[bpt/emacs.git] / lisp / calc / calc-cplx.el

;;; calc-cplx.el --- Complex number functions for Calc

;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
;;   2005, 2006, 2007, 2008 Free Software Foundation, Inc.

;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>

;; This file is part of GNU Emacs.

;; GNU Emacs is free software; you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation; either version 3, or (at your option)
;; any later version.

;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
;; GNU General Public License for more details.

;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs; see the file COPYING.  If not, write to the
;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
;; Boston, MA 02110-1301, USA.

;;; Commentary:

;;; Code:

;; This file is autoloaded from calc-ext.el.

(require 'calc-ext)
(require 'calc-macs)

(defun calc-argument (arg)
  (interactive "P")
  (calc-slow-wrapper
   (calc-unary-op "arg" 'calcFunc-arg arg)))

(defun calc-re (arg)
  (interactive "P")
  (calc-slow-wrapper
   (calc-unary-op "re" 'calcFunc-re arg)))

(defun calc-im (arg)
  (interactive "P")
  (calc-slow-wrapper
   (calc-unary-op "im" 'calcFunc-im arg)))


(defun calc-polar ()
  (interactive)
  (calc-slow-wrapper
   (let ((arg (calc-top-n 1)))
     (if (or (calc-is-inverse)
	     (eq (car-safe arg) 'polar))
	 (calc-enter-result 1 "p-r" (list 'calcFunc-rect arg))
       (calc-enter-result 1 "r-p" (list 'calcFunc-polar arg))))))


(defun calc-complex-notation ()
  (interactive)
  (calc-wrapper
   (calc-change-mode 'calc-complex-format nil t)
   (message "Displaying complex numbers in (X,Y) format")))

(defun calc-i-notation ()
  (interactive)
  (calc-wrapper
   (calc-change-mode 'calc-complex-format 'i t)
   (message "Displaying complex numbers in X+Yi format")))

(defun calc-j-notation ()
  (interactive)
  (calc-wrapper
   (calc-change-mode 'calc-complex-format 'j t)
   (message "Displaying complex numbers in X+Yj format")))


(defun calc-polar-mode (n)
  (interactive "P")
  (calc-wrapper
   (if (if n
	   (> (prefix-numeric-value n) 0)
	 (eq calc-complex-mode 'cplx))
       (progn
	 (calc-change-mode 'calc-complex-mode 'polar)
	 (message "Preferred complex form is polar"))
     (calc-change-mode 'calc-complex-mode 'cplx)
     (message "Preferred complex form is rectangular"))))


;;;; Complex numbers.

(defun math-normalize-polar (a)
  (let ((r (math-normalize (nth 1 a)))
	(th (math-normalize (nth 2 a))))
    (cond ((math-zerop r)
	   '(polar 0 0))
	  ((or (math-zerop th))
	   r)
	  ((and (not (eq calc-angle-mode 'rad))
		(or (equal th '(float 18 1))
		    (equal th 180)))
	   (math-neg r))
	  ((math-negp r)
	   (math-neg (list 'polar (math-neg r) th)))
	  (t
	   (list 'polar r th)))))


;;; Coerce A to be complex (rectangular form).  [c N]
(defun math-complex (a)
  (cond ((eq (car-safe a) 'cplx) a)
	((eq (car-safe a) 'polar)
	 (if (math-zerop (nth 1 a))
	     (nth 1 a)
	   (let ((sc (calcFunc-sincos (nth 2 a))))
	     (list 'cplx
		   (math-mul (nth 1 a) (nth 1 sc))
		   (math-mul (nth 1 a) (nth 2 sc))))))
	(t (list 'cplx a 0))))

;;; Coerce A to be complex (polar form).  [c N]
(defun math-polar (a)
  (cond ((eq (car-safe a) 'polar) a)
	((math-zerop a) '(polar 0 0))
	(t
	 (list 'polar
	       (math-abs a)
	       (calcFunc-arg a)))))

;;; Multiply A by the imaginary constant i.  [N N] [Public]
(defun math-imaginary (a)
  (if (and (or (Math-objvecp a) (math-infinitep a))
	   (not calc-symbolic-mode))
      (math-mul a
		(if (or (eq (car-safe a) 'polar)
			(and (not (eq (car-safe a) 'cplx))
			     (eq calc-complex-mode 'polar)))
		    (list 'polar 1 (math-quarter-circle nil))
		  '(cplx 0 1)))
    (math-mul a '(var i var-i))))


(defun math-want-polar (a b)
  (cond ((eq (car-safe a) 'polar)
	 (if (eq (car-safe b) 'cplx)
	     (eq calc-complex-mode 'polar)
	   t))
	((eq (car-safe a) 'cplx)
	 (if (eq (car-safe b) 'polar)
	     (eq calc-complex-mode 'polar)
	   nil))
	((eq (car-safe b) 'polar)
	 t)
	((eq (car-safe b) 'cplx)
	 nil)
	(t (eq calc-complex-mode 'polar))))

;;; Force A to be in the (-pi,pi] or (-180,180] range.
(defun math-fix-circular (a &optional dir)   ; [R R]
  (cond ((eq (car-safe a) 'hms)
	 (cond ((and (Math-lessp 180 (nth 1 a)) (not (eq dir 1)))
		(math-fix-circular (math-add a '(float -36 1)) -1))
	       ((or (Math-lessp -180 (nth 1 a)) (eq dir -1))
		a)
	       (t
		(math-fix-circular (math-add a '(float 36 1)) 1))))
	((eq calc-angle-mode 'rad)
	 (cond ((and (Math-lessp (math-pi) a) (not (eq dir 1)))
		(math-fix-circular (math-sub a (math-two-pi)) -1))
	       ((or (Math-lessp (math-neg (math-pi)) a) (eq dir -1))
		a)
	       (t
		(math-fix-circular (math-add a (math-two-pi)) 1))))
	(t
	 (cond ((and (Math-lessp '(float 18 1) a) (not (eq dir 1)))
		(math-fix-circular (math-add a '(float -36 1)) -1))
	       ((or (Math-lessp '(float -18 1) a) (eq dir -1))
		a)
	       (t
		(math-fix-circular (math-add a '(float 36 1)) 1))))))


;;;; Complex numbers.

(defun calcFunc-polar (a)   ; [C N] [Public]
  (cond ((Math-vectorp a)
	 (math-map-vec 'calcFunc-polar a))
	((Math-realp a) a)
	((Math-numberp a)
	 (math-normalize (math-polar a)))
	(t (list 'calcFunc-polar a))))

(defun calcFunc-rect (a)   ; [N N] [Public]
  (cond ((Math-vectorp a)
	 (math-map-vec 'calcFunc-rect a))
	((Math-realp a) a)
	((Math-numberp a)
	 (math-normalize (math-complex a)))
	(t (list 'calcFunc-rect a))))

;;; Compute the complex conjugate of A.  [O O] [Public]
(defun calcFunc-conj (a)
  (let (aa bb)
    (cond ((Math-realp a)
	   a)
	  ((eq (car a) 'cplx)
	   (list 'cplx (nth 1 a) (math-neg (nth 2 a))))
	  ((eq (car a) 'polar)
	   (list 'polar (nth 1 a) (math-neg (nth 2 a))))
	  ((eq (car a) 'vec)
	   (math-map-vec 'calcFunc-conj a))
	  ((eq (car a) 'calcFunc-conj)
	   (nth 1 a))
	  ((math-known-realp a)
	   a)
	  ((and (equal a '(var i var-i))
		(math-imaginary-i))
	   (math-neg a))
	  ((and (memq (car a) '(+ - * /))
		(progn
		  (setq aa (calcFunc-conj (nth 1 a))
			bb (calcFunc-conj (nth 2 a)))
		  (or (not (eq (car-safe aa) 'calcFunc-conj))
		      (not (eq (car-safe bb) 'calcFunc-conj)))))
	   (if (eq (car a) '+)
	       (math-add aa bb)
	     (if (eq (car a) '-)
		 (math-sub aa bb)
	       (if (eq (car a) '*)
		   (math-mul aa bb)
		 (math-div aa bb)))))
	  ((eq (car a) 'neg)
	   (math-neg (calcFunc-conj (nth 1 a))))
	  ((let ((inf (math-infinitep a)))
	     (and inf
		  (math-mul (calcFunc-conj (math-infinite-dir a inf)) inf))))
	  (t (calc-record-why 'numberp a)
	     (list 'calcFunc-conj a)))))


;;; Compute the complex argument of A.  [F N] [Public]
(defun calcFunc-arg (a)
  (cond ((Math-anglep a)
	 (if (math-negp a) (math-half-circle nil) 0))
	((eq (car-safe a) 'cplx)
	 (calcFunc-arctan2 (nth 2 a) (nth 1 a)))
	((eq (car-safe a) 'polar)
	 (nth 2 a))
	((eq (car a) 'vec)
	 (math-map-vec 'calcFunc-arg a))
	((and (equal a '(var i var-i))
	      (math-imaginary-i))
	 (math-quarter-circle t))
	((and (equal a '(neg (var i var-i)))
	      (math-imaginary-i))
	 (math-neg (math-quarter-circle t)))
	((let ((signs (math-possible-signs a)))
	   (or (and (memq signs '(2 4 6)) 0)
	       (and (eq signs 1) (math-half-circle nil)))))
	((math-infinitep a)
	 (if (or (equal a '(var uinf var-uinf))
		 (equal a '(var nan var-nan)))
	     '(var nan var-nan)
	   (calcFunc-arg (math-infinite-dir a))))
	(t (calc-record-why 'numvecp a)
	   (list 'calcFunc-arg a))))

(defun math-imaginary-i ()
  (let ((val (calc-var-value 'var-i)))
    (or (eq (car-safe val) 'special-const)
	(equal val '(cplx 0 1))
	(and (eq (car-safe val) 'polar)
	     (eq (nth 1 val) 0)
	     (Math-equal (nth 1 val) (math-quarter-circle nil))))))

;;; Extract the real or complex part of a complex number.  [R N] [Public]
;;; Also extracts the real part of a modulo form.
(defun calcFunc-re (a)
  (let (aa bb)
    (cond ((Math-realp a) a)
	  ((memq (car a) '(mod cplx))
	   (nth 1 a))
	  ((eq (car a) 'polar)
	   (math-mul (nth 1 a) (calcFunc-cos (nth 2 a))))
	  ((eq (car a) 'vec)
	   (math-map-vec 'calcFunc-re a))
	  ((math-known-realp a) a)
	  ((eq (car a) 'calcFunc-conj)
	   (calcFunc-re (nth 1 a)))
	  ((and (equal a '(var i var-i))
		(math-imaginary-i))
	   0)
	  ((and (memq (car a) '(+ - *))
		(progn
		  (setq aa (calcFunc-re (nth 1 a))
			bb (calcFunc-re (nth 2 a)))
		  (or (not (eq (car-safe aa) 'calcFunc-re))
		      (not (eq (car-safe bb) 'calcFunc-re)))))
	   (if (eq (car a) '+)
	       (math-add aa bb)
	     (if (eq (car a) '-)
		 (math-sub aa bb)
	       (math-sub (math-mul aa bb)
			 (math-mul (calcFunc-im (nth 1 a))
				   (calcFunc-im (nth 2 a)))))))
	  ((and (eq (car a) '/)
		(math-known-realp (nth 2 a)))
	   (math-div (calcFunc-re (nth 1 a)) (nth 2 a)))
	  ((eq (car a) 'neg)
	   (math-neg (calcFunc-re (nth 1 a))))
	  (t (calc-record-why 'numberp a)
	     (list 'calcFunc-re a)))))

(defun calcFunc-im (a)
  (let (aa bb)
    (cond ((Math-realp a)
	   (if (math-floatp a) '(float 0 0) 0))
	  ((eq (car a) 'cplx)
	   (nth 2 a))
	  ((eq (car a) 'polar)
	   (math-mul (nth 1 a) (calcFunc-sin (nth 2 a))))
	  ((eq (car a) 'vec)
	   (math-map-vec 'calcFunc-im a))
	  ((math-known-realp a)
	   0)
	  ((eq (car a) 'calcFunc-conj)
	   (math-neg (calcFunc-im (nth 1 a))))
	  ((and (equal a '(var i var-i))
		(math-imaginary-i))
	   1)
	  ((and (memq (car a) '(+ - *))
		(progn
		  (setq aa (calcFunc-im (nth 1 a))
			bb (calcFunc-im (nth 2 a)))
		  (or (not (eq (car-safe aa) 'calcFunc-im))
		      (not (eq (car-safe bb) 'calcFunc-im)))))
	   (if (eq (car a) '+)
	       (math-add aa bb)
	     (if (eq (car a) '-)
		 (math-sub aa bb)
	       (math-add (math-mul (calcFunc-re (nth 1 a)) bb)
			 (math-mul aa (calcFunc-re (nth 2 a)))))))
	  ((and (eq (car a) '/)
		(math-known-realp (nth 2 a)))
	   (math-div (calcFunc-im (nth 1 a)) (nth 2 a)))
	  ((eq (car a) 'neg)
	   (math-neg (calcFunc-im (nth 1 a))))
	  (t (calc-record-why 'numberp a)
	     (list 'calcFunc-im a)))))

(provide 'calc-cplx)

;; arch-tag: de73a331-941c-4507-ae76-46c76adc70dd
;;; calc-cplx.el ends here
Commit	Line	Data
3132f345 CW	1	;;; calc-cplx.el --- Complex number functions for Calc
3132f345 CW	2
58ba2f8f	3	;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
8b72699e	4	;; 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
3132f345 CW	5
3132f345 CW	6	;; Author: David Gillespie <daveg@synaptics.com>
e8fff8ed	7	;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
136211a9 EZ	8
	9	;; This file is part of GNU Emacs.
	10
7c671b23 GM	11	;; GNU Emacs is free software; you can redistribute it and/or modify
7c671b23 GM	12	;; it under the terms of the GNU General Public License as published by
075969b4	13	;; the Free Software Foundation; either version 3, or (at your option)
7c671b23 GM	14	;; any later version.
7c671b23 GM	15
136211a9	16	;; GNU Emacs is distributed in the hope that it will be useful,
7c671b23 GM	17	;; but WITHOUT ANY WARRANTY; without even the implied warranty of
	18	;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	19	;; GNU General Public License for more details.
	20
	21	;; You should have received a copy of the GNU General Public License
	22	;; along with GNU Emacs; see the file COPYING. If not, write to the
	23	;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
	24	;; Boston, MA 02110-1301, USA.
136211a9	25
3132f345	26	;;; Commentary:
136211a9	27
3132f345	28	;;; Code:
136211a9 EZ	29
136211a9 EZ	30	;; This file is autoloaded from calc-ext.el.
136211a9	31
b96bd98c	32	(require 'calc-ext)
136211a9 EZ	33	(require 'calc-macs)
136211a9 EZ	34
136211a9 EZ	35	(defun calc-argument (arg)
	36	(interactive "P")
	37	(calc-slow-wrapper
bf77c646	38	(calc-unary-op "arg" 'calcFunc-arg arg)))
136211a9 EZ	39
	40	(defun calc-re (arg)
	41	(interactive "P")
	42	(calc-slow-wrapper
bf77c646	43	(calc-unary-op "re" 'calcFunc-re arg)))
136211a9 EZ	44
	45	(defun calc-im (arg)
	46	(interactive "P")
	47	(calc-slow-wrapper
bf77c646	48	(calc-unary-op "im" 'calcFunc-im arg)))
136211a9 EZ	49
	50
	51	(defun calc-polar ()
	52	(interactive)
	53	(calc-slow-wrapper
	54	(let ((arg (calc-top-n 1)))
	55	(if (or (calc-is-inverse)
	56	(eq (car-safe arg) 'polar))
	57	(calc-enter-result 1 "p-r" (list 'calcFunc-rect arg))
bf77c646	58	(calc-enter-result 1 "r-p" (list 'calcFunc-polar arg))))))
136211a9 EZ	59
	60
	61
	62
	63	(defun calc-complex-notation ()
	64	(interactive)
	65	(calc-wrapper
	66	(calc-change-mode 'calc-complex-format nil t)
3132f345	67	(message "Displaying complex numbers in (X,Y) format")))
136211a9 EZ	68
	69	(defun calc-i-notation ()
	70	(interactive)
	71	(calc-wrapper
	72	(calc-change-mode 'calc-complex-format 'i t)
3132f345	73	(message "Displaying complex numbers in X+Yi format")))
136211a9 EZ	74
	75	(defun calc-j-notation ()
	76	(interactive)
	77	(calc-wrapper
	78	(calc-change-mode 'calc-complex-format 'j t)
3132f345	79	(message "Displaying complex numbers in X+Yj format")))
136211a9 EZ	80
	81
	82	(defun calc-polar-mode (n)
	83	(interactive "P")
	84	(calc-wrapper
	85	(if (if n
	86	(> (prefix-numeric-value n) 0)
	87	(eq calc-complex-mode 'cplx))
	88	(progn
	89	(calc-change-mode 'calc-complex-mode 'polar)
3132f345	90	(message "Preferred complex form is polar"))
136211a9	91	(calc-change-mode 'calc-complex-mode 'cplx)
3132f345	92	(message "Preferred complex form is rectangular"))))
136211a9 EZ	93
	94
	95	;;;; Complex numbers.
	96
	97	(defun math-normalize-polar (a)
	98	(let ((r (math-normalize (nth 1 a)))
	99	(th (math-normalize (nth 2 a))))
	100	(cond ((math-zerop r)
	101	'(polar 0 0))
	102	((or (math-zerop th))
	103	r)
	104	((and (not (eq calc-angle-mode 'rad))
	105	(or (equal th '(float 18 1))
	106	(equal th 180)))
	107	(math-neg r))
	108	((math-negp r)
	109	(math-neg (list 'polar (math-neg r) th)))
	110	(t
bf77c646	111	(list 'polar r th)))))
136211a9 EZ	112
	113
	114	;;; Coerce A to be complex (rectangular form). [c N]
	115	(defun math-complex (a)
	116	(cond ((eq (car-safe a) 'cplx) a)
	117	((eq (car-safe a) 'polar)
	118	(if (math-zerop (nth 1 a))
	119	(nth 1 a)
	120	(let ((sc (calcFunc-sincos (nth 2 a))))
	121	(list 'cplx
	122	(math-mul (nth 1 a) (nth 1 sc))
	123	(math-mul (nth 1 a) (nth 2 sc))))))
bf77c646	124	(t (list 'cplx a 0))))
136211a9 EZ	125
	126	;;; Coerce A to be complex (polar form). [c N]
	127	(defun math-polar (a)
	128	(cond ((eq (car-safe a) 'polar) a)
	129	((math-zerop a) '(polar 0 0))
	130	(t
	131	(list 'polar
	132	(math-abs a)
bf77c646	133	(calcFunc-arg a)))))
136211a9 EZ	134
	135	;;; Multiply A by the imaginary constant i. [N N] [Public]
	136	(defun math-imaginary (a)
	137	(if (and (or (Math-objvecp a) (math-infinitep a))
	138	(not calc-symbolic-mode))
	139	(math-mul a
	140	(if (or (eq (car-safe a) 'polar)
	141	(and (not (eq (car-safe a) 'cplx))
	142	(eq calc-complex-mode 'polar)))
	143	(list 'polar 1 (math-quarter-circle nil))
	144	'(cplx 0 1)))
bf77c646	145	(math-mul a '(var i var-i))))
136211a9 EZ	146
	147
	148
	149
	150	(defun math-want-polar (a b)
	151	(cond ((eq (car-safe a) 'polar)
	152	(if (eq (car-safe b) 'cplx)
	153	(eq calc-complex-mode 'polar)
	154	t))
	155	((eq (car-safe a) 'cplx)
	156	(if (eq (car-safe b) 'polar)
	157	(eq calc-complex-mode 'polar)
	158	nil))
	159	((eq (car-safe b) 'polar)
	160	t)
	161	((eq (car-safe b) 'cplx)
	162	nil)
bf77c646	163	(t (eq calc-complex-mode 'polar))))
136211a9 EZ	164
	165	;;; Force A to be in the (-pi,pi] or (-180,180] range.
	166	(defun math-fix-circular (a &optional dir) ; [R R]
	167	(cond ((eq (car-safe a) 'hms)
	168	(cond ((and (Math-lessp 180 (nth 1 a)) (not (eq dir 1)))
	169	(math-fix-circular (math-add a '(float -36 1)) -1))
	170	((or (Math-lessp -180 (nth 1 a)) (eq dir -1))
	171	a)
	172	(t
	173	(math-fix-circular (math-add a '(float 36 1)) 1))))
	174	((eq calc-angle-mode 'rad)
	175	(cond ((and (Math-lessp (math-pi) a) (not (eq dir 1)))
	176	(math-fix-circular (math-sub a (math-two-pi)) -1))
	177	((or (Math-lessp (math-neg (math-pi)) a) (eq dir -1))
	178	a)
	179	(t
	180	(math-fix-circular (math-add a (math-two-pi)) 1))))
	181	(t
	182	(cond ((and (Math-lessp '(float 18 1) a) (not (eq dir 1)))
	183	(math-fix-circular (math-add a '(float -36 1)) -1))
	184	((or (Math-lessp '(float -18 1) a) (eq dir -1))
	185	a)
	186	(t
bf77c646	187	(math-fix-circular (math-add a '(float 36 1)) 1))))))
136211a9 EZ	188
	189
	190	;;;; Complex numbers.
	191
	192	(defun calcFunc-polar (a) ; [C N] [Public]
	193	(cond ((Math-vectorp a)
	194	(math-map-vec 'calcFunc-polar a))
	195	((Math-realp a) a)
	196	((Math-numberp a)
	197	(math-normalize (math-polar a)))
bf77c646	198	(t (list 'calcFunc-polar a))))
136211a9 EZ	199
	200	(defun calcFunc-rect (a) ; [N N] [Public]
	201	(cond ((Math-vectorp a)
	202	(math-map-vec 'calcFunc-rect a))
	203	((Math-realp a) a)
	204	((Math-numberp a)
	205	(math-normalize (math-complex a)))
bf77c646	206	(t (list 'calcFunc-rect a))))
136211a9 EZ	207
	208	;;; Compute the complex conjugate of A. [O O] [Public]
	209	(defun calcFunc-conj (a)
	210	(let (aa bb)
	211	(cond ((Math-realp a)
	212	a)
	213	((eq (car a) 'cplx)
	214	(list 'cplx (nth 1 a) (math-neg (nth 2 a))))
	215	((eq (car a) 'polar)
	216	(list 'polar (nth 1 a) (math-neg (nth 2 a))))
	217	((eq (car a) 'vec)
	218	(math-map-vec 'calcFunc-conj a))
	219	((eq (car a) 'calcFunc-conj)
	220	(nth 1 a))
	221	((math-known-realp a)
	222	a)
	223	((and (equal a '(var i var-i))
	224	(math-imaginary-i))
	225	(math-neg a))
	226	((and (memq (car a) '(+ - * /))
	227	(progn
	228	(setq aa (calcFunc-conj (nth 1 a))
	229	bb (calcFunc-conj (nth 2 a)))
	230	(or (not (eq (car-safe aa) 'calcFunc-conj))
	231	(not (eq (car-safe bb) 'calcFunc-conj)))))
	232	(if (eq (car a) '+)
	233	(math-add aa bb)
	234	(if (eq (car a) '-)
	235	(math-sub aa bb)
	236	(if (eq (car a) '*)
	237	(math-mul aa bb)
	238	(math-div aa bb)))))
	239	((eq (car a) 'neg)
	240	(math-neg (calcFunc-conj (nth 1 a))))
	241	((let ((inf (math-infinitep a)))
	242	(and inf
	243	(math-mul (calcFunc-conj (math-infinite-dir a inf)) inf))))
	244	(t (calc-record-why 'numberp a)
bf77c646	245	(list 'calcFunc-conj a)))))
136211a9 EZ	246
	247
	248	;;; Compute the complex argument of A. [F N] [Public]
	249	(defun calcFunc-arg (a)
	250	(cond ((Math-anglep a)
	251	(if (math-negp a) (math-half-circle nil) 0))
	252	((eq (car-safe a) 'cplx)
	253	(calcFunc-arctan2 (nth 2 a) (nth 1 a)))
	254	((eq (car-safe a) 'polar)
	255	(nth 2 a))
	256	((eq (car a) 'vec)
	257	(math-map-vec 'calcFunc-arg a))
	258	((and (equal a '(var i var-i))
	259	(math-imaginary-i))
	260	(math-quarter-circle t))
	261	((and (equal a '(neg (var i var-i)))
	262	(math-imaginary-i))
	263	(math-neg (math-quarter-circle t)))
	264	((let ((signs (math-possible-signs a)))
	265	(or (and (memq signs '(2 4 6)) 0)
	266	(and (eq signs 1) (math-half-circle nil)))))
	267	((math-infinitep a)
	268	(if (or (equal a '(var uinf var-uinf))
	269	(equal a '(var nan var-nan)))
	270	'(var nan var-nan)
	271	(calcFunc-arg (math-infinite-dir a))))
	272	(t (calc-record-why 'numvecp a)
bf77c646	273	(list 'calcFunc-arg a))))
136211a9 EZ	274
	275	(defun math-imaginary-i ()
	276	(let ((val (calc-var-value 'var-i)))
	277	(or (eq (car-safe val) 'special-const)
	278	(equal val '(cplx 0 1))
	279	(and (eq (car-safe val) 'polar)
	280	(eq (nth 1 val) 0)
bf77c646	281	(Math-equal (nth 1 val) (math-quarter-circle nil))))))
136211a9 EZ	282
	283	;;; Extract the real or complex part of a complex number. [R N] [Public]
	284	;;; Also extracts the real part of a modulo form.
	285	(defun calcFunc-re (a)
	286	(let (aa bb)
	287	(cond ((Math-realp a) a)
	288	((memq (car a) '(mod cplx))
	289	(nth 1 a))
	290	((eq (car a) 'polar)
	291	(math-mul (nth 1 a) (calcFunc-cos (nth 2 a))))
	292	((eq (car a) 'vec)
	293	(math-map-vec 'calcFunc-re a))
	294	((math-known-realp a) a)
	295	((eq (car a) 'calcFunc-conj)
	296	(calcFunc-re (nth 1 a)))
	297	((and (equal a '(var i var-i))
	298	(math-imaginary-i))
	299	0)
	300	((and (memq (car a) '(+ - *))
	301	(progn
	302	(setq aa (calcFunc-re (nth 1 a))
	303	bb (calcFunc-re (nth 2 a)))
	304	(or (not (eq (car-safe aa) 'calcFunc-re))
	305	(not (eq (car-safe bb) 'calcFunc-re)))))
	306	(if (eq (car a) '+)
	307	(math-add aa bb)
	308	(if (eq (car a) '-)
	309	(math-sub aa bb)
	310	(math-sub (math-mul aa bb)
	311	(math-mul (calcFunc-im (nth 1 a))
	312	(calcFunc-im (nth 2 a)))))))
	313	((and (eq (car a) '/)
	314	(math-known-realp (nth 2 a)))
	315	(math-div (calcFunc-re (nth 1 a)) (nth 2 a)))
	316	((eq (car a) 'neg)
	317	(math-neg (calcFunc-re (nth 1 a))))
	318	(t (calc-record-why 'numberp a)
bf77c646	319	(list 'calcFunc-re a)))))
136211a9 EZ	320
	321	(defun calcFunc-im (a)
	322	(let (aa bb)
	323	(cond ((Math-realp a)
	324	(if (math-floatp a) '(float 0 0) 0))
	325	((eq (car a) 'cplx)
	326	(nth 2 a))
	327	((eq (car a) 'polar)
	328	(math-mul (nth 1 a) (calcFunc-sin (nth 2 a))))
	329	((eq (car a) 'vec)
	330	(math-map-vec 'calcFunc-im a))
	331	((math-known-realp a)
	332	0)
	333	((eq (car a) 'calcFunc-conj)
	334	(math-neg (calcFunc-im (nth 1 a))))
	335	((and (equal a '(var i var-i))
	336	(math-imaginary-i))
	337	1)
	338	((and (memq (car a) '(+ - *))
	339	(progn
	340	(setq aa (calcFunc-im (nth 1 a))
	341	bb (calcFunc-im (nth 2 a)))
	342	(or (not (eq (car-safe aa) 'calcFunc-im))
	343	(not (eq (car-safe bb) 'calcFunc-im)))))
	344	(if (eq (car a) '+)
	345	(math-add aa bb)
	346	(if (eq (car a) '-)
	347	(math-sub aa bb)
	348	(math-add (math-mul (calcFunc-re (nth 1 a)) bb)
	349	(math-mul aa (calcFunc-re (nth 2 a)))))))
	350	((and (eq (car a) '/)
	351	(math-known-realp (nth 2 a)))
	352	(math-div (calcFunc-im (nth 1 a)) (nth 2 a)))
	353	((eq (car a) 'neg)
	354	(math-neg (calcFunc-im (nth 1 a))))
	355	(t (calc-record-why 'numberp a)
bf77c646	356	(list 'calcFunc-im a)))))
136211a9	357
b96bd98c JB	358	(provide 'calc-cplx)
b96bd98c JB	359
cbee283d	360	;; arch-tag: de73a331-941c-4507-ae76-46c76adc70dd
bf77c646	361	;;; calc-cplx.el ends here