HermiteDecomposition

with unimodular and upper triangular in Hermite normal form.

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HermiteDecomposition(m)a unimodular and in Hermite normal form

Domain: Number theory

Details

• is upper triangular with positive pivots, and every entry above a pivot is reduced into — the row-reduced convention that makes unique for a given .
• : , so is invertible over , not merely over .
• Used by ProfiniteDecomposition to put a matrix over into strong-approximation form (Hertogh's Algorithm 8.4).

Examples

See also: ProfiniteDecomposition, ExtendedGCD