SlackIdeals swMATH ID: 33429 Software Authors: Antonio Macchia, Amy Wiebe Description: Slack Ideals in Macaulay2. Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matrix, the matrix obtained by evaluating each facet inequality at each vertex. Unlike the classical model, the slack model naturally mods out projective transformations. It is inherently algebraic, arising as the positive part of a variety of a saturated determinantal ideal, and provides a new computational tool to study classical realizability problems for polytopes. We introduce the package SlackIdeals for Macaulay2, that provides methods for creating and manipulating slack matrices and slack ideals of convex polytopes and matroids. Slack ideals are often difficult to compute. To improve the power of the slack model, we develop two strategies to simplify computations: we scale as many entries of the slack matrix as possible to one; we then obtain a reduced slack model combining the slack variety with the more compact Grassmannian realization space model. This allows us to study slack ideals that were previously out of computational reach. As applications, we show that the well-known Perles polytope does not admit rational realizations and prove the non-realizability of a large simplicial sphere. Homepage: https://arxiv.org/abs/2003.07382 Source Code: https://bitbucket.org/macchia/slackideals/src/master/SlackIdeals.m2 Dependencies: Macaulay2 Keywords: Combinatorics; arXiv_math.CO; arXiv_Commutative Algebra; math.AC; Algebraic Geometry; arXiv_math.AG; Macaulay2; Polytopes; Slack matrices; Slack ideals; Matroids Related Software: Macaulay2; 2L_enum Cited in: 2 Documents Standard Articles 1 Publication describing the Software Year Slack Ideals in Macaulay2 arXiv Antonio Macchia, Amy Wiebe 2020 Cited by 5 Authors 2 Gouveia, Joao 1 Bogart, Tristram 1 Macchia, Antonio 1 Torres, Juan Camilo 1 Wiebe, Amy Cited in 1 Serial 2 Discrete & Computational Geometry all top 5 Cited in 6 Fields 2 Convex and discrete geometry (52-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) Citations by Year