1500 Reputation

19 years, 104 days

I dont see......

@asa12 I dont see what eq2, eq3, eq4 are.

Collect....

@shzan It seems collect, distributed was needed in this example.

function_coeffs := proc(A, v::set(name))
local S, T;
S := indets(A, {function});
S := select(has, S, v);
T := {Non(map(identical, S))};
frontend(proc(A, S) local V; (proc(E, S, N) [coeffs](collect(E, S, distributed), S, N) end)(A, S, 'V'), [V] end, [A, S union v], [T, {}])
end;

A:=a[1](x)*v*u+a[2](x)*v*D(u)-(D(a[2](x))*v+a[2](x)*D(v))*u;

function_coeffs(A,{u,v});

[-a[2](x), a[1](x)-D(a[2](x)), a[2](x)], [u*D(v), u*v, D(u)*v]

A cleaner version follows (there was a remainder from a previous attempt):

function_coeffs := proc(A, v::set(name))
local S, T;
S := indets(A, {function});
S := select(has, S, v);
T := {Non(map(identical, S))};
frontend(proc(A, S) local V; [coeffs](collect(A, S, distributed), S, 'V'), [V] end, [A, S union v], [T, {}])
end;

Verify....

Can you verify this is your formula:

f2_new:=1/2*N*(cos(theta[2])+cos(theta[1]))*Omega+(1/2*(X+Y)*sin(theta[1])*cos(phi[1])*lambda[a]+1/2*(X-Y)*sin(theta[2])*cos(phi[2])*lambda[b])*N^(1/2)*omega^(1/2)+(1/2*omega*X^2+1/2/omega*P[X]^2)*(-kappa+omega)+(1/2*omega*Y^2+1/2/omega*P[Y]^2)*(kappa+omega);

No solutions?...

@AfshinK Maple gave a solution with a parameter: _NN1. Maybe you need to explore this option.

{t__ij = -1/(-m+1)*LambertW(_NN1,(-m+1)*m*d^2/theta*exp(-(-m+1)*(-1-c*t__kj-m^2*eta*((exp(t)-1)/exp(t))^m/(exp(t)-1)/theta)))+1+c*t__kj+m^2*eta*((exp(t)-1)/exp(t))^m/(exp(t)-1)/theta};

Old problem....

@Carl Love This Maple is one of the very early versions. It is quite limited. I now recall this very problem from ago. For ill conditioned  polynomials, at higher precision, factor and fsolve runs into "Unable to compute maxnorm". evalf(fsolve(rho_poly),31); fails and evalf(fsolve(rho_poly),30); succeeds. Refining RootOfs fails for select roots, but isolating them enables progress and higher accuracy at a slow rate. 24 roots were identified with least precision of 371 digits. Maximum residual for these is .56481e-347.

These problems were unexpected. I thought this occurence explained difficulties in the originating problem, but I was mistaken.

Precision....

@Carl Love I tried alot. My Maple gave me some trouble. I think this old version is weak or even bugged in this task. Do you see any precision issues? At 500 Digits with most factors I've obtained remainder of 10^(-460), but with a few (8 total I think) only 10^(-12).

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