Dear all,
  I have a  Boolean polynomial f with huge degree & variables.
Also it has huge number of monomials.
I want to delete all monomials from f with degree greater
than 20. For that I have written the following approach.

V=BooleanPolynomialRing(4,['r%d'%(i) for i in range(4)])
V.inject_variables()
f=r0+r1*r2+r1*r2*r3
print f.degree()
A=f.monomials()
g=0
for i in range(Set(A).cardinality()):
 if((A[i]).degree()>=2):
    g=g+V(A[i])

f=f+g
print f

But observed that for my actual case, it is very slow. Will you
kindly give any better idea?

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