Re: gp: subst() anomaly

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

On Tue, 25 Feb 2003, Michael Somos wrote:
> ? E=ellinit([0,0,0,1,0]);
> ? P=[x,y];
> ? Q=elladd(E,P,P);
> ? subst(Q,y^2,x^3+x)
> %4 = [0, 0]
> ? subst(Q[1],y^2,x^3+x)
> %5 = (1/4*x^4 - 1/2*x^2 + 1/4)/(x^3 + x)
>
> seems a bit peculiar to me. I can't seem to find a simpler example
> of this behavior, although this example is a natural one. Shalom,

Here's a simpler one:

(01:06) gp > subst(y*x,y^2,x)
%1 = 0

which in turn is due to

(01:06) gp > Mod(x*y, y^2)
%2 = 0 \\ x*y viewed in Q(y)[x]

The latter feature is debatable [ although documented ], but it is easy to
fix subst. Have done the latter.

    Karim.
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