Help:=proc(): print(`Imply(R,L,W), ES(R,L,W,m)`): 
print(`Closure1(R,L,F,m) `):
end:

with(combinat):

#Implementing p. 5 of the Alon-Boppana paper
#Combinaorica 7(1)  (1987) 1-22

#Imply(R,L,W): inputs pos. integers R and L
#and a list of length R of sets (of integers) W
#and outputs the set of all elements that belong
#to AT LEAST two of the sets in the list W
#If its cardinality <=L OR returs FAIL if it >L
Imply:=proc(R,L,W) local S,i,j:



if nops(W)<>R then
  ERROR(`Size of W should be equal to`, R):
fi:

if {seq(type(W[i],set),i=1..R)}<>{true} then
  ERROR(`W should be a list of sets`):
fi:

if {seq( evalb(nops(W[i])<=L),i=1..R)}<>{true} then
ERROR(`W should be a list of sets of at most `, L, ` elements `):
 
fi:

S:= {seq(seq(op(W[i] intersect W[j]),j=i+1..R),i=1..R) }:

if nops(S)>L then
 RETURN(FAIL):
else
 RETURN(S):
fi:

end:




#ES(R,L,W,m): inputs pos. integers R and L
#and a list of length R of sets (of integers) W
#and a positive integer m,
#and outputs the set of sets of all elements that belong
#to AT LEAST two of the sets in W and
#all their supersets in {1, ..., m}
#If its cardinality is <=L OR returs FAIL if it >L
ES:=proc(R,L,W,m) local S,extra,i,F,susan,WCBI, susan1:
S:=Imply(R,L,W):

if S=FAIL then
  RETURN({}):
fi:

F:={S}:

extra:=L-nops(S):

WCBI:={seq(i,i=1..m)} minus S:

for i from 1 to extra do

susan:=choose(WCBI,i):

 F:= F union {seq(S union susan1, susan1 in susan)}:

od:

F:

end:









#Closure(R,L,F): Inputs pos. integers R and L
#and a family of sets of integers, F
#and outputs its closure (aS defined in page 5 of
#the Alon-Boppana paper
Closure:=proc(R,L,F) local F1:

F1:=F:




end:

#Closure1(R,L,F,m): Inputs pos. integers R and L
#and a family of sets of integers, F
#and outputs ONE extra set implied by SOME
#subfamily of R sets in F
Closure1:=proc(R,L,F,m) local Jake,Clubs, club,tay:




Clubs:=choose(F,R):

for club in Clubs do

tay:=ES(R,L,convert(club,list),m):

if tay minus F<>{} then
  RETURN(F union tay):
fi:

od:
FAIL:
 




end: