triangle-of-power.scm

;; Triangle of Power operator in Scheme.
;; Tested in Racket, Guile, and Chicken; portable under R6RS+.

;; See https://mathcenter.oxford.emory.edu/site/math108/logs/
;; and https://www.youtube.com/watch?v=sULa9Lc4pck
;; and https://math.stackexchange.com/questions/30046/alternative-notation-for-exponents-logs-and-roots/165225#165225
;; to learn about "Triangle of Power" notation

;; Exponents Logs Radicals (triangle) operation
(define-syntax elr
  ;; Argument order is counterclockwise from bottom right. 
  (syntax-rules (?)
    [(_ a b ?) (expt a b)]
    [(_ a ? c) (/ (log c) (log a))]
    [(_ ? b c) (expt c (/ 1 b))]
    [(_ a b c) (= (expt a b) c)]))

;; ^ looks a bit like a △, but Racket already uses it and
;; it may look too similar to exponentiation
(define-syntax △
  (syntax-rules ()
    [(_ a b c) (elr a b c)]))

;; Examples:
(= (△ 3 #;raised-to 2 #;is ?) 9) ;; Exponentiation
(= (△ 3 ? 9) 2) ;; Logarithm
(= (△ ? 2 9) 3) ;; Root
(eq? (△ 3 2 9) #t) ;; Complete triangle