code.delx.au - gnu-emacs/blob - lisp/calc/calc-cplx.el

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