Abstract
We present generic, type safe Groebner bases software. The implemented algorithms distinguish Groebner base computation in polynomials rings over fields, rings with pseudo division, parameter rings, regular rings, Euclidean rings, non-commutative fields in commuting, solvable and free-non-commuting main variables. The interface, class organization is described in the object-oriented programming environment of the Java Algebra System (JAS). Different critical pair selection strategies and reduction algorithms can be provided by dependency injection. Different implementations can be selected for the mentioned coefficient rings through factory classes and methods. Groebner bases algorithms can be composed according to application needs and/or hardware availability. For example, versions for shared memory sequential or parallel computation, term order optimization or fraction free coefficient ring computation can be composed. For distributed memory compute clusters there are OpenMPI and MPJ implementations of Buchberger’s algorithm with optimized distributed storage of reduction polynomials.
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References
Böge, W., Gebauer, R., Kredel, H.: Some examples for solving systems of algebraic equations by calculating Gröbner bases. J. Symb. Comp. 2/1(1), 83–98 (1986)
Buchberger, B.: Gröbner bases: An algorithmic method in polynomial ideal theory. In: Bose, N. (ed.) Recent Trends in Multidimensional Systems Theory, Reidel, pp. 184–232 (1985)
Faugère, J.C., Gianni, P., Lazard, D., Mora, T.: Efficient computation of zero-dimensional Gröbner bases by change of ordering. J. Symbolic Computation 16(4), 329–344 (1994)
Gebauer, R., Möller, H.M.: On an installation of Buchberger’s algorithm. J. Symb. Comput. 6(2/3), 275–286 (1988)
Kredel, H.: On a Java Computer Algebra System, its performance and applications. Science of Computer Programming 70(2-3), 185–207 (2008)
Kredel, H.: Unique factorization domains in the java computer algebra system. In: Sturm, T., Zengler, C. (eds.) ADG 2008. LNCS, vol. 6301, pp. 86–115. Springer, Heidelberg (2011)
Kredel, H.: Distributed Gröbner bases computation with MPJ. In: IEEE AINA Workshops, Barcelona, Spain, pp. 1429–1435 (2013)
Kredel, H.: The Java algebra system (JAS). Technical report (2000), http://krum.rz.uni-mannheim.de/jas/
Taboada, G.L., Ramos, S., Expósito, R.R., Touriño, J., Doallo, R.: FastMPJ a high performance Java message passing library. Technical report (2011), http://fastmpj.com/
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Kredel, H. (2014). Generic and Parallel Groebner Bases in JAS. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_60
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DOI: https://doi.org/10.1007/978-3-662-44199-2_60
Publisher Name: Springer, Berlin, Heidelberg
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