Aaaand the test that was using that "unused" function.

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

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index 8adc51cdd4836e8d1a405fb342f6c4bb8fa50fb6..2d84337fda1cb5275add8171ba8e982559dc1853 100644 (file)
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -126,28 +126,7 @@ def ips_iso(K):
     return (phi,phi_inv)
 
 
-
-def unrestrict_span(K, K2=None):
-    if K2 is None:
-        K2 = K
-
-    _,phi_inv = ips_iso(K2)
-    V_iso = iso_space(K2)
-    (W, W_perp) = V_iso.cartesian_factors()
-
-    rays = []
-    for r in K.rays():
-        w = sum([ r[idx]*W.basis()[idx] for idx in range(0,len(r)) ])
-        pair = V_iso( (w, W_perp.zero()) )
-        rays.append( phi_inv(pair) )
-
-    L = ToricLattice(W.dimension() + W_perp.dimension())
-
-    return Cone(rays, lattice=L)
-
-
-
-def restrict_span(K, K2=None):
+def rho(K, K2=None):
     r"""
     Restrict ``K`` into its own span, or the span of another cone.
 
@@ -195,14 +174,6 @@ def restrict_span(K, K2=None):
         sage: K_S.lattice_dim() == K.dual().dim()
         True
 
-    This function has ``unrestrict_span()`` as its inverse::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8, solid=True)
-        sage: J = restrict_span(K)
-        sage: K == unrestrict_span(J,K)
-        True
-
     This function should not affect the dimension of a cone::
 
         sage: set_random_seed()
@@ -408,100 +379,6 @@ def lineality(K):
     return K.linear_subspace().dimension()
 
 
-def codim(K):
-    r"""
-    Compute the codimension of this cone.
-
-    The codimension of a cone is the dimension of the space of all
-    elements perpendicular to every element of the cone. In other words,
-    the codimension is the difference between the dimension of the
-    ambient space and the dimension of the cone itself.
-
-    OUTPUT:
-
-    A nonnegative integer representing the dimension of the space of all
-    elements perpendicular to this cone.
-
-    .. seealso::
-
-        :meth:`dim`, :meth:`lattice_dim`
-
-    EXAMPLES:
-
-    The codimension of the nonnegative orthant is zero, since the span of
-    its generators equals the entire ambient space::
-
-        sage: K = Cone([(1,0,0), (0,1,0), (0,0,1)])
-        sage: codim(K)
-        0
-
-    However, if we remove a ray so that the entire cone is contained
-    within the `x-y`-plane, then the resulting cone will have
-    codimension one, because the `z`-axis is perpendicular to every
-    element of the cone::
-
-        sage: K = Cone([(1,0,0), (0,1,0)])
-        sage: codim(K)
-        1
-
-    If our cone is all of `\mathbb{R}^{2}`, then its codimension is zero::
-
-        sage: K = Cone([(1,0), (-1,0), (0,1), (0,-1)])
-        sage: codim(K)
-        0
-
-    And if the cone is trivial in any space, then its codimension is
-    equal to the dimension of the ambient space::
-
-        sage: K = Cone([], lattice=ToricLattice(0))
-        sage: K.lattice_dim()
-        0
-        sage: codim(K)
-        0
-
-        sage: K = Cone([(0,)])
-        sage: K.lattice_dim()
-        1
-        sage: codim(K)
-        1
-
-        sage: K = Cone([(0,0)])
-        sage: K.lattice_dim()
-        2
-        sage: codim(K)
-        2
-
-    TESTS:
-
-    The codimension of a cone should be an integer between zero and
-    the dimension of the ambient space, inclusive::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8)
-        sage: c = codim(K)
-        sage: c in ZZ
-        True
-        sage: (0 <= c) and (c <= K.lattice_dim())
-        True
-
-    A solid cone should have codimension zero::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8, solid = True)
-        sage: codim(K)
-        0
-
-    The codimension of a cone is equal to the lineality of its dual::
-
-        sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8, solid = True)
-        sage: codim(K) == lineality(K.dual())
-        True
-
-    """
-    return (K.lattice_dim() - K.dim())
-
-
 def discrete_complementarity_set(K):
     r"""
     Compute the discrete complementarity set of this cone.