Changeset a7cb00 in git

Timestamp:

Sep 30, 2016, 1:32:51 PM (8 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', '73c62e0961bcfc8f1a00420b41eec2ea3c0ef6e9')

Children:

6b5e56f646727b9c59f35f2dddeaf888f39e5493

Parents:

6dddc1749bb9cabb0076e15b222acb41142d9d8b

Message:

doc: polytopeVia... -> gfan.lib

Files:

• Singular/LIB/gfan.lib (modified) (2 diffs)
• Singular/LIB/polymakeInterface.lib (modified) (2 diffs)
• doc/cones.yes.doc (modified) (previous)

Singular/LIB/gfan.lib

@@ -40 +40 @@
        linealitySpace(c);    the lineality space of c
        negatedCone(c);       the negative of c
+       polytopeViaInequalities();
+       polytopeViaPoints();
        quotientLatticeBasis(c);  basis of Z^n intersected with the span of c modulo Z^n intersected with the lineality space of c
        randomPoint(c);       a random point in the relative interior of c
@@ -1540 +1542 @@
 }
 
+proc polytopeViaPoints()
+"USAGE: polytopeViaPoints(V [, flags]);  intmat V, int flags
+RETURN: polytope which is the intersection of the cone generated by the row vectors
+of V with the hyperplane, in which the first coordinate equals 1;
+flags may be 0 or 1,@*
+if flags is 1, then program assumes that each row vector of M generates a ray in the cone,
+if flags is 0, then program computes that information itself
+EXAMPLE: example polytopeViaPoints; shows an example
+"
+{
+
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  // This is a polytope in R^2 generated by (0,0), (1,0), (0,1), (0,0);
+  intmat V[4][3]=
+  1,0,0,
+  1,1,0,
+  1,0,1,
+  1,1,1;
+  polytope p1=polytopeViaPoints(V);
+  p1;
+  // This is a polytope in R^2 generated by (1/2,2/3), (3/4,4/5), (5/6,6/7):
+  intmat V[3][3]=
+  6,3,4,
+  20,15,16,
+  42,35,36;
+  polytope p2=polytopeViaPoints(V);
+  p2;
+  // This polytope is the positive orthant in R^2:
+  // (0,1,0) and (0,0,1) imply that the polytope is unbounded in that direction
+  intmat V[3][3]=
+  1,0,0,
+  0,1,0,
+  0,0,1;
+  polytope p3=polytopeViaPoints(V);
+  p3;
+}
+
+proc polytopeViaInequalities()
+"USAGE: polytopeViaInequalities(EV [, E [, flags]]);  intmat EV,E, int flags
+RETURN: polytope consisting of all points x, such that IE*x >= 0 in each component
+and (if stated) E*x = 0;
+flags may range between 0,..,3 defining an upper and lower bit
+(0=0*2+0, 1=0*2+1, 2=1*2+0, 3=1*2+1),
+if higher bit is 1, then program assumes each inequality yields a facet,
+if lower bit is 1, then program assumes the kernel of E is the span of the cone,
+if either bit is 0, then program computes the information itself.
+EXAMPLE: example polytopeViaPoints; shows an example
+"
+{
+
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  intmat IE[2][3]=
+  1,0,0,
+  0,1,0;
+  intmat E[1][3]=
+  0,0,1;
+  polytope p=polytopeViaInequalities(IE,E);
+  p;
+}
+
 proc vertices()
 "USAGE:   vertices(p);  p polytope

Singular/LIB/polymakeInterface.lib

@@ -43 +43 @@
     nLatticePoints();
     normalFan();
+    polytopeViaInequalities();
+    polytopeViaPoints();
     vertexAdjacencyGraph();
     vertexEdgeGraph();
@@ -957 +959 @@
 }
 
+proc polytopeViaPoints()
+"USAGE: polytopeViaPoints(V [, flags]);  intmat V, int flags
+RETURN: polytope which is the intersection of the cone generated by the row vectors
+of V with the hyperplane, in which the first coordinate equals 1;
+flags may be 0 or 1,@*
+if flags is 1, then program assumes that each row vector of M generates a ray in the cone,
+if flags is 0, then program computes that information itself
+EXAMPLE: example polytopeViaPoints; shows an example
+"
+{
+
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  // This is a polytope in R^2 generated by (0,0), (1,0), (0,1), (0,0);
+  intmat V[4][3]=
+  1,0,0,
+  1,1,0,
+  1,0,1,
+  1,1,1;
+  polytope p1=polytopeViaPoints(V);
+  p1;
+  // This is a polytope in R^2 generated by (1/2,2/3), (3/4,4/5), (5/6,6/7):
+  intmat V[3][3]=
+  6,3,4,
+  20,15,16,
+  42,35,36;
+  polytope p2=polytopeViaPoints(V);
+  p2;
+  // This polytope is the positive orthant in R^2:
+  // (0,1,0) and (0,0,1) imply that the polytope is unbounded in that direction
+  intmat V[3][3]=
+  1,0,0,
+  0,1,0,
+  0,0,1;
+  polytope p3=polytopeViaPoints(V);
+  p3;
+}
+
+proc polytopeViaInequalities()
+"USAGE: polytopeViaInequalities(EV [, E [, flags]]);  intmat EV,E, int flags
+RETURN: polytope consisting of all points x, such that IE*x >= 0 in each component
+and (if stated) E*x = 0;
+flags may range between 0,..,3 defining an upper and lower bit
+(0=0*2+0, 1=0*2+1, 2=1*2+0, 3=1*2+1),
+if higher bit is 1, then program assumes each inequality yields a facet,
+if lower bit is 1, then program assumes the kernel of E is the span of the cone,
+if either bit is 0, then program computes the information itself.
+EXAMPLE: example polytopeViaPoints; shows an example
+"
+{
+
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  intmat IE[2][3]=
+  1,0,0,
+  0,1,0;
+  intmat E[1][3]=
+  0,0,1;
+  polytope p=polytopeViaInequalities(IE,E);
+  p;
+}
+
 proc vertexAdjacencyGraph()
 "USAGE:   vertexAdjacencyGraph(p);  p polytope