Hello, I would like to do the following computation concerning a subring of a quotient of a polynomial ring:
The first task is easily solvable: compute the dimension of the coinvariant ring of the symmetric group: sage: R.<x1,x2,x3> = QQ['x1, x2, x3'] sage: I = R.ideal( x1+x2+x3, x1^2+x2^2+x3^2, x1^3+x2^3+x3^3 ) sage: I.vector_space_dimension() 6 This is the dimension of the the quotient of the ring R by the ideal I. Now imagine that R is replaced by QQ['x1, x2, x3, y1, y2, y3']. I would like to mod out by the same ideal and then compute the vector space dimension of a subring of this quotient having again finite vector space dimension. In the example, the subring is generated by x1, x2, x3, x1*y1+x2*y2+x3*y3, x1^2*y1+x2^2*y2+x3^2*y3, x1^3*y1+x2^3*y2+x3^3*y3. Is there any construction solving this kind of problem? Thanks for your help, Christian Stump -- 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
