def consequences_of_nonnegative_solution_assumption(self, eqs):
r"""
Return equations implied by the assumption of the existence of nonnegative solutions.
"""
n_zeros_prev = -1
zeros = []
gb = eqs
while n_zeros_prev!=len(zeros):
n_zeros_prev = len(zeros)
gb = self._ring_ramification.ideal(gb + zeros).groebner_basis()
# gb = self._ring_ramification.ideal(gb + zeros).groebner_basis()
zeros = []
for eq in gb:
coefs = eq.coefficients()
if sum([sgn(a)*sgn(b) for a,b in zip(coefs[:-1],coefs[1:])])==len(coefs)-1:
zeros += eq.variables()
return [zeros, gb]
def _sage_(self):
import sage.all as sage
return sage.sgn(self.args[0]._sage_())
def _sage_(self):
import sage.all as sage
return sage.sgn(self.args[0]._sage_())
def fundamental_discriminants(A, B):
"""Return the fundamental discriminants between A and B (inclusive), as Sage integers,
ordered by absolute value, with negatives first when abs same."""
v = [ZZ(D) for D in range(A, B + 1) if is_fundamental_discriminant(D)]
v.sort(key=lambda x: (abs(x), sgn(x)))
return v
def gen_fricterm( rbt ):
from sage.all import zero_matrix, SR, sgn
fric = zero_matrix(SR, rbt.dof, 1 )
for i in xrange(1,rbt.dof+1):
fric[i-1,0] = rbt.fvi[i] * rbt.dq[i-1,0] + rbt.fci[i] * sgn(rbt.dq[i-1,0])
return fric
