src/tlimit.lisp

   1 ;;; -*-  Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- ;;;;
   2 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
   3 ;;;     The data in this file contains enhancements.                   ;;;;;
   4 ;;;                                                                    ;;;;;
   5 ;;;  Copyright (c) 1984,1987 by William Schelter,University of Texas   ;;;;;
   6 ;;;     All rights reserved                                            ;;;;;
   7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
   8 ;;;     (c) Copyright 1980 Massachusetts Institute of Technology         ;;;
   9 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
  10
  11 (in-package :maxima)
  12
  13 (macsyma-module tlimit)
  14
  15 (load-macsyma-macros rzmac)
  16
  17 ;; TOP LEVEL FUNCTION(S): $TLIMIT $TLDEFINT
  18
  19 (defmfun $tlimit (&rest args)
  20   (let ((limit-using-taylor t))
  21     (declare (special limit-using-taylor))
  22     (apply #'$limit args)))
  23
  24 (defmfun $tldefint (exp var ll ul)
  25   (let ((limit-using-taylor t))
  26     (declare (special limit-using-taylor))
  27     ($ldefint exp var ll ul)))
  28
  29 (defun tlimp (expr)             ; TO BE EXPANDED TO BE SMARTER (MAYBE)
  30   (declare (ignore expr))
  31   t)
  32
  33 ;; compute limit of exp by finding its taylor series expansion.
  34 ;; asks for $lhospitallim terms of taylor series.
  35 ;; this is an arbitrary limit: with default value $lhospitallim = 4,
  36 ;;  tlimit(2^n/n^5, n, inf)  =>  0
  37 (defun taylim (exp var val *i*)
  38   (prog (ex)
  39      (setq ex (catch 'taylor-catch
  40                 (let ((silent-taylor-flag t))
  41                   ($taylor exp var (ridofab val) $lhospitallim))))
  42      (or ex (return (cond ((eq *i* t)
  43                            (limit1 exp var val))
  44                           ((eq *i* 'think)
  45                            (if (member (caar exp) '(mtimes mexpt) :test #'eq)
  46                                (limit1 exp var val)
  47                                (simplimit exp var val)))
  48                           (t
  49                            (simplimit exp var val)))))
  50      (return
  51        (let ((taylored t))
  52          (declare (special taylored))
  53          (limit (simplify ($ratdisrep ex)) var val 'think)))))