{"id":4795,"date":"2020-02-29T05:55:03","date_gmt":"2020-02-28T21:55:03","guid":{"rendered":"https:\/\/www.highflybird.com\/blog\/?p=4795"},"modified":"2020-02-29T07:13:49","modified_gmt":"2020-02-28T23:13:49","slug":"%e9%98%bf%e6%96%af%e8%92%82%e8%8a%ac%e6%96%af%e8%92%82%e8%8a%ac","status":"publish","type":"post","link":"https:\/\/www.highflybird.com\/blog\/?p=4795","title":{"rendered":"\u4e00\u5143\u4e8c\u6b21\u3001\u4e09\u6b21\u3001\u56db\u6b21\u65b9\u7a0b\u6c42\u89e3\u548c\u590d\u6570\u7684\u8fd0\u7b97"},"content":{"rendered":"

\u5bf9\u4e00\u5143\u4e09\u6b21\u6216\u8005\u56db\u6b21\u65b9\u7a0b\uff0c\u662f\u6709\u6570\u5b66\u516c\u5f0f\u6c42\u7cbe\u786e\u89e3\u7684\uff0c\u53ef\u4ee5\u4e0d\u7528\u8fed\u4ee3\u6cd5\u3002\u53c2\u8003\u4e86\u7ef4\u57fa\u7684\u4e0a\u7684\u65b9\u6cd5\uff0c\u73b0\u5728\u6211\u8d34\u51fa\u4e00\u5143\u4e8c\u6b21\u3001\u4e09\u6b21\u6216\u8005\u56db\u6b21\u65b9\u7a0b\u7684LISP\u6c42\u89e3\u65b9\u6cd5\u3002\u4f7f\u5f97\u5728\u6c42\u89e3\u6548\u7387\u53ef\u4ee5\u5f97\u5230\u6781\u5927\u63d0\u9ad8\u3002
\n\u6ce8\u660e\uff1a \u56e0\u4e3a\u8fd9\u51e0\u4e2a\u65b9\u7a0b\u7684\u89e3\u6709\u53ef\u80fd\u662f\u590d\u6570\uff0c\u6240\u4ee5\u6211\u5bf9\u6bcf\u4e2a\u89e3\u90fd\u7528\u8868\u7684\u5f62\u5f0f\u6765\u5217\u51fa\u3002
\n\u5982\u679c\u8fd9\u4e2a\u8868\u7684\u7b2c\u4e8c\u9879\u4e3a0\uff0c\u90a3\u4e48\u8fd9\u4e2a\u89e3\u662f\u5b9e\u6570\uff0c\u5426\u5219\u662f\u590d\u6570\u3002
\n\u8b6c\u5982 \uff1a\\({x^4+3x^3+7x^2+2x-5 = 0}\\)<\/p>\n

(Math:Quartic_Equation 1 3 7 2 -5)\n<\/pre>\n
==\u300b((-1.19281 -2.21406) (-1.19281 2.21406) (-1.24789 0) (0.633498 0))<\/p>\n
\u610f\u5473\u7740\u8fd9\u4e2a\u65b9\u7a0b\u6709\u4e24\u4e2a\u5b9e\u6570\u89e3\uff1a-1.24789 , 0.633498
\n\u4e24\u4e2a\u865a\u6570\u89e3\uff1a-1.19281-2.21406 i ,-1.19281+2.21406i
\n\u53e6\u5916\u5728\u672b\u5c3e\u9644\u4e0a\u9a8c\u7b97\u6d4b\u8bd5\u51fd\u6570\u3002<\/p>\n
\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684LISP\u6e90\u7801\uff1a<\/p>\n
 \n;;;=============================================================\n;;;\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u89e3                                     \t\n;;;f(x) = a*x^2+b*x+c = 0                               \t\n;;;Input: the coefficients a, b, c are real numbers     \t\n;;;Output: when a \/= 0,one or Two solutions,all of them like \t\n;;;        this: (x y),means: x + y * i,if it's a real number,  \n;;;        then y = 0.Otherwise ,  return a real number or nil  \n;;;Ref: http:\/\/en.wikipedia.org\/wiki\/Quadratic_equation \t\n;;;=============================================================\n(defun Math:Quadratic_Equation (a b c \/ d e g)\n  (if (zerop a)\n    (if (not (zerop b))\n      (list (list (\/ (- c) (float b)) 0))\n    )\n    (progn\n      (setq a (float a))\n      (if (not (equal a 1 1e-14))\n        (setq b (\/ b a)\n              c (\/ c a)\n        )\n      )\n      (setq d (- (* b b) (* 4 c)))\n      (setq e (* b -0.5))\n      (cond\n        ( (equal d 0 1e-14)\n          (list (list e 0) (list e 0))\n        )\n        ( (> d 0)\n          (setq g (* (sqrt d) -0.5))\n          (list (list (- e g) 0) (list (+ e g) 0))\n        )\n        ( (< d 0)\n          (setq g (* (sqrt (- d)) -0.5))\n          (list (list e (- g)) (list e g))\n        )\n      )\n    )\n  )\n)\n<\/pre>\n
\u89e3\u4e00\u5143\u4e09\u6b21\u65b9\u7a0b\u7684LISP\u6e90\u7801\uff1a<\/p>\n
;;;=============================================================\n;;;\u4e00\u5143\u4e09\u6b21\u65b9\u7a0b\u7684\u89e3                                     \t\n;;;f(x) = a*x^3+b*x^2+c*x+d = 0                         \t\n;;;Input: the coefficients a, b, c, d are real numbers  \t\n;;;Output: when a \/= 0,Three solutions,all of them like this: \t\n;;;        (x y),means: x+y*i,if it's a real number,then y = 0; \n;;;        otherwise goto \"Math:Quadratic_Equation\"     \t\n;;;Ref: http:\/\/en.wikipedia.org\/wiki\/Cubic_function     \t\n;;;=============================================================\n(defun Math:Cubic_Equation (a b c d \/ e f g h u w x y)\n  (cond\n    ( (zerop a)\n      (Math:Quadratic_Equation b c d)\n    )\n    ( (zerop d)\n      (cons '(0 0) (Math:Quadratic_Equation a b c))\n    )\n    (t\n      (setq b (\/ b a 3.0))\n      (setq c (\/ c a 6.0))\n      (setq d (\/ d a 2.0))\n     \n      (setq e (- (* b (- (+ c c c) (* b b))) d))        \t;Alpha\n      (setq f (- (* b b) c c))                          \t;Beta\n      (setq g (- (* e e) (* f f f)))                    \t;Delta,The nature of the roots\n      (cond\n        ( (equal g 0 1e-14)\n          (setq u (MATH:CubeRoot e))\n          (list (list (- (+ u u) b) 0.0)\n                (list (- (+ b u)) 0.0)\n                (list (- (+ b u)) 0.0)\n          )\n        )\n        ( (> g 0)\n          (setq h (sqrt g))\n          (setq u (MATH:CubeRoot (+ e h)))\n          (setq w (MATH:CubeRoot (- e h)))\n          (setq x (- (+ b (* (+ u w) 0.5))))\n          (setq y (* (sqrt 3) (- u w) 0.5))\n          (list (list (+ u w (- b)) 0)\n                (list x y)\n                (list x (- y))\n          )\n        )\n        ( (< g 0)\n          (setq x (\/ e f (sqrt f)))\n          (setq y (sqrt (abs (- 1 (* x x)))))\n\n          (setq u (\/ (atan y x) 3))\n          (setq w (\/ (+ pi pi) 3))\n          (setq h (* 2 (sqrt f)))\n          (list (list (- (* (cos u) h) b) 0)\n                (list (- (* (cos (+ u w)) h) b) 0)\n                (list (- (* (cos (- u w)) h) b) 0)\n          )\n        )\n      )\n    )\n  )\n)\n<\/pre>\n
\u89e3\u4e00\u5143\u56db\u6b21\u65b9\u7a0b\u7684\u89e3\uff1a<\/p>\n
 \n;;;=============================================================\n;;;\u4e00\u5143\u56db\u6b21\u65b9\u7a0b\u7684\u89e3                                     \t\n;;;f(x) = a*x^4+b*x^3+c*x^2+d*x+e= 0                    \t\n;;;Input: the coefficients a,b,c,d,e are real numbers.  \t\n;;;Output: when a \/= 0,Three solutions,all of them like this: \t\n;;;        (x y),means: x+y*i,if it's a real number,then y = 0, \n;;;        otherwise goto \"Math:Quadratic_Equation\".            \n;;;Ref: http:\/\/en.wikipedia.org\/wiki\/Quartic_function   \t\n;;;=============================================================\n(defun Math:Quartic_Equation (a b c d e \/ B2 B3 B4 EPS F G H P Q R V W X Y Z S)\n  (setq eps 1e-8)\n  (cond\n    ( (equal a 0 eps)\n      (Math:Cubic_Equation b c d e)\n    )\n    ( (equal e 0 eps)\n      (cons '(0 0) (Math:Cubic_Equation a b c d))\n    )\n    ( (and (equal b 0 eps) (equal d 0 eps))\n      (foreach x (Math:Quadratic_Equation a c e)\n        (foreach y (Math:CSqrt x)\n          (setq s (cons y s))\n        )\n      )\n    )  \n    ( (setq a (float a))\n      (setq b (\/ b a))\n      (setq c (\/ c a))\n      (setq d (\/ d a))\n      (setq e (\/ e a))\n      (setq b2 (* b b))\n      (setq b3 (* b2 b))\n      (setq b4 (* b3 b))\n     \n      (setq f (+ (* b2 -0.375) c))                      \t;alpha\n      (setq g (+ (* b3 0.125) (* b c -0.5) d))          \t;beta\n      (setq h (+ (* -0.01171875 b4) (* 0.0625 c b2) (* -0.25 b d) e))\n\n      (if (equal g 0 eps)\n        (progn \n          (setq x (* b -0.25))\n          (mapcar\n            (function (lambda (e) (list (+ (car e) x) (cadr e))))\n            (Math:Quartic_Equation 1 0 f 0 h)           \t;Recursion \n          )\n        )\n        (progn \n          (setq p (- (* f f 2) h))\n          (setq q (- (* f f f 0.5) (* f h 0.5) (* g g 0.125)))\n          (setq r (Math:Cubic_Equation 1 (* 2.5 f) p q))\n          (while (not (equal (cadar r) 0 eps))\n            (setq r (cdr r))\n          )\n          (setq r (caar r))\n          (setq w (sqrt (abs (+ f r r))))\n          (foreach i (list + -)\n            (foreach j (list + -)\n              (setq x (i (* b -0.25) (* w 0.5)))\n              (setq y (- (+ f f f r r (i (\/ g 0.5 w)))))\n              (if (< y 0)\n                (setq z (list x (j (* (sqrt (- y)) 0.5))))\n                (setq z (list (+ x (j (* (sqrt y) 0.5))) 0)) \n              )\n              (setq S (cons z S))\n            )\n          )\n        )\n      )\n    )\n  )\n)\n<\/pre>\n
\u590d\u6570\u76f8\u5173\u4ee3\u7801\uff1a<\/p>\n
;;;=============================================================\n;;;\u7acb\u65b9\u6839(\u4e3a\u89e3\u4e09\u6b21\u548c\u56db\u6b21\u65b9\u7a0b\u7f16\u5199\uff0c\u56e0expt\u51fd\u6570\u7b2c\u4e00\u4e2a\u53c2\u6570\u4e0d\u80fd\u4e3a\u8d1f) \n;;;\u8f93\u5165\uff1ax \u5b9e\u6570                                                 \n;;;\u8f93\u51fa\uff1ax \u7684\u7acb\u65b9\u6839                                             \n;;;=============================================================\n(defun MATH:CubeRoot (x)\n  (if (< x 0)\n    (- (expt (- x) 0.33333333333333333333333))\n    (expt x 0.33333333333333333333333)\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u52a0\u590d\u6570                                                   \n;;;\u8f93\u5165\uff1aZ1--\u590d\u6570\uff0cZ2--\u590d\u6570                                     \n;;;\u8f93\u51fa\uff1a\u590d\u6570\u8ddf\u5b9e\u6570\u76f8\u52a0\u7684\u7ed3\u679c                                   \n;;;=============================================================\n(defun Math:C+C (z1 z2)\n  (mapcar '+ z1 z2)\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u51cf\u590d\u6570                                                   \n;;;\u8f93\u5165\uff1aZ1--\u590d\u6570\uff0cZ2--\u590d\u6570                                     \n;;;\u8f93\u51fa\uff1a\u590d\u6570\u8ddf\u5b9e\u6570\u76f8\u51cf\u7684\u7ed3\u679c                                   \n;;;=============================================================\n(defun math:C-C (z1 z2)\n  (mapcar '- Z1 Z2)\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u4e58\u590d\u6570                                                   \n;;;\u8f93\u5165\uff1aZ1--\u590d\u6570\uff0cZ2--\u590d\u6570                             \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u8ddf\u5b9e\u6570\u76f8\u4e58\u7684\u7ed3\u679c                           \t\n;;;=============================================================\n(defun Math:C*C (Z1 Z2)\n  (list\n    (- (* (car Z1) (car z2)) (* (cadr z1) (cadr z2)))\n    (+ (* (car Z1) (cadr Z2)) (* (cadr z1) (car Z2)))\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u9664\u4ee5\u590d\u6570                                         \t\n;;;\u8f93\u5165\uff1aZ1--\u590d\u6570\uff0cZ2--\u590d\u6570                             \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u8ddf\u5b9e\u6570\u76f8\u9664\u7684\u7ed3\u679c                           \t\n;;;=============================================================\n(defun Math:C\/C (Z1 Z2 \/ a b c d N)\n  (setq a (car  z1))\n  (setq b (cadr z1))\n  (setq c (car  z2))\n  (setq d (cadr z2))\n  (setq N (float (+ (* c c) (* d d))))\n  (if (not (zerop N))\n    (list\n      (\/ (+ (* a c) (* b d)) N)\n      (\/ (- (* b c) (* a d)) N)\n    )\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u52a0\u5b9e\u6570                                           \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570\uff0cR --\u5b9e\u6570                             \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u8ddf\u5b9e\u6570\u76f8\u52a0\u7684\u7ed3\u679c                           \t\n;;;=============================================================\n(defun Math:C+R (Z R)\n  (list (+ (car z) R) (cadr z))\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u51cf\u5b9e\u6570                                           \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570\uff0cR --\u5b9e\u6570                             \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u8ddf\u5b9e\u6570\u76f8\u51cf\u7684\u7ed3\u679c                           \t\n;;;=============================================================\n(defun Math:C-R (Z R)\n  (list (- (car z) R) (cadr z))\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u4e58\u5b9e\u6570                                           \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570\uff0cR --\u5b9e\u6570                             \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u8ddf\u5b9e\u6570\u76f8\u4e58\u7684\u7ed3\u679c                           \t\n;;;=============================================================\n(defun Math:C*R (Z R)\n  (list (* (car z) R) (* (cadr z) R))\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u9664\u4ee5\u5b9e\u6570                                         \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570\uff0cR --\u5b9e\u6570                             \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u8ddf\u5b9e\u6570\u76f8\u9664\u7684\u7ed3\u679c                           \t\n;;;=============================================================\n(defun Math:C\/R (Z R)\n  (if (not (zerop R))\n    (list (\/ (car z) R) (\/ (cadr z) R))\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u6a21                                             \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570                                       \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u7684\u6a21\uff0c\u5373\u590d\u6570\u4ee3\u8868\u7684\u77e2\u91cf\u957f\u5ea6                 \t\n;;;=============================================================\n(defun MATH:CNormal (Z)\n  (distance '(0 0) Z)\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u5e73\u65b9\u6839                                         \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570                                       \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u7684\u5e73\u65b9\u6839\uff0c\u4ee5\u590d\u6570\u5f62\u5f0f\u8868\u8fbe\uff0c\u6709\u4e24\u4e2a\u89e3         \t\n;;;=============================================================\n(defun Math:CSqrt (Z \/ x y a r)\n  (setq x (car z))\n  (setq y (cadr z))\n  (if (equal y 0 1e-14)\n    (if (> x 0)\n      (list (list (setq x (sqrt x)) 0) (list (- x) 0))\n      (list (list 0 (setq y (sqrt (- x)))) (list 0 (- y)))\n    )\n    (progn\n      (setq a (* (atan y x) 0.5))\n      (setq r (sqrt (distance '(0 0) Z)))\n      (setq x (* r (cos a)))\n      (setq y (* r (sin a)))\n      (list (list x y) (list (- x) (- y)))\n    )\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u65b9\u6839                                           \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570, n --\u6b63\u6574\u6570                           \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570\u7684n\u6b21\u65b9\u6839\uff0c\u4ee5\u590d\u6570\u5f62\u5f0f\u8868\u8fbe\uff0c\u6709n\u4e2a\u89e3\u3002       \t\n;;;=============================================================\n(defun MATH:CRoot (Z n \/ r a b i s 2Pi)\n  (if (and (= (type n) 'INT) (> n 0))\n    (progn\n      (setq r (expt (distance '(0 0) z) (\/ 1. n)))\n      (setq a (atan (cadr z) (car z)))\n      (setq i 0)\n      (setq 2Pi (+ pi pi))\n      (repeat n\n        (setq b (\/ (+ a (* i 2Pi)) n))\n        (setq s (cons (list (* r (cos b)) (* r (sin b))) s))\n        (setq i (1+ i))\n      )\n      (reverse s)\n    )\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u5b9e\u5e42\u6307\u6570                                       \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570, x -- \u5b9e\u6570                            \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570Z \u7684x\u6b21\u5e42\uff0c\u4ee5\u590d\u6570\u5f62\u5f0f\u8868\u8fbe\u3002                \t\n;;;=============================================================\n(defun MATH:CRPower (Z x \/ a r)\n  (setq a (atan (cadr Z) (car Z)))\n  (setq r (expt (distance '(0 0) Z) x))\n  (list (* r (cos (* a x))) (* r (sin (* a x))))\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u590d\u5e42\u6307\u6570                                       \t\n;;;\u8f93\u5165\uff1aZ1 --\u590d\u6570, Z2 -- \u590d\u6570                          \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570Z1\u7684Z2\u6b21\u5e42\uff0c\u4ee5\u590d\u6570\u5f62\u5f0f\u8868\u8fbe\u3002               \t\n;;;=============================================================\n(defun MATH:CZPower (Z1 Z2 \/ a r x y k)\n  (if (> (setq r (distance '(0 0) Z1)) 1e-20)\n    (progn \n      (setq a (atan (cadr Z1) (car Z1)))\n      (setq x (car z2))\n      (setq y (cadr z2))\n      (setq k (log r))\n      (setq r (exp (- (* k x) (* y a))))\n      (setq a (+ (* k y) (* x a)))\n      (list (* r (cos a)) (* r (sin a)))\n    )\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u81ea\u7136\u5bf9\u6570                                        \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570                                       \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570Z \u7684\u81ea\u7136\u5bf9\u6570\uff0c\u4ee5\u590d\u6570\u5f62\u5f0f\u8868\u8fbe\u3002             \t\n;;;=============================================================\n(defun MATH:CExp (Z \/ r)\n  (if (> (setq r (distance '(0 0) Z)) 1e-20)\n    (list (log r) (atan (cadr Z) (car Z)))\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u4f59\u5f26                                           \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570                                          \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570Z \u7684\u4f59\u5f26\uff0c\u4ee5\u590d\u6570\u5f62\u5f0f\u8868\u8fbe\u3002                 \t\n;;;=============================================================\n(defun MATH:CCOS (Z \/ x y c s u v)\n  (setq x (car z))\n  (setq y (cadr z))\n  (if (equal y 0 1e-20)\n    (list (cos x) 0)\n    (progn\n      (setq c (* 0.5 (cos x)))\n      (setq s (* 0.5 (sin x)))\n      (setq u (exp y))\n      (setq v (exp (- y)))\n      (list (* c (+ v u)) (* s (- v u)))\n    )\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u6b63\u5f26                                          \t\t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570                                       \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570Z \u7684\u6b63\u5f26\uff0c\u4ee5\u590d\u6570\u5f62\u5f0f\u8868\u8fbe\u3002                 \t\n;;;=============================================================\n(defun MATH:CSIN (Z \/ x y c s u v)\n  (setq x (car z))\n  (setq y (cadr z))\n  (if (equal y 0 1e-20)\n    (list (sin x) 0)\n    (progn\n      (setq s (* 0.5 (sin x)))\n      (setq c (* 0.5 (cos x)))\n      (setq u (exp (- y)))\n      (setq v (exp y))\n      (list (* s (+ v u)) (* c (- v u)))\n    )\n  )\n)\n\n;;;=============================================================\n;;;\u590d\u6570\u7684\u6b63\u5207                                           \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570                                       \t\n;;;\u8f93\u51fa\uff1a\u590d\u6570Z \u7684\u6b63\u5207\uff0c\u4ee5\u590d\u6570\u5f62\u5f0f\u8868\u8fbe\u3002                 \t\n;;;=============================================================\n(defun MATH:CTAN (Z \/ x y c s u v)\n  (MATH:C\/C (MATH:CSIN Z) (MATH:CCOS Z))\n)\n\n;;;=============================================================\n;;;\u5b9e\u7cfb\u6570\u7684\u590d\u6570\u591a\u9879\u5f0f\u8fd0\u7b97                               \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570, RealNumbers --\u5b9e\u7cfb\u6570\u5217\u8868             \t\n;;;\u8f93\u51fa\uff1a\u6839\u636e\u5b9e\u7cfb\u6570\u591a\u9879\u5f0f\u590d\u6570\u65b9\u7a0b\u503c\uff0c\u7528\u590d\u6570\u8868\u793a\u3002       \t\n;;;=============================================================\n(defun MATH:CReal_Polynomial (Z RealNumbers \/ f)\n  (cond\n    ( (cdr RealNumbers) \n      (setq f (MATH:C*R Z (car RealNumbers)))\n      (repeat (- (length RealNumbers) 2)\n        (setq RealNumbers (cdr RealNumbers))\n        (setq f (MATH:C+R f (car RealNumbers)))\n        (setq f (MATH:C*C f Z))\n      )\n      (setq f (MATH:C+R f (cadr RealNumbers)))\n    )\n    ( (car RealNumbers) (list (car RealNumbers) 0))\n  )\n)\n\n;;;=============================================================\n;;;\u865a\u7cfb\u6570\u7684\u590d\u6570\u591a\u9879\u5f0f\u8fd0\u7b97                               \t\n;;;\u8f93\u5165\uff1aZ --\u590d\u6570, ImaginaryNumbers--\u590d\u7cfb\u6570\u5217\u8868         \t\n;;;\u8f93\u51fa\uff1a\u6839\u636e\u590d\u7cfb\u6570\u591a\u9879\u5f0f\u590d\u6570\u65b9\u7a0b\u503c\uff0c\u7528\u590d\u6570\u8868\u793a\u3002       \t\n;;;=============================================================\n(defun MATH:CImaginary_Polynomial (Z ImaginaryNumbers \/ f)\n  (if (setq f (car ImaginaryNumbers))\n    (progn\n      (repeat (1- (length ImaginaryNumbers))\n        (setq ImaginaryNumbers (cdr ImaginaryNumbers))\n        (setq f (MATH:C*C f Z)) \n        (setq f (MATH:C+C f (car ImaginaryNumbers)))\n      )\n      f\n    )\n  )\n)\n<\/pre>\n
\u6d4b\u8bd5\u4ee3\u7801\uff1a<\/p>\n
;;;=============================================================\n;;;\u4ee5\u4e0b\u7a0b\u5e8f\u4e3a\u6d4b\u8bd5\u7528:                                    \t\n;;;Test for \"Math:Quartic_Equation\"                     \t\n;;;If the difference between the Coefficients is big,it will get\n;;;some float point error.                   \t\t\t\n;;;=============================================================\n(defun C:t4 (\/ a b c d e S z z1 z2 z3 z4)\n  (initget 1)\n  (setq a (getreal \"\\nCoefficient a:\"))\n  (initget 1)\n  (setq b (getreal \"\\nCoefficient b:\"))\n  (initget 1)\n  (setq c (getreal \"\\nCoefficient c:\"))\n  (initget 1)\n  (setq d (getreal \"\\nCoefficient d:\"))\n  (initget 1)\n  (setq e (getreal \"\\nCoefficient e:\"))\n  ;(MISC:test 1000 '((Math:Quartic_Equation a b c d e)))\n  (setq S (Math:Quartic_Equation a b c d e))            \t;get the solutions\n  (foreach z S\n    (princ \"\\n\")\n    (princ (mapcar '(lambda (x) (rtos x 2 20)) z))      \t;print them.\n  )\n  (foreach z S                                          \t;Check every solution\n    (setq f (MATH:CReal_Polynomial z (list a b c d e)))\n    (if (not (equal f '(0 0) 1e-6))                     \t;if f(z) \/= 0.0,maybe it's caused by floating point operation;\n      (alert\n        (strcat\n          \"Maybe it's a Wrong solution: f(\"\n          (vl-princ-to-string z)\n          \") = \"\n          (VL-PRINC-TO-STRING f)\n        )\n      )\n    )\n  )\n  (princ)\n)\n\n(defun C:t3 (\/ a b c d e S z z1 z2 z3 z4)\n  (initget 1)\n  (setq a (getreal \"\\nCoefficient a:\"))\n  (initget 1)\n  (setq b (getreal \"\\nCoefficient b:\"))\n  (initget 1)\n  (setq c (getreal \"\\nCoefficient c:\"))\n  (initget 1)\n  (setq d (getreal \"\\nCoefficient d:\"))\n  (UTI:BENCH\n    20000 \n    (list\n      (list 'Math:Cubic_Equation a b c d)\n      (list 'Math:Cubic_Equation1 a b c d)\n    )\n  )\n  (foreach n '(Math:Cubic_Equation Math:Cubic_Equation1)\n    (setq S (apply n (list a b c d)))            \t\t;get the solutions\n    (foreach z S\n      (princ \"\\n\")\n      (princ (mapcar '(lambda (x) (rtos x 2 20)) z))      \t;print them.\n    )\n    (foreach z S                                          \t;Check every solution\n      (setq f (MATH:CReal_Polynomial z (list a b c d)))\n      (if (not (equal f '(0 0) 1e-6))                     \t;if f(z) \/= 0.0,maybe it's caused by floating point operation;\n        (alert\n          (strcat\n\t    \"Use \"\n\t    (VL-PRINC-TO-STRING n)\n            \",Maybe it's a Wrong solution: f(\"\n            (vl-princ-to-string z)\n            \") = \"\n            (VL-PRINC-TO-STRING f)\n          )\n        )\n      )\n    )\n  )\n  (princ)\n)\n(princ \"\\nThe command is : test.\")\n(vl-load-com)\n(princ)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
\u5bf9\u4e00\u5143\u4e09\u6b21\u6216\u8005\u56db\u6b21\u65b9\u7a0b\uff0c\u662f\u6709\u6570\u5b66\u516c\u5f0f\u6c42\u7cbe\u786e\u89e3\u7684\uff0c\u53ef\u4ee5\u4e0d\u7528\u8fed\u4ee3\u6cd5\u3002\u53c2\u8003\u4e86\u7ef4\u57fa\u7684\u4e0a\u7684\u65b9\u6cd5\uff0c\u73b0\u5728\u6211\u8d34\u51fa\u4e00\u5143\u4e8c\u6b21\u3001\u4e09\u6b21<\/p>\n
Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4795","post","type-post","status-publish","format-standard","hentry","category-programming"],"_links":{"self":[{"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4795","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4795"}],"version-history":[{"count":0,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/4795\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4795"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4795"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.highflybird.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}