cino hilliard on Tue, 14 Feb 2006 02:34:26 +0100


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Re: x^n + x^n

Thanks for your input. Pari does some symbolics so well it has spoiled me into thinking it can do 
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^n
The 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