This ticket implements multivector fields (i.e. alternating contravariant tensor fields) on differentiable manifolds, via the parent classes

• MultivectorModule: set A^p(M) of multivector fields of a degree p on a manifold M, considered as a module over the commutative algebra C^k(M) of differentiable scalar fields
• MultivectorFreeModule: set A^p(M) of multivector fields of a degree p on a parallelizable manifold M, considered as a free module of rank binomial(n,p) over C^k(M) (where n=dimM)

and the element classes

• MultivectorField: multivector field on a differentiable manifold
• MultivectorFieldParal: multivector field on a parallelizable differentiable manifold

The classes MultivectorFreeModule and MultivectorFieldParal inherit from respectively ExtPowerFreeModule and AlternatingContrTensor, which have been introduced in #23207.

The classes VectorField and VectorFieldParal inherit now from the new classes MultivectorField and MultivectorFieldParal, since a vector field is a multivector field of degree 1.

The ticket implements the exterior product A^p(M) x A^q(M) ---> A^p+q(M) (method wedge), as well as the interior products

• A^p(M) x Omega*^q(M)* ---> Omega*^q-p(M)*
• Omega*^p(M)* x A^q(M) ---> A^q-p(M)
  for p<=q, where Omega*^p(M)* is the C^k(M)-module of differential forms of degree p on M (method interior_product).
  The ticket also implements the Schouten-Nijenhuis bracket A^p(M)xA^q(M) ---> A^p+q-1(M) (method bracket), extending the Lie bracket of vector fields.

This is a follow up of #23207 within the SageManifolds project (see the metaticket #18528 for an overview).

Depends on #23207

CC: @sagetrac-bpym @tscrim

Component: geometry

Keywords: multivector, Schouten-Nijenhuis bracket

Author: Eric Gourgoulhon

Branch/Commit: 18df6e6

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/23429