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|
;;; calc-cplx.el --- Complex number functions for Calc
;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
;; 2005, 2006 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainer: Jay Belanger <belanger@truman.edu>
;; This file is part of GNU Emacs.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY. No author or distributor
;; accepts responsibility to anyone for the consequences of using it
;; or for whether it serves any particular purpose or works at all,
;; unless he says so in writing. Refer to the GNU Emacs General Public
;; License for full details.
;; Everyone is granted permission to copy, modify and redistribute
;; GNU Emacs, but only under the conditions described in the
;; GNU Emacs General Public License. A copy of this license is
;; supposed to have been given to you along with GNU Emacs so you
;; can know your rights and responsibilities. It should be in a
;; file named COPYING. Among other things, the copyright notice
;; and this notice must be preserved on all copies.
;;; Commentary:
;;; Code:
;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)
(require 'calc-macs)
(defun calc-argument (arg)
(interactive "P")
(calc-slow-wrapper
(calc-unary-op "arg" 'calcFunc-arg arg)))
(defun calc-re (arg)
(interactive "P")
(calc-slow-wrapper
(calc-unary-op "re" 'calcFunc-re arg)))
(defun calc-im (arg)
(interactive "P")
(calc-slow-wrapper
(calc-unary-op "im" 'calcFunc-im arg)))
(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))
(calc-enter-result 1 "r-p" (list 'calcFunc-polar arg))))))
(defun calc-complex-notation ()
(interactive)
(calc-wrapper
(calc-change-mode 'calc-complex-format nil t)
(message "Displaying complex numbers in (X,Y) format")))
(defun calc-i-notation ()
(interactive)
(calc-wrapper
(calc-change-mode 'calc-complex-format 'i t)
(message "Displaying complex numbers in X+Yi format")))
(defun calc-j-notation ()
(interactive)
(calc-wrapper
(calc-change-mode 'calc-complex-format 'j t)
(message "Displaying complex numbers in X+Yj format")))
(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)
(message "Preferred complex form is polar"))
(calc-change-mode 'calc-complex-mode 'cplx)
(message "Preferred complex form is rectangular"))))
;;;; 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
(list 'polar r th)))))
;;; 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))))))
(t (list 'cplx a 0))))
;;; 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)
(calcFunc-arg a)))))
;;; 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)))
(math-mul a '(var i var-i))))
(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)
(t (eq calc-complex-mode 'polar))))
;;; 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
(math-fix-circular (math-add a '(float 36 1)) 1))))))
;;;; 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)))
(t (list 'calcFunc-polar a))))
(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)))
(t (list 'calcFunc-rect a))))
;;; 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)
(list 'calcFunc-conj a)))))
;;; 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)
(list 'calcFunc-arg a))))
(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)
(Math-equal (nth 1 val) (math-quarter-circle nil))))))
;;; 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)
(list 'calcFunc-re a)))))
(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)
(list 'calcFunc-im a)))))
(provide 'calc-cplx)
;;; arch-tag: de73a331-941c-4507-ae76-46c76adc70dd
;;; calc-cplx.el ends here
|
