Do you know some mathematical theory that might help writing a procedure?
Some classic algorithm for computing the GCD, for example?
Something known 2000 years ago?
---
G A Edgar

libname := "/Users/edgar/Documents/Maple/advisor",libname,"/Users/edgar/Document
s/Maple/algolib 8":
currentdir("/Users/edgar/tmp/"):
plouffe := "/Users/edgar/Documents/Maple/ myfiles/inverter.mpl":

I think I may have found the source of this error. Basically, the
driver requires the fonts in the 'afm' folder of the Maple installation.
However, it will only attempt to find the folder by moving up one
directory from 'currentdir()'.
Try running the command:
>currentdir("Library/Frameworks/Maple.framework/Versions/10/bin.APPLE_UN
IVERSAL_OSX");
at the beginning of your worksheet. Then, when you set the plotoutput,
use a full pathname like:
plotsetup=(ps,plotoutput=`/Users//Desktop/aa.ps`);
where is your OSX login name. Maple should be able to find
the proper fonts to render the .ps file, and write this file to your
Desktop.
It appears that this behaviour has been corrected in Maple 11.
Sincerely,
Bill
Maplesoft Technical Support
www.maplesoft.com/support

To get the closed form for A^k ...
Diagonalize A, say A = U D U^(-1) where D is a diagonal matrix. The entries of
D are the eigenvalues of A, and the columns of U are the eigenvectors.
[Let's assume r2^2+2*r2*r1*X+r1^2*X^2+4*X-4*r1*X-4*X*r2 is
not zero, so the two eigenvalues are different. Then the symbolic
solution for the eigenvectors is OK.]
Then D^k is easy to compute, and A^k = U D^k U^(-1) is your answer.
---
G A Edgar

You have some sort of strange evaluation. After your stuff, I get this...
> D5(14);
-770
> sum('D4(14-i)',i=1..10);
715
> sum(D4(14-i),i=1..10);
-770
> sum(D4(14-j),j=1..10);
715
I normally use expressions and not functions, so I cannot say what is going on here...
Something like: the expression in D4 involves a sum on the variable i,
and now you are doing ANOTHER sum on the same variable i, so they get confused?

Maple 10 ...
> G := (i,j) -> if is(i,even) and is(j,even) then 1; else 0; fi;
(i, j) -> if is(i, even) and is(j, even) then 1 else 0 fi;
> G(2,3);
0
> G(2,4);
1
---
G A Edgar

try some of the Tutors...
Tools > Tutors > Precalculus > ...
---
G A Edgar

What is a dae? An acronym I don't know? A misspelled word?
---
G A Edgar

For this
Int((x^2+x+1)/sinh(x-1/x)*exp(-I*(x-1/x)*theta),x=–infinity+I*0.. +infinity+I*0)
I would do something like this:
f := x -> (x^2+x+1)/sinh(x-1/x)*exp(-I*(x-1/x)*theta);
Int(f(s+I*0),s=-infinity..infinity);
But in this case you can just say
Int(f(s),s=-infinity..infinity);
---
G A Edgar

You wrote:
f(x) = 2.3x
which is probably not what you want.
To define a function f, write:
f := x -> 2.3*x;
or
f := unapply(2.3*x,x);
To define an expression instead, write:
f := 2.3*x;
---
G A Edgar

The point is, the "simplification" b^u*b^v -> b^(u+v) is WRONG in general for complex b.
That is (perhaps) why Maple does not do it automatically.
If you really want it, you can say:
simplify(%,symbolic);
or
simplify(E) assuming b::real;
---
G A Edgar

Learning math will help in your engineering studies. And getting us to do your math for you is not the best way. However, one of these is related to Maple, so I provide a hint...
sketch the following: 1.)x=t^(3), y=t^(2);
> plot([t^3,t^2,t=-5..5],x=-2..2,y=-2..2);
Try the others yourself: adjust the numbers to get a graph that looks good,
showing the main features of the particular problem.
The rest are math (convert to rectangular, find dy.dx, find area), not Maple, so you should try to do them yourself.
---
G A Edgar

**> eq1 := a+b+c=k*h-h-h*h+1;**

**> eq2 := (p-k+h)*(p-h-1)*(p-1)-(p-k)*(p-2)*(p)=a*(p-1)+b*(p-h-1)+c*(p-k+h);**

**> kk := solve(eq1,k);**

**> subs(k=kk,eq2);**

**> i1 := isolve(%);**

So the integer solution of this has arbitrary values for and

**> subs(i1,kk);**

So for k to be an integer, we need divides . That is, where is an integer.

**> j1 := {c=1,b=1,a=r*h-1,k=h+r+1};**

Check that this is a solution:

**> expand(subs(j1,eq1));**

**> expand(subs(j1,eq2));**

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You might use : everywhere, so nothing prints automatically, then put in "print" statements for what you actually want to print. The "print" statements can be inside "for" loops and
"if" blocks, for example.
---
G A Edgar

Look up "variation of parameters" in a standard textbook, and see if it is related.
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G A Edgar