Changeset 1f36cef in git

Timestamp:

Sep 29, 2016, 11:48:55 AM (8 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'b4f17ed1d25f93d46dbe29e4b499baecc2fd51bb')

Children:

1cca2257b0e482d23bff22027d4e66c3c8f4c508

Parents:

a163b285f10edfeeb40f2314bfc7233a710282c5

Message:

chg: new doc for gfanlib and polymake, p2

Files:

• Singular/LIB/gfan.lib (modified) (4 diffs)
• doc/cones.yes.doc (modified) (previous)

Singular/LIB/gfan.lib

@@ -15 +15 @@
        canonicalizeCone(c); a unique representation of the cone c
        codimension(c);      the codimension of the input
+       coneViaPoints();     define a cone
+       coneViaInequalities(); define a cone
        coneLink(c,w);       the link of c around w
        containsAsFace(c,d); is d a face of c
        containsInSupport(c,d); is d contained in c
        containsPositiveVector(c); contains a vector with only positive entries?
+       containsRelatively(c,p); p in c?
        convexHull(c1,c2);   convex hull
        convexIntersection(c1,c2); convex hull
@@ -30 +33 @@
        getLinearForms(c);    linear forms previously stored in c
        getMultiplicity(c);   multiplicity previously stored in c
-       inequalities(c);      inequalities of c 
+       inequalities(c);      inequalities of c
        isFullSpace(c);       is the entire ambient space?
        isOrigin(c);          is the origin?
@@ -222 +225 @@
 }
 
+proc coneViaPoints()
+"USAGE:   coneViaPoints(HL); intmat HL
+          coneViaPoints(HL,L); intmat HL, intmat L
+          coneViaPoints(HL,L,flags); intmat HL, intmat L, int flags
+RETURN:  cone
+PURPOSE: cone generated by half lines generated by the row vectors of HL
+  and (if stated) by lines generated by the row vectors of L;
+  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 upper bit is 1, then program assumes that each row vector in HL
+  generates a ray of the cone,
+  if lower bit is 1, then program assumes that the span of the row
+  vectors of L is the lineality space of the cone,
+  if either bit is 0, then program computes the information itself.
+EXAMPLE: example coneViaPoints; shows an example
+"
+{
+
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  // Let's define a cone in R^3 generated by the following half lines:
+  intmat HL[5][3]=
+   1,0, 0,
+  -1,0, 0,
+   0,1, 1,
+   0,1,-1,
+   0,0, 1;
+  cone c=coneViaPoints(HL);
+  c;
+  kill HL,c;
+  // Note that (1,0,0) and (-1,0,0) form a line, hence also possible:
+  intmat HL[3][3]=
+  0,1, 1,
+  0,1,-1,
+  0,0, 1;
+  intmat L[1][3]=
+  1,0,0;
+  cone c=coneViaPoints(HL,L);
+  c;
+  kill HL,L,c;
+  // lineality space is exactly Lin(1,0,0)
+  intmat HL[3][3]=
+  0,1, 1,
+  0,1,-1,
+  0,0, 1;
+  intmat L[1][3]=
+  1,0,0;
+  cone c=coneViaPoints(HL,L,1);
+  c;
+  kill HL,L,c;
+  // and that (0,1,-1), (0,1,1) generate rays
+  intmat HL[3][3]=
+  0,1, 1,
+  0,1,-1;
+  intmat L[1][3]=
+  1,0,0;
+  cone c=coneViaPoints(HL,L,1);
+  c;
+  kill HL,L,c;
+  // and that (0,1,-1), (0,1,1) generate rays
+  intmat HL[3][3]=
+  0,1, 1,
+  0,1,-1;
+  intmat L[1][3]=
+  1,0,0;
+  cone c=coneViaPoints(HL,L,3);
+  c;
+}
+
+proc coneViaInequalities()
+"USAGE:   coneViaInequalities(IE); intmat IE
+          coneViaInequalities(IE,E); intmat IE, intmat E
+          coneViaInequalities(IE,E,flags); intmat IE, intmat E, int flags
+RETURN:  cone
+PURPOSE: cone consisting of all points x, such that IE*x >= 0 in each component
+  and (if stated) E*x = 0;
+  inequalities and (if stated) equations will be transformed, getting rid of
+  redundancies;
+  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 coneViaInequalities; shows an example
+"
+{
+
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  // Let's define a cone in R^3 given by the following inequalities:
+  intmat IE[6][3]=
+  1,3,5,
+  1,5,3,
+  0,1,-1,
+  0,1,1,
+  1,0,0,
+  -1,0,0;
+  cone c=coneViaInequalities(IE);
+  c;
+  // Note that the last two inequalities yield x1 = 0, hence also possible:
+  intmat IE[4][3]=
+  0,1,-1,
+  0,1,1;
+  intmat E[1][3]=
+  1,0,0;
+  cone c=coneViaInequalities(IE,E);
+  c;
+  // each inequalities gives rise to a facet
+  intmat IE[2][3]=
+  0,1,-1,
+  0,1,1;
+  intmat E[1][3]=
+  1,0,0;
+  cone c=coneViaInequalities(IE,E,1);
+  c;
+  // and the kernel of E is the span of the cone
+  intmat IE[2][3]=
+  0,1,-1,
+  0,1,1;
+  intmat E[1][3]=
+  1,0,0;
+  cone c=coneViaInequalities(IE,E,3);
+  c;
+}
+
 proc coneLink()
 "USAGE:   coneLink(c,w);  c cone, w intvec/bigintmat
@@ -273 +405 @@
   containsInSupport(c,d2);
   containsAsFace(c,d2);
+}
+
+proc containsRelatively()
+"USAGE:   containsRelatively(c,p);  c cone, intvec p
+RETURN:  1 iff the given cone contains the given point in its relative interior; 0 otherwise
+EXAMPLE: example containsRelatively; shows an example
+"
+{
+
+}
+example
+{
+  "EXAMPLE:"; echo = 2;
+  intmat M[2][2]=
+  1,0,
+  0,1;
+  cone c=coneViaPoints(M);
+  intvec p1=1,1;
+  containsRelatively(c,p1);
+  intvec p2=0,1;
+  containsRelatively(c,p2);
 }