Hi all: I'm trying to get Sage to compute in a multivariate polynomial ring over a transcendental field extension but am running into difficulties. For example, Sage crashes when trying to compute a radical ideal as demonstrated by the example below. I tried the same example in Singular, which gave me the correct answer (the ideal generated by x*y).
So is the failure below a Singular interface bug or am i doing something wrong? I suspect Singular doesn't like Sage's fraction field construction of a transcendental extension. Alex ---------------------------------------------------------------------- | Sage Version 4.3, Release Date: 2009-12-24 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- WARNING: There is one major unsolved bug in some versions of Sage on OS X 10.6 that causes an 'Abort trap' crash when doing certain symbolic computations. See http://trac.sagemath.org/sage_trac/ticket/7095/. sage: R0.<q> = 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: 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() --------------------------------------------------------------------------- RuntimeError 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) 400 if not R.base_ring().is_field(): 401 raise ValueError("Coefficient ring must be a field for function '%s'."%(self.f.__name__)) --> 402 return self.f(self._instance, *args, **kwds) 403 404 require_field = RequireField /Applications/sage/local/lib/python2.6/site-packages/sage/rings/ polynomial/multi_polynomial_ideal.pyc in wrapper(*args, **kwds) 362 """ 363 with RedSBContext(): --> 364 return func(*args, **kwds) 365 366 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) 1385 I.parent().lib('primdec.lib') 1386 r = I.radical() -> 1387 return S.ideal(r) 1388 1389 @require_field /Applications/sage/local/lib/python2.6/site-packages/sage/rings/ polynomial/multi_polynomial_ring.pyc in ideal(self, *gens, **kwds) 496 if (kwds.has_key('coerce') and kwds['coerce']) or do_coerce: 497 gens = [self(x) for x in gens] # this will even coerce from singular ideals correctly! --> 498 return multi_polynomial_ideal.MPolynomialIdeal(self, gens, **kwds) 499 500 /Applications/sage/local/lib/python2.6/site-packages/sage/rings/ polynomial/multi_polynomial_ideal.pyc in __init__(self, ring, gens, coerce) 2250 Ideal (x0^2, x1^3) of Multivariate Polynomial Ring in x0, x1 over Finite Field of size 3 2251 """ -> 2252 Ideal_generic.__init__(self, ring, gens, coerce=coerce) 2253 2254 def __cmp__(self, other): /Applications/sage/local/lib/python2.6/site-packages/sage/rings/ ideal.pyc in __init__(self, ring, gens, coerce) 238 gens = [gens] 239 if coerce: --> 240 gens = [ring(x) for x in gens] 241 242 gens = tuple(gens) /Applications/sage/local/lib/python2.6/site-packages/sage/rings/ polynomial/multi_polynomial_ring.pyc in __call__(self, x, check) 425 self._singular_().set_ring() 426 try: --> 427 return x.sage_poly(self) 428 except TypeError: 429 raise TypeError, "unable to coerce singular object" /Applications/sage/local/lib/python2.6/site-packages/sage/interfaces/ singular.pyc in sage_poly(self, R, kcache) 1400 1401 singular_poly_list = self.parent().eval("string(coef (%s,%s))"%(\ -> 1402 self.name (),variable_str)).split(",") 1403 1404 if singular_poly_list == ['1','0'] : /Applications/sage/local/lib/python2.6/site-packages/sage/interfaces/ singular.pyc in eval(self, x, allow_semicolon, strip, **kwds) 547 548 if s.find("error") != -1 or s.find("Segment fault") != -1: --> 549 raise RuntimeError, 'Singular error:\n%s'%s 550 551 if get_verbose() > 0: RuntimeError: Singular error: ? coef(`ideal`,`poly`) failed ? expected coef(`poly`,`poly`) ? error occurred in STDIN line 81: `string(coef(sage18,x*y));` ? wrong type declaration. type 'help string;' sage:
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