def from_polyhedron_to_linear_system(cls, p, poly_ring=None):
"""
Convert a instance of Polyhedron to a instance of BasicSemialgebraicSet_polyhedral_linear_system
"""
if p.__class__ == cls:
return p
base_ring = p.base_ring().fraction_field()
ambient_dim = p.ambient_dim()
if poly_ring is None:
poly_ring = PolynomialRing(base_ring, "x", ambient_dim)
else:
if ambient_dim != poly_ring.ambient_dim():
raise ValueError(
"Ambient dimensions of p and poly_ring do not match.")
self = cls(base_ring=base_ring,
ambient_dim=ambient_dim,
poly_ring=poly_ring)
i = 1
for lhs in p.inequalities_list():
self.add_linear_constraint(lhs[1:], lhs[0], operator.ge)
self.history_set[-sum(lhs[1:][i] * self.poly_ring().gens()[i]
for i in range(len(lhs) - 1)) -
lhs[0]] = {i}
i += 1
for lhs in p.equations_list():
self.add_linear_constraint(lhs[1:], lhs[0], operator.eq)
self.history_set[sum(lhs[1:][i] * self.poly_ring().gens()[i]
for i in range(len(lhs) - 1)) + lhs[0]] = {i}
i += 1
return self
