#Please do not post homework
#James Betti, 2 Feb 2025, Assignment 2

TotClique := proc(G,k):
    [nops(Cliques(G,k)),nops(Cliques(Comp(G),k))];
end:

CheckRamsey := proc(k,K) local i,G,c,m:
    m := infinity;
    for i from 1 to K do
        G := RG(18,1/2);
        c := TotClique(G,k);
        m := min(m, min(c[1], c[2]));
    od:
    m;
end:

EstimateAverageClique := proc(n,p,k,K) local tot,i,G:
    tot := 0;
    for i from 1 to K do
        G := RG(n,p);
        tot := tot + nops(Cliques(G,k));
    od:
    tot / K;
end:

# Takes quite a while to run…
EstimateAverageClique(10,1/2,4,10000);
# My estimate is 6547/2000 ≈ 3.2735

# Below is some ``Maple V Primer'' scrap work.

L := a+b+2*c+3*d;
op(L);
nop(L);
ops(3,L);

L1 := [x,y,z,y];
L2 := [a,b,c];
L := [op(L1),op(L2)];

f := x->x^2-3*x+5;
g := (x,y)->x*y/(1+x^2+y^2);
simplify(g(sin(t),cos(t)));

sum(i^2,i=1..10);
sum(i^2,i=1..n);

Limit((x^2-4)/(x-2),x=2);
value(%);
limit((x^2-4)/(x-2),x=2);

D(x->exp(x));

Int(Int(y*sin(2*x+3*y^2),x),y);
value(%);

y := 1/sqrt(1-x);
taylor(y,x=0,5);