cino hilliard on Tue, 14 Feb 2006 02:34:26 +0100 |
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Re: x^n + x^n |
more.
From: Jeroen Demeyer <jdemeyer@cage.ugent.be> To: pari-users@list.cr.yp.to Subject: Re: x^n + x^n Date: Sun, 12 Feb 2006 13:46:56 +0100 cino hilliard wrote:x^n+x^n gives (04:00) gp > x^n+x^n *** gpow: need integer exponent if series valuation != 0. Maple gives x^n+x^n; 2x^nThe reason is that Maple is a different kind of program. PARI/GP is really just a fancy calculator, it does not know about symbolic expressions like x^n. However, it can work with polynomials and power series, which can act somewhat like symbolic expressions. For example,(x + 1)^2 will give what you expect: x^2 + 2*x + 1.Maple on the other hand, can really do symbolic manipulations, so it really treats x^n as "x to the power n". I don't have Maple here, but I suppose you could differentiate x^n and get nx^(n-1) as the answer.The upshot of this is that PARI/GP is really specialized on the mathematics, so it is much faster than Maple for mathematical computations (factoring a large number for example).This is the idea, I'm sure someone else can explain better. Jeroen Demeyer
Cino