# hw 6 - Pablo Blanco
# OK to post

######
# Outputs ALL 2 by 2 matrices of the form
#
# [[a,b+I*c],[b-I*c,d]]
#
# where a,b,c,d, are integers such that 1 <= a,b,c,d <= K
#####
AllHM2:=proc(K) local a,b,c,d:
{seq(seq(seq(seq( [[a,b+I*c],[b-I*c,d]],a=1..K ),b=1..K  ),c=1..K ),d=1..K )}:
end:

#####
# Normalize(v): Helper function that returns a vector which is v normalized.
#####
Normalize:=proc(v) local n,N,i:
 n:=nops(v):
 N:=add(expand(v[i]*conjugate(v[i])) ,i=1..n):
 [seq(v[i]/sqrt(N) ,i=1..n)]:
end:

#####
# Generates all [a,b] with 1<=a,b<=K, then outputs the normalized [a,b]. 
# Note that this outputs FEWER than K^2 vectors. e.g., [3,3] and [4,4] are the same once normalized.
#####
RealSV2:=proc(K) local a,b:
 {seq(seq( Normalize([a,b]),a=1..K),b=1..K)}:
end:


UncertaintyContest:= proc(K):


end: