sage: K.is_full_space()
True
sage: pi_of_K = positive_operator_gens(K)
- sage: actual = Cone([p.list() for p in pi_of_K], lattice=L).lineality()
- sage: actual == n^2
+ sage: pi_cone = Cone([p.list() for p in pi_of_K], lattice=L)
+ sage: pi_cone.lineality() == n^2
True
sage: K = Cone([(1,0),(0,1),(0,-1)])
sage: pi_of_K = positive_operator_gens(K)
sage: set_random_seed()
sage: K = random_cone(max_ambient_dim=4)
sage: L = ToricLattice(K.lattice_dim()**2)
- sage: z_cone = Cone([ z.list() for z in Z_transformation_gens(K) ],
+ sage: Z_cone = Cone([ z.list() for z in Z_transformation_gens(K) ],
....: lattice=L,
....: check=False)
sage: ll_basis = [ vector(l.list()) for l in K.lyapunov_like_basis() ]
sage: lls = L.vector_space().span(ll_basis)
- sage: z_cone.linear_subspace() == lls
+ sage: Z_cone.linear_subspace() == lls
True
The lineality of the Z-transformations on a cone is the Lyapunov
sage: K = random_cone(max_ambient_dim=4)
sage: Z_of_K = Z_transformation_gens(K)
sage: L = ToricLattice(K.lattice_dim()**2)
- sage: z_cone = Cone([ z.list() for z in Z_of_K ],
+ sage: Z_cone = Cone([ z.list() for z in Z_of_K ],
....: lattice=L,
....: check=False)
- sage: z_cone.lineality() == K.lyapunov_rank()
+ sage: Z_cone.lineality() == K.lyapunov_rank()
True
The lineality spaces of the duals of the positive operator and
sage: pi_cone = Cone([p.list() for p in pi_of_K],
....: lattice=L,
....: check=False)
- sage: z_cone = Cone([ z.list() for z in Z_of_K],
+ sage: Z_cone = Cone([ z.list() for z in Z_of_K],
....: lattice=L,
....: check=False)
- sage: pi_cone.dim() == z_cone.dim()
+ sage: pi_cone.dim() == Z_cone.dim()
True
sage: pi_star = pi_cone.dual()
- sage: z_star = z_cone.dual()
+ sage: z_star = Z_cone.dual()
sage: pi_star.linear_subspace() == z_star.linear_subspace()
True
True
sage: L = ToricLattice(n^2)
sage: Z_of_K = Z_transformation_gens(K)
- sage: z_cone = Cone([z.list() for z in Z_of_K],
+ sage: Z_cone = Cone([z.list() for z in Z_of_K],
....: lattice=L,
....: check=False)
- sage: actual = z_cone.dim()
+ sage: actual = Z_cone.dim()
sage: actual == n^2
True
sage: K = K.dual()
sage: K.is_full_space()
True
- sage: z_of_K = Z_transformation_gens(K)
- sage: z_cone = Cone([z.list() for z in Z_of_K],
+ sage: Z_of_K = Z_transformation_gens(K)
+ sage: Z_cone = Cone([z.list() for z in Z_of_K],
....: lattice=L,
....: check=False)
- sage: actual = z_cone.dim()
+ sage: actual = Z_cone.dim()
sage: actual == n^2
True
sage: K = Cone([(1,0),(0,1),(0,-1)])
sage: Z_of_K = Z_transformation_gens(K)
- sage: actual = Cone([z.list() for z in Z_of_K], check=False).dim()
- sage: actual == 3
+ sage: Z_cone = Cone([z.list() for z in Z_of_K], check=False)
+ sage: Z_cone.dim() == 3
True
"""
# Matrices are not vectors in Sage, so we have to convert them