- The isomorphism should be an inner product space isomorphism, and
- thus it should preserve dual cones (and commute with the "dual"
- operation). But beware the automatic renaming of the dual lattice.
- OH AND YOU HAVE TO SORT THE CONES::
-
- sage: K = random_cone(max_dim=10, strictly_convex=False, solid=True)
- sage: L = K.lattice()
- sage: rename_lattice(L, 'L')
- sage: (phi, phi_inv) = span_iso(K)
- sage: sorted(phi_inv( phi(K).dual() )) == sorted(K.dual())
- True
-
- We may need to isomorph twice to make sure we stop moving down to
- smaller spaces. (Once you've done this on a cone and its dual, the
- result should be proper.) OH AND YOU HAVE TO SORT THE CONES::
-
- sage: K = random_cone(max_dim=10, strictly_convex=False, solid=False)
- sage: L = K.lattice()
- sage: rename_lattice(L, 'L')
- sage: (phi, phi_inv) = span_iso(K)
- sage: K_S = phi(K)
- sage: (phi_dual, phi_dual_inv) = span_iso(K_S.dual())
- sage: J_T = phi_dual(K_S.dual()).dual()
- sage: phi_inv(phi_dual_inv(J_T)) == K
- True
-