Дифференцирование

Носов Иван/README.md

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+# Дифференцирование 
+## Ссылка на видеоразбор
+https://youtu.be/Kh0shn9UW6Y
+## Код из книги
+    #let rec differentiate x tm = match tm with
+    Var y -> if y = x then Const "1" else Const "0"
+    | Const c -> Const "0"
+    | Fn("-",[t]) -> Fn("-",[differentiate x t])
+    | Fn("+",[t1;t2]) -> Fn("+",[differentiate x t1;
+    differentiate x t2])
+    | Fn("-",[t1;t2]) -> Fn("-",[differentiate x t1;
+    differentiate x t2])
+    |    Fn("*",[t1;t2]) ->
+    Fn("+",[Fn("*",[differentiate x t1; t2]);
+    Fn("*",[t1; differentiate x t2])])
+    | Fn("inv",[t]) -> chain x t
+    (Fn("-",[Fn("inv",[Fn("^",[t;Const "2"])])]))
+    | Fn("^",[t;n]) -> chain x t
+    (Fn("*",[n; Fn("^",[t; Fn("-",[n; Const "1"])])]))
+    | Fn("exp",[t]) -> chain x t tm
+    | Fn("ln",[t]) -> chain x t (Fn("inv",[t]))
+    | Fn("sin",[t]) -> chain x t (Fn("cos",[t]))
+    | Fn("cos",[t]) -> chain x t
+    (Fn("-",[Fn("sin",[t])]))
+    | Fn("/",[t1;t2]) -> differentiate x
+    (Fn("*",[t1; Fn("inv",[t2])]))
+    | Fn("tan",[t]) -> differentiate x
+    (Fn("/",[Fn("sin",[t]); Fn("cos",[t])]))
+    and chain x t u = Fn("*",[differentiate x t; u]);;

Носов Иван/proizvodnaya.rkt

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+#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))
+