Covector Basis

Since \(k\)-forms use covector bundles as basis for different components, utilities for dealing with these in Python are provided by the CovectorBasis. This type supports the wedge product using the XOR ^ operator, as well as the Hodge using the inversion ~ operator.

The CovectorBasis type is primarily intended to be used to help with sorting and classifying different \(k\)-form components.

class fdg.CovectorBasis(n: int, /, *idx: int)

Type used to specify covector basis bundle.

Parameters:

• n (int) – Dimension of the space basis bundle is in.

• *idx (int) – Indices of basis present in the bundle. Should be sorted and non-repeating.

normalize() → tuple[int, CovectorBasis]

Normalize the basis by splitting the sign.

index

Index of the basis for the k-form.

Type:

int

ndim

Number of dimensions of the space the basis are in.

Type:

int

rank

Number of basis contained.

Type:

int

sign

The sign of the basis.

Type:

int