isomorphism -- retrieve an isomorphism of modules

• Usage:

  f = isomorphism(N, M)

• Inputs:
  • M, a module,
  • N, a module,
• Optional inputs:
  • Homogeneous => a Boolean value, default value true, if false, allow an inhomogeneous isomorphism;
  • Verbose => a Boolean value, default value false, whether to print debugging information;
  • Strict => a Boolean value, default value false, whether to force strict equality of degrees;
  • Tries => an integer, default value null, the number of attempts at generating random map;
  • Strategy (missing documentation) => ..., default value null,
• Outputs:
  • f, a matrix, an isomorphism $M \to N$;

i1 : S = ZZ/32003[x_0..x_3]

o1 = S

o1 : PolynomialRing

i2 : m = random(S^3, S^{4:-2});

             3      4
o2 : Matrix S  <-- S

i3 : A = random(target m, target m);

             3      3
o3 : Matrix S  <-- S

i4 : B = random(source m, source m);

             4      4
o4 : Matrix S  <-- S

i5 : N = coker(A*m*B);

i6 : M = coker m;

i7 : f = isomorphism(N, M)

o7 = | 1     4078 4892  |
     | -2922 6959 -89   |
     | -5122 -889 -1064 |

o7 : Matrix N <-- M

i8 : isIsomorphism f

o8 = true