Singular Manual: coneViaInequalities

  | ### 4.22.2 coneViaInequalities `Syntax:` `coneViaInequalities(` intmat IE `)` `coneViaInequalities(` intmat IE, intmat E `)` `coneViaInequalities(` intmat IE, intmat E, int flags `)` `Type:` 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:`
      LIB"gfanlib.so";
      // 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;
      ==> AMBIENT_DIM
      ==> 3
      ==> INEQUALITIES
      ==> 0,1,-1,
      ==> 0,1, 1,
      ==> 1,3, 5,
      ==> 1,5, 3
      ==> LINEAR_SPAN
      ==> -1,0,0
      ==>
      // Note that the last two inequalities yield x1 = 0, hence also possible:
      intmat IE[4][3]=
      ==> // ** redefining IE **
      0,1,-1,
      0,1,1;
      intmat E[1][3]=
      1,0,0;
      cone c=coneViaInequalities(IE,E);
      ==> // ** redefining c **
      c;
      ==> AMBIENT_DIM
      ==> 3
      ==> INEQUALITIES
      ==> 0,1,-1,
      ==> 0,1, 1
      ==> LINEAR_SPAN
      ==> 1,0,0
      ==>
      // each inequalities gives rise to a facet
      intmat IE[2][3]=
      ==> // ** redefining IE **
      0,1,-1,
      0,1,1;
      intmat E[1][3]=
      ==> // ** redefining E **
      1,0,0;
      cone c=coneViaInequalities(IE,E,1);
      ==> // ** redefining c **
      c;
      ==> AMBIENT_DIM
      ==> 3
      ==> INEQUALITIES
      ==> 0,1,-1,
      ==> 0,1, 1
      ==> LINEAR_SPAN
      ==> 1,0,0
      ==>
      // and the kernel of E is the span of the cone
      intmat IE[2][3]=
      ==> // ** redefining IE **
      0,1,-1,
      0,1,1;
      intmat E[1][3]=
      ==> // ** redefining E **
      1,0,0;
      cone c=coneViaInequalities(IE,E,3);
      ==> // ** redefining c **
      c;
      ==> AMBIENT_DIM
      ==> 3
      ==> FACETS
      ==> 0,1,-1,
      ==> 0,1, 1
      ==> LINEAR_SPAN
      ==> 1,0,0
      ==>

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