X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Fcone%2Fschur.py;h=1fa1e52407fe2782b3852cf1482970724abb2003;hb=928b7d49fda98ff105c92293b5797bb7a2b9873a;hp=53607a948ef26a3cb9f5fae2d86c8d895a4fab71;hpb=7fe29009a2fa2e6a2ceaf623e860e23a0fa22b1a;p=sage.d.git

diff --git a/mjo/cone/schur.py b/mjo/cone/schur.py
index 53607a9..1fa1e52 100644
--- a/mjo/cone/schur.py
+++ b/mjo/cone/schur.py
@@ -5,17 +5,26 @@ Iusem, Seeger, and Sossa. It defines the Schur ordering on `R^{n}`.
 
 from sage.all import *
 
-def schur_cone(n):
+def schur_cone(n, lattice=None):
     r"""
-    Return the Schur cone in ``n`` dimensions.
+    Return the Schur cone in ``n`` dimensions that induces the
+    majorization ordering.
 
     INPUT:
 
-    - ``n`` -- the dimension the ambient space.
+      - ``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``.
+    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:
 
@@ -56,11 +65,10 @@ def schur_cone(n):
     [GourionSeeger]_, whose elements' entries are in non-increasing
     order::
 
-        sage: set_random_seed()
         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 xrange(n-1) )
+        sage: all( x[i] >= x[i+1] for i in range(n-1) )
         True
 
     TESTS:
@@ -72,10 +80,9 @@ def schur_cone(n):
 
     The Schur cone induces the majorization ordering::
 
-        sage: set_random_seed()
         sage: def majorized_by(x,y):
         ....:     return (all(sum(x[0:i]) <= sum(y[0:i])
-        ....:                 for i in xrange(x.degree()-1))
+        ....:                 for i in range(x.degree()-1))
         ....:             and sum(x) == sum(y))
         sage: n = ZZ.random_element(10)
         sage: V = VectorSpace(QQ, n)
@@ -87,7 +94,28 @@ def schur_cone(n):
         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:
@@ -100,5 +128,4 @@ def schur_cone(n):
     # The "max" below catches the trivial case where n == 0.
     S = matrix(ZZ, max(0,n-1), n, _f)
 
-    # Likewise, when n == 0, we need to specify the lattice.
-    return Cone(S.rows(), ToricLattice(n))
+    return Cone(S.rows(), lattice)