Functional Differential Geometry

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(define e0
  (+ (* (literal-manifold-function 'e0x R2-rect)
        d/dx)
     (* (literal-manifold-function 'e0y R2-rect)
        d/dy)))

This code is misleading because:

1. The term d/dx is undefined:

1 ]=> (pp d/dx)

;Unbound variable: d/dx

2. It is defined only implicitly, making it difficult to follow:

(define-coordinates (up x y) R2-rect)

(define-coordinates (up r theta) R2-polar)

(define R2-rect-chi-inverse
  (point R2-rect))

(define R2-rect-point
  (R2-rect-chi-inverse (up 'x_0 'y_0)))

Once implicitly defined, we can print its definition:

1 ]=> (pp d/dx)
(lambda (f)
  (compose ((apply partial i) (compose f (coordinate-system '->point)))
           (coordinate-system '->coords)))

;No return value.

1 ]=> 

However, we still do not know where d/dx is defined.

— Me@2025-03-19 02:35:03 PM

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2025.03.20 Thursday (c) All rights reserved by ACHK