#include <sources/headers/Complex.h>

template<typename Obj, template<typename> typename Mor, typename Coeff>

Complex_Base class

base class for complexes

A complex consists of a list objects of objects, a matrix diffs of morphisms that defines a differential and a list cancelled_indices of cancelled indices.

Derived classes

template<typename Obj, template<typename> typename Mor, typename Coeff>

class Complex

generic child of Complex_Base

Constructors, destructors, conversion operators

Complex_Base()

constructor of zero object in the category of complexes

Complex_Base(std::vector<Obj> objects, Eigen::SparseMatrix<Mor<Coeff>> diffs)

standard constructor

Public functions

void cancel()

computes fully reduced complex obtained by repeated application of the Cancellation Lemma from [4]

void cancel(const ssize_t& sourceindex, const ssize_t& targetindex)

implements the Cancellation Lemma from [4] for a single component of the differential

auto check() const -> bool

true if the components of the differential d are well-defined and d²=0. Otherwise, this function will give a warning.

auto find_invertible() -> std::pair<int, int>

component of the differential to which one can apply the Cancellation Lemma from [4]; if there is no such component, this returns (n,n), where n is the number of objects in the complex

auto get_cancelled_indices() const -> std::list<unsigned int>

list of cancelled indices

auto get_diffs() const -> Eigen::SparseMatrix<Mor<Coeff>>

Eigen matrix defining the differential.

auto get_objects() const -> std::vector<Obj>

list of objects in the complex

void isotopy(const ssize_t& start, const ssize_t& end, const Mor<Coeff>& mor)

implements the Clean-Up Lemma from [4], ie performs a basic isotopy along start—(mor)—>end

void print(const ssize_t& index_from, const ssize_t& index_to) const

print a component of the differential of a complex in terminal

void resize()

resizes the list of objects and matrix of differentials according to the list of cancelled indices

auto to_string() const -> std::string

string representative of a complex

Protected variables

std::list<unsigned int> cancelled_indices

list of cancelled indices, which is empty by default; cancel() adds the indices of the cancelled generators, but keeps objects and diffs intact; resize() then actually deletes the objects and resizes diffs according to this list.

Eigen::SparseMatrix<Mor<Coeff>> diffs

matrix defining the differential of the complex

std::vector<Obj> objects

list of objects of the complex (corresponds to the underlying 'chain module')

size_t start_find_invertible

starting index for finding invertible generators