Trigonometric definite integral resulting in sinc-likefunction
Subject: Trigonometric definite integral resulting in sinc-likefunction
From: Dan
Date: Fri, 16 Jul 2010 11:49:07 +0100 (BST)
On Thu, 15 Jul 2010, Richard Hennessy wrote:
> This could be the answer.
> (%i12) integrate(cos(2*%pi*m*x),x,0,1);
> (out12) if equal(m,0) then 1 else sin(2*%pi*m)/(2*%pi*m)
That's the kind of output you'd get by using asksign in the
integration routine, then loading the noninteractive package, yes?
On the other hand, the sin(2*%pi*m)/(2*%pi*m) expression is correct
even when m = 0, so perhaps any asksign work should be in the trig
simplifier, not in the integration routine - perhaps producing
something like
(%i1) declare(m,integer) ;
(%o1) done
(%i2) sin(2*%pi*m) ;
(%o2) if equal(m,0) then 2*%pi*m else 0
There was a thread a while back about implementing sinc
<http://www.math.utexas.edu/pipermail/maxima/2003/006259.html>;, which
ended with an asksign-based suggestion by Wolfgang Jenkner.
Incidentally, you may remember that some time ago, I asked about the
degree of independence of the Maxima and Axiom codebases, because I
was getting the same surprising result from both CAS
<http://www.math.utexas.edu/pipermail/maxima/2009/018685.html>;. The
surprising result came (at least in part) from this error - although
in the Axiom version, the trig simplification that wasn't uniformly
correct was implemented in my script, rather than internally in Axiom.
--
Regards,
Dan