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emmy.calculus.covariant

Cartan->basisclj/s

(Cartan->basis C)
source

Cartan->Cartan-over-mapclj/s

(Cartan->Cartan-over-map Cartan map)
source

Cartan->Christoffelclj/s

(Cartan->Christoffel Cartan)
source

Cartan->formsclj/s

(Cartan->forms C)
source

Cartan-transformclj/s

(Cartan-transform cartan basis-prime)
source

Cartan?clj/s

(Cartan? x)
source

Christoffel->basisclj/s

(Christoffel->basis C)
source

Christoffel->Cartanclj/s

(Christoffel->Cartan Christoffel)
source

Christoffel->symbolsclj/s

(Christoffel->symbols C)
source

Christoffel?clj/s

(Christoffel? x)
source

covariant-derivativeclj/s

(covariant-derivative Cartan)
(covariant-derivative Cartan map)
source

covariant-differentialclj/s

(covariant-differential Cartan)
source

geodesic-equationclj/s

(geodesic-equation source-coordsys target-coordsys Cartan-on-target)
source

interior-productclj/s

(interior-product X)
source

Lie-Dclj/s

(Lie-D R)

Takes a system derivative R and returns a operator that takes a function F of coordinatized state and performs the operation described below, from ODE.scm in scmutils:

Let (sigma t) be the state of a system at time t. Let the (first-order) system of differential equations governing the evolution of this state be:

((D sigma) t) = (R (sigma t))

(D sigma) = (compose R sigma)

i.e. R is a system derivative.

Let F be any function of state, then a differential equation for the evolution of F, as it is dragged along the integral curve sigma is:

(D (compose F sigma)) = (* (compose (D F) sigma) (D sigma))
= (compose (* (D F) R) sigma)

Let's call this operation Lie-D (the Lie derivative for coordinates).

Takes a system derivative `R` and returns a operator that takes a function `F`
of coordinatized state and performs the operation described below, from
ODE.scm in scmutils:

Let `(sigma t)` be the state of a system at time `t`. Let the
(first-order) system of differential equations governing the evolution of
this state be:

```clojure
((D sigma) t) = (R (sigma t))
```

```clojure
(D sigma) = (compose R sigma)
```

i.e. `R` is a system derivative.

Let `F` be any function of state, then a differential equation for the
evolution of `F`, as it is dragged along the integral curve sigma is:

```clojure
(D (compose F sigma)) = (* (compose (D F) sigma) (D sigma))
= (compose (* (D F) R) sigma)
```

Let's call this operation `Lie-D` (the Lie derivative for coordinates).
sourceraw docstring

make-Cartanclj/s

(make-Cartan forms basis)
source

make-Christoffelclj/s

(make-Christoffel symbols basis)

Returns a data structure representing Christoffel symbols of the second kind.

Returns a data structure representing [Christoffel symbols of the second
kind](https://en.wikipedia.org/wiki/Christoffel_symbols#Christoffel_symbols_of_the_second_kind_(symmetric_definition)).
sourceraw docstring

parallel-transport-equationclj/s

(parallel-transport-equation source-coordsys target-coordsys Cartan-on-target)
source

symmetrize-Cartanclj/s

(symmetrize-Cartan Cartan)
source

symmetrize-Christoffelclj/s

(symmetrize-Christoffel G)
source

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