exterior_objects.hpp File Reference

Compute the action of Kozsul and Diff on the exterior algebra. More...

#include "exterior_algebra.hpp"
#include <unsupported/Eigen/KroneckerProduct>

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Classes
class	Manicore::Koszul_exterior< l, d >
	Koszul operator on the exterior algebra. More...
class	Manicore::Diff_exterior< l, d >
	Diff operator on the exterior algebra. More...
struct	Manicore::Koszul_homogeneous_mat< d, index >
	Generate the matrices for the Koszul operator on homogeneous monomial. More...
struct	Manicore::Diff_homogeneous_mat< d, index >
	Generate the matrices for the Differential operator on homogeneous monomial. More...
struct	Manicore::Koszul_full< l, d >
	Koszul operator from \(\mathcal{P}_r\Lambda^l(\mathbb{R}^d)\) to \(\mathcal{P}_{r+1}\Lambda^{l-1}(\mathbb{R}^d)\). More...
struct	Manicore::Diff_full< l, d >
	Differential operator from \(\mathcal{P}_r\Lambda^l(\mathbb{R}^d)\) to \(\mathcal{P}_{r-1}\Lambda^{l+1}(\mathbb{R}^d)\). More...
struct	Manicore::Initialize_exterior_module< d >
	Initialize every class related to the polynomial degree r. More...

Namespaces
	Manicore

Detailed Description

Compute the action of Kozsul and Diff on the exterior algebra.

The action is returned as a list of matrix between the exterior algebra basis To get the full action, one must take the Kronecker product between the action on the exterior algebra and the action on the polynomial space. In the case of Koszul, the action is to multiply by \(x_i\), and in the case of Diff, it is the differentiated by \(x_i\).

The basis are those given in exterior_algebra.hpp. The basis of \(\mathcal{P}_r\Lambda^l(\mathbb{R}^d)\) is the Kronecker product \(\Lambda^l \otimes \mathcal{P}_r\).

The most useful are: Koszul_full : gives the matrix of the Koszul operator Diff_full : gives the matrix of the Diff operator

Call Manicore::Initialize_exterior_module<d>::init(int r) to initialize every module on dimension d