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((qxy)^2); I Ideal (q^2x^2y^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'="">'
