Algorithms for "Ideals" in polynomial algebras over the max-plus semi-ring - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T21:41:07Z http://mathoverflow.net/feeds/question/97578 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/97578/algorithms-for-ideals-in-polynomial-algebras-over-the-max-plus-semi-ring Algorithms for "Ideals" in polynomial algebras over the max-plus semi-ring Drew 2012-05-21T17:40:59Z 2012-05-21T17:40:59Z <p>I'm a beginner in tropical geometry, and I'm running into the following question:</p> <p>In the usual polynomial ring over a field, one has algorithms (i.e. using a Groebner basis) for determining whether an element of the ring in in an ideal given by some generators.</p> <p>Suppose now I'm looking at an polynomial algebra over the max-plus semi-ring, and I have some relations, say \$f_i = g_i\$. Are there algorithms known (or better yet, has someone already written code) to determine whether a given relation, say \$h=k\$, lies in the the equivalence relation generated by the \$f_i=g_i\$? </p> <p>I put "ideal" in quotes because as I understand it, kernels of semi-ring maps can not be thought of as subsets of the domain as in the case of rings, but rather are just equivalence relations.</p> <p>So far Google searching hasn't turned up anything promising.</p>