Groebner bases seem to do this relatively quickly. Here's your last
example done in a crude way, seems almost instantaneous.
R.<x0,x1,x2,x3,e1,e2,e3> = PolynomialRing(QQ,order = TermOrder
('degrevlex',4)+TermOrder('degrevlex',3))
foo= (x0 + x1 + x2 + x3)^3
sym = []
xvars = [x0,x1,x2,x3]
for i in range(1,4):
temp = 0
for p in combinations([0,1,2,3],i):
temp = temp + prod([xvars[p[j]] for j in range(i)])
sym.append(sage_eval('e'+str(i), locals=locals())-temp)
symid = R.ideal(sym+[foo]).elimination_ideal([x0,x1,x2,x3])
list(symid.gens())
[e1^3]
-Marshall
On Oct 19, 9:47 am, Pierre <[email protected]> wrote:
> Thanks. This works, but it is sooooo very slow :
>
> sage: foo= (x0 + x1 + x2 + x3)^1;
> sage.libs.symmetrica.all.t_POLYNOM_ELMSYM( foo )
> e[1] #immediate
>
> sage: foo= (x0 + x1 + x2 + x3)^2;
> sage.libs.symmetrica.all.t_POLYNOM_ELMSYM( foo )
> e[1, 1] #also immediate
>
> sage: foo= (x0 + x1 + x2 + x3)^3;
> sage.libs.symmetrica.all.t_POLYNOM_ELMSYM( foo )
> #nothing after several minutes, i had to go C-c (on a macbook)
>
> My original polynomial just about fits on the screen, so needless to
> say after 30 minutes i had nothing.
>
> Is this normal ? Using groebner basis techniques my guess is that
> things should not quite be that slow.
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