# [Maxima] simplification

Barton Willis willisb at unk.edu
Fri Apr 13 10:17:31 CDT 2012

```The general simplifier for trigonometric functions has a method for deciding when to apply a reflection identity; for example

(%i1) sin(-x);
(%o1) -sin(x)

(%i2) cos(-x);
(%o2) cos(x)

(%i3) makelist(cos(x + (1-e) * %pi/2),e,[-1,0,1]);
(%o3) [-cos(x),-sin(x),cos(x)]

Maxima uses an ordering predicate (defined on expressions, not just numbers)  to decide when to use the reflection identity:

(%i4) sin(b-x);
(%o4) -sin(x-b)

(%i5) sin(b-a);
(%o5) sin(b-a)

The aim of the algorithm is to simplify as many expressions to zero as possible:

(%i7) sin(b-x) + sin(x-b);
(%o7) 0

(%i8) sin(a-b) + sin(b-a);
(%o8) 0

Also, the function trigrat might be useful to you?  I didn't answer your question, but maybe some of this is useful.

--bw

________________________________________
From: maxima-bounces at math.utexas.edu [maxima-bounces at math.utexas.edu] on behalf of Jean Vittor [jean.vittor at free.fr]
Sent: Friday, April 13, 2012 06:39
To: maxima at math.utexas.edu
Subject: [Maxima] simplification

Hi,

I'm new to maxima and I have a hard time understanding how
simplification works.

My point is to use "sign" values (I mean integers which take their value
from {-1;1}) and to be able to automate some trigo simplifications like
(in the following, e is a sign and x a real expression):
- sin(e*x) -> e*sin(x)
- cos(e*x) -> cos(x)
- cos(x+(1-e)*%pi/2) -> e*cos(x)
- ...
- and, of course, e^2 -> 1

Is there a way to do this with maxima ?

Thanks,

Jean

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