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;;
;; Copyright (C) 2010, 2011 Mark H. Weaver <mhw@netris.org>
;;
;; hstep: Heaviside step function support for Maxima
;;
;; This program 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
;; of the License, or (at your option) any later version.
;;
;; This program is distributed in the hope that it will be useful,
;; 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 this program; if not, write to the Free Software
;; Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
;;
(in-package :maxima)
($put '$hstep 1 '$version)
(defprop $hstep %hstep verb)
(defprop %hstep $hstep noun)
(defprop $hstep %hstep alias)
(defprop %hstep $hstep reversealias)
(defprop %hstep simp-hstep operators)
(setf (get '%hstep 'simplim%function) 'simplim%hstep)
(setf (get '%hstep 'real-valued) t)
;; TODO: other properties which would be nice to declare about hstep:
;; non-negative
;; non-decreasing
(defprop %hstep ((x) (($delta) x)) grad)
(defprop $delta ((x) ((%hstep) x)) integral)
(defun $hstep (z) (take '(%hstep) z))
;;
;; TODO: should the following rule be included somehow?
;;
;; hstep(-x) --> 1 - hstep(x)
;;
;; It would also be nice to simplify products
;; containing more than one hstep.
;;
(defun simp-hstep (expr z simpflag)
(oneargcheck expr)
(setq z (simpcheck (cadr expr) simpflag))
(let ((sgn (csign z)))
(cond ((eq sgn '$neg) 0)
((eq sgn '$zero) 1//2)
((eq sgn '$pos) 1)
(t
;; positive * x --> x and negative * x --> -1 * x.
(if (mtimesp z)
(setq z (muln (mapcar #'(lambda (s)
(let ((sgn (csign s)))
(cond ((eq sgn '$neg) -1)
((eq sgn '$pos) 1)
(t s))))
(margs z))
t)))
(eqtest (list '(%hstep) z) expr)))))
(defun simplim%hstep (e x pt)
(let* ((e (limit (cadr e) x pt 'think))
(sgn (mnqp e 0)))
(cond ((eq t sgn) ($hstep e)) ;; limit of arg is not zero
((eq nil sgn) '$und) ;; limit of arg is zero
(t (throw 'limit nil))))) ;; don't know
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