1;;; calc-cplx.el --- Complex number functions for Calc
2
3;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
4;;   2005, 2006, 2007 Free Software Foundation, Inc.
5
6;; Author: David Gillespie <daveg@synaptics.com>
7;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
8
9;; This file is part of GNU Emacs.
10
11;; GNU Emacs is free software; you can redistribute it and/or modify
12;; it under the terms of the GNU General Public License as published by
13;; the Free Software Foundation; either version 2, or (at your option)
14;; any later version.
15
16;; GNU Emacs is distributed in the hope that it will be useful,
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.
25
26;;; Commentary:
27
28;;; Code:
29
30;; This file is autoloaded from calc-ext.el.
31
32(require 'calc-ext)
33(require 'calc-macs)
34
35(defun calc-argument (arg)
36  (interactive "P")
37  (calc-slow-wrapper
38   (calc-unary-op "arg" 'calcFunc-arg arg)))
39
40(defun calc-re (arg)
41  (interactive "P")
42  (calc-slow-wrapper
43   (calc-unary-op "re" 'calcFunc-re arg)))
44
45(defun calc-im (arg)
46  (interactive "P")
47  (calc-slow-wrapper
48   (calc-unary-op "im" 'calcFunc-im arg)))
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))
58       (calc-enter-result 1 "r-p" (list 'calcFunc-polar arg))))))
59
60
61
62
63(defun calc-complex-notation ()
64  (interactive)
65  (calc-wrapper
66   (calc-change-mode 'calc-complex-format nil t)
67   (message "Displaying complex numbers in (X,Y) format")))
68
69(defun calc-i-notation ()
70  (interactive)
71  (calc-wrapper
72   (calc-change-mode 'calc-complex-format 'i t)
73   (message "Displaying complex numbers in X+Yi format")))
74
75(defun calc-j-notation ()
76  (interactive)
77  (calc-wrapper
78   (calc-change-mode 'calc-complex-format 'j t)
79   (message "Displaying complex numbers in X+Yj format")))
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)
90	 (message "Preferred complex form is polar"))
91     (calc-change-mode 'calc-complex-mode 'cplx)
92     (message "Preferred complex form is rectangular"))))
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
111	   (list 'polar r th)))))
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))))))
124	(t (list 'cplx a 0))))
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)
133	       (calcFunc-arg a)))))
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)))
145    (math-mul a '(var i var-i))))
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)
163	(t (eq calc-complex-mode 'polar))))
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
187		(math-fix-circular (math-add a '(float 36 1)) 1))))))
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)))
198	(t (list 'calcFunc-polar a))))
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)))
206	(t (list 'calcFunc-rect a))))
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)
245	     (list 'calcFunc-conj a)))))
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)
273	   (list 'calcFunc-arg a))))
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)
281	     (Math-equal (nth 1 val) (math-quarter-circle nil))))))
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)
319	     (list 'calcFunc-re a)))))
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)
356	     (list 'calcFunc-im a)))))
357
358(provide 'calc-cplx)
359
360;;; arch-tag: de73a331-941c-4507-ae76-46c76adc70dd
361;;; calc-cplx.el ends here
362