+def project_span(K, K2 = None):
+ r"""
+ Return a "copy" of ``K`` embeded in a lower-dimensional space.
+
+ By default, we will project ``K`` into the subspace spanned by its
+ rays. However, if ``K2`` is not ``None``, we will project into the
+ space spanned by the rays of ``K2`` instead.
+
+ EXAMPLES::
+
+ sage: K = Cone([(1,0,0), (0,1,0)])
+ sage: project_span(K)
+ 2-d cone in 2-d lattice N
+ sage: project_span(K).rays()
+ N(1, 0),
+ N(0, 1)
+ in 2-d lattice N
+
+ sage: K = Cone([(1,0,0), (0,1,0)])
+ sage: K2 = Cone([(0,1)])
+ sage: project_span(K, K2).rays()
+ N(1)
+ in 1-d lattice N
+
+ """
+ # Allow us to use a second cone to generate the subspace into
+ # which we're "projecting."
+ if K2 is None:
+ K2 = K
+
+ # Use these to generate the new cone.
+ cs1 = K.rays().matrix().columns()
+
+ # And use these to figure out which indices to drop.
+ cs2 = K2.rays().matrix().columns()
+
+ perp_idxs = []
+
+ for idx in range(0, len(cs2)):
+ if cs2[idx].is_zero():
+ perp_idxs.append(idx)
+
+ solid_cols = [ cs1[idx] for idx in range(0,len(cs1))
+ if not idx in perp_idxs
+ and not idx >= len(cs2) ]
+
+ m = matrix(solid_cols)
+ L = ToricLattice(len(m.rows()))
+ J = Cone(m.transpose(), lattice=L)
+ return J
+
+