### Some BCMATH integer matrix programs

- Finding small multipliers for the extended gcd of n positive integers using the Havas-Majewski-Matthews LLL-based approach: first version, improved version.
- Finding the Hermite normal form of an integer matrix using the Havas-Majewski-Matthews LLL-based algorithm.
- Finding a small solution of a system of linear diophantine equations AX=b using the Hermite normal form of an integer matrix and the Havas-Majewski-Matthews LLL-based algorithm.
- Finding a LLL reduced basis for an integer matrix whose rows are LI.
- Finding a LLL reduced basis for an integer matrix whose rows may be LD, using the MLLL algorithm.
- Finding the Smith normal form of an integer matrix using the Hermite normal form.
- Finding the shortest vectors of a lattice using the Fincke-Pohst algorithm.
- Finding the closest lattice points to a given point.
- Solving a system of linear congruences AX
≡ B (mod m) using the Smith normal form of an integer matrix.
- Solving a system of linear congruences with possibly differing moduli, using the Smith normal form of an integer matrix.

*Last modified 16th February 2017*

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