Re: Finding the inverse of a function.

[Dusko Pavlovic <dusko@kestrel.edu>]

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 
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

> 
> (This is entertaining but is not categorical: http://www.cs.dartmouth.edu/~doug/music.ps.gz)
> 
> Martin
> 
> 
> 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=5684#
>> 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.
>> 
>> 2c,
>> -- dusko
>> 
>> On Sep 16, 2011, at 5:42 PM, peasthope@shaw.ca wrote:
>> 
>>> Is CT any help in getting an overview of infinite series?
>>> 
>>> I'm curious to find an inverse of f(\theta) = \theta \sin \theta
>>> and wonder whether there is an approach more insightful than
>>> the traditional course in applied analysis.
>>> 
>>> Thanks,             ... Peter E.


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