mjo/cone/schur.py: bye, use sage's cones.schur() instead

diff --git a/mjo/cone/all.py b/mjo/cone/all.py
index 7ce56c0bf41f6f18123155c6b232bd52594b5905..18fb052297b8ce1e4ef5a21d378638b6379d0379 100644 (file)
--- a/mjo/cone/all.py
+++ b/mjo/cone/all.py
@@ -9,7 +9,6 @@ from mjo.cone.faces import *
 from mjo.cone.nonnegative_orthant import *
 from mjo.cone.permutation_invariant import *
 from mjo.cone.rearrangement import *
-from mjo.cone.schur import *
 from mjo.cone.symmetric_pd import *
 from mjo.cone.symmetric_psd import *
 from mjo.cone.trivial_cone import *

diff --git a/mjo/cone/schur.py b/mjo/cone/schur.py
deleted file mode 100644 (file)
index 1fa1e52..0000000
--- a/mjo/cone/schur.py
+++ /dev/null
@@ -1,131 +0,0 @@
-"""
-The Schur cone, as described in the "Critical angles..." papers by
-Iusem, Seeger, and Sossa. It defines the Schur ordering on `R^{n}`.
-"""
-
-from sage.all import *
-
-def schur_cone(n, lattice=None):
-    r"""
-    Return the Schur cone in ``n`` dimensions that induces the
-    majorization ordering.
-
-    INPUT:
-
-      - ``n`` -- the dimension the ambient space.
-
-      - ``lattice`` -- (default: ``None``) an ambient lattice of rank ``n``
-                       to be passed to the :func:`Cone` constructor.
-
-    OUTPUT:
-
-    A rational closed convex Schur cone of dimension ``n``. Each
-    generating ray will have the integer ring as its base ring.
-
-    If a ``lattice`` was specified, then the resulting cone will live in
-    that lattice unless its rank is incompatible with the dimension
-    ``n`` (in which case a ``ValueError`` is raised).
-
-    REFERENCES:
-
-    .. [GourionSeeger] Daniel Gourion and Alberto Seeger.
-       Critical angles in polyhedral convex cones: numerical and
-       statistical considerations. Mathematical Programming, 123:173-198,
-       2010, doi:10.1007/s10107-009-0317-2.
-
-    .. [IusemSeegerOnPairs] Alfredo Iusem and Alberto Seeger.
-       On pairs of vectors achieving the maximal angle of a convex cone.
-       Mathematical Programming, 104(2-3):501-523, 2005,
-       doi:10.1007/s10107-005-0626-z.
-
-    .. [SeegerSossaI] Alberto Seeger and David Sossa.
-       Critical angles between two convex cones I. General theory.
-       TOP, 24(1):44-65, 2016, doi:10.1007/s11750-015-0375-y.
-
-    SETUP::
-
-        sage: from mjo.cone.nonnegative_orthant import nonnegative_orthant
-        sage: from mjo.cone.schur import schur_cone
-
-    EXAMPLES:
-
-    Verify the claim that the maximal angle between any two generators
-    of the Schur cone and the nonnegative quintant is ``3*pi/4``::
-
-        sage: P = schur_cone(5)
-        sage: Q = nonnegative_orthant(5)
-        sage: G = ( g.change_ring(QQbar).normalized() for g in P )
-        sage: H = ( h.change_ring(QQbar).normalized() for h in Q )
-        sage: actual = max(arccos(u.inner_product(v)) for u in G for v in H)
-        sage: expected = 3*pi/4
-        sage: abs(actual - expected).n() < 1e-12
-        True
-
-    The dual of the Schur cone is the "downward monotonic cone"
-    [GourionSeeger]_, whose elements' entries are in non-increasing
-    order::
-
-        sage: n = ZZ.random_element(10)
-        sage: K = schur_cone(n).dual()
-        sage: x = K.random_element()
-        sage: all( x[i] >= x[i+1] for i in range(n-1) )
-        True
-
-    TESTS:
-
-    We get the trivial cone when ``n`` is zero::
-
-        sage: schur_cone(0).is_trivial()
-        True
-
-    The Schur cone induces the majorization ordering::
-
-        sage: def majorized_by(x,y):
-        ....:     return (all(sum(x[0:i]) <= sum(y[0:i])
-        ....:                 for i in range(x.degree()-1))
-        ....:             and sum(x) == sum(y))
-        sage: n = ZZ.random_element(10)
-        sage: V = VectorSpace(QQ, n)
-        sage: S = schur_cone(n)
-        sage: majorized_by(V.zero(), S.random_element())
-        True
-        sage: x = V.random_element()
-        sage: y = V.random_element()
-        sage: majorized_by(x,y) == ( (y-x) in S )
-        True
-
-    If a ``lattice`` was given, it is actually used::
-
-        sage: L = ToricLattice(3, 'M')
-        sage: schur_cone(3, lattice=L)
-        2-d cone in 3-d lattice M
-
-    Unless the rank of the lattice disagrees with ``n``::
-
-        sage: L = ToricLattice(1, 'M')
-        sage: schur_cone(3, lattice=L)
-        Traceback (most recent call last):
-        ...
-        ValueError: lattice rank=1 and dimension n=3 are incompatible
-
-    """
-    if lattice is None:
-        lattice = ToricLattice(n)
-
-    if lattice.rank() != n:
-        raise ValueError('lattice rank=%d and dimension n=%d are incompatible'
-                         %
-                         (lattice.rank(), n))
-
-    def _f(i,j):
-        if i == j:
-            return 1
-        elif j - i == 1:
-            return -1
-        else:
-            return 0
-
-    # The "max" below catches the trivial case where n == 0.
-    S = matrix(ZZ, max(0,n-1), n, _f)
-
-    return Cone(S.rows(), lattice)