#OK to post homework #Joseph Koutsoutis, 03-02-2025, Assignment 11 read `C11.txt`: #1 VerifyMulAnBn := proc(k) local n, eq, A, B, i1, j1: for n from 1 to k do: A := An(n): B := Bn(n): if Mul(A, B) = [seq([seq(sqrt(n) * B[i1][j1], j1=1..nops(B[1]))], i1=1..nops(B))] then: printf("\#for n=%d evalb(Mul(An(%d)Bn(%d)) = sqrt(%d)Bn(%d) outputted true\n", n, n, n, n, n): else: return FAIL: fi: od: end: #I verified that Mul(An(n)Bn(n)) = sqrt(n)Bn(n) for n from 1 to 11 #2 IndNu := proc(G) local n, r: n := G[1]: for r from 1 to n do: if MinMaxNNpablo(G, r) > 0 then return r-1: fi: od: return n: end: #seq(IndNu(Gnd(n, 2)), n=3..15) outputted 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5 #seq(IndNu(Gnd(n, 3)), n=4..15) outputted 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 #3 UpperBoundMinMaxNN := proc(G, r, K) local n, V, i, ub, curr: n := G[1]: V := {seq(i, i=1..n)}: ub := infinity: for i from 1 to K do: curr := MaxNN(G, combinat[randcomb](V, r)): if curr < ub then: ub := curr: fi: od: ub: end: #UpperBoundMinMaxNN(Ck(8), 129, 5000) outputted 6