Valence Smith Form of a matrix A

• Valence Computation

  • Product of at least all the primes appearing in the invariant factors of A

• Set of primes

  • factor the valence v, L is the set of primes dividing v

• Integer Rank

  • q ? L, r = rankq(A) ? there are r non-zero invariant factors

• Non-trivial invariant factors

  • ?p?L, compute Sp, the local Smith form at p. S = S ? Sp

• Return S

• Valence Computation
  • Product of at least all the primes appearing in the invariant factors of A

• Set of primes
  • factor the valence v, L is the set of primes dividing v

• Integer Rank
  • q ? L, r = rankq(A) ? there are r non-zero invariant factors

• Non-trivial invariant factors
  • ?p?L, compute Sp, the local Smith form at p. S = S ? Sp

• Return S

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