#C16.txt, Dr. Z. ExpMath, March 25, 2019
Help:=proc(): print(` GuessWhoS(x,N), ManyGWS(N,K,t), GuessWhoC(x,N) , SEnt(P) `): 
print(`Profile(n,k), ABTP(N,k) `):
end:

#Simulating a stupid guess who game with a nunmber from 0 to N
GuessWhoS:=proc(x,N) local co,i:
co:=0:
for i from 0 to N do
#print(`Is the number equal to`, i):
 co:=co+1:
 if x=i then
   RETURN(co):
 fi:
od:
FAIL:
end:

#ManyGHS(N,K,t): the prob. generating function using variable t
#fof K Guess who games, followed by the average and s.d.
ManyGWS:=proc(N,K,t) local ra,i,f,mu,sig,f1:

ra:=rand(0..N):

f:=add(t^GuessWhoS(ra(),N),i=1..K)/K:
mu:=subs(t=1,diff(f,t)):
f1:=f/t^mu:
sig:= sqrt(subs(t=1,diff(t*diff(f1,t),t))):
[evalf([mu,sig]),sort(evalf(f))]:
end:


#Simulating a clever guess who game with a nunmber from 0 to N
GuessWhoC:=proc(x,N) local co,L,U,U0:
L:=0:
U:=trunc((N-1)/2):

co:=0:

while L<U do
#print(`Is the nunber between`, L,` and `, U , `including both`):
 co:=co+1:
if x>=L and x<=U then
 
   U:=trunc((U+L)/2):
  
else
   U0:=U:
   U:=trunc(U+(U-L)/2):
   L:=U0+1:
fi:
od:
co:
end:

#SEent(P): The (Shannon) amount of information in bits of the discere prob. distribution P
SEnt:=proc(P) local i:
if not (type(P,list) and min(op(P))>0 and convert(P,`+`)=1) then
 print(`bad input`):
 RETURN(FAIL):
fi:
-add(P[i]*log[2](P[i]),i=1..nops(P)):
end:

 
#[[Name,[DescriptiveFeature1, ..., DescriptiveFeature],targetFeature] , ...]

#Profile(n,k): inputs a positive integer n and k outputs
#a list of 0,1 of length k whose i-th item is "Is n divisible by prime[i]" for i from 1 to k
#For example
#Profile(10,3) should output [1,0,1]
Profile:=proc(n,k) local i:
subs({true=1, false=0},[ seq(evalb(n mod ithprime(i)=0),i=1..k)]):
end:

 
#Inputs a positive integer N and pos. integer k outputs an ABT
#for the data generated from them using the k descriptive features
#is it divisible by the k-th prime 
ABTP:=proc(N,k) local n:
[ seq([n,Profile(n,k), isprime(n)],n=1..N)]:
end: