#OK to post homework
#Joseph Koutsoutis, 02-16-2025, Assignment 6

read `C6.txt`:

#1

AllHM2 := proc(K) local a,b,c,d,matrices:
  matrices := {}:
  for a from 1 to K do:
    for b from 1 to K do:
      for c from 1 to K do:
        for d from 1 to K do:
          matrices := matrices union {[[a, b+I*c], [b-I*c, d]]}:
        od:
      od:
    od:
  od:
  matrices:
end:


#2

RealSV2 := proc(K) local a,b,k,vectors:
  vectors := {}:
  for a from 1 to K do:
    for b from 1 to K do:
      k := sqrt(a^2 + b^2):
      vectors := vectors union {[a / k, b / k]}:
    od:
  od:
  vectors:
end:


#3

UncertaintyContest := proc(K) local matrices, vectors, A, B, V, smallest, biggest, ratio:
  matrices := AllHM2(K):
  vectors := RealSV2(K):
  smallest := [none, infinity]:
  biggest := [none, 0]:

  for A in matrices do:
    for B in matrices do:
      if Com(A,B) <> [[0,0], [0,0]] then:
        for V in vectors do:
          ratio := CheckUP(A,B,V):
          if ratio <> FAIL then:
            if ratio < smallest[2] then smallest := [[A,B,V], ratio]: fi:
            if ratio > biggest[2] then biggest := [[A,B,V], ratio]: fi:
          fi:
        od:
      fi:
    od:
  od:

  smallest, biggest:
end:


#UncertaintyContest(2) outputted 

# [[[[1, 2 + I], [2 - I, 2]], [[2, 2 + I], [2 - I, 1]], [sqrt(2)/2, sqrt(2)/2]], 0.6249999982], 
# [[[[1, 1 + I], [1 - I, 1]], [[1, 1 + 2*I], [1 - 2*I, 2]], [(2*sqrt(5))/5, sqrt(5)/5]], 6.519202426]

#UncertaintyContest(3) outputted

# [[[[1, 2 + I], [2 - I, 3]], [[3, 2 + I], [2 - I, 1]], [sqrt(2)/2, sqrt(2)/2]], 0.4999999972], 
# [[[[1, 2 + 3*I], [2 - 3*I, 3]], [[2, 3 + 2*I], [3 - 2*I, 2]], [(3*sqrt(13))/13, (2*sqrt(13))/13]], 51.69472778]

#where we note that simplify(CheckUP([[1, 2 + I], [2 - I, 3]], [[3, 2 + I], [2 - I, 1]], [sqrt(2)/2, sqrt(2)/2]))
#outputs 1/2 if the evalf is removed.