DenseTensorDependence

class differential_geometry.dependence.DenseTensorDependence(coordinate_system: _CoordinateSystemBase, rank: int, /, *, dependent_axes: str | Sequence[str] | None = None)

Dense symbolic tensor dependence with attached tensor-aware operators.

This subclass uses the tensor rank to define the shape and supports symbolic tensor operations (e.g., raising/lowering indices, divergence), in addition to element-wise operations.

Parameters:

• coordinate_system (_CoordinateSystemBase) – The coordinate system in which the tensor is defined.

• rank (int) – The rank (number of tensor indices) for the tensor. Shape will be (ndim,)*rank.

• dependent_axes (str or Sequence[str], optional) – The coordinate axes on which the tensor depends.

Methods

__init__(coordinate_system, rank, /, *[, ...])	Initialize a dense tensor dependence object with a given rank and coordinate dependence.
adjust_tensor_signature(variance_in, ...[, ...])	Adjust the tensor variance (covariant/contravariant) of each index.
depends_on(axis)	Check whether this object symbolically depends on a given coordinate axis.
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.
from_symbolic_proxy(coordinate_system, ...)	Rebuild a DenseTensorDependence from a symbolic proxy.
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.
to_symbolic_proxy()	Construct a symbolic proxy representing this tensor or scalar field.

Attributes

axes_symbols	The symbolic representations of the dependent coordinate axes.
coordinate_system	The coordinate system associated with this dependence object.
coordinates_ndim	Number of coordinate dimensions in the associated coordinate system.
dependent_axes	The list of coordinate axis names this field depends on.
is_scalar	Whether this object represents a scalar field (i.e., rank 0).
rank	The tensor rank [number of indices] of this field.
shape	The tensor shape of this symbolic field.
symbolic_proxy	A symbolic proxy field or tensor that represents coordinate dependence.