Singular dense solve with Method::Dixon with SolutionType::Determinist fails

[Breush]

With this minimal example, we get x = [ 0 0 0 ] as a solution, which is wrong.

#include <linbox/solutions/solve.h>

using namespace LinBox;

int main(void)
{
    using Ring = Givaro::ZRing<Integer>;
    using Matrix = DenseMatrix<Ring>;
    using Vector = DenseVector<Ring>;

    Ring ZZ;

    Matrix A(ZZ, 1, 3);
    Vector x(ZZ, A.coldim());
    Vector b(ZZ, A.rowdim());
    Ring::Element d;

    A.setEntry(0, 1, 1);
    A.setEntry(0, 2, 2);
    ZZ.assign(b[0], 1);

    // Calling Dixon
    solve(x, d, A, b, Method::Dixon(Method::Dixon::SolutionType::DETERMINIST));

    std::cout << "[ 0 1 2 ] x = [ 1 ] => xNum/xDen = [ " << x[0] << " " << x[1] << " " << x[2] << " ] /" << d << std::endl;

    return 0;
}

First investigation shows that FFPACK::LQUPtoInverseOfFullRankMinor within RationalSolver<...>::monolithicSolve might be the culprit.

[bdsaunders]

I'd like to see "determinist" spelled "deterministic". The former word, "one who determines" is seldom used and is jarring to the ear in our context.

On Fri, Mar 8, 2019 at 5:50 AM A. Breust notifications@github.com wrote:

With this minimal example, we get x = [ 0 0 0 ] as a solution, which is wrong.

include <linbox/solutions/solve.h>

using namespace LinBox; int main(void) { using Ring = Givaro::ZRing; using Matrix = DenseMatrix; using Vector = DenseVector;

Ring ZZ;

Matrix A(ZZ, 1, 3);
Vector x(ZZ, A.coldim());
Vector b(ZZ, A.rowdim());
Ring::Element d;

A.setEntry(0, 1, 1);
A.setEntry(0, 2, 2);
ZZ.assign(b[0], 1);

// Calling Dixon
solve(x, d, A, b, Method::Dixon(Method::Dixon::SolutionType::DETERMINIST));

std::cout << "[ 0 1 2 ] x = [ 1 ] => xNum/xDen = [ " << x[0] << " " << x[1] << " " << x[2] << " ] /" << d << std::endl;

return 0;

}

First investigation shows that FFPACK::LQUPtoInverseOfFullRankMinor within RationalSolver<...>::monolithicSolve might be the culprit.

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[Breush]

@bdsaunders All right, I changed "Determinist" to "Deterministic" in my WIP branch #169.

[jgdumas]

Solved by fflas-ffpack PR#230