Structure representing the coefficient field \(\mathbb{Z}/p\mathbb{Z}\). More...

Public Member Functions
Element	plus_times_equal (const Element &x, const Element &y, const Element &w)

Element	times (const Element &y, const Element &w)

Element	additive_identity () const
	Returns the additive idendity \(0_{\Bbbk}\) of the field.

Element	multiplicative_identity (Element=0) const
	Returns the multiplicative identity \(1_{\Bbbk}\) of the field.

std::pair< Element, Element >	inverse (Element x, Element P)

Element	times_minus (Element x, Element y)

int	characteristic () const
	Returns the characteristic \(p\) of the field.

Public Member Functions inherited from CoefficientField
	CoefficientField ()

Element	characteristic ()

Element	multiplicative_identity ()

Element	additive_identity ()

void	plus_equal (Element x, Element y)

Additional Inherited Members
Public Types inherited from CoefficientField
typedef unspecified	Element
	Type of element of the field. More...

Detailed Description

Structure representing the coefficient field \(\mathbb{Z}/p\mathbb{Z}\).

Examples:: Bitmap_cubical_complex/cubical_complex_persistence.cpp, Bitmap_cubical_complex/periodic_cubical_complex_persistence.cpp, Bitmap_cubical_complex/Random_bitmap_cubical_complex.cpp, Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp, Persistent_cohomology/custom_persistence_sort.cpp, Persistent_cohomology/persistence_from_file.cpp, Persistent_cohomology/persistence_from_simple_simplex_tree.cpp, Persistent_cohomology/plain_homology.cpp, Persistent_cohomology/rips_persistence_step_by_step.cpp, Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp, Rips_complex/rips_distance_matrix_persistence.cpp, Rips_complex/rips_persistence.cpp, Witness_complex/example_nearest_landmark_table.cpp, Witness_complex/strong_witness_persistence.cpp, and Witness_complex/weak_witness_persistence.cpp.

Member Function Documentation

std::pair<Element, Element> Gudhi::persistent_cohomology::Field_Zp::inverse	(	Element	x,
		Element	P
	)

inline

Returns the inverse in the field. Modifies P. ???

Element Gudhi::persistent_cohomology::Field_Zp::plus_times_equal	(	const Element &	x,
		const Element &	y,
		const Element &	w
	)

inline

Set x <- x + w * y

Element Gudhi::persistent_cohomology::Field_Zp::times	(	const Element &	y,
		const Element &	w
	)

inline

Returns y * w

Element Gudhi::persistent_cohomology::Field_Zp::times_minus	(	Element	x,
		Element	y
	)

inline

Returns -x * y.

The documentation for this class was generated from the following file: