Hello,

I need to check if Maple can solve a specific PDE. Since I don't know much about the PDEtools package, I wonder if a user familiar with it and experienced in solving PDEs could help me.

with(PDEtools);
declare(u(x,y,z,w));
PDE1:=alpha*(y+b*(w))*diff(u(x,y,z,w),x)+(x+z-b*(w))*diff(u(x,y,z,w),y)-c*y*diff(u(x,y,z,w),z)+d*(y-x)*diff(u(x,y,z,w),w)=0;
Sol1:=pdsolve(PDE1);

Maple returns NULL as the solution. Any ideas on how to obtain a solution, if possible? In other similar PDEs, u(x,y,w,z) has a quadratic form.

Many thanks,

Hello

I am trying to solve some PDEs using Maple.  In one of them, Maple returns

SolL:= HL(x, y, z) = f__1(1/2*(2*sigma*z - x^2)/sigma, rho^2 - 2*rho*z + y^2 + z^2)

How to retrieve only the arguments of f__1?  

Many thanks

Hello

I have the following procedure that uses the Lie Derivatives of a vector field to build a set of equations.

LieDerList:=proc(h::symbol,f::list,vars::list)
description "This function returns the system of equations based on the Lie derivative.":
local i,n:=numelems(vars),L:=Array(0..n):
L[0]:=h:
for i from 1 to n do
    L[i]:=inner(f,map((a,b) -> diff(b,a),vars,L[i-1])):
end do:
return(zip((w,v)->simplify(w-v),[seq(L)],[seq](cat(h,i),i=0..n))):
end proc:

Below it is an example on how to call the procedure.

I used CodeTools:-ThreadSafetyCheck to check all the procedures used within LieDerList and LieDerList itself, but nothing wrong came out. However when I try to run 

LieEq4:=Threads:-Map(w->LieDerList(x,w,[x,y,z]),models4):

where models4 is a list of 1765 elements, maple returns "Error, (in factors) attempting to assign to `LinearAlgebra:-Modular:-Create` which is protected". If I change Threads to Grid, there is no problem at all.  

What am I overlooking? Is there a method to ensure the procedure is thread-safe?

Many thanks.   

PS.  I found one problem - inner, which is related to LinearAlgebra package, is not thread-safe.  

Hello,

I'm seeking an efficient solution to a particular problem. To illustrate, I'll provide a simplified example, though in practice, I'm handling lists with millions of elements.

Let's take the list, l: [1, 2, 3, 4, 5, 6, 7, 8]. Each element in this list has a corresponding twin. For instance, 1 has twins [4, 5], and 2 has twins [9, 12] (note that 12 is not in the original list, but that's not problematic). The complete list of twins is represented as t: [[4, 5], [9, 12], [6, 8], [1, 5], [1, 4], [3, 8], [13, 14, 17], [3, 6], [2, 12], [11, 12, 15]], and the twins are made available as they are needed.

The objective is to remove all twins starting from the first element of the list. Once a twin is removed, there's no need to check for twins for that particular element. For example, consider the first element, 1; the twins [4, 5] are removed, and there's no need to find the twins for those elements. The desired outcome would be the list [1, 2, 3, 7,10].

My solution utilizes a combination of a while loop and sets. However, it's painfully slow when dealing with lists larger than a few hundred thousand elements. 

Many thanks.  

Hello

I need to share some results with a colleague who is not a user of Maple, and a way to do this is by using the Tabulate (plain command and not from DocumentTools) function to format them. In the worksheet, the output looks good, but when I try to print it or save it as a PDF, only a few lines are printed. It appears that Maple is not able to break the tables into multiple pages for printing.

The output is a table with 77 rows and 30 columns.   

I welcome alternative solutions to the problem of displaying the results. 

Many thanks