LiDIA

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 52 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. Konstantinou, Elisavet; Kontogeorgis, Aristides; Stamatiou, Yannis C; Zaroliagis, Christos: On the efficient generation of prime-order elliptic curves (2010)
  4. Mikuš, Michal; Savicky, Petr: Remarks on Gödel’s code as a hash function (2010)
  5. Najman, Filip: Compact representation of quadratic integers and integer points on some elliptic curves (2010)
  6. Tanaka, Satoru; Ogura, Naoki; Nakamula, Ken; Matsui, Tetsushi; Uchiyama, Shigenori: NZMATH 1.0 (2010)
  7. Miret, J.; Moreno, R.; Rio, A.; Valls, M.: Computing the (\ell)-power torsion of an elliptic curve over a finite field (2009)
  8. Mihailescu, Preda: Fast convolutions meet Montgomery (2008)
  9. de Haan, R.; Jacobson, M. J. jun.; Williams, H. C.: A fast, rigorous technique for computing the regulator of a real quadratic field (2007)
  10. Konstantinou, Elisavet; Stamatiou, Yannis C.; Zaroliagis, Christos: Efficient generation of secure elliptic curves (2007) ioport
  11. Miret, J.; Moreno, R.; Sadornil, D.; Tena Ayuso, Juan Gabriel; Valls, M.: An algorithm to compute volcanoes of 2-isogenies of elliptic curves over finite fields (2006)
  12. Schömer, Elmar; Wolpert, Nicola: An exact and efficient approach for computing a cell in an arrangement of quadrics (2006)
  13. Gregor, Douglas; Järvi, Jaakko; Kulkarni, Mayuresh; Lumsdaine, Andrew; Musser, David; Schupp, Sibylle: Generic programming and high-performance libraries (2005) ioport
  14. Miret, J.; Moreno, R.; Rio, A.; Valls, M.: Determining the (2)-Sylow subgroup of an elliptic curve over a finite field (2005)
  15. Biehl, Ingrid; Paulus, Sacher; Takagi, Tsuyoshi: Efficient undeniable signature schemes based on ideal arithmetic in quadratic orders (2004)
  16. Culver, Tim; Keyser, John; Manocha, Dinesh: Exact computation of the medial axis of a polyhedron (2004)
  17. Jacobson, Michael J. jun.; Williams, Hugh C.: New quadratic polynomials with high densities of prime values (2003)
  18. Jacobson, M. J. jun.; Pintér, Á.; Walsh, P. G.: A computational approach for solving (y^2=1^k+2^k+\dotsb+x^k) (2003)
  19. Teske, Edlyn: Computing discrete logarithms with the parallelized kangaroo method. (2003)
  20. Aardal, Karen; Weismantel, Robert; Wolsey, Laurence A.: Non-standard approaches to integer programming (2002)

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