Linear Algebra over different fields (`LinearAlgebra.det` does not respect the `+` and `*` multimethods)

Julia’s LinearAlgebra library doesn’t have built-in functions for exact determinants of integer matrices, which is more appropriate for a number-theory package. Instead, its det function works by first computing the LU factorization (i.e. doing Gaussian elimination), which requires conversion to floating point (and is accurate up to roundoff errors).

See also the discussion in another thread.

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