From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6950 Path: news.gmane.org!not-for-mail From: Dusko Pavlovic Newsgroups: gmane.science.mathematics.categories Subject: Re: Finding the inverse of a function. Date: Wed, 5 Oct 2011 13:52:25 +0100 Message-ID: References: <4E79E072.8050104@cs.bham.ac.uk> Reply-To: Dusko Pavlovic NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v1084) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1317904176 20418 80.91.229.12 (6 Oct 2011 12:29:36 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 6 Oct 2011 12:29:36 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Thu Oct 06 14:29:32 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RBn4r-0005cA-Rs for gsmc-categories@m.gmane.org; Thu, 06 Oct 2011 14:29:30 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:42972) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1RBn2p-0002FU-E3; Thu, 06 Oct 2011 09:27:23 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RBn2n-0005mp-8A for categories-list@mlist.mta.ca; Thu, 06 Oct 2011 09:27:21 -0300 In-Reply-To: <4E79E072.8050104@cs.bham.ac.uk> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6950 Archived-At: hi martin, On Sep 21, 2011, at 2:02 PM, Martin Escardo wrote: > This has been further developed in several papers by Rutten and other = people. i know, of course, that jan rutten developed theory of power series to a = great length, as used in combinatorics and automata theory. he has a = paper about coalgebraic differential calculus --- but of *bitstreams*. = the query on the list concerned the function=20 x sin(x), i think, as studied by undergraduates in calculus I. did jan = really work on such things? i would be really interested in that. i used to think that it might be worth while to rework widder's book on = transform theory coalgebraically. but even the coalgebraic laplace = transform in our paper does not seem to have been useful for anything. i = thought no one noticed it. it would be good to know that it was further = developed. all the best, -- dusko >=20 > (This is entertaining but is not categorical: = http://www.cs.dartmouth.edu/~doug/music.ps.gz) >=20 > Martin >=20 >=20 > On 20/09/11 18:55, Dusko Pavlovic wrote: >> infinite series and analytic functions can be simply and conveniently = manipulated in categories of coalgebras. their taylor and laplace = transforms turn up as coalgebra isomorphims. the basics of this approach = are in my LICS 98 paper with martin escardo, >> http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=3D5684# >> or >> http://www.isg.rhul.ac.uk/dusko/coalgebra.html >> neither martin nor i really pursued this path, which is perhaps a = mistake, since it seems that a powerful categorical tool lies there. >>=20 >> 2c, >> -- dusko >>=20 >> On Sep 16, 2011, at 5:42 PM, peasthope@shaw.ca wrote: >>=20 >>> Is CT any help in getting an overview of infinite series? >>>=20 >>> I'm curious to find an inverse of f(\theta) =3D \theta \sin \theta >>> and wonder whether there is an approach more insightful than >>> the traditional course in applied analysis. >>>=20 >>> Thanks, ... Peter E. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]