AbstractChainComplex Concept Reference

Definition

The concept AbstractChainComplex describes the requirements for (topological) chain complexes associated to abstract complexes used in the concept HDVF.

It provides methods to:

• get the dimension of the complex, the number of cells in each dimension
• get the boundary and co-boundary of cell(s)
• get the vertices of a given cell
• output the complex in text format

Cells are indexed along each dimension and thus identified by their index together with their dimension.

Has models

CGAL::Homological_discrete_vector_field::Abstract_simplicial_chain_complex<IntegralDomainWithoutDivision>

CGAL::Homological_discrete_vector_field::Sub_chain_complex_mask<IntegralDomainWithoutDivision, AbstractChainComplex>

Related Functions
(Note that these are not member functions.)
std::ostream &	operator<< (std::ostream &out, const AbstractChainComplex &complex) const
	Inserts the chain complex in text mode in the stream.

Types
typedef CoefficientRing	Coefficient_ring
	Type of coefficients ring used to compute homology, model of IntegralDomainWithoutDivision
typedef CGAL::OSM::Sparse_chain< CoefficientRing, CGAL::OSM::COLUMN >	Column_chain
	Type of column-major chains (returned by the boundary operator)
typedef CGAL::OSM::Sparse_chain< CoefficientRing, CGAL::OSM::ROW >	Row_chain
	Type of row-major chains (returned by the co-boundary operator)
typedef CGAL::OSM::Sparse_matrix< CoefficientRing, CGAL::OSM::COLUMN >	Column_matrix
	Type of column-major sparse matrices (used to store the boundary operator)

Verification operations
bool	is_valid_cell_dimension (int q)
	Checks if q belongs to the range of dimensions of cells in the complex.
bool	is_valid_cell (size_t id, int q)
	Checks if a cell of index i and dimension q belongs to the range of dimensions of cells in the complex.

Operators
AbstractChainComplex &	operator= (const AbstractChainComplex &complex)
	Assignment operator.

Member Typedef Documentation

Coefficient_ring

typedef CoefficientRing AbstractChainComplex::Coefficient_ring

Type of coefficients ring used to compute homology, model of IntegralDomainWithoutDivision

Member Function Documentation

operator=()

AbstractChainComplex & AbstractChainComplex::operator=

(

const AbstractChainComplex &

complex

)

Assignment operator.

The operator creates a copy of complex.