Hi, On 7 Dez., 17:03, 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
No. The problem is not that I does not lie in R. The problem is that I1 does not lie in P: sage: P.<x0,x1,y0,y1,y2,y3> = PolynomialRing(QQ,order='degrevlex') sage: I = Ideal(x0^4-y0,x0^3*x1-y1,x0*x1^3-y2,x1^4-y3) sage: R.<y0,y1,y2,y3> = PolynomialRing(QQ,order='degrevlex') sage: I1=Ideal(1) sage: I.ring() is P True sage: I1.ring() Integer Ring There is no reason to believe that any CAS could guess that you want Ideal(1) to be an ideal in P or R or whatever ring if you don't state it -- 1 is an integer, and thus Ideal(1) is an ideal in ZZ. This is an answer to your question. But it seems to me that your question is actually not relevant to your problem. If I understand correctly, you want to eliminate the variables x0 and x1, right? So, you could do sage: I.elimination_ideal([x0,x1]) Ideal (y1*y2 - y0*y3, y2^3 - y1*y3^2, y0*y2^2 - y1^2*y3, y1^3 - y0^2*y2) of Multivariate Polynomial Ring in x0, x1, y0, y1, y2, y3 over Rational Field Of course, the elimination ideal still belongs to P, not to R, although the variables x0,x1 are not used anymore. If you want to obtain an ideal in R, you could do sage: R.ideal_monoid()(I.elimination_ideal([x0,x1])) Ideal (y1*y2 - y0*y3, y2^3 - y1*y3^2, y0*y2^2 - y1^2*y3, y1^3 - y0^2*y2) of Multivariate Polynomial Ring in y0, y1, y2, y3 over Rational Field or sage: I.elimination_ideal([x0,x1]).change_ring(R) Ideal (y1*y2 - y0*y3, y2^3 - y1*y3^2, y0*y2^2 - y1^2*y3, y1^3 - y0^2*y2) of Multivariate Polynomial Ring in y0, y1, y2, y3 over Rational Field Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
