polymake: a Framework for Analyzing Convex Polytopes

By Ewgenij Gawrilow, Michael Joswig. 2000

765 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/39e12377e6b7ad66538e87d4840638ca9a5e4e5e

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In Computer Graphics and Computer-Aided Design

In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

Citations in the corpus

Roots of Ehrhart polynomials arising from graphs (2010, positive): “Step 2 is performed with Polymake [9, 24].”
An Update on the Hirsch Conjecture (2009, neutral): “Our suggestion for this is polymake [27].”
Tropical and Ordinary Convexity Combined (2008, methodology): “We implemented this enumeration scheme in polymake [11], and the result of the computation for d = 3 is given in Table 1.”
Causal Bounds and Observable Constraints for Non-deterministic Models (2012, methodology): “A program such as Polymake (Gawrilow and Joswig, 2000) or PORTA (Christof and Loebel, 1998) can be used to transform the representation of Ĥ in terms of its extreme vertices to a representation in terms of its facets or inequalities.”
FAVOURABLE MODULES: FILTRATIONS, POLYTOPES, NEWTON–OKOUNKOV BODIES AND FLAT DEGENERATIONS (2013, methodology): “In this case our toric variety is isomorphic to the one in [AB] associated to this reduced decomposition (for most of these computations we used the program polymake ([GJ]).”
DRESSIANS, TROPICAL GRASSMANNIANS, AND THEIR RAYS (2011, methodology): “Our second main result is the explicit computation of the entire fan Dr(3, 8) via polymake [7].”
Minimal half-spaces and external representation of tropical polyhedra (2009, methodology): “The pictures of the max-plus polytopes were generated with POLYMAKE [25], the latest version of which contains an extension dealing with tropical polytopes [27].”
Chern classes of conformal blocks (2009, methodology): “ the beginning of §6 shows that the Chern classes in cohomology lie in the subring generated by the classes of divisors. We therefore ask the following: 2These were carried out in part using polymake [8]. 30 NAJMUDDINFAKHRUDDIN Question 7.3. Do the Chern classes in CH∗(M g,n)Q of all conformal block”
Potential unsatisfiability of cyclic constraints on stochastic biological networks biases selection towards hierarchical architectures (2015, methodology): “For standard computations on polytopes, we make use of the standard algorithms incorporated by the polymake project [52].”
Convex Hull Realizations of the Multiplihedra (2007, methodology): “Indeed polymake was instrumental in the experimental phase of this research [ 11 ].”
What are higher-order networks? (2021, methodology): “There are other software including simcomp toolbox in GAP [89], or the topology application ‘topaz’ in polymake [105].”
Moduli of tropical plane curves (2014, methodology): “The objects in Equations 1 to 3 are carefully defined, and we explain our algorithms for computing these explicitly, using the software packages TOPCOM [28] and polymake [2,16].”