Re: [Axiom-developer] choose the better expand

[Francois Maltey]

Dear Bill, Martin, William, and other... thanks a lot !

Yesterday I finish a first version of expand sin_cos, 
expand sinh_cosh, expand tan_tanh, ...

Now I will improve it thanks to your previous reponses.

And I have theses other questions. This time every one is very short :

1/ what is the << import >> command in a *.spad file.
Martin and Bill give me exemples with import complex or import list.

2/ I can extract an integer from EXPR INTEGER by       
   fct (x:R) == if R is Integer then x::Integer else -999 
but this doesn't work for Expression Complex Integer 
or Expression Fraction Integer. 
Can I test in an unknow Ring R if x is a (n:Integer) * 1$R or not. 
No one of my tries with a lot of
retractIfCan(x)@Union(Integer, "failed") compile.

3/ I find pretty to expand cos (a+%i*b) with sin/sinh/cos/cosh
but I don't find how to detect a ring as R = Complex S, use real
and imag, and make conversion back as cos a + %i*sinh b,...

4/ Do you want [for Martin I believe] a 
expand (factorial (n+1)) and an expand (factorial (n-1)) to
(n+1)*factorial n and factorial n / n. 

5/ Do you prefer :
a-expand (sin (2*x+y)) gives an Expression in sin x, sin y, cos x... of corse.
b-expand (sin (3)) remains sin (3) [or do you prefer with sin 1 and cos 1]
c-expand (sin (3*expressions without variables)) remains the same. 

I believe that everybody agree to a and b.
But what do I choose for c ? 
must I transform sin (sqrt (2) + sqrt (3)) or not ?

6/ Do you see other usefull expand ?

7/ Do you prefer only one expand as above, or do I make a 
expand (..., "sincos"), expand (..., "sinhcosh"), 
expand (..., "tantanh") or expand (..., "exp").
In this case what is the second argument in others functions of axiom : 
a String, a Symbol, a list of ...

8/ In the package TRMANIP, I divide an expression with an Integer by :
  n := c::Integer
  a1 := (a::F)/(n::R::F)
is it the shortest way in use or not ?

9/ at every call of expand there is a       
  num := numer arg
  den := denom arg
  b := reductum num / den
  b ^= 0 =>
Is the computation of b at each call is short (1 single machine operation) 
or long (with a factor or a gcd call) ?
Perhaps it's maybe possible to compute with leadingMonomial num, reductum num
without quotient. Do you have any advise ?

Thanks a lot !

François, in France