PolyLib
The Polyhedral Library (PolyLib for short) operates on objects made up of unions of polyhedra of any dimension. It was first developed by Doran Wilde at IRISA, in Rennes, France, in connection with the ALPHA project. This first version (1.1) manipulates non parameterized unions of polyhedra through the following operations: intersection, difference, union, convex hull, simplify, image and preimage, plus some input and output functions. The polyhedra are computed in their dual implicit and Minkowski representations, in homogeneous spaces. Version 2 of the PolyLib included parameterized vertices computation. PolyLib3.14 includes Ehrhart polynomials computation, which permits to count the number of integer points contained in a parameterized polyhedron. PolyLib4 included the GNU MP library (as a compilation option), and 64 bits computations, in order to avoid integer overflows. Polylib5 is a merge of Strasbourg, Rennes and BYU Polylib.
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References in zbMATH (referenced in 44 articles )
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Sorted by year (- Maréchal, Alexandre; Périn, Michaël: Efficient elimination of redundancies in polyhedra by raytracing (2017)
- Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
- Grégoire, Thomas; Chlipala, Adam: Mostly automated formal verification of loop dependencies with applications to distributed stencil algorithms (2016)
- Muller, Jean-Michel: Elementary functions. Algorithms and implementation (2016)
- Cimatti, Alessandro; Micheli, Andrea; Roveri, Marco: Solving strong controllability of temporal problems with uncertainty using SMT (2015)
- Roux, Alet; Zastawniak, Tomasz: Linear vector optimization and European option pricing under proportional transaction costs (2015)
- Ben-Amram, Amir M.; Genaim, Samir: Ranking functions for linear-constraint loops (2014)
- Feller, Christian; Johansen, Tor Arne; Olaru, Sorin: An improved algorithm for combinatorial multi-parametric quadratic programming (2013)
- Le Chenadec, Vincent; Pitsch, Heinz: A 3D unsplit forward/backward volume-of-fluid approach and coupling to the level set method (2013)
- Diss, Mostapha; Louichi, Ahmed; Merlin, Vincent; Smaoui, Hatem: An example of probability computations under the IAC assumption: the stability of scoring rules (2012)
- Eirinakis, Pavlos; Ruggieri, Salvatore; Subramani, K.; Wojciechowski, Piotr: A complexity perspective on entailment of parameterized linear constraints (2012)
- Motallebi, Hassan; Azgomi, Mohammad Abdollahi: Modeling and verification of hybrid dynamic systems using multisingular hybrid Petri nets (2012)
- Beck, Matthias; van Herick, Andrew: Enumeration of $4 \times 4$ magic squares (2011)
- Simon, Axel; King, Andy: The two variable per inequality abstract domain (2010)
- Verdoolaege, Sven: isl: An integer set library for the polyhedral model (2010)
- Bagnara, Roberto; Hill, Patricia M.; Zaffanella, Enea: Applications of polyhedral computations to the analysis and verification of hardware and software systems (2009)
- Olaru, S.; Dumitrache, I.; Dumur, D.: Geometrical analysis of model predictive control: A parameterized polyhedra approach (2009)
- Chen, Liangyu; Zeng, Zhenbing: Which symmetric homogeneous polynomials can be proved positive semi-definite by difference substitution method? (2008)
- Lepelley, Dominique; Louichi, Ahmed; Smaoui, Hatem: On Ehrhart polynomials and probability calculations in voting theory (2008)
- Olaru, Sorin; Dumur, Didier; Thomas, Jean; Zainea, Marius: Predictive control for hybrid systems. Implications of polyhedral pre-computations (2008)