\begin{theindex}

  \item $<$domain description$>$, 133
  \item $<$domain symbol$>$, 133
  \item .masrc, 264
  \item \verb./., 31, 63, 254
  \item \verb./\., 254
  \item \verb.\/., 254
  \item \verb/#/, 31, 254
  \item \verb/$/, 254
  \item \verb/%/, 31
  \item \verb/'/, 33, 254
  \item \verb/(*/, 33
  \item \verb/(/, 31, 254
  \item \verb/)/, 31, 254
  \item \verb/*)/, 33
  \item \verb/*/, 31, 63, 254
  \item \verb/+/, 31, 63, 254
  \item \verb/,...,/, 254
  \item \verb/,/, 31, 254
  \item \verb/--command=COMMAND/, 263
  \item \verb/--copyright/, 263
  \item \verb/--exit-on-error/, 264
  \item \verb/--exit/, 264
  \item \verb/--file=FILE/, 264
  \item \verb/--help/, 263
  \item \verb/--memorysize=SIZE/, 264
  \item \verb/--no-readline/, 264
  \item \verb/--output[=FILE]/, 264
  \item \verb/--version/, 263
  \item \verb/-/, 31, 63, 254
  \item \verb/->/, 31
  \item \verb/-C/, 263
  \item \verb/-E/, 264
  \item \verb/-R/, 264
  \item \verb/-c COMMAND/, 263
  \item \verb/-e/, 264
  \item \verb/-f FILE/, 264
  \item \verb/-m SIZE/, 264
  \item \verb/-o[FILE]/, 264
  \item \verb/./, 31, 254
  \item \verb//, 33, 254
  \item \verb/:/, 31, 254
  \item \verb/;/, 31, 254
  \item \verb/</, 31, 254
  \item \verb/<=/, 31, 254
  \item \verb/<>/, 31
  \item \verb/=/, 31, 254
  \item \verb/=>/, 31
  \item \verb/>/, 31, 254
  \item \verb/>=/, 31, 254
  \item \verb/[/, 254, 255
  \item \verb/]/, 254, 255
  \item \verb/^/, 63, 254
  \item \verb/{}/, 31, 254
  \item \verb/||/, 254
  \item \verb/~/, 254

  \indexspace

  \item abelian group, 56
  \item abelian monoid, 56
  \item abstract objects, 22, 51
  \item actual parameter, 37, 39, 45
  \item ADCNST, 131
  \item ADCONV, 132
  \item ADD, 264
  \item ADDDREAD, 133
  \item ADDDWRIT, 133
  \item ADDIF, 131
  \item ADEXP, 132
  \item ADEXTRA, 247
  \item ADFACT, 132
  \item ADFI, 132
  \item ADFIP, 132
  \item ADGCD, 132
  \item ADGCDC, 132
  \item ADGCDE, 132
  \item ADINV, 131
  \item ADINVT, 131
  \item ADLCM, 132
  \item ADNEG, 131
  \item ADNOR, 247
  \item ADONE, 131
  \item ADPROD, 131
  \item ADQUOT, 132
  \item ADREAD, 132
  \item ADSIGN, 131
  \item ADSUM, 131
  \item ADTOIP, 132
  \item ADV, 24, 66, 72, 264
  \item ADVLDD, 133
  \item ADWRIT, 133
  \item AF (x, p(x), $\lbrack$ (l,r) $\lbrack$, s$\rbrack$ $\rbrack$), 
		143
  \item AIX, 1
  \item ALDES, 253, 261
    \subitem  syntax error, 255
    \subitem  syntax warning, 255
  \item algebra, 22, 51
  \item algebraic number, 276
  \item Algebraic Numbers, 134, 144
  \item ALGOL, 269
  \item algorithm, 15, 18
    \subitem  Buchberger, 153, 200
  \item ALIST, 270
  \item AmigaDOS, 1
  \item AND, 265
    \subitem  keyword, 31
  \item APABS, 92
  \item APCMPR, 92
  \item APDIFF, 93
  \item APEXP, 93
  \item APF $\lbrack s \rbrack$, 138
  \item APFINT, 92, 94
  \item APFRN, 24, 92, 93
  \item APNEG, 92
  \item APPI, 17, 93
  \item APPLY, 265
  \item APPROD, 92
  \item approximation, 89
  \item APQ, 92
  \item APREAD, 93
  \item APROOT, 93
  \item APSIGN, 92
  \item APSPRE, 92
  \item APSUM, 92
  \item APWRIT, 17, 93
  \item arbitrary domain, 129
    \subitem  polynomial, 129, 277
  \item Arbitrary Precision Floating Point Numbers, 134, 139
  \item arithmetic, 20, 74, 269, 270, 274
  \item ARRAY, 265
  \item array, 255
    \subitem  keyword, 254
  \item ASCII, 30, 253
  \item ASSIGN, 265
  \item assignment, 16, 17, 38
  \item ASSOC, 265
  \item atom, 20, 31
  \item average computing time, 71
  \item AXIOMS, 265
    \subitem  keyword, 31
  \item axioms, 51, 61

  \indexspace

  \item back track, 62
  \item base, involutive, 247
  \item basic arithmetic, 74, 274
  \item basis
    \subitem  submodule, 200
  \item BCPL, 269
  \item BEGIN
    \subitem  keyword, 31
  \item BEGIN-END
    \subitem  statement, 43
  \item big $O$ notation, 72
  \item binding, 40
  \item BIOS, 261, 269
  \item blank, 33, 255
  \item browse, 23, 25
  \item Buchberger algorithm, 153, 154, 200, 276
  \item Buchbergers graduated term order, 108

  \indexspace

  \item C, 28
  \item CAR, 264, 271
  \item CASE, 265
  \item case
    \subitem  keyword, 254
  \item CATCH, 265
  \item category theory, 22, 51
  \item CCONC, 66, 73
  \item CDR, 264
  \item cell, 71
  \item center, 189
    \subitem  computation, 190
  \item CenterPol, 128
  \item centralizer, 189
  \item character set, 30, 253
  \item CINV, 66, 73
  \item closure, 57
  \item CLOUT, 69
  \item command, 27
    \subitem  line, 263
  \item comment, 16, 31, 33, 254, 255
  \item common multiples, 198
  \item commutator relation, 127
  \item COMP, 65, 72, 264
  \item compatible
    \subitem  homogeneity, 199
  \item compiled
    \subitem  code, 269, 270
    \subitem  function, 16
    \subitem  procedure, 271
  \item compiler, 18, 265, 269
  \item complex number, 74
  \item Complex Numbers, 134
  \item complexity, 71, 85, 92, 102, 112, 127
  \item comprehensive Gr\"obner base, 171, 277
  \item computation
    \subitem  center, 190
  \item computing in solvable polynomial rings, 126, 183
  \item computing time, 71
  \item CON, 48, 263
  \item CONC, 66, 73, 264
  \item concrete objects, 22, 51
  \item COND, 265
  \item condition, 38
  \item conditional rewriting, 62
  \item configuration, 269, 271
  \item confluence, 62
  \item confusion, 27
  \item CONS, 264
  \item const, 255
    \subitem  keyword, 254
  \item construction, 65
  \item counting, real roots, 237, 239
  \item critical pairs, 154
  \item cross reference, 25

  \indexspace

  \item data type, 268
  \item DE, 265
  \item DEBUG, 262
  \item debug, 27
  \item declaration, 16
  \item definition, 23
  \item denotational semantics, 51
  \item dependencies, 269
  \item Derive, 15, 270
  \item DESC, 60
  \item descriptor, 59
  \item design, 268
  \item destruction, 66
  \item det, 82
  \item determinant, 80
  \item DF, 265
  \item DG, 265
  \item diagram, 66
  \item DIFIP, 130
  \item digit, 21, 30, 74, 253, 274
  \item DIIFGB, 130
  \item DIIFLS, 130
  \item DIIFNF, 130
  \item DIIFRP, 115
  \item DIILIS, 247
  \item DIIPI, 248
  \item DIIPIB, 248
  \item DIIPNF, 247
  \item DILIS, 130, 247
  \item DILRD, 131
  \item DILWR, 131
  \item dimension, 155
  \item DINCCO, 127
  \item DINCCP, 128
  \item DINCCPpre, 128
  \item DINCGB, 128
  \item DINLGB, 128
  \item DINLIS, 128
  \item DINLNF, 127
  \item DINPEX, 127
  \item DINPPR, 127
  \item DIP2SYM, 121
  \item DIPBSO, 113
  \item DIPC, 247
  \item DIPDCI, 247
  \item DIPDEG, 113
  \item DIPDIF, 129
  \item DIPEVL, 113
  \item DIPFMO, 113
  \item DIPFP, 115
  \item DIPGB, 130
  \item DIPI, 247, 248
  \item DIPIB, 248
  \item DIPII, 247
  \item DIPLBC, 113
  \item DIPMAD, 113
  \item DIPMCP, 113
  \item DIPNEG, 129
  \item DIPNOR, 130
  \item DIPRNI, 247
  \item DIPROD, 129
  \item DIPSUM, 129
  \item DIPTODEF, 122
  \item DIPVDEF, 122
  \item directory, 15, 16, 50, 262
  \item DIRFIP, 115
  \item DIRLIS, 114, 247
  \item DIRPAB, 113
  \item DIRPDF, 114
  \item DIRPGB, 114
  \item DIRPI, 248
  \item DIRPIB, 248
  \item DIRPNF, 114, 247
  \item DIRPNG, 113
  \item DIRPPR, 114
  \item DIRPSG, 113
  \item DIRPSM, 113
  \item distributive polynomial, 112, 121, 127, 129, 275
  \item DO
    \subitem  keyword, 31
  \item do
    \subitem  keyword, 254
  \item domain
    \subitem  description, 133
    \subitem  symbol, 133
  \item DOS, 1, 262
  \item DPGEN, 78
  \item DUMPENV, 261
  \item dynamic scope, 46

  \indexspace

  \item EBNF, 34, 52, 255
  \item EDIT, 262
  \item editor, 19, 25, 50, 262
  \item elimination, quantifier, 239
  \item ELSE
    \subitem  keyword, 31
  \item else
    \subitem  keyword, 254
  \item EMACS, 262
  \item embedding, 200
  \item emergency, 27
  \item END
    \subitem  keyword, 31
  \item EQ, 265
  \item EQUAL, 73
  \item error, 27, 36, 257
  \item EVAL, 265
  \item evaluation, 19, 52, 63, 64
  \item EVLGIL, 128
  \item EVLGTD, 128
  \item EVOWRITE, 122
  \item executable program, 271
  \item EXIT, 27, 262, 265
  \item EXP, 59
  \item Exp, 90
  \item EXPLODE, 265
  \item exponential series, 89
  \item EXPOSE, 57, 59, 61, 63
    \subitem  keyword, 31
  \item expression, 34
  \item EXTENT, 73
  \item external function, 40
  \item EXTPROCS, 23, 260

  \indexspace

  \item factor, 37
  \item fatal error, 27
  \item FIELD, 56
  \item field, 55, 60
  \item finite field, 74
  \item Finite Field Numbers, 134
  \item FIRST, 66, 72, 264, 271
  \item FLAMBDA, 265
  \item floating point, 17, 74, 91, 272, 274
    \subitem  algorithms, 91
    \subitem  representation, 91
    \subitem  syntax, 93
  \item fluid
    \subitem  variable, 46
  \item FOR, 28
  \item for
    \subitem  keyword, 254
  \item formal parameter, 45
    \subitem  list, 45
  \item formulas
    \subitem  syntax, 241
  \item FORTRAN, 253
  \item function, 37
    \subitem  overload, 60
  \item FUSSY, 262

  \indexspace

  \item GCD, 26
  \item GCM, 261
  \item GEM, 1, 19
  \item generic, 23, 261
    \subitem  function, 60
    \subitem  operators, 262
    \subitem  parse, 63
  \item GENERICS, 23, 261
  \item GENPARSE, 262
  \item GENSYM, 265
  \item GET, 265
  \item GINBAS, 231
  \item GINCHK, 230
  \item GINCUT, 230
  \item GINORP, 230
  \item GINRED, 230
  \item GLAMBDA, 265
  \item global, 255
    \subitem  keyword, 254
    \subitem  variable, 46
  \item go to
    \subitem  keyword, 254
  \item GOTO, 265
  \item goto, 255
    \subitem  keyword, 254
  \item Gr\"obner base, 154
    \subitem  comprehensive, 171
    \subitem  left, 185
    \subitem  partial, 199
    \subitem  submodule, 201
    \subitem  two-sided, 185
    \subitem  universal, 207
  \item GRA, 48, 263
  \item graded structure, 199
  \item graphic, 48, 263, 265
  \item greatest common divisor, 80, 276
  \item GRNBAS, 231
  \item GRNCHK, 231
  \item GRNCUT, 231
  \item GRNGGB, 231
  \item GRNORP, 231
  \item GRNRED, 231
  \item GSYINF, 230
  \item GSYNSP, 230
  \item GSYORD, 230
  \item GSYPGR, 230
  \item GSYPGW, 230
  \item GSYSPG, 230

  \indexspace

  \item header, 54
  \item HELP, 23, 40, 74, 260
  \item help, 17, 23--25, 260
    \subitem  facilities, 23
  \item homogeneity compatible, 199
  \item homogeneous, 199
    \subitem  ideal, 199

  \indexspace

  \item IABS, 76
  \item IBM
    \subitem  RS6000, 1
  \item ICOMP, 76, 79
  \item ideal
    \subitem  decomposition, 276
    \subitem  homogeneous, 199
    \subitem  intersection, 197
    \subitem  quotient, 198
  \item identifier, 31, 32, 254
    \subitem  list, 45
  \item IDIF, 76
  \item IEXP, 77
  \item IF, 16, 265
    \subitem  keyword, 31
    \subitem  statement, 43
  \item if
    \subitem  keyword, 254
  \item IFACT, 78
  \item IGCD, 77
  \item ILCM, 77
  \item ILWRIT, 78
  \item IMPL, 265
  \item IMPLEMENTATION
    \subitem  keyword, 31
  \item implementation, 19, 51, 57, 126, 184, 269
  \item IMPLODE, 265
  \item IMPORT, 55, 57, 59, 61
    \subitem  keyword, 31
  \item IN, 263
  \item independent sets, 155
  \item INEG, 76
  \item infinite loop, 41
  \item InitExternals, 271
  \item input, 15, 19, 27, 28, 48, 269, 273
  \item INT, 134
  \item integer, 20, 21, 74, 75, 102, 272, 274
    \subitem  algorithms, 75
    \subitem  factorization, 74, 272, 274
    \subitem  representation, 75
    \subitem  syntax, 77
  \item Integral Digit modulo Digit, 133
  \item Integral Numbers, 133, 134
  \item Integral Numbers modulo Integer, 133, 137
  \item Integral Polynomial, 140
  \item integral polynomial, 102
  \item Integral Polynomials, 134
  \item interactive, 30, 268, 270
  \item internal function, 40
  \item interpretation, 64
  \item interpreter, 271, 273, 274
  \item intersection
    \subitem  ideal, 197
  \item intrinsic, 255
    \subitem  keyword, 254
  \item INV, 66, 73, 264
  \item invariant polynomials, 229, 277
  \item inverse graduated term order, 109
  \item inverse lexicographical term order, 109
  \item involutive base, 247
  \item involutive bases, 277, 278
  \item IP (x1,...,xr), 140
  \item IPABS, 103
  \item IPDIF, 103
  \item IPNEG, 103
  \item IPPGSD, 105
  \item IPPROD, 103, 105
  \item IPPSR, 104
  \item IPQR, 104
  \item IPREAD, 104
  \item IPROD, 20, 76, 80
  \item IPRODK, 76
  \item IPSIGN, 103
  \item IPSUM, 103
  \item IPWRIT, 104
  \item IQ, 77
  \item IQR, 77
  \item IRAND, 77
  \item IREAD, 77
  \item IREM, 77
  \item ISIGN, 76
  \item ISUM, 76
  \item IWRITE, 20, 77

  \indexspace

  \item JOIN, 264
  \item join, 22, 51
    \subitem  specifications, 55

  \indexspace

  \item kernel, 271, 273
  \item keyword, 31, 254
  \item knowledge, 15, 18, 19

  \indexspace

  \item LABEL, 265
  \item LAMBDA, 265
  \item lambda calculus, 52
  \item language, 16, 28, 30, 264, 269, 271
  \item left, 70
  \item left common multiples, 198
  \item left Gr\"obner base, 185
  \item LENGTH, 65, 72
  \item letter, 30, 253
  \item lexical conventions, 30
  \item LFCHECK, 120
  \item LGBASE, 128
  \item library, 19, 268, 272
  \item linear algebra, 277
  \item linear form, 119, 199
  \item linker, 271
  \item LIRRSET, 128
  \item LISP, 16, 18, 27, 28, 261, 264, 269
  \item LIST, 65, 73, 265
  \item list, 16, 20
    \subitem  processing, 16, 65, 72, 273
    \subitem  representation, 75, 84, 91
  \item list expression, 37
  \item LISTENV, 23, 261
  \item listexpr, 37
  \item local
    \subitem  variable, 46
  \item logic formulas, 278
  \item LOOP, 265
  \item lower level routine, 271
  \item LT, 265

  \indexspace

  \item macro, 25, 28, 265
  \item Macsyma, 15
  \item main program, 273
  \item MAP, 60, 265
    \subitem  keyword, 31
  \item mapcar, 69, 265
  \item Maple, 15
  \item MAS
    \subitem  expression, 121
  \item MAS.RC, 262
  \item MASLOAD, 247
  \item Mathematica, 15
  \item maximal computing time, 71
  \item MD m, 137
  \item memory, 71
  \item MI m, 137
  \item minimal computing time, 71
  \item MLAMBDA, 265
  \item MODEL, 265
    \subitem  keyword, 31
  \item model, 52, 59
  \item model theory, 22, 51
  \item MODULA, 28, 261
  \item modular integer, 61, 74, 274
  \item module, 200
    \subitem  arithmetic, 277
    \subitem  of syzygies, 195
    \subitem  structure, 268
  \item MUL, 264
  \item muLISP, 270

  \indexspace

  \item NE, 265
  \item NIL, 264
  \item NOEINF, 231
  \item NOENSP, 231
  \item NOERED, 231
  \item Noether, 229
  \item Noetherian relation, 62
  \item non-commutative polynomial, 276
  \item NOT, 265
    \subitem  keyword, 31
  \item NPREAD, 127
  \item NUL, 48, 263
  \item number, 31, 254
  \item numeric, 268, 270, 272

  \indexspace

  \item OBJECT, 56
  \item octonion number, 74
  \item Octonion Numbers, 134
  \item of
    \subitem  keyword, 254
  \item operating system, 19, 48, 263
  \item operator
    \subitem  overloading, 63, 262
  \item optimal variable ordering, 124
  \item optimized linking, 271
  \item OR, 265
    \subitem  keyword, 31
  \item ORDER, 73
  \item Ore condition, 198
  \item OS2, 1
  \item OUT, 263
  \item output, 17, 19, 48, 263, 269, 273
  \item overflow, 94
  \item overload, 60

  \indexspace

  \item package, 271
  \item parameter, 24, 28, 37, 39
  \item parametric real root counting, 239
  \item parser, 16, 18, 28, 30, 63, 262, 269, 273, 274
    \subitem  ALDES, 253
  \item partial
    \subitem  Gr\"obner~base, 199
    \subitem  reduction, 199
  \item PDEG, 102
  \item Peano arithmetic, 64
  \item Peano axioms, 63
  \item Peano structure, 62
  \item permutations, 229
  \item PFDIP, 115
  \item PL/0, 30
  \item PLBCF, 103
  \item PLDCF, 103
  \item POLY, 121
  \item polynomial, 102, 112, 121, 127, 129
    \subitem  arithmetic, 275
    \subitem  ideals, 276
  \item polynomial invariants, 229, 277
  \item polynomials
    \subitem  syntax, 242
  \item power, 37
  \item PQELIMXOPS, 243
  \item PQIREAD, 243
  \item PQMKCNF, 243
  \item PQMKDNF, 243
  \item PQMKPOS, 243
  \item PQMKPRENEX, 243
  \item PQMKVD, 244
  \item PQPPRT, 243
  \item PQPRING, 244
  \item PQPRINGWR, 244
  \item PQSIMPLIFY, 243
  \item PQTEXW, 243
  \item PRAGMA, 28, 63, 253, 261
  \item pragma, 255
    \subitem  keyword, 254
  \item PREAD, 115, 119
  \item PRED, 103
  \item primary ideal
    \subitem  decomposition, 158, 160
  \item print
    \subitem  keyword, 254
  \item PROCEDURE, 58
    \subitem  declaration, 45
  \item procedure, 64
    \subitem  call, 39
    \subitem  type, 18, 270, 271
  \item PROCEDURE 
    \subitem keyword, 31
  \item PROGA, 265
  \item PROGN, 265
  \item program, 34, 52
  \item PSL, 270
  \item PTBCF, 103
  \item PTRCF, 103
  \item PUT, 265
  \item PWRITE, 115

  \indexspace

  \item quantifier elimination, 239, 278
  \item quaternion number, 74
  \item Quaternion Numbers, 134
  \item QUOT, 264
  \item QUOTE, 265
  \item quote character, 33, 254
  \item quotient
    \subitem  ideal, 198

  \indexspace

  \item RAM, 48, 263
  \item rational, 21
  \item Rational Functions, 134, 142
  \item rational number, 55, 57, 58, 60, 74, 85, 112, 121, 127, 272, 
		274
    \subitem  algorithms, 85
    \subitem  representation, 84
    \subitem  syntax, 87
  \item Rational Numbers, 133, 136
  \item Rational Polynomial, 141
  \item rational polynomial, 112, 121, 127
  \item Rational Polynomials, 134
  \item read, 48
  \item real root
    \subitem  isolation, 276
  \item real root counting, 237, 239, 278
  \item real roots
    \subitem  of zero--dimensional ideals, 166
  \item recursive polynomial, 275
  \item RED, 66, 72, 264
  \item Reduce, 15, 269, 270
  \item reduced univariate polynomial, 124
  \item reduction
    \subitem  partial, 199
  \item relation table, 185
  \item relink, 271
  \item REM, 264
  \item rename, 22, 51
  \item REPEAT, 265
    \subitem  keyword, 31
    \subitem  statement, 44
  \item repeat
    \subitem  keyword, 254
  \item representation, 75, 84, 91
  \item resultant, 276
  \item RETURN
    \subitem  statement, 46
  \item return
    \subitem  keyword, 254
  \item REVERSE, 264
  \item rewrite rule, 64
  \item RF (x1,...,xr), 142
  \item right, 70
  \item ring, 275
  \item RLISP, 269
  \item RN $\lbrack s \rbrack$, 135
  \item RNABS, 21, 85
  \item RNCOMP, 21, 85
  \item RNDEN, 85
  \item RNDIF, 87
  \item RNDRD, 87
  \item RNDWR, 21, 87, 93
  \item RNEXP, 86
  \item RNFAP, 92
  \item RNINT, 21, 85
  \item RNINV, 86
  \item RNNEG, 85
  \item RNNUM, 85
  \item RNPROD, 21, 86, 88
  \item RNQ, 86
  \item RNRAND, 87
  \item RNREAD, 87
  \item RNRED, 21, 85
  \item RNSIGN, 85
  \item RNSUM, 21, 87, 89
  \item RNWRIT, 21, 87
  \item root counting, 278
  \item roots
    \subitem  of ideals, 276
  \item RP (x1,...,xr), 141
  \item RQEOPTSET, 240
  \item RQEOPTWRITE, 240
  \item RQEPRRC, 239
  \item RQEQE, 239
  \item RULE, 62, 265
    \subitem  keyword, 31

  \indexspace

  \item S-expression, 16, 19, 65, 121
  \item S-polynomial, 154
  \item safe, 255
    \subitem  keyword, 254
  \item scope, 46
  \item Scratchpad, 15
  \item Scratchpad II, 22, 51
  \item Scratchpad II term order, 109
  \item semantics, 22, 51
  \item set of integer, 74, 274
  \item SetDCIBop, 249
  \item SetDIPIBop, 249
  \item SETQ, 28, 265
  \item SHOW, 261
  \item SHUT, 263
  \item SIG, 265
  \item SIGNATURE, 55
    \subitem  keyword, 31
  \item signature, 17, 23
    \subitem  definition, 260
  \item SIGS, 23, 26, 260
  \item SLISP, 269, 270
  \item SLOPPY, 262
  \item SML, 52
  \item SMPRM, 78
  \item solvable polynomial ring, computing in, 126, 183
  \item SORT, 54, 57, 59, 61, 265
    \subitem  keyword, 31
  \item sort
    \subitem  name, 261
  \item SORTS, 261
  \item space, 71
  \item SPEC, 265
  \item SPECIFICATION
    \subitem  keyword, 31
  \item specification, 17, 51, 54
    \subitem  component, 51
    \subitem  syntax, 53
  \item statement, 38
    \subitem  sequence, 42
  \item static scope, 46
  \item storage, 16, 19, 261, 269
  \item storage management, 273
  \item string, 31, 33, 69, 254
  \item structure, 15, 268
    \subitem  graded, 199
  \item SUB, 264
  \item SUBCHK, 232
  \item SUBINF, 231
  \item SUBLIS, 265
  \item sublist, 71
  \item submodule, 200
    \subitem  basis, 200
    \subitem  Gr\"obner base, 201
    \subitem  syzygies, 201
  \item SUBORD, 232
  \item SUBORP, 232
  \item SUBRED, 232
  \item SUBSGR, 232
  \item SUBSGW, 232
  \item substitution, 62
  \item substitutions, 229
  \item substr, 71
  \item SUBSYM, 232
  \item SYM2DIP, 121
  \item symbol, 15, 32, 261, 269
    \subitem  handling, 273, 274
  \item SYMTB, 261
  \item syntax, 16, 27, 28, 34, 35, 52, 77, 87, 93, 255, 256, 261
    \subitem  diagram, 35, 53, 241, 242, 256
    \subitem  error, 34, 36
    \subitem  formulas, 241
    \subitem  polynomials, 242
    \subitem  warning, 34, 36
  \item syntax error, 257
    \subitem  ALDES, 255
  \item syntax warning, 257
    \subitem  ALDES, 255
  \item system
    \subitem  components, 267
  \item systems of equations, 276
  \item syzygies, 195
    \subitem  submodule, 201
  \item syzygy, 277
  \item syzygy module, 195

  \indexspace

  \item TERM, 121
  \item term, 34
    \subitem  algebra, 62
    \subitem  rewriting, 62
  \item term order, 199
  \item TfComputeTf, 240
  \item TFORM, 239
  \item TfUseDb, 240
  \item THEN
    \subitem  keyword, 31
  \item then
    \subitem  keyword, 254
  \item THROW, 265
  \item TIME, 262
  \item time, 71
  \item token, 31, 253
  \item TOS, 1, 19
  \item TRACE, 262
  \item transliteration, 32, 259
  \item TSGBASE, 128
  \item two-sided Gr\"obner base, 185
  \item type, 18, 19, 23, 270
    \subitem  checking, 271
  \item TYPES, 23

  \indexspace

  \item UGBBIN, 209
  \item underflow, 94
  \item unification, 62, 64
  \item UNIT, 265
  \item unit, 54
    \subitem  name, 261
  \item UNITS, 261
  \item universal algebra, 22, 51
  \item universal Gr\"obner base, 207
  \item UNTIL
    \subitem  keyword, 31
  \item until
    \subitem  keyword, 254

  \indexspace

  \item VAL, 60
  \item VAR, 58, 265
    \subitem  declaration, 45
    \subitem  keyword, 31
    \subitem  parameter, 42, 45
  \item variable, 17, 19, 23, 32, 37, 39, 62, 261
  \item VARS, 23, 261

  \indexspace

  \item warning, 36, 257
  \item WHEN, 60, 62
    \subitem  keyword, 31
  \item WHILE, 16, 265
    \subitem  keyword, 31
    \subitem  statement, 44
  \item while
    \subitem  keyword, 254
  \item WIN, 48, 263
  \item write, 48

\end{theindex}
