REDUCE

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
ADD_TO_COLUMNS operator, 79
ADD_TO_ROWS operator, 80
ADD_COLUMNS operator, 81
ADD_ROWS operator, 82
ADJ, 83
ADJOINT_CDIFFOP operator (CDE), 84
ADJPREC switch, 85
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
    loading, 264
    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
CDE_GRADING operator (CDE), 298
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
DOTGRAD operator, 530, 531
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 loading of code, 660
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
GRAD
    operator, 749
GRAD operator, 750
Graded ordering, 751
Gradient
    vector field, 752
gradlex
    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
        graded, 772
        grouped, 773
        matrix, 774
        weighted, 775
    term order
        default, 776
        gradlex, 777
        lex, 778
        revgradlex, 779
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
LAMBDA reserved word, 956
Lambert’s W, 957
LAPLACE package, 958
Laplacian
    vector field, 959
Laurent series, 960
LCM, 961, 962
LCOF, 963
LDOT operator, 964
Leading coefficient, 965
Legendre polynomials, 966, 967
LEGENDRE_BASE, 968
LEGENDRE_SYMBOL, 969
LegendreP, 970
LENGTH, 971, 972, 973, 974, 975
LENGTH operator, 976
    use on lists, 977
LET, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987
Levi-Cevita tensor, 988
LEX, 989
lex
    term order, 990
LHS operator, 991
LHYP switch, 992
Lie Derivative, 993
LIE package, 994
LIEPDE, 995
LIMIT, 996, 997
LIMIT+, 998
LIMIT-, 999
LIMITS package, 1000
LIMITS package, 1001
LINALG package, 1002
Line integrals, 1003
LINEAR, 1004
Linear Algebra package, 1005, 1006
LINEAR declaration, 1007
Linear operator, 1008, 1009, 1010
LINEINT, 1011
LINEINT function, 1012
LINELENGTH operator, 1013
LISP, 1014
Lisp, 1015
LIST, 1016
List, 1017
    vector operations, 1018
list, 1019
List operation, 1020, 1021
LIST switch, 1022
LISTARGP declaration, 1023
LISTARGS switch, 1024
LISTPROC keyword, 1025
LISTVECOPS package, 1026
LMON switch, 1027
LN, 1028, 1029
LNTH operator, 1030
LOAD, 1031
LOAD_PACKAGE, 1032, 1033
LOADGROUPS, 1034
LOG, 1035, 1036, 1037
LOG10, 1038, 1039
LOGB, 1040, 1041
Lommel functions, 1042
Lommel1, 1043, 1044
Lommel2, 1045, 1046
LOOKING_GOOD switch, 1047
Loop, 1048, 1049
LOW_POW, 1050
LOWER_MATRIX switch, 1051
LPDO package, 1052
LPOWER, 1053
LTERM, 1054, 1055
LTRIG switch, 1056
LU_DECOM operator, 1057

M_ROOTS operator, 1058
M_SOLVE operator, 1059
MACRO, 1060
MAINVAR, 1061
MAKE_BLOC_DIAGONAL, 1062, 1063
MAKE_PARTIC_TENS, 1064, 1065, 1066, 1067
MAKE_TENSOR_BELONG_SPACE, 1068, 1069
MAKE_TENSOR_BELONG_SPACE declaration, 1070
MAKE_TENSOR_BELONG_SPACE operator, 1071
MAKE_IDENTITY operator, 1072
MAKE_VARIABLES, 1073
MAP, 1074
map, 1075
MASS, 1076, 1077
MAT, 1078, 1079, 1080
MATCH, 1081
MATEIGEN, 1082
Mathematical function, 1083
MATRIX, 1084
Matrix assignment, 1085
Matrix calculations, 1086
Matrix ordering, 1087
MATRIX_AUGMENT operator, 1088
MATRIX_STACK operator, 1089
MATRIXP, 1090, 1091
MATRIXPROC, 1092
MAX, 1093
MCD, 1094, 1095
MCD switch, 1096, 1097
Meijer’s G function, 1098
MEMBER, 1099
metric, 1100, 1101
METRIC command, 1102
Metric structure, 1103
Metric tensor
    CANTENS package, 1104
MIN, 1105
Minimum, 1106
Minkowski, 1107, 1108, 1109
MINOR operator, 1110
Mixed symmetry
    CANTENS package, 1111
MK_IDS_BELONG_ANYSPACE, 1112
MK_IDS_BELONG_SPACE, 1113
MK_IDS_BELONG_ANYSPACE operator, 1114
MK_IDS_BELONG_SPACE, 1115
MK_IDS_BELONG_SPACE operator, 1116
MK_CDIFFOP operator (CDE), 1117
MK_SUPERFUN operator (CDE), 1118
MKALLLINODD operator (CDE), 1119
MKID, 1120
MKPOLY, 1121
MKSET, 1122
MM, 1123
MOD operator, 1124
Mode, 1125
    algebraic, 1126
    symbolic, 1127
Mode communication, 1128
Mode handling declarations, 1129
MODSR package, 1130
Modular coefficient, 1131
MODULAR switch, 1132, 1133, 1134
MONOMIAL_BASE, 1135
Motzkin, 1136
Motzkin number, 1137
MSG switch, 1138
MSHELL, 1139
MULT_COLUMNS operator, 1140
MULT_ROWS operator, 1141
Multiple assignment statement, 1142
MULTIPLICITIES switch, 1143
MULTIROOT switch, 1144

NAT switch, 1145, 1146
NCPOLY package, 1147
NEARESTROOT, 1148, 1149
NEARESTROOTS, 1150
NEGATIVE, 1151, 1152
NEGATIVE reserved variable, 1153
negativity, 1154
NERO switch, 1155, 1156
Newton’s method, 1157
NEXTPRIME, 1158
NIL reserved variable, 1159
NN, 1160
NOCOMMUTEDF switch, 1161
NOCONVERT switch, 1162
NODEPEND command, 1163
NODEPEND statement, 1164
NOETHER function, 1165, 1166
NOEXPAND_TD command, 1167
NOINTSUBST switch, 1168
NOLNR switch, 1169
Non-commuting operator, 1170
NONCOM, 1171
NONCOM declaration, 1172
NONZERO declaration, 1173
NORMFORM package, 1174
NORMFORM package, 1175
NOSPLIT, 1176
NOSPLIT switch, 1177
NOSPUR, 1178
NOSUM command, 1179, 1180
NOSUM switch, 1181
NOT_NEGATIVE switch, 1182
NOTREALVALUED, 1183
NOXPND
    @, 1184
    D, 1185
NOXPND@ command, 1186
NOXPND command, 1187
NS dummy variable, 1188
NULLSPACE, 1189
NUM, 1190
NUM_FIT, 1191
NUM_INT, 1192, 1193
NUM_MIN, 1194, 1195
NUM_ODESOLVE, 1196, 1197
NUM_SOLVE, 1198, 1199
Number, 1200, 1201
NUMBERP boolean operator, 1202
Numeric indices
    CANTENS package, 1203
NUMERIC package, 1204
NUMERIC package, 1205
Numerical operator, 1206
Numerical precision, 1207

ODD declaration, 1208
Odd operator, 1209
ODD_VAR global variable (CDE), 1210
ODESOLVE package, 1211
OFF, 1212, 1213
ON, 1214, 1215
ON keyword, 1216
ONE_OF operator, 1217
ONESPACE switch, 1218, 1219, 1220
    Off, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228
    On, 1229, 1230, 1231, 1232, 1233, 1234, 1235
ONLY_INTEGER switch, 1236
OPAPPLY, 1237
OPERATOR, 1238
Operator, 1239, 1240, 1241, 1242
    antisymmetric, 1243
    CANTENS package, 1244
    double slash, 1245
    even, 1246
    infix, 1247
    linear, 1248
    non-commuting, 1249
    numerical, 1250
    odd, 1251
    precedence, 1252, 1253
    symmetric, 1254
    unary prefix, 1255
OPERATOR declaration, 1256
    CANTENS package, 1257
Operators
    free, in rules, 1258
OPORDER, 1259
OR logical operator, 1260
ORDER declaration, 1261, 1262
Ordering
    exterior form, 1263
ORDP boolean operator, 1264, 1265
Orthogonal polynomials, 1266
ORTHOVEC package, 1267
ORTHOVEC package
    example, 1268, 1269, 1270, 1271, 1272, 1273
OUT command, 1274
Output, 1275, 1276
Output declaration, 1277, 1278
OUTPUT switch, 1279

Packages
    ALGINT, 1280, 1281
    APPLYSYM, 1282
    ARNUM, 1283
    ASSERT, 1284
    ASSIST, 1285
    AVECTOR, 1286
    BIBASIS, 1287
    BOOLEAN, 1288
    CALI, 1289
    CAMAL, 1290
    CANTENS, 1291
    CDE, 1292
    CDIff, 1293
    CGB, 1294
    COMPACT, 1295
    CRACK, 1296
    CVIT, 1297
    DEfiNT, 1298, 1299
    DEfiNT, 1300
    DESIR, 1301
    DFPART, 1302
    DUMMY, 1303
    EXCALC, 1304
    FIDE, 1305
    FPS, 1306
    GCREF, 1307
    GENTRAN, 1308
    GNUPLOT, 1309
    GROEBNER, 1310
    GROEBNER, 1311
    GUARDIAN, 1312
    IDEALS, 1313
    INEQ, 1314
    INVBASE, 1315
    LALR, 1316
    LAPLACE, 1317
    LIE, 1318
    LIMITS, 1319
    LINALG, 1320
    LISTVECOPS, 1321
    LPDO, 1322
    MODSR, 1323
    NCPOLY, 1324
    NORMFORM, 1325
    NUMERIC, 1326
    ODESOLVE, 1327
    ORTHOVEC, 1328
    PHYSOP, 1329
    PLOT, 1330
    PM, 1331
    POLYDIV, 1332
    QSUM, 1333
    RANDPOLY, 1334
    RATAPRX, 1335
    REACTEQN, 1336
    REDLOG, 1337
    RESET, 1338
    RESIDUE, 1339
    RLfi, 1340
    ROOTS, 1341
    RSOLVE, 1342
    RTRACE, 1343
    SCOPE, 1344
    SETS, 1345
    SPARSE, 1346
    SPDE, 1347
    SPECFN, 1348
    SPECFN2, 1349
    SSTOOLS, 1350
    SUM, 1351
    SYMMETRY, 1352
    TAYLOR, 1353
    TPS, 1354
    TRI, 1355
    TRIGSIMP, 1356, 1357
    TURTLE, 1358
    WU, 1359
    XCOLOR, 1360
    XIDEAL, 1361
    ZEILBERG, 1362
    ZTRANS, 1363
Padé Approximation, 1364
PADE operator, 1365
Padget, Julian, 1366
PART operator, 1367, 1368
    use on lists, 1369
    use on Taylor kernel, 1370, 1371
partial derivatives, 1372
Partial differentiation, 1373
partial fraction, 1374
partial fraction decomposition, 1375
Partial symmetry
    CANTENS package, 1376
PAUSE command, 1377
PCLASS, 1378, 1379, 1380
Percent sign, 1381
PERIOD switch, 1382
Periodic decimal representation, 1383
PERIODIC operator, 1384
PERIODIC2RATIONAL operator, 1385
PF operator, 1386
PFORM command, 1387
PFORM statement, 1388
PHYSINDEX, 1389
PHYSOP package, 1390
PI reserved variable, 1391
PIVOT operator, 1392
PLOT, 1393
PLOT package, 1394
PLOTKEEP switch, 1395
PLOTRESET, 1396
PM package, 1397
POCHHAMMER, 1398, 1399
Pochhammer, 1400
Pochhammer notation, 1401
Pochhammer’s symbol, 1402, 1403
POLYDIV package, 1404
POLYGAMMA, 1405, 1406
Polygamma functions, 1407
Polynomial, 1408
Polynomial equations, 1409
POSITIVE, 1410, 1411
POSITIVE reserved variable, 1412
positivity, 1413
Power series, 1414
    arithmetic, 1415
    composition, 1416
    differentiation, 1417
    of integral, 1418
    of user defined function, 1419
Power series expansions, 1420
PRECEDENCE declaration, 1421
PRECISE switch, 1422, 1423
PRECISE_COMPLEX switch, 1424
PRECISION operator, 1425
    in ROOTS package, 1426
preduce, 1427
preducet, 1428
Prefix, 1429, 1430
Prefix operator, 1431
    declaring new one, 1432
Prefix operator, unary, 1433
PRET switch, 1434, 1435
PRETTYPRINT, 1436
Prettyprinting, 1437, 1438
PRGEN, 1439
PRI switch, 1440
PRIMEP boolean operator, 1441
PRINCIPAL_DER global variable (CDE), 1442
PRINT_PRECISION command, 1443
PRINTGROUP, 1444
Procedure
    body, 1445, 1446
    heading, 1447
    list-valued, 1448
    matrix-valued, 1449
    using LET inside body, 1450
PROCEDURE command, 1451
PROD operator, 1452
PRODUCT, 1453
PRODUCT keyword, 1454
Program, 1455
Program structure, 1456
Proper statement, 1457, 1458, 1459, 1460, 1461
PRSYS, 1462, 1463
PS, 1464
PS operator, 1465
PSCHANGEVAR operator, 1466
PSCOMPOSE operator, 1467
PSCOPY operator, 1468
PSDEPVAR operator, 1469
PSEUDO_DIVIDE, 1470
PSEUDO_DIVIDE operator, 1471
PSEUDO_INVERSE operator, 1472
PSEUDO_QUOTIENT operator, 1473
PSEUDO_REMAINDER, 1474
PSEUDO_REMAINDER operator, 1475
PSEXPANSIONPT operator, 1476
PSEXPLIM Operator, 1477
PSEXPLIM operator, 1478
PSFUNCTION operator, 1479
PSI, 1480, 1481, 1482
Psi function, 1483
PSORDER operator, 1484
PSORDLIM operator, 1485
PSPRINTORDER switch, 1486
PSREVERSE operator, 1487
PSSETORDER operator, 1488
PSSUM operator, 1489
PSTAYLOR operator, 1490
PSTERM operator, 1491
PSTRUNCATE operator, 1492
Puiseux expansion, 1493
Puiseux series, 1494
PUT_EQUATIONS_USED operator (CDE), 1495
PUTCSYSTEM command, 1496
PVAR_DF operator (CDE), 1497

QBINOMIAL operator, 1498
QBRACKETS operator, 1499
QFACTORIAL operator, 1500
QGOSPER operator, 1501
QGOSPER_DOWN switch, 1502, 1503
QGOSPER_SPECIALSOL switch, 1504
QPHIHYPERTERM operator, 1505
QPOCHHAMMER operator, 1506
QPSIHYPERTERM operator, 1507
QRATIO operator, 1508
QSIMPCOMB operator, 1509, 1510
QSUM package, 1511
QSUM_NULLSPACE switch, 1512, 1513
QSUM_TRACE switch, 1514
QSUMRECURSION operator, 1515
QSUMRECURSION_CERTIFICATE switch, 1516, 1517
QSUMRECURSION_DOWN switch, 1518
QSUMRECURSION_EXP switch, 1519
Quadrature, 1520
QUASILINPDE, 1521
QUIT, 1522
QUOTE, 1523

R_SOLVE, 1524
RANDOM, 1525
RANDOM_NEW_SEED, 1526
RANDOM_MATRIX operator, 1527
RANDPOLY package, 1528
RANK, 1529
RAT, 1530
RAT switch, 1531
RATAPRX package, 1532
RATARG switch, 1533, 1534
Rational coefficient, 1535
Rational function, 1536
rational number, 1537
RATIONAL switch, 1538
RATIONAL2PERIODIC operator, 1539
RATIONALIZE switch, 1540
RATJORDAN operator, 1541
RATPRI, 1542
RATPRI switch, 1543
RATROOT switch, 1544
REACTEQN package, 1545
REAL, 1546
Real coefficient, 1547, 1548
Real number, 1549, 1550
REALROOTS, 1551, 1552
REALVALUED, 1553
REALVALUEDP, 1554
REDERR, 1555
REDLOG package, 1556
REDUCE, 1557
REDUCT, 1558
REM_SPACES, 1559
REM_DUMMY_IDS, 1560
REM_DUMMY_INDICES, 1561, 1562
REM_VALUE_TENS, 1563, 1564
REM_SPACES, 1565
REM_TENSOR, 1566
REMAINDER, 1567
REMAINDER operator, 1568
REMANTICOM, 1569
REMEMBER, 1570
REMFAC, 1571
REMFORDER command, 1572, 1573
REMIND, 1574
REMOVE_COLUMNS operator, 1575, 1576
REMOVE_ROWS operator, 1577
REMOVE_VARIABLES, 1578
REMSYM, 1579, 1580
RENOSUM command, 1581, 1582
REPART, 1583, 1584, 1585
REPEAT, 1586, 1587, 1588, 1589
REPEAT statement, 1590
REPPRINCPARAM_DER shared global variable (CDE), 1591
REPPRINCPARAM_ODD shared global variable (CDE), 1592
REQUIREMENTS shared variable, 1593
Reserved variable, 1594, 1595
Reserved variable
    HIGH_POW, 1596
    LOW_POW, 1597
    CATALAN, 1598
    EULER_GAMMA, 1599
    GOLDEN_RATIO, 1600
    I, 1601
    INFINITY, 1602
    KHINCHIN, 1603
    NEGATIVE, 1604
    NIL, 1605
    PI, 1606
    POSITIVE, 1607
    T, 1608
RESET package, 1609
RESIDUE package, 1610
REST operator, 1611
RESULT, 1612
RESULTANT, 1613
RETRY, 1614
RETURN, 1615, 1616, 1617, 1618
RETURN statement, 1619
REVERSE operator, 1620
REVGRADLEX, 1621
revgradlex
    term order, 1622
REVPRI, 1623
REVPRI switch, 1624
Rewriting rules
    CANTENS package, 1625
RHS operator, 1626
Riemann tensor
    CANTENS package, 1627
RIEMANNCONX command, 1628, 1629
Riemannian Connections, 1630
RLfi package, 1631
Rlisp, 1632
RLISP88, 1633
RLROOTNO, 1634
root finding, 1635
ROOT_MULTIPLICITIES global variable, 1636
ROOT_OF operator, 1637, 1638
ROOT_VAL, 1639, 1640
ROOTACC operator (ROOTS package), 1641
ROOTACC!# global variable (ROOTS package), 1642
ROOTMSG switch, 1643
ROOTPREC operator (ROOTS package), 1644
ROOTS, 1645, 1646
ROOTS package, 1647
ROOTS package, 1648
ROOTS_AT_PREC, 1649
ROOTSCOMPLEX, 1650
ROOTSREAL, 1651
ROUND, 1652
ROUNDALL switch, 1653
ROUNDBF switch, 1654
ROUNDED, 1655, 1656
ROUNDED switch, 1657, 1658, 1659, 1660, 1661
ROW_DIM operator, 1662
ROWS_PIVOT operator, 1663
RSETREPRESENTATION, 1664
RSOLVE package, 1665
RTR command, 1666
RTRACE package, 1667
RTRACE switch, 1668, 1669
RTROUT command, 1670
RTRST command, 1671
Rule lists, 1672
Rules
    Double slash operators, 1673
    Double tilde variables, 1674
    Free operators, 1675

saturation, 1676
SAVE_CDE_STATE operator, 1677
SAVEAS statement, 1678
SAVESTRUCTR switch, 1679
Saving an expression, 1680
SCALAR, 1681, 1682
Scalar, 1683, 1684
Scalar variable, 1685
SCALEFACTORS operator, 1686
SCALOP, 1687
SCHOUTEN_BRACKET operator (CDE), 1688
SCIENTIFIC_NOTATION declaration, 1689
SCOPE package, 1690
SDER(I), 1691
SEC, 1692, 1693
SECH, 1694, 1695
SECOND operator, 1696
SELECT, 1697
Selector, 1698
SELECTVARS operator, 1699
Semicolon, 1700
SET statement, 1701, 1702
Set Statement, 1703
SET_EQ, 1704
SETAVAILABLE, 1705
SETDIFF, 1706
SETELEMENTS, 1707
SETGENERATORS, 1708
SETGROUPTABLE, 1709
SETMOD, 1710
SETS package, 1711
SGN
    indeterminate sign, 1712
SHARE declaration, 1713
SHOW_DUMMY_NAMES, 1714
SHOW_EPSILONS, 1715, 1716, 1717
SHOW_SPACES, 1718, 1719, 1720
SHOWRULES, 1721
SHOWTIME command, 1722
SHUT command, 1723
SI, 1724
Side effect, 1725
SIGN, 1726, 1727
SIGNATURE, 1728
Signature
    CANTENS package, 1729, 1730, 1731, 1732
signature, 1733, 1734, 1735
SIGNATURE command, 1736
SIMPLEDE, 1737
SIMPLEX operator, 1738
Simplification, 1739, 1740, 1741
simplify_combinatorial, 1742
SIMPLIFY_GAMMA, 1743
simplify_gamma2, 1744
simplify_gamman, 1745
SIMPNONCOMDF switch, 1746
SIMPSYS, 1747, 1748, 1749
SIN, 1750, 1751
SINH, 1752, 1753
SixjSymbol, 1754
SMACRO reserved identifier, 1755
SMITHEX operator, 1756
SMITHEX_INT operator, 1757
SolidHarmonicY, 1758
SOLVE operator, 1759, 1760, 1761
    ASSUMPTIONS variable, 1762
    REQUIREMENTS shared variable, 1763
    ROOT_MULTIPLICITIES global variable, 1764
    use of GROEBNER package, 1765
SOLVE package
    with ROOTS package, 1766
SOLVESINGULAR switch, 1767
space, 1768
SPACEDIM command, 1769, 1770
Spaces
    CANTENS package, 1771, 1772, 1773
spaces, 1774, 1775, 1776, 1777
SPADD_TO_COLUMNS operator, 1778
SPADD_TO_ROWS operator, 1779
SPADD_COLUMNS operator, 1780
SPADD_ROWS operator, 1781
SPARSE declaration, 1782
SPARSE package, 1783
SPARSEMATP predicate, 1784
SPAUGMENT_COLUMNS operator, 1785
SPBAND_MATRIX operator, 1786
SPBLOCK_MATRIX operator, 1787
SPCHAR_MATRIX operator, 1788
SPCHAR_POLY operator, 1789
SPCHOLESKY operator, 1790
SPCOEFF_MATRIX operator, 1791
SPCOL_DIM operator, 1792
SPCOMPANION operator, 1793
SPCOPY_INTO operator, 1794
SPDE package, 1795
SPDIAGONAL operator, 1796
SPECFN, 1797
SPECFN package, 1798
SPECFN2 package, 1799
SPEXTEND operator, 1800
SPFIND_COMPANION operator, 1801
SPGET_COLUMNS operator, 1802
SPGET_ROWS operator, 1803
SPGRAM_SCHMIDT operator, 1804
Spherical and Solid Harmonics, 1805
Spherical coordinates, 1806, 1807
SphericalHarmonicY, 1808
SPHERMITIAN_TP operator, 1809
SPHESSIAN operator, 1810
Spinor
    CANTENS package, 1811
SPJACOBIAN operator, 1812
SPJORDAN_BLOCK operator, 1813
SPLIT_FIELD function, 1814
SPLITEXT_LIST operator (CDE), 1815
SPLITEXT_OPEQU operator (CDE), 1816
SPLITVARS_OPEQU operator (CDE), 1817
SPLU_DECOM operator, 1818
SPMAKE_IDENTITY operator, 1819
SPMATRIX_AUGMENT operator, 1820
SPMATRIX_STACK operator, 1821
SPMINOR operator, 1822
SPMULT_COLUMNS operator, 1823
SPMULT_ROWS operator, 1824
SPPIVOT operator, 1825
SPPSEUDO_INVERSE operator, 1826
SPREMOVE_ROWS operator, 1827
SPROW_DIM operator, 1828
SPROWS_PIVOT operator, 1829
SPSUB_MATRIX operator, 1830
SPSVD operator, 1831
SPSWAP_COLUMNS operator, 1832
SPSWAP_ENTRIES operator, 1833
SPSWAP_ROWS operator, 1834
SPUR, 1835
SQFRF, 1836
SQRT, 1837, 1838
SQUAREP predicate, 1839, 1840
SSTOOLS package, 1841
STACK_ROWS operator, 1842, 1843
Standard form, 1844
Standard quotient, 1845
STATE, 1846
Statement, 1847
    assignment, 1848
    compound, 1849
    conditional, 1850
    FOR, 1851
    FOREACH, 1852
    GO TO, 1853
    Group, 1854
    REPEAT, 1855
    RETURN, 1856
    SAVEAS, 1857
    Set, 1858
    Unset, 1859
    WHILE, 1860
Statement terminator, 1861
Stirling numbers, 1862
Stirling1, 1863
Stirling2, 1864
STOREGROUP, 1865
String, 1866
STRUCTR, 1867, 1868
Structuring, 1869
Struve functions, 1870
StruveH, 1871, 1872
StruveL, 1873, 1874
Sturm Sequences, 1875
SUB, 1876
SUB operator, 1877
SUB_MATRIX operator, 1878
SUBSET_EQ, 1879
Subspaces
    CANTENS package, 1880
subspaces, 1881
Substitution, 1882
SUCHTHAT, 1883
SUM, 1884
SUM keyword, 1885
SUM operator, 1886
SUM package, 1887
SUM!-SQ operator, 1888
SUMRECURSION, 1889
SUMTOHYPER, 1890
SUPER_PRODUCT operator (CDE), 1891
SVD operator, 1892
SVEC, 1893
SWAP_COLUMNS operator, 1894
SWAP_ENTRIES operator, 1895
SWAP_ROWS operator, 1896
Switch, 1897, 1898
    ADJPREC, 1899
    ALGINT, 1900
    ALLBRANCH, 1901
    ALLFAC, 1902, 1903, 1904
    ALLOWDFINT, 1905
    ANTICOM, 1906
    ARBVARS, 1907
    BALANCED_MOD, 1908, 1909
    BEZOUT, 1910
    BFSPACE, 1911
    CHECKORD, 1912
    COMBINEEXPT, 1913
    COMBINELOGS, 1914
    COMMUTEDF, 1915
    COMP, 1916
    COMPLEX, 1917, 1918
    CRAMER, 1919, 1920
    CREF, 1921
    DEFN, 1922, 1923, 1924
    DFINT, 1925
    DISPJACOBIAN, 1926
    DIV, 1927, 1928
    ECHO, 1929
    ERRCONT, 1930
    EVALLHSEQP, 1931
    EXP, 1932, 1933
    EXPANDDF, 1934
    EXPANDLOGS, 1935
    EZGCD, 1936
    FACTOR, 1937, 1938
    FAILHARD, 1939
    FAST_LA, 1940, 1941
    FASTSIMPLEX, 1942
    FORT, 1943
    FORTUPPER, 1944
    FULLROOTS, 1945
    GCD, 1946
    GLTBASIS, 1947, 1948
    GROEBFULLREDUCTION, 1949, 1950
    GROEBOPT, 1951, 1952, 1953
    GROEBPROT, 1954
    GROEBSTAT, 1955, 1956
    HEUGCD, 1957
    IFACTOR, 1958
    IMAGINARY, 1959
    INTSTR, 1960
    LHYP, 1961
    LIST, 1962
    LISTARGS, 1963
    LMON, 1964
    LOOKING_GOOD, 1965
    LOWER_MATRIX, 1966
    LTRIG, 1967
    MCD, 1968, 1969
    MODULAR, 1970, 1971, 1972
    MSG, 1973
    MULTIPLICITIES, 1974
    MULTIROOT, 1975
    NAT, 1976, 1977
    NERO, 1978
    NOCOMMUTEDF, 1979
    NOCONVERT, 1980
    NOINTSUBST, 1981
    NOLNR, 1982
    NOSPLIT, 1983
    NOSUM, 1984
    NOT_NEGATIVE, 1985
    ONESPACE, 1986, 1987, 1988
    ONLY_INTEGER, 1989
    OUTPUT, 1990
    PERIOD, 1991
    PLOTKEEP, 1992
    PRECISE, 1993, 1994
    PRECISE_COMPLEX, 1995
    PRET, 1996, 1997
    PRI, 1998
    PSPRINTORDER, 1999
    QGOSPER_DOWN, 2000, 2001
    QGOSPER_SPECIALSOL, 2002
    QSUM_NULLSPACE, 2003, 2004
    QSUM_TRACE, 2005
    QSUMRECURSION_CERTIFICATE, 2006, 2007
    QSUMRECURSION_DOWN, 2008
    QSUMRECURSION_EXP, 2009
    RAT, 2010
    RATARG, 2011, 2012
    RATIONAL, 2013
    RATIONALIZE, 2014
    RATPRI, 2015
    RATROOT, 2016
    REVPRI, 2017
    ROOTMSG, 2018
    ROUNDALL, 2019
    ROUNDBF, 2020
    ROUNDED, 2021, 2022, 2023, 2024, 2025
    RTRACE, 2026, 2027
    SAVESTRUCTR, 2028
    SIMPNONCOMDF, 2029
    SOLVESINGULAR, 2030
    SYMMETRIC, 2031
    TAYLORAUTOCOMBINE, 2032
    TAYLORAUTOEXPAND, 2033, 2034
    TAYLORKEEPORIGINAL, 2035, 2036, 2037, 2038
    TAYLORPRINTORDER, 2039
    TR_LIE, 2040
    TRA, 2041
    TRCOMPACT, 2042
    TRFAC, 2043
    TRGROEB, 2044, 2045
    TRGROEB1, 2046, 2047
    TRGROEBR, 2048
    TRGROEBS, 2049, 2050
    TRIGFORM, 2051
    TRINT, 2052, 2053
    TRINTSUBST, 2054
    TRNUMERIC, 2055
    TRPLOT, 2056
    TRROOT, 2057
    TRSOLVE, 2058
    TRSUM, 2059
    TRWU, 2060
    UPPER_MATRIX, 2061
    VAROPT, 2062
    VERBOSELOAD, 2063
    ZB_FACTOR, 2064
    ZB_PROOF, 2065
    ZB_TRACE, 2066, 2067
Switches by package
    REDUCE Core
        ADJPREC, 2068
        ALLBRANCH, 2069
        ALLFAC, 2070, 2071, 2072
        ALLOWDFINT, 2073
        ARBVARS, 2074
        BALANCED_MOD, 2075, 2076
        BEZOUT, 2077
        BFSPACE, 2078
        COMBINEEXPT, 2079
        COMBINELOGS, 2080
        COMMUTEDF, 2081
        COMP, 2082
        COMPLEX, 2083, 2084
        CRAMER, 2085, 2086
        CREF, 2087
        DEFN, 2088, 2089, 2090
        DFINT, 2091
        DISPJACOBIAN, 2092
        DIV, 2093, 2094
        ECHO, 2095
        ERRCONT, 2096
        EVALLHSEQP, 2097
        EXP, 2098, 2099
        EXPANDDF, 2100
        EXPANDLOGS, 2101
        EZGCD, 2102
        FACTOR, 2103, 2104
        FAILHARD, 2105
        FORT, 2106
        FORTUPPER, 2107
        FULLROOTS, 2108
        GCD, 2109
        HEUGCD, 2110
        IFACTOR, 2111
        INTSTR, 2112
        LIST, 2113
        LISTARGS, 2114
        MCD, 2115, 2116
        MODULAR, 2117, 2118, 2119
        MSG, 2120
        MULTIPLICITIES, 2121
        NAT, 2122, 2123
        NERO, 2124
        NOCOMMUTEDF, 2125
        NOCONVERT, 2126
        NOINTSUBST, 2127
        NOLNR, 2128
        NOSPLIT, 2129
        OUTPUT, 2130
        PERIOD, 2131
        PLOTKEEP, 2132
        PRECISE, 2133, 2134
        PRECISE_COMPLEX, 2135
        PRET, 2136, 2137
        PRI, 2138
        RAT, 2139
        RATARG, 2140, 2141
        RATIONAL, 2142
        RATIONALIZE, 2143
        RATPRI, 2144
        REVPRI, 2145
        ROUNDALL, 2146
        ROUNDBF, 2147
        ROUNDED, 2148, 2149, 2150, 2151, 2152
        SAVESTRUCTR, 2153
        SIMPNONCOMDF, 2154
        SOLVESINGULAR, 2155
        TRFAC, 2156
        TRIGFORM, 2157
        TRINT, 2158
        TRINTSUBST, 2159
        VAROPT, 2160
    ALGINT package
        ALGINT, 2161
        TRA, 2162
        TRINT, 2163
    CANTENS package
        ONESPACE, 2164, 2165, 2166
    CDE package
        CHECKORD, 2167
    COMPACT package
        TRCOMPACT, 2168
    EXCALC package
        NOSUM, 2169
    GNUPLOT package
        TRPLOT, 2170
    GROEBNER package
        GLTBASIS, 2171, 2172
        GROEBFULLREDUCTION, 2173, 2174
        GROEBOPT, 2175, 2176, 2177
        GROEBPROT, 2178
        GROEBSTAT, 2179, 2180
        TRGROEB, 2181, 2182
        TRGROEB1, 2183, 2184
        TRGROEBR, 2185
        TRGROEBS, 2186, 2187
    LAPLACE package
        LHYP, 2188
        LMON, 2189
        LTRIG, 2190
    LIE package
        TR_LIE, 2191
    LINALG package
        FAST_LA, 2192
        FASTSIMPLEX, 2193
        IMAGINARY, 2194
        LOWER_MATRIX, 2195
        NOT_NEGATIVE, 2196
        ONLY_INTEGER, 2197
        SYMMETRIC, 2198
        UPPER_MATRIX, 2199
    NORMFORM package
        LOOKING_GOOD, 2200
    NUMERIC package
        TRNUMERIC, 2201
    PHYSOP package
        ANTICOM, 2202
    QSUM package
        QGOSPER_DOWN, 2203, 2204
        QGOSPER_SPECIALSOL, 2205
        QSUM_NULLSPACE, 2206, 2207
        QSUM_TRACE, 2208
        QSUMRECURSION_CERTIFICATE, 2209, 2210
        QSUMRECURSION_DOWN, 2211
        QSUMRECURSION_EXP, 2212
    ROOTS package
        MULTIROOT, 2213
        RATROOT, 2214
        ROOTMSG, 2215
        TRROOT, 2216
    RSOLVE package
        TRSOLVE, 2217
    RTRACE package
        RTRACE, 2218, 2219
    SPARSE package
        FAST_LA, 2220
    SUM package
        TRSUM, 2221
    TAYLOR package
        TAYLORAUTOCOMBINE, 2222
        TAYLORAUTOEXPAND, 2223, 2224
        TAYLORKEEPORIGINAL, 2225, 2226, 2227, 2228
        TAYLORPRINTORDER, 2229
        VERBOSELOAD, 2230
    TPS package
        PSPRINTORDER, 2231
    WU package
        TRWU, 2232
    ZEILBERG package
        ZB_FACTOR, 2233
        ZB_PROOF, 2234
        ZB_TRACE, 2235, 2236
SYMBOLIC, 2237
Symbolic indices
    CANTENS package, 2238
Symbolic mode, 2239, 2240, 2241, 2242, 2243
Symbolic procedure, 2244
symmetric
    tensor, 2245
SYMMETRIC declaration, 2246, 2247
Symmetric operator, 2248
SYMMETRIC switch, 2249
SYMMETRICP predicate, 2250, 2251
Symmetries
    CANTENS package, 2252
SYMMETRIZE, 2253
SYMMETRY package, 2254
SYMMETRY package, 2255
SYMMETRYBASIS, 2256
SYMMETRYBASISPART, 2257
SYMTREE, 2258
SYMTREE declaration, 2259
systemprecision, 2260

T reserved variable, 2261
TAN, 2262, 2263, 2264
Tangent vector, 2265
TANH, 2266, 2267
TAYLOR operator, 2268
TAYLOR package, 2269
Taylor series, 2270
    arithmetic, 2271
    differentiation, 2272
    integration, 2273
    reversion, 2274
    substitution, 2275
TAYLORAUTOCOMBINE switch, 2276
TAYLORAUTOEXPAND switch, 2277, 2278
TAYLORCOMBINE operator, 2279, 2280
TAYLORKEEPORIGINAL switch, 2281, 2282, 2283, 2284
TAYLORORIGINAL operator, 2285, 2286
TAYLORPRINTORDER switch, 2287
TAYLORPRINTTERMS variable, 2288, 2289
TAYLORREVERT operator, 2290, 2291
TAYLORSERIESP operator, 2292
TAYLORTEMPLATE operator, 2293, 2294
TAYLORTOSTANDARD operator, 2295
TENSOP, 2296
TENSOR, 2297
Tensor contractions
    CANTENS package, 2298
Tensor derivatives
    CANTENS package, 2299
Tensor polynomial
    CANTENS package, 2300
Terminator, statement, 2301
THIRD operator, 2302
ThreejSymbol, 2303
TIME, 2304
TOEPLITZ operator, 2305
torder, 2306, 2307, 2308, 2309, 2310
TORDER operator, 2311
TOTAL_ORDER global variable (CDE), 2312
TOTALDEG, 2313
TP, 2314
TPS package, 2315
TR_LIE switch, 2316
TRA switch, 2317
TRACE, 2318
Trace
    CANTENS package, 2319
Tracing
    EXCALC package, 2320
    GNUPLOT package, 2321
    ROOTS package, 2322
    SPDE package, 2323
    SUM package, 2324
TRCOMPACT switch, 2325
TRFAC switch, 2326
TRGROEB switch, 2327, 2328
TRGROEB1 switch, 2329, 2330
TRGROEBR switch, 2331
TRGROEBS switch, 2332, 2333
TRI package, 2334
TRIANG_ADJOINT operator, 2335
TRIGFORM switch, 2336
TRIGONOMETRIC_BASE, 2337
TRIGSIMP, 2338
TRIGSIMP package, 2339, 2340
TRINT switch, 2341, 2342
TRINTSUBST switch, 2343
TRNUMERIC switch, 2344
TRPLOT switch, 2345
TRRL command, 2346
TRRLID command, 2347
TRROOT switch, 2348
TRSOLVE switch, 2349
TRSUM switch, 2350
truncated power series, 2351
TRWU switch, 2352
TRXIDEAL switch, 2353
TRXMOD switch, 2354
TURTLE package, 2355
TURTLE package, 2356
TVECTOR command, 2357, 2358

U(ALFA), 2359
U(ALFA,I), 2360
Unary prefix operator, 2361
UNION, 2362
UNIT, 2363
UNRTR command, 2364
UNRTRST command, 2365
UNSET statement, 2366, 2367
Unset Statement, 2368
UNTIL, 2369
UNTRRL command, 2370
UNTRRLID command, 2371
UP_QRATIO operator, 2372
UPPER_MATRIX switch, 2373
UPWARD_ANTIDIFFERENCE, 2374
User packages, 2375

VANDERMONDE operator, 2376
VARDF, 2377
VARDF (variational derivative) operator), 2378
Variable, 2379
    double tilde, 2380
Variable elimination, 2381
Variational derivative, 2382
VARNAME, 2383, 2384
VAROPT switch, 2385
VDF, 2386
VEC command, 2387
VECDIM, 2388
VECOP, 2389
VECTOR, 2390
Vector
    addition, 2391
    cross product, 2392
    differentiation, 2393
    division, 2394
    dot product, 2395
    exponentiation, 2396
    inner product, 2397
    integration, 2398
    modulus, 2399
    multiplication, 2400
    subtraction, 2401
Vector algebra, 2402
VECTORADD, 2403
VECTORCROSS, 2404
VECTORDIFFERENCE, 2405
VECTOREXPT, 2406
VECTORMINUS, 2407
VECTORPLUS, 2408
VECTORQUOTIENT, 2409
VECTORRECIP, 2410
VECTORTIMES, 2411
VERBOSELOAD switch, 2412
VINT, 2413
VMOD, 2414
VMOD operator, 2415
VOLINT, 2416
VOLINTEGRAL function, 2417
VOLINTORDER vector, 2418
VORDER, 2419
VOUT, 2420
VSTART, 2421
VTAYLOR, 2422

Warnings
    TAYLOR package, 2423
Wedge, 2424
WEIGHT, 2425
Weighted ordering, 2426
WHEN, 2427
WHERE, 2428
WHILE, 2429, 2430, 2431, 2432
WHILE statement, 2433
Whittaker functions, 2434
WhittakerM, 2435, 2436
WhittakerU, 2437
WhittakerW, 2438
wholespace, 2439, 2440, 2441, 2442, 2443, 2444
WHOLESPACE_DIM, 2445, 2446
Workspace, 2447
WRITE, 2448
WS, 2449, 2450
WTLEVEL, 2451
WU package, 2452

X(I), 2453
XAUTO, 2454
XCOLOR package, 2455
XFULLREDUCE switch, 2456
XI(I), 2457
XIDEAL, 2458
XIDEAL package, 2459
XMOD, 2460
XMODIDEAL, 2461
XORDER, 2462
XPND
    XPND
        @, 2463
XPND
    @, 2464
    D, 2465
XPND command, 2466
XVARS, 2467

ZB_DIRECTION variable, 2468
ZB_FACTOR switch, 2469
ZB_ORDER variable, 2470
ZB_PROOF switch, 2471
ZB_TRACE switch, 2472, 2473
ZEILBERG package, 2474
ZEILBERGER_REPRESENTATION variable, 2475
ZETA, 2476, 2477
Zeta function (Riemann’s), 2478
ZETA(ALFA,I), 2479
ZTRANS, 2480
ZTRANS package, 2481