forms.cppm File Reference

The Exterior Algebra (Differential Forms). More...

#include <concepts>
#include <cstddef>
import dedekind.geometry;

Include dependency graph for forms.cppm:

Classes
class	dedekind::analysis::OneForm< F, N >
	The cotangent vector (The 'Gradient' components). More...

Concepts
concept	dedekind::analysis::IsDifferentialForm
	A mapping from a Tangent Space to a Scalar.

Functions
template<IsMatrixScalar F, std::size_t N>
constexpr Covector< F, N >	dedekind::analysis::to_covector (const OneForm< F, N > &w)
	Convert a OneForm to its Covector (row-vector) representation.
template<IsMatrixScalar F, std::size_t N>
constexpr OneForm< F, N >	dedekind::analysis::from_covector (const Covector< F, N > &cov)
	Convert a Covector to its OneForm representation.

Detailed Description

The Exterior Algebra (Differential Forms).

@partition :forms

Copyright

2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

Note

"To new concepts correspond, necessarily, new signs." – David Hilbert, Mathematical Problems (1900)

See also

#272 Denotational Automatic Differentiation (work in progress): the OneForm ↔ Dual bridge.

#286 undergraduate calculus (work in progress): the integral theorems of vector calculus.

Function Documentation

from_covector()

template<IsMatrixScalar F, std::size_t N>

OneForm< F, N > dedekind::analysis::from_covector ( const Covector< F, N > & cov )

constexprexport

Convert a Covector to its OneForm representation.

This is the inverse view of to_covector for the current dense row-vector representation of linear functionals.

to_covector()

template<IsMatrixScalar F, std::size_t N>

Covector< F, N > dedekind::analysis::to_covector ( const OneForm< F, N > & w )

constexprexport

Convert a OneForm to its Covector (row-vector) representation.

A OneForm<F,N> and a Covector<F,N> (= LinearMap<F,1,N>) are two representations of the same linear functional F^N -> F. This function constructs the Covector whose single row holds the OneForm's components, making the bijection explicit.