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 ;; Maintainers: D. Goel <deego@gnufans.org>
7 ;; Colin Walters <walters@debian.org>
9 ;; This file is part of GNU Emacs.
11 ;; GNU Emacs is distributed in the hope that it will be useful,
12 ;; but WITHOUT ANY WARRANTY. No author or distributor
13 ;; accepts responsibility to anyone for the consequences of using it
14 ;; or for whether it serves any particular purpose or works at all,
15 ;; unless he says so in writing. Refer to the GNU Emacs General Public
16 ;; License for full details.
18 ;; Everyone is granted permission to copy, modify and redistribute
19 ;; GNU Emacs, but only under the conditions described in the
20 ;; GNU Emacs General Public License. A copy of this license is
21 ;; supposed to have been given to you along with GNU Emacs so you
22 ;; can know your rights and responsibilities. It should be in a
23 ;; file named COPYING. Among other things, the copyright notice
24 ;; and this notice must be preserved on all copies.
30 ;; This file is autoloaded from calc-ext.el.
35 (defun calc-Need-calc-cplx () nil
)
38 (defun calc-argument (arg)
41 (calc-unary-op "arg" 'calcFunc-arg arg
)))
46 (calc-unary-op "re" 'calcFunc-re arg
)))
51 (calc-unary-op "im" 'calcFunc-im arg
)))
57 (let ((arg (calc-top-n 1)))
58 (if (or (calc-is-inverse)
59 (eq (car-safe arg
) 'polar
))
60 (calc-enter-result 1 "p-r" (list 'calcFunc-rect arg
))
61 (calc-enter-result 1 "r-p" (list 'calcFunc-polar arg
))))))
66 (defun calc-complex-notation ()
69 (calc-change-mode 'calc-complex-format nil t
)
70 (message "Displaying complex numbers in (X,Y) format")))
72 (defun calc-i-notation ()
75 (calc-change-mode 'calc-complex-format
'i t
)
76 (message "Displaying complex numbers in X+Yi format")))
78 (defun calc-j-notation ()
81 (calc-change-mode 'calc-complex-format
'j t
)
82 (message "Displaying complex numbers in X+Yj format")))
85 (defun calc-polar-mode (n)
89 (> (prefix-numeric-value n
) 0)
90 (eq calc-complex-mode
'cplx
))
92 (calc-change-mode 'calc-complex-mode
'polar
)
93 (message "Preferred complex form is polar"))
94 (calc-change-mode 'calc-complex-mode
'cplx
)
95 (message "Preferred complex form is rectangular"))))
100 (defun math-normalize-polar (a)
101 (let ((r (math-normalize (nth 1 a
)))
102 (th (math-normalize (nth 2 a
))))
103 (cond ((math-zerop r
)
105 ((or (math-zerop th
))
107 ((and (not (eq calc-angle-mode
'rad
))
108 (or (equal th
'(float 18 1))
112 (math-neg (list 'polar
(math-neg r
) th
)))
114 (list 'polar r th
)))))
117 ;;; Coerce A to be complex (rectangular form). [c N]
118 (defun math-complex (a)
119 (cond ((eq (car-safe a
) 'cplx
) a
)
120 ((eq (car-safe a
) 'polar
)
121 (if (math-zerop (nth 1 a
))
123 (let ((sc (calcFunc-sincos (nth 2 a
))))
125 (math-mul (nth 1 a
) (nth 1 sc
))
126 (math-mul (nth 1 a
) (nth 2 sc
))))))
127 (t (list 'cplx a
0))))
129 ;;; Coerce A to be complex (polar form). [c N]
130 (defun math-polar (a)
131 (cond ((eq (car-safe a
) 'polar
) a
)
132 ((math-zerop a
) '(polar 0 0))
138 ;;; Multiply A by the imaginary constant i. [N N] [Public]
139 (defun math-imaginary (a)
140 (if (and (or (Math-objvecp a
) (math-infinitep a
))
141 (not calc-symbolic-mode
))
143 (if (or (eq (car-safe a
) 'polar
)
144 (and (not (eq (car-safe a
) 'cplx
))
145 (eq calc-complex-mode
'polar
)))
146 (list 'polar
1 (math-quarter-circle nil
))
148 (math-mul a
'(var i var-i
))))
153 (defun math-want-polar (a b
)
154 (cond ((eq (car-safe a
) 'polar
)
155 (if (eq (car-safe b
) 'cplx
)
156 (eq calc-complex-mode
'polar
)
158 ((eq (car-safe a
) 'cplx
)
159 (if (eq (car-safe b
) 'polar
)
160 (eq calc-complex-mode
'polar
)
162 ((eq (car-safe b
) 'polar
)
164 ((eq (car-safe b
) 'cplx
)
166 (t (eq calc-complex-mode
'polar
))))
168 ;;; Force A to be in the (-pi,pi] or (-180,180] range.
169 (defun math-fix-circular (a &optional dir
) ; [R R]
170 (cond ((eq (car-safe a
) 'hms
)
171 (cond ((and (Math-lessp 180 (nth 1 a
)) (not (eq dir
1)))
172 (math-fix-circular (math-add a
'(float -
36 1)) -
1))
173 ((or (Math-lessp -
180 (nth 1 a
)) (eq dir -
1))
176 (math-fix-circular (math-add a
'(float 36 1)) 1))))
177 ((eq calc-angle-mode
'rad
)
178 (cond ((and (Math-lessp (math-pi) a
) (not (eq dir
1)))
179 (math-fix-circular (math-sub a
(math-two-pi)) -
1))
180 ((or (Math-lessp (math-neg (math-pi)) a
) (eq dir -
1))
183 (math-fix-circular (math-add a
(math-two-pi)) 1))))
185 (cond ((and (Math-lessp '(float 18 1) a
) (not (eq dir
1)))
186 (math-fix-circular (math-add a
'(float -
36 1)) -
1))
187 ((or (Math-lessp '(float -
18 1) a
) (eq dir -
1))
190 (math-fix-circular (math-add a
'(float 36 1)) 1))))))
193 ;;;; Complex numbers.
195 (defun calcFunc-polar (a) ; [C N] [Public]
196 (cond ((Math-vectorp a
)
197 (math-map-vec 'calcFunc-polar a
))
200 (math-normalize (math-polar a
)))
201 (t (list 'calcFunc-polar a
))))
203 (defun calcFunc-rect (a) ; [N N] [Public]
204 (cond ((Math-vectorp a
)
205 (math-map-vec 'calcFunc-rect a
))
208 (math-normalize (math-complex a
)))
209 (t (list 'calcFunc-rect a
))))
211 ;;; Compute the complex conjugate of A. [O O] [Public]
212 (defun calcFunc-conj (a)
214 (cond ((Math-realp a
)
217 (list 'cplx
(nth 1 a
) (math-neg (nth 2 a
))))
219 (list 'polar
(nth 1 a
) (math-neg (nth 2 a
))))
221 (math-map-vec 'calcFunc-conj a
))
222 ((eq (car a
) 'calcFunc-conj
)
224 ((math-known-realp a
)
226 ((and (equal a
'(var i var-i
))
229 ((and (memq (car a
) '(+ -
* /))
231 (setq aa
(calcFunc-conj (nth 1 a
))
232 bb
(calcFunc-conj (nth 2 a
)))
233 (or (not (eq (car-safe aa
) 'calcFunc-conj
))
234 (not (eq (car-safe bb
) 'calcFunc-conj
)))))
243 (math-neg (calcFunc-conj (nth 1 a
))))
244 ((let ((inf (math-infinitep a
)))
246 (math-mul (calcFunc-conj (math-infinite-dir a inf
)) inf
))))
247 (t (calc-record-why 'numberp a
)
248 (list 'calcFunc-conj a
)))))
251 ;;; Compute the complex argument of A. [F N] [Public]
252 (defun calcFunc-arg (a)
253 (cond ((Math-anglep a
)
254 (if (math-negp a
) (math-half-circle nil
) 0))
255 ((eq (car-safe a
) 'cplx
)
256 (calcFunc-arctan2 (nth 2 a
) (nth 1 a
)))
257 ((eq (car-safe a
) 'polar
)
260 (math-map-vec 'calcFunc-arg a
))
261 ((and (equal a
'(var i var-i
))
263 (math-quarter-circle t
))
264 ((and (equal a
'(neg (var i var-i
)))
266 (math-neg (math-quarter-circle t
)))
267 ((let ((signs (math-possible-signs a
)))
268 (or (and (memq signs
'(2 4 6)) 0)
269 (and (eq signs
1) (math-half-circle nil
)))))
271 (if (or (equal a
'(var uinf var-uinf
))
272 (equal a
'(var nan var-nan
)))
274 (calcFunc-arg (math-infinite-dir a
))))
275 (t (calc-record-why 'numvecp a
)
276 (list 'calcFunc-arg a
))))
278 (defun math-imaginary-i ()
279 (let ((val (calc-var-value 'var-i
)))
280 (or (eq (car-safe val
) 'special-const
)
281 (equal val
'(cplx 0 1))
282 (and (eq (car-safe val
) 'polar
)
284 (Math-equal (nth 1 val
) (math-quarter-circle nil
))))))
286 ;;; Extract the real or complex part of a complex number. [R N] [Public]
287 ;;; Also extracts the real part of a modulo form.
288 (defun calcFunc-re (a)
290 (cond ((Math-realp a
) a
)
291 ((memq (car a
) '(mod cplx
))
294 (math-mul (nth 1 a
) (calcFunc-cos (nth 2 a
))))
296 (math-map-vec 'calcFunc-re a
))
297 ((math-known-realp a
) a
)
298 ((eq (car a
) 'calcFunc-conj
)
299 (calcFunc-re (nth 1 a
)))
300 ((and (equal a
'(var i var-i
))
303 ((and (memq (car a
) '(+ -
*))
305 (setq aa
(calcFunc-re (nth 1 a
))
306 bb
(calcFunc-re (nth 2 a
)))
307 (or (not (eq (car-safe aa
) 'calcFunc-re
))
308 (not (eq (car-safe bb
) 'calcFunc-re
)))))
313 (math-sub (math-mul aa bb
)
314 (math-mul (calcFunc-im (nth 1 a
))
315 (calcFunc-im (nth 2 a
)))))))
316 ((and (eq (car a
) '/)
317 (math-known-realp (nth 2 a
)))
318 (math-div (calcFunc-re (nth 1 a
)) (nth 2 a
)))
320 (math-neg (calcFunc-re (nth 1 a
))))
321 (t (calc-record-why 'numberp a
)
322 (list 'calcFunc-re a
)))))
324 (defun calcFunc-im (a)
326 (cond ((Math-realp a
)
327 (if (math-floatp a
) '(float 0 0) 0))
331 (math-mul (nth 1 a
) (calcFunc-sin (nth 2 a
))))
333 (math-map-vec 'calcFunc-im a
))
334 ((math-known-realp a
)
336 ((eq (car a
) 'calcFunc-conj
)
337 (math-neg (calcFunc-im (nth 1 a
))))
338 ((and (equal a
'(var i var-i
))
341 ((and (memq (car a
) '(+ -
*))
343 (setq aa
(calcFunc-im (nth 1 a
))
344 bb
(calcFunc-im (nth 2 a
)))
345 (or (not (eq (car-safe aa
) 'calcFunc-im
))
346 (not (eq (car-safe bb
) 'calcFunc-im
)))))
351 (math-add (math-mul (calcFunc-re (nth 1 a
)) bb
)
352 (math-mul aa
(calcFunc-re (nth 2 a
)))))))
353 ((and (eq (car a
) '/)
354 (math-known-realp (nth 2 a
)))
355 (math-div (calcFunc-im (nth 1 a
)) (nth 2 a
)))
357 (math-neg (calcFunc-im (nth 1 a
))))
358 (t (calc-record-why 'numberp a
)
359 (list 'calcFunc-im a
)))))
361 ;;; calc-cplx.el ends here
