[sage-support] Re: Decomposing polynomials from other polynomials using Gröbner bases

2011-04-05 Thread Johan S. R. Nielsen
This is really cool and seems to be exactly what I need. Thank you very much! Cheers, Johan On Apr 5, 3:19 pm, luisfe wrote: > On Apr 5, 2:10 pm, "Johan S. R. Nielsen" wrote: > > > Oops, continuing: > > > more precisely, we wish to find a q in Q[Y1, Y2] such that q(f1, f2) = > > g. In this case

[sage-support] Re: Decomposing polynomials from other polynomials using Gröbner bases

2011-04-05 Thread luisfe
On Apr 5, 2:10 pm, "Johan S. R. Nielsen" wrote: > Oops, continuing: > > more precisely, we wish to find a q in Q[Y1, Y2] such that q(f1, f2) = > g. In this case, we have > q(Y1, Y2) = Y1^2 + Y1*Y2 - Y2 > as a solution, as > f1^2 + f1*f2 - f2 = g This is an elimination problem. Note that it is n

[sage-support] Re: Decomposing polynomials from other polynomials using Gröbner bases

2011-04-05 Thread Johan S. R. Nielsen
Oops, continuing: more precisely, we wish to find a q in Q[Y1, Y2] such that q(f1, f2) = g. In this case, we have q(Y1, Y2) = Y1^2 + Y1*Y2 - Y2 as a solution, as f1^2 + f1*f2 - f2 = g As far as I can see, I can't easily use the lift function for this, as the ideal's polynomials will always be lin

[sage-support] Re: Decomposing polynomials from other polynomials using Gröbner bases

2011-04-05 Thread Johan S. R. Nielsen
Thanks for the swift reply! That is a neat function, but I don't think it is what I need. I was being too unclear, so here is an example: Let R = Q[x], f1 = x^2 + 1 and f2 = x + 3 and g = x4+x3+4x2+x+3. We wish to write g as a polynomial in f1 and f2 over Q; more precisely, we wish to find a q