Thanks :-) On Tue, Nov 16, 2010 at 1:02 PM, luisfe <lftab...@yahoo.es> wrote:
> > > On Nov 16, 12:28 pm, Niels <niels.lub...@gmail.com> wrote: > > Hi, > > > > I would like to compute the gcd of two bi-variate polynomials over a > number > > field: > > > > sage: R = PolynomialRing( QQ, var( 't' ), order = 'lex' ) > > sage: t = R.gens()[0] > > sage: T = NumberFieldTower( [t ** 2 - t + 1], 'a0' ) > > sage: a0 = T.gens()[0] > > sage: R = R.change_ring( T ) > > sage: > > sage: P = PolynomialRing( T, var( 'x,y' ), order = 'lex' ) > > sage: x, y = P.gens() > > sage: > > sage: gcd( [( a0 + 1 ) * x , ( a0 + 1 ) * x * y] ) > > x > > > > # This should be ( a0 + 1 ) * x. > > I disagree, the gcd of two polynomials is defined up to constant > multiplication. Probably the answer is monic wrt the monomial order. > > > > sage: > > sage: t = R.gens()[0] > > sage: T = NumberFieldTower( [ t ** 2 - a0], 'a1' ) > > sage: a1 = T.gens()[0] > > sage: > > sage: P = PolynomialRing( T, var( 'x,y' ), order = 'lex' ) > > sage: x, y = P.gens() > > sage: > > > > # Computing the gcd in QQ(a0,a1)[x,y] gives problems. > > # (btw qou_rem and divides also don't work over this ring) > > multivariate polynomials over towers of number fields are currently > generic multivariate polynomials and there is no gcd implemented in > Sage for multivariate polynomials over generic fields. Try to compute > in this case a primitive element and pass to a simple extension so it > will use Singular. > > > > sage: gcd( [( a0 + 1 ) * x , ( a0 + 1 ) * x * y] ) > > > > > --------------------------------------------------------------------------- > > AttributeError Traceback (most recent call > last) > > > > /home/niels/<ipython console> in <module>() > > > > > /home/niels/Desktop/n/app/sage/local/lib/python2.6/site-packages/sage/rings/arith.pyc > > in gcd(a, b, **kwargs) > > 1434 if U is ZZ or U is int or U is long:# > ZZ.has_coerce_map_from(U): > > 1435 return sage.rings.integer.GCD_list(a) > > -> 1436 return __GCD_sequence(seq, **kwargs) > > 1437 > > 1438 GCD = gcd > > > > > /home/niels/Desktop/n/app/sage/local/lib/python2.6/site-packages/sage/rings/arith.pyc > > in __GCD_sequence(v, **kwargs) > > 1476 one = v.universe()(1) > > 1477 for vi in v: > > -> 1478 g = vi.gcd(g, **kwargs) > > 1479 if g == one: > > 1480 return g > > > > > /home/niels/Desktop/n/app/sage/local/lib/python2.6/site-packages/sage/structure/element.so > > in sage.structure.element.Element.__getattr__ > > (sage/structure/element.c:2666)() > > > > > /home/niels/Desktop/n/app/sage/local/lib/python2.6/site-packages/sage/structure/parent.so > > in sage.structure.parent.getattr_from_other_class > > (sage/structure/parent.c:2840)() > > > > > /home/niels/Desktop/n/app/sage/local/lib/python2.6/site-packages/sage/structure/parent.so > > in sage.structure.parent.raise_attribute_error > > (sage/structure/parent.c:2638)() > > > > AttributeError: 'MPolynomial_polydict' object has no attribute 'gcd' > > sage: > > > --------------------------------------------------------------------------- > > > > # giving 2 elements to gcd instead of a list, gives rise to different > > exception > > > > sage: gcd( ( a0 + 1 ) * x , ( a0 + 1 ) * x * y ) > > > --------------------------------------------------------------------------- > > TypeError Traceback (most recent call > last) > > > > /home/niels/<ipython console> in <module>() > > > > > /home/niels/Desktop/n/app/sage/local/lib/python2.6/site-packages/sage/rings/arith.pyc > > in gcd(a, b, **kwargs) > > 1427 return ZZ(a).gcd(ZZ(b)) > > 1428 except TypeError: > > -> 1429 raise TypeError, "unable to find gcd of %s and > > %s"%(a,b) > > 1430 > > 1431 from sage.structure.sequence import Sequence > > > > TypeError: unable to find gcd of (a0 + 1)*x and (a0 + 1)*x*y > > sage: > > > --------------------------------------------------------------------------- > > > > Kind regards, > > > > Niels > > > > > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com<sage-devel%2bunsubscr...@googlegroups.com> > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
