calc-cplx.el 10 KB
Newer Older
1 2
;;; calc-cplx.el --- Complex number functions for Calc

Jay Belanger's avatar
Jay Belanger committed
3
;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
Glenn Morris's avatar
Glenn Morris committed
4
;;   2005, 2006, 2007 Free Software Foundation, Inc.
5 6

;; Author: David Gillespie <daveg@synaptics.com>
Jay Belanger's avatar
Jay Belanger committed
7
;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
Eli Zaretskii's avatar
Eli Zaretskii committed
8 9 10

;; This file is part of GNU Emacs.

11 12 13 14 15
;; GNU Emacs is free software; you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation; either version 2, or (at your option)
;; any later version.

Eli Zaretskii's avatar
Eli Zaretskii committed
16
;; GNU Emacs is distributed in the hope that it will be useful,
17 18 19 20 21 22 23 24
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
;; GNU General Public License for more details.

;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs; see the file COPYING.  If not, write to the
;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
;; Boston, MA 02110-1301, USA.
Eli Zaretskii's avatar
Eli Zaretskii committed
25

26
;;; Commentary:
Eli Zaretskii's avatar
Eli Zaretskii committed
27

28
;;; Code:
Eli Zaretskii's avatar
Eli Zaretskii committed
29 30 31

;; This file is autoloaded from calc-ext.el.

Jay Belanger's avatar
Jay Belanger committed
32
(require 'calc-ext)
Eli Zaretskii's avatar
Eli Zaretskii committed
33 34 35 36 37
(require 'calc-macs)

(defun calc-argument (arg)
  (interactive "P")
  (calc-slow-wrapper
38
   (calc-unary-op "arg" 'calcFunc-arg arg)))
Eli Zaretskii's avatar
Eli Zaretskii committed
39 40 41 42

(defun calc-re (arg)
  (interactive "P")
  (calc-slow-wrapper
43
   (calc-unary-op "re" 'calcFunc-re arg)))
Eli Zaretskii's avatar
Eli Zaretskii committed
44 45 46 47

(defun calc-im (arg)
  (interactive "P")
  (calc-slow-wrapper
48
   (calc-unary-op "im" 'calcFunc-im arg)))
Eli Zaretskii's avatar
Eli Zaretskii committed
49 50 51 52 53 54 55 56 57


(defun calc-polar ()
  (interactive)
  (calc-slow-wrapper
   (let ((arg (calc-top-n 1)))
     (if (or (calc-is-inverse)
	     (eq (car-safe arg) 'polar))
	 (calc-enter-result 1 "p-r" (list 'calcFunc-rect arg))
58
       (calc-enter-result 1 "r-p" (list 'calcFunc-polar arg))))))
Eli Zaretskii's avatar
Eli Zaretskii committed
59 60 61 62 63 64 65 66




(defun calc-complex-notation ()
  (interactive)
  (calc-wrapper
   (calc-change-mode 'calc-complex-format nil t)
67
   (message "Displaying complex numbers in (X,Y) format")))
Eli Zaretskii's avatar
Eli Zaretskii committed
68 69 70 71 72

(defun calc-i-notation ()
  (interactive)
  (calc-wrapper
   (calc-change-mode 'calc-complex-format 'i t)
73
   (message "Displaying complex numbers in X+Yi format")))
Eli Zaretskii's avatar
Eli Zaretskii committed
74 75 76 77 78

(defun calc-j-notation ()
  (interactive)
  (calc-wrapper
   (calc-change-mode 'calc-complex-format 'j t)
79
   (message "Displaying complex numbers in X+Yj format")))
Eli Zaretskii's avatar
Eli Zaretskii committed
80 81 82 83 84 85 86 87 88 89


(defun calc-polar-mode (n)
  (interactive "P")
  (calc-wrapper
   (if (if n
	   (> (prefix-numeric-value n) 0)
	 (eq calc-complex-mode 'cplx))
       (progn
	 (calc-change-mode 'calc-complex-mode 'polar)
90
	 (message "Preferred complex form is polar"))
Eli Zaretskii's avatar
Eli Zaretskii committed
91
     (calc-change-mode 'calc-complex-mode 'cplx)
92
     (message "Preferred complex form is rectangular"))))
Eli Zaretskii's avatar
Eli Zaretskii committed
93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110


;;;; Complex numbers.

(defun math-normalize-polar (a)
  (let ((r (math-normalize (nth 1 a)))
	(th (math-normalize (nth 2 a))))
    (cond ((math-zerop r)
	   '(polar 0 0))
	  ((or (math-zerop th))
	   r)
	  ((and (not (eq calc-angle-mode 'rad))
		(or (equal th '(float 18 1))
		    (equal th 180)))
	   (math-neg r))
	  ((math-negp r)
	   (math-neg (list 'polar (math-neg r) th)))
	  (t
111
	   (list 'polar r th)))))
Eli Zaretskii's avatar
Eli Zaretskii committed
112 113 114 115 116 117 118 119 120 121 122 123


;;; Coerce A to be complex (rectangular form).  [c N]
(defun math-complex (a)
  (cond ((eq (car-safe a) 'cplx) a)
	((eq (car-safe a) 'polar)
	 (if (math-zerop (nth 1 a))
	     (nth 1 a)
	   (let ((sc (calcFunc-sincos (nth 2 a))))
	     (list 'cplx
		   (math-mul (nth 1 a) (nth 1 sc))
		   (math-mul (nth 1 a) (nth 2 sc))))))
124
	(t (list 'cplx a 0))))
Eli Zaretskii's avatar
Eli Zaretskii committed
125 126 127 128 129 130 131 132

;;; Coerce A to be complex (polar form).  [c N]
(defun math-polar (a)
  (cond ((eq (car-safe a) 'polar) a)
	((math-zerop a) '(polar 0 0))
	(t
	 (list 'polar
	       (math-abs a)
133
	       (calcFunc-arg a)))))
Eli Zaretskii's avatar
Eli Zaretskii committed
134 135 136 137 138 139 140 141 142 143 144

;;; Multiply A by the imaginary constant i.  [N N] [Public]
(defun math-imaginary (a)
  (if (and (or (Math-objvecp a) (math-infinitep a))
	   (not calc-symbolic-mode))
      (math-mul a
		(if (or (eq (car-safe a) 'polar)
			(and (not (eq (car-safe a) 'cplx))
			     (eq calc-complex-mode 'polar)))
		    (list 'polar 1 (math-quarter-circle nil))
		  '(cplx 0 1)))
145
    (math-mul a '(var i var-i))))
Eli Zaretskii's avatar
Eli Zaretskii committed
146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162




(defun math-want-polar (a b)
  (cond ((eq (car-safe a) 'polar)
	 (if (eq (car-safe b) 'cplx)
	     (eq calc-complex-mode 'polar)
	   t))
	((eq (car-safe a) 'cplx)
	 (if (eq (car-safe b) 'polar)
	     (eq calc-complex-mode 'polar)
	   nil))
	((eq (car-safe b) 'polar)
	 t)
	((eq (car-safe b) 'cplx)
	 nil)
163
	(t (eq calc-complex-mode 'polar))))
Eli Zaretskii's avatar
Eli Zaretskii committed
164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186

;;; Force A to be in the (-pi,pi] or (-180,180] range.
(defun math-fix-circular (a &optional dir)   ; [R R]
  (cond ((eq (car-safe a) 'hms)
	 (cond ((and (Math-lessp 180 (nth 1 a)) (not (eq dir 1)))
		(math-fix-circular (math-add a '(float -36 1)) -1))
	       ((or (Math-lessp -180 (nth 1 a)) (eq dir -1))
		a)
	       (t
		(math-fix-circular (math-add a '(float 36 1)) 1))))
	((eq calc-angle-mode 'rad)
	 (cond ((and (Math-lessp (math-pi) a) (not (eq dir 1)))
		(math-fix-circular (math-sub a (math-two-pi)) -1))
	       ((or (Math-lessp (math-neg (math-pi)) a) (eq dir -1))
		a)
	       (t
		(math-fix-circular (math-add a (math-two-pi)) 1))))
	(t
	 (cond ((and (Math-lessp '(float 18 1) a) (not (eq dir 1)))
		(math-fix-circular (math-add a '(float -36 1)) -1))
	       ((or (Math-lessp '(float -18 1) a) (eq dir -1))
		a)
	       (t
187
		(math-fix-circular (math-add a '(float 36 1)) 1))))))
Eli Zaretskii's avatar
Eli Zaretskii committed
188 189 190 191 192 193 194 195 196 197


;;;; Complex numbers.

(defun calcFunc-polar (a)   ; [C N] [Public]
  (cond ((Math-vectorp a)
	 (math-map-vec 'calcFunc-polar a))
	((Math-realp a) a)
	((Math-numberp a)
	 (math-normalize (math-polar a)))
198
	(t (list 'calcFunc-polar a))))
Eli Zaretskii's avatar
Eli Zaretskii committed
199 200 201 202 203 204 205

(defun calcFunc-rect (a)   ; [N N] [Public]
  (cond ((Math-vectorp a)
	 (math-map-vec 'calcFunc-rect a))
	((Math-realp a) a)
	((Math-numberp a)
	 (math-normalize (math-complex a)))
206
	(t (list 'calcFunc-rect a))))
Eli Zaretskii's avatar
Eli Zaretskii committed
207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244

;;; Compute the complex conjugate of A.  [O O] [Public]
(defun calcFunc-conj (a)
  (let (aa bb)
    (cond ((Math-realp a)
	   a)
	  ((eq (car a) 'cplx)
	   (list 'cplx (nth 1 a) (math-neg (nth 2 a))))
	  ((eq (car a) 'polar)
	   (list 'polar (nth 1 a) (math-neg (nth 2 a))))
	  ((eq (car a) 'vec)
	   (math-map-vec 'calcFunc-conj a))
	  ((eq (car a) 'calcFunc-conj)
	   (nth 1 a))
	  ((math-known-realp a)
	   a)
	  ((and (equal a '(var i var-i))
		(math-imaginary-i))
	   (math-neg a))
	  ((and (memq (car a) '(+ - * /))
		(progn
		  (setq aa (calcFunc-conj (nth 1 a))
			bb (calcFunc-conj (nth 2 a)))
		  (or (not (eq (car-safe aa) 'calcFunc-conj))
		      (not (eq (car-safe bb) 'calcFunc-conj)))))
	   (if (eq (car a) '+)
	       (math-add aa bb)
	     (if (eq (car a) '-)
		 (math-sub aa bb)
	       (if (eq (car a) '*)
		   (math-mul aa bb)
		 (math-div aa bb)))))
	  ((eq (car a) 'neg)
	   (math-neg (calcFunc-conj (nth 1 a))))
	  ((let ((inf (math-infinitep a)))
	     (and inf
		  (math-mul (calcFunc-conj (math-infinite-dir a inf)) inf))))
	  (t (calc-record-why 'numberp a)
245
	     (list 'calcFunc-conj a)))))
Eli Zaretskii's avatar
Eli Zaretskii committed
246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272


;;; Compute the complex argument of A.  [F N] [Public]
(defun calcFunc-arg (a)
  (cond ((Math-anglep a)
	 (if (math-negp a) (math-half-circle nil) 0))
	((eq (car-safe a) 'cplx)
	 (calcFunc-arctan2 (nth 2 a) (nth 1 a)))
	((eq (car-safe a) 'polar)
	 (nth 2 a))
	((eq (car a) 'vec)
	 (math-map-vec 'calcFunc-arg a))
	((and (equal a '(var i var-i))
	      (math-imaginary-i))
	 (math-quarter-circle t))
	((and (equal a '(neg (var i var-i)))
	      (math-imaginary-i))
	 (math-neg (math-quarter-circle t)))
	((let ((signs (math-possible-signs a)))
	   (or (and (memq signs '(2 4 6)) 0)
	       (and (eq signs 1) (math-half-circle nil)))))
	((math-infinitep a)
	 (if (or (equal a '(var uinf var-uinf))
		 (equal a '(var nan var-nan)))
	     '(var nan var-nan)
	   (calcFunc-arg (math-infinite-dir a))))
	(t (calc-record-why 'numvecp a)
273
	   (list 'calcFunc-arg a))))
Eli Zaretskii's avatar
Eli Zaretskii committed
274 275 276 277 278 279 280

(defun math-imaginary-i ()
  (let ((val (calc-var-value 'var-i)))
    (or (eq (car-safe val) 'special-const)
	(equal val '(cplx 0 1))
	(and (eq (car-safe val) 'polar)
	     (eq (nth 1 val) 0)
281
	     (Math-equal (nth 1 val) (math-quarter-circle nil))))))
Eli Zaretskii's avatar
Eli Zaretskii committed
282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318

;;; Extract the real or complex part of a complex number.  [R N] [Public]
;;; Also extracts the real part of a modulo form.
(defun calcFunc-re (a)
  (let (aa bb)
    (cond ((Math-realp a) a)
	  ((memq (car a) '(mod cplx))
	   (nth 1 a))
	  ((eq (car a) 'polar)
	   (math-mul (nth 1 a) (calcFunc-cos (nth 2 a))))
	  ((eq (car a) 'vec)
	   (math-map-vec 'calcFunc-re a))
	  ((math-known-realp a) a)
	  ((eq (car a) 'calcFunc-conj)
	   (calcFunc-re (nth 1 a)))
	  ((and (equal a '(var i var-i))
		(math-imaginary-i))
	   0)
	  ((and (memq (car a) '(+ - *))
		(progn
		  (setq aa (calcFunc-re (nth 1 a))
			bb (calcFunc-re (nth 2 a)))
		  (or (not (eq (car-safe aa) 'calcFunc-re))
		      (not (eq (car-safe bb) 'calcFunc-re)))))
	   (if (eq (car a) '+)
	       (math-add aa bb)
	     (if (eq (car a) '-)
		 (math-sub aa bb)
	       (math-sub (math-mul aa bb)
			 (math-mul (calcFunc-im (nth 1 a))
				   (calcFunc-im (nth 2 a)))))))
	  ((and (eq (car a) '/)
		(math-known-realp (nth 2 a)))
	   (math-div (calcFunc-re (nth 1 a)) (nth 2 a)))
	  ((eq (car a) 'neg)
	   (math-neg (calcFunc-re (nth 1 a))))
	  (t (calc-record-why 'numberp a)
319
	     (list 'calcFunc-re a)))))
Eli Zaretskii's avatar
Eli Zaretskii committed
320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355

(defun calcFunc-im (a)
  (let (aa bb)
    (cond ((Math-realp a)
	   (if (math-floatp a) '(float 0 0) 0))
	  ((eq (car a) 'cplx)
	   (nth 2 a))
	  ((eq (car a) 'polar)
	   (math-mul (nth 1 a) (calcFunc-sin (nth 2 a))))
	  ((eq (car a) 'vec)
	   (math-map-vec 'calcFunc-im a))
	  ((math-known-realp a)
	   0)
	  ((eq (car a) 'calcFunc-conj)
	   (math-neg (calcFunc-im (nth 1 a))))
	  ((and (equal a '(var i var-i))
		(math-imaginary-i))
	   1)
	  ((and (memq (car a) '(+ - *))
		(progn
		  (setq aa (calcFunc-im (nth 1 a))
			bb (calcFunc-im (nth 2 a)))
		  (or (not (eq (car-safe aa) 'calcFunc-im))
		      (not (eq (car-safe bb) 'calcFunc-im)))))
	   (if (eq (car a) '+)
	       (math-add aa bb)
	     (if (eq (car a) '-)
		 (math-sub aa bb)
	       (math-add (math-mul (calcFunc-re (nth 1 a)) bb)
			 (math-mul aa (calcFunc-re (nth 2 a)))))))
	  ((and (eq (car a) '/)
		(math-known-realp (nth 2 a)))
	   (math-div (calcFunc-im (nth 1 a)) (nth 2 a)))
	  ((eq (car a) 'neg)
	   (math-neg (calcFunc-im (nth 1 a))))
	  (t (calc-record-why 'numberp a)
356
	     (list 'calcFunc-im a)))))
Eli Zaretskii's avatar
Eli Zaretskii committed
357

Jay Belanger's avatar
Jay Belanger committed
358 359
(provide 'calc-cplx)

Miles Bader's avatar
Miles Bader committed
360
;;; arch-tag: de73a331-941c-4507-ae76-46c76adc70dd
361
;;; calc-cplx.el ends here