Cubic |

This the home of the CUBIC software. The program computes a list of (isomorphism classes of) cubic number fields of bounded discriminant. I wrote this program back in 1995-96 as a toy project, rewrote it in 2003 for a different project involving the 3-ranks of quadratic fields, and eventually made it publicly available in 2009. The current version requires a fairly recent version of the PARI/GP library. I no longer work on this or related projects but I update the code from time to time when the PARI interface changes, and I will try to fix bugs if you find and report them. Have fun !

[Download] (version 1.3)

The README file |

CUBIC, vestion 1.3. 0) Prerequisite: make sure the PARI/GP library is installed on your system 1) Configuration: the default Makefile, assumes that your PARI/GP library is recent (e.g. 2.9.0), was compiled with gmp, and is installed in the standard location. As would be produced by the standard procedure ./Configure && make install Have a look at the numbered configuration options at the top of 'Makefile'; modify if your installation is non-standard. 2) Compilation: simply type make This will produce two binaries : cubic-noprint: only *count* the fields cubic : also *output* the fields (about ten times slower). 3) Usage: both binaries use the same syntax, with a single argument describing a range of discriminants. Restriction: the discriminants considered must all have the same signs. 1000 : discriminants in [0, 1000] -1000 : discriminants in [-1000, 0] [1000, 2000] : discriminants in [1000, 2000] [-2000, -1000]: discriminants in [-2000, -1000] [-2000, 2000] : FORBIDDEN (different signs!) [58343207081] : discriminants EXACTLY 58343207081 You may use any arithmetic expression in the GP language provided it is enclosed within quotes: ./cubic-noprint "2*10^10" Extra Flags: -g: be increasingly verbose [ default: 0 ] 4) References Author: Karim Belabas, IMB (UMR 5251) Univ. Bordeaux, 351 cours de la Liberation, F-33405 Talence (France) http://www.math.u-bordeaux.fr/~kbelabas/ @article {MR1415795, AUTHOR = {Belabas, Karim}, TITLE = {A fast algorithm to compute cubic fields}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {66}, YEAR = {1997}, NUMBER = {219}, PAGES = {1213--1237}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {11Y40 (11R16)}, MRNUMBER = {MR1415795 (97m:11159)}, MRREVIEWER = {Joe P. Buhler}, } @article {MR2059751, AUTHOR = {Belabas, Karim}, TITLE = {On quadratic fields with large 3-rank}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {73}, YEAR = {2004}, NUMBER = {248}, PAGES = {2061--2074 (electronic)}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {11R11 (11R16 11R29 11Y40)}, MRNUMBER = {MR2059751 (2005c:11132)}, MRREVIEWER = {Michel Olivier}, } 5) License: This software (the 'cubic' package) is released under the GNU General Public License (version 2 or above at your convenience). It is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. PARI/GP is free software, covered by the GNU General Public License. 6) Version history: CUBIC, v1.3, 25/07/2016: update for pari-2.9 CUBIC, v1.2, 22/07/2011: remove most 'printf' CUBIC, v1.1, 22/06/2011: fix Makefile, improve README. CUBIC, v1.0, 15/07/2009: initial public release (stable version).

Karim Belabas 2018-03-01 10:11:25