KANT/KASH

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.

This software is also referenced in ORMS.


References in zbMATH (referenced in 149 articles , 1 standard article )

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  1. Ballet, Stéphane; Pieltant, Julia; Rambaud, Matthieu; Sijsling, Jeroen: On some bounds for symmetric tensor rank of multiplication in finite fields (2017)
  2. Khodaiemehr, Hassan; Kiani, Dariush: High-rate space-time block codes from twisted Laurent series rings (2015)
  3. Gaál, István; Petrányi, Gábor: Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields. (2014)
  4. Maier, P.; Stewart, R.; Trinder, P. W.: Reliable scalable symbolic computation: the design of SymGridPar2 (2014) ioport
  5. Fieker, Claus; Gaál, István; Pohst, Michael: On computing integral points of a Mordell curve over rational function fields in characteristic (>3) (2013)
  6. Aguilar-Zavoznik, Alejandro; Pineda-Ruelas, Mario: A relation between ideals, Diophantine equations and factorization in quadratic fields (F) with (h_F=2) (2012)
  7. Ahn, Jeoung-Hwan; Kwon, Soun-Hi: The imaginary abelian number fields of 2-power degrees with ideal class groups of exponent (\leq2) (2012)
  8. Szekrényesi, Gergő: Parallel algorithm for determining the “small solutions” of Thue equations (2012)
  9. Aguilar-Zavoznik, Alejandro; Pineda-Ruelas, Mario: 2-class group of quadratic fields (2011)
  10. Ballet, Stéphane; Pieltant, Julia: On the tensor rank of multiplication in any extension of (\mathbbF_2) (2011)
  11. Gaál, István; Pohst, Michael: Solving explicitly (F(x,y)=G(x,y)) over function fields (2011)
  12. Cannon, John; Donnelly, Steve; Fieker, Claus; Watkins, Mark: Magma -- a tool for number theory (2010)
  13. Gaál, István; Pohst, Michael: Diophantine equations over global function fields. IV: S-unit equations in several variables with an application to norm form equations (2010)
  14. Tanaka, Satoru; Ogura, Naoki; Nakamula, Ken; Matsui, Tetsushi; Uchiyama, Shigenori: NZMATH 1.0 (2010)
  15. Hajdu, Lajos: Optimal systems of fundamental (S)-units for LLL-reduction (2009)
  16. Horn, Peter; Roozemond, Dan: The SCIEnce EU program: Symbolic Computation Infrastructure for Europe (2009) MathEduc
  17. Louboutin, Stéphane R.: On the divisibility of the class number of imaginary quadratic number fields (2009)
  18. Pohst, M. E.; Wagner, Marcus: On the computation of Hermite-Humbert constants: the algorithm of Cohn revisited (2009)
  19. Yoshimura, Yusuke: Abelian number fields satisfying the Hilbert-Speiser condition at (p=2) or (3) (2009)
  20. Fieker, Claus; Pohst, Michael E.: A lower regulator bound for number fields (2008)

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Further publications can be found at: http://page.math.tu-berlin.de/~kant/publications.html