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Most of this change is to boilerplate commentary such as license URLs. This change was prompted by ftp://ftp.gnu.org's going-away party, planned for November. Change these FTP URLs to https://ftp.gnu.org instead. Make similar changes for URLs to other organizations moving away from FTP. Also, change HTTP to HTTPS for URLs to gnu.org and fsf.org when this works, as this will further help defend against man-in-the-middle attacks (for this part I omitted the MS-DOS and MS-Windows sources and the test tarballs to keep the workload down). HTTPS is not fully working to lists.gnu.org so I left those URLs alone for now.
356 lines
9.8 KiB
EmacsLisp
356 lines
9.8 KiB
EmacsLisp
;;; calc-cplx.el --- Complex number functions for Calc
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;; Copyright (C) 1990-1993, 2001-2017 Free Software Foundation, Inc.
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;; Author: David Gillespie <daveg@synaptics.com>
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;; This file is part of GNU Emacs.
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;; GNU Emacs is free software: you can redistribute it and/or modify
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;; it under the terms of the GNU General Public License as published by
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;; the Free Software Foundation, either version 3 of the License, or
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;; (at your option) any later version.
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;; GNU Emacs is distributed in the hope that it will be useful,
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;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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;; GNU General Public License for more details.
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;; You should have received a copy of the GNU General Public License
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;; along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>.
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;;; Commentary:
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;;; Code:
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;; This file is autoloaded from calc-ext.el.
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(require 'calc-ext)
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(require 'calc-macs)
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(defun calc-argument (arg)
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(interactive "P")
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(calc-slow-wrapper
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(calc-unary-op "arg" 'calcFunc-arg arg)))
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(defun calc-re (arg)
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(interactive "P")
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(calc-slow-wrapper
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(calc-unary-op "re" 'calcFunc-re arg)))
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(defun calc-im (arg)
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(interactive "P")
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(calc-slow-wrapper
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(calc-unary-op "im" 'calcFunc-im arg)))
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(defun calc-polar ()
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(interactive)
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(calc-slow-wrapper
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(let ((arg (calc-top-n 1)))
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(if (or (calc-is-inverse)
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(eq (car-safe arg) 'polar))
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(calc-enter-result 1 "p-r" (list 'calcFunc-rect arg))
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(calc-enter-result 1 "r-p" (list 'calcFunc-polar arg))))))
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(defun calc-complex-notation ()
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(interactive)
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(calc-wrapper
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(calc-change-mode 'calc-complex-format nil t)
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(message "Displaying complex numbers in (X,Y) format")))
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(defun calc-i-notation ()
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(interactive)
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(calc-wrapper
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(calc-change-mode 'calc-complex-format 'i t)
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(message "Displaying complex numbers in X+Yi format")))
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(defun calc-j-notation ()
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(interactive)
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(calc-wrapper
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(calc-change-mode 'calc-complex-format 'j t)
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(message "Displaying complex numbers in X+Yj format")))
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(defun calc-polar-mode (n)
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(interactive "P")
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(calc-wrapper
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(if (if n
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(> (prefix-numeric-value n) 0)
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(eq calc-complex-mode 'cplx))
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(progn
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(calc-change-mode 'calc-complex-mode 'polar)
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(message "Preferred complex form is polar"))
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(calc-change-mode 'calc-complex-mode 'cplx)
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(message "Preferred complex form is rectangular"))))
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;;;; Complex numbers.
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(defun math-normalize-polar (a)
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(let ((r (math-normalize (nth 1 a)))
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(th (math-normalize (nth 2 a))))
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(cond ((math-zerop r)
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'(polar 0 0))
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((or (math-zerop th))
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r)
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((and (not (eq calc-angle-mode 'rad))
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(or (equal th '(float 18 1))
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(equal th 180)))
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(math-neg r))
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((math-negp r)
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(math-neg (list 'polar (math-neg r) th)))
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(t
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(list 'polar r th)))))
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;;; Coerce A to be complex (rectangular form). [c N]
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(defun math-complex (a)
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(cond ((eq (car-safe a) 'cplx) a)
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((eq (car-safe a) 'polar)
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(if (math-zerop (nth 1 a))
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(nth 1 a)
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(let ((sc (calcFunc-sincos (nth 2 a))))
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(list 'cplx
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(math-mul (nth 1 a) (nth 1 sc))
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(math-mul (nth 1 a) (nth 2 sc))))))
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(t (list 'cplx a 0))))
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;;; Coerce A to be complex (polar form). [c N]
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(defun math-polar (a)
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(cond ((eq (car-safe a) 'polar) a)
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((math-zerop a) '(polar 0 0))
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(t
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(list 'polar
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(math-abs a)
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(calcFunc-arg a)))))
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;;; Multiply A by the imaginary constant i. [N N] [Public]
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(defun math-imaginary (a)
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(if (and (or (Math-objvecp a) (math-infinitep a))
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(not calc-symbolic-mode))
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(math-mul a
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(if (or (eq (car-safe a) 'polar)
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(and (not (eq (car-safe a) 'cplx))
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(eq calc-complex-mode 'polar)))
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(list 'polar 1 (math-quarter-circle nil))
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'(cplx 0 1)))
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(math-mul a '(var i var-i))))
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(defun math-want-polar (a b)
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(cond ((eq (car-safe a) 'polar)
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(if (eq (car-safe b) 'cplx)
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(eq calc-complex-mode 'polar)
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t))
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((eq (car-safe a) 'cplx)
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(if (eq (car-safe b) 'polar)
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(eq calc-complex-mode 'polar)
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nil))
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((eq (car-safe b) 'polar)
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t)
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((eq (car-safe b) 'cplx)
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nil)
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(t (eq calc-complex-mode 'polar))))
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;;; Force A to be in the (-pi,pi] or (-180,180] range.
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(defun math-fix-circular (a &optional dir) ; [R R]
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(cond ((eq (car-safe a) 'hms)
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(cond ((and (Math-lessp 180 (nth 1 a)) (not (eq dir 1)))
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(math-fix-circular (math-add a '(float -36 1)) -1))
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((or (Math-lessp -180 (nth 1 a)) (eq dir -1))
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a)
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(t
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(math-fix-circular (math-add a '(float 36 1)) 1))))
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((eq calc-angle-mode 'rad)
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(cond ((and (Math-lessp (math-pi) a) (not (eq dir 1)))
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(math-fix-circular (math-sub a (math-two-pi)) -1))
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((or (Math-lessp (math-neg (math-pi)) a) (eq dir -1))
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a)
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(t
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(math-fix-circular (math-add a (math-two-pi)) 1))))
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(t
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(cond ((and (Math-lessp '(float 18 1) a) (not (eq dir 1)))
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(math-fix-circular (math-add a '(float -36 1)) -1))
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((or (Math-lessp '(float -18 1) a) (eq dir -1))
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a)
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(t
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(math-fix-circular (math-add a '(float 36 1)) 1))))))
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;;;; Complex numbers.
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(defun calcFunc-polar (a) ; [C N] [Public]
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(cond ((Math-vectorp a)
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(math-map-vec 'calcFunc-polar a))
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((Math-realp a) a)
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((Math-numberp a)
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(math-normalize (math-polar a)))
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(t (list 'calcFunc-polar a))))
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(defun calcFunc-rect (a) ; [N N] [Public]
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(cond ((Math-vectorp a)
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(math-map-vec 'calcFunc-rect a))
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((Math-realp a) a)
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((Math-numberp a)
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(math-normalize (math-complex a)))
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(t (list 'calcFunc-rect a))))
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;;; Compute the complex conjugate of A. [O O] [Public]
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(defun calcFunc-conj (a)
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(let (aa bb)
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(cond ((Math-realp a)
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a)
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((eq (car a) 'cplx)
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(list 'cplx (nth 1 a) (math-neg (nth 2 a))))
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((eq (car a) 'polar)
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(list 'polar (nth 1 a) (math-neg (nth 2 a))))
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((eq (car a) 'vec)
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(math-map-vec 'calcFunc-conj a))
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((eq (car a) 'calcFunc-conj)
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(nth 1 a))
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((math-known-realp a)
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a)
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((and (equal a '(var i var-i))
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(math-imaginary-i))
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(math-neg a))
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((and (memq (car a) '(+ - * /))
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(progn
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(setq aa (calcFunc-conj (nth 1 a))
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bb (calcFunc-conj (nth 2 a)))
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(or (not (eq (car-safe aa) 'calcFunc-conj))
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(not (eq (car-safe bb) 'calcFunc-conj)))))
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(if (eq (car a) '+)
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(math-add aa bb)
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(if (eq (car a) '-)
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(math-sub aa bb)
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(if (eq (car a) '*)
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(math-mul aa bb)
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(math-div aa bb)))))
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((eq (car a) 'neg)
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(math-neg (calcFunc-conj (nth 1 a))))
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((let ((inf (math-infinitep a)))
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(and inf
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(math-mul (calcFunc-conj (math-infinite-dir a inf)) inf))))
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(t (calc-record-why 'numberp a)
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(list 'calcFunc-conj a)))))
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;;; Compute the complex argument of A. [F N] [Public]
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(defun calcFunc-arg (a)
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(cond ((Math-anglep a)
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(if (math-negp a) (math-half-circle nil) 0))
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((eq (car-safe a) 'cplx)
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(calcFunc-arctan2 (nth 2 a) (nth 1 a)))
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((eq (car-safe a) 'polar)
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(nth 2 a))
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((eq (car a) 'vec)
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(math-map-vec 'calcFunc-arg a))
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((and (equal a '(var i var-i))
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(math-imaginary-i))
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(math-quarter-circle t))
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((and (equal a '(neg (var i var-i)))
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(math-imaginary-i))
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(math-neg (math-quarter-circle t)))
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((let ((signs (math-possible-signs a)))
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(or (and (memq signs '(2 4 6)) 0)
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(and (eq signs 1) (math-half-circle nil)))))
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((math-infinitep a)
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(if (or (equal a '(var uinf var-uinf))
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(equal a '(var nan var-nan)))
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'(var nan var-nan)
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(calcFunc-arg (math-infinite-dir a))))
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(t (calc-record-why 'numvecp a)
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(list 'calcFunc-arg a))))
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(defun math-imaginary-i ()
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(let ((val (calc-var-value 'var-i)))
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(or (eq (car-safe val) 'special-const)
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(equal val '(cplx 0 1))
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(and (eq (car-safe val) 'polar)
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(eq (nth 1 val) 0)
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(Math-equal (nth 1 val) (math-quarter-circle nil))))))
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;;; Extract the real or complex part of a complex number. [R N] [Public]
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;;; Also extracts the real part of a modulo form.
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(defun calcFunc-re (a)
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(let (aa bb)
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(cond ((Math-realp a) a)
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((memq (car a) '(mod cplx))
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(nth 1 a))
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((eq (car a) 'polar)
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(math-mul (nth 1 a) (calcFunc-cos (nth 2 a))))
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((eq (car a) 'vec)
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(math-map-vec 'calcFunc-re a))
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((math-known-realp a) a)
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((eq (car a) 'calcFunc-conj)
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(calcFunc-re (nth 1 a)))
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((and (equal a '(var i var-i))
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(math-imaginary-i))
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0)
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((and (memq (car a) '(+ - *))
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(progn
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(setq aa (calcFunc-re (nth 1 a))
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bb (calcFunc-re (nth 2 a)))
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(or (not (eq (car-safe aa) 'calcFunc-re))
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(not (eq (car-safe bb) 'calcFunc-re)))))
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(if (eq (car a) '+)
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(math-add aa bb)
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(if (eq (car a) '-)
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(math-sub aa bb)
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(math-sub (math-mul aa bb)
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(math-mul (calcFunc-im (nth 1 a))
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(calcFunc-im (nth 2 a)))))))
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((and (eq (car a) '/)
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(math-known-realp (nth 2 a)))
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(math-div (calcFunc-re (nth 1 a)) (nth 2 a)))
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((eq (car a) 'neg)
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(math-neg (calcFunc-re (nth 1 a))))
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(t (calc-record-why 'numberp a)
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(list 'calcFunc-re a)))))
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(defun calcFunc-im (a)
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(let (aa bb)
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(cond ((Math-realp a)
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(if (math-floatp a) '(float 0 0) 0))
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((eq (car a) 'cplx)
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(nth 2 a))
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((eq (car a) 'polar)
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(math-mul (nth 1 a) (calcFunc-sin (nth 2 a))))
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((eq (car a) 'vec)
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(math-map-vec 'calcFunc-im a))
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((math-known-realp a)
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0)
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((eq (car a) 'calcFunc-conj)
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(math-neg (calcFunc-im (nth 1 a))))
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((and (equal a '(var i var-i))
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(math-imaginary-i))
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1)
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((and (memq (car a) '(+ - *))
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(progn
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(setq aa (calcFunc-im (nth 1 a))
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bb (calcFunc-im (nth 2 a)))
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(or (not (eq (car-safe aa) 'calcFunc-im))
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(not (eq (car-safe bb) 'calcFunc-im)))))
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(if (eq (car a) '+)
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(math-add aa bb)
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(if (eq (car a) '-)
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(math-sub aa bb)
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(math-add (math-mul (calcFunc-re (nth 1 a)) bb)
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(math-mul aa (calcFunc-re (nth 2 a)))))))
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((and (eq (car a) '/)
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(math-known-realp (nth 2 a)))
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(math-div (calcFunc-im (nth 1 a)) (nth 2 a)))
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((eq (car a) 'neg)
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(math-neg (calcFunc-im (nth 1 a))))
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(t (calc-record-why 'numberp a)
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(list 'calcFunc-im a)))))
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(provide 'calc-cplx)
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;;; calc-cplx.el ends here
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