Re: [Axiom-developer] choose the better expand

[Martin Rubey]

Francois Maltey <address@hidden> writes:

> So expand : expand ! 
> I ask for me if I do only one expand (Expr) 
> or expand (Expr, "sincos") with one parameter and
>    expand (Expr, ["sincos", ...) with many parameters. Do you have an idea ?

You probably should provide the three of them.

Could you define (exactly!) what expand is supposed to do. I guess that it's
similar to

Function: TRIGEXPAND (exp) 

expands trigonometric and hyperbolic functions of sums of angles and of
multiple angles occurring in exp. For best results, exp should be expanded. To
enhance user control of simplification, this function expands only one level at
a time, expanding sums of angles or multiple angles. To obtain full expansion
into sines and cosines immediately, set the switch TRIGEXPAND:TRUE. TRIGEXPAND
default: [FALSE] - if TRUE causes expansion of all expressions containing SINs
and COSs occurring subsequently. HALFANGLES[FALSE] - if TRUE causes half-angles
to be simplified away. TRIGEXPANDPLUS[TRUE] - controls the "sum" rule for
TRIGEXPAND, expansion of sums (e.g. SIN(X+Y)) will take place only if
TRIGEXPANDPLUS is TRUE. TRIGEXPANDTIMES[TRUE] - controls the "product" rule for
TRIGEXPAND, expansion of products (e.g. SIN(2*X)) will take place only if
TRIGEXPANDTIMES is TRUE.

(C1) X+SIN(3*X)/SIN(X),TRIGEXPAND=TRUE,EXPAND;
                              2           2
(D1)                     - SIN (X) + 3 COS (X) + X
(C2) TRIGEXPAND(SIN(10*X+Y));
(D2)               COS(10 X) SIN(Y) + SIN(10 X) COS(Y)


Variable: TRIGEXPANDPLUS 

default: [TRUE] - controls the "sum" rule for TRIGEXPAND. Thus, when the
TRIGEXPAND command is used or the TRIGEXPAND switch set to TRUE, expansion of
sums (e.g. SIN(X+Y)) will take place only if TRIGEXPANDPLUS is TRUE.

Variable: TRIGEXPANDTIMES 

default: [TRUE] - controls the "product" rule for TRIGEXPAND. Thus, when the
TRIGEXPAND command is used or the TRIGEXPAND switch set to TRUE, expansion of
products (e.g. SIN(2*X)) will take place only if TRIGEXPANDTIMES is TRUE.

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Martin