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Re: [Axiom-developer] severe (!) bug in normalize


From: Francois Maltey
Subject: Re: [Axiom-developer] severe (!) bug in normalize
Date: 05 Dec 2006 22:16:23 +0100
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

Francois Maltey <address@hidden> writes:


And I let a error :

replace line 205     

                  numexpo := numexpo -$MP cst1::Integer::R *$MP k::MP
                  cst := cst * (first argument k **$Rep cst1::Integer)
        output([cst, numexpo::%]::OutputForm)$OutputPackage

The old one was : 
                  cst := first argument k ** cst1::Integer


What do you want for Gosper algorithm in the famus quotient u(n)/u(n-1).

With or without exp ? with or without power ?

the expr.spad I send you don't suppose (a,b,c) in R+

So we don't have (a^b)^c = a^(bc)

But other simplifications are done where n is a real number, not a letter.

                (a^u)^n = a^(nu) 
           exp (n ln a) = a^n, the fraction.
(exp a)^n exp b / exp c = exp (na+b-c)
                 (na)^u = n^u a^u 
                (a/n)^u = a^n / n^u
  exp (n log a - log c) = a^n / c

I hope I let no error in mathematics formula :
1 / (z^u) = z^(-u) \neq (1/z)^u -- try with z=-1 and u=1/2

It seems that my expr.spad is right for the sum function :
sum   (    q^n, n)
sum   (n * q^n, n)
sum (n^2 * q^n, n)
sum     (exp n, n)
sum ((n-1)*n^2 * q^n, n)

but have an error in :
sum (n * exp n, n)
sum (n^3 * q^n, n)

Even with print-spy I don't understand where is the mistake.

Hope this help you !

Francois




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