Chinese remainder code raises an error when called with Python ints

[davidloeffler]

Lots of the congruence subgroup code works intensively with small integers, and represents these as Python ints rather than Sage integers for speed reasons. This brought to light the following irritating bug:

sage: crt(int(2), int(3), int(5), int(7))
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)

/storage/masiao/sage-4.6.1.alpha3/devel/sage-reviewing/<ipython console> in <module>()

/usr/local/sage/sage-4.6/local/lib/python2.6/site-packages/sage/rings/arith.pyc in crt(a, b, m, n)
   2737         return CRT_list(a, b)
   2738     g, alpha, beta = XGCD(m, n)
-> 2739     q, r = (b - a).quo_rem(g)
   2740     if r != 0:
   2741         raise ValueError("No solution to crt problem since gcd(%s,%s) does not divide %s-%s" % (m, n, a, b))

AttributeError: 'int' object has no attribute 'quo_rem'

[davidloeffler]

Here's a tiny little patch (one line, one comment, one doctest).

[mhansen]

Shouldn't you use Integer(a) instead of ZZ(a) since it's about 3.5 times faster (on boxen)?

[davidloeffler]

new version

[davidloeffler]

Here's a new patch using Integer. Sorry, I meant to overwrite the original patch -- apply only the second one.

[mhansen]

Thanks!