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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 4183461\Chapter{Introduction}23A number field is a finite extension of the field of rational numbers.4{\Alnuth} provides various methods to compute with number fields5which are given by a defining polynomial or by generators. For background6on number fields we refer to \cite{Sta79}.78Some of the methods provided in this package are written in {\GAP} code.9The other part of the methods is imported from the Computer Algebra10System PARI/GP \cite{PARI2}. Hence this package contains some {\GAP}11functions and an interface to some functions in the computer algebra12system PARI/GP. Therefore one has to have PARI/GP installed to use the13full functionality of {\Alnuth}.1415We note that only a very small part of the functions available in PARI/GP16are linked to {\GAP} and PARI/GP provides many more methods for17computations in number fields.1819The main methods included in {\Alnuth} are: creating a number field,20computing its maximal order (using PARI/GP), computing its unit group (using21PARI/GP) and a presentation of this unit group, computing the elements of a22given norm of the number field (using PARI/GP), determining a presentation23for a finitely generated multiplicative subgroup (using PARI/GP), and24factoring polynomials defined over number fields (using PARI/GP). For25background on algorithms for number fields we refer to \cite{Poh93},26\cite{PZa89} and \cite{Coh93}.2728The functions provided by {\Alnuth} are introduced in the following29chapter. Then an example application is outlined. In the final chapter30of this manual the installation of the package and configuration of31the interface, including hints on the installation of PARI/GP, are32described.3334%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%35\Section{Acknowledgements}3637To begin with we are very grateful for all the feedback by users of38former versions of {\Alnuth}.3940We thank Bill Allombert who wrote the GP code for the interface to41PARI/GP and who was extremely helpful in the transition from KANT42to PARI/GP.4344For feedback on the development version, including a code patch, we45are much obliged to Max Horn.4647The second author acknowledges the financial support at CAUL within48the projects PTDC/MAT/101993/2008 and ISFL-1-143, financed by FEDER49and FCT, in the development of Version 3 of {\Alnuth}.5051%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%52\Section{License}5354This program is free software: you can redistribute it and/or modify55it under the terms of the GNU General Public License as published by56the Free Software Foundation, either version 2 of the license, or57(at your option) any later version.5859This program is distributed in the hope that it will be useful,60but WITHOUT ANY WARRANTY; without even the implied warranty of61MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the62GNU General Public License for more details.6364You should have received a copy of the GNU General Public License65along with this program. If not, see \URL{http://www.gnu.org/licenses/}6667%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%68%%69%E707172