Changeset 6b5e56 in git


Ignore:
Timestamp:
Sep 30, 2016, 3:17:04 PM (8 years ago)
Author:
Hans Schoenemann <hannes@…>
Branches:
(u'fieker-DuVal', '117eb8c30fc9e991c4decca4832b1d19036c4c65')(u'spielwiese', 'b4f17ed1d25f93d46dbe29e4b499baecc2fd51bb')
Children:
5d51cc663dae53ce9fbf7b3e9c6d91552065e9ee
Parents:
a7cb003033a5f0d241c506361d12833f4c05be5d
Message:
doc: references
Location:
Singular/LIB
Files:
2 edited

Legend:

Unmodified
Added
Removed
  • Singular/LIB/normal.lib

    ra7cb00 r6b5e56  
    77@*        S. Laplagne,   slaplagn@dm.uba.ar,
    88@*        G. Pfister,    pfister@mathematik.uni-kl.de
     9@*        Peter Chini,   chini@rhrk.uni-kl.de (normalConductor)
    910
    1011
  • Singular/LIB/polymakeInterface.lib

    ra7cb00 r6b5e56  
    959959}
    960960
    961 proc polytopeViaPoints()
    962 "USAGE: polytopeViaPoints(V [, flags]);  intmat V, int flags
    963 RETURN: polytope which is the intersection of the cone generated by the row vectors
    964 of V with the hyperplane, in which the first coordinate equals 1;
    965 flags may be 0 or 1,@*
    966 if flags is 1, then program assumes that each row vector of M generates a ray in the cone,
    967 if flags is 0, then program computes that information itself
    968 EXAMPLE: example polytopeViaPoints; shows an example
    969 "
    970 {
    971 
    972 }
    973 example
    974 {
    975   "EXAMPLE:"; echo = 2;
    976   // This is a polytope in R^2 generated by (0,0), (1,0), (0,1), (0,0);
    977   intmat V[4][3]=
    978   1,0,0,
    979   1,1,0,
    980   1,0,1,
    981   1,1,1;
    982   polytope p1=polytopeViaPoints(V);
    983   p1;
    984   // This is a polytope in R^2 generated by (1/2,2/3), (3/4,4/5), (5/6,6/7):
    985   intmat V[3][3]=
    986   6,3,4,
    987   20,15,16,
    988   42,35,36;
    989   polytope p2=polytopeViaPoints(V);
    990   p2;
    991   // This polytope is the positive orthant in R^2:
    992   // (0,1,0) and (0,0,1) imply that the polytope is unbounded in that direction
    993   intmat V[3][3]=
    994   1,0,0,
    995   0,1,0,
    996   0,0,1;
    997   polytope p3=polytopeViaPoints(V);
    998   p3;
    999 }
    1000 
    1001 proc polytopeViaInequalities()
    1002 "USAGE: polytopeViaInequalities(EV [, E [, flags]]);  intmat EV,E, int flags
    1003 RETURN: polytope consisting of all points x, such that IE*x >= 0 in each component
    1004 and (if stated) E*x = 0;
    1005 flags may range between 0,..,3 defining an upper and lower bit
    1006 (0=0*2+0, 1=0*2+1, 2=1*2+0, 3=1*2+1),
    1007 if higher bit is 1, then program assumes each inequality yields a facet,
    1008 if lower bit is 1, then program assumes the kernel of E is the span of the cone,
    1009 if either bit is 0, then program computes the information itself.
    1010 EXAMPLE: example polytopeViaPoints; shows an example
    1011 "
    1012 {
    1013 
    1014 }
    1015 example
    1016 {
    1017   "EXAMPLE:"; echo = 2;
    1018   intmat IE[2][3]=
    1019   1,0,0,
    1020   0,1,0;
    1021   intmat E[1][3]=
    1022   0,0,1;
    1023   polytope p=polytopeViaInequalities(IE,E);
    1024   p;
    1025 }
    1026 
    1027961proc vertexAdjacencyGraph()
    1028962"USAGE:   vertexAdjacencyGraph(p);  p polytope
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