On Tue, Dec 7, 2010 at 4:29 PM, luisfe <lftab...@yahoo.es> wrote:

> On Dec 7, 5:03 pm, andrew ewart <aewartma...@googlemail.com> wrote:
> > I have the following code
> >
> > P.<x0,x1,y0,y1,y2,y3> = PolynomialRing(QQ,order='degrevlex')
> > I = Ideal(x0^4-y0,x0^3*x1-y1,x0*x1^3-y2,x1^4-y3)
> > print I
> > R.<y0,y1,y2,y3> = PolynomialRing(QQ,order='degrevlex')
> > I1=Ideal(1)
> > J=I.intersection(I1)
> > print J
> > but gives error
> > File "/usr/local/sage/sage-4.6/local/lib/python2.6/site-packages/sage/
> > rings/polynomial/multi_polynomial_ideal.py", line 369, in wrapper
> >     return func(*args, **kwds)
> >   File "/usr/local/sage/sage-4.6/local/lib/python2.6/site-packages/
> > sage/rings/polynomial/multi_polynomial_ideal.py", line 1327, in
> > intersection
> >     raise ValueError, "other must be an ideal in the ring of self, but
> > it isn't."
> > ValueError: other must be an ideal in the ring of self, but it isn't.
> >
> > becuase I doesnt lie in R
> > so how do I change this so that sage will be happy for I, an ideal in
> > P, intersecting with any ideal in R
> > (also R is supposed to be a subring of P where the x0 and x1 are
> > removed)
>
> Sort answer, you cannot intersect ideals in different rings.
> Note that I1 is an ideal of ZZ since you wrote Ideal(1) which is
> assumed to be 1 in ZZ.
>
> You could define the ideal 1 in R as (for instance)
>
> I1 = Ideal(R(1))
> I2 = I1.change_ring(P) # Now it is an ideal in P with the same
> generators as I1
> I2.intersection(I)
> Ideal (x1^4 - y3, x0*x1^3 - y2, x0^3*x1 - y1, x0^4 - y0) of
> Multivariate Polynomial Ring in x0, x1, y0, y1, y2, y3 over Rational
> Field
>
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I thought I1=R=<1>
also the intersection should be in R, not just in P, so how is this
achieved?

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