emmy.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.
coordinate-system->Lame-coefficientsclj/s
(coordinate-system->Lame-coefficients coordinate-system)coordinate-system->orthonormal-vector-basisclj/s
(coordinate-system->orthonormal-vector-basis coordsys)curlclj/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.
Curlclj/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 $\mathbb{R}^3 \to \mathbb{R}^3$.Divclj/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.
divergenceclj/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.
Gradclj/s
Operator that takes a function f and returns a new function that
calculates the Gradient of f.
The related emmy.env/D operator returns a function that produces a
structure of the opposite orientation as Grad. Both of these functions use
reverse-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 [[emmy.env/D]] operator returns a function that produces a structure of the opposite orientation as [[Grad]]. Both of these functions use reverse-mode automatic differentiation.
gradientclj/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.
Lapclj/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.
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