Computing the binomial part of a polynomial ideal
References
[1]
A. Altman, S. Kleiman, A Term of Commutative Algebra, Worldwide Center of Mathematics, Cambridge, 2013.
[2]
L. Babai, R. Beals, J.-y. Cai, G. Ivanyos, E.M. Luks, Multiplicative equations over commuting matrices, in: Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1996, pp. 498–507.
[3]
T. Becker, V. Weispfenning, Gröbner Bases, Springer-Verlag, New York, 1993.
[4]
D.J. Bernstein, Factoring into coprimes in essentially linear time, J. Algorithms 54 (1) (2005) 1–30.
[5]
J.P. Brennan, W.V. Vasconcelos, Effective computation of the integral closure of a morphism, J. Pure Appl. Algebra 86 (1993) 2.
[6]
J. Buchmann, M. Jacobson Jr, E. Teske, On some computational problems in finite abelian groups, Math. Comput. 66 (220) (1997) 1663–1687.
[7]
J. Buchmann, A. Schmidt, Computing the structure of a finite abelian group, Math. Comput. 74 (252) (2005) 2017–2026.
[8]
I.O.M. de Castilla, R.P. Sánchez, Cellular binomial ideals. Primary decomposition of binomial ideals, J. Symb. Comput. 30 (4) (2000) 383–400.
[9]
H. Derksen, E. Jeandel, P. Koiran, Quantum automata and algebraic groups, J. Symb. Comput. 39 (3) (2005) 357–371.
[10]
D. Eisenbud, B. Sturmfels, Binomial ideals, Duke Math. J. 84 (1) (1996) 1–45.
[11]
G. Ge, Algorithms related to multiplicative representations of algebraic numbers, PhD thesis University of California, Berkeley, 1993.
[12]
G. Ge, Recognizing units in number fields, Math. Comput. 63 (1994) 377–387.
[13]
M. Giesbrecht, D.S. Roche, H. Tilak, Computing sparse multiples of polynomials, Algorithmica 64 (3) (2012) 454–480.
[14]
G.-M. Greuel, S. Laplagne, F. Seelisch, Normalization of rings, J. Symb. Comput. 45 (2010) 9.
[15]
G.-M. Greuel, G. Pfister, A Singular Introduction to Commutative Algebra, Springer Verlag, Berlin, Heidelberg, 2008.
[16]
J.D. Hauenstein, L. Matusevich, C. Peterson, S.N. Sherman, Binomiality testing and computing sparse polynomials via witness sets, Vietnam J. Math. 50 (3) (2022) 653–678.
[17]
R. Hemmecke, P.N. Malkin, Computing generating sets of lattice ideals and Markov bases of lattices, J. Symb. Comput. 44 (10) (2009) 1463–1476.
[18]
J. Herzog, T. Hibi, H. Ohsugi, Binomial Ideals, Springer Int. Publ., Cham, 2018.
[19]
A. Jensen, T. Kahle, L. Katthän, Finding binomials in polynomial ideals, Res. Math. Sci. 4 (2017).
[20]
Kahle, T. (2022): Short polynomials and where to find them. Retrieved July 13, 2023 from https://thomas-kahle.de/material/shortPoly.pdf.
[21]
L. Katthän, M. Michalek, E. Miller, When is a polynomial ideal binomial after an ambient automorphism?, Found. Comput. Math. 19 (2019) 1363–1385.
[22]
M. Kauers, Algorithms for nonlinear higher order difference equations, PhD thesis RISC Institute, Linz, 2005.
[23]
M. Kauers, P. Nuspl, V. Pillwein, Order bounds for c2-finite sequences, in: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, in: Association for Computing Machinery, New York, NY, USA, 2023, pp. 389–397.
[24]
M. Kauers, B. Zimmermann, Computing the algebraic relations of c-finite sequences and multisequences, J. Symb. Comput. 43 (11) (2008) 787–803.
[25]
G. Kemper, The calculation of radical ideals in positive characteristic, J. Symb. Comput. 34 (3) (2002) 229–238.
[26]
M. Kreuzer, L. Robbiano, Computational Commutative Algebra 1, Springer-Verlag, Heidelberg, 2000.
[27]
M. Kreuzer, L. Robbiano, Computational Commutative Algebra 2, Springer-Verlag, Heidelberg, 2005.
[28]
M. Kreuzer, L. Robbiano, Computational Linear and Commutative Algebra, Springer Int. Publ., Cham, 2016.
[29]
H.W. Lenstra, A. Silverberg, Algorithms for commutative algebras over the rational numbers, Found. Comput. Math. 18 (1) (2018) 159–180.
[30]
D.W. Masser, Linear relations on algebraic groups, in: A. Baker (Ed.), New Advances in Transcendence Theory, Cambridge University Press, Cambridge, 1988, pp. 248–262.
[31]
J. Neukirch, Algebraic Number Theory, Springer-Verlag, Berlin, Heidelberg, 2013.
[32]
E.D. Sontag, A technique for determining the signs of sensitivities of steady states in chemical reaction networks, IET Syst. Biol. 8 (6) (2014) 251–267.
[33]
A. Steel, Conquering inseparability: primary decomposition and multivariate factorization over algebraic function fields of positive characteristic, J. Symb. Comput. 40 (3) (2005) 1053–1075.
[34]
E. Teske, A space efficient algorithm for group structure computation, Math. Comput. 67 (1998) 224.
[35]
The Sage Developers (2023): Sagemath, the sage mathematics software system. Version 10.0. https://www.sagemath.org.
[36]
R.H. Villarreal, Monomial Algebras, Chapman and Hall/CRC, New York, 2018.
[37]
J. Von Zur Gathen, J. Gerhard, Modern Computer Algebra, Cambridge University Press, Cambridge, 2013.
[38]
Walsh, F. (November 2023): Binomial part, a Sagemath package. Version 1.0. Available at https://github.com/abacus42/binomial-part.
[39]
T. Zheng, B. Xia, An effective framework for constructing exponent lattice basis of nonzero algebraic numbers, in: Proceedings of the 2019 ACM International Symposium on Symbolic and Algebraic Computation, in: Association for Computing Machinery, New York, NY, 2019, pp. 371–378.
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Published: 25 June 2024
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