799	linSyzSolve sing_512.htm#SEC566
2800	linalg.lib sing_1207.htm#SEC1288
2801	linalg_lib sing_1207.htm#SEC1288
2802	linealityDimension sing_2412.htm#SEC2493
2803	linealitySpace sing_2413.htm#SEC2494
2804	linear algebra sing_211.htm#SEC251
2805	linear algebra sing_292.htm#SEC332
2806	linear algebra sing_293.htm#SEC333
2807	linear algebra sing_294.htm#SEC334
2808	linear code, dual sing_2172.htm#IDX942
2809	linear code, systematic sing_2173.htm#IDX943
2810	linear interreduction sing_502.htm#IDX320
2811	linearCombinations sing_531.htm#SEC585
2812	linearMapKernel sing_530.htm#SEC584
2813	linear_relations sing_1199.htm#SEC1280
2814	linearlyEquivalent sing_1581.htm#SEC1662
2815	linearpart sing_2054.htm#SEC2135
2816	linesHypersurface sing_1723.htm#SEC1804
2817	link Parallelization with ssi links sing_113.htm#SEC153
2818	link sing_924.htm#SEC981
2819	link declarations sing_114.htm#SEC154
2820	link expressions sing_115.htm#SEC155
2821	link related functions link related functions sing_116.htm#SEC156
2822	links sing_2977.htm#IDX1265
2823	list sing_123.htm#SEC163
2824	list sing_2695.htm#IDX1151
2825	list sing_2696.htm#IDX1153
2826	list declarations sing_124.htm#SEC164
2827	list expressions sing_125.htm#SEC165
2828	list operations sing_126.htm#SEC166
2829	list related functions list related functions sing_127.htm#SEC167
2830	lists sing_2666.htm#IDX1093
2831	lists, elements sing_2668.htm#IDX1095
2832	listvar sing_290.htm#SEC330
2833	lll sing_2911.htm#SEC2992
2834	load sing_393.htm#SEC433
2835	loadLib, option sing_318.htm#IDX178
2836	loadProc, option sing_318.htm#IDX179
2837	locAtZero sing_1400.htm#SEC1481
2838	locNormal sing_1326.htm#SEC1407
2839	locStatus sing_756.htm#SEC810
2840	local methods sing_1325.htm#IDX626
2841	local methods sing_1326.htm#IDX629
2842	local names sing_46.htm#SEC83
2843	local rings, computing in Rings associated to monomial orderings sing_919.htm#SEC976
2844	local weighted lexicographical ordering sing_970.htm#IDX461
2845	local weighted reverse lexicographical ordering Local orderings sing_970.htm#IDX458
2846	localInvar sing_1999.htm#SEC2080
2847	localization Rings associated to monomial orderings sing_919.htm#SEC976
2848	localization sing_2603.htm#IDX1011
2849	localization of D-module sing_560.htm#IDX345
2850	localization of D-module sing_668.htm#IDX384
2851	locally closed set sing_1038.htm#IDX485
2852	locally closed set sing_1039.htm#IDX487
2853	locally closed set sing_1040.htm#IDX489
2854	locally closed set sing_1041.htm#IDX493
2855	locally closed set sing_1055.htm#IDX531
2856	locally closed set sing_1057.htm#IDX536
2857	localstd sing_2339.htm#SEC2420
2858	locnormal.lib sing_1325.htm#SEC1406
2859	locnormal_lib sing_1325.htm#SEC1406
2860	locstd sing_1928.htm#SEC2009
2861	locus FamElemsAtEnvCompPoints sing_1043.htm#SEC1124
2862	locus sing_1043.htm#IDX503
2863	locus sing_1044.htm#IDX506
2864	locus sing_1045.htm#IDX509
2865	locus sing_1046.htm#IDX512
2866	locus sing_1047.htm#IDX515
2867	locus sing_1048.htm#IDX517
2868	locus sing_1049.htm#IDX521
2869	locusdg sing_1044.htm#SEC1125
2870	locusto sing_1046.htm#SEC1127
2871	log2 sing_2229.htm#SEC2310
2872	logHessian sing_2797.htm#SEC2878
2873	logarithmic annihilator ideal sing_537.htm#IDX334
2874	logarithmic annihilator ideal sing_592.htm#IDX359
2875	logg sing_1728.htm#SEC1809
2876	lp, global ordering sing_969.htm#IDX439
2877	lpCalcSubstDegBound sing_862.htm#SEC916
2878	lpDegBound sing_865.htm#SEC919
2879	lpDivision sing_868.htm#SEC922
2880	lpGBPres2Poly sing_869.htm#SEC923
2881	lpGlDimBound sing_860.htm#SEC914
2882	lpHilbert sing_825.htm#SEC879
2883	lpIsPrime sing_859.htm#SEC913
2884	lpIsSemiPrime sing_858.htm#SEC912
2885	lpKDim sing_823.htm#SEC877
2886	lpKDimCheck sing_822.htm#SEC876
2887	lpMonomialBasis sing_824.htm#SEC878
2888	lpNcgenCount sing_867.htm#SEC921
2889	lpNoetherian sing_857.htm#SEC911
2890	lpSickleDim sing_826.htm#SEC880
2891	lpSubstitute sing_861.htm#SEC915
2892	lpVarBlockSize sing_866.htm#SEC920
2893	lprint sing_1061.htm#SEC1142
2894	lres sing_291.htm#SEC331
2895	ls, local ordering sing_970.htm#IDX452
2896	lsum sing_1284.htm#SEC1365
2897	ludecomp sing_292.htm#SEC332
2898	luinverse sing_293.htm#SEC333
2899	lusolve sing_294.htm#SEC334
2900	mRes sing_2815.htm#SEC2896
2901	m_merkle_hellman_decryption m_merkle_hellman_decryption sing_2301.htm#SEC2382
2902	m_merkle_hellman_encryption m_merkle_hellman_encryption sing_2300.htm#SEC2381
2903	m_merkle_hellman_transformation m_merkle_hellman_transformation sing_2299.htm#SEC2380
2904	magnitude sing_2223.htm#SEC2304
2905	makeDivisor sing_1573.htm#SEC1654
2906	makeFormalDivisor sing_1583.htm#SEC1664
2907	makeGraph sing_1275.htm#SEC1356
2908	makeGraphVE sing_1714.htm#SEC1795
2909	makeHeisenberg sing_736.htm#SEC790
2910	makeIdeal sing_2807.htm#SEC2888
2911	makeLetterplaceRing sing_871.htm#SEC925
2912	makeLinks sing_2977.htm#SEC3058
2913	makeMalgrange sing_604.htm#SEC658
2914	makeMatrix sing_2806.htm#SEC2887
2915	makeModElimRing sing_753.htm#SEC807
2916	makePDivisor sing_1589.htm#SEC1670
2917	makePoly sing_2950.htm#SEC3031
2918	makeQPoly sing_2974.htm#SEC3055
2919	makeQsl2 sing_638.htm#SEC692
2920	makeQsl3 sing_639.htm#SEC693
2921	makeQso3 sing_637.htm#SEC691
2922	makeSheaf sing_1702.htm#SEC1783
2923	makeUe6 sing_634.htm#SEC688
2924	makeUe7 sing_635.htm#SEC689
2925	makeUe8 sing_636.htm#SEC690
2926	makeUf4 sing_633.htm#SEC687
2927	makeUg2 sing_632.htm#SEC686
2928	makeUgl sing_618.htm#SEC672
2929	makeUsl sing_617.htm#SEC671
2930	makeUsl2 sing_616.htm#SEC670
2931	makeUso10 sing_624.htm#SEC678
2932	makeUso11 sing_625.htm#SEC679
2933	makeUso12 sing_626.htm#SEC680
2934	makeUso5 sing_619.htm#SEC673
2935	makeUso6 sing_620.htm#SEC674
2936	makeUso7 sing_621.htm#SEC675
2937	makeUso8 sing_622.htm#SEC676
2938	makeUso9 sing_623.htm#SEC677
2939	makeUsp1 sing_627.htm#SEC681
2940	makeUsp2 sing_628.htm#SEC682
2941	makeUsp3 sing_629.htm#SEC683
2942	makeUsp4 sing_630.htm#SEC684
2943	makeUsp5 sing_631.htm#SEC685
2944	makeVariety sing_1694.htm#SEC1775
2945	makeVector sing_2835.htm#SEC2916
2946	makeWeyl sing_735.htm#SEC789
2947	map sing_128.htm#SEC168
2948	map (plural) sing_432.htm#SEC472
2949	map declarations sing_129.htm#SEC169
2950	map declarations (plural) map declarations (plural) sing_433.htm#SEC473
2951	map expressions sing_130.htm#SEC170
2952	map expressions (plural) map expressions (plural) sing_434.htm#SEC474
2953	map operations sing_131.htm#IDX129
2954	map operations (plural) map operations (plural) sing_435.htm#IDX300
2955	map related functions map related functions sing_132.htm#IDX131
2956	map related functions (plural) map related functions (plural) sing_436.htm#IDX301
2957	mapIsFinite sing_1247.htm#SEC1328
2958	mapToRatNormCurve sing_1624.htm#SEC1705
2959	mapall sing_1141.htm#SEC1222
2960	mappingcone sing_2789.htm#SEC2870
2961	mappingcone3 sing_2791.htm#SEC2872
2962	markov4ti2 sing_1491.htm#SEC1572 9163
2963	mat2arr sing_2588.htm#SEC2669
2964	mat2carr sing_2589.htm#SEC2670
2965	mat_rk sing_1221.htm#SEC1302
2966	matbil sing_2350.htm#SEC2431
2967	mathematical objects Representation of mathematical objects sing_965.htm#SEC1022
2968	mathinit sing_2135.htm#SEC2216
2969	matmult sing_2351.htm#SEC2432
2970	matrix sing_133.htm#SEC173
2971	matrix sing_2588.htm#IDX979
2972	matrix sing_2589.htm#IDX982
2973	matrix sing_2590.htm#IDX986
2974	matrix declarations sing_134.htm#SEC174
2975	matrix diagonalization sing_2212.htm#IDX953
2976	matrix expressions sing_135.htm#SEC175
2977	matrix operations sing_137.htm#SEC177
2978	matrix related functions matrix related functions sing_138.htm#SEC178
2979	matrix type cast sing_136.htm#SEC176
2980	matrix.lib sing_1175.htm#SEC1256
2981	matrixExp sing_1614.htm#SEC1695
2982	matrixLog sing_1615.htm#SEC1696
2983	matrixT1 sing_1942.htm#SEC2023
2984	matrix_lib sing_1175.htm#SEC1256
2985	matrixpres sing_2794.htm#SEC2875
2986	matrixsystem sing_2730.htm#SEC2811
2987	max sing_295.htm#SEC335
2988	maxEord sing_1639.htm#SEC1720
2989	maxExp sing_210.htm#IDX136
2990	maxIntRoot sing_685.htm#SEC739
2991	maxPoints sing_2799.htm#SEC2880
2992	maxPointsProb sing_2800.htm#SEC2881
2993	maxZeros sing_1617.htm#SEC1698
2994	maxabs sing_2369.htm#SEC2450
2995	maxcoef sing_1084.htm#SEC1165
2996	maxdeg sing_1085.htm#SEC1166
2997	maxdeg1 sing_1086.htm#SEC1167
2998	maxideal sing_296.htm#SEC336
2999	maximalFace sing_2515.htm#SEC2596
3000	maximalGroebnerCone sing_2569.htm#SEC2650
3001	maximalValue sing_2516.htm#SEC2597
3002	maximum sing_2242.htm#SEC2323
3003	maximum likelihood estimate sing_2795.htm#IDX1209
3004	maximum number of zeroes sing_1617.htm#IDX715
3005	maxlike.lib sing_2795.htm#SEC2876
3006	maxlike_lib sing_2795.htm#SEC2876
3007	mdouble sing_56.htm#SEC93
3008	mem, option sing_318.htm#IDX180
3009	member sing_2668.htm#SEC2749
3010	memberpos sing_1100.htm#SEC1181
3011	membershipMon sing_1341.htm#SEC1422
3012	memory sing_297.htm#SEC337
3013	memory management sing_297.htm#SEC337
3014	merkle_hellman_decryption merkle_hellman_decryption sing_2303.htm#SEC2384
3015	merkle_hellman_encryption merkle_hellman_encryption sing_2302.htm#SEC2383
3016	methods, hashtables sing_2801.htm#IDX1210
3017	methods.lib sing_2801.htm#SEC2882
3018	methods_lib sing_2801.htm#SEC2882
3019	midpoint sing_2726.htm#SEC2807
3020	milnor sing_1929.htm#SEC2010
3021	milnorcode sing_1785.htm#SEC1866
3022	milnornumber sing_1916.htm#SEC1997
3023	min sing_298.htm#SEC338
3024	minAssChar sing_1445.htm#SEC1526
3025	minAssCharE sing_1446.htm#SEC1527
3026	minAssGTZ sing_1443.htm#SEC1524
3027	minAssGTZE sing_1444.htm#SEC1525
3028	minAssZ sing_1463.htm#SEC1544
3029	minEcart sing_2332.htm#SEC2413
3030	minIntRoot sing_558.htm#SEC612
3031	minIntRoot2 sing_684.htm#SEC738
3032	minMult sing_1254.htm#SEC1335
3033	minbase sing_299.htm#SEC339
3034	minbaseMon sing_1338.htm#SEC1419
3035	mindeg sing_1087.htm#SEC1168
3036	mindeg1 sing_1088.htm#SEC1169
3037	mindist sing_2187.htm#SEC2268
3038	minimal display time, setting the sing_361.htm#IDX284
3039	minimal representations sing_880.htm#IDX438
3040	minimalAfaceOrbits sing_2456.htm#SEC2537
3041	minimalAfaces sing_2447.htm#SEC2528
3042	minimalFace sing_2517.htm#SEC2598
3043	minimalOrbitConeOrbits minimalOrbitConeOrbits sing_2458.htm#SEC2539
3044	minimalValue sing_2518.htm#SEC2599
3045	minipoly sing_1226.htm#SEC1307
3046	minkowskiSum sing_2519.htm#SEC2600
3047	minor sing_300.htm#SEC340
3048	minpoly sing_401.htm#SEC441
3049	minres sing_301.htm#SEC341
3050	minres (plural) sing_471.htm#SEC511
3051	minus sing_2684.htm#IDX1127
3052	minus sing_2685.htm#IDX1129
3053	minus sing_2706.htm#IDX1175
3054	minus sing_2707.htm#IDX1177
3055	mirror symmetry sing_1274.htm#IDX594
3056	mixed Hodge structure sing_1845.htm#IDX801
3057	mixed Hodge structure sing_1851.htm#IDX829
3058	mixed Hodge structure sing_1852.htm#IDX835
3059	mixed Hodge structure sing_1853.htm#IDX843
3060	mixed Hodge structure sing_1854.htm#IDX849
3061	mixed Hodge structure sing_1855.htm#IDX857
3062	mixed Hodge structure sing_1856.htm#IDX867
3063	mixed Hodge structure sing_1867.htm#IDX873
3064	mixed Hodge structure sing_1869.htm#IDX884
3065	mod sing_81.htm#SEC121
3066	mod sing_98.htm#SEC138
3067	mod sing_147.htm#SEC187
3068	mod sing_155.htm#SEC195
3069	mod2id sing_1092.htm#SEC1173
3070	modBorder sing_1481.htm#SEC1562
3071	modDec sing_1357.htm#SEC1438
3072	modIntersect sing_1335.htm#SEC1416
3073	modJanet sing_1483.htm#SEC1564
3074	modNPos sing_1385.htm#SEC1466
3075	modNormal sing_1331.htm#SEC1412
3076	modNpos_test sing_1383.htm#SEC1464
3077	modQuotient sing_1328.htm#SEC1409
3078	modSagbiAlg sing_1807.htm#SEC1888
3079	modSat sing_1329.htm#SEC1410
3080	modStd sing_1333.htm#SEC1414
3081	modSyz sing_1334.htm#SEC1415
3082	modVStd sing_1818.htm#SEC1899
3083	modVStd0 sing_1819.htm#SEC1900
3084	modWalk sing_2856.htm#SEC2937
3085	mod_versal sing_1836.htm#SEC1917
3086	modality sing_1793.htm#SEC1874
3087	modberlekampMassey sing_1290.htm#SEC1371
3088	moddiq.lib sing_1327.htm#SEC1408
3089	moddiq_lib sing_1327.htm#SEC1408
3090	modfWalk sing_2858.htm#SEC2939
3091	modfrWalk sing_2859.htm#SEC2940
3092	modnormal.lib sing_1330.htm#SEC1411
3093	modnormal_lib sing_1330.htm#SEC1411
3094	modrWalk sing_2857.htm#SEC2938
3095	modrationalInterpolation modrationalInterpolation sing_1288.htm#SEC1369
3096	modregCM sing_1389.htm#SEC1470
3097	modsatiety sing_1387.htm#SEC1468
3098	modstd.lib sing_1332.htm#SEC1413
3099	modstd_lib sing_1332.htm#SEC1413
3100	modular sing_1070.htm#SEC1151
3101	modular methods sing_1325.htm#IDX627
3102	modular methods sing_1330.htm#IDX633
3103	modular methods. sing_1326.htm#IDX630
3104	modular techniques. sing_1331.htm#IDX635
3105	modular.lib sing_1069.htm#SEC1150
3106	modular_lib sing_1069.htm#SEC1150
3107	modular_lib sing_1069.htm#IDX540
3108	module sing_139.htm#SEC179
3109	module (plural) sing_437.htm#SEC477
3110	module declarations sing_140.htm#SEC180
3111	module declarations (plural) module declarations (plural) sing_438.htm#SEC478
3112	module expressions sing_141.htm#SEC181
3113	module expressions (plural) module expressions (plural) sing_439.htm#SEC479
3114	module operations sing_142.htm#SEC182
3115	module operations (plural) module operations (plural) sing_440.htm#SEC480
3116	module ordering C sing_971.htm#IDX464
3117	module ordering c sing_971.htm#IDX466
3118	module related functions module related functions sing_143.htm#SEC183
3119	module related functions (plural) module related functions (plural) sing_441.htm#SEC481
3120	module_containment sing_1239.htm#SEC1320
3121	modules.lib sing_2802.htm#SEC2883
3122	modules_lib sing_2802.htm#SEC2883
3123	moduliSpace sing_1716.htm#SEC1797
3124	modulo sing_302.htm#SEC342
3125	modulo (plural) sing_472.htm#SEC512
3126	moduloSlim sing_743.htm#SEC797
3127	modwalk.lib sing_2855.htm#SEC2936
3128	modwalk_lib sing_2855.htm#SEC2936
3129	moebius sing_2624.htm#SEC2705
3130	moebius function sing_2624.htm#IDX1052
3131	molien sing_1965.htm#SEC2046
3132	mondim sing_667.htm#SEC721
3133	mondromy.lib sing_1897.htm#SEC1978
3134	mondromy_lib sing_1897.htm#SEC1978
3135	monitor sing_303.htm#SEC343
3136	monodromy sing_1845.htm#IDX805
3137	monodromy sing_1850.htm#SEC1931
3138	monodromy sing_1850.htm#IDX825
3139	monodromy sing_1855.htm#IDX860
3140	monodromy sing_1867.htm#IDX876
3141	monodromy sing_1869.htm#IDX887
3142	monodromyB sing_1901.htm#SEC1982
3143	monoideal, dimension sing_667.htm#IDX377
3144	monomial sing_304.htm#SEC344
3145	monomial ordering sing_1150.htm#IDX566
3146	monomial orderings General definitions for orderings sing_919.htm#SEC976
3147	monomial orderings sing_968.htm#SEC1025
3148	monomial orderings introduction Introduction to orderings sing_967.htm#SEC1024
3149	monomial output sing_405.htm#SEC445
3150	monomial, write sing_405.htm#SEC445
3151	monomialInIdeal sing_682.htm#SEC736
3152	monomialLcm sing_2330.htm#SEC2411
3153	monomialabortstd sing_2631.htm#SEC2712
3154	monomialideal.lib sing_1336.htm#SEC1417
3155	monomialideal_lib sing_1336.htm#SEC1417
3156	monomials and precedence Miscellaneous oddities sing_422.htm#IDX290
3157	mons2intmat sing_1430.htm#SEC1511 15555
3158	morsesplit sing_1786.htm#SEC1867
3159	movingCone sing_2454.htm#SEC2535
3160	mp_res_mat sing_2065.htm#SEC2146
3161	mplot sing_2136.htm#SEC2217
3162	mpresmat sing_305.htm#SEC345
3163	mprimdec.lib sing_1353.htm#SEC1434
3164	mprimdec_lib sing_1353.htm#SEC1434
3165	mrcgs sing_1109.htm#SEC1190
3166	mrcgs, rcgs, buildtree, cantreetoMaple, cantodiffcgs crcgs sing_1111.htm#IDX558
3167	mrcgs, rcgs, crcgs, Maple sing_1112.htm#IDX559
3168	mregular.lib sing_1368.htm#SEC1449
3169	mregular_lib sing_1368.htm#SEC1449
3170	mres sing_306.htm#SEC346
3171	mres (plural) sing_473.htm#SEC513
3172	mstd sing_307.htm#SEC347
3173	msum sing_58.htm#SEC95
3174	mtriple sing_57.htm#SEC94
3175	mult Miscellaneous oddities sing_308.htm#SEC348
3176	mult sing_422.htm#IDX291
3177	multBound sing_402.htm#SEC442
3178	multRat sing_690.htm#SEC744
3179	multarr2arr sing_2619.htm#SEC2700
3180	multarrMultRestrict sing_2621.htm#SEC2702
3181	multarrRestrict sing_2620.htm#SEC2701
3182	multcol sing_1193.htm#SEC1274
3183	multdivisor sing_1575.htm#SEC1656
3184	multformaldivisor sing_1587.htm#SEC1668
3185	multi sing_2317.htm#SEC2398
3186	multi indices sing_37.htm#SEC65
3187	multi-graded Hilbert series sing_877.htm#IDX432
3188	multiDeg sing_2890.htm#SEC2971
3189	multiDegBasis sing_2891.htm#SEC2972
3190	multiDegGroebner sing_2899.htm#SEC2980
3191	multiDegModulo sing_2901.htm#SEC2982
3192	multiDegPartition sing_2892.htm#SEC2973
3193	multiDegResolution sing_2902.htm#SEC2983
3194	multiDegSyzygy sing_2900.htm#SEC2981
3195	multiDegTensor sing_2903.htm#SEC2984
3196	multiDegTor sing_2904.htm#SEC2985
3197	multiarrangement sing_2615.htm#IDX1032
3198	multiarrangement sing_2616.htm#IDX1034
3199	multiarrangement sing_2617.htm#IDX1037
3200	multiarrangement sing_2618.htm#IDX1038
3201	multiarrangement sing_2619.htm#IDX1041
3202	multiarrangement sing_2620.htm#IDX1044
3203	multiarrangement sing_2621.htm#IDX1046
3204	multidimensional_knapsack multidimensional_knapsack sing_2295.htm#SEC2376
3205	multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2860.htm#IDX1217
3206	multigrading.lib sing_2860.htm#IDX1215
3207	multigrading_lib sing_2860.htm#IDX1216
3208	multipleCover sing_1722.htm#SEC1803
3209	multiplication sing_2686.htm#IDX1131
3210	multiplication sing_2708.htm#IDX1179
3211	multiplicities, sequence of sing_1876.htm#IDX899
3212	multiplicity sing_661.htm#IDX372
3213	multiplicity sing_1261.htm#IDX586
3214	multiplicity sequence sing_1758.htm#IDX772
3215	multiplicity sequence sing_1761.htm#IDX784
3216	multiplicity sequence sing_1878.htm#IDX900
3217	multiplyLeftFractions multiplyLeftFractions sing_766.htm#SEC820
3218	multiplylist sing_1659.htm#SEC1740
3219	multivariate equations sing_2030.htm#IDX924
3220	multrow sing_1194.htm#SEC1275
3221	multseq2charexp sing_1757.htm#SEC1838
3222	multsequence sing_1878.htm#SEC1959
3223	nBoundaryLatticePoints nBoundaryLatticePoints sing_2520.htm#SEC2601
3224	nHilbertBasis sing_2521.htm#SEC2602
3225	nInteriorLatticePoints nInteriorLatticePoints sing_2522.htm#SEC2603
3226	nLatticePoints sing_2523.htm#SEC2604
3227	naccache_stern_decryption naccache_stern_decryption sing_2298.htm#SEC2379
3228	naccache_stern_encryption naccache_stern_encryption sing_2297.htm#SEC2378
3229	naccache_stern_generation naccache_stern_generation sing_2296.htm#SEC2377
3230	nameof sing_309.htm#SEC349
3231	names sing_310.htm#SEC350
3232	nashmult sing_1765.htm#SEC1846
3233	nblocks sing_361.htm#IDX219
3234	ncExt_R sing_709.htm#SEC763
3235	ncHilb sing_662.htm#SEC716
3236	ncHilb.lib sing_877.htm#SEC931
3237	ncHilb_lib sing_877.htm#SEC931
3238	ncHilbertMultiplicity ncHilbertMultiplicity sing_665.htm#SEC719
3239	ncHilbertPolynomial sing_664.htm#SEC718
3240	ncHilbertSeries sing_663.htm#SEC717
3241	ncHom sing_710.htm#SEC764
3242	ncInit sing_881.htm#SEC935
3243	ncModslimgb.lib sing_720.htm#SEC774
3244	ncModslimgb_lib sing_720.htm#SEC774
3245	ncRelations sing_744.htm#SEC798
3246	ncVarsAdd sing_883.htm#SEC937
3247	ncVarsGet sing_882.htm#SEC936
3248	nc_algebra sing_474.htm#SEC514
3249	nc_hilb sing_361.htm#IDX221
3250	ncalg.lib sing_615.htm#SEC669
3251	ncalg_lib sing_615.htm#SEC669
3252	ncalgebra sing_475.htm#SEC515
3253	ncdecomp.lib sing_642.htm#SEC696
3254	ncdecomp_lib sing_642.htm#SEC696
3255	ncdetection sing_609.htm#SEC663
3256	ncfactor sing_648.htm#SEC702
3257	ncfactor.lib sing_647.htm#SEC701
3258	ncfactor_lib sing_647.htm#SEC701
3259	ncfrac.lib sing_694.htm#SEC748
3260	ncfrac_lib sing_694.htm#SEC748
3261	ncgen sing_808.htm#SEC862
3262	nchilb sing_878.htm#SEC932
3263	nchilbert.lib sing_661.htm#SEC715
3264	nchilbert_lib sing_661.htm#SEC715
3265	nchomolog.lib sing_708.htm#IDX390
3266	nchomolog_lib sing_708.htm#IDX391
3267	ncloc.lib sing_716.htm#SEC770
3268	ncloc_lib sing_716.htm#SEC770
3269	ncmodslimgb sing_721.htm#SEC775
3270	ncols sing_311.htm#SEC351
3271	ncones sing_2436.htm#SEC2517
3272	ncpreim.lib sing_722.htm#SEC776
3273	ncpreim_lib sing_722.htm#SEC776
3274	ncrat.lib sing_880.htm#IDX433
3275	ncratAdd sing_885.htm#SEC939
3276	ncratDefine sing_884.htm#SEC938
3277	ncratEvaluateAt sing_894.htm#SEC948
3278	ncratFromPoly sing_892.htm#SEC946
3279	ncratFromString sing_891.htm#SEC945
3280	ncratInvert sing_888.htm#SEC942
3281	ncratMultiply sing_887.htm#SEC941
3282	ncratPower sing_893.htm#SEC947
3283	ncratPrint sing_890.htm#SEC944
3284	ncratSPrint sing_889.htm#SEC943
3285	ncratSubstract sing_886.htm#SEC940
3286	ncrat_lib sing_880.htm#IDX434
3287	ncrepAdd sing_896.htm#SEC950
3288	ncrepDim sing_901.htm#SEC955
3289	ncrepEvaluate sing_903.htm#SEC957
3290	ncrepEvaluateAt sing_904.htm#SEC958
3291	ncrepGet sing_895.htm#SEC949
3292	ncrepGetRegularMinimal ncrepGetRegularMinimal sing_911.htm#SEC965
3293	ncrepGetRegularZeroMinimal ncrepGetRegularZeroMinimal sing_910.htm#SEC964
3294	ncrepInvert sing_899.htm#SEC953
3295	ncrepIsDefined sing_906.htm#SEC960
3296	ncrepIsDefinedDim sing_905.htm#SEC959
3297	ncrepIsRegular sing_907.htm#SEC961
3298	ncrepMultiply sing_898.htm#SEC952
3299	ncrepPencilCombine sing_913.htm#SEC967
3300	ncrepPencilGet sing_912.htm#SEC966
3301	ncrepPrint sing_900.htm#SEC954
3302	ncrepRegularMinimize ncrepRegularMinimize sing_909.htm#SEC963
3303	ncrepRegularZeroMinimize ncrepRegularZeroMinimize sing_908.htm#SEC962
3304	ncrepSubstitute sing_902.htm#SEC956
3305	ncrepSubstract sing_897.htm#SEC951
3306	nctools.lib sing_730.htm#SEC784
3307	nctools_lib sing_730.htm#SEC784
3308	ndcond sing_733.htm#SEC787
3309	negateNcfrac sing_703.htm#SEC757
3310	negatedCone sing_2414.htm#SEC2495
3311	negation sing_2685.htm#IDX1130
3312	negative degree lexicographical ordering sing_970.htm#IDX455
3313	negative degree reverse lexicographical ordering Local orderings sing_970.htm#IDX453
3314	negative lexicographical ordering sing_970.htm#IDX451
3315	negativedivisor sing_1576.htm#SEC1657
3316	negativeformaldivisor negativeformaldivisor sing_1586.htm#SEC1667
3317	net sing_2912.htm#IDX1218
3318	net sing_2914.htm#SEC2995
3319	net access Command line options sing_19.htm#IDX40
3320	netBigInt sing_2920.htm#SEC3001
3321	netBigIntMat sing_2915.htm#SEC2996
3322	netBigIntMatShort sing_2916.htm#SEC2997
3323	netCoefficientRing sing_2917.htm#SEC2998
3324	netIdeal sing_2918.htm#SEC2999
3325	netInt sing_2919.htm#SEC3000
3326	netIntMat sing_2921.htm#SEC3002
3327	netIntMatShort sing_2922.htm#SEC3003
3328	netIntVector sing_2923.htm#SEC3004
3329	netIntVectorShort sing_2924.htm#SEC3005
3330	netList sing_2926.htm#SEC3007
3331	netMap sing_2927.htm#SEC3008
3332	netMap2 sing_2928.htm#SEC3009
3333	netMatrix sing_2837.htm#SEC2918
3334	netNumber sing_2925.htm#SEC3006
3335	netPoly sing_2931.htm#SEC3012
3336	netPrimePower sing_2932.htm#SEC3013
3337	netRing sing_2933.htm#SEC3014
3338	netString sing_2934.htm#SEC3015
3339	netVector sing_2836.htm#SEC2917
3340	netmatrix sing_2929.htm#SEC3010
3341	netmatrixShort sing_2930.htm#SEC3011
3342	nets.lib sing_2912.htm#SEC2993
3343	nets_lib sing_2912.htm#SEC2993
3344	netvector sing_2935.htm#SEC3016
3345	netvectorShort sing_2936.htm#SEC3017
3346	newTest sing_2237.htm#SEC2318
3347	newline sing_172.htm#SEC212
3348	news sing_2994.htm#SEC3075
3349	newstruct sing_183.htm#SEC223
3350	newstruct sing_2638.htm#IDX1068
3351	newtonDiag sing_1096.htm#SEC1177
3352	newtonPolygonNegSlopes newtonPolygonNegSlopes sing_2578.htm#SEC2659
3353	newtonPolytope sing_2440.htm#SEC2521
3354	newtonPolytopeLP sing_2477.htm#SEC2558
3355	newtonPolytopeP sing_2476.htm#SEC2557
3356	newtonpoly sing_1883.htm#SEC1964
3357	nf_icis sing_1930.htm#SEC2011
3358	nfmodStd sing_1378.htm#SEC1459
3359	nfmodSyz sing_1380.htm#SEC1461
3360	nfmodstd.lib sing_1376.htm#SEC1457
3361	nfmodstd_lib sing_1376.htm#SEC1457
3362	nfmodsyz.lib sing_1379.htm#SEC1460
3363	nfmodsyz_lib sing_1379.htm#SEC1460
3364	nilpotent Lie algebras sing_1612.htm#IDX700
3365	nmaxcones sing_2435.htm#SEC2516
3366	noElements sing_2957.htm#SEC3038
3367	noether sing_403.htm#SEC443
3368	noether.lib sing_1381.htm#SEC1462
3369	noetherNormal sing_1246.htm#SEC1327
3370	noether_lib sing_1381.htm#SEC1462
3371	non-english special characters sing_411.htm#IDX286
3372	nonMonomials sing_1434.htm#SEC1515
3373	nonZeroEntry sing_1249.htm#SEC1330
3374	noncommutative, rational expressions sing_880.htm#IDX435
3375	none, option sing_318.htm#IDX150
3376	norTest sing_1401.htm#SEC1482
3377	norm sing_2316.htm#SEC2397
3378	normaform (up to a bound) sing_361.htm#IDX244
3379	normal sing_1391.htm#SEC1472
3380	normal bundle, graph, rational curves, multiple covers, lines on normalBundle sing_1721.htm#IDX751
3381	normal form sing_977.htm#IDX467
3382	normal.lib sing_1390.htm#SEC1471
3383	normalBundle sing_1721.htm#SEC1802
3384	normalC sing_1393.htm#SEC1474
3385	normalConductor sing_1405.htm#SEC1486
3386	normalFan sing_2524.htm#SEC2605
3387	normalForm sing_1577.htm#SEC1658
3388	normalI sing_1478.htm#SEC1559
3389	normalP sing_1392.htm#SEC1473
3390	normalToricRing sing_1408.htm#SEC1489 29638
3391	normalToricRingFromBinomials normalToricRingFromBinomials sing_1409.htm#SEC1490 2301
3392	normal_lib sing_1390.htm#SEC1471
3393	normalform sing_1790.htm#SEC1871
3394	normalform sing_1806.htm#IDX794
3395	normaliz sing_1.htm#IDX14 18426
3396	normaliz sing_1421.htm#SEC1502
3397	normaliz.lib sing_1406.htm#SEC1487
3398	normaliz_lib sing_1406.htm#SEC1487
3399	normalization sing_1260.htm#IDX584
3400	normalization sing_1325.htm#IDX625
3401	normalization sing_1326.htm#IDX628
3402	normalization sing_1330.htm#IDX632
3403	normalization sing_1331.htm#IDX634
3404	normalization sing_1391.htm#IDX643
3405	normalization sing_1392.htm#IDX646
3406	normalization sing_1393.htm#IDX649
3407	normalization sing_1405.htm#IDX655
3408	normalization sing_1406.htm#IDX657
3409	normalization. sing_1322.htm#IDX624
3410	normalization. sing_1619.htm#IDX722
3411	normalize sing_1089.htm#SEC1170
3412	normalizeMonoidal sing_772.htm#SEC826
3413	normalizeRational sing_773.htm#SEC827
3414	not sing_101.htm#SEC141
3415	not equal sing_2689.htm#IDX1138
3416	not equal sing_2710.htm#IDX1185
3417	notBuckets, option sing_318.htm#IDX160
3418	notRegularity, option sing_318.htm#IDX158
3419	notSugar, option sing_318.htm#IDX159
3420	notWarnSB, option sing_318.htm#IDX181
3421	npar sing_2222.htm#SEC2303
3422	npars sing_312.htm#SEC352
3423	nrRootsDeterm sing_2347.htm#SEC2428
3424	nrRootsProbab sing_2346.htm#SEC2427
3425	nres sing_313.htm#SEC353
3426	nres (plural) sing_476.htm#SEC516
3427	nrows sing_314.htm#SEC354
3428	nrroots sing_2376.htm#SEC2457
3429	nsatiety sing_1386.htm#SEC1467
3430	nselect sing_1270.htm#SEC1351
3431	nt_solve sing_2080.htm#SEC2161
3432	ntsolve.lib sing_2079.htm#SEC2160
3433	ntsolve_lib sing_2079.htm#SEC2160
3434	num_elim sing_2097.htm#SEC2178
3435	num_elim1 sing_2098.htm#SEC2179
3436	num_prime_decom sing_2091.htm#SEC2172
3437	num_prime_decom1 sing_2092.htm#SEC2173
3438	num_radical1 sing_2095.htm#SEC2176
3439	num_radical2 sing_2096.htm#SEC2177
3440	num_radical_via_decom num_radical_via_decom sing_2093.htm#SEC2174
3441	num_radical_via_randlincom num_radical_via_randlincom sing_2094.htm#SEC2175
3442	number sing_144.htm#SEC184
3443	number sing_2592.htm#IDX992
3444	number declarations sing_145.htm#SEC185
3445	number expressions sing_146.htm#SEC186
3446	number operations sing_147.htm#SEC187
3447	number related functions number related functions sing_148.htm#SEC188
3448	numberOfConesOfDimension numberOfConesOfDimension sing_2437.htm#SEC2518
3449	number_e sing_1022.htm#SEC1103
3450	number_pi sing_1023.htm#SEC1104
3451	numerAlg.lib sing_1594.htm#IDX689
3452	numerAlg_lib sing_1594.htm#IDX690
3453	numerAlg_lib sing_1599.htm#IDX699
3454	numerDecom.lib sing_1599.htm#IDX693
3455	numerDecom_lib sing_1594.htm#IDX692
3456	numerDecom_lib sing_1599.htm#IDX694
3457	numerator sing_315.htm#SEC355
3458	numerical algebraic geometry sing_2082.htm#IDX926
3459	numerical irreducible decomposition sing_1599.htm#IDX695
3460	nvars sing_316.htm#SEC356
3461	olga.lib sing_755.htm#SEC809
3462	olga_lib sing_755.htm#SEC809
3463	oneDimBelongSemigroup oneDimBelongSemigroup sing_1256.htm#SEC1337
3464	oneNcfrac sing_700.htm#SEC754
3465	onesVector sing_2442.htm#SEC2523
3466	online help The online help system sing_16.htm#SEC22
3467	open sing_317.htm#SEC357
3468	opentex sing_2139.htm#SEC2220
3469	operatorAlgebra sing_828.htm#SEC882
3470	operatorBM sing_544.htm#SEC598
3471	operatorModulo sing_545.htm#SEC599
3472	oppose sing_477.htm#SEC517
3473	opposite sing_478.htm#SEC518
3474	opposite polynomial sing_361.htm#IDX229
3475	opposite ring sing_361.htm#IDX226
3476	option sing_318.htm#SEC358
3477	option(warn) sing_70.htm#SEC110
3478	optionIsSet sing_1147.htm#SEC1228
3479	or Evaluation of logical expressions sing_101.htm#SEC141
3480	or sing_415.htm#SEC455
3481	orbit sing_1612.htm#IDX702
3482	orbit sing_1613.htm#IDX706
3483	orbit sing_1616.htm#IDX711
3484	orbit sing_1617.htm#IDX714
3485	orbitConeOrbits sing_2457.htm#SEC2538
3486	orbitCones sing_2448.htm#SEC2529
3487	orbit_variety sing_1989.htm#SEC2070
3488	orbitparam.lib sing_1612.htm#SEC1693
3489	orbitparam_lib sing_1612.htm#SEC1693
3490	ord sing_319.htm#SEC359
3491	ord_test sing_1142.htm#SEC1223
3492	order ideal, border basis sing_1480.htm#IDX666
3493	order ideal, border basis sing_1481.htm#IDX667
3494	ordering diffAlgebraChangeOrd sing_2674.htm#IDX1107
3495	ordering sing_2690.htm#IDX1141
3496	ordering sing_2691.htm#IDX1144
3497	orderings General definitions for orderings sing_968.htm#SEC1025
3498	orderings introduction Introduction to orderings sing_967.htm#SEC1024
3499	orderings, L sing_975.htm#SEC1032
3500	orderings, M sing_972.htm#SEC1029
3501	orderings, a sing_974.htm#SEC1031
3502	orderings, global sing_969.htm#SEC1026
3503	orderings, local sing_970.htm#SEC1027
3504	orderings, product sing_973.htm#SEC1030
3505	ordstr sing_320.htm#SEC360
3506	origin sing_2385.htm#SEC2466
3507	orthogonalize sing_1212.htm#SEC1293
3508	outer sing_1183.htm#SEC1264
3509	output sing_41.htm#SEC71
3510	outputting monomials sing_405.htm#SEC445
3511	p-adic numbers sing_32.htm#SEC46
3512	pFactor sing_2271.htm#SEC2352
3513	pIntersect sing_508.htm#SEC562
3514	pIntersectSyz sing_509.htm#SEC563
3515	package sing_149.htm#SEC189
3516	package declarations package declarations sing_150.htm#SEC190
3517	package related functions package related functions sing_151.htm#SEC191
3518	pairset sing_2336.htm#SEC2417
3519	par sing_321.htm#SEC361
3520	par2varRing sing_1005.htm#SEC1086
3521	paraConic sing_1627.htm#SEC1708
3522	paraPlaneCurve sing_1621.htm#SEC1702
3523	parallel computing sing_2981.htm#IDX1268
3524	parallel skeletons sing_1071.htm#IDX546
3525	parallel.lib sing_1071.htm#SEC1152
3526	parallelTestAND sing_1075.htm#SEC1156
3527	parallelTestOR sing_1076.htm#SEC1157
3528	parallelWaitAll sing_1074.htm#SEC1155
3529	parallelWaitFirst sing_1073.htm#SEC1154
3530	parallelWaitN sing_1072.htm#SEC1153
3531	parallel_lib sing_1071.htm#SEC1152
3532	parallelization sing_1071.htm#IDX545
3533	parallelization sing_1126.htm#IDX560
3534	parallelization sing_1159.htm#IDX570
3535	param sing_1874.htm#SEC1955
3536	parameter, as numbers sing_144.htm#SEC184
3537	parameterSubstitute sing_2564.htm#SEC2645
3538	parametric annihilator sing_537.htm#IDX335
3539	parametric annihilator for variety sing_600.htm#IDX365
3540	parametric ideal sing_1034.htm#IDX473
3541	parametric ideal sing_1041.htm#IDX492
3542	parametric ideal sing_1041.htm#IDX494
3543	parametric ideal sing_1042.htm#IDX499
3544	parametrization sing_1612.htm#IDX703
3545	parametrization sing_1616.htm#IDX712
3546	parametrization sing_1874.htm#IDX894
3547	parametrizeOrbit sing_1616.htm#SEC1697
3548	paraplanecurves.lib sing_1618.htm#SEC1699
3549	paraplanecurves_lib sing_1618.htm#SEC1699
3550	pardeg sing_322.htm#SEC362
3551	parstr sing_323.htm#SEC363
3552	part sing_1559.htm#SEC1640
3553	partOver sing_1562.htm#SEC1643
3554	partUnder sing_1563.htm#SEC1644
3555	partial fraction sing_2938.htm#IDX1243
3556	partial_molien sing_1967.htm#SEC2048
3557	partitions sing_1282.htm#SEC1363
3558	partitions sing_1282.htm#IDX613
3559	path Used environment variables sing_3003.htm#SEC3100
3560	path integral sing_1274.htm#IDX600
3561	paths Used environment variables sing_3003.htm#SEC3100
3562	pause sing_1068.htm#SEC1149
3563	pdivi sing_1036.htm#SEC1117
3564	pdivi sing_1037.htm#IDX483
3565	pdivi2 sing_1102.htm#SEC1183
3566	pdivisorplus sing_1591.htm#SEC1672
3567	permcol sing_1195.htm#SEC1276
3568	permrow sing_1196.htm#SEC1277
3569	permutationFromIntvec permutationFromIntvec sing_2463.htm#SEC2544
3570	permutationToIntvec sing_2464.htm#SEC2545
3571	permutations sing_1283.htm#IDX614
3572	permutations, sum, max, min sing_2665.htm#IDX1092
3573	permute sing_1283.htm#SEC1364
3574	permute_L sing_2174.htm#SEC2255
3575	perron sing_777.htm#SEC831
3576	perron.lib sing_776.htm#SEC830
3577	perron_lib sing_776.htm#SEC830
3578	pfd sing_2939.htm#SEC3020
3579	pfd.lib sing_2938.htm#SEC3019
3580	pfdMat sing_2947.htm#SEC3028
3581	pfd_lib sing_2938.htm#SEC3019
3582	phindex.lib sing_2633.htm#IDX1059
3583	phindex_lib sing_2633.htm#IDX1060
3584	picksFormula sing_2486.htm#SEC2567
3585	pid sing_361.htm#IDX238
3586	plainInvariants sing_1833.htm#SEC1914
3587	planeCur sing_1804.htm#SEC1885
3588	plot sing_2152.htm#SEC2233
3589	plotRot sing_2156.htm#SEC2237
3590	plotRotated sing_2155.htm#SEC2236
3591	plotRotatedDirect sing_2158.htm#SEC2239
3592	plotRotatedList sing_2157.htm#SEC2238
3593	plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_2159.htm#SEC2240
3594	plural sing_1149.htm#IDX565
3595	pmat sing_1062.htm#SEC1143
3596	pnormalf sing_1037.htm#SEC1118
3597	pnormalform sing_1105.htm#SEC1186
3598	pointid.lib sing_1433.htm#SEC1514
3599	pointid_lib sing_1433.htm#SEC1514
3600	polSol sing_674.htm#SEC728
3601	polSolFiniteRank sing_675.htm#SEC729
3602	pollTask sing_1169.htm#SEC1250
3603	poly sing_152.htm#SEC192
3604	poly (plural) sing_442.htm#SEC482
3605	poly declarations sing_153.htm#SEC193
3606	poly declarations (plural) poly declarations (plural) sing_443.htm#SEC483
3607	poly expressions sing_154.htm#SEC194
3608	poly expressions (plural) poly expressions (plural) sing_444.htm#SEC484
3609	poly operations sing_155.htm#SEC195
3610	poly operations (plural) poly operations (plural) sing_445.htm#SEC485
3611	poly related functions poly related functions sing_156.htm#SEC196
3612	poly related functions (plural) poly related functions (plural) sing_446.htm#SEC486
3613	poly2list sing_586.htm#SEC640
3614	poly2zdd sing_2654.htm#SEC2735 61839
3615	polyInterpolation sing_1287.htm#SEC1368
3616	polyVars sing_681.htm#SEC735
3617	polybori sing_2638.htm#IDX1064
3618	polybori.lib sing_2638.htm#IDX1061
3619	polybori.lib sing_2638.htm#IDX1065
3620	polybori_lib sing_2638.htm#IDX1062
3621	polyclass.lib sing_2949.htm#SEC3030
3622	polyclass_lib sing_2949.htm#SEC3030
3623	polylib.lib sing_1077.htm#SEC1158
3624	polylib_lib sing_1077.htm#SEC1158
3625	polymake sing_2474.htm#IDX964
3626	polymake.lib sing_2474.htm#SEC2555
3627	polymakePolytope sing_2475.htm#SEC2556
3628	polymake_lib sing_2474.htm#SEC2555
3629	polynomial sing_2701.htm#IDX1166
3630	polynomial functions sing_2953.htm#IDX1249
3631	polynomial solutions sing_668.htm#IDX387
3632	polynomial, opposite sing_361.htm#IDX230
3633	polynomials sing_2949.htm#IDX1246
3634	polytope sing_191.htm#SEC231
3635	polytope sing_2474.htm#IDX960
3636	polytopeViaInequalities polytopeViaInequalities sing_2415.htm#SEC2496
3637	polytopeViaPoints sing_2416.htm#SEC2497
3638	pos_def sing_1223.htm#SEC1304
3639	poset sing_2623.htm#IDX1050
3640	positiveOrthant sing_2386.htm#SEC2467
3641	posweight sing_1947.htm#SEC2028
3642	powSumSym sing_1516.htm#SEC1597
3643	power sing_1184.htm#SEC1265
3644	power set sing_2667.htm#IDX1094
3645	powerN sing_2255.htm#SEC2336
3646	powerX sing_2264.htm#SEC2345
3647	power_products sing_1981.htm#SEC2062
3648	powerpolyX sing_2234.htm#SEC2315
3649	powersums sing_2357.htm#SEC2438
3650	preComp sing_1364.htm#SEC1445
3651	preimage sing_324.htm#SEC364
3652	preimage sing_722.htm#IDX392
3653	preimage (plural) sing_479.htm#SEC519
3654	preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1145.htm#IDX563
3655	preimageLattice sing_2880.htm#SEC2961
3656	preimageLoc sing_1145.htm#SEC1226
3657	preimageNC sing_724.htm#SEC778
3658	prepEmbDiv sing_1689.htm#SEC1770
3659	prepMat sing_2027.htm#SEC2108
3660	prepRealclassify sing_1795.htm#SEC1876
3661	prepSV sing_2169.htm#SEC2250
3662	prepareAss sing_1452.htm#SEC1533
3663	presentTree sing_1676.htm#SEC1757
3664	presentation sing_2838.htm#SEC2919
3665	presolve.lib sing_2046.htm#SEC2127
3666	presolve_lib sing_2046.htm#SEC2127
3667	primL sing_2259.htm#SEC2340
3668	primList sing_2258.htm#SEC2339
3669	primRoot sing_1497.htm#SEC1578
3670	primTest sing_1363.htm#SEC1444
3671	primary decomposition sing_1437.htm#IDX659
3672	primary decomposition sing_1460.htm#IDX660
3673	primary decomposition of modules sing_1353.htm#IDX636
3674	primary decomposition, numerical sing_1599.htm#IDX697
3675	primary_char0 sing_1971.htm#SEC2052
3676	primary_char0_no_molien primary_char0_no_molien sing_1973.htm#SEC2054
3677	primary_char0_no_molien_random primary_char0_no_molien_random sing_1978.htm#SEC2059
3678	primary_char0_random primary_char0_random sing_1976.htm#SEC2057
3679	primary_charp sing_1972.htm#SEC2053
3680	primary_charp_no_molien primary_charp_no_molien sing_1974.htm#SEC2055
3681	primary_charp_no_molien_random primary_charp_no_molien_random sing_1979.htm#SEC2060
3682	primary_charp_random primary_charp_random sing_1977.htm#SEC2058
3683	primary_charp_without primary_charp_without sing_1975.htm#SEC2056
3684	primary_charp_without_random primary_charp_without_random sing_1980.htm#SEC2061
3685	primary_invariants sing_1959.htm#SEC2040
3686	primary_invariants_random primary_invariants_random sing_1960.htm#SEC2041
3687	primdec.lib sing_1437.htm#SEC1518
3688	primdecGTZ sing_1439.htm#SEC1520
3689	primdecGTZE sing_1440.htm#SEC1521
3690	primdecMon sing_1352.htm#SEC1433
3691	primdecSY sing_1441.htm#SEC1522
3692	primdecSYE sing_1442.htm#SEC1523
3693	primdecZ sing_1461.htm#SEC1542
3694	primdecZM sing_1462.htm#SEC1543
3695	primdec_lib sing_1437.htm#SEC1518
3696	primdecint.lib sing_1460.htm#SEC1541
3697	primdecint_lib sing_1460.htm#SEC1541
3698	prime sing_325.htm#SEC365
3699	primeClosure sing_1396.htm#SEC1477
3700	primecoeffs sing_1029.htm#SEC1110
3701	primefactors sing_326.htm#SEC366
3702	primes sing_1024.htm#SEC1105
3703	primitiv.lib sing_1468.htm#SEC1549
3704	primitiv_lib sing_1468.htm#SEC1549
3705	primitive sing_1469.htm#SEC1550
3706	primitive element sing_1469.htm#IDX661
3707	primitiveSpan sing_2887.htm#SEC2968
3708	primitive_extra sing_1470.htm#SEC1551
3709	primparam sing_1828.htm#SEC1909
3710	principal intersection sing_502.htm#IDX319
3711	print sing_327.htm#SEC367
3712	print sing_2590.htm#IDX985
3713	print sing_2678.htm#IDX1116
3714	print sing_2680.htm#IDX1121
3715	print sing_2681.htm#IDX1122
3716	print sing_2703.htm#IDX1170
3717	print sing_2704.htm#IDX1171
3718	printBetti sing_2819.htm#SEC2900
3719	printFreeModule sing_2811.htm#SEC2892
3720	printGraph sing_1276.htm#SEC1357
3721	printGraphG sing_1715.htm#SEC1796
3722	printGroup sing_2868.htm#SEC2949
3723	printHom sing_2814.htm#SEC2895
3724	printMatrix sing_2810.htm#SEC2891
3725	printModule sing_2813.htm#SEC2894
3726	printMoebius sing_2629.htm#SEC2710
3727	printNormalFormEquation printNormalFormEquation sing_2952.htm#SEC3033
3728	printPoly sing_2951.htm#SEC3032
3729	printResolution sing_2812.htm#SEC2893
3730	printSheaf sing_1703.htm#SEC1784
3731	printStack sing_1717.htm#SEC1798
3732	printTask sing_1164.htm#SEC1245
3733	printVariety sing_1695.htm#SEC1776
3734	printf sing_328.htm#SEC368
3735	printlevel sing_404.htm#SEC444
3736	proc sing_157.htm#SEC197
3737	proc declaration sing_158.htm#SEC198
3738	proc expression sing_159.htm#SEC199
3739	procedure, ASCII help sing_56.htm#IDX125
3740	procedure, ASCII/Texinfo help sing_58.htm#IDX127
3741	procedure, texinfo help sing_57.htm#IDX126
3742	procedures, help string sing_45.htm#SEC82
3743	procedures, static Procedure definition sing_43.htm#SEC78
3744	procs with different argument types procs with different argument types sing_160.htm#SEC200
3745	prodcrit sing_2334.htm#SEC2415
3746	product sing_1025.htm#SEC1106
3747	product sing_2686.htm#IDX1132
3748	product sing_2708.htm#IDX1180
3749	product variety, abstract variety sing_1696.htm#IDX739
3750	productVariety sing_1696.htm#SEC1777
3751	productgroup sing_2889.htm#SEC2970
3752	progress watch sing_318.htm#IDX163
3753	projectLattice sing_2881.htm#SEC2962
3754	projective bundle, abstract variety, sheaf, enumeration of conics projectiveBundle sing_1700.htm#IDX743
3755	projective dimension purityfiltration_lib sing_778.htm#IDX401
3756	projective limes sing_32.htm#SEC46
3757	projective space, abstract variety sing_1699.htm#IDX742
3758	projectiveBundle sing_1700.htm#SEC1781
3759	projectiveDimension sing_779.htm#SEC833
3760	projectiveSpace sing_1699.htm#SEC1780
3761	prompt sing_15.htm#SEC21
3762	prompt, option sing_318.htm#IDX182
3763	propagator sing_1274.htm#IDX598
3764	propagator sing_1277.htm#SEC1358
3765	prot, option sing_318.htm#IDX161
3766	protocol of computations sing_318.htm#IDX162
3767	proximitymatrix sing_1756.htm#SEC1837
3768	prune sing_329.htm#SEC369
3769	pruneModule sing_2845.htm#SEC2926
3770	prwalk sing_2959.htm#SEC3040
3771	psigncnd sing_2115.htm#SEC2196
3772	puiseux2generators sing_1886.htm#SEC1967
3773	puiseuxExpansion sing_2535.htm#SEC2616
3774	pure tensor sing_495.htm#IDX307
3775	purelist sing_789.htm#SEC843
3776	purity purityfiltration_lib sing_778.htm#IDX403
3777	purityFiltration sing_780.htm#SEC834
3778	purityTriang sing_781.htm#SEC835
3779	purityfiltration.lib purityfiltration_lib sing_778.htm#IDX396
3780	purityfiltration_lib purityfiltration_lib sing_778.htm#IDX397
3781	pushForward sing_2906.htm#SEC2987
3782	pwalk sing_1298.htm#SEC1379
3783	pyobject sing_192.htm#SEC232
3784	pyobject sing_2638.htm#IDX1067
3785	pyobject declarations pyobject declarations sing_193.htm#SEC233
3786	pyobject expressions pyobject expressions sing_194.htm#SEC234
3787	pyobject operations sing_195.htm#SEC235
3788	pyobject related functions pyobject related functions sing_196.htm#SEC236
3789	pyramid sing_2727.htm#SEC2808
3790	python_eval sing_197.htm#SEC237
3791	python_import sing_198.htm#SEC238
3792	python_run sing_199.htm#SEC239
3793	qbase sing_2360.htm#SEC2441
3794	qepcad sing_2737.htm#SEC2818
3795	qepcadsystem sing_2738.htm#SEC2819
3796	qhmatrix sing_1945.htm#SEC2026
3797	qhmoduli.lib sing_1903.htm#SEC1984
3798	qhmoduli_lib sing_1903.htm#SEC1984
3799	qhspectrum sing_1932.htm#SEC2013
3800	qhweight sing_330.htm#SEC370
3801	qmatrix.lib sing_790.htm#SEC844
3802	qmatrix_lib sing_790.htm#SEC844
3803	qminor sing_792.htm#SEC846
3804	qrds sing_331.htm#SEC371
3805	qring Miscellaneous oddities sing_166.htm#SEC206
3806	qring sing_422.htm#IDX295
3807	qring (plural) sing_447.htm#SEC487
3808	qring declaration sing_170.htm#SEC210
3809	qring declaration (plural) qring declaration (plural) sing_448.htm#SEC488
3810	qring related functions (plural) qring related functions (plural) sing_449.htm#SEC489
3811	qring ring ideal 'factor ring' sing_1154.htm#IDX569
3812	qringNF, option sing_318.htm#IDX164
3813	qslimgb sing_1004.htm#SEC1085
3814	quadraticSieve sing_2272.htm#SEC2353
3815	quantMat sing_791.htm#SEC845
3816	quickclass sing_1787.htm#SEC1868
3817	quit sing_394.htm#SEC434
3818	quotSheaf sing_1712.htm#SEC1793
3819	quote sing_332.htm#SEC372
3820	quotient sing_333.htm#SEC373
3821	quotient (plural) sing_480.htm#SEC520
3822	quotientLatticeBasis quotientLatticeBasis sing_2417.htm#SEC2498
3823	quotientMain sing_2126.htm#SEC2207
3824	quotientMon sing_1343.htm#SEC1424
3825	rHRR sing_1556.htm#SEC1637
3826	rJanet sing_1482.htm#SEC1563
3827	rMacaulay sing_1063.htm#SEC1144
3828	rad_con sing_1090.htm#SEC1171
3829	radical sing_1449.htm#SEC1530
3830	radicalEHV sing_1450.htm#SEC1531
3831	radicalMemberShip sing_2557.htm#SEC2638
3832	radicalMon sing_1344.htm#SEC1425
3833	radicalZ sing_1464.htm#SEC1545
3834	randcharpoly sing_2354.htm#SEC2435
3835	randlinpoly sing_2356.htm#SEC2437
3836	random sing_334.htm#SEC374
3837	random sing_361.htm#IDX242
3838	random sing_2611.htm#IDX1024
3839	random sing_2612.htm#IDX1026
3840	random number generator, seed sing_361.htm#IDX240
3841	random.lib sing_1113.htm#SEC1194
3842	randomBinomial sing_1125.htm#SEC1206
3843	randomCheck sing_2185.htm#SEC2266
3844	randomLast sing_1124.htm#SEC1205
3845	randomPoint sing_2418.htm#SEC2499
3846	randomPolyInT sing_2566.htm#SEC2647
3847	random_lib sing_1113.htm#SEC1194
3848	randomid sing_1115.htm#SEC1196
3849	randommat sing_1116.htm#SEC1197
3850	rank sing_210.htm#IDX137
3851	rank sing_335.htm#SEC375
3852	rankSheaf sing_1704.htm#SEC1785
3853	ratSol sing_676.htm#SEC730
3854	ratgb.lib sing_796.htm#IDX404
3855	ratgb_lib sing_796.htm#IDX405
3856	rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1621.htm#IDX724
3857	rational functions sing_880.htm#IDX436
3858	rational normal curve, projection. sing_1622.htm#IDX725
3859	rational normal curve, projection. sing_1625.htm#IDX726
3860	rational normal curve, projection. sing_1626.htm#IDX727
3861	rational solutions sing_668.htm#IDX388
3862	rational univariate projection sing_2354.htm#IDX956
3863	rationalCurve sing_1724.htm#SEC1805
3864	rationalPointConic sing_1623.htm#SEC1704
3865	ratstd sing_797.htm#SEC851
3866	rays sing_2419.htm#SEC2500
3867	rcgs sing_1110.htm#SEC1191
3868	rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs rcgs sing_1109.htm#IDX556
3869	rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs sing_1110.htm#IDX557
3870	rcolon sing_879.htm#SEC933
3871	re2squ sing_1600.htm#SEC1681
3872	read sing_336.htm#SEC376
3873	readInputTXT sing_2946.htm#SEC3027
3874	readNmzData sing_1424.htm#SEC1505 18957
3875	reading, option sing_318.htm#IDX183
3876	readline sing_1.htm#IDX5
3877	real sing_28.htm#IDX74
3878	real root isolation sing_2100.htm#IDX931
3879	real roots, univariate polynomial sing_2361.htm#IDX958
3880	real roots, univariate projection sing_2345.htm#IDX954
3881	real roots,sign conditions sing_2113.htm#IDX934
3882	realLLL sing_2099.htm#SEC2180
3883	realclassify sing_1914.htm#SEC1995
3884	realclassify.lib sing_1913.htm#SEC1994
3885	realclassify_lib sing_1913.htm#SEC1994
3886	realizationDim sing_2529.htm#SEC2610
3887	realizationDimPoly sing_2531.htm#SEC2612
3888	realizationMatroids.lib realizationMatroids_lib sing_2528.htm#SEC2609
3889	realizationMatroids_lib realizationMatroids_lib sing_2528.htm#SEC2609
3890	realmorsesplit sing_1915.htm#SEC1996
3891	realpoly sing_1473.htm#SEC1554
3892	realrad sing_1475.htm#SEC1556
3893	realrad.lib sing_1472.htm#SEC1553
3894	realrad_lib sing_1472.htm#SEC1553
3895	realzero sing_1474.htm#SEC1555
3896	recover.lib sing_2082.htm#SEC2163
3897	recover_lib sing_2082.htm#SEC2163
3898	recursive_boolean_poly recursive_boolean_poly sing_2644.htm#SEC2725 17045
3899	recursive_from_boolean_poly recursive_from_boolean_poly sing_2650.htm#SEC2731 37794
3900	redSB, option sing_318.htm#IDX165
3901	redTail, option sing_318.htm#IDX167
3902	redThrough, option sing_318.htm#IDX168
3903	redcgs.lib sing_1098.htm#SEC1179
3904	redcgs_lib sing_1098.htm#SEC1179
3905	redefine, option sing_318.htm#IDX184
3906	redspec sing_1104.htm#SEC1185
3907	reduce sing_337.htm#SEC377
3908	reduce sing_516.htm#IDX324
3909	reduce sing_1036.htm#IDX481
3910	reduce sing_1037.htm#IDX484
3911	reduce (letterplace) reduce (letterplace) sing_809.htm#SEC863
3912	reduce (plural) sing_481.htm#SEC521
3913	reduce (up to a bound) sing_361.htm#IDX243
3914	reduceIntChain sing_2850.htm#SEC2931
3915	reduced sing_1035.htm#IDX478
3916	reduced standard basis sing_318.htm#IDX166
3917	reduction sing_1997.htm#SEC2078
3918	reesclos.lib sing_1476.htm#SEC1557
3919	reesclos_lib sing_1476.htm#SEC1557
3920	reference sing_200.htm#SEC240
3921	reference declarations reference declarations sing_201.htm#SEC241
3922	reference expressions reference expressions sing_202.htm#SEC242
3923	reference operations reference and shared operations sing_205.htm#SEC245
3924	reference related functions reference and shared related functions sing_206.htm#SEC246
3925	regCM sing_1388.htm#SEC1469
3926	regIdeal sing_1369.htm#SEC1450
3927	regMonCurve sing_1372.htm#SEC1453
3928	regularity Syzygies and resolutions sing_338.htm#SEC378
3929	regularity sing_979.htm#SEC1041
3930	regularity sing_1388.htm#IDX641
3931	regularity sing_1389.htm#IDX642
3932	reiffen sing_555.htm#SEC609
3933	rel_orbit_variety sing_1990.htm#SEC2071
3934	relations sing_776.htm#IDX395
3935	relativeInteriorPoint relativeInteriorPoint sing_2420.htm#SEC2501
3936	relative_orbit_variety relative_orbit_variety sing_1991.htm#SEC2072
3937	relweight sing_1946.htm#SEC2027
3938	remainder sing_2119.htm#SEC2200
3939	remainderMain sing_2127.htm#SEC2208
3940	removeCone sing_2438.htm#SEC2519
3941	removepower sing_1766.htm#SEC1847
3942	repart sing_339.htm#SEC379
3943	replace sing_2224.htm#SEC2305
3944	representation, math objects Representation of mathematical objects sing_965.htm#SEC1022
3945	res sing_340.htm#SEC380
3946	resbinomial.lib sing_1630.htm#IDX730
3947	resbinomial_lib sing_1630.htm#IDX731
3948	reservedName sing_341.htm#SEC381
3949	resfunction sing_1644.htm#SEC1725
3950	resgraph.lib sing_1662.htm#SEC1743
3951	resgraph_lib sing_1662.htm#SEC1743
3952	resjung.lib sing_1666.htm#SEC1747
3953	resjung_lib sing_1666.htm#SEC1747
3954	reslist sing_1658.htm#SEC1739
3955	resolution purityfiltration_lib sing_161.htm#SEC201
3956	resolution sing_778.htm#IDX402
3957	resolution (plural) sing_450.htm#SEC490
3958	resolution declarations resolution declarations sing_162.htm#SEC202
3959	resolution declarations (plural) resolution declarations (plural) sing_451.htm#SEC491
3960	resolution expressions resolution expressions sing_163.htm#SEC203
3961	resolution expressions (plural) resolution expressions (plural) sing_452.htm#SEC492
3962	resolution graph sing_1751.htm#IDX768
3963	resolution related functions resolution related functions sing_164.htm#SEC204
3964	resolution related functions (plural) resolution related functions (plural) sing_453.htm#SEC493
3965	resolution, La Scala's method sing_291.htm#SEC331
3966	resolution, computation of sing_340.htm#IDX186
3967	resolution, hilbert-driven sing_266.htm#SEC306
3968	resolutionInLocalization resolutionInLocalization sing_2757.htm#SEC2838
3969	resolutiongraph sing_1752.htm#SEC1833
3970	resolve sing_1674.htm#SEC1755
3971	resolve.lib sing_1670.htm#SEC1751
3972	resolve_lib sing_1670.htm#SEC1751
3973	resources.lib sing_1126.htm#SEC1207
3974	resources_lib sing_1126.htm#SEC1207
3975	restriction sing_2604.htm#IDX1012
3976	restriction sing_2620.htm#IDX1045
3977	restriction sing_2621.htm#IDX1047
3978	restriction of sing_560.htm#IDX347
3979	restrictionIdeal sing_570.htm#SEC624
3980	restrictionModule sing_571.htm#SEC625
3981	resultant sing_305.htm#SEC345
3982	resultant sing_342.htm#SEC382
3983	reszeta.lib sing_1683.htm#SEC1764
3984	reszeta_lib sing_1683.htm#SEC1764
3985	return sing_395.htm#SEC435
3986	return type of procedures Return type of procedures sing_420.htm#SEC460
3987	returnSB, option sing_318.htm#IDX152
3988	reverse sing_2375.htm#SEC2456
3989	reverse lexicographical ordering sing_969.htm#IDX442
3990	reynolds_molien sing_1966.htm#SEC2047
3991	rho sing_2266.htm#SEC2347
3992	rightInverse sing_2204.htm#SEC2285
3993	rightKernel sing_2202.htm#SEC2283
3994	rightModulo sing_742.htm#SEC796
3995	rightNF sing_741.htm#SEC795
3996	rightNFWeyl sing_693.htm#SEC747
3997	rightOre sing_762.htm#SEC816
3998	rightStd sing_740.htm#SEC794
3999	rightstd (letterplace) rightstd (letterplace) sing_810.htm#SEC864
4000	ring sing_165.htm#SEC205
4001	ring (plural) sing_454.htm#SEC494
4002	ring coefficients hasTransExtensionCoefficient sing_1152.htm#IDX567
4003	ring coefficients sing_1153.htm#IDX568
4004	ring declarations sing_167.htm#SEC207
4005	ring declarations (plural) ring declarations (plural) sing_455.htm#SEC495
4006	ring operations sing_169.htm#SEC209
4007	ring operations (plural) ring operations (plural) sing_456.htm#SEC496
4008	ring related functions ring related functions sing_168.htm#SEC208
4009	ring related functions (plural) ring related functions (plural) sing_457.htm#SEC497
4010	ring theory sing_856.htm#IDX417
4011	ring, opposite sing_361.htm#IDX227
4012	ring, rings sing_1099.htm#IDX548
4013	ring.lib sing_1131.htm#SEC1212
4014	ring_cf sing_210.htm#IDX138
4015	ring_lib sing_1131.htm#SEC1212
4016	ring_list sing_344.htm#SEC384
4017	ring_variable sing_2591.htm#IDX989
4018	ring_variable sing_2592.htm#IDX991
4019	ring_variable sing_2593.htm#IDX995
4020	ring_variable sing_2594.htm#IDX997
4021	ringgb.lib sing_2953.htm#SEC3034
4022	ringgb.lib, functions for coefficient rings sing_2953.htm#IDX1251
4023	ringgb_lib sing_2953.htm#SEC3034
4024	ringlist sing_343.htm#SEC383
4025	ringlist (plural) sing_482.htm#SEC522
4026	ringtensor sing_1143.htm#SEC1224
4027	ringweights sing_1144.htm#SEC1225
4028	rinvar.lib sing_2002.htm#SEC2083
4029	rinvar_lib sing_2002.htm#SEC2083
4030	rmNmzFiles sing_1429.htm#SEC1510 32601
4031	rm_unitcol sing_1201.htm#SEC1282
4032	rm_unitrow sing_1200.htm#SEC1281
4033	rmx sing_2149.htm#SEC2230
4034	rncAntiCanonicalMap sing_1622.htm#SEC1703
4035	rncItProjEven sing_1626.htm#SEC1707
4036	rncItProjOdd sing_1625.htm#SEC1706
4037	root of Bernstein-Sato polynomial sing_537.htm#IDX336
4038	rootIsolation sing_2111.htm#SEC2192
4039	rootIsolationNoPreprocessing rootIsolationNoPreprocessing sing_2110.htm#SEC2191
4040	rootIsolationPrimdec rootIsolationPrimdec sing_2112.htm#SEC2193
4041	rootisolation.lib sing_2100.htm#SEC2181
4042	rootisolation_lib sing_2100.htm#SEC2181
4043	rootofUnity sing_1146.htm#SEC1227
4044	roots sing_2120.htm#SEC2201
4045	rootsMain sing_2128.htm#SEC2209
4046	rootsModp sing_2248.htm#SEC2329
4047	rootsmr.lib sing_2345.htm#SEC2426
4048	rootsmr_lib sing_2345.htm#SEC2426
4049	rootsur.lib sing_2361.htm#SEC2442
4050	rootsur_lib sing_2361.htm#SEC2442
4051	round sing_2246.htm#SEC2327
4052	rowShift sing_210.htm#IDX141
4053	rowShift sing_212.htm#SEC252
4054	rowred sing_1197.htm#SEC1278
4055	rp, global ordering sing_969.htm#IDX441
4056	rstandard.lib sing_1479.htm#SEC1560
4057	rstandard_lib sing_1479.htm#SEC1560
4058	rswalk sing_2980.htm#SEC3061
4059	rtimer sing_408.htm#SEC448
4060	rvalue No rvalue of increments and assignments sing_414.htm#SEC454
4061	rvar sing_345.htm#SEC385
4062	rwalk sing_2960.htm#SEC3041
4063	rwalk.lib sing_2958.htm#SEC3039
4064	rwalk_lib sing_2958.htm#SEC3039
4065	sPiece sing_2976.htm#SEC3057
4066	sRes sing_2816.htm#SEC2897
4067	sa_poly_reduce sing_525.htm#SEC579
4068	sa_reduce sing_524.htm#SEC578
4069	sagbi sing_1487.htm#SEC1568
4070	sagbi basis sing_1807.htm#IDX795
4071	sagbi.lib sing_1484.htm#SEC1565
4072	sagbiAlg sing_1800.htm#SEC1881
4073	sagbiMod sing_1801.htm#SEC1882
4074	sagbiPart sing_1488.htm#SEC1569
4075	sagbiReduce sing_1486.htm#SEC1567
4076	sagbiSPoly sing_1485.htm#SEC1566
4077	sagbi_lib sing_1484.htm#SEC1565
4078	salida sing_1655.htm#SEC1736
4079	sameComponent sing_2328.htm#SEC2409
4080	sameQ sing_2131.htm#SEC2212
4081	sat sing_1271.htm#SEC1352
4082	satiety sing_1371.htm#SEC1452
4083	satstd sing_2632.htm#SEC2713
4084	saturation sing_1271.htm#IDX592
4085	saturation sing_1329.htm#IDX631
4086	saturation sing_1386.htm#IDX639
4087	saturation sing_1387.htm#IDX640
4088	sba sing_346.htm#SEC386
4089	scalarProd sing_514.htm#SEC568
4090	scheme sing_2718.htm#SEC2799
4091	schubert.lib sing_1693.htm#SEC1774
4092	schubert_lib sing_1693.htm#SEC1774
4093	sdb, source code debugger Source code debugger sing_66.htm#SEC103
4094	second degree sing_1050.htm#IDX524
4095	second order deformation. sing_2973.htm#IDX1261
4096	secondary fan sing_2474.htm#IDX962
4097	secondary polytope sing_2474.htm#IDX963
4098	secondaryPolytope sing_2479.htm#SEC2560
4099	secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1987.htm#SEC2068
4100	secondary_char0 sing_1982.htm#SEC2063
4101	secondary_charp sing_1984.htm#SEC2065
4102	secondary_no_molien sing_1985.htm#SEC2066
4103	secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1988.htm#SEC2069
4104	segre sing_1511.htm#SEC1592
4105	select sing_1272.htm#SEC1353
4106	select1 sing_1273.htm#SEC1354
4107	semaphore sing_361.htm#IDX247
4108	semaphore sing_1130.htm#SEC1211
4109	semaphores sing_1126.htm#IDX562
4110	semi-prime ideal sing_856.htm#IDX422
4111	semiCMcod2 sing_1943.htm#SEC2024
4112	semiGroup sing_1802.htm#SEC1883
4113	semiMod sing_1803.htm#SEC1884
4114	semidiv sing_2320.htm#SEC2401
4115	semigroup sing_1755.htm#SEC1836
4116	semigroup sing_1759.htm#IDX775
4117	semigroup of values sing_1876.htm#IDX896
4118	semigroupGenerator sing_2421.htm#SEC2502
4119	sep sing_1459.htm#SEC1540
4120	separateHNE sing_1887.htm#SEC1968
4121	separator sing_1354.htm#SEC1435
4122	serreRelations sing_829.htm#SEC883
4123	set sing_2586.htm#IDX975
4124	set sing_2963.htm#SEC3044
4125	set, intersectionSet, union, complement, equality, isEqual sets_lib sing_2962.htm#IDX1257
4126	setBaseMultigrading sing_2861.htm#SEC2942
4127	setLetterplaceAttributes setLetterplaceAttributes sing_874.htm#SEC928
4128	setLinearForms sing_2422.htm#SEC2503
4129	setModuleGrading sing_2873.htm#SEC2954
4130	setMultiplicity sing_2423.htm#SEC2504
4131	setNmzDataPath sing_1426.htm#SEC1507 18123
4132	setNmzExecPath sing_1422.htm#SEC1503 38993
4133	setNmzFilename sing_1425.htm#SEC1506 20206
4134	setNmzOption sing_1419.htm#SEC1500 9012
4135	setUniformizingParameter setUniformizingParameter sing_2576.htm#SEC2657
4136	set_is_injective sing_2308.htm#SEC2389
4137	setcores sing_1128.htm#SEC1209
4138	setenv sing_361.htm#IDX250
4139	setglobalrings sing_1099.htm#SEC1180
4140	setinitials sing_2728.htm#SEC2809
4141	setring sing_347.htm#SEC387
4142	sets.lib sing_2962.htm#SEC3043
4143	sets_lib sing_2962.htm#SEC3043
4144	sh sing_361.htm#IDX252
4145	shared sing_200.htm#SEC240
4146	shared declarations sing_203.htm#SEC243
4147	shared expressions sing_204.htm#SEC244
4148	shared operations reference and shared operations sing_205.htm#SEC245
4149	shared related functions reference and shared related functions sing_206.htm#SEC246
4150	sheaf cohomology sing_1732.htm#IDX756
4151	sheafCoh sing_1738.htm#SEC1819 64501
4152	sheafCohBGG sing_1736.htm#SEC1817 13439
4153	sheafCohBGG2 sing_1737.htm#SEC1818 3338
4154	sheafcoh.lib sing_1732.htm#SEC1813
4155	sheafcoh_lib sing_1732.htm#SEC1813
4156	short sing_405.htm#SEC445
4157	show sing_1064.htm#SEC1145
4158	showBO sing_1675.htm#SEC1756
4159	showDataTypes sing_1677.htm#SEC1758
4160	showNmzOptions sing_1420.htm#SEC1501 64955
4161	showNuminvs sing_1417.htm#SEC1498 18934
4162	showgrades sing_783.htm#SEC837
4163	showrecursive sing_1065.htm#SEC1146
4164	signal handler sing_3001.htm#SEC3098
4165	signatureBrieskorn sing_1952.htm#SEC2033
4166	signatureL sing_2634.htm#SEC2715
4167	signatureLqf sing_2635.htm#SEC2716
4168	signatureNemethi sing_1954.htm#SEC2035
4169	signaturePuiseux sing_1953.htm#SEC2034
4170	signcnd sing_2114.htm#SEC2195
4171	signcond.lib sing_2113.htm#SEC2194
4172	signcond_lib sing_2113.htm#SEC2194
4173	simplePrune sing_2854.htm#SEC2935
4174	simplesolver sing_2033.htm#SEC2114
4175	simplex sing_348.htm#SEC388
4176	simplexOut sing_2069.htm#SEC2150
4177	simplify sing_349.htm#SEC389
4178	simplifyRat sing_688.htm#SEC742
4179	sing.lib sing_1919.htm#SEC2000
4180	sing4ti2.lib sing_1490.htm#SEC1571
4181	sing4ti2_lib sing_1490.htm#SEC1571
4182	sing_lib sing_1919.htm#SEC2000
4183	singular locus of D-module sing_668.htm#IDX382
4184	singularities sing_1769.htm#IDX786
4185	singularities sing_1796.htm#IDX790
4186	singularities sing_1845.htm#IDX798
4187	singularities sing_1846.htm#IDX809
4188	singularities sing_1847.htm#IDX812
4189	singularities sing_1848.htm#IDX815
4190	singularities sing_1849.htm#IDX818
4191	singularities sing_1850.htm#IDX822
4192	singularities sing_1851.htm#IDX826
4193	singularities sing_1852.htm#IDX832
4194	singularities sing_1853.htm#IDX840
4195	singularities sing_1854.htm#IDX846
4196	singularities sing_1855.htm#IDX854
4197	singularities sing_1856.htm#IDX864
4198	singularities sing_1950.htm#IDX918
4199	singularities, resolution of Resolution of singularities sing_952.htm#SEC1009
4200	singularity sing_1788.htm#SEC1869
4201	singularrc sing_20.htm#IDX73
4202	size Miscellaneous oddities sing_350.htm#SEC390
4203	size sing_422.htm#IDX294
4204	skewmat sing_1185.htm#SEC1266
4205	sleep sing_356.htm#SEC396
4206	slimgb sing_351.htm#SEC391
4207	slimgb sing_929.htm#SEC986
4208	slimgb (plural) sing_483.htm#SEC523
4209	slocus sing_1931.htm#SEC2012
4210	smaller sing_2691.htm#IDX1142
4211	smatrix sing_171.htm#SEC211
4212	smith sing_2213.htm#SEC2294
4213	smithNormalForm sing_2909.htm#SEC2990
4214	solutionsMod2 sing_2263.htm#SEC2344
4215	solve sing_282.htm#SEC322
4216	solve sing_1050.htm#IDX525
4217	solve sing_2063.htm#SEC2144
4218	solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_294.htm#SEC334
4219	solve.lib sing_2061.htm#SEC2142
4220	solveTInitialFormPar solveTInitialFormPar sing_2560.htm#SEC2641
4221	solve_IP sing_1324.htm#SEC1405
4222	solve_lib sing_2061.htm#SEC2142
4223	solvelinearpart sing_2056.htm#SEC2137
4224	solving sing_2082.htm#IDX929
4225	sort sing_1026.htm#SEC1107
4226	sort sing_2696.htm#IDX1152
4227	sortIntvec sing_591.htm#SEC645
4228	sortandmap sing_2057.htm#SEC2138
4229	sortier sing_2001.htm#SEC2082
4230	sortvars sing_2058.htm#SEC2139
4231	sortvec sing_352.htm#SEC392
4232	source sing_2832.htm#SEC2913
4233	source code debugger, sdb Source code debugger sing_66.htm#SEC103
4234	spaceCur sing_1805.htm#SEC1886
4235	spadd sing_1859.htm#SEC1940
4236	span sing_2424.htm#SEC2505
4237	sparseHomogIdeal sing_1122.htm#SEC1203
4238	sparseInterpolation sing_1291.htm#SEC1372
4239	sparseid sing_1117.htm#SEC1198
4240	sparsemat sing_1119.htm#SEC1200
4241	sparsematrix sing_1118.htm#SEC1199
4242	sparsepoly sing_1120.htm#SEC1201
4243	sparsetriag sing_1121.htm#SEC1202
4244	spcurve.lib sing_1939.htm#SEC2020
4245	spcurve_lib sing_1939.htm#SEC2020
4246	special characters, non-english sing_411.htm#IDX287
4247	specification sing_1104.htm#IDX551
4248	spectral pairs sing_1845.htm#IDX807
4249	spectral pairs sing_1852.htm#IDX839
4250	spectral pairs sing_1854.htm#IDX853
4251	spectral pairs sing_1855.htm#IDX862
4252	spectral pairs sing_1867.htm#IDX878
4253	spectral pairs sing_1869.htm#IDX889
4254	spectralNeg sing_1685.htm#SEC1766
4255	spectrum sing_1845.htm#IDX806
4256	spectrum sing_1851.htm#SEC1932
4257	spectrum sing_1851.htm#IDX831
4258	spectrum sing_1852.htm#IDX838
4259	spectrum sing_1853.htm#IDX845
4260	spectrum sing_1854.htm#IDX852
4261	spectrum sing_1855.htm#IDX861
4262	spectrum sing_1867.htm#IDX877
4263	spectrum sing_1869.htm#IDX888
4264	spectrum sing_1950.htm#IDX920
4265	spectrum.lib sing_1949.htm#SEC2030
4266	spectrum_lib sing_1949.htm#SEC2030
4267	spectrumnd sing_1950.htm#SEC2031
4268	spgamma sing_1866.htm#SEC1947
4269	spgeomgenus sing_1865.htm#SEC1946
4270	spissemicont sing_1862.htm#SEC1943
4271	split sing_1066.htm#SEC1147
4272	splitPolygon sing_2481.htm#SEC2562
4273	splitring sing_1471.htm#SEC1552
4274	splitting sing_1362.htm#SEC1443
4275	spmilnor sing_1864.htm#SEC1945
4276	spmul sing_1861.htm#SEC1942
4277	spnf sing_1227.htm#SEC1308
4278	spoly sing_2331.htm#SEC2412
4279	sppairs sing_1852.htm#SEC1933
4280	sppnf sing_1857.htm#SEC1938
4281	sppprint sing_1858.htm#SEC1939
4282	spprint sing_1228.htm#SEC1309
4283	sprintf sing_354.htm#SEC394
4284	spsemicont sing_1863.htm#SEC1944
4285	spsub sing_1860.htm#SEC1941
4286	sqfrNorm sing_2121.htm#SEC2202
4287	sqfrNormMain sing_2129.htm#SEC2210
4288	sqr sing_2243.htm#SEC2324
4289	sqrfree sing_353.htm#SEC393
4290	squareRoot sing_2262.htm#SEC2343
4291	squarefree sing_1888.htm#SEC1969
4292	sres sing_355.htm#SEC395
4293	ssi Parallelization with ssi links sing_924.htm#SEC981
4294	stabilizer sing_2662.htm#SEC2743
4295	stack, moduli space of stable maps sing_1717.htm#IDX747
4296	stack, moduli space of stable maps, rational curves moduliSpace sing_1716.htm#IDX746
4297	stackNets sing_2937.htm#SEC3018
4298	staircase sing_2134.htm#SEC2215
4299	standard sing_2338.htm#SEC2419
4300	standard bases, saturation sing_2632.htm#IDX1058
4301	standard bases. sing_2631.htm#IDX1057
4302	standard.lib sing_1003.htm#IDX469
4303	standard_lib sing_1003.htm#IDX470
4304	stanleyreisner.lib sing_2971.htm#SEC3052
4305	stanleyreisner_lib sing_2971.htm#SEC3052
4306	startNmz sing_1428.htm#SEC1509 21925
4307	startTasks sing_1165.htm#SEC1246
4308	static procedures Procedure definition sing_43.htm#SEC78
4309	status sing_356.htm#SEC396
4310	std sing_357.htm#SEC397
4311	std sing_927.htm#SEC984
4312	std (letterplace) sing_811.htm#SEC865
4313	std (plural) sing_484.htm#SEC524
4314	stdfglm sing_358.htm#SEC398
4315	stdhilb sing_359.htm#SEC399
4316	stdlocus sing_1047.htm#SEC1128
4317	stopTask sing_1166.htm#SEC1247
4318	storeActionOnOrbitConeIndices storeActionOnOrbitConeIndices sing_2462.htm#SEC2543
4319	stratify sing_2028.htm#SEC2109
4320	stratify.lib sing_2026.htm#SEC2107
4321	stratify_lib sing_2026.htm#SEC2107
4322	string Miscellaneous oddities sing_172.htm#SEC212
4323	string sing_422.htm#IDX297
4324	string sing_2678.htm#IDX1115
4325	string sing_2680.htm#IDX1120
4326	string sing_2681.htm#IDX1123
4327	string sing_2703.htm#IDX1169
4328	string sing_2704.htm#IDX1172
4329	string declarations sing_173.htm#SEC213
4330	string expressions sing_174.htm#SEC214
4331	string operations sing_176.htm#SEC216
4332	string related functions string related functions sing_177.htm#SEC217
4333	string type cast sing_175.htm#SEC215
4334	stripHNE sing_1885.htm#SEC1966
4335	structure sing_2700.htm#IDX1163
4336	sturm sing_2371.htm#SEC2452
4337	sturmha sing_2373.htm#SEC2454
4338	sturmhaseq sing_2374.htm#SEC2455
4339	sturmquery sing_2349.htm#SEC2430
4340	sturmseq sing_2372.htm#SEC2453
4341	sublists sing_2667.htm#SEC2748
4342	submat sing_1186.htm#SEC1267
4343	subquotient sing_2824.htm#SEC2905
4344	subrInterred sing_1095.htm#SEC1176
4345	subset sing_1101.htm#SEC1182
4346	subset_sum01 sing_2292.htm#SEC2373
4347	subset_sum02 sing_2293.htm#SEC2374
4348	subst sing_360.htm#SEC400
4349	subst (plural) sing_485.htm#SEC525
4350	substAll sing_2083.htm#SEC2164
4351	substitute sing_1094.htm#SEC1175
4352	sugarCrit, option sing_318.htm#IDX169
4353	sum sing_1027.htm#SEC1108
4354	sum sing_2683.htm#IDX1126
4355	sum sing_2705.htm#IDX1174
4356	sum_of_powers sing_1515.htm#SEC1596
4357	sumlist sing_1657.htm#SEC1738
4358	sumofquotients sing_1725.htm#SEC1806
4359	super-commutative algebras Graded commutative algebras (SCA) sing_798.htm#SEC852
4360	superCommutative sing_739.htm#SEC793
4361	super_increasing_knapsack super_increasing_knapsack sing_2304.htm#SEC2385
4362	surf.lib sing_2151.htm#SEC2232
4363	surf_lib sing_2151.htm#SEC2232
4364	surfacesignature.lib surfacesignature_lib sing_1951.htm#SEC2032
4365	surfacesignature_lib surfacesignature_lib sing_1951.htm#SEC2032
4366	surfer sing_1.htm#IDX8
4367	surfer sing_2153.htm#SEC2234
4368	surfex sing_1.htm#IDX7
4369	surfex.lib sing_2154.htm#SEC2235
4370	surfex_lib sing_2154.htm#SEC2235
4371	suspend sing_356.htm#SEC396
4372	swalk sing_2979.htm#SEC3060
4373	swalk.lib sing_2978.htm#SEC3059
4374	swalk_lib sing_2978.htm#SEC3059
4375	swap sing_1792.htm#SEC1873
4376	swap sing_2593.htm#IDX993
4377	switch No case or switch statement sing_416.htm#SEC456
4378	switchRingsAndComputeInitialIdeal switchRingsAndComputeInitialIdeal sing_2581.htm#SEC2662
4379	syModStd sing_1500.htm#SEC1581
4380	symNsym sing_1509.htm#SEC1590
4381	sym_gauss sing_1211.htm#SEC1292
4382	symm sing_1508.htm#SEC1589
4383	symmStd sing_1499.htm#SEC1580
4384	symmat sing_1187.htm#SEC1268
4385	symmetric basis sing_1203.htm#IDX573
4386	symmetric power sing_1205.htm#IDX575
4387	symmetric product sing_2739.htm#IDX1203
4388	symmetricBasis sing_1203.htm#SEC1284
4389	symmetricPower sing_1205.htm#SEC1286
4390	symmetricPowerSheaf sing_1711.htm#SEC1792
4391	symmetries sing_2658.htm#IDX1091
4392	symmfunc sing_2358.htm#SEC2439
4393	symodstd.lib sing_1494.htm#SEC1575
4394	symodstd_lib sing_1494.htm#SEC1575
4395	sympower sing_2022.htm#SEC2103
4396	symsignature sing_2348.htm#SEC2429
4397	syndrome sing_2181.htm#SEC2262
4398	sysBin sing_2179.htm#SEC2260
4399	sysCRHT sing_2176.htm#SEC2257
4400	sysCRHTMindist sing_2177.htm#SEC2258
4401	sysFL sing_2192.htm#SEC2273
4402	sysNewton sing_2178.htm#SEC2259
4403	sysQE sing_2182.htm#SEC2263
4404	sys_code sing_2173.htm#SEC2254
4405	system sing_361.htm#SEC401
4406	system, -- sing_361.htm#IDX277
4407	system, --long_option_name sing_361.htm#IDX280
4408	system, --long_option_name=value sing_361.htm#IDX282
4409	system, HC sing_361.htm#IDX213
4410	system, LLL sing_361.htm#IDX217
4411	system, Singular sing_361.htm#IDX256
4412	system, SingularLib sing_361.htm#IDX258
4413	system, absFact sing_361.htm#IDX190
4414	system, alarm sing_361.htm#IDX189
4415	system, blackbox sing_361.htm#IDX191
4416	system, bracket sing_361.htm#IDX196
4417	system, browsers sing_361.htm#IDX195
4418	system, complexNearZero sing_361.htm#IDX198
4419	system, contributors sing_361.htm#IDX200
4420	system, cpu sing_361.htm#IDX202
4421	system, cpu sing_361.htm#IDX276
4422	system, denom_list sing_361.htm#IDX204
4423	system, eigenvals sing_361.htm#IDX205
4424	system, env sing_361.htm#IDX206
4425	system, executable sing_361.htm#IDX208
4426	system, getPrecDigits sing_361.htm#IDX211
4427	system, getenv sing_361.htm#IDX210
4428	system, gmsnf sing_361.htm#IDX212
4429	system, hessenberg sing_361.htm#IDX214
4430	system, install sing_361.htm#IDX216
4431	system, nblocks sing_361.htm#IDX220
4432	system, nc_hilb sing_361.htm#IDX222
4433	system, neworder sing_361.htm#IDX223
4434	system, newstruct sing_361.htm#IDX224
4435	system, opp sing_361.htm#IDX225
4436	system, oppose sing_361.htm#IDX228
4437	system, pcvBasis sing_361.htm#IDX237
4438	system, pcvCV2P sing_361.htm#IDX235
4439	system, pcvDim sing_361.htm#IDX236
4440	system, pcvLAddL sing_361.htm#IDX231
4441	system, pcvMinDeg sing_361.htm#IDX233
4442	system, pcvP2CV sing_361.htm#IDX234
4443	system, pcvPMulL sing_361.htm#IDX232
4444	system, pid sing_361.htm#IDX239
4445	system, random sing_361.htm#IDX241
4446	system, reserve sing_361.htm#IDX245
4447	system, reservedLink sing_361.htm#IDX246
4448	system, semaphore sing_361.htm#IDX248
4449	system, semic sing_361.htm#IDX249
4450	system, setenv sing_361.htm#IDX251
4451	system, sh sing_361.htm#IDX253
4452	system, shrinktest sing_361.htm#IDX254
4453	system, spadd sing_361.htm#IDX259
4454	system, spectrum sing_361.htm#IDX260
4455	system, spmul sing_361.htm#IDX261
4456	system, std_syz sing_361.htm#IDX262
4457	system, tensorModuleMult sing_361.htm#IDX263
4458	system, twostd sing_361.htm#IDX264
4459	system, uname sing_361.htm#IDX267
4460	system, verifyGB sing_361.htm#IDX270
4461	system, version sing_361.htm#IDX273
4462	system, with sing_361.htm#IDX274
4463	systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2754.htm#SEC2835
4464	systhreads.lib sing_2981.htm#SEC3062
4465	systhreads_lib sing_2981.htm#SEC3062
4466	syz sing_362.htm#SEC402
4467	syz (letterplace) sing_812.htm#SEC866
4468	syz (plural) sing_486.htm#SEC526
4469	tDetropicalise sing_2562.htm#SEC2643
4470	tInitialForm sing_2546.htm#SEC2627
4471	tInitialFormPar sing_2558.htm#SEC2639
4472	tInitialFormParMax sing_2559.htm#SEC2640
4473	tInitialIdeal sing_2547.htm#SEC2628
4474	tab sing_1067.htm#SEC1148
4475	tail sing_2327.htm#SEC2408
4476	tame polynomial sing_1867.htm#IDX870
4477	tame polynomial sing_1868.htm#IDX880
4478	tame polynomial sing_1869.htm#IDX881
4479	tangentGens sing_1613.htm#SEC1694
4480	tangentcone sing_1938.htm#SEC2019
4481	target sing_2831.htm#SEC2912
4482	task sing_1159.htm#IDX572
4483	tasks.lib sing_1159.htm#SEC1240
4484	tasks_lib sing_1159.htm#SEC1240
4485	tau_es sing_1840.htm#SEC1921
4486	tau_es2 sing_1763.htm#SEC1844
4487	tdCf sing_1544.htm#SEC1625
4488	tdFactor sing_1546.htm#SEC1627
4489	tdProj sing_1549.htm#SEC1630
4490	tdTerms sing_1545.htm#SEC1626
4491	teachstd.lib sing_2325.htm#SEC2406
4492	teachstd_lib sing_2325.htm#SEC2406
4493	template.lib sing_55.htm#IDX120
4494	template.lib sing_55.htm#IDX123
4495	template_lib sing_55.htm#SEC92
4496	template_lib sing_55.htm#IDX121
4497	tensor sing_363.htm#SEC403
4498	tensor sing_495.htm#IDX311
4499	tensor algebra sing_863.htm#IDX425
4500	tensorFreeModule sing_2843.htm#SEC2924
4501	tensorFreemodMod sing_2842.htm#SEC2923
4502	tensorMatrix sing_2839.htm#SEC2920
4503	tensorMod sing_1319.htm#SEC1400
4504	tensorModFreemod sing_2841.htm#SEC2922
4505	tensorModule sing_2840.htm#SEC2921
4506	tensorProduct sing_2844.htm#SEC2925
4507	tensorSheaf sing_1710.htm#SEC1791
4508	term orderings General definitions for orderings sing_968.htm#SEC1025
4509	term orderings introduction Introduction to orderings sing_967.htm#SEC1024
4510	testFraction sing_760.htm#SEC814
4511	testLift sing_875.htm#SEC929
4512	testLocData sing_757.htm#SEC811
4513	testNCfac sing_651.htm#SEC705
4514	testNcfrac sing_706.htm#SEC760
4515	testNcfracExamples sing_707.htm#SEC761
4516	testNcloc sing_718.htm#SEC772
4517	testNclocExamples sing_719.htm#SEC773
4518	testOlga sing_774.htm#SEC828
4519	testOlgaExamples sing_775.htm#SEC829
4520	testParametrization sing_1628.htm#SEC1709
4521	testPointConic sing_1629.htm#SEC1710
4522	testPrimary sing_1447.htm#SEC1528
4523	testPrimaryE sing_1448.htm#SEC1529
4524	testSyz sing_876.htm#SEC930
4525	testZero sing_2956.htm#SEC3037
4526	tetrahedronGroup sing_854.htm#SEC908
4527	tex sing_2140.htm#SEC2221
4528	texDrawBasic sing_2553.htm#SEC2634
4529	texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2555.htm#SEC2636
4530	texDrawTriangulation texDrawTriangulation sing_2556.htm#SEC2637
4531	texDrawTropical sing_2554.htm#SEC2635
4532	texMatrix sing_2552.htm#SEC2633
4533	texNumber sing_2550.htm#SEC2631
4534	texPolynomial sing_2551.htm#SEC2632
4535	texcoef sing_2221.htm#SEC2302
4536	texdemo sing_2141.htm#SEC2222
4537	texfactorize sing_2142.htm#SEC2223
4538	texmap sing_2143.htm#SEC2224
4539	texname sing_2144.htm#SEC2225
4540	texobj sing_2145.htm#SEC2226
4541	texpoly sing_2146.htm#SEC2227
4542	texproc sing_2147.htm#SEC2228
4543	texring sing_2148.htm#SEC2229
4544	the first alternative algorithm sing_1296.htm#IDX619
4545	three_elements sing_2311.htm#SEC2392
4546	timeFactorize sing_1031.htm#SEC1112
4547	timeStd sing_1030.htm#SEC1111
4548	timer sing_406.htm#SEC446
4549	timer resolution, setting the sing_361.htm#IDX283
4550	timestep sing_2731.htm#SEC2812
4551	tjurina sing_1934.htm#SEC2015
4552	tmatrix sing_1855.htm#SEC1936
4553	todd sing_1541.htm#SEC1622
4554	toddE sing_1542.htm#SEC1623
4555	toddPoly sing_1555.htm#SEC1636
4556	tolessvars sing_2055.htm#SEC2136
4557	topChernClass sing_1707.htm#SEC1788
4558	topological invariants sing_1751.htm#IDX766
4559	topological invariants sing_1758.htm#IDX773
4560	topological invariants sing_1759.htm#IDX777
4561	topological invariants sing_1760.htm#IDX781
4562	topological invariants sing_1761.htm#IDX785
4563	toric ideals sing_983.htm#SEC1045
4564	toric ring sing_1406.htm#IDX658
4565	toric.lib sing_1501.htm#SEC1582
4566	toric_ideal sing_1502.htm#SEC1583
4567	toric_lib sing_1501.htm#SEC1582
4568	toric_std sing_1503.htm#SEC1584
4569	torus sing_2019.htm#SEC2100
4570	torusInvariants sing_1412.htm#SEC1493 911
4571	torusrep sing_2020.htm#SEC2101
4572	torusreynolds sing_2025.htm#SEC2106
4573	total divisors sing_495.htm#IDX308
4574	total multiplicities sing_1751.htm#IDX769
4575	totalChernClass sing_1705.htm#SEC1786
4576	totalSegreClass sing_1708.htm#SEC1789
4577	totalmultiplicities sing_1753.htm#SEC1834
4578	trace sing_364.htm#SEC404
4579	tracemult sing_2352.htm#SEC2433
4580	transpose sing_365.htm#SEC405
4581	trapezoid sing_2725.htm#SEC2806
4582	triMNewton sing_2081.htm#SEC2162
4583	triagmatrix sing_1123.htm#SEC1204
4584	triang.lib sing_2074.htm#SEC2155
4585	triangL sing_2075.htm#SEC2156
4586	triangL_solve sing_2072.htm#SEC2153
4587	triangLf_solve sing_2070.htm#SEC2151
4588	triangLfak sing_2076.htm#SEC2157
4589	triangM sing_2077.htm#SEC2158
4590	triangMH sing_2078.htm#SEC2159
4591	triangM_solve sing_2071.htm#SEC2152
4592	triang_lib sing_2074.htm#SEC2155
4593	triang_solve sing_2073.htm#SEC2154
4594	triangularGroup sing_855.htm#SEC909
4595	triangulations sing_2478.htm#SEC2559
4596	tropical curves sing_2532.htm#IDX967
4597	tropical geometry sing_1274.htm#IDX593
4598	tropical geometry sing_2575.htm#IDX969
4599	tropical mirror symmetry sing_1274.htm#IDX595
4600	tropical polynomials sing_2532.htm#IDX968
4601	tropical varieties sing_2575.htm#IDX970
4602	tropical.lib sing_2532.htm#SEC2613
4603	tropicalCurve sing_2537.htm#SEC2618
4604	tropicalJInvariant sing_2540.htm#SEC2621
4605	tropicalLifting sing_2533.htm#SEC2614
4606	tropicalLinkNewton sing_2583.htm#SEC2664
4607	tropicalNewton.lib sing_2575.htm#SEC2656
4608	tropicalNewton_lib sing_2575.htm#SEC2656
4609	tropicalPointNewton sing_2580.htm#SEC2661
4610	tropicalSubst sing_2565.htm#SEC2646
4611	tropicalVariety sing_2572.htm#SEC2653
4612	tropicalVarietyNewton tropicalVarietyNewton sing_2582.htm#SEC2663
4613	tropical_lib sing_2532.htm#SEC2613
4614	tropicalise sing_2544.htm#SEC2625
4615	tropicaliseSet sing_2545.htm#SEC2626
4616	truncate sing_1733.htm#SEC1814 13545
4617	truncateFast sing_1734.htm#SEC1815 22046
4618	truncated module sing_1733.htm#IDX757
4619	truncated module sing_1734.htm#IDX758
4620	tst_ncfactor sing_660.htm#SEC714
4621	twalk sing_1295.htm#SEC1376
4622	two-sided sing_495.htm#IDX309
4623	two-sided Groebner basis sing_495.htm#IDX310
4624	twostd sing_361.htm#IDX265
4625	twostd (letterplace) twostd (letterplace) sing_813.htm#SEC867
4626	twostd (plural) sing_487.htm#SEC527
4627	type sing_366.htm#SEC406
4628	type B sing_2609.htm#IDX1020
4629	type D sing_2610.htm#IDX1022
4630	type,custom Definition of a user defined type sing_184.htm#SEC224
4631	type2arr sing_2587.htm#SEC2668
4632	typecasting sing_2587.htm#IDX976
4633	typecasting sing_2588.htm#IDX978
4634	typecasting sing_2589.htm#IDX981
4635	typeof sing_367.htm#SEC407
4636	u sing_2717.htm#SEC2798
4637	uname sing_361.htm#IDX266
4638	unbounded_knapsack sing_2294.htm#SEC2375
4639	union sing_2964.htm#SEC3045
4640	unipotent groups sing_1612.htm#IDX701
4641	uniquePoint sing_2425.htm#SEC2506
4642	unitMatrix sing_2106.htm#SEC2187
4643	unitMatrix2 sing_2041.htm#SEC2122
4644	unitmat sing_1188.htm#SEC1269
4645	univariate sing_368.htm#SEC408
4646	univarpoly sing_2359.htm#SEC2440
4647	universal sing_2697.htm#IDX1155
4648	universal sing_2698.htm#IDX1157
4649	universal derivation diffAlgebraUnivDerIdeal sing_2673.htm#IDX1106
4650	unknown syndrome Decoding method based on quadratic equations sing_999.htm#SEC1075
4651	unset sing_279.htm#SEC319
4652	untyped definitions sing_88.htm#SEC128
4653	untyped definitions sing_427.htm#SEC467
4654	updatePairs sing_2337.htm#SEC2418
4655	ures_solve sing_2064.htm#SEC2145
4656	uressolve sing_369.htm#SEC409
4657	usage, option sing_318.htm#IDX185
4658	used environment variables Used environment variables sing_3003.htm#SEC3100
4659	user interface, Emacs Emacs user interface sing_21.htm#SEC28
4660	vStd sing_1817.htm#SEC1898
4661	val sing_2577.htm#SEC2658
4662	valvars sing_2059.htm#SEC2140
4663	vandermonde sing_370.htm#SEC410
4664	vanishId sing_2191.htm#SEC2272
4665	vanishing polynomial sing_2953.htm#IDX1247
4666	var sing_371.htm#SEC411
4667	varMat sing_2591.htm#SEC2672
4668	varNum sing_2592.htm#SEC2673
4669	variables sing_372.htm#SEC412
4670	variables sing_2591.htm#IDX988
4671	variables sing_2592.htm#IDX990
4672	variables sing_2593.htm#IDX994
4673	variables sing_2594.htm#IDX996
4674	variablesSorted sing_533.htm#SEC587
4675	variablesStandard sing_532.htm#SEC586
4676	vars2pars sing_683.htm#SEC737
4677	varsigns sing_2364.htm#SEC2445
4678	varstr sing_373.htm#SEC413
4679	vdim sing_374.htm#SEC414
4680	vdim (plural) sing_488.htm#SEC528
4681	vec2poly sing_515.htm#SEC569
4682	vecFieldToMatrix sing_2989.htm#SEC3070
4683	vector sing_178.htm#SEC218
4684	vector declarations sing_179.htm#SEC219
4685	vector expressions sing_180.htm#SEC220
4686	vector operations sing_181.htm#SEC221
4687	vector related functions vector related functions sing_182.htm#SEC222
4688	verify sing_2355.htm#SEC2436
4689	verify Groebner base sing_361.htm#IDX269
4690	verifyGB sing_361.htm#IDX271
4691	veronese sing_2084.htm#SEC2165
4692	versal sing_1835.htm#SEC1916
4693	version sing_361.htm#IDX272
4694	vertexAdjacencyGraph vertexAdjacencyGraph sing_2525.htm#SEC2606
4695	vertexEdgeGraph sing_2526.htm#SEC2607
4696	vertices sing_2441.htm#SEC2522
4697	vfilt sing_1853.htm#SEC1934
4698	view sing_2211.htm#SEC2292
4699	visual sing_2527.htm#SEC2608
4700	visualize sing_2716.htm#SEC2797
4701	voice sing_409.htm#SEC449
4702	vwfilt sing_1854.htm#SEC1935
4703	wUnit sing_2249.htm#SEC2330
4704	waitAllTasks sing_1168.htm#SEC1249
4705	waitTasks sing_1167.htm#SEC1248
4706	waitall sing_375.htm#SEC415
4707	waitfirst sing_376.htm#SEC416
4708	walk, groebner sing_1293.htm#IDX615
4709	walk, groebner sing_2855.htm#IDX1213
4710	walk, groebner sing_2958.htm#IDX1252
4711	walk, groebner sing_2978.htm#IDX1266
4712	warkedPreimageStd sing_2756.htm#SEC2837
4713	warn, option sing_70.htm#SEC110
4714	warn, option sing_318.htm#IDX151
4715	watchdog sing_1028.htm#SEC1109
4716	wedge sing_377.htm#SEC417
4717	weierstr.lib sing_2340.htm#SEC2421
4718	weierstrDiv sing_2341.htm#SEC2422
4719	weierstrPrep sing_2342.htm#SEC2423
4720	weierstr_lib sing_2340.htm#SEC2421
4721	weierstrassForm sing_2541.htm#SEC2622
4722	weight sing_378.htm#SEC418
4723	weight filtration sing_1845.htm#IDX803
4724	weight filtration sing_1852.htm#IDX837
4725	weight filtration sing_1854.htm#IDX851
4726	weight filtration sing_1855.htm#IDX859
4727	weight filtration sing_1867.htm#IDX875
4728	weight filtration sing_1869.htm#IDX886
4729	weightKB sing_379.htm#SEC419
4730	weightM, option sing_318.htm#IDX170
4731	weighted lexicographical ordering sing_969.htm#IDX449
4732	weighted reverse lexicographical ordering Global orderings sing_969.htm#IDX447
4733	weightedRing sing_732.htm#SEC786
4734	whichvariable sing_2363.htm#SEC2444
4735	while sing_396.htm#SEC436
4736	withDim sing_210.htm#IDX145
4737	withHilb sing_210.htm#IDX143
4738	withMult sing_210.htm#IDX146
4739	withRes sing_210.htm#IDX144
4740	withSB sing_210.htm#IDX142
4741	wp, global ordering sing_969.htm#IDX448
4742	write sing_380.htm#SEC420
4743	writeBertiniInput sing_2090.htm#SEC2171
4744	writeNmzData sing_1423.htm#SEC1504 38467
4745	writeNmzPaths sing_1427.htm#SEC1508 sprintf
4746	writing monomials sing_405.htm#SEC445
4747	ws, local ordering sing_970.htm#IDX459
4748	wurzel sing_2231.htm#SEC2312
4749	xchange sing_2225.htm#SEC2306
4750	xdvi sing_2150.htm#SEC2231
4751	zdd sing_2638.htm#IDX1069
4752	zdd2poly sing_2655.htm#SEC2736 55047
4753	zero sing_2804.htm#SEC2885
4754	zero-dimensional sing_2360.htm#IDX957
4755	zeroMod sing_1358.htm#SEC1439
4756	zeroNcfrac sing_699.htm#SEC753
4757	zeroOpt sing_1367.htm#SEC1448
4758	zeroRadical sing_1251.htm#SEC1332
4759	zeroReduce sing_2955.htm#SEC3036
4760	zeroSet sing_2122.htm#SEC2203
4761	zerodec sing_1456.htm#SEC1537
4762	zeroreduce sing_2953.htm#IDX1248
4763	zeroset.lib sing_2117.htm#SEC2198
4764	zeroset_lib sing_2117.htm#SEC2198
4765	zetaDL sing_1687.htm#SEC1768
4766	{ sing_36.htm#IDX78
4767	\|\| sing_36.htm#IDX103
4768	\|\| sing_101.htm#SEC141
4769	} sing_36.htm#IDX79
4770	~ sing_36.htm#IDX117
4771	~ sing_397.htm#SEC437

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

Download in other formats:

Original Format