Is this the intended behaviour? First, for an ordinary polynomial ring:
sage: R0.<x,y> = QQ[]
sage: (x*y)/x
y
sage: _.parent()
Fraction Field of Multivariate Polynomial Ring in x, y over Rational Field
sage: R0((x*y)/x)
y
sage: _.parent()
Multivariate Polynomial Ring in x, y over Rational Field
kind of makes sense to me. But if the coefficients are not just numbers then
it doesn't work any more:
sage: Rt.<x,y> = QQ['t'][]
sage: (x*y)/x
x*y/x
sage: _.parent()
Fraction Field of Multivariate Polynomial Ring in x, y over Univariate
Polynomial Ring in t over Rational Field
sage: Rt((x*y)/x)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/vbraun/Sage/24cell/<ipython console> in <module>()
/home/vbraun/Sage/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_ring.pyc
in __call__(self, x, check)
430 return x.numerator()
431 else:
--> 432 raise TypeError, "unable to coerce since the
denominator is not 1"
433
434 elif is_SingularElement(x) and self._has_singular:
TypeError: unable to coerce since the denominator is not 1
I think this is the problem, but I'm not sure:
sage: ((x*y)/x).reduce()
---------------------------------------------------------------------------
ArithmeticError Traceback (most recent call last)
/home/vbraun/Sage/24cell/<ipython console> in <module>()
/home/vbraun/Sage/sage/local/lib/python2.6/site-packages/sage/rings/fraction_field_element.so
in sage.rings.fraction_field_element.FractionFieldElement.reduce
(sage/rings/fraction_field_element.c:2736)()
ArithmeticError: unable to reduce because lack of gcd or quo_rem algorithm
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