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hereditary-base.scm
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hereditary-base.scm
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;; (number->hereditary-base-2 #b10110)
;; -> '(+ (^ 2 (^ 2 (^ 2 (^ 2 0)))) (^ 2 (^ 2 (^ 2 0))) (^ 2 (^ 2 0)))
;;
;; (number->hereditary-base-2 35) -> (+ (^ 2 (+ (^ 2 2) 1)) 2 1)
(define (number->hereditary-base-2 n)
(let ((deg 0) ;; polynom degree
(poly-prefix '())
(poly-prefix-simp '()))
(letrec
((number->hereditary-base-2-rec
(lambda (n)
;;(dv deg)
(cond
((zero? n) '(0))
;;((= 1 n) (quasiquote ((^ 2 ,(number->hereditary-base-2 deg)))))
((= (modulo n 2) 1)
(let ((monomial
(quasiquote ((^ 2 ,(number->hereditary-base-2 deg))))))
(set! deg (+ 1 deg))
(append
(number->hereditary-base-2-rec (quotient n 2))
monomial)))
(else
(set! deg (+ 1 deg))
(append (number->hereditary-base-2-rec (quotient n 2)) (list 0)))))))
(set! poly-prefix (cons '+ (number->hereditary-base-2-rec n)))
(dv poly-prefix)
(set! poly-prefix-simp (simplify poly-prefix))
(dv poly-prefix-simp)
poly-prefix-simp)))
;; (number->hereditary-base-k 100 3) -> '(+ (^ 3 (+ 3 1)) (* 2 (^ 3 2)) 1)
(define (number->hereditary-base-k n k)
(let ((deg 0) ;; polynom degree
(poly-prefix '())
(poly-prefix-simp '()))
(letrec
((number->hereditary-base-k-rec
(lambda (n k)
(if (zero? n)
'(0)
(let ((r (modulo n k))) ;; remainder
;;(dv deg)
(if (not (zero? r))
(let ((monomial
(quasiquote ((* ,r (^ ,k ,(number->hereditary-base-k deg k))))))
(q (quotient n k)))
(set! deg (+ 1 deg))
(append
(number->hereditary-base-k-rec q k)
monomial))
(begin
(set! deg (+ 1 deg))
(append
(number->hereditary-base-k-rec (quotient n k) k)
(list 0)))))))))
(set! poly-prefix (cons '+ (number->hereditary-base-k-rec n k)))
;;(dv poly-prefix)
(set! poly-prefix-simp (simplify poly-prefix))
;;(dv poly-prefix-simp)
poly-prefix-simp)))
;; (number->hereditary-base-k-expt 100 3) -> '(+ (expt 3 (+ 3 1)) (* 2 (expt 3 2)) 1)
;;
;; (number->hereditary-base-k-expt 22876792454964 3) -> '(+ (expt 3 (+ (expt 3 3) 1)) 3)
;;
;; (number->hereditary-base-k-expt 7625597484990 3) -> '(+ (expt 3 (expt 3 3)) 3)
;;
;; (number->hereditary-base-k-expt 173646739038364 5)
;;
;; '(+
;; (expt 5 (* 4 5))
;; (* 4 (expt 5 (+ (* 3 5) 4)))
;; (* 2 (expt 5 (+ (* 3 5) 2)))
;; (* 3 (expt 5 (+ (* 3 5) 1)))
;; (expt 5 (+ (* 2 5) 3))
;; (* 2 (expt 5 (+ (* 2 5) 2)))
;; (expt 5 (* 2 5))
;; (expt 5 (+ 5 3))
;; (* 4 (expt 5 (+ 5 2)))
;; (* 3 (expt 5 (+ 5 1)))
;; (* 2 (expt 5 5))
;; (expt 5 4)
;; (expt 5 3)
;; (* 4 (expt 5 2))
;; (* 2 5)
;; 4)
(define (number->hereditary-base-k-expt n k)
(let ((deg 0) ;; polynom degree
(poly-prefix '())
(poly-prefix-simp '()))
(letrec
((number->hereditary-base-k-rec-expt
(lambda (n k)
(if (zero? n)
'(0)
(let ((r (modulo n k))) ;; remainder
;;(dv deg)
(if (not (zero? r))
(let ((monomial
(quasiquote ((* ,r (expt ,k ,(number->hereditary-base-k-expt deg k))))))
(q (quotient n k)))
(set! deg (+ 1 deg))
(append
(number->hereditary-base-k-rec-expt q k)
monomial))
(begin
(set! deg (+ 1 deg))
(append
(number->hereditary-base-k-rec-expt (quotient n k) k)
(list 0)))))))))
(set! poly-prefix (cons '+ (number->hereditary-base-k-rec-expt n k)))
;;(dv poly-prefix)
(set! poly-prefix-simp (simplify poly-prefix))
;;(dv poly-prefix-simp)
poly-prefix-simp)))
;; (number->hereditary-base-2-infix #b10110)
;; -> '((2 ^ (2 ^ (2 ^ (2 ^ 0)))) + (2 ^ (2 ^ (2 ^ 0))) + (2 ^ (2 ^ 0)))
;;
;; (number->hereditary-base-2-infix 26)
;; -> '((2 ^ (2 ^ 2)) + (2 ^ (2 + 1)) + 2)
;; previous -> '((2 ^ (2 ^ (2 ^ (2 ^ 0)))) + (2 ^ ((2 ^ (2 ^ 0)) + (2 ^ 0))) + (2 ^ (2 ^ 0)))
;;
(define (number->hereditary-base-2-infix n)
(prefix->infix (number->hereditary-base-2 n)))
;; (number->hereditary-base-k-infix 22876792454964 3)
;; -> '((3 ^ ((3 ^ 3) + 1)) + 3)
;;
;; (number->hereditary-base-k-infix 109 7) -> '((2 * (7 ^ 2)) + 7 + 4)
;;
;; (number->hereditary-base-k-infix 299 12) -> '((2 * (12 ^ 2)) + 11)
;;
(define (number->hereditary-base-k-infix n k)
(prefix->infix (number->hereditary-base-k n k)))