On Wednesday, May 13, 2015 at 10:33:23 AM UTC-7, N. Du Hamel wrote:
>
> I do something like that for the substitution, where eq is my equation in
> terms of e_i and g_j :
> eq =
> eq.subs_expr({e1^2:-G2.resultant(G3),e2^2:-G1.resultant(G3),e3^2:-G1.resultant(G2)})
> eq =
> eq.subs_expr({e1^3:e1*(-G2.resultant(G3)),e2^3:e2*(-G1.resultant(G3)),e3^3:e3*(-G1.resultant(G2))})
> eq =
> eq.subs_expr({e1^4:(-G2.resultant(G3))^2,e2^4:(-G1.resultant(G3))^2,e3^4:(-G1.resultant(G2))^2})
>
Well, you could generate the list of substitutions programmatically:
r23= G2.resultant(G3)
eq = eq.subs({e1^i: e1^(i % 2)*(-r23)^(i//2) for i in [1..4]})
etc.
A more general approach would be to construct the appropriate polynomial
ring (with an elimination order for e1,e2,e3) and make the ideal generated
by your relations:
e1^2= ... (etc)
and then reduce your expression eq with respect to that ideal. For more
complicated sets of relations, this is a good approach, but in your case
the substitution method is basically equivalent.
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