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1. For the cube
1 0 0 0
is a missing vertex in cube-1.ext and
1 1/2 0 0
is a point not in the CH of these 7 points
cube-1.ext.lp
is formed by adding a leading col of zeroes, making it an H-rep,
with the missing point (with leading zero) as objective.
mai6% lrs cube-1.ext.lp
lrs:lrslib_v.7.2_2022.3.6(64bit,lrslong.h,hybrid_arithmetic)
*Input taken from cube-1.ext.lp
cube-1
*lponly mode: Dantzig's rule
minimize 0 2 1 0 0
*Unbounded solution
1 0 0 0 0
0 -1 1 1 1
*overflow checking on lrslong arithmetic
*lrs:lrslib_v.7.2_2022.3.6(64bit,lrslong.h,hybrid arithmetic)
We use a *ray* (without leading zero) as an objective function in
cube.ine.lp
which solves to give the missing vertex
mai6% lrs cube.ine.lp
lrs:lrslib_v.7.2_2022.3.6(64bit,lrslong.h,hybrid_arithmetic)
*Input taken from cube.ine.lp
cube
minimize-1 1 1 1
*lponly mode: Dantzig's rule
1 0 0 0
*Obj=-1 pivots=6
2.cp6-1.ext misses the origin of cp6.ext.
mai6% lrs cp6-1.ext.lp
lrs:lrslib_v.7.2_2022.3.6(64bit,lrslong.h,hybrid_arithmetic)
*Input taken from cp6-1.ext.lp
cp6.ext.lp
*lponly mode: Dantzig's rule
minimize 0 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
*Unbounded solution
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -2 0 0 0 1 1 0 0 1 1 0 1 1 1 1 -2
*overflow checking on lrslong arithmetic
Take the ray to give the objective in cp6.ine
mai6% lrs cp6.ine
lrs:lrslib_v.7.2_2022.3.6(64bit,lrslong.h,hybrid_arithmetic)
*Input taken from cp6.ine
cp6.ine
*lponly mode: Dantzig's rule
minimize-2 0 0 0 1 1 0 0 1 1 0 1 1 1 1 -2
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
*Obj=-2 pivots=312
3. cp6-half.ext misses 16 vertices of cp6.ext and the extra point is
1 23/216 199/216 103/108 199/216 25/27 35/36 203/216 35/36 67/72 7/216 1/18 7/72 19/216 7/108 7/72
mai6% lrs cp6-half.ext.lp
lrs:lrslib_v.7.2_2022.3.6(64bit,lrslong.h,hybrid_arithmetic)
*Input taken from cp6-half.ext.lp
cp6-half
minimize 0 216 23 199 206 199 200 210 203 210 201 7 12 21 19 14 21
*lponly mode: Dantzig's rule
*Unbounded solution
0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 -1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -2 1 1 1 1 -1 -1 -1 -1 0 1 -1 -1 1 0
0 0 -1 0 1 0 0 0 0 0 -1 0 0 0 0 1 0
0 0 -1 0 0 1 0 0 0 0 -1 -1 1 0 0 1 0
0 0 -1 1 0 0 0 0 0 0 -1 0 1 0 -1 1 0
0 0 -1 0 0 0 1 0 0 0 -1 -1 1 0 -1 2 0
0 0 0 0 0 0 0 0 -1 0 1 1 -1 0 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 1 0
0 0 0 0 0 0 0 0 0 -1 1 0 0 0 1 -1 0
0 0 0 0 0 0 0 -1 0 0 1 1 0 0 0 -1 0
We get 10 rays, each could be used as an objective in cp6.ine and the four I chose all gave
different missing vertices. Eg:
mai6% lrs cp6.ine
lrs:lrslib_v.7.2_2022.3.6(64bit,lrslong.h,hybrid_arithmetic)
*Input taken from cp6.ine
cp6.ine
*lponly mode: Dantzig's rule
minimize 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 -1 1
1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0
*Obj=-2 pivots=165
*overflow checking on lrslong arithmetic
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