- Referenced in 210 articles
- 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...
- Referenced in 288 articles
- research in polyhedral geometry. It deals with polytopes, polyhedra and fans as well as simplicial...
- Referenced in 147 articles
- 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...
- Referenced in 112 articles
- 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...
- Referenced in 116 articles
- collection of routines for analyzing polytopes and polyhedra. The polyhedra are either given...
- Referenced in 65 articles
- 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...
- Referenced in 59 articles
- 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...
- Referenced in 35 articles
- 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...
- Referenced in 36 articles
- PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element...
- Referenced in 32 articles
- 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
- polygons and the smooth Fano polytopes. These classifications can be queried using the forms...
- Referenced in 16 articles
- 01poly [OPTIONS] you get information about 01-polytopes of dimension 2-6 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...
- Referenced in 25 articles
- threefolds which can be obtained from each polytope, up to current computational limits. We then...
- Referenced in 21 articles
- computing the mixed volume of the Newton polytopes of a general semi-mixed polynomial system...
- Referenced in 20 articles
- difficult class of polyhedra, called configuration polytopes, that have application to determining the ground states...
- Referenced in 18 articles
- tool for computing vertices of Newton polytopes of A-discriminants, are both available online...
- Referenced in 9 articles
- 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...
- Referenced in 12 articles
- 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...
- Referenced in 8 articles
- Enumeration of 2-level polytopes. A (convex) polytope P is said to be 2-level ... translate of H. The study of these polytopes is motivated by questions in combinatorial optimization ... enumerating all combinatorial types of 2-level polytopes of a given dimension d, and provide ... each fixed (𝑑−1) -dimensional 2-level polytope 𝑃0 , we enumerate all d-dimensional...
- Referenced in 16 articles
- find an interesting interplay with systems for polytopes in the project. References and current implementations...