## LiDIA - A library for computational number theory (1995)

Venue: | SFB 124-C1, Fachbereich Informatik, Universitt des Saarlandes |

Citations: | 20 - 2 self |

### BibTeX

@TECHREPORT{Biehl95lidia-,

author = {Ingrid Biehl and Johannes Buchmann and Thomas Papanikolaou},

title = {LiDIA - A library for computational number theory},

institution = {SFB 124-C1, Fachbereich Informatik, Universitt des Saarlandes},

year = {1995}

}

### Years of Citing Articles

### OpenURL

### Abstract

this paper we describe LiDIA, a new library for computational number theory. Why do we work on a new library for computational number theory when such powerful tools as Pari [1], Kant

### Citations

675 | Mathematica, A system for Doing Mathematics by Computer - Wolfram - 1991 |

80 |
The GNU multiple precision arithmetic library
- Granlund
- 2010
(Show Context)
Citation Context ...a serious problem to decide which multiprecision integer package and which memory manager should be used in LiDIA. There are competing multiprecision integer packages, for example the GNU gmp-package =-=[7]-=-, the libI-package [6], and the lip-package [9]. Some of those packages are more efficient on one architecture and some on others. Also, new architectures will lead to new multiprecision packages. We ... |

31 | Factoring integers and computing discrete logarithms via diophantine approximations
- Schnorr
- 1991
(Show Context)
Citation Context ...d Korkine-Zolotaref-reduced bases etc. In the following table we list the running times needed by a SUN Sparc8 for the calculation of the LLL-reduced matrix of a n \Theta n Schnorr-Factor-matrix (see =-=[12]-=-). n LiDIA Pari Maple Mathematica 5 0.57 0.78 75.43 5.58 10 4.30 6.39 470.25 28.30 15 15.10 22.67 - 69.10 20 37.21 55.70 - - 25 72.35 107.75 - - 30 126.50 185.69 - - 35 199.36 300.55 - - 40 296.74 435... |

15 | On the Factorization of RSA120
- Denny, Dodson, et al.
- 1994
(Show Context)
Citation Context ...of our research group is developed independently of other computer algebra systems. Over the past years we have been working on many problems of computational number theory such as factoring integers =-=[5]-=-, computing discrete logarithms over finite fields [13], counting the number of points on an elliptic curve over a finite field [8], computing the class number of number fields [2], etc. In those proj... |

7 |
libI: eine lange ganzzahlige Arithmetik
- Dentzer
- 1991
(Show Context)
Citation Context ...ecide which multiprecision integer package and which memory manager should be used in LiDIA. There are competing multiprecision integer packages, for example the GNU gmp-package [7], the libI-package =-=[6]-=-, and the lip-package [9]. Some of those packages are more efficient on one architecture and some on others. Also, new architectures will lead to new multiprecision packages. We decided to make LiDIA ... |

3 |
User's Guide to PARI - GP", available with PARI-package by anonymous ftp on megrez.math.u-bordeaux.fr
- Batut, Bernardi, et al.
(Show Context)
Citation Context ...brucken 1 Introduction In this paper we describe LiDIA, a new library for computational number theory. Why do we work on a new library for computational number theory when such powerful tools as Pari =-=[1]-=-, Kant [11], Simath [10] already exist? In fact, those systems are very useful for solving problems for which there exist efficient system routines. For example, using Pari or Kant it is possible to c... |

3 |
A probabilistic class group and regular algorithm and its implementation", Computational Number Theory (Petho
- Buchmann, Dullmann
- 1991
(Show Context)
Citation Context ... factoring integers [5], computing discrete logarithms over finite fields [13], counting the number of points on an elliptic curve over a finite field [8], computing the class number of number fields =-=[2]-=-, etc. In those projects software for many basic tasks was needed, for example a multiprecision integer and floating point arithmetic, a polynomial arithmetic, linear algebra routines, etc. However, r... |

3 |
lip: long integer package", Bellcore
- Lenstra
- 1989
(Show Context)
Citation Context ...n integer package and which memory manager should be used in LiDIA. There are competing multiprecision integer packages, for example the GNU gmp-package [7], the libI-package [6], and the lip-package =-=[9]-=-. Some of those packages are more efficient on one architecture and some on others. Also, new architectures will lead to new multiprecision packages. We decided to make LiDIA independent of a particul... |

3 |
A Programmer's Guide", available with the KANT package by anonymous ftp on math.tuberlin. de
- Schmettow, Juntgen, et al.
(Show Context)
Citation Context ...Introduction In this paper we describe LiDIA, a new library for computational number theory. Why do we work on a new library for computational number theory when such powerful tools as Pari [1], Kant =-=[11]-=-, Simath [10] already exist? In fact, those systems are very useful for solving problems for which there exist efficient system routines. For example, using Pari or Kant it is possible to compute inva... |

3 | An implementation of the general number field sieve to compute discrete logarithms mod p", submitted
- Weber
- 1994
(Show Context)
Citation Context ...her computer algebra systems. Over the past years we have been working on many problems of computational number theory such as factoring integers [5], computing discrete logarithms over finite fields =-=[13]-=-, counting the number of points on an elliptic curve over a finite field [8], computing the class number of number fields [2], etc. In those projects software for many basic tasks was needed, for exam... |

2 |
V.,"Counting the number of points on elliptic curves over finite fields of characteristic greater than three
- Lehmann, Maurer, et al.
- 1994
(Show Context)
Citation Context ...y problems of computational number theory such as factoring integers [5], computing discrete logarithms over finite fields [13], counting the number of points on an elliptic curve over a finite field =-=[8]-=-, computing the class number of number fields [2], etc. In those projects software for many basic tasks was needed, for example a multiprecision integer and floating point arithmetic, a polynomial ari... |

1 |
LiDIA manual
- Buchmann, Papanikolaou
- 1994
(Show Context)
Citation Context ...ystems and we make our improvements available to the groups developing the other systems. Currently the classes of LiDIA are documented in manual pages which are similar to the UNIX manual pages (see =-=[3]-=-). We are working on a tool that makes the documentation interactively available and which in particular supports search in the LiDIA documentation. That documentation tool will be part of a LiDIA dev... |