Hi, Just realized that gcd( [( a0 + 1 ) * x , ( a0 + 1 ) * x * y] )=x is correct.
This makes me wonder whether to exception of the second gcd (after adjoining a1) is a bug, or whether my construction of the numberfield is incorrect. Maybe i should have asked this question at sage-support Kind regards, Niels On Tue, Nov 16, 2010 at 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. > > 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) > > 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 For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
