Deprecated: Creation of dynamic property wpdb::$categories is deprecated in /usr/home/bugyo/public_html/b-log/wp-includes/wp-db.php on line 668

Deprecated: Creation of dynamic property wpdb::$post2cat is deprecated in /usr/home/bugyo/public_html/b-log/wp-includes/wp-db.php on line 668

Deprecated: Creation of dynamic property wpdb::$link2cat is deprecated in /usr/home/bugyo/public_html/b-log/wp-includes/wp-db.php on line 668

Deprecated: Return type of WP_Theme::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-theme.php on line 554

Deprecated: Return type of WP_Theme::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-theme.php on line 595

Deprecated: Return type of WP_Theme::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-theme.php on line 535

Deprecated: Return type of WP_Theme::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-theme.php on line 544

Deprecated: Using ${var} in strings is deprecated, use {$var} instead in /usr/home/bugyo/public_html/b-log/wp-includes/comment-template.php on line 1739

Deprecated: Return type of WP_REST_Request::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/rest-api/class-wp-rest-request.php on line 960

Deprecated: Return type of WP_REST_Request::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/rest-api/class-wp-rest-request.php on line 980

Deprecated: Return type of WP_REST_Request::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/rest-api/class-wp-rest-request.php on line 992

Deprecated: Return type of WP_REST_Request::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/rest-api/class-wp-rest-request.php on line 1003

Deprecated: Return type of WP_Block_List::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 151

Deprecated: Return type of WP_Block_List::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 175

Deprecated: Return type of WP_Block_List::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 164

Deprecated: Return type of WP_Block_List::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 186

Deprecated: Return type of WP_Block_List::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 138

Deprecated: Return type of WP_Block_List::offsetExists($index) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 75

Deprecated: Return type of WP_Block_List::offsetGet($index) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 89

Deprecated: Return type of WP_Block_List::offsetSet($index, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 110

Deprecated: Return type of WP_Block_List::offsetUnset($index) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 127

Deprecated: Return type of WP_Block_List::count() should either be compatible with Countable::count(): int, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-block-list.php on line 199

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /usr/home/bugyo/public_html/b-log/wp-includes/class-wp-term.php on line 198
[数式処理][Scheme] 微分する – B-LOG
B-LOG

[数式処理][Scheme] 微分する

複雑な微分をするときは計算機に任せた方が良いように思う。

Scheme で微分するには次のようにする。

(define (deriv exp var)
  (cond ((eq? exp var) 1)
	((not (pair? exp)) 0)
	((eq? (car exp) '-)
	 `(- ,(deriv (cadr exp) var)))
	((eq? (car exp) '+)
	 `(+ ,(deriv (cadr exp) var) ,(deriv (caddr exp) var)))
	((eq? (car exp) '*)
	 `(+ (* ,(deriv (cadr exp) var)
		,(caddr exp))
	     (* ,(cadr exp)
		,(deriv (caddr exp) var))))
	((eq? (car exp) 'expt)
	 (let ((g (cadr exp))
	       (n (caddr exp)))
	   `(* (* ,n (expt ,g ,(- n 1))) ,(deriv g var))))
	((eq? (car exp) 'sin)
	 `(* (cos ,(cadr exp)) ,(deriv (cadr exp) var)))
	((eq? (car exp) 'cos)
	 `(* (- (sin ,(cadr exp))) ,(deriv (cadr exp) var)))
        ((eq? (car exp) 'tan)
         `(* (+ 1 (expt ,exp 2)) ,(deriv (cadr exp) var)))
	(else (error "not yet."))))
> (deriv '(expt (* (sin x) (cos x)) 1/2)) 'x)
=> (* (* 1/2
         (expt (* (sin x) (cos x)) -1/2))
      (+ (* (* (cos x) 1)
	    (cos x))
         (* (sin x)
	    (* (- (sin x)) 1))))

`-‘ 演算子は単項演算子としてのみ使える。