exterior_algebra.hpp File Reference

The methods in this file are meant to compute the action of everything that is independent of the atlas. More...

#include "exterior_dimension.hpp"
#include <vector>
#include <array>
#include <unordered_map>
#include <algorithm>
#include <cstdlib>
#include <cassert>
#include <Eigen/Dense>
#include <unsupported/Eigen/KroneckerProduct>

Include dependency graph for exterior_algebra.hpp:

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Go to the source code of this file.

Classes
class	Manicore::ExteriorBasis< l, d >
	Class to handle the exterior algebra basis. More...
class	Manicore::ComplBasis< l, d >
	Return a mapping from the basis of l-forms in dimension d to the basis of (d-l)-forms. More...
struct	Manicore::Compute_pullback< l, d1, d2 >
	Generic pullback computation. More...
struct	Manicore::Compute_pullback< 0, d1, d2 >
struct	Manicore::Compute_pullback< 1, d1, d2 >
struct	Manicore::Compute_pullback< d, d, d >
struct	Manicore::Compute_pullback< 1, 1, 1 >
struct	Manicore::Compute_pullback< 2, 2, 3 >
struct	Manicore::Compute_pullback< 2, 3, 2 >
struct	Manicore::Compute_pullback< 2, 3, 3 >
struct	Manicore::Compute_ExtGram< l >
	Wrapper for the \(L^2\) product on the exterior algebra. More...
struct	Manicore::Monomial_powers< d >
	Generate a basis of monomial powers of degree r. More...

Namespaces
	Manicore

Functions
template<typename V , typename Derived >
double	Manicore::Compute_partial_det (const V &a1, const V &a2, const Eigen::MatrixBase< Derived > &A)
	Generic determinant computation. More...

Detailed Description

The methods in this file are meant to compute the action of everything that is independent of the atlas.

The most useful are: Compute_pullback : computes the action of a pullback to the exterior algebra Monomial_full : gives a mapping between index and monomial powers

The polynomial basis must be initialized before use.

The explicit ordering for low dimensions is available here.