find integral solutions to matrix equations over PIDs#38019
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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. |
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sagemathgh-38019: find integral solutions to matrix equations over PIDs 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
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Jun 16, 2024
sagemathgh-38019: find integral solutions to matrix equations over PIDs 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.