find integral solutions to matrix equations over PIDs #38019
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mkoeppe
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May 17, 2024
mkoeppe
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Thanks, all done. |
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Of course, the same can be done with a weaker normal form, the Hermite form. matrix_integer_dense has many algorithm options for that one... |
…_smith_form SageMath version 10.4.beta9, Release Date: 2024-06-09
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That's a good suggestion, thanks. I gave it a try. |
vbraun
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Even for matrices explicitly defined over ℤ, the `.solve_left()` and
`.solve_right()` methods may return solutions over ℚ. In this patch, we
add an optional flag `integral=` to these methods which forces the
computation of an integral solution if one exists (and throws an
exception otherwise).
The algorithm is completely standard, using the (pre-existing)
`.smith_form()` method, but so far users had to implement the rest of
the solution method on their own each time.
Computing integral solutions to underdetermined systems is a common task
when working with lattices.
URL: sagemath#38019
Reported by: Lorenz Panny
Reviewer(s): Matthias Köppe
vbraun
pushed a commit
to vbraun/sage
that referenced
this pull request
Jun 16, 2024
Even for matrices explicitly defined over ℤ, the `.solve_left()` and
`.solve_right()` methods may return solutions over ℚ. In this patch, we
add an optional flag `integral=` to these methods which forces the
computation of an integral solution if one exists (and throws an
exception otherwise).
The algorithm is completely standard, using the (pre-existing)
`.smith_form()` method, but so far users had to implement the rest of
the solution method on their own each time.
Computing integral solutions to underdetermined systems is a common task
when working with lattices.
URL: sagemath#38019
Reported by: Lorenz Panny
Reviewer(s): Matthias Köppe
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Even for matrices explicitly defined over ℤ, the
.solve_left()and.solve_right()methods may return solutions over ℚ. In this patch, we add an optional flagintegral=to these methods which forces the computation of an integral solution if one exists (and throws an exception otherwise).The algorithm is completely standard, using the (pre-existing)
.smith_form()method, but so far users had to implement the rest of the solution method on their own each time.Computing integral solutions to underdetermined systems is a common task when working with lattices.