[Axiom-math] (no subject)

[cf]

5 December 2004

Dear Colleagues,
 
     I have started slowly translating my Matlab programs to axiom, and
     am experiencing some difficulties. The type system of axiom is
     very advanced. However, its not clear to me at this stage
     how to implement in axiom certain basic operations that I can
     implement relatively easily in Matlab. I have written a test program
     file test.input with some questions (as comments) and pasted this
 below. 
     You can  run this in axiom with: )read test.input;
 
 
 
 --Test program file test.input for basic manipulations.
 --qi, i=1,..,n=3 are the generalized co-ordinates (functions of time t),
 --and pi = derivative of qi wrt to time t, i=1,..,n=3.
 
 
 --In Matlab it is possible to "convert" strings to symbolic variables
 --as follows: n=3; qt = sym(zeros(n,1)); pt = sym(zeros(n,1)); 
 --for i=1:n, qt(i)=sym(['q',int2str(i),'(t)']); 
 --pt(i) = sym(['p',int2str(i),'(t)']); end;
 
-- IS THERE A WAY OF DOING THE ABOVE IN AXIOM ??? So far I could only
--find  the following method.
 
 q1:=operator 'q1
 q2:=operator 'q2
 q3:=operator 'q3
 
 p1:=operator 'p1
 p2:=operator 'p2
 p3:=operator 'p3
 
 gt := q1(t)*q1(t) + p1(t)*sin(q2(t)) + p2(t)*cos(q3(t)) + p3(t)
 
 dgtdt:= D(gt,t)
 
 
 dgtdt := (rule D(q1(t),t) == p1(t)) dgtdt;
 dgtdt := (rule D(q2(t),t) == p2(t)) dgtdt;
 dgtdt := (rule D(q3(t),t) == p3(t)) dgtdt
 
 
 --I want to "supress the t" in the expression gt and
 --obtain: g = q1*q1 + p1*sin(q2) + p2*cos(q3) + p3.
 --Then take the derivative of g wrt the qi's, and pi's, i=1,..,n=3.
 
 --In Matlab I do this as follows: 
 --q = sym(zeros(n,1)); p = sym(zeros(n,1)); 
 --for i=1:n, q(i)=sym(['q',int2str(i)]); p(i) = sym(['p',int2str(i)]);
--end;
 --g = subs(g,qt,q); g = subs(g,pt,p);
 
 --IS THERE A WAY OF DOING THE ABOVE IN AXIOM ??? So far I could only find
 --the following method. 
 
 
 g := (rule (q1(t) == qw1; q2(t) == qw2; q3(t) == qw3; p1(t) == pw1; p2(t)
== pw2; p3(t) == pw3))gt
 
 dgdqw1 := D(g,qw1)
 dgdqw2 := D(g,qw2)
 dgdqw3 := D(g,qw3)
 
 dgdpw1 := D(g,pw1)
 dgdpw2 := D(g,pw2)
 dgdpw3 := D(g,pw3)
 
 --end of program.


Thanks very much.

Regards,

C. Frangos.

------
Constantine Frangos.
Professor
Dept. of Mathematics and Statistics
Rand Afrikaans University
P O Box 524
Auckland Park 2006
South Africa

Tel: +27-11-489-2452
Fax: +27-11-489-2832
e-mail: address@hidden (work)
              address@hidden (home)