Computing the nullspace of a moderate matrix blows up RAM

[emanuel-sygal]

I am trying to find a basis for the nullspace of some matrix $A$ in sympy of size (384, 120).
When calling
A.nullspace()
The RAM usage keeps rising until it crashes, even on a machine with 400 GB free RAM.

The matrix consists of elements that are just 1,-1,0 and mostly zero.
I create the matix like this:
A = sympy.Matrix(vectors_list)

where every element of vectors_list is a tuple of elements of type sympy.core.numbers.
I tried setting the environment variables
"SYMPY_USE_CACHE", "SYMPY_INT_TRACE" to "no"
and it did not make a change.

I posted here a txt file containing a reproducible matrix with the bug: https://groups.google.com/forum/m/#!topic/sympy/R5DQsaIDJbg

[asmeurer]

I wasn't able to keyboard interrupt the operation, suggesting it is stuck in a C function somewhere.

[rlamy]

The problem is that matrix elements grow to humongous sizes (millions of digits, and probably more).

The following patch makes the problem tractable:

diff --git a/sympy/matrices/matrices.py b/sympy/matrices/matrices.py
index 1dd0867..b64d4f1 100644
--- a/sympy/matrices/matrices.py
+++ b/sympy/matrices/matrices.py
@@ -639,6 +639,7 @@ def _row_reduce(self, iszerofunc, simpfunc, normalize_last=True,
         zero_above : whether entries above the pivot should be zeroed.
             If `zero_above=False`, an echelon matrix will be returned.
         """
+        from sympy.core.numbers import igcd
         rows, cols = self.rows, self.cols
         mat = list(self)
         def get_col(i):
@@ -701,7 +702,8 @@ def cross_cancel(a, i, b, j):
                 if iszerofunc(val):
                     continue
 
-                cross_cancel(pivot_val, row, val, piv_row)
+                g = igcd(pivot_val, val)
+                cross_cancel(pivot_val // g, row, val // g, piv_row)
             piv_row += 1
 
         # normalize each row

The patch is obviously incorrect as it only works for integers, but I guess the idea can be generalised.