Trigonometric functions with symbolic argument an even multiple of pi
Subject: Trigonometric functions with symbolic argument an even multiple of pi
From: George Leeman
Date: Wed, 6 Apr 2011 17:11:38 -0400
Maxima has an elegant way of handling such evaluations if we know that
integer m is even:
declare(m,even);
cos(m*%pi);
The answer is 1, as expected. However, the case where the argument is an
even integer raised to
a symbolic positive integer power seems more difficult. I wonder if there
is a simple solution.
One possible attempt is:
declare(positive, feature);
matchdeclare(ep, lambda([x],is(op(x)="^") and evenp(part(x,1))
and member(part(x,2),propvars(integer)) and
member(part(x,2),propvars(positive))));
tellsimpafter(cos(ep*%pi),1);
After this sequence the statements
kill(m);
declare(m,[integer,positive]);
cos(4^m*%pi);
give an answer of 1, but the approach seems rather complicated.
-- George Leeman