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Determinant

 Property

Summary

The determinant, by fraction-free elimination where the entries are polynomials
over the rationals and by Laplace expansion otherwise.

Remarks

Both are exact and neither divides in a way that could exclude a point, so the
two agree wherever both apply; which one ran is a fact about cost, not about the
answer. Laplace is optimal for a fully symbolic matrix, whose determinant
genuinely has n! terms.

























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