Re: Fast substitutions in Pari

[Franck MICHEL <Franck.Michel@univ.u-3mrs.fr>]

>Normaly you should rather do
>subst(u,x,taylor(phi,t))
>If it is slower, then this is probably a inefficiency problem in PARI.

It is slower, I was surprised of it.

>What kind of coefficients phi have ? (integers, rationals, reals ?)

Below is an example. I don't use this u but the function phi is exactly one
of those I'm using.

\ps 16;
u=sum(i=1,15,(-1)^i*i^2*x^i);
a = 3741/2996+34323/2630*I; 
b =
2771/3873+1653/2366*I; 
c = 1264/1653+1883/2922*I; 
d =
-2159/2174+91/776*I;
phi=a*t*(1-t*b)*I/(1-t)/(1-c*t)/(1-d*t);
subst(u,x,tayl
or(phi,t));
taylor(subst(u,x,phi),t);

On my PC, subst(u,x,taylor(phi,t)) is done in 1502ms, and
taylor(subst(u,x,phi),t) is done in 552ms. 

--
Franck