User:Spekkio: Difference between revisions
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maclaurin series for different functions sin/cos/sqrt/pow etc... (see my recent post in [[Talk:Nth root]]) |
maclaurin series for different functions sin/cos/sqrt/pow etc... (see my recent post in [[Talk:Nth root]]) |
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<lang lisp> |
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(defun factorial (n) |
(defun factorial (n) |
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(defun powint (a b) |
(defun powint (a b) |
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(if (= b 0) |
(if (= b 0) |
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1 |
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( |
(if (> b 0) |
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(* a (powint a (- b 1))) |
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(* (/ 1 a) (powint a (+ b 1))) |
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) |
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) |
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) |
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(defun binom (alpha n) |
(defun binom (alpha n) |
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(+ (* (binom b n) (powint (- a 1) n)) (power a b (- n 1))))) |
(+ (* (binom b n) (powint (- a 1) n)) (power a b (- n 1))))) |
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(defun powertest(a b n) |
(defun powertest(a b n prev) |
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(let (( power10 (power a b (+ 10 n)) )) |
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(if |
(if |
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(= (* |
(= (* power10 1.0) (* prev 1.0)) |
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power10 |
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(powertest a b (+ 10 n)) |
(powertest a b (+ 10 n) power10) |
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) |
) |
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) |
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) |
) |
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(defun pow (a b |
(defun pow (a b) |
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(if (< a 0) |
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(if (< b 1) |
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0 |
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(powertest a b 1 1) |
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) |
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(if (< a 2) |
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(powertest a b 1 1) |
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0 |
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) |
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) |
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) |
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(defun logS(x n) (if (= n 0) (* 2 x) (+ (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1))) (logS x (- n 1)) ) )) |
(defun logS(x n) (if (= n 0) (* 2 x) (+ (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1))) (logS x (- n 1)) ) )) |
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(defun squaren(x n) (expon (* 1/2 (loge x n)) n)) |
(defun squaren(x n) (expon (* 1/2 (loge x n)) n)) |
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(defun squarentest(a n) |
(defun squarentest(a n prev) |
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(let (( square10 (squaren a (+ 10 n)) )) |
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(if |
(if |
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(= (* |
(= (* square10 1.0) (* prev 1.0)) |
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square10 |
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(squarentest a (+ 10 n)) |
(squarentest a (+ 10 n) square10) |
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) |
) |
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) |
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) |
) |
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(defun sqrtn (a) (squarentest a 1)) |
(defun sqrtn (a) (squarentest a 1 0)) |
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(defun powern(x a n) (expon (* a (loge x n)) n)) |
(defun powern(x a n) (expon (* a (loge x n)) n)) |
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(defun powerntest(a b n) |
(defun powerntest(a b n prev) |
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(let ((n10 (+ 10 n))) |
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(let (( power10 (powern a b n10) )) |
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(if |
(if |
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(= (* |
(= (* power10 1.0) (* prev 1.0)) |
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power10 |
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(powerntest a b |
(powerntest a b n10 power10) |
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) |
) |
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) |
) |
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)) |
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(defun pown (a b) (powerntest a b 1)) |
(defun pown (a b) (powerntest a b 1 0)) |
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(defun sine(x n) |
(defun sine(x n) |
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(defun asinetest(x n) |
(defun asinetest(x n prev) |
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(let (( asine10 (asine x (+ 10 n)) )) |
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(if |
(if |
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(= (* |
(= (* asine10 1.0) (* prev 1.0)) |
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asine10 |
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(asinetest x (+ 10 n)) |
(asinetest x (+ 10 n) asine10) |
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) |
) |
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) |
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) |
) |
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(if (< x 1) |
(if (< x 1) |
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(if (> x -1) |
(if (> x -1) |
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(asinetest x 1) |
(asinetest x 1 0) |
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(/ (pie) -2) |
(/ (pie) -2) |
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) |
) |
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