sicmutils.calculus.vector-calculus

This namespace contains vector calculus operators, in versions built on top of derivative/D and in Functional Differential Geometry style.

The former transform functions of scalars or vectors, while the latter take a metric and basis.

This namespace contains vector calculus operators, in versions built on top
of [[derivative/D]] _and_ in Functional Differential Geometry style.

The former transform functions of scalars or vectors, while the latter take a
metric and basis.

raw docstring

coordinate-system->Lame-coefficients^clj/s

(coordinate-system->Lame-coefficients coordinate-system)

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coordinate-system->orthonormal-vector-basis^clj/s

(coordinate-system->orthonormal-vector-basis coordsys)

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curl^clj/s

(curl metric orthonormal-basis)

curl implements equation (10.7) of Functional Differential Geometry, defined on page 155.

[[curl]] implements equation (10.7) of Functional Differential Geometry,
defined on page 155.

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Curl^clj/s

Operator that takes a function f and returns a function that calculates the Curl of f at its input point.

f must be a function from $\mathbb{R}^3 \to \mathbb{R}^3$.

Operator that takes a function `f` and returns a function that
calculates the [Curl](https://en.wikipedia.org/wiki/Curl_(mathematics)) of `f`
at its input point.

`f` must be a function from $\mathbb{R}^3 \to \mathbb{R}^3$.

source raw docstring

Div^clj/s

Operator that takes a function f and returns a function that calculates the Divergence of f at its input point.

The divergence is a one-level contraction of the gradient.

Operator that takes a function `f` and returns a function that
 calculates the [Divergence](https://en.wikipedia.org/wiki/Divergence) of
 `f` at its input point.

The divergence is a one-level contraction of the gradient.

source raw docstring

divergence^clj/s

(divergence Cartan)

(divergence metric orthonormal-basis)

Both arities of divergence are defined on page 156 of Functional Differential Geometry.

Both arities of [[divergence]] are defined on page 156 of Functional Differential Geometry.

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Grad^clj/s

Operator that takes a function f and returns a new function that calculates the Gradient of f.

The related [[D]] operator returns a function that produces a structure of the opposite orientation as Grad. Both of these functions use forward-mode automatic differentiation.

Operator that takes a function `f` and returns a new function that
calculates the [Gradient](https://en.wikipedia.org/wiki/Gradient) of `f`.

The related [[D]] operator returns a function that produces a structure of the
opposite orientation as [[Grad]]. Both of these functions use forward-mode
automatic differentiation.

source raw docstring

gradient^clj/s

(gradient metric basis)

gradient implements equation (10.3) in Functional Differential Geometry, defined on page 154.

[[gradient]] implements equation (10.3) in Functional Differential Geometry,
defined on page 154.

source raw docstring

Lap^clj/s

Operator that takes a function f and returns a function that calculates the Vector Laplacian of f at its input point.

Operator that takes a function `f` and returns a function that
calculates the [Vector
Laplacian](https://en.wikipedia.org/wiki/Laplace_operator#Vector_Laplacian) of
`f` at its input point.

source raw docstring