GRIN swMATH ID: 8940 Software Authors: Serkan Hosten, Bernd Sturmfels Description: GRIN: An implementation of Gröbner bases for integer programming. this paper we present a computer program (GRIN) for solving and analyzinginteger programs using Grobner bases. The algorithms coded in GRIN aredrawn from both commutative algebra and the standard IP repertoire (e.g. Lovasz’reduced lattice bases). We present two new algorithms for computing generatorsof toric ideals. One of them is due to DiBiase and Urbanke. The emphasis ofour discussion lies on experiments and practical computability... Homepage: http://link.springer.com/chapter/10.1007/3-540-59408-6_57 Related Software: Macaulay2; CoCoA; SINGULAR; 4ti2; Gfan; SageMath; GAP; Binomials.m2; posets; Maple; Normaliz; OSL; PARI/GP; Mathematica Cited in: 27 Publications all top 5 Cited by 42 Authors 5 Thomas, Rekha R. 3 Pisón-Casares, Pilar 3 Vigneron-Tenorio, Alberto 3 Weismantel, Robert 2 Briales Morales, Emilio 2 Charalambous, Hara 2 Craw, Alastair 2 Hemmecke, Raymond 2 Hoşten, Serkan 2 Maclagan, Diane 2 Schultz, Rüdiger 2 Sturmfels, Bernd 2 Thoma, Apostolos 2 Vladoiu, Marius 1 Bigatti, Anna Maria 1 Blanco, Víctor 1 Bogart, Tristram 1 Braun, Volker 1 Campillo, Antonio 1 Carra’Ferro, Giuseppa 1 Crema, Alejandro 1 Darlington, John 1 Di Biase, Fausto 1 Ferrarello, Daniela 1 Guo, Yike 1 Haus, Utz-Uwe 1 Ida, Tetsuo 1 Jensen, Anders Nedergaard 1 Kahle, Thomas 1 Kesh, Deepanjan 1 Li, Qiang 1 Malkin, Peter N. 1 Mehta, Shashank K. 1 Pokutta, Sebastian 1 Puerto Albandoz, Justo 1 Robbiano, Lorenzo 1 Shapiro, Jay Allen 1 Stougie, Leen 1 Urbaniak, Regina 1 Urbanke, Rüdiger L. 1 van der Vlerk, Maarten H. 1 Ziegler, Günter Matthias all top 5 Cited in 19 Serials 3 Journal of Algebra 3 Journal of Symbolic Computation 2 SIAM Journal on Discrete Mathematics 2 Mathematical Programming. Series A. Series B 1 Communications in Algebra 1 Discrete Mathematics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Annals of the Institute of Statistical Mathematics 1 Collectanea Mathematica 1 Proceedings of the London Mathematical Society. Third Series 1 Revista Matemática Iberoamericana 1 European Journal of Operational Research 1 Applicable Algebra in Engineering, Communication and Computing 1 Experimental Mathematics 1 Matemática Contemporânea 1 Journal of Mathematical Chemistry 1 Mathematical Methods of Operations Research 1 Journal of High Energy Physics 1 Discrete Mathematics, Algorithms and Applications all top 5 Cited in 13 Fields 16 Commutative algebra (13-XX) 11 Operations research, mathematical programming (90-XX) 9 Algebraic geometry (14-XX) 5 Computer science (68-XX) 4 Combinatorics (05-XX) 3 Associative rings and algebras (16-XX) 2 Probability theory and stochastic processes (60-XX) 1 Number theory (11-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX) Citations by Year