share/algebra/charsets/test.mac

   1 /* Test File for CharSets Version 2.0 (with Maple V.3) */
   2 /* Copyright (C) 1990-1996 by Dongming Wang */
   3 /* the test function for CharSets */
   4
   5 known_good: [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,
   6 21,22,24,26,27,28,29,30,32]$
   7
   8 charsets_test : lambda ([], block(
   9   [ aa,ps,ps1,ord,orda,ordb,as,f,test_in,test_out,rr,i,
  10     x4, x1, x2, x3, x, y, b, c2, basset, wbasset, qbasset,
  11     charsetn, wcharsetn, qcharsetn, triset, trisetc],
  12    ps : [ x4 ^ 2 + x4 ^ 2 * x1 -x4 * x2 -x1 * x2 * x4 + x1 * x2 + 3 * x2,
  13        x1 * x4 + x3 -x1 * x2, x4 * x3 -2 * x2 ^ 2 -x1 * x2 -1],
  14    ps1 : [ x ^ 2 + y, x ^ 4 * y -x ^ 3],
  15    ord : [ x1, x2, x3, x4],
  16    orda : [ x, y],
  17    ordb : [ b, c2],
  18    as : [ -1 + b + 6 * b ^ 2 + 12 * b ^ 3],
  19    f : -6156 + 29484 * b + 23328 * c2 + 11664 * c2 ^ 3 -17712 * c2 ^ 2 + 67392 * c2 ^ 2
  20      * b ^ 2 + 58320 * c2 ^ 2 * b -58320 * b * c2 -50544 * b ^ 2 * c2 + 17496 * b ^ 2,
  21    test_in : [ [ charsets_charset, [ ps, ord]], /* 1 */
  22              [ charsets_charset, [ ps, ord, basset]], /* 2 */
  23              [ charsets_charset, [ ps, ord, wbasset]], /* 3 */
  24              [ charsets_charset, [ ps, ord, qbasset]], /* 4 */
  25              [ charsets_charset, [ ps, ord, charsetn]], /* 5 */
  26              [ charsets_charset, [ ps, ord, wcharsetn]], /* 6 */
  27              [ charsets_charset, [ ps, ord, qcharsetn]], /* 7 */
  28              [ charsets_charset, [ ps, ord, triset]], /* 8 */
  29              [ charsets_charset, [ ps, ord, trisetc]], /* 9 */
  30              [ charsets_mcharset, [ ps, ord]], /* 10 */
  31              [ charsets_mcharset, [ ps, ord, basset]], /* 11 */
  32              [ charsets_mcharset, [ ps, ord, wbasset]], /* 12 */
  33              [ charsets_mcharset, [ ps, ord, qbasset]], /* 13 */
  34              [ charsets_mcharset, [ ps, ord, charsetn]], /* 14 */
  35              [ charsets_mcharset, [ ps, ord, wcharsetn]], /* 15 */
  36              [ charsets_mcharset, [ ps, ord, qcharsetn]], /* 16 */
  37              [ charsets_mcharset, [ ps, ord, triset]], /* 17 */
  38              [ charsets_mcharset, [ ps, ord, trisetc]], /* 18 */
  39              [ charsets_iniset,[[as[1],((4*b^2-1))*f-11],ordb]], /* 19 */
  40              [ charsets_remset,[[as[1]-f,f^2,2*f-b^2],[as[1],f],ordb]], /* 20 */
  41              [ charsets_charser, [ ps, ord]], /* 21 */
  42              [ charsets_charser, [ ps, ord, basset]], /* 22 */
  43              [ charsets_charser, [ ps, ord, wbasset]], /* 23 */
  44              [ charsets_charser, [ ps, ord, charsetn]], /* 24 */
  45              [ charsets_charser, [ ps, ord, wcharsetn]], /* 25 */
  46              [ charsets_charser, [ ps, ord, trisetc]], /* 26 */
  47              [ charsets_mcs, [ ps, ord]], /* 27 */
  48              [ charsets_mcs, [ ps, ord, basset]], /* 28 */
  49              [ charsets_mcs, [ ps, ord, wbasset]], /* 29 */
  50              [ charsets_mcs, [ ps, ord, charsetn]], /* 30 */
  51              [ charsets_mcs, [ ps, ord, wcharsetn]], /* 31 */
  52              [ charsets_mcs, [ ps, ord, trisetc]], /* 32 */
  53              [ charsets_ecs, [ ps, ord]], /* 33 */
  54              [ charsets_ecs, [ ps, ord, basset]], /* 34 */
  55              [ charsets_ecs, [ ps, ord, wbasset]], /* 35 */
  56              [ charsets_ecs, [ [ ps, x2-x3], ord, charsetn]], /* 36 */
  57              [ charsets_ecs, [ ps, ord, wcharsetn]], /* 37 */
  58              [ charsets_ecs, [ ps, ord, trisetc]], /* 38 */
  59              [ charsets_mecs, [ ps, ord]], /* 39 */
  60              [ charsets_mecs, [ ps, ord, basset]], /* 40 */
  61              [ charsets_mecs, [ ps, ord, wbasset]], /* 41 */
  62              [ charsets_mecs, [ [ ps, x2], ord, charsetn]], /* 42 */
  63              [ charsets_mecs, [ ps, ord, wcharsetn]], /* 43 */
  64              [ charsets_mecs, [ ps, ord, trisetc]], /* 44 */
  65              [ charsets_triser, [ ps, ord]], /* 45 */
  66              [ charsets_csolve,[subst(x1=3,ps),charsets_setify([x4,x2,x3])]],/* 46 */
  67              [ charsets_ics, [ ps, ord]], /* 47 */
  68              [ charsets_ics, [ ps, ord, basset]], /* 48 */
  69              [ charsets_ics, [ ps, ord, charsetn]], /* 49 */
  70              [ charsets_ics, [ ps, ord, trisetc]], /* 50 */
  71              [ charsets_cfactor, [ f, as, ordb]], /* 51 */
  72              [ charsets_qics, [ ps, ord]], /* 52 */
  73              [ charsets_qics, [ ps, ord, basset]], /* 53 */
  74              [ charsets_qics, [ ps, ord, wbasset]], /* 54 */
  75              [ charsets_qics, [ ps, ord, charsetn]], /* 55 */
  76              [ charsets_qics, [ ps, ord, wcharsetn]], /* 56 */
  77              [ charsets_qics, [ ps, ord, trisetc]], /* 57 */
  78              [ charsets_eics, [ ps, ord]], /* 58 */
  79              [ charsets_eics, [ ps, ord, basset]], /* 59 */
  80              [ charsets_eics, [ [ ps, x3], ord, charsetn]], /* 60 */
  81              [ charsets_eics, [ ps, ord, trisetc]], /* 61 */
  82              [ charsets_ivd, [ ps, ord]], /* 62 */
  83              [ charsets_ivd, [ ps, ord, basset]], /* 63 */
  84              [ charsets_ivd, [ ps, ord, charsetn]], /* 64 */
  85              [ charsets_ivd, [ ps, ord, trisetc]], /* 65 */
  86              [ charsets_pid, [ ps1, orda]], /* 66 */
  87              [ charsets_pid, [ ps1, orda, basset]], /* 67 */
  88              [ charsets_pid, [ ps1, orda, charsetn]], /* 68 */
  89              [ charsets_pid, [ ps1, orda, trisetc]]], /* 69 */
  90    test_out : [
  91 /* 1 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
  92          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2]]),
  93 /* 2 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
  94          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2]]),
  95 /* 3 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
  96          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]]),
  97 /* 4 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
  98          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]]),
  99 /* 5 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 100          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2]]),
 101 /* 6 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 102          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]]),
 103 /* 7 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 104          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]]),
 105 /* 8 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 106          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]]),
 107 /* 9 */ charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 108          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2]]),
 109 /*10 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 110          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2]])]),
 111 /*11 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 112          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2]])]),
 113 /*12 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 114          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]])]),
 115 /*13 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 116          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]])]),
 117 /*14 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 118          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2]])]),
 119 /*15 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 120          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]])]),
 121 /*16 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 122          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]])]),
 123 /*17 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 124          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2]])]),
 125 /*18 */ charsets_setify([charsets_setify([charsets_setify([x1]),[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 126          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2]])]),
 127 /*19 */ charsets_setify([charsets_setify([2*b+1,2*b-1])]),
 128 /*20 */ charsets_setify([charsets_setify([b^2])]),
 129 /*21 */ charsets_setify([charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 130          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 131          [1+x1,x2,-1+x3^2,-x3+x4],[x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2]])]),
 132 /*22 */ charsets_setify([charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 133          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 134          [1+x1,x2,-1+x3^2,-x3+x4],[x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2]])]),
 135 /*23 */ charsets_setify([charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 136          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 137          [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],[x1,4*x2^4+4*x2^2+1,
 138          -2*x2^3*x3+4*x2^4+4*x2^2-x2*x3+1,x4^2-x4*x2+3*x2],
 139          [1+x1,x2,-x3^2+2*x2^2+1-x2*x3-x2,x4*x3-2*x2^2-x1*x2-1]])]),
 140 /*24 */ charsets_setify([charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 141          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3 -x1*x2],
 142          [1+x1,x2,-1+x3^2,-x3+x4],[x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2]])]),
 143 /*25 */ charsets_setify([charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 144          2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 145          [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 146          [x1,4*x2^4+4*x2^2+1,-2*x2^3*x3+4*x2^4+4*x2^2-x2*x3+1,x4^2-x4*x2+3*x2],
 147          [1+x1,x2,-1+x3^2,x4*x3-2*x2^2-x1*x2-1]])]),
 148 /* 26 */ charsets_setify([charsets_setify([[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 149          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 150          [1+x1,x2,-1+x3^2,-x3+x4],[x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2]])]),
 151 /* 27 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 152          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 153          [1+x1,x2,-1+x3^2,-x3+x4],[x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2]])]),
 154 /* 28 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 155          x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 156          [1+x1,x2,-1+x3^2,-x3+x4],[x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2]])]),
 157 /* 29 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 158           2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 159           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 160           [1+x1,x2,x3^2-2*x2^2-1+x2*x3+x2,x4*x3-2*x2^2-x1*x2-1]]),
 161           charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 162            2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 163            [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 164            [1+x1,x2,-1+x3^2,x4*x3-2*x2^2-x1*x2-1]])]),
 165 /* 30 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 166           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 167           [1+x1,x2,-1+x3^2,-x3+x4],[x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2]])]),
 168 /* 31 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 169           2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 170           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 171           [1+x1,x2,x3^2-2*x2^2-1+x2*x3+x2,x4*x3-2*x2^2-x1*x2-1]]),
 172           charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 173            2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 174            [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 175            [1+x1,x2,-1+x3^2,x4*x3-2*x2^2-x1*x2-1]])]),
 176 /* 32 */ charsets_setify([charsets_setify([[-2 *x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 177           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 178           [1 +x1,x2,-1+x3^2,-x3+x4],[x1,2*x2^2+1,x3,x4^2-x4*x2 +3*x2]])]),
 179 /* 33 */ charsets_setify([charsets_setify([[1+x1,x2,-1+x3^2,-x3+x4],
 180           [x1,2 *x2^2+1,x3,x4^2-x4*x2+3*x2],
 181           [[x1*((-2*x1*x2+2 *x2^2+2*x1*x2^2+1+x1)),
 182           x1^3*x2+3*x1^2*x2+x3^2+x3 ^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 183           x1*((1 +x1))]])]),
 184 /* 34 */ charsets_setify([charsets_setify([[1+x1,x2,-1+x3^2,-x3+x4],
 185           [x1,2 *x2^2+1,x3,x4^2-x4*x2+3*x2],
 186           [[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 187           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 188           x1*((1 +x1))]])]),
 189 /* 35 */ charsets_setify([charsets_setify([[x1,2*x2^2+1,x3,x4^2-x4*x2 +3*x2],
 190           [[1+x1,x2,-x3^2+2*x2^2+1-x2*x3-x2,x4*x3 -2*x2^2-x1*x2-1],x3],
 191           [[x1*((-2*x1*x2+2*x2^2 +2*x1*x2^2+1+x1)),
 192           2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2 *x3,x1*x4+x3-x1*x2],x1*((1+x1))],
 193           [[x1,4*x2^4+4 *x2^2+1,-2*x2^3*x3+4*x2^4+4*x2^2-x2*x3+1,
 194           x4^2 -x4*x2+3*x2],2*x2^2+1]])]),
 195 /* 36 */ charsets_setify([charsets_setify([[1+x1,x2,-1+x3^2,-x3+x4],
 196           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 197           [[x1*((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 198           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 199           x1*((x2-x3))*((1+x1))]])]),
 200 /* 37 */ charsets_setify([charsets_setify([[x1,2 *x2^2+1,x3,x4^2-x4*x2+3*x2],
 201           [1+x1,x2,-1+x3^2,x4 *x3-2*x2^2-x1*x2-1],
 202           [[x1*((-2*x1*x2+2*x2^2+2 *x1*x2^2+1+x1)),
 203           2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2 *x3,x1*x4+x3-x1*x2],x1*((1+x1))],
 204           [[x1,4*x2^4+4 *x2^2+1,-2*x2^3*x3+4*x2^4+4*x2^2-x2*x3+1,
 205           x4^2 -x4*x2+3*x2],2*x2^2+1]])]),
 206 /* 38 */ charsets_setify([charsets_setify([[1+x1,x2,-1 +x3^2,-x3+x4],
 207           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 208           [[x1 *((-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1)),
 209           x1^3*x2+3 *x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3 -x1*x2],
 210           x1*((1+x1))]])]),
 211 /* 39 */ charsets_setify([charsets_setify([[1+x1,x2,-1 +x3^2,-x3+x4],
 212           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 213           [[-2 *x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 214           x1^3*x2+3*x1^2*x2+x3 ^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 215           x1 *((1+x1))]])]),
 216 /* 40 */ charsets_setify([charsets_setify([[1+x1,x2,-1+x3^2,-x3 +x4],
 217           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 218           [[-2*x1 *x2+2*x2^2+2*x1*x2^2+1+x1,
 219           x1^3*x2+3*x1^2*x2+x3^2 +x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 220           x1*((1 +x1))]])]),
 221 /* 41 */ charsets_setify([charsets_setify([[x1,2*x2^2+1,x3,x4^2-x4*x2 +3*x2],
 222           [[1+x1,x2,-x3^2+2*x2^2+1-x2*x3-x2,x4*x3 -2*x2^2-x1*x2-1],x3],
 223           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,
 224           x1 *x4+x3-x1*x2],x1*((1+x1))],
 225           [[x1,4*x2^4+4*x2^2 +1,2*x2^2+1-x2*x3,x4^2-x4*x2+3*x2],2*x2^2+1]])]),
 226 /* 42 */ charsets_setify([charsets_setify([[x1,2 *x2^2+1,x3,x4^2-x4*x2+3*x2],
 227           [[-2*x1*x2+2*x2^2 +2*x1*x2^2+1+x1,
 228           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 229           x1*x2*((1+x1))]])]),
 230 /* 43 */ charsets_setify([charsets_setify([[x1,2 *x2^2+1,x3,x4^2-x4*x2+3*x2],
 231           [1+x1,x2,-1+x3^2,x4 *x3-2*x2^2-x1*x2-1],
 232           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,
 233           x1*x4 +x3-x1*x2],x1*((1+x1))],
 234           [[x1,4*x2^4+4*x2^2+1,2 *x2^2+1-x2*x3,x4^2-x4*x2+3*x2],2*x2^2+1]])]),
 235 /* 44 */ charsets_setify([charsets_setify([[1 +x1,x2,-1+x3^2,-x3+x4],
 236           [x1,2*x2^2+1,x3,x4^2-x4*x2 +3*x2],
 237           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 238           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 239           x1*((1+x1))]])]),
 240 /* 45 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 241           2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 242           [x1,2*x2^2+1,x3,x4 ^2-x4*x2+3*x2],
 243           [1+x1,x2,x3^2-2*x2^2-1+x2*x3+x2,x4*x3-2*x2^2-x1*x2-1]]),
 244           charsets_setify([[-2*x1*x2+2*x2^2 +2*x1*x2^2+1+x1,
 245            2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2 *x3,x1*x4+x3-x1*x2],
 246            [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 247            [1 +x1,x2,-1+x3^2,x4*x3-2*x2^2-x1*x2-1]])]),
 248 /* 46 */ charsets_setify([charsets_setify([charsets_setify([x3 =((-3))/4+3/4*%I*23^((1/2)),
 249           x2=3/8+1/8*%I*23 ^((1/2)),
 250           x4=3/16+1/16*%I*23^((1/2))+1/16*2^((1 /2))*
 251              ((-79-21*%I*23^((1/2))))^((1/2))]),
 252           charsets_setify([x4 =3/16-1/16*%I*23^((1/2))+1/16*2^((1/2))*
 253              ((-79 +21*%I*23^((1/2))))^((1/2)),
 254              x3=((-3))/4-3/4 *%I*23^((1/2)),x2=3/8-1/8*%I*23^((1/2))]),
 255           charsets_setify([x2 =3/8-1/8*%I*23^((1/2)),
 256              x4=3/16-1/16*%I*23^((1/2)) -1/16*2^((1/2))*
 257                 ((-79+21*%I*23^((1/2))))^((1 /2)),
 258              x3=15/8+3/8*%I*23^((1/2))]),
 259           charsets_setify([x2=3/8+1 /8*%I*23^((1/2)),
 260              x3=15/8-3/8*%I*23^((1/2)),
 261              x4=3 /16+1/16*%I*23^((1/2))-1/16*2^((1/2))*
 262                 ((-79-21 *%I*23^((1/2))))^((1/2))])]),
 263           charsets_setify([charsets_setify([x3=15 /8+3/8*%I*23^((1/2)),
 264              x4=-1/4-1/4*%I*23^((1/2)),
 265              x2 =-1/2*((-11+%I*23^((1/2))))/((7+%I*23^((1/2))))]),
 266           charsets_setify([x3 =-3/4+3/4*%I*23^((1/2)),x4=5/8-1/8*%I*23^((1 /2)),
 267              x2=1/4*((-1+5*%I*23^((1/2))))/((7+%I*23 ^((1/2))))]),
 268           charsets_setify([x3=15/8-3/8*%I*23^((1/2)),
 269              x2 =-1/2*((11+%I*23^((1/2))))/((-7+%I*23^((1/2)))),
 270              x4 =-1/4+1/4*%I*23^((1/2))]),
 271           charsets_setify([x3=-3/4-3/4 *%I*23^((1/2)),x4=5/8+1/8*%I*23^((1/2)),
 272              x2=1/4 *((1+5*%I*23^((1/2))))/((-7+%I*23^((1/2))))])]),
 273           charsets_setify([charsets_setify([x2 =3/8+1/8*%I*23^((1/2)),
 274              x4=3/16+1/16*%I*23^((1/2))+1/16*((-158-42*%I*23^((1/2))))^((1/2)),
 275              x3=-3 /4+3/4*%I*23^((1/2))]),
 276           charsets_setify([x2=3/8+1/8*%I*23^((1 /2)),
 277              x4=3/16+1/16*%I*23^((1/2))-1/16*((-158-42*%I*23^((1/2))))^((1/2)),
 278              x3=15/8-3/8*%I*23^((1 /2))]),
 279           charsets_setify([x2=3/8-1/8*%I*23^((1/2)),
 280              x4=3/16-1/16*%I*23^((1/2))+1/16*((-158+42*%I*23^((1/2))))^((1/2)),
 281              x3=-3/4-3/4*%I*23^((1/2))]),
 282           charsets_setify([x2 =3/8-1/8*%I*23^((1/2)),
 283              x4=3/16-1/16*%I*23^((1/2))-1/16*((-158+42*%I*23^((1/2))))^((1/2)),
 284              x3=15 /8+3/8*%I*23^((1/2))])])]),
 285 /* 47 */ charsets_setify([charsets_setify([[1+x1,x2,x3 -1,x4-1],[1+x1,x2,1+x3,1+x4],
 286           [-2*x1*x2+2*x2^2 +2*x1*x2^2+1+x1,x3-x1+x1*x2,x4+1-2*x2],
 287           [-2*x1*x2 +2*x2^2+2*x1*x2^2+1+x1,-x3-x1+2*x1*x2,x4+x2-1]])]),
 288 /* 48 */ charsets_setify([charsets_setify([[1 +x1,x2,x3-1,x4-1],[1+x1,x2,1+x3,1+x4],
 289           [-2*x1*x2 +2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,x4+1-2*x2],
 290           [-2 *x1*x2+2*x2^2+2*x1*x2^2+1+x1,-x3-x1+2*x1*x2,x4+x2 -1]])]),
 291 /* 49 */ charsets_setify([charsets_setify([[1+x1,x2,x3-1,x4-1],[1+x1,x2,1 +x3,1+x4],
 292           [-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1 +x1*x2,x4+1-2*x2],
 293           [-2*x1*x2+2*x2^2+2*x1*x2^2+1 +x1,-x3-x1+2*x1*x2,x4+x2-1]])]),
 294 /* 50 */ charsets_setify([charsets_setify([[1 +x1,x2,x3-1,x4-1],[1+x1,x2,1+x3,1+x4],
 295           [-2*x1*x2 +2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,x4+1-2*x2],
 296           [-2 *x1*x2+2*x2^2+2*x1*x2^2+1+x1,-x3-x1+2*x1*x2,x4+x2 -1]])]),
 297 /* 51 */ charsets_setify([charsets_setify([144*
 298           ((-27*b-32*c2+48*b^2*c2+27*b^2+27*c2^2+72*b*c2+18))*
 299           ((12*b^2+7*b+3*c2 -1))])]),
 300 /* 52 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2 ^2+1+x1,
 301           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3 -x1^2*x2*x3,x1*x4+x3-x1*x2],
 302           [x1,2*x2^2+1,x3,x4^2-x4 *x2+3*x2],[1+x1,x2,x3-1,x4-1],
 303           [1+x1,x2,1+x3,1+x4]])]),
 304 /* 53 */ charsets_setify([charsets_setify([[-2 *x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 305           x1^3*x2+3*x1^2*x2+x3 ^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 306           [x1,2 *x2^2+1,x3,x4^2-x4*x2+3*x2],[1+x1,x2,x3-1,x4-1],
 307           [1 +x1,x2,1+x3,1+x4]])]),
 308 /* 54 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2 ^2+2*x1*x2^2+1+x1,
 309           2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2 *x3,x1*x4+x3-x1*x2],
 310           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 311           [1 +x1,x2,x3^2-2*x2^2-1+x2*x3+x2,x4*x3-2*x2^2-x1*x2-1]]),
 312           charsets_setify([[-2 *x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 313           2*x1*x2^2+x1^2*x2+x1 +x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 314           [x1,2*x2^2+1,x3,x4 ^2-x4*x2+3*x2],[1+x1,x2,x3-1,x4-1],
 315           [1+x1,x2,1+x3,1 +x4]])]),
 316 /* 55 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2 ^2+1+x1,
 317           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3 -x1^2*x2*x3,x1*x4+x3-x1*x2],
 318           [x1,2*x2^2+1,x3,x4^2-x4 *x2+3*x2],[1+x1,x2,x3-1,x4-1],
 319           [1+x1,x2,1+x3,1+x4]])]),
 320 /* 56 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 321           2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 322           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],
 323           [1+x1,x2,x3^2-2*x2^2-1+x2*x3+x2,x4 *x3-2*x2^2-x1*x2-1]]),
 324           charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 325            2*x1*x2^2+x1^2*x2+x1+x3^2-x1*x2*x3,x1*x4+x3-x1*x2],
 326            [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],[1+x1,x2,x3-1,x4-1],
 327            [1+x1,x2,1+x3,1+x4]])]),
 328 /* 57 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,
 329           x1^3*x2+3*x1^2*x2+x3^2+x3^2*x1-x1*x2*x3-x1^2*x2*x3,x1*x4+x3-x1*x2],
 330           [x1,2*x2^2+1,x3,x4^2-x4*x2+3*x2],[1+x1,x2,x3-1,x4-1],
 331           [1+x1,x2,1+x3,1+x4]])]),
 332 /* 58 */ charsets_setify([charsets_setify([[1+x1,x2,x3-1,x4-1],[1+x1,x2,1+x3,1+x4],
 333           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,-x3-x1+2*x1*x2,x4+x2-1],
 334           x1*((1+x1))],[x1,2*x2^2+1,x3,x4+x2-1],
 335           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,x4+1-2*x2],
 336           x1*((1+x1))],[x1,2*x2^2+1,x3,x4+1-2*x2]])]),
 337 /* 58 */ charsets_setify([charsets_setify([[1+x1,x2,x3-1,x4-1],[1+x1,x2,1+x3,1+x4],
 338           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,-x3-x1+2*x1*x2,x4+x2-1],
 339           x1*((1+x1))],[x1,2*x2^2+1,x3,x4+x2-1],
 340           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,x4+1-2*x2],
 341           x1*((1+x1))],[x1,2*x2^2+1,x3,x4+1-2*x2]])]),
 342 /* 59 */ charsets_setify([charsets_setify([[1+x1,x2,x3-1,x4-1],[1+x1,x2,1+x3,1+x4],
 343           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,-x3-x1+2*x1*x2,x4+x2-1],
 344           x1*x3*((1+x1))],[[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,
 345           x4+1-2*x2],x1*x3*((1+x1))]])]),
 346 /* 60 */ charsets_setify([charsets_setify([[1+x1,x2,x3-1,x4-1],[1+x1,x2,1+x3,1+x4],
 347           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,-x3-x1+2*x1*x2,x4+x2-1],
 348           x1*((1+x1))],[x1,2*x2^2+1,x3,x4+x2-1],
 349           [[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,x4+1-2*x2],
 350           x1*((1+x1))],[x1,2*x2^2+1,x3,x4+1-2*x2]])]),
 351 /* 61 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,
 352           x4+1-2*x2],[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3+x1-2*x1*x2,x4+x2-1]])]),
 353 /* 62 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,
 354           x4+1-2*x2],[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3+x1-2*x1*x2,x4+x2-1]])]),
 355 /* 63 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,
 356           x4+1-2*x2],[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3+x1-2*x1*x2,x4+x2-1]])]),
 357 /* 64 */ charsets_setify([charsets_setify([[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3-x1+x1*x2,
 358           x4+1-2*x2],[-2*x1*x2+2*x2^2+2*x1*x2^2+1+x1,x3+x1-2*x1*x2,x4+x2-1]])]),
 359 /* 65 */ charsets_setify([charsets_setify([[[x^2-x+1,y+x-1],[x^2-x+1,y+x-1]],[[x^3,x^2+y],[x,y]],
 360           [[x+1,y+1],[x+1,y+1]]])]),
 361 /* 66 */ charsets_setify([charsets_setify([[[x^2-x+1,y+x-1],[x^2-x+1,y+x-1]],[[x^3,x^2+y],[x,y]],
 362           [[x+1,y+1],[x+1,y+1]]])]),
 363 /* 67 */ charsets_setify([charsets_setify([[[x^2-x+1,y+x-1],[x^2-x+1,y+x-1]],[[x^3,x^2+y],[x,y]],
 364           [[x+1,y+1],[x+1,y+1]]])]),
 365 /* 68 */ charsets_setify([charsets_setify([[[x^2-x+1,y+x-1],[x^2-x+1,y+x-1]],[[x^3,x^2+y],[x,y]],
 366           [[x+1,y+1],[x+1,y+1]]])])],
 367
 368      /* for i : 1 thru length(test_in) do (     */
 369      for i in known_good  do (
 370      print("Executing test number ",i),
 371      print("Test", i, "input:"),
 372      grind (funmake (first (test_in[i]), second (test_in[i]))),
 373      print ("Test", i, "expected output:"),
 374      grind (test_out[i]),
 375      /* errcatch  */
 376      /* (  */
 377        rr : setify1(apply(first(test_in[i]), second(test_in[i]))),
 378        if charsets_testsub( rr, test_out[i])
 379        then (
 380          print("CharSets_Test:",i,"Good"))
 381        else (
 382          print("CharSets_Test:",i,"Bad; actual output:",rr))
 383       /* ) */ ,
 384      if %% = [] then print ("CharSets_Test: error in test."))
 385 ))$
 386 /* subroutine for test */
 387
 388 charsets_testsub( rr,ss):=block( [ i,ii,_ind],
 389    rr:map(expand,rr),ss:map(expand,ss),
 390    if member(rr, ss) then ( true)
 391    else (
 392       _ind:false,
 393       for i in ss do (
 394         ii:if listp(i) then i else setify1(i),
 395         if charsets_equal ( charsets_setdifference ( rr, ii), charsets_setdifference ( ii, rr))
 396           then (
 397            return ( _ind:true))) ,
 398       return(_ind))
 399 )$
 400 /* subroutine for testsub */
 401
 402 charsets_equal ( a,b):= block(
 403    [ i,j,_ind],
 404    if listp(a) then (
 405       if length ( a) # length ( b)  then (
 406          print("charsets_equal: lists of different lengths",length ( a),a,length ( b),b),
 407          return ( false)),
 408       _ind:true,
 409       for i : 1 thru length ( a) do (
 410         if not charsets_equal ( a[i], b[i]) then return ( _ind:false)),
 411       return( _ind))
 412      else if /* WARNING: listp should be setp */listp(a) then (
 413       if length ( a) # length ( b) then (
 414          print("charsets_equal: sets of different lengths",length ( a),a,length ( b),b),
 415          return ( false)),
 416       _ind:true,
 417       for i in a do (
 418         for j in b do (
 419           if not charsets_equal ( i, j) then return (_ind : false)),
 420         if not _ind then return ( false)),
 421       return (_ind))
 422      else if charsets_operatorp(b, charsets_ListOrSet) then ( false)
 423      else if polynomialp(a,listofvars(a)) then (
 424       if second(divide ( a, b)) = 0 and second(divide ( b, a)) = 0 then ( true)
 425         else (
 426          print("charsets_equal: polynomials dont divide",a,b),
 427          false))
 428      else if a = b then ( true)
 429      else (
 430         if a = -b then true
 431         else (
 432          print("charsets_equal: a not equal b",a,b),
 433       false))
 434 )$