print(`This is Project 1.txt`);
print(`by Rachel Adelman, Sophie Droppa, Anna Janik, and Sydney Yao`);

Help := proc()
    if nargs = 0 then
        print("Table of Contents");

    elif nargs = 1 and args[1] = HW then
        print(`HW(u,v): The classical Hardy-Weinberg underlying transformation`);
        print(`with genotype frequencies (u,v,w) using w = 1 - u - v.`);
        print(`Try:`);
        print(`HW(u,v);`);

    elif nargs = 1 and args[1] = HWg then
        print(`HWg(u,v,M): The generalized Hardy-Weinberg transformation`);
        print(`that uses a positive 3×3 mating/survival matrix M.`);
        print(`Based on the full three-type system (u,v,w).`);
        print(`Try:`);
        print(`HWg(u,v, [[1,1,1],[1,1,1],[1,1,1]]);`);
    end if;
end proc:

#Classical HW 3 Variable Transformation 

HW := proc(u,v,w)
    [u^2 + u*v + (1/4)*v^2,
     u*v + 2*u*w + (1/2)*v^2 + v*w,
     (1/4)*v^2 + v*w + w^2];
end proc:

#HW 2 Variable transformation
HW:= proc(u,v)
    local w;
    w := 1 - u - v;
    expand([
        u^2 + u*v + (1/4)*v^2,
        u*v + 2*u*w + (1/2)*v^2 + v*w
    ]);
end proc:

# Generalized HW with 3 variable 
HWg := proc(u,v,w,M)
    local LI, tot;

    LI := [
        M[1][1]*u^2 + (M[1][2] + M[2][1])/2 * u*v + M[2][2]*(1/4)*v^2,

        (M[1][2]+M[2][1])/2*u*v
           + (M[1][3]+M[3][1])*u*w
           + M[2][2]/2*v^2
           + (M[2][3]+M[3][2])/2*v*w,

        M[2][2]*(1/4)*v^2
           + (M[2][3]+M[3][2])/2*v*w
           + M[3][3]*w^2
    ];

    tot := LI[1] + LI[2] + LI[3];

    [LI[1]/tot, LI[2]/tot, LI[3]/tot];
end proc:


#HW Generalized 2 Variable 

HWg := proc(u,v,M)
    local w, LI;
    w := 1 - u - v;
    LI := HW3g(u,v,w,M);
    normal([LI[1], LI[2]]);
end proc: