Back to main (Karim Belabas)
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
the PARI/GP
library, version 2.9.0 or more recent. 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)
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).
