Re: [Axiom-math] input files, functions

[Martin Rubey]

Dear Constantine,

I tried your files, but it seems to me that they do work, in fact.

Given the two files

--testkinemat1.input

)read expandsincos.input

Acon := matrix([[1, 0, Lo2*cos(phi)+Lo1*sin(phi), -sin(delta1)*a, 0, 0, 0],_
                [0, 1, Lo2*sin(phi)-Lo1*cos(phi),  a*cos(delta1), 0, 0, 0],_
                [0, 1, Lo2*sin(phi)+Lo1*cos(phi), 0,  a*cos(delta1), 0, 0],_
                [1, 0,-Lo2*cos(phi)+Lo1*sin(phi), 0, 0, -sin(delta2)*a, 0],_
                [0, 1,-Lo2*sin(phi)-Lo1*cos(phi), 0, 0,  a*cos(delta2), 0],_
                [1, 0,-Lo2*cos(phi)-Lo1*sin(phi), 0, 0, 0, -sin(delta2)*a],_
                [0, 1,-Lo2*sin(phi)+Lo1*cos(phi), 0, 0, 0, a*cos(delta2)]])

detAcon:=determinant(Acon)

--detAcon:=factor(detAcon)

detAcon:=expandsincos(detAcon)

detAcon:=simplify(detAcon)

-- expandsincos.input
-- Basic trigonometric expansion rules for axiom.
-- cos(2*x) == cos(x)**2 - sin(x)**2

expandsincos := rule (sin(x+y) == sin(x)*cos(y) + sin(y)*cos(x); _
                      cos(x+y) == cos(x)*cos(y) - sin(x)*sin(y); _
                      sin(2*x) == 2*sin(x)*cos(x); _
                      cos(2*x) == cos(x)*cos(x) - sin(x)*sin(x)); 

typing

)read testkinemat1.input

does what is expected. Note that there must not be a semicolon after the
filename!
 
 > (1) I am trying to read expandsincos.input from within
 >     testkinemat1.input but this gives an error. Not clear why ??

I suspect that the error was something like

The file expandsincos.input; is needed but does not exist.

 > (3) I tried to write the script testkinemat1.input like a function
 >     without input or output variables (see below) but this gave
 >     errors. Not clear why ??

No! )read is a system command, not a "usual" operation. Sytem commands always
start with a ")". I believe that the want to be quite on their own, one per
line. 
 
 > (4) Any examples of how to write user functions calling other user
 >     functions, etc would be much appreciated. Especially the case
 >     where a function can return multiple variables eg. in matlab: 
 > 
 >     [x1,x2,x3] = func1(y1,y2,y3);

This just means that func1 is a function that returns a list. For example

(9) -> f:=(a,b,c)+->[a,b,c,a+b+c]

   Loading /home/martin/axiom/mnt/linux/algebra/ANON.o for domain 
      AnonymousFunction 
   (9)  (a,b,c) +-> [a,b,c,a + b + c]
                                                      Type: AnonymousFunction
(10) -> f(1,2,3)

   (10)  [1,2,3,6]
                                                   Type: List PositiveInteger


 > (5) In axiom what is the instruction to "pause" after the execution of
 >     a line, and continue after hitting enter ? eg in matlab: 
 >     a = 1 
 >     pause; 
 >     b = 3 
 >     pause;

Sorry, I don't know. Quite possible that such a thing does not exist.

All the best,

Martin

PS: do you use the Windows or Linux version?