Running out of primes in a Chinese Remainder algorithm

[David Roe]

Hi Linbox developers,
We've been running into the following issue from Sage in a number of ways (see http://trac.sagemath.org/ticket/15535, http://trac.sagemath.org/ticket/12883 and http://trac.sagemath.org/ticket/17640).  When running various algorithms with integer matrices, we see the following error message:

you are running out of primes. 1000 coprime primes found

So far, this has occurred in computing both characteristic polynomials and eigenvalues, but only after running thousands or millions of examples.

Looking at the Linbox source code, this error message is printed in linbox/algorithms/cra-domain-seq.h, linbox/algorithms/cra-domain-omp.h and linbox/algorithms/rational-cra2.h.  In each case, there's a counter coprime and a termination threshold maxnoncoprime (set to 1000 in the source code).  Presumably this counter is not getting reset between calls, eventually triggering the problem.

I'm not familiar with linbox, so help would be appreciated.  Thanks,
David