Incorrect answers given for ranks of large matrices.

[elarson314]

Is there an existing issue for this?

• [X] I have searched the existing issues for a bug report that matches the one I want to file, without success.

Did you read the documentation and troubleshoot guide?

• [X] I have read the documentation and troubleshoot guide

Environment

- **OS**: RedHat EL 7.7
- **Sage Version**: 9.5

Steps To Reproduce

On a machine with ample RAM, compute the rank of a matrix with more than 2^32 entries. For example, a Vandermonde matrix like so:

def vandermonde_rank(x, y):
   F = GF(8388593)
   M = matrix(F, x, y)

   for i in range(x):
      row = []
      i = F(i)
      ij = F(1)
      for j in range(y):
         row.append(ij)
         ij *= i
      M[i] = row

   M.echelonize()
   return M.rank()

print(vandermonde_rank(65537, 65537))

Expected Behavior

The rank should be computed correctly (or, failing that, an error should be raised saying that the matrix is too large).

Actual Behavior

The rank is computed incorrectly once there are more than 2^32 entries. For example, the above code prints 65536 for the rank of the 65537 x 65537 Vandermonde matrix. The user is not warned that the answer might not be correct.

Additional Information

No response

[jhpalmieri]

Here's something:

sage: M = identity_matrix(GF(8388593), 10)
sage: type(M.rank())
<class 'sage.rings.integer.Integer'>
sage: M.echelonize()
sage: type(M.rank())
<class 'int'>

The echelonize method caches the rank as part of its computations, but it caches a Python int rather than a Sage Integer.