print(`This is PIE, a Maple package written by the`);
print(`Experimental Math class taught by Dr. Z during`);
print(`Spring 2011.`);

with(combinat):

#====================================================================
Help := proc()
if nargs=0 then
        print(`contains the following procedures:`);
        print(`PIE(L),AND1(C1,C2,n)`);
elif nargs=1 and args[1]=PIE then
        print(`PIE(L):`);
        print(`Inputs a list of sets, L, and outputs the number`);
        print(`of elements in their union `);
        print(`For example, try:`);
        print(`PIE([{1,3},{2,3}])`);
elif nargs=1 and args[1]=AND1 then
        print(`AND1(C1,C2,n):`);
        print(`Inputs two clauses, C1 and C2, in n variables (expressed`);
        print(`as sets of integers from the set {-n,...,-1,1,...,n}) finds`);
        print(`their AND`);
fi;
end:

#====================================================================
PIE := proc(L)
local co,i,S,s,m;

m := nops(L);
co := add(nops(L[i]),i=1..m);

for i from 2 to m do
        S := choose(L,i); #print(S);
        co := co + (-1)^(i-1)*add(nops(`intersect`(op(s))),s in S);
od;

RETURN(co);

end:

#====================================================================
AND1 := proc(C1,C2,n)
local C,i;

C := C1 union C2;
for i from 1 to n do
        if member(i,C) and member(-i,C) then
                RETURN(0);
        fi;
od;

RETURN(C);


end: