LiDIA: A library for computational number theory. LiDIA is a C++ library for number theory. The present version only contains tools for rational integers and some floating point arithmetic, however. Emphasis is put on easy usability, modularity (e.g. it can be used with different multi-precision packages) and speed. In this report the authors present several illustrative examples. In particular, they compare their running times with those of the software packages Pari, Maple and Mathematica. Computer algebra system (CAS).

This software is also referenced in ORMS.

References in zbMATH (referenced in 21 articles , 1 standard article )

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  1. Velichka, M.D.; Jacobson, M.J. jun.; Stein, A.: Computing discrete logarithms in the Jacobian of high-genus hyperelliptic curves over even characteristic finite fields (2014)
  2. Welschenbach, Michael: Cryptography in C and C++ (2013)
  3. Tanaka, Satoru; Ogura, Naoki; Nakamula, Ken; Matsui, Tetsushi; Uchiyama, Shigenori: NZMATH 1.0 (2010)
  4. Biehl, Ingrid; Paulus, Sacher; Takagi, Tsuyoshi: Efficient undeniable signature schemes based on ideal arithmetic in quadratic orders (2004)
  5. Backes, Werner; Wetzel, Susanne: Heuristics on lattice basis reduction in practice (2002)
  6. Krishnan, Shankar; Foskey, Mark; Culver, Tim; Keyser, John; Manocha, Dinesh: PRECISE: efficient multiprecision evaluation of algebraic roots and predicates for reliable geometric computation (2001)
  7. Backes, Werner; Wetzel, Susanne: New results on lattice basis reduction in practice (2000)
  8. Keyser, J.; Culver, T.; Manocha, D.; Krishnan, S.: Efficient and exact manipulation of algebraic points and curves (2000)
  9. Maurer, Markus Hartmut: Regulator approximation and fundamental unit computation for real-quadratic orders (2000)
  10. Paulus, Sachar; Takagi, Tsuyoshi: A new public-key cryptosystem over a quadratic order with quadratic decryption time. (2000)
  11. Jacobson, Michael J. jun.: Applying sieving to the computation of quadratic class groups (1999)
  12. Keyser, John; Krishnan, Shankar; Manocha, Dinesh: Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic. II: Computation (1999)
  13. Hühnlein, Detlef; Jacobson, Michael J.jun.; Sachar, Paulus; Takagi, Tsuyoshi: A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption (1998)
  14. Weber, Damian; Denny, Thomas: The solution of McCurley’s discrete log challenge (1998)
  15. Wetzel, Susanne: An efficient parallel block-reduction algorithm (1998)
  16. Buchmann, Johannes; Jacobson, Michael J.jun.; Teske, Edlyn: On some computational problems in finite abelian groups (1997)
  17. Green, Edward L.; Heath, Lenwood S.; Keller, Benjamin J.: Opal: a system for computing noncommutative Gröbner bases (1997)
  18. Schirokauer, Oliver; Weber, Damian; Denny, Thomas: Discrete logarithms: The effectiveness of the index calculus method (1996)
  19. Weber, Damian: Computing discrete logarithms with the general number field sieve (1996)
  20. Biehl, Ingrid; Buchmann, Johannes; Papanikolaou, Thomas: LiDIA: A library for computational number theory (1995)

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