SETUP::
- sage: from mjo.cone.faces import dual_face
+ sage: from mjo.cone.faces import (dual_face, face_generated_by)
EXAMPLES:
sage: dual_face(K,trivial_face).is_equivalent(K.dual())
True
+ The dual of the cone of ``K`` at ``y`` is the dual face of the face
+ of ``K`` generated by ``y`` ([Tam]_ Corollary 3.2)::
+
+ sage: set_random_seed()
+ sage: K = random_cone(max_ambient_dim=8, max_rays=10)
+ sage: y = K.random_element()
+ sage: S = [y]
+ sage: phi_y = face_generated_by(K,S)
+ sage: points_cone_gens = list(K.rays()) + [-z for z in phi_y.rays()]
+ sage: points_cone = Cone(points_cone_gens, K.lattice())
+ sage: points_cone.dual().is_equivalent(dual_face(K, phi_y))
+ True
+
"""
# Ensure that F is actually a face of K before continuing.
if not F.is_face_of(K):