Дифференцирование

Носов Иван/proizvodnaya.rkt

@@ -0,0 +1,113 @@
+#lang racket
+(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)))
+        
+        ((dif? exp)
+         (make-dif (deriv (addend exp) var)
+                   (deriv (augend exp) var)))
+        
+        ((product? exp)
+         (make-sum
+          (make-product (multiplier exp)
+                        (deriv (multipicand exp) var))
+          (make-product (deriv (multiplier exp) var)
+                        (multipicand exp))))
+
+        ((exponentiation? exp)
+         (make-product
+          (make-product (exponent exp)
+                        (make-exponentiation (base exp) (- (exponent exp) 1)))
+          (deriv (base exp)
+                 var)))
+        
+        ((sinus? exp)
+         (make-product
+          (deriv (base exp)
+                 var)(make-cos (base exp))))
+        
+        ((cosinus? exp)
+         (make-product
+          (deriv (base exp)var)(make-sin (base exp))))
+
+        ((ex? exp)
+         (make-product
+          (deriv (base exp)
+                 var)(make-exp (base exp))))
+         
+
+        (else
+         error "unknow expression type -- DERIV" exp)))
+
+(define (ex? x)
+  (and (pair? x) (eq? 'exp (car x))))
+
+(define (make-exp a0)(list 'exp a0))
+
+(define (sinus? x)
+  (and (pair? x) (eq? 'sin (car x) )))
+
+(define (make-cos a0)(list 'cos a0))
+
+(define (cosinus? x)
+  (and (pair? x) (eq? 'cos (car x) )))
+
+(define (make-sin a0)(list '-sin a0))
+
+(define (=number? exp num)
+  (and (number? exp) (= exp num)))
+
+(define (multipicand p) (caddr p))
+
+(define (variable? x) (symbol? x))
+
+(define (same-variable? v0 v1)
+  (and (variable? v0) (variable? v1) (eq? v0 v1)))
+
+(define (make-sum a0 a1)
+  (cond ((and (number? a0) (number? a1)) (+ a0 a1))
+        (else (list '+ a0 a1))))
+
+(define (sum? x)
+  (and (pair? x) (eq? (car x) '+)))
+
+(define (dif? x)
+  (and (pair? x) (eq? (car x) '-)))
+
+(define (make-dif a0 a1)
+  (cond ((and (number? a0) (number? a1)) (- a0 a1))
+        (else (list '- a0 a1))))
+
+(define (addend s) (cadr s))
+
+(define (augend s) (caddr s))
+
+(define (make-product m0 m1)
+  (cond ((or (=number? m0 0) (=number? m1 0)) 0)
+        ((=number? m0 1) m1)
+        ((=number? m1 1) m0)
+        ((and (number? m0) (number? m1)) (* m0 m1))
+        (else (list '* m0 m1))))
+
+(define (product? x)
+  (and (pair? x) (eq? (car x) '*)))
+
+(define (multiplier p) (cadr p))
+
+(define (make-exponentiation x n)
+  (cond ((= n 0) 1)
+        ((= n 1) x)
+        (else (list '** x n))))
+
+(define (exponentiation? x)
+  (and (pair? x) (eq? (car x) '**)))
+
+(define (base s) (cadr s))
+
+(define (exponent s) (caddr s))
+