Help:=proc():print(`p(x,d,n),LS(x,n),LLS(x,n),Pol(x,y,n)`):
print(`h(x,n,d)`):
end:
with(Groebner):


p:=proc(x,d,n) local i:
add(x[i]^d,i=1..n):
end:

LS:=proc(x,n) local i,WL:
WL:=[seq(p(x,i,n),i=1..n)]:
WL:=gbasis(WL,plex(seq(x[n-i+1],i=1..n))):
end:

LLS:=proc(x,n) local W,i,i1:
W:=LS(x,n):

[seq(leadmon(W[i],plex(seq(x[n-i1+1],i1=1..n)))[2],
i=1..nops(W))]:
end:

#h(x,n,d): the complete homog. symm. polynomial
# in x[1], ..., x[n]
# of degree d
h:=proc(x,n,d) local i:
option remember:


if n=1 then
   RETURN(x[1]^d):
fi:

if d=0 then
   RETURN(1):
fi:

expand(add(h(x,n-1,d-j)*x[n]^j,j=0..d)):
end:

H:=proc(x,n) local i:
[seq(h(x,i,n+1-i),i=1..n)]:end:

Pol:=proc(f,x,y,n) local i,F,t:
F:=expand(subs( {seq(x[i]=x[i]+t*y[i],i=1..n)},f)):
{seq(coeff(F,t,i),i=0..degree(F,t))}:
end: