+ sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=6)
+ sage: all([ is_lyapunov_like_on(L,K)
+ ....: for L in K.lyapunov_like_basis() ])
+ True
+ sage: all([ is_lyapunov_like_on(L.change_ring(SR),K)
+ ....: for L in K.lyapunov_like_basis() ])
+ True
+
+ """
+ if L.base_ring().is_exact() or L.base_ring() is SR:
+ # The "fast method" of creating a vector space based on a
+ # ``lyapunov_like_basis`` is actually slower than this.
+ return all([ s*(L*x) == 0
+ for (x,s) in K.discrete_complementarity_set() ])
+ else:
+ # The only inexact ring that we're willing to work with is SR,
+ # since it can still be exact when working with symbolic
+ # constants like pi and e.
+ raise ValueError('base ring of operator L is neither SR nor exact')
+
+def LL_cone(K):
+ gens = K.lyapunov_like_basis()
+ L = ToricLattice(K.lattice_dim()**2)
+ return Cone([ g.list() for g in gens ], lattice=L, check=False)
+
+def Sigma_cone(K):
+ gens = K.cross_positive_operators_gens()
+ L = ToricLattice(K.lattice_dim()**2)
+ return Cone([ g.list() for g in gens ], lattice=L, check=False)
+
+def Z_cone(K):
+ gens = K.Z_operators_gens()
+ L = ToricLattice(K.lattice_dim()**2)
+ return Cone([ g.list() for g in gens ], lattice=L, check=False)
+
+def pi_cone(K1, K2=None):
+ if K2 is None:
+ K2 = K1
+ gens = K1.positive_operators_gens(K2)
+ L = ToricLattice(K1.lattice_dim()*K2.lattice_dim())
+ return Cone([ g.list() for g in gens ], lattice=L, check=False)