Question: Equate two expressions

Hello!

Hope everything fine with you. Please check the following program

restart; a := 0; b := 1; Rd := .5; Ra := .2; Nc := .6; e := .2; Nr := .3; H := .9; Digits := 20;
with(LinearAlgebra);
L[0] := 1; L[1] := a+1-x;
M := 4; K := 1;
for n while n <= M do
L[n+1] := expand(-((x-2*n-a-1)*L[n]+(n+a)*L[n-1])/(n+1))
end do; printlevel := 2;
for m from 0 while m < M do
for n to 2^(K-1) do
psi[n, m] := simplify(sqrt(m+1/2.)*2^((1/2)*K)*(eval(L[m], x = 2^K*x-2*n+1)))
end do
end do;
f1 := simplify(sum(sum(c[p, q]*psi[p, q], q = 0 .. M-1), p = 1 .. 2^(K-1)));
u := collect(f1, [x], recursive);

u := -3.5276684147527874541*c[1, 3]*x^3+(4.4721359549995793928*c[1, 2]+21.166010488516724724*c[1, 3])*x^2+(-3.4641016151377545871*c[1, 1]-13.416407864998738178*c[1, 2]-34.394767043839677677*c[1, 3])*x+c[1, 0]+3.4641016151377545871*c[1, 1]+7.8262379212492639373*c[1, 2]+14.992590762699346680*c[1, 3]

f := 1+sum(A[i]*(x^(i+1)-(i+1)*x), i = 1 .. M-2)

f:=1+A[1]*(x^2-2*x)+A[2]*(x^3-3*x)

I want to equate the like powers of "x" in f ( mention as red) and u ( mention as red) for any values of M make a system of equations as

Eq[1]:=-3.5276684147527874541*c[1, 3] = A[2];

Eq[2]:=4.4721359549995793928*c[1, 2]+21.166010488516724724*c[1, 3] = A[1];

Eq[3]:=-3.4641016151377545871*c[1, 1]-13.416407864998738178*c[1, 2]-34.394767043839677677*c[1, 3] = -2*A[1]-3*A[2];

Eq[4]:=c[1, 0]+3.4641016151377545871*c[1, 1]+7.8262379212492639373*c[1, 2]+14.992590762699346680*c[1, 3] = 1;

and solve them for any values of A[1] and A[2];

Also attached the program Equate.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China