1 ;;; calc-cplx.el --- Complex number functions for Calc
3 ;; Copyright (C) 1990-1993, 2001-2018 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
7 ;; This file is part of GNU Emacs.
9 ;; GNU Emacs is free software: you can redistribute it and/or modify
10 ;; it under the terms of the GNU General Public License as published by
11 ;; the Free Software Foundation, either version 3 of the License, or
12 ;; (at your option) any later version.
14 ;; GNU Emacs is distributed in the hope that it will be useful,
15 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
16 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
17 ;; GNU General Public License for more details.
19 ;; You should have received a copy of the GNU General Public License
20 ;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>.
26 ;; This file is autoloaded from calc-ext.el.
31 (defun calc-argument (arg)
34 (calc-unary-op "arg" 'calcFunc-arg arg
)))
39 (calc-unary-op "re" 'calcFunc-re arg
)))
44 (calc-unary-op "im" 'calcFunc-im arg
)))
50 (let ((arg (calc-top-n 1)))
51 (if (or (calc-is-inverse)
52 (eq (car-safe arg
) 'polar
))
53 (calc-enter-result 1 "p-r" (list 'calcFunc-rect arg
))
54 (calc-enter-result 1 "r-p" (list 'calcFunc-polar arg
))))))
59 (defun calc-complex-notation ()
62 (calc-change-mode 'calc-complex-format nil t
)
63 (message "Displaying complex numbers in (X,Y) format")))
65 (defun calc-i-notation ()
68 (calc-change-mode 'calc-complex-format
'i t
)
69 (message "Displaying complex numbers in X+Yi format")))
71 (defun calc-j-notation ()
74 (calc-change-mode 'calc-complex-format
'j t
)
75 (message "Displaying complex numbers in X+Yj format")))
78 (defun calc-polar-mode (n)
82 (> (prefix-numeric-value n
) 0)
83 (eq calc-complex-mode
'cplx
))
85 (calc-change-mode 'calc-complex-mode
'polar
)
86 (message "Preferred complex form is polar"))
87 (calc-change-mode 'calc-complex-mode
'cplx
)
88 (message "Preferred complex form is rectangular"))))
93 (defun math-normalize-polar (a)
94 (let ((r (math-normalize (nth 1 a
)))
95 (th (math-normalize (nth 2 a
))))
100 ((and (not (eq calc-angle-mode
'rad
))
101 (or (equal th
'(float 18 1))
105 (math-neg (list 'polar
(math-neg r
) th
)))
107 (list 'polar r th
)))))
110 ;;; Coerce A to be complex (rectangular form). [c N]
111 (defun math-complex (a)
112 (cond ((eq (car-safe a
) 'cplx
) a
)
113 ((eq (car-safe a
) 'polar
)
114 (if (math-zerop (nth 1 a
))
116 (let ((sc (calcFunc-sincos (nth 2 a
))))
118 (math-mul (nth 1 a
) (nth 1 sc
))
119 (math-mul (nth 1 a
) (nth 2 sc
))))))
120 (t (list 'cplx a
0))))
122 ;;; Coerce A to be complex (polar form). [c N]
123 (defun math-polar (a)
124 (cond ((eq (car-safe a
) 'polar
) a
)
125 ((math-zerop a
) '(polar 0 0))
131 ;;; Multiply A by the imaginary constant i. [N N] [Public]
132 (defun math-imaginary (a)
133 (if (and (or (Math-objvecp a
) (math-infinitep a
))
134 (not calc-symbolic-mode
))
136 (if (or (eq (car-safe a
) 'polar
)
137 (and (not (eq (car-safe a
) 'cplx
))
138 (eq calc-complex-mode
'polar
)))
139 (list 'polar
1 (math-quarter-circle nil
))
141 (math-mul a
'(var i var-i
))))
146 (defun math-want-polar (a b
)
147 (cond ((eq (car-safe a
) 'polar
)
148 (if (eq (car-safe b
) 'cplx
)
149 (eq calc-complex-mode
'polar
)
151 ((eq (car-safe a
) 'cplx
)
152 (if (eq (car-safe b
) 'polar
)
153 (eq calc-complex-mode
'polar
)
155 ((eq (car-safe b
) 'polar
)
157 ((eq (car-safe b
) 'cplx
)
159 (t (eq calc-complex-mode
'polar
))))
161 ;;; Force A to be in the (-pi,pi] or (-180,180] range.
162 (defun math-fix-circular (a &optional dir
) ; [R R]
163 (cond ((eq (car-safe a
) 'hms
)
164 (cond ((and (Math-lessp 180 (nth 1 a
)) (not (eq dir
1)))
165 (math-fix-circular (math-add a
'(float -
36 1)) -
1))
166 ((or (Math-lessp -
180 (nth 1 a
)) (eq dir -
1))
169 (math-fix-circular (math-add a
'(float 36 1)) 1))))
170 ((eq calc-angle-mode
'rad
)
171 (cond ((and (Math-lessp (math-pi) a
) (not (eq dir
1)))
172 (math-fix-circular (math-sub a
(math-two-pi)) -
1))
173 ((or (Math-lessp (math-neg (math-pi)) a
) (eq dir -
1))
176 (math-fix-circular (math-add a
(math-two-pi)) 1))))
178 (cond ((and (Math-lessp '(float 18 1) a
) (not (eq dir
1)))
179 (math-fix-circular (math-add a
'(float -
36 1)) -
1))
180 ((or (Math-lessp '(float -
18 1) a
) (eq dir -
1))
183 (math-fix-circular (math-add a
'(float 36 1)) 1))))))
186 ;;;; Complex numbers.
188 (defun calcFunc-polar (a) ; [C N] [Public]
189 (cond ((Math-vectorp a
)
190 (math-map-vec 'calcFunc-polar a
))
193 (math-normalize (math-polar a
)))
194 (t (list 'calcFunc-polar a
))))
196 (defun calcFunc-rect (a) ; [N N] [Public]
197 (cond ((Math-vectorp a
)
198 (math-map-vec 'calcFunc-rect a
))
201 (math-normalize (math-complex a
)))
202 (t (list 'calcFunc-rect a
))))
204 ;;; Compute the complex conjugate of A. [O O] [Public]
205 (defun calcFunc-conj (a)
207 (cond ((Math-realp a
)
210 (list 'cplx
(nth 1 a
) (math-neg (nth 2 a
))))
212 (list 'polar
(nth 1 a
) (math-neg (nth 2 a
))))
214 (math-map-vec 'calcFunc-conj a
))
215 ((eq (car a
) 'calcFunc-conj
)
217 ((math-known-realp a
)
219 ((and (equal a
'(var i var-i
))
222 ((and (memq (car a
) '(+ -
* /))
224 (setq aa
(calcFunc-conj (nth 1 a
))
225 bb
(calcFunc-conj (nth 2 a
)))
226 (or (not (eq (car-safe aa
) 'calcFunc-conj
))
227 (not (eq (car-safe bb
) 'calcFunc-conj
)))))
236 (math-neg (calcFunc-conj (nth 1 a
))))
237 ((let ((inf (math-infinitep a
)))
239 (math-mul (calcFunc-conj (math-infinite-dir a inf
)) inf
))))
240 (t (calc-record-why 'numberp a
)
241 (list 'calcFunc-conj a
)))))
244 ;;; Compute the complex argument of A. [F N] [Public]
245 (defun calcFunc-arg (a)
246 (cond ((Math-anglep a
)
247 (if (math-negp a
) (math-half-circle nil
) 0))
248 ((eq (car-safe a
) 'cplx
)
249 (calcFunc-arctan2 (nth 2 a
) (nth 1 a
)))
250 ((eq (car-safe a
) 'polar
)
253 (math-map-vec 'calcFunc-arg a
))
254 ((and (equal a
'(var i var-i
))
256 (math-quarter-circle t
))
257 ((and (equal a
'(neg (var i var-i
)))
259 (math-neg (math-quarter-circle t
)))
260 ((let ((signs (math-possible-signs a
)))
261 (or (and (memq signs
'(2 4 6)) 0)
262 (and (eq signs
1) (math-half-circle nil
)))))
264 (if (or (equal a
'(var uinf var-uinf
))
265 (equal a
'(var nan var-nan
)))
267 (calcFunc-arg (math-infinite-dir a
))))
268 (t (calc-record-why 'numvecp a
)
269 (list 'calcFunc-arg a
))))
271 (defun math-imaginary-i ()
272 (let ((val (calc-var-value 'var-i
)))
273 (or (eq (car-safe val
) 'special-const
)
274 (equal val
'(cplx 0 1))
275 (and (eq (car-safe val
) 'polar
)
277 (Math-equal (nth 1 val
) (math-quarter-circle nil
))))))
279 ;;; Extract the real or complex part of a complex number. [R N] [Public]
280 ;;; Also extracts the real part of a modulo form.
281 (defun calcFunc-re (a)
283 (cond ((Math-realp a
) a
)
284 ((memq (car a
) '(mod cplx
))
287 (math-mul (nth 1 a
) (calcFunc-cos (nth 2 a
))))
289 (math-map-vec 'calcFunc-re a
))
290 ((math-known-realp a
) a
)
291 ((eq (car a
) 'calcFunc-conj
)
292 (calcFunc-re (nth 1 a
)))
293 ((and (equal a
'(var i var-i
))
296 ((and (memq (car a
) '(+ -
*))
298 (setq aa
(calcFunc-re (nth 1 a
))
299 bb
(calcFunc-re (nth 2 a
)))
300 (or (not (eq (car-safe aa
) 'calcFunc-re
))
301 (not (eq (car-safe bb
) 'calcFunc-re
)))))
306 (math-sub (math-mul aa bb
)
307 (math-mul (calcFunc-im (nth 1 a
))
308 (calcFunc-im (nth 2 a
)))))))
309 ((and (eq (car a
) '/)
310 (math-known-realp (nth 2 a
)))
311 (math-div (calcFunc-re (nth 1 a
)) (nth 2 a
)))
313 (math-neg (calcFunc-re (nth 1 a
))))
314 (t (calc-record-why 'numberp a
)
315 (list 'calcFunc-re a
)))))
317 (defun calcFunc-im (a)
319 (cond ((Math-realp a
)
320 (if (math-floatp a
) '(float 0 0) 0))
324 (math-mul (nth 1 a
) (calcFunc-sin (nth 2 a
))))
326 (math-map-vec 'calcFunc-im a
))
327 ((math-known-realp a
)
329 ((eq (car a
) 'calcFunc-conj
)
330 (math-neg (calcFunc-im (nth 1 a
))))
331 ((and (equal a
'(var i var-i
))
334 ((and (memq (car a
) '(+ -
*))
336 (setq aa
(calcFunc-im (nth 1 a
))
337 bb
(calcFunc-im (nth 2 a
)))
338 (or (not (eq (car-safe aa
) 'calcFunc-im
))
339 (not (eq (car-safe bb
) 'calcFunc-im
)))))
344 (math-add (math-mul (calcFunc-re (nth 1 a
)) bb
)
345 (math-mul aa
(calcFunc-re (nth 2 a
)))))))
346 ((and (eq (car a
) '/)
347 (math-known-realp (nth 2 a
)))
348 (math-div (calcFunc-im (nth 1 a
)) (nth 2 a
)))
350 (math-neg (calcFunc-im (nth 1 a
))))
351 (t (calc-record-why 'numberp a
)
352 (list 'calcFunc-im a
)))))
356 ;;; calc-cplx.el ends here
