The following is apparently not implemented (see 3.1.2 traceback at
bottom):
---
sage: R.<x1, x2> = PolynomialRing(Integers(), 2)
sage: (x1*x2).factor()
---
However, I think it would be trivial to implement: change the base
ring of the polynomial to Rationals() and then factor. I believe the
result returned by Singular is then guaranteed to have integer
coefficients, so it can be coerced back.

Can someone more familiar with Singular confirm that? And if I am
correct, would it be worth hacking factor() to enable this?

Kiran
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call
last)

/home/sdb1/r1/kedlaya/<ipython console> in <module>()

/scratch/sage-x64/local/lib/python2.5/site-packages/sage/rings/
polynomial/multi_polynomial_element.py in factor(self)
   1349             pass
   1350
-> 1351         R._singular_().set_ring()
   1352         S = self._singular_().factorize()
   1353         factors = S[1]

/scratch/sage-x64/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_singular_interface.py in _singular_(self,
singular, force)
    172             return R
    173         except (AttributeError, ValueError):
--> 174             return self._singular_init_(singular, force)
    175
    176     def _singular_init_(self, singular=singular_default,
force=False):

/scratch/sage-x64/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_singular_interface.py in _singular_init_(self,
singular, force)
    243
    244         else:
--> 245             raise TypeError, "no conversion to a Singular ring
defined"
    246
    247         return self.__singular

TypeError: no conversion to a Singular ring defined

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