TensorDependenceMixin

class differential_geometry.dependence.TensorDependenceMixin

Mixin class providing tensor-specific operations for symbolic dependence objects.

This mixin extends OperatorsMixin by adding operations that rely on tensor structure, such as raising/lowering indices, adjusting variance signatures, and computing divergence in addition to the general-purpose gradient and Laplacian.

It assumes the object exposes:

• coordinate_system: a coordinate system with symbolic metric data,

• rank: an integer rank for the tensor (0 = scalar, 1 = vector, etc.),

• symbolic_proxy: a SymPy scalar or array-like expression,

• from_symbolic_proxy: a method to reconstruct a new instance from a proxy.

Notes

Unlike OperatorsMixin, which applies differential operators to each component independently, this mixin enables true tensorial operations that respect index variance (covariant/contravariant behavior).

Methods

__init__()
adjust_tensor_signature(variance_in, ...[, ...])	Adjust the tensor variance (covariant/contravariant) of each index.
divergence(*[, basis, as_field])	Compute the divergence of a rank-1 tensor field.
element_wise_gradient(*[, basis, as_field])	Compute the component-wise gradient of the field.
element_wise_laplacian(*[, as_field])	Compute the component-wise Laplacian of the field.
gradient(*[, basis, as_field])	Compute the elementwise gradient of the tensor field.
laplacian(*[, as_field])	Compute the Laplacian of the tensor field (component-wise).
lower_index(axis, /, *[, as_field])	Lower a tensor index along the specified axis using the metric tensor.
raise_index(axis, /, *[, as_field])	Raise a tensor index along the specified axis using the inverse metric tensor.