Resultants of real polynomials

[shreevatsa]

Hello,

If I try to compute the resultant of two polynomials in RR['x','y'],
it fails with a NotImplemented error. Like:

R.<x,y> = RR[]
p = x + y
q = x*y
p.resultant(q)

It works when I use QQ[] instead. I don't know how resultants are
computed (it seems to be done by libsingular), but if is done using a
determinant, say, then shouldn't it work for real polynomials too? Is
this perchance just an error translating Sage's real polynomials to
Singular's terms?

[Carl Witty]

This issue is now being tracked at http://trac.sagemath.org/sage_trac/ticket/2693

As a workaround, you can instead do:

R.<x,y> = RR[]
p = x + y
q = x*y

p.polynomial(x).resultant(q.polynomial(x))

where p.polynomial(x) gives a univariate polynomial in x over the ring
RR['y']. Sage's univariate resultant implementation is more generic
than the multivariate implementation, and handles this case.

Carl