Finish test cleanup, notation updates, and dead code removal.

diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py
index ba5f51ea880ccdc2cc3344cb8b91022ff3e5b8cf..c6d26829f32a6efedf927dc542fdcfc453c22e30 100644 (file)
--- a/mjo/cone/cone.py
+++ b/mjo/cone/cone.py
@@ -8,23 +8,12 @@ addsitedir(abspath('../../'))
 from sage.all import *
 
 
-def drop_dependent(vs):
-    r"""
-    Return the largest linearly-independent subset of ``vs``.
-    """
-    result = []
-    m = matrix(vs).echelon_form()
-    for idx in range(0, m.nrows()):
-        if not m[idx].is_zero():
-            result.append(m[idx])
-
-    return result
-
-
 def basically_the_same(K1,K2):
     r"""
     ``True`` if ``K1`` and ``K2`` are basically the same, and ``False``
-    otherwise.
+    otherwise. This is intended as a lazy way to check whether or not
+    ``K1`` and ``K2`` are linearly isomorphic (i.e. ``A(K1) == K2`` for
+    some invertible linear transformation ``A``).
     """
     if K1.lattice_dim() != K2.lattice_dim():
         return False
@@ -65,7 +54,8 @@ def rho(K, K2=None):
 
     INPUT:
 
-    - ``K2`` -- another cone whose lattice has the same rank as this cone.
+    - ``K2`` -- another cone whose lattice has the same rank as this
+                cone.
 
     OUTPUT:
 
@@ -136,11 +126,11 @@ def rho(K, K2=None):
         sage: set_random_seed()
         sage: K = random_cone(max_dim = 8, strictly_convex=False, solid=False)
         sage: K_S = rho(K)
-        sage: P = rho(K_S.dual()).dual()
-        sage: P.is_proper()
+        sage: K_SP = rho(K_S.dual()).dual()
+        sage: K_SP.is_proper()
         True
-        sage: P = rho(K_S, K_S.dual())
-        sage: P.is_proper()
+        sage: K_SP = rho(K_S, K_S.dual())
+        sage: K_SP.is_proper()
         True
 
     ::
@@ -148,11 +138,11 @@ def rho(K, K2=None):
         sage: set_random_seed()
         sage: K = random_cone(max_dim = 8, strictly_convex=True, solid=False)
         sage: K_S = rho(K)
-        sage: P = rho(K_S.dual()).dual()
-        sage: P.is_proper()
+        sage: K_SP = rho(K_S.dual()).dual()
+        sage: K_SP.is_proper()
         True
-        sage: P = rho(K_S, K_S.dual())
-        sage: P.is_proper()
+        sage: K_SP = rho(K_S, K_S.dual())
+        sage: K_SP.is_proper()
         True
 
     ::
@@ -160,11 +150,11 @@ def rho(K, K2=None):
         sage: set_random_seed()
         sage: K = random_cone(max_dim = 8, strictly_convex=False, solid=True)
         sage: K_S = rho(K)
-        sage: P = rho(K_S.dual()).dual()
-        sage: P.is_proper()
+        sage: K_SP = rho(K_S.dual()).dual()
+        sage: K_SP.is_proper()
         True
-        sage: P = rho(K_S, K_S.dual())
-        sage: P.is_proper()
+        sage: K_SP = rho(K_S, K_S.dual())
+        sage: K_SP.is_proper()
         True
 
     ::
@@ -172,47 +162,52 @@ def rho(K, K2=None):
         sage: set_random_seed()
         sage: K = random_cone(max_dim = 8, strictly_convex=True, solid=True)
         sage: K_S = rho(K)
-        sage: P = rho(K_S.dual()).dual()
-        sage: P.is_proper()
+        sage: K_SP = rho(K_S.dual()).dual()
+        sage: K_SP.is_proper()
         True
-        sage: P = rho(K_S, K_S.dual())
-        sage: P.is_proper()
+        sage: K_SP = rho(K_S, K_S.dual())
+        sage: K_SP.is_proper()
         True
 
-    Test the proposition in our paper concerning the duals, where the
-    subspace `W` is the span of `K^{*}`::
+    Test the proposition in our paper concerning the duals and
+    restrictions. Generate a random cone, then create a subcone of
+    it. The operation of dual-taking should then commute with rho::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8, solid=False, strictly_convex=False)
-        sage: K_W = rho(K, K.dual())
-        sage: K_star_W_star = rho(K.dual()).dual()
+        sage: J = random_cone(max_dim = 8, solid=False, strictly_convex=False)
+        sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
+        sage: K_W = rho(K, J)
+        sage: K_star_W_star = rho(K.dual(), J).dual()
         sage: basically_the_same(K_W, K_star_W_star)
         True
 
     ::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8, solid=True, strictly_convex=False)
-        sage: K_W = rho(K, K.dual())
-        sage: K_star_W_star = rho(K.dual()).dual()
+        sage: J = random_cone(max_dim = 8, solid=True, strictly_convex=False)
+        sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
+        sage: K_W = rho(K, J)
+        sage: K_star_W_star = rho(K.dual(), J).dual()
         sage: basically_the_same(K_W, K_star_W_star)
         True
 
     ::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8, solid=False, strictly_convex=True)
-        sage: K_W = rho(K, K.dual())
-        sage: K_star_W_star = rho(K.dual()).dual()
+        sage: J = random_cone(max_dim = 8, solid=False, strictly_convex=True)
+        sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
+        sage: K_W = rho(K, J)
+        sage: K_star_W_star = rho(K.dual(), J).dual()
         sage: basically_the_same(K_W, K_star_W_star)
         True
 
     ::
 
         sage: set_random_seed()
-        sage: K = random_cone(max_dim = 8, solid=True, strictly_convex=True)
-        sage: K_W = rho(K, K.dual())
-        sage: K_star_W_star = rho(K.dual()).dual()
+        sage: J = random_cone(max_dim = 8, solid=True, strictly_convex=True)
+        sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
+        sage: K_W = rho(K, J)
+        sage: K_star_W_star = rho(K.dual(), J).dual()
         sage: basically_the_same(K_W, K_star_W_star)
         True
 
@@ -220,18 +215,16 @@ def rho(K, K2=None):
     if K2 is None:
         K2 = K
 
-    # First we project K onto the span of K2. This can be done with
-    # cones (i.e. without converting to vector spaces), but it's
-    # annoying to deal with lattice mismatches.
+    # First we project K onto the span of K2. This will explode if the
+    # rank of ``K2.lattice()`` doesn't match ours.
     span_K2 = Cone(K2.rays() + (-K2).rays(), lattice=K.lattice())
     K = K.intersection(span_K2)
 
-    V = K.lattice().vector_space()
-
-    # Create the space W \times W^{\perp} isomorphic to V.
-    # First we get an orthogonal (but not normal) basis...
-    W_basis = drop_dependent(K2.rays())
-    W = V.subspace_with_basis(W_basis)
+    # Cheat a little to get the subspace span(K2). The paper uses the
+    # rays of K2 as a basis, but everything is invariant under linear
+    # isomorphism (i.e. a change of basis), and this is a little
+    # faster.
+    W = span_K2.linear_subspace()
 
     # We've already intersected K with the span of K2, so every
     # generator of K should belong to W now.
@@ -420,9 +413,7 @@ def discrete_complementarity_set(K):
 
     A list of pairs `(x,s)` such that,
 
-      * `x` is in this cone.
       * `x` is a generator of this cone.
-      * `s` is in this cone's dual.
       * `s` is a generator of this cone's dual.
       * `x` and `s` are orthogonal.
 
@@ -827,10 +818,10 @@ def lyapunov_rank(K):
         sage: K = random_cone(max_dim=8)
         sage: actual = lyapunov_rank(K)
         sage: K_S = rho(K)
-        sage: P = rho(K_S.dual()).dual()
+        sage: K_SP = rho(K_S.dual()).dual()
         sage: l = lineality(K)
         sage: c = codim(K)
-        sage: expected = lyapunov_rank(P) + K.dim()*(l + c) + c**2
+        sage: expected = lyapunov_rank(K_SP) + K.dim()*(l + c) + c**2
         sage: actual == expected
         True
 
@@ -864,7 +855,6 @@ def lyapunov_rank(K):
         True
 
     """
-    K_orig = K
     beta = 0
 
     m = K.dim()
@@ -872,16 +862,16 @@ def lyapunov_rank(K):
     l = lineality(K)
 
     if m < n:
-        # K is not solid, project onto its span.
+        # K is not solid, restrict to its span.
         K = rho(K)
 
         # Lemma 2
         beta += m*(n - m) + (n - m)**2
 
     if l > 0:
-        # K is not pointed, project its dual onto its span.
-        # Uses a proposition from our paper, i.e. this is
-        # equivalent to K = rho(K.dual()).dual()
+        # K is not pointed, restrict to the span of its dual. Uses a
+        # proposition from our paper, i.e. this is equivalent to K =
+        # rho(K.dual()).dual().
         K = rho(K, K.dual())
 
         # Lemma 3