KANT/KASH swMATH ID: 481 Software Authors: Anita Krahmann, Carolin Just, Claus Fieker, Florian Heß, Jose Mendez, Jürgen Klüners, Marcus Wagner, Michael Pohst, Oliver Voigt, Robert Fraatz, Sebastian Freundt, Sebastian Pauli;Former authors: Andreas Hoppe, Carsten Friedrichs, Georg Baier, Harald Bartel, Hartmut Bauer, Johannes Graf v. Schmettow, Katharina Geißler, Klaus Wildanger, Maike Henningsen, Mario Daberkow, Martin Schörnig, Max Jüntgen KANT group, Institut für Mathematik, Technische Universität Berlin Description: KASH/KANT is a computer algebra system (CAS) for sophisticated computations in algebraic number fields and global function fields. It has been developed under the project leadership of Prof. Dr. M. Pohst at Technische Universität Berlin. KANT is a program library for computations in algebraic number fields, algebraic function fields and local fields. In the number field case, algebraic integers are considered to be elements of a specified order of an appropriate field F. The available algorithms provide the user with the means to compute many invariants of F. It is possible to solve tasks like calculating the solutions of Diophantine equations related to F. Furthermore subfields of F can be generated and F can be embedded into an overfield. The potential of moving elements between different fields (orders) is a significant feature of our system. In the function field case, for example, genus computations and the construction of Riemann-Roch spaces are available. Homepage: http://www.math.tu-berlin.de/~kant/ Keywords: orms; computational algebraic number theory; subroutine library Related Software: Magma; Maple; PARI/GP; GAP; SIMATH; SageMath; Polycyclic; ecdata; Macaulay2; TECC; AClib; SCSCP; NZMATH; GiANT; MuPAD; Matlab; Mathematica; KANTOO; ALNUTH; Polenta Referenced in: 155 Publications This software is also referenced in ORMS. Further Publications: http://page.math.tu-berlin.de/~kant/publications.html Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year KANT - a tool for computations in algebraic number fields. Zbl 0731.11070Schmettow, J. Graf v. 1991 all top 5 Referenced by 151 Authors 32 Pohst, Michael E. 18 Gaál, István 11 Klüners, Jürgen 9 Kwon, Soun-Hi 7 Fieker, Claus 5 Pauli, Sebastian 4 Chang, Ku-Young 4 Eick, Bettina 4 Kida, Masanari 4 Maharaj, Hiren 4 Togbé, Alain 4 Wildanger, Klaus 3 Acciaro, Vincenzo 3 Daberkow, Mario 3 de Weger, Benjamin M. M. 3 Graf von Schmettow, Johannes 3 Hess, Florian 3 Malle, Gunter 3 Mitamura, Teruko 3 Nyberg, Eric 3 Selmane, Schehrazad 2 Aguilar-Zavoznik, Alejandro 2 Ahn, Jeoung-Hwan 2 Baker, Kathryn 2 Ballet, Stéphane 2 Belabas, Karim 2 Bley, Werner 2 Bruin, Nils 2 Buchmann, Johannes A. 2 Diaz y Diaz, Francisco 2 Freundt, Sebastian 2 Hachimori, Yoshitaka 2 Heuberger, Clemens 2 Karve, Aneesh 2 Louboutin, Stéphane R. 2 Matthews, Gretchen L. 2 Narkiewicz, Władysław 2 Park, Sun-Mi 2 Pieltant, Julia 2 Pineda Ruelas, Mario 2 Roblot, Xavier-François 2 Smart, Nigel P. 2 Svoboda, David 2 Takayama, Nobuki 2 Wagner, Marcus M. 2 Wakabayashi, Isao 2 Yamamura, Ken 2 Yang, Hee-Sun 1 Aguilera-Venegas, Gabriel 1 Allombert, Bill 1 Assmann, Björn 1 Atencia-Mc. Killop, Iván 1 Baake, Michael 1 Bennett, Michael A. 1 Bosma, Wieb 1 Boston, Nigel 1 Burns, David John 1 Bush, Michael R. 1 Cannon, John J. 1 Cohen, Arjeh Marcel 1 Cramer, Peter 1 Donnelly, Steve 1 Dorfer, Gerhard 1 Duggan, Michael A. 1 Elkies, Noam David 1 Everest, Graham Robert 1 Flynn, Eugene Victor 1 Galán-García, José Luis 1 Galán-García, María-Ángeles 1 Galbraith, Steven D. 1 Gao, Xiaoshan 1 Geissler, Katharina 1 Grimm, Uwe 1 Grundman, Helen G. 1 Győry, Kálmán 1 Hajdu, Lajos 1 Hajir, Farshid 1 Halbritter, Ulrich 1 Hanke, Timo 1 Henningsen, M. 1 Horn, Peter D. 1 Hubbard, David 1 Hulpke, Alexander Jörg 1 Iglesias, Andrés 1 Itoh, Tsuyoshi 1 Jadrijević, Borka 1 Járási, István 1 Jüntgen, Max 1 Jurk, Andreas 1 Kawakita, Motoko Qiu 1 Khodaiemehr, Hassan 1 Kiani, Dariush 1 Kim, Hyunkwang 1 Kim, Jungsoo 1 Ko, Jeongwoo 1 Konovalov, Olexandr 1 Krahmann, Anita 1 Le, Maohua 1 Leedham-Green, Charles R. 1 Lemmermeyer, Franz Josef ...and 51 more Authors all top 5 Referenced in 37 Serials 22 Mathematics of Computation 20 Journal of Number Theory 17 Journal of Symbolic Computation 12 Journal de Théorie des Nombres de Bordeaux 6 Experimental Mathematics 4 Journal of Algebra 4 Transactions of the American Mathematical Society 3 Acta Arithmetica 3 Tokyo Journal of Mathematics 3 Acta Mathematica et Informatica Universitatis Ostraviensis 2 Functiones et Approximatio. Commentarii Mathematici 2 Glasgow Mathematical Journal 2 Journal of Pure and Applied Algebra 2 Proceedings of the American Mathematical Society 2 JP Journal of Algebra, Number Theory and Applications 1 Bulletin of the Australian Mathematical Society 1 Periodica Mathematica Hungarica 1 Zeitschrift für Kristallographie 1 Applied Mathematics and Computation 1 Archiv der Mathematik 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Czechoslovak Mathematical Journal 1 Japanese Journal of Mathematics. New Series 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Journal of Complexity 1 Glasnik Matematički. Serija III 1 Applicable Algebra in Engineering, Communication and Computing 1 Finite Fields and their Applications 1 The Ramanujan Journal 1 Bulletin of the Brazilian Mathematical Society. New Series 1 DMV Seminar 1 Lecture Notes in Computer Science 1 International Journal of Algebra 1 Advances in Mathematics of Communications 1 Annales Mathematicae et Informaticae all top 5 Referenced in 14 Fields 135 Number theory (11-XX) 21 Computer science (68-XX) 13 Field theory and polynomials (12-XX) 12 Algebraic geometry (14-XX) 8 Information and communication theory, circuits (94-XX) 5 Group theory and generalizations (20-XX) 4 Numerical analysis (65-XX) 3 Commutative algebra (13-XX) 2 General and overarching topics; collections (00-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Probability theory and stochastic processes (60-XX) Referencing Publications by Year