I do not know this is easier, but it is more transparent.

A := (Cq = Cao*k1*t/(1+k1*t)/(1+k2*t));
X := {A}, {Cq}(t), {Cq};
Aextremas := `@`(S -> collect(S, RootOf, distributed, factor), evala, proc () _EnvExplicit := false;[solve](args) end proc)({A, D(Cq) = 0} union implicitdiff(X, t) union implicitdiff(X, t, t), {t} union map2(`@@`, D, {`$`(0 .. 2)})(Cq));
map(allvalues, Aextremas);

Plainly:

A:=[2,4,6,8,10,12];
m:=proc(x,L) local i; if member(x,L,'i') then i else NULL end if end proc;
m(4,A);
m(3,A);

 gives:

.

AFAIK thre is no way to sort those. Maple will display sum terms according to "in-memory address" ordering and you can not change that. You can always try this:

Look up ?extrema

Simply put you are trying to compute this:

@Honigmelone 

Please test the above code. Let me know the cases that dont work.

Try the above.

posting:
http://www.mapleprimes.com/questions/207267-Coefficients-Of-Differential-Polynomial#comment223370

Lookup ?frontend. It is intended precisely for your task.

Try with:

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 proc, [A, S union v], [T, {}])
end proc;

eq := (-Omega^2*a*A[2]-Omega^2*m*B[1]+Omega*A[1]*c[1]+B[1]*k[1])*cos(Omega*t)+(Omega^2*a*B[2]-Omega^2*m*A[1]-Omega*B[1]*c[1]+A[1]*k[1])*sin(Omega*t) = 0;

function_coeffs(lhs(eq),{t});

gives:

[-Omega^2*a*A[2]-Omega^2*m*B[1]+Omega*A[1]*c[1]+B[1]*k[1], Omega^2*a*B[2]-Omega^2*m*A[1]-Omega*B[1]*c[1]+A[1]*k[1]], [cos(Omega*t), sin(Omega*t)]

I think this is safe to use:

restart;
A := a, positive, k, positive, Omega, positive, m, positive, -something - 2, positive; assume(A);
Q := -4*k*m+2*Omega^2*a^2*something+Omega^2*a^2*something^2;
u:=-Omega*a*sqrt(2)*sqrt(-Omega^2*a^2-2*k*m+sqrt(Omega^2*a^2*(Omega^2*a^2+4*k*m)))/(-Omega^2*a^2+sqrt(Omega^2*a^2*(Omega^2*a^2+4*k*m)));

`@`(normal,simplify)(u,[Q],[k,something]);

F1 := proc(S, F) local x, f; f := unapply('hastype'(x, F(map(identical, S))), x); (remove, select)(f, S) end proc;
A := F1(indets(eq, anyfunc(dependent(t))), anyfunc);
subs(seq(A[2][i] = cat(K, i), i = 1 .. nops(A[2])), eq);

restart;
A:=a,positive,k,positive,Omega,positive,m,positive,Z,positive,-1+V,positive;interface(showassumed=0),assume(A);
u:=-Omega*a*sqrt(2)*sqrt(-Omega^2*a^2-2*k*m+sqrt(Omega^2*a^2*(Omega^2*a^2+4*k*m)))/(-Omega^2*a^2+sqrt(Omega^2*a^2*(Omega^2*a^2+4*k*m)));

P := Z^2*Omega^2*a^2-k*m, 1+4*Z^2-V^2;
`@`(factor,simplify)(u,[P],[k,Z,V]); #m works too
`@`(expand,solve)({P},{Z^2,V^2});
about(V,Z);

this should work too:

createModule3 := proc(A::Matrix(square))
    local dim;
    dim := RowDimension(A);
    module()
        export det;
        det := (proc(dim) (x::Matrix(1..dim,1..dim)) -> Determinant(x) end proc)(dim);
    end module
end proc:

createModule3(Matrix(2)):-det(IdentityMatrix(2));

Does the above work?

Arguments to procedures are themselves not variables and in your createModule2 you use dim as variable and not parameter.

restart;
A:=interface(showassumed=0),assume(x,real),factor(ln(sqrt(x-12)/(-x^(2)+15*x)));((expr,var)->solve({`@`(evalc,Re)(expr)>=0,`@`(evalc,Im)(expr)=0},var))(op(1,A),{x});
plot(A,x=12..15,scaling=constrained,axes=boxed,thickness=3);

#Gives
# A := ln(-(x-12)^(1/2)/x/(x-15))
# {x < 15, 12 <= x}

With small expressions it is hard to observe facilities at work.

interface(version);
mf:=unapply('unapply(F(n),n),F,n'):
phi:=(1+sqrt(5))/2:

#   Maple Worksheet Interface, Release 4, IBM INTEL NT, Apr 16 1996

fn:=unapply(1/2*sqrt(-(u-1)*(u+1)*(u^2-u-1))*u*(4*u-3)/sqrt(u*(u-1)),u):
fn2:=assume(u1>1,u1<phi),mf(`@`(factor,combine,simplify,fn),u1):
fn2(u);

Gives:

#1/2*(4*u-3)*(-(u+1)*(u^2-u-1)*u)^(1/2)

plot([fn,fn2],1..phi,color=[khaki,black],thickness=[4,0],numpoints=100,adaptive=false);