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• Basic Structures : array (0, 1, 2 dimensional), bit array, hashtable, stack.

• Arithmetic with arbitrary precision over the Integers (Karatsuba with GMP) plus
• Chinese remaindering.
• Primality testing (Miller, Lehmann, Pepin for Fermat numbers, ...).
• Factorization (Pollard, ...).
• Euler's phi.
• Primitive roots.
• RSA coding system.

• Arithmetic over Z/mZ.

• Arithmetic with arbitrary precision over the Rationals.

• Fractions.

• Linear Algebra : dense and sparse (reduced coordinate format) vectors, dense matrices and submatrices.
• Visualisation tools.
• Linear recurring sequence :
• Pade/Euclide algorithm over a field.
• Reeds-Sloane algorithm modulo any integer.
• System solving :
• Elimination (Gauss) over a field.
• Fraction-free elimination (Gauss-Bareiss) over a ring.
• Matrix-Free algorithm (Coppersmith's Block Wiedemann) over a field .
• Rank computation :
• Elimination over a field.
• Fraction-free elimination over a ring.
• Specialized elimination implementations (GF(2), GF(p^k)).
• Matrix-Free algorithm over a field with Toepliz, diagonal and/or tranpose precondtionning.
• Valence computation over the Integers :
• Fraction-free elimination (Heuristic Storjohan).
• Matrix-Free and Chinese remaindering.
• Smith form :
• Elimination or Matrix-Free over a field, elimination over GF(p^k) and Fraction-free elimination (Heuristic Storjohan).
• Elimination or Matrix-Free over a field, elimination over GF(p^k) and Valence computation.

• Polynomial arithmetic.
• Square free decomposition.
• Sturm query.
• Factorization (Berlekamp, Cantor-Zassenhaus).

• Arithmetic with algebraic numbers.
• Equality testing (D5, lazy).
• Sign testing (Sylvester-Habicht).

• Timer (microseconds).
• user time, system time, real time.

, : Distributed.
: Available via e-mail.

 Last update: Tuesday, January 10th 2012 Givaro