factoring broken in 0 variable polynomial ring

[burcin]

sage: P = PolynomialRing(QQ,0,'')
sage: P
Multivariate Polynomial Ring in no variables over Rational Field
sage: t = P.random_element()
sage: t.factor()
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)

/home/burcin/.sage/temp/karr/24426/_home_burcin__sage_init_sage_0.py in <module>()

/home/burcin/sage/sage-4.3.alpha0/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_element.pyc in factor(self, proof)
   1422         # try to use univariate factoring first

   1423         try:
-> 1424             F = self.univariate_polynomial().factor()
   1425             return Factorization([(R(f),m) for f,m in F], unit=F.unit())
   1426         except TypeError:

/home/burcin/sage/sage-4.3.alpha0/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_element.pyc in univariate_polynomial(self, R)
   1055         #construct ring if None

   1056         if R is None:
-> 1057             R = self.base_ring()[str(self.variables()[0])]
   1058 
   1059         monomial_coefficients = self._MPolynomial_element__element.dict()

IndexError: tuple index out of range

Component: commutative algebra

Author: Burcin Erocal

Reviewer: William Stein, Alex Ghitza

Merged: sage-4.3.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7950

[burcin]

factor zero variable polynomials

[burcin]

comment:1

Attachment: trac_7950-zero_variable_factor.patch.gz

trivial review please?

[burcin]

Author: Burcin Erocal

[williamstein]

comment:2

1. Factoring of 0 should raise an error like it does over ZZ, but doesn't right now:

sage: P = PolynomialRing(ZZ,0,'')
sage: P(10).factor()
10
sage: P(0).factor()
0
sage: factor(0)
---------------------------------------------------------------------------
ArithmeticError                           Traceback (most recent call last)

2. The element 10 in the polynomial ring "ZZ[]" in 0-variables is actually not a unit. So it is wrong that it is put in the "unit" slot of the factorization. Notice how factoring 10 works:

sage: R.<x> = ZZ[]
sage: (10*x).factor()
2 * 5 * x
sage: list((10*x).factor())
[(2, 1), (5, 1), (x, 1)]

In particular, the 10 is not treated incorrectly as a unit.

So I think this patch needs work.

[burcin]

Attachment: trac_7950-zero_variable_factor.take2.patch.gz

only apply this patch

[burcin]

Reviewer: William Stein

[burcin]

comment:3

Thanks for the review!

New patch addressing both points is available at attachment: trac_7950-zero_variable_factor.take2.patchI hope it doesn't contain more stupid mistakes. :)