InnerPoint finds a not valid point

[Víctor de Buen Remiro]

This is an example of InnerPoint failing, due to it returns a point that not matches the inequations but there exists a inner point x2 that I've found with Mathematica

Matrix A = SetMat(SetOfSet(

SetOfReal( -1, +0, +0, +0, +0, +0),
SetOfReal( +1, +0, +0, +0, +0, +0),
SetOfReal( +0, -1, +0, +0, +0, +0),
SetOfReal( +0, +1, +0, +0, +0, +0),
SetOfReal( +0, +0, -1, +0, +0, +0),
SetOfReal( +0, +0, +1, +0, +0, +0),
SetOfReal( +0, +0, +0, -1, +0, +0),
SetOfReal( +0, +0, +0, +1, +0, +0),
SetOfReal( +0, +0, +0, +0, -1, +0),
SetOfReal( +0, +0, +0, +0, +1, +0),
SetOfReal( +0, +0, +0, +0, +0, -1),
SetOfReal( +0, +0, +0, +0, +0, +1),
SetOfReal( +0, +1, +0, +0, +0, -1),
SetOfReal( +0, +0, +0, -1, +0, +1),
SetOfReal( +1, +0, +0, +0, -1, +0),
SetOfReal( +0, +0, -1, +0, +1, +0),
SetOfReal( +0, +0, -1, +1, +0, +0),
SetOfReal( -1, +1, +0, +0, +0, +0),
SetOfReal( +0, +0, +0, +0, -1, +1)

));
Matrix a = Col( +2, -1.21, +1.3, -1.19, +2, -1.108, +1.3, -1.1, +2, -1.159, +1.3, -1.15, +0, +0, +0, +0, +0, +0, +0);
Set X = InnerPoint(A,a);
Matrix check_1 = A*X::InnerPoint-a;
Real ok_1 = MatMax(check_1)<=1.E-15;

Matrix x2 = Col(-1.21, -1.21, -1.108, -1.108, -1.159, -1.159);
Matrix check_2 = A*x2-a;
Real ok_2 = MatMax(check_2)<=1.E-15;

[Víctor de Buen Remiro]

A standard test has been added to

​http://cvs.tol-project.org/viewcvs.cgi/tol_tests/tol/Bugzilla/bug_000533

[Víctor de Buen Remiro]

I think that this information could be usefull. If we draw points around the inner point x2 with normal distribution N(0,0.0001), it's to say, points that are very close to x2, the ratio of inner points is very low (about 0.2%). I conclude that is a very narrow but non empty region. You can check it with this TOL code:

Real probInnerEnvironment = SetAvr(For(1,100000,Real(Real k)
{

Matrix x3 = x2+Gaussian(Rows(x2),1,0,0.0001);
Matrix check_3 = A*x3-a;
MatMax(check_3)<=1.E-15

}));