1 ;;; calc-cplx.el --- Complex number functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainer: Colin Walters <walters@debian.org>
8 ;; This file is part of GNU Emacs.
10 ;; GNU Emacs is distributed in the hope that it will be useful,
11 ;; but WITHOUT ANY WARRANTY. No author or distributor
12 ;; accepts responsibility to anyone for the consequences of using it
13 ;; or for whether it serves any particular purpose or works at all,
14 ;; unless he says so in writing. Refer to the GNU Emacs General Public
15 ;; License for full details.
17 ;; Everyone is granted permission to copy, modify and redistribute
18 ;; GNU Emacs, but only under the conditions described in the
19 ;; GNU Emacs General Public License. A copy of this license is
20 ;; supposed to have been given to you along with GNU Emacs so you
21 ;; can know your rights and responsibilities. It should be in a
22 ;; file named COPYING. Among other things, the copyright notice
23 ;; and this notice must be preserved on all copies.
29 ;; This file is autoloaded from calc-ext.el.
34 (defun calc-Need-calc-cplx () nil)
37 (defun calc-argument (arg)
40 (calc-unary-op "arg" 'calcFunc-arg arg)))
45 (calc-unary-op "re" 'calcFunc-re arg)))
50 (calc-unary-op "im" 'calcFunc-im arg)))
56 (let ((arg (calc-top-n 1)))
57 (if (or (calc-is-inverse)
58 (eq (car-safe arg) 'polar))
59 (calc-enter-result 1 "p-r" (list 'calcFunc-rect arg))
60 (calc-enter-result 1 "r-p" (list 'calcFunc-polar arg))))))
65 (defun calc-complex-notation ()
68 (calc-change-mode 'calc-complex-format nil t)
69 (message "Displaying complex numbers in (X,Y) format")))
71 (defun calc-i-notation ()
74 (calc-change-mode 'calc-complex-format 'i t)
75 (message "Displaying complex numbers in X+Yi format")))
77 (defun calc-j-notation ()
80 (calc-change-mode 'calc-complex-format 'j t)
81 (message "Displaying complex numbers in X+Yj format")))
84 (defun calc-polar-mode (n)
88 (> (prefix-numeric-value n) 0)
89 (eq calc-complex-mode 'cplx))
91 (calc-change-mode 'calc-complex-mode 'polar)
92 (message "Preferred complex form is polar"))
93 (calc-change-mode 'calc-complex-mode 'cplx)
94 (message "Preferred complex form is rectangular"))))
99 (defun math-normalize-polar (a)
100 (let ((r (math-normalize (nth 1 a)))
101 (th (math-normalize (nth 2 a))))
102 (cond ((math-zerop r)
104 ((or (math-zerop th))
106 ((and (not (eq calc-angle-mode 'rad))
107 (or (equal th '(float 18 1))
111 (math-neg (list 'polar (math-neg r) th)))
113 (list 'polar r th)))))
116 ;;; Coerce A to be complex (rectangular form). [c N]
117 (defun math-complex (a)
118 (cond ((eq (car-safe a) 'cplx) a)
119 ((eq (car-safe a) 'polar)
120 (if (math-zerop (nth 1 a))
122 (let ((sc (calcFunc-sincos (nth 2 a))))
124 (math-mul (nth 1 a) (nth 1 sc))
125 (math-mul (nth 1 a) (nth 2 sc))))))
126 (t (list 'cplx a 0))))
128 ;;; Coerce A to be complex (polar form). [c N]
129 (defun math-polar (a)
130 (cond ((eq (car-safe a) 'polar) a)
131 ((math-zerop a) '(polar 0 0))
137 ;;; Multiply A by the imaginary constant i. [N N] [Public]
138 (defun math-imaginary (a)
139 (if (and (or (Math-objvecp a) (math-infinitep a))
140 (not calc-symbolic-mode))
142 (if (or (eq (car-safe a) 'polar)
143 (and (not (eq (car-safe a) 'cplx))
144 (eq calc-complex-mode 'polar)))
145 (list 'polar 1 (math-quarter-circle nil))
147 (math-mul a '(var i var-i))))
152 (defun math-want-polar (a b)
153 (cond ((eq (car-safe a) 'polar)
154 (if (eq (car-safe b) 'cplx)
155 (eq calc-complex-mode 'polar)
157 ((eq (car-safe a) 'cplx)
158 (if (eq (car-safe b) 'polar)
159 (eq calc-complex-mode 'polar)
161 ((eq (car-safe b) 'polar)
163 ((eq (car-safe b) 'cplx)
165 (t (eq calc-complex-mode 'polar))))
167 ;;; Force A to be in the (-pi,pi] or (-180,180] range.
168 (defun math-fix-circular (a &optional dir) ; [R R]
169 (cond ((eq (car-safe a) 'hms)
170 (cond ((and (Math-lessp 180 (nth 1 a)) (not (eq dir 1)))
171 (math-fix-circular (math-add a '(float -36 1)) -1))
172 ((or (Math-lessp -180 (nth 1 a)) (eq dir -1))
175 (math-fix-circular (math-add a '(float 36 1)) 1))))
176 ((eq calc-angle-mode 'rad)
177 (cond ((and (Math-lessp (math-pi) a) (not (eq dir 1)))
178 (math-fix-circular (math-sub a (math-two-pi)) -1))
179 ((or (Math-lessp (math-neg (math-pi)) a) (eq dir -1))
182 (math-fix-circular (math-add a (math-two-pi)) 1))))
184 (cond ((and (Math-lessp '(float 18 1) a) (not (eq dir 1)))
185 (math-fix-circular (math-add a '(float -36 1)) -1))
186 ((or (Math-lessp '(float -18 1) a) (eq dir -1))
189 (math-fix-circular (math-add a '(float 36 1)) 1))))))
192 ;;;; Complex numbers.
194 (defun calcFunc-polar (a) ; [C N] [Public]
195 (cond ((Math-vectorp a)
196 (math-map-vec 'calcFunc-polar a))
199 (math-normalize (math-polar a)))
200 (t (list 'calcFunc-polar a))))
202 (defun calcFunc-rect (a) ; [N N] [Public]
203 (cond ((Math-vectorp a)
204 (math-map-vec 'calcFunc-rect a))
207 (math-normalize (math-complex a)))
208 (t (list 'calcFunc-rect a))))
210 ;;; Compute the complex conjugate of A. [O O] [Public]
211 (defun calcFunc-conj (a)
213 (cond ((Math-realp a)
216 (list 'cplx (nth 1 a) (math-neg (nth 2 a))))
218 (list 'polar (nth 1 a) (math-neg (nth 2 a))))
220 (math-map-vec 'calcFunc-conj a))
221 ((eq (car a) 'calcFunc-conj)
223 ((math-known-realp a)
225 ((and (equal a '(var i var-i))
228 ((and (memq (car a) '(+ - * /))
230 (setq aa (calcFunc-conj (nth 1 a))
231 bb (calcFunc-conj (nth 2 a)))
232 (or (not (eq (car-safe aa) 'calcFunc-conj))
233 (not (eq (car-safe bb) 'calcFunc-conj)))))
242 (math-neg (calcFunc-conj (nth 1 a))))
243 ((let ((inf (math-infinitep a)))
245 (math-mul (calcFunc-conj (math-infinite-dir a inf)) inf))))
246 (t (calc-record-why 'numberp a)
247 (list 'calcFunc-conj a)))))
250 ;;; Compute the complex argument of A. [F N] [Public]
251 (defun calcFunc-arg (a)
252 (cond ((Math-anglep a)
253 (if (math-negp a) (math-half-circle nil) 0))
254 ((eq (car-safe a) 'cplx)
255 (calcFunc-arctan2 (nth 2 a) (nth 1 a)))
256 ((eq (car-safe a) 'polar)
259 (math-map-vec 'calcFunc-arg a))
260 ((and (equal a '(var i var-i))
262 (math-quarter-circle t))
263 ((and (equal a '(neg (var i var-i)))
265 (math-neg (math-quarter-circle t)))
266 ((let ((signs (math-possible-signs a)))
267 (or (and (memq signs '(2 4 6)) 0)
268 (and (eq signs 1) (math-half-circle nil)))))
270 (if (or (equal a '(var uinf var-uinf))
271 (equal a '(var nan var-nan)))
273 (calcFunc-arg (math-infinite-dir a))))
274 (t (calc-record-why 'numvecp a)
275 (list 'calcFunc-arg a))))
277 (defun math-imaginary-i ()
278 (let ((val (calc-var-value 'var-i)))
279 (or (eq (car-safe val) 'special-const)
280 (equal val '(cplx 0 1))
281 (and (eq (car-safe val) 'polar)
283 (Math-equal (nth 1 val) (math-quarter-circle nil))))))
285 ;;; Extract the real or complex part of a complex number. [R N] [Public]
286 ;;; Also extracts the real part of a modulo form.
287 (defun calcFunc-re (a)
289 (cond ((Math-realp a) a)
290 ((memq (car a) '(mod cplx))
293 (math-mul (nth 1 a) (calcFunc-cos (nth 2 a))))
295 (math-map-vec 'calcFunc-re a))
296 ((math-known-realp a) a)
297 ((eq (car a) 'calcFunc-conj)
298 (calcFunc-re (nth 1 a)))
299 ((and (equal a '(var i var-i))
302 ((and (memq (car a) '(+ - *))
304 (setq aa (calcFunc-re (nth 1 a))
305 bb (calcFunc-re (nth 2 a)))
306 (or (not (eq (car-safe aa) 'calcFunc-re))
307 (not (eq (car-safe bb) 'calcFunc-re)))))
312 (math-sub (math-mul aa bb)
313 (math-mul (calcFunc-im (nth 1 a))
314 (calcFunc-im (nth 2 a)))))))
315 ((and (eq (car a) '/)
316 (math-known-realp (nth 2 a)))
317 (math-div (calcFunc-re (nth 1 a)) (nth 2 a)))
319 (math-neg (calcFunc-re (nth 1 a))))
320 (t (calc-record-why 'numberp a)
321 (list 'calcFunc-re a)))))
323 (defun calcFunc-im (a)
325 (cond ((Math-realp a)
326 (if (math-floatp a) '(float 0 0) 0))
330 (math-mul (nth 1 a) (calcFunc-sin (nth 2 a))))
332 (math-map-vec 'calcFunc-im a))
333 ((math-known-realp a)
335 ((eq (car a) 'calcFunc-conj)
336 (math-neg (calcFunc-im (nth 1 a))))
337 ((and (equal a '(var i var-i))
340 ((and (memq (car a) '(+ - *))
342 (setq aa (calcFunc-im (nth 1 a))
343 bb (calcFunc-im (nth 2 a)))
344 (or (not (eq (car-safe aa) 'calcFunc-im))
345 (not (eq (car-safe bb) 'calcFunc-im)))))
350 (math-add (math-mul (calcFunc-re (nth 1 a)) bb)
351 (math-mul aa (calcFunc-re (nth 2 a)))))))
352 ((and (eq (car a) '/)
353 (math-known-realp (nth 2 a)))
354 (math-div (calcFunc-im (nth 1 a)) (nth 2 a)))
356 (math-neg (calcFunc-im (nth 1 a))))
357 (t (calc-record-why 'numberp a)
358 (list 'calcFunc-im a)))))
360 ;;; calc-cplx.el ends here