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3132f345 CW |
1 | ;;; calc-cplx.el --- Complex number functions for Calc |
2 | ||
bf77c646 | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc. |
3132f345 CW |
4 | |
5 | ;; Author: David Gillespie <daveg@synaptics.com> | |
a1506d29 | 6 | ;; Maintainers: D. Goel <deego@gnufans.org> |
6e1c888a | 7 | ;; Colin Walters <walters@debian.org> |
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8 | |
9 | ;; This file is part of GNU Emacs. | |
10 | ||
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. | |
17 | ||
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. | |
25 | ||
3132f345 | 26 | ;;; Commentary: |
136211a9 | 27 | |
3132f345 | 28 | ;;; Code: |
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29 | |
30 | ;; This file is autoloaded from calc-ext.el. | |
31 | (require 'calc-ext) | |
32 | ||
33 | (require 'calc-macs) | |
34 | ||
35 | (defun calc-Need-calc-cplx () nil) | |
36 | ||
37 | ||
38 | (defun calc-argument (arg) | |
39 | (interactive "P") | |
40 | (calc-slow-wrapper | |
bf77c646 | 41 | (calc-unary-op "arg" 'calcFunc-arg arg))) |
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42 | |
43 | (defun calc-re (arg) | |
44 | (interactive "P") | |
45 | (calc-slow-wrapper | |
bf77c646 | 46 | (calc-unary-op "re" 'calcFunc-re arg))) |
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47 | |
48 | (defun calc-im (arg) | |
49 | (interactive "P") | |
50 | (calc-slow-wrapper | |
bf77c646 | 51 | (calc-unary-op "im" 'calcFunc-im arg))) |
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52 | |
53 | ||
54 | (defun calc-polar () | |
55 | (interactive) | |
56 | (calc-slow-wrapper | |
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)) | |
bf77c646 | 61 | (calc-enter-result 1 "r-p" (list 'calcFunc-polar arg)))))) |
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62 | |
63 | ||
64 | ||
65 | ||
66 | (defun calc-complex-notation () | |
67 | (interactive) | |
68 | (calc-wrapper | |
69 | (calc-change-mode 'calc-complex-format nil t) | |
3132f345 | 70 | (message "Displaying complex numbers in (X,Y) format"))) |
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71 | |
72 | (defun calc-i-notation () | |
73 | (interactive) | |
74 | (calc-wrapper | |
75 | (calc-change-mode 'calc-complex-format 'i t) | |
3132f345 | 76 | (message "Displaying complex numbers in X+Yi format"))) |
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77 | |
78 | (defun calc-j-notation () | |
79 | (interactive) | |
80 | (calc-wrapper | |
81 | (calc-change-mode 'calc-complex-format 'j t) | |
3132f345 | 82 | (message "Displaying complex numbers in X+Yj format"))) |
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83 | |
84 | ||
85 | (defun calc-polar-mode (n) | |
86 | (interactive "P") | |
87 | (calc-wrapper | |
88 | (if (if n | |
89 | (> (prefix-numeric-value n) 0) | |
90 | (eq calc-complex-mode 'cplx)) | |
91 | (progn | |
92 | (calc-change-mode 'calc-complex-mode 'polar) | |
3132f345 | 93 | (message "Preferred complex form is polar")) |
136211a9 | 94 | (calc-change-mode 'calc-complex-mode 'cplx) |
3132f345 | 95 | (message "Preferred complex form is rectangular")))) |
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96 | |
97 | ||
98 | ;;;; Complex numbers. | |
99 | ||
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) | |
104 | '(polar 0 0)) | |
105 | ((or (math-zerop th)) | |
106 | r) | |
107 | ((and (not (eq calc-angle-mode 'rad)) | |
108 | (or (equal th '(float 18 1)) | |
109 | (equal th 180))) | |
110 | (math-neg r)) | |
111 | ((math-negp r) | |
112 | (math-neg (list 'polar (math-neg r) th))) | |
113 | (t | |
bf77c646 | 114 | (list 'polar r th))))) |
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115 | |
116 | ||
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)) | |
122 | (nth 1 a) | |
123 | (let ((sc (calcFunc-sincos (nth 2 a)))) | |
124 | (list 'cplx | |
125 | (math-mul (nth 1 a) (nth 1 sc)) | |
126 | (math-mul (nth 1 a) (nth 2 sc)))))) | |
bf77c646 | 127 | (t (list 'cplx a 0)))) |
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128 | |
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)) | |
133 | (t | |
134 | (list 'polar | |
135 | (math-abs a) | |
bf77c646 | 136 | (calcFunc-arg a))))) |
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137 | |
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)) | |
142 | (math-mul a | |
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)) | |
147 | '(cplx 0 1))) | |
bf77c646 | 148 | (math-mul a '(var i var-i)))) |
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149 | |
150 | ||
151 | ||
152 | ||
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) | |
157 | t)) | |
158 | ((eq (car-safe a) 'cplx) | |
159 | (if (eq (car-safe b) 'polar) | |
160 | (eq calc-complex-mode 'polar) | |
161 | nil)) | |
162 | ((eq (car-safe b) 'polar) | |
163 | t) | |
164 | ((eq (car-safe b) 'cplx) | |
165 | nil) | |
bf77c646 | 166 | (t (eq calc-complex-mode 'polar)))) |
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167 | |
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)) | |
174 | a) | |
175 | (t | |
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)) | |
181 | a) | |
182 | (t | |
183 | (math-fix-circular (math-add a (math-two-pi)) 1)))) | |
184 | (t | |
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)) | |
188 | a) | |
189 | (t | |
bf77c646 | 190 | (math-fix-circular (math-add a '(float 36 1)) 1)))))) |
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191 | |
192 | ||
193 | ;;;; Complex numbers. | |
194 | ||
195 | (defun calcFunc-polar (a) ; [C N] [Public] | |
196 | (cond ((Math-vectorp a) | |
197 | (math-map-vec 'calcFunc-polar a)) | |
198 | ((Math-realp a) a) | |
199 | ((Math-numberp a) | |
200 | (math-normalize (math-polar a))) | |
bf77c646 | 201 | (t (list 'calcFunc-polar a)))) |
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202 | |
203 | (defun calcFunc-rect (a) ; [N N] [Public] | |
204 | (cond ((Math-vectorp a) | |
205 | (math-map-vec 'calcFunc-rect a)) | |
206 | ((Math-realp a) a) | |
207 | ((Math-numberp a) | |
208 | (math-normalize (math-complex a))) | |
bf77c646 | 209 | (t (list 'calcFunc-rect a)))) |
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210 | |
211 | ;;; Compute the complex conjugate of A. [O O] [Public] | |
212 | (defun calcFunc-conj (a) | |
213 | (let (aa bb) | |
214 | (cond ((Math-realp a) | |
215 | a) | |
216 | ((eq (car a) 'cplx) | |
217 | (list 'cplx (nth 1 a) (math-neg (nth 2 a)))) | |
218 | ((eq (car a) 'polar) | |
219 | (list 'polar (nth 1 a) (math-neg (nth 2 a)))) | |
220 | ((eq (car a) 'vec) | |
221 | (math-map-vec 'calcFunc-conj a)) | |
222 | ((eq (car a) 'calcFunc-conj) | |
223 | (nth 1 a)) | |
224 | ((math-known-realp a) | |
225 | a) | |
226 | ((and (equal a '(var i var-i)) | |
227 | (math-imaginary-i)) | |
228 | (math-neg a)) | |
229 | ((and (memq (car a) '(+ - * /)) | |
230 | (progn | |
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))))) | |
235 | (if (eq (car a) '+) | |
236 | (math-add aa bb) | |
237 | (if (eq (car a) '-) | |
238 | (math-sub aa bb) | |
239 | (if (eq (car a) '*) | |
240 | (math-mul aa bb) | |
241 | (math-div aa bb))))) | |
242 | ((eq (car a) 'neg) | |
243 | (math-neg (calcFunc-conj (nth 1 a)))) | |
244 | ((let ((inf (math-infinitep a))) | |
245 | (and inf | |
246 | (math-mul (calcFunc-conj (math-infinite-dir a inf)) inf)))) | |
247 | (t (calc-record-why 'numberp a) | |
bf77c646 | 248 | (list 'calcFunc-conj a))))) |
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249 | |
250 | ||
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) | |
258 | (nth 2 a)) | |
259 | ((eq (car a) 'vec) | |
260 | (math-map-vec 'calcFunc-arg a)) | |
261 | ((and (equal a '(var i var-i)) | |
262 | (math-imaginary-i)) | |
263 | (math-quarter-circle t)) | |
264 | ((and (equal a '(neg (var i var-i))) | |
265 | (math-imaginary-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))))) | |
270 | ((math-infinitep a) | |
271 | (if (or (equal a '(var uinf var-uinf)) | |
272 | (equal a '(var nan var-nan))) | |
273 | '(var nan var-nan) | |
274 | (calcFunc-arg (math-infinite-dir a)))) | |
275 | (t (calc-record-why 'numvecp a) | |
bf77c646 | 276 | (list 'calcFunc-arg a)))) |
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277 | |
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) | |
283 | (eq (nth 1 val) 0) | |
bf77c646 | 284 | (Math-equal (nth 1 val) (math-quarter-circle nil)))))) |
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285 | |
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) | |
289 | (let (aa bb) | |
290 | (cond ((Math-realp a) a) | |
291 | ((memq (car a) '(mod cplx)) | |
292 | (nth 1 a)) | |
293 | ((eq (car a) 'polar) | |
294 | (math-mul (nth 1 a) (calcFunc-cos (nth 2 a)))) | |
295 | ((eq (car a) 'vec) | |
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)) | |
301 | (math-imaginary-i)) | |
302 | 0) | |
303 | ((and (memq (car a) '(+ - *)) | |
304 | (progn | |
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))))) | |
309 | (if (eq (car a) '+) | |
310 | (math-add aa bb) | |
311 | (if (eq (car a) '-) | |
312 | (math-sub aa bb) | |
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))) | |
319 | ((eq (car a) 'neg) | |
320 | (math-neg (calcFunc-re (nth 1 a)))) | |
321 | (t (calc-record-why 'numberp a) | |
bf77c646 | 322 | (list 'calcFunc-re a))))) |
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323 | |
324 | (defun calcFunc-im (a) | |
325 | (let (aa bb) | |
326 | (cond ((Math-realp a) | |
327 | (if (math-floatp a) '(float 0 0) 0)) | |
328 | ((eq (car a) 'cplx) | |
329 | (nth 2 a)) | |
330 | ((eq (car a) 'polar) | |
331 | (math-mul (nth 1 a) (calcFunc-sin (nth 2 a)))) | |
332 | ((eq (car a) 'vec) | |
333 | (math-map-vec 'calcFunc-im a)) | |
334 | ((math-known-realp a) | |
335 | 0) | |
336 | ((eq (car a) 'calcFunc-conj) | |
337 | (math-neg (calcFunc-im (nth 1 a)))) | |
338 | ((and (equal a '(var i var-i)) | |
339 | (math-imaginary-i)) | |
340 | 1) | |
341 | ((and (memq (car a) '(+ - *)) | |
342 | (progn | |
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))))) | |
347 | (if (eq (car a) '+) | |
348 | (math-add aa bb) | |
349 | (if (eq (car a) '-) | |
350 | (math-sub aa bb) | |
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))) | |
356 | ((eq (car a) 'neg) | |
357 | (math-neg (calcFunc-im (nth 1 a)))) | |
358 | (t (calc-record-why 'numberp a) | |
bf77c646 | 359 | (list 'calcFunc-im a))))) |
136211a9 | 360 | |
bf77c646 | 361 | ;;; calc-cplx.el ends here |