#hw8, Isaac Lam, February 15 2024

#Old code

# returns matrix M in standard form
SFde:=proc(q,M) local k,n,i,j,S,rj,cj,ri:
    k:=nops(M);
    n:=nops(M[1]);
    S:=copy(M);

    for i from 1 to k do: # algorithm is iterated from 1 to k
        # if S_ii = 0, then we need to perform a swap:
        if S[i,i] = 0 then 
            for j from i+1 to k while S[j,i] = 0 do od; # look for available row

            if j<=k then # swap rows
                rj:=GetRow(S,j);
                S:=SetRow(S,j, GetRow(S,i));
                S:=SetRow(S,i,rj);

            else # look to swap columns

                for j from i+1 to n while S[i,j] = 0 do od; # look for available col

                # swap cols
                cj:=GetCol(S,j);
                S:=SetCol(S,j, GetCol(S,i));
                S:=SetCol(S,i,cj);
            fi;
        fi;

        # scale row to have leading entry 1
        ri:=GetRow(S,i);
        ri:=(ri*(ri[i]&^(-1) mod q)) mod q;
        S:=SetRow(S,i,ri);

        for j from 1 to k do:
            if j <> i then
                rj:=GetRow(S,j);
                rj:=(rj - (rj[i] * ri mod q)) mod q;
                S:=SetRow(S,j,rj);
            fi;
        od;
    od;

    return S;
end;

#End of old code

with(NumberTheory);
with(LinearAlgebra[Modular]);
WtEnumerator := proc(q, M, t) local totalWeight, currWeight, currVector, alph, i, j, currNum, currLinCombo, sF;
alph := [0, 1]; 
sF := SFde(q, M); 
for i to t do 
     if nops(PrimeFactors(i)) = 1 then alph := [op(alph), i]; end if; 
end do; 
for i from 0 to nops(sF)*nops(alph) do 
     currLinCombo := convert(i, 'base', nops(alph)); 
     currVector := seq(0, i = 1 .. q); 
     for j from nops(sF) - nops(currLinCombo) + 1 to nops(sF) do 
         currVector := Mod(t, currVector + sF[j]*alph[currLinCombo[j + nops(currLinCombo) - nops(sF) - 1]]); 
     end do; currWeight := 0; 
     for j to q do 
         if currVector[j] <> 0 then currWeight := currWeight + 1; end if; 
     end do; 
     totalWeight := totalWeight + t^currWeight; 
end do; 
totalWeight; 
end;