Concepts

Concepts
concept	AbstractChainComplex
	The concept AbstractChainComplex describes the requirements for (topological) chain complexes associated to abstract complexes used in the concept CGAL::HDVF. More...
concept	Filtration
	The concept Filtration describes the requirements for persistent filtrations associated to persistent homology computation. More...
concept	GeometricChainComplex
	The concept GeometricChainComplex refines the concept AbstractChainComplex and describes the requirements for (topological) chain complexes associated to geometric complexes used in the concept CGAL::HDVF. It adds to AbstractChainComplex methods to get vertices coordinates. More...
concept	HDVF
	The concept HDVF describes the requirements for Homological Discrete Vector Fields (HDVF for short) , a theory of computational homology unifying discrete Morse theory and effective homology. HDVFs were introduced by Aldo Gonzalez-Lorenzo in his PhD (see [AGL,2017], [AGL,2016]). More...
concept	Ring
	The concept Ring describes the requirements for the ring of coefficients used to compute homology in the HomologicalDiscreteVectorField concept. Besides ring operators, it also specifies the functions needed to test invertibility in the ring. More...
concept	SparseChain
	The concept SparseChain describes the requirements for sparse vectors (called sparse chains in homology) optimized for topological computations. More precisely, SparseChain provides all the operations on chains required by the SparseMatrix concept. More...
concept	SparseMatrix
	The concept SparseMatrix describes the requirements for sparse matrices optimized for topological computations. Traditionally, sparse matrices data structures encode non zero coefficients of (sparse) matrices in order to optimize either matrices memory footprint, or linear algebra operations (which usually comes to optimize iterators over non zero coefficients and access to coefficients). However, topological operations require slightly different features: More...