4.22.1 coneViaPoints

Syntax:

coneViaPoints( intmat HL )
coneViaPoints( intmat HL, intmat L )
coneViaPoints( intmat HL, intmat L, int flags )

Type:

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:

LIB"gfanlib.so"; // 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; ==> AMBIENT_DIM ==> 3 ==> FACETS ==> 0,1,0, ==> 0,1,1 ==> LINEAR_SPAN ==> ==> 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; ==> AMBIENT_DIM ==> 3 ==> FACETS ==> 0,1,0, ==> 0,1,1 ==> LINEAR_SPAN ==> ==> 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; ==> AMBIENT_DIM ==> 3 ==> FACETS ==> 0,1,0, ==> 0,1,1 ==> LINEAR_SPAN ==> ==> 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; ==> AMBIENT_DIM ==> 3 ==> FACETS ==> 0,1,-1, ==> 0,1, 1 ==> LINEAR_SPAN ==> ==>