X-Git-Url: https://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Frearrangement.py;h=0bbf95bb7603bed819d4b9e91a4b148856dc464c;hb=refs%2Fheads%2Fmaster;hp=0df1daf054ecefecafac59e09f00559e7fa1cad8;hpb=090b2c77aa4bd371d66885451f9df44c6b6d818f;p=sage.d.git

diff --git a/mjo/cone/rearrangement.py b/mjo/cone/rearrangement.py
deleted file mode 100644
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--- a/mjo/cone/rearrangement.py
+++ /dev/null
@@ -1,141 +0,0 @@
-# Sage doesn't load ~/.sage/init.sage during testing (sage -t), so we
-# have to explicitly mangle our sitedir here so that "mjo.cone"
-# resolves.
-from os.path import abspath
-from site import addsitedir
-addsitedir(abspath('../../'))
-
-from sage.all import *
-
-def rearrangement_cone(p,n):
-    r"""
-    Return the rearrangement cone of order ``p`` in ``n`` dimensions.
-
-    The rearrangement cone in ``n`` dimensions has as its elements
-    vectors of length ``n``. For inclusion in the cone, the smallest
-    ``p`` components of a vector must sum to a nonnegative number.
-
-    For example, the rearrangement cone of order ``p == 1`` has its
-    single smallest component nonnegative. This implies that all
-    components are nonnegative, and that therefore the rearrangement
-    cone of order one is the nonnegative orthant.
-
-    When ``p == n``, the sum of all components of a vector must be
-    nonnegative for inclusion in the cone. That is, the cone is a
-    half-space in ``n`` dimensions.
-
-    INPUT:
-
-    - ``p`` -- The number of components to "rearrange."
-
-    - ``n`` -- The dimension of the ambient space for the resulting cone.
-
-    OUTPUT:
-
-    A polyhedral closed convex cone object representing a rearrangement
-    cone of order ``p`` in ``n`` dimensions.
-
-    EXAMPLES:
-
-    The rearrangement cones of order one are nonnegative orthants::
-
-        sage: rearrangement_cone(1,1) == Cone([(1,)])
-        True
-        sage: rearrangement_cone(1,2) == Cone([(0,1),(1,0)])
-        True
-        sage: rearrangement_cone(1,3) == Cone([(0,0,1),(0,1,0),(1,0,0)])
-        True
-
-    When ``p == n``, the resulting cone will be a half-space, so we
-    expect its lineality to be one less than ``n`` because it will
-    contain a hyperplane but is not the entire space::
-
-        sage: rearrangement_cone(5,5).lineality()
-        4
-
-    All rearrangement cones are proper::
-
-        sage: all([ rearrangement_cone(p,n).is_proper()
-        ....:               for n in range(10)
-        ....:               for p in range(n) ])
-        True
-
-    The Lyapunov rank of the rearrangement cone of order ``p`` in ``n``
-    dimensions is ``n`` for ``p == 1`` or ``p == n`` and one otherwise::
-
-        sage: all([ rearrangement_cone(p,n).lyapunov_rank() == n
-        ....:               for n in range(2, 10)
-        ....:               for p in [1, n-1] ])
-        True
-        sage: all([ rearrangement_cone(p,n).lyapunov_rank() == 1
-        ....:               for n in range(3, 10)
-        ....:               for p in range(2, n-1) ])
-        True
-
-    TESTS:
-
-    The rearrangement cone is permutation-invariant::
-
-        sage: n = ZZ.random_element(2,10).abs()
-        sage: p = ZZ.random_element(1,n)
-        sage: K = rearrangement_cone(p,n)
-        sage: P = SymmetricGroup(n).random_element().matrix()
-        sage: all([ K.contains(P*r) for r in K.rays() ])
-        True
-
-    """
-
-    def d(j):
-        v = [1]*n    # Create the list of all ones...
-        v[j] = 1 - p # Now "fix" the ``j``th entry.
-        return v
-
-    V = VectorSpace(QQ, n)
-    G = V.basis() + [ d(j) for j in range(n) ]
-    return Cone(G)
-
-
-def has_rearrangement_property(v, p):
-    r"""
-    Test if the vector ``v`` has the "rearrangement property."
-
-    The rearrangement cone of order ``p`` in `n` dimensions has its
-    members vectors of length `n`. The "rearrangement property,"
-    satisfied by its elements, is to have its smallest ``p`` components
-    sum to a nonnegative number.
-
-    We believe that we have a description of the extreme vectors of the
-    rearrangement cone: see ``rearrangement_cone()``. This function is
-    used to test that conic combinations of those extreme vectors are in
-    fact elements of the rearrangement cone. We can't test all conic
-    combinations, obviously, but we can test a random one.
-
-    To become more sure of the result, generate a bunch of vectors with
-    ``random_element()`` and test them with this function.
-
-    INPUT:
-
-    - ``v`` -- An element of a cone suspected of being the rearrangement
-               cone of order ``p``.
-
-    - ``p`` -- The suspected order of the rearrangement cone.
-
-    OUTPUT:
-
-    If ``v`` has the rearrangement property (that is, if its smallest ``p``
-    components sum to a nonnegative number), ``True`` is returned. Otherwise
-    ``False`` is returned.
-
-    EXAMPLES:
-
-    Every element of a rearrangement cone should have the property::
-
-        sage: for n in range(2,10):
-        ....:     for p in range(1, n-1):
-        ....:         K = rearrangement_cone(p,n)
-        ....:         v = K.random_element()
-        ....:         if not has_rearrangement_property(v,p): print v
-
-    """
-    components = sorted(v)[0:p]
-    return sum(components) >= 0