# polynomials rings over transcendental field extensions

Hi all:

It looks like working with polynomial rings over transcendental field extensions still doesn't work in Sage. Am i doing something wrong below? The same computation works in Singular, giving the correct answer of the ideal generated by x*y.

Alex

| Sage Version 4.6, Release Date: 2010-10-30 |

## | Type notebook() for the GUI, and license() for information. |

sage: R0. = PolynomialRing(QQ); R0
Univariate Polynomial Ring in q over Rational Field

sage: k= FractionField(R0); k Fraction Field of Univariate Polynomial Ring in q over Rational Field

sage: R.<x,y> = PolynomialRing(k); R Multivariate Polynomial Ring in x, y over Fraction Field of Univariate Polynomial Ring in q over Rational Field

sage: I = R.ideal((q*x*y)^2); I
Ideal (q^2*x^2*y^2) of Multivariate Polynomial Ring in x, y over Fraction Field of Univariate Polynomial Ring in q over Rational Field

## sage: I.radical()

TypeError Traceback (most recent call last)

/Users/arai021/<ipython console=""> in <module>()

/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in __call__(self, *args, **kwds)
405 if not R.base_ring().is_field():
406 raise ValueError("Coefficient ring must be a field for function '%s'."%(self.f.__name__))
--> 407 return self.f(self._instance, *args, **kwds)
408
409 require_field = RequireField

/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in wrapper(*args, **kwds)
367 """
368 with RedSBContext():
--> 369 return func(*args, **kwds)
370
371 from sage.misc.sageinspect import sage_getsource

/Applications/sage/local/lib/python2.6/site-packages/sage/rings/polynomial/multi_polynomial_ideal.pyc in radical(self) 1404 import sage.libs.singular 1405 radical = sage.libs.singular.ff.primdec__lib.radical -> 1406 r = radical(self) 1407 1408 S = self.ring()

/Applications/sage/local/lib/python2.6/site-packages/sage/libs/singular/function.so in sage.libs.singular.function.SingularFunction.__call__ (sage/libs/singular/function.cpp:9618)()

TypeError: Cannot call Singular function 'radical' with ring parameter of type '<class 'sage.rings.polynomial.multi_polynomial_ring.mpolynomialring_polydict_domain'="">'

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