Date: 16 DEC 1980 2010-EST
From: LSH at MIT-MC (Lars S. Hornfeldt)
Subject: Human-like new TRIG-SIMPLIFIER and SUMSUBSTITUTOR
To: INFO-MACSYM at MIT-MC, INFO-TENSOR at MIT-MC, HEP at MIT-MC


TRIGSUM(exp);  is a new function (autoloading) that exploits the
TRIG-onometric SUM-relation:     2         2
                              sin (x) + cos (x) - 1  ==> 0

in an optimal fashion; ie it uses DIFFERENT formulations:
   2      2                   2        2             2        2
sin  + cos  ==> 1,     1 - sin  ==> cos ,     1 - cos  ==> sin

selectively only where they are BENEFICIAL, and the program returns
THAT mixture of sin and cos that constitutes the least number of terms.
For instance, TRIGSUM on the 6-term-expression:

  (ONE - C     )*SIN(X)^2 \  Returns 3 terms: /    (      S)*SIN(X)^2
+ (ONE      - S)*COS(X)^2  >      ===>       <   + (    C  )*COS(X)^2
+ (    + C  + S)          /                   \  + (ONE    )

This works equally well and fast if multiplied with any sin-cos power.

TRIGSUM uses the sum-substitutor (=1yr work) in STENSR. For references
and pointers see SHARE;STENSR USAGE.  Any arb.-length-sum of arb.-length-
products of tensors can be substituted, and in PRINCIPLE also of scalars.
Send bugs, and such sum-relations that you want to exploit, to me.

Being a complicated program, it's not small, but you can ALWAYS type
TRIGSUM(..);  since it tests space to fit the program before it autoloads.
Also the workspace consumption =0, in contrast to explicit subst. sin=>cos.

Do   :PRINT LSH;TRGSUM DEMOUT    to see a demo writefile, or run the demo
itself by  DEMO(TRGSUM,DEMO,DSK,LSH)$   which takes 5 cpu-min to end
[but (a curiosum): substituting sin=>cos would give results requiring
an Earthsized machine to store, and would take 10^7 Universe-lifetimes].

-lsh