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## Index

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

ABS, 65, 66
ACOS, 67, 68
ACOSH, 69, 70
ACOT, 71, 72
ACOTH, 73, 74
ACSC, 75, 76
ACSCH, 77, 78
affine, 86
Affine space
CANTENS package, 87
Airy functions, 88
Airy_Ai, 89, 90
Airy_Aiprime, 91, 92
Airy_Bi, 93, 94
Airy_Biprime, 95, 96
ALGEBRAIC, 97
Algebraic mode, 98, 99, 100
Algebraic number fields, 101
Algebraic numbers, 102
ALGINT package, 103, 104
ALGINT switch, 105
ALL_PARAMETRIC_DER shared global variable (CDE), 106
ALL_PARAMETRIC_ODD shared global variable (CDE), 107
ALL_PARAMTERIC_DER shared global variable (CDE), 108
ALL_PRINCIPAL_DER shared global variable (CDE), 109
ALL_PRINCIPAL_ODD shared global variable (CDE), 110
ALLBRANCH switch, 111
ALLFAC switch, 112, 113, 114
ALLOWDFINT switch, 115
ALLSYMMETRYBASES, 116
AND logical operator, 117
ansatz of symmetry generator, 118
ANTICOM switch, 119
ANTICOMM operator, 120
Anticommutative
CANTENS package, 121
ANTICOMMUTE, 122
Antisymmetric
CANTENS package, 123
ANTISYMMETRIC declaration, 124, 125
Antisymmetric operator, 126
APPEND operator, 127
APPLYSYM, 128
APPLYSYM package
example, 129
APPLYSYM package, 130
approximation, 131
ARBCOMPLEX, 132
ARBINT, 133
ARBVARS switch, 134
ARGLENGTH operator, 135
ARNUM package, 136
ARNUM package
example, 137, 138, 139, 140
ARRAY, 141
Array declaration, 142
ASEC, 143, 144
ASECH, 145, 146
ASIN, 147, 148
ASINH, 149, 150
ASSERT package, 151
Assignment, 152, 153, 154, 155, 156, 157, 158, 159
Assignment statement, 160
multiple, 161
ASSIST, 162, 163
ASSIST package, 164
ASSUMPTIONS variable, 165
Asymptotic command, 166, 167
ATAN, 168, 169, 170
ATAN2, 171, 172
ATANH, 173, 174
AUGMENT_COLUMNS operator, 175
AVAILABLEGROUPS, 176
AVEC function, 177
AVECTOR package, 178
example, 179, 180, 181, 182, 183
AVECTOR package, 184

BALANCED_MOD switch, 185, 186
BAND_MATRIX operator, 187
Barnes, Alan, 188
BEGIN…END, 189, 190, 191, 192
BERNOULLI, 193
Bernoulli, 194
Bernoulli numbers, 195, 196
BERNSTEIN_BASE, 197
Bessel functions, 198
BesselI, 199, 200
BesselJ, 201, 202
BesselK, 203, 204
BesselY, 205, 206
BETA, 207, 208
Beta function, 209
BEZOUT switch, 210
BFSPACE switch, 211
BIBASIS, 212
BIBASIS package, 213
bibasis_print_statistics, 214
Binomial, 215
Binomial coefficients, 216
bloc-diagonal, 217, 218, 219
Block, 220, 221
BLOCK_MATRIX operator, 222
BNDEQ!* shared variable, 223
Boolean expression, 224
BOOLEAN operator, 225
BOOLEAN package, 226
BOUNDS, 227, 228
Buchberger’s Algorithm, 229, 230
BYE command, 231

C(I), 232
CALI package, 233
Call by value, 234, 235
CAMAL package, 236
CANONICAL, 237
Canonical form, 238, 239
CANONICAL operator, 240, 241, 242, 243, 244, 245, 246, 247
CANONICALDECOMPOSITION, 248
CANTENS package, 249
CANTENS package
== operator, 250
affine space, 251
anticommutative indexed objects, 252
antisymmetric tensor, 253
DEPEND, 254
dummy indices, 255
epsilon tensor, 256
FORALL, 257
indices, 258, 259
indices, dummy, 260
indices, numeric, 261
indices, symbolic, 262
LET, 263
metric tensor, 265
mixed symmetry, 266
numeric indices, 267
partial symmetry, 268
rewriting rules, 269
Riemann tensor, 270
signature, 271, 272, 273, 274
spaces, 275, 276, 277
spinor, 278
SUB, 279, 280
subspaces, 281
symbolic indices, 282, 283
symmetries, 284
tensor contractions, 285
tensor derivatives, 286
tensor polynomial, 287
trace, 288
variables, 289, 290, 291
CARD_NO shared global variable, 292
Cartesian coordinates, 293
CATALAN reserved variable, 294
Caveats
TAYLOR package, 295
CDE operator, 296
CDE package, 297
CDIff package, 299
CEILING, 300
CFRAC operator, 301
CGB operator, 302
CGB package, 303
CGBFULLRED switch, 304
CGBGEN switch, 305
CGBGS switch, 306
CGBREAL switch, 307
CGBSTAT switch, 308
Chain rule, 309
CHANGEVAR operator, 310
CHAR_MATRIX operator, 311
CHAR_POLY operator, 312
CHARACTER, 313
Character set, 314
CHARACTERN, 315
Chebyshev fit, 316
Chebyshev polynomials, 317
CHEBYSHEV_BASE_T, 318
CHEBYSHEV_BASE_U, 319
CHEBYSHEV_DF, 320
CHEBYSHEV_EVAL, 321
CHEBYSHEV_FIT, 322
CHEBYSHEV_INT, 323
ChebyshevT, 324
ChebyshevU, 325
CHECKORD switch, 326
CHOLESKY operator, 327
CI, 328
CLEAR, 329, 330
CLEAR_DUMMY_BASE, 331
CLEARPHYSOP, 332
CLEARRULES, 333
Clebsch Gordan coefficients, 334
Clebsch_Gordan, 335
COEFF operator, 336
COEFF_MATRIX operator, 337
Coefficient, 338, 339, 340, 341, 342
COEFFN operator, 343
COFACTOR, 344
COFRAME
WITH METRIC, 345
WITH SIGNATURE, 346
Coframe, 347, 348
COFRAME command, 349
COLLECT keyword, 350
COLUMN_DIM operator, 351
COMBINEEXPT switch, 352
COMBINELOGS switch, 353
COMM, 354
COMM operator, 355
Command, 356
BYE, 357
CONT, 358
DEFINE, 359
PAUSE, 360
SHOWTIME, 361
Command terminator
IN command, 362
COMMENT keyword, 363
COMMUTE, 364
COMMUTEDF switch, 365
COMP switch, 366
COMPACT operator, 367
COMPACT package, 368
COMPANION operator, 369
Compiler, 370
COMPLEX, 371
Complex coefficient, 372
COMPLEX switch, 373, 374
Compound statement, 375, 376
Computations with supersymmetric algebraic and differential expressions, 377
Conditional statement, 378, 379
CONJ, 380
Constructor, 381
CONT COMMAND, 382
CONTFRAC operator, 383
Continued fractions, 384
CONTINUED_FRACTION operator, 385
CONTRACT, 386
CONV_CDIFF2SUPERFUN operator (CDE), 387
CONV_SUPERFUN2CDIFF operator (CDE), 388
Coordinates
cartesian, 389
cylindrical, 390
coordinates
spherical, 391
COORDINATES operator, 392
COORDS vector, 393
COPY_INTO operator, 394
COS, 395, 396
COSH, 397, 398
COT, 399, 400
COTH, 401, 402
CRACK package, 403
crack, running in CDE package, 404
CRAMER switch, 405, 406
CREF, 407
CREF switch, 408
CRESYS, 409, 410
CROSS
vector, 411
Cross product, 412, 413
Cross reference, 414
CSC, 415, 416
CSCH, 417, 418
CSETREPRESENTATION, 419
Curl
vector field, 420
CURL
operator, 421
CURL operator, 422
CVIT package, 423
Cylindrical coordinates, 424

d
exterior differentiation, 425
dd_groebner, 426
Declaration, 427
array, 428
KORDER, 429
mode handling, 430
DECOMPOSE, 431
decomposition
partial fraction, 432
Default
term order, 433
Defaults
TAYLOR package, 434
DEFINE command, 435
DEFINE_SPACES, 436, 437
Definite integration (simple), 438
DEFINT function, 439
DEfiNT package, 440, 441
DEfiNT package, 442
DEFLINEINT function, 443
DEFN switch, 444, 445, 446
DEFPOLY statement, 447
DEG, 448
Degree, 449
del, 450, 451, 452
DELSQ
operator, 453
DELSQ operator, 454
delta, 455, 456, 457, 458, 459, 460, 461
deltafunction, 462, 463
DEMO, 464
DEN, 465, 466
DEP_VAR global variable (CDE), 467
DEPEND, 468
DEPEND
CANTENS package, 469
DEPEND command, 470
DEPEND declaration, 471
DEPEND statement, 472
DEQ(I), 473
DER_DEG_ORDERING operator (CDE), 474
Derivative
variational, 475
derivatives, 476
DESIR package, 477
DET, 478
DET operator, 479
Determinant
in DETM!*, 480
DETM!* variable, 481
DETRAFO, 482
DF, 483
DF operator, 484, 485
DF_ODD operator (CDE), 486
DFINT switch, 487
DFP, 488
DFPART package, 489
DIAGONAL operator, 490
DIAGONALIZE, 491
Differential geometry, 492
Differentiation, 493, 494, 495
partial, 496
vector, 497, 498
Digamma, 499
Digamma function, 500
DILOG, 501, 502, 503
Dilogarithm function, 504
Dimension, 505
Dirac γ matrix, 506
DISPJACOBIAN switch, 507
DISPLAY, 508
Display, 509
DISPLAYFRAME command, 510, 511
Displaying structure, 512
DIV
operator, 513
DIV operator, 514
DIV switch, 515, 516
Divergence
vector field, 517
DIVIDE operator, 518
DLINEINT, 519
DO, 520, 521, 522
DO keyword, 523
Dollar sign, 524
DOT, 525
DOT
vector, 526
Dot product, 527, 528, 529
Double slash operator
in rules, 532
Double tilde variables
in rules, 533
DOWN_QRATIO operator, 534
DOWNWARD_ANTIDIFFERENCE, 535
DUMMY, 536, 537, 538, 539, 540, 541
dummy, 542, 543
Dummy indices
CANTENS package, 544
dummy indices, 545
DUMMY package, 546
DUMMY_BASE, 547
DUMMY_INDICES, 548
DUMMY_NAME, 549
DVINT, 550
DVOLINT, 551

E reserved variable, 552
ECHO switch, 553
ED, 554, 555
EDITDEF, 556
Ei, 557
ELL_FUNCTION operator (CDE), 558
EllipticE, 559
EllipticF, 560
EllipticTheta, 561
END, 562
EPS, 563, 564
EPS
Levi-Civita tensor, 565
epsilon, 566, 567, 568
Epsilon tensor
CANTENS package, 569
Equation, 570, 571
ERF, 572
ERRCONT switch, 573
Errors
TAYLOR package, 574
eta, 575, 576, 577, 578
ETA(ALFA), 579
Euclidean metric, 580
euclidian, 581
EULER, 582
Euler, 583
Euler numbers, 584, 585
Euler polynomials, 586
EULER_DF operator (CDE), 587
EULER_GAMMA reserved variable, 588
EulerP, 589
EVAL_MODE shared global variable, 590
EVALB, 591
EVALLHSEQP switch, 592
EVEN declaration, 593
Even operator, 594
EVENP boolean operator, 595
EXCALC, 596
EXCALC package
example, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612
tracing, 613
EXCALC package, 614
Exclamation mark, 615
EXCLUDE, 616, 617
EXCOEFFS, 618
EXDEGREE, 619
EXDEGREE command, 620
EXDELT, 621, 622
EXP, 623, 624, 625, 626
EXP switch, 627, 628
EXPAND_CASES operator, 629
EXPAND_TD command, 630
EXPANDDF switch, 631
EXPANDLOGS switch, 632
EXPR, 633
Expression, 634
boolean, 635
EXT operator (CDE), 636
EXTEND operator, 637
EXTENDED_GOSPER, 638
EXTENDED_SUMRECURSION, 639
Exterior calculus, 640
Exterior differentiation, 641
Exterior form
declaration, 642
ordering, 643
vector, 644
with indices, 645, 646
Exterior product, 647, 648
EXVARS, 649
EZGCD switch, 650

FACTOR declaration, 651
FACTOR switch, 652, 653
FACTORIAL, 654, 655
Factorization, 656
FACTORIZE, 657, 658
FAILHARD switch, 659
FAST_LA switch, 661, 662
FASTSIMPLEX switch, 663
FDOMAIN command, 664, 665
FEXPR reserved identifier, 666
Fibonacci, 667
Fibonacci numbers, 668
Fibonacci Polynomials, 669
FibonacciP, 670
FIDE package, 671
File handling, 672
FIND_COMPANION operator, 673
FIRST operator, 674
FIRSTROOT, 675
FIX, 676
FIXP boolean operator, 677
FLOOR, 678
FOR, 679
FORALL, 680, 681
FORALL
CANTENS package, 682
FOREACH, 683, 684, 685, 686
FOREACH statement, 687
FOR statement, 688
FORDER command, 689, 690
FORT, 691
FORT switch, 692
FORTRAN, 693, 694
FORTUPPER switch, 695
FPS, 696
FPS package, 697
FRAME command, 698, 699
Free operators
in rules, 700
FREEOF boolean operator, 701
FROBENIUS operator, 702
FULLROOTS switch, 703, 704
Function, 705

G, 706
GAMMA, 707, 708
Gamma function, 709
GAMMATOFACTORIAL, 710
GCD, 711
GCD switch, 712
GCREF package, 713
gdimension, 714
Gegenbauer polynomials, 715
GegenbauerP, 716
GEN(I), 717
Generalized Hypergeometric functions, 718
GENERATORS, 719
generic function, 720
generic tensor, 721
GENERIC_FUNCTION, 722
GENTRAN package, 723
GET_COLUMNS operator, 724
GET_ROWS operator, 725
GETCSYSTEM command, 726
GETROOT, 727
GFNEWT, 728
GFROOT, 729
gindependent_sets, 730
GL(I), 731
glexconvert, 732
GLOBAL_SIGN, 733, 734, 735
GLTBASIS switch, 736, 737
GNUPLOT command, 738
GNUPLOT package, 739
GNUPLOT package, 740
GOTO, 741, 742
GO TO statement, 743
GOLDEN_RATIO reserved variable, 744
GOSPER, 745
Gosper’s Algorithm, 746
GOSPER_REPRESENTATION variable, 747
Gröbner Bases, 748
operator, 749
vector field, 752
term order, 753
GRAM_SCHMIDT operator, 754
greduce, 755
greduce_orders, 756
GROEBFULLREDUCTION switch, 757, 758
groebmonfac, 759, 760
groebner, 761
Groebner Bases, 762
GROEBNER package, 763
Groebner package, 764
example, 765, 766, 767, 768, 769, 770, 771
ordering
grouped, 773
matrix, 774
weighted, 775
term order
default, 776
lex, 778
GROEBNER package, 780
groebner_walk, 781
groebnerf, 782, 783, 784
groebnert, 785
GROEBOPT switch, 786, 787, 788
GROEBPROT switch, 789
groebprotfile, 790
groebresmax, 791
groebrestriction, 792
GROEBSTAT switch, 793, 794
groepostproc, 795
groesolve, 796
Group statement, 797, 798, 799
Grouped ordering, 800
gsort, 801
gsplit, 802
gspoly, 803
GSYS operator, 804
GSYS2CGB operator, 805
GUARDIAN package, 806
gvars, 807
gvarslast, 808, 809
gzerodim?, 810

Hankel functions, 811
Hankel1, 812, 813
Hankel2, 814, 815
Hermite polynomials, 816
HERMITE_BASE, 817
HermiteP, 818
HERMITIAN_TP operator, 819
HESSIAN operator, 820
HEUGCD switch, 821
HFACTORS scale factors, 822
High energy trace, 823
High energy vector expression, 824, 825
HIGH_POW, 826
HILBERT operator, 827
Hilbert polynomial, 828
Hilbertpolynomial, 829
History, 830
Hodge-* duality operator, 831, 832
HYPERRECURSION, 833
HYPERSUM, 834
HYPERTERM, 835
HYPOT, 836, 837

i, 838
I reserved variable, 839
I_SOLVE, 840
IBETA, 841
idealdimension, 842
Ideal quotient, 843
idealquotient, 844
IDEALS package, 845
Identifier, 846
IF, 847, 848
IFACTOR switch, 849
IGAMMA, 850
IMAGINARY switch, 851
imaginary unit, 852
IMPART, 853, 854, 855, 856
IMPLICIT_TAYLOR operator, 857
IN command, 858
IN keyword, 859
Indefinite integration, 860
INDEP_VAR global variable (CDE), 861
independentsets, 862
INDEX, 863
INDEX_SYMMETRIES command, 864, 865
indexrange, 866, 867, 868
INDEXRANGE command, 869
Indices
CANTENS package, 870, 871
INEQ package, 872
INEQ_SOLVE operator, 873
INFINITY, 874, 875
INFINITY reserved variable, 876
INFIX declaration, 877
Infix operator, 878, 879, 880, 881, 882, 883, 884
INITIALIZE_EQUATIONS operator (CDE), 885
Inner product, 886
exterior form, 887
INPUT, 888
Input, 889
Instant evaluation, 890, 891, 892, 893, 894
INT, 895, 896
INTEGER, 897
Integer, 898
INTEGRATE_EQUATION operator (CDE), 899
Integration, 900, 901
definite (simple), 902
line, 903
volume, 904
Interactive use, 905, 906
INTERPOL, 907
INTERSECTION, 908
Introduction, 909
INTSTR switch, 910
INVBASE package, 911
INVZTRANS, 912
IRREDUCIBLEREPNR, 913
IRREDUCIBLEREPTABLE, 914
ISOLATER, 915

Jacobi Elliptic Functions and Integrals, 916
Jacobi’s polynomials, 917
Jacobiamplitude, 918
JACOBIAN operator, 919
Jacobicn, 920
Jacobidn, 921
JacobiP, 922
Jacobisn, 923
JacobiZeta, 924
JET_FIBER_DIM operator, 925
JET_DIM operator, 926
JOIN keyword, 927
JORDAN operator, 928
JORDAN_BLOCK operator, 929
JORDANSYMBOLIC operator, 930

KEEP command, 931, 932
Kernel, 933, 934, 935, 936
CANTENS package, 937
kernel form, 938
KHINCHIN reserved variable, 939
KORDER, 940
KORDER declaration, 941
KRONECKER_PRODUCT operator, 942
Kummer functions, 943
KummerM, 944, 945
KummerU, 946, 947

l’Hôpital’s rule, 948, 949
Label, 950, 951
Laguerre polynomials, 952
LAGUERRE_BASE, 953
LaguerreP, 954
LALR package, 955
LALR_CONSTRUCT_PARSER operator, 956
LALR_PRECEDENCE operator, 957
LAMBDA reserved word, 958
Lambert’s W, 959
LAPLACE package, 960
Laplacian
vector field, 961
Laurent series, 962
LCM, 963, 964
LCOF, 965
LDOT operator, 966
Legendre polynomials, 968, 969
LEGENDRE_BASE, 970
LEGENDRE_SYMBOL, 971
LegendreP, 972
LENGTH, 973, 974, 975, 976, 977
LENGTH operator, 978
use on lists, 979
LET, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989
Levi-Cevita tensor, 990
LEX, 991
lex
term order, 992
LHS operator, 993
LHYP switch, 994
Lie Derivative, 995
LIE package, 996
LIEPDE, 997
LIMIT, 998, 999
LIMIT+, 1000
LIMIT-, 1001
LIMITS package, 1002
LIMITS package, 1003
LINALG package, 1004
Line integrals, 1005
LINEAR, 1006
Linear Algebra package, 1007, 1008
LINEAR declaration, 1009
Linear operator, 1010, 1011, 1012
LINEINT, 1013
LINEINT function, 1014
LINELENGTH operator, 1015
LISP, 1016
Lisp, 1017
LIST, 1018
List, 1019
vector operations, 1020
list, 1021
List operation, 1022, 1023
LIST switch, 1024
LISTARGP declaration, 1025
LISTARGS switch, 1026
LISTPROC keyword, 1027
LISTVECOPS package, 1028
LMON switch, 1029
LN, 1030, 1031
LNTH operator, 1032
LOG, 1037, 1038, 1039
LOG10, 1040, 1041
LOGB, 1042, 1043
Lommel functions, 1044
Lommel1, 1045, 1046
Lommel2, 1047, 1048
LOOKING_GOOD switch, 1049
Loop, 1050, 1051
LOW_POW, 1052
LOWER_MATRIX switch, 1053
LPDO package, 1054
LPOWER, 1055
LTERM, 1056, 1057
LTRIG switch, 1058
LU_DECOM operator, 1059

M_ROOTS operator, 1060
M_SOLVE operator, 1061
MACRO, 1062
MAINVAR, 1063
MAKE_BLOC_DIAGONAL, 1064, 1065
MAKE_PARTIC_TENS, 1066, 1067, 1068, 1069
MAKE_TENSOR_BELONG_SPACE, 1070, 1071
MAKE_TENSOR_BELONG_SPACE declaration, 1072
MAKE_TENSOR_BELONG_SPACE operator, 1073
MAKE_IDENTITY operator, 1074
MAKE_VARIABLES, 1075
MAP, 1076
map, 1077
MASS, 1078, 1079
MAT, 1080, 1081, 1082
MATCH, 1083
MATEIGEN, 1084
Mathematical function, 1085
MATRIX, 1086
Matrix assignment, 1087
Matrix calculations, 1088
Matrix ordering, 1089
MATRIX_AUGMENT operator, 1090
MATRIX_STACK operator, 1091
MATRIXP, 1092, 1093
MATRIXPROC, 1094
MAX, 1095
MCD, 1096, 1097
MCD switch, 1098, 1099
Meijer’s G function, 1100
MEMBER, 1101
metric, 1102, 1103
METRIC command, 1104
Metric structure, 1105
Metric tensor
CANTENS package, 1106
MIN, 1107
Minimum, 1108
Minkowski, 1109, 1110, 1111
MINOR operator, 1112
Mixed symmetry
CANTENS package, 1113
MK_IDS_BELONG_ANYSPACE, 1114
MK_IDS_BELONG_SPACE, 1115
MK_IDS_BELONG_ANYSPACE operator, 1116
MK_IDS_BELONG_SPACE, 1117
MK_IDS_BELONG_SPACE operator, 1118
MK_CDIFFOP operator (CDE), 1119
MK_SUPERFUN operator (CDE), 1120
MKALLLINODD operator (CDE), 1121
MKID, 1122
MKPOLY, 1123
MKSET, 1124
MM, 1125
MOD operator, 1126
Mode, 1127
algebraic, 1128
symbolic, 1129
Mode communication, 1130
Mode handling declarations, 1131
MODSR package, 1132
Modular coefficient, 1133
MODULAR switch, 1134, 1135, 1136
MONOMIAL_BASE, 1137
Motzkin, 1138
Motzkin number, 1139
MSG switch, 1140
MSHELL, 1141
MULT_COLUMNS operator, 1142
MULT_ROWS operator, 1143
Multiple assignment statement, 1144
MULTIPLICITIES switch, 1145
MULTIROOT switch, 1146

NAT switch, 1147, 1148
NCPOLY package, 1149
NEARESTROOT, 1150, 1151
NEARESTROOTS, 1152
NEGATIVE, 1153, 1154
NEGATIVE reserved variable, 1155
negativity, 1156
NERO switch, 1157, 1158
Newton’s method, 1159
NEXTPRIME, 1160
NIL reserved variable, 1161
NN, 1162
NOCOMMUTEDF switch, 1163
NOCONVERT switch, 1164
NODEPEND command, 1165
NODEPEND statement, 1166
NOETHER function, 1167, 1168
NOEXPAND_TD command, 1169
NOINTSUBST switch, 1170
NOLNR switch, 1171
Non-commuting operator, 1172
NONCOM, 1173
NONCOM declaration, 1174
NONZERO declaration, 1175
NORMFORM package, 1176
NORMFORM package, 1177
NOSPLIT, 1178
NOSPLIT switch, 1179
NOSPUR, 1180
NOSUM command, 1181, 1182
NOSUM switch, 1183
NOT_NEGATIVE switch, 1184
NOTREALVALUED, 1185
NOXPND
@, 1186
D, 1187
NOXPND@ command, 1188
NOXPND command, 1189
NS dummy variable, 1190
NULLSPACE, 1191
NUM, 1192
NUM_FIT, 1193
NUM_INT, 1194, 1195
NUM_MIN, 1196, 1197
NUM_ODESOLVE, 1198, 1199
NUM_SOLVE, 1200, 1201
Number, 1202, 1203
NUMBERP boolean operator, 1204
Numeric indices
CANTENS package, 1205
NUMERIC package, 1206
NUMERIC package, 1207
Numerical operator, 1208
Numerical precision, 1209

ODD declaration, 1210
Odd operator, 1211
ODD_VAR global variable (CDE), 1212
ODESOLVE package, 1213
OFF, 1214, 1215
ON, 1216, 1217
ON keyword, 1218
ONE_OF operator, 1219
ONESPACE switch, 1220, 1221, 1222
Off, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230
On, 1231, 1232, 1233, 1234, 1235, 1236, 1237
ONLY_INTEGER switch, 1238
OPAPPLY, 1239
OPERATOR, 1240
Operator, 1241, 1242, 1243, 1244
antisymmetric, 1245
CANTENS package, 1246
double slash, 1247
even, 1248
infix, 1249
linear, 1250
non-commuting, 1251
numerical, 1252
odd, 1253
precedence, 1254, 1255
symmetric, 1256
unary prefix, 1257
OPERATOR declaration, 1258
CANTENS package, 1259
Operators
free, in rules, 1260
OPORDER, 1261
OR logical operator, 1262
ORDER declaration, 1263, 1264
Ordering
exterior form, 1265
ORDP boolean operator, 1266, 1267
Orthogonal polynomials, 1268
ORTHOVEC package, 1269
ORTHOVEC package
example, 1270, 1271, 1272, 1273, 1274, 1275
OUT command, 1276
Output, 1277, 1278
Output declaration, 1279, 1280
OUTPUT switch, 1281

Packages
ALGINT, 1282, 1283
APPLYSYM, 1284
ARNUM, 1285
ASSERT, 1286
ASSIST, 1287
AVECTOR, 1288
BIBASIS, 1289
BOOLEAN, 1290
CALI, 1291
CAMAL, 1292
CANTENS, 1293
CDE, 1294
CDIff, 1295
CGB, 1296
COMPACT, 1297
CRACK, 1298
CVIT, 1299
DEfiNT, 1300, 1301
DEfiNT, 1302
DESIR, 1303
DFPART, 1304
DUMMY, 1305
EXCALC, 1306
FIDE, 1307
FPS, 1308
GCREF, 1309
GENTRAN, 1310
GNUPLOT, 1311
GROEBNER, 1312
GROEBNER, 1313
GUARDIAN, 1314
IDEALS, 1315
INEQ, 1316
INVBASE, 1317
LALR, 1318
LAPLACE, 1319
LIE, 1320
LIMITS, 1321
LINALG, 1322
LISTVECOPS, 1323
LPDO, 1324
MODSR, 1325
NCPOLY, 1326
NORMFORM, 1327
NUMERIC, 1328
ODESOLVE, 1329
ORTHOVEC, 1330
PHYSOP, 1331
PLOT, 1332
PM, 1333
POLYDIV, 1334
QSUM, 1335
RANDPOLY, 1336
RATAPRX, 1337
REACTEQN, 1338
REDLOG, 1339
RESET, 1340
RESIDUE, 1341
RLfi, 1342
ROOTS, 1343
RSOLVE, 1344
RTRACE, 1345
SCOPE, 1346
SETS, 1347
SPARSE, 1348
SPDE, 1349
SPECFN, 1350
SPECFN2, 1351
SSTOOLS, 1352
SUM, 1353
SYMMETRY, 1354
TAYLOR, 1355
TPS, 1356
TRI, 1357
TRIGSIMP, 1358, 1359
TURTLE, 1360
WU, 1361
XCOLOR, 1362
XIDEAL, 1363
ZEILBERG, 1364
ZTRANS, 1365
PART operator, 1369, 1370
use on lists, 1371
use on Taylor kernel, 1372, 1373
partial derivatives, 1374
Partial differentiation, 1375
partial fraction, 1376
partial fraction decomposition, 1377
Partial symmetry
CANTENS package, 1378
PAUSE command, 1379
PCLASS, 1380, 1381, 1382
Percent sign, 1383
PERIOD switch, 1384
Periodic decimal representation, 1385
PERIODIC operator, 1386
PERIODIC2RATIONAL operator, 1387
PF operator, 1388
PFORM command, 1389
PFORM statement, 1390
PHYSINDEX, 1391
PHYSOP package, 1392
PI reserved variable, 1393
PIVOT operator, 1394
PLOT, 1395
PLOT package, 1396
PLOTKEEP switch, 1397
PLOTRESET, 1398
PM package, 1399
POCHHAMMER, 1400, 1401
Pochhammer, 1402
Pochhammer notation, 1403
Pochhammer’s symbol, 1404, 1405
POLYDIV package, 1406
POLYGAMMA, 1407, 1408
Polygamma functions, 1409
Polynomial, 1410
Polynomial equations, 1411
POSITIVE, 1412, 1413
POSITIVE reserved variable, 1414
positivity, 1415
Power series, 1416
arithmetic, 1417
composition, 1418
differentiation, 1419
of integral, 1420
of user defined function, 1421
Power series expansions, 1422
PRECEDENCE declaration, 1423
PRECISE switch, 1424, 1425
PRECISE_COMPLEX switch, 1426
PRECISION operator, 1427
in ROOTS package, 1428
preduce, 1429
preducet, 1430
Prefix, 1431, 1432
Prefix operator, 1433
declaring new one, 1434
Prefix operator, unary, 1435
PRET switch, 1436, 1437
PRETTYPRINT, 1438
Prettyprinting, 1439, 1440
PRGEN, 1441
PRI switch, 1442
PRIMEP boolean operator, 1443
PRINCIPAL_DER global variable (CDE), 1444
PRINT_PRECISION command, 1445
PRINTGROUP, 1446
Procedure
body, 1447, 1448
list-valued, 1450
matrix-valued, 1451
using LET inside body, 1452
PROCEDURE command, 1453
PROD operator, 1454
PRODUCT, 1455
PRODUCT keyword, 1456
Program, 1457
Program structure, 1458
Proper statement, 1459, 1460, 1461, 1462, 1463
PRSYS, 1464, 1465
PS, 1466
PS operator, 1467
PSCHANGEVAR operator, 1468
PSCOMPOSE operator, 1469
PSCOPY operator, 1470
PSDEPVAR operator, 1471
PSEUDO_DIVIDE, 1472
PSEUDO_DIVIDE operator, 1473
PSEUDO_INVERSE operator, 1474
PSEUDO_QUOTIENT operator, 1475
PSEUDO_REMAINDER, 1476
PSEUDO_REMAINDER operator, 1477
PSEXPANSIONPT operator, 1478
PSEXPLIM Operator, 1479
PSEXPLIM operator, 1480
PSFUNCTION operator, 1481
PSI, 1482, 1483, 1484
Psi function, 1485
PSORDER operator, 1486
PSORDLIM operator, 1487
PSPRINTORDER switch, 1488
PSREVERSE operator, 1489
PSSETORDER operator, 1490
PSSUM operator, 1491
PSTAYLOR operator, 1492
PSTERM operator, 1493
PSTRUNCATE operator, 1494
Puiseux expansion, 1495
Puiseux series, 1496
PUT_EQUATIONS_USED operator (CDE), 1497
PUTCSYSTEM command, 1498
PVAR_DF operator (CDE), 1499

QBINOMIAL operator, 1500
QBRACKETS operator, 1501
QFACTORIAL operator, 1502
QGOSPER operator, 1503
QGOSPER_DOWN switch, 1504, 1505
QGOSPER_SPECIALSOL switch, 1506
QPHIHYPERTERM operator, 1507
QPOCHHAMMER operator, 1508
QPSIHYPERTERM operator, 1509
QRATIO operator, 1510
QSIMPCOMB operator, 1511, 1512
QSUM package, 1513
QSUM_NULLSPACE switch, 1514, 1515
QSUM_TRACE switch, 1516
QSUMRECURSION operator, 1517
QSUMRECURSION_CERTIFICATE switch, 1518, 1519
QSUMRECURSION_DOWN switch, 1520
QSUMRECURSION_EXP switch, 1521
QUASILINPDE, 1523
QUIT, 1524
QUOTE, 1525

R_SOLVE, 1526
RANDOM, 1527
RANDOM_NEW_SEED, 1528
RANDOM_MATRIX operator, 1529
RANDPOLY package, 1530
RANK, 1531
RAT, 1532
RAT switch, 1533
RATAPRX package, 1534
RATARG switch, 1535, 1536
Rational coefficient, 1537
Rational function, 1538
rational number, 1539
RATIONAL switch, 1540
RATIONAL2PERIODIC operator, 1541
RATIONALIZE switch, 1542
RATJORDAN operator, 1543
RATPRI, 1544
RATPRI switch, 1545
RATROOT switch, 1546
REACTEQN package, 1547
REAL, 1548
Real coefficient, 1549, 1550
Real number, 1551, 1552
REALROOTS, 1553, 1554
REALVALUED, 1555
REALVALUEDP, 1556
REDERR, 1557
REDLOG package, 1558
REDUCE, 1559
REDUCT, 1560
REM_SPACES, 1561
REM_DUMMY_IDS, 1562
REM_DUMMY_INDICES, 1563, 1564
REM_VALUE_TENS, 1565, 1566
REM_SPACES, 1567
REM_TENSOR, 1568
REMAINDER, 1569
REMAINDER operator, 1570
REMANTICOM, 1571
REMEMBER, 1572
REMFAC, 1573
REMFORDER command, 1574, 1575
REMIND, 1576
REMOVE_COLUMNS operator, 1577, 1578
REMOVE_ROWS operator, 1579
REMOVE_VARIABLES, 1580
REMSYM, 1581, 1582
RENOSUM command, 1583, 1584
REPART, 1585, 1586, 1587
REPEAT, 1588, 1589, 1590, 1591
REPEAT statement, 1592
REPPRINCPARAM_DER shared global variable (CDE), 1593
REPPRINCPARAM_ODD shared global variable (CDE), 1594
REQUIREMENTS shared variable, 1595
Reserved variable, 1596, 1597
Reserved variable
HIGH_POW, 1598
LOW_POW, 1599
CATALAN, 1600
EULER_GAMMA, 1601
GOLDEN_RATIO, 1602
I, 1603
INFINITY, 1604
KHINCHIN, 1605
NEGATIVE, 1606
NIL, 1607
PI, 1608
POSITIVE, 1609
T, 1610
RESET package, 1611
RESIDUE package, 1612
REST operator, 1613
RESULT, 1614
RESULTANT, 1615
RETRY, 1616
RETURN, 1617, 1618, 1619, 1620
RETURN statement, 1621
REVERSE operator, 1622
term order, 1624
REVPRI, 1625
REVPRI switch, 1626
Rewriting rules
CANTENS package, 1627
RHS operator, 1628
Riemann tensor
CANTENS package, 1629
RIEMANNCONX command, 1630, 1631
Riemannian Connections, 1632
RLfi package, 1633
Rlisp, 1634
RLISP88, 1635
RLROOTNO, 1636
root finding, 1637
ROOT_MULTIPLICITIES global variable, 1638
ROOT_OF operator, 1639, 1640
ROOT_VAL, 1641, 1642
ROOTACC operator (ROOTS package), 1643
ROOTACC!# global variable (ROOTS package), 1644
ROOTMSG switch, 1645
ROOTPREC operator (ROOTS package), 1646
ROOTS, 1647, 1648
ROOTS package, 1649
ROOTS package, 1650
ROOTS_AT_PREC, 1651
ROOTSCOMPLEX, 1652
ROOTSREAL, 1653
ROUND, 1654
ROUNDALL switch, 1655
ROUNDBF switch, 1656
ROUNDED, 1657, 1658
ROUNDED switch, 1659, 1660, 1661, 1662, 1663
ROW_DIM operator, 1664
ROWS_PIVOT operator, 1665
RSETREPRESENTATION, 1666
RSOLVE package, 1667
RTR command, 1668
RTRACE package, 1669
RTRACE switch, 1670, 1671
RTROUT command, 1672
RTRST command, 1673
Rule lists, 1674
Rules
Double slash operators, 1675
Double tilde variables, 1676
Free operators, 1677

saturation, 1678
SAVE_CDE_STATE operator, 1679
SAVEAS statement, 1680
SAVESTRUCTR switch, 1681
Saving an expression, 1682
SCALAR, 1683, 1684
Scalar, 1685, 1686
Scalar variable, 1687
SCALEFACTORS operator, 1688
SCALOP, 1689
SCHOUTEN_BRACKET operator (CDE), 1690
SCIENTIFIC_NOTATION declaration, 1691
SCOPE package, 1692
SDER(I), 1693
SEC, 1694, 1695
SECH, 1696, 1697
SECOND operator, 1698
SELECT, 1699
Selector, 1700
SELECTVARS operator, 1701
Semicolon, 1702
SET statement, 1703, 1704
Set Statement, 1705
SET_EQ, 1706
SETAVAILABLE, 1707
SETDIFF, 1708
SETELEMENTS, 1709
SETGENERATORS, 1710
SETGROUPTABLE, 1711
SETMOD, 1712
SETS package, 1713
SGN
indeterminate sign, 1714
SHARE declaration, 1715
SHOW_DUMMY_NAMES, 1716
SHOW_EPSILONS, 1717, 1718, 1719
SHOW_SPACES, 1720, 1721, 1722
SHOWRULES, 1723
SHOWTIME command, 1724
SHUT command, 1725
SI, 1726
Side effect, 1727
SIGN, 1728, 1729
SIGNATURE, 1730
Signature
CANTENS package, 1731, 1732, 1733, 1734
signature, 1735, 1736, 1737
SIGNATURE command, 1738
SIMPLEDE, 1739
SIMPLEX operator, 1740
Simplification, 1741, 1742, 1743
simplify_combinatorial, 1744
SIMPLIFY_GAMMA, 1745
simplify_gamma2, 1746
simplify_gamman, 1747
SIMPNONCOMDF switch, 1748
SIMPSYS, 1749, 1750, 1751
SIN, 1752, 1753
SINH, 1754, 1755
SixjSymbol, 1756
SMACRO reserved identifier, 1757
SMITHEX operator, 1758
SMITHEX_INT operator, 1759
SolidHarmonicY, 1760
SOLVE operator, 1761, 1762, 1763
ASSUMPTIONS variable, 1764
REQUIREMENTS shared variable, 1765
ROOT_MULTIPLICITIES global variable, 1766
use of GROEBNER package, 1767
SOLVE package
with ROOTS package, 1768
SOLVESINGULAR switch, 1769
space, 1770
SPACEDIM command, 1771, 1772
Spaces
CANTENS package, 1773, 1774, 1775
spaces, 1776, 1777, 1778, 1779
SPARSE declaration, 1784
SPARSE package, 1785
SPARSEMATP predicate, 1786
SPAUGMENT_COLUMNS operator, 1787
SPBAND_MATRIX operator, 1788
SPBLOCK_MATRIX operator, 1789
SPCHAR_MATRIX operator, 1790
SPCHAR_POLY operator, 1791
SPCHOLESKY operator, 1792
SPCOEFF_MATRIX operator, 1793
SPCOL_DIM operator, 1794
SPCOMPANION operator, 1795
SPCOPY_INTO operator, 1796
SPDE package, 1797
SPDIAGONAL operator, 1798
SPECFN, 1799
SPECFN package, 1800
SPECFN2 package, 1801
SPEXTEND operator, 1802
SPFIND_COMPANION operator, 1803
SPGET_COLUMNS operator, 1804
SPGET_ROWS operator, 1805
SPGRAM_SCHMIDT operator, 1806
Spherical and Solid Harmonics, 1807
Spherical coordinates, 1808, 1809
SphericalHarmonicY, 1810
SPHERMITIAN_TP operator, 1811
SPHESSIAN operator, 1812
Spinor
CANTENS package, 1813
SPJACOBIAN operator, 1814
SPJORDAN_BLOCK operator, 1815
SPLIT_FIELD function, 1816
SPLITEXT_LIST operator (CDE), 1817
SPLITEXT_OPEQU operator (CDE), 1818
SPLITVARS_OPEQU operator (CDE), 1819
SPLU_DECOM operator, 1820
SPMAKE_IDENTITY operator, 1821
SPMATRIX_AUGMENT operator, 1822
SPMATRIX_STACK operator, 1823
SPMINOR operator, 1824
SPMULT_COLUMNS operator, 1825
SPMULT_ROWS operator, 1826
SPPIVOT operator, 1827
SPPSEUDO_INVERSE operator, 1828
SPREMOVE_ROWS operator, 1829
SPROW_DIM operator, 1830
SPROWS_PIVOT operator, 1831
SPSUB_MATRIX operator, 1832
SPSVD operator, 1833
SPSWAP_COLUMNS operator, 1834
SPSWAP_ENTRIES operator, 1835
SPSWAP_ROWS operator, 1836
SPUR, 1837
SQFRF, 1838
SQRT, 1839, 1840
SQUAREP predicate, 1841, 1842
SSTOOLS package, 1843
STACK_ROWS operator, 1844, 1845
Standard form, 1846
Standard quotient, 1847
STATE, 1848
Statement, 1849
assignment, 1850
compound, 1851
conditional, 1852
FOR, 1853
FOREACH, 1854
GO TO, 1855
Group, 1856
REPEAT, 1857
RETURN, 1858
SAVEAS, 1859
Set, 1860
Unset, 1861
WHILE, 1862
Statement terminator, 1863
Stirling numbers, 1864
Stirling1, 1865
Stirling2, 1866
STOREGROUP, 1867
String, 1868
STRUCTR, 1869, 1870
Structuring, 1871
Struve functions, 1872
StruveH, 1873, 1874
StruveL, 1875, 1876
Sturm Sequences, 1877
SUB, 1878
SUB operator, 1879
SUB_MATRIX operator, 1880
SUBSET_EQ, 1881
Subspaces
CANTENS package, 1882
subspaces, 1883
Substitution, 1884
SUCHTHAT, 1885
SUM, 1886
SUM keyword, 1887
SUM operator, 1888
SUM package, 1889
SUM!-SQ operator, 1890
SUMRECURSION, 1891
SUMTOHYPER, 1892
SUPER_PRODUCT operator (CDE), 1893
SVD operator, 1894
SVEC, 1895
SWAP_COLUMNS operator, 1896
SWAP_ENTRIES operator, 1897
SWAP_ROWS operator, 1898
Switch, 1899, 1900
ALGINT, 1902
ALLBRANCH, 1903
ALLFAC, 1904, 1905, 1906
ALLOWDFINT, 1907
ANTICOM, 1908
ARBVARS, 1909
BALANCED_MOD, 1910, 1911
BEZOUT, 1912
BFSPACE, 1913
CHECKORD, 1914
COMBINEEXPT, 1915
COMBINELOGS, 1916
COMMUTEDF, 1917
COMP, 1918
COMPLEX, 1919, 1920
CRAMER, 1921, 1922
CREF, 1923
DEFN, 1924, 1925, 1926
DFINT, 1927
DISPJACOBIAN, 1928
DIV, 1929, 1930
ECHO, 1931
ERRCONT, 1932
EVALLHSEQP, 1933
EXP, 1934, 1935
EXPANDDF, 1936
EXPANDLOGS, 1937
EZGCD, 1938
FACTOR, 1939, 1940
FAILHARD, 1941
FAST_LA, 1942, 1943
FASTSIMPLEX, 1944
FORT, 1945
FORTUPPER, 1946
FULLROOTS, 1947
GCD, 1948
GLTBASIS, 1949, 1950
GROEBFULLREDUCTION, 1951, 1952
GROEBOPT, 1953, 1954, 1955
GROEBPROT, 1956
GROEBSTAT, 1957, 1958
HEUGCD, 1959
IFACTOR, 1960
IMAGINARY, 1961
INTSTR, 1962
LHYP, 1963
LIST, 1964
LISTARGS, 1965
LMON, 1966
LOOKING_GOOD, 1967
LOWER_MATRIX, 1968
LTRIG, 1969
MCD, 1970, 1971
MODULAR, 1972, 1973, 1974
MSG, 1975
MULTIPLICITIES, 1976
MULTIROOT, 1977
NAT, 1978, 1979
NERO, 1980
NOCOMMUTEDF, 1981
NOCONVERT, 1982
NOINTSUBST, 1983
NOLNR, 1984
NOSPLIT, 1985
NOSUM, 1986
NOT_NEGATIVE, 1987
ONESPACE, 1988, 1989, 1990
ONLY_INTEGER, 1991
OUTPUT, 1992
PERIOD, 1993
PLOTKEEP, 1994
PRECISE, 1995, 1996
PRECISE_COMPLEX, 1997
PRET, 1998, 1999
PRI, 2000
PSPRINTORDER, 2001
QGOSPER_DOWN, 2002, 2003
QGOSPER_SPECIALSOL, 2004
QSUM_NULLSPACE, 2005, 2006
QSUM_TRACE, 2007
QSUMRECURSION_CERTIFICATE, 2008, 2009
QSUMRECURSION_DOWN, 2010
QSUMRECURSION_EXP, 2011
RAT, 2012
RATARG, 2013, 2014
RATIONAL, 2015
RATIONALIZE, 2016
RATPRI, 2017
RATROOT, 2018
REVPRI, 2019
ROOTMSG, 2020
ROUNDALL, 2021
ROUNDBF, 2022
ROUNDED, 2023, 2024, 2025, 2026, 2027
RTRACE, 2028, 2029
SAVESTRUCTR, 2030
SIMPNONCOMDF, 2031
SOLVESINGULAR, 2032
SYMMETRIC, 2033
TAYLORAUTOCOMBINE, 2034
TAYLORAUTOEXPAND, 2035, 2036
TAYLORKEEPORIGINAL, 2037, 2038, 2039, 2040
TAYLORPRINTORDER, 2041
TR_LIE, 2042
TRA, 2043
TRCOMPACT, 2044
TRFAC, 2045
TRGROEB, 2046, 2047
TRGROEB1, 2048, 2049
TRGROEBR, 2050
TRGROEBS, 2051, 2052
TRIGFORM, 2053
TRINT, 2054, 2055
TRINTSUBST, 2056
TRNUMERIC, 2057
TRPLOT, 2058
TRROOT, 2059
TRSOLVE, 2060
TRSUM, 2061
TRWU, 2062
UPPER_MATRIX, 2063
VAROPT, 2064
ZB_FACTOR, 2066
ZB_PROOF, 2067
ZB_TRACE, 2068, 2069
Switches by package
REDUCE Core
ALLBRANCH, 2071
ALLFAC, 2072, 2073, 2074
ALLOWDFINT, 2075
ARBVARS, 2076
BALANCED_MOD, 2077, 2078
BEZOUT, 2079
BFSPACE, 2080
COMBINEEXPT, 2081
COMBINELOGS, 2082
COMMUTEDF, 2083
COMP, 2084
COMPLEX, 2085, 2086
CRAMER, 2087, 2088
CREF, 2089
DEFN, 2090, 2091, 2092
DFINT, 2093
DISPJACOBIAN, 2094
DIV, 2095, 2096
ECHO, 2097
ERRCONT, 2098
EVALLHSEQP, 2099
EXP, 2100, 2101
EXPANDDF, 2102
EXPANDLOGS, 2103
EZGCD, 2104
FACTOR, 2105, 2106
FAILHARD, 2107
FORT, 2108
FORTUPPER, 2109
FULLROOTS, 2110
GCD, 2111
HEUGCD, 2112
IFACTOR, 2113
INTSTR, 2114
LIST, 2115
LISTARGS, 2116
MCD, 2117, 2118
MODULAR, 2119, 2120, 2121
MSG, 2122
MULTIPLICITIES, 2123
NAT, 2124, 2125
NERO, 2126
NOCOMMUTEDF, 2127
NOCONVERT, 2128
NOINTSUBST, 2129
NOLNR, 2130
NOSPLIT, 2131
OUTPUT, 2132
PERIOD, 2133
PLOTKEEP, 2134
PRECISE, 2135, 2136
PRECISE_COMPLEX, 2137
PRET, 2138, 2139
PRI, 2140
RAT, 2141
RATARG, 2142, 2143
RATIONAL, 2144
RATIONALIZE, 2145
RATPRI, 2146
REVPRI, 2147
ROUNDALL, 2148
ROUNDBF, 2149
ROUNDED, 2150, 2151, 2152, 2153, 2154
SAVESTRUCTR, 2155
SIMPNONCOMDF, 2156
SOLVESINGULAR, 2157
TRFAC, 2158
TRIGFORM, 2159
TRINT, 2160
TRINTSUBST, 2161
VAROPT, 2162
ALGINT package
ALGINT, 2163
TRA, 2164
TRINT, 2165
CANTENS package
ONESPACE, 2166, 2167, 2168
CDE package
CHECKORD, 2169
COMPACT package
TRCOMPACT, 2170
EXCALC package
NOSUM, 2171
GNUPLOT package
TRPLOT, 2172
GROEBNER package
GLTBASIS, 2173, 2174
GROEBFULLREDUCTION, 2175, 2176
GROEBOPT, 2177, 2178, 2179
GROEBPROT, 2180
GROEBSTAT, 2181, 2182
TRGROEB, 2183, 2184
TRGROEB1, 2185, 2186
TRGROEBR, 2187
TRGROEBS, 2188, 2189
LAPLACE package
LHYP, 2190
LMON, 2191
LTRIG, 2192
LIE package
TR_LIE, 2193
LINALG package
FAST_LA, 2194
FASTSIMPLEX, 2195
IMAGINARY, 2196
LOWER_MATRIX, 2197
NOT_NEGATIVE, 2198
ONLY_INTEGER, 2199
SYMMETRIC, 2200
UPPER_MATRIX, 2201
NORMFORM package
LOOKING_GOOD, 2202
NUMERIC package
TRNUMERIC, 2203
PHYSOP package
ANTICOM, 2204
QSUM package
QGOSPER_DOWN, 2205, 2206
QGOSPER_SPECIALSOL, 2207
QSUM_NULLSPACE, 2208, 2209
QSUM_TRACE, 2210
QSUMRECURSION_CERTIFICATE, 2211, 2212
QSUMRECURSION_DOWN, 2213
QSUMRECURSION_EXP, 2214
ROOTS package
MULTIROOT, 2215
RATROOT, 2216
ROOTMSG, 2217
TRROOT, 2218
RSOLVE package
TRSOLVE, 2219
RTRACE package
RTRACE, 2220, 2221
SPARSE package
FAST_LA, 2222
SUM package
TRSUM, 2223
TAYLOR package
TAYLORAUTOCOMBINE, 2224
TAYLORAUTOEXPAND, 2225, 2226
TAYLORKEEPORIGINAL, 2227, 2228, 2229, 2230
TAYLORPRINTORDER, 2231
TPS package
PSPRINTORDER, 2233
WU package
TRWU, 2234
ZEILBERG package
ZB_FACTOR, 2235
ZB_PROOF, 2236
ZB_TRACE, 2237, 2238
SYMBOLIC, 2239
Symbolic indices
CANTENS package, 2240
Symbolic mode, 2241, 2242, 2243, 2244, 2245
Symbolic procedure, 2246
symmetric
tensor, 2247
SYMMETRIC declaration, 2248, 2249
Symmetric operator, 2250
SYMMETRIC switch, 2251
SYMMETRICP predicate, 2252, 2253
Symmetries
CANTENS package, 2254
SYMMETRIZE, 2255
SYMMETRY package, 2256
SYMMETRY package, 2257
SYMMETRYBASIS, 2258
SYMMETRYBASISPART, 2259
SYMTREE, 2260
SYMTREE declaration, 2261
systemprecision, 2262

T reserved variable, 2263
TAN, 2264, 2265, 2266
Tangent vector, 2267
TANH, 2268, 2269
TAYLOR operator, 2270
TAYLOR package, 2271
Taylor series, 2272
arithmetic, 2273
differentiation, 2274
integration, 2275
reversion, 2276
substitution, 2277
TAYLORAUTOCOMBINE switch, 2278
TAYLORAUTOEXPAND switch, 2279, 2280
TAYLORCOMBINE operator, 2281, 2282
TAYLORKEEPORIGINAL switch, 2283, 2284, 2285, 2286
TAYLORORIGINAL operator, 2287, 2288
TAYLORPRINTORDER switch, 2289
TAYLORPRINTTERMS variable, 2290, 2291
TAYLORREVERT operator, 2292, 2293
TAYLORSERIESP operator, 2294
TAYLORTEMPLATE operator, 2295, 2296
TAYLORTOSTANDARD operator, 2297
TENSOP, 2298
TENSOR, 2299
Tensor contractions
CANTENS package, 2300
Tensor derivatives
CANTENS package, 2301
Tensor polynomial
CANTENS package, 2302
Terminator, statement, 2303
THIRD operator, 2304
ThreejSymbol, 2305
TIME, 2306
TOEPLITZ operator, 2307
torder, 2308, 2309, 2310, 2311, 2312
TORDER operator, 2313
TOTAL_ORDER global variable (CDE), 2314
TOTALDEG, 2315
TP, 2316
TPS package, 2317
TR_LIE switch, 2318
TRA switch, 2319
TRACE, 2320
Trace
CANTENS package, 2321
Tracing
EXCALC package, 2322
GNUPLOT package, 2323
ROOTS package, 2324
SPDE package, 2325
SUM package, 2326
TRCOMPACT switch, 2327
TRFAC switch, 2328
TRGROEB switch, 2329, 2330
TRGROEB1 switch, 2331, 2332
TRGROEBR switch, 2333
TRGROEBS switch, 2334, 2335
TRI package, 2336
TRIGFORM switch, 2338
TRIGONOMETRIC_BASE, 2339
TRIGSIMP, 2340
TRIGSIMP package, 2341, 2342
TRINT switch, 2343, 2344
TRINTSUBST switch, 2345
TRNUMERIC switch, 2346
TRPLOT switch, 2347
TRRL command, 2348
TRRLID command, 2349
TRROOT switch, 2350
TRSOLVE switch, 2351
TRSUM switch, 2352
truncated power series, 2353
TRWU switch, 2354
TRXIDEAL switch, 2355
TRXMOD switch, 2356
TURTLE package, 2357
TURTLE package, 2358
TVECTOR command, 2359, 2360

U(ALFA), 2361
U(ALFA,I), 2362
Unary prefix operator, 2363
UNION, 2364
UNIT, 2365
UNRTR command, 2366
UNRTRST command, 2367
UNSET statement, 2368, 2369
Unset Statement, 2370
UNTIL, 2371
UNTRRL command, 2372
UNTRRLID command, 2373
UP_QRATIO operator, 2374
UPPER_MATRIX switch, 2375
UPWARD_ANTIDIFFERENCE, 2376
User packages, 2377

VANDERMONDE operator, 2378
VARDF, 2379
VARDF (variational derivative) operator), 2380
Variable, 2381
double tilde, 2382
Variable elimination, 2383
Variational derivative, 2384
VARNAME, 2385, 2386
VAROPT switch, 2387
VDF, 2388
VEC command, 2389
VECDIM, 2390
VECOP, 2391
VECTOR, 2392
Vector
cross product, 2394
differentiation, 2395
division, 2396
dot product, 2397
exponentiation, 2398
inner product, 2399
integration, 2400
modulus, 2401
multiplication, 2402
subtraction, 2403
Vector algebra, 2404
VECTORCROSS, 2406
VECTORDIFFERENCE, 2407
VECTOREXPT, 2408
VECTORMINUS, 2409
VECTORPLUS, 2410
VECTORQUOTIENT, 2411
VECTORRECIP, 2412
VECTORTIMES, 2413
VINT, 2415
VMOD, 2416
VMOD operator, 2417
VOLINT, 2418
VOLINTEGRAL function, 2419
VOLINTORDER vector, 2420
VORDER, 2421
VOUT, 2422
VSTART, 2423
VTAYLOR, 2424

Warnings
TAYLOR package, 2425
Wedge, 2426
WEIGHT, 2427
Weighted ordering, 2428
WHEN, 2429
WHERE, 2430
WHILE, 2431, 2432, 2433, 2434
WHILE statement, 2435
Whittaker functions, 2436
WhittakerM, 2437, 2438
WhittakerU, 2439
WhittakerW, 2440
wholespace, 2441, 2442, 2443, 2444, 2445, 2446
WHOLESPACE_DIM, 2447, 2448
Workspace, 2449
WRITE, 2450
WS, 2451, 2452
WTLEVEL, 2453
WU package, 2454

X(I), 2455
XAUTO, 2456
XCOLOR package, 2457
XFULLREDUCE switch, 2458
XI(I), 2459
XIDEAL, 2460
XIDEAL package, 2461
XMOD, 2462
XMODIDEAL, 2463
XORDER, 2464
XPND
XPND
@, 2465
XPND
@, 2466
D, 2467
XPND command, 2468
XVARS, 2469

ZB_DIRECTION variable, 2470
ZB_FACTOR switch, 2471
ZB_ORDER variable, 2472
ZB_PROOF switch, 2473
ZB_TRACE switch, 2474, 2475
ZEILBERG package, 2476
ZEILBERGER_REPRESENTATION variable, 2477
ZETA, 2478, 2479
Zeta function (Riemann’s), 2480
ZETA(ALFA,I), 2481
ZTRANS, 2482
ZTRANS package, 2483

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