Date: 2020-10-07 18:10:00

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## Index

!!FLIM global variable, 1
!!NFPD global variable, 2
!*CSYSTEMS global (AVECTOR), 3
!__FILE__ (special identiﬁer), 4
!__LINE__ (special identiﬁer), 5
B function, 6
Γ function, 7
ψ function, 8
ψ(n) functions, 9
ζ function, 10
* operator, 11
3-D vectors, 12
algebraic numbers, 13
lists, 14
power series, 15
vectors, 16
** operator, 17
lists, 18
power series, 19
*. (ldot) operator, 20
+ operator, 21
3-D vectors, 22
algebraic numbers, 23
lists, 24
power series, 25
vectors, 26
- operator, 27
3-D vectors, 28
lists, 29
power series, 30
vectors, 31
.(CONS) operator, 32
.. operator, 33
/ operator, 34
3-D vectors, 35
algebraic numbers, 36
lists, 37
power series, 38
vectors, 39
// operator, 40
:= (assignment) operator, 41, 42
; (statement terminator), 43
< operator, 44
<< (begin group), 45
<= operator, 46
== operator (CANTENS) PACKAGE), 47
> operator, 48
>< (cross product) operator
3-D vectors, 49
>= operator, 50
>> (end group), 51
@ operator, 52
partial diﬀerentiation, 53
tangent vector, 54
# (Hodge-*) operator, 55, 56
$ (statement terminator), 57
% (Percent sign), 58
\ operator (SETDIFF), 59
operator, 60
3-D vectors, 61
exterior multiplication, 62, 63
lists, 64
_ (lnth) operator for lists, 65
_| (inner product) operator, 66, 67
|_ (Lie derivative) operator, 68, 69
3j and 6j symbols, 70

ABS, 71, 72
ACOS, 73, 74
ACOSH, 75, 76
ACOT, 77, 78
ACOTH, 79, 80
ACSC, 81, 82
ACSCH, 83, 84
ADD_TO_COLUMNS operator, 85
ADD_TO_ROWS operator, 86
ADD_COLUMNS operator, 87
ADD_ROWS operator, 88
ADJ, 89
ADJOINT_CDIFFOP operator (CDE), 90
ADJPREC switch, 91
affine, 92
Aﬃne space
CANTENS package, 93
aﬃne_points (CALI), 94
aﬃne_points1
* (CALI), 95
affine_monomial_curve, 96
affine_monomial_curve!*, 97
affine_points, 98
affine_points!*, 99
Airy Functions, 100
Airy functions, 101
Airy_Ai, 102, 103, 104
Airy_Aiprime, 105, 106, 107
Airy_Bi, 108, 109, 110
Airy_Biprime, 111, 112, 113
ALGEBRAIC, 114
Algebraic mode, 115, 116, 117
Algebraic number ﬁelds, 118
Algebraic numbers, 119
algebraic numbers (CALI), 120
ALGINT package, 121, 122
ALGINT switch, 123
ALL_PARAMETRIC_DER shared global variable (CDE), 124
ALL_PARAMETRIC_ODD shared global variable (CDE), 125
ALL_PARAMTERIC_DER shared global variable (CDE), 126
ALL_PRINCIPAL_DER shared global variable (CDE), 127
ALL_PRINCIPAL_ODD shared global variable (CDE), 128
ALLBRANCH switch, 129
ALLFAC switch, 130, 131, 132
ALLOWDFINT switch, 133
ALLSYMMETRYBASES, 134
analytic_spread, 135
analytic_spread!*, 136
AND logical operator, 137
annihilator, 138
annihilator!*, 139
ansatz of symmetry generator, 140
ANTICOM switch, 141
ANTICOMM operator, 142
Anticommutative
CANTENS package, 143
ANTICOMMUTE, 144
Antisymmetric
CANTENS package, 145
ANTISYMMETRIC declaration, 146, 147
Antisymmetric operator, 148
APPEND operator, 149
APPLYSYM, 150
APPLYSYM package
example, 151
APPLYSYM package, 152
approximation, 153
ARBCOMPLEX, 154
ARBINT, 155
ARBVARS switch, 156
ARGLENGTH operator, 157
ARNUM package, 158
ARNUM package
example, 159, 160, 161, 162
ARRAY, 163
Array declaration, 164
ASEC, 165, 166
ASECH, 167, 168
ASIN, 169, 170
ASINH, 171, 172
ASSERT package, 173
assgrad, 174
assgrad!*, 175
Assignment, 176, 177, 178, 179, 180, 181, 182, 183
Assignment statement, 184
multiple, 185
ASSIST, 186, 187
ASSIST package, 188
ASSUMPTIONS variable, 189
Asymptotic command, 190, 191
ATAN, 192, 193, 194
ATAN2, 195, 196
ATANH, 197, 198
AUGMENT_COLUMNS operator, 199
AVAILABLEGROUPS, 200
AVEC function, 201
AVECTOR package, 202
example, 203, 204, 205, 206, 207
AVECTOR package, 208

BALANCED_MOD switch, 209, 210
BAND_MATRIX operator, 211
Barnes, Alan, 212, 213
bas_detectunits (CALI), 214
bas_factorunits (CALI), 215
bas_getrelations, 216
bas_removerelations, 217
bas_setrelations, 218
base coeﬃcients (CALI), 219
base elements (CALI), 220
base ring (CALI), 221, 222
basis (CALI), 223
bcsimp (CALI), 224
BEGIN…END, 225, 226, 227, 228
BERNOULLI, 229
Bernoulli, 230, 231
Bernoulli numbers, 232, 233, 234
BERNSTEIN_BASE, 235
Bessel functions, 236, 237
BesselI, 238, 239, 240
BesselJ, 241, 242, 243
BesselK, 244, 245, 246
BesselY, 247, 248, 249
BETA, 250, 251
Beta, 252
Beta function, 253, 254
bettiNumbers, 255
BettiNumbers!*, 256
BEZOUT switch, 257
BFSPACE switch, 258
BIBASIS, 259
BIBASIS package, 260
bibasis_print_statistics, 261
Binomial, 262
Binomial coeﬃcients, 263
binomial switch, 264
bloc-diagonal, 265, 266, 267
Block, 268, 269
BLOCK_MATRIX operator, 270
blockorder procedure (CALI), 271
blockorder!*, 272
blowup, 273
blowup (CALI), 274
blowup!*, 275
BNDEQ!* shared variable, 276
Boolean expression, 277
BOOLEAN operator, 278
BOOLEAN package, 279
border basis (CALI), 280
bounded identiﬁer, 281
bounded identiﬁer (CALI), 282
BOUNDS, 283, 284
Buchberger’s Algorithm, 285, 286
BYE command, 287

C(I), 288
CALI package, 289
cali!=basering global variable (CALI), 290, 291, 292
cali!=degrees global variable (CALI), 293, 294, 295
cali!=monset global variable (CALI), 296, 297
Call by value, 298, 299
CAMAL package, 300
CANONICAL, 301
Canonical form, 302, 303
CANONICAL operator, 304, 305, 306, 307, 308, 309, 310, 311
CANONICALDECOMPOSITION, 312
CANTENS package, 313
CANTENS package
== operator, 314
aﬃne space, 315
anticommutative indexed objects, 316
antisymmetric tensor, 317
DEPEND, 318
dummy indices, 319
epsilon tensor, 320
FORALL, 321
indices, 322, 323
indices, dummy, 324
indices, numeric, 325
indices, symbolic, 326
LET, 327
loading, 328
metric tensor, 329
mixed symmetry, 330
numeric indices, 331
partial symmetry, 332
rewriting rules, 333
Riemann tensor, 334
signature, 335, 336, 337, 338
spaces, 339, 340, 341
spinor, 342
SUB, 343, 344
subspaces, 345
symbolic indices, 346, 347
symmetries, 348
tensor contractions, 349
tensor derivatives, 350
tensor polynomial, 351
trace, 352
variables, 353, 354, 355
CARD_NO shared global variable, 356
Cartesian coordinates, 357
Catalan, 358
CATALAN reserved variable, 359
Caveats
TAYLOR package, 360
CDE operator, 361
CDE package, 362
CDE_GRADING operator (CDE), 363
CDIﬀ package, 364
CEILING, 365
CF operator, 366, 367
CF_EVEN_ODD operator, 368
CF_REMOVE_CONSTANT operator, 369
CF_REMOVE_FRACTIONS operator, 370
CF_UNIT_DENOMINATORS operator, 371
CF_UNIT_NUMERATORS operator, 372
CF_CONTINUENTS operator, 373
CF_CONVERGENT operator, 374
CF_CONVERGENTS operator, 375
CF_EULER operator, 376, 377
cf_euler operator, 378
CF_EXPRESSION operator, 379
CF_TAYLOR switch, 380
CF_TRANSFORM operator, 381
CFRAC operator, 382
cfrac operator, 383
CGB operator, 384
CGB package, 385
CGBFULLRED switch, 386
CGBGEN switch, 387
CGBGS switch, 388
CGBREAL switch, 389
CGBSTAT switch, 390
Chain rule, 391
change of term orders (CALI), 392
change_termorder, 393
change_termorder!*, 394
change_termorder1, 395
change_termorder1!*, 396
CHANGEVAR operator, 397
CHAR_MATRIX operator, 398
CHAR_POLY operator, 399
CHARACTER, 400
Character set, 401
CHARACTERN, 402
Chebyshev ﬁt, 403
Chebyshev polynomials, 404
CHEBYSHEV_BASE_T, 405
CHEBYSHEV_BASE_U, 406
CHEBYSHEV_DF, 407
CHEBYSHEV_EVAL, 408
CHEBYSHEV_FIT, 409
CHEBYSHEV_INT, 410
ChebyshevT, 411
ChebyshevU, 412
CHECKORD switch, 413
CHOLESKY operator, 414
CI, 415
CLEAR, 416, 417
CLEAR_DUMMY_BASE, 418
clearcaliprintterms, 419
CLEARPHYSOP, 420
CLEARRULES, 421
Clebsch Gordan coeﬃcients, 422
Clebsch_Gordan, 423
codim, 424
codim!*, 425
COEFF operator, 426
COEFF2 operator, 427
COEﬀ2 package, 428
COEFF_MATRIX operator, 429
Coeﬃcient, 430, 431, 432, 433, 434
COEFFN operator, 435
COFACTOR, 436
COFRAME
WITH METRIC, 437
WITH SIGNATURE, 438
Coframe, 439, 440
COFRAME command, 441
COLLECT keyword, 442
column degree (CALI), 443
COLUMN_DIM operator, 444
COMBINEEXPT switch, 445
COMBINELOGS switch, 446
COMM, 447
COMM operator, 448
Command, 449
BYE, 450
CONT, 451
DEFINE, 452
PAUSE, 453
SHOWTIME, 454
Command terminator
IN command, 455
COMMENT keyword, 456
COMMUTE, 457
COMMUTEDF switch, 458
COMP switch, 459
COMPACT operator, 460
COMPACT package, 461
COMPANION operator, 462
Compiler, 463
COMPLEX, 464
Complex coeﬃcient, 465
COMPLEX switch, 466, 467
Compound statement, 468, 469
Computations with supersymmetric algebraic and diﬀerential expressions, 470
Conditional statement, 471, 472
CONJ, 473
Constructor, 474
CONT COMMAND, 475
CONTFRAC operator, 476
contfrac operator, 477
Continued fractions, 478
CONTINUED_FRACTION operator, 479
CONTRACT, 480
CONV_CDIFF2SUPERFUN operator (CDE), 481
CONV_SUPERFUN2CDIFF operator (CDE), 482
Coordinates
cartesian, 483
cylindrical, 484
coordinates
spherical, 485
COORDINATES operator, 486
COORDS vector, 487
COPY_INTO operator, 488
COS, 489, 490
COSH, 491, 492
COT, 493, 494
COTH, 495, 496
CRACK package, 497
crack, running in CDE package, 498
CRAMER switch, 499, 500
CREF, 501
CREF switch, 502
CRESYS, 503, 504
CROSS
vector, 505
Cross product, 506, 507
Cross reference, 508
CSC, 509, 510
CSCH, 511, 512
CSETREPRESENTATION, 513
Curl
vector ﬁeld, 514
CURL
operator, 515
CURL operator, 516
CVIT package, 517
Cylindrical coordinates, 518

d
exterior diﬀerentiation, 519
dd_groebner, 520
Declaration, 521
array, 522
KORDER, 523
mode handling, 524
DECOMPOSE, 525
decomposition
partial fraction, 526
Default
term order, 527
Defaults
TAYLOR package, 528
DEFINE command, 529
DEFINE_SPACES, 530, 531
Deﬁnite integration (simple), 532
DEFINT function, 533
DEﬁNT package, 534, 535
DEﬁNT package, 536
DEFLINEINT function, 537
DEFN switch, 538, 539, 540
DEFPOLY statement, 541
DEG, 542
Degree, 543
degree, 544
degree arguments, 545
degree vectors (CALI), 546
degree!*, 547
degreeorder procedure (CALI), 548
degreeorder!*, 549
degsfromresolution, 550
del, 551, 552, 553
deleteunits
* (CALI), 554
deleteunits, 555
DELSQ
operator, 556
DELSQ operator, 557
delta, 558, 559, 560, 561, 562, 563, 564
deltafunction, 565, 566
DEMO, 567
DEN, 568, 569
DEP_VAR global variable (CDE), 570
DEPEND, 571
DEPEND
CANTENS package, 572
DEPEND command, 573
DEPEND declaration, 574
DEPEND statement, 575
DEQ(I), 576
DER_DEG_ORDERING operator (CDE), 577
Derivative
variational, 578
derivatives, 579
DESIR package, 580
DET, 581
DET operator, 582
detectunits (CALI), 583, 584
Determinant
in DETM!*, 585
DETM!* variable, 586
DETRAFO, 587
DF, 588
DF operator, 589, 590
DF_ODD operator (CDE), 591
DFINT switch, 592
DFP, 593
DFPART package, 594
DFPRINT switch, 595
DIAGONAL operator, 596
DIAGONALIZE, 597
Diﬀerential geometry, 598
Diﬀerentiation, 599, 600, 601
partial, 602
vector, 603, 604
Digamma, 605
Digamma function, 606, 607
DILOG, 608, 609, 610
Dilogarithm function, 611
dim, 612
dim (CALI), 613
dim!*, 614
Dimension, 615
dimzerop, 616
dimzerop!*, 617
Dirac γ matrix, 618
directsum, 619
DISPJACOBIAN switch, 620
DISPLAY, 621
Display, 622
DISPLAYFRAME command, 623, 624
Displaying structure, 625
DIV
operator, 626
DIV operator, 627
DIV switch, 628, 629
Divergence
vector ﬁeld, 630
divide operator, 631
DLINEINT, 632
dmode (CALI), 633
DO, 634, 635, 636
DO keyword, 637
Dollar sign, 638
DOT, 639
DOT
vector, 640
Dot product, 641, 642, 643
DOTGRAD operator, 644, 645
Double slash operator
in rules, 646
Double tilde variables
in rules, 647
DOWN_QRATIO operator, 648
DOWNWARD_ANTIDIFFERENCE, 649
dp_pseudodivmod (CALI), 650
dp_pseudodivmod, 651, 652
dpgcd, 653, 654
dpmat (CALI), 655, 656, 657, 658, 659
dpmat_coldegs (CALI), 660
dpmat_cols (CALI), 661
dpmat_gbtag (CALI), 662
dpmat_list (CALI), 663
dpmat_rows (CALI), 664
dual bases (CALI), 665
dualbases (CALI), 666, 667, 668
dualhbases (CALI), 669, 670
DUMMY, 671, 672, 673, 674, 675, 676
dummy, 677, 678
Dummy indices
CANTENS package, 679
dummy indices, 680
DUMMY package, 681
DUMMY_BASE, 682
DUMMY_INDICES, 683
DUMMY_NAME, 684
DVINT, 685
DVOLINT, 686

E reserved variable, 687
easydim, 688
easydim (CALI), 689
easydim!*, 690
easyindepset, 691
easyindepset!*, 692
easyprimarydecomposition, 693
easyprimarydecomposition!*, 694
ecart (CALI), 695, 696
ecart vector (CALI), 697, 698, 699
ECHO switch, 700
ED, 701, 702
EDITDEF, 703
efgb (CALI), 704
Ei, 705
eliminate, 706
eliminate (CALI), 707
eliminate!*, 708
eliminationorder procedure (CALI), 709
eliminationorder!*, 710
ELL_FUNCTION operator (CDE), 711
EllipticD, 712
EllipticE, 713
EllipticF, 714
EllipticK, 715
EllipticTheta1, 716
EllipticTheta2, 717
EllipticTheta3, 718
EllipticTheta4, 719
END, 720
EPS, 721, 722
EPS
Levi-Civita tensor, 723
epsilon, 724, 725, 726
Epsilon tensor
CANTENS package, 727
eqhull, 728
eqhull!*, 729
Equation, 730, 731
ERF, 732
ERRCONT switch, 733
Errors
TAYLOR package, 734
eta, 735, 736, 737, 738
ETA(ALFA), 739
Euclidean metric, 740
euclidian, 741
EULER, 742
Euler, 743, 744
Euler numbers, 745, 746, 747
Euler polynomials, 748
EULER_DF operator (CDE), 749
Euler_Gamma, 750
EULER_GAMMA reserved variable, 751
EulerP, 752
EVAL2 operator, 753
EVAL_MODE shared global variable, 754
EVALB, 755
EVALLHSEQP switch, 756
EVEN declaration, 757
Even operator, 758
EVENP boolean operator, 759
evlf (CALI), 760
EXCALC, 761
EXCALC package
example, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777
tracing, 778
EXCALC package, 779
EXCALC package
example, 780
Exclamation mark, 781
EXCLUDE, 782, 783
EXCOEFFS, 784
EXDEGREE, 785
EXDEGREE command, 786
EXDELT, 787, 788
EXP, 789, 790, 791, 792
EXP switch, 793, 794
EXPAND_CASES operator, 795
EXPAND_TD command, 796
EXPANDDF switch, 797
EXPANDLOGS switch, 798
EXPR, 799
Expression, 800
boolean, 801
EXT operator (CDE), 802
EXTEND operator, 803
extended Gröbner factorizer (CALI), 804, 805, 806
EXTENDED_GOSPER, 807
EXTENDED_SUMRECURSION, 808
extendedgroebfactor, 809
extendedgroebfactor!*, 810
extendedgroebfactor1, 811
extendedgroebfactor1!*, 812
extendible power series, 813
Exterior calculus, 814
Exterior diﬀerentiation, 815
Exterior form
declaration, 816
ordering, 817
vector, 818
with indices, 819, 820
Exterior product, 821, 822
EXVARS, 823
EZGCD switch, 824

FACTOR declaration, 825
FACTOR switch, 826, 827
FACTORIAL, 828, 829
Factorization, 830
FACTORIZE, 831, 832
factorprimes (CALI), 833, 834
factorunits (CALI), 835, 836
FAILHARD switch, 837
FANCY_LOWER_DIGITS, 838
FANCY_PRINT_DF, 839
Fast loading of code, 840
FAST_LA switch, 841, 842
FASTSIMPLEX switch, 843
FDOMAIN command, 844, 845
FEXPR reserved identiﬁer, 846
Fibonacci, 847, 848
Fibonacci numbers, 849, 850
Fibonacci Polynomials, 851
FibonacciPolynomials, 852
FibonacciP, 853
FIDE package, 854
File handling, 855
File, startup, 856
FIND_COMPANION operator, 857
FIRST operator, 858
FIRSTROOT, 859
FIX, 860
FIXP boolean operator, 861
ﬂatten (CALI), 862
FLOOR, 863
FOR, 864
FORALL, 865, 866
FORALL
CANTENS package, 867
FOREACH, 868, 869, 870, 871
FOREACH statement, 872
FOR statement, 873
FORDER command, 874, 875
FORT, 876
FORT switch, 877
FORTRAN, 878, 879
FORTUPPER switch, 880
FPS, 881
FPS package, 882
FRAME command, 883, 884
free identiﬁer, 885
Free operators
in rules, 886
FREEOF boolean operator, 887
FROBENIUS operator, 888
FULLROOTS switch, 889, 890
Function, 891

G, 892
GAMMA, 893, 894
Gamma, 895
Gamma function, 896, 897
GAMMATOFACTORIAL, 898
gb-tag (CALI), 899, 900
gbasis, 901
gbasis!*, 902
gbtestversion (CALI), 903, 904, 905, 906
GCD, 907
GCD switch, 908
GCREF package, 909
gdimension, 910
Gegenbauer polynomials, 911
GegenbauerP, 912
GEN(I), 913
Generalized Hypergeometric functions, 914
GENERATORS, 915
generic function, 916
generic tensor, 917
GENERIC_FUNCTION, 918
GENTRAN package, 919
GET_COLUMNS operator, 920
GET_ROWS operator, 921
GETCSYSTEM command, 922
getdegrees, 923
getecart, 924
getkbase, 925
getkbase!*, 926
getleadterms, 927
getring procedure (CALI), 928
GETROOT, 929
getrules, 930
GFNEWT, 931
GFROOT, 932
gindependent_sets, 933
GL(I), 934
glexconvert, 935
global procedures (CALI), 936
GLOBAL_SIGN, 937, 938, 939
GLTBASIS switch, 940, 941
GNUPLOT command, 942
GNUPLOT package, 943
GNUPLOT package, 944
GOTO, 945, 946
GO TO statement, 947
Golden_Ratio, 948
GOLDEN_RATIO reserved variable, 949
GOSPER, 950
Gosper’s Algorithm, 951
GOSPER_REPRESENTATION variable, 952
Gröbner Bases, 953
GRAD
operator, 954
GRAD operator, 955
Graded ordering, 956
GradedBettinumbers, 957
GradedBettiNumbers!*, 958
Gradient
vector ﬁeld, 959
gradlex
term order, 960
GRAM_SCHMIDT operator, 961
greduce, 962
greduce_orders, 963
groeb
=rf (CALI), 964
groeb (CALI), 965
groeb_homstbasis (CALI), 966
groeb_lazystbasis (CALI), 967
groeb_mingb, 968
groeb_minimize, 969
groeb_stbasis, 970
groebf_zeroprimes1 (CALI), 971
groebfactor, 972
groebfactor!*, 973
GROEBFULLREDUCTION switch, 974, 975
groebmonfac, 976, 977
groebner, 978
Groebner Bases, 979
GROEBNER package, 980
Groebner package, 981
example, 982, 983, 984, 985, 986, 987, 988
ordering
graded, 989
grouped, 990
matrix, 991
weighted, 992
term order
default, 993
gradlex, 994
lex, 995
revgradlex, 996
GROEBNER package, 997
groebner_walk, 998
groebnerf, 999, 1000, 1001
groebnert, 1002
GROEBOPT switch, 1003, 1004, 1005
GROEBPROT switch, 1006
groebprotfile, 1007
groebresmax, 1008
groebrestriction, 1009
GROEBSTAT switch, 1010, 1011
groepostproc, 1012
groesolve, 1013
Group statement, 1014, 1015, 1016
Grouped ordering, 1017
gsort, 1018
gsplit, 1019
gspoly, 1020
GSYS operator, 1021
GSYS2CGB operator, 1022
GUARDIAN package, 1023
gvars, 1024
gvarslast, 1025, 1026
gzerodim?, 1027

Hankel functions, 1028, 1029
Hankel1, 1030, 1031, 1032
Hankel2, 1033, 1034, 1035
hardzerotest (CALI), 1036
Hermite polynomials, 1037
HERMITE_BASE, 1038
HermiteP, 1039
HERMITIAN_TP operator, 1040
HESSIAN operator, 1041
HEUGCD switch, 1042
hf
=hf (CALI), 1043
hf_whs_from_resolution, 1044
hf_whilb, 1045
hf_whilb3, 1046
HFACTORS scale factors, 1047
hftestversion (CALI), 1048, 1049, 1050, 1051
High energy trace, 1052
High energy vector expression, 1053, 1054
HIGH_POW, 1055
HILBERT operator, 1056
Hilbert polynomial, 1057
Hilbert series (CALI), 1058
Hilbertpolynomial, 1059
HilbertSeries, 1060
HilbertSeries (CALI), 1061
HilbertSeries!*, 1062
History, 1063
Hodge-* duality operator, 1064, 1065
homstbasis, 1066
homstbasis!*, 1067
HORNER, 1068
HORNER switch, 1069
Hypergeometric functions, 1070
HYPERRECURSION, 1071
HYPERSUM, 1072
HYPERTERM, 1073
HYPOT, 1074, 1075

i, 1076
I reserved variable, 1077
I_SOLVE, 1078
IBETA, 1079
idealdimension, 1080
Ideal quotient, 1081
ideal quotient (CALI), 1082
ideal2mat, 1083
ideal2mat (CALI), 1084
ideal_of_minors, 1085, 1086
ideal_of_pfaffians, 1087, 1088
idealpower, 1089
idealprod, 1090
idealquotient, 1091, 1092
idealquotient!*, 1093
ideals (CALI), 1094
IDEALS package, 1095
idealsum, 1096
Identiﬁer, 1097
IF, 1098, 1099
IFACTOR switch, 1100
IGAMMA, 1101
IMAGINARY switch, 1102
imaginary unit, 1103
IMPART, 1104, 1105, 1106, 1107, 1108
IMPLICIT_TAYLOR operator, 1109
IN command, 1110
IN keyword, 1111
Indeﬁnite integration, 1112
INDEP_VAR global variable (CDE), 1113
independentsets, 1114
indepvarsets, 1115
indepvarsets!*, 1116
INDEX, 1117
INDEX_SYMMETRIES command, 1118, 1119
INDEXED, 1120
indexrange, 1121, 1122, 1123
INDEXRANGE command, 1124
Indices
CANTENS package, 1125, 1126
INEQ package, 1127
INEQ_SOLVE operator, 1128
INFINITY, 1129, 1130
INFINITY reserved variable, 1131
INFIX declaration, 1132
Inﬁx operator, 1133, 1134, 1135, 1136, 1137, 1138, 1139
INITIALIZE_EQUATIONS operator (CDE), 1140
initmat, 1141
Inner product, 1142
exterior form, 1143
INPUT, 1144
Input, 1145
Instant evaluation, 1146, 1147, 1148, 1149, 1150
INT, 1151, 1152
INTEGER, 1153
Integer, 1154
INTEGRATE_EQUATION operator (CDE), 1155
Integration, 1156, 1157
deﬁnite (simple), 1158
line, 1159
volume, 1160
Interactive use, 1161, 1162
internal procedures (CALI), 1163
INTERPOL, 1164
interreduce, 1165
interreduce!*, 1166
INTERSECTION, 1167
Introduction, 1168
INTSTR switch, 1169
INVBASE package, 1170
INVZTRANS, 1171
IRREDUCIBLEREPNR, 1172
IRREDUCIBLEREPTABLE, 1173
isolatedprimes, 1174
isolatedprimes!*, 1175
ISOLATER, 1176
isprime, 1177
isprime!*, 1178
iszeroradical, 1179

Jacobi Elliptic Functions and Integrals, 1180
Jacobi’s polynomials, 1181
Jacobiam, 1182
JACOBIAN operator, 1183
Jacobicn, 1184
Jacobidn, 1185
JacobiP, 1186
Jacobisn, 1187
JacobiZeta, 1188
JET_FIBER_DIM operator, 1189
JET_DIM operator, 1190
JOIN keyword, 1191
JORDAN operator, 1192
JORDAN_BLOCK operator, 1193
JORDANSYMBOLIC operator, 1194

KEEP command, 1195, 1196
Kernel, 1197, 1198, 1199, 1200
CANTENS package, 1201
kernel form, 1202
Khinchin, 1203
KHINCHIN reserved variable, 1204
Killing Vectors, 1205
KILLING_VECTOR command, 1206, 1207
KORDER, 1208
KORDER declaration, 1209
KRONECKER_PRODUCT operator, 1210
Kummer functions, 1211, 1212
KummerM, 1213, 1214, 1215
KummerU, 1216, 1217, 1218

l’Hôpital’s rule, 1219, 1220
Label, 1221, 1222
Laguerre polynomials, 1223
LAGUERRE_BASE, 1224
LaguerreP, 1225
LALR package, 1226
LAMBDA reserved word, 1227
Lambert’s W, 1228
LAPLACE package, 1229
Laplacian
vector ﬁeld, 1230
Laurent series, 1231
lazy switch, 1232
lazystbasis, 1233
lazystbasis!*, 1234
LCM, 1235, 1236
LCOF, 1237
LDOT operator, 1238
Leading coeﬃcient, 1239
Legendre polynomials, 1240, 1241
LEGENDRE_BASE, 1242
LEGENDRE_SYMBOL, 1243
LegendreP, 1244
LENGTH, 1245, 1246, 1247, 1248, 1249
LENGTH operator, 1250
use on lists, 1251
LET, 1252, 1253, 1254, 1255, 1256, 1257, 1258, 1259, 1260, 1261
Levi-Cevita tensor, 1262
LEX, 1263
lex
term order, 1264
lexefgb (CALI), 1265, 1266
lexicographic (CALI), 1267
LHS operator, 1268
LHYP switch, 1269
Lie Derivative, 1270
LIE package, 1271
LIEPDE, 1272
LIMIT, 1273, 1274
LIMIT+, 1275
LIMIT-, 1276
LIMITS package, 1277
LIMITS package, 1278
LINALG package, 1279
Line integrals, 1280
LINEAR, 1281
Linear Algebra package, 1282, 1283
LINEAR declaration, 1284
Linear operator, 1285, 1286, 1287
LINEINT, 1288
LINEINT function, 1289
LINELENGTH operator, 1290
LISP, 1291
Lisp, 1292
LIST, 1293
List, 1294
vector operations, 1295
list, 1296
List operation, 1297, 1298
LIST switch, 1299
LISTARGP declaration, 1300
LISTARGS switch, 1301
listgroebfactor, 1302
listgroebfactor!*, 1303
listminimize (CALI), 1304
LISTPROC keyword, 1305
listtest (CALI), 1306
LISTVECOPS package, 1307
LMON switch, 1308
LN, 1309
LNTH operator, 1310
LOAD, 1311
LOAD_PACKAGE, 1312, 1313
LOADGROUPS, 1314
local procedures (CALI), 1315
localorder procedure (CALI), 1316
localorder!*, 1317
LOG, 1318, 1319, 1320
LOG10, 1321, 1322
LOGB, 1323, 1324
Lommel functions, 1325, 1326
Lommel1, 1327, 1328, 1329
Lommel2, 1330, 1331, 1332
LOOKING_GOOD switch, 1333
Loop, 1334, 1335
LOW_POW, 1336
LOWER_MATRIX switch, 1337
LPDO package, 1338
LPOWER, 1339
LTERM, 1340, 1341
LTRIG switch, 1342
LU_DECOM operator, 1343

M_ROOTS operator, 1344
M_SOLVE operator, 1345
MACRO, 1346
MAINVAR, 1347
MAKE_BLOC_DIAGONAL, 1348, 1349
MAKE_PARTIC_TENS, 1350, 1351, 1352, 1353
MAKE_TENSOR_BELONG_SPACE, 1354, 1355
MAKE_TENSOR_BELONG_SPACE declaration, 1356
MAKE_TENSOR_BELONG_SPACE operator, 1357
MAKE_IDENTITY operator, 1358
MAKE_VARIABLES, 1359
MAP, 1360
map, 1361
map (CALI), 1362
MASS, 1363, 1364
MAT, 1365, 1366, 1367
mat2list, 1368
mat2list (CALI), 1369, 1370
matappend, 1371
MATCH, 1372
MATEIGEN, 1373
Mathematical function, 1374
mathomogenize, 1375
mathprint (CALI), 1376
matintersect, 1377
matintersect (CALI), 1378
matintersect!*, 1379
matjac, 1380, 1381
matqquot, 1382
matqquot!*, 1383
matquot
* (CALI), 1384
matquot, 1385
matquot!*, 1386
MATRIX, 1387
Matrix assignment, 1388
Matrix calculations, 1389
Matrix ordering, 1390
MATRIX_AUGMENT operator, 1391
MATRIX_STACK operator, 1392
MATRIXP, 1393, 1394
MATRIXPROC, 1395
matstabquot, 1396
matstabquot!*, 1397
matsum, 1398
MAX, 1399
MCD, 1400, 1401
MCD switch, 1402, 1403
Meijer’s G function, 1404
MEMBER, 1405
metric, 1406, 1407
METRIC command, 1408
Metric structure, 1409
Metric tensor
CANTENS package, 1410
MIN, 1411
minimal_generators, 1412
minimal_generators!*, 1413
Minimum, 1414
Minkowski, 1415, 1416, 1417
MINOR operator, 1418
minors, 1419, 1420
Mixed symmetry
CANTENS package, 1421
MK_IDS_BELONG_ANYSPACE, 1422
MK_IDS_BELONG_SPACE, 1423
MK_IDS_BELONG_ANYSPACE operator, 1424
MK_IDS_BELONG_SPACE, 1425
MK_IDS_BELONG_SPACE operator, 1426
MK_CDIFFOP operator (CDE), 1427
MK_SUPERFUN operator (CDE), 1428
MKALLLINODD operator (CDE), 1429
MKID, 1430
MKPOLY, 1431
MKSET, 1432
MM, 1433
mod, 1434
mod operator, 1435, 1436
mod!*, 1437
Mode, 1438
algebraic, 1439
symbolic, 1440
Mode communication, 1441
Mode handling declarations, 1442
modequalp, 1443
modequalp (CALI), 1444
modequalp!*, 1445
MODSR package, 1446
Modular coeﬃcient, 1447
MODULAR switch, 1448, 1449, 1450
module bcsf (CALI), 1451
module cali (CALI), 1452
module calimat (CALI), 1453, 1454
module dpmat (CALI), 1455
module groeb (CALI), 1456
module groebf (CALI), 1457, 1458
module lf (CALI), 1459, 1460
module moid (CALI), 1461
module mora (CALI), 1462
module odim (CALI), 1463, 1464
module prime (CALI), 1465
module quotient (CALI), 1466
module ring (CALI), 1467
module scripts (CALI), 1468, 1469
module term order (CALI), 1470
module triang (CALI), 1471, 1472
modulequotient, 1473
modulequotient!*, 1474
modules (CALI), 1475
moid_primes, 1476
MONOMIAL_BASE, 1477
Motzkin, 1478
Motzkin number, 1479
MRV_LIMIT operator, 1480
MRVLIMIT package, 1481
MSG switch, 1482
MSHELL, 1483
MULT_COLUMNS operator, 1484
MULT_ROWS operator, 1485
Multiple assignment statement, 1486
MULTIPLICITIES switch, 1487
MULTIROOT switch, 1488

NAT switch, 1489, 1490
NCPOLY package, 1491
NEARESTROOT, 1492, 1493
NEARESTROOTS, 1494
NEGATIVE, 1495, 1496
NEGATIVE reserved variable, 1497
negativity, 1498
NERO switch, 1499, 1500
Newton’s method, 1501
NEXTPRIME, 1502
NIL reserved variable, 1503
NM operator, 1504
NN, 1505
NOCOMMUTEDF switch, 1506
NOCONVERT switch, 1507
NODEPEND command, 1508
NODEPEND statement, 1509
NOETHER function, 1510, 1511
Noetherian (CALI), 1512
Noetherian switch, 1513, 1514
NOEXPAND_TD command, 1515
NOINTSUBST switch, 1516
NOLNR switch, 1517
Non-commuting operator, 1518
NONCOM, 1519
NONCOM declaration, 1520
NONZERO declaration, 1521
normalform, 1522
normalform!*, 1523
NORMFORM package, 1524
NORMFORM package, 1525
NOSPLIT, 1526
NOSPLIT switch, 1527
NOSPUR, 1528
NOSUM command, 1529, 1530
NOSUM switch, 1531
NOT_NEGATIVE switch, 1532
NOTREALVALUED declaration, 1533
NOXPND
@, 1534
D, 1535
NOXPND@ command, 1536
NOXPND command, 1537
NS dummy variable, 1538
NULLSPACE, 1539
NUM, 1540
NUM_FIT, 1541
NUM_INT, 1542, 1543
NUM_MIN, 1544, 1545
NUM_ODESOLVE, 1546, 1547
NUM_SOLVE, 1548, 1549
Number, 1550, 1551
NUMBERP boolean operator, 1552
Numeric indices
CANTENS package, 1553
NUMERIC package, 1554
NUMERIC package, 1555
Numerical operator, 1556
Numerical precision, 1557
nzdp, 1558
nzdp!*, 1559

ODD declaration, 1560
Odd operator, 1561
ODD_VAR global variable (CDE), 1562
ODESOLVE package, 1563
odim_borderbasis, 1564
odim_parameter, 1565
odim_up, 1566
OFF, 1567, 1568
oldbasis (CALI), 1569
oldborderbasis (CALI), 1570
oldring (CALI), 1571
ON, 1572, 1573
ON keyword, 1574
ONE_OF operator, 1575
ONESPACE switch, 1576, 1577, 1578
Oﬀ, 1579, 1580, 1581, 1582, 1583, 1584, 1585, 1586
On, 1587, 1588, 1589, 1590, 1591, 1592, 1593
ONLY_INTEGER switch, 1594
OPAPPLY, 1595
OPERATOR, 1596
Operator, 1597, 1598, 1599, 1600
antisymmetric, 1601
CANTENS package, 1602
double slash, 1603
even, 1604
inﬁx, 1605
linear, 1606
non-commuting, 1607
numerical, 1608
odd, 1609
precedence, 1610, 1611
symmetric, 1612
unary preﬁx, 1613
OPERATOR declaration, 1614
CANTENS package, 1615
Operators
free, in rules, 1616
OPORDER, 1617
OR logical operator, 1618
ORDER declaration, 1619, 1620
Ordering
exterior form, 1621
ORDP boolean operator, 1622, 1623
Orthogonal polynomials, 1624
ORTHOVEC package, 1625
ORTHOVEC package
example, 1626, 1627, 1628, 1629, 1630, 1631
OUT command, 1632
Output, 1633, 1634
Output declaration, 1635, 1636
OUTPUT switch, 1637

Packages
ALGINT, 1638, 1639
APPLYSYM, 1640
ARNUM, 1641
ASSERT, 1642
ASSIST, 1643
AVECTOR, 1644
BIBASIS, 1645
BOOLEAN, 1646
CALI, 1647
CAMAL, 1648
CANTENS, 1649
CDE, 1650
CDIﬀ, 1651
CGB, 1652
COEﬀ2, 1653
COMPACT, 1654
CRACK, 1655
CVIT, 1656
DEﬁNT, 1657, 1658
DEﬁNT, 1659
DESIR, 1660
DFPART, 1661
DUMMY, 1662
EXCALC, 1663
FIDE, 1664
FPS, 1665
GCREF, 1666
GENTRAN, 1667
GNUPLOT, 1668
GROEBNER, 1669
GROEBNER, 1670
GUARDIAN, 1671
IDEALS, 1672
INEQ, 1673
INVBASE, 1674
LALR, 1675
LAPLACE, 1676
LIE, 1677
LIMITS, 1678
LINALG, 1679
LISTVECOPS, 1680
LPDO, 1681
MODSR, 1682
MRVLIMIT, 1683
NCPOLY, 1684
NORMFORM, 1685
NUMERIC, 1686
ODESOLVE, 1687
ORTHOVEC, 1688
PHYSOP, 1689
PLOT, 1690
PM, 1691
QHULL, 1692
QSUM, 1693
RANDPOLY, 1694
RATAPRX, 1695
RATINT, 1696
REACTEQN, 1697
REDLOG, 1698
RESET, 1699
RESIDUE, 1700
RLﬁ, 1701
ROOTS, 1702
RSOLVE, 1703
RTRACE, 1704
SCOPE, 1705
SETS, 1706
SPARSE, 1707
SPDE, 1708
SPECFN, 1709
SPECFN2, 1710
SSTOOLS, 1711
SUM, 1712
SYMMETRY, 1713
TAYLOR, 1714
TPS, 1715
TRI, 1716
TRIGD, 1717
TRIGINT, 1718
TRIGSIMP, 1719, 1720
TURTLE, 1721
WU, 1722
XCOLOR, 1723
XIDEAL, 1724
ZEILBERG, 1725
ZTRANS, 1726
Padé Approximation, 1727
PADE operator, 1728
Padget, Julian, 1729
PART operator, 1730, 1731
use on lists, 1732
use on Taylor kernel, 1733, 1734
PARTIAL, 1735
partial derivatives, 1736
Partial diﬀerentiation, 1737
partial fraction, 1738
partial fraction decomposition, 1739
Partial symmetry
CANTENS package, 1740
PAUSE command, 1741
PCLASS, 1742, 1743, 1744
Percent sign, 1745
PERIOD switch, 1746
Periodic decimal representation, 1747
PERIODIC operator, 1748
PERIODIC2RATIONAL operator, 1749
PF operator, 1750
pfaffian, 1751, 1752
PFORM command, 1753
PFORM statement, 1754
PHYSINDEX, 1755
PHYSOP package, 1756
PI reserved variable, 1757
PIVOT operator, 1758
PLOT, 1759
PLOT package, 1760
PLOTKEEP switch, 1761
PLOTRESET, 1762
PM package, 1763
POCHHAMMER, 1764, 1765
Pochhammer, 1766, 1767
Pochhammer notation, 1768, 1769
Pochhammer’s symbol, 1770, 1771
POLYGAMMA, 1772, 1773
Polygamma, 1774
Polygamma functions, 1775, 1776
Polynomial, 1777
Polynomial equations, 1778
Polynomial Pseudo-Division, 1779
POSITIVE, 1780, 1781
POSITIVE reserved variable, 1782
positivity, 1783
Power series, 1784
arithmetic, 1785
composition, 1786
diﬀerentiation, 1787
of integral, 1788
of user deﬁned function, 1789
Power series expansions, 1790
PRECEDENCE declaration, 1791
PRECISE switch, 1792, 1793
PRECISE_COMPLEX switch, 1794
PRECISION operator, 1795
in ROOTS package, 1796
preduce, 1797
preducet, 1798
Preﬁx, 1799, 1800
Preﬁx operator, 1801
declaring new one, 1802
Preﬁx operator, unary, 1803
preimage, 1804
preimage (CALI), 1805
preimage!*, 1806
PRET switch, 1807, 1808
PRETTYPRINT, 1809
Prettyprinting, 1810, 1811
PRGEN, 1812
PRI switch, 1813
primary decomposition (CALI), 1814
primarydecomposition, 1815
primarydecomposition!*, 1816
prime
=decompose2 (CALI), 1817
PRIMEP boolean operator, 1818
PRINCIPAL_DER global variable (CDE), 1819
PRINT_INDEXED declaration, 1820
PRINT_NOINDEXED declaration, 1821
PRINT_PRECISION command, 1822
PRINTGROUP, 1823
printterms (CALI), 1824
Procedure
body, 1825, 1826
heading, 1827
list-valued, 1828
matrix-valued, 1829
using LET inside body, 1830
PROCEDURE command, 1831
PROD operator, 1832
PRODUCT, 1833
PRODUCT keyword, 1834
Program, 1835
Program structure, 1836
proj_points (CALI), 1837
proj_points1
* (CALI), 1838
proj_monomial_curve, 1839
proj_monomial_curve!*, 1840
proj_points, 1841
proj_points!*, 1842
Proper statement, 1843, 1844, 1845, 1846, 1847
PRSYS, 1848, 1849
PS, 1850
PS operator, 1851
PSCHANGEVAR operator, 1852
PSCOMPOSE operator, 1853
PSCOPY operator, 1854
PSDEPVAR operator, 1855
Pseudo-Division, 1856
pseudo_div operator, 1857
pseudo_divide operator, 1858
PSEUDO_INVERSE operator, 1859
pseudo_quotient operator, 1860
pseudo_remainder operator, 1861
PSEXPANSIONPT operator, 1862
PSEXPLIM Operator, 1863
PSEXPLIM operator, 1864
PSFUNCTION operator, 1865
PSI, 1866, 1867, 1868, 1869
Psi function, 1870
psi function, 1871
PSORDER operator, 1872
PSORDLIM operator, 1873
PSPRINTORDER switch, 1874
PSREVERSE operator, 1875
PSSETORDER operator, 1876
PSSUM operator, 1877
PSTAYLOR operator, 1878
PSTERM operator, 1879
PSTRUNCATE operator, 1880
Puiseux expansion, 1881
Puiseux series, 1882
PUT_EQUATIONS_USED operator (CDE), 1883
PUTCSYSTEM command, 1884
PVAR_DF operator (CDE), 1885

QBINOMIAL operator, 1886
QBRACKETS operator, 1887
QFACTORIAL operator, 1888
QGOSPER operator, 1889
QGOSPER_DOWN switch, 1890, 1891
QGOSPER_SPECIALSOL switch, 1892
QHULL package, 1893
QPHIHYPERTERM operator, 1894
QPOCHHAMMER operator, 1895
QPSIHYPERTERM operator, 1896
QRATIO operator, 1897
QSIMPCOMB operator, 1898, 1899
QSUM package, 1900
QSUM_NULLSPACE switch, 1901, 1902
QSUM_TRACE switch, 1903
QSUMRECURSION operator, 1904
QSUMRECURSION_CERTIFICATE switch, 1905, 1906
QSUMRECURSION_DOWN switch, 1907
QSUMRECURSION_EXP switch, 1908
Quadrature, 1909
QUASILINPDE, 1910
QUIT, 1911
QUOTE, 1912

R_SOLVE, 1913
radical, 1914
radical (CALI), 1915
radical!*, 1916
RANDOM, 1917
random_linear_form, 1918, 1919
RANDOM_NEW_SEED, 1920
RANDOM_MATRIX operator, 1921
RANDPOLY package, 1922
RANK, 1923
RAT, 1924
RAT switch, 1925
RATAPRX package, 1926
RATARG switch, 1927, 1928
RATINT package, 1929
Rational coeﬃcient, 1930
Rational function, 1931
rational number, 1932
RATIONAL switch, 1933
RATIONAL2PERIODIC operator, 1934
RATIONALIZE switch, 1935
RATJORDAN operator, 1936
ratpreimage, 1937
ratpreimage!*, 1938
RATPRI, 1939
RATPRI switch, 1940
RATROOT switch, 1941
REACTEQN package, 1942
REAL, 1943
Real coeﬃcient, 1944, 1945
Real number, 1946, 1947
REALROOTS, 1948, 1949
REALVALUED declaration, 1950
REALVALUEDP, 1951
red (CALI), 1952
red_better (CALI), 1953
red_extract (CALI), 1954
red_prepare (CALI), 1955
red_TailRedDriver (CALI), 1956
red_TopRedBE (CALI), 1957
red_total (CALI), 1958
red_Interreduce, 1959
red_redpol, 1960
red_Straight, 1961
red_TailRed, 1962
red_TopInterreduce, 1963
red_TopRed, 1964
red_TopRedBE, 1965
red_TotalRed, 1966
REDERR, 1967
REDLOG package, 1968
REDUCE, 1969
reducerc ﬁle, 1970, 1971
REDUCT, 1972
REM_SPACES, 1973
REM_DUMMY_IDS, 1974
REM_DUMMY_INDICES, 1975, 1976
REM_VALUE_TENS, 1977, 1978
REM_SPACES, 1979
REM_TENSOR, 1980
remainder operator, 1981
REMANTICOM, 1982
REMEMBER, 1983
REMFAC, 1984
REMFORDER command, 1985, 1986
REMIND, 1987
REMOVE_COLUMNS operator, 1988, 1989
REMOVE_ROWS operator, 1990
REMOVE_VARIABLES, 1991
REMSYM, 1992, 1993
RENOSUM command, 1994, 1995
REPART, 1996, 1997, 1998, 1999
REPEAT, 2000, 2001, 2002, 2003
REPEAT statement, 2004
REPPRINCPARAM_DER shared global variable (CDE), 2005
REPPRINCPARAM_ODD shared global variable (CDE), 2006
REQUIREMENTS shared variable, 2007
Reserved variable, 2008, 2009
Reserved variable
HIGH_POW, 2010
LOW_POW, 2011
CATALAN, 2012
EULER_GAMMA, 2013
GOLDEN_RATIO, 2014
I, 2015
INFINITY, 2016
KHINCHIN, 2017
NEGATIVE, 2018
NIL, 2019
PI, 2020
POSITIVE, 2021
T, 2022
RESET operator, 2023
RESET package, 2024
RESIDUE package, 2025
resolve, 2026
resolve (CALI), 2027
Resolve!*, 2028
REST operator, 2029
RESULT, 2030
RESULTANT, 2031
RETRY, 2032
RETURN, 2033, 2034, 2035, 2036
RETURN statement, 2037
reverse lexicographic (CALI), 2038
REVERSE operator, 2039
REVGRADLEX, 2040
revgradlex
term order, 2041
revlex term order (CALI), 2042
REVPRI, 2043
REVPRI switch, 2044
Rewriting rules
CANTENS package, 2045
RHS operator, 2046
Riemann tensor
CANTENS package, 2047
Riemann Zeta function, 2048
RIEMANNCONX command, 2049, 2050
Riemannian Connections, 2051
ring (CALI), 2052
ring_2a (CALI), 2053
ring_degrees (CALI), 2054
ring_ecart (CALI), 2055
ring_from_a (CALI), 2056
ring_isnoetherian (CALI), 2057
ring_names (CALI), 2058
ring_tag (CALI), 2059
ring_define, 2060
ring_lp, 2061
ring_rlp, 2062
ring_sum, 2063
RLﬁ package, 2064
Rlisp, 2065
RLISP88, 2066
RLROOTNO, 2067
root ﬁnding, 2068
ROOT_MULTIPLICITIES global variable, 2069
ROOT_OF operator, 2070, 2071
ROOT_VAL, 2072, 2073
ROOTACC operator (ROOTS package), 2074
ROOTACC!# global variable (ROOTS package), 2075
ROOTMSG switch, 2076
ROOTPREC operator (ROOTS package), 2077
ROOTS, 2078, 2079
ROOTS package, 2080
ROOTS package, 2081
ROOTS_AT_PREC, 2082
ROOTSCOMPLEX, 2083
ROOTSREAL, 2084
ROUND, 2085
ROUNDALL switch, 2086
ROUNDBF switch, 2087
ROUNDED, 2088, 2089
ROUNDED switch, 2090, 2091, 2092, 2093, 2094
ROW_DIM operator, 2095
ROWS_PIVOT operator, 2096
RSETREPRESENTATION, 2097
RSOLVE package, 2098
RTR command, 2099
RTRACE package, 2100
RTRACE switch, 2101, 2102
RTROUT command, 2103
RTRST command, 2104
Rule lists, 2105
Rules
Double slash operators, 2106
Double tilde variables, 2107
Free operators, 2108
rules (CALI), 2109

saturation, 2110
SAVE_CDE_STATE operator, 2111
SAVEAS statement, 2112
savemat, 2113
savesfs switch, 2114
SAVESTRUCTR switch, 2115
Saving an expression, 2116
SCALAR, 2117, 2118
Scalar, 2119, 2120
Scalar variable, 2121
SCALEFACTORS operator, 2122
SCALOP, 2123
SCHOUTEN_BRACKET operator (CDE), 2124
SCIENTIFIC_NOTATION declaration, 2125
SCOPE package, 2126
SDER(I), 2127
SEC, 2128, 2129
SECH, 2130, 2131
SECOND operator, 2132
SELECT, 2133
Selector, 2134
SELECTVARS operator, 2135
SELFCONJUGATE declaration, 2136, 2137
Semicolon, 2138
SET statement, 2139, 2140
Set Statement, 2141
SET_EQ, 2142
SETAVAILABLE, 2143
setcaliprintterms, 2144
setcalitrace, 2145
setcalitrace (CALI), 2146
setdegrees, 2147
setdegrees (CALI), 2148
SETDIFF, 2149
SETELEMENTS, 2150
setgbasis, 2151
setgbasis (CALI), 2152
SETGENERATORS, 2153
SETGROUPTABLE, 2154
setideal, 2155
setideal (CALI), 2156
setkorder (CALI), 2157
SETMOD, 2158
setmodule, 2159
setmodule (CALI), 2160
setmonset (CALI), 2161
setmonset!*, 2162
setring (CALI), 2163, 2164, 2165, 2166
setring command (CALI), 2167
setring!*, 2168
setrules, 2169
setrules (CALI), 2170, 2171, 2172
setrules!*, 2173
SETS package, 2174
SGN
indeterminate sign, 2175
SHARE declaration, 2176
SHOW_DUMMY_NAMES, 2177
SHOW_EPSILONS, 2178, 2179, 2180
SHOW_SPACES, 2181, 2182, 2183
SHOWRULES, 2184
SHOWTIME command, 2185
SHUT command, 2186
SI, 2187
Side eﬀect, 2188
sieve, 2189
SIGN, 2190, 2191
SIGNATURE, 2192
Signature
CANTENS package, 2193, 2194, 2195, 2196
signature, 2197, 2198, 2199
SIGNATURE command, 2200
SIMPLEDE, 2201
SIMPLEX operator, 2202
Simpliﬁcation, 2203, 2204, 2205
simplify_combinatorial, 2206
SIMPLIFY_GAMMA, 2207
simplify_gamma2, 2208
simplify_gamman, 2209
SIMPNONCOMDF switch, 2210
SIMPSYS, 2211, 2212, 2213
SIN, 2214, 2215
singular_locus, 2216
singular_locus!*, 2217
SINH, 2218, 2219
SixjSymbol, 2220
SMACRO reserved identiﬁer, 2221
SMITHEX operator, 2222
SMITHEX_INT operator, 2223
SolidHarmonicY, 2224, 2225
SOLVE operator, 2226, 2227, 2228
ASSUMPTIONS variable, 2229
REQUIREMENTS shared variable, 2230
ROOT_MULTIPLICITIES global variable, 2231
use of GROEBNER package, 2232
SOLVE package
with ROOTS package, 2233
SOLVESINGULAR switch, 2234
space, 2235
SPACEDIM command, 2236, 2237
Spaces
CANTENS package, 2238, 2239, 2240
spaces, 2241, 2242, 2243, 2244
SPADD_TO_COLUMNS operator, 2245
SPADD_TO_ROWS operator, 2246
SPADD_COLUMNS operator, 2247
SPADD_ROWS operator, 2248
SPARSE declaration, 2249
SPARSE package, 2250
SPARSEMATP predicate, 2251
SPAUGMENT_COLUMNS operator, 2252
SPBAND_MATRIX operator, 2253
SPBLOCK_MATRIX operator, 2254
SPCHAR_MATRIX operator, 2255
SPCHAR_POLY operator, 2256
SPCHOLESKY operator, 2257
SPCOEFF_MATRIX operator, 2258
SPCOL_DIM operator, 2259
SPCOMPANION operator, 2260
SPCOPY_INTO operator, 2261
SPDE package, 2262
SPDIAGONAL operator, 2263
SPECFN, 2264
SPECFN package, 2265
SPECFN2 package, 2266
SPEXTEND operator, 2267
SPFIND_COMPANION operator, 2268
SPGET_COLUMNS operator, 2269
SPGET_ROWS operator, 2270
SPGRAM_SCHMIDT operator, 2271
Spherical and Solid Harmonics, 2272
Spherical coordinates, 2273, 2274
SphericalHarmonicY, 2275, 2276
SPHERMITIAN_TP operator, 2277
SPHESSIAN operator, 2278
Spinor
CANTENS package, 2279
SPJACOBIAN operator, 2280
SPJORDAN_BLOCK operator, 2281
SPLIT_FIELD function, 2282
SPLITEXT_LIST operator (CDE), 2283
SPLITEXT_OPEQU operator (CDE), 2284
SPLITVARS_OPEQU operator (CDE), 2285
SPLU_DECOM operator, 2286
SPMAKE_IDENTITY operator, 2287
SPMATRIX_AUGMENT operator, 2288
SPMATRIX_STACK operator, 2289
SPMINOR operator, 2290
SPMULT_COLUMNS operator, 2291
SPMULT_ROWS operator, 2292
SPPIVOT operator, 2293
SPPSEUDO_INVERSE operator, 2294
SPREMOVE_ROWS operator, 2295
SPROW_DIM operator, 2296
SPROWS_PIVOT operator, 2297
SPSUB_MATRIX operator, 2298
SPSVD operator, 2299
SPSWAP_COLUMNS operator, 2300
SPSWAP_ENTRIES operator, 2301
SPSWAP_ROWS operator, 2302
SPUR, 2303
SQFRF, 2304
SQRT, 2305, 2306
SQUAREP predicate, 2307, 2308
SSTOOLS package, 2309
stable quotient (CALI), 2310
STACK_ROWS operator, 2311, 2312
Standard form, 2313
Standard quotient, 2314
Startup ﬁle, 2315, 2316
STATE, 2317
Statement, 2318
assignment, 2319
compound, 2320
conditional, 2321
FOR, 2322
FOREACH, 2323
GO TO, 2324
Group, 2325
REPEAT, 2326
RETURN, 2327
SAVEAS, 2328
Set, 2329
Unset, 2330
WHILE, 2331
Statement terminator, 2332
Stirling Numbers, 2333
Stirling numbers, 2334
Stirling1, 2335, 2336
Stirling2, 2337, 2338
STOREGROUP, 2339
String, 2340
STRUCTR, 2341, 2342
Structuring, 2343
Struve functions, 2344, 2345
StruveH, 2346, 2347, 2348
StruveL, 2349, 2350, 2351
Sturm Sequences, 2352
SUB, 2353
SUB operator, 2354
SUB_MATRIX operator, 2355
sublist (CALI), 2356
submodulep, 2357
submodulep!*, 2358
SUBSET_EQ, 2359
Subspaces
CANTENS package, 2360
subspaces, 2361
Substitution, 2362
SUCHTHAT, 2363
SUM, 2364
SUM keyword, 2365
SUM operator, 2366
SUM package, 2367
SUM!-SQ operator, 2368
SUMRECURSION, 2369
SUMTOHYPER, 2370
SUPER_PRODUCT operator (CDE), 2371
SVD operator, 2372
SVEC, 2373
SWAP_COLUMNS operator, 2374
SWAP_ENTRIES operator, 2375
SWAP_ROWS operator, 2376
Switch, 2377, 2378
ADJPREC, 2379
ALGINT, 2380
ALLBRANCH, 2381
ALLFAC, 2382, 2383, 2384
ALLOWDFINT, 2385
ANTICOM, 2386
ARBVARS, 2387
BALANCED_MOD, 2388, 2389
BEZOUT, 2390
BFSPACE, 2391
binomial, 2392
CHECKORD, 2393
COMBINEEXPT, 2394
COMBINELOGS, 2395
COMMUTEDF, 2396
COMP, 2397
COMPLEX, 2398, 2399
CRAMER, 2400, 2401
CREF, 2402
DEFN, 2403, 2404, 2405
DFINT, 2406
DFPRINT, 2407
DISPJACOBIAN, 2408
DIV, 2409, 2410
ECHO, 2411
ERRCONT, 2412
EVALLHSEQP, 2413
EXP, 2414, 2415
EXPANDDF, 2416
EXPANDLOGS, 2417
EZGCD, 2418
FACTOR, 2419, 2420
FAILHARD, 2421
FAST_LA, 2422, 2423
FASTSIMPLEX, 2424
FORT, 2425
FORTUPPER, 2426
FULLROOTS, 2427
GCD, 2428
GLTBASIS, 2429, 2430
GROEBFULLREDUCTION, 2431, 2432
GROEBOPT, 2433, 2434, 2435
GROEBPROT, 2436
GROEBSTAT, 2437, 2438
HEUGCD, 2439
HORNER, 2440
IFACTOR, 2441
IMAGINARY, 2442
INTSTR, 2443
lazy, 2444
LHYP, 2445
LIST, 2446
LISTARGS, 2447
LMON, 2448
LOOKING_GOOD, 2449
LOWER_MATRIX, 2450
LTRIG, 2451
MCD, 2452, 2453
MODULAR, 2454, 2455, 2456
MSG, 2457
MULTIPLICITIES, 2458
MULTIROOT, 2459
NAT, 2460, 2461
NERO, 2462
NOCOMMUTEDF, 2463
NOCONVERT, 2464
Noetherian, 2465, 2466
NOINTSUBST, 2467
NOLNR, 2468
NOSPLIT, 2469
NOSUM, 2470
NOT_NEGATIVE, 2471
ONESPACE, 2472, 2473, 2474
ONLY_INTEGER, 2475
OUTPUT, 2476
PERIOD, 2477
PLOTKEEP, 2478
PRECISE, 2479, 2480
PRECISE_COMPLEX, 2481
PRET, 2482, 2483
PRI, 2484
PSPRINTORDER, 2485
QGOSPER_DOWN, 2486, 2487
QGOSPER_SPECIALSOL, 2488
QSUM_NULLSPACE, 2489, 2490
QSUM_TRACE, 2491
QSUMRECURSION_CERTIFICATE, 2492, 2493
QSUMRECURSION_DOWN, 2494
QSUMRECURSION_EXP, 2495
RAT, 2496
RATARG, 2497, 2498
RATIONAL, 2499
RATIONALIZE, 2500
RATPRI, 2501
RATROOT, 2502
REVPRI, 2503
ROOTMSG, 2504
ROUNDALL, 2505
ROUNDBF, 2506
ROUNDED, 2507, 2508, 2509, 2510, 2511
RTRACE, 2512, 2513
savesfs, 2514
SAVESTRUCTR, 2515
SIMPNONCOMDF, 2516
SOLVESINGULAR, 2517
SYMMETRIC, 2518
TAYLORAUTOCOMBINE, 2519
TAYLORAUTOEXPAND, 2520, 2521
TAYLORKEEPORIGINAL, 2522, 2523, 2524, 2525
TAYLORPRINTORDER, 2526
TR_LIE, 2527
TRA, 2528
TRCOMPACT, 2529
TRFAC, 2530
TRGROEB, 2531, 2532
TRGROEB1, 2533, 2534
TRGROEBR, 2535
TRGROEBS, 2536, 2537
TRIGFORM, 2538
TRINT, 2539, 2540
TRINTSUBST, 2541
TRNUMERIC, 2542
TRPLOT, 2543
TRROOT, 2544
TRSOLVE, 2545
TRSUM, 2546
TRWU, 2547
UPPER_MATRIX, 2548
VAROPT, 2549
VERBOSELOAD, 2550
ZB_FACTOR, 2551
ZB_PROOF, 2552
ZB_TRACE, 2553, 2554
switch ASSERT, 2555
switch ASSERTBREAK, 2556
switch ASSERTSTATISTICS, 2557
switch bcsimp (CALI), 2558
switch hardzerotest (CALI), 2559
switch lexefgb (CALI), 2560, 2561
switch Noetherian (CALI), 2562
Switches by package
REDUCE Core
ADJPREC, 2563
ALLBRANCH, 2564
ALLFAC, 2565, 2566, 2567
ALLOWDFINT, 2568
ARBVARS, 2569
BALANCED_MOD, 2570, 2571
BEZOUT, 2572
BFSPACE, 2573
COMBINEEXPT, 2574
COMBINELOGS, 2575
COMMUTEDF, 2576
COMP, 2577
COMPLEX, 2578, 2579
CRAMER, 2580, 2581
CREF, 2582
DEFN, 2583, 2584, 2585
DFINT, 2586
DFPRINT, 2587
DISPJACOBIAN, 2588
DIV, 2589, 2590
ECHO, 2591
ERRCONT, 2592
EVALLHSEQP, 2593
EXP, 2594, 2595
EXPANDDF, 2596
EXPANDLOGS, 2597
EZGCD, 2598
FACTOR, 2599, 2600
FAILHARD, 2601
FORT, 2602
FORTUPPER, 2603
FULLROOTS, 2604
GCD, 2605
HEUGCD, 2606
HORNER, 2607
IFACTOR, 2608
INTSTR, 2609
LIST, 2610
LISTARGS, 2611
MCD, 2612, 2613
MODULAR, 2614, 2615, 2616
MSG, 2617
MULTIPLICITIES, 2618
NAT, 2619, 2620
NERO, 2621
NOCOMMUTEDF, 2622
NOCONVERT, 2623
NOINTSUBST, 2624
NOLNR, 2625
NOSPLIT, 2626
OUTPUT, 2627
PERIOD, 2628
PLOTKEEP, 2629
PRECISE, 2630, 2631
PRECISE_COMPLEX, 2632
PRET, 2633, 2634
PRI, 2635
RAT, 2636
RATARG, 2637, 2638
RATIONAL, 2639
RATIONALIZE, 2640
RATPRI, 2641
REVPRI, 2642
ROUNDALL, 2643
ROUNDBF, 2644
ROUNDED, 2645, 2646, 2647, 2648, 2649
savesfs, 2650
SAVESTRUCTR, 2651
SIMPNONCOMDF, 2652
SOLVESINGULAR, 2653
TRFAC, 2654
TRIGFORM, 2655
TRINT, 2656
TRINTSUBST, 2657
VAROPT, 2658
ALGINT package
ALGINT, 2659
TRA, 2660
TRINT, 2661
CALI package
binomial, 2662
lazy, 2663
Noetherian, 2664, 2665
CANTENS package
ONESPACE, 2666, 2667, 2668
CDE package
CHECKORD, 2669
COMPACT package
TRCOMPACT, 2670
EXCALC package
NOSUM, 2671
GNUPLOT package
TRPLOT, 2672
GROEBNER package
GLTBASIS, 2673, 2674
GROEBFULLREDUCTION, 2675, 2676
GROEBOPT, 2677, 2678, 2679
GROEBPROT, 2680
GROEBSTAT, 2681, 2682
TRGROEB, 2683, 2684
TRGROEB1, 2685, 2686
TRGROEBR, 2687
TRGROEBS, 2688, 2689
LAPLACE package
LHYP, 2690
LMON, 2691
LTRIG, 2692
LIE package
TR_LIE, 2693
LINALG package
FAST_LA, 2694
FASTSIMPLEX, 2695
IMAGINARY, 2696
LOWER_MATRIX, 2697
NOT_NEGATIVE, 2698
ONLY_INTEGER, 2699
SYMMETRIC, 2700
UPPER_MATRIX, 2701
NORMFORM package
LOOKING_GOOD, 2702
NUMERIC package
TRNUMERIC, 2703
PHYSOP package
ANTICOM, 2704
QSUM package
QGOSPER_DOWN, 2705, 2706
QGOSPER_SPECIALSOL, 2707
QSUM_NULLSPACE, 2708, 2709
QSUM_TRACE, 2710
QSUMRECURSION_CERTIFICATE, 2711, 2712
QSUMRECURSION_DOWN, 2713
QSUMRECURSION_EXP, 2714
ROOTS package
MULTIROOT, 2715
RATROOT, 2716
ROOTMSG, 2717
TRROOT, 2718
RSOLVE package
TRSOLVE, 2719
RTRACE package
RTRACE, 2720, 2721
SPARSE package
FAST_LA, 2722
SUM package
TRSUM, 2723
TAYLOR package
TAYLORAUTOCOMBINE, 2724
TAYLORAUTOEXPAND, 2725, 2726
TAYLORKEEPORIGINAL, 2727, 2728, 2729, 2730
TAYLORPRINTORDER, 2731
VERBOSELOAD, 2732
TPS package
PSPRINTORDER, 2733
WU package
TRWU, 2734
ZEILBERG package
ZB_FACTOR, 2735
ZB_PROOF, 2736
ZB_TRACE, 2737, 2738
sym, 2739
sym (CALI), 2740
sym!*, 2741
SYMBOLIC, 2742
Symbolic indices
CANTENS package, 2743
Symbolic mode, 2744, 2745, 2746, 2747, 2748
Symbolic procedure, 2749
symbolic_power, 2750
symbolic_power!*, 2751
symmetric
tensor, 2752
SYMMETRIC declaration, 2753, 2754
Symmetric operator, 2755
SYMMETRIC switch, 2756
SYMMETRICP predicate, 2757, 2758
Symmetries
CANTENS package, 2759
SYMMETRIZE, 2760
SYMMETRY package, 2761
SYMMETRY package, 2762
SYMMETRYBASIS, 2763
SYMMETRYBASISPART, 2764
SYMTREE, 2765
SYMTREE declaration, 2766
systemprecision, 2767
syzygies, 2768
syzygies!*, 2769
syzygies1!*, 2770

T, 2771
T reserved variable, 2772
TAN, 2773, 2774, 2775
Tangent vector, 2776
tangentcone, 2777
TANH, 2778, 2779
TAYLOR operator, 2780
TAYLOR package, 2781
Taylor series, 2782
arithmetic, 2783
diﬀerentiation, 2784
integration, 2785
reversion, 2786
substitution, 2787
TAYLORAUTOCOMBINE switch, 2788
TAYLORAUTOEXPAND switch, 2789, 2790
TAYLORCOMBINE operator, 2791, 2792
TAYLORKEEPORIGINAL switch, 2793, 2794, 2795, 2796
TAYLORORIGINAL operator, 2797, 2798
TAYLORPRINTORDER switch, 2799
TAYLORPRINTTERMS variable, 2800, 2801
TAYLORREVERT operator, 2802, 2803
TAYLORSERIESP operator, 2804
TAYLORTEMPLATE operator, 2805, 2806
TAYLORTOSTANDARD operator, 2807
TENSOP, 2808
TENSOR, 2809
Tensor contractions
CANTENS package, 2810
Tensor derivatives
CANTENS package, 2811
Tensor polynomial
CANTENS package, 2812
term (CALI), 2813
Terminator, statement, 2814
THIRD operator, 2815
ThreejSymbol, 2816
TIME, 2817
TOEPLITZ operator, 2818
torder, 2819, 2820, 2821, 2822, 2823
TORDER operator, 2824
TOTAL, 2825
TOTAL_ORDER global variable (CDE), 2826
TOTALDEG, 2827
TP, 2828
TPS package, 2829
TR_LIE switch, 2830
TRA switch, 2831
TRACE, 2832
Trace
CANTENS package, 2833
trace (CALI), 2834
Tracing
EXCALC package, 2835
GNUPLOT package, 2836
ROOTS package, 2837
SPDE package, 2838
SUM package, 2839
tracing (CALI), 2840
TRCOMPACT switch, 2841
TRFAC switch, 2842
TRGROEB switch, 2843, 2844
TRGROEB1 switch, 2845, 2846
TRGROEBR switch, 2847
TRGROEBS switch, 2848, 2849
TRI package, 2850
triang (CALI), 2851
TRIANG_ADJOINT operator, 2852
triangular systems (CALI), 2853, 2854, 2855
trig functions, 2856
TRIGD package, 2857
TRIGFORM switch, 2858
TRIGINT package, 2859
TRIGONOMETRIC_BASE, 2860
TRIGSIMP, 2861
TRIGSIMP package, 2862, 2863
TRINT switch, 2864, 2865
TRINTSUBST switch, 2866
TRNUMERIC switch, 2867
TRPLOT switch, 2868
TRRL command, 2869
TRRLID command, 2870
TRROOT switch, 2871
TRSOLVE switch, 2872
TRSUM switch, 2873
TRWU switch, 2874
TRXIDEAL switch, 2875
TRXMOD switch, 2876
TURTLE package, 2877
TURTLE package, 2878
TVECTOR command, 2879, 2880

U(ALFA), 2881
U(ALFA,I), 2882
Unary preﬁx operator, 2883
UNION, 2884
UNIT, 2885
unmixedradical, 2886
unmixedradical!*, 2887
UNRTR command, 2888
UNRTRST command, 2889
UNSET statement, 2890, 2891
Unset Statement, 2892
UNTIL, 2893
UNTRRL command, 2894
UNTRRLID command, 2895
UP_QRATIO operator, 2896
UPPER_MATRIX switch, 2897
UPWARD_ANTIDIFFERENCE, 2898
User packages, 2899

VANDERMONDE operator, 2900
VARDF, 2901
VARDF (variational derivative) operator), 2902
Variable, 2903
double tilde, 2904
Variable elimination, 2905
Variational derivative, 2906
varlessp (CALI), 2907
VARNAME, 2908, 2909
varnames (CALI), 2910
varopt, 2911
VAROPT switch, 2912
varopt!*, 2913
VDF, 2914
VEC command, 2915
VECDIM, 2916
VECOP, 2917
VECTOR, 2918
Vector
addition, 2919
cross product, 2920
diﬀerentiation, 2921
division, 2922
dot product, 2923
exponentiation, 2924
inner product, 2925
integration, 2926
modulus, 2927
multiplication, 2928
subtraction, 2929
Vector algebra, 2930
VECTORADD, 2931
VECTORCROSS, 2932
VECTORDIFFERENCE, 2933
VECTOREXPT, 2934
VECTORMINUS, 2935
VECTORPLUS, 2936
VECTORQUOTIENT, 2937
VECTORRECIP, 2938
VECTORTIMES, 2939
VERBOSELOAD switch, 2940
VINT, 2941
VMOD, 2942
VMOD operator, 2943
VOLINT, 2944
VOLINTEGRAL function, 2945
VOLINTORDER vector, 2946
VORDER, 2947
VOUT, 2948
VSTART, 2949
VTAYLOR, 2950

Warnings
TAYLOR package, 2951
Wedge, 2952
WEIGHT, 2953
weighted Hilbert series (CALI), 2954, 2955
Weighted ordering, 2956
WeightedHilbertSeries, 2957
WeightedHilbertSeries (CALI), 2958
WeightedHilbertSeries!*, 2959
WHEN, 2960
WHERE, 2961
WHILE, 2962, 2963, 2964, 2965
WHILE statement, 2966
Whittaker functions, 2967, 2968
WhittakerM, 2969, 2970, 2971
WhittakerU, 2972
WhittakerW, 2973, 2974
wholespace, 2975, 2976, 2977, 2978, 2979, 2980
WHOLESPACE_DIM, 2981, 2982
Workspace, 2983
WRITE, 2984
WS, 2985, 2986
WTLEVEL, 2987
WU package, 2988

X(I), 2989
XAUTO, 2990
XCOLOR package, 2991
XFULLREDUCE switch, 2992
XI(I), 2993
XIDEAL, 2994
XIDEAL package, 2995
XMOD, 2996
XMODIDEAL, 2997
XORDER, 2998
XPND
XPND
@, 2999
XPND
@, 3000
D, 3001
XPND command, 3002
XVARS, 3003

ZB_DIRECTION variable, 3004
ZB_FACTOR switch, 3005
ZB_ORDER variable, 3006
ZB_PROOF switch, 3007
ZB_TRACE switch, 3008, 3009
ZEILBERG package, 3010
ZEILBERGER_REPRESENTATION variable, 3011
zeroprimarydecomposition, 3012
zeroprimarydecomposition!*, 3013
zeroprimes, 3014
zeroprimes!*, 3015
zeroradical, 3016
zeroradical!*, 3017
zerosolve
* (CALI), 3018, 3019
zerosolve, 3020
zerosolve (CALI), 3021
zerosolve1
* (CALI), 3022, 3023
zerosolve1, 3024
zerosolve1 (CALI), 3025
zerosolve2
* (CALI), 3026
zerosolve2, 3027
ZETA, 3028, 3029
Zeta, 3030
Zeta function, 3031
Zeta function (Riemann’s), 3032
ZETA(ALFA,I), 3033
ZTRANS, 3034
ZTRANS package, 3035

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