thank you very much for your input.
I guess I have a little catching up to do with regard to what a lab "workstation" is supposed to be. And I bet switching to linux and setting up the network will be an interesting challenge..

This is a good question, I have often asked myself the same thing.. :-)
Well, to begin with, I am currently doing it the hard way because the relations between some of the quantities involved are still unclear and I'm trying to draw some general conclusions. To be frank, I had not anticipated reaching the limits of Maple's symbolic solver so quickly. I'm solving a singular PDE via recursive taylor series and I need a lot more terms to ensure convergence.

*Does the matrix have some special structure that could make it easier (symmetric or sparse or a tree graph, perhaps)?*

I suspect that the investigation on the matrix's structure will be very interesting and it will probably be among the next things I do. I have a feeling it will turn out sparse but I have no idea whether it will have any symmetries etc.

*Do you want to see how the solution varies with some parameter? *

Yes that's also part of what I want to do. X[ i ]s are functions of several independent variables and I need to find the values that optimize a given function F of X[ i ]s

This is a good question, I have often asked myself the same thing.. :-)
Well, to begin with, I am currently doing it the hard way because the relations between some of the quantities involved are still unclear and I'm trying to draw some general conclusions. To be frank, I had not anticipated reaching the limits of Maple's symbolic solver so quickly. I'm solving a singular PDE via recursive taylor series and I need a lot more terms to ensure convergence.

*Does the matrix have some special structure that could make it easier (symmetric or sparse or a tree graph, perhaps)?*

I suspect that the investigation on the matrix's structure will be very interesting and it will probably be among the next things I do. I have a feeling it will turn out sparse but I have no idea whether it will have any symmetries etc.

*Do you want to see how the solution varies with some parameter? *

Yes that's also part of what I want to do. X[ i ]s are functions of several independent variables and I need to find the values that optimize a given function F of X[ i ]s

yes, i believe that is what I was looking for.
Thank you

yes, i believe that is what I was looking for.
Thank you

in windows XP Pro when I include the line
currentdir("c:\\workfolder"):
in maple.ini I get the warning
"Warning, system/ssystem calls have been disabled in the options dialog."
That didn't happen in Maple 10.
Also, when maple.ini was in \lib\ folder it was for some reason executed twice.. to stop this from happening I had to move it to \users\

in windows XP Pro when I include the line
currentdir("c:\\workfolder"):
in maple.ini I get the warning
"Warning, system/ssystem calls have been disabled in the options dialog."
That didn't happen in Maple 10.
Also, when maple.ini was in \lib\ folder it was for some reason executed twice.. to stop this from happening I had to move it to \users\

I tried using makeproc and it worked, now I have F as a function of X and ci_js (of X).
> F:=X->a1*c8_2(X) + a2*c6_5(X) + a3*c4_3(X) + {...} ;
> for i from MaxOrder by -1 to 1 do
> for j from 1 to op(1,Sols[i]) do
> cat(lhs(Sols[i][j])):=makeproc(rhs(Sols)[i][j],X): # this produces the various ci_js
> end:
> end:
The problem is that as I call eg. F(1), each ci_j is being evaluated again and again thousands of times inside higher order ci_js. The result is that the function does not return a value (I let it run for more than 24h)!
Obviously evaluating the same function thousands of times for the same point does not make much sense. Its value should be stored somewhere for quick access. I thought about using option remember but I could not figure how to use it with makeproc. codegen[optimize] claims to to something similar (using option remember). I tried creating the procedures with cat(lhs(Sols[i][j])):=optimize(makeproc(rhs(Sols)[i][j],X)): but saw no difference.
The above is only the latest method I have devised to solve this problem. I'm not at all certain it's the most efficient. What I'm looking for is a quick way to construct and use F(X) to produce numerical results.
thanks in advance
PS. to give a feel of the memory required: an 8th order coefficient c8_j(X) contains about 10000 c1_1(X)(+10000 c1_2(X)+ ...), 5000 c2_1(X)(+5000 c2_2(X)+...), 2500 c3_1(X)(+2500 c3_2(X)+...), etc

I tried using makeproc and it worked, now I have F as a function of X and ci_js (of X).
> F:=X->a1*c8_2(X) + a2*c6_5(X) + a3*c4_3(X) + {...} ;
> for i from MaxOrder by -1 to 1 do
> for j from 1 to op(1,Sols[i]) do
> cat(lhs(Sols[i][j])):=makeproc(rhs(Sols)[i][j],X): # this produces the various ci_js
> end:
> end:
The problem is that as I call eg. F(1), each ci_j is being evaluated again and again thousands of times inside higher order ci_js. The result is that the function does not return a value (I let it run for more than 24h)!
Obviously evaluating the same function thousands of times for the same point does not make much sense. Its value should be stored somewhere for quick access. I thought about using option remember but I could not figure how to use it with makeproc. codegen[optimize] claims to to something similar (using option remember). I tried creating the procedures with cat(lhs(Sols[i][j])):=optimize(makeproc(rhs(Sols)[i][j],X)): but saw no difference.
The above is only the latest method I have devised to solve this problem. I'm not at all certain it's the most efficient. What I'm looking for is a quick way to construct and use F(X) to produce numerical results.
thanks in advance
PS. to give a feel of the memory required: an 8th order coefficient c8_j(X) contains about 10000 c1_1(X)(+10000 c1_2(X)+ ...), 5000 c2_1(X)(+5000 c2_2(X)+...), 2500 c3_1(X)(+2500 c3_2(X)+...), etc