Simplicial blowups and discrete normal surfaces in the GAP package simpcomp
نویسنده
چکیده
simpcomp is an extension to GAP, the well known system for computational discrete algebra. It allows the user to work with simplicial complexes. In the latest version, support for simplicial blowups and discrete normal surfaces was added, both features unique to simpcomp. Furthermore, new functions for constructing certain infinite series of triangulations have been implemented and interfaces to other software packages have been improved to previous versions.
منابع مشابه
A GAP toolbox for simplicial complexes
simpcomp is a GAP package for working with simplicial complexes. It allows the computation of many properties of simplicial complexes (such as the f -, gand h-vectors, the face lattice, the automorphism group, (co-)homology with explicit basis computation, intersection form, etc.) and provides the user with functions to compute new complexes from old (simplex links and stars, connected sums, ca...
متن کاملGAP toolbox for simplicial complexes
simpcomp is a GAP package for working with simplicial complexes. It allows the computation of many properties of simplicial complexes (such as the f -, gand h-vectors, the face lattice, the automorphism group, (co-)homology with explicit basis computation, intersection form, etc.) and provides the user with functions to compute new complexes from old (simplex links and stars, connected sums, ca...
متن کاملCombinatorial Properties of the K3 Surface: Simplicial Blowups and Slicings
The 4-dimensional abstract Kummer variety K4 with 16 nodes leads to the K3 surface by resolving the 16 singularities. Here we present a simplicial realization of this minimal resolution. Starting with the minimal 16-vertex triangulation (K)16 we resolve its 16 isolated singularities – step by step – by simplicial blowups. A key step is the construction of a triangulated version of the mapping c...
متن کاملSimplicial Homology a Proposed Share Package for Gap
Preface 1 About the Package The development of the package was driven by two diierent targets. The rst target is to design eecient algorithms for exact matrix computations (e.g. Smith Normal from) for sparse matrices with entries in the integers. The second target is eecient software to calculate homology of simplicial complexes. Since the crucial step for the second target is the calculation o...
متن کاملComputing Simplicial Homology Based on Efficient Smith Normal Form Algorithms
We recall that the calculation of homology with integer coefficients of a simplicial complex reduces to the calculation of the Smith Normal Form of the boundary matrices which in general are sparse. We provide a review of several algorithms for the calculation of Smith Normal Form of sparse matrices and compare their running times for actual boundary matrices. Then we describe alternative appro...
متن کامل