#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