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singular.idx @ 3a9ee05

fieker-DuValspielwiese

Last change on this file since 3a9ee05 was 3a9ee05, checked in by Hans Schoenemann <hannes@…>, 8 years ago
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1	! sing_36.htm#IDX102
2	!= sing_36.htm#IDX96
3	!= sing_95.htm#SEC134
4	" sing_36.htm#IDX105
5	# sing_36.htm#IDX119
6	$ sing_36.htm#IDX120
7	% sing_36.htm#IDX92
8	% sing_76.htm#SEC115
9	% sing_93.htm#SEC132
10	% sing_105.htm#SEC144
11	&& sing_36.htm#IDX103
12	&& sing_96.htm#SEC135
13	( sing_36.htm#IDX81
14	) sing_36.htm#IDX82
15	* bigintmat operations sing_36.htm#IDX90
16	* sing_76.htm#SEC115
17	* sing_82.htm#SEC121
18	* sing_88.htm#SEC127
19	* sing_93.htm#SEC132
20	* sing_101.htm#SEC140
21	* sing_105.htm#SEC144
22	** sing_36.htm#IDX94
23	+ bigintmat operations sing_36.htm#IDX86
24	+ sing_76.htm#SEC115
25	+ sing_82.htm#SEC121
26	+ sing_88.htm#SEC127
27	+ sing_93.htm#SEC132
28	+ sing_101.htm#SEC140
29	+ sing_105.htm#SEC144
30	++ sing_36.htm#IDX87
31	- bigintmat operations sing_36.htm#IDX88
32	- sing_76.htm#SEC115
33	- sing_82.htm#SEC121
34	- sing_93.htm#SEC132
35	- sing_101.htm#SEC140
36	- sing_105.htm#SEC144
37	-- sing_36.htm#IDX89
38	--MPhost sing_19.htm#IDX67
39	--MPport sing_19.htm#IDX66
40	--allow-net sing_19.htm#IDX39
41	--batch sing_19.htm#IDX65
42	--browser sing_19.htm#IDX43
43	--echo sing_19.htm#IDX35
44	--emacs sing_19.htm#IDX68
45	--emacs-dir sing_19.htm#IDX69
46	--emacs-load sing_19.htm#IDX70
47	--execute sing_19.htm#IDX57
48	--help sing_19.htm#IDX37
49	--min-time sing_19.htm#IDX62
50	--no-out sing_19.htm#IDX49
51	--no-rc sing_19.htm#IDX45
52	--no-shell sing_19.htm#IDX50
53	--no-stdlib sing_19.htm#IDX47
54	--no-tty sing_19.htm#IDX51
55	--no-warn sing_19.htm#IDX48
56	--quiet sing_19.htm#IDX53
57	--random sing_19.htm#IDX61
58	--sdb sing_19.htm#IDX32
59	--singular sing_19.htm#IDX71
60	--ticks-per-sec sing_19.htm#IDX63
61	--user-option sing_19.htm#IDX59
62	--verbose sing_19.htm#IDX54
63	-> sing_154.htm#SEC193
64	-MPhost Command line options
65	-MPport Command line options
66	-allow-net Command line options
67	-b Command line options sing_19.htm#IDX64
68	-batch Command line options
69	-browser Command line options
70	-c Command line options sing_19.htm#IDX56
71	-d Command line options sing_19.htm#IDX31
72	-e Command line options sing_19.htm#IDX34
73	-echo Command line options
74	-emacs Command line options
75	-emacs-dir Command line options
76	-emacs-load Command line options
77	-execute Command line options
78	-h Command line options sing_19.htm#IDX36
79	-help Command line options
80	-min-time Command line options
81	-no-out Command line options
82	-no-rc Command line options
83	-no-shell Command line options
84	-no-stdlib Command line options
85	-no-tty Command line options
86	-no-warn Command line options
87	-q Command line options sing_19.htm#IDX52
88	-quiet Command line options
89	-r Command line options sing_19.htm#IDX60
90	-random Command line options
91	-sdb Command line options
92	-singular Command line options
93	-ticks-per-sec Command line options
94	-u Command line options sing_19.htm#IDX58
95	-user-option Command line options
96	-v Command line options sing_19.htm#IDX55
97	-verbose Command line options
98	.. sing_36.htm#IDX114
99	.singularrc file sing_20.htm#IDX73
100	.singularrc file, no loading Command line options sing_19.htm#IDX46
101	/ sing_36.htm#IDX91
102	/ sing_105.htm#SEC144
103	// sing_36.htm#IDX108
104	// sing_36.htm#IDX110
105	// sing_36.htm#IDX111
106	: sing_36.htm#IDX115
107	: sing_105.htm#SEC144
108	:: sing_36.htm#IDX116
109	:: sing_144.htm#SEC183
110	; sing_36.htm#IDX112
111	< sing_36.htm#IDX101
112	< sing_298.htm#SEC337
113	<= sing_36.htm#IDX100
114	<= sing_95.htm#SEC134
115	<> sing_36.htm#IDX97
116	<> sing_95.htm#SEC134
117	= sing_36.htm#IDX78
118	== sing_36.htm#IDX95
119	== sing_95.htm#SEC134
120	> sing_36.htm#IDX99
121	>= sing_36.htm#IDX98
122	>= sing_95.htm#SEC134
123	? sing_36.htm#IDX107
124	? sing_308.htm#IDX144
125	AG codes sing_887.htm#SEC938
126	AGcode_L sing_1826.htm#SEC1901
127	AGcode_Omega sing_1827.htm#SEC1902
128	ASCII sing_936.htm#SEC1011
129	ASCII links sing_112.htm#SEC151
130	ASSUME sing_64.htm#SEC100
131	A_L sing_1525.htm#SEC1600
132	A_Z sing_935.htm#SEC1010
133	Access to elements of a user defined type Access to elements of a user defined type sing_180.htm#SEC219
134	Adj_div sing_1821.htm#SEC1896
135	Adjoint ideal sing_1402.htm#IDX535
136	Alexander polynomial sing_1496.htm#IDX559
137	Algebraic Geometry codes sing_1820.htm#IDX707
138	Algebraic dependence Algebraic dependence sing_868.htm#SEC919
139	Algebraic geometry sing_1377.htm#SEC1452
140	AltVarEnd sing_781.htm#SEC832
141	AltVarStart sing_780.htm#SEC831
142	Ann sing_1316.htm#SEC1391
143	Appel function sing_611.htm#IDX340
144	Appel hypergeometric function sing_611.htm#IDX341
145	Applications sing_885.htm#SEC936
146	ArnoldAction sing_1618.htm#SEC1693
147	Assignments for user defined types Assignments for user defined types sing_182.htm#SEC221
148	Atkin sing_1909.htm#SEC1984
149	Authors sing_1.htm#IDX16
150	BINresol sing_1415.htm#SEC1490
151	Background sing_3.htm#SEC5
152	Basic programming sing_843.htm#SEC894
153	Basic programming sing_843.htm#SEC894
154	BelongSemig sing_2225.htm#SEC2300
155	Bern sing_2203.htm#SEC2278
156	Bernstein operator sing_588.htm#IDX322
157	Bernstein-Sato polynomial sing_553.htm#IDX303
158	Bernstein-Sato polynomial sing_588.htm#IDX319
159	Bernstein-Sato polynomial sing_1559.htm#IDX590
160	Bernstein-Sato polynomial sing_1563.htm#IDX607
161	Bernstein-Sato polynomial for variety sing_644.htm#IDX344
162	Betti number Syzygies and resolutions sing_902.htm#SEC958
163	Bigatti-La Scala-Robbiano algorithm Bigatti and La Scala and Robbiano sing_912.htm#SEC968
164	BlowingUp sing_1538.htm#SEC1613
165	Blowupcenter sing_1418.htm#SEC1493
166	BorelCheck sing_1493.htm#SEC1568
167	Branches of space curve singularities Branches of space curve singularities sing_876.htm#SEC927
168	Briancon-Maisonobe algorithm sing_588.htm#IDX328
169	Brieskorn lattice sing_1559.htm#IDX586
170	Brieskorn lattice sing_1560.htm#IDX597
171	Brieskorn lattice sing_1561.htm#IDX600
172	Brieskorn lattice sing_1562.htm#IDX603
173	Brieskorn lattice sing_1563.htm#IDX606
174	Brieskorn lattice sing_1564.htm#IDX610
175	Brieskorn lattice sing_1565.htm#IDX614
176	Brieskorn lattice sing_1566.htm#IDX620
177	Brieskorn lattice sing_1567.htm#IDX628
178	Brieskorn lattice sing_1568.htm#IDX634
179	Brieskorn lattice sing_1569.htm#IDX642
180	Brieskorn lattice sing_1570.htm#IDX652
181	Brieskorn lattice sing_1581.htm#IDX658
182	Brieskorn lattice sing_1583.htm#IDX669
183	Brieskorn lattice sing_1611.htm#IDX696
184	Brill-Noether algorithm sing_1820.htm#IDX708
185	BrillNoether sing_1823.htm#SEC1898
186	Buchberger algorithm for toric ideals Buchberger algorithm sing_913.htm#SEC969
187	Budur-Mustata-Saito approach sing_644.htm#IDX348
188	Building Singular sing_2456.htm#SEC2543
189	C programming language Major differences to the C programming language sing_457.htm#SEC496
190	C, module ordering sing_895.htm#IDX402
191	CGS, disjoint, reduced, Comprehensive Groebner System cgsdr sing_957.htm#IDX412
192	CM_regularity sing_1480.htm#SEC1555 33865
193	CMtype sing_1649.htm#SEC1724
194	CRHT-ideal sing_919.htm#SEC982
195	Castelnuovo-Mumford regularity sing_1480.htm#IDX551
196	Category string sing_51.htm#SEC87
197	CenCharDec sing_738.htm#SEC789
198	Center sing_1457.htm#SEC1532
199	CenterBO sing_1464.htm#SEC1539
200	CentralQuot sing_736.htm#SEC787
201	CentralSaturation sing_737.htm#SEC788
202	Change of rings sing_9.htm#SEC15
203	Characteristic sets sing_903.htm#SEC959
204	CharacteristicExponents CharacteristicExponents sing_1544.htm#SEC1619
205	ChernRootsDual sing_2184.htm#SEC2259
206	ChernRootsHom sing_2191.htm#SEC2266
207	ChernRootsProd sing_2186.htm#SEC2261
208	ChernRootsSum sing_2182.htm#SEC2257
209	ChernRootsSymm sing_2193.htm#SEC2268
210	ChernRootsWedge sing_2194.htm#SEC2269
211	Chevalley-Rosenlicht theorem sing_1396.htm#IDX520
212	Chevalley-Rosenlicht theorem sing_1397.htm#IDX523
213	Classification of hypersurface singularities Classification of hypersurface singularities sing_877.htm#SEC928
214	Classification of singularities sing_2393.htm#IDX891
215	Code Codes and the decoding problem sing_918.htm#SEC975
216	Codes and the decoding problem Codes and the decoding problem sing_918.htm#SEC974
217	Coding theory sing_1819.htm#SEC1894
218	Coefficient rings Notes for Singular users sing_2454.htm#SEC2535
219	Command line options Command line options sing_19.htm#SEC26
220	Commands Functions and system variables sing_258.htm#SEC297
221	Commands for user defined types Commands for user defined types sing_181.htm#SEC220
222	Commutative Algebra sing_856.htm#SEC907
223	Commutative algebra sing_1135.htm#SEC1210
224	CompDecomp sing_550.htm#SEC601
225	CompInt sing_2227.htm#SEC2302
226	CompleteHomog sing_2172.htm#SEC2247
227	ComplexValue sing_2267.htm#SEC2342
228	Computing Groebner and Standard Bases Computing Groebner and Standard Bases sing_852.htm#SEC903
229	ConsLevels sing_964.htm#SEC1039
230	ContactMatrix sing_1546.htm#SEC1621
231	Conti-Traverso algorithm sing_908.htm#SEC964
232	Contributors sing_1.htm#IDX15
233	Control structures sing_425.htm#SEC464
234	Control theory System and Control theory sing_1853.htm#SEC1928
235	Cooper philosophy sing_919.htm#SEC980
236	Cornacchia sing_1899.htm#SEC1974
237	CornacchiaModified sing_1900.htm#SEC1975
238	Crep sing_960.htm#SEC1035
239	Critical points sing_871.htm#SEC922
240	CurveParam sing_1540.htm#SEC1615
241	CurveRes sing_1539.htm#SEC1614
242	Curves sing_1402.htm#IDX532
243	Customization of the Emacs interface Customization of the Emacs interface sing_25.htm#SEC35
244	Cyclic code sing_1834.htm#IDX715
245	Cyclic roots sing_849.htm#SEC900
246	D-integration sing_611.htm#IDX337
247	D-localization sing_611.htm#IDX333
248	D-localization sing_815.htm#IDX371
249	D-module purityfiltration_lib sing_553.htm#IDX301
250	D-module sing_588.htm#IDX316
251	D-module sing_611.htm#IDX330
252	D-module sing_644.htm#IDX342
253	D-module sing_793.htm#IDX356
254	D-module sing_815.htm#IDX368
255	D-module structure sing_588.htm#IDX317
256	D-module structure sing_644.htm#IDX343
257	D-restriction sing_611.htm#IDX335
258	DBM links sing_117.htm#SEC156
259	DISPLAY environment variable The online help system sing_16.htm#IDX28
260	DLoc sing_614.htm#SEC665
261	DLoc0 sing_616.htm#SEC667
262	Data types sing_72.htm#SEC111
263	Data types (plural) sing_470.htm#IDX287
264	Debugging tools sing_63.htm#SEC99
265	Decker, Wolfram sing_1.htm#IDX17
266	Declaration of objects of a user defined type Declaration of objects of a user defined type sing_179.htm#SEC218
267	Decoding sing_1834.htm#IDX717
268	Decoding codes with Groebner bases Decoding codes with Groebner bases sing_917.htm#SEC973
269	Decoding method based on quadratic equations Decoding method based on quadratic equations sing_922.htm#SEC991
270	Definition of a user defined type Definition of a user defined type sing_178.htm#SEC217
271	Deformations sing_874.htm#SEC925
272	Deformations, T1 and T2 sing_873.htm#SEC924
273	Degree sing_1381.htm#SEC1456
274	Delta sing_1465.htm#SEC1540
275	DeltaList sing_1466.htm#SEC1541
276	Demo mode sing_24.htm#SEC34
277	Depth sing_863.htm#SEC914
278	Determinacy sing_2396.htm#IDX895
279	Di Biase-Urbanke algorithm Di Biase and Urbanke sing_911.htm#SEC967
280	Distributed computing sing_980.htm#IDX426
281	Dlocalization sing_816.htm#SEC867
282	Documentation Tool sing_60.htm#SEC96
283	Dp, global ordering sing_893.htm#IDX385
284	Ds, local ordering sing_894.htm#IDX395
285	DsingularLocus sing_820.htm#SEC871
286	Dynamic loading sing_71.htm#SEC110
287	Dynamic modules sing_851.htm#SEC902
288	ECPP sing_1943.htm#SEC2018
289	ECoef sing_1424.htm#SEC1499
290	EOrdlist sing_1422.htm#SEC1497
291	ERROR sing_287.htm#SEC326
292	Edatalist sing_1421.htm#SEC1496
293	Edelman-Reiner sing_2150.htm#IDX826
294	Editing SINGULAR input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC36
295	Editing input sing_18.htm#SEC25
296	Elimination sing_859.htm#SEC910
297	Emacs Emacs user interface sing_21.htm#SEC28
298	Emacs, Singular demo mode sing_24.htm#SEC34
299	Emacs, a quick guide A quick guide to Emacs sing_22.htm#SEC29
300	Emacs, customization of Singular mode Customization of the Emacs interface sing_25.htm#SEC35
301	Emacs, editing Singular input files Editing SINGULAR input files with Emacs sing_26.htm#SEC36
302	Emacs, important commands Top 20 Emacs commands sing_27.htm#SEC37
303	Emacs, overview A quick guide to Emacs sing_22.htm#SEC29
304	Emacs, running Singular under Running SINGULAR under Emacs sing_23.htm#SEC30
305	Emacs, user interface Emacs user interface sing_21.htm#SEC28
306	Emaxcont sing_1426.htm#SEC1501
307	Equal sing_1380.htm#SEC1455
308	Eresol sing_1416.htm#SEC1491
309	Evaluation of logical expressions Evaluation of logical expressions sing_459.htm#SEC498
310	Examples sing_841.htm#SEC892
311	Examples of ring declarations Examples of ring declarations sing_29.htm#SEC39
312	Exp for matrices sing_1398.htm#IDX524
313	Experimental libraries Experimental libraries sing_2121.htm#SEC2196
314	Ext sing_1195.htm#SEC1270
315	Ext, computation of sing_862.htm#SEC913
316	Ext_R sing_1194.htm#SEC1269
317	Exterior sing_767.htm#SEC818
318	Extra weight vector sing_898.htm#SEC949
319	Factorization sing_864.htm#SEC915
320	Feynman graph sing_1171.htm#IDX461
321	Finite fields sing_858.htm#SEC909
322	First steps sing_6.htm#SEC12
323	Fitzgerald-Lax method Fitzgerald-Lax method sing_921.htm#SEC988
324	Flow control sing_40.htm#SEC69
325	Formal Checker sing_59.htm#SEC95
326	Formatting output sing_848.htm#SEC899
327	Free resolution sing_860.htm#SEC911
328	Free resolution, graded Handling graded modules sing_861.htm#SEC912
329	Functions sing_259.htm#SEC298
330	Future benefits of Singular 4 Notes for Singular users sing_2454.htm#SEC2541
331	G-algebra sing_534.htm#SEC573
332	G-algebra sing_534.htm#SEC575
333	G-algebra, setup sing_534.htm#SEC577
334	GBWeight sing_617.htm#SEC668
335	GBsolve sing_1733.htm#SEC1808
336	GIT sing_2279.htm#IDX877
337	GKZsystem sing_734.htm#SEC785
338	GKdim sing_707.htm#SEC758
339	GMP sing_1.htm#IDX3
340	GND.lib sing_2286.htm#SEC2361
341	GND_lib sing_2286.htm#SEC2361
342	GTZmod sing_1243.htm#SEC1318
343	GTZopt sing_1250.htm#SEC1325
344	G_a -Invariants sing_880.htm#SEC931
345	Gamma sing_1431.htm#SEC1506
346	Gauss-Manin connection Gauss-Manin connection sing_904.htm#SEC960
347	Gauss-Manin connection sing_1611.htm#IDX695
348	Gauss-Manin connection sing_1658.htm#IDX698
349	Gauss-Manin system sing_1559.htm#IDX585
350	Gauss-Manin system sing_1560.htm#IDX596
351	Gauss-Manin system sing_1561.htm#IDX599
352	Gauss-Manin system sing_1562.htm#IDX602
353	Gauss-Manin system sing_1563.htm#IDX605
354	Gauss-Manin system sing_1564.htm#IDX609
355	Gauss-Manin system sing_1565.htm#IDX613
356	Gauss-Manin system sing_1566.htm#IDX619
357	Gauss-Manin system sing_1567.htm#IDX627
358	Gauss-Manin system sing_1568.htm#IDX633
359	Gauss-Manin system sing_1569.htm#IDX641
360	Gauss-Manin system sing_1570.htm#IDX651
361	Gauss-Manin system sing_1581.htm#IDX657
362	Gauss-Manin system sing_1583.htm#IDX668
363	General command syntax General command syntax sing_35.htm#SEC58
364	General concepts sing_12.htm#SEC18
365	General purpose sing_929.htm#SEC1004
366	General syntax of a ring declaration General syntax of a ring declaration sing_30.htm#SEC40
367	Generalized Hilbert Syzygy Theorem Syzygies and resolutions (plural) sing_536.htm#SEC585
368	Generalized Newton identities Generalized Newton identities sing_920.htm#SEC985
369	Geometric genus sing_1402.htm#IDX536
370	German Umlaute sing_455.htm#IDX274
371	Getting started sing_5.htm#SEC11
372	Global orderings sing_893.htm#SEC944
373	Graded commutative algebras Graded commutative algebras (SCA) sing_538.htm#SEC589
374	Greuel, Gert-Martin sing_1.htm#IDX18
375	Groebner Bases Computing Groebner and Standard Bases sing_852.htm#SEC903
376	Groebner bases in G-algebras Groebner bases in G-algebras sing_535.htm#SEC578
377	Groebner bases in free associative algebras Groebner bases for two-sided ideals in free associative algebras sing_541.htm#SEC592
378	Groebner bases, decodeGB sing_1834.htm#IDX719
379	Groebner bases, slim sing_855.htm#SEC906
380	Groebner basis conversion Groebner basis conversion sing_854.htm#SEC905
381	Groebner cover, parametric ideal, canonical, discussion of extend sing_956.htm#IDX411
382	Groebner cover, parametric ideal, canonical, discussion of sing_963.htm#IDX415
383	Groebner fan sing_2038.htm#IDX736
384	Groebner walk sing_1186.htm#IDX480
385	Groebner walk sing_1188.htm#IDX482
386	Groebner walk sing_2386.htm#IDX888
387	Groebner walk sing_2387.htm#IDX889
388	Gromov-Witten invariants sing_1171.htm#IDX458
389	Gromov-Witten invariants sing_1177.htm#IDX467
390	Gromov-Witten invariants sing_1178.htm#IDX471
391	Gweights sing_761.htm#SEC812
392	H2basis sing_1616.htm#SEC1691
393	Hamburger-Noether expansion sing_1496.htm#IDX555
394	Hamburger-Noether expansion sing_1584.htm#IDX677
395	Hamburger-Noether expansions sing_1821.htm#IDX709
396	Handling graded modules Handling graded modules sing_861.htm#SEC912
397	Hcode sing_1518.htm#SEC1593
398	Help string sing_45.htm#SEC81
399	Hensel sing_292.htm#SEC331
400	Hilbert function sing_404.htm#IDX184
401	Hilbert function sing_901.htm#SEC954
402	Hilbert series sing_901.htm#SEC954
403	Hilbert-driven GB algorithm Groebner basis conversion sing_854.htm#SEC905
404	HilbertClassPoly sing_1906.htm#SEC1981
405	HilbertSeries sing_1711.htm#SEC1786
406	HilbertWeights sing_1712.htm#SEC1787
407	Hom sing_1198.htm#SEC1273
408	HomJJ sing_1273.htm#SEC1348
409	Hosten-Sturmfels algorithm Hosten and Sturmfels sing_910.htm#SEC966
410	How to enter and exit How to enter and exit sing_14.htm#SEC20
411	How to use this manual How to use this manual sing_4.htm#SEC6
412	Hurwitz numbers sing_1177.htm#IDX470
413	Hurwitz numbers sing_1178.htm#IDX474
414	Hypersurface singularities, classification of Classification of hypersurface singularities sing_877.htm#SEC928
415	IN sing_329.htm#IDX145
416	Ideal membership sing_900.htm#IDX407
417	Identifiers, syntax of sing_37.htm#SEC64
418	ImageGroup sing_1714.htm#SEC1789
419	ImageVariety sing_1713.htm#SEC1788
420	Imap, option sing_364.htm#IDX171
421	Implemented algorithms Implemented algorithms sing_33.htm#SEC46
422	Incl sing_1379.htm#SEC1454
423	Index sing_2462.htm#SEC2549
424	Info string sing_52.htm#SEC88
425	InterDiv sing_1447.htm#SEC1522
426	Interactive use sing_13.htm#SEC19
427	Interrupting SINGULAR Interrupting SINGULAR sing_17.htm#SEC24
428	IntersectWithSub sing_739.htm#SEC790
429	IntersectionMatrix sing_1545.htm#SEC1620
430	Introduction sing_2.htm#SEC4
431	Invariant Theory sing_879.htm#SEC930
432	Invariant theory sing_1663.htm#SEC1738
433	InvariantQ sing_1716.htm#SEC1791
434	InvariantRing sing_1715.htm#SEC1790
435	Invariants of a finite group Invariants of a finite group sing_881.htm#SEC932
436	Invariants of plane curve singularities Invariants of plane curve singularities sing_875.htm#SEC926
437	IsSCA sing_782.htm#SEC833
438	J-marked schemes sing_1487.htm#IDX553
439	J-marked schemes, Borel ideals sing_1492.htm#IDX554
440	JMBTest.lib sing_1487.htm#SEC1562
441	JMBTest_lib sing_1487.htm#SEC1562
442	JMSConst.lib sing_1492.htm#SEC1567
443	JMSConst_lib sing_1492.htm#SEC1567
444	JMarkedScheme sing_1494.htm#SEC1569
445	Jacobi sing_1916.htm#SEC1991
446	Jacobson form sing_1871.htm#IDX720
447	Jacobson normal form sing_1871.htm#IDX721
448	JuReTopDim sing_1389.htm#SEC1464
449	JuReZeroDim sing_1390.htm#SEC1465
450	KScoef sing_1609.htm#SEC1684
451	KSconvert sing_1607.htm#SEC1682
452	KSker sing_1606.htm#SEC1681
453	KSlinear sing_1608.htm#SEC1683
454	KSpencerKernel sing_1656.htm#SEC1731
455	KeneshlouMatrixPresentation KeneshlouMatrixPresentation sing_2305.htm#SEC2380
456	Kernel of module homomorphisms Kernel of module homomorphisms sing_867.htm#SEC918
457	KoszulHomology sing_1207.htm#SEC1282
458	LETTERPLACE sing_539.htm#SEC590
459	LIB sing_333.htm#SEC372
460	LIB commands sing_53.htm#SEC89
461	LIBs sing_925.htm#SEC1000
462	LLL sing_406.htm#IDX214
463	LOT algorithm sing_588.htm#IDX329
464	LU-decomposition of a matrix of numbers sing_338.htm#SEC377
465	Laurent series sing_1175.htm#IDX466
466	Left and two-sided Groebner bases Left and two-sided Groebner bases sing_883.htm#SEC934
467	Left ideal membership Groebner bases in G-algebras sing_535.htm#SEC581
468	Left normal form Groebner bases in G-algebras sing_535.htm#SEC580
469	LengthSym sing_792.htm#SEC843
470	LengthSymElement sing_791.htm#SEC842
471	Letterplace sing_539.htm#SEC590
472	Lexicographic Groebner bases, computation of Groebner basis conversion sing_854.htm#SEC905
473	Libraries Writing procedures and libraries sing_48.htm#SEC84
474	Libraries sing_844.htm#SEC895
475	Libraries in the SINGULAR Documentation Libraries in the SINGULAR Documentation sing_49.htm#SEC85
476	Library versioning Notes for Singular users sing_2454.htm#SEC2539
477	Lie algebra sing_1397.htm#IDX521
478	Lie group sing_1400.htm#IDX526
479	Lie group sing_1401.htm#IDX529
480	Limitations sing_455.htm#SEC494
481	Linear algebra sing_1075.htm#SEC1150
482	Linear code sing_1834.htm#IDX716
483	LinearActionQ sing_1718.htm#SEC1793
484	LinearCombinationQ sing_1719.htm#SEC1794
485	LinearizeAction sing_1717.htm#SEC1792
486	Loading a library sing_62.htm#SEC98
487	Local orderings sing_894.htm#SEC945
488	Log for matrices sing_1399.htm#IDX525
489	Long coefficients sing_846.htm#SEC897
490	M, ordering sing_896.htm#SEC947
491	MVComplex sing_2399.htm#SEC2474
492	Macintosh installation Macintosh installation instructions sing_2461.htm#SEC2548
493	Mathematical background Mathematical background sing_899.htm#SEC950
494	Mathematical background (plural) Mathematical background (plural) sing_533.htm#SEC572
495	Matrix orderings sing_896.htm#SEC947
496	Max sing_1625.htm#SEC1700
497	Maximus sing_1489.htm#SEC1564
498	Maxord sing_1430.htm#SEC1505
499	MillerRabin sing_1926.htm#SEC2001
500	Milnor number Milnor and Tjurina number sing_870.htm#SEC921
501	Milnor number sing_2395.htm#IDX894
502	Min sing_1626.htm#SEC1701
503	MinMult sing_2226.htm#SEC2301
504	MinimalDecomposition MinimalDecomposition sing_1720.htm#SEC1795
505	Minimum distance sing_1834.htm#IDX718
506	Minimus sing_1488.htm#SEC1563
507	Miscellaneous libraries Miscellaneous libraries sing_2096.htm#SEC2171
508	ModEqn sing_1619.htm#SEC1694
509	Modular techniques sing_980.htm#IDX423
510	Module orderings sing_895.htm#SEC946
511	Modules and and their annihilator Modules and their annihilator sing_10.htm#SEC16
512	Monodromy sing_1611.htm#IDX693
513	Monomial orderings sing_890.htm#SEC941
514	Monomial orderings, Term orderings sing_31.htm#SEC43
515	Morse lemma sing_2394.htm#IDX892
516	MultiplicitySequence MultiplicitySequence sing_1543.htm#SEC1618
517	NF sing_383.htm#SEC422
518	NF sing_525.htm#SEC564
519	NFMora sing_1992.htm#SEC2067
520	NPos sing_1263.htm#SEC1338
521	NPos_test sing_1261.htm#SEC1336
522	NSplaces sing_1822.htm#SEC1897
523	NTL sing_1.htm#IDX4
524	Names sing_37.htm#SEC64
525	Names in procedures sing_46.htm#SEC82
526	Names, indexed sing_37.htm#SEC64
527	New libraries depending on Singular 4 Notes for Singular users sing_2454.htm#SEC2537
528	New orderings for modules Notes for Singular users sing_2454.htm#SEC2540
529	Newton non-degenerate sing_1598.htm#IDX691
530	Newton polygon sing_1597.htm#IDX690
531	Newton polygon sing_1598.htm#IDX692
532	Newton polytope sing_2038.htm#IDX735
533	NoetherPosition sing_1257.htm#SEC1332
534	Non-commutative LIBs Non-commutative libraries sing_545.htm#SEC596
535	Non-commutative algebra Non-commutative algebra sing_882.htm#SEC933
536	Non-commutative algebra sing_916.htm#SEC972
537	Non-commutative libraries Non-commutative libraries sing_545.htm#SEC596
538	Non-commutative subsystem Non-commutative subsystem sing_468.htm#SEC507
539	Nonhyp sing_1419.htm#SEC1494
540	Normal form sing_900.htm#IDX406
541	Normalization sing_866.htm#SEC917
542	Notes for Singular users Notes for Singular users sing_2454.htm#SEC2534
543	Notes for developers Notes for developers sing_2455.htm#SEC2542
544	NullCone sing_1721.htm#SEC1796
545	NumIrrDecom sing_1393.htm#SEC1468
546	NumLocalDim sing_1382.htm#SEC1457
547	NumPrimDecom sing_1395.htm#SEC1470
548	Oaku-Takayama algorithm sing_588.htm#IDX327
549	Objects sing_38.htm#SEC65
550	Orlik-Solomon sing_2151.htm#IDX827
551	Output, formatting of sing_848.htm#SEC899
552	PBW sing_567.htm#IDX315
553	PBW basis sing_534.htm#SEC574
554	PBW_eqDeg sing_585.htm#SEC636
555	PBW_maxDeg sing_586.htm#SEC637
556	PBW_maxMonom sing_587.htm#SEC638
557	PEsolve sing_1731.htm#SEC1806
558	PH_ais sing_2100.htm#SEC2175
559	PH_nais sing_2101.htm#SEC2176
560	PLURAL sing_469.htm#SEC508
561	PLURAL LIBs Non-commutative libraries sing_545.htm#SEC596
562	ParToVar sing_2269.htm#SEC2344
563	Parallelization Parallelization with ssi links sing_850.htm#SEC901
564	Parallelization sing_980.htm#IDX424
565	Parameter list sing_44.htm#SEC80
566	Parameters sing_847.htm#SEC898
567	Parametrization sing_1402.htm#IDX533
568	Parametrization, image. sing_1412.htm#IDX545
569	PartC sing_2221.htm#SEC2296
570	PartitionVar sing_2266.htm#SEC2341
571	Path names Notes for Singular users sing_2454.htm#SEC2538
572	PerfectPowerTest sing_1889.htm#SEC1964
573	Perturbation walk sing_1187.htm#IDX481
574	Pfister, Gerhard sing_1.htm#IDX19
575	Pipe links sing_116.htm#SEC155
576	PocklingtonLehmer sing_1928.htm#SEC2003
577	Poincare polynomial sing_2163.htm#IDX851
578	Polar curves sing_872.htm#SEC923
579	PollardRho sing_1929.htm#SEC2004
580	PolyBoRi, Boolean Groebner Basis recursive_from_boolean_poly sing_2103.htm#IDX752
581	PolyBoRi, Boolean Groebner Basis sing_2105.htm#IDX753
582	PolyBoRi, Boolean Groebner Basis sing_2106.htm#IDX754
583	PolyBoRi, Boolean Groebner Basis sing_2107.htm#IDX755
584	PolyBoRi, Boolean Groebner Basis sing_2108.htm#IDX756
585	PolyBoRi, Boolean Groebner Basis sing_2109.htm#IDX757
586	PolyBoRi, Boolean Groebner Basis sing_2110.htm#IDX758
587	PolyBoRi, Boolean Groebner Basis sing_2111.htm#IDX759
588	PolyBoRi, Boolean Groebner Basis sing_2112.htm#IDX760
589	PolyBoRi, Boolean Groebner Basis sing_2113.htm#IDX761
590	PolyBoRi, Boolean Groebner Basis sing_2114.htm#IDX762
591	PolyBoRi, Boolean Groebner Basis sing_2115.htm#IDX763
592	PolyBoRi, Boolean Groebner Basis sing_2116.htm#IDX764
593	PolyBoRi, Boolean Groebner Basis sing_2117.htm#IDX765
594	PolyBoRi, Boolean Groebner Basis sing_2119.htm#IDX767
595	PolyBoRi, zero-supressed decision diagram sing_2118.htm#IDX766
596	Polybori, Boolean Groebner Basis sing_2120.htm#IDX768
597	Polynomial data sing_888.htm#SEC939
598	Pottier algorithm sing_909.htm#SEC965
599	Preface sing_1.htm#SEC1
600	Prep sing_961.htm#SEC1036
601	Primary decomposition Primary decomposition sing_865.htm#SEC916
602	PrimdecA sing_1239.htm#SEC1314
603	PrimdecB sing_1240.htm#SEC1315
604	Procedure definition Procedure definition sing_43.htm#SEC77
605	Procedure-specific commands Procedure-specific commands sing_47.htm#SEC83
606	Procedures sing_42.htm#SEC76
607	Procedures and libraries Writing procedures and libraries sing_8.htm#SEC14
608	Procedures and libraries sing_844.htm#SEC895
609	Procedures in a library Procedures in a library sing_54.htm#SEC90
610	Product orderings sing_897.htm#SEC948
611	Programming sing_842.htm#SEC893
612	PtoCrep sing_962.htm#SEC1037
613	Puiseux expansion sing_1496.htm#IDX556
614	Puiseux expansion sing_1584.htm#IDX678
615	Puiseux pairs Invariants of plane curve singularities sing_875.htm#SEC926
616	Puiseux pairs sing_1590.htm#IDX683
617	Qso3Casimir sing_733.htm#SEC784
618	Quotient sing_1773.htm#SEC1848
619	QuotientEquations sing_1620.htm#SEC1695
620	Rational curves sing_1402.htm#IDX534
621	ReJunkUseHomo sing_1388.htm#SEC1463
622	ReesAlgebra sing_1355.htm#SEC1430
623	References sing_924.htm#SEC997
624	References (plural) sing_537.htm#SEC586
625	Release Notes sing_2450.htm#SEC2525
626	ResTree sing_1448.htm#SEC1523
627	Resolution sing_11.htm#SEC17
628	Resolution of singularities Resolution of singularities sing_878.htm#SEC929
629	Resolution, free sing_860.htm#SEC911
630	ReynoldsImage sing_1722.htm#SEC1797
631	ReynoldsOperator sing_1723.htm#SEC1798
632	RiemannRochBN sing_2168.htm#SEC2243
633	RiemannRochHess sing_2324.htm#SEC2399
634	Right Groebner bases and syzygies Right Groebner bases and syzygies sing_884.htm#SEC935
635	Ring-dependent options Notes for Singular users sing_2454.htm#SEC2536
636	Rings and orderings sing_28.htm#SEC38
637	Rings and standard bases Rings and standard bases sing_7.htm#SEC13
638	Running SINGULAR under Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
639	SCA Graded commutative algebras (SCA) sing_538.htm#SEC589
640	SDB breakpoint Source code debugger sing_66.htm#SEC105
641	SDB debugger Source code debugger sing_66.htm#SEC105
642	SDLoc sing_615.htm#SEC666
643	SINGULAR libraries sing_925.htm#SEC1000
644	SINGULARHIST sing_18.htm#SEC25
645	SV-decoding algorithm sing_1829.htm#IDX712
646	SV-decoding algorithm, preprocessing sing_1828.htm#IDX711
647	Sannfs sing_591.htm#SEC642
648	SannfsBFCT sing_600.htm#SEC651
649	SannfsVar sing_647.htm#SEC698
650	Sannfslog sing_592.htm#SEC643
651	Saturation sing_857.htm#SEC908
652	Sch@"onemann, Hans sing_1.htm#IDX20
653	Schoof sing_1940.htm#SEC2015
654	Schreyer ordering sing_1055.htm#IDX440
655	Schreyer resolution sing_1055.htm#IDX441
656	SchurCh sing_2218.htm#SEC2293
657	SchurS sing_2217.htm#SEC2292
658	Scontinue sing_1059.htm#SEC1134
659	Semigroup sing_1536.htm#SEC1611
660	Setting up a G-algebra sing_534.htm#SEC577
661	ShanksMestre sing_1939.htm#SEC2014
662	SimplifyIdeal sing_1724.htm#SEC1799
663	Singular sing_406.htm#IDX246
664	Singular 3 and Singular 4 Singular 3 and Singular 4 sing_2452.htm#SEC2532
665	Singular, customization of Emacs user interface Customization of the Emacs interface sing_25.htm#SEC35
666	Singular, demo mode sing_24.htm#SEC34
667	Singular, editing input files with Emacs Editing SINGULAR input files with Emacs sing_26.htm#SEC36
668	Singular, important commands of Emacs interface Top 20 Emacs commands sing_27.htm#SEC37
669	Singular, running within Emacs Running SINGULAR under Emacs sing_23.htm#SEC30
670	Singular2bertini sing_1386.htm#SEC1461
671	SingularLib sing_406.htm#IDX248
672	Singularities sing_1495.htm#SEC1570
673	Singularity Theory sing_869.htm#SEC920
674	Skeletons for parallelization sing_980.htm#IDX425
675	Smith form sing_1871.htm#IDX722
676	Smith normal form sing_1871.htm#IDX723
677	SolowayStrassen sing_1927.htm#SEC2002
678	Solving systems of polynomial equations Solving systems of polynomial equations sing_886.htm#SEC937
679	Source code debugger, invocation Command line options sing_19.htm#IDX33
680	Space curve singularities, branches of Branches of space curve singularities sing_876.htm#SEC927
681	Special characters sing_36.htm#SEC63
682	Splitting lemma sing_2394.htm#IDX893
683	Sres sing_1057.htm#SEC1132
684	Ssi file links sing_114.htm#SEC153
685	Ssi links sing_113.htm#SEC152
686	Ssi tcp links sing_115.htm#SEC154
687	Ssyz sing_1058.htm#SEC1133
688	StabEqn sing_1621.htm#SEC1696
689	StabEqnId sing_1622.htm#SEC1697
690	StabOrder sing_1623.htm#SEC1698
691	Standard Bases Computing Groebner and Standard Bases sing_852.htm#SEC903
692	Standard bases sing_900.htm#SEC951
693	StartOrderingV sing_1490.htm#SEC1565
694	Startup sequence sing_20.htm#SEC27
695	StringF sing_1610.htm#SEC1685
696	SymGroup sing_790.htm#SEC841
697	Symbolic-numerical solving Symbolic-numerical solving sing_886.htm#SEC937
698	Symbolic-numerical solving sing_1728.htm#SEC1803
699	System and Control theory System and Control theory sing_1853.htm#SEC1928
700	System dependent limitations System dependent limitations sing_456.htm#SEC495
701	System variables sing_442.htm#SEC481
702	Syzygies and resolutions Syzygies and resolutions sing_902.htm#SEC955
703	Syzygies and resolutions (plural) Syzygies and resolutions (plural) sing_536.htm#SEC582
704	T1 sing_873.htm#SEC924
705	T2 sing_873.htm#SEC924
706	TRACE Tracing of procedures sing_65.htm#SEC101
707	TRACE sing_451.htm#SEC490
708	T_1 sing_1643.htm#SEC1718
709	T_12 sing_1645.htm#SEC1720
710	T_2 sing_1644.htm#SEC1719
711	Teaching sing_1885.htm#SEC1960
712	Template for writing a library sing_55.htm#SEC91
713	TestGRRes sing_2304.htm#SEC2379
714	TestJMark sing_1491.htm#SEC1566
715	The SINGULAR language The SINGULAR language sing_34.htm#SEC55
716	The Tran algorithm sing_1184.htm#IDX478
717	The fractal walk algorithm sing_1183.htm#IDX477
718	The fractal walk algorithm sing_2388.htm#IDX890
719	The online help system The online help system sing_16.htm#SEC22
720	Tjurina sing_1641.htm#SEC1716
721	Tjurina number Milnor and Tjurina number sing_870.htm#SEC921
722	Tjurina number sing_1278.htm#IDX505
723	Top 20 Emacs commands Top 20 Emacs commands sing_27.htm#SEC37
724	Tor sing_1209.htm#SEC1284
725	Toric ideals and integer programming Toric ideals and integer programming sing_905.htm#SEC961
726	Tricks and pitfalls sing_454.htm#SEC493
727	Tropical Geometry sing_2037.htm#SEC2112
728	Type casting Type conversion and casting sing_39.htm#SEC68
729	Type conversion Type conversion and casting sing_39.htm#SEC67
730	Typesetting of help and info strings Typesetting of help and info strings sing_61.htm#SEC97
731	U_D_O sing_1124.htm#SEC1199
732	Unix installation Unix installation instructions sing_2459.htm#SEC2546
733	UpOneMatrix sing_779.htm#SEC830
734	UpperMonomials sing_1624.htm#SEC1699
735	UseBertini sing_1385.htm#SEC1460
736	User defined types sing_177.htm#SEC216
737	V-filtration sing_1559.htm#IDX588
738	V-filtration sing_1565.htm#IDX616
739	V-filtration sing_1566.htm#IDX622
740	V-filtration sing_1567.htm#IDX630
741	V-filtration sing_1568.htm#IDX636
742	V-filtration sing_1569.htm#IDX644
743	V-filtration sing_1570.htm#IDX654
744	V-filtration sing_1581.htm#IDX660
745	V-filtration sing_1583.htm#IDX671
746	VarToPar sing_2268.htm#SEC2343
747	Variables, indexed sing_37.htm#SEC64
748	Version number Version schema for Singular sing_2453.htm#SEC2533
749	Version schema for Singular Version schema for Singular sing_2453.htm#SEC2533
750	Version string sing_50.htm#SEC86
751	Visualization sing_1791.htm#SEC1866
752	WP, global ordering sing_893.htm#IDX389
753	WSemigroup sing_1541.htm#SEC1616
754	Weierstrass sing_1824.htm#SEC1899
755	Weierstrass semigroup sing_1820.htm#IDX706
756	Weyl sing_764.htm#SEC815
757	Weyl algebra sing_588.htm#IDX321
758	Weyl algebra sing_644.htm#IDX346
759	Weyl closure sing_815.htm#IDX374
760	WeylClosure sing_817.htm#SEC868
761	WeylClosure1 sing_818.htm#SEC869
762	Windows installation Windows installation instructions sing_2460.htm#SEC2547
763	WitSet sing_1392.htm#SEC1467
764	WitSupSet sing_1391.htm#SEC1466
765	Ws, local ordering sing_894.htm#IDX401
766	XLsolve sing_1734.htm#SEC1809
767	ZZsolve sing_1735.htm#SEC1810
768	[ sing_36.htm#IDX84
769	\ sing_36.htm#IDX113
770	] sing_36.htm#IDX85
771	^ sing_36.htm#IDX93
772	^ sing_76.htm#SEC115
773	^ sing_88.htm#SEC127
774	_ sing_36.htm#IDX117
775	` sing_36.htm#IDX106
776	a, ordering sing_898.htm#SEC949
777	absFactorize sing_1137.htm#SEC1212
778	absFactorizeBCG sing_1138.htm#SEC1213
779	absPrimdecGTZ sing_1335.htm#SEC1410
780	absPrimdecGTZE sing_1336.htm#SEC1411
781	absValue sing_937.htm#SEC1012
782	absfact.lib sing_1136.htm#SEC1211
783	absfact_lib sing_1136.htm#SEC1211
784	absolute factorization. sing_1136.htm#IDX452
785	abstractR sing_1474.htm#SEC1549
786	actionIsProper sing_1704.htm#SEC1779
787	addNvarsTo sing_1054.htm#SEC1129
788	addRat sing_836.htm#SEC887
789	addcol sing_1093.htm#SEC1168
790	addcores sing_1023.htm#SEC1098
791	addrow sing_1094.htm#SEC1169
792	addvarsTo sing_1053.htm#SEC1128
793	ademRelations sing_697.htm#SEC748
794	adjoint sing_1118.htm#SEC1193
795	adjointIdeal sing_1403.htm#SEC1478
796	adjunction divisor sing_1821.htm#IDX710
797	admissibleSub sing_755.htm#SEC806
798	afaces sing_2280.htm#SEC2355
799	affine code Fitzgerald-Lax method sing_921.htm#SEC989
800	ainvar.lib sing_1701.htm#SEC1776
801	ainvar_lib sing_1701.htm#SEC1776
802	aksaka.lib sing_1886.htm#SEC1961
803	aksaka_lib sing_1886.htm#SEC1961
804	alexanderpolynomial sing_1499.htm#SEC1574
805	alexpoly.lib sing_1496.htm#SEC1571
806	alexpoly_lib sing_1496.htm#SEC1571
807	algDependent sing_1143.htm#SEC1218
808	alg_kernel sing_1144.htm#SEC1219
809	algebra.lib sing_1139.htm#SEC1214
810	algebra_containment sing_1140.htm#SEC1215
811	algebra_lib sing_1139.htm#SEC1214
812	algebraic dependence sing_785.htm#IDX352
813	algebraic field extension sing_1349.htm#IDX510
814	algebraicDependence sing_1362.htm#SEC1437
815	algorithm of Bigatti, La Scala and Robbiano Bigatti and La Scala and Robbiano sing_912.htm#SEC968
816	algorithm of Conti and Traverso sing_908.htm#SEC964
817	algorithm of Di Biase and Urbanke Di Biase and Urbanke sing_911.htm#SEC967
818	algorithm of Hosten and Sturmfels Hosten and Sturmfels sing_910.htm#SEC966
819	algorithm of Pottier sing_909.htm#SEC965
820	align sing_260.htm#SEC299
821	all.lib sing_930.htm#SEC1005
822	allDoubleExt sing_802.htm#SEC853
823	allExtOfLeft sing_799.htm#SEC850
824	allExtOfRight sing_800.htm#SEC851
825	allPositive sing_564.htm#SEC615
826	all_lib sing_930.htm#SEC1005
827	allowing net access Command line options sing_19.htm#IDX41
828	allprint sing_971.htm#SEC1046
829	allreal sing_2029.htm#SEC2104
830	allrealst sing_2027.htm#SEC2102
831	allsquarefree sing_1603.htm#SEC1678
832	ambientDimension sing_187.htm#SEC226
833	and Evaluation of logical expressions sing_96.htm#SEC135
834	and sing_459.htm#SEC498
835	annPoly sing_612.htm#SEC663
836	annRat sing_613.htm#SEC664
837	annRatSyz sing_825.htm#SEC876
838	annfs sing_589.htm#SEC640
839	annfs0 sing_601.htm#SEC652
840	annfs2 sing_602.htm#SEC653
841	annfsBMI sing_598.htm#SEC649
842	annfsParamBM sing_597.htm#SEC648
843	annfsRB sing_603.htm#SEC654
844	annfspecial sing_590.htm#SEC641
845	annihilator of polynomial sing_611.htm#IDX331
846	annihilator of rational function sing_611.htm#IDX332
847	annihilator of rational function sing_815.htm#IDX377
848	annil sing_1245.htm#SEC1320
849	appelF1 sing_630.htm#SEC681
850	appelF2 sing_631.htm#SEC682
851	appelF4 sing_632.htm#SEC683
852	appendWeight2Ord sing_757.htm#SEC808
853	apply sing_426.htm#SEC465
854	applyAdF sing_580.htm#SEC631
855	arcpoint.lib sing_1509.htm#SEC1584
856	arcpoint_lib sing_1509.htm#SEC1584
857	areZeroElements sing_2366.htm#SEC2441
858	argument, default sing_44.htm#SEC80
859	argument, optional sing_44.htm#SEC80
860	arr.lib sing_2122.htm#SEC2197
861	arr2multarr sing_2155.htm#SEC2230
862	arrBoolean sing_2144.htm#SEC2219
863	arrBoundedChambers sing_2165.htm#SEC2240
864	arrBraid sing_2145.htm#SEC2220
865	arrCenter sing_2132.htm#SEC2207
866	arrCentered sing_2134.htm#SEC2209
867	arrCentral sing_2133.htm#SEC2208
868	arrCentralize sing_2135.htm#SEC2210
869	arrChambers sing_2164.htm#SEC2239
870	arrCharPoly sing_2162.htm#SEC2237
871	arrCone sing_2138.htm#SEC2213
872	arrCoordChange sing_2136.htm#SEC2211
873	arrCoordNormalize sing_2137.htm#SEC2212
874	arrDecone sing_2139.htm#SEC2214
875	arrDer sing_2152.htm#SEC2227
876	arrEdelmanReiner sing_2150.htm#SEC2225
877	arrEssentialize sing_2143.htm#SEC2218
878	arrExponents sing_2154.htm#SEC2229
879	arrFlats sing_2159.htm#SEC2234
880	arrIsEssential sing_2142.htm#SEC2217
881	arrIsFree sing_2153.htm#SEC2228
882	arrLastVar sing_2131.htm#SEC2206
883	arrLattice sing_2160.htm#SEC2235
884	arrLocalize sing_2140.htm#SEC2215
885	arrOrlikSolomon sing_2151.htm#SEC2226
886	arrPoincare sing_2163.htm#SEC2238
887	arrPrintMatrix sing_2127.htm#SEC2202
888	arrRandom sing_2148.htm#SEC2223
889	arrRandomCentral sing_2149.htm#SEC2224
890	arrRestrict sing_2141.htm#SEC2216
891	arrSet sing_2123.htm#SEC2198
892	arrSwapVar sing_2130.htm#SEC2205
893	arrTypeB sing_2146.htm#SEC2221
894	arrTypeD sing_2147.htm#SEC2222
895	arr_lib sing_2122.htm#SEC2197
896	arrange sing_605.htm#SEC656
897	arrangement sing_2123.htm#IDX769
898	arrangement sing_2124.htm#IDX774
899	arrangement sing_2155.htm#IDX836
900	arrangement sing_2156.htm#IDX839
901	ask sing_1894.htm#SEC1969
902	assPrimes sing_1154.htm#SEC1229
903	assign sing_2123.htm#IDX771
904	assignment,custom Assignments for user defined types sing_182.htm#SEC221
905	assprimeszerodim.lib assprimeszerodim_lib sing_1152.htm#SEC1227
906	assprimeszerodim_lib assprimeszerodim_lib sing_1152.htm#SEC1227
907	atkins.lib sing_1895.htm#SEC1970
908	atkins_lib sing_1895.htm#SEC1970
909	attrib sing_261.htm#SEC300
910	autonom sing_1858.htm#SEC1933
911	autonomDim sing_1859.htm#SEC1934
912	awalk1 sing_1185.htm#SEC1260
913	awalk2 sing_1186.htm#SEC1261
914	b-function sing_553.htm#IDX304
915	bFactor sing_635.htm#SEC686
916	babyGiant sing_1924.htm#SEC1999
917	backward sing_2255.htm#SEC2330
918	bareiss sing_262.htm#SEC301
919	base2str sing_933.htm#SEC1008
920	basering sing_28.htm#IDX77
921	basering sing_83.htm#SEC122
922	basicinvariants sing_1515.htm#SEC1590
923	belongSemigroup sing_1157.htm#SEC1232
924	bernstein sing_1563.htm#SEC1638
925	bernsteinBM sing_593.htm#SEC644
926	bernsteinLift sing_594.htm#SEC645
927	bertini2Singular sing_1387.htm#SEC1462
928	betti sing_263.htm#SEC302
929	betti (plural) sing_503.htm#SEC542
930	bfct sing_554.htm#SEC605
931	bfctAnn sing_556.htm#SEC607
932	bfctBound sing_824.htm#SEC875
933	bfctIdeal sing_558.htm#SEC609
934	bfctOneGB sing_557.htm#SEC608
935	bfctSyz sing_555.htm#SEC606
936	bfctVarAnn sing_646.htm#SEC697
937	bfctVarIn sing_645.htm#SEC696
938	bfun.lib sing_553.htm#SEC604
939	bfun_lib sing_553.htm#SEC604
940	bigint sing_73.htm#SEC112
941	bigint declarations sing_74.htm#SEC113
942	bigint expressions sing_75.htm#SEC114
943	bigint operations sing_76.htm#SEC115
944	bigint related functions bigint related functions sing_77.htm#SEC116
945	bigintmat sing_78.htm#SEC117
946	bigintmat declarations bigintmat declarations sing_79.htm#SEC118
947	bigintmat expressions bigintmat expressions sing_80.htm#SEC119
948	bigintmat operations bigintmat operations sing_82.htm#SEC121
949	bigintmat type cast sing_81.htm#SEC120
950	bimodules sing_546.htm#IDX292
951	bimodules.lib sing_546.htm#SEC597
952	bimodules_lib sing_546.htm#SEC597
953	binary_add sing_1947.htm#SEC2022
954	binomial sing_938.htm#SEC1013
955	binomials2intmat sing_1310.htm#SEC1385 58804
956	birational map, image, inverse. sing_1404.htm#IDX539
957	bistd sing_547.htm#SEC598
958	bisyzygies sing_546.htm#IDX293
959	bitrinity sing_548.htm#SEC599
960	blackbox sing_243.htm#SEC282
961	blackbox sing_251.htm#SEC290
962	block sing_40.htm#SEC69
963	block sing_425.htm#SEC464
964	blowUp sing_1455.htm#SEC1530
965	blowUp2 sing_1456.htm#SEC1531
966	blowUpBO sing_1462.htm#SEC1537
967	blowup0 sing_1162.htm#SEC1237
968	boolean sing_2144.htm#IDX813
969	boolean expressions sing_95.htm#SEC134
970	boolean operations sing_96.htm#SEC135
971	boolean_constant sing_2105.htm#SEC2180 52873
972	boolean_ideal sing_2109.htm#SEC2184 53515
973	boolean_poly sing_2106.htm#SEC2181 41652
974	boolean_poly_ring sing_2104.htm#SEC2179 sprintf
975	boolean_set sing_2110.htm#SEC2185 58235
976	boolean_std sing_2103.htm#SEC2178 5921
977	boundBuFou sing_2024.htm#SEC2099
978	boundDes sing_2026.htm#SEC2101
979	boundaryLatticePoints boundaryLatticePoints sing_2411.htm#SEC2486
980	boundposDes sing_2025.htm#SEC2100
981	bracket sing_406.htm#IDX192
982	bracket sing_462.htm#SEC501
983	bracket sing_504.htm#SEC543
984	braid sing_2145.htm#IDX815
985	branchTo procs with different argument types sing_155.htm#SEC194
986	break sing_427.htm#SEC466
987	break point sing_441.htm#SEC480
988	breakpoint sing_428.htm#SEC467
989	brillnoether.lib sing_2167.htm#SEC2242
990	brillnoether_lib sing_2167.htm#SEC2242
991	brnoeth.lib sing_1820.htm#SEC1895
992	brnoeth_lib sing_1820.htm#SEC1895
993	browser, command line option Command line options sing_19.htm#IDX44
994	browser, setting the sing_406.htm#IDX188
995	browsers The online help system sing_16.htm#IDX21
996	browsers, setting the sing_406.htm#IDX187
997	bubblesort sing_1897.htm#SEC1972
998	busadj sing_1116.htm#SEC1191
999	bvar sing_2117.htm#SEC2192 52773
1000	c, module ordering sing_895.htm#IDX404
1001	cProj sing_2207.htm#SEC2282
1002	calculateI sing_1429.htm#SEC1504
1003	calculate_max_sum sing_1966.htm#SEC2041
1004	calculate_ordering sing_1944.htm#SEC2019
1005	cancelunit, option sing_364.htm#IDX167
1006	canonMap sing_1190.htm#SEC1265
1007	canonicalizeCone sing_188.htm#SEC227
1008	canonize sing_1866.htm#SEC1941
1009	cantoradd sing_1980.htm#SEC2055
1010	cantormult sing_1983.htm#SEC2058
1011	cantorred sing_1981.htm#SEC2056
1012	cardGroup sing_1159.htm#SEC1234
1013	case No case or switch statement sing_460.htm#SEC499
1014	cdd sing_1.htm#IDX10
1015	cddlib sing_1.htm#IDX11
1016	center sing_567.htm#IDX311
1017	center sing_573.htm#SEC624
1018	center sing_2132.htm#IDX795
1019	center sing_2133.htm#IDX796
1020	center sing_2134.htm#IDX798
1021	center sing_2135.htm#IDX800
1022	centerRed sing_572.htm#SEC623
1023	centerVS sing_571.htm#SEC622
1024	central sing_2126.htm#IDX781
1025	central sing_2133.htm#IDX797
1026	central sing_2135.htm#IDX799
1027	central sing_2149.htm#IDX824
1028	central.lib sing_567.htm#SEC618
1029	central1st sing_2256.htm#SEC2331
1030	central2nd sing_2257.htm#SEC2332
1031	central_lib sing_567.htm#SEC618
1032	centralize sing_567.htm#IDX314
1033	centralizeSet sing_568.htm#SEC619
1034	centralizer sing_567.htm#IDX312
1035	centralizer sing_574.htm#SEC625
1036	centralizerRed sing_570.htm#SEC621
1037	centralizerVS sing_569.htm#SEC620
1038	cgs sing_932.htm#SEC1007
1039	cgsdr sing_957.htm#SEC1032
1040	chAll sing_2179.htm#SEC2254
1041	chAllInv sing_2180.htm#SEC2255
1042	chDual sing_2185.htm#SEC2260
1043	chHE sing_2181.htm#SEC2256
1044	chHom sing_2192.htm#SEC2267
1045	chNum sing_2175.htm#SEC2250
1046	chNumbers sing_2176.htm#SEC2251
1047	chNumbersProj sing_2211.htm#SEC2286
1048	chProd sing_2187.htm#SEC2262
1049	chProdE sing_2188.htm#SEC2263
1050	chProdL sing_2189.htm#SEC2264
1051	chProdLP sing_2190.htm#SEC2265
1052	chProj sing_2208.htm#SEC2283
1053	chSum sing_2183.htm#SEC2258
1054	chSymm sing_2195.htm#SEC2270
1055	chSymm2L sing_2196.htm#SEC2271
1056	chSymm2LP sing_2197.htm#SEC2272
1057	chWedge sing_2198.htm#SEC2273
1058	chWedge2L sing_2199.htm#SEC2274
1059	chWedge2LP sing_2200.htm#SEC2275
1060	chaincrit sing_1994.htm#SEC2069
1061	chambers sing_2164.htm#IDX852
1062	chambers sing_2165.htm#IDX853
1063	changeDenominator sing_1283.htm#SEC1358
1064	changechar sing_1028.htm#SEC1103
1065	changeord sing_1029.htm#SEC1104
1066	changeordTo sing_1052.htm#SEC1127
1067	changes sing_2451.htm#SEC2526
1068	changevar sing_1030.htm#SEC1105
1069	char sing_264.htm#SEC303
1070	charInfo sing_628.htm#SEC679
1071	charVariety sing_627.htm#SEC678
1072	char_series sing_265.htm#SEC304
1073	characteristic exponents sing_1503.htm#IDX563
1074	characteristic exponents sing_1504.htm#IDX568
1075	characteristic exponents sing_1505.htm#IDX571
1076	characteristic exponents sing_1506.htm#IDX575
1077	characteristic exponents sing_1590.htm#IDX681
1078	characteristic polynomial sing_2162.htm#IDX850
1079	characteristic variety sing_611.htm#IDX339
1080	characteristic variety sing_815.htm#IDX373
1081	charexp2conductor sing_1506.htm#SEC1581
1082	charexp2generators sing_1504.htm#SEC1579
1083	charexp2inter sing_1505.htm#SEC1580
1084	charexp2multseq sing_1503.htm#SEC1578
1085	charexp2poly sing_1507.htm#SEC1582
1086	charpoly sing_1117.htm#SEC1192
1087	charstr sing_266.htm#SEC305
1088	checkFactor sing_604.htm#SEC655
1089	checkRoot sing_599.htm#SEC650
1090	chern sing_2174.htm#SEC2249
1091	chern.lib sing_2169.htm#SEC2244
1092	chernCharPoly sing_2214.htm#SEC2289
1093	chernPoly sing_2213.htm#SEC2288
1094	chern_lib sing_2169.htm#SEC2244
1095	chineseRem sing_1915.htm#SEC1990
1096	chinrem sing_267.htm#SEC306
1097	chinrempoly sing_2383.htm#SEC2458
1098	chinrestp sing_1974.htm#SEC2049
1099	cimonom.lib sing_2224.htm#SEC2299
1100	cimonom_lib sing_2224.htm#SEC2299
1101	cisimplicial.lib sing_1155.htm#SEC1230
1102	cisimplicial_lib sing_1155.htm#SEC1230
1103	classify sing_1516.htm#SEC1591
1104	classify.lib sing_1514.htm#SEC1589
1105	classifyCeq sing_1533.htm#SEC1608
1106	classify_lib sing_1514.htm#SEC1589
1107	classifyceq.lib sing_1532.htm#IDX578
1108	classifyceq_lib sing_1532.htm#IDX579
1109	classifyci.lib sing_1534.htm#IDX580
1110	classifyci_lib sing_1534.htm#IDX581
1111	classifyicis sing_1535.htm#SEC1610
1112	classpoly sing_2212.htm#SEC2287
1113	cleanTmp sing_2095.htm#SEC2170
1114	cleanunit sing_1427.htm#SEC1502
1115	cleardenom sing_268.htm#SEC307
1116	close sing_269.htm#SEC308
1117	closed_points sing_1830.htm#SEC1905
1118	closetex sing_1797.htm#SEC1872
1119	closureFrac sing_1276.htm#SEC1351
1120	coHom sing_808.htm#SEC859
1121	codim sing_1628.htm#SEC1703
1122	codimension sing_189.htm#SEC228
1123	coding theory sing_887.htm#SEC938
1124	coef sing_270.htm#SEC309
1125	coefficient sing_2125.htm#IDX777
1126	coefficient sing_2126.htm#IDX780
1127	coefficient sing_2127.htm#IDX784
1128	coefficient field sing_139.htm#SEC178
1129	coefficient rings, ring of integers, zero divisors, p-adic numbers Coefficient rings sing_32.htm#SEC44
1130	coefficients, long sing_846.htm#SEC897
1131	coeffmod sing_1892.htm#SEC1967
1132	coeffs sing_271.htm#SEC310
1133	collectDiv sing_1472.htm#SEC1547
1134	colrank sing_1864.htm#SEC1939
1135	colred sing_1100.htm#SEC1175
1136	commRing sing_839.htm#SEC890
1137	comma sing_461.htm#SEC500
1138	command,custom Commands for user defined types sing_181.htm#SEC220
1139	command-line option, setting value of sing_406.htm#IDX270
1140	command-line option, value of sing_406.htm#IDX268
1141	command-line options, print all values of sing_406.htm#IDX267
1142	command-line options, short help Command line options sing_19.htm#IDX38
1143	commands (plural) sing_502.htm#IDX291
1144	comment sing_36.htm#IDX109
1145	compareTasks sing_1064.htm#SEC1139
1146	completeReduction sing_1706.htm#SEC1781
1147	complex sing_28.htm#IDX76
1148	complexSingType sing_1530.htm#SEC1605
1149	compregb.lib sing_931.htm#SEC1006
1150	compregb_lib sing_931.htm#SEC1006
1151	comprehensive Groebner system sing_931.htm#IDX410
1152	compress sing_1077.htm#SEC1152
1153	computeConstant sing_1175.htm#SEC1250
1154	computeGromovWitten sing_1178.htm#SEC1253
1155	computeN sing_1476.htm#SEC1551
1156	computeV sing_1475.htm#SEC1550
1157	computemcm sing_1434.htm#SEC1509
1158	concat sing_1078.htm#SEC1153
1159	conductor sing_1506.htm#IDX574
1160	conductor, degree sing_1590.htm#IDX684
1161	cone sing_183.htm#SEC222
1162	cone sing_2138.htm#IDX804
1163	cone sing_2139.htm#IDX806
1164	cone related functions cone related functions sing_186.htm#SEC225
1165	coneLink sing_190.htm#SEC229
1166	coneViaInequalities sing_185.htm#SEC224
1167	coneViaPoints sing_184.htm#SEC223
1168	conic, parametrization, rational point. sing_1411.htm#IDX544
1169	conicWithTangents sing_2071.htm#SEC2146
1170	constructH sing_1435.htm#SEC1510
1171	constructblwup sing_1436.htm#SEC1511
1172	constructlastblwup sing_1437.htm#SEC1512
1173	constructor sing_2155.htm#IDX837
1174	constructor sing_2156.htm#IDX840
1175	contact matrix sing_1505.htm#IDX570
1176	containedQ sing_1785.htm#SEC1860
1177	containsAsFace sing_191.htm#SEC230
1178	containsInCollection containsInCollection sing_223.htm#SEC262
1179	containsInSupport sing_192.htm#SEC231
1180	containsPositiveVector containsPositiveVector sing_193.htm#SEC232
1181	containsRelatively sing_194.htm#SEC233
1182	content sing_1002.htm#SEC1077
1183	contentSB, option sing_364.htm#IDX168
1184	continue Behavior of continue sing_429.htm#SEC468
1185	continue sing_463.htm#SEC502
1186	contraHom sing_809.htm#SEC860
1187	contract sing_272.htm#SEC311
1188	contributors sing_406.htm#IDX195
1189	control sing_1856.htm#SEC1931
1190	control.lib sing_1855.htm#SEC1930
1191	controlDim sing_1857.htm#SEC1932
1192	controlExample sing_1869.htm#SEC1944
1193	control_Matrix sing_1558.htm#SEC1633
1194	control_lib sing_1855.htm#SEC1930
1195	convertdata sing_1432.htm#SEC1507
1196	convex geometry sing_2400.htm#SEC2475
1197	convexHull sing_195.htm#SEC234
1198	convexIntersection sing_196.htm#SEC235
1199	convloc sing_608.htm#SEC659
1200	coordinate change sing_2135.htm#IDX801
1201	coordinate change sing_2136.htm#IDX802
1202	coordinate change sing_2137.htm#IDX803
1203	coordinates sing_2012.htm#IDX726
1204	coords sing_2012.htm#SEC2087
1205	copyTask sing_1063.htm#SEC1138
1206	copyright sing_1.htm#IDX1
1207	corank sing_1517.htm#SEC1592
1208	cornerMonomials sing_1313.htm#SEC1388
1209	countPoints sing_1937.htm#SEC2012
1210	coverings sing_1177.htm#IDX469
1211	coverings sing_1178.htm#IDX473
1212	cpu sing_406.htm#IDX197
1213	cpu sing_406.htm#IDX264
1214	createBO sing_1463.htm#SEC1538
1215	createGradedRingHomomorphism createGradedRingHomomorphism sing_2342.htm#SEC2417
1216	createGroup sing_2335.htm#SEC2410
1217	createQuotientGroup sing_2336.htm#SEC2411
1218	createTask sing_1061.htm#SEC1136
1219	createTorsionFreeGroup createTorsionFreeGroup sing_2337.htm#SEC2412
1220	createlist sing_1445.htm#SEC1520
1221	crypto.lib sing_1910.htm#SEC1985
1222	crypto_lib sing_1910.htm#SEC1985
1223	cup sing_1191.htm#SEC1266
1224	cupproduct sing_1192.htm#SEC1267
1225	curve singularities sing_1496.htm#IDX557
1226	curve singularities sing_1584.htm#IDX679
1227	curvepar.lib sing_1537.htm#SEC1612
1228	curvepar_lib sing_1537.htm#SEC1612
1229	custom assignment Assignments for user defined types sing_182.htm#SEC221
1230	custom command Commands for user defined types sing_181.htm#SEC220
1231	custom type Definition of a user defined type sing_178.htm#SEC217
1232	cycleLength sing_2047.htm#SEC2122
1233	cyclePoints sing_2051.htm#SEC2126
1234	cyclic sing_989.htm#SEC1064
1235	cyclic code Codes and the decoding problem sing_918.htm#SEC976
1236	cyclotomic sing_1671.htm#SEC1746
1237	datetime sing_273.htm#SEC312
1238	dbprint sing_274.htm#SEC313
1239	deRham.lib sing_2397.htm#IDX896
1240	deRhamCohom sing_625.htm#SEC676
1241	deRhamCohomIdeal sing_626.htm#SEC677
1242	deRhamCohomology sing_2398.htm#SEC2473
1243	deRham_lib sing_2397.htm#IDX897
1244	debugLib, option sing_364.htm#IDX172
1245	debug_log sing_1527.htm#SEC1602
1246	debugger Source code debugger sing_66.htm#SEC102
1247	debugging library code Source code debugger sing_66.htm#SEC102
1248	dec1var sing_1244.htm#SEC1319
1249	decimal sing_1911.htm#SEC1986
1250	decode sing_1847.htm#SEC1922
1251	decodeCode sing_1849.htm#SEC1924
1252	decodeRandom sing_1848.htm#SEC1923
1253	decodeRandomFL sing_1852.htm#SEC1927
1254	decodeSV sing_1829.htm#SEC1904
1255	decodegb.lib sing_1834.htm#SEC1909
1256	decodegb_lib sing_1834.htm#SEC1909
1257	decoding, decoding problem Codes and the decoding problem sing_918.htm#SEC977
1258	decoef sing_1877.htm#SEC1952
1259	decone sing_2138.htm#IDX805
1260	decone sing_2139.htm#IDX807
1261	def sing_83.htm#SEC122
1262	def declarations sing_84.htm#SEC123
1263	defRes, option sing_364.htm#IDX173
1264	default argument sing_44.htm#SEC80
1265	defineHomogeneous sing_2375.htm#SEC2450
1266	defined sing_275.htm#SEC314
1267	defl sing_1394.htm#SEC1469
1268	deform sing_1629.htm#SEC1704
1269	deform.lib sing_1548.htm#SEC1623
1270	deform_lib sing_1548.htm#SEC1623
1271	defring sing_1031.htm#SEC1106
1272	defringp sing_1033.htm#SEC1108
1273	defrings sing_1032.htm#SEC1107
1274	deg sing_276.htm#SEC315
1275	degBound sing_443.htm#SEC482
1276	degree Miscellaneous oddities sing_277.htm#SEC316
1277	degree sing_466.htm#IDX281
1278	degree lexicographical ordering sing_893.htm#IDX384
1279	degree of a polynomial Miscellaneous oddities sing_466.htm#IDX285
1280	degree reverse lexicographical ordering sing_893.htm#IDX382
1281	degreeDivisor sing_2236.htm#SEC2311
1282	degreeFormalDivisor sing_2244.htm#SEC2319
1283	degreepart sing_1737.htm#SEC1812
1284	delete sing_278.htm#SEC317
1285	delete sing_325.htm#SEC364
1286	deleteGenerator sing_640.htm#SEC691
1287	deleteSublist sing_939.htm#SEC1014
1288	delta sing_1596.htm#SEC1671
1289	delta invariant sing_1278.htm#IDX504
1290	delta invariant sing_1596.htm#IDX689
1291	delta invariant. sing_1270.htm#IDX497
1292	delta invariant. sing_1271.htm#IDX500
1293	delta invariant. sing_1272.htm#IDX503
1294	deltaLoc sing_1278.htm#SEC1353
1295	denom_list sing_406.htm#IDX199
1296	denominator sing_279.htm#SEC318
1297	depth sing_1193.htm#SEC1268
1298	depthIdeal sing_1254.htm#SEC1329
1299	derivate sing_1703.htm#SEC1778
1300	derivation sing_2152.htm#IDX828
1301	desingularization sing_2286.htm#IDX880
1302	desingularization sing_2287.htm#SEC2362
1303	det sing_280.htm#SEC319
1304	det_B sing_1119.htm#SEC1194
1305	detadj sing_1612.htm#SEC1687
1306	determinacy sing_2396.htm#SEC2471
1307	determinecenter sing_1417.htm#SEC1492
1308	detropicalise sing_2089.htm#SEC2164
1309	develop sing_1586.htm#SEC1661
1310	diag sing_1079.htm#SEC1154
1311	diagInvariants sing_1292.htm#SEC1367 62096
1312	diag_test sing_1115.htm#SEC1190
1313	diff sing_281.htm#SEC320
1314	diffRat sing_838.htm#SEC889
1315	difpoly2tex sing_1878.htm#SEC1953
1316	dim sing_282.htm#SEC321
1317	dim (plural) sing_505.htm#SEC544
1318	dimGradedPart sing_1485.htm#SEC1560 11262
1319	dimH sing_1484.htm#SEC1559 38534
1320	dimMon sing_1234.htm#SEC1309
1321	dim_slocus sing_1630.htm#SEC1705
1322	dimension sing_197.htm#SEC236
1323	dimensionOfLocalization dimensionOfLocalization sing_2274.htm#SEC2349
1324	direct_boolean_poly sing_2107.htm#SEC2182 49893
1325	direct_from_boolean_poly direct_from_boolean_poly sing_2113.htm#SEC2188 36941
1326	disc sing_1898.htm#SEC1973
1327	discr sing_1652.htm#SEC1727
1328	discrepancy sing_1470.htm#SEC1545
1329	disp_zdd sing_2120.htm#SEC2195 41439
1330	displayCohom sing_1486.htm#SEC1561 22633
1331	displayHNE sing_1589.htm#SEC1664
1332	displayInvariants sing_1591.htm#SEC1666
1333	displayMultsequence sing_1593.htm#SEC1668
1334	displayPuiseuxExpansion displayPuiseuxExpansion sing_2064.htm#SEC2139
1335	displayTropicalLifting displayTropicalLifting sing_2062.htm#SEC2137
1336	distributed computing sing_982.htm#IDX429
1337	distributed computing sing_1022.htm#IDX431
1338	distributed computing sing_1060.htm#IDX444
1339	div Miscellaneous oddities sing_76.htm#SEC115
1340	div sing_93.htm#SEC132
1341	div sing_466.htm#IDX278
1342	divideUnits sing_1874.htm#SEC1949
1343	dividelist sing_1444.htm#SEC1519
1344	division sing_283.htm#SEC322
1345	division (plural) sing_506.htm#SEC545
1346	division, pdivi, reduce sing_959.htm#IDX414
1347	division, reduce sing_958.htm#IDX413
1348	divisor sing_1977.htm#SEC2052
1349	divisorplus sing_2230.htm#SEC2305
1350	divisors negativeformaldivisor sing_2229.htm#IDX854
1351	divisors sing_2230.htm#IDX855
1352	divisors sing_2231.htm#IDX856
1353	divisors sing_2232.htm#IDX857
1354	divisors sing_2233.htm#IDX858
1355	divisors sing_2234.htm#IDX859
1356	divisors sing_2235.htm#IDX860
1357	divisors sing_2236.htm#IDX861
1358	divisors sing_2237.htm#IDX862
1359	divisors sing_2238.htm#IDX863
1360	divisors sing_2239.htm#IDX864
1361	divisors sing_2240.htm#IDX865
1362	divisors sing_2241.htm#IDX866
1363	divisors sing_2242.htm#IDX867
1364	divisors sing_2243.htm#IDX868
1365	divisors sing_2244.htm#IDX869
1366	divisors, polyhedra sing_2245.htm#IDX870
1367	divisors, polyhedra sing_2246.htm#IDX871
1368	divisors, polyhedra sing_2247.htm#IDX872
1369	divisors.lib sing_2228.htm#SEC2303
1370	divisors_lib sing_2228.htm#SEC2303
1371	dmod.lib sing_588.htm#SEC639
1372	dmodAction sing_833.htm#SEC884
1373	dmodActionRat sing_834.htm#SEC885
1374	dmodGeneralAssumptionCheck dmodGeneralAssumptionCheck sing_826.htm#SEC877
1375	dmod_lib sing_588.htm#SEC639
1376	dmodapp.lib sing_611.htm#SEC662
1377	dmodapp_lib sing_611.htm#SEC662
1378	dmodloc.lib sing_815.htm#IDX366
1379	dmodloc_lib sing_815.htm#IDX367
1380	dmodoublext sing_810.htm#SEC861
1381	dmodvar.lib sing_644.htm#SEC695
1382	dmodvar_lib sing_644.htm#SEC695
1383	double sing_1982.htm#SEC2057
1384	doubleExt sing_801.htm#SEC852
1385	downloading Download instructions sing_2458.htm#SEC2545
1386	dp, global ordering sing_893.htm#IDX383
1387	drawNewtonSubdivision drawNewtonSubdivision sing_2067.htm#SEC2142
1388	drawTropicalCurve sing_2066.htm#SEC2141
1389	ds, local ordering sing_894.htm#IDX393
1390	dsum sing_1080.htm#SEC1155
1391	dualCone sing_198.htm#SEC237
1392	dualConic sing_2091.htm#SEC2166
1393	dualPart sing_2220.htm#SEC2295
1394	dualPolytope sing_240.htm#SEC279
1395	dual_code sing_1831.htm#SEC1906
1396	dump sing_284.htm#SEC323
1397	ecart sing_1985.htm#SEC2060
1398	echo sing_444.htm#SEC483
1399	eexgcdN sing_1912.htm#SEC1987
1400	effective sing_2238.htm#SEC2313
1401	egcdMain sing_1778.htm#SEC1853
1402	ehrhartPolynomialCoeff ehrhartPolynomialCoeff sing_2412.htm#SEC2487
1403	ehrhartRing sing_1288.htm#SEC1363 16966
1404	eigenvals sing_1127.htm#SEC1202
1405	eigenvalue sing_377.htm#SEC416
1406	eigenvalue sing_1127.htm#IDX450
1407	eigenvalues sing_1371.htm#SEC1446
1408	elemSymmId sing_990.htm#SEC1065
1409	elim sing_1164.htm#SEC1239
1410	elim.lib sing_1161.htm#SEC1236
1411	elim1 sing_1165.htm#SEC1240
1412	elim2 sing_1166.htm#SEC1241
1413	elimRing sing_1163.htm#SEC1238
1414	elimWeight sing_758.htm#SEC809
1415	elim_lib sing_1161.htm#SEC1236
1416	eliminate sing_285.htm#SEC324
1417	eliminate (plural) sing_507.htm#SEC546
1418	eliminateNC sing_753.htm#SEC804
1419	elimination sing_752.htm#IDX351
1420	elimlinearpart sing_1738.htm#SEC1813
1421	elimpart sing_1739.htm#SEC1814
1422	elimpartanyr sing_1740.htm#SEC1815
1423	elimrep sing_1425.htm#SEC1500
1424	elliptic curve sing_1174.htm#IDX465
1425	elliptic curves sing_1171.htm#IDX459
1426	elliptic curves sing_1177.htm#IDX468
1427	elliptic curves sing_1178.htm#IDX472
1428	ellipticAdd sing_1933.htm#SEC2008
1429	ellipticAllPoints sing_1938.htm#SEC2013
1430	ellipticMult sing_1934.htm#SEC2009
1431	ellipticNF sing_2054.htm#SEC2129
1432	ellipticNFDB sing_2055.htm#SEC2130
1433	ellipticRandomCurve sing_1935.htm#SEC2010
1434	ellipticRandomPoint sing_1936.htm#SEC2011
1435	ellipticcovers.lib sing_1171.htm#IDX453
1436	ellipticcovers_lib sing_1171.htm#IDX454
1437	else sing_434.htm#SEC473
1438	embedMat sing_784.htm#SEC835
1439	emptyFan sing_224.htm#SEC263
1440	encode sing_1839.htm#SEC1914
1441	endomorphism filtration sing_1570.htm#IDX655
1442	endvfilt sing_1570.htm#SEC1645
1443	engine sing_641.htm#SEC692
1444	envelop sing_967.htm#SEC1042
1445	envelopdg sing_968.htm#SEC1043
1446	envelope sing_508.htm#SEC547
1447	enveloping algebra sing_406.htm#IDX203
1448	enveloping algebra sing_546.htm#IDX295
1449	environment variable, DISPLAY The online help system sing_16.htm#IDX29
1450	equalJinI sing_1513.htm#SEC1588
1451	equalMultiDeg sing_2368.htm#SEC2443
1452	equations sing_199.htm#SEC238
1453	equiRadical sing_1329.htm#SEC1404
1454	equidim sing_1331.htm#SEC1406
1455	equidimMax sing_1332.htm#SEC1407
1456	equidimMaxEHV sing_1333.htm#SEC1408
1457	equidimZ sing_1344.htm#SEC1419
1458	equising.lib sing_1553.htm#SEC1628
1459	equising_lib sing_1553.htm#SEC1628
1460	equisingular Tjurina number sing_1496.htm#IDX562
1461	equisingularity ideal sing_1555.htm#IDX582
1462	equisingularity stratum sing_1556.htm#IDX583
1463	error recovery sing_15.htm#SEC21
1464	errorInsert sing_1842.htm#SEC1917
1465	errorRand sing_1843.htm#SEC1918
1466	errormap sing_2262.htm#SEC2337
1467	esIdeal sing_1555.htm#SEC1630
1468	esStratum sing_1556.htm#SEC1631
1469	essential sing_2142.htm#IDX810
1470	essential sing_2143.htm#IDX811
1471	eta sing_2049.htm#SEC2124
1472	euler sing_1891.htm#SEC1966
1473	eulerChProj sing_2210.htm#SEC2285
1474	eval sing_286.htm#SEC325
1475	evaluateFormalDivisor evaluateFormalDivisor sing_2240.htm#SEC2315
1476	evaluatePDivisor sing_2246.htm#SEC2321
1477	evaluate_reynolds sing_1676.htm#SEC1751
1478	evalutateIntegral sing_1176.htm#SEC1251
1479	example sing_288.htm#SEC327
1480	example sing_2144.htm#IDX812
1481	example sing_2145.htm#IDX814
1482	example sing_2146.htm#IDX816
1483	example sing_2147.htm#IDX818
1484	example sing_2148.htm#IDX820
1485	example sing_2149.htm#IDX822
1486	example sing_2150.htm#IDX825
1487	execute sing_289.htm#SEC328
1488	exit sing_438.htm#SEC477
1489	exp2pt sing_1879.htm#SEC1954
1490	expo sing_1903.htm#SEC1978
1491	exponents sing_2154.htm#IDX833
1492	export sing_431.htm#SEC470
1493	exportNuminvs sing_1296.htm#SEC1371 10423
1494	exportto sing_432.htm#SEC471
1495	expression list sing_72.htm#IDX129
1496	expression list sing_470.htm#IDX288
1497	ext-module purityfiltration_lib sing_793.htm#IDX357
1498	extcurve sing_1825.htm#SEC1900
1499	extdevelop sing_1587.htm#SEC1662
1500	extend sing_963.htm#SEC1038
1501	extendWeyl sing_827.htm#SEC878
1502	extendedTensor sing_759.htm#SEC810
1503	extendring sing_1034.htm#SEC1109
1504	extension of rings sing_1349.htm#IDX511
1505	exterior basis sing_1106.htm#IDX447
1506	exterior power sing_1108.htm#IDX449
1507	exteriorBasis sing_1106.htm#SEC1181
1508	exteriorPower sing_1108.htm#SEC1183
1509	extgcd sing_290.htm#SEC329
1510	fVector sing_227.htm#SEC266
1511	fVector sing_2416.htm#SEC2491
1512	fVectorP(polymake) sing_2416.htm#SEC2491
1513	facFirstShift sing_746.htm#SEC797
1514	facFirstWeyl sing_742.htm#SEC793
1515	facGBIdeal sing_1314.htm#SEC1389
1516	facShift sing_745.htm#SEC796
1517	facSubWeyl sing_744.htm#SEC795
1518	facWeyl sing_741.htm#SEC792
1519	facetVertexLatticeDistances facetVertexLatticeDistances sing_2413.htm#SEC2488
1520	facetWidth sing_2414.htm#SEC2489
1521	facetWidths sing_2415.htm#SEC2490
1522	facets sing_200.htm#SEC239
1523	facstd sing_291.htm#SEC330
1524	factmodd sing_292.htm#SEC331
1525	factorH sing_954.htm#SEC1029
1526	factorLenstraECM sing_1942.htm#SEC2017
1527	factorMain sing_1779.htm#SEC1854
1528	factorgroup sing_2358.htm#SEC2433
1529	factorial sing_940.htm#SEC1015
1530	factorization sing_1136.htm#IDX451
1531	factorize sing_293.htm#SEC332
1532	factory sing_1.htm#IDX2
1533	fan sing_221.htm#SEC260
1534	fan sing_2038.htm#IDX731
1535	fan related functions fan related functions sing_222.htm#SEC261
1536	fanViaCones sing_225.htm#SEC264
1537	farey sing_294.htm#SEC333
1538	fastExpt sing_1887.htm#SEC1962
1539	fastHC, option sing_364.htm#IDX149
1540	fastelim sing_1741.htm#SEC1816
1541	fetch sing_295.htm#SEC334
1542	fetch (plural) sing_509.htm#SEC548
1543	fetchall sing_1035.htm#SEC1110
1544	ffsolve sing_1730.htm#SEC1805
1545	ffsolve.lib sing_1729.htm#SEC1804
1546	ffsolve_lib sing_1729.htm#SEC1804
1547	fglm sing_296.htm#SEC335
1548	fglm sing_403.htm#IDX183
1549	fglm_solve sing_1757.htm#SEC1832
1550	fglmquot sing_297.htm#SEC336
1551	fibonacci sing_941.htm#SEC1016
1552	field sing_139.htm#SEC178
1553	file, .singularrc sing_20.htm#IDX72
1554	filecmd sing_298.htm#SEC337
1555	filtration purityfiltration_lib sing_793.htm#IDX358
1556	finalCharts sing_1449.htm#SEC1524
1557	find sing_299.htm#SEC338
1558	findAuto sing_701.htm#SEC752
1559	findInvo sing_699.htm#SEC750
1560	findInvoDiag sing_700.htm#SEC751
1561	findOrientedBoundary findOrientedBoundary sing_2050.htm#SEC2125
1562	findTorsion sing_1868.htm#SEC1943
1563	find_first_primitive_root find_first_primitive_root sing_1946.htm#SEC2021
1564	find_index sing_1950.htm#SEC2025
1565	findifs.lib sing_1875.htm#SEC1950
1566	findifs_example sing_1876.htm#SEC1951
1567	findifs_lib sing_1875.htm#SEC1950
1568	findimAlgebra sing_768.htm#SEC819
1569	finduni sing_300.htm#SEC339
1570	findvars sing_1742.htm#SEC1817
1571	finite field sing_139.htm#SEC178
1572	finite field sing_1729.htm#IDX704
1573	finiteDiagInvariants finiteDiagInvariants sing_1291.htm#SEC1366 3508
1574	finitediff.lib sing_2248.htm#IDX873
1575	finitediff_lib sing_2248.htm#IDX874
1576	finitenessTest sing_1150.htm#SEC1225
1577	finvar.lib sing_1664.htm#SEC1739
1578	finvar_lib sing_1664.htm#SEC1739
1579	first index is 1 sing_465.htm#SEC504
1580	firstoct sing_1790.htm#SEC1865
1581	fitting sing_1196.htm#SEC1271
1582	fl2poly sing_638.htm#SEC689
1583	flatten sing_1081.htm#SEC1156
1584	flatteningStrat sing_1197.htm#SEC1272
1585	floating point sing_1044.htm#IDX434
1586	for sing_433.htm#SEC472
1587	formaldivisorplus sing_2241.htm#SEC2316
1588	forward sing_2254.htm#SEC2329
1589	fourier sing_633.htm#SEC684
1590	fouriersystem sing_2265.htm#SEC2340
1591	fpadim.lib sing_649.htm#SEC700
1592	fpadim_lib sing_649.htm#SEC700
1593	fprintf sing_301.htm#SEC340
1594	frandwalk sing_2388.htm#SEC2463
1595	free sing_2153.htm#IDX830
1596	free sing_2154.htm#IDX832
1597	free associative algebra, tensor algebra Free associative algebras sing_540.htm#SEC591
1598	freeGBasis sing_684.htm#SEC735
1599	freegb.lib sing_680.htm#SEC731
1600	freegb_lib sing_680.htm#SEC731
1601	freemodule sing_302.htm#SEC341
1602	freerank sing_992.htm#SEC1067
1603	from_boolean_constant from_boolean_constant sing_2111.htm#SEC2186 44881
1604	from_boolean_ideal sing_2115.htm#SEC2190 62698
1605	from_boolean_poly sing_2112.htm#SEC2187 27864
1606	from_boolean_set sing_2116.htm#SEC2191 60615
1607	frwalk sing_303.htm#SEC342
1608	fullFan sing_226.htm#SEC265
1609	fullSerreRelations sing_695.htm#SEC746
1610	furtherInvar sing_1708.htm#SEC1783
1611	further_hn_proc sing_1604.htm#SEC1679
1612	fwalk sing_1183.htm#SEC1258
1613	galois field sing_139.htm#SEC178
1614	gauss_col sing_1091.htm#SEC1166
1615	gauss_nf sing_1122.htm#SEC1197
1616	gauss_row sing_1092.htm#SEC1167
1617	gaussred sing_1120.htm#SEC1195
1618	gaussred_pivot sing_1121.htm#SEC1196
1619	gcd sing_304.htm#SEC343
1620	gcdMon sing_1223.htm#SEC1298
1621	gcddivisor sing_1978.htm#SEC2053
1622	gen sing_305.htm#SEC344
1623	genMDSMat sing_1845.htm#SEC1920
1624	genSymId sing_1368.htm#SEC1443
1625	general error-locator polynomial sing_919.htm#SEC983
1626	general neron. sing_2286.htm#IDX881
1627	general weighted lexicographical ordering sing_894.htm#IDX399
1628	general weighted reverse lexicographical ordering Local orderings sing_894.htm#IDX396
1629	general.lib sing_934.htm#SEC1009
1630	generalOrder sing_2003.htm#SEC2078
1631	general_lib sing_934.htm#SEC1009
1632	generateG sing_1941.htm#SEC2016
1633	generators sing_1504.htm#IDX566
1634	generatorsOfLinealitySpace generatorsOfLinealitySpace sing_201.htm#SEC240
1635	generatorsOfSpan sing_202.htm#SEC241
1636	genericid sing_1010.htm#SEC1085
1637	genericity sing_1865.htm#SEC1940
1638	genericmat sing_1082.htm#SEC1157
1639	genoutput sing_1438.htm#SEC1513
1640	genus sing_1274.htm#SEC1349
1641	geometric invariant theory sing_2279.htm#IDX878
1642	geometrical locus, locus, loci, dynamic geometry sing_966.htm#IDX418
1643	geometrical locus, locus, loci, envelop sing_967.htm#IDX419
1644	geometrical locus, locus, loci, envelop. sing_968.htm#IDX420
1645	geometrical locus, locus, loci. sing_965.htm#IDX417
1646	geometrical locus, locus, loci. sing_969.htm#IDX421
1647	getArguments sing_1072.htm#SEC1147
1648	getCommand sing_1071.htm#SEC1146
1649	getCone sing_228.htm#SEC267
1650	getGradingGroup sing_2333.htm#SEC2408
1651	getLattice sing_2334.htm#SEC2409
1652	getLinearForms sing_203.htm#SEC242
1653	getModuleGrading sing_2344.htm#SEC2419
1654	getMultiplicity sing_204.htm#SEC243
1655	getOneVar sing_1282.htm#SEC1357
1656	getResult sing_1073.htm#SEC1148
1657	getSmallest sing_1281.htm#SEC1356
1658	getState sing_1074.htm#SEC1149
1659	getVariableWeights sing_2332.htm#SEC2407
1660	getcores sing_1025.htm#SEC1100
1661	getdump sing_306.htm#SEC345
1662	getenv sing_406.htm#IDX205
1663	gfanlib sing_1.htm#IDX9
1664	gfanlib_so sing_2401.htm#IDX898
1665	gitCone sing_2281.htm#SEC2356
1666	gitFan sing_2282.htm#SEC2357
1667	gitfan sing_2279.htm#IDX876
1668	gitfan.lib sing_2279.htm#SEC2354
1669	gitfan_lib sing_2279.htm#SEC2354
1670	gkdim.lib sing_706.htm#SEC757
1671	gkdim_lib sing_706.htm#SEC757
1672	gkzFan sing_2283.htm#SEC2358
1673	global Bernstein-Sato polynomial sing_553.htm#IDX302
1674	global Bernstein-Sato polynomial sing_588.htm#IDX320
1675	global Bernstein-Sato polynomial for variety sing_644.htm#IDX345
1676	globalSections sing_2235.htm#SEC2310
1677	gmscoeffs sing_1562.htm#SEC1637
1678	gmsnf sing_1561.htm#SEC1636
1679	gmspoly.lib sing_1581.htm#SEC1656
1680	gmspoly_lib sing_1581.htm#SEC1656
1681	gmsring sing_1560.htm#SEC1635
1682	gmssing.lib sing_1559.htm#SEC1634
1683	gmssing_lib sing_1559.htm#SEC1634
1684	good basis sing_1559.htm#IDX594
1685	good basis sing_1569.htm#IDX649
1686	good basis sing_1581.htm#IDX665
1687	good basis sing_1583.htm#IDX676
1688	goodBasis sing_1583.htm#SEC1658
1689	gorensteinIndex sing_2417.htm#SEC2492
1690	gorensteinVector sing_2418.htm#SEC2493
1691	graal.lib sing_2272.htm#SEC2347
1692	graalMixed sing_2273.htm#SEC2348
1693	graal_lib sing_2272.htm#SEC2347
1694	gradeNumber sing_797.htm#SEC848
1695	graded Weyl algebra sing_553.htm#IDX305
1696	graded module, graded piece sing_1485.htm#IDX552
1697	graded modules, graded homomorphisms, syzygies gradedModules_lib sing_2288.htm#IDX882
1698	graded modules, handling of Handling graded modules sing_861.htm#SEC912
1699	gradedModules.lib sing_2288.htm#SEC2363
1700	gradedModules_lib sing_2288.htm#SEC2363
1701	gradiator sing_2377.htm#SEC2452
1702	graph sing_1172.htm#IDX463
1703	graph sing_1173.htm#IDX464
1704	graphics.lib sing_1792.htm#SEC1867
1705	graphics_lib sing_1792.htm#SEC1867
1706	graphviz sing_1.htm#IDX13
1707	graver4ti2 sing_1366.htm#SEC1441 39635
1708	grconcat sing_2311.htm#SEC2386
1709	grdeg sing_2291.htm#SEC2366
1710	grgens sing_2300.htm#SEC2375
1711	grgroebner sing_2310.htm#SEC2385
1712	grlift sing_2308.htm#SEC2383
1713	grlifting sing_2315.htm#SEC2390
1714	grlifting2 sing_2316.htm#SEC2391
1715	grlifting3 sing_2318.htm#SEC2393
1716	grneg sing_2321.htm#SEC2396
1717	grobcov sing_956.htm#SEC1031
1718	grobcov.lib sing_955.htm#SEC1030
1719	grobcov_lib sing_955.htm#SEC1030
1720	grobj sing_2289.htm#SEC2364
1721	groebner sing_307.htm#SEC346
1722	groebner sing_853.htm#SEC904
1723	groebner basis computations sing_307.htm#IDX143
1724	groebnerComplex sing_2408.htm#SEC2483
1725	groebnerCone sing_2404.htm#SEC2479
1726	groebnerFan sing_2406.htm#SEC2481
1727	groebnerFanP sing_2043.htm#SEC2118
1728	gromovWitten sing_1177.htm#SEC1252
1729	grorder sing_2302.htm#SEC2377
1730	ground field sing_139.htm#SEC178
1731	group_reynolds sing_1672.htm#SEC1747
1732	grpower sing_2298.htm#SEC2373
1733	grpres sing_2301.htm#SEC2376
1734	grprod sing_2309.htm#SEC2384
1735	grrange sing_2320.htm#SEC2395
1736	grres sing_2307.htm#SEC2382
1737	grrndmap sing_2313.htm#SEC2388
1738	grrndmap2 sing_2314.htm#SEC2389
1739	grrndmat sing_2312.htm#SEC2387
1740	grshift sing_2293.htm#SEC2368
1741	grsum sing_2297.htm#SEC2372
1742	grsyz sing_2306.htm#SEC2381
1743	grtest sing_2290.htm#SEC2365
1744	grtranspose sing_2299.htm#SEC2374
1745	grtranspose1 sing_2303.htm#SEC2378
1746	grtwist sing_2295.htm#SEC2370
1747	grtwists sing_2296.htm#SEC2371
1748	grview sing_2292.htm#SEC2367
1749	grwalk.lib sing_1182.htm#SEC1257
1750	grwalk_lib sing_1182.htm#SEC1257
1751	grzero sing_2294.htm#SEC2369
1752	gwalk sing_1188.htm#SEC1263
1753	hStarVector sing_2420.htm#SEC2495
1754	hVector sing_2421.htm#SEC2496
1755	h_increasing_knapsack h_increasing_knapsack sing_1964.htm#SEC2039
1756	hardware platform sing_406.htm#IDX260
1757	hasAlgExtensionCoefficient hasAlgExtensionCoefficient sing_1049.htm#SEC1124
1758	hasCommutativeVars sing_1045.htm#SEC1120
1759	hasFieldCoefficient sing_1048.htm#SEC1123
1760	hasGlobalOrdering sing_1046.htm#SEC1121
1761	hasMixedOrdering sing_1047.htm#SEC1122
1762	hasNumericCoeffs sing_1044.htm#SEC1119
1763	headStand sing_1104.htm#SEC1179
1764	heightZ sing_1343.htm#SEC1418
1765	help sing_308.htm#SEC347
1766	help browsers The online help system sing_16.htm#IDX22
1767	help browsers, dummy The online help system sing_16.htm#IDX25
1768	help browsers, dummy sing_16.htm#IDX27
1769	help browsers, emacs The online help system sing_16.htm#IDX26
1770	help browsers, html The online help system sing_16.htm#IDX23
1771	help browsers, setting command to use The online help system sing_16.htm#IDX30
1772	help browsers, setting the sing_406.htm#IDX189
1773	help, accessing over the net Command line options sing_19.htm#IDX42
1774	help, online help system The online help system sing_16.htm#SEC22
1775	hermiteNormalForm sing_2378.htm#SEC2453
1776	hess.lib sing_2323.htm#SEC2398
1777	hess_lib sing_2323.htm#SEC2398
1778	hessenberg sing_406.htm#IDX211
1779	hessenberg sing_1126.htm#SEC1201
1780	highcorner sing_309.htm#SEC348
1781	hilb sing_310.htm#SEC349
1782	hilbPoly sing_1008.htm#SEC1083
1783	hilbert4ti2 sing_1365.htm#SEC1440 13993
1784	hilbertBasis sing_2419.htm#SEC2494
1785	hilbertSeries sing_2380.htm#SEC2455
1786	hilbvec sing_1743.htm#SEC1818
1787	hnexpansion sing_1585.htm#SEC1660
1788	hnoether.lib sing_1584.htm#SEC1659
1789	hnoether_lib sing_1584.htm#SEC1659
1790	holonomic rank sing_815.htm#IDX369
1791	holonomicRank sing_819.htm#SEC870
1792	hom_kernel sing_1204.htm#SEC1279
1793	homog sing_311.htm#SEC350
1794	homogeneitySpace sing_2403.htm#SEC2478
1795	homogfacFirstQWeyl sing_748.htm#SEC799
1796	homogfacFirstQWeyl_all homogfacFirstQWeyl_all sing_750.htm#SEC801
1797	homogfacNthQWeyl sing_747.htm#SEC798
1798	homogfacNthQWeyl_all homogfacNthQWeyl_all sing_749.htm#SEC800
1799	homolog.lib sing_1189.htm#SEC1264
1800	homolog_lib sing_1189.htm#SEC1264
1801	homology sing_1199.htm#SEC1274
1802	howto, download Download instructions sing_2458.htm#SEC2545
1803	howto, install on Macintosh Macintosh installation instructions sing_2461.htm#SEC2548
1804	howto, install on Unix Unix installation instructions sing_2459.htm#SEC2546
1805	howto, install on Windows Windows installation instructions sing_2460.htm#SEC2547
1806	hres sing_312.htm#SEC351
1807	html, default help The online help system sing_16.htm#IDX24
1808	hyperel.lib sing_1971.htm#SEC2046
1809	hyperel_lib sing_1971.htm#SEC2046
1810	hyperplane sing_2123.htm#IDX770
1811	hyperplane arrangement sing_588.htm#IDX326
1812	hypersurface singularity sing_1611.htm#IDX694
1813	iMult sing_1277.htm#SEC1352
1814	id2mod sing_1004.htm#SEC1079
1815	ideal sing_85.htm#SEC124
1816	ideal declarations sing_86.htm#SEC125
1817	ideal declarations (plural) ideal declarations (plural) sing_472.htm#SEC511
1818	ideal expressions sing_87.htm#SEC126
1819	ideal expressions (plural) ideal expressions (plural) sing_473.htm#SEC512
1820	ideal operations sing_88.htm#SEC127
1821	ideal operations (plural) ideal operations (plural) sing_474.htm#SEC513
1822	ideal related functions ideal related functions sing_89.htm#SEC128
1823	ideal related functions (plural) ideal related functions (plural) sing_475.htm#SEC514
1824	ideal, toric sing_906.htm#SEC962
1825	idealSplit sing_1750.htm#SEC1825
1826	ideals Miscellaneous oddities sing_466.htm#IDX282
1827	idealsimplify sing_1512.htm#SEC1587
1828	identifier Identifier resolution sing_467.htm#SEC506
1829	identifyvar sing_1420.htm#SEC1495
1830	if sing_434.htm#SEC473
1831	imageLattice sing_2346.htm#SEC2421
1832	image_of_variety sing_1700.htm#SEC1775
1833	imap sing_313.htm#SEC352
1834	imap (plural) sing_510.htm#SEC549
1835	imapall sing_1036.htm#SEC1111
1836	impart sing_314.htm#SEC353
1837	importfrom sing_435.htm#SEC474
1838	inCenter sing_577.htm#SEC628
1839	inCentralizer sing_578.htm#SEC629
1840	inForm sing_620.htm#SEC671
1841	inSubring sing_1142.htm#SEC1217
1842	indSet sing_1249.htm#SEC1324
1843	indepSet sing_315.htm#SEC354
1844	indexed names sing_36.htm#IDX83
1845	indexed names sing_37.htm#SEC64
1846	inequalities sing_205.htm#SEC244
1847	infRedTail, option sing_364.htm#IDX150
1848	info The online help system sing_16.htm#SEC23
1849	iniD sing_1440.htm#SEC1515
1850	init_debug sing_1519.htm#SEC1594
1851	initial sing_2402.htm#SEC2477
1852	initial form sing_553.htm#IDX307
1853	initial ideal sing_553.htm#IDX306
1854	initial ideal approach sing_553.htm#IDX310
1855	initial ideal approach sing_644.htm#IDX349
1856	initialForm sing_2076.htm#SEC2151
1857	initialIdeal sing_2077.htm#SEC2152
1858	initialIdealW sing_619.htm#SEC670
1859	initialMalgrange sing_618.htm#SEC669
1860	injective_knapsack sing_1965.htm#SEC2040
1861	inout.lib sing_970.htm#SEC1045
1862	inout_lib sing_970.htm#SEC1045
1863	input sing_41.htm#SEC70
1864	insert sing_316.htm#SEC355
1865	insertCone sing_229.htm#SEC268
1866	insertGenerator sing_639.htm#SEC690
1867	instructions, Macintosh installation Macintosh installation instructions sing_2461.htm#SEC2548
1868	instructions, Unix installation Unix installation instructions sing_2459.htm#SEC2546
1869	instructions, Windows installation Windows installation instructions sing_2460.htm#SEC2547
1870	instructions, downloading Download instructions sing_2458.htm#SEC2545
1871	int sing_90.htm#SEC129
1872	int declarations sing_91.htm#SEC130
1873	int expressions sing_92.htm#SEC131
1874	int operations sing_93.htm#SEC132
1875	int related functions int related functions sing_94.htm#SEC133
1876	intInverse sing_2355.htm#SEC2430
1877	intPart sing_1919.htm#SEC1994
1878	intRank sing_2347.htm#SEC2422
1879	intRoot sing_1920.htm#SEC1995
1880	intRoots sing_636.htm#SEC687
1881	intStrategy, option sing_364.htm#IDX151
1882	intclMonIdeal sing_1289.htm#SEC1364 22338
1883	intclToricRing sing_1285.htm#SEC1360 62143
1884	integer division Miscellaneous oddities sing_466.htm#IDX277
1885	integer programming sing_914.htm#SEC970
1886	integral basis sing_1211.htm#IDX483
1887	integral basis sing_1403.htm#IDX537
1888	integral closure sing_1270.htm#IDX496
1889	integral closure sing_1271.htm#IDX499
1890	integral closure sing_1272.htm#IDX502
1891	integral closure sing_1284.htm#IDX506
1892	integralBasis sing_1211.htm#SEC1286
1893	integralIdeal sing_623.htm#SEC674
1894	integralModule sing_624.htm#SEC675
1895	integralSection sing_2356.htm#SEC2431
1896	integralbasis.lib sing_1210.htm#SEC1285
1897	integralbasis_lib sing_1210.htm#SEC1285
1898	integration of D-module sing_611.htm#IDX338
1899	interface, Emacs Emacs user interface sing_21.htm#SEC28
1900	interiorLatticePoints interiorLatticePoints sing_2422.htm#SEC2497
1901	internalfunctions sing_1520.htm#SEC1595
1902	interpolate sing_1756.htm#SEC1831
1903	interpolation sing_317.htm#SEC356
1904	interred sing_318.htm#SEC357
1905	intersect sing_319.htm#SEC358
1906	intersect (plural) sing_511.htm#SEC550
1907	intersectElim, option sing_364.htm#IDX169
1908	intersectLattices sing_2352.htm#SEC2427
1909	intersectMon sing_1226.htm#SEC1301
1910	intersectSyz, option sing_364.htm#IDX170
1911	intersectZ sing_1345.htm#SEC1420
1912	intersection sing_1594.htm#SEC1669
1913	intersection lattice sing_2159.htm#IDX845
1914	intersection lattice sing_2160.htm#IDX846
1915	intersection multiplicity sing_1505.htm#IDX572
1916	intersection multiplicity sing_1594.htm#IDX687
1917	intersectionDiv sing_1468.htm#SEC1543
1918	intersectionValRingIdeals intersectionValRingIdeals sing_1294.htm#SEC1369 38773
1919	intersectionValRings intersectionValRings sing_1293.htm#SEC1368 35761
1920	intmat sing_97.htm#SEC136
1921	intmat declarations sing_98.htm#SEC137
1922	intmat expressions sing_99.htm#SEC138
1923	intmat operations sing_101.htm#SEC140
1924	intmat related functions intmat related functions sing_102.htm#SEC141
1925	intmat type cast sing_100.htm#SEC139
1926	intmat2mons sing_1309.htm#SEC1384 21150
1927	intprog.lib sing_1212.htm#SEC1287
1928	intprog_lib sing_1212.htm#SEC1287
1929	intvec sing_103.htm#SEC142
1930	intvec declarations sing_104.htm#SEC143
1931	intvec expressions sing_105.htm#SEC144
1932	intvec operations sing_106.htm#SEC145
1933	intvec related functions intvec related functions sing_107.htm#SEC146
1934	invariant ring minimal generating set matrix group invariant_algebra_reynolds sing_1669.htm#IDX700
1935	invariant ring minimal generating set permutation group invariant_algebra_perm sing_1670.htm#IDX701
1936	invariantRing sing_1702.htm#SEC1777
1937	invariant_algebra_perm invariant_algebra_perm sing_1670.htm#SEC1745
1938	invariant_algebra_reynolds invariant_algebra_reynolds sing_1669.htm#SEC1744
1939	invariant_basis sing_1677.htm#SEC1752
1940	invariant_basis_reynolds invariant_basis_reynolds sing_1678.htm#SEC1753
1941	invariant_ring sing_1665.htm#SEC1740
1942	invariant_ring_random invariant_ring_random sing_1666.htm#SEC1741
1943	invariants sing_1590.htm#SEC1665
1944	inverse sing_1110.htm#SEC1185
1945	inverse of a matrix via its LU-decomposition sing_339.htm#SEC378
1946	inverseFourier sing_634.htm#SEC685
1947	inverse_B sing_1111.htm#SEC1186
1948	inverse_L sing_1112.htm#SEC1187
1949	inverse_modulus sing_1948.htm#SEC2023
1950	invertBirMap sing_1404.htm#SEC1479
1951	invertNumberMain sing_1780.htm#SEC1855
1952	involut.lib sing_698.htm#SEC749
1953	involut_lib sing_698.htm#SEC749
1954	involution sing_703.htm#SEC754
1955	invunit sing_1613.htm#SEC1688
1956	iostruct sing_1867.htm#SEC1942
1957	irrRealizationDim sing_2058.htm#SEC2133
1958	irred_secondary_char0 irred_secondary_char0 sing_1691.htm#SEC1766
1959	irred_secondary_no_molien irred_secondary_no_molien sing_1694.htm#SEC1769
1960	irreddecMon sing_1235.htm#SEC1310
1961	irreducible power series sing_1595.htm#IDX688
1962	irreducible secondary invariant irred_secondary_char0 sing_1691.htm#IDX702
1963	isAface sing_2284.htm#SEC2359
1964	isAntiEndo sing_705.htm#SEC756
1965	isBounded sing_2423.htm#SEC2498
1966	isCI sing_261.htm#IDX136
1967	isCI sing_1160.htm#SEC1235
1968	isCM sing_261.htm#IDX137
1969	isCM sing_1200.htm#SEC1275
1970	isCMcod2 sing_1648.htm#SEC1723
1971	isCanonical sing_2424.htm#SEC2499
1972	isCartan sing_579.htm#SEC630
1973	isCentral sing_775.htm#SEC826
1974	isCommutative sing_777.htm#SEC828
1975	isCompatible sing_230.htm#SEC269
1976	isCompressed sing_2425.htm#SEC2500
1977	isEqualDivisor sing_2234.htm#SEC2309
1978	isEquising sing_1557.htm#SEC1632
1979	isFlat sing_1201.htm#SEC1276
1980	isFsat sing_629.htm#SEC680
1981	isFullSpace sing_206.htm#SEC245
1982	isGorenstein sing_2426.htm#SEC2501
1983	isGradedRingHomomorphism isGradedRingHomomorphism sing_2341.htm#SEC2416
1984	isGroup sing_2339.htm#SEC2414
1985	isGroupHomomorphism sing_2340.htm#SEC2415
1986	isHolonomic sing_607.htm#SEC658
1987	isHomg sing_261.htm#IDX133
1988	isHomogeneous sing_2367.htm#SEC2442
1989	isInt sing_642.htm#SEC693
1990	isIntegralSurjective isIntegralSurjective sing_2353.htm#SEC2428
1991	isInvolution sing_704.htm#SEC755
1992	isLatticeEmpty sing_2427.htm#SEC2502
1993	isLocalizationRegular isLocalizationRegular sing_2276.htm#SEC2351
1994	isLocallyFree sing_1202.htm#SEC1277
1995	isMonomial sing_1221.htm#SEC1296
1996	isNC sing_776.htm#SEC827
1997	isNormal sing_2428.htm#SEC2503
1998	isOnCurve sing_1932.htm#SEC2007
1999	isOrigin sing_207.htm#SEC246
2000	isPositive sing_2364.htm#SEC2439
2001	isPrimitiveSublattice isPrimitiveSublattice sing_2354.htm#SEC2429
2002	isPure sing_231.htm#SEC270
2003	isPureTensor sing_551.htm#SEC602
2004	isQuotientRing sing_1050.htm#SEC1125
2005	isRational sing_610.htm#SEC661
2006	isReflexive sing_2429.htm#SEC2504
2007	isReg sing_1203.htm#SEC1278
2008	isSB sing_261.htm#IDX132
2009	isSimplicial sing_208.htm#SEC247
2010	isSmooth sing_2430.htm#SEC2505
2011	isSubModule sing_1051.htm#SEC1126
2012	isSublattice sing_2345.htm#SEC2420
2013	isSymmetric sing_1369.htm#SEC1444
2014	isTame sing_1582.htm#SEC1657
2015	isTerminal sing_2431.htm#SEC2506
2016	isTorsionFree sing_2363.htm#SEC2438
2017	isTwoSidedGB sing_552.htm#SEC603
2018	isUpperTriangular sing_756.htm#SEC807
2019	isVar sing_696.htm#SEC747
2020	isVeryAmple sing_2432.htm#SEC2507
2021	isWeyl sing_778.htm#SEC829
2022	isZeroElement sing_2365.htm#SEC2440
2023	is_NND sing_1598.htm#SEC1673
2024	is_NP sing_1258.htm#SEC1333
2025	is_active sing_1631.htm#SEC1706
2026	is_bijective sing_1147.htm#SEC1222
2027	is_cenBimodule sing_811.htm#SEC862
2028	is_cenSubbimodule sing_812.htm#SEC863
2029	is_ci sing_1632.htm#SEC1707
2030	is_complex sing_1083.htm#SEC1158
2031	is_fix_injective sing_1969.htm#SEC2044
2032	is_h_injective sing_1968.htm#SEC2043
2033	is_injective sing_1145.htm#SEC1220
2034	is_irred sing_1595.htm#SEC1670
2035	is_is sing_1633.htm#SEC1708
2036	is_nested sing_1259.htm#SEC1334
2037	is_prime sing_1949.htm#SEC2024
2038	is_primitive_root sing_1945.htm#SEC2020
2039	is_pure sing_803.htm#SEC854
2040	is_reg sing_1634.htm#SEC1709
2041	is_regs sing_1635.htm#SEC1710
2042	is_surjective sing_1146.htm#SEC1221
2043	is_zero sing_993.htm#SEC1068
2044	isartinianMon sing_1232.htm#SEC1307
2045	isgenericMon sing_1233.htm#SEC1308
2046	ishyper sing_1972.htm#SEC2047
2047	isirreducibleMon sing_1231.htm#SEC1306
2048	isoncurve sing_1973.htm#SEC2048
2049	isparam sing_2036.htm#SEC2111
2050	isprimaryMon sing_1230.htm#SEC1305
2051	isprimeMon sing_1229.htm#SEC1304
2052	isuni sing_2021.htm#SEC2096
2053	iv2lp sing_674.htm#SEC725
2054	iv2lpList sing_675.htm#SEC726
2055	iv2lpMat sing_676.htm#SEC727
2056	ivDHilbert sing_650.htm#SEC701
2057	ivDHilbertSickle sing_651.htm#SEC702
2058	ivDimCheck sing_652.htm#SEC703
2059	ivHilbert sing_653.htm#SEC704
2060	ivKDim sing_654.htm#SEC705
2061	ivL2lpI sing_673.htm#SEC724
2062	ivMis2Base sing_655.htm#SEC706
2063	ivMis2Dim sing_656.htm#SEC707
2064	ivOrdMisLex sing_657.htm#SEC708
2065	ivSickle sing_658.htm#SEC709
2066	ivSickleDim sing_660.htm#SEC711
2067	ivSickleHil sing_659.htm#SEC710
2068	jInvariant sing_2070.htm#SEC2145
2069	jOft sing_1904.htm#SEC1979
2070	jacob sing_320.htm#SEC359
2071	jacoblift sing_1614.htm#SEC1689
2072	jacobson sing_1873.htm#SEC1948
2073	jacobson.lib sing_1871.htm#SEC1946
2074	jacobson_lib sing_1871.htm#SEC1946
2075	janet sing_321.htm#SEC360
2076	jet sing_322.htm#SEC361
2077	jordan sing_1131.htm#SEC1206
2078	jordanbasis sing_1132.htm#SEC1207
2079	jordanmatrix sing_1133.htm#SEC1208
2080	jordannf sing_1134.htm#SEC1209
2081	jungfib sing_1453.htm#SEC1528
2082	jungnormal sing_1452.htm#SEC1527
2083	jungresolve sing_1451.htm#SEC1526
2084	katsura sing_991.htm#SEC1066
2085	kbase sing_323.htm#SEC362
2086	kbase (plural) sing_512.htm#SEC551
2087	keepring sing_436.htm#SEC475
2088	kernel sing_324.htm#SEC363
2089	kernelLattice sing_2348.htm#SEC2423
2090	kill sing_325.htm#SEC364
2091	killTask sing_1062.htm#SEC1137
2092	killall sing_943.htm#SEC1018
2093	killattrib sing_326.htm#SEC365
2094	kmemory sing_942.htm#SEC1017
2095	kohom sing_1205.htm#SEC1280
2096	kontrahom sing_1206.htm#SEC1281
2097	koszul sing_327.htm#SEC366
2098	kskernel.lib sing_1605.htm#SEC1680
2099	kskernel_lib sing_1605.htm#SEC1680
2100	l-adic numbers sing_32.htm#SEC45
2101	laguerre sing_328.htm#SEC367
2102	laguerre_solve sing_1752.htm#SEC1827
2103	lastvarGeneral sing_2002.htm#SEC2077
2104	latex.lib sing_1796.htm#SEC1871
2105	latex_lib sing_1796.htm#SEC1871
2106	lattice sing_2160.htm#IDX848
2107	latticeArea sing_2052.htm#SEC2127
2108	latticeBasis sing_2349.htm#SEC2424
2109	latticeCodegree sing_2433.htm#SEC2508
2110	latticeDegree sing_2434.htm#SEC2509
2111	latticePoints sing_2435.htm#SEC2510
2112	latticeVolume sing_2436.htm#SEC2511
2113	laxfrT sing_2252.htm#SEC2327
2114	laxfrX sing_2253.htm#SEC2328
2115	lazy, option sing_364.htm#IDX152
2116	lcm sing_994.htm#SEC1069
2117	lcmMon sing_1224.htm#SEC1299
2118	lcmN sing_1913.htm#SEC1988
2119	lcmofall sing_1433.htm#SEC1508
2120	lead sing_329.htm#SEC368
2121	leadcoef sing_330.htm#SEC369
2122	leadexp sing_331.htm#SEC370
2123	leadmonom sing_332.htm#SEC371
2124	leadmonomial sing_1988.htm#SEC2063
2125	left annihilator ideal sing_588.htm#IDX318
2126	leftInverse sing_1862.htm#SEC1937
2127	leftKernel sing_1860.htm#SEC1935
2128	length, option sing_364.htm#IDX153
2129	letplaceGBasis sing_682.htm#SEC733
2130	letterplace correspondence Letterplace correspondence sing_542.htm#SEC593
2131	lex_solve sing_1758.htm#SEC1833
2132	lexicographical ordering sing_893.htm#IDX379
2133	lib2doc sing_60.htm#SEC96
2134	libcdd sing_1.htm#IDX12
2135	libfac sing_1.htm#IDX6
2136	libparse sing_69.htm#SEC108
2137	library sing_2102.htm#IDX748
2138	library sing_2279.htm#IDX875
2139	library, info string sing_55.htm#IDX125
2140	library, polybori.lib sing_2102.htm#IDX745
2141	library, template sing_55.htm#SEC91
2142	library, template.lib sing_55.htm#IDX123
2143	lieBracket sing_693.htm#SEC744
2144	lift sing_334.htm#SEC373
2145	lift sing_546.htm#IDX294
2146	lift (plural) sing_513.htm#SEC552
2147	lift_kbase sing_1551.htm#SEC1626
2148	lift_rel_kb sing_1552.htm#SEC1627
2149	liftenvelope sing_549.htm#SEC600
2150	liftstd sing_335.htm#SEC374
2151	liftstd (plural) sing_514.htm#SEC553
2152	linReduce sing_561.htm#SEC612
2153	linReduceIdeal sing_562.htm#SEC613
2154	linSyzSolve sing_563.htm#SEC614
2155	linalg.lib sing_1109.htm#SEC1184
2156	linalg_lib sing_1109.htm#SEC1184
2157	linealityDimension sing_209.htm#SEC248
2158	linealitySpace sing_210.htm#SEC249
2159	linear algebra sing_262.htm#SEC301
2160	linear algebra sing_338.htm#SEC377
2161	linear algebra sing_339.htm#SEC378
2162	linear algebra sing_340.htm#SEC379
2163	linear code, dual sing_1831.htm#IDX713
2164	linear code, systematic sing_1832.htm#IDX714
2165	linear interreduction sing_553.htm#IDX309
2166	linearCombinations sing_582.htm#SEC633
2167	linearMapKernel sing_581.htm#SEC632
2168	linear_relations sing_1101.htm#SEC1176
2169	linearlyEquivalent sing_2237.htm#SEC2312
2170	linearpart sing_1744.htm#SEC1819
2171	link Parallelization with ssi links sing_108.htm#SEC147
2172	link sing_850.htm#SEC901
2173	link declarations sing_109.htm#SEC148
2174	link expressions sing_110.htm#SEC149
2175	link related functions link related functions sing_111.htm#SEC150
2176	list sing_118.htm#SEC157
2177	list declarations sing_119.htm#SEC158
2178	list expressions sing_120.htm#SEC159
2179	list operations sing_121.htm#SEC160
2180	list related functions list related functions sing_122.htm#SEC161
2181	listvar sing_336.htm#SEC375
2182	lll sing_2381.htm#SEC2456
2183	load sing_437.htm#SEC476
2184	loadLib, option sing_364.htm#IDX174
2185	loadProc, option sing_364.htm#IDX175
2186	locAtZero sing_1279.htm#SEC1354
2187	locNormal sing_1215.htm#SEC1290
2188	local methods sing_1214.htm#IDX486
2189	local methods sing_1215.htm#IDX489
2190	local names sing_46.htm#SEC82
2191	local rings, computing in Rings associated to monomial orderings sing_845.htm#SEC896
2192	local weighted lexicographical ordering sing_894.htm#IDX400
2193	local weighted reverse lexicographical ordering Local orderings sing_894.htm#IDX397
2194	localInvar sing_1707.htm#SEC1782
2195	localization Rings associated to monomial orderings sing_845.htm#SEC896
2196	localization sing_2140.htm#IDX808
2197	localization of D-module sing_611.htm#IDX334
2198	localization of D-module sing_815.htm#IDX372
2199	locally closed set, constructible set sing_964.htm#IDX416
2200	localstd sing_1998.htm#SEC2073
2201	locnormal.lib sing_1214.htm#SEC1289
2202	locnormal_lib sing_1214.htm#SEC1289
2203	locstd sing_1636.htm#SEC1711
2204	locus sing_965.htm#SEC1040
2205	locusdg sing_966.htm#SEC1041
2206	locusto sing_969.htm#SEC1044
2207	log2 sing_1888.htm#SEC1963
2208	logarithmic annihilator ideal sing_588.htm#IDX323
2209	lowerHomogeneitySpace lowerHomogeneitySpace sing_2407.htm#SEC2482
2210	lp, global ordering sing_893.htm#IDX378
2211	lp2iv sing_677.htm#SEC728
2212	lp2ivId sing_678.htm#SEC729
2213	lp2lstr sing_689.htm#SEC740
2214	lpDHilbert sing_661.htm#SEC712
2215	lpDHilbertSickle sing_662.htm#SEC713
2216	lpDimCheck sing_664.htm#SEC715
2217	lpHilbert sing_663.htm#SEC714
2218	lpId2ivLi sing_679.htm#SEC730
2219	lpKDim sing_665.htm#SEC716
2220	lpMis2Base sing_666.htm#SEC717
2221	lpMis2Dim sing_667.htm#SEC718
2222	lpMult sing_686.htm#SEC737
2223	lpNF sing_683.htm#SEC734
2224	lpOrdMisLex sing_668.htm#SEC719
2225	lpPower sing_688.htm#SEC739
2226	lpSickle sing_669.htm#SEC720
2227	lpSickleDim sing_671.htm#SEC722
2228	lpSickleHil sing_670.htm#SEC721
2229	lprint sing_972.htm#SEC1047
2230	lres sing_337.htm#SEC376
2231	ls, local ordering sing_894.htm#IDX391
2232	lst2str sing_690.htm#SEC741
2233	lsum sing_1181.htm#SEC1256
2234	ludecomp sing_338.htm#SEC377
2235	luinverse sing_339.htm#SEC378
2236	lusolve sing_340.htm#SEC379
2237	m_merkle_hellman_decryption m_merkle_hellman_decryption sing_1960.htm#SEC2035
2238	m_merkle_hellman_encryption m_merkle_hellman_encryption sing_1959.htm#SEC2034
2239	m_merkle_hellman_transformation m_merkle_hellman_transformation sing_1958.htm#SEC2033
2240	magnitude sing_1882.htm#SEC1957
2241	makeDivisor sing_2229.htm#SEC2304
2242	makeFormalDivisor sing_2239.htm#SEC2314
2243	makeGraph sing_1172.htm#SEC1247
2244	makeHeisenberg sing_766.htm#SEC817
2245	makeLetterplaceRing sing_681.htm#SEC732
2246	makeMalgrange sing_648.htm#SEC699
2247	makeModElimRing sing_783.htm#SEC834
2248	makePDivisor sing_2245.htm#SEC2320
2249	makeQsl2 sing_731.htm#SEC782
2250	makeQsl3 sing_732.htm#SEC783
2251	makeQso3 sing_730.htm#SEC781
2252	makeUe6 sing_727.htm#SEC778
2253	makeUe7 sing_728.htm#SEC779
2254	makeUe8 sing_729.htm#SEC780
2255	makeUf4 sing_726.htm#SEC777
2256	makeUg2 sing_725.htm#SEC776
2257	makeUgl sing_711.htm#SEC762
2258	makeUsl sing_710.htm#SEC761
2259	makeUsl2 sing_709.htm#SEC760
2260	makeUso10 sing_717.htm#SEC768
2261	makeUso11 sing_718.htm#SEC769
2262	makeUso12 sing_719.htm#SEC770
2263	makeUso5 sing_712.htm#SEC763
2264	makeUso6 sing_713.htm#SEC764
2265	makeUso7 sing_714.htm#SEC765
2266	makeUso8 sing_715.htm#SEC766
2267	makeUso9 sing_716.htm#SEC767
2268	makeUsp1 sing_720.htm#SEC771
2269	makeUsp2 sing_721.htm#SEC772
2270	makeUsp3 sing_722.htm#SEC773
2271	makeUsp4 sing_723.htm#SEC774
2272	makeUsp5 sing_724.htm#SEC775
2273	makeWeyl sing_765.htm#SEC816
2274	map sing_123.htm#SEC162
2275	map (plural) sing_476.htm#SEC515
2276	map declarations sing_124.htm#SEC163
2277	map declarations (plural) map declarations (plural) sing_477.htm#SEC516
2278	map expressions sing_125.htm#SEC164
2279	map expressions (plural) map expressions (plural) sing_478.htm#SEC517
2280	map operations sing_126.htm#IDX130
2281	map operations (plural) map operations (plural) sing_479.htm#IDX289
2282	map related functions map related functions sing_127.htm#IDX131
2283	map related functions (plural) map related functions (plural) sing_480.htm#IDX290
2284	mapIsFinite sing_1149.htm#SEC1224
2285	mapToRatNormCurve sing_1408.htm#SEC1483
2286	mapall sing_1037.htm#SEC1112
2287	mappingcone sing_2317.htm#SEC2392
2288	mappingcone3 sing_2319.htm#SEC2394
2289	markov4ti2 sing_1364.htm#SEC1439 9163
2290	mat2arr sing_2125.htm#SEC2200
2291	mat2carr sing_2126.htm#SEC2201
2292	mat_rk sing_1123.htm#SEC1198
2293	matbil sing_2009.htm#SEC2084
2294	mathematical objects Representation of mathematical objects sing_889.htm#SEC940
2295	mathinit sing_1794.htm#SEC1869
2296	matmult sing_2010.htm#SEC2085
2297	matrix sing_128.htm#SEC167
2298	matrix sing_2125.htm#IDX776
2299	matrix sing_2126.htm#IDX779
2300	matrix sing_2127.htm#IDX783
2301	matrix declarations sing_129.htm#SEC168
2302	matrix diagonalization sing_1871.htm#IDX724
2303	matrix expressions sing_130.htm#SEC169
2304	matrix operations sing_132.htm#SEC171
2305	matrix related functions matrix related functions sing_133.htm#SEC172
2306	matrix type cast sing_131.htm#SEC170
2307	matrix.lib sing_1076.htm#SEC1151
2308	matrixExp sing_1398.htm#SEC1473
2309	matrixLog sing_1399.htm#SEC1474
2310	matrixT1 sing_1650.htm#SEC1725
2311	matrix_lib sing_1076.htm#SEC1151
2312	matrixpres sing_2322.htm#SEC2397
2313	matrixsystem sing_2263.htm#SEC2338
2314	max sing_341.htm#SEC380
2315	maxEord sing_1423.htm#SEC1498
2316	maxIntRoot sing_832.htm#SEC883
2317	maxZeros sing_1401.htm#SEC1476
2318	maxabs sing_2028.htm#SEC2103
2319	maxcoef sing_995.htm#SEC1070
2320	maxdeg sing_996.htm#SEC1071
2321	maxdeg1 sing_997.htm#SEC1072
2322	maxideal sing_342.htm#SEC381
2323	maximalFace sing_2437.htm#SEC2512
2324	maximalGroebnerCone sing_2405.htm#SEC2480
2325	maximalValue sing_2438.htm#SEC2513
2326	maximum sing_1901.htm#SEC1976
2327	maximum number of zeroes sing_1401.htm#IDX531
2328	mdouble sing_56.htm#SEC92
2329	mem, option sing_364.htm#IDX176
2330	membershipMon sing_1225.htm#SEC1300
2331	memory sing_343.htm#SEC382
2332	memory managment sing_343.htm#SEC382
2333	merkle_hellman_decryption merkle_hellman_decryption sing_1962.htm#SEC2037
2334	merkle_hellman_encryption merkle_hellman_encryption sing_1961.htm#SEC2036
2335	midpoint sing_2259.htm#SEC2334
2336	milnor sing_1637.htm#SEC1712
2337	milnorcode sing_1521.htm#SEC1596
2338	milnornumber sing_2395.htm#SEC2470
2339	min sing_344.htm#SEC383
2340	minAssChar sing_1323.htm#SEC1398
2341	minAssCharE sing_1324.htm#SEC1399
2342	minAssGTZ sing_1321.htm#SEC1396
2343	minAssGTZE sing_1322.htm#SEC1397
2344	minAssZ sing_1341.htm#SEC1416
2345	minEcart sing_1991.htm#SEC2066
2346	minIntRoot sing_609.htm#SEC660
2347	minIntRoot2 sing_831.htm#SEC882
2348	minMult sing_1156.htm#SEC1231
2349	minbase sing_345.htm#SEC384
2350	minbaseMon sing_1222.htm#SEC1297
2351	mindeg sing_998.htm#SEC1073
2352	mindeg1 sing_999.htm#SEC1074
2353	mindist sing_1846.htm#SEC1921
2354	minimal display time, setting the sing_406.htm#IDX273
2355	minimalFace sing_2439.htm#SEC2514
2356	minimalValue sing_2440.htm#SEC2515
2357	minipoly sing_1128.htm#SEC1203
2358	minkowskiSum sing_2441.htm#SEC2516
2359	minor sing_346.htm#SEC385
2360	minpoly sing_445.htm#SEC484
2361	minres sing_347.htm#SEC386
2362	minres (plural) sing_515.htm#SEC554
2363	mirror symmetry sing_1171.htm#IDX456
2364	mixed Hodge structure sing_1559.htm#IDX587
2365	mixed Hodge structure sing_1565.htm#IDX615
2366	mixed Hodge structure sing_1566.htm#IDX621
2367	mixed Hodge structure sing_1567.htm#IDX629
2368	mixed Hodge structure sing_1568.htm#IDX635
2369	mixed Hodge structure sing_1569.htm#IDX643
2370	mixed Hodge structure sing_1570.htm#IDX653
2371	mixed Hodge structure sing_1581.htm#IDX659
2372	mixed Hodge structure sing_1583.htm#IDX670
2373	mod sing_76.htm#SEC115
2374	mod sing_93.htm#SEC132
2375	mod sing_142.htm#SEC181
2376	mod2id sing_1003.htm#SEC1078
2377	mod2str sing_691.htm#SEC742
2378	modDec sing_1241.htm#SEC1316
2379	modNPos sing_1264.htm#SEC1339
2380	modNormal sing_1217.htm#SEC1292
2381	modNpos_test sing_1262.htm#SEC1337
2382	modStd sing_1219.htm#SEC1294
2383	modWalk sing_2326.htm#SEC2401
2384	mod_versal sing_1550.htm#SEC1625
2385	modality sing_1529.htm#SEC1604
2386	modfWalk sing_2328.htm#SEC2403
2387	modfrWalk sing_2329.htm#SEC2404
2388	modnormal.lib sing_1216.htm#SEC1291
2389	modnormal_lib sing_1216.htm#SEC1291
2390	modrWalk sing_2327.htm#SEC2402
2391	modregCM sing_1268.htm#SEC1343
2392	modsatiety sing_1266.htm#SEC1341
2393	modstd.lib sing_1218.htm#SEC1293
2394	modstd_lib sing_1218.htm#SEC1293
2395	modular sing_981.htm#SEC1056
2396	modular methods sing_1214.htm#IDX487
2397	modular methods sing_1216.htm#IDX492
2398	modular methods. sing_1215.htm#IDX490
2399	modular techniques. sing_1217.htm#IDX494
2400	modular.lib sing_980.htm#SEC1055
2401	modular_lib sing_980.htm#SEC1055
2402	modular_lib sing_980.htm#IDX422
2403	module sing_134.htm#SEC173
2404	module (plural) sing_481.htm#SEC520
2405	module declarations sing_135.htm#SEC174
2406	module declarations (plural) module declarations (plural) sing_482.htm#SEC521
2407	module expressions sing_136.htm#SEC175
2408	module expressions (plural) module expressions (plural) sing_483.htm#SEC522
2409	module operations sing_137.htm#SEC176
2410	module operations (plural) module operations (plural) sing_484.htm#SEC523
2411	module ordering C sing_895.htm#IDX403
2412	module ordering c sing_895.htm#IDX405
2413	module related functions module related functions sing_138.htm#SEC177
2414	module related functions (plural) module related functions (plural) sing_485.htm#SEC524
2415	module_containment sing_1141.htm#SEC1216
2416	modulo sing_348.htm#SEC387
2417	modulo (plural) sing_516.htm#SEC555
2418	moduloSlim sing_773.htm#SEC824
2419	modwalk.lib sing_2325.htm#IDX883
2420	modwalk_lib sing_2325.htm#IDX884
2421	moebius sing_2161.htm#SEC2236
2422	moebius function sing_2161.htm#IDX849
2423	molien sing_1673.htm#SEC1748
2424	mondromy.lib sing_1611.htm#SEC1686
2425	mondromy_lib sing_1611.htm#SEC1686
2426	monitor sing_349.htm#SEC388
2427	monodromy sing_1559.htm#IDX591
2428	monodromy sing_1564.htm#SEC1639
2429	monodromy sing_1564.htm#IDX611
2430	monodromy sing_1569.htm#IDX646
2431	monodromy sing_1581.htm#IDX662
2432	monodromy sing_1583.htm#IDX673
2433	monodromyB sing_1615.htm#SEC1690
2434	monomial sing_350.htm#SEC389
2435	monomial ordering sing_1046.htm#IDX436
2436	monomial orderings General definitions for orderings sing_845.htm#SEC896
2437	monomial orderings sing_892.htm#SEC943
2438	monomial orderings introduction Introduction to orderings sing_891.htm#SEC942
2439	monomialInIdeal sing_829.htm#SEC880
2440	monomialLcm sing_1989.htm#SEC2064
2441	monomialideal.lib sing_1220.htm#SEC1295
2442	monomialideal_lib sing_1220.htm#SEC1295
2443	monomials and precedence Miscellaneous oddities sing_466.htm#IDX279
2444	mons2intmat sing_1308.htm#SEC1383 15555
2445	morsesplit sing_1522.htm#SEC1597
2446	mp_res_mat sing_1755.htm#SEC1830
2447	mplot sing_1795.htm#SEC1870
2448	mpresmat sing_351.htm#SEC390
2449	mprimdec.lib sing_1237.htm#SEC1312
2450	mprimdec_lib sing_1237.htm#SEC1312
2451	mregular.lib sing_1252.htm#SEC1327
2452	mregular_lib sing_1252.htm#SEC1327
2453	mres sing_352.htm#SEC391
2454	mres (plural) sing_517.htm#SEC556
2455	mstd sing_353.htm#SEC392
2456	msum sing_58.htm#SEC94
2457	mtriple sing_57.htm#SEC93
2458	mult Miscellaneous oddities sing_354.htm#SEC393
2459	mult sing_466.htm#IDX280
2460	multBound sing_446.htm#SEC485
2461	multRat sing_837.htm#SEC888
2462	multarr2arr sing_2156.htm#SEC2231
2463	multarrMultRestrict sing_2158.htm#SEC2233
2464	multarrRestrict sing_2157.htm#SEC2232
2465	multcol sing_1095.htm#SEC1170
2466	multdivisor sing_2231.htm#SEC2306
2467	multformaldivisor sing_2243.htm#SEC2318
2468	multi sing_1976.htm#SEC2051
2469	multi indices sing_37.htm#SEC64
2470	multiDeg sing_2360.htm#SEC2435
2471	multiDegBasis sing_2361.htm#SEC2436
2472	multiDegGroebner sing_2369.htm#SEC2444
2473	multiDegModulo sing_2371.htm#SEC2446
2474	multiDegPartition sing_2362.htm#SEC2437
2475	multiDegResolution sing_2372.htm#SEC2447
2476	multiDegSyzygy sing_2370.htm#SEC2445
2477	multiDegTensor sing_2373.htm#SEC2448
2478	multiDegTor sing_2374.htm#SEC2449
2479	multiarrangement sing_2152.htm#IDX829
2480	multiarrangement sing_2153.htm#IDX831
2481	multiarrangement sing_2154.htm#IDX834
2482	multiarrangement sing_2155.htm#IDX835
2483	multiarrangement sing_2156.htm#IDX838
2484	multiarrangement sing_2157.htm#IDX841
2485	multiarrangement sing_2158.htm#IDX843
2486	multidimensional_knapsack multidimensional_knapsack sing_1954.htm#SEC2029
2487	multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra multigrading_lib sing_2330.htm#IDX887
2488	multigrading.lib sing_2330.htm#IDX885
2489	multigrading_lib sing_2330.htm#IDX886
2490	multiplicities, sequence of sing_1590.htm#IDX685
2491	multiplicity sequence sing_1503.htm#IDX564
2492	multiplicity sequence sing_1506.htm#IDX576
2493	multiplicity sequence sing_1592.htm#IDX686
2494	multiplylist sing_1443.htm#SEC1518
2495	multivariate equations sing_1729.htm#IDX703
2496	multrow sing_1096.htm#SEC1171
2497	multseq2charexp sing_1502.htm#SEC1577
2498	multsequence sing_1592.htm#SEC1667
2499	nBoundaryLatticePoints nBoundaryLatticePoints sing_2442.htm#SEC2517
2500	nHilbertBasis sing_2443.htm#SEC2518
2501	nInteriorLatticePoints nInteriorLatticePoints sing_2444.htm#SEC2519
2502	nLatticePoints sing_2445.htm#SEC2520
2503	naccache_stern_decryption naccache_stern_decryption sing_1957.htm#SEC2032
2504	naccache_stern_encryption naccache_stern_encryption sing_1956.htm#SEC2031
2505	naccache_stern_generation naccache_stern_generation sing_1955.htm#SEC2030
2506	nameof sing_355.htm#SEC394
2507	names sing_356.htm#SEC395
2508	nashmult sing_1510.htm#SEC1585
2509	nblocks sing_406.htm#IDX215
2510	ncExt_R sing_806.htm#SEC857
2511	ncHom sing_807.htm#SEC858
2512	ncRelations sing_774.htm#SEC825
2513	nc_algebra sing_518.htm#SEC557
2514	ncalg.lib sing_708.htm#SEC759
2515	ncalg_lib sing_708.htm#SEC759
2516	ncalgebra sing_519.htm#SEC558
2517	ncdecomp.lib sing_735.htm#SEC786
2518	ncdecomp_lib sing_735.htm#SEC786
2519	ncdetection sing_702.htm#SEC753
2520	ncfactor.lib sing_740.htm#SEC791
2521	ncfactor_lib sing_740.htm#SEC791
2522	nchomolog.lib sing_805.htm#IDX362
2523	nchomolog_lib sing_805.htm#IDX363
2524	ncols sing_357.htm#SEC396
2525	ncones sing_233.htm#SEC272
2526	ncpreim.lib sing_752.htm#SEC803
2527	ncpreim_lib sing_752.htm#SEC803
2528	nctools.lib sing_760.htm#SEC811
2529	nctools_lib sing_760.htm#SEC811
2530	ndcond sing_763.htm#SEC814
2531	negatedCone sing_211.htm#SEC250
2532	negative degree lexicographical ordering sing_894.htm#IDX394
2533	negative degree reverse lexicographical ordering Local orderings sing_894.htm#IDX392
2534	negative lexicographical ordering sing_894.htm#IDX390
2535	negativedivisor sing_2232.htm#SEC2307
2536	negativeformaldivisor negativeformaldivisor sing_2242.htm#SEC2317
2537	net access Command line options sing_19.htm#IDX40
2538	newTest sing_1896.htm#SEC1971
2539	newline sing_166.htm#SEC205
2540	news sing_2451.htm#SEC2526
2541	newstruct sing_177.htm#SEC216
2542	newstruct sing_2102.htm#IDX750
2543	newtonDiag sing_1007.htm#SEC1082
2544	newtonPolytope sing_241.htm#SEC280
2545	newtonPolytopeLP sing_2041.htm#SEC2116
2546	newtonPolytopeP sing_2040.htm#SEC2115
2547	newtonpoly sing_1597.htm#SEC1672
2548	nf_icis sing_1638.htm#SEC1713
2549	nfmodStd sing_2384.htm#SEC2459
2550	nfmodstd.lib sing_2382.htm#SEC2457
2551	nfmodstd_lib sing_2382.htm#SEC2457
2552	nilpotent Lie algebras sing_1396.htm#IDX516
2553	nmaxcones sing_232.htm#SEC271
2554	noether sing_447.htm#SEC486
2555	noether.lib sing_1260.htm#SEC1335
2556	noetherNormal sing_1148.htm#SEC1223
2557	noether_lib sing_1260.htm#SEC1335
2558	non-english special characters sing_455.htm#IDX275
2559	nonMonomials sing_1312.htm#SEC1387
2560	nonZeroEntry sing_1151.htm#SEC1226
2561	none, option sing_364.htm#IDX146
2562	norTest sing_1280.htm#SEC1355
2563	norm sing_1975.htm#SEC2050
2564	normal sing_1270.htm#SEC1345
2565	normal.lib sing_1269.htm#SEC1344
2566	normalC sing_1272.htm#SEC1347
2567	normalFan sing_2446.htm#SEC2521
2568	normalFanL sing_2042.htm#SEC2117
2569	normalForm sing_2233.htm#SEC2308
2570	normalI sing_1356.htm#SEC1431
2571	normalP sing_1271.htm#SEC1346
2572	normalToricRing sing_1286.htm#SEC1361 29638
2573	normalToricRingFromBinomials normalToricRingFromBinomials sing_1287.htm#SEC1362 2301
2574	normal_lib sing_1269.htm#SEC1344
2575	normalform sing_1526.htm#SEC1601
2576	normaliz sing_1.htm#IDX14 18426
2577	normaliz sing_1299.htm#SEC1374
2578	normaliz.lib sing_1284.htm#SEC1359
2579	normaliz_lib sing_1284.htm#SEC1359
2580	normalization sing_1214.htm#IDX485
2581	normalization sing_1215.htm#IDX488
2582	normalization sing_1216.htm#IDX491
2583	normalization sing_1217.htm#IDX493
2584	normalization sing_1270.htm#IDX495
2585	normalization sing_1271.htm#IDX498
2586	normalization sing_1272.htm#IDX501
2587	normalization sing_1284.htm#IDX507
2588	normalization. sing_1211.htm#IDX484
2589	normalization. sing_1403.htm#IDX538
2590	normalize sing_1000.htm#SEC1075
2591	not sing_96.htm#SEC135
2592	notBuckets, option sing_364.htm#IDX156
2593	notRegularity, option sing_364.htm#IDX154
2594	notSugar, option sing_364.htm#IDX155
2595	notWarnSB, option sing_364.htm#IDX177
2596	npar sing_1881.htm#SEC1956
2597	npars sing_358.htm#SEC397
2598	nrRootsDeterm sing_2006.htm#SEC2081
2599	nrRootsProbab sing_2005.htm#SEC2080
2600	nres sing_359.htm#SEC398
2601	nres (plural) sing_520.htm#SEC559
2602	nrows sing_360.htm#SEC399
2603	nrroots sing_2035.htm#SEC2110
2604	nsatiety sing_1265.htm#SEC1340
2605	nselect sing_1167.htm#SEC1242
2606	nt_solve sing_1770.htm#SEC1845
2607	ntsolve.lib sing_1769.htm#SEC1844
2608	ntsolve_lib sing_1769.htm#SEC1844
2609	number sing_139.htm#SEC178
2610	number sing_2129.htm#IDX789
2611	number declarations sing_140.htm#SEC179
2612	number expressions sing_141.htm#SEC180
2613	number operations sing_142.htm#SEC181
2614	number related functions number related functions sing_143.htm#SEC182
2615	numberOfConesOfDimension numberOfConesOfDimension sing_234.htm#SEC273
2616	number_e sing_944.htm#SEC1019
2617	number_pi sing_945.htm#SEC1020
2618	numerAlg.lib sing_1378.htm#IDX512
2619	numerAlg_lib sing_1378.htm#IDX513
2620	numerDecom.lib sing_1383.htm#IDX514
2621	numerDecom_lib sing_1383.htm#IDX515
2622	numerator sing_361.htm#SEC400
2623	nvars sing_362.htm#SEC401
2624	oneDimBelongSemigroup oneDimBelongSemigroup sing_1158.htm#SEC1233
2625	online help The online help system sing_16.htm#SEC22
2626	open sing_363.htm#SEC402
2627	opentex sing_1798.htm#SEC1873
2628	operatorBM sing_595.htm#SEC646
2629	operatorModulo sing_596.htm#SEC647
2630	oppose sing_521.htm#SEC560
2631	opposite sing_522.htm#SEC561
2632	opposite polynomial sing_406.htm#IDX222
2633	opposite ring sing_406.htm#IDX219
2634	option sing_364.htm#SEC403
2635	option(warn) sing_70.htm#SEC109
2636	optionIsSet sing_1043.htm#SEC1118
2637	or Evaluation of logical expressions sing_96.htm#SEC135
2638	or sing_459.htm#SEC498
2639	orbit sing_1396.htm#IDX518
2640	orbit sing_1397.htm#IDX522
2641	orbit sing_1400.htm#IDX527
2642	orbit sing_1401.htm#IDX530
2643	orbitCones sing_2285.htm#SEC2360
2644	orbit_variety sing_1697.htm#SEC1772
2645	orbitparam.lib sing_1396.htm#SEC1471
2646	orbitparam_lib sing_1396.htm#SEC1471
2647	ord sing_365.htm#SEC404
2648	ord_test sing_1038.htm#SEC1113
2649	orderings General definitions for orderings sing_892.htm#SEC943
2650	orderings introduction Introduction to orderings sing_891.htm#SEC942
2651	orderings, M sing_896.htm#SEC947
2652	orderings, a sing_898.htm#SEC949
2653	orderings, global sing_893.htm#SEC944
2654	orderings, local sing_894.htm#SEC945
2655	orderings, product sing_897.htm#SEC948
2656	ordstr sing_366.htm#SEC405
2657	orthogonalize sing_1114.htm#SEC1189
2658	outer sing_1084.htm#SEC1159
2659	output sing_41.htm#SEC70
2660	p-adic numbers sing_32.htm#SEC45
2661	pFactor sing_1930.htm#SEC2005
2662	pIntersect sing_559.htm#SEC610
2663	pIntersectSyz sing_560.htm#SEC611
2664	package sing_144.htm#SEC183
2665	package declarations package declarations sing_145.htm#SEC184
2666	package related functions package related functions sing_146.htm#SEC185
2667	pairset sing_1995.htm#SEC2070
2668	par sing_367.htm#SEC406
2669	par2varRing sing_928.htm#SEC1003
2670	paraConic sing_1411.htm#SEC1486
2671	paraPlaneCurve sing_1405.htm#SEC1480
2672	parallel skeletons sing_982.htm#IDX428
2673	parallel.lib sing_982.htm#SEC1057
2674	parallelTestAND sing_986.htm#SEC1061
2675	parallelTestOR sing_987.htm#SEC1062
2676	parallelWaitAll sing_985.htm#SEC1060
2677	parallelWaitFirst sing_984.htm#SEC1059
2678	parallelWaitN sing_983.htm#SEC1058
2679	parallel_lib sing_982.htm#SEC1057
2680	parallelization sing_982.htm#IDX427
2681	parallelization sing_1022.htm#IDX430
2682	parallelization sing_1060.htm#IDX443
2683	param sing_1588.htm#SEC1663
2684	parameter, as numbers sing_139.htm#SEC178
2685	parameterSubstitute sing_2092.htm#SEC2167
2686	parametric annihilator sing_588.htm#IDX324
2687	parametric annihilator for variety sing_644.htm#IDX347
2688	parametrization sing_1396.htm#IDX519
2689	parametrization sing_1400.htm#IDX528
2690	parametrization sing_1588.htm#IDX680
2691	parametrizeOrbit sing_1400.htm#SEC1475
2692	paraplanecurves.lib sing_1402.htm#SEC1477
2693	paraplanecurves_lib sing_1402.htm#SEC1477
2694	pardeg sing_368.htm#SEC407
2695	parstr sing_369.htm#SEC408
2696	part sing_2219.htm#SEC2294
2697	partOver sing_2222.htm#SEC2297
2698	partUnder sing_2223.htm#SEC2298
2699	partial_molien sing_1675.htm#SEC1750
2700	partitions sing_1179.htm#SEC1254
2701	partitions sing_1179.htm#IDX475
2702	path integral sing_1171.htm#IDX462
2703	pause sing_979.htm#SEC1054
2704	pdivi sing_958.htm#SEC1033
2705	pdivisorplus sing_2247.htm#SEC2322
2706	permcol sing_1097.htm#SEC1172
2707	permrow sing_1098.htm#SEC1173
2708	permutations sing_1180.htm#IDX476
2709	permute sing_1180.htm#SEC1255
2710	permute_L sing_1833.htm#SEC1908
2711	perron sing_786.htm#SEC837
2712	perron.lib sing_785.htm#SEC836
2713	perron_lib sing_785.htm#SEC836
2714	phindex.lib sing_2097.htm#IDX741
2715	phindex_lib sing_2097.htm#IDX742
2716	picksFormula sing_2053.htm#SEC2128
2717	pid sing_406.htm#IDX231
2718	plainInvariants sing_1547.htm#SEC1622
2719	plot sing_1811.htm#SEC1886
2720	plotRot sing_1815.htm#SEC1890
2721	plotRotated sing_1814.htm#SEC1889
2722	plotRotatedDirect sing_1817.htm#SEC1892
2723	plotRotatedList sing_1816.htm#SEC1891
2724	plotRotatedListFromSpecifyList plotRotatedListFromSpecifyList sing_1818.htm#SEC1893
2725	plural sing_1045.htm#IDX435
2726	pmat sing_973.htm#SEC1048
2727	pnormalf sing_959.htm#SEC1034
2728	pointid.lib sing_1311.htm#SEC1386
2729	pointid_lib sing_1311.htm#SEC1386
2730	polSol sing_821.htm#SEC872
2731	polSolFiniteRank sing_822.htm#SEC873
2732	pollTask sing_1070.htm#SEC1145
2733	poly sing_147.htm#SEC186
2734	poly (plural) sing_486.htm#SEC525
2735	poly declarations sing_148.htm#SEC187
2736	poly declarations (plural) poly declarations (plural) sing_487.htm#SEC526
2737	poly expressions sing_149.htm#SEC188
2738	poly expressions (plural) poly expressions (plural) sing_488.htm#SEC527
2739	poly operations sing_150.htm#SEC189
2740	poly operations (plural) poly operations (plural) sing_489.htm#SEC528
2741	poly related functions poly related functions sing_151.htm#SEC190
2742	poly related functions (plural) poly related functions (plural) sing_490.htm#SEC529
2743	poly.lib sing_988.htm#SEC1063
2744	poly2list sing_637.htm#SEC688
2745	poly2zdd sing_2118.htm#SEC2193 61839
2746	polyVars sing_828.htm#SEC879
2747	poly_lib sing_988.htm#SEC1063
2748	polybori sing_2102.htm#IDX746
2749	polybori.lib sing_2102.htm#IDX743
2750	polybori.lib sing_2102.htm#IDX747
2751	polybori_lib sing_2102.htm#IDX744
2752	polymake sing_2038.htm#IDX734
2753	polymake.lib sing_2038.htm#SEC2113
2754	polymakePolytope sing_2039.htm#SEC2114
2755	polymake_lib sing_2038.htm#SEC2113
2756	polymake_so sing_2410.htm#IDX899
2757	polynomial solutions sing_815.htm#IDX375
2758	polynomial, opposite sing_406.htm#IDX223
2759	polytope sing_236.htm#SEC275
2760	polytope sing_2038.htm#IDX730
2761	polytope related functions polytope related functions sing_239.htm#SEC278
2762	polytopeViaInequalities polytopeViaInequalities sing_238.htm#SEC277
2763	polytopeViaPoints sing_237.htm#SEC276
2764	pos_def sing_1125.htm#SEC1200
2765	poset sing_2160.htm#IDX847
2766	posweight sing_1655.htm#SEC1730
2767	powSumSym sing_2178.htm#SEC2253
2768	power sing_1085.htm#SEC1160
2769	powerN sing_1914.htm#SEC1989
2770	powerX sing_1923.htm#SEC1998
2771	power_products sing_1689.htm#SEC1764
2772	powerpolyX sing_1893.htm#SEC1968
2773	powersums sing_2016.htm#SEC2091
2774	preComp sing_1248.htm#SEC1323
2775	preimage sing_370.htm#SEC409
2776	preimage sing_752.htm#IDX350
2777	preimage (plural) sing_523.htm#SEC562
2778	preimage under a map between local rings, map between local rings, map between local and global rings preimageLoc sing_1041.htm#IDX433
2779	preimageLattice sing_2350.htm#SEC2425
2780	preimageLoc sing_1041.htm#SEC1116
2781	preimageNC sing_754.htm#SEC805
2782	prepEmbDiv sing_1473.htm#SEC1548
2783	prepMat sing_1726.htm#SEC1801
2784	prepRealclassify sing_1531.htm#SEC1606
2785	prepSV sing_1828.htm#SEC1903
2786	prepareAss sing_1330.htm#SEC1405
2787	presentTree sing_1460.htm#SEC1535
2788	presolve.lib sing_1736.htm#SEC1811
2789	presolve_lib sing_1736.htm#SEC1811
2790	primL sing_1918.htm#SEC1993
2791	primList sing_1917.htm#SEC1992
2792	primRoot sing_1370.htm#SEC1445
2793	primTest sing_1247.htm#SEC1322
2794	primary_char0 sing_1679.htm#SEC1754
2795	primary_char0_no_molien primary_char0_no_molien sing_1681.htm#SEC1756
2796	primary_char0_no_molien_random primary_char0_no_molien_random sing_1686.htm#SEC1761
2797	primary_char0_random primary_char0_random sing_1684.htm#SEC1759
2798	primary_charp sing_1680.htm#SEC1755
2799	primary_charp_no_molien primary_charp_no_molien sing_1682.htm#SEC1757
2800	primary_charp_no_molien_random primary_charp_no_molien_random sing_1687.htm#SEC1762
2801	primary_charp_random primary_charp_random sing_1685.htm#SEC1760
2802	primary_charp_without primary_charp_without sing_1683.htm#SEC1758
2803	primary_charp_without_random primary_charp_without_random sing_1688.htm#SEC1763
2804	primary_invariants sing_1667.htm#SEC1742
2805	primary_invariants_random primary_invariants_random sing_1668.htm#SEC1743
2806	primdec.lib sing_1315.htm#SEC1390
2807	primdecGTZ sing_1317.htm#SEC1392
2808	primdecGTZE sing_1318.htm#SEC1393
2809	primdecMon sing_1236.htm#SEC1311
2810	primdecSY sing_1319.htm#SEC1394
2811	primdecSYE sing_1320.htm#SEC1395
2812	primdecZ sing_1339.htm#SEC1414
2813	primdecZM sing_1340.htm#SEC1415
2814	primdec_lib sing_1315.htm#SEC1390
2815	primdecint.lib sing_1338.htm#SEC1413
2816	primdecint_lib sing_1338.htm#SEC1413
2817	prime sing_371.htm#SEC410
2818	primeClosure sing_1275.htm#SEC1350
2819	primecoeffs sing_951.htm#SEC1026
2820	primefactors sing_372.htm#SEC411
2821	primes sing_946.htm#SEC1021
2822	primitiv.lib sing_1346.htm#SEC1421
2823	primitiv_lib sing_1346.htm#SEC1421
2824	primitive sing_1347.htm#SEC1422
2825	primitive element sing_1347.htm#IDX509
2826	primitiveSpan sing_2357.htm#SEC2432
2827	primitive_extra sing_1348.htm#SEC1423
2828	primparam sing_1542.htm#SEC1617
2829	principal intersection sing_553.htm#IDX308
2830	print sing_373.htm#SEC412
2831	print sing_2127.htm#IDX782
2832	printGraph sing_1173.htm#SEC1248
2833	printGroup sing_2338.htm#SEC2413
2834	printMoebius sing_2166.htm#SEC2241
2835	printTask sing_1065.htm#SEC1140
2836	printf sing_374.htm#SEC413
2837	printlevel sing_448.htm#SEC487
2838	proc sing_152.htm#SEC191
2839	proc declaration sing_153.htm#SEC192
2840	proc expression sing_154.htm#SEC193
2841	procedure, ASCII help sing_56.htm#IDX126
2842	procedure, ASCII/Texinfo help sing_58.htm#IDX128
2843	procedure, texinfo help sing_57.htm#IDX127
2844	procedures, help string sing_45.htm#SEC81
2845	procedures, static Procedure definition sing_43.htm#SEC77
2846	procs with different argument types procs with different argument types sing_155.htm#SEC194
2847	prodcrit sing_1993.htm#SEC2068
2848	product sing_947.htm#SEC1022
2849	productgroup sing_2359.htm#SEC2434
2850	progress watch sing_364.htm#IDX159
2851	projectLattice sing_2351.htm#SEC2426
2852	projective dimension purityfiltration_lib sing_793.htm#IDX359
2853	projective limes sing_32.htm#SEC45
2854	projectiveDimension sing_794.htm#SEC845
2855	prompt sing_15.htm#SEC21
2856	prompt, option sing_364.htm#IDX178
2857	propagator sing_1171.htm#IDX460
2858	propagator sing_1174.htm#SEC1249
2859	prot, option sing_364.htm#IDX157
2860	protocol of computations sing_364.htm#IDX158
2861	proximitymatrix sing_1501.htm#SEC1576
2862	prune sing_375.htm#SEC414
2863	prwalk sing_2386.htm#SEC2461
2864	psigncnd sing_1789.htm#SEC1864
2865	puiseux2generators sing_1600.htm#SEC1675
2866	puiseuxExpansion sing_2063.htm#SEC2138
2867	pure tensor sing_546.htm#IDX296
2868	purelist sing_804.htm#SEC855
2869	purity purityfiltration_lib sing_793.htm#IDX361
2870	purityFiltration sing_795.htm#SEC846
2871	purityTriang sing_796.htm#SEC847
2872	purityfiltration.lib purityfiltration_lib sing_793.htm#IDX354
2873	purityfiltration_lib purityfiltration_lib sing_793.htm#IDX355
2874	pushForward sing_2376.htm#SEC2451
2875	pwalk sing_1187.htm#SEC1262
2876	pyobject sing_243.htm#SEC282
2877	pyobject sing_2102.htm#IDX749
2878	pyobject declarations pyobject declarations sing_244.htm#SEC283
2879	pyobject expressions pyobject expressions sing_245.htm#SEC284
2880	pyobject operations sing_246.htm#SEC285
2881	pyobject related functions pyobject related functions sing_247.htm#SEC286
2882	pyramid sing_2260.htm#SEC2335
2883	python_eval sing_248.htm#SEC287
2884	python_import sing_249.htm#SEC288
2885	python_run sing_250.htm#SEC289
2886	qbase sing_2019.htm#SEC2094
2887	qepcad sing_2270.htm#SEC2345
2888	qepcadsystem sing_2271.htm#SEC2346
2889	qhmatrix sing_1653.htm#SEC1728
2890	qhmoduli.lib sing_1617.htm#SEC1692
2891	qhmoduli_lib sing_1617.htm#SEC1692
2892	qhspectrum sing_1640.htm#SEC1715
2893	qhweight sing_376.htm#SEC415
2894	qmatrix.lib sing_787.htm#SEC838
2895	qmatrix_lib sing_787.htm#SEC838
2896	qminor sing_789.htm#SEC840
2897	qrds sing_377.htm#SEC416
2898	qring Miscellaneous oddities sing_161.htm#SEC200
2899	qring sing_466.htm#IDX284
2900	qring (plural) sing_491.htm#SEC530
2901	qring declaration sing_165.htm#SEC204
2902	qring declaration (plural) qring declaration (plural) sing_492.htm#SEC531
2903	qring related functions (plural) qring related functions (plural) sing_493.htm#SEC532
2904	qring ring ideal 'factor ring' sing_1050.htm#IDX439
2905	qringNF, option sing_364.htm#IDX160
2906	qslimgb sing_927.htm#SEC1002
2907	quadraticSieve sing_1931.htm#SEC2006
2908	quantMat sing_788.htm#SEC839
2909	quickclass sing_1523.htm#SEC1598
2910	quit sing_438.htm#SEC477
2911	quote sing_378.htm#SEC417
2912	quotient sing_379.htm#SEC418
2913	quotient (plural) sing_524.htm#SEC563
2914	quotientLatticeBasis quotientLatticeBasis sing_212.htm#SEC251
2915	quotientMain sing_1781.htm#SEC1856
2916	quotientMon sing_1227.htm#SEC1302
2917	quotients sing_2279.htm#IDX879
2918	rHRR sing_2216.htm#SEC2291
2919	rMacaulay sing_974.htm#SEC1049
2920	rad_con sing_1001.htm#SEC1076
2921	radical sing_1327.htm#SEC1402
2922	radicalEHV sing_1328.htm#SEC1403
2923	radicalMemberShip sing_2085.htm#SEC2160
2924	radicalMon sing_1228.htm#SEC1303
2925	radicalZ sing_1342.htm#SEC1417
2926	randcharpoly sing_2013.htm#SEC2088
2927	randlinpoly sing_2015.htm#SEC2090
2928	random sing_380.htm#SEC419
2929	random sing_406.htm#IDX235
2930	random sing_2148.htm#IDX821
2931	random sing_2149.htm#IDX823
2932	random number generator, seed sing_406.htm#IDX233
2933	random.lib sing_1009.htm#SEC1084
2934	randomBinomial sing_1021.htm#SEC1096
2935	randomCheck sing_1844.htm#SEC1919
2936	randomLast sing_1020.htm#SEC1095
2937	randomPoint sing_213.htm#SEC252
2938	randomPolyInT sing_2094.htm#SEC2169
2939	random_lib sing_1009.htm#SEC1084
2940	randomid sing_1011.htm#SEC1086
2941	randommat sing_1012.htm#SEC1087
2942	rank sing_261.htm#IDX134
2943	rank sing_381.htm#SEC420
2944	ratSol sing_823.htm#SEC874
2945	ratgb.lib sing_813.htm#IDX364
2946	ratgb_lib sing_813.htm#IDX365
2947	rational curves, rational parametrization of rational curves. paraPlaneCurve sing_1405.htm#IDX540
2948	rational normal curve, projection. sing_1406.htm#IDX541
2949	rational normal curve, projection. sing_1409.htm#IDX542
2950	rational normal curve, projection. sing_1410.htm#IDX543
2951	rational solutions sing_815.htm#IDX376
2952	rational univariate projection sing_2013.htm#IDX727
2953	rationalPointConic sing_1407.htm#SEC1482
2954	ratstd sing_814.htm#SEC865
2955	rays sing_214.htm#SEC253
2956	re2squ sing_1384.htm#SEC1459
2957	read sing_382.htm#SEC421
2958	readNmzData sing_1302.htm#SEC1377 18957
2959	reading, option sing_364.htm#IDX179
2960	readline sing_1.htm#IDX5
2961	real sing_28.htm#IDX75
2962	real roots, univariate polynomial sing_2020.htm#IDX729
2963	real roots, univariate projection sing_2004.htm#IDX725
2964	real roots,sign conditions sing_1787.htm#IDX705
2965	realclassify sing_2393.htm#SEC2468
2966	realclassify.lib sing_2392.htm#SEC2467
2967	realclassify_lib sing_2392.htm#SEC2467
2968	realizationDim sing_2057.htm#SEC2132
2969	realizationDimPoly sing_2059.htm#SEC2134
2970	realizationMatroids.lib realizationMatroids_lib sing_2056.htm#SEC2131
2971	realizationMatroids_lib realizationMatroids_lib sing_2056.htm#SEC2131
2972	realmorsesplit sing_2394.htm#SEC2469
2973	realpoly sing_1351.htm#SEC1426
2974	realrad sing_1353.htm#SEC1428
2975	realrad.lib sing_1350.htm#SEC1425
2976	realrad_lib sing_1350.htm#SEC1425
2977	realzero sing_1352.htm#SEC1427
2978	recursive_boolean_poly recursive_boolean_poly sing_2108.htm#SEC2183 17045
2979	recursive_from_boolean_poly recursive_from_boolean_poly sing_2114.htm#SEC2189 37794
2980	redSB, option sing_364.htm#IDX161
2981	redTail, option sing_364.htm#IDX163
2982	redThrough, option sing_364.htm#IDX164
2983	redefine, option sing_364.htm#IDX180
2984	reduce sing_383.htm#SEC422
2985	reduce sing_567.htm#IDX313
2986	reduce (plural) sing_525.htm#SEC564
2987	reduced standard basis sing_364.htm#IDX162
2988	reduction sing_1705.htm#SEC1780
2989	reesclos.lib sing_1354.htm#SEC1429
2990	reesclos_lib sing_1354.htm#SEC1429
2991	reference sing_251.htm#SEC290
2992	reference declarations reference declarations sing_252.htm#SEC291
2993	reference expressions reference expressions sing_253.htm#SEC292
2994	reference operations reference and shared operations sing_256.htm#SEC295
2995	reference related functions reference and shared related functions sing_257.htm#SEC296
2996	regCM sing_1267.htm#SEC1342
2997	regIdeal sing_1253.htm#SEC1328
2998	regMonCurve sing_1256.htm#SEC1331
2999	regularity Syzygies and resolutions sing_384.htm#SEC423
3000	regularity sing_902.htm#SEC958
3001	reiffen sing_606.htm#SEC657
3002	rel_orbit_variety sing_1698.htm#SEC1773
3003	relations sing_785.htm#IDX353
3004	relativeInteriorPoint relativeInteriorPoint sing_215.htm#SEC254
3005	relative_orbit_variety relative_orbit_variety sing_1699.htm#SEC1774
3006	relweight sing_1654.htm#SEC1729
3007	remainder sing_1774.htm#SEC1849
3008	remainderMain sing_1782.htm#SEC1857
3009	removeCone sing_235.htm#SEC274
3010	removepower sing_1511.htm#SEC1586
3011	repart sing_385.htm#SEC424
3012	replace sing_1883.htm#SEC1958
3013	representation, math objects Representation of mathematical objects sing_889.htm#SEC940
3014	res sing_386.htm#SEC425
3015	resbinomial.lib sing_1414.htm#IDX546
3016	resbinomial_lib sing_1414.htm#IDX547
3017	reservedName sing_387.htm#SEC426
3018	resfunction sing_1428.htm#SEC1503
3019	resgraph.lib sing_1446.htm#SEC1521
3020	resgraph_lib sing_1446.htm#SEC1521
3021	resjung.lib sing_1450.htm#SEC1525
3022	resjung_lib sing_1450.htm#SEC1525
3023	reslist sing_1442.htm#SEC1517
3024	resolution purityfiltration_lib sing_156.htm#SEC195
3025	resolution sing_793.htm#IDX360
3026	resolution (plural) sing_494.htm#SEC533
3027	resolution declarations resolution declarations sing_157.htm#SEC196
3028	resolution declarations (plural) resolution declarations (plural) sing_495.htm#SEC534
3029	resolution expressions resolution expressions sing_158.htm#SEC197
3030	resolution expressions (plural) resolution expressions (plural) sing_496.htm#SEC535
3031	resolution graph sing_1496.htm#IDX560
3032	resolution related functions resolution related functions sing_159.htm#SEC198
3033	resolution related functions (plural) resolution related functions (plural) sing_497.htm#SEC536
3034	resolution, La Scala's method sing_337.htm#SEC376
3035	resolution, computation of sing_386.htm#IDX182
3036	resolution, hilbert-driven sing_312.htm#SEC351
3037	resolutionInLocalization resolutionInLocalization sing_2278.htm#SEC2353
3038	resolutiongraph sing_1497.htm#SEC1572
3039	resolve sing_1458.htm#SEC1533
3040	resolve.lib sing_1454.htm#SEC1529
3041	resolve_lib sing_1454.htm#SEC1529
3042	resources.lib sing_1022.htm#SEC1097
3043	resources_lib sing_1022.htm#SEC1097
3044	restriction sing_2141.htm#IDX809
3045	restriction sing_2157.htm#IDX842
3046	restriction sing_2158.htm#IDX844
3047	restriction of sing_611.htm#IDX336
3048	restrictionIdeal sing_621.htm#SEC672
3049	restrictionModule sing_622.htm#SEC673
3050	resultant sing_351.htm#SEC390
3051	resultant sing_388.htm#SEC427
3052	reszeta.lib sing_1467.htm#SEC1542
3053	reszeta_lib sing_1467.htm#SEC1542
3054	return sing_439.htm#SEC478
3055	return type of procedures Return type of procedures sing_464.htm#SEC503
3056	returnSB, option sing_364.htm#IDX148
3057	reverse sing_2034.htm#SEC2109
3058	reverse lexicographical ordering sing_893.htm#IDX381
3059	reynolds_molien sing_1674.htm#SEC1749
3060	rho sing_1925.htm#SEC2000
3061	rightInverse sing_1863.htm#SEC1938
3062	rightKernel sing_1861.htm#SEC1936
3063	rightModulo sing_772.htm#SEC823
3064	rightNF sing_771.htm#SEC822
3065	rightNFWeyl sing_840.htm#SEC891
3066	rightStd sing_770.htm#SEC821
3067	ring sing_160.htm#SEC199
3068	ring (plural) sing_498.htm#SEC537
3069	ring coefficients hasAlgExtensionCoefficient sing_1048.htm#IDX437
3070	ring coefficients sing_1049.htm#IDX438
3071	ring declarations sing_162.htm#SEC201
3072	ring declarations (plural) ring declarations (plural) sing_499.htm#SEC538
3073	ring operations sing_164.htm#SEC203
3074	ring operations (plural) ring operations (plural) sing_500.htm#SEC539
3075	ring related functions ring related functions sing_163.htm#SEC202
3076	ring related functions (plural) ring related functions (plural) sing_501.htm#SEC540
3077	ring, opposite sing_406.htm#IDX220
3078	ring.lib sing_1027.htm#SEC1102
3079	ring_cf sing_261.htm#IDX135
3080	ring_lib sing_1027.htm#SEC1102
3081	ring_variable sing_2128.htm#IDX786
3082	ring_variable sing_2129.htm#IDX788
3083	ring_variable sing_2130.htm#IDX792
3084	ring_variable sing_2131.htm#IDX794
3085	ringlist sing_389.htm#SEC428
3086	ringlist (plural) sing_526.htm#SEC565
3087	ringtensor sing_1039.htm#SEC1114
3088	ringweights sing_1040.htm#SEC1115
3089	rinvar.lib sing_1710.htm#SEC1785
3090	rinvar_lib sing_1710.htm#SEC1785
3091	rmNmzFiles sing_1307.htm#SEC1382 32601
3092	rm_unitcol sing_1103.htm#SEC1178
3093	rm_unitrow sing_1102.htm#SEC1177
3094	rmx sing_1808.htm#SEC1883
3095	rncAntiCanonicalMap sing_1406.htm#SEC1481
3096	rncItProjEven sing_1410.htm#SEC1485
3097	rncItProjOdd sing_1409.htm#SEC1484
3098	root of Bernstein-Sato polynomial sing_588.htm#IDX325
3099	rootofUnity sing_1042.htm#SEC1117
3100	roots sing_1775.htm#SEC1850
3101	rootsMain sing_1783.htm#SEC1858
3102	rootsModp sing_1907.htm#SEC1982
3103	rootsmr.lib sing_2004.htm#SEC2079
3104	rootsmr_lib sing_2004.htm#SEC2079
3105	rootsur.lib sing_2020.htm#SEC2095
3106	rootsur_lib sing_2020.htm#SEC2095
3107	round sing_1905.htm#SEC1980
3108	rowred sing_1099.htm#SEC1174
3109	rp, global ordering sing_893.htm#IDX380
3110	rswalk sing_2391.htm#SEC2466
3111	rtimer sing_452.htm#SEC491
3112	rvalue No rvalue of increments and assignments sing_458.htm#SEC497
3113	rvar sing_390.htm#SEC429
3114	rwalk sing_2387.htm#SEC2462
3115	rwalk.lib sing_2385.htm#SEC2460
3116	rwalk_lib sing_2385.htm#SEC2460
3117	s_res sing_1056.htm#SEC1131
3118	sa_poly_reduce sing_576.htm#SEC627
3119	sa_reduce sing_575.htm#SEC626
3120	sagbi sing_1360.htm#SEC1435
3121	sagbi.lib sing_1357.htm#SEC1432
3122	sagbiPart sing_1361.htm#SEC1436
3123	sagbiReduce sing_1359.htm#SEC1434
3124	sagbiSPoly sing_1358.htm#SEC1433
3125	sagbi_lib sing_1357.htm#SEC1432
3126	salida sing_1439.htm#SEC1514
3127	sameComponent sing_1987.htm#SEC2062
3128	sameQ sing_1786.htm#SEC1861
3129	sat sing_1168.htm#SEC1243
3130	satiety sing_1255.htm#SEC1330
3131	sba sing_391.htm#SEC430
3132	scalarProd sing_565.htm#SEC616
3133	scheme sing_2251.htm#SEC2326
3134	schreyer.lib sing_1055.htm#SEC1130
3135	schreyer_lib sing_1055.htm#SEC1130
3136	sdb, source code debugger Source code debugger sing_66.htm#SEC102
3137	secondary fan sing_2038.htm#IDX732
3138	secondary polytope sing_2038.htm#IDX733
3139	secondaryFan sing_2046.htm#SEC2121
3140	secondaryPolytope sing_2045.htm#SEC2120
3141	secondary_and_irreducibles_no_molien secondary_and_irreducibles_no_molien sing_1695.htm#SEC1770
3142	secondary_char0 sing_1690.htm#SEC1765
3143	secondary_charp sing_1692.htm#SEC1767
3144	secondary_no_molien sing_1693.htm#SEC1768
3145	secondary_not_cohen_macaulay secondary_not_cohen_macaulay sing_1696.htm#SEC1771
3146	segre sing_2173.htm#SEC2248
3147	select sing_1169.htm#SEC1244
3148	select1 sing_1170.htm#SEC1245
3149	semaphore sing_406.htm#IDX238
3150	semaphore sing_1026.htm#SEC1101
3151	semaphores sing_1022.htm#IDX432
3152	semiCMcod2 sing_1651.htm#SEC1726
3153	semidiv sing_1979.htm#SEC2054
3154	semigroup sing_1500.htm#SEC1575
3155	semigroup sing_1504.htm#IDX567
3156	semigroup of values sing_1590.htm#IDX682
3157	semigroupGenerator sing_216.htm#SEC255
3158	sep sing_1337.htm#SEC1412
3159	separateHNE sing_1601.htm#SEC1676
3160	separator sing_1238.htm#SEC1313
3161	serreRelations sing_694.htm#SEC745
3162	set sing_2123.htm#IDX772
3163	setBaseMultigrading sing_2331.htm#SEC2406
3164	setLetterplaceAttributes setLetterplaceAttributes sing_685.htm#SEC736
3165	setLinearForms sing_217.htm#SEC256
3166	setModuleGrading sing_2343.htm#SEC2418
3167	setMultiplicity sing_218.htm#SEC257
3168	setNmzDataPath sing_1304.htm#SEC1379 18123
3169	setNmzExecPath sing_1300.htm#SEC1375 38993
3170	setNmzFilename sing_1303.htm#SEC1378 20206
3171	setNmzOption sing_1297.htm#SEC1372 9012
3172	set_is_injective sing_1967.htm#SEC2042
3173	setcores sing_1024.htm#SEC1099
3174	setenv sing_406.htm#IDX241
3175	setinitials sing_2261.htm#SEC2336
3176	setring sing_392.htm#SEC431
3177	sh sing_406.htm#IDX243
3178	shared sing_251.htm#SEC290
3179	shared declarations sing_254.htm#SEC293
3180	shared expressions sing_255.htm#SEC294
3181	shared operations reference and shared operations sing_256.htm#SEC295
3182	shared related functions reference and shared related functions sing_257.htm#SEC296
3183	sheaf cohomology sing_1477.htm#IDX548
3184	sheafCoh sing_1483.htm#SEC1558 64501
3185	sheafCohBGG sing_1481.htm#SEC1556 13439
3186	sheafCohBGG2 sing_1482.htm#SEC1557 3338
3187	sheafcoh.lib sing_1477.htm#SEC1552
3188	sheafcoh_lib sing_1477.htm#SEC1552
3189	shiftPoly sing_687.htm#SEC738
3190	short sing_449.htm#SEC488
3191	show sing_975.htm#SEC1050
3192	showBO sing_1459.htm#SEC1534
3193	showDataTypes sing_1461.htm#SEC1536
3194	showNmzOptions sing_1298.htm#SEC1373 64955
3195	showNuminvs sing_1295.htm#SEC1370 18934
3196	showgrades sing_798.htm#SEC849
3197	showrecursive sing_976.htm#SEC1051
3198	sickle sing_672.htm#SEC723
3199	signatureBrieskorn sing_1660.htm#SEC1735
3200	signatureL sing_2098.htm#SEC2173
3201	signatureLqf sing_2099.htm#SEC2174
3202	signatureNemethi sing_1662.htm#SEC1737
3203	signaturePuiseux sing_1661.htm#SEC1736
3204	signcnd sing_1788.htm#SEC1863
3205	signcond.lib sing_1787.htm#SEC1862
3206	signcond_lib sing_1787.htm#SEC1862
3207	simplesolver sing_1732.htm#SEC1807
3208	simplex sing_393.htm#SEC432
3209	simplexOut sing_1759.htm#SEC1834
3210	simplify sing_394.htm#SEC433
3211	simplifyRat sing_835.htm#SEC886
3212	sing.lib sing_1627.htm#SEC1702
3213	sing4ti2.lib sing_1363.htm#SEC1438
3214	sing4ti2_lib sing_1363.htm#SEC1438
3215	sing_lib sing_1627.htm#SEC1702
3216	singular locus of D-module sing_815.htm#IDX370
3217	singularities sing_1559.htm#IDX584
3218	singularities sing_1560.htm#IDX595
3219	singularities sing_1561.htm#IDX598
3220	singularities sing_1562.htm#IDX601
3221	singularities sing_1563.htm#IDX604
3222	singularities sing_1564.htm#IDX608
3223	singularities sing_1565.htm#IDX612
3224	singularities sing_1566.htm#IDX618
3225	singularities sing_1567.htm#IDX626
3226	singularities sing_1568.htm#IDX632
3227	singularities sing_1569.htm#IDX640
3228	singularities sing_1570.htm#IDX650
3229	singularities sing_1658.htm#IDX697
3230	singularities, resolution of Resolution of singularities sing_878.htm#SEC929
3231	singularity sing_1524.htm#SEC1599
3232	singularrc sing_20.htm#IDX74
3233	size Miscellaneous oddities sing_395.htm#SEC434
3234	size sing_466.htm#IDX283
3235	skewmat sing_1086.htm#SEC1161
3236	sleep sing_401.htm#SEC440
3237	slimgb sing_396.htm#SEC435
3238	slimgb sing_855.htm#SEC906
3239	slimgb (plural) sing_527.htm#SEC566
3240	slocus sing_1639.htm#SEC1714
3241	smith sing_1872.htm#SEC1947
3242	smithNormalForm sing_2379.htm#SEC2454
3243	solutionsMod2 sing_1922.htm#SEC1997
3244	solve sing_1753.htm#SEC1828
3245	solve a linear equation system A*x = b via the LU-decomposition of A lusolve sing_340.htm#SEC379
3246	solve.lib sing_1751.htm#SEC1826
3247	solveTInitialFormPar solveTInitialFormPar sing_2088.htm#SEC2163
3248	solve_IP sing_1213.htm#SEC1288
3249	solve_lib sing_1751.htm#SEC1826
3250	solvelinearpart sing_1746.htm#SEC1821
3251	sort sing_948.htm#SEC1023
3252	sortIntvec sing_643.htm#SEC694
3253	sortandmap sing_1747.htm#SEC1822
3254	sortier sing_1709.htm#SEC1784
3255	sortvars sing_1748.htm#SEC1823
3256	sortvec sing_397.htm#SEC436
3257	source code debugger, sdb Source code debugger sing_66.htm#SEC102
3258	spadd sing_1573.htm#SEC1648
3259	span sing_219.htm#SEC258
3260	sparseHomogIdeal sing_1018.htm#SEC1093
3261	sparseid sing_1013.htm#SEC1088
3262	sparsemat sing_1015.htm#SEC1090
3263	sparsematrix sing_1014.htm#SEC1089
3264	sparsepoly sing_1016.htm#SEC1091
3265	sparsetriag sing_1017.htm#SEC1092
3266	spcurve.lib sing_1647.htm#SEC1722
3267	spcurve_lib sing_1647.htm#SEC1722
3268	special characters, non-english sing_455.htm#IDX276
3269	spectral pairs sing_1559.htm#IDX593
3270	spectral pairs sing_1566.htm#IDX625
3271	spectral pairs sing_1568.htm#IDX639
3272	spectral pairs sing_1569.htm#IDX648
3273	spectral pairs sing_1581.htm#IDX664
3274	spectral pairs sing_1583.htm#IDX675
3275	spectralNeg sing_1469.htm#SEC1544
3276	spectrum sing_1559.htm#IDX592
3277	spectrum sing_1565.htm#SEC1640
3278	spectrum sing_1565.htm#IDX617
3279	spectrum sing_1566.htm#IDX624
3280	spectrum sing_1567.htm#IDX631
3281	spectrum sing_1568.htm#IDX638
3282	spectrum sing_1569.htm#IDX647
3283	spectrum sing_1581.htm#IDX663
3284	spectrum sing_1583.htm#IDX674
3285	spectrum sing_1658.htm#IDX699
3286	spectrum.lib sing_1657.htm#SEC1732
3287	spectrum_lib sing_1657.htm#SEC1732
3288	spectrumnd sing_1658.htm#SEC1733
3289	spgamma sing_1580.htm#SEC1655
3290	spgeomgenus sing_1579.htm#SEC1654
3291	spissemicont sing_1576.htm#SEC1651
3292	split sing_977.htm#SEC1052
3293	splitPolygon sing_2048.htm#SEC2123
3294	splitring sing_1349.htm#SEC1424
3295	splitting sing_1246.htm#SEC1321
3296	spmilnor sing_1578.htm#SEC1653
3297	spmul sing_1575.htm#SEC1650
3298	spnf sing_1129.htm#SEC1204
3299	spoly sing_1990.htm#SEC2065
3300	sppairs sing_1566.htm#SEC1641
3301	sppnf sing_1571.htm#SEC1646
3302	sppprint sing_1572.htm#SEC1647
3303	spprint sing_1130.htm#SEC1205
3304	sprintf sing_399.htm#SEC438
3305	spsemicont sing_1577.htm#SEC1652
3306	spsub sing_1574.htm#SEC1649
3307	sqfrNorm sing_1776.htm#SEC1851
3308	sqfrNormMain sing_1784.htm#SEC1859
3309	sqr sing_1902.htm#SEC1977
3310	sqrfree sing_398.htm#SEC437
3311	squareRoot sing_1921.htm#SEC1996
3312	squarefree sing_1602.htm#SEC1677
3313	sres sing_400.htm#SEC439
3314	ssi Parallelization with ssi links sing_850.htm#SEC901
3315	staircase sing_1793.htm#SEC1868
3316	standard sing_1997.htm#SEC2072
3317	standard.lib sing_926.htm#IDX408
3318	standard_lib sing_926.htm#IDX409
3319	startNmz sing_1306.htm#SEC1381 21925
3320	startTasks sing_1066.htm#SEC1141
3321	static procedures Procedure definition sing_43.htm#SEC77
3322	status sing_401.htm#SEC440
3323	std sing_402.htm#SEC441
3324	std sing_853.htm#SEC904
3325	std (plural) sing_528.htm#SEC567
3326	stdfglm sing_403.htm#SEC442
3327	stdhilb sing_404.htm#SEC443
3328	stopTask sing_1067.htm#SEC1142
3329	stratify sing_1727.htm#SEC1802
3330	stratify.lib sing_1725.htm#SEC1800
3331	stratify_lib sing_1725.htm#SEC1800
3332	string Miscellaneous oddities sing_166.htm#SEC205
3333	string sing_466.htm#IDX286
3334	string declarations sing_167.htm#SEC206
3335	string expressions sing_168.htm#SEC207
3336	string operations sing_170.htm#SEC209
3337	string related functions string related functions sing_171.htm#SEC210
3338	string type cast sing_169.htm#SEC208
3339	stripHNE sing_1599.htm#SEC1674
3340	sturm sing_2030.htm#SEC2105
3341	sturmha sing_2032.htm#SEC2107
3342	sturmhaseq sing_2033.htm#SEC2108
3343	sturmquery sing_2008.htm#SEC2083
3344	sturmseq sing_2031.htm#SEC2106
3345	submat sing_1087.htm#SEC1162
3346	subrInterred sing_1006.htm#SEC1081
3347	subset_sum01 sing_1951.htm#SEC2026
3348	subset_sum02 sing_1952.htm#SEC2027
3349	subst sing_405.htm#SEC444
3350	subst (plural) sing_529.htm#SEC568
3351	substitute sing_1005.htm#SEC1080
3352	sugarCrit, option sing_364.htm#IDX165
3353	sum sing_949.htm#SEC1024
3354	sum_of_powers sing_2177.htm#SEC2252
3355	sumlist sing_1441.htm#SEC1516
3356	super-commutative algebras Graded commutative algebras (SCA) sing_538.htm#SEC589
3357	superCommutative sing_769.htm#SEC820
3358	super_increasing_knapsack super_increasing_knapsack sing_1963.htm#SEC2038
3359	surf.lib sing_1810.htm#SEC1885
3360	surf_lib sing_1810.htm#SEC1885
3361	surfacesignature.lib surfacesignature_lib sing_1659.htm#SEC1734
3362	surfacesignature_lib surfacesignature_lib sing_1659.htm#SEC1734
3363	surfer sing_1.htm#IDX8
3364	surfer sing_1812.htm#SEC1887
3365	surfex sing_1.htm#IDX7
3366	surfex.lib sing_1813.htm#SEC1888
3367	surfex_lib sing_1813.htm#SEC1888
3368	suspend sing_401.htm#SEC440
3369	swalk sing_2390.htm#SEC2465
3370	swalk.lib sing_2389.htm#SEC2464
3371	swalk_lib sing_2389.htm#SEC2464
3372	swap sing_1528.htm#SEC1603
3373	swap sing_2130.htm#IDX790
3374	switch No case or switch statement sing_460.htm#SEC499
3375	syModStd sing_1373.htm#SEC1448
3376	symNsym sing_2171.htm#SEC2246
3377	sym_gauss sing_1113.htm#SEC1188
3378	symm sing_2170.htm#SEC2245
3379	symmStd sing_1372.htm#SEC1447
3380	symmat sing_1088.htm#SEC1163
3381	symmetric basis sing_1105.htm#IDX446
3382	symmetric power sing_1107.htm#IDX448
3383	symmetricBasis sing_1105.htm#SEC1180
3384	symmetricPower sing_1107.htm#SEC1182
3385	symmfunc sing_2017.htm#SEC2092
3386	symodstd.lib sing_1367.htm#SEC1442
3387	symodstd_lib sing_1367.htm#SEC1442
3388	symsignature sing_2007.htm#SEC2082
3389	syndrome sing_1840.htm#SEC1915
3390	sysBin sing_1838.htm#SEC1913
3391	sysCRHT sing_1835.htm#SEC1910
3392	sysCRHTMindist sing_1836.htm#SEC1911
3393	sysFL sing_1851.htm#SEC1926
3394	sysNewton sing_1837.htm#SEC1912
3395	sysQE sing_1841.htm#SEC1916
3396	sys_code sing_1832.htm#SEC1907
3397	system sing_406.htm#SEC445
3398	system, -- sing_406.htm#IDX266
3399	system, --long_option_name sing_406.htm#IDX269
3400	system, --long_option_name=value sing_406.htm#IDX271
3401	system, HC sing_406.htm#IDX209
3402	system, LLL sing_406.htm#IDX213
3403	system, Singular sing_406.htm#IDX247
3404	system, SingularLib sing_406.htm#IDX249
3405	system, absFact sing_406.htm#IDX185
3406	system, blackbox sing_406.htm#IDX186
3407	system, bracket sing_406.htm#IDX191
3408	system, browsers sing_406.htm#IDX190
3409	system, btest sing_406.htm#IDX193
3410	system, complexNearZero sing_406.htm#IDX194
3411	system, contributors sing_406.htm#IDX196
3412	system, cpu sing_406.htm#IDX198
3413	system, cpu sing_406.htm#IDX265
3414	system, denom_list sing_406.htm#IDX200
3415	system, eigenvals sing_406.htm#IDX201
3416	system, env sing_406.htm#IDX202
3417	system, freegb sing_406.htm#IDX204
3418	system, getPrecDigits sing_406.htm#IDX207
3419	system, getenv sing_406.htm#IDX206
3420	system, gmsnf sing_406.htm#IDX208
3421	system, hessenberg sing_406.htm#IDX210
3422	system, install sing_406.htm#IDX212
3423	system, nblocks sing_406.htm#IDX216
3424	system, newstruct sing_406.htm#IDX217
3425	system, opp sing_406.htm#IDX218
3426	system, oppose sing_406.htm#IDX221
3427	system, pcvBasis sing_406.htm#IDX230
3428	system, pcvCV2P sing_406.htm#IDX228
3429	system, pcvDim sing_406.htm#IDX229
3430	system, pcvLAddL sing_406.htm#IDX224
3431	system, pcvMinDeg sing_406.htm#IDX226
3432	system, pcvP2CV sing_406.htm#IDX227
3433	system, pcvPMulL sing_406.htm#IDX225
3434	system, pid sing_406.htm#IDX232
3435	system, random sing_406.htm#IDX234
3436	system, reserve sing_406.htm#IDX236
3437	system, reservedLink sing_406.htm#IDX237
3438	system, semaphore sing_406.htm#IDX239
3439	system, semic sing_406.htm#IDX240
3440	system, setenv sing_406.htm#IDX242
3441	system, sh sing_406.htm#IDX244
3442	system, shrinktest sing_406.htm#IDX245
3443	system, spadd sing_406.htm#IDX250
3444	system, spectrum sing_406.htm#IDX251
3445	system, spmul sing_406.htm#IDX252
3446	system, std_syz sing_406.htm#IDX253
3447	system, stest sing_406.htm#IDX254
3448	system, tensorModuleMult sing_406.htm#IDX255
3449	system, twostd sing_406.htm#IDX256
3450	system, uname sing_406.htm#IDX259
3451	system, version sing_406.htm#IDX262
3452	system, with sing_406.htm#IDX263
3453	systemOfParametersOfLocalization systemOfParametersOfLocalization sing_2275.htm#SEC2350
3454	syz sing_407.htm#SEC446
3455	syz (plural) sing_530.htm#SEC569
3456	syzygy sing_1055.htm#IDX442
3457	tDetropicalise sing_2090.htm#SEC2165
3458	tInitialForm sing_2074.htm#SEC2149
3459	tInitialFormPar sing_2086.htm#SEC2161
3460	tInitialFormParMax sing_2087.htm#SEC2162
3461	tInitialIdeal sing_2075.htm#SEC2150
3462	tab sing_978.htm#SEC1053
3463	tail sing_1986.htm#SEC2061
3464	tame polynomial sing_1581.htm#IDX656
3465	tame polynomial sing_1582.htm#IDX666
3466	tame polynomial sing_1583.htm#IDX667
3467	tangentGens sing_1397.htm#SEC1472
3468	tangentcone sing_1646.htm#SEC1721
3469	task sing_1060.htm#IDX445
3470	tasks.lib sing_1060.htm#SEC1135
3471	tasks_lib sing_1060.htm#SEC1135
3472	tau_es sing_1554.htm#SEC1629
3473	tau_es2 sing_1508.htm#SEC1583
3474	tdCf sing_2204.htm#SEC2279
3475	tdFactor sing_2206.htm#SEC2281
3476	tdProj sing_2209.htm#SEC2284
3477	tdTerms sing_2205.htm#SEC2280
3478	teachstd.lib sing_1984.htm#SEC2059
3479	teachstd_lib sing_1984.htm#SEC2059
3480	template.lib sing_55.htm#IDX121
3481	template.lib sing_55.htm#IDX124
3482	template_lib sing_55.htm#SEC91
3483	template_lib sing_55.htm#IDX122
3484	tensor sing_546.htm#IDX300
3485	tensor sing_1089.htm#SEC1164
3486	tensorMod sing_1208.htm#SEC1283
3487	term orderings General definitions for orderings sing_892.htm#SEC943
3488	term orderings introduction Introduction to orderings sing_891.htm#SEC942
3489	testNCfac sing_743.htm#SEC794
3490	testParametrization sing_1412.htm#SEC1487
3491	testPointConic sing_1413.htm#SEC1488
3492	testPrimary sing_1325.htm#SEC1400
3493	testPrimaryE sing_1326.htm#SEC1401
3494	tex sing_1799.htm#SEC1874
3495	texDrawBasic sing_2081.htm#SEC2156
3496	texDrawNewtonSubdivision texDrawNewtonSubdivision sing_2083.htm#SEC2158
3497	texDrawTriangulation texDrawTriangulation sing_2084.htm#SEC2159
3498	texDrawTropical sing_2082.htm#SEC2157
3499	texMatrix sing_2080.htm#SEC2155
3500	texNumber sing_2078.htm#SEC2153
3501	texPolynomial sing_2079.htm#SEC2154
3502	texcoef sing_1880.htm#SEC1955
3503	texdemo sing_1800.htm#SEC1875
3504	texfactorize sing_1801.htm#SEC1876
3505	texmap sing_1802.htm#SEC1877
3506	texname sing_1803.htm#SEC1878
3507	texobj sing_1804.htm#SEC1879
3508	texpoly sing_1805.htm#SEC1880
3509	texproc sing_1806.htm#SEC1881
3510	texring sing_1807.htm#SEC1882
3511	the first alternative algorithm sing_1185.htm#IDX479
3512	three_elements sing_1970.htm#SEC2045
3513	timeFactorize sing_953.htm#SEC1028
3514	timeStd sing_952.htm#SEC1027
3515	timer sing_450.htm#SEC489
3516	timer resolution, setting the sing_406.htm#IDX272
3517	timestep sing_2264.htm#SEC2339
3518	tjurina sing_1642.htm#SEC1717
3519	tmatrix sing_1569.htm#SEC1644
3520	todd sing_2201.htm#SEC2276
3521	toddE sing_2202.htm#SEC2277
3522	toddPoly sing_2215.htm#SEC2290
3523	tolessvars sing_1745.htm#SEC1820
3524	topological invariants sing_1496.htm#IDX558
3525	topological invariants sing_1503.htm#IDX565
3526	topological invariants sing_1504.htm#IDX569
3527	topological invariants sing_1505.htm#IDX573
3528	topological invariants sing_1506.htm#IDX577
3529	toric ideals sing_906.htm#SEC962
3530	toric ring sing_1284.htm#IDX508
3531	toric.lib sing_1374.htm#SEC1449
3532	toric_ideal sing_1375.htm#SEC1450
3533	toric_lib sing_1374.htm#SEC1449
3534	toric_std sing_1376.htm#SEC1451
3535	torusInvariants sing_1290.htm#SEC1365 911
3536	total divisors sing_546.htm#IDX297
3537	total multiplicities sing_1496.htm#IDX561
3538	totalmultiplicities sing_1498.htm#SEC1573
3539	trace sing_408.htm#SEC447
3540	tracemult sing_2011.htm#SEC2086
3541	transpose sing_409.htm#SEC448
3542	trapezoid sing_2258.htm#SEC2333
3543	triMNewton sing_1771.htm#SEC1846
3544	triagmatrix sing_1019.htm#SEC1094
3545	triang.lib sing_1764.htm#SEC1839
3546	triangL sing_1765.htm#SEC1840
3547	triangL_solve sing_1762.htm#SEC1837
3548	triangLf_solve sing_1760.htm#SEC1835
3549	triangLfak sing_1766.htm#SEC1841
3550	triangM sing_1767.htm#SEC1842
3551	triangMH sing_1768.htm#SEC1843
3552	triangM_solve sing_1761.htm#SEC1836
3553	triang_lib sing_1764.htm#SEC1839
3554	triang_solve sing_1763.htm#SEC1838
3555	triangulations sing_2044.htm#SEC2119
3556	tropical curves sing_2060.htm#IDX739
3557	tropical geometry sing_1171.htm#IDX455
3558	tropical mirror symmetry sing_1171.htm#IDX457
3559	tropical polynomials sing_2060.htm#IDX740
3560	tropical.lib sing_2060.htm#IDX737
3561	tropicalCurve sing_2065.htm#SEC2140
3562	tropicalJInvariant sing_2068.htm#SEC2143
3563	tropicalLifting sing_2061.htm#SEC2136
3564	tropicalSubst sing_2093.htm#SEC2168
3565	tropicalVariety sing_2409.htm#SEC2484
3566	tropical_lib sing_2060.htm#IDX738
3567	tropicalise sing_2072.htm#SEC2147
3568	tropicaliseSet sing_2073.htm#SEC2148
3569	truncate sing_1478.htm#SEC1553 13545
3570	truncateFast sing_1479.htm#SEC1554 5124
3571	truncated module sing_1478.htm#IDX549
3572	truncated module sing_1479.htm#IDX550
3573	tst_ncfactor sing_751.htm#SEC802
3574	twalk sing_1184.htm#SEC1259
3575	two-sided sing_546.htm#IDX298
3576	two-sided Groebner basis sing_546.htm#IDX299
3577	twostd sing_406.htm#IDX257
3578	twostd sing_531.htm#SEC570
3579	type sing_410.htm#SEC449
3580	type B sing_2146.htm#IDX817
3581	type D sing_2147.htm#IDX819
3582	type,custom Definition of a user defined type sing_178.htm#SEC217
3583	type2arr sing_2124.htm#SEC2199
3584	typecasting sing_2124.htm#IDX773
3585	typecasting sing_2125.htm#IDX775
3586	typecasting sing_2126.htm#IDX778
3587	typeof sing_411.htm#SEC450
3588	u sing_2250.htm#SEC2325
3589	uname sing_406.htm#IDX258
3590	unbounded_knapsack sing_1953.htm#SEC2028
3591	unipotent groups sing_1396.htm#IDX517
3592	uniquePoint sing_220.htm#SEC259
3593	unitmat sing_1090.htm#SEC1165
3594	univariate sing_412.htm#SEC451
3595	univarpoly sing_2018.htm#SEC2093
3596	unknown syndrome Decoding method based on quadratic equations sing_922.htm#SEC992
3597	unset sing_325.htm#SEC364
3598	untyped definitions sing_83.htm#SEC122
3599	untyped definitions sing_471.htm#SEC510
3600	updatePairs sing_1996.htm#SEC2071
3601	ures_solve sing_1754.htm#SEC1829
3602	uressolve sing_413.htm#SEC452
3603	usage, option sing_364.htm#IDX181
3604	user interface, Emacs Emacs user interface sing_21.htm#SEC28
3605	valvars sing_1749.htm#SEC1824
3606	vandermonde sing_414.htm#SEC453
3607	vanishId sing_1850.htm#SEC1925
3608	var sing_415.htm#SEC454
3609	varMat sing_2128.htm#SEC2203
3610	varNum sing_2129.htm#SEC2204
3611	variables sing_416.htm#SEC455
3612	variables sing_2128.htm#IDX785
3613	variables sing_2129.htm#IDX787
3614	variables sing_2130.htm#IDX791
3615	variables sing_2131.htm#IDX793
3616	variablesSorted sing_584.htm#SEC635
3617	variablesStandard sing_583.htm#SEC634
3618	vars2pars sing_830.htm#SEC881
3619	varsigns sing_2023.htm#SEC2098
3620	varstr sing_417.htm#SEC456
3621	vct2str sing_692.htm#SEC743
3622	vdim sing_418.htm#SEC457
3623	vdim (plural) sing_532.htm#SEC571
3624	vec2poly sing_566.htm#SEC617
3625	vector sing_172.htm#SEC211
3626	vector declarations sing_173.htm#SEC212
3627	vector expressions sing_174.htm#SEC213
3628	vector operations sing_175.htm#SEC214
3629	vector related functions vector related functions sing_176.htm#SEC215
3630	verify sing_2014.htm#SEC2089
3631	versal sing_1549.htm#SEC1624
3632	version sing_406.htm#IDX261
3633	vertexAdjacencyGraph vertexAdjacencyGraph sing_2447.htm#SEC2522
3634	vertexEdgeGraph sing_2448.htm#SEC2523
3635	vertices sing_242.htm#SEC281
3636	vfilt sing_1567.htm#SEC1642
3637	view sing_1870.htm#SEC1945
3638	visual sing_2449.htm#SEC2524
3639	visualize sing_2249.htm#SEC2324
3640	voice sing_453.htm#SEC492
3641	vwfilt sing_1568.htm#SEC1643
3642	wUnit sing_1908.htm#SEC1983
3643	waitAllTasks sing_1069.htm#SEC1144
3644	waitTasks sing_1068.htm#SEC1143
3645	waitall sing_419.htm#SEC458
3646	waitfirst sing_420.htm#SEC459
3647	warkedPreimageStd sing_2277.htm#SEC2352
3648	warn, option sing_70.htm#SEC109
3649	warn, option sing_364.htm#IDX147
3650	watchdog sing_950.htm#SEC1025
3651	wedge sing_421.htm#SEC460
3652	weierstr.lib sing_1999.htm#SEC2074
3653	weierstrDiv sing_2000.htm#SEC2075
3654	weierstrPrep sing_2001.htm#SEC2076
3655	weierstr_lib sing_1999.htm#SEC2074
3656	weierstrassForm sing_2069.htm#SEC2144
3657	weight sing_422.htm#SEC461
3658	weight filtration sing_1559.htm#IDX589
3659	weight filtration sing_1566.htm#IDX623
3660	weight filtration sing_1568.htm#IDX637
3661	weight filtration sing_1569.htm#IDX645
3662	weight filtration sing_1581.htm#IDX661
3663	weight filtration sing_1583.htm#IDX672
3664	weightKB sing_423.htm#SEC462
3665	weightM, option sing_364.htm#IDX166
3666	weighted lexicographical ordering sing_893.htm#IDX388
3667	weighted reverse lexicographical ordering Global orderings sing_893.htm#IDX386
3668	weightedRing sing_762.htm#SEC813
3669	whichvariable sing_2022.htm#SEC2097
3670	while sing_440.htm#SEC479
3671	withDim sing_261.htm#IDX141
3672	withHilb sing_261.htm#IDX139
3673	withMult sing_261.htm#IDX142
3674	withRes sing_261.htm#IDX140
3675	withSB sing_261.htm#IDX138
3676	wp, global ordering sing_893.htm#IDX387
3677	write sing_424.htm#SEC463
3678	writeNmzData sing_1301.htm#SEC1376 38467
3679	writeNmzPaths sing_1305.htm#SEC1380 sprintf
3680	ws, local ordering sing_894.htm#IDX398
3681	wurzel sing_1890.htm#SEC1965
3682	xchange sing_1884.htm#SEC1959
3683	xdvi sing_1809.htm#SEC1884
3684	zdd sing_2102.htm#IDX751
3685	zdd2poly sing_2119.htm#SEC2194 55047
3686	zero-dimensional sing_2019.htm#IDX728
3687	zeroMod sing_1242.htm#SEC1317
3688	zeroOpt sing_1251.htm#SEC1326
3689	zeroRadical sing_1153.htm#SEC1228
3690	zeroSet sing_1777.htm#SEC1852
3691	zerodec sing_1334.htm#SEC1409
3692	zeroset.lib sing_1772.htm#SEC1847
3693	zeroset_lib sing_1772.htm#SEC1847
3694	zetaDL sing_1471.htm#SEC1546
3695	{ sing_36.htm#IDX79
3696	\|\| sing_36.htm#IDX104
3697	\|\| sing_96.htm#SEC135
3698	} sing_36.htm#IDX80
3699	~ sing_36.htm#IDX118
3700	~ sing_441.htm#SEC480

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