[Axiom-mail] Re: CAS for the "masses"

[Francois Maltey]

I'm very iteresting by the question.
   Is there a CAS for "masses" ?

Let me tell my point of view...

I must use Maple with my beginning graduate students. 
About 1 hour per week for them.

Maple isnot a great idea because the language isn't typed.
There is only one type of matrix, 0 in Integer = 0 in Float, and so.
This makes problems almost at every course. 
Computations with Mupad was more right because the language was typed.

My exercices uses both algebra and calculus abilities.

By example study the Tchebytcheff scalarProduct :

<P,Q> = integrate (P(t)*Q(t)/sqrt(1-t^2), t=-1..1)
  creates matrix in LinearAlgebra                   (1)
     uses Risch method for Integrate                (2)
      and eigenValues in linearAlgebra 
     calls polynomialSolve in polynomial algebra    (3)
  or calls numericalSolve in numerical analysis.    (4)

I don't forget differential equation (5) for orthogonal polynomial 
or recurrent (more or less) linear sequents         (6)
I'm also looking for combinatorial analysis         (7) 
power-series with theses coefficients (8) or Fourier series (9), 
and plots (10) abilities.

So I need a large CAS which all theses 10 domains. 
If only one is missing I only can do 70% of the exercices, 
        two are missing ... .... ... 0.7x0.7 = 49% 
       three ... ...                 35 %, and so.

Little systems as derive or maxima hasn't all these chapters.

Maybe it's easiest to write a naivePackage which uses big algorithms 
for axiom than to improve a too little systems.

So axiom has advantages ! but... hasn't yet all these purposes.
By example Expression are irrelevant with analysis course.

The axiom/aldor/spad interpreter allows to choose the package we prefer.
For this use, Expressions isn't right. I might write a Calculus domain 
which uses almost the same code that Expression and then call the 
axiom Risch algorithm or the standard limit functions. 
I'll don't have to rewrite these functions They are already in Axiom.

But...

Find the good domain in the typed language as axiom isn't so easy.

It's quicker to insert the good test in a low typed language
(see the maple or the mupad code...) 
Of corse there are more bugs by this way, 
but we get quickly an often(?) right result.

I'm impressed how axiom results are right 
(as other typed languages, caml is fine also)
but it's really complex to analysis. One example : 
In almost all CAS abs z = sqrt (z * conjugate z) without any question.
but I don't find so obvious the use of abs in axiom if there is no sqrt 
function in the domain. 

Many reefs in axiom force me to use axiom less I would like :

My code isn't pretty because I write it line after line with a lot of
assigment after each operation. It's the only way I found to get a compiled
package. 
When I use functional way with map, select or composed functions,
my functions don't compile. I make too errors and don't find them.

After this, I must enter in pamphlet files tricks, it's not nice.
Of corse pamphlet files is a good idea in order to keep an homogenous 
system.
    
So Yesterday when I was working arround
cos (4*a), cos a^4 + sin a^4,... , I used axiom with 
subst (expand cos (a+b+c+d), [b=a, c=a, d=a]) 
even if others CAS allows the expand (cos (4*a)).
Lacks as this one make axiom not interesting for my colleagues.

My work isn't to be an axiom developper, 
I only use few hours CAS per weeks in my work and 
I can't bid pehaps around 100 hours for improving expand.

F. in France.