Bill Allombert on Mon, 24 Feb 2003 17:23:36 +0100 |
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Re: Fast substitutions in Pari |
On Sun, Feb 23, 2003 at 12:33:15PM +0100, Franck MICHEL wrote: > Hi, > > Assume u is a polynomial in x of degree n, and phi is a rational fraction > in t. > I would like to transform u to a truncated series in t, i.e: > - replace x by phi in u; > - and expand in t (to the degree n). > > I set seriesprecision to n and use: > taylor(subst(u,x,phi),t); > > It is very simple; but is it the best way to do it? Normaly you should rather do subst(u,x,taylor(phi,t)) If it is slower, then this is probably a inefficiency problem in PARI. > I've tried to first expand phi in t; and to substitute the series in t into > the polynomial in x. But it is slower, even if we add an O(t^p) to the > series in t, with p chosen in function of x^k. Perhaps this kind of > manipulation is already done by Pari with taylor(subst(u,x,phi),t) and > there is no need to search to improve it (?) > > Thanks in advance for your advices. What kind of coefficients phi have ? (integers, rationals, reals ?) If the coefficients are rationals, try to reduce everything to a common denominator. The way PARI handle polynomials and formal series with rationals coefficients is sub-optimal. In fact even if phi has integral coefficients, the power series development will not, so this may explain the problem. Cheers, Bill.