#JUNIPER GREEN
#VERY PRELIMINARY VERSION

Help:=proc(): print(`M(n,P), e.g. M([10,[10,{}]);, WM(n,P), Wh(n,P), WMh(n,P) , mex(A) , G(n,P), Gh(n,P)   `):end:

with(numtheory):

mex:=proc(A) local i: 
if A={} then
 RETURN(FAIL):
fi:
for i from 0 while member(i,A) do od:i:end:


#EASY VERSION
#M(n,P): All the legal moves in Juniper Green with starting integer n, P=[m,S], where m is current integer m and "already used set" S. Try:
#M(10,[10,{}]);
M:=proc(n,P) local m,S,i,S1,m1:
option remember:
m:=P[1]:
S:=P[2]:

if P[1]=n and S={} then
S1:={seq(i,i=1..n)}:
else
S1:=divisors(m) union {seq(m*i,i=1..trunc(n/m))}:
fi:

S1:=S1 minus S:
{seq([m1, S union {m1}],m1 in S1)}:
end:

#WM(n,P): The set of winning moves in Juniper-Green starting with n and current state P. Try:
#WM(10,[10,{}]);
WM:=proc(n,P)  local gu,gu1,mu:
option remember:
gu:=M(n,P):
if gu={} then
 RETURN({}):
fi:

mu:={}:

for gu1 in gu do
 if WM(n,gu1)={} then
  mu:=mu union {gu1}:
fi:
od:
mu:


end:

#G(n,P): The Sprague-Grundy value of position P in EASY Juniper Green with starting integer n
G:=proc(n,P) local S,s:
option remember:

S:=M(n,P):

if S={} then
 0:
else
mex({seq(G(n,s),s in S)}):
fi:


end:

#HARD VERSION

#Mh(n,P): All the legal moves in Juniper Green Hard with starting integer n, P=[m,S], where m is current integer m and "already used set" S. Try:
#Mh(10,[10,{}]);
Mh:=proc(n,P) local m,S,i,S1,m1:
option remember:
m:=P[1]:
S:=P[2]:

if P[1]=n and S={} then
S1:={seq(2*i,i=1..trunc(n/2))}:
else
S1:=divisors(m) union {seq(m*i,i=1..trunc(n/m))}:
fi:

S1:=S1 minus S:
{seq([m1, S union {m1}],m1 in S1)}:
end:

#WMh(n,P): The set of winning moves in Juniper-Green starting with n and current state P. Try:
#WMh(10,[10,{}]);
WMh:=proc(n,P)  local gu,gu1,mu:
option remember:
gu:=Mh(n,P):
if gu={} then
 RETURN({}):
fi:

mu:={}:

for gu1 in gu do
 if WMh(n,gu1)={} then
  mu:=mu union {gu1}:
fi:
od:
mu:


end:

#Gh(n,P): The Sprague-Grundy value of position P in Hard Juniper Green with starting integer n
Gh:=proc(n,P) local S,s:
option remember:

S:=Mh(n,P):

if S={} then
 0:
else
mex({seq(Gh(n,s),s in S)}):
fi:


end: