#C12.txt

Help12:=proc(): print(`Ex1(), RG(n,K), FM(f,n), BM(f,n) `): end:

Ex1:=proc():table([({3})=18,({2})=12,({})=0,({1, 3})=60,({2, 3})=90,({1, 2})=30,({1})=6,({1, 2, 3})=120]):end:


with(combinat):

#RG(n,K): inputs an and K outputs a random "n-person game" with entries in [0,K]
RG:=proc(n,K) local ra,PS,S,f:
ra:=rand(0..K):
f[{}]:=0:
PS:=powerset(n):

for S in PS minus {{}} do
f[S]:=ra():
od:
op(f):
end:

#FM(f,n): inputs a function from 2^{1,...n} to pos. real numbres
#we want g(T)= Sum of g(S) over all subsets S of T
FM:=proc(f,n) local S,PS,PN,g,S1:
PN:=powerset(n):
for S in PN do
PS:=powerset(S):
g[S]:=add(f[S1], S1 in PS):
od:
op(g):
end:

#BM(f,n): inputs a function from 2^{1,...n} to pos. real numbres
#we want g(T)= Sum of (-1)^(|T|-|S|)*g(S) over all subsets S of T
BM:=proc(f,n) local S,PS,PN,g,S1:
PN:=powerset(n):
for S in PN do
PS:=powerset(S):
g[S]:=add( (-1)^(nops(S)-nops(S1))*f[S1], S1 in PS):
od:
op(g):
end: