1;;; calc-cplx.el --- Complex number functions for Calc 2 3;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004, 4;; 2005, 2006, 2007 Free Software Foundation, Inc. 5 6;; Author: David Gillespie <daveg@synaptics.com> 7;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> 8 9;; This file is part of GNU Emacs. 10 11;; GNU Emacs is free software; you can redistribute it and/or modify 12;; it under the terms of the GNU General Public License as published by 13;; the Free Software Foundation; either version 2, or (at your option) 14;; any later version. 15 16;; GNU Emacs is distributed in the hope that it will be useful, 17;; but WITHOUT ANY WARRANTY; without even the implied warranty of 18;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 19;; GNU General Public License for more details. 20 21;; You should have received a copy of the GNU General Public License 22;; along with GNU Emacs; see the file COPYING. If not, write to the 23;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, 24;; Boston, MA 02110-1301, USA. 25 26;;; Commentary: 27 28;;; Code: 29 30;; This file is autoloaded from calc-ext.el. 31 32(require 'calc-ext) 33(require 'calc-macs) 34 35(defun calc-argument (arg) 36 (interactive "P") 37 (calc-slow-wrapper 38 (calc-unary-op "arg" 'calcFunc-arg arg))) 39 40(defun calc-re (arg) 41 (interactive "P") 42 (calc-slow-wrapper 43 (calc-unary-op "re" 'calcFunc-re arg))) 44 45(defun calc-im (arg) 46 (interactive "P") 47 (calc-slow-wrapper 48 (calc-unary-op "im" 'calcFunc-im arg))) 49 50 51(defun calc-polar () 52 (interactive) 53 (calc-slow-wrapper 54 (let ((arg (calc-top-n 1))) 55 (if (or (calc-is-inverse) 56 (eq (car-safe arg) 'polar)) 57 (calc-enter-result 1 "p-r" (list 'calcFunc-rect arg)) 58 (calc-enter-result 1 "r-p" (list 'calcFunc-polar arg)))))) 59 60 61 62 63(defun calc-complex-notation () 64 (interactive) 65 (calc-wrapper 66 (calc-change-mode 'calc-complex-format nil t) 67 (message "Displaying complex numbers in (X,Y) format"))) 68 69(defun calc-i-notation () 70 (interactive) 71 (calc-wrapper 72 (calc-change-mode 'calc-complex-format 'i t) 73 (message "Displaying complex numbers in X+Yi format"))) 74 75(defun calc-j-notation () 76 (interactive) 77 (calc-wrapper 78 (calc-change-mode 'calc-complex-format 'j t) 79 (message "Displaying complex numbers in X+Yj format"))) 80 81 82(defun calc-polar-mode (n) 83 (interactive "P") 84 (calc-wrapper 85 (if (if n 86 (> (prefix-numeric-value n) 0) 87 (eq calc-complex-mode 'cplx)) 88 (progn 89 (calc-change-mode 'calc-complex-mode 'polar) 90 (message "Preferred complex form is polar")) 91 (calc-change-mode 'calc-complex-mode 'cplx) 92 (message "Preferred complex form is rectangular")))) 93 94 95;;;; Complex numbers. 96 97(defun math-normalize-polar (a) 98 (let ((r (math-normalize (nth 1 a))) 99 (th (math-normalize (nth 2 a)))) 100 (cond ((math-zerop r) 101 '(polar 0 0)) 102 ((or (math-zerop th)) 103 r) 104 ((and (not (eq calc-angle-mode 'rad)) 105 (or (equal th '(float 18 1)) 106 (equal th 180))) 107 (math-neg r)) 108 ((math-negp r) 109 (math-neg (list 'polar (math-neg r) th))) 110 (t 111 (list 'polar r th))))) 112 113 114;;; Coerce A to be complex (rectangular form). [c N] 115(defun math-complex (a) 116 (cond ((eq (car-safe a) 'cplx) a) 117 ((eq (car-safe a) 'polar) 118 (if (math-zerop (nth 1 a)) 119 (nth 1 a) 120 (let ((sc (calcFunc-sincos (nth 2 a)))) 121 (list 'cplx 122 (math-mul (nth 1 a) (nth 1 sc)) 123 (math-mul (nth 1 a) (nth 2 sc)))))) 124 (t (list 'cplx a 0)))) 125 126;;; Coerce A to be complex (polar form). [c N] 127(defun math-polar (a) 128 (cond ((eq (car-safe a) 'polar) a) 129 ((math-zerop a) '(polar 0 0)) 130 (t 131 (list 'polar 132 (math-abs a) 133 (calcFunc-arg a))))) 134 135;;; Multiply A by the imaginary constant i. [N N] [Public] 136(defun math-imaginary (a) 137 (if (and (or (Math-objvecp a) (math-infinitep a)) 138 (not calc-symbolic-mode)) 139 (math-mul a 140 (if (or (eq (car-safe a) 'polar) 141 (and (not (eq (car-safe a) 'cplx)) 142 (eq calc-complex-mode 'polar))) 143 (list 'polar 1 (math-quarter-circle nil)) 144 '(cplx 0 1))) 145 (math-mul a '(var i var-i)))) 146 147 148 149 150(defun math-want-polar (a b) 151 (cond ((eq (car-safe a) 'polar) 152 (if (eq (car-safe b) 'cplx) 153 (eq calc-complex-mode 'polar) 154 t)) 155 ((eq (car-safe a) 'cplx) 156 (if (eq (car-safe b) 'polar) 157 (eq calc-complex-mode 'polar) 158 nil)) 159 ((eq (car-safe b) 'polar) 160 t) 161 ((eq (car-safe b) 'cplx) 162 nil) 163 (t (eq calc-complex-mode 'polar)))) 164 165;;; Force A to be in the (-pi,pi] or (-180,180] range. 166(defun math-fix-circular (a &optional dir) ; [R R] 167 (cond ((eq (car-safe a) 'hms) 168 (cond ((and (Math-lessp 180 (nth 1 a)) (not (eq dir 1))) 169 (math-fix-circular (math-add a '(float -36 1)) -1)) 170 ((or (Math-lessp -180 (nth 1 a)) (eq dir -1)) 171 a) 172 (t 173 (math-fix-circular (math-add a '(float 36 1)) 1)))) 174 ((eq calc-angle-mode 'rad) 175 (cond ((and (Math-lessp (math-pi) a) (not (eq dir 1))) 176 (math-fix-circular (math-sub a (math-two-pi)) -1)) 177 ((or (Math-lessp (math-neg (math-pi)) a) (eq dir -1)) 178 a) 179 (t 180 (math-fix-circular (math-add a (math-two-pi)) 1)))) 181 (t 182 (cond ((and (Math-lessp '(float 18 1) a) (not (eq dir 1))) 183 (math-fix-circular (math-add a '(float -36 1)) -1)) 184 ((or (Math-lessp '(float -18 1) a) (eq dir -1)) 185 a) 186 (t 187 (math-fix-circular (math-add a '(float 36 1)) 1)))))) 188 189 190;;;; Complex numbers. 191 192(defun calcFunc-polar (a) ; [C N] [Public] 193 (cond ((Math-vectorp a) 194 (math-map-vec 'calcFunc-polar a)) 195 ((Math-realp a) a) 196 ((Math-numberp a) 197 (math-normalize (math-polar a))) 198 (t (list 'calcFunc-polar a)))) 199 200(defun calcFunc-rect (a) ; [N N] [Public] 201 (cond ((Math-vectorp a) 202 (math-map-vec 'calcFunc-rect a)) 203 ((Math-realp a) a) 204 ((Math-numberp a) 205 (math-normalize (math-complex a))) 206 (t (list 'calcFunc-rect a)))) 207 208;;; Compute the complex conjugate of A. [O O] [Public] 209(defun calcFunc-conj (a) 210 (let (aa bb) 211 (cond ((Math-realp a) 212 a) 213 ((eq (car a) 'cplx) 214 (list 'cplx (nth 1 a) (math-neg (nth 2 a)))) 215 ((eq (car a) 'polar) 216 (list 'polar (nth 1 a) (math-neg (nth 2 a)))) 217 ((eq (car a) 'vec) 218 (math-map-vec 'calcFunc-conj a)) 219 ((eq (car a) 'calcFunc-conj) 220 (nth 1 a)) 221 ((math-known-realp a) 222 a) 223 ((and (equal a '(var i var-i)) 224 (math-imaginary-i)) 225 (math-neg a)) 226 ((and (memq (car a) '(+ - * /)) 227 (progn 228 (setq aa (calcFunc-conj (nth 1 a)) 229 bb (calcFunc-conj (nth 2 a))) 230 (or (not (eq (car-safe aa) 'calcFunc-conj)) 231 (not (eq (car-safe bb) 'calcFunc-conj))))) 232 (if (eq (car a) '+) 233 (math-add aa bb) 234 (if (eq (car a) '-) 235 (math-sub aa bb) 236 (if (eq (car a) '*) 237 (math-mul aa bb) 238 (math-div aa bb))))) 239 ((eq (car a) 'neg) 240 (math-neg (calcFunc-conj (nth 1 a)))) 241 ((let ((inf (math-infinitep a))) 242 (and inf 243 (math-mul (calcFunc-conj (math-infinite-dir a inf)) inf)))) 244 (t (calc-record-why 'numberp a) 245 (list 'calcFunc-conj a))))) 246 247 248;;; Compute the complex argument of A. [F N] [Public] 249(defun calcFunc-arg (a) 250 (cond ((Math-anglep a) 251 (if (math-negp a) (math-half-circle nil) 0)) 252 ((eq (car-safe a) 'cplx) 253 (calcFunc-arctan2 (nth 2 a) (nth 1 a))) 254 ((eq (car-safe a) 'polar) 255 (nth 2 a)) 256 ((eq (car a) 'vec) 257 (math-map-vec 'calcFunc-arg a)) 258 ((and (equal a '(var i var-i)) 259 (math-imaginary-i)) 260 (math-quarter-circle t)) 261 ((and (equal a '(neg (var i var-i))) 262 (math-imaginary-i)) 263 (math-neg (math-quarter-circle t))) 264 ((let ((signs (math-possible-signs a))) 265 (or (and (memq signs '(2 4 6)) 0) 266 (and (eq signs 1) (math-half-circle nil))))) 267 ((math-infinitep a) 268 (if (or (equal a '(var uinf var-uinf)) 269 (equal a '(var nan var-nan))) 270 '(var nan var-nan) 271 (calcFunc-arg (math-infinite-dir a)))) 272 (t (calc-record-why 'numvecp a) 273 (list 'calcFunc-arg a)))) 274 275(defun math-imaginary-i () 276 (let ((val (calc-var-value 'var-i))) 277 (or (eq (car-safe val) 'special-const) 278 (equal val '(cplx 0 1)) 279 (and (eq (car-safe val) 'polar) 280 (eq (nth 1 val) 0) 281 (Math-equal (nth 1 val) (math-quarter-circle nil)))))) 282 283;;; Extract the real or complex part of a complex number. [R N] [Public] 284;;; Also extracts the real part of a modulo form. 285(defun calcFunc-re (a) 286 (let (aa bb) 287 (cond ((Math-realp a) a) 288 ((memq (car a) '(mod cplx)) 289 (nth 1 a)) 290 ((eq (car a) 'polar) 291 (math-mul (nth 1 a) (calcFunc-cos (nth 2 a)))) 292 ((eq (car a) 'vec) 293 (math-map-vec 'calcFunc-re a)) 294 ((math-known-realp a) a) 295 ((eq (car a) 'calcFunc-conj) 296 (calcFunc-re (nth 1 a))) 297 ((and (equal a '(var i var-i)) 298 (math-imaginary-i)) 299 0) 300 ((and (memq (car a) '(+ - *)) 301 (progn 302 (setq aa (calcFunc-re (nth 1 a)) 303 bb (calcFunc-re (nth 2 a))) 304 (or (not (eq (car-safe aa) 'calcFunc-re)) 305 (not (eq (car-safe bb) 'calcFunc-re))))) 306 (if (eq (car a) '+) 307 (math-add aa bb) 308 (if (eq (car a) '-) 309 (math-sub aa bb) 310 (math-sub (math-mul aa bb) 311 (math-mul (calcFunc-im (nth 1 a)) 312 (calcFunc-im (nth 2 a))))))) 313 ((and (eq (car a) '/) 314 (math-known-realp (nth 2 a))) 315 (math-div (calcFunc-re (nth 1 a)) (nth 2 a))) 316 ((eq (car a) 'neg) 317 (math-neg (calcFunc-re (nth 1 a)))) 318 (t (calc-record-why 'numberp a) 319 (list 'calcFunc-re a))))) 320 321(defun calcFunc-im (a) 322 (let (aa bb) 323 (cond ((Math-realp a) 324 (if (math-floatp a) '(float 0 0) 0)) 325 ((eq (car a) 'cplx) 326 (nth 2 a)) 327 ((eq (car a) 'polar) 328 (math-mul (nth 1 a) (calcFunc-sin (nth 2 a)))) 329 ((eq (car a) 'vec) 330 (math-map-vec 'calcFunc-im a)) 331 ((math-known-realp a) 332 0) 333 ((eq (car a) 'calcFunc-conj) 334 (math-neg (calcFunc-im (nth 1 a)))) 335 ((and (equal a '(var i var-i)) 336 (math-imaginary-i)) 337 1) 338 ((and (memq (car a) '(+ - *)) 339 (progn 340 (setq aa (calcFunc-im (nth 1 a)) 341 bb (calcFunc-im (nth 2 a))) 342 (or (not (eq (car-safe aa) 'calcFunc-im)) 343 (not (eq (car-safe bb) 'calcFunc-im))))) 344 (if (eq (car a) '+) 345 (math-add aa bb) 346 (if (eq (car a) '-) 347 (math-sub aa bb) 348 (math-add (math-mul (calcFunc-re (nth 1 a)) bb) 349 (math-mul aa (calcFunc-re (nth 2 a))))))) 350 ((and (eq (car a) '/) 351 (math-known-realp (nth 2 a))) 352 (math-div (calcFunc-im (nth 1 a)) (nth 2 a))) 353 ((eq (car a) 'neg) 354 (math-neg (calcFunc-im (nth 1 a)))) 355 (t (calc-record-why 'numberp a) 356 (list 'calcFunc-im a))))) 357 358(provide 'calc-cplx) 359 360;;; arch-tag: de73a331-941c-4507-ae76-46c76adc70dd 361;;; calc-cplx.el ends here 362