SOME BCMATH INTEGER MATRIX PROGRAMS

Some BCMATH integer matrix programs

  1. Finding small multipliers for the extended gcd of n positive integers using the Havas-Majewski-Matthews LLL-based approach: first version, improved version.
  2. Finding the Hermite normal form of an integer matrix using the Havas-Majewski-Matthews LLL-based algorithm.
  3. 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.
  4. Finding a LLL reduced basis for an integer matrix whose rows are LI.
  5. Finding a LLL reduced basis for an integer matrix whose rows may be LD, using the MLLL algorithm.
  6. Finding the Smith normal form of an integer matrix using the Hermite normal form.
  7. Finding the shortest vectors of a lattice using the Fincke-Pohst algorithm.
  8. Finding the closest lattice points to a given point.
  9. Solving a system of linear congruences AX ≡ B (mod m) using the Smith normal form of an integer matrix.
  10. 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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