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- fglm(I, from_ring, to_ring)
- converts *reduced* Groebner Basis in from_ring to a GroebnerBasis in to_ring.
It acts independend of the global ring, which is restored at the end of the
computation,
>>> from polybori.PyPolyBoRi import OrderCode
>>> dp_asc = OrderCode.dp_asc
>>> r=declare_ring(['x','y','z'],dict())
>>> old_ring = r
>>> new_ring = old_ring.clone(ordering=dp_asc)
>>> (x,y,z) = [old_ring.variable(i) for i in xrange(3)]
>>> ideal=[x+z, y+z]# lp Groebner basis
>>> list(fglm(ideal, old_ring, new_ring))
[y + x, z + x]
- m_k_plus_one(completed_elements, variables)
- calculates $m_{k+1}$ from the FGLM algorithm as described in Wichmanns diploma thesis
It would be nice to be able to efficiently extract the smallest term of a polynomial
>>> from polybori.PyPolyBoRi import OrderCode
>>> dp_asc = OrderCode.dp_asc
>>> r=Ring(1000)
>>> x = r.variable
>>> s=BooleSet([x(1)*x(2),x(1),x(2),Monomial(r),x(3)])
>>> variables=BooleSet([x(1),x(2),x(3)])
>>> m_k_plus_one(s,variables)
x(2)*x(3)
>>> r2 = r.clone(ordering=dp_asc)
>>> m_k_plus_one(r2(s).set(),r2(variables).set())
x(1)*x(3)
- vars_real_divisors(monomial, monomial_set)
- returns all elements of of monomial_set, which result multiplied by a variable in monomial.
>>> from polybori.PyPolyBoRi import OrderCode
>>> dp_asc = OrderCode.dp_asc
>>> from polybori.PyPolyBoRi import Ring
>>> r=Ring(1000)
>>> x = r.variable
>>> b=BooleSet([x(1)*x(2),x(2)])
>>> vars_real_divisors(x(1)*x(2)*x(3),b)
{{x(1),x(2)}}
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