def less_than_n_solutions(ideal,n):
l=interred(ideal)
if not l:
return False
g=GroebnerStrategy(l[0].ring())
all_monomials=Monomial([Variable(i) for i
in xrange(number_of_variables())]).divisors()
monomials_not_in_leading_ideal=all_monomials
for p in l:
g.add_generator(p)
while g.npairs()>0:
monomials_not_in_leading_ideal=monomials_not_in_leading_ideal\
% g.reduction_strategy.minimal_leading_terms
if len(monomials_not_in_leading_ideal)<n:
return True
g.clean_top_by_chain_criterion()
p=g.next_spoly()
p=g.nf(p)
if not p.is_zero():
g.add_generator(p)
monomials_not_in_leading_ideal=monomials_not_in_leading_ideal\
% g.reduction_strategy.minimal_leading_terms
if len(monomials_not_in_leading_ideal)<n:
return True
else:
return False
def less_than_n_solutions(ideal, n):
l = interred(ideal)
if not l:
return False
g = GroebnerStrategy(l[0].ring())
all_monomials = Monomial(
[Variable(i) for i in xrange(number_of_variables())]).divisors()
monomials_not_in_leading_ideal = all_monomials
for p in l:
g.add_generator(p)
while g.npairs() > 0:
monomials_not_in_leading_ideal = monomials_not_in_leading_ideal \
% g.reduction_strategy.minimal_leading_terms
if len(monomials_not_in_leading_ideal) < n:
return True
g.clean_top_by_chain_criterion()
p = g.next_spoly()
p = g.nf(p)
if not p.is_zero():
g.add_generator(p)
monomials_not_in_leading_ideal = monomials_not_in_leading_ideal \
% g.reduction_strategy.minimal_leading_terms
if len(monomials_not_in_leading_ideal) < n:
return True
else:
return False
def buchberger(l):
"calculates a (non minimal) Groebner basis"
l=interred(l)
#for making sure, that every polynomial has a different leading term
#needed for add_generator
if not l:
return []
g=GroebnerStrategy(l[0].ring())
for p in l:
g.add_generator(p)
while g.npairs()>0:
g.clean_top_by_chain_criterion()
p=g.next_spoly()
p=g.nf(p)
if not p.is_zero():
g.add_generator(p)
return list(g)
def buchberger(l):
"calculates a (non minimal) Groebner basis"
l = interred(l)
#for making sure, that every polynomial has a different leading term
#needed for add_generator
if not l:
return []
g = GroebnerStrategy(l[0].ring())
for p in l:
g.add_generator(p)
while g.npairs() > 0:
g.clean_top_by_chain_criterion()
p = g.next_spoly()
p = g.nf(p)
if not p.is_zero():
g.add_generator(p)
return list(g)