mjo/matrix_vector: replace isomorphism with basis_representation().

[sage.d.git] / mjo / cone / cone.py

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 7e9c549eec66ede6dc0c94bd67e0e16d4d999538..b7456e21abc170d6479f9010a2b7ccdd5ab9438d 100644 (file)
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -1,93 +1,23 @@
 from sage.all import *
 
-def is_lyapunov_like(L,K):
-    r"""
-    Determine whether or not ``L`` is Lyapunov-like on ``K``.
-
-    We say that ``L`` is Lyapunov-like on ``K`` if `\left\langle
-    L\left\lparenx\right\rparen,s\right\rangle = 0` for all pairs
-    `\left\langle x,s \right\rangle` in the complementarity set of
-    ``K``. It is known [Orlitzky]_ that this property need only be
-    checked for generators of ``K`` and its dual.
-
-    There are faster ways of checking this property. For example, we
-    could compute a `lyapunov_like_basis` of the cone, and then test
-    whether or not the given matrix is contained in the span of that
-    basis. The value of this function is that it works on symbolic
-    matrices.
-
-    INPUT:
-
-    - ``L`` -- A linear transformation or matrix.
-
-    - ``K`` -- A polyhedral closed convex cone.
-
-    OUTPUT:
-
-    ``True`` if it can be proven that ``L`` is Lyapunov-like on ``K``,
-    and ``False`` otherwise.
-
-    .. WARNING::
-
-        If this function returns ``True``, then ``L`` is Lyapunov-like
-        on ``K``. However, if ``False`` is returned, that could mean one
-        of two things. The first is that ``L`` is definitely not
-        Lyapunov-like on ``K``. The second is more of an "I don't know"
-        answer, returned (for example) if we cannot prove that an inner
-        product is zero.
-
-    REFERENCES:
-
-    M. Orlitzky. The Lyapunov rank of an improper cone.
-    http://www.optimization-online.org/DB_HTML/2015/10/5135.html
-
-    EXAMPLES:
-
-    The identity is always Lyapunov-like in a nontrivial space::
-
-        sage: set_random_seed()
-        sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8)
-        sage: L = identity_matrix(K.lattice_dim())
-        sage: is_lyapunov_like(L,K)
-        True
-
-    As is the "zero" transformation::
-
-        sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=8)
-        sage: R = K.lattice().vector_space().base_ring()
-        sage: L = zero_matrix(R, K.lattice_dim())
-        sage: is_lyapunov_like(L,K)
-        True
-
-        Everything in ``K.lyapunov_like_basis()`` should be Lyapunov-like
-        on ``K``::
-
-        sage: K = random_cone(min_ambient_dim=1, max_ambient_dim=6)
-        sage: all([ is_lyapunov_like(L,K) for L in K.lyapunov_like_basis() ])
-        True
-
-    """
-    return all([(L*x).inner_product(s) == 0
-                for (x,s) in K.discrete_complementarity_set()])
-
 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)
+    return Cone(( g.list() for g in gens ), lattice=L, check=False)
 
 def Sigma_cone(K):
-    gens = K.cross_positive_operator_gens()
+    gens = K.cross_positive_operators_gens()
     L = ToricLattice(K.lattice_dim()**2)
-    return Cone([ g.list() for g in gens ], lattice=L, check=False)
+    return Cone(( g.list() for g in gens ), lattice=L, check=False)
 
 def Z_cone(K):
-    gens = K.Z_operator_gens()
+    gens = K.Z_operators_gens()
     L = ToricLattice(K.lattice_dim()**2)
-    return Cone([ g.list() for g in gens ], lattice=L, check=False)
+    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_operator_gens(K2)
+    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)
+    return Cone(( g.list() for g in gens ), lattice=L, check=False)