
MPT
 Referenced in 210 articles
[sw04732]
 handling of systems with persistent additive and polytopic uncertainties. Users can add custom constraints, such ... polytopic, contraction, or collision avoidance constraints, or create custom objective functions. Resulting optimal control laws...

polymake
 Referenced in 288 articles
[sw00724]
 research in polyhedral geometry. It deals with polytopes, polyhedra and fans as well as simplicial...

Normaliz
 Referenced in 147 articles
[sw00630]
 computations in affine monoids, vector configurations, lattice polytopes, and rational cones. Its input data ... cone, the lattice points of a rational polytope or unbounded polyhedron, the integer hull ... grading (for example, for rational polytopes), generalized (or weighted) Ehrhart series and Lebesgue integrals ... polynomials over rational polytopes via NmzIntegrate, a description of the cone and lattice under consideration...

LattE
 Referenced in 112 articles
[sw04654]
 counting lattice points and integration inside convex polytopes. LattE contains the first ever implementation ... directly compute integrals of polynomial functions over polytopes and in particular to do volume computations...

PORTA
 Referenced in 116 articles
[sw04869]
 collection of routines for analyzing polytopes and polyhedra. The polyhedra are either given...

PALP
 Referenced in 65 articles
[sw00672]
 programs for calculations with lattice polytopes and applications to toric geometry, which is freely available ... addition, there are procedures specialised to reflexive polytopes such as the enumeration of reflexive subpolytopes...

plantri
 Referenced in 59 articles
[sw10864]
 planar graphs, including triangulations, quadrangulations and convex polytopes. Many applications in the natural sciences ... given. These include triangulations, quadrangulations, convex polytopes, several classes of cubic and quartic graphs...

Ellipsoidal Toolbox
 Referenced in 35 articles
[sw10826]
 intersections of ellipsoids with halfspaces and polytopes; distances between ellipsoids, between ellipsoids and hyperplanes, between ... ellipsoids and polytopes; and projections onto given subspaces. Ellipsoidal methods are used to compute forward ... sets intersect with given ellipsoids, hyperplanes, or polytopes...

PolyTop
 Referenced in 36 articles
[sw07629]
 PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element...

Convex
 Referenced in 32 articles
[sw07770]
 bounded polyhedron is also called a polytope. In the Convex package, polyhedra are represented ... type POLYHEDRON and polytopes by the subtype POLYTOPE. A POLYHEDRON may contain lines...

Graded Ring Database
 Referenced in 31 articles
[sw11291]
 polygons and the smooth Fano polytopes. These classifications can be queried using the forms...

01poly
 Referenced in 16 articles
[sw14281]
 01poly [OPTIONS] you get information about 01polytopes of dimension 26 with desired properties ... Dimension 5. The output includes the polytope(s) as bitvector (e.g. a 1 for every ... equivalence classes and their cardinalities. All known polytopes can immediately be accessed by their unique...

CalabiYau database
 Referenced in 25 articles
[sw24665]
 threefolds which can be obtained from each polytope, up to current computational limits. We then...

DEMiCs
 Referenced in 21 articles
[sw00196]
 computing the mixed volume of the Newton polytopes of a general semimixed polynomial system...

lrs
 Referenced in 20 articles
[sw04730]
 difficult class of polyhedra, called configuration polytopes, that have application to determining the ground states...

TropLi
 Referenced in 18 articles
[sw10180]
 tool for computing vertices of Newton polytopes of Adiscriminants, are both available online...

TiGERS
 Referenced in 9 articles
[sw12585]
 bijection with the vertices of a convex polytope known as the state polytope ... normal fan of its state polytope. In this paper we present a software system called ... enumerating the edge graph of its state polytope. The key contributions are an inexpensive algorithm ... tree on the vertices of the state polytope. Using these ideas we obtain a combinatorial...

isl
 Referenced in 12 articles
[sw09841]
 polyhedral model. In compiler research, polytopes and related mathematical objects have been successfully used ... integer points in a (parametric) polytope and manipulated as a whole, rather than as individual...

2L_enum
 Referenced in 8 articles
[sw31753]
 Enumeration of 2level polytopes. A (convex) polytope P is said to be 2level ... translate of H. The study of these polytopes is motivated by questions in combinatorial optimization ... enumerating all combinatorial types of 2level polytopes of a given dimension d, and provide ... each fixed (𝑑−1) dimensional 2level polytope 𝑃0 , we enumerate all ddimensional...

hgm R
 Referenced in 16 articles
[sw08770]
 find an interesting interplay with systems for polytopes in the project. References and current implementations...