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document exact BigInt determinants #53579

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merged 1 commit into from Mar 9, 2024
Merged

document exact BigInt determinants #53579

merged 1 commit into from Mar 9, 2024

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stevengj
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@stevengj stevengj commented Mar 4, 2024

New users are commonly surprised that determinants of integer matrices give an approximate floating-point answer (#40128), and are unaware that an exact algorithm is implemented for BigInt matrices (#40868). This PR comments on both of these facts in the det documentation.

(At some point, we may want to mark LinearAlgebra.det_bareiss as public, and document it, but that can be done in a future PR.)

@stevengj stevengj added domain:docs This change adds or pertains to documentation domain:linear algebra Linear algebra labels Mar 4, 2024
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jmichel7 commented Mar 4, 2024

Something worth documenting with det_bareiss is exactdiv. This routine is fundamental for making this kind of linear algebra to work over a ring.

For instance, it is sufficient to define exactdiv for polynomials to have det_bareiss work for a matrix of polynomials. I have implemented quite a few similar linear algebra algorithms over a ring where exactdiv is useful in the same way, for instance computing the characteristic polynomial or the comatrix (the inverse times the determinant).

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stevengj commented Mar 4, 2024

Yes, but documenting det_bareiss is a topic for another issue, as I mentioned above — I agree that one would want to document exactdiv as well in that case. This PR is just focused on documenting det.

@oscardssmith oscardssmith merged commit c705a25 into master Mar 9, 2024
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@oscardssmith oscardssmith deleted the stevengj-patch-3 branch March 9, 2024 15:42
mkitti pushed a commit to mkitti/julia that referenced this pull request Apr 13, 2024
New users are commonly surprised that determinants of integer matrices
give an approximate floating-point answer (JuliaLang#40128), and are unaware that
an exact algorithm is implemented for `BigInt` matrices (JuliaLang#40868). This
PR comments on both of these facts in the `det` documentation.

(At some point, we may want to mark `LinearAlgebra.det_bareiss` as
`public`, and document it, but that can be done in a future PR.)
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4 participants