#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);