# hw14 - Pablo Blanco
# OK to post

read(`C14.txt`):


RandomBell1:=proc(K) local V,ra,i,N,T,A0,A1,B0,B1:
 A0:=C1QG()[4]:
 A1:=C1QG()[2]:
 B0:=-expand((C1QG()[2]+C1QG()[4])/sqrt(2)):
 B1:=expand((C1QG()[2]-C1QG()[4])/sqrt(2)):

 ra:= rand(-K..K):
 T:=[seq(ra(),i=1..8)]:       # generates coefficients of un-normalized V
 N:=sqrt(add(T[i]^2,i=1..8)): # determines normalization scalar
 V:=[seq(T[2*i+1]/N+I*T[2*i+2]/N,i=0..3)]: # reads off coefficients and scales them]

 simplify(Bell(A0,A1,B0,B1,V));
end:

##############
# results of RandomBell(10,1000):
# average: ~0.03310509368                     --- guess of true value: 0
# refuted counter: 13                         --- this was often 12
################

RandomBell:=proc(K,N) local val,vioCo,i,curr:
 val:=0: # total value obtained
 vioCo:=0: # counts the number of times Einstein is refuted
 for i from 1 to N do:
  curr:=RandomBell1(K):
  val+=curr:
  if curr^2 > 4 then
   vioCo++:
  fi:
 od:


 val/N,vioCo:
end: