diff options
Diffstat (limited to 'semestr-2/racket/deriv.rkt')
| -rw-r--r-- | semestr-2/racket/deriv.rkt | 47 |
1 files changed, 47 insertions, 0 deletions
diff --git a/semestr-2/racket/deriv.rkt b/semestr-2/racket/deriv.rkt new file mode 100644 index 0000000..0eef9d2 --- /dev/null +++ b/semestr-2/racket/deriv.rkt @@ -0,0 +1,47 @@ +#lang racket + +(define (variable? x) (symbol? x)) + +(define (same-variable? v1 v2) + (and (variable? v1) (variable? v2) (eq? v1 v2))) + +(define (=number? exp num) + (and (number? exp) (= exp num))) + +(define (make-sum a1 a2) + (cond ((=number? a1 0) a2) + ((=number? a2 0) a1) + ((and (number? a1) (number? a2) (+ a1 a2))) + (else (list '+ a1 a2)))) +(define (sum? x) + (and (pair? x) (eq? (car x) '+))) +(define (addend s) (cadr s)) +(define (augend s) (caddr s)) + +(define (make-product m1 m2) + (cond ((or (=number? m1 0) (=number? m2 0)) 0) + ((=number? m1 1) m2) + ((=number? m2 1) m1) + ((and (number? m1) (number? m2)) (* m1 m2)) + (else (list '* m1 m2)))) +(define (product? x) + (and (pair? x) (eq? (car x) '*))) +(define (multiplier p) (cadr p)) +(define (multiplicand p) (caddr p)) + +(define (deriv exp var) + (cond ((number? exp) 0) + ((variable? exp) + (if (same-variable? exp var) 1 0)) + ((sum? exp) + (make-sum (deriv (addend exp) var) + (deriv (augend exp) var))) + ((product? exp) + (make-sum + (make-product (multiplier exp) + (deriv (multiplicand exp) var)) + (make-product (deriv (multiplier exp) var) + (multiplicand exp)))) + (else + (error "Nieznany rodzaj wyrazenia -- DERIV" exp)))) +
\ No newline at end of file |