tests/rtest_gcd.mac

   1 (kill(all),0);
   2 0$
   3
   4 (gcd_all_options(f,g) := append(makelist((gcd:option, gcd(f,g)), option, [ez, subres, red, spmod]),
   5                                 makelist((gcd:option, gcd(g,f)), option, [ez, subres, red, spmod])),
   6  check_gcd(f,g,expected_result) := block([gcds], gcds:gcd_all_options(expand(f), expand(g)),
   7                                          if every (lambda ([e], equal (e, expected_result)), gcds)
   8                                          then true
   9                                          else FAILED_GCDS ('expected = expected_result, 'actual = gcds)),
  10  0);
  11 0$
  12
  13 /* Basic tests: numbers */
  14
  15 check_gcd(1, 1, 1);
  16 true$
  17
  18 check_gcd(1, -1, 1);
  19 true$
  20
  21 check_gcd(6, 2, 2);
  22 true$
  23
  24 check_gcd(6, -2, 2);
  25 true$
  26
  27 check_gcd(3/2, 1/2, 1/2);
  28 true$
  29
  30 check_gcd(3/2, -1/2, 1/2);
  31 true$
  32
  33 check_gcd(1+%i, 2+2*%i, 1+%i);
  34 true$
  35
  36 check_gcd(1+%i, -1/2-1/2*%i, 1/2+1/2*%i);
  37 true$
  38
  39 /* Basic tests: univariate polynomials */
  40
  41 check_gcd(x, 1, 1);
  42 true$
  43
  44 check_gcd(6*x, 2, 2);
  45 true$
  46
  47 check_gcd(2*x*(3*x-1), 2*x, 2*x);
  48 true$
  49
  50 check_gcd(2*x*(3*x-1), 3*x-1, 3*x-1);
  51 true$
  52
  53 check_gcd(2*x*(3*x-1), 6*x*(3*x-1), 2*x*(3*x-1));
  54 true$
  55
  56 check_gcd(2*x*(3*x-1), 3*x+1, 1);
  57 true$
  58
  59 /* Basic tests: multivariate polynomials */
  60
  61 check_gcd(y*x, 1, 1);
  62 true$
  63
  64 check_gcd(6*y*x, 2, 2);
  65 true$
  66
  67 check_gcd(2*y*(3*x-1)*(y+1), 2*y, 2*y);
  68 true$
  69
  70 check_gcd(2*y*(3*x-1)*(y+1), (3*x-1)*(y-1), 3*x-1);
  71 true$
  72
  73 check_gcd(2*y*(3*x-1)*(y+1), 2*y*(3*x-1)*(y-1), 2*y*(3*x-1));
  74 true$
  75
  76 check_gcd(2*y*(3*x-1)*(y+1), 6*y*(3*x-1)*(y+1), 2*y*(3*x-1)*(y+1));
  77 true$
  78
  79 check_gcd(2*y*(3*x-1)*(y+1), (3*x+1)*(y-1), 1);
  80 true$
  81
  82 /* Randomized tests */
  83
  84 (random_polynomial(var) := product(random(3)+1+sum((random(4)-2)*var^i, i, 1, random(3)), j, 0, random(3)),
  85  check_gcd_common_factor(f,g,common_factor,vars) :=
  86  block([gcds], gcds: gcd_all_options (expand (f), expand (g)),
  87        if every (lambda ([x], equal (remainder (x, common_factor), 0)), gcds)
  88        then true
  89        else FAILED_GCDS ('common_factor = common_factor, 'gcd_results = gcds)),
  90  0);
  91 0$
  92
  93 makelist(block([common_factor],
  94                common_factor:random_polynomial(x),
  95                check_gcd_common_factor(common_factor*random_polynomial(x),
  96                                        common_factor*random_polynomial(x),
  97                                        common_factor,
  98                                        [x])),
  99          10);
 100 [true, true, true, true, true, true, true, true, true, true]$
 101
 102 makelist(block([common_factor],
 103                common_factor:random_polynomial(x)*random_polynomial(y),
 104                check_gcd_common_factor(common_factor*random_polynomial(x)*random_polynomial(y),
 105                                        common_factor*random_polynomial(x)*random_polynomial(y),
 106                                        common_factor,
 107                                        [x, y])),
 108          10);
 109 [true, true, true, true, true, true, true, true, true, true]$
 110
 111 makelist(block([common_factor],
 112                common_factor:random_polynomial(x)*random_polynomial(y)*random_polynomial(z),
 113                check_gcd_common_factor(common_factor*random_polynomial(x)*random_polynomial(y)*random_polynomial(z),
 114                                        common_factor*random_polynomial(x)*random_polynomial(y)*random_polynomial(z),
 115                                        common_factor,
 116                                        [x, y, z])),
 117          10);
 118 [true, true, true, true, true, true, true, true, true, true]$
 119
 120 /* SF bug 3832 and merge request 25 */
 121
 122 is(equal(gcd(expand((r^2-2*m+a^2)*(a^2*s^2+r^2)^3*(a^2*s^2+r^2-2*m)), expand((r^2-2*m+a^2)*(a^2*s^2+r^2)^2)),
 123          expand((r^2-2*m+a^2)*(a^2*s^2+r^2)^2)));
 124 true$