Dear Sven, dear Forum,
You can use NormalizInterface
https://gap-packages.github.io/NormalizInterface/doc/chap3_mj.html#X8570F3C87B5B7DD7
or 4ti2Interface
https://homalg-project.github.io/homalg_project/4ti2Interface/doc/chap3.html#X7F5D3AAB7834A607
or numericalsgps FactorizationsVectorWRTList
https://gap-packages.github.io/numericalsgps/doc/chap11.html#X8780C7E5830B9AE2
Depending on what do you have installed in your system it will use
NormalizInterface or 4ti2Interface. By default it tries to solve the
problem "by hand", so I recommend either loading first NormalizInterface
or 4ti2Interface. You may want to have a look at
https://gap-packages.github.io/numericalsgps/doc/chap13.html#X84A2793F7A9F3E6A
The easiest way may be installing NormalizInterface and load it prior to
numericalsgps.
Hope this helps,
Pedro
El 29/12/2020 a las 13:30, Sven Reichard escribió:
Dear Forum,
I have a system Ax=b of linear Diophantine equations and I would like to find
the set of all non-negative solutions x.
This looks like a reasonable problem, but so far I have not found anything on
it. My current solution works but not very efficiently. It does the following:
- Lattice reduction on A
- Find a rational solution x' (by SolutionMat)
- Find an integral basis of the nullspace of A (by TriangulizedNullspaceMat)
- Perform a backtrack search for non-negative integer solutions.
If anybody could point me in the direction of other things to try I would be
grateful.
Best wishes for the New Year,
Sven Reichard.
Dresden International University
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Pedro A. Garcia-Sanchez :: https://www.ugr.es/local/pedro
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