[Axiom-math] trigs and factor

[Martin Rubey]

(I'm forwarding this also to axiom-math, since I believe that it is of general
interest. I hope I'm not disturbing privacy)

Dear CF,

> (1) One of my main interests in axiom is to investigate whether it can be
> used to efficiently perform complicated symbolic computations and
> SIMPLIFICATIONS of the resulting symbolic expressions. My present
> applications involve expressions with mainly trigonometric terms, ie
> sin(x)cos(y), sin^2(x)cos(z), etc. Please send me some of the built in axiom
> simplification commands. I have printed part of the axiom manual but have
> only been able to find the "factor" command so far.

As far as I know, factor has no (or not much) effect on fields, and EXPR INT is
one. In fact, this is a topic that should go on mathaction. To find out about
various factorisation operations you can try

)di op fact

giving you all operations that contain "fact" in their names. After that you
can inspect promising ones --- find out where they are defined with -- for
example --

grep "sqfrFactor.*==" *.spad

in the algebra/src directory, and then: read the source. It is often very well
documented.

There are also various trig operations:

)di op trig

Sorry, I don't know much more at the moment. Maxima has a command "trigrat"
that works well. Maybe Axiom needs some work here. It would be great if you
document your findings on MathAction!

> (2) I want to define functions, each in a separate .input file. I then want
> (2) to
>     write a main script file test.input, and run this in the backround under
>     linux using the following command:
> 
> time nohup AXIOMsys < test.input > test.dat &
> 
>     The file test.input will call the above-mentioned functions. Each of the
>     functions can also call each other. I am using this approach in Matlab
>     extensively, but it is not clear how to do this in axiom (issues of
>     declaration/definition of functions in separate files, etc).  Any advice
>     would be much appreciated.

I'm not sure what's the problem. Maybe you want a .input file containing

)read funs1.input
)read funs2.input
...

?

If your operations are reusable, you might prefer "packages". These group
together operations that work for any domain in a specified category. If you
are interested, I'll expand.

> (The axiom manual seems to cover at length interactive command line
> programming while I am mainly interested in writing programs (in files) with
> calls to functions, also defined in files, etc.)
 
True.

Good luck,

Martin

PS: what's your scientific domain?