Waldek Hebisch <[EMAIL PROTECTED]> writes:

> Martin Rubey wrote:
> > 
> > Waldek Hebisch <[EMAIL PROTECTED]> writes:
> > 
> > > 2) I think we have all tools to do actual computations: we can factorise
> > >    in algebraic extensions, so we can verify irreducibility assumptions.
> > >    We have functions to compute primitive elements.
> > 
> > I was unable to use the latter.  Do you think you could compute the example 
> > I
> > gave with FriCAS?
> > 
> 
> Is te following what you want?
> 
> pol1 := x^2+1
> pol2 := z^3-2
> primrec := primitiveElement([pol1, pol2], [x, z])$PrimitiveElement(Fraction 
> Integer)
> Ae := SAE(Fraction(Integer), SparseUnivariatePolynomial(Fraction(Integer)), 
> primrec.prim)
> (primrec.poly.1::Ae)^2
> (primrec.poly.2::Ae)^3


Oh, how very very nice!  I didn't know about PrimitiveElement. Many thanks,
I'll sent this to my colleague!

BTW: this also means that the polynomial is not unique?  I got a different one
using Sage/pari...

Martin


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