emmy.calculus.coordinate — org.mentat/emmy 0.32.0

coordinate-functions clj/s

(coordinate-functions coordinate-system)

Returns a structure similar to the manifold/coordinate-prototype of coordinate-system, where every entry is a function from manifold point => the associated component of the point in the coordinate representation described by coordinate-system.

define-coordinates clj/s

(define-coordinates coordinate-prototype coordinate-system)

Give some coordinate-system like R2-rect and a coordinate-prototype like [x y] or (up x y),binds the following definitions into the namespace where define-coordinates is invoked:

• R2-rect binds to a new version of the coordinate system with its coordinate-prototype replaced by the supplied prototype

• x and y bind to coordinate functions, i.e., functions from manifold point to that particular coordinate

• d:dx and d:dy bind to the corresponding vector field procedures

• dx and dy bind to 1-forms for each coordinate.

let-coordinates clj/s

(let-coordinates bindings & body)

similar to a let binding that holds pairs of

<coordinate-structure-prototype>, <coordinate-system>

And internally binds, for each pair: (take [x y] and m/R2-rect as examples):

• The coordinate system symbol R2-rect to a new version of the coordinate system with its coordinate-prototype replaced by the one you supplied. That's (up x y) in this example.

• the entries x and y to coordinate functions, i.e., functions from manifold point to this particular coordinate

• d:dx and d:dy vector field procedures (I'm fuzzy here!)

• dx and dy 1-forms for each coordinate (fuzzy here too!)

Example:

(let-coordinates [[x y]    R2-rect
                 [r theta] R2-polar]
  ;; bindings:
  ;; R2-rect, x, y, d:dx, d:dy, dx, dy
  ;; R2-polar, r, theta, d:dr, d:dtheta, dr, dtheta
  body...)

quotify-coordinate-prototype clj/s

(quotify-coordinate-prototype p)

Scmutils wants to allow forms like this:

(using-coordinates (up x y) R2-rect ...)

Note that x, y are unquoted. This function converts such an unquoted form into a quoted one that could be evaluated to return an up-tuple of the symbols:

(up 'x 'y)

Such an object is useful for [[structure/mapr]].

using-coordinates clj/s

(using-coordinates coordinate-prototype coordinate-system & body)

using-coordinates wraps let-coordinates and allows you to supply a single coordinate prototype and a single coordinate system. See let-coordinates for details about what symbols are bound inside the body.

Example:

(using-coordinates (up x y) R2-rect
                   body...)