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--MPhost	sing_19.htm#IDX66
--MPport	sing_19.htm#IDX65
--allow-net	sing_19.htm#IDX39
--batch	sing_19.htm#IDX64
--browser	sing_19.htm#IDX43
--echo	sing_19.htm#IDX35
--emacs	sing_19.htm#IDX67
--emacs-dir	sing_19.htm#IDX68
--emacs-load	sing_19.htm#IDX69
--execute	sing_19.htm#IDX56
--help	sing_19.htm#IDX37
--min-time	sing_19.htm#IDX61
--no-out	sing_19.htm#IDX49
--no-rc	sing_19.htm#IDX45
--no-shell	sing_19.htm#IDX50
--no-stdlib	sing_19.htm#IDX47
--no-tty	sing_19.htm#IDX51
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--random	sing_19.htm#IDX60
--sdb	sing_19.htm#IDX32
--singular	sing_19.htm#IDX70
--ticks-per-sec	sing_19.htm#IDX62
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-d	sing_19.htm#IDX31
-e	sing_19.htm#IDX34
-h	sing_19.htm#IDX36
-q	sing_19.htm#IDX52
-r	sing_19.htm#IDX59
-u	sing_19.htm#IDX57
-v	sing_19.htm#IDX54
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.singularrc file	sing_20.htm#IDX72
.singularrc file, no loading	sing_19.htm#IDX46
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?	sing_36.htm#IDX106
? 	sing_262.htm#IDX148
ADGT	sing_1063.htm#SEC1144
AG codes	sing_972.htm#SEC1029
AGcode_L	sing_2253.htm#SEC2334
AGcode_Omega	sing_2254.htm#SEC2335
ASCII	sing_1023.htm#SEC1104
ASCII links	sing_117.htm#SEC157
ASSUME	sing_64.htm#SEC101
A_L	sing_1875.htm#SEC1956
A_Z	sing_1021.htm#SEC1102
A_Z_L	sing_1022.htm#SEC1103
Access to elements of a user defined type	sing_186.htm#SEC226
Adj_div	sing_2248.htm#SEC2329
Adjoint ideal	sing_1704.htm#IDX729
Alexander polynomial	sing_1837.htm#IDX777
Algebraic Geometry codes	sing_2247.htm#IDX946
Algebraic dependence	sing_951.htm#SEC1008
Algebraic geometry	sing_1573.htm#SEC1654
AltVarEnd	sing_751.htm#SEC805
AltVarStart	sing_750.htm#SEC804
Ann	sing_1507.htm#SEC1588
Appel function	sing_561.htm#IDX352
Appel hypergeometric function	sing_561.htm#IDX353
Applications	sing_970.htm#SEC1027
Arnol'd	sing_1855.htm#IDX797
Arnold, classification.	sing_1883.htm#IDX802
Arnold, classification. 	sing_1884.htm#IDX803
ArnoldAction	sing_1990.htm#SEC2071
Assignments for user defined types	sing_188.htm#SEC228
AssocTanToEnv	sing_1057.htm#SEC1138
Atkin	sing_2336.htm#SEC2417
Authors	sing_1.htm#IDX16
Automatic Deduction	sing_1063.htm#IDX528
Automatic Demonstration	sing_1063.htm#IDX529
BFBoundsBudur	sing_598.htm#SEC652
BINresol	sing_1717.htm#SEC1798
BSidealFromAnn	sing_596.htm#SEC650
Background	sing_3.htm#SEC5
Basic programming	sing_926.htm#SEC983
Basic programming 	sing_926.htm#SEC983
BelongSemig	sing_2466.htm#SEC2547
BerlekampMassey	sing_1305.htm#SEC1386
Bern	sing_1612.htm#SEC1693
Bernstein operator	sing_537.htm#IDX334
Bernstein-Sato ideal	sing_593.htm#IDX355
Bernstein-Sato polynomial	sing_502.htm#IDX315
Bernstein-Sato polynomial 	sing_537.htm#IDX331
Bernstein-Sato polynomial  	sing_1931.htm#IDX814
Bernstein-Sato polynomial   	sing_1935.htm#IDX831
Bernstein-Sato polynomial for variety	sing_601.htm#IDX363
BernsteinSatoIdeal	sing_597.htm#SEC651
Betti	sing_1364.htm#SEC1445
Betti number	sing_988.htm#SEC1050
BettiNumsH	sing_1662.htm#SEC1743
BettiNumsN	sing_1670.htm#SEC1751
BettiNumsQp	sing_1665.htm#SEC1746
BettiNumsS	sing_1668.htm#SEC1749
Betty number	sing_1659.htm#IDX691
Bigatti-La Scala-Robbiano algorithm	sing_998.htm#SEC1060
Bimodules	sing_824.htm#SEC878
Bisyzygy	sing_824.htm#SEC878
BlowingUp	sing_1910.htm#SEC1991
Blowupcenter	sing_1720.htm#SEC1801
BorelCheck	sing_1834.htm#SEC1915
Bott's formula	sing_1779.htm#IDX745
Branches of space curve singularities	sing_959.htm#SEC1016
Briancon-Maisonobe algorithm	sing_537.htm#IDX340
Brieskorn lattice	sing_1931.htm#IDX810
Brieskorn lattice 	sing_1932.htm#IDX821
Brieskorn lattice  	sing_1933.htm#IDX824
Brieskorn lattice   	sing_1934.htm#IDX827
Brieskorn lattice    	sing_1935.htm#IDX830
Brieskorn lattice     	sing_1936.htm#IDX834
Brieskorn lattice      	sing_1937.htm#IDX838
Brieskorn lattice       	sing_1938.htm#IDX844
Brieskorn lattice        	sing_1939.htm#IDX852
Brieskorn lattice         	sing_1940.htm#IDX858
Brieskorn lattice          	sing_1941.htm#IDX866
Brieskorn lattice           	sing_1942.htm#IDX876
Brieskorn lattice            	sing_1953.htm#IDX882
Brieskorn lattice             	sing_1955.htm#IDX893
Brieskorn lattice              	sing_1983.htm#IDX920
Brill-Noether algorithm	sing_2247.htm#IDX947
BrillNoether	sing_2250.htm#SEC2331
Buchberger algorithm for toric ideals	sing_999.htm#SEC1061
Budur-Mustata-Saito approach	sing_601.htm#IDX367
Building Singular	sing_2998.htm#SEC3096
C programming language	sing_413.htm#SEC453
C, module ordering	sing_980.htm#IDX464
CGS	sing_1044.htm#IDX477
CGS, disjoint, reduced, comprehensive Groebner system	sing_1115.htm#IDX554
CM_regularity	sing_1821.htm#SEC1902
CMtype	sing_2027.htm#SEC2108
CRHT-ideal	sing_1005.htm#SEC1074
CSMA	sing_1635.htm#SEC1716
CYGWIN and ESingular	sing_23.htm#SEC33
Castelnuovo-Mumford regularity	sing_1821.htm#IDX769
Category string	sing_51.htm#SEC88
CenCharDec	sing_646.htm#SEC700
Center	sing_1759.htm#SEC1840
CenterBO	sing_1766.htm#SEC1847
CentralQuot	sing_644.htm#SEC698
CentralSaturation	sing_645.htm#SEC699
Change of rings	sing_9.htm#SEC15
Characteristic sets	sing_989.htm#SEC1051
CharacteristicExponents	sing_1916.htm#SEC1997
ChernClass	sing_1792.htm#SEC1873
ChernRootsDual	sing_1591.htm#SEC1672
ChernRootsHom	sing_1600.htm#SEC1681
ChernRootsProd	sing_1593.htm#SEC1674
ChernRootsSum	sing_1589.htm#SEC1670
ChernRootsSymm	sing_1602.htm#SEC1683
ChernRootsWedge	sing_1603.htm#SEC1684
Chevalley-Rosenlicht theorem	sing_1698.htm#IDX714
Chevalley-Rosenlicht theorem 	sing_1699.htm#IDX717
Chow ring, abstract variety, projective space, Grassmannian	sing_1783.htm#IDX750
ChowRing	sing_1783.htm#SEC1864
Classification of hypersurface singularities	sing_960.htm#SEC1017
Classification of singularities	sing_2000.htm#IDX921
Code	sing_1004.htm#SEC1067
Codes and the decoding problem	sing_1004.htm#SEC1066
Coding theory	sing_2246.htm#SEC2327
Coefficient rings	sing_2996.htm#SEC3089
Command line options	sing_19.htm#SEC26
Commands	sing_207.htm#SEC247
Commands for user defined types	sing_187.htm#SEC227
Commutative Algebra	sing_939.htm#SEC996
Commutative algebra	sing_1242.htm#SEC1323
CompDecomp	sing_499.htm#SEC553
CompInt	sing_2468.htm#SEC2549
CompleteHomog	sing_1579.htm#SEC1660
ComplexValue	sing_2812.htm#SEC2893
Comprehensive Groebner System	sing_1044.htm#IDX480
Comprehensive Groebner Systems	sing_1042.htm#SEC1123
Comprehensive Groebner Systems 	sing_1107.htm#SEC1188
Computing Groebner and Standard Bases	sing_935.htm#SEC992
ConsLevels	sing_1064.htm#SEC1145
ContactMatrix	sing_1918.htm#SEC1999
Conti-Traverso algorithm	sing_994.htm#SEC1056
Contributors	sing_1.htm#IDX15
Control structures	sing_381.htm#SEC421
Control theory	sing_2280.htm#SEC2361
Cooper philosophy	sing_1005.htm#SEC1072
Cornacchia	sing_2326.htm#SEC2407
CornacchiaModified	sing_2327.htm#SEC2408
Crep	sing_1047.htm#SEC1128
Critical points	sing_954.htm#SEC1011
CurveParam	sing_1912.htm#SEC1993
CurveRes	sing_1911.htm#SEC1992
Curves	sing_1704.htm#IDX726
Customization of the Emacs interface	sing_25.htm#SEC36
Cyclic code	sing_2261.htm#IDX954
Cyclic roots	sing_932.htm#SEC989
D-integration	sing_561.htm#IDX349
D-localization	sing_561.htm#IDX345
D-localization 	sing_668.htm#IDX384
D-module	sing_502.htm#IDX313
D-module 	sing_537.htm#IDX328
D-module  	sing_561.htm#IDX342
D-module   	sing_593.htm#IDX354
D-module    	sing_601.htm#IDX361
D-module     	sing_668.htm#IDX381
D-module      	sing_778.htm#IDX399
D-module structure	sing_537.htm#IDX329
D-module structure 	sing_593.htm#IDX357
D-module structure  	sing_601.htm#IDX362
D-restriction	sing_561.htm#IDX347
DBM links	sing_122.htm#SEC162
DISPLAY environment variable	sing_16.htm#IDX28
DLoc	sing_564.htm#SEC618
DLoc0	sing_566.htm#SEC620
Data types	sing_72.htm#SEC112
Data types (plural)	sing_426.htm#IDX299
Debugging tools	sing_63.htm#SEC100
Decker, Wolfram	sing_1.htm#IDX17
Declaration of objects of a user defined type	sing_185.htm#SEC225
Decoding	sing_2261.htm#IDX956
Decoding codes with Groebner bases	sing_1003.htm#SEC1065
Decoding method based on quadratic equations	sing_1008.htm#SEC1083
Definition of a user defined type	sing_184.htm#SEC224
Deformations	sing_957.htm#SEC1014
Deformations, T1 and T2	sing_956.htm#SEC1013
Deg	sing_1367.htm#SEC1448
Degree	sing_1368.htm#SEC1449
DegreePure	sing_1683.htm#SEC1764
Degrees	sing_1369.htm#SEC1450
Delta	sing_1767.htm#SEC1848
DeltaList	sing_1768.htm#SEC1849
Demo mode	sing_24.htm#SEC35
Depth	sing_946.htm#SEC1003
Determinacy	sing_2003.htm#IDX925
Di Biase-Urbanke algorithm	sing_997.htm#SEC1059
DifConsLCSets	sing_1067.htm#SEC1148
Distributed computing	sing_1078.htm#IDX545
Dlocalization	sing_669.htm#SEC723
Documentation Tool	sing_60.htm#SEC97
Dp, global ordering	sing_978.htm#IDX447
Ds, local ordering	sing_979.htm#IDX457
DsingularLocus	sing_673.htm#SEC727
Dynamic loading	sing_71.htm#SEC111
Dynamic modules	sing_934.htm#SEC991
ECPP	sing_2370.htm#SEC2451
ECoef	sing_1726.htm#SEC1807
EOrdlist	sing_1724.htm#SEC1805
ERROR	sing_238.htm#SEC278
ESingular, CYGWIN	sing_23.htm#SEC33
Edatalist	sing_1723.htm#SEC1804
Edelman-Reiner	sing_2655.htm#IDX1038
Editing SINGULAR input files with Emacs	sing_26.htm#SEC37
Editing input	sing_18.htm#SEC25
Elimination	sing_942.htm#SEC999
Emacs	sing_21.htm#SEC28
Emacs, Singular demo mode	sing_24.htm#SEC35
Emacs, a quick guide	sing_22.htm#SEC29
Emacs, customization of Singular mode	sing_25.htm#SEC36
Emacs, editing Singular input files	sing_26.htm#SEC37
Emacs, important commands	sing_27.htm#SEC38
Emacs, overview	sing_22.htm#SEC29
Emacs, running Singular under	sing_23.htm#SEC30
Emacs, user interface	sing_21.htm#SEC28
Emaxcont	sing_1728.htm#SEC1809
Enumerative geometry	sing_1779.htm#IDX743
Equal	sing_1682.htm#SEC1763
Eresol	sing_1718.htm#SEC1799
EulerAff	sing_1636.htm#SEC1717
EulerProj	sing_1637.htm#SEC1718
Evaluation of logical expressions	sing_415.htm#SEC455
Examples	sing_924.htm#SEC981
Examples of ring declarations	sing_29.htm#SEC40
Examples of use of Letterplace	sing_800.htm#SEC854
Examples of use of Letterplace over Z	sing_801.htm#SEC855
Exp for matrices	sing_1700.htm#IDX718
Experimental libraries	sing_2739.htm#SEC2820
Ext	sing_1322.htm#SEC1403
Ext, computation of	sing_945.htm#SEC1002
Ext_R	sing_1321.htm#SEC1402
Exterior	sing_737.htm#SEC791
Extra weight vector	sing_983.htm#SEC1040
Factorization	sing_947.htm#SEC1004
FamElemsAtEnvCompPoints	sing_1058.htm#SEC1139
Feynman graph	sing_1290.htm#IDX601
Finite fields	sing_941.htm#SEC998
First steps	sing_6.htm#SEC12
Fitzgerald-Lax method	sing_1007.htm#SEC1080
Float	sing_253.htm#SEC293
Flow control	sing_40.htm#SEC70
Formal Checker	sing_59.htm#SEC96
Formatting output	sing_931.htm#SEC988
Free associative algebras	sing_821.htm#SEC875
Free resolution	sing_943.htm#SEC1000
Free resolution, graded	sing_944.htm#SEC1001
FultonA	sing_1634.htm#SEC1715
Functional decomposition	sing_1273.htm#IDX593
Functionality and release notes of Letterplace	sing_802.htm#SEC856
Functions	sing_208.htm#SEC248
Functions (letterplace)	sing_804.htm#SEC858
Future benefits of Singular 4	sing_2996.htm#SEC3094
G-algebra	sing_490.htm#SEC530
G-algebra 	sing_490.htm#SEC532
G-algebra  	sing_661.htm#IDX369
G-algebra   	sing_662.htm#IDX376
G-algebra, setup	sing_490.htm#SEC534
GBWeight	sing_567.htm#SEC621
GBsolve	sing_2120.htm#SEC2201
GIT-Fans	sing_966.htm#SEC1023
GITcone	sing_2535.htm#SEC2616
GITfan	sing_2536.htm#SEC2617
GITfanFromOrbitCones	sing_2537.htm#SEC2618
GITfanParallel	sing_2538.htm#SEC2619
GITfanParallelSymmetric	sing_2553.htm#SEC2634
GITfanSymmetric	sing_2552.htm#SEC2633
GKExp	sing_666.htm#SEC720
GKZfan	sing_2539.htm#SEC2620
GKZsystem	sing_642.htm#SEC696
GKdim	sing_615.htm#SEC669
GMP	sing_1.htm#IDX3
GMP 	sing_3000.htm#SEC3098
GND.lib	sing_2817.htm#SEC2898
GND_lib	sing_2817.htm#SEC2898
GTZmod	sing_1428.htm#SEC1509
GTZopt	sing_1435.htm#SEC1516
G_a -Invariants	sing_963.htm#SEC1020
Gamma	sing_1733.htm#SEC1814
Gauss-Manin connection	sing_990.htm#SEC1052
Gauss-Manin connection 	sing_1983.htm#IDX919
Gauss-Manin connection  	sing_2036.htm#IDX929
Gauss-Manin system	sing_1931.htm#IDX809
Gauss-Manin system 	sing_1932.htm#IDX820
Gauss-Manin system  	sing_1933.htm#IDX823
Gauss-Manin system   	sing_1934.htm#IDX826
Gauss-Manin system    	sing_1935.htm#IDX829
Gauss-Manin system     	sing_1936.htm#IDX833
Gauss-Manin system      	sing_1937.htm#IDX837
Gauss-Manin system       	sing_1938.htm#IDX843
Gauss-Manin system        	sing_1939.htm#IDX851
Gauss-Manin system         	sing_1940.htm#IDX857
Gauss-Manin system          	sing_1941.htm#IDX865
Gauss-Manin system           	sing_1942.htm#IDX875
Gauss-Manin system            	sing_1953.htm#IDX881
Gauss-Manin system             	sing_1955.htm#IDX892
Gelfand-Kirillov dimension	sing_863.htm#IDX421
Gelfand-Kirillov dimension, G-Algebra	sing_666.htm#IDX377
General command syntax	sing_35.htm#SEC59
General concepts	sing_12.htm#SEC18
General purpose	sing_1015.htm#SEC1096
General syntax of a ring declaration	sing_30.htm#SEC41
Generalized Hilbert Syzygy Theorem	sing_492.htm#SEC544
Generalized Newton identities	sing_1006.htm#SEC1077
Geometric Invariant Theory	sing_965.htm#SEC1022
Geometric Theorems	sing_1063.htm#IDX530
Geometric genus	sing_1704.htm#IDX730
German Umlaute	sing_411.htm#IDX286
Getting started	sing_5.htm#SEC11
Global orderings	sing_978.htm#SEC1035
Goettsche's formula	sing_1659.htm#IDX692
GoettscheF	sing_1660.htm#SEC1741
Graded commutative algebras	sing_798.htm#SEC852
Grassmannian	sing_1784.htm#SEC1865
Grassmannian, abstract variety, Schubert calculus	sing_1784.htm#IDX751
Greuel, Gert-Martin	sing_1.htm#IDX18
Grob1Levels	sing_1066.htm#SEC1147
Groebner Bases	sing_935.htm#SEC992
Groebner bases for two-sided ideals in free associative algebras	sing_823.htm#SEC877
Groebner bases in G-algebras	sing_491.htm#SEC535
Groebner bases in free associative algebras	sing_823.htm#SEC877
Groebner bases, decodeGB	sing_2261.htm#IDX958
Groebner bases, slim	sing_938.htm#SEC995
Groebner basis conversion	sing_937.htm#SEC994
Groebner cover	sing_1043.htm#IDX473
Groebner cover 	sing_1050.htm#IDX492
Groebner cover  	sing_1051.htm#IDX499
Groebner fan	sing_2560.htm#IDX975
Groebner walk	sing_1313.htm#IDX622
Groebner walk 	sing_1315.htm#IDX624
Groebner walk  	sing_2950.htm#IDX1255
Groebner walk   	sing_2951.htm#IDX1256
Groebner-Shirshov bases	sing_823.htm#SEC877
Groebner-Shirshov bases in free associative algebras	sing_823.htm#SEC877
Groebnerwalk	sing_1309.htm#IDX618
Groebnerwalk 	sing_2872.htm#IDX1240
Groebnerwalk  	sing_2949.htm#IDX1254
Groebnerwalk   	sing_2960.htm#IDX1266
Gromov-Witten invariants	sing_1290.htm#IDX598
Gromov-Witten invariants 	sing_1296.htm#IDX607
Gromov-Witten invariants  	sing_1297.htm#IDX611
Gromov-Witten invariants, lines on hypersurfaces	sing_1809.htm#IDX763
Gromov-Witten invariants, multiple covers	sing_1808.htm#IDX762
Gromov-Witten invariants, rational curves on Calabi-Yau threefolds	sing_1810.htm#IDX764
Gromov-Witten invariants, rational curves on Calabi-Yau threefolds 	sing_1811.htm#IDX765
Gromov-Witten invariants.	sing_1779.htm#IDX746
Gweights	sing_731.htm#SEC785
H2basis	sing_1988.htm#SEC2069
HHnormalForm	sing_1892.htm#SEC1973
Hamburger-Noether expansion	sing_1837.htm#IDX773
Hamburger-Noether expansion 	sing_1956.htm#IDX901
Hamburger-Noether expansions	sing_2248.htm#IDX948
Handling graded modules	sing_944.htm#SEC1001
Hcode	sing_1868.htm#SEC1949
Help string	sing_45.htm#SEC82
Hensel	sing_243.htm#SEC283
Hilbert function	sing_359.htm#IDX189
Hilbert function 	sing_661.htm#IDX370
Hilbert function  	sing_662.htm#IDX374
Hilbert function   	sing_987.htm#SEC1046
Hilbert polynomial	sing_661.htm#IDX372
Hilbert scheme	sing_1659.htm#IDX695
Hilbert series	sing_661.htm#IDX371
Hilbert series 	sing_662.htm#IDX375
Hilbert series  	sing_827.htm#IDX412
Hilbert series   	sing_987.htm#SEC1046
Hilbert-driven GB algorithm	sing_937.htm#SEC994
HilbertClassPoly	sing_2333.htm#SEC2414
HilbertSeries	sing_2089.htm#SEC2170
HilbertWeights	sing_2090.htm#SEC2171
Hodge ideals	sing_2854.htm#IDX1232
Hom	sing_1325.htm#SEC1406
HomJJ	sing_1463.htm#SEC1544
Hosten-Sturmfels algorithm	sing_996.htm#SEC1058
How to enter and exit	sing_14.htm#SEC20
How to use this manual	sing_4.htm#SEC6
Hurwitz numbers	sing_1296.htm#IDX610
Hurwitz numbers 	sing_1297.htm#IDX614
Hypersurface singularities, classification of	sing_960.htm#SEC1017
I-regular function	sing_1050.htm#IDX498
IN	sing_283.htm#IDX149
Ideal membership	sing_986.htm#IDX469
Identifiers, syntax of	sing_37.htm#SEC65
ImageGroup	sing_2092.htm#SEC2173
ImageVariety	sing_2091.htm#SEC2172
Imap, option	sing_318.htm#IDX175
Implemented algorithms	sing_33.htm#SEC47
Incl	sing_1681.htm#SEC1762
Index	sing_3006.htm#SEC3104
Info string	sing_52.htm#SEC89
InterDiv	sing_1749.htm#SEC1830
Interactive use	sing_13.htm#SEC19
Interrupting SINGULAR	sing_17.htm#SEC24
IntersectWithSub	sing_647.htm#SEC701
Intersection theory	sing_1779.htm#IDX742
IntersectionMatrix	sing_1917.htm#SEC1998
Introduction	sing_2.htm#SEC4
Invariant Theory	sing_962.htm#SEC1019
Invariant theory	sing_2041.htm#SEC2122
InvariantQ	sing_2094.htm#SEC2175
InvariantRing	sing_2093.htm#SEC2174
Invariants of a finite group	sing_964.htm#SEC1021
Invariants of plane curve singularities	sing_958.htm#SEC1015
IsSCA	sing_752.htm#SEC806
J-marked schemes	sing_1828.htm#IDX771
J-marked schemes, Borel ideals	sing_1833.htm#IDX772
JMBTest.lib	sing_1828.htm#SEC1909
JMBTest_lib	sing_1828.htm#SEC1909
JMSConst.lib	sing_1833.htm#SEC1914
JMSConst_lib	sing_1833.htm#SEC1914
JMarkedScheme	sing_1835.htm#SEC1916
Jacobi	sing_2343.htm#SEC2424
Jacobson form	sing_2298.htm#IDX959
Jacobson normal form	sing_2298.htm#IDX960
Janet basis	sing_1552.htm#IDX673
Janet division, Janet basis	sing_1551.htm#IDX672
JuReTopDim	sing_1691.htm#SEC1772
JuReZeroDim	sing_1692.htm#SEC1773
Jumping numbers	sing_2854.htm#IDX1235
K-basis	sing_827.htm#IDX410
K-dimension	sing_827.htm#IDX411
KScoef	sing_1981.htm#SEC2062
KSconvert	sing_1979.htm#SEC2060
KSker	sing_1978.htm#SEC2059
KSlinear	sing_1980.htm#SEC2061
KSpencerKernel	sing_2034.htm#SEC2115
KeneshlouMatrixPresentation	sing_2836.htm#SEC2917
Ker	sing_1373.htm#SEC1454
Kernel of module homomorphisms	sing_950.htm#SEC1007
KoszulHomology	sing_1334.htm#SEC1415
Kronecker module	sing_1659.htm#IDX694
Kronecker product	sing_363.htm#SEC403
L, ordering	sing_984.htm#SEC1041
LETTERPLACE	sing_799.htm#SEC853
LETTERPLACE libraries	sing_826.htm#SEC880
LIB	sing_287.htm#SEC327
LIB commands	sing_53.htm#SEC90
LIBs	sing_1011.htm#SEC1092
LLL	sing_361.htm#IDX219
LOT algorithm	sing_537.htm#IDX341
LRcoef	sing_2861.htm#SEC2942
LRcoprod	sing_2864.htm#SEC2945
LRinstall	sing_2860.htm#SEC2941
LRmult	sing_2863.htm#SEC2944
LRschubmult	sing_2865.htm#SEC2946
LRskew	sing_2862.htm#SEC2943
LU-decomposition of a matrix of numbers	sing_292.htm#SEC332
Laurent series	sing_1294.htm#IDX606
Left and two-sided Groebner bases	sing_968.htm#SEC1025
Left ideal membership (plural)	sing_491.htm#SEC538
Left normal form	sing_491.htm#SEC537
Leinartas	sing_2929.htm#IDX1246
LengthSym	sing_795.htm#SEC849
LengthSymElement	sing_794.htm#SEC848
Letterplace	sing_799.htm#SEC853
Letterplace Groebner basis	sing_827.htm#IDX409
Letterplace Groebner basis 	sing_863.htm#IDX419
Letterplace Groebner basis  	sing_872.htm#IDX428
Letterplace correspondence	sing_825.htm#SEC879
Letterplace libraries	sing_826.htm#SEC880
Letterplace ring	sing_357.htm#SEC397
Levels	sing_1065.htm#SEC1146
Lexicographic Groebner bases, computation of	sing_937.htm#SEC994
Libraries	sing_48.htm#SEC85
Libraries 	sing_927.htm#SEC984
Libraries in the SINGULAR Documentation	sing_49.htm#SEC86
Library versioning	sing_2996.htm#SEC3092
Lie	sing_2792.htm#IDX1225
Lie algebra	sing_1699.htm#IDX715
Lie bracket	sing_460.htm#SEC500
Lie group	sing_1702.htm#IDX720
Lie group 	sing_1703.htm#IDX723
Limitations	sing_411.htm#SEC451
Linear algebra	sing_1183.htm#SEC1264
Linear code	sing_2261.htm#IDX955
LinearActionQ	sing_2096.htm#SEC2177
LinearCombinationQ	sing_2097.htm#SEC2178
LinearizeAction	sing_2095.htm#SEC2176
Loading a library	sing_62.htm#SEC99
Local orderings	sing_979.htm#SEC1036
Log for matrices	sing_1701.htm#IDX719
Long coefficients	sing_929.htm#SEC986
M, ordering	sing_981.htm#SEC1038
MVComplex	sing_1640.htm#SEC1721
Macdonald's formula	sing_1659.htm#IDX693
MacdonaldF	sing_1666.htm#SEC1747
Macintosh installation	sing_3005.htm#SEC3103
Mathematical background	sing_985.htm#SEC1042
Mathematical background (letterplace)	sing_820.htm#SEC874
Mathematical background (plural)	sing_489.htm#SEC529
Matrix orderings	sing_981.htm#SEC1038
Max	sing_1997.htm#SEC2078
Maximus	sing_1830.htm#SEC1911
Maxord	sing_1732.htm#SEC1813
MillerRabin	sing_2353.htm#SEC2434
Milnor code	sing_1855.htm#IDX799
Milnor number	sing_953.htm#SEC1010
Milnor number 	sing_2002.htm#IDX924
Min	sing_1998.htm#SEC2079
MinMult	sing_2467.htm#SEC2548
MinimalDecomposition	sing_2098.htm#SEC2179
Minimum distance	sing_2261.htm#IDX957
Minimus	sing_1829.htm#SEC1910
Miscellaneous libraries	sing_2626.htm#SEC2707
ModEqn	sing_1991.htm#SEC2072
Modular techniques	sing_1078.htm#IDX542
Module orderings	sing_980.htm#SEC1037
Modules and and their annihilator	sing_10.htm#SEC16
Monodromy	sing_1983.htm#IDX917
Monomial orderings	sing_975.htm#SEC1032
Monomial orderings on free algebras	sing_822.htm#SEC876
Monomial orderings, Term orderings	sing_31.htm#SEC44
Mori dream spaces	sing_2740.htm#IDX1126
Morse lemma	sing_2001.htm#IDX922
Morse lemma 	sing_2004.htm#IDX926
MultiplicitySequence	sing_1915.htm#SEC1996
Multiplier ideals	sing_2854.htm#IDX1234
NF	sing_337.htm#SEC377
NF (letterplace)	sing_813.htm#SEC867
NF (plural)	sing_481.htm#SEC521
NFMora	sing_2419.htm#SEC2500
NPos	sing_1453.htm#SEC1534
NPos_test	sing_1451.htm#SEC1532
NSplaces	sing_2249.htm#SEC2330
NTL	sing_1.htm#IDX4
NakYoshF	sing_1663.htm#SEC1744
Names	sing_37.htm#SEC65
Names in procedures	sing_46.htm#SEC83
Names, indexed	sing_37.htm#SEC65
New orderings for modules	sing_2996.htm#SEC3093
Newton non-degenerate	sing_1970.htm#IDX915
Newton polygon	sing_1969.htm#IDX914
Newton polygon 	sing_1970.htm#IDX916
Newton polygons	sing_2617.htm#IDX980
Newton polytope	sing_2560.htm#IDX974
Newton step	sing_2186.htm#IDX943
Noether position	sing_1453.htm#IDX642
NoetherPosition	sing_1442.htm#SEC1523
Non-commutative algebra	sing_967.htm#SEC1024
Non-commutative algebra 	sing_1002.htm#SEC1064
Non-commutative subsystem	sing_424.htm#SEC464
Nonhyp	sing_1721.htm#SEC1802
Normalization	sing_949.htm#SEC1006
Notes for Singular users	sing_2996.htm#SEC3088
Notes for developers	sing_2997.htm#SEC3095
NullCone	sing_2099.htm#SEC2180
NumIrrDecom	sing_1695.htm#SEC1776
NumLocalDim	sing_1684.htm#SEC1765
NumPrimDecom	sing_1697.htm#SEC1778
Oaku-Takayama algorithm	sing_537.htm#IDX339
Objects	sing_38.htm#SEC66
Orlik-Solomon	sing_2656.htm#IDX1039
Output	sing_1383.htm#IDX639
Output 	sing_2681.htm#IDX1074
Output  	sing_2683.htm#IDX1075
Output   	sing_2684.htm#IDX1076
Output    	sing_2685.htm#IDX1077
Output     	sing_2686.htm#IDX1078
Output      	sing_2687.htm#IDX1079
Output       	sing_2688.htm#IDX1080
Output        	sing_2689.htm#IDX1081
Output         	sing_2690.htm#IDX1082
Output          	sing_2691.htm#IDX1083
Output           	sing_2692.htm#IDX1084
Output            	sing_2693.htm#IDX1085
Output             	sing_2694.htm#IDX1086
Output              	sing_2695.htm#IDX1087
Output               	sing_2696.htm#IDX1088
Output                	sing_2697.htm#IDX1089
Output                 	sing_2698.htm#IDX1090
Output                  	sing_2699.htm#IDX1091
Output                   	sing_2700.htm#IDX1092
Output                    	sing_2701.htm#IDX1093
Output                     	sing_2702.htm#IDX1094
Output                      	sing_2703.htm#IDX1095
Output                       	sing_2704.htm#IDX1096
Output                        	sing_2705.htm#IDX1097
Output, formatting of	sing_931.htm#SEC988
PBW	sing_516.htm#IDX327
PBW basis	sing_490.htm#SEC531
PBW_eqDeg	sing_534.htm#SEC588
PBW_maxDeg	sing_535.htm#SEC589
PBW_maxMonom	sing_536.htm#SEC590
PEsolve	sing_2118.htm#SEC2199
PH_ais	sing_2709.htm#SEC2790
PH_nais	sing_2710.htm#SEC2791
PLURAL	sing_425.htm#SEC465
PLURAL LIBs	sing_494.htm#SEC548
PLURAL libraries	sing_494.htm#SEC548
PPolyH	sing_1661.htm#SEC1742
PPolyN	sing_1669.htm#SEC1750
PPolyQp	sing_1664.htm#SEC1745
PPolyS	sing_1667.htm#SEC1748
ParToVar	sing_2814.htm#SEC2895
Parallelization	sing_933.htm#SEC990
Parallelization 	sing_1078.htm#IDX543
Parameter list	sing_44.htm#SEC81
Parameters	sing_930.htm#SEC987
Parametrization	sing_1704.htm#IDX727
Parametrization, image.	sing_1714.htm#IDX739
PartC	sing_1630.htm#SEC1711
PartitionVar	sing_2811.htm#SEC2892
Path names	sing_2996.htm#SEC3091
PerfectPowerTest	sing_2316.htm#SEC2397
Perturbation walk	sing_1314.htm#IDX623
Pfister, Gerhard	sing_1.htm#IDX19
Pipe links	sing_121.htm#SEC161
PocklingtonLehmer	sing_2355.htm#SEC2436
Poincare polynomial	sing_2668.htm#IDX1063
Polar curves	sing_955.htm#SEC1012
PollardRho	sing_2356.htm#SEC2437
PolyBoRi, Boolean Groebner Basis	sing_2712.htm#IDX1105
PolyBoRi, Boolean Groebner Basis 	sing_2714.htm#IDX1106
PolyBoRi, Boolean Groebner Basis  	sing_2715.htm#IDX1107
PolyBoRi, Boolean Groebner Basis   	sing_2716.htm#IDX1108
PolyBoRi, Boolean Groebner Basis    	sing_2717.htm#IDX1109
PolyBoRi, Boolean Groebner Basis     	sing_2718.htm#IDX1110
PolyBoRi, Boolean Groebner Basis      	sing_2719.htm#IDX1111
PolyBoRi, Boolean Groebner Basis       	sing_2720.htm#IDX1112
PolyBoRi, Boolean Groebner Basis        	sing_2721.htm#IDX1113
PolyBoRi, Boolean Groebner Basis         	sing_2722.htm#IDX1114
PolyBoRi, Boolean Groebner Basis          	sing_2723.htm#IDX1115
PolyBoRi, Boolean Groebner Basis           	sing_2724.htm#IDX1116
PolyBoRi, Boolean Groebner Basis            	sing_2725.htm#IDX1117
PolyBoRi, Boolean Groebner Basis             	sing_2726.htm#IDX1118
PolyBoRi, Boolean Groebner Basis              	sing_2728.htm#IDX1120
PolyBoRi, zero-supressed decision diagram	sing_2727.htm#IDX1119
Polybori, Boolean Groebner Basis	sing_2729.htm#IDX1121
Polynomial data	sing_973.htm#SEC1030
Pottier algorithm	sing_995.htm#SEC1057
Preface	sing_1.htm#SEC1
Prep	sing_1048.htm#SEC1129
Primary decomposition	sing_948.htm#SEC1005
PrimdecA	sing_1424.htm#SEC1505
PrimdecB	sing_1425.htm#SEC1506
Procedure definition	sing_43.htm#SEC78
Procedure-specific commands	sing_47.htm#SEC84
Procedures	sing_42.htm#SEC77
Procedures and libraries	sing_8.htm#SEC14
Procedures and libraries 	sing_927.htm#SEC984
Procedures in a library	sing_54.htm#SEC91
Product orderings	sing_982.htm#SEC1039
Programming	sing_925.htm#SEC982
Pseudo ordering L	sing_984.htm#SEC1041
PtoCrep	sing_1049.htm#SEC1130
Puiseux expansion	sing_1837.htm#IDX774
Puiseux expansion 	sing_1956.htm#IDX902
Puiseux pairs	sing_958.htm#SEC1015
Puiseux pairs 	sing_1962.htm#IDX907
QPoly, quotient ring.	sing_2956.htm#IDX1261
QQ	sing_28.htm#SEC39
QQ 	sing_75.htm#SEC115
Qso3Casimir	sing_641.htm#SEC695
Quot-scheme	sing_1659.htm#IDX696
Quotient	sing_2204.htm#SEC2285
QuotientEquations	sing_1992.htm#SEC2073
Rational curves	sing_1704.htm#IDX728
ReJunkUseHomo	sing_1690.htm#SEC1771
Reduced Comprehensive Groebner Systems	sing_1107.htm#SEC1188
ReesAlgebra	sing_1546.htm#SEC1627
References	sing_1010.htm#SEC1089
References (plural)	sing_493.htm#SEC545
References and history of Letterplace	sing_803.htm#SEC857
Release Notes	sing_2992.htm#SEC3073
Release Notes (letterplace)	sing_923.htm#SEC977
Res	sing_1363.htm#SEC1444
ResTree	sing_1750.htm#SEC1831
Resolution	sing_11.htm#SEC17
Resolution of singularities	sing_961.htm#SEC1018
Resolution, free	sing_943.htm#SEC1000
ReynoldsImage	sing_2100.htm#SEC2181
ReynoldsOperator	sing_2101.htm#SEC2182
RiemannRochBN	sing_1575.htm#SEC1656
RiemannRochHess	sing_1679.htm#SEC1760
Right Groebner bases and syzygies	sing_969.htm#SEC1026
Right ideal membership (plural)	sing_491.htm#SEC539
Ring-dependent options	sing_2996.htm#SEC3090
Rings and orderings	sing_28.htm#SEC39
Rings and standard bases	sing_7.htm#SEC13
Running SINGULAR under Emacs	sing_23.htm#SEC30
SCA	sing_798.htm#SEC852
SDB breakpoint	sing_66.htm#SEC106
SDB debugger	sing_66.htm#SEC106
SDLoc	sing_565.htm#SEC619
SINGULAR libraries	sing_1011.htm#SEC1092
SINGULARHIST	sing_18.htm#SEC25
SL	sing_2104.htm#SEC2185
SLreynolds	sing_2110.htm#SEC2191
SV-decoding algorithm	sing_2256.htm#IDX951
SV-decoding algorithm, preprocessing	sing_2255.htm#IDX950
SaitoBase	sing_2986.htm#SEC3067
Sannfs	sing_541.htm#SEC595
SannfsBFCT	sing_550.htm#SEC604
SannfsVar	sing_604.htm#SEC658
Sannfslog	sing_542.htm#SEC596
Saturation	sing_940.htm#SEC997
Sch@"onemann, Hans	sing_1.htm#IDX20
Schoof	sing_2367.htm#SEC2448
Schubert calculus	sing_1779.htm#IDX744
SchubertClass	sing_1816.htm#SEC1897
SchurCh	sing_1627.htm#SEC1708
SchurS	sing_1626.htm#SEC1707
SegreA	sing_1633.htm#SEC1714
Semigroup	sing_1899.htm#SEC1980
Serre relations	sing_834.htm#IDX416
SetDeg	sing_1366.htm#SEC1447
Setting up a G-algebra	sing_490.htm#SEC534
ShanksMestre	sing_2366.htm#SEC2447
SimplifyIdeal	sing_2102.htm#SEC2183
Singular	sing_361.htm#IDX256
Singular 3 and Singular 4	sing_2994.htm#SEC3086
Singular, customization of Emacs user interface	sing_25.htm#SEC36
Singular, demo mode	sing_24.htm#SEC35
Singular, editing input files with Emacs	sing_26.htm#SEC37
Singular, important commands of Emacs interface	sing_27.htm#SEC38
Singular, running within Emacs	sing_23.htm#SEC30
Singular2bertini	sing_1688.htm#SEC1769
SingularLib	sing_361.htm#IDX258
Singularities	sing_1836.htm#SEC1917
Singularity Theory	sing_952.htm#SEC1009
SingularityDBM.lib	sing_1855.htm#SEC1936
SingularityDBM_lib	sing_1855.htm#SEC1936
Skeletons for parallelization	sing_1078.htm#IDX544
Smith form	sing_2298.htm#IDX961
Smith normal form	sing_2298.htm#IDX962
SolowayStrassen	sing_2354.htm#SEC2435
Solving systems of polynomial equations	sing_971.htm#SEC1028
Source	sing_1355.htm#SEC1436
Source code debugger, invocation	sing_19.htm#IDX33
Space curve singularities, branches of	sing_959.htm#SEC1016
Special characters	sing_36.htm#SEC64
Splitting lemma	sing_2001.htm#IDX923
Splitting lemma 	sing_2004.htm#IDX927
Ssi file links	sing_119.htm#SEC159
Ssi links	sing_118.htm#SEC158
Ssi tcp links	sing_120.htm#SEC160
StabEqn	sing_1993.htm#SEC2074
StabEqnId	sing_1994.htm#SEC2075
StabOrder	sing_1995.htm#SEC2076
Standard Bases	sing_935.htm#SEC992
Standard bases	sing_986.htm#SEC1043
Stanely-Reisner ideals, Stanley-Reisner rings, deformations	sing_2953.htm#IDX1258
StartOrderingV	sing_1831.htm#SEC1912
Startup sequence	sing_20.htm#SEC27
StringF	sing_1982.htm#SEC2063
SymGroup	sing_793.htm#SEC847
Symbolic-numerical solving	sing_971.htm#SEC1028
Symbolic-numerical solving 	sing_2115.htm#SEC2196
System and Control theory	sing_2280.htm#SEC2361
System dependent limitations	sing_412.htm#SEC452
System variables	sing_398.htm#SEC438
Syzygies and resolutions	sing_988.htm#SEC1047
Syzygies and resolutions (plural)	sing_492.htm#SEC541
Syzygy bimodule	sing_824.htm#SEC878
T1	sing_956.htm#SEC1013
T1 	sing_2954.htm#SEC3035
T2	sing_956.htm#SEC1013
T2 	sing_2955.htm#SEC3036
TRACE	sing_65.htm#SEC102
TRACE 	sing_407.htm#SEC447
T_1	sing_2021.htm#SEC2102
T_12	sing_2023.htm#SEC2104
T_2	sing_2022.htm#SEC2103
Target	sing_1354.htm#SEC1435
Teaching	sing_2312.htm#SEC2393
Template for writing a library	sing_55.htm#SEC92
TestGRRes	sing_2835.htm#SEC2916
TestJMark	sing_1832.htm#SEC1913
The SINGULAR language	sing_34.htm#SEC56
The Tran algorithm	sing_1311.htm#IDX620
The fractal walk algorithm	sing_1310.htm#IDX619
The fractal walk algorithm 	sing_2952.htm#IDX1257
The online help system	sing_16.htm#SEC22
Tjurina	sing_2019.htm#SEC2100
Tjurina number	sing_953.htm#SEC1010
Tjurina number 	sing_1468.htm#IDX657
Top 20 Emacs commands	sing_27.htm#SEC38
Tor	sing_1336.htm#SEC1417
Toric ideals and integer programming	sing_991.htm#SEC1053
Tricks and pitfalls	sing_410.htm#SEC450
Tropical Geometry	sing_2464.htm#SEC2545
Two-sided ideal membership (plural)	sing_491.htm#SEC540
Type casting	sing_39.htm#SEC69
Type conversion	sing_39.htm#SEC68
Typesetting of help and info strings	sing_61.htm#SEC98
U_D_O	sing_1231.htm#SEC1312
Ufnarovski graph	sing_863.htm#IDX424
Unix installation	sing_3003.htm#SEC3101
UpOneMatrix	sing_749.htm#SEC803
UpperMonomials	sing_1996.htm#SEC2077
UseBertini	sing_1687.htm#SEC1768
User defined types	sing_183.htm#SEC223
V-filtration	sing_1931.htm#IDX812
V-filtration 	sing_1937.htm#IDX840
V-filtration  	sing_1938.htm#IDX846
V-filtration   	sing_1939.htm#IDX854
V-filtration    	sing_1940.htm#IDX860
V-filtration     	sing_1941.htm#IDX868
V-filtration      	sing_1942.htm#IDX878
V-filtration       	sing_1953.htm#IDX884
V-filtration        	sing_1955.htm#IDX895
V-filtration         	sing_2854.htm#IDX1233
VarToPar	sing_2813.htm#SEC2894
Variables, indexed	sing_37.htm#SEC65
VecField.lib	sing_2981.htm#SEC3062
VecField_lib	sing_2981.htm#SEC3062
Version number	sing_2995.htm#SEC3087
Version schema for Singular	sing_2995.htm#SEC3087
Version string	sing_50.htm#SEC87
Vfiltration	sing_2855.htm#SEC2936
Visualization	sing_2218.htm#SEC2299
WLCGS	sing_1061.htm#SEC1142
WLemma	sing_1060.htm#SEC1141
WP, global ordering	sing_978.htm#IDX451
WSemigroup	sing_1913.htm#SEC1994
Weierstrass	sing_2251.htm#SEC2332
Weierstrass semigroup	sing_2247.htm#IDX945
Weyl	sing_734.htm#SEC788
Weyl algebra	sing_537.htm#IDX333
Weyl algebra 	sing_593.htm#IDX359
Weyl algebra  	sing_601.htm#IDX365
Weyl closure	sing_668.htm#IDX387
WeylClosure	sing_670.htm#SEC724
WeylClosure1	sing_671.htm#SEC725
Wibmer's Lemma	sing_1060.htm#IDX527
Windows installation	sing_3004.htm#SEC3102
WitSet	sing_1694.htm#SEC1775
WitSupSet	sing_1693.htm#SEC1774
Ws, local ordering	sing_979.htm#IDX463
XLsolve	sing_2121.htm#SEC2202
ZZ	sing_28.htm#SEC39
ZZ 	sing_75.htm#SEC115
ZZ/m	sing_28.htm#SEC39
ZZ/p	sing_28.htm#SEC39
ZZsolve	sing_2122.htm#SEC2203
[	sing_36.htm#IDX83
[]	sing_142.htm#SEC182
[] 	sing_155.htm#SEC195
[]  	sing_176.htm#SEC216
[]   	sing_181.htm#SEC221
\	sing_36.htm#IDX112
]	sing_36.htm#IDX84
^	sing_36.htm#IDX92
^ 	sing_81.htm#SEC121
^  	sing_93.htm#SEC133
^   	sing_147.htm#SEC187
^    	sing_155.htm#SEC195
_	sing_36.htm#IDX116
`	sing_36.htm#IDX105
a, ordering	sing_983.htm#SEC1040
absFactorize	sing_1244.htm#SEC1325
absFactorizeBCG	sing_1245.htm#SEC1326
absPrimdecGTZ	sing_1526.htm#SEC1607
absPrimdecGTZE	sing_1527.htm#SEC1608
absValue	sing_1024.htm#SEC1105
absfact.lib	sing_1243.htm#SEC1324
absfact_lib	sing_1243.htm#SEC1324
absolute factorization.	sing_1243.htm#IDX580
abstract variety, projective space, Grassmannian	sing_1780.htm#IDX747
abstract variety, projective space, Grassmannian 	sing_1781.htm#IDX748
abstractR	sing_1776.htm#SEC1857
actionIsProper	sing_2082.htm#SEC2163
add	sing_2761.htm#IDX1158
add 	sing_2783.htm#IDX1206
addElement	sing_2738.htm#SEC2819
addLeftFractions	sing_765.htm#SEC819
addModules	sing_1375.htm#SEC1456
addNvarsTo	sing_1167.htm#SEC1248
addRat	sing_689.htm#SEC743
addSheaf	sing_1799.htm#SEC1880
addcol	sing_1200.htm#SEC1281
addcores	sing_1136.htm#SEC1217
addnondegeneratevariables	sing_2004.htm#SEC2085
addrow	sing_1201.htm#SEC1282
addvarsTo	sing_1166.htm#SEC1247
ademRelations	sing_838.htm#SEC892
adjoint	sing_1225.htm#SEC1306
adjointIdeal	sing_1705.htm#SEC1786
adjunction divisor	sing_2248.htm#IDX949
admissibleSub	sing_725.htm#SEC779
afaces	sing_2531.htm#SEC2612
affine code	sing_1007.htm#SEC1081
ainvar.lib	sing_2079.htm#SEC2160
ainvar_lib	sing_2079.htm#SEC2160
aksaka.lib	sing_2313.htm#SEC2394
aksaka_lib	sing_2313.htm#SEC2394
alexanderpolynomial	sing_1840.htm#SEC1921
alexpoly.lib	sing_1837.htm#SEC1918
alexpoly_lib	sing_1837.htm#SEC1918
algDependent	sing_1250.htm#SEC1331
alg_kernel	sing_1251.htm#SEC1332
algebra.lib	sing_1246.htm#SEC1327
algebra_containment	sing_1247.htm#SEC1328
algebra_lib	sing_1246.htm#SEC1327
algebraic dependence	sing_776.htm#IDX395
algebraic field extension	sing_1540.htm#IDX666
algebraic statistics	sing_2866.htm#IDX1236
algebraicDependence	sing_1558.htm#SEC1639
algorithm of Bigatti, La Scala and Robbiano	sing_998.htm#SEC1060
algorithm of Conti and Traverso	sing_994.htm#SEC1056
algorithm of Di Biase and Urbanke	sing_997.htm#SEC1059
algorithm of Hosten and Sturmfels	sing_996.htm#SEC1058
algorithm of Pottier	sing_995.htm#SEC1057
alias	sing_35.htm#SEC59
align	sing_209.htm#SEC249
all.lib	sing_1016.htm#SEC1097
allDoubleExt	sing_787.htm#SEC841
allExtOfLeft	sing_784.htm#SEC838
allExtOfRight	sing_785.htm#SEC839
allPositive	sing_513.htm#SEC567
all_lib	sing_1016.htm#SEC1097
allowing net access	sing_19.htm#IDX41
allprint	sing_1069.htm#SEC1150
allreal	sing_2456.htm#SEC2537
allrealst	sing_2454.htm#SEC2535
allsquarefree	sing_1975.htm#SEC2056
ambientDimension	sing_2473.htm#SEC2554
and	sing_101.htm#SEC141
and 	sing_415.htm#SEC455
annPoly	sing_562.htm#SEC616
annRat	sing_563.htm#SEC617
annRatSyz	sing_678.htm#SEC732
annfalphaI	sing_599.htm#SEC653
annfs	sing_538.htm#SEC592
annfs0	sing_551.htm#SEC605
annfs2	sing_552.htm#SEC606
annfsBMI	sing_548.htm#SEC602
annfsLogIdeal	sing_594.htm#SEC648
annfsParamBM	sing_547.htm#SEC601
annfsRB	sing_553.htm#SEC607
annfspecial	sing_539.htm#SEC593
annfspecialOld	sing_540.htm#SEC594
annihilator of polynomial	sing_561.htm#IDX343
annihilator of rational function	sing_561.htm#IDX344
annihilator of rational function 	sing_668.htm#IDX390
annihilatorMultiFs	sing_595.htm#SEC649
annil	sing_1430.htm#SEC1511
appelF1	sing_580.htm#SEC634
appelF2	sing_581.htm#SEC635
appelF4	sing_582.htm#SEC636
appendWeight2Ord	sing_727.htm#SEC781
application	sing_2789.htm#IDX1221
apply	sing_382.htm#SEC422
applyAdF	sing_529.htm#SEC583
applyMatrix	sing_2128.htm#SEC2209
applyPermutationToIntvec	sing_2556.htm#SEC2637
applyVecField	sing_2982.htm#SEC3063
arcpoint.lib	sing_1850.htm#SEC1931
arcpoint_lib	sing_1850.htm#SEC1931
areEqualLeftFractions	sing_767.htm#SEC821
areZeroElements	sing_2913.htm#SEC2994
argument, default	sing_44.htm#SEC81
argument, optional	sing_44.htm#SEC81
arnoldClassify	sing_1859.htm#SEC1940
arnoldCorank	sing_1860.htm#SEC1941
arnoldDeterminacy	sing_1861.htm#SEC1942
arnoldListAllSeries	sing_1856.htm#SEC1937
arnoldMilnorCode	sing_1862.htm#SEC1943
arnoldMorseSplit	sing_1863.htm#SEC1944
arnoldNormalForm	sing_1858.htm#SEC1939
arnoldShowSeries	sing_1857.htm#SEC1938
arnoldclassify.lib	sing_1855.htm#SEC1936
arnoldclassify_lib	sing_1855.htm#SEC1936
arr.lib	sing_2627.htm#SEC2708
arr2multarr	sing_2660.htm#SEC2741
arrBoolean	sing_2649.htm#SEC2730
arrBoundedChambers	sing_2670.htm#SEC2751
arrBraid	sing_2650.htm#SEC2731
arrCenter	sing_2637.htm#SEC2718
arrCentered	sing_2639.htm#SEC2720
arrCentral	sing_2638.htm#SEC2719
arrCentralize	sing_2640.htm#SEC2721
arrChambers	sing_2669.htm#SEC2750
arrCharPoly	sing_2667.htm#SEC2748
arrCone	sing_2643.htm#SEC2724
arrCoordChange	sing_2641.htm#SEC2722
arrCoordNormalize	sing_2642.htm#SEC2723
arrDecone	sing_2644.htm#SEC2725
arrDer	sing_2657.htm#SEC2738
arrEdelmanReiner	sing_2655.htm#SEC2736
arrEssentialize	sing_2648.htm#SEC2729
arrExponents	sing_2659.htm#SEC2740
arrFlats	sing_2664.htm#SEC2745
arrIsEssential	sing_2647.htm#SEC2728
arrIsFree	sing_2658.htm#SEC2739
arrLastVar	sing_2636.htm#SEC2717
arrLattice	sing_2665.htm#SEC2746
arrLocalize	sing_2645.htm#SEC2726
arrOrlikSolomon	sing_2656.htm#SEC2737
arrPoincare	sing_2668.htm#SEC2749
arrPrintMatrix	sing_2632.htm#SEC2713
arrRandom	sing_2653.htm#SEC2734
arrRandomCentral	sing_2654.htm#SEC2735
arrRestrict	sing_2646.htm#SEC2727
arrSet	sing_2628.htm#SEC2709
arrSwapVar	sing_2635.htm#SEC2716
arrTypeB	sing_2651.htm#SEC2732
arrTypeD	sing_2652.htm#SEC2733
arr_lib	sing_2627.htm#SEC2708
arrange	sing_555.htm#SEC609
arrangement	sing_2628.htm#IDX981
arrangement 	sing_2629.htm#IDX986
arrangement  	sing_2660.htm#IDX1048
arrangement   	sing_2661.htm#IDX1051
ask	sing_2321.htm#SEC2402
assPrimes	sing_1261.htm#SEC1342
assign	sing_2628.htm#IDX983
assignment,custom	sing_188.htm#SEC228
associated tangent	sing_1057.htm#IDX520
associated tangent 	sing_1058.htm#IDX524
assprimeszerodim.lib	sing_1259.htm#SEC1340
assprimeszerodim_lib	sing_1259.htm#SEC1340
atkins.lib	sing_2322.htm#SEC2403
atkins_lib	sing_2322.htm#SEC2403
attrib	sing_210.htm#SEC250
autGenWeights	sing_2743.htm#SEC2824
autGradAlg	sing_2742.htm#SEC2823
autKS	sing_2741.htm#SEC2822
autX	sing_2746.htm#SEC2827
autXhat	sing_2745.htm#SEC2826
autgradalg.lib	sing_2740.htm#SEC2821
autgradalg_lib	sing_2740.htm#SEC2821
automorphism group	sing_2740.htm#IDX1127
automorphisms	sing_2740.htm#IDX1124
autonom	sing_2285.htm#SEC2366
autonomDim	sing_2286.htm#SEC2367
awalk1	sing_1312.htm#SEC1393
awalk2	sing_1313.htm#SEC1394
b-function	sing_502.htm#IDX316
bFactor	sing_585.htm#SEC639
babyGiant	sing_2351.htm#SEC2432
backward	sing_2800.htm#SEC2881
bareiss	sing_211.htm#SEC251
base2str	sing_1019.htm#SEC1100
basering	sing_28.htm#IDX76
basering 	sing_88.htm#SEC128
basicinvariants	sing_1865.htm#SEC1946
baumslagGroup	sing_840.htm#SEC894
baumslagSolitar	sing_839.htm#SEC893
beilinsonWindow	sing_2976.htm#SEC3057
belongSemigroup	sing_1264.htm#SEC1345
bernstein	sing_1935.htm#SEC2016
bernsteinBM	sing_543.htm#SEC597
bernsteinLift	sing_544.htm#SEC598
bertini	sing_1680.htm#IDX701
bertini 	sing_1685.htm#IDX708
bertini  	sing_2168.htm#IDX940
bertini2Singular	sing_1689.htm#SEC1770
betti	sing_212.htm#SEC252
betti (plural)	sing_459.htm#SEC499
bfct	sing_503.htm#SEC557
bfctAnn	sing_505.htm#SEC559
bfctBound	sing_677.htm#SEC731
bfctIdeal	sing_507.htm#SEC561
bfctOneGB	sing_506.htm#SEC560
bfctSyz	sing_504.htm#SEC558
bfctVarAnn	sing_603.htm#SEC657
bfctVarIn	sing_602.htm#SEC656
bfun.lib	sing_502.htm#SEC556
bfun_lib	sing_502.htm#SEC556
bigger	sing_2768.htm#IDX1172
bigint	sing_78.htm#SEC118
bigint declarations	sing_79.htm#SEC119
bigint expressions	sing_80.htm#SEC120
bigint operations	sing_81.htm#SEC121
bigint related functions	sing_82.htm#SEC122
bigintToBinary	sing_2554.htm#SEC2635
bigintmat	sing_83.htm#SEC123
bigintmat declarations	sing_84.htm#SEC124
bigintmat expressions	sing_85.htm#SEC125
bigintmat operations	sing_87.htm#SEC127
bigintmat type cast	sing_86.htm#SEC126
bimodules	sing_495.htm#IDX304
bimodules.lib	sing_495.htm#SEC549
bimodules_lib	sing_495.htm#SEC549
binaryToBigint	sing_2555.htm#SEC2636
binary_add	sing_2374.htm#SEC2455
binomial	sing_1025.htm#SEC1106
binomials2intmat	sing_1501.htm#SEC1582
birational map, image, inverse.	sing_1706.htm#IDX733
bistd	sing_496.htm#SEC550
bisyzygies	sing_495.htm#IDX305
bitrinity	sing_497.htm#SEC551
blackbox	sing_192.htm#SEC232
blackbox 	sing_200.htm#SEC240
block	sing_40.htm#SEC70
block 	sing_381.htm#SEC421
blowUp	sing_1757.htm#SEC1838
blowUp2	sing_1758.htm#SEC1839
blowUpBO	sing_1764.htm#SEC1845
blowup0	sing_1281.htm#SEC1362
boolean	sing_2649.htm#IDX1025
boolean expressions	sing_100.htm#SEC140
boolean operations	sing_101.htm#SEC141
boolean_constant	sing_2714.htm#SEC2795
boolean_ideal	sing_2718.htm#SEC2799
boolean_poly	sing_2715.htm#SEC2796
boolean_poly_ring	sing_2713.htm#SEC2794
boolean_set	sing_2719.htm#SEC2800
boolean_std	sing_2712.htm#SEC2793
border basis	sing_1548.htm#IDX668
borderBasis	sing_1549.htm#SEC1630
boundBuFou	sing_2451.htm#SEC2532
boundDes	sing_2453.htm#SEC2534
boundposDes	sing_2452.htm#SEC2533
bounds	sing_2187.htm#SEC2268
bounds2	sing_2125.htm#SEC2206
boxSet	sing_2189.htm#SEC2270
bracket	sing_361.htm#IDX198
bracket 	sing_418.htm#SEC458
bracket  	sing_460.htm#SEC500
braid	sing_2650.htm#IDX1027
branchTo	sing_160.htm#SEC200
break	sing_383.htm#SEC423
break point	sing_397.htm#SEC437
breakpoint	sing_384.htm#SEC424
brillnoether.lib	sing_1574.htm#SEC1655
brillnoether_lib	sing_1574.htm#SEC1655
brnoeth.lib	sing_2247.htm#SEC2328
brnoeth_lib	sing_2247.htm#SEC2328
browser, command line option	sing_19.htm#IDX44
browser, setting the	sing_361.htm#IDX194
browsers	sing_16.htm#IDX21
browsers, setting the	sing_361.htm#IDX193
bubblesort	sing_2324.htm#SEC2405
buildtree	sing_1115.htm#SEC1196
buildtree, Maple	sing_1116.htm#IDX555
buildtree, buildtreetoMaple, CGS	sing_1117.htm#IDX556
buildtreetoMaple	sing_1116.htm#SEC1197
busadj	sing_1223.htm#SEC1304
bvar	sing_2726.htm#SEC2807
c, module ordering	sing_980.htm#IDX466
cProj	sing_1616.htm#SEC1697
calculateI	sing_1731.htm#SEC1812
calculate_max_sum	sing_2393.htm#SEC2474
calculate_ordering	sing_2371.htm#SEC2452
cancelunit, option	sing_318.htm#IDX171
canonMap	sing_1317.htm#SEC1398
canoncial form	sing_1047.htm#IDX487
canoncial form 	sing_1048.htm#IDX489
canoncial form  	sing_1049.htm#IDX491
canonical	sing_1043.htm#IDX475
canonical form	sing_1064.htm#IDX533
canonical form 	sing_1065.htm#IDX535
canonical form  	sing_1066.htm#IDX538
canonical form   	sing_1067.htm#IDX540
canonical,	sing_1051.htm#IDX501
canonicalizeCone	sing_2474.htm#SEC2555
canonize	sing_2293.htm#SEC2374
cantodiffcgs	sing_1121.htm#SEC1202
cantoradd	sing_2407.htm#SEC2488
cantormult	sing_2410.htm#SEC2491
cantorred	sing_2408.htm#SEC2489
cardGroup	sing_1266.htm#SEC1347
case	sing_416.htm#SEC456
catNets	sing_2681.htm#SEC2762
cccMatrixToPositiveIntvec	sing_2621.htm#SEC2702
cdd	sing_1.htm#IDX10
cddlib	sing_1.htm#IDX11
center	sing_516.htm#IDX323
center 	sing_522.htm#SEC576
center  	sing_2637.htm#IDX1007
center   	sing_2638.htm#IDX1008
center    	sing_2639.htm#IDX1010
center     	sing_2640.htm#IDX1012
centerRed	sing_521.htm#SEC575
centerVS	sing_520.htm#SEC574
central	sing_2631.htm#IDX993
central 	sing_2638.htm#IDX1009
central  	sing_2640.htm#IDX1011
central   	sing_2654.htm#IDX1036
central.lib	sing_516.htm#SEC570
central1st	sing_2801.htm#SEC2882
central2nd	sing_2802.htm#SEC2883
central_lib	sing_516.htm#SEC570
centralize	sing_516.htm#IDX326
centralizeSet	sing_517.htm#SEC571
centralizer	sing_516.htm#IDX324
centralizer 	sing_523.htm#SEC577
centralizerRed	sing_519.htm#SEC573
centralizerVS	sing_518.htm#SEC572
cf_class	sing_210.htm#IDX132
cgs	sing_1018.htm#SEC1099
cgsdr	sing_1044.htm#SEC1125
chAll	sing_1586.htm#SEC1667
chAllInv	sing_1587.htm#SEC1668
chDual	sing_1592.htm#SEC1673
chHE	sing_1588.htm#SEC1669
chHom	sing_1601.htm#SEC1682
chNum	sing_1582.htm#SEC1663
chNumbers	sing_1583.htm#SEC1664
chNumbersProj	sing_1620.htm#SEC1701
chProd	sing_1594.htm#SEC1675
chProdE	sing_1595.htm#SEC1676
chProdL	sing_1596.htm#SEC1677
chProdLP	sing_1597.htm#SEC1678
chProdM	sing_1598.htm#SEC1679
chProdMP	sing_1599.htm#SEC1680
chProj	sing_1617.htm#SEC1698
chSum	sing_1590.htm#SEC1671
chSymm	sing_1604.htm#SEC1685
chSymm2L	sing_1605.htm#SEC1686
chSymm2LP	sing_1606.htm#SEC1687
chWedge	sing_1607.htm#SEC1688
chWedge2L	sing_1608.htm#SEC1689
chWedge2LP	sing_1609.htm#SEC1690
chaincrit	sing_2421.htm#SEC2502
chambers	sing_2669.htm#IDX1064
chambers 	sing_2670.htm#IDX1065
changeCoordinates	sing_2983.htm#SEC3064
changeDenominator	sing_1473.htm#SEC1554
changechar	sing_1141.htm#SEC1222
changeord	sing_1142.htm#SEC1223
changeordTo	sing_1165.htm#SEC1246
changes	sing_2993.htm#SEC3074
changevar	sing_1143.htm#SEC1224
char	sing_213.htm#SEC253
charInfo	sing_578.htm#SEC632
charVariety	sing_577.htm#SEC631
char_series	sing_214.htm#SEC254
characteristic exponents	sing_1844.htm#IDX781
characteristic exponents 	sing_1845.htm#IDX786
characteristic exponents  	sing_1846.htm#IDX789
characteristic exponents   	sing_1847.htm#IDX793
characteristic exponents    	sing_1962.htm#IDX905
characteristic polynomial	sing_2667.htm#IDX1062
characteristic variety	sing_561.htm#IDX351
characteristic variety 	sing_668.htm#IDX386
charexp2conductor	sing_1847.htm#SEC1928
charexp2generators	sing_1845.htm#SEC1926
charexp2inter	sing_1846.htm#SEC1927
charexp2multseq	sing_1844.htm#SEC1925
charexp2poly	sing_1848.htm#SEC1929
charpoly	sing_1224.htm#SEC1305
charstr	sing_215.htm#SEC255
chebyshev	sing_1277.htm#SEC1358
checkFactor	sing_554.htm#SEC608
checkRoot	sing_549.htm#SEC603
checkpfd	sing_2931.htm#SEC3012
checkpfdMat	sing_2939.htm#SEC3020
chern	sing_1581.htm#SEC1662
chern.lib	sing_1576.htm#SEC1657
chernCharPoly	sing_1623.htm#SEC1704
chernPoly	sing_1622.htm#SEC1703
chern_lib	sing_1576.htm#SEC1657
chineseRem	sing_2342.htm#SEC2423
chinrem	sing_216.htm#SEC256
chinrempoly	sing_1446.htm#SEC1527
chinrestp	sing_2401.htm#SEC2482
cimonom.lib	sing_2465.htm#SEC2546
cimonom_lib	sing_2465.htm#SEC2546
cisimplicial.lib	sing_1262.htm#SEC1343
cisimplicial_lib	sing_1262.htm#SEC1343
classSpaceCurve	sing_1894.htm#SEC1975
classification	sing_1855.htm#IDX798
classification 	sing_1882.htm#IDX801
classify	sing_1866.htm#SEC1947
classify.lib	sing_1864.htm#SEC1945
classify2.lib	sing_1882.htm#SEC1963
classify2_lib	sing_1882.htm#SEC1963
classifyCeq	sing_1896.htm#SEC1977
classifyMapGerms.lib	sing_1900.htm#SEC1981
classifyMapGerms_lib	sing_1900.htm#SEC1981
classifySimpleMaps	sing_1906.htm#SEC1987
classifySimpleMaps1	sing_1907.htm#SEC1988
classifyUnimodalMaps	sing_1908.htm#SEC1989
classify_aeq.lib	sing_1885.htm#SEC1966
classify_aeq_lib	sing_1885.htm#SEC1966
classify_lib	sing_1864.htm#SEC1945
classifyceq.lib	sing_1895.htm#SEC1976
classifyceq_lib	sing_1895.htm#SEC1976
classifyci.lib	sing_1897.htm#SEC1978
classifyci_lib	sing_1897.htm#SEC1978
classifyicis	sing_1898.htm#SEC1979
classpoly	sing_1621.htm#SEC1702
cleanTmp	sing_2609.htm#SEC2690
cleanunit	sing_1729.htm#SEC1810
cleardenom	sing_217.htm#SEC257
close	sing_218.htm#SEC258
closed_points	sing_2257.htm#SEC2338
closetex	sing_2224.htm#SEC2305
closureFrac	sing_1466.htm#SEC1547
coDim	sing_1902.htm#SEC1983
coDimMap	sing_1901.htm#SEC1982
coHom	sing_711.htm#SEC765
codim	sing_2006.htm#SEC2087
codimension	sing_2475.htm#SEC2556
coding theory	sing_972.htm#SEC1029
coef	sing_219.htm#SEC259
coefficient	sing_2630.htm#IDX989
coefficient 	sing_2631.htm#IDX992
coefficient  	sing_2632.htm#IDX996
coefficient field	sing_144.htm#SEC184
coefficient rings, ring of integers, zero divisors, p-adic numbers	sing_32.htm#SEC45
coefficients	sing_2755.htm#IDX1147
coefficients, long	sing_929.htm#SEC986
coeffmod	sing_2319.htm#SEC2400
coeffs	sing_220.htm#SEC260
cohomologyHashTable	sing_2974.htm#SEC3055
cohomologyMatrix	sing_2971.htm#SEC3052
cohomologyMatrixFromResolution	sing_2972.htm#SEC3053
coker	sing_1371.htm#SEC1452
colength of derivations	sing_1272.htm#IDX592
collectDiv	sing_1774.htm#SEC1855
colrank	sing_2291.htm#SEC2372
colred	sing_1207.htm#SEC1288
combinat.lib	sing_2672.htm#SEC2753
combinat_lib	sing_2672.htm#SEC2753
commRing	sing_692.htm#SEC746
comma	sing_417.htm#SEC457
command,custom	sing_187.htm#SEC227
command-line option, setting value of	sing_361.htm#IDX282
command-line option, value of	sing_361.htm#IDX280
command-line options, print all values of	sing_361.htm#IDX279
command-line options, short help	sing_19.htm#IDX38
commands (letterplace)	sing_804.htm#SEC858
commands (plural)	sing_458.htm#IDX303
comment	sing_36.htm#IDX108
compare	sing_2766.htm#IDX1167
compare 	sing_2767.htm#IDX1169
compare  	sing_2768.htm#IDX1173
compare   	sing_2769.htm#IDX1176
compare    	sing_2787.htm#IDX1214
compare     	sing_2788.htm#IDX1216
compareMatrix	sing_1379.htm#SEC1460
compareModules	sing_1374.htm#SEC1455
compareTasks	sing_1172.htm#SEC1253
compareVectors	sing_1399.htm#SEC1480
complement	sing_2734.htm#SEC2815
completeReduction	sing_2084.htm#SEC2165
complex	sing_28.htm#IDX75
complexClassify	sing_1883.htm#SEC1964
complexSingType	sing_1880.htm#SEC1961
complexType	sing_1884.htm#SEC1965
compose	sing_1278.htm#SEC1359
compregb.lib	sing_1017.htm#SEC1098
compregb_lib	sing_1017.htm#SEC1098
comprehensive Groebner system	sing_1017.htm#IDX472
compress	sing_1185.htm#SEC1266
computeAfaceOrbits	sing_2541.htm#SEC2622
computeConstant	sing_1294.htm#SEC1375
computeGromovWitten	sing_1297.htm#SEC1378
computeN	sing_1778.htm#SEC1859
computeV	sing_1777.htm#SEC1858
computemcm	sing_1736.htm#SEC1817
concat	sing_1186.htm#SEC1267
conductor	sing_1270.htm#IDX586
conductor 	sing_1474.htm#IDX658
conductor  	sing_1847.htm#IDX792
conductor, degree	sing_1962.htm#IDX908
cone	sing_189.htm#SEC229
cone 	sing_2643.htm#IDX1016
cone  	sing_2644.htm#IDX1018
coneLink	sing_2478.htm#SEC2559
coneViaInequalities	sing_2477.htm#SEC2558
coneViaPoints	sing_2476.htm#SEC2557
conic, parametrization, rational point.	sing_1713.htm#IDX738
conicWithTangents	sing_2585.htm#SEC2666
constructH	sing_1737.htm#SEC1818
constructblwup	sing_1738.htm#SEC1819
constructible set	sing_1064.htm#IDX531
constructible set 	sing_1066.htm#IDX536
constructible sets	sing_1065.htm#IDX534
constructible sets 	sing_1067.htm#IDX539
constructlastblwup	sing_1739.htm#SEC1820
constructor	sing_2660.htm#IDX1049
constructor 	sing_2661.htm#IDX1052
constructor  	sing_2754.htm#IDX1143
constructor   	sing_2777.htm#IDX1192
constructor    	sing_2778.htm#IDX1194
constructor     	sing_2779.htm#IDX1197
constructor      	sing_2780.htm#IDX1200
contact matrix	sing_1846.htm#IDX788
containedQ	sing_2216.htm#SEC2297
containment	sing_2773.htm#IDX1183
containsAsFace	sing_2479.htm#SEC2560
containsInCollection	sing_2512.htm#SEC2593
containsInSupport	sing_2480.htm#SEC2561
containsPositiveVector	sing_2481.htm#SEC2562
containsRelatively	sing_2482.htm#SEC2563
content	sing_1100.htm#SEC1181
contentSB, option	sing_318.htm#IDX172
continue	sing_385.htm#SEC425
continue 	sing_419.htm#SEC459
contraHom	sing_712.htm#SEC766
contract	sing_221.htm#SEC261
contraction	sing_2790.htm#IDX1222
contraction 	sing_2791.htm#IDX1224
contraction  	sing_2792.htm#IDX1226
contribution bundle, graph, multiple cover, rational curve,	sing_1806.htm#IDX760
contributionBundle	sing_1806.htm#SEC1887
contributors	sing_361.htm#IDX200
control	sing_2283.htm#SEC2364
control.lib	sing_2282.htm#SEC2363
controlDim	sing_2284.htm#SEC2365
controlExample	sing_2296.htm#SEC2377
control_Matrix	sing_1930.htm#SEC2011
control_lib	sing_2282.htm#SEC2363
convertLeftToRightFraction	sing_764.htm#SEC818
convertRightToLeftFraction	sing_763.htm#SEC817
convertdata	sing_1734.htm#SEC1815
convexHull	sing_2483.htm#SEC2564
convexIntersection	sing_2484.htm#SEC2565
convloc	sing_558.htm#SEC612
coordinate change	sing_2640.htm#IDX1013
coordinate change 	sing_2641.htm#IDX1014
coordinate change  	sing_2642.htm#IDX1015
coordinates	sing_2439.htm#IDX965
coords	sing_2439.htm#SEC2520
copyTask	sing_1171.htm#SEC1252
copyright	sing_1.htm#IDX1
corank	sing_1867.htm#SEC1948
cornerMonomials	sing_1504.htm#SEC1585
countPoints	sing_2364.htm#SEC2445
coverings	sing_1296.htm#IDX609
coverings 	sing_1297.htm#IDX613
cpu	sing_361.htm#IDX202
cpu 	sing_361.htm#IDX276
crcgs	sing_1120.htm#SEC1201
createBO	sing_1765.htm#SEC1846
createGradedRingHomomorphism	sing_2889.htm#SEC2970
createGroup	sing_2882.htm#SEC2963
createQuotientGroup	sing_2883.htm#SEC2964
createTask	sing_1169.htm#SEC1250
createTorsionFreeGroup	sing_2884.htm#SEC2965
create_ring	sing_222.htm#SEC262
createlist	sing_1747.htm#SEC1828
cring	sing_73.htm#SEC113
cring declarations	sing_74.htm#SEC114
cring expressions	sing_75.htm#SEC115
cring operations	sing_76.htm#SEC116
cring related functions	sing_77.htm#SEC117
crossprod	sing_223.htm#SEC263
crypto.lib	sing_2337.htm#SEC2418
crypto_lib	sing_2337.htm#SEC2418
crystallographicGroupC2MM	sing_848.htm#SEC902
crystallographicGroupCM	sing_847.htm#SEC901
crystallographicGroupP1	sing_841.htm#SEC895
crystallographicGroupP2	sing_845.htm#SEC899
crystallographicGroupP2GG	sing_846.htm#SEC900
crystallographicGroupP2MM	sing_844.htm#SEC898
crystallographicGroupP3	sing_852.htm#SEC906
crystallographicGroupP31M	sing_853.htm#SEC907
crystallographicGroupP3M1	sing_854.htm#SEC908
crystallographicGroupP4	sing_849.htm#SEC903
crystallographicGroupP4GM	sing_851.htm#SEC905
crystallographicGroupP4MM	sing_850.htm#SEC904
crystallographicGroupP6	sing_855.htm#SEC909
crystallographicGroupP6MM	sing_856.htm#SEC910
crystallographicGroupPG	sing_843.htm#SEC897
crystallographicGroupPM	sing_842.htm#SEC896
cup	sing_1318.htm#SEC1399
cupproduct	sing_1319.htm#SEC1400
curve singularities	sing_1837.htm#IDX775
curve singularities 	sing_1956.htm#IDX903
curve singularity	sing_1268.htm#IDX581
curveColengthDerivations	sing_1272.htm#SEC1353
curveConductorMult	sing_1270.htm#SEC1351
curveDeligneNumber	sing_1271.htm#SEC1352
curveDeltaInv	sing_1269.htm#SEC1350
curveInv.lib	sing_1268.htm#SEC1349
curveInv_lib	sing_1268.htm#SEC1349
curvepar.lib	sing_1909.htm#SEC1990
curvepar_lib	sing_1909.htm#SEC1990
custom assignment	sing_188.htm#SEC228
custom command	sing_187.htm#SEC227
custom type	sing_184.htm#SEC224
customstd.lib	sing_2676.htm#SEC2757
customstd_lib	sing_2676.htm#SEC2757
cycleLength	sing_2563.htm#SEC2644
cyclePoints	sing_2567.htm#SEC2648
cyclic	sing_1087.htm#SEC1168
cyclic code	sing_1004.htm#SEC1068
cyclotomic	sing_2049.htm#SEC2130
datetime	sing_224.htm#SEC264
dbprint	sing_225.htm#SEC265
deRham.lib	sing_1638.htm#SEC1719
deRhamCohom	sing_575.htm#SEC629
deRhamCohomIdeal	sing_576.htm#SEC630
deRhamCohomology	sing_1639.htm#SEC1720
deRham_lib	sing_1638.htm#SEC1719
debugLib, option	sing_318.htm#IDX177
debug_log	sing_1877.htm#SEC1958
debugger	sing_66.htm#SEC103
debugging library code	sing_66.htm#SEC103
dec1var	sing_1429.htm#SEC1510
decimal	sing_2338.htm#SEC2419
decode	sing_2274.htm#SEC2355
decodeCode	sing_2276.htm#SEC2357
decodeRandom	sing_2275.htm#SEC2356
decodeRandomFL	sing_2279.htm#SEC2360
decodeSV	sing_2256.htm#SEC2337
decodegb.lib	sing_2261.htm#SEC2342
decodegb_lib	sing_2261.htm#SEC2342
decoding, decoding problem	sing_1004.htm#SEC1069
decoef	sing_2304.htm#SEC2385
decomp.lib	sing_1273.htm#SEC1354
decomp_lib	sing_1273.htm#SEC1354
decompopts	sing_1274.htm#SEC1355
decompose	sing_1275.htm#SEC1356
decomposeVecField	sing_2989.htm#SEC3070
decomposition	sing_2755.htm#IDX1145
decomposition 	sing_2929.htm#IDX1245
decomposition of modules	sing_1422.htm#IDX641
decomposition, numerical	sing_1685.htm#IDX706
decone	sing_2643.htm#IDX1017
decone 	sing_2644.htm#IDX1019
def	sing_88.htm#SEC128
def declarations	sing_89.htm#SEC129
defRes, option	sing_318.htm#IDX178
default argument	sing_44.htm#SEC81
defineHomogeneous	sing_2922.htm#SEC3003
defined	sing_226.htm#SEC266
defl	sing_1696.htm#SEC1777
deform	sing_2007.htm#SEC2088
deform.lib	sing_1920.htm#SEC2001
deform_lib	sing_1920.htm#SEC2001
defring	sing_1144.htm#SEC1225
defringp	sing_1146.htm#SEC1227
defrings	sing_1145.htm#SEC1226
deg	sing_227.htm#SEC267
degBound	sing_399.htm#SEC439
degree	sing_228.htm#SEC268
degree 	sing_422.htm#IDX293
degree  	sing_2770.htm#IDX1178
degree   	sing_2772.htm#IDX1182
degree lexicographical ordering	sing_978.htm#IDX446
degree of a polynomial	sing_422.htm#IDX297
degree reverse lexicographical ordering	sing_978.htm#IDX444
degreeDivisor	sing_1649.htm#SEC1730
degreeFormalDivisor	sing_1657.htm#SEC1738
degreepart	sing_2133.htm#SEC2214
delete	sing_126.htm#SEC166
delete 	sing_229.htm#SEC269
delete  	sing_279.htm#SEC319
deleteGenerator	sing_590.htm#SEC644
deleteSublist	sing_1026.htm#SEC1107
deligne number	sing_1268.htm#IDX583
deligne number 	sing_1271.htm#IDX588
deligne number  	sing_1272.htm#IDX590
delta	sing_1968.htm#SEC2049
delta invariant	sing_1269.htm#IDX584
delta invariant 	sing_1468.htm#IDX656
delta invariant  	sing_1968.htm#IDX913
delta invariant.	sing_1460.htm#IDX649
delta invariant. 	sing_1461.htm#IDX652
delta invariant.  	sing_1462.htm#IDX655
deltaLoc	sing_1468.htm#SEC1549
denom_list	sing_361.htm#IDX204
denominator	sing_230.htm#SEC270
depth	sing_1320.htm#SEC1401
depthIdeal	sing_1439.htm#SEC1520
derivate	sing_2081.htm#SEC2162
derivation	sing_2657.htm#IDX1040
derivation 	sing_2775.htm#IDX1187
derivation  	sing_2776.htm#IDX1191
derivation   	sing_2777.htm#IDX1193
derivation    	sing_2778.htm#IDX1195
derivation     	sing_2779.htm#IDX1198
derivation      	sing_2780.htm#IDX1201
derivation       	sing_2789.htm#IDX1220
derivationAdd	sing_2783.htm#SEC2864
derivationCheckList	sing_2778.htm#SEC2859
derivationConstructor	sing_2780.htm#SEC2861
derivationContraction	sing_2791.htm#SEC2872
derivationContractionGen	sing_2790.htm#SEC2871
derivationEqu	sing_2787.htm#SEC2868
derivationEval	sing_2789.htm#SEC2870
derivationFromList	sing_2777.htm#SEC2858
derivationFromPoly	sing_2779.htm#SEC2860
derivationLie	sing_2792.htm#SEC2873
derivationMul	sing_2786.htm#SEC2867
derivationNeg	sing_2785.htm#SEC2866
derivationNeq	sing_2788.htm#SEC2869
derivationPrint	sing_2782.htm#SEC2863
derivationSub	sing_2784.htm#SEC2865
derivationToString	sing_2781.htm#SEC2862
desingularization	sing_2817.htm#IDX1229
desingularization 	sing_2818.htm#SEC2899
det	sing_231.htm#SEC271
det_B	sing_1226.htm#SEC1307
detadj	sing_1984.htm#SEC2065
determinacy	sing_2003.htm#SEC2084
determinecenter	sing_1719.htm#SEC1800
detropicalise	sing_2603.htm#SEC2684
develop	sing_1958.htm#SEC2039
diag	sing_1187.htm#SEC1268
diagInvariants	sing_1483.htm#SEC1564
diag_test	sing_1222.htm#SEC1303
diagonalizeMatrixSimul	sing_2990.htm#SEC3071
diagonalizeVecField	sing_2987.htm#SEC3068
diagonalizeVecFieldLin	sing_2985.htm#SEC3066
diff	sing_232.htm#SEC272
diffAlgebra	sing_2748.htm#SEC2829
diffAlgebraChangeOrd	sing_2752.htm#SEC2833
diffAlgebraGens	sing_2750.htm#SEC2831
diffAlgebraListGen	sing_2753.htm#SEC2834
diffAlgebraStructure	sing_2749.htm#SEC2830
diffAlgebraUnivDerIdeal	sing_2751.htm#SEC2832
diffRat	sing_691.htm#SEC745
difference	sing_2762.htm#IDX1161
difference 	sing_2784.htm#IDX1209
difference  	sing_2785.htm#IDX1211
differential	sing_2754.htm#IDX1144
differential 	sing_2776.htm#IDX1189
differential algebra	sing_2747.htm#IDX1131
differential algebra 	sing_2748.htm#IDX1132
differential algebra  	sing_2749.htm#IDX1135
differential algebra   	sing_2750.htm#IDX1136
differential algebra    	sing_2751.htm#IDX1138
differential forms	sing_2747.htm#IDX1129
differential forms 	sing_2748.htm#IDX1133
differentials	sing_2747.htm#IDX1130
differentials 	sing_2748.htm#IDX1134
difform.lib	sing_2747.htm#SEC2828
difformAdd	sing_2761.htm#SEC2842
difformCoef	sing_2755.htm#SEC2836
difformDeg	sing_2770.htm#SEC2851
difformDiff	sing_2776.htm#SEC2857
difformDiv	sing_2765.htm#SEC2846
difformEqu	sing_2766.htm#SEC2847
difformFromPoly	sing_2754.htm#SEC2835
difformGenToString	sing_2756.htm#SEC2837
difformHomogDecomp	sing_2757.htm#SEC2838
difformIsBigger	sing_2768.htm#SEC2849
difformIsGen	sing_2760.htm#SEC2841
difformIsHomog	sing_2771.htm#SEC2852
difformIsHomogDeg	sing_2772.htm#SEC2853
difformIsSmaller	sing_2769.htm#SEC2850
difformListCont	sing_2773.htm#SEC2854
difformListSort	sing_2774.htm#SEC2855
difformMul	sing_2764.htm#SEC2845
difformNeg	sing_2763.htm#SEC2844
difformNeq	sing_2767.htm#SEC2848
difformPrint	sing_2759.htm#SEC2840
difformSub	sing_2762.htm#SEC2843
difformToString	sing_2758.htm#SEC2839
difformUnivDer	sing_2775.htm#SEC2856
difform_lib	sing_2747.htm#SEC2828
difpoly2tex	sing_2305.htm#SEC2386
dim	sing_233.htm#SEC273
dim (letterplace)	sing_805.htm#SEC859
dim (plural)	sing_461.htm#SEC501
dimGradedPart	sing_1826.htm#SEC1907
dimH	sing_1825.htm#SEC1906
dimMon	sing_1419.htm#SEC1500
dimStack	sing_1804.htm#SEC1885
dim_slocus	sing_2008.htm#SEC2089
dimension	sing_2485.htm#SEC2566
dimension, moduli space of stable maps, rational curves	sing_1804.htm#IDX758
dimensionOfLocalization	sing_1673.htm#SEC1754
direct_boolean_poly	sing_2716.htm#SEC2797
direct_from_boolean_poly	sing_2722.htm#SEC2803
disc	sing_2325.htm#SEC2406
discr	sing_2030.htm#SEC2111
discrepancy	sing_1772.htm#SEC1853
discrim	sing_1059.htm#SEC1140
discussion of parametric ideal	sing_1043.htm#IDX476
disjoint	sing_1044.htm#IDX478
disp_zdd	sing_2729.htm#SEC2810
displayCohom	sing_1827.htm#SEC1908
displayHNE	sing_1961.htm#SEC2042
displayInvariants	sing_1963.htm#SEC2044
displayMultsequence	sing_1965.htm#SEC2046
displayPuiseuxExpansion	sing_2579.htm#SEC2660
displayTropicalLifting	sing_2577.htm#SEC2658
displaypfd	sing_2933.htm#SEC3014
displaypfd_long	sing_2934.htm#SEC3015
distributed computing	sing_1080.htm#IDX548
distributed computing 	sing_1135.htm#IDX562
distributed computing  	sing_1168.htm#IDX572
div	sing_81.htm#SEC121
div 	sing_98.htm#SEC138
div  	sing_155.htm#SEC195
div   	sing_422.htm#IDX290
divideUnits	sing_2301.htm#SEC2382
dividelist	sing_1746.htm#SEC1827
division	sing_234.htm#SEC274
division 	sing_1045.htm#IDX481
division  	sing_1046.htm#IDX483
division   	sing_2765.htm#IDX1166
division (plural)	sing_462.htm#SEC502
division, pdivi2, reduce	sing_1114.htm#IDX553
division, reduce	sing_1111.htm#IDX550
divisor	sing_2404.htm#SEC2485
divisorplus	sing_1643.htm#SEC1724
divisors	sing_1642.htm#IDX674
divisors 	sing_1643.htm#IDX675
divisors  	sing_1644.htm#IDX676
divisors   	sing_1645.htm#IDX677
divisors    	sing_1646.htm#IDX678
divisors     	sing_1647.htm#IDX679
divisors      	sing_1648.htm#IDX680
divisors       	sing_1649.htm#IDX681
divisors        	sing_1650.htm#IDX682
divisors         	sing_1651.htm#IDX683
divisors          	sing_1652.htm#IDX684
divisors           	sing_1653.htm#IDX685
divisors            	sing_1654.htm#IDX686
divisors             	sing_1655.htm#IDX687
divisors              	sing_1656.htm#IDX688
divisors               	sing_1657.htm#IDX689
divisors, polyhedra	sing_1658.htm#IDX690
divisors.lib	sing_1641.htm#SEC1722
divisors_lib	sing_1641.htm#SEC1722
dmod.lib	sing_537.htm#SEC591
dmodAction	sing_686.htm#SEC740
dmodActionRat	sing_687.htm#SEC741
dmodGeneralAssumptionCheck	sing_679.htm#SEC733
dmod_lib	sing_537.htm#SEC591
dmodapp.lib	sing_561.htm#SEC615
dmodapp_lib	sing_561.htm#SEC615
dmodideal.lib	sing_593.htm#SEC647
dmodideal_lib	sing_593.htm#SEC647
dmodloc.lib	sing_668.htm#IDX379
dmodloc_lib	sing_668.htm#IDX380
dmodoublext	sing_713.htm#SEC767
dmodvar.lib	sing_601.htm#SEC655
dmodvar_lib	sing_601.htm#SEC655
double	sing_2409.htm#SEC2490
doubleExt	sing_786.htm#SEC840
downloading	sing_3001.htm#SEC3099
dp, global ordering	sing_978.htm#IDX445
drawNewtonSubdivision	sing_2582.htm#SEC2663
drawTropicalCurve	sing_2581.htm#SEC2662
ds, local ordering	sing_979.htm#IDX455
dsum	sing_1188.htm#SEC1269
dualCone	sing_2486.htm#SEC2567
dualConic	sing_2605.htm#SEC2686
dualPart	sing_1629.htm#SEC1710
dualPartition	sing_1817.htm#SEC1898
dualPolytope	sing_2525.htm#SEC2606
dualSheaf	sing_1795.htm#SEC1876
dual_code	sing_2258.htm#SEC2339
dump	sing_235.htm#SEC275
dyckGroup1	sing_857.htm#SEC911
dyckGroup2	sing_858.htm#SEC912
dyckGroup3	sing_859.htm#SEC913
dynamic geometry	sing_1052.htm#IDX505
dynamic geometry 	sing_1053.htm#IDX508
ecart	sing_2412.htm#SEC2493
echo	sing_400.htm#SEC440
eexgcdN	sing_2339.htm#SEC2420
effective	sing_1651.htm#SEC1732
egcdMain	sing_2209.htm#SEC2290
ehrhartRing	sing_1479.htm#SEC1560
eigenvals	sing_1234.htm#SEC1315
eigenvalue	sing_331.htm#SEC371
eigenvalue 	sing_1234.htm#IDX578
eigenvalues	sing_1567.htm#SEC1648
elemSymmId	sing_1088.htm#SEC1169
elim	sing_1283.htm#SEC1364
elim.lib	sing_1280.htm#SEC1361
elim1	sing_1284.htm#SEC1365
elim2	sing_1285.htm#SEC1366
elimRing	sing_1282.htm#SEC1363
elimWeight	sing_728.htm#SEC782
elim_lib	sing_1280.htm#SEC1361
eliminate	sing_236.htm#SEC276
eliminate (plural)	sing_463.htm#SEC503
eliminateNC	sing_723.htm#SEC777
elimination	sing_722.htm#IDX394
elimlinearpart	sing_2134.htm#SEC2215
elimpart	sing_2135.htm#SEC2216
elimpartanyr	sing_2136.htm#SEC2217
elimrep	sing_1727.htm#SEC1808
elliptic curve	sing_1293.htm#IDX605
elliptic curves	sing_1290.htm#IDX599
elliptic curves 	sing_1296.htm#IDX608
elliptic curves  	sing_1297.htm#IDX612
ellipticAdd	sing_2360.htm#SEC2441
ellipticAllPoints	sing_2365.htm#SEC2446
ellipticMult	sing_2361.htm#SEC2442
ellipticNF	sing_2570.htm#SEC2651
ellipticRandomCurve	sing_2362.htm#SEC2443
ellipticRandomPoint	sing_2363.htm#SEC2444
ellipticcovers.lib	sing_1290.htm#SEC1371
ellipticcovers_lib	sing_1290.htm#SEC1371
else	sing_390.htm#SEC430
embedMat	sing_754.htm#SEC808
emptyFan	sing_2513.htm#SEC2594
encode	sing_2266.htm#SEC2347
endomorphism filtration	sing_1942.htm#IDX879
endvfilt	sing_1942.htm#SEC2023
ensureLeftNcfrac	sing_701.htm#SEC755
ensureRightNcfrac	sing_702.htm#SEC756
envelop	sing_1054.htm#SEC1135
envelop 	sing_1054.htm#IDX511
envelop  	sing_1055.htm#IDX514
envelop   	sing_1057.htm#IDX519
envelop    	sing_1058.htm#IDX523
envelope	sing_464.htm#SEC504
enveloping algebra	sing_361.htm#IDX208
enveloping algebra 	sing_495.htm#IDX307
environment variable, DISPLAY	sing_16.htm#IDX29
environment variables	sing_3002.htm#SEC3100
equal	sing_2766.htm#IDX1168
equal 	sing_2767.htm#IDX1170
equal  	sing_2787.htm#IDX1215
equal   	sing_2788.htm#IDX1217
equalJinI	sing_1854.htm#SEC1935
equalMultiDeg	sing_2915.htm#SEC2996
equations	sing_2487.htm#SEC2568
equiRadical	sing_1520.htm#SEC1601
equidim	sing_1522.htm#SEC1603
equidimMax	sing_1523.htm#SEC1604
equidimMaxEHV	sing_1524.htm#SEC1605
equidimZ	sing_1535.htm#SEC1616
equising.lib	sing_1925.htm#SEC2006
equising_lib	sing_1925.htm#SEC2006
equisingular Tjurina number	sing_1837.htm#IDX780
equisingularity ideal	sing_1927.htm#IDX806
equisingularity stratum	sing_1928.htm#IDX807
error recovery	sing_15.htm#SEC21
errorInsert	sing_2269.htm#SEC2350
errorRand	sing_2270.htm#SEC2351
errormap	sing_2807.htm#SEC2888
esIdeal	sing_1927.htm#SEC2008
esStratum	sing_1928.htm#SEC2009
essential	sing_2647.htm#IDX1022
essential 	sing_2648.htm#IDX1023
eta	sing_2565.htm#SEC2646
euler	sing_2318.htm#SEC2399
eulerChProj	sing_1619.htm#SEC1700
eulerPolynomialTable	sing_2973.htm#SEC3054
eval	sing_237.htm#SEC277
evalJacobianAtBox	sing_2195.htm#SEC2276
evalPolyAtBox	sing_2194.htm#SEC2275
evalPolyAtBox2	sing_2130.htm#SEC2211
evaluateFormalDivisor	sing_1653.htm#SEC1734
evaluateProduct	sing_2551.htm#SEC2632
evaluate_reynolds	sing_2054.htm#SEC2135
evaluatepfd	sing_2932.htm#SEC3013
evaluation	sing_2789.htm#IDX1219
evalutateIntegral	sing_1295.htm#SEC1376
exactness recovery	sing_2168.htm#IDX938
example	sing_239.htm#SEC279
example 	sing_2649.htm#IDX1024
example  	sing_2650.htm#IDX1026
example   	sing_2651.htm#IDX1028
example    	sing_2652.htm#IDX1030
example     	sing_2653.htm#IDX1032
example      	sing_2654.htm#IDX1034
example       	sing_2655.htm#IDX1037
exclusionTest	sing_2131.htm#SEC2212
execute	sing_240.htm#SEC280
exit	sing_394.htm#SEC434
exp2pt	sing_2306.htm#SEC2387
expo	sing_2330.htm#SEC2411
exponents	sing_2659.htm#IDX1045
export	sing_387.htm#SEC427
exportNuminvs	sing_1487.htm#SEC1568
exportto	sing_388.htm#SEC428
expp	sing_1815.htm#SEC1896
expression list	sing_72.htm#IDX128
expression list 	sing_426.htm#IDX300
ext-module	sing_778.htm#IDX400
extcurve	sing_2252.htm#SEC2333
extdevelop	sing_1959.htm#SEC2040
extendGC	sing_1051.htm#SEC1132
extendWeyl	sing_680.htm#SEC734
extendedTensor	sing_729.htm#SEC783
extendpoly	sing_1050.htm#SEC1131
extendring	sing_1147.htm#SEC1228
extension of rings	sing_1540.htm#IDX667
exterior basis	sing_1213.htm#IDX575
exterior power	sing_1215.htm#IDX577
exteriorBasis	sing_1213.htm#SEC1294
exteriorPower	sing_1215.htm#SEC1296
extgcd	sing_241.htm#SEC281
extractS	sing_600.htm#SEC654
fPiece	sing_2957.htm#SEC3038
fVector	sing_2516.htm#SEC2597
facFirstShift	sing_655.htm#SEC709
facFirstWeyl	sing_651.htm#SEC705
facGBIdeal	sing_1505.htm#SEC1586
facShift	sing_654.htm#SEC708
facSubWeyl	sing_653.htm#SEC707
facWeyl	sing_650.htm#SEC704
faceContaining	sing_2488.htm#SEC2569
facets	sing_2489.htm#SEC2570
facstd	sing_242.htm#SEC282
factmodd	sing_243.htm#SEC283
factor	sing_325.htm#SEC365
factor 	sing_1112.htm#IDX551
factorH	sing_1041.htm#SEC1122
factorLenstraECM	sing_2369.htm#SEC2450
factorMain	sing_2210.htm#SEC2291
factorgroup	sing_2905.htm#SEC2986
factorial	sing_1027.htm#SEC1108
factorization	sing_326.htm#SEC366
factorization 	sing_1243.htm#IDX579
factorize	sing_244.htm#SEC284
factorize 	sing_325.htm#SEC365
factory	sing_1.htm#IDX2
facvar	sing_1112.htm#SEC1193
fan	sing_190.htm#SEC230
fan 	sing_2560.htm#IDX971
fanViaCones	sing_2514.htm#SEC2595
farey	sing_245.htm#SEC285
fareypoly	sing_1302.htm#SEC1383
fastExpt	sing_2314.htm#SEC2395
fastHC, option	sing_318.htm#IDX153
fastelim	sing_2137.htm#SEC2218
fetch	sing_246.htm#SEC286
fetch (letterplace)	sing_806.htm#SEC860
fetch (plural)	sing_465.htm#SEC505
fetchall	sing_1148.htm#SEC1229
ffmodStd	sing_1308.htm#SEC1389
ffmodstd.lib	sing_1301.htm#SEC1382
ffmodstd_lib	sing_1301.htm#SEC1382
ffsolve	sing_2117.htm#SEC2198
ffsolve.lib	sing_2116.htm#SEC2197
ffsolve_lib	sing_2116.htm#SEC2197
fglm	sing_247.htm#SEC287
fglm 	sing_358.htm#IDX188
fglm_solve	sing_2153.htm#SEC2234
fglmquot	sing_248.htm#SEC288
fibonacci	sing_1028.htm#SEC1109
fibonacciGroup	sing_860.htm#SEC914
field	sing_144.htm#SEC184
file, .singularrc	sing_20.htm#IDX71
filecmd	sing_249.htm#SEC289
filtration	sing_778.htm#IDX401
finalCharts	sing_1751.htm#SEC1832
finalcases	sing_1117.htm#SEC1198
find	sing_250.htm#SEC290
findAuto	sing_609.htm#SEC663
findInvo	sing_607.htm#SEC661
findInvoDiag	sing_608.htm#SEC662
findOrientedBoundary	sing_2566.htm#SEC2647
findTorsion	sing_2295.htm#SEC2376
findZeroPoly	sing_2945.htm#SEC3026
find_first_primitive_root	sing_2373.htm#SEC2454
find_index	sing_2377.htm#SEC2458
findifs.lib	sing_2302.htm#SEC2383
findifs_example	sing_2303.htm#SEC2384
findifs_lib	sing_2302.htm#SEC2383
findimAlgebra	sing_738.htm#SEC792
finduni	sing_251.htm#SEC291
findvars	sing_2138.htm#SEC2219
finite field	sing_144.htm#SEC184
finite field 	sing_2116.htm#IDX935
finiteDiagInvariants	sing_1482.htm#SEC1563
finitediff.lib	sing_2793.htm#IDX1227
finitediff_lib	sing_2793.htm#IDX1228
finitely presented algebra	sing_827.htm#IDX408
finitely presented algebra 	sing_834.htm#IDX414
finitely presented algebra  	sing_863.htm#IDX417
finitely presented algebra   	sing_872.htm#IDX429
finitely presented algebra    	sing_886.htm#IDX430
finitely presented algebra, standard finitely presented algebra	sing_821.htm#IDX407
finitely presented group	sing_834.htm#IDX415
finitenessTest	sing_1257.htm#SEC1338
finiterep	sing_2107.htm#SEC2188
finvar.lib	sing_2042.htm#SEC2123
finvar_lib	sing_2042.htm#SEC2123
first index is 1	sing_421.htm#SEC461
first order deformation	sing_2954.htm#IDX1259
first order deformation 	sing_2957.htm#IDX1262
firstQuadrantComplex	sing_2979.htm#SEC3060
firstoct	sing_2202.htm#SEC2283
fitting	sing_1323.htm#SEC1404
fixed points, moduli space of stable maps, graph	sing_1805.htm#IDX759
fixedPoints	sing_1805.htm#SEC1886
fl2poly	sing_588.htm#SEC642
flatten	sing_1189.htm#SEC1270
flatteningStrat	sing_1324.htm#SEC1405
flintQ	sing_252.htm#SEC292
floating point	sing_1157.htm#IDX565
for	sing_389.htm#SEC429
formal linear representations	sing_889.htm#IDX438
formaldivisorplus	sing_1654.htm#SEC1735
forward	sing_2799.htm#SEC2880
fourier	sing_583.htm#SEC637
fouriersystem	sing_2810.htm#SEC2891
fpadim.lib	sing_827.htm#SEC881
fpadim_lib	sing_827.htm#SEC881
fpalgebras.lib	sing_834.htm#SEC888
fpalgebras_lib	sing_834.htm#SEC888
fpaprops.lib	sing_863.htm#SEC917
fpaprops_lib	sing_863.htm#SEC917
fprintf	sing_254.htm#SEC294
fracStatus	sing_759.htm#SEC813
framed sheaves	sing_1659.htm#IDX697
frandwalk	sing_2952.htm#SEC3033
free	sing_2658.htm#IDX1042
free 	sing_2659.htm#IDX1044
free associative algebra	sing_834.htm#IDX413
free associative algebra 	sing_872.htm#IDX425
free associative algebra, tensor algebra	sing_821.htm#SEC875
free noncommutative Groebner basis	sing_872.htm#IDX427
freeAlgebra (letterplace)	sing_807.htm#SEC861
freeModule	sing_1351.htm#SEC1432
freeModule2Module	sing_1380.htm#SEC1461
freegb.lib	sing_872.htm#SEC926
freegb_lib	sing_872.htm#SEC926
freemodule	sing_255.htm#SEC295
freerank	sing_1090.htm#SEC1171
fres	sing_256.htm#SEC296
from_boolean_constant	sing_2720.htm#SEC2801
from_boolean_ideal	sing_2724.htm#SEC2805
from_boolean_poly	sing_2721.htm#SEC2802
from_boolean_set	sing_2725.htm#SEC2806
frwalk	sing_257.htm#SEC297
full representation	sing_1050.htm#IDX497
full representation 	sing_1051.htm#IDX502
fullDimImages	sing_2532.htm#SEC2613
fullFan	sing_2515.htm#SEC2596
fullSerreRelations	sing_837.htm#SEC891
fullSpace	sing_2470.htm#SEC2551
furtherInvar	sing_2086.htm#SEC2167
further_hn_proc	sing_1976.htm#SEC2057
fwalk	sing_1310.htm#SEC1391
galois field	sing_144.htm#SEC184
gaussColWithoutPerm	sing_2174.htm#SEC2255
gaussRowWithoutPerm	sing_2173.htm#SEC2254
gauss_col	sing_1198.htm#SEC1279
gauss_nf	sing_1229.htm#SEC1310
gauss_row	sing_1199.htm#SEC1280
gaussred	sing_1227.htm#SEC1308
gaussred_pivot	sing_1228.htm#SEC1309
gcd	sing_258.htm#SEC298
gcdMon	sing_1408.htm#SEC1489
gcddivisor	sing_2405.htm#SEC2486
gen	sing_259.htm#SEC299
genMDSMat	sing_2272.htm#SEC2353
genSymId	sing_1564.htm#SEC1645
general error-locator polynomial	sing_1005.htm#SEC1075
general neron.	sing_2817.htm#IDX1230
general weighted lexicographical ordering	sing_979.htm#IDX461
general weighted reverse lexicographical ordering	sing_979.htm#IDX458
general.lib	sing_1020.htm#SEC1101
generalOrder	sing_2430.htm#SEC2511
general_lib	sing_1020.htm#SEC1101
generateG	sing_2368.htm#SEC2449
generator	sing_2750.htm#IDX1137
generator 	sing_2760.htm#IDX1157
generator  	sing_2790.htm#IDX1223
generators	sing_1845.htm#IDX784
generators 	sing_2753.htm#IDX1141
generators  	sing_2755.htm#IDX1146
generators   	sing_2756.htm#IDX1150
generatorsOfLinealitySpace	sing_2490.htm#SEC2571
generatorsOfSpan	sing_2491.htm#SEC2572
generic representation	sing_1050.htm#IDX496
genericid	sing_1123.htm#SEC1204
genericity	sing_2292.htm#SEC2373
genericmat	sing_1190.htm#SEC1271
genoutput	sing_1740.htm#SEC1821
genus	sing_1464.htm#SEC1545
geometrical locus	sing_1052.htm#IDX503
geometrical locus 	sing_1053.htm#IDX506
geometrical locus  	sing_1054.htm#IDX509
geometrical locus   	sing_1055.htm#IDX512
geometrical locus    	sing_1056.htm#IDX515
geometrical locus     	sing_1057.htm#IDX517
geometrical locus      	sing_1058.htm#IDX521
getArguments	sing_1180.htm#SEC1261
getCommand	sing_1179.htm#SEC1260
getCone	sing_2517.htm#SEC2598
getGradingGroup	sing_2880.htm#SEC2961
getLattice	sing_2881.htm#SEC2962
getLinearForms	sing_2492.htm#SEC2573
getMaxPoints	sing_2869.htm#SEC2950
getModuleGrading	sing_2891.htm#SEC2972
getMultiplicity	sing_2493.htm#SEC2574
getOneVar	sing_1472.htm#SEC1553
getRelations	sing_2171.htm#SEC2252
getRelationsRadical	sing_2172.htm#SEC2253
getResult	sing_1181.htm#SEC1262
getSmallest	sing_1471.htm#SEC1552
getState	sing_1182.htm#SEC1263
getStringpfd	sing_2935.htm#SEC3016
getStringpfd_indexed	sing_2936.htm#SEC3017
getVariableWeights	sing_2879.htm#SEC2960
getWitnessSet	sing_2175.htm#SEC2256
getcores	sing_1138.htm#SEC1219
getdump	sing_260.htm#SEC300
getenv	sing_361.htm#IDX210
gfan.lib	sing_2469.htm#SEC2550
gfan_lib	sing_2469.htm#SEC2550
gfanlib	sing_1.htm#IDX9
gitCone	sing_2559.htm#SEC2640
gitfan.lib	sing_2529.htm#SEC2610
gitfan_lib	sing_2529.htm#SEC2610
gkdim.lib	sing_614.htm#SEC668
gkdim_lib	sing_614.htm#SEC668
global	sing_210.htm#IDX133
global Bernstein-Sato ideal	sing_593.htm#IDX356
global Bernstein-Sato polynomial	sing_502.htm#IDX314
global Bernstein-Sato polynomial 	sing_537.htm#IDX332
global Bernstein-Sato polynomial for variety	sing_601.htm#IDX364
global homological dimension	sing_863.htm#IDX422
globalSections	sing_1648.htm#SEC1729
gmscoeffs	sing_1934.htm#SEC2015
gmsnf	sing_1933.htm#SEC2014
gmspoly.lib	sing_1953.htm#SEC2034
gmspoly_lib	sing_1953.htm#SEC2034
gmsring	sing_1932.htm#SEC2013
gmssing.lib	sing_1931.htm#SEC2012
gmssing_lib	sing_1931.htm#SEC2012
goettsche.lib	sing_1659.htm#SEC1740
goettsche_lib	sing_1659.htm#SEC1740
good basis	sing_1931.htm#IDX818
good basis 	sing_1941.htm#IDX873
good basis  	sing_1953.htm#IDX889
good basis   	sing_1955.htm#IDX900
goodBasis	sing_1955.htm#SEC2036
graal.lib	sing_1671.htm#SEC1752
graalMixed	sing_1672.htm#SEC1753
graal_lib	sing_1671.htm#SEC1752
gradeNumber	sing_782.htm#SEC836
graded	sing_2753.htm#IDX1142
graded Hilbert series	sing_886.htm#IDX432
graded Weyl algebra	sing_502.htm#IDX317
graded algebra	sing_2740.htm#IDX1125
graded module, graded piece	sing_1826.htm#IDX770
graded modules, graded homomorphisms, syzygies	sing_2819.htm#IDX1231
graded modules, handling of	sing_944.htm#SEC1001
graded piece,  second order piece	sing_2958.htm#IDX1263
graded-module, graded-resolution, homogenoues-matrix, R-module-homomorphism	sing_1348.htm#IDX638
gradedModules.lib	sing_2819.htm#SEC2900
gradedModules_lib	sing_2819.htm#SEC2900
gradiator	sing_2924.htm#SEC3005
graph	sing_1291.htm#IDX603
graph 	sing_1292.htm#IDX604
graph  	sing_1800.htm#IDX754
graph   	sing_1801.htm#IDX755
graphics.lib	sing_2219.htm#SEC2300
graphics_lib	sing_2219.htm#SEC2300
graphviz	sing_1.htm#IDX13
graver4ti2	sing_1562.htm#SEC1643
grconcat	sing_2842.htm#SEC2923
grdeg	sing_2822.htm#SEC2903
grgens	sing_2831.htm#SEC2912
grgroebner	sing_2841.htm#SEC2922
grlift	sing_2839.htm#SEC2920
grlifting	sing_2846.htm#SEC2927
grlifting2	sing_2847.htm#SEC2928
grlifting3	sing_2849.htm#SEC2930
grneg	sing_2852.htm#SEC2933
grobcov	sing_1043.htm#SEC1124
grobcov.lib	sing_1042.htm#SEC1123
grobcov_lib	sing_1042.htm#SEC1123
grobj	sing_2820.htm#SEC2901
groebner	sing_261.htm#SEC301
groebner 	sing_936.htm#SEC993
groebner basis computations	sing_261.htm#IDX147
groebnerComplex	sing_2616.htm#SEC2697
groebnerCone	sing_2610.htm#SEC2691
groebnerFan	sing_2615.htm#SEC2696
gromovWitten	sing_1296.htm#SEC1377
grorder	sing_2833.htm#SEC2914
ground field	sing_144.htm#SEC184
groupActionOnHashes	sing_2547.htm#SEC2628
groupActionOnQImage	sing_2546.htm#SEC2627
group_reynolds	sing_2050.htm#SEC2131
growth of algebra	sing_863.htm#IDX420
grpower	sing_2829.htm#SEC2910
grpres	sing_2832.htm#SEC2913
grprod	sing_2840.htm#SEC2921
grrange	sing_2851.htm#SEC2932
grres	sing_2838.htm#SEC2919
grrndmap	sing_2844.htm#SEC2925
grrndmap2	sing_2845.htm#SEC2926
grrndmat	sing_2843.htm#SEC2924
grshift	sing_2824.htm#SEC2905
grsum	sing_2828.htm#SEC2909
grsyz	sing_2837.htm#SEC2918
grtest	sing_2821.htm#SEC2902
grtranspose	sing_2830.htm#SEC2911
grtranspose1	sing_2834.htm#SEC2915
grtwist	sing_2826.htm#SEC2907
grtwists	sing_2827.htm#SEC2908
grview	sing_2823.htm#SEC2904
grwalk.lib	sing_1309.htm#SEC1390
grwalk_lib	sing_1309.htm#SEC1390
grzero	sing_2825.htm#SEC2906
gwalk	sing_1315.htm#SEC1396
h_increasing_knapsack	sing_2391.htm#SEC2472
hardware platform	sing_361.htm#IDX269
hasAlgExtensionCoefficient	sing_1161.htm#SEC1242
hasCommutativeVars	sing_1158.htm#SEC1239
hasGlobalOrdering	sing_1159.htm#SEC1240
hasLeftDenom	sing_695.htm#SEC749
hasMixedOrdering	sing_1160.htm#SEC1241
hasNumericCoeffs	sing_1157.htm#SEC1238
hasRightDenom	sing_696.htm#SEC750
hasTransExtensionCoefficient	sing_1162.htm#SEC1243
hashToCone	sing_2557.htm#SEC2638
hashesToFan	sing_2558.htm#SEC2639
headStand	sing_1211.htm#SEC1292
heightZ	sing_1534.htm#SEC1615
help	sing_262.htm#SEC302
help browsers	sing_16.htm#IDX22
help browsers, dummy	sing_16.htm#IDX25
help browsers, dummy 	sing_16.htm#IDX27
help browsers, emacs	sing_16.htm#IDX26
help browsers, html	sing_16.htm#IDX23
help browsers, setting command to use	sing_16.htm#IDX30
help browsers, setting the	sing_361.htm#IDX195
help, accessing over the net	sing_19.htm#IDX42
help, online help system	sing_16.htm#SEC22
hermiteNormalForm	sing_2925.htm#SEC3006
hess.lib	sing_1678.htm#SEC1759
hess_lib	sing_1678.htm#SEC1759
hessenberg	sing_361.htm#IDX216
hessenberg 	sing_1233.htm#SEC1314
highcorner	sing_263.htm#SEC303
hilb	sing_264.htm#SEC304
hilbPoly	sing_1106.htm#SEC1187
hilbert4ti2	sing_1561.htm#SEC1642
hilbertSeries	sing_2927.htm#SEC3008
hilbvec	sing_2139.htm#SEC2220
hnexpansion	sing_1957.htm#SEC2038
hnoether.lib	sing_1956.htm#SEC2037
hnoether_lib	sing_1956.htm#SEC2037
hodge.lib	sing_2854.htm#SEC2935
hodgeIdeals	sing_2856.htm#SEC2937
hodge_lib	sing_2854.htm#SEC2935
holonomic rank	sing_668.htm#IDX382
holonomicRank	sing_672.htm#SEC726
hom	sing_1392.htm#SEC1473
hom_kernel	sing_1331.htm#SEC1412
homog	sing_265.htm#SEC305
homog 	sing_2771.htm#IDX1180
homog_part	sing_1812.htm#SEC1893
homog_parts	sing_1813.htm#SEC1894
homogeneitySpace	sing_2612.htm#SEC2693
homogeneous	sing_265.htm#SEC305
homogeneous 	sing_2757.htm#IDX1151
homogeneous  	sing_2771.htm#IDX1179
homogeneous   	sing_2772.htm#IDX1181
homogeneous decomposition	sing_2757.htm#IDX1152
homogfacFirstQWeyl	sing_658.htm#SEC712
homogfacFirstQWeyl_all	sing_660.htm#SEC714
homogfacNthQWeyl	sing_657.htm#SEC711
homogfacNthQWeyl_all	sing_659.htm#SEC713
homogfacNthWeyl	sing_656.htm#SEC710
homolog.lib	sing_1316.htm#SEC1397
homolog_lib	sing_1316.htm#SEC1397
homology	sing_1326.htm#SEC1407
homomorphism	sing_1376.htm#SEC1457
howto, download	sing_3001.htm#SEC3099
howto, install on Macintosh	sing_3005.htm#SEC3103
howto, install on Unix	sing_3003.htm#SEC3101
howto, install on Windows	sing_3004.htm#SEC3102
hres	sing_266.htm#SEC306
html, default help	sing_16.htm#IDX24
hybrid algorithms	sing_2168.htm#IDX937
hyperel.lib	sing_2398.htm#SEC2479
hyperel_lib	sing_2398.htm#SEC2479
hyperplane	sing_2628.htm#IDX982
hyperplane arrangement	sing_537.htm#IDX338
hypersurface singularity	sing_1983.htm#IDX918
iMult	sing_1467.htm#SEC1548
id	sing_1349.htm#SEC1430
id2mod	sing_1102.htm#SEC1183
ideal	sing_90.htm#SEC130
ideal (plural)	sing_427.htm#SEC467
ideal declarations	sing_91.htm#SEC131
ideal declarations (plural)	sing_428.htm#SEC468
ideal expressions	sing_92.htm#SEC132
ideal expressions (plural)	sing_429.htm#SEC469
ideal operations	sing_93.htm#SEC133
ideal operations (plural)	sing_430.htm#SEC470
ideal related functions	sing_94.htm#SEC134
ideal related functions (plural)	sing_431.htm#SEC471
ideal, toric	sing_992.htm#SEC1054
idealSplit	sing_2146.htm#SEC2227
ideals	sing_422.htm#IDX294
idealsimplify	sing_1853.htm#SEC1934
identifier	sing_423.htm#SEC463
identifyvar	sing_1722.htm#SEC1803
if	sing_390.htm#SEC430
image	sing_1372.htm#SEC1453
imageLattice	sing_2893.htm#SEC2974
image_of_variety	sing_2078.htm#SEC2159
imap	sing_267.htm#SEC307
imap (letterplace)	sing_808.htm#SEC862
imap (plural)	sing_466.htm#SEC506
imapall	sing_1149.htm#SEC1230
impart	sing_268.htm#SEC308
importfrom	sing_391.htm#SEC431
inCenter	sing_526.htm#SEC580
inCentralizer	sing_527.htm#SEC581
inForm	sing_570.htm#SEC624
inSubring	sing_1249.htm#SEC1330
indSet	sing_1434.htm#SEC1515
indepSet	sing_269.htm#SEC309
indexed names	sing_36.htm#IDX82
indexed names 	sing_37.htm#SEC65
indices, multi	sing_37.htm#SEC65
inequalities	sing_2494.htm#SEC2575
infRedTail, option	sing_318.htm#IDX154
infinitely presented algebra	sing_886.htm#IDX431
info	sing_16.htm#SEC23
iniD	sing_1742.htm#SEC1823
init_debug	sing_1869.htm#SEC1950
initial	sing_2613.htm#SEC2694
initial form	sing_502.htm#IDX319
initial ideal	sing_502.htm#IDX318
initial ideal approach	sing_502.htm#IDX322
initial ideal approach 	sing_601.htm#IDX368
initialForm	sing_2590.htm#SEC2671
initialIdeal	sing_2591.htm#SEC2672
initialIdealW	sing_569.htm#SEC623
initialMalgrange	sing_568.htm#SEC622
injective_knapsack	sing_2392.htm#SEC2473
inout.lib	sing_1068.htm#SEC1149
inout_lib	sing_1068.htm#SEC1149
input	sing_41.htm#SEC71
insert	sing_126.htm#SEC166
insert 	sing_270.htm#SEC310
insertCone	sing_2518.htm#SEC2599
insertGenerator	sing_589.htm#SEC643
instructions, Macintosh installation	sing_3005.htm#SEC3103
instructions, Unix installation	sing_3003.htm#SEC3101
instructions, Windows installation	sing_3004.htm#SEC3102
instructions, downloading	sing_3001.htm#SEC3099
int	sing_95.htm#SEC135
int declarations	sing_96.htm#SEC136
int expressions	sing_97.htm#SEC137
int operations	sing_98.htm#SEC138
int related functions	sing_99.htm#SEC139
intInverse	sing_2902.htm#SEC2983
intPart	sing_2346.htm#SEC2427
intRank	sing_2894.htm#SEC2975
intRoot	sing_2347.htm#SEC2428
intRoots	sing_586.htm#SEC640
intStrategy, option	sing_318.htm#IDX155
intclMonIdeal	sing_1480.htm#SEC1561
intclToricRing	sing_1476.htm#SEC1557
integer division	sing_422.htm#IDX289
integer programming	sing_1000.htm#SEC1062
integral	sing_1787.htm#SEC1868
integral basis	sing_1338.htm#IDX625
integral basis 	sing_1705.htm#IDX731
integral closure	sing_1460.htm#IDX648
integral closure 	sing_1461.htm#IDX651
integral closure  	sing_1462.htm#IDX654
integral closure   	sing_1475.htm#IDX660
integralBasis	sing_1338.htm#SEC1419
integralIdeal	sing_573.htm#SEC627
integralModule	sing_574.htm#SEC628
integralSection	sing_2903.htm#SEC2984
integralbasis.lib	sing_1337.htm#SEC1418
integralbasis_lib	sing_1337.htm#SEC1418
integration of D-module	sing_561.htm#IDX350
interface, Emacs	sing_21.htm#SEC28
internalfunctions	sing_1870.htm#SEC1951
interpolate	sing_2152.htm#SEC2233
interpolation	sing_271.htm#SEC311
interpret	sing_1394.htm#SEC1475
interpretElem	sing_1397.htm#SEC1478
interpretInv	sing_1395.htm#SEC1476
interpretList	sing_1398.htm#SEC1479
interred	sing_272.htm#SEC312
intersect	sing_273.htm#SEC313
intersect (plural)	sing_467.htm#SEC507
intersectElim, option	sing_318.htm#IDX173
intersectLattices	sing_2899.htm#SEC2980
intersectLists	sing_2673.htm#SEC2754
intersectMon	sing_1411.htm#SEC1492
intersectOrbitsWithMovingCone	sing_2545.htm#SEC2626
intersectSyz, option	sing_318.htm#IDX174
intersectZ	sing_1536.htm#SEC1617
intersection	sing_1966.htm#SEC2047
intersection 	sing_2733.htm#IDX1123
intersection lattice	sing_2664.htm#IDX1057
intersection lattice 	sing_2665.htm#IDX1058
intersection multiplicity	sing_1846.htm#IDX790
intersection multiplicity 	sing_1966.htm#IDX911
intersectionDiv	sing_1770.htm#SEC1851
intersectionSet	sing_2733.htm#SEC2814
intersectionValRingIdeals	sing_1485.htm#SEC1566
intersectionValRings	sing_1484.htm#SEC1565
intersectpar	sing_1062.htm#SEC1143
interval arithmetic	sing_2186.htm#IDX942
interval.lib	sing_2123.htm#SEC2204
interval_lib	sing_2123.htm#SEC2204
intervalmatrixInit	sing_2126.htm#SEC2207
intmat	sing_102.htm#SEC142
intmat declarations	sing_103.htm#SEC143
intmat expressions	sing_104.htm#SEC144
intmat operations	sing_106.htm#SEC146
intmat related functions	sing_107.htm#SEC147
intmat type cast	sing_105.htm#SEC145
intmat2mons	sing_1500.htm#SEC1581
intprog.lib	sing_1339.htm#SEC1420
intprog_lib	sing_1339.htm#SEC1420
intvec	sing_108.htm#SEC148
intvec declarations	sing_109.htm#SEC149
intvec expressions	sing_110.htm#SEC150
intvec operations	sing_111.htm#SEC151
intvec related functions	sing_112.htm#SEC152
invar	sing_2109.htm#SEC2190
invar.lib	sing_2103.htm#SEC2184
invar_lib	sing_2103.htm#SEC2184
invariant	sing_1271.htm#IDX589
invariant ring minimal generating set matrix group	sing_2047.htm#IDX931
invariant ring minimal generating set permutation group	sing_2048.htm#IDX932
invariantRing	sing_2080.htm#SEC2161
invariant_algebra_perm	sing_2048.htm#SEC2129
invariant_algebra_reynolds	sing_2047.htm#SEC2128
invariant_basis	sing_2055.htm#SEC2136
invariant_basis_reynolds	sing_2056.htm#SEC2137
invariant_ring	sing_2043.htm#SEC2124
invariant_ring_random	sing_2044.htm#SEC2125
invariants	sing_1268.htm#IDX582
invariants 	sing_1272.htm#IDX591
invariants  	sing_1962.htm#SEC2043
inverse	sing_1217.htm#SEC1298
inverse of a matrix via its LU-decomposition	sing_293.htm#SEC333
inverseFourier	sing_584.htm#SEC638
inverse_B	sing_1218.htm#SEC1299
inverse_L	sing_1219.htm#SEC1300
inverse_modulus	sing_2375.htm#SEC2456
invertAlgebraMorphism	sing_2991.htm#SEC3072
invertBirMap	sing_1706.htm#SEC1787
invertLeftFraction	sing_769.htm#SEC823
invertNcfrac	sing_705.htm#SEC759
invertNumberMain	sing_2211.htm#SEC2292
involut.lib	sing_606.htm#SEC660
involut_lib	sing_606.htm#SEC660
involution	sing_611.htm#SEC665
invunit	sing_1985.htm#SEC2066
iostruct	sing_2294.htm#SEC2375
irrRealizationDim	sing_2573.htm#SEC2654
irred_secondary_char0	sing_2069.htm#SEC2150
irred_secondary_no_molien	sing_2072.htm#SEC2153
irreddecMon	sing_1420.htm#SEC1501
irreducible power series	sing_1967.htm#IDX912
irreducible secondary invariant	sing_2069.htm#IDX933
isAface	sing_2530.htm#SEC2611
isAntiEndo	sing_613.htm#SEC667
isCI	sing_210.htm#IDX139
isCI 	sing_1267.htm#SEC1348
isCM	sing_210.htm#IDX140
isCM 	sing_1327.htm#SEC1408
isCMcod2	sing_2026.htm#SEC2107
isCartan	sing_528.htm#SEC582
isCentral	sing_745.htm#SEC799
isCommutative	sing_747.htm#SEC801
isCompatible	sing_2519.htm#SEC2600
isDenom	sing_717.htm#SEC771
isElement	sing_2735.htm#SEC2816
isEqualDivisor	sing_1647.htm#SEC1728
isEquising	sing_1929.htm#SEC2010
isFlat	sing_1328.htm#SEC1409
isFreeAlgebra	sing_873.htm#SEC927
isFsat	sing_579.htm#SEC633
isFullSpace	sing_2495.htm#SEC2576
isGradedRingHomomorphism	sing_2888.htm#SEC2969
isGroup	sing_2886.htm#SEC2967
isGroupHomomorphism	sing_2887.htm#SEC2968
isHolonomic	sing_557.htm#SEC611
isHomog	sing_210.htm#IDX135
isHomogeneous	sing_2914.htm#SEC2995
isInS	sing_758.htm#SEC812
isInt	sing_591.htm#SEC645
isIntegralSurjective	sing_2900.htm#SEC2981
isInvertibleLeftFraction	sing_768.htm#SEC822
isInvertibleNcfrac	sing_704.htm#SEC758
isInvolution	sing_612.htm#SEC666
isLocalizationRegular	sing_1675.htm#SEC1756
isLocallyFree	sing_1329.htm#SEC1410
isMonomial	sing_1406.htm#SEC1487
isNC	sing_746.htm#SEC800
isOnCurve	sing_2359.htm#SEC2440
isOneFraction	sing_771.htm#SEC825
isOneNcfrac	sing_698.htm#SEC752
isOrderingShiftInvariant	sing_879.htm#SEC933
isOrigin	sing_2496.htm#SEC2577
isPositive	sing_2911.htm#SEC2992
isPrimitiveSublattice	sing_2901.htm#SEC2982
isPure	sing_2520.htm#SEC2601
isPureTensor	sing_500.htm#SEC554
isQuotientRing	sing_1163.htm#SEC1244
isRational	sing_560.htm#SEC614
isReg	sing_1330.htm#SEC1411
isSB	sing_210.htm#IDX134
isSimplicial	sing_2497.htm#SEC2578
isSubModule	sing_1164.htm#SEC1245
isSublattice	sing_2892.htm#SEC2973
isSubset	sing_2736.htm#SEC2817
isSuperset	sing_2737.htm#SEC2818
isSymmetric	sing_1565.htm#SEC1646
isTame	sing_1954.htm#SEC2035
isTorsionFree	sing_2910.htm#SEC2991
isTwoSidedGB	sing_501.htm#SEC555
isUpperTriangular	sing_726.htm#SEC780
isWeyl	sing_748.htm#SEC802
isZeroElement	sing_2912.htm#SEC2993
isZeroFraction	sing_770.htm#SEC824
isZeroNcfrac	sing_697.htm#SEC751
is_NND	sing_1970.htm#SEC2051
is_NP	sing_1443.htm#SEC1524
is_active	sing_2009.htm#SEC2090
is_bijective	sing_1254.htm#SEC1335
is_cenBimodule	sing_714.htm#SEC768
is_cenSubbimodule	sing_715.htm#SEC769
is_ci	sing_2010.htm#SEC2091
is_complex	sing_1191.htm#SEC1272
is_composite	sing_1276.htm#SEC1357
is_fix_injective	sing_2396.htm#SEC2477
is_h_injective	sing_2395.htm#SEC2476
is_injective	sing_1252.htm#SEC1333
is_irred	sing_1967.htm#SEC2048
is_is	sing_2011.htm#SEC2092
is_nested	sing_1444.htm#SEC1525
is_prime	sing_2376.htm#SEC2457
is_primitive_root	sing_2372.htm#SEC2453
is_pure	sing_788.htm#SEC842
is_reg	sing_2012.htm#SEC2093
is_regs	sing_2013.htm#SEC2094
is_surjective	sing_1253.htm#SEC1334
is_zero	sing_1091.htm#SEC1172
isartinianMon	sing_1417.htm#SEC1498
isgenericMon	sing_1418.htm#SEC1499
ishyper	sing_2399.htm#SEC2480
isirreducibleMon	sing_1416.htm#SEC1497
isoncurve	sing_2400.htm#SEC2481
isparam	sing_2463.htm#SEC2544
isprimaryMon	sing_1415.htm#SEC1496
isprimeMon	sing_1414.htm#SEC1495
isuni	sing_2448.htm#SEC2529
ivmatGaussian	sing_2193.htm#SEC2274
ivmatGaussian2	sing_2129.htm#SEC2210
ivmatInit	sing_2190.htm#SEC2271
ivmatSet	sing_2191.htm#SEC2272
jOft	sing_2331.htm#SEC2412
jacob	sing_274.htm#SEC314
jacoblift	sing_1986.htm#SEC2067
jacobson	sing_2300.htm#SEC2381
jacobson.lib	sing_2298.htm#SEC2379
jacobson_lib	sing_2298.htm#SEC2379
janet	sing_275.htm#SEC315
janet basis	sing_1548.htm#IDX669
jet	sing_276.htm#SEC316
jordan	sing_1238.htm#SEC1319
jordanVecField	sing_2984.htm#SEC3065
jordanbasis	sing_1239.htm#SEC1320
jordanmatrix	sing_1240.htm#SEC1321
jordannf	sing_1241.htm#SEC1322
jungfib	sing_1755.htm#SEC1836
jungnormal	sing_1754.htm#SEC1835
jungresolve	sing_1753.htm#SEC1834
katsura	sing_1089.htm#SEC1170
kbase	sing_277.htm#SEC317
kbase (plural)	sing_468.htm#SEC508
keepring	sing_392.htm#SEC432
kerHom	sing_1393.htm#SEC1474
kernel	sing_278.htm#SEC318
kernelLattice	sing_2895.htm#SEC2976
kill	sing_279.htm#SEC319
killTask	sing_1170.htm#SEC1251
killall	sing_1030.htm#SEC1111
killattrib	sing_280.htm#SEC320
kmemory	sing_1029.htm#SEC1110
kohom	sing_1332.htm#SEC1413
kontrahom	sing_1333.htm#SEC1414
koszul	sing_281.htm#SEC321
kskernel.lib	sing_1977.htm#SEC2058
kskernel_lib	sing_1977.htm#SEC2058
l-adic numbers	sing_32.htm#SEC46
laguerre	sing_282.htm#SEC322
laguerre_solve	sing_2148.htm#SEC2229
lastQuadrantComplex	sing_2980.htm#SEC3061
lastvarGeneral	sing_2429.htm#SEC2510
latex.lib	sing_2223.htm#SEC2304
latex_lib	sing_2223.htm#SEC2304
lattice	sing_2665.htm#IDX1060
latticeArea	sing_2568.htm#SEC2649
latticeBasis	sing_2896.htm#SEC2977
laxfrT	sing_2797.htm#SEC2878
laxfrX	sing_2798.htm#SEC2879
lazy, option	sing_318.htm#IDX156
lcm	sing_1092.htm#SEC1173
lcmMon	sing_1409.htm#SEC1490
lcmN	sing_2340.htm#SEC2421
lcmofall	sing_1735.htm#SEC1816
lead	sing_283.htm#SEC323
leadcoef	sing_284.htm#SEC324
leadexp	sing_285.htm#SEC325
leadmonom	sing_286.htm#SEC326
leadmonomial	sing_2415.htm#SEC2496
left annihilator ideal	sing_537.htm#IDX330
left annihilator ideal 	sing_593.htm#IDX358
leftInverse	sing_2289.htm#SEC2370
leftKernel	sing_2287.htm#SEC2368
leftOre	sing_761.htm#SEC815
length	sing_2188.htm#SEC2269
length, option	sing_318.htm#IDX157
length2	sing_2124.htm#SEC2205
letplaceGBasis	sing_881.htm#SEC935
letterplace	sing_296.htm#SEC336
letterplace 	sing_337.htm#SEC377
lex_solve	sing_2154.htm#SEC2235
lexicographical ordering	sing_978.htm#IDX441
lib2doc	sing_60.htm#SEC97
libSingular	sing_3000.htm#SEC3098
libcdd	sing_1.htm#IDX12
libfac	sing_1.htm#IDX6
libparse	sing_69.htm#SEC109
library	sing_2711.htm#IDX1101
library, gitfan, GIT, geometric invariant theory, quotients	sing_2529.htm#IDX969
library, info string	sing_55.htm#IDX124
library, polybori.lib	sing_2711.htm#IDX1098
library, ringgb.lib	sing_2944.htm#IDX1251
library, template	sing_55.htm#SEC92
library, template.lib	sing_55.htm#IDX122
lieBracket	sing_882.htm#SEC936
lift	sing_288.htm#SEC328
lift 	sing_495.htm#IDX306
lift (letterplace)	sing_809.htm#SEC863
lift (plural)	sing_469.htm#SEC509
lift_kbase	sing_1923.htm#SEC2004
lift_rel_kb	sing_1924.htm#SEC2005
liftenvelope	sing_498.htm#SEC552
liftstd	sing_289.htm#SEC329
liftstd (letterplace)	sing_810.htm#SEC864
liftstd (plural)	sing_470.htm#SEC510
likeIdeal	sing_2867.htm#SEC2948
likelihood ideal	sing_2866.htm#IDX1237
linReduce	sing_510.htm#SEC564
linReduceIdeal	sing_511.htm#SEC565
linSyzSolve	sing_512.htm#SEC566
linalg.lib	sing_1216.htm#SEC1297
linalg_lib	sing_1216.htm#SEC1297
linealityDimension	sing_2498.htm#SEC2579
linealitySpace	sing_2499.htm#SEC2580
linear algebra	sing_211.htm#SEC251
linear algebra 	sing_292.htm#SEC332
linear algebra  	sing_293.htm#SEC333
linear algebra   	sing_294.htm#SEC334
linear code, dual	sing_2258.htm#IDX952
linear code, systematic	sing_2259.htm#IDX953
linear interreduction	sing_502.htm#IDX321
linearCombinations	sing_531.htm#SEC585
linearMapKernel	sing_530.htm#SEC584
linear_relations	sing_1208.htm#SEC1289
linearlyEquivalent	sing_1650.htm#SEC1731
linearpart	sing_2140.htm#SEC2221
linesHypersurface	sing_1809.htm#SEC1890
link	sing_113.htm#SEC153
link 	sing_933.htm#SEC990
link declarations	sing_114.htm#SEC154
link expressions	sing_115.htm#SEC155
link related functions	sing_116.htm#SEC156
links	sing_2959.htm#IDX1264
list	sing_123.htm#SEC163
list 	sing_2773.htm#IDX1184
list  	sing_2774.htm#IDX1186
list declarations	sing_124.htm#SEC164
list expressions	sing_125.htm#SEC165
list operations	sing_126.htm#SEC166
list related functions	sing_127.htm#SEC167
lists	sing_2673.htm#IDX1067
lists, elements	sing_2675.htm#IDX1069
listvar	sing_290.htm#SEC330
lll	sing_2928.htm#SEC3009
load	sing_393.htm#SEC433
loadLib, option	sing_318.htm#IDX179
loadProc, option	sing_318.htm#IDX180
locAtZero	sing_1469.htm#SEC1550
locNormal	sing_1342.htm#SEC1423
locStatus	sing_756.htm#SEC810
local methods	sing_1341.htm#IDX628
local methods 	sing_1342.htm#IDX631
local names	sing_46.htm#SEC83
local rings, computing in	sing_928.htm#SEC985
local weighted lexicographical ordering	sing_979.htm#IDX462
local weighted reverse lexicographical ordering	sing_979.htm#IDX459
localInvar	sing_2085.htm#SEC2166
localization	sing_928.htm#SEC985
localization 	sing_2645.htm#IDX1020
localization of D-module	sing_561.htm#IDX346
localization of D-module 	sing_668.htm#IDX385
locally closed set	sing_1047.htm#IDX486
locally closed set 	sing_1048.htm#IDX488
locally closed set  	sing_1049.htm#IDX490
locally closed set   	sing_1050.htm#IDX494
locally closed set    	sing_1064.htm#IDX532
locally closed set     	sing_1066.htm#IDX537
localstd	sing_2425.htm#SEC2506
locnormal.lib	sing_1341.htm#SEC1422
locnormal_lib	sing_1341.htm#SEC1422
locstd	sing_2014.htm#SEC2095
locus	sing_1052.htm#SEC1133
locus 	sing_1052.htm#IDX504
locus  	sing_1053.htm#IDX507
locus   	sing_1054.htm#IDX510
locus    	sing_1055.htm#IDX513
locus     	sing_1056.htm#IDX516
locus      	sing_1057.htm#IDX518
locus       	sing_1058.htm#IDX522
locusdg	sing_1053.htm#SEC1134
locusto	sing_1055.htm#SEC1136
log2	sing_2315.htm#SEC2396
logHessian	sing_2868.htm#SEC2949
logarithmic annihilator ideal	sing_537.htm#IDX335
logarithmic annihilator ideal 	sing_593.htm#IDX360
logg	sing_1814.htm#SEC1895
lp, global ordering	sing_978.htm#IDX440
lpCalcSubstDegBound	sing_871.htm#SEC925
lpDegBound	sing_874.htm#SEC928
lpDivision	sing_877.htm#SEC931
lpGBPres2Poly	sing_878.htm#SEC932
lpGkDim	sing_867.htm#SEC921
lpGlDimBound	sing_869.htm#SEC923
lpHilbert	sing_832.htm#SEC886
lpIsPrime	sing_866.htm#SEC920
lpIsSemiPrime	sing_865.htm#SEC919
lpKDim	sing_829.htm#SEC883
lpMonomialBasis	sing_831.htm#SEC885
lpNcgenCount	sing_876.htm#SEC930
lpNoetherian	sing_864.htm#SEC918
lpSubstitute	sing_870.htm#SEC924
lpVarBlockSize	sing_875.htm#SEC929
lprint	sing_1070.htm#SEC1151
lrcalc.lib	sing_2859.htm#SEC2940
lrcalc_lib	sing_2859.htm#SEC2940
lres	sing_291.htm#SEC331
ls, local ordering	sing_979.htm#IDX453
lsum	sing_1300.htm#SEC1381
ludecomp	sing_292.htm#SEC332
luinverse	sing_293.htm#SEC333
lusolve	sing_294.htm#SEC334
mRes	sing_1361.htm#SEC1442
m_merkle_hellman_decryption	sing_2387.htm#SEC2468
m_merkle_hellman_encryption	sing_2386.htm#SEC2467
m_merkle_hellman_transformation	sing_2385.htm#SEC2466
magnitude	sing_2309.htm#SEC2390
makeDivisor	sing_1642.htm#SEC1723
makeFormalDivisor	sing_1652.htm#SEC1733
makeGraph	sing_1291.htm#SEC1372
makeGraphVE	sing_1800.htm#SEC1881
makeHeisenberg	sing_736.htm#SEC790
makeIdeal	sing_1353.htm#SEC1434
makeLetterplaceRing	sing_880.htm#SEC934
makeLinks	sing_2959.htm#SEC3040
makeMalgrange	sing_605.htm#SEC659
makeMatrix	sing_1352.htm#SEC1433
makeModElimRing	sing_753.htm#SEC807
makePDivisor	sing_1658.htm#SEC1739
makePoly	sing_2941.htm#SEC3022
makeQPoly	sing_2956.htm#SEC3037
makeQsl2	sing_639.htm#SEC693
makeQsl3	sing_640.htm#SEC694
makeQso3	sing_638.htm#SEC692
makeSheaf	sing_1788.htm#SEC1869
makeUe6	sing_635.htm#SEC689
makeUe7	sing_636.htm#SEC690
makeUe8	sing_637.htm#SEC691
makeUf4	sing_634.htm#SEC688
makeUg2	sing_633.htm#SEC687
makeUgl	sing_619.htm#SEC673
makeUsl	sing_618.htm#SEC672
makeUsl2	sing_617.htm#SEC671
makeUso10	sing_625.htm#SEC679
makeUso11	sing_626.htm#SEC680
makeUso12	sing_627.htm#SEC681
makeUso5	sing_620.htm#SEC674
makeUso6	sing_621.htm#SEC675
makeUso7	sing_622.htm#SEC676
makeUso8	sing_623.htm#SEC677
makeUso9	sing_624.htm#SEC678
makeUsp1	sing_628.htm#SEC682
makeUsp2	sing_629.htm#SEC683
makeUsp3	sing_630.htm#SEC684
makeUsp4	sing_631.htm#SEC685
makeUsp5	sing_632.htm#SEC686
makeVariety	sing_1780.htm#SEC1861
makeVector	sing_1381.htm#SEC1462
makeWeyl	sing_735.htm#SEC789
makedistinguished	sing_1279.htm#SEC1360
map	sing_128.htm#SEC168
map (plural)	sing_432.htm#SEC472
map declarations	sing_129.htm#SEC169
map declarations (plural)	sing_433.htm#SEC473
map expressions	sing_130.htm#SEC170
map expressions (plural)	sing_434.htm#SEC474
map operations	sing_131.htm#IDX129
map operations (plural)	sing_435.htm#IDX301
map related functions	sing_132.htm#IDX131
map related functions  (plural)	sing_436.htm#IDX302
mapIsFinite	sing_1256.htm#SEC1337
mapToRatNormCurve	sing_1710.htm#SEC1791
mapall	sing_1150.htm#SEC1231
mappingcone	sing_2848.htm#SEC2929
mappingcone3	sing_2850.htm#SEC2931
markov4ti2	sing_1560.htm#SEC1641
mat2arr	sing_2630.htm#SEC2711
mat2carr	sing_2631.htm#SEC2712
mat_rk	sing_1230.htm#SEC1311
matbil	sing_2436.htm#SEC2517
mathematical objects	sing_974.htm#SEC1031
mathinit	sing_2221.htm#SEC2302
matmult	sing_2437.htm#SEC2518
matrix	sing_133.htm#SEC173
matrix 	sing_2630.htm#IDX988
matrix  	sing_2631.htm#IDX991
matrix   	sing_2632.htm#IDX995
matrix declarations	sing_134.htm#SEC174
matrix diagonalization	sing_2298.htm#IDX963
matrix expressions	sing_135.htm#SEC175
matrix operations	sing_137.htm#SEC177
matrix related functions	sing_138.htm#SEC178
matrix type cast	sing_136.htm#SEC176
matrix.lib	sing_1184.htm#SEC1265
matrixExp	sing_1700.htm#SEC1781
matrixLog	sing_1701.htm#SEC1782
matrixT1	sing_2028.htm#SEC2109
matrix_lib	sing_1184.htm#SEC1265
matrixpres	sing_2853.htm#SEC2934
matrixsystem	sing_2808.htm#SEC2889
max	sing_295.htm#SEC335
maxEord	sing_1725.htm#SEC1806
maxExp	sing_210.htm#IDX136
maxIntRoot	sing_685.htm#SEC739
maxPoints	sing_2870.htm#SEC2951
maxPointsProb	sing_2871.htm#SEC2952
maxZeros	sing_1703.htm#SEC1784
maxabs	sing_2455.htm#SEC2536
maxcoef	sing_1093.htm#SEC1174
maxdeg	sing_1094.htm#SEC1175
maxdeg1	sing_1095.htm#SEC1176
maxideal	sing_296.htm#SEC336
maximalGroebnerCone	sing_2611.htm#SEC2692
maximum	sing_2328.htm#SEC2409
maximum likelihood estimate	sing_2866.htm#IDX1238
maximum number of zeroes	sing_1703.htm#IDX725
maxlike.lib	sing_2866.htm#SEC2947
maxlike_lib	sing_2866.htm#SEC2947
mdouble	sing_56.htm#SEC93
mem, option	sing_318.htm#IDX181
member	sing_2675.htm#SEC2756
memberpos	sing_1109.htm#SEC1190
membershipMon	sing_1410.htm#SEC1491
memory	sing_297.htm#SEC337
memory management	sing_297.htm#SEC337
merkle_hellman_decryption	sing_2389.htm#SEC2470
merkle_hellman_encryption	sing_2388.htm#SEC2469
methods, hashtables	sing_2679.htm#IDX1072
methods.lib	sing_2679.htm#SEC2760
methods_lib	sing_2679.htm#SEC2760
midpoint	sing_2804.htm#SEC2885
milnor	sing_2015.htm#SEC2096
milnorcode	sing_1871.htm#SEC1952
milnornumber	sing_2002.htm#SEC2083
min	sing_298.htm#SEC338
minAssChar	sing_1514.htm#SEC1595
minAssCharE	sing_1515.htm#SEC1596
minAssGTZ	sing_1512.htm#SEC1593
minAssGTZE	sing_1513.htm#SEC1594
minAssZ	sing_1532.htm#SEC1613
minEcart	sing_2418.htm#SEC2499
minIntRoot	sing_559.htm#SEC613
minIntRoot2	sing_684.htm#SEC738
minMult	sing_1263.htm#SEC1344
minbase	sing_299.htm#SEC339
minbaseMon	sing_1407.htm#SEC1488
mindeg	sing_1096.htm#SEC1177
mindeg1	sing_1097.htm#SEC1178
mindist	sing_2273.htm#SEC2354
minimal display time, setting the	sing_361.htm#IDX285
minimal representations	sing_889.htm#IDX439
minimalAfaceOrbits	sing_2542.htm#SEC2623
minimalAfaces	sing_2533.htm#SEC2614
minimalOrbitConeOrbits	sing_2544.htm#SEC2625
minipoly	sing_1235.htm#SEC1316
minor	sing_300.htm#SEC340
minpoly	sing_401.htm#SEC441
minres	sing_301.htm#SEC341
minres (plural)	sing_471.htm#SEC511
minus	sing_2762.htm#IDX1160
minus 	sing_2763.htm#IDX1162
minus  	sing_2784.htm#IDX1208
minus   	sing_2785.htm#IDX1210
mirror symmetry	sing_1290.htm#IDX596
mixed Hodge structure	sing_1931.htm#IDX811
mixed Hodge structure 	sing_1937.htm#IDX839
mixed Hodge structure  	sing_1938.htm#IDX845
mixed Hodge structure   	sing_1939.htm#IDX853
mixed Hodge structure    	sing_1940.htm#IDX859
mixed Hodge structure     	sing_1941.htm#IDX867
mixed Hodge structure      	sing_1942.htm#IDX877
mixed Hodge structure       	sing_1953.htm#IDX883
mixed Hodge structure        	sing_1955.htm#IDX894
mod	sing_81.htm#SEC121
mod 	sing_98.htm#SEC138
mod  	sing_147.htm#SEC187
mod   	sing_155.htm#SEC195
mod2id	sing_1101.htm#SEC1182
modBorder	sing_1550.htm#SEC1631
modDec	sing_1426.htm#SEC1507
modIntersect	sing_1404.htm#SEC1485
modJanet	sing_1552.htm#SEC1633
modNPos	sing_1454.htm#SEC1535
modNormal	sing_1347.htm#SEC1428
modNpos_test	sing_1452.htm#SEC1533
modQuotient	sing_1344.htm#SEC1425
modSagbiAlg	sing_1893.htm#SEC1974
modSat	sing_1345.htm#SEC1426
modStd	sing_1402.htm#SEC1483
modSyz	sing_1403.htm#SEC1484
modVStd	sing_1904.htm#SEC1985
modVStd0	sing_1905.htm#SEC1986
modWalk	sing_2873.htm#SEC2954
mod_versal	sing_1922.htm#SEC2003
modality	sing_1879.htm#SEC1960
modberlekampMassey	sing_1306.htm#SEC1387
moddiq.lib	sing_1343.htm#SEC1424
moddiq_lib	sing_1343.htm#SEC1424
modfWalk	sing_2875.htm#SEC2956
modfrWalk	sing_2876.htm#SEC2957
modnormal.lib	sing_1346.htm#SEC1427
modnormal_lib	sing_1346.htm#SEC1427
modrWalk	sing_2874.htm#SEC2955
modrationalInterpolation	sing_1304.htm#SEC1385
modregCM	sing_1458.htm#SEC1539
modsatiety	sing_1456.htm#SEC1537
modstd.lib	sing_1401.htm#SEC1482
modstd_lib	sing_1401.htm#SEC1482
modular	sing_1079.htm#SEC1160
modular methods	sing_1341.htm#IDX629
modular methods 	sing_1346.htm#IDX635
modular methods.	sing_1342.htm#IDX632
modular techniques.	sing_1347.htm#IDX637
modular.lib	sing_1078.htm#SEC1159
modular_lib	sing_1078.htm#SEC1159
modular_lib 	sing_1078.htm#IDX541
module	sing_139.htm#SEC179
module (plural)	sing_437.htm#SEC477
module declarations	sing_140.htm#SEC180
module declarations (plural)	sing_438.htm#SEC478
module expressions	sing_141.htm#SEC181
module expressions (plural)	sing_439.htm#SEC479
module operations	sing_142.htm#SEC182
module operations (plural)	sing_440.htm#SEC480
module ordering C	sing_980.htm#IDX465
module ordering c	sing_980.htm#IDX467
module related functions	sing_143.htm#SEC183
module related functions (plural)	sing_441.htm#SEC481
module_containment	sing_1248.htm#SEC1329
modules.lib	sing_1348.htm#SEC1429
modules_lib	sing_1348.htm#SEC1429
moduliSpace	sing_1802.htm#SEC1883
modulo	sing_302.htm#SEC342
modulo (letterplace)	sing_811.htm#SEC865
modulo (plural)	sing_472.htm#SEC512
moduloSlim	sing_743.htm#SEC797
modwalk.lib	sing_2872.htm#SEC2953
modwalk_lib	sing_2872.htm#SEC2953
moebius	sing_2666.htm#SEC2747
moebius function	sing_2666.htm#IDX1061
molien	sing_2051.htm#SEC2132
mondim	sing_667.htm#SEC721
mondromy.lib	sing_1983.htm#SEC2064
mondromy_lib	sing_1983.htm#SEC2064
monitor	sing_303.htm#SEC343
monodromy	sing_1931.htm#IDX815
monodromy 	sing_1936.htm#SEC2017
monodromy  	sing_1936.htm#IDX835
monodromy   	sing_1941.htm#IDX870
monodromy    	sing_1953.htm#IDX886
monodromy     	sing_1955.htm#IDX897
monodromyB	sing_1987.htm#SEC2068
monoideal, dimension	sing_667.htm#IDX378
monomial	sing_304.htm#SEC344
monomial ordering	sing_1159.htm#IDX567
monomial orderings	sing_928.htm#SEC985
monomial orderings 	sing_977.htm#SEC1034
monomial orderings introduction	sing_976.htm#SEC1033
monomial output	sing_405.htm#SEC445
monomial, write	sing_405.htm#SEC445
monomialInIdeal	sing_682.htm#SEC736
monomialLcm	sing_2416.htm#SEC2497
monomialabortstd	sing_2677.htm#SEC2758
monomialideal.lib	sing_1405.htm#SEC1486
monomialideal_lib	sing_1405.htm#SEC1486
monomials and precedence	sing_422.htm#IDX291
mons2intmat	sing_1499.htm#SEC1580
morsesplit	sing_1872.htm#SEC1953
movingCone	sing_2540.htm#SEC2621
mp_res_mat	sing_2151.htm#SEC2232
mplot	sing_2222.htm#SEC2303
mpresmat	sing_305.htm#SEC345
mprimdec.lib	sing_1422.htm#SEC1503
mprimdec_lib	sing_1422.htm#SEC1503
mrcgs	sing_1118.htm#SEC1199
mrcgs, rcgs, buildtree, cantreetoMaple, cantodiffcgs	sing_1120.htm#IDX559
mrcgs, rcgs, crcgs, Maple	sing_1121.htm#IDX560
mregular.lib	sing_1437.htm#SEC1518
mregular_lib	sing_1437.htm#SEC1518
mres	sing_306.htm#SEC346
mres (plural)	sing_473.htm#SEC513
mstd	sing_307.htm#SEC347
msum	sing_58.htm#SEC95
mtriple	sing_57.htm#SEC94
mult	sing_308.htm#SEC348
mult 	sing_422.htm#IDX292
multBound	sing_402.htm#SEC442
multIdeals	sing_2857.htm#SEC2938
multRat	sing_690.htm#SEC744
multarr2arr	sing_2661.htm#SEC2742
multarrMultRestrict	sing_2663.htm#SEC2744
multarrRestrict	sing_2662.htm#SEC2743
multcol	sing_1202.htm#SEC1283
multdivisor	sing_1644.htm#SEC1725
multformaldivisor	sing_1656.htm#SEC1737
multi	sing_2403.htm#SEC2484
multi indices	sing_37.htm#SEC65
multi-graded Hilbert series	sing_886.htm#IDX433
multiDeg	sing_2907.htm#SEC2988
multiDegBasis	sing_2908.htm#SEC2989
multiDegGroebner	sing_2916.htm#SEC2997
multiDegModulo	sing_2918.htm#SEC2999
multiDegPartition	sing_2909.htm#SEC2990
multiDegResolution	sing_2919.htm#SEC3000
multiDegSyzygy	sing_2917.htm#SEC2998
multiDegTensor	sing_2920.htm#SEC3001
multiDegTor	sing_2921.htm#SEC3002
multiarrangement	sing_2657.htm#IDX1041
multiarrangement 	sing_2658.htm#IDX1043
multiarrangement  	sing_2659.htm#IDX1046
multiarrangement   	sing_2660.htm#IDX1047
multiarrangement    	sing_2661.htm#IDX1050
multiarrangement     	sing_2662.htm#IDX1053
multiarrangement      	sing_2663.htm#IDX1055
multidimensional_knapsack	sing_2381.htm#SEC2462
multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra	sing_2877.htm#IDX1243
multigrading.lib	sing_2877.htm#IDX1241
multigrading_lib	sing_2877.htm#IDX1242
multipleCover	sing_1808.htm#SEC1889
multiplication	sing_2764.htm#IDX1164
multiplication 	sing_2786.htm#IDX1212
multiplicities, sequence of	sing_1962.htm#IDX909
multiplicity	sing_661.htm#IDX373
multiplicity 	sing_1270.htm#IDX587
multiplicity sequence	sing_1844.htm#IDX782
multiplicity sequence 	sing_1847.htm#IDX794
multiplicity sequence  	sing_1964.htm#IDX910
multiplyLeftFractions	sing_766.htm#SEC820
multiplylist	sing_1745.htm#SEC1826
multivariate equations	sing_2116.htm#IDX934
multrow	sing_1203.htm#SEC1284
multseq2charexp	sing_1843.htm#SEC1924
multsequence	sing_1964.htm#SEC2045
naccache_stern_decryption	sing_2384.htm#SEC2465
naccache_stern_encryption	sing_2383.htm#SEC2464
naccache_stern_generation	sing_2382.htm#SEC2463
nameof	sing_309.htm#SEC349
names	sing_310.htm#SEC350
nashmult	sing_1851.htm#SEC1932
nblocks	sing_361.htm#IDX220
ncExt_R	sing_709.htm#SEC763
ncHilb	sing_662.htm#SEC716
ncHilb.lib	sing_886.htm#SEC940
ncHilb_lib	sing_886.htm#SEC940
ncHilbertMultiplicity	sing_665.htm#SEC719
ncHilbertPolynomial	sing_664.htm#SEC718
ncHilbertSeries	sing_663.htm#SEC717
ncHom	sing_710.htm#SEC764
ncInit	sing_890.htm#SEC944
ncModslimgb.lib	sing_720.htm#SEC774
ncModslimgb_lib	sing_720.htm#SEC774
ncRelations	sing_744.htm#SEC798
ncVarsAdd	sing_892.htm#SEC946
ncVarsGet	sing_891.htm#SEC945
nc_algebra	sing_474.htm#SEC514
nc_hilb	sing_361.htm#IDX222
ncalg.lib	sing_616.htm#SEC670
ncalg_lib	sing_616.htm#SEC670
ncalgebra	sing_475.htm#SEC515
ncdecomp.lib	sing_643.htm#SEC697
ncdecomp_lib	sing_643.htm#SEC697
ncdetection	sing_610.htm#SEC664
ncfactor	sing_649.htm#SEC703
ncfactor.lib	sing_648.htm#SEC702
ncfactor_lib	sing_648.htm#SEC702
ncfrac.lib	sing_694.htm#SEC748
ncfrac_lib	sing_694.htm#SEC748
ncgen	sing_812.htm#SEC866
nchilb	sing_887.htm#SEC941
nchilbert.lib	sing_661.htm#SEC715
nchilbert_lib	sing_661.htm#SEC715
nchomolog.lib	sing_708.htm#IDX391
nchomolog_lib	sing_708.htm#IDX392
ncloc.lib	sing_716.htm#SEC770
ncloc_lib	sing_716.htm#SEC770
ncmodslimgb	sing_721.htm#SEC775
ncols	sing_311.htm#SEC351
ncones	sing_2522.htm#SEC2603
ncpreim.lib	sing_722.htm#SEC776
ncpreim_lib	sing_722.htm#SEC776
ncrat.lib	sing_889.htm#IDX434
ncratAdd	sing_894.htm#SEC948
ncratDefine	sing_893.htm#SEC947
ncratEvaluateAt	sing_903.htm#SEC957
ncratFromPoly	sing_901.htm#SEC955
ncratFromString	sing_900.htm#SEC954
ncratInvert	sing_897.htm#SEC951
ncratMultiply	sing_896.htm#SEC950
ncratPower	sing_902.htm#SEC956
ncratPrint	sing_899.htm#SEC953
ncratSPrint	sing_898.htm#SEC952
ncratSubstract	sing_895.htm#SEC949
ncrat_lib	sing_889.htm#IDX435
ncrepAdd	sing_905.htm#SEC959
ncrepDim	sing_910.htm#SEC964
ncrepEvaluate	sing_912.htm#SEC966
ncrepEvaluateAt	sing_913.htm#SEC967
ncrepGet	sing_904.htm#SEC958
ncrepGetRegularMinimal	sing_920.htm#SEC974
ncrepGetRegularZeroMinimal	sing_919.htm#SEC973
ncrepInvert	sing_908.htm#SEC962
ncrepIsDefined	sing_915.htm#SEC969
ncrepIsDefinedDim	sing_914.htm#SEC968
ncrepIsRegular	sing_916.htm#SEC970
ncrepMultiply	sing_907.htm#SEC961
ncrepPencilCombine	sing_922.htm#SEC976
ncrepPencilGet	sing_921.htm#SEC975
ncrepPrint	sing_909.htm#SEC963
ncrepRegularMinimize	sing_918.htm#SEC972
ncrepRegularZeroMinimize	sing_917.htm#SEC971
ncrepSubstitute	sing_911.htm#SEC965
ncrepSubstract	sing_906.htm#SEC960
nctools.lib	sing_730.htm#SEC784
nctools_lib	sing_730.htm#SEC784
ndcond	sing_733.htm#SEC787
negateNcfrac	sing_703.htm#SEC757
negatedCone	sing_2500.htm#SEC2581
negation	sing_2763.htm#IDX1163
negative degree lexicographical ordering	sing_979.htm#IDX456
negative degree reverse lexicographical ordering	sing_979.htm#IDX454
negative lexicographical ordering	sing_979.htm#IDX452
negativedivisor	sing_1645.htm#SEC1726
negativeformaldivisor	sing_1655.htm#SEC1736
net	sing_2680.htm#IDX1073
net 	sing_2682.htm#SEC2763
net access	sing_19.htm#IDX40
netBigInt	sing_2688.htm#SEC2769
netBigIntMat	sing_2683.htm#SEC2764
netBigIntMatShort	sing_2684.htm#SEC2765
netCoefficientRing	sing_2685.htm#SEC2766
netIdeal	sing_2686.htm#SEC2767
netInt	sing_2687.htm#SEC2768
netIntMat	sing_2689.htm#SEC2770
netIntMatShort	sing_2690.htm#SEC2771
netIntVector	sing_2691.htm#SEC2772
netIntVectorShort	sing_2692.htm#SEC2773
netList	sing_2694.htm#SEC2775
netMap	sing_2695.htm#SEC2776
netMap2	sing_2696.htm#SEC2777
netMatrix	sing_1383.htm#SEC1464
netNumber	sing_2693.htm#SEC2774
netPoly	sing_2699.htm#SEC2780
netPrimePower	sing_2700.htm#SEC2781
netRing	sing_2701.htm#SEC2782
netString	sing_2702.htm#SEC2783
netVector	sing_1382.htm#SEC1463
netmatrix	sing_2697.htm#SEC2778
netmatrixShort	sing_2698.htm#SEC2779
nets.lib	sing_2680.htm#SEC2761
nets_lib	sing_2680.htm#SEC2761
netvector	sing_2703.htm#SEC2784
netvectorShort	sing_2704.htm#SEC2785
newTest	sing_2323.htm#SEC2404
newline	sing_172.htm#SEC212
news	sing_2993.htm#SEC3074
newstruct	sing_183.htm#SEC223
newstruct 	sing_2711.htm#IDX1103
newtonDiag	sing_1105.htm#SEC1186
newtonPolygonNegSlopes	sing_2620.htm#SEC2701
newtonPolytope	sing_2526.htm#SEC2607
newtonpoly	sing_1969.htm#SEC2050
nextHodgeIdeal	sing_2858.htm#SEC2939
nf_icis	sing_2016.htm#SEC2097
nfmodStd	sing_1447.htm#SEC1528
nfmodSyz	sing_1449.htm#SEC1530
nfmodstd.lib	sing_1445.htm#SEC1526
nfmodstd_lib	sing_1445.htm#SEC1526
nfmodsyz.lib	sing_1448.htm#SEC1529
nfmodsyz_lib	sing_1448.htm#SEC1529
nilpotent Lie algebras	sing_1698.htm#IDX710
nmaxcones	sing_2521.htm#SEC2602
noElements	sing_2948.htm#SEC3029
noether	sing_403.htm#SEC443
noether.lib	sing_1450.htm#SEC1531
noetherNormal	sing_1255.htm#SEC1336
noether_lib	sing_1450.htm#SEC1531
non-english special characters	sing_411.htm#IDX287
nonMonomials	sing_1503.htm#SEC1584
nonZeroEntry	sing_1258.htm#SEC1339
noncommutative, rational expressions	sing_889.htm#IDX436
none, option	sing_318.htm#IDX150
norTest	sing_1470.htm#SEC1551
norm	sing_2402.htm#SEC2483
normaform (up to a bound)	sing_361.htm#IDX245
normal	sing_1460.htm#SEC1541
normal bundle, graph, rational curves, multiple covers, lines on	sing_1807.htm#IDX761
normal form	sing_986.htm#IDX468
normal.lib	sing_1459.htm#SEC1540
normalBundle	sing_1807.htm#SEC1888
normalC	sing_1462.htm#SEC1543
normalConductor	sing_1474.htm#SEC1555
normalForm	sing_1646.htm#SEC1727
normalI	sing_1547.htm#SEC1628
normalP	sing_1461.htm#SEC1542
normalToricRing	sing_1477.htm#SEC1558
normalToricRingFromBinomials	sing_1478.htm#SEC1559
normal_lib	sing_1459.htm#SEC1540
normalform	sing_1876.htm#SEC1957
normalform 	sing_1892.htm#IDX804
normaliz	sing_1.htm#IDX14
normaliz 	sing_1490.htm#SEC1571
normaliz.lib	sing_1475.htm#SEC1556
normaliz_lib	sing_1475.htm#SEC1556
normalization	sing_1269.htm#IDX585
normalization 	sing_1341.htm#IDX627
normalization  	sing_1342.htm#IDX630
normalization   	sing_1346.htm#IDX634
normalization    	sing_1347.htm#IDX636
normalization     	sing_1460.htm#IDX647
normalization      	sing_1461.htm#IDX650
normalization       	sing_1462.htm#IDX653
normalization        	sing_1474.htm#IDX659
normalization         	sing_1475.htm#IDX661
normalization.	sing_1338.htm#IDX626
normalization. 	sing_1705.htm#IDX732
normalize	sing_1098.htm#SEC1179
normalizeMonoidal	sing_772.htm#SEC826
normalizeRational	sing_773.htm#SEC827
not	sing_101.htm#SEC141
not equal	sing_2767.htm#IDX1171
not equal 	sing_2788.htm#IDX1218
notBuckets, option	sing_318.htm#IDX160
notRegularity, option	sing_318.htm#IDX158
notSugar, option	sing_318.htm#IDX159
notWarnSB, option	sing_318.htm#IDX182
npar	sing_2308.htm#SEC2389
npars	sing_312.htm#SEC352
nrRootsDeterm	sing_2433.htm#SEC2514
nrRootsProbab	sing_2432.htm#SEC2513
nres	sing_313.htm#SEC353
nres (plural)	sing_476.htm#SEC516
nrows	sing_314.htm#SEC354
nrroots	sing_2462.htm#SEC2543
nsatiety	sing_1455.htm#SEC1536
nselect	sing_1286.htm#SEC1367
nt_solve	sing_2166.htm#SEC2247
ntsolve.lib	sing_2165.htm#SEC2246
ntsolve_lib	sing_2165.htm#SEC2246
num_elim	sing_2183.htm#SEC2264
num_elim1	sing_2184.htm#SEC2265
num_prime_decom	sing_2177.htm#SEC2258
num_prime_decom1	sing_2178.htm#SEC2259
num_radical1	sing_2181.htm#SEC2262
num_radical2	sing_2182.htm#SEC2263
num_radical_via_decom	sing_2179.htm#SEC2260
num_radical_via_randlincom	sing_2180.htm#SEC2261
number	sing_144.htm#SEC184
number 	sing_2634.htm#IDX1001
number declarations	sing_145.htm#SEC185
number expressions	sing_146.htm#SEC186
number operations	sing_147.htm#SEC187
number related functions	sing_148.htm#SEC188
numberOfConesOfDimension	sing_2523.htm#SEC2604
number_e	sing_1031.htm#SEC1112
number_pi	sing_1032.htm#SEC1113
numerAlg.lib	sing_1680.htm#IDX699
numerAlg_lib	sing_1680.htm#IDX700
numerAlg_lib 	sing_1685.htm#IDX709
numerDecom.lib	sing_1685.htm#IDX703
numerDecom_lib	sing_1680.htm#IDX702
numerDecom_lib 	sing_1685.htm#IDX704
numerator	sing_315.htm#SEC355
numerical algebraic geometry	sing_2168.htm#IDX936
numerical irreducible decomposition	sing_1685.htm#IDX705
nvars	sing_316.htm#SEC356
olga.lib	sing_755.htm#SEC809
olga_lib	sing_755.htm#SEC809
oneDimBelongSemigroup	sing_1265.htm#SEC1346
oneNcfrac	sing_700.htm#SEC754
onesVector	sing_2528.htm#SEC2609
online help	sing_16.htm#SEC22
open	sing_317.htm#SEC357
opentex	sing_2225.htm#SEC2306
operatorAlgebra	sing_835.htm#SEC889
operatorBM	sing_545.htm#SEC599
operatorModulo	sing_546.htm#SEC600
oppose	sing_477.htm#SEC517
opposite	sing_478.htm#SEC518
opposite polynomial	sing_361.htm#IDX230
opposite ring	sing_361.htm#IDX227
option	sing_318.htm#SEC358
option Imap	sing_318.htm#IDX176
option(warn)	sing_70.htm#SEC110
optionIsSet	sing_1156.htm#SEC1237
or	sing_101.htm#SEC141
or 	sing_415.htm#SEC455
orbit	sing_1698.htm#IDX712
orbit 	sing_1699.htm#IDX716
orbit  	sing_1702.htm#IDX721
orbit   	sing_1703.htm#IDX724
orbitConeOrbits	sing_2543.htm#SEC2624
orbitCones	sing_2534.htm#SEC2615
orbit_variety	sing_2075.htm#SEC2156
orbitparam.lib	sing_1698.htm#SEC1779
orbitparam_lib	sing_1698.htm#SEC1779
ord	sing_319.htm#SEC359
ord_test	sing_1151.htm#SEC1232
order ideal, border basis	sing_1549.htm#IDX670
order ideal, border basis 	sing_1550.htm#IDX671
ordering	sing_2752.htm#IDX1140
ordering 	sing_2768.htm#IDX1174
ordering  	sing_2769.htm#IDX1177
orderings	sing_977.htm#SEC1034
orderings introduction	sing_976.htm#SEC1033
orderings, L	sing_984.htm#SEC1041
orderings, M	sing_981.htm#SEC1038
orderings, a	sing_983.htm#SEC1040
orderings, global	sing_978.htm#SEC1035
orderings, local	sing_979.htm#SEC1036
orderings, product	sing_982.htm#SEC1039
ordstr	sing_320.htm#SEC360
origin	sing_2471.htm#SEC2552
orthogonalize	sing_1221.htm#SEC1302
outer	sing_1192.htm#SEC1273
output	sing_41.htm#SEC71
outputting monomials	sing_405.htm#SEC445
p-adic numbers	sing_32.htm#SEC46
pFactor	sing_2357.htm#SEC2438
pIntersect	sing_508.htm#SEC562
pIntersectSyz	sing_509.htm#SEC563
package	sing_149.htm#SEC189
package declarations	sing_150.htm#SEC190
package related functions	sing_151.htm#SEC191
pairset	sing_2422.htm#SEC2503
par	sing_321.htm#SEC361
par2varRing	sing_1014.htm#SEC1095
paraConic	sing_1713.htm#SEC1794
paraPlaneCurve	sing_1707.htm#SEC1788
parallel computing	sing_2963.htm#IDX1267
parallel skeletons	sing_1080.htm#IDX547
parallel.lib	sing_1080.htm#SEC1161
parallelTestAND	sing_1084.htm#SEC1165
parallelTestOR	sing_1085.htm#SEC1166
parallelWaitAll	sing_1083.htm#SEC1164
parallelWaitFirst	sing_1082.htm#SEC1163
parallelWaitN	sing_1081.htm#SEC1162
parallel_lib	sing_1080.htm#SEC1161
parallelization	sing_1080.htm#IDX546
parallelization 	sing_1135.htm#IDX561
parallelization  	sing_1168.htm#IDX571
param	sing_1960.htm#SEC2041
parameter, as numbers	sing_144.htm#SEC184
parameter, default	sing_44.htm#SEC81
parameter, optional	sing_44.htm#SEC81
parameterSubstitute	sing_2606.htm#SEC2687
parametric annihilator	sing_537.htm#IDX336
parametric annihilator for variety	sing_601.htm#IDX366
parametric ideal	sing_1043.htm#IDX474
parametric ideal 	sing_1050.htm#IDX493
parametric ideal  	sing_1050.htm#IDX495
parametric ideal   	sing_1051.htm#IDX500
parametrization	sing_1698.htm#IDX713
parametrization 	sing_1702.htm#IDX722
parametrization  	sing_1960.htm#IDX904
parametrizeOrbit	sing_1702.htm#SEC1783
paraplanecurves.lib	sing_1704.htm#SEC1785
paraplanecurves_lib	sing_1704.htm#SEC1785
pardeg	sing_322.htm#SEC362
parstr	sing_323.htm#SEC363
part	sing_1628.htm#SEC1709
partOver	sing_1631.htm#SEC1712
partUnder	sing_1632.htm#SEC1713
partial fraction	sing_2929.htm#IDX1244
partial_molien	sing_2053.htm#SEC2134
partitions	sing_1298.htm#SEC1379
partitions 	sing_1298.htm#IDX615
path	sing_3002.htm#SEC3100
path integral	sing_1290.htm#IDX602
paths	sing_3002.htm#SEC3100
pause	sing_1077.htm#SEC1158
pdivi	sing_1045.htm#SEC1126
pdivi 	sing_1046.htm#IDX484
pdivi2	sing_1111.htm#SEC1192
permcol	sing_1204.htm#SEC1285
permrow	sing_1205.htm#SEC1286
permutationFromIntvec	sing_2549.htm#SEC2630
permutationToIntvec	sing_2550.htm#SEC2631
permutations	sing_1299.htm#IDX616
permutations, sum, max, min	sing_2672.htm#IDX1066
permute	sing_1299.htm#SEC1380
permute_L	sing_2260.htm#SEC2341
perron	sing_777.htm#SEC831
perron.lib	sing_776.htm#SEC830
perron_lib	sing_776.htm#SEC830
pfd	sing_2930.htm#SEC3011
pfd.lib	sing_2929.htm#SEC3010
pfdMat	sing_2938.htm#SEC3019
pfd_lib	sing_2929.htm#SEC3010
phindex.lib	sing_2706.htm#SEC2787
phindex_lib	sing_2706.htm#SEC2787
picksFormula	sing_2569.htm#SEC2650
pid	sing_361.htm#IDX239
plainInvariants	sing_1919.htm#SEC2000
planeCur	sing_1890.htm#SEC1971
plot	sing_2238.htm#SEC2319
plotRot	sing_2242.htm#SEC2323
plotRotated	sing_2241.htm#SEC2322
plotRotatedDirect	sing_2244.htm#SEC2325
plotRotatedList	sing_2243.htm#SEC2324
plotRotatedListFromSpecifyList	sing_2245.htm#SEC2326
plural	sing_1158.htm#IDX566
pmat	sing_1071.htm#SEC1152
pnormalf	sing_1046.htm#SEC1127
pnormalform	sing_1114.htm#SEC1195
pointid.lib	sing_1502.htm#SEC1583
pointid_lib	sing_1502.htm#SEC1583
polSol	sing_674.htm#SEC728
polSolFiniteRank	sing_675.htm#SEC729
pollTask	sing_1178.htm#SEC1259
poly	sing_152.htm#SEC192
poly (plural)	sing_442.htm#SEC482
poly declarations	sing_153.htm#SEC193
poly declarations (plural)	sing_443.htm#SEC483
poly expressions	sing_154.htm#SEC194
poly expressions (plural)	sing_444.htm#SEC484
poly operations	sing_155.htm#SEC195
poly operations (plural)	sing_445.htm#SEC485
poly related functions	sing_156.htm#SEC196
poly related functions (plural)	sing_446.htm#SEC486
poly2list	sing_587.htm#SEC641
poly2zdd	sing_2727.htm#SEC2808
polyInterpolation	sing_1303.htm#SEC1384
polyVars	sing_681.htm#SEC735
polybori	sing_2711.htm#IDX1099
polybori.lib	sing_2711.htm#SEC2792
polybori.lib 	sing_2711.htm#IDX1100
polybori_lib	sing_2711.htm#SEC2792
polyclass.lib	sing_2940.htm#SEC3021
polyclass_lib	sing_2940.htm#SEC3021
polylib.lib	sing_1086.htm#SEC1167
polylib_lib	sing_1086.htm#SEC1167
polymake.lib	sing_2560.htm#SEC2641
polymake_lib	sing_2560.htm#SEC2641
polynomial	sing_2779.htm#IDX1199
polynomial functions	sing_2944.htm#IDX1250
polynomial solutions	sing_668.htm#IDX388
polynomial, opposite	sing_361.htm#IDX231
polynomials	sing_2940.htm#IDX1247
polytope	sing_191.htm#SEC231
polytope 	sing_2560.htm#IDX970
polytopeViaInequalities	sing_2501.htm#SEC2582
polytopeViaPoints	sing_2502.htm#SEC2583
pos_def	sing_1232.htm#SEC1313
poset	sing_2665.htm#IDX1059
positiveOrthant	sing_2472.htm#SEC2553
posweight	sing_2033.htm#SEC2114
powSumSym	sing_1585.htm#SEC1666
power	sing_1193.htm#SEC1274
power set	sing_2674.htm#IDX1068
powerN	sing_2341.htm#SEC2422
powerX	sing_2350.htm#SEC2431
power_products	sing_2067.htm#SEC2148
powerpolyX	sing_2320.htm#SEC2401
powersums	sing_2443.htm#SEC2524
preComp	sing_1433.htm#SEC1514
preimage	sing_324.htm#SEC364
preimage 	sing_722.htm#IDX393
preimage (plural)	sing_479.htm#SEC519
preimage under a map between local rings, map between local rings, map between local and global rings	sing_1154.htm#IDX564
preimageLattice	sing_2897.htm#SEC2978
preimageLoc	sing_1154.htm#SEC1235
preimageNC	sing_724.htm#SEC778
prepEmbDiv	sing_1775.htm#SEC1856
prepMat	sing_2113.htm#SEC2194
prepRealclassify	sing_1881.htm#SEC1962
prepSV	sing_2255.htm#SEC2336
prepareAss	sing_1521.htm#SEC1602
presentTree	sing_1762.htm#SEC1843
presentation	sing_1384.htm#SEC1465
presolve.lib	sing_2132.htm#SEC2213
presolve_lib	sing_2132.htm#SEC2213
primL	sing_2345.htm#SEC2426
primList	sing_2344.htm#SEC2425
primRoot	sing_1566.htm#SEC1647
primTest	sing_1432.htm#SEC1513
primary decomposition	sing_1506.htm#IDX663
primary decomposition 	sing_1529.htm#IDX664
primary decomposition of modules	sing_1422.htm#IDX640
primary decomposition, numerical	sing_1685.htm#IDX707
primary_char0	sing_2057.htm#SEC2138
primary_char0_no_molien	sing_2059.htm#SEC2140
primary_char0_no_molien_random	sing_2064.htm#SEC2145
primary_char0_random	sing_2062.htm#SEC2143
primary_charp	sing_2058.htm#SEC2139
primary_charp_no_molien	sing_2060.htm#SEC2141
primary_charp_no_molien_random	sing_2065.htm#SEC2146
primary_charp_random	sing_2063.htm#SEC2144
primary_charp_without	sing_2061.htm#SEC2142
primary_charp_without_random	sing_2066.htm#SEC2147
primary_invariants	sing_2045.htm#SEC2126
primary_invariants_random	sing_2046.htm#SEC2127
primdec.lib	sing_1506.htm#SEC1587
primdecGTZ	sing_1508.htm#SEC1589
primdecGTZE	sing_1509.htm#SEC1590
primdecMon	sing_1421.htm#SEC1502
primdecSY	sing_1510.htm#SEC1591
primdecSYE	sing_1511.htm#SEC1592
primdecZ	sing_1530.htm#SEC1611
primdecZM	sing_1531.htm#SEC1612
primdec_lib	sing_1506.htm#SEC1587
primdecint.lib	sing_1529.htm#SEC1610
primdecint_lib	sing_1529.htm#SEC1610
prime	sing_325.htm#SEC365
primeClosure	sing_1465.htm#SEC1546
primecoeffs	sing_1038.htm#SEC1119
primefactors	sing_326.htm#SEC366
primes	sing_1033.htm#SEC1114
primitiv.lib	sing_1537.htm#SEC1618
primitiv_lib	sing_1537.htm#SEC1618
primitive	sing_1538.htm#SEC1619
primitive element	sing_1538.htm#IDX665
primitiveSpan	sing_2904.htm#SEC2985
primitive_extra	sing_1539.htm#SEC1620
primparam	sing_1914.htm#SEC1995
principal intersection	sing_502.htm#IDX320
print	sing_327.htm#SEC367
print 	sing_2632.htm#IDX994
print  	sing_2756.htm#IDX1149
print   	sing_2758.htm#IDX1154
print    	sing_2759.htm#IDX1155
print     	sing_2781.htm#IDX1203
print      	sing_2782.htm#IDX1204
printBetti	sing_1365.htm#SEC1446
printFreeModule	sing_1357.htm#SEC1438
printGraph	sing_1292.htm#SEC1373
printGraphG	sing_1801.htm#SEC1882
printGroup	sing_2885.htm#SEC2966
printHom	sing_1360.htm#SEC1441
printMatrix	sing_1356.htm#SEC1437
printModule	sing_1359.htm#SEC1440
printMoebius	sing_2671.htm#SEC2752
printNormalFormEquation	sing_2943.htm#SEC3024
printPoly	sing_2942.htm#SEC3023
printResolution	sing_1358.htm#SEC1439
printSheaf	sing_1789.htm#SEC1870
printStack	sing_1803.htm#SEC1884
printTask	sing_1173.htm#SEC1254
printVariety	sing_1781.htm#SEC1862
printf	sing_328.htm#SEC368
printlevel	sing_404.htm#SEC444
proc	sing_157.htm#SEC197
proc declaration	sing_158.htm#SEC198
proc expression	sing_159.htm#SEC199
procedure, ASCII help	sing_56.htm#IDX125
procedure, ASCII/Texinfo help	sing_58.htm#IDX127
procedure, texinfo help	sing_57.htm#IDX126
procedures, help string	sing_45.htm#SEC82
procedures, static	sing_43.htm#SEC78
procs with different argument types	sing_160.htm#SEC200
prodcrit	sing_2420.htm#SEC2501
product	sing_1034.htm#SEC1115
product 	sing_2764.htm#IDX1165
product  	sing_2786.htm#IDX1213
product variety, abstract variety	sing_1782.htm#IDX749
productOfProjectiveSpaces	sing_2965.htm#SEC3046
productVariety	sing_1782.htm#SEC1863
productgroup	sing_2906.htm#SEC2987
progress watch	sing_318.htm#IDX163
projectLattice	sing_2898.htm#SEC2979
projective bundle, abstract variety, sheaf, enumeration of conics	sing_1786.htm#IDX753
projective dimension	sing_778.htm#IDX402
projective limes	sing_32.htm#SEC46
projective space, abstract variety	sing_1785.htm#IDX752
projectiveBundle	sing_1786.htm#SEC1867
projectiveDimension	sing_779.htm#SEC833
projectiveSpace	sing_1785.htm#SEC1866
prompt	sing_15.htm#SEC21
prompt, option	sing_318.htm#IDX183
propagator	sing_1290.htm#IDX600
propagator 	sing_1293.htm#SEC1374
prot, option	sing_318.htm#IDX161
protocol of computations	sing_318.htm#IDX162
proximitymatrix	sing_1842.htm#SEC1923
prune	sing_329.htm#SEC369
pruneModule	sing_1391.htm#SEC1472
prwalk	sing_2950.htm#SEC3031
psigncnd	sing_2201.htm#SEC2282
puiseux2generators	sing_1972.htm#SEC2053
puiseuxExpansion	sing_2578.htm#SEC2659
pure tensor	sing_495.htm#IDX308
purelist	sing_789.htm#SEC843
purity	sing_778.htm#IDX404
purityFiltration	sing_780.htm#SEC834
purityTriang	sing_781.htm#SEC835
purityfiltration.lib	sing_778.htm#IDX397
purityfiltration_lib	sing_778.htm#IDX398
pushForward	sing_2923.htm#SEC3004
pwalk	sing_1314.htm#SEC1395
pyobject	sing_192.htm#SEC232
pyobject 	sing_2711.htm#IDX1102
pyobject declarations	sing_193.htm#SEC233
pyobject expressions	sing_194.htm#SEC234
pyobject operations	sing_195.htm#SEC235
pyobject related functions	sing_196.htm#SEC236
pyramid	sing_2805.htm#SEC2886
python_eval	sing_197.htm#SEC237
python_import	sing_198.htm#SEC238
python_run	sing_199.htm#SEC239
qbase	sing_2446.htm#SEC2527
qepcad	sing_2815.htm#SEC2896
qepcadsystem	sing_2816.htm#SEC2897
qhmatrix	sing_2031.htm#SEC2112
qhmoduli.lib	sing_1989.htm#SEC2070
qhmoduli_lib	sing_1989.htm#SEC2070
qhspectrum	sing_2018.htm#SEC2099
qhweight	sing_330.htm#SEC370
qmatrix.lib	sing_790.htm#SEC844
qmatrix_lib	sing_790.htm#SEC844
qminor	sing_792.htm#SEC846
qrds	sing_331.htm#SEC371
qring	sing_166.htm#SEC206
qring 	sing_422.htm#IDX296
qring (plural)	sing_447.htm#SEC487
qring declaration	sing_170.htm#SEC210
qring declaration (plural)	sing_448.htm#SEC488
qring related functions (plural)	sing_449.htm#SEC489
qring ring ideal 'factor ring'	sing_1163.htm#IDX570
qringNF, option	sing_318.htm#IDX164
qslimgb	sing_1013.htm#SEC1094
quadraticSieve	sing_2358.htm#SEC2439
quantMat	sing_791.htm#SEC845
quickclass	sing_1873.htm#SEC1954
quit	sing_394.htm#SEC434
quotSheaf	sing_1798.htm#SEC1879
quote	sing_332.htm#SEC372
quotient	sing_333.htm#SEC373
quotient (plural)	sing_480.htm#SEC520
quotientLatticeBasis	sing_2503.htm#SEC2584
quotientMain	sing_2212.htm#SEC2293
quotientMon	sing_1412.htm#SEC1493
rHRR	sing_1625.htm#SEC1706
rJanet	sing_1551.htm#SEC1632
rMacaulay	sing_1072.htm#SEC1153
rad_con	sing_1099.htm#SEC1180
radical	sing_1518.htm#SEC1599
radicalEHV	sing_1519.htm#SEC1600
radicalMemberShip	sing_2599.htm#SEC2680
radicalMon	sing_1413.htm#SEC1494
radicalZ	sing_1533.htm#SEC1614
randcharpoly	sing_2440.htm#SEC2521
randlinpoly	sing_2442.htm#SEC2523
random	sing_334.htm#SEC374
random 	sing_361.htm#IDX243
random  	sing_2653.htm#IDX1033
random   	sing_2654.htm#IDX1035
random number generator, seed	sing_361.htm#IDX241
random.lib	sing_1122.htm#SEC1203
randomBinomial	sing_1134.htm#SEC1215
randomCheck	sing_2271.htm#SEC2352
randomLast	sing_1133.htm#SEC1214
randomPoint	sing_2504.htm#SEC2585
randomPolyInT	sing_2608.htm#SEC2689
random_lib	sing_1122.htm#SEC1203
randomid	sing_1124.htm#SEC1205
randommat	sing_1125.htm#SEC1206
rank	sing_210.htm#IDX137
rank 	sing_335.htm#SEC375
rankSheaf	sing_1790.htm#SEC1871
ratSol	sing_676.htm#SEC730
ratgb.lib	sing_796.htm#IDX405
ratgb_lib	sing_796.htm#IDX406
rational curves, rational parametrization of rational curves.	sing_1707.htm#IDX734
rational functions	sing_889.htm#IDX437
rational normal curve, projection.	sing_1708.htm#IDX735
rational normal curve, projection. 	sing_1711.htm#IDX736
rational normal curve, projection.  	sing_1712.htm#IDX737
rational solutions	sing_668.htm#IDX389
rational univariate projection	sing_2440.htm#IDX966
rationalCurve	sing_1810.htm#SEC1891
rationalPointConic	sing_1709.htm#SEC1790
ratstd	sing_797.htm#SEC851
rays	sing_2505.htm#SEC2586
rcgs	sing_1119.htm#SEC1200
rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs	sing_1118.htm#IDX557
rcgs, crcgs, buildtree, cantreetoMaple, cantodiffcgs 	sing_1119.htm#IDX558
rcolon	sing_888.htm#SEC942
re2squ	sing_1686.htm#SEC1767
read	sing_336.htm#SEC376
readInputTXT	sing_2937.htm#SEC3018
readNmzData	sing_1493.htm#SEC1574
reading, option	sing_318.htm#IDX184
readline	sing_1.htm#IDX5
real	sing_28.htm#IDX74
real root isolation	sing_2186.htm#IDX941
real roots, univariate polynomial	sing_2447.htm#IDX968
real roots, univariate projection	sing_2431.htm#IDX964
real roots,sign conditions	sing_2199.htm#IDX944
realLLL	sing_2185.htm#SEC2266
realclassify	sing_2000.htm#SEC2081
realclassify.lib	sing_1999.htm#SEC2080
realclassify_lib	sing_1999.htm#SEC2080
realizationDim	sing_2572.htm#SEC2653
realizationDimPoly	sing_2574.htm#SEC2655
realizationMatroids.lib	sing_2571.htm#SEC2652
realizationMatroids_lib	sing_2571.htm#SEC2652
realmorsesplit	sing_2001.htm#SEC2082
realpoly	sing_1542.htm#SEC1623
realrad	sing_1544.htm#SEC1625
realrad.lib	sing_1541.htm#SEC1622
realrad_lib	sing_1541.htm#SEC1622
realzero	sing_1543.htm#SEC1624
recover.lib	sing_2168.htm#SEC2249
recover_lib	sing_2168.htm#SEC2249
recursive_boolean_poly	sing_2717.htm#SEC2798
recursive_from_boolean_poly	sing_2723.htm#SEC2804
redSB, option	sing_318.htm#IDX165
redTail, option	sing_318.htm#IDX167
redThrough, option	sing_318.htm#IDX168
redcgs.lib	sing_1107.htm#SEC1188
redcgs_lib	sing_1107.htm#SEC1188
redefine, option	sing_318.htm#IDX185
redspec	sing_1113.htm#SEC1194
reduce	sing_337.htm#SEC377
reduce 	sing_516.htm#IDX325
reduce  	sing_1045.htm#IDX482
reduce   	sing_1046.htm#IDX485
reduce (letterplace)	sing_813.htm#SEC867
reduce (plural)	sing_481.htm#SEC521
reduce (up to a bound)	sing_361.htm#IDX244
reduceIntChain	sing_1396.htm#SEC1477
reduced	sing_1044.htm#IDX479
reduced standard basis	sing_318.htm#IDX166
reduction	sing_2083.htm#SEC2164
reesclos.lib	sing_1545.htm#SEC1626
reesclos_lib	sing_1545.htm#SEC1626
reference	sing_200.htm#SEC240
reference declarations	sing_201.htm#SEC241
reference expressions	sing_202.htm#SEC242
reference operations	sing_205.htm#SEC245
reference related functions	sing_206.htm#SEC246
regCM	sing_1457.htm#SEC1538
regIdeal	sing_1438.htm#SEC1519
regMonCurve	sing_1441.htm#SEC1522
regionComplex	sing_2977.htm#SEC3058
regularity	sing_338.htm#SEC378
regularity 	sing_988.htm#SEC1050
regularity  	sing_1457.htm#IDX645
regularity   	sing_1458.htm#IDX646
reiffen	sing_556.htm#SEC610
rel_orbit_variety	sing_2076.htm#SEC2157
relations	sing_776.htm#IDX396
relativeInteriorPoint	sing_2506.htm#SEC2587
relative_orbit_variety	sing_2077.htm#SEC2158
relweight	sing_2032.htm#SEC2113
remainder	sing_2205.htm#SEC2286
remainderMain	sing_2213.htm#SEC2294
removeCone	sing_2524.htm#SEC2605
removepower	sing_1852.htm#SEC1933
repart	sing_339.htm#SEC379
replace	sing_2310.htm#SEC2391
representation, math objects	sing_974.htm#SEC1031
res	sing_340.htm#SEC380
resbinomial.lib	sing_1716.htm#IDX740
resbinomial_lib	sing_1716.htm#IDX741
reservedName	sing_341.htm#SEC381
resfunction	sing_1730.htm#SEC1811
resgraph.lib	sing_1748.htm#SEC1829
resgraph_lib	sing_1748.htm#SEC1829
resjung.lib	sing_1752.htm#SEC1833
resjung_lib	sing_1752.htm#SEC1833
reslist	sing_1744.htm#SEC1825
resolution	sing_161.htm#SEC201
resolution 	sing_778.htm#IDX403
resolution (plural)	sing_450.htm#SEC490
resolution declarations	sing_162.htm#SEC202
resolution declarations (plural)	sing_451.htm#SEC491
resolution expressions	sing_163.htm#SEC203
resolution expressions (plural)	sing_452.htm#SEC492
resolution graph	sing_1837.htm#IDX778
resolution related functions	sing_164.htm#SEC204
resolution related functions (plural)	sing_453.htm#SEC493
resolution, La Scala's method	sing_291.htm#SEC331
resolution, computation of	sing_340.htm#IDX187
resolution, hilbert-driven	sing_266.htm#SEC306
resolutionInLocalization	sing_1677.htm#SEC1758
resolutiongraph	sing_1838.htm#SEC1919
resolve	sing_1760.htm#SEC1841
resolve.lib	sing_1756.htm#SEC1837
resolve_lib	sing_1756.htm#SEC1837
resources.lib	sing_1135.htm#SEC1216
resources_lib	sing_1135.htm#SEC1216
restriction	sing_2646.htm#IDX1021
restriction 	sing_2662.htm#IDX1054
restriction  	sing_2663.htm#IDX1056
restriction of	sing_561.htm#IDX348
restrictionIdeal	sing_571.htm#SEC625
restrictionModule	sing_572.htm#SEC626
resultant	sing_305.htm#SEC345
resultant 	sing_342.htm#SEC382
reszeta.lib	sing_1769.htm#SEC1850
reszeta_lib	sing_1769.htm#SEC1850
return	sing_395.htm#SEC435
return type of procedures	sing_420.htm#SEC460
returnSB, option	sing_318.htm#IDX152
reverse	sing_2461.htm#SEC2542
reverse lexicographical ordering	sing_978.htm#IDX443
reynolds_molien	sing_2052.htm#SEC2133
rho	sing_2352.htm#SEC2433
rightInverse	sing_2290.htm#SEC2371
rightKernel	sing_2288.htm#SEC2369
rightModulo	sing_742.htm#SEC796
rightNF	sing_741.htm#SEC795
rightNFWeyl	sing_693.htm#SEC747
rightOre	sing_762.htm#SEC816
rightStd	sing_740.htm#SEC794
rightstd (letterplace)	sing_814.htm#SEC868
ring	sing_165.htm#SEC205
ring (plural)	sing_454.htm#SEC494
ring coefficients	sing_1161.htm#IDX568
ring coefficients 	sing_1162.htm#IDX569
ring declarations	sing_167.htm#SEC207
ring declarations (plural)	sing_455.htm#SEC495
ring operations	sing_169.htm#SEC209
ring operations (plural)	sing_456.htm#SEC496
ring related functions	sing_168.htm#SEC208
ring related functions (plural)	sing_457.htm#SEC497
ring theory	sing_863.htm#IDX418
ring, opposite	sing_361.htm#IDX228
ring, rings	sing_1108.htm#IDX549
ring.lib	sing_1140.htm#SEC1221
ring_cf	sing_210.htm#IDX138
ring_lib	sing_1140.htm#SEC1221
ring_list	sing_344.htm#SEC384
ring_variable	sing_2633.htm#IDX998
ring_variable 	sing_2634.htm#IDX1000
ring_variable  	sing_2635.htm#IDX1004
ring_variable   	sing_2636.htm#IDX1006
ringgb.lib	sing_2944.htm#SEC3025
ringgb.lib, functions for coefficient rings	sing_2944.htm#IDX1252
ringgb_lib	sing_2944.htm#SEC3025
ringlist	sing_343.htm#SEC383
ringlist (plural)	sing_482.htm#SEC522
ringtensor	sing_1152.htm#SEC1233
ringweights	sing_1153.htm#SEC1234
rinvar.lib	sing_2088.htm#SEC2169
rinvar_lib	sing_2088.htm#SEC2169
rmNmzFiles	sing_1498.htm#SEC1579
rm_unitcol	sing_1210.htm#SEC1291
rm_unitrow	sing_1209.htm#SEC1290
rmx	sing_2235.htm#SEC2316
rncAntiCanonicalMap	sing_1708.htm#SEC1789
rncItProjEven	sing_1712.htm#SEC1793
rncItProjOdd	sing_1711.htm#SEC1792
root of Bernstein-Sato polynomial	sing_537.htm#IDX337
rootIsolation	sing_2197.htm#SEC2278
rootIsolationNoPreprocessing	sing_2196.htm#SEC2277
rootIsolationPrimdec	sing_2198.htm#SEC2279
rootisolation.lib	sing_2186.htm#SEC2267
rootisolation_lib	sing_2186.htm#SEC2267
rootofUnity	sing_1155.htm#SEC1236
roots	sing_2206.htm#SEC2287
rootsMain	sing_2214.htm#SEC2295
rootsModp	sing_2334.htm#SEC2415
rootsmr.lib	sing_2431.htm#SEC2512
rootsmr_lib	sing_2431.htm#SEC2512
rootsur.lib	sing_2447.htm#SEC2528
rootsur_lib	sing_2447.htm#SEC2528
round	sing_2332.htm#SEC2413
rowShift	sing_210.htm#IDX141
rowShift 	sing_212.htm#SEC252
rowred	sing_1206.htm#SEC1287
rp, global ordering	sing_978.htm#IDX442
rstandard.lib	sing_1548.htm#SEC1629
rstandard_lib	sing_1548.htm#SEC1629
rswalk	sing_2962.htm#SEC3043
rtimer	sing_408.htm#SEC448
rvalue	sing_414.htm#SEC454
rvar	sing_345.htm#SEC385
rwalk	sing_2951.htm#SEC3032
rwalk.lib	sing_2949.htm#SEC3030
rwalk_lib	sing_2949.htm#SEC3030
sPiece	sing_2958.htm#SEC3039
sRes	sing_1362.htm#SEC1443
sa_poly_reduce	sing_525.htm#SEC579
sa_reduce	sing_524.htm#SEC578
sagbi	sing_1556.htm#SEC1637
sagbi basis	sing_1893.htm#IDX805
sagbi.lib	sing_1553.htm#SEC1634
sagbiAlg	sing_1886.htm#SEC1967
sagbiMod	sing_1887.htm#SEC1968
sagbiPart	sing_1557.htm#SEC1638
sagbiReduce	sing_1555.htm#SEC1636
sagbiSPoly	sing_1554.htm#SEC1635
sagbi_lib	sing_1553.htm#SEC1634
salida	sing_1741.htm#SEC1822
sameComponent	sing_2414.htm#SEC2495
sameQ	sing_2217.htm#SEC2298
sat	sing_1287.htm#SEC1368
satiety	sing_1440.htm#SEC1521
satstd	sing_2678.htm#SEC2759
saturation	sing_1287.htm#IDX594
saturation 	sing_1345.htm#IDX633
saturation  	sing_1455.htm#IDX643
saturation   	sing_1456.htm#IDX644
sba	sing_346.htm#SEC386
scalarProd	sing_514.htm#SEC568
scheme	sing_2796.htm#SEC2877
schubert.lib	sing_1779.htm#SEC1860
schubert_lib	sing_1779.htm#SEC1860
sdb, source code debugger	sing_66.htm#SEC103
second degree	sing_1059.htm#IDX525
second order deformation.	sing_2955.htm#IDX1260
secondary fan	sing_2560.htm#IDX972
secondary polytope	sing_2560.htm#IDX973
secondaryPolytope	sing_2562.htm#SEC2643
secondary_and_irreducibles_no_molien	sing_2073.htm#SEC2154
secondary_char0	sing_2068.htm#SEC2149
secondary_charp	sing_2070.htm#SEC2151
secondary_no_molien	sing_2071.htm#SEC2152
secondary_not_cohen_macaulay	sing_2074.htm#SEC2155
segre	sing_1580.htm#SEC1661
select	sing_1288.htm#SEC1369
select1	sing_1289.htm#SEC1370
semaphore	sing_361.htm#IDX248
semaphore 	sing_1139.htm#SEC1220
semaphores	sing_1135.htm#IDX563
semi-prime ideal	sing_863.htm#IDX423
semiCMcod2	sing_2029.htm#SEC2110
semiGroup	sing_1888.htm#SEC1969
semiMod	sing_1889.htm#SEC1970
semidiv	sing_2406.htm#SEC2487
semigroup	sing_1841.htm#SEC1922
semigroup 	sing_1845.htm#IDX785
semigroup of values	sing_1962.htm#IDX906
semigroupGenerator	sing_2507.htm#SEC2588
sep	sing_1528.htm#SEC1609
separateHNE	sing_1973.htm#SEC2054
separator	sing_1423.htm#SEC1504
serreRelations	sing_836.htm#SEC890
set	sing_2628.htm#IDX984
set 	sing_2731.htm#SEC2812
set, intersectionSet, union, complement, equality, isEqual	sing_2730.htm#IDX1122
setBaseMultigrading	sing_2878.htm#SEC2959
setLetterplaceAttributes	sing_883.htm#SEC937
setLinearForms	sing_2508.htm#SEC2589
setModuleGrading	sing_2890.htm#SEC2971
setMultiplicity	sing_2509.htm#SEC2590
setNmzDataPath	sing_1495.htm#SEC1576
setNmzExecPath	sing_1491.htm#SEC1572
setNmzFilename	sing_1494.htm#SEC1575
setNmzOption	sing_1488.htm#SEC1569
setUniformizingParameter	sing_2618.htm#SEC2699
set_is_injective	sing_2394.htm#SEC2475
setcores	sing_1137.htm#SEC1218
setenv	sing_361.htm#IDX251
setglobalrings	sing_1108.htm#SEC1189
setinitials	sing_2806.htm#SEC2887
setring	sing_347.htm#SEC387
sets.lib	sing_2730.htm#SEC2811
sets_lib	sing_2730.htm#SEC2811
sh	sing_361.htm#IDX253
shared	sing_200.htm#SEC240
shared declarations	sing_203.htm#SEC243
shared expressions	sing_204.htm#SEC244
shared operations	sing_205.htm#SEC245
shared related functions	sing_206.htm#SEC246
sheaf cohomology	sing_1818.htm#IDX766
sheafCoh	sing_1824.htm#SEC1905
sheafCohBGG	sing_1822.htm#SEC1903
sheafCohBGG2	sing_1823.htm#SEC1904
sheafcoh.lib	sing_1818.htm#SEC1899
sheafcoh_lib	sing_1818.htm#SEC1899
short	sing_405.htm#SEC445
show	sing_1073.htm#SEC1154
showBO	sing_1761.htm#SEC1842
showDataTypes	sing_1763.htm#SEC1844
showNmzOptions	sing_1489.htm#SEC1570
showNuminvs	sing_1486.htm#SEC1567
showgrades	sing_783.htm#SEC837
showrecursive	sing_1074.htm#SEC1155
signal handler	sing_3000.htm#SEC3098
signatureBrieskorn	sing_2038.htm#SEC2119
signatureL	sing_2707.htm#SEC2788
signatureLqf	sing_2708.htm#SEC2789
signatureNemethi	sing_2040.htm#SEC2121
signaturePuiseux	sing_2039.htm#SEC2120
signcnd	sing_2200.htm#SEC2281
signcond.lib	sing_2199.htm#SEC2280
signcond_lib	sing_2199.htm#SEC2280
simplePrune	sing_1400.htm#SEC1481
simplesolver	sing_2119.htm#SEC2200
simplex	sing_348.htm#SEC388
simplexOut	sing_2155.htm#SEC2236
simplify	sing_349.htm#SEC389
simplifyRat	sing_688.htm#SEC742
sing.lib	sing_2005.htm#SEC2086
sing4ti2.lib	sing_1559.htm#SEC1640
sing4ti2_lib	sing_1559.htm#SEC1640
sing_lib	sing_2005.htm#SEC2086
singular locus of D-module	sing_668.htm#IDX383
singularities	sing_1855.htm#IDX796
singularities 	sing_1882.htm#IDX800
singularities  	sing_1931.htm#IDX808
singularities   	sing_1932.htm#IDX819
singularities    	sing_1933.htm#IDX822
singularities     	sing_1934.htm#IDX825
singularities      	sing_1935.htm#IDX828
singularities       	sing_1936.htm#IDX832
singularities        	sing_1937.htm#IDX836
singularities         	sing_1938.htm#IDX842
singularities          	sing_1939.htm#IDX850
singularities           	sing_1940.htm#IDX856
singularities            	sing_1941.htm#IDX864
singularities             	sing_1942.htm#IDX874
singularities              	sing_2036.htm#IDX928
singularities, resolution of	sing_961.htm#SEC1018
singularity	sing_1874.htm#SEC1955
singularrc	sing_20.htm#IDX73
size	sing_350.htm#SEC390
size 	sing_422.htm#IDX295
skewmat	sing_1194.htm#SEC1275
sleep	sing_356.htm#SEC396
slimgb	sing_351.htm#SEC391
slimgb 	sing_938.htm#SEC995
slimgb (plural)	sing_483.htm#SEC523
slocus	sing_2017.htm#SEC2098
smaller	sing_2769.htm#IDX1175
smatrix	sing_171.htm#SEC211
smith	sing_2299.htm#SEC2380
smithNormalForm	sing_2926.htm#SEC3007
solutionsMod2	sing_2349.htm#SEC2430
solve	sing_282.htm#SEC322
solve 	sing_1059.htm#IDX526
solve  	sing_2149.htm#SEC2230
solve a linear equation system A*x = b via the LU-decomposition of A	sing_294.htm#SEC334
solve.lib	sing_2147.htm#SEC2228
solveTInitialFormPar	sing_2602.htm#SEC2683
solve_IP	sing_1340.htm#SEC1421
solve_lib	sing_2147.htm#SEC2228
solvelinearpart	sing_2142.htm#SEC2223
solving	sing_2168.htm#IDX939
sort	sing_1035.htm#SEC1116
sort 	sing_2774.htm#IDX1185
sortIntvec	sing_592.htm#SEC646
sortandmap	sing_2143.htm#SEC2224
sortier	sing_2087.htm#SEC2168
sortvars	sing_2144.htm#SEC2225
sortvec	sing_352.htm#SEC392
source	sing_1378.htm#SEC1459
source code debugger, sdb	sing_66.htm#SEC103
spaceCur	sing_1891.htm#SEC1972
spadd	sing_1945.htm#SEC2026
span	sing_2510.htm#SEC2591
sparseHomogIdeal	sing_1131.htm#SEC1212
sparseInterpolation	sing_1307.htm#SEC1388
sparseid	sing_1126.htm#SEC1207
sparsemat	sing_1128.htm#SEC1209
sparsematrix	sing_1127.htm#SEC1208
sparsepoly	sing_1129.htm#SEC1210
sparsetriag	sing_1130.htm#SEC1211
spcurve.lib	sing_2025.htm#SEC2106
spcurve_lib	sing_2025.htm#SEC2106
special characters, non-english	sing_411.htm#IDX288
specification	sing_1113.htm#IDX552
spectral pairs	sing_1931.htm#IDX817
spectral pairs 	sing_1938.htm#IDX849
spectral pairs  	sing_1940.htm#IDX863
spectral pairs   	sing_1941.htm#IDX872
spectral pairs    	sing_1953.htm#IDX888
spectral pairs     	sing_1955.htm#IDX899
spectralNeg	sing_1771.htm#SEC1852
spectrum	sing_1931.htm#IDX816
spectrum 	sing_1937.htm#SEC2018
spectrum  	sing_1937.htm#IDX841
spectrum   	sing_1938.htm#IDX848
spectrum    	sing_1939.htm#IDX855
spectrum     	sing_1940.htm#IDX862
spectrum      	sing_1941.htm#IDX871
spectrum       	sing_1953.htm#IDX887
spectrum        	sing_1955.htm#IDX898
spectrum         	sing_2036.htm#IDX930
spectrum.lib	sing_2035.htm#SEC2116
spectrum_lib	sing_2035.htm#SEC2116
spectrumnd	sing_2036.htm#SEC2117
spgamma	sing_1952.htm#SEC2033
spgeomgenus	sing_1951.htm#SEC2032
spissemicont	sing_1948.htm#SEC2029
split	sing_1075.htm#SEC1156
splitPolygon	sing_2564.htm#SEC2645
splitring	sing_1540.htm#SEC1621
splitting	sing_1431.htm#SEC1512
spmilnor	sing_1950.htm#SEC2031
spmul	sing_1947.htm#SEC2028
spnf	sing_1236.htm#SEC1317
spoly	sing_2417.htm#SEC2498
sppairs	sing_1938.htm#SEC2019
sppnf	sing_1943.htm#SEC2024
sppprint	sing_1944.htm#SEC2025
spprint	sing_1237.htm#SEC1318
sprintf	sing_354.htm#SEC394
spsemicont	sing_1949.htm#SEC2030
spsub	sing_1946.htm#SEC2027
sqfrNorm	sing_2207.htm#SEC2288
sqfrNormMain	sing_2215.htm#SEC2296
sqr	sing_2329.htm#SEC2410
sqrfree	sing_353.htm#SEC393
squareRoot	sing_2348.htm#SEC2429
squarefree	sing_1974.htm#SEC2055
sres	sing_355.htm#SEC395
ssi	sing_933.htm#SEC990
stabilizer	sing_2744.htm#SEC2825
stack, moduli space of stable maps	sing_1803.htm#IDX757
stack, moduli space of stable maps, rational curves	sing_1802.htm#IDX756
stackNets	sing_2705.htm#SEC2786
staircase	sing_2220.htm#SEC2301
standard	sing_2424.htm#SEC2505
standard bases, saturation	sing_2678.htm#IDX1071
standard bases.	sing_2677.htm#IDX1070
standard.lib	sing_1012.htm#IDX470
standard_lib	sing_1012.htm#IDX471
stanleyreisner.lib	sing_2953.htm#SEC3034
stanleyreisner_lib	sing_2953.htm#SEC3034
startNmz	sing_1497.htm#SEC1578
startTasks	sing_1174.htm#SEC1255
static procedures	sing_43.htm#SEC78
status	sing_356.htm#SEC396
std	sing_357.htm#SEC397
std 	sing_936.htm#SEC993
std (letterplace)	sing_815.htm#SEC869
std (plural)	sing_484.htm#SEC524
stdfglm	sing_358.htm#SEC398
stdhilb	sing_359.htm#SEC399
stdlocus	sing_1056.htm#SEC1137
stopTask	sing_1175.htm#SEC1256
storeActionOnOrbitConeIndices	sing_2548.htm#SEC2629
strand	sing_2978.htm#SEC3059
stratify	sing_2114.htm#SEC2195
stratify.lib	sing_2112.htm#SEC2193
stratify_lib	sing_2112.htm#SEC2193
string	sing_172.htm#SEC212
string 	sing_422.htm#IDX298
string  	sing_2756.htm#IDX1148
string   	sing_2758.htm#IDX1153
string    	sing_2759.htm#IDX1156
string     	sing_2781.htm#IDX1202
string      	sing_2782.htm#IDX1205
string declarations	sing_173.htm#SEC213
string expressions	sing_174.htm#SEC214
string operations	sing_176.htm#SEC216
string related functions	sing_177.htm#SEC217
string type cast	sing_175.htm#SEC215
stripHNE	sing_1971.htm#SEC2052
structure	sing_2778.htm#IDX1196
sturm	sing_2457.htm#SEC2538
sturmha	sing_2459.htm#SEC2540
sturmhaseq	sing_2460.htm#SEC2541
sturmquery	sing_2435.htm#SEC2516
sturmseq	sing_2458.htm#SEC2539
sublists	sing_2674.htm#SEC2755
submat	sing_1195.htm#SEC1276
subquotient	sing_1370.htm#SEC1451
subrInterred	sing_1104.htm#SEC1185
subset	sing_1110.htm#SEC1191
subset_sum01	sing_2378.htm#SEC2459
subset_sum02	sing_2379.htm#SEC2460
subst	sing_360.htm#SEC400
subst (letterplace)	sing_816.htm#SEC870
subst (plural)	sing_485.htm#SEC525
substAll	sing_2169.htm#SEC2250
substitute	sing_1103.htm#SEC1184
sufficientlyPositiveMultidegree	sing_2969.htm#SEC3050
sugarCrit, option	sing_318.htm#IDX169
sum	sing_1036.htm#SEC1117
sum 	sing_2761.htm#IDX1159
sum  	sing_2783.htm#IDX1207
sum_of_powers	sing_1584.htm#SEC1665
sumlist	sing_1743.htm#SEC1824
sumofquotients	sing_1811.htm#SEC1892
super-commutative algebras	sing_798.htm#SEC852
superCommutative	sing_739.htm#SEC793
super_increasing_knapsack	sing_2390.htm#SEC2471
surf.lib	sing_2237.htm#SEC2318
surf_lib	sing_2237.htm#SEC2318
surfacesignature.lib	sing_2037.htm#SEC2118
surfacesignature_lib	sing_2037.htm#SEC2118
surfer	sing_1.htm#IDX8
surfer 	sing_2239.htm#SEC2320
surfex	sing_1.htm#IDX7
surfex.lib	sing_2240.htm#SEC2321
surfex_lib	sing_2240.htm#SEC2321
suspend	sing_356.htm#SEC396
swalk	sing_2961.htm#SEC3042
swalk.lib	sing_2960.htm#SEC3041
swalk_lib	sing_2960.htm#SEC3041
swap	sing_1878.htm#SEC1959
swap 	sing_2635.htm#IDX1002
switch	sing_416.htm#SEC456
switchRingsAndComputeInitialIdeal	sing_2623.htm#SEC2704
syModStd	sing_1569.htm#SEC1650
symExt	sing_2968.htm#SEC3049
symNsym	sing_1578.htm#SEC1659
sym_gauss	sing_1220.htm#SEC1301
symm	sing_1577.htm#SEC1658
symmStd	sing_1568.htm#SEC1649
symmat	sing_1196.htm#SEC1277
symmetric basis	sing_1212.htm#IDX574
symmetric power	sing_1214.htm#IDX576
symmetric product	sing_1659.htm#IDX698
symmetricBasis	sing_1212.htm#SEC1293
symmetricPower	sing_1214.htm#SEC1295
symmetricPowerSheaf	sing_1797.htm#SEC1878
symmetries	sing_2740.htm#IDX1128
symmfunc	sing_2444.htm#SEC2525
symodstd.lib	sing_1563.htm#SEC1644
symodstd_lib	sing_1563.htm#SEC1644
sympower	sing_2108.htm#SEC2189
symsignature	sing_2434.htm#SEC2515
syndrome	sing_2267.htm#SEC2348
sysBin	sing_2265.htm#SEC2346
sysCRHT	sing_2262.htm#SEC2343
sysCRHTMindist	sing_2263.htm#SEC2344
sysFL	sing_2278.htm#SEC2359
sysNewton	sing_2264.htm#SEC2345
sysQE	sing_2268.htm#SEC2349
sys_code	sing_2259.htm#SEC2340
system	sing_361.htm#SEC401
system, --	sing_361.htm#IDX278
system, --long_option_name	sing_361.htm#IDX281
system, --long_option_name=value	sing_361.htm#IDX283
system, HC	sing_361.htm#IDX214
system, LLL	sing_361.htm#IDX218
system, Singular	sing_361.htm#IDX257
system, SingularLib	sing_361.htm#IDX259
system, absFact	sing_361.htm#IDX191
system, alarm	sing_361.htm#IDX190
system, blackbox	sing_361.htm#IDX192
system, bracket	sing_361.htm#IDX197
system, browsers	sing_361.htm#IDX196
system, complexNearZero	sing_361.htm#IDX199
system, contributors	sing_361.htm#IDX201
system, cpu	sing_361.htm#IDX203
system, cpu 	sing_361.htm#IDX277
system, denom_list	sing_361.htm#IDX205
system, eigenvals	sing_361.htm#IDX206
system, env	sing_361.htm#IDX207
system, executable	sing_361.htm#IDX209
system, getPrecDigits	sing_361.htm#IDX212
system, getenv	sing_361.htm#IDX211
system, gmsnf	sing_361.htm#IDX213
system, hessenberg	sing_361.htm#IDX215
system, install	sing_361.htm#IDX217
system, nblocks	sing_361.htm#IDX221
system, nc_hilb	sing_361.htm#IDX223
system, neworder	sing_361.htm#IDX224
system, newstruct	sing_361.htm#IDX225
system, opp	sing_361.htm#IDX226
system, oppose	sing_361.htm#IDX229
system, pcvBasis	sing_361.htm#IDX238
system, pcvCV2P	sing_361.htm#IDX236
system, pcvDim	sing_361.htm#IDX237
system, pcvLAddL	sing_361.htm#IDX232
system, pcvMinDeg	sing_361.htm#IDX234
system, pcvP2CV	sing_361.htm#IDX235
system, pcvPMulL	sing_361.htm#IDX233
system, pid	sing_361.htm#IDX240
system, random	sing_361.htm#IDX242
system, reserve	sing_361.htm#IDX246
system, reservedLink	sing_361.htm#IDX247
system, semaphore	sing_361.htm#IDX249
system, semic	sing_361.htm#IDX250
system, setenv	sing_361.htm#IDX252
system, sh	sing_361.htm#IDX254
system, shrinktest	sing_361.htm#IDX255
system, spadd	sing_361.htm#IDX260
system, spectrum	sing_361.htm#IDX261
system, spmul	sing_361.htm#IDX262
system, std_syz	sing_361.htm#IDX263
system, tensorModuleMult	sing_361.htm#IDX264
system, twostd	sing_361.htm#IDX265
system, uname	sing_361.htm#IDX268
system, verifyGB	sing_361.htm#IDX271
system, version	sing_361.htm#IDX274
system, with	sing_361.htm#IDX275
systemOfParametersOfLocalization	sing_1674.htm#SEC1755
systhreads.lib	sing_2963.htm#SEC3044
systhreads_lib	sing_2963.htm#SEC3044
syz	sing_362.htm#SEC402
syz (letterplace)	sing_817.htm#SEC871
syz (plural)	sing_486.htm#SEC526
tDetropicalise	sing_2604.htm#SEC2685
tInitialForm	sing_2588.htm#SEC2669
tInitialFormPar	sing_2600.htm#SEC2681
tInitialFormParMax	sing_2601.htm#SEC2682
tInitialIdeal	sing_2589.htm#SEC2670
tab	sing_1076.htm#SEC1157
tail	sing_2413.htm#SEC2494
tame polynomial	sing_1953.htm#IDX880
tame polynomial 	sing_1954.htm#IDX890
tame polynomial  	sing_1955.htm#IDX891
tangentGens	sing_1699.htm#SEC1780
tangentcone	sing_2024.htm#SEC2105
target	sing_1377.htm#SEC1458
task	sing_1168.htm#IDX573
tasks.lib	sing_1168.htm#SEC1249
tasks_lib	sing_1168.htm#SEC1249
tateProdCplxNegGrad.lib	sing_2964.htm#SEC3045
tateProdCplxNegGrad_lib	sing_2964.htm#SEC3045
tateResolution	sing_2970.htm#SEC3051
tau_es	sing_1926.htm#SEC2007
tau_es2	sing_1849.htm#SEC1930
tdCf	sing_1613.htm#SEC1694
tdFactor	sing_1615.htm#SEC1696
tdProj	sing_1618.htm#SEC1699
tdTerms	sing_1614.htm#SEC1695
teach_lpGkDim	sing_868.htm#SEC922
teach_lpKDim	sing_830.htm#SEC884
teach_lpKDimCheck	sing_828.htm#SEC882
teach_lpSickleDim	sing_833.htm#SEC887
teachstd.lib	sing_2411.htm#SEC2492
teachstd_lib	sing_2411.htm#SEC2492
template.lib	sing_55.htm#IDX120
template.lib 	sing_55.htm#IDX123
template_lib	sing_55.htm#SEC92
template_lib 	sing_55.htm#IDX121
tensor	sing_363.htm#SEC403
tensor 	sing_495.htm#IDX312
tensor algebra	sing_872.htm#IDX426
tensorFreeModule	sing_1389.htm#SEC1470
tensorFreemodMod	sing_1388.htm#SEC1469
tensorMatrix	sing_1385.htm#SEC1466
tensorMod	sing_1335.htm#SEC1416
tensorModFreemod	sing_1387.htm#SEC1468
tensorModule	sing_1386.htm#SEC1467
tensorProduct	sing_1390.htm#SEC1471
tensorSheaf	sing_1796.htm#SEC1877
term orderings	sing_977.htm#SEC1034
term orderings introduction	sing_976.htm#SEC1033
testFraction	sing_760.htm#SEC814
testLift	sing_884.htm#SEC938
testLocData	sing_757.htm#SEC811
testNCfac	sing_652.htm#SEC706
testNcfrac	sing_706.htm#SEC760
testNcfracExamples	sing_707.htm#SEC761
testNcloc	sing_718.htm#SEC772
testNclocExamples	sing_719.htm#SEC773
testOlga	sing_774.htm#SEC828
testOlgaExamples	sing_775.htm#SEC829
testParametrization	sing_1714.htm#SEC1795
testPointConic	sing_1715.htm#SEC1796
testPrimary	sing_1516.htm#SEC1597
testPrimaryE	sing_1517.htm#SEC1598
testSyz	sing_885.htm#SEC939
testZero	sing_2947.htm#SEC3028
tetrahedronGroup	sing_861.htm#SEC915
tex	sing_2226.htm#SEC2307
texDrawBasic	sing_2595.htm#SEC2676
texDrawNewtonSubdivision	sing_2597.htm#SEC2678
texDrawTriangulation	sing_2598.htm#SEC2679
texDrawTropical	sing_2596.htm#SEC2677
texMatrix	sing_2594.htm#SEC2675
texNumber	sing_2592.htm#SEC2673
texPolynomial	sing_2593.htm#SEC2674
texcoef	sing_2307.htm#SEC2388
texdemo	sing_2227.htm#SEC2308
texfactorize	sing_2228.htm#SEC2309
texmap	sing_2229.htm#SEC2310
texname	sing_2230.htm#SEC2311
texobj	sing_2231.htm#SEC2312
texpoly	sing_2232.htm#SEC2313
texproc	sing_2233.htm#SEC2314
texring	sing_2234.htm#SEC2315
the first alternative algorithm	sing_1312.htm#IDX621
three_elements	sing_2397.htm#SEC2478
timeFactorize	sing_1040.htm#SEC1121
timeStd	sing_1039.htm#SEC1120
timer	sing_406.htm#SEC446
timer resolution, setting the	sing_361.htm#IDX284
timestep	sing_2809.htm#SEC2890
tjurina	sing_2020.htm#SEC2101
tmatrix	sing_1941.htm#SEC2022
todd	sing_1610.htm#SEC1691
toddE	sing_1611.htm#SEC1692
toddPoly	sing_1624.htm#SEC1705
tolessvars	sing_2141.htm#SEC2222
topChernClass	sing_1793.htm#SEC1874
topological invariants	sing_1837.htm#IDX776
topological invariants 	sing_1844.htm#IDX783
topological invariants  	sing_1845.htm#IDX787
topological invariants   	sing_1846.htm#IDX791
topological invariants    	sing_1847.htm#IDX795
toric ideals	sing_992.htm#SEC1054
toric ring	sing_1475.htm#IDX662
toric.lib	sing_1570.htm#SEC1651
toric_ideal	sing_1571.htm#SEC1652
toric_lib	sing_1570.htm#SEC1651
toric_std	sing_1572.htm#SEC1653
torus	sing_2105.htm#SEC2186
torusInvariants	sing_1481.htm#SEC1562
torusrep	sing_2106.htm#SEC2187
torusreynolds	sing_2111.htm#SEC2192
total divisors	sing_495.htm#IDX309
total multiplicities	sing_1837.htm#IDX779
totalChernClass	sing_1791.htm#SEC1872
totalSegreClass	sing_1794.htm#SEC1875
totalmultiplicities	sing_1839.htm#SEC1920
trace	sing_364.htm#SEC404
tracemult	sing_2438.htm#SEC2519
transpose	sing_365.htm#SEC405
trapezoid	sing_2803.htm#SEC2884
triMNewton	sing_2167.htm#SEC2248
triagmatrix	sing_1132.htm#SEC1213
triang.lib	sing_2160.htm#SEC2241
triangL	sing_2161.htm#SEC2242
triangL_solve	sing_2158.htm#SEC2239
triangLf_solve	sing_2156.htm#SEC2237
triangLfak	sing_2162.htm#SEC2243
triangM	sing_2163.htm#SEC2244
triangMH	sing_2164.htm#SEC2245
triangM_solve	sing_2157.htm#SEC2238
triang_lib	sing_2160.htm#SEC2241
triang_solve	sing_2159.htm#SEC2240
triangularGroup	sing_862.htm#SEC916
triangulations	sing_2561.htm#SEC2642
tropical curves	sing_2575.htm#IDX976
tropical geometry	sing_1290.htm#IDX595
tropical geometry 	sing_2617.htm#IDX978
tropical mirror symmetry	sing_1290.htm#IDX597
tropical polynomials	sing_2575.htm#IDX977
tropical varieties	sing_2617.htm#IDX979
tropical.lib	sing_2575.htm#SEC2656
tropicalCurve	sing_2580.htm#SEC2661
tropicalJInvariant	sing_2583.htm#SEC2664
tropicalLifting	sing_2576.htm#SEC2657
tropicalLinkNewton	sing_2625.htm#SEC2706
tropicalNewton.lib	sing_2617.htm#SEC2698
tropicalNewton_lib	sing_2617.htm#SEC2698
tropicalPointNewton	sing_2622.htm#SEC2703
tropicalSubst	sing_2607.htm#SEC2688
tropicalVariety	sing_2614.htm#SEC2695
tropicalVarietyNewton	sing_2624.htm#SEC2705
tropical_lib	sing_2575.htm#SEC2656
tropicalise	sing_2586.htm#SEC2667
tropicaliseSet	sing_2587.htm#SEC2668
truncate	sing_1819.htm#SEC1900
truncateCoker	sing_2967.htm#SEC3048
truncateFast	sing_1820.htm#SEC1901
truncateM	sing_2966.htm#SEC3047
truncated module	sing_1819.htm#IDX767
truncated module 	sing_1820.htm#IDX768
twalk	sing_1311.htm#SEC1392
twist	sing_2975.htm#SEC3056
two-sided	sing_495.htm#IDX310
two-sided Groebner basis	sing_495.htm#IDX311
twostd	sing_361.htm#IDX266
twostd (letterplace)	sing_818.htm#SEC872
twostd (plural)	sing_487.htm#SEC527
type	sing_366.htm#SEC406
type B	sing_2651.htm#IDX1029
type D	sing_2652.htm#IDX1031
type,custom	sing_184.htm#SEC224
type2arr	sing_2629.htm#SEC2710
typecasting	sing_2629.htm#IDX985
typecasting 	sing_2630.htm#IDX987
typecasting  	sing_2631.htm#IDX990
typeof	sing_367.htm#SEC407
u	sing_2795.htm#SEC2876
uname	sing_361.htm#IDX267
unbounded_knapsack	sing_2380.htm#SEC2461
union	sing_2732.htm#SEC2813
unipotent groups	sing_1698.htm#IDX711
uniquePoint	sing_2511.htm#SEC2592
unitMatrix	sing_2192.htm#SEC2273
unitMatrix2	sing_2127.htm#SEC2208
unitmat	sing_1197.htm#SEC1278
univariate	sing_368.htm#SEC408
univarpoly	sing_2445.htm#SEC2526
universal	sing_2775.htm#IDX1188
universal 	sing_2776.htm#IDX1190
universal derivation	sing_2751.htm#IDX1139
unknown syndrome	sing_1008.htm#SEC1084
unset	sing_279.htm#SEC319
untyped definitions	sing_88.htm#SEC128
untyped definitions 	sing_427.htm#SEC467
updatePairs	sing_2423.htm#SEC2504
ures_solve	sing_2150.htm#SEC2231
uressolve	sing_369.htm#SEC409
usage, option	sing_318.htm#IDX186
used environment variables	sing_3002.htm#SEC3100
user interface, Emacs	sing_21.htm#SEC28
vStd	sing_1903.htm#SEC1984
val	sing_2619.htm#SEC2700
valvars	sing_2145.htm#SEC2226
vandermonde	sing_370.htm#SEC410
vanishId	sing_2277.htm#SEC2358
vanishing polynomial	sing_2944.htm#IDX1248
var	sing_371.htm#SEC411
varMat	sing_2633.htm#SEC2714
varNum	sing_2634.htm#SEC2715
variables	sing_372.htm#SEC412
variables 	sing_2633.htm#IDX997
variables  	sing_2634.htm#IDX999
variables   	sing_2635.htm#IDX1003
variables    	sing_2636.htm#IDX1005
variablesSorted	sing_533.htm#SEC587
variablesStandard	sing_532.htm#SEC586
vars2pars	sing_683.htm#SEC737
varsigns	sing_2450.htm#SEC2531
varstr	sing_373.htm#SEC413
vdim	sing_374.htm#SEC414
vdim (letterplace)	sing_819.htm#SEC873
vdim (plural)	sing_488.htm#SEC528
vec2poly	sing_515.htm#SEC569
vecFieldToMatrix	sing_2988.htm#SEC3069
vector	sing_178.htm#SEC218
vector declarations	sing_179.htm#SEC219
vector expressions	sing_180.htm#SEC220
vector operations	sing_181.htm#SEC221
vector related functions	sing_182.htm#SEC222
verify	sing_2441.htm#SEC2522
verify Groebner base	sing_361.htm#IDX270
verifyGB	sing_361.htm#IDX272
veronese	sing_2170.htm#SEC2251
versal	sing_1921.htm#SEC2002
version	sing_361.htm#IDX273
vertices	sing_2527.htm#SEC2608
vfilt	sing_1939.htm#SEC2020
view	sing_2297.htm#SEC2378
visualize	sing_2794.htm#SEC2875
voice	sing_409.htm#SEC449
vwfilt	sing_1940.htm#SEC2021
wUnit	sing_2335.htm#SEC2416
waitAllTasks	sing_1177.htm#SEC1258
waitTasks	sing_1176.htm#SEC1257
waitall	sing_375.htm#SEC415
waitfirst	sing_376.htm#SEC416
walk, groebner	sing_1309.htm#IDX617
walk, groebner 	sing_2872.htm#IDX1239
walk, groebner  	sing_2949.htm#IDX1253
walk, groebner   	sing_2960.htm#IDX1265
warkedPreimageStd	sing_1676.htm#SEC1757
warn, option	sing_70.htm#SEC110
warn, option 	sing_318.htm#IDX151
watchdog	sing_1037.htm#SEC1118
wedge	sing_377.htm#SEC417
weierstr.lib	sing_2426.htm#SEC2507
weierstrDiv	sing_2427.htm#SEC2508
weierstrPrep	sing_2428.htm#SEC2509
weierstr_lib	sing_2426.htm#SEC2507
weierstrassForm	sing_2584.htm#SEC2665
weight	sing_378.htm#SEC418
weight filtration	sing_1931.htm#IDX813
weight filtration 	sing_1938.htm#IDX847
weight filtration  	sing_1940.htm#IDX861
weight filtration   	sing_1941.htm#IDX869
weight filtration    	sing_1953.htm#IDX885
weight filtration     	sing_1955.htm#IDX896
weightKB	sing_379.htm#SEC419
weightM, option	sing_318.htm#IDX170
weighted lexicographical ordering	sing_978.htm#IDX450
weighted reverse lexicographical ordering	sing_978.htm#IDX448
weightedRing	sing_732.htm#SEC786
whichvariable	sing_2449.htm#SEC2530
while	sing_396.htm#SEC436
withDim	sing_210.htm#IDX145
withHilb	sing_210.htm#IDX143
withMult	sing_210.htm#IDX146
withRes	sing_210.htm#IDX144
withSB	sing_210.htm#IDX142
wp, global ordering	sing_978.htm#IDX449
write	sing_380.htm#SEC420
writeBertiniInput	sing_2176.htm#SEC2257
writeNmzData	sing_1492.htm#SEC1573
writeNmzPaths	sing_1496.htm#SEC1577
writing monomials	sing_405.htm#SEC445
ws, local ordering	sing_979.htm#IDX460
wurzel	sing_2317.htm#SEC2398
xchange	sing_2311.htm#SEC2392
xdvi	sing_2236.htm#SEC2317
zdd	sing_2711.htm#IDX1104
zdd2poly	sing_2728.htm#SEC2809
zero	sing_1350.htm#SEC1431
zero-dimensional	sing_2446.htm#IDX967
zeroMod	sing_1427.htm#SEC1508
zeroNcfrac	sing_699.htm#SEC753
zeroOpt	sing_1436.htm#SEC1517
zeroRadical	sing_1260.htm#SEC1341
zeroReduce	sing_2946.htm#SEC3027
zeroSet	sing_2208.htm#SEC2289
zerodec	sing_1525.htm#SEC1606
zeroreduce	sing_2944.htm#IDX1249
zeroset.lib	sing_2203.htm#SEC2284
zeroset_lib	sing_2203.htm#SEC2284
zetaDL	sing_1773.htm#SEC1854
{	sing_36.htm#IDX78
||	sing_36.htm#IDX103
|| 	sing_101.htm#SEC141
}	sing_36.htm#IDX79
~	sing_36.htm#IDX117
~ 	sing_397.htm#SEC437
