8 years, 17 days

## How to retrieve the coefficients of a tr...

Maple 2024

Hello

Consider,  as an example,  the following (simple) transcendental equation.

`alpha*((epsilon-1)*x+y-3*x*z-epsilon/3*x^3+b*sin(w)+3)`

How to retrieve the coefficients and the terms considering that the unknowns are x,y,z and w?   Something like [x,y,x*z,x^3,sin(w),1] and their coefficients.

many thanks

## Given that the solution of a PDE is know...

Maple 2024

Hello

I am trying to understand how to use Maple to solve a PDE.  Below it is a problem (Henon-Heilles system) where the answer is known.

```with(PDEtools);

infolevel[pdsolve]:=3:

declare(Hamil(x,y,u,v));

PDEHamil := u*diff(Hamil(x, y, u, v), x) + v*diff(Hamil(x, y, u, v), y) + (-2*x*y - x)*diff(Hamil(x, y, u, v), u) + (-x^2 + y^2 - y)*diff(Hamil(x, y, u, v), v) = 0;

pdsolve(PDEHamil)
```

Maple returns no solution, but one solution is:

```sH:=1/2*(u^2+v^2)+1/2*(x^2+y^2-2/3*y^3)+x^2*y;

simplify(eval(subs(Hamil(x,y,u,v)=sH,PDEHamil)));
0=0
```

What am I missing?

Many thanks.

## Help on how to solve (if possible) a PDE...

Maple 2024

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,

## How to retrieve the arguments of f_1 , t...

Maple 2024

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

## How to make (if possible) this procedure...

Maple 2024

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.

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