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[Axiom-developer] how to expand trig functions ?

From: Francois Maltey
Subject: [Axiom-developer] how to expand trig functions ?
Date: Fri, 03 Jun 2005 15:01:54 +0200
User-agent: Gnus/5.1006 (Gnus v5.10.6) XEmacs/21.5 (chestnut, linux)


I play with expand(sin(...)) :

expand (sin (x+y)) is right, but 

1/ I can't get expand (sin (2*x)) 

2/ The result of expand (sin (x+y+z)) doesn't seem complete. 
   axiom only apply twice the expanded sin (a+b) and cos (a+b).
   I prefer the maple and mupad method. The formula is completly expanded.

Is there a reason for this ?

Do you think the axiom-code must remain as now ?
or is it possible to improve it ? If you think so, I propose to look at this.

Am I right when I see it's comming from this src/algebra/manip.spad file ?

)abbrev package TRMANIP TranscendentalManipulations
++ Transformations on transcendental objects
++ Author: Bob Sutor, Manuel Bronstein
++ Date Created: Way back
++ Date Last Updated: 22 January 1996, added simplifyLog MCD.
++ Description:
++   TranscendentalManipulations provides functions to simplify and
++   expand expressions involving transcendental operators.
++ Keywords: transcendental, manipulation.
TranscendentalManipulations(R, F): Exports == Implementation where
  R : Join(OrderedSet, GcdDomain)
  F : Join(FunctionSpace R, TranscendentalFunctionCategory)

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