# [om] different representations for a/b and a*b^(-1)

Richard Fateman fateman at cs.berkeley.edu
Mon May 20 17:29:41 CEST 2002


David Carlisle wrote:

>>The definition of cosine in OM is
>>not useful.
>>
>
> OM itself doesn't have a definition of cosine of course. The definition
> in the dictionary transc1 is
>
> http://monet.nag.co.uk/cocoon/openmath/cd/transc1.html#cos
>
>
>>This symbol represents the cos function as described in Abramowitz and
>>Stegun, section 4.3. It takes one argument.

A&S was published in 1964, I think.
This was in the dawn of the computer age. the tables in it
were produced by mechanical calculators. When NIST comes
out with a new version, will you instantly change to it,
even if it means moving branch cuts (not in cos, of course,
but other functions)?

The information there is generally useful, and especially useful if
your intention is to convey "the contents of A&S".  It is not
so useful if have two computer algebra systems at your disposal
and they do different things with cosine.
1. How precise and how accurate should any numerical operations
be?  If they are unspecified, one system may say "cos(1/3)" and
mean something rather different from another, say "cos(0.333333334)"
2. How about those areas in which there is room for choice?
domain of arctan?  which n  in  n*pi*i ?

Now maybe you will say "we don't specify everything".  OK, it
seems to me it would be much more useful to have an operational
definition (some might prefer an axiomatic definition), but
here's a proposal. When I say Cos[x]  I mean exactly what
Mathematica means.  (or choose some other CAS).  Version 2.0.

Then at least I can refer to an authority for the meaning.

Encoding an object could be
<begin>
<annotation-Mathematica> "Cos[x]" </annotation>
<annotation-Maple> cos(x)</annotation>
<annotation-TeX> \cos x   ...
<\begin>

This is more useful.

RJF

>>
>
> This definition is as useful as the referenced book. Maybe you don't
> find that useful but apparently a lot of people have, the book has
> sold a lot of copies in many editions, I believe.

At least 100,000, I read.

>
>>I haven't looked at it in years,
>>
> Hmmm.
>
>
>
> David
>
>
>
> _____________________________________________________________________
> This message has been checked for all known viruses by Star Internet
> delivered through the MessageLabs Virus Scanning Service. For further
> information visit http://www.star.net.uk/stats.asp or alternatively call
> Star Internet for details on the Virus Scanning Service.
> --
> om at openmath.org  -  general discussion on OpenMath
> Post public announcements to om-announce at openmath.org
> Automatic list maintenance software at majordomo at openmath.org
> Mail om-owner at openmath.org for assistance with any problems
>

--
om at openmath.org  -  general discussion on OpenMath
Post public announcements to om-announce at openmath.org
Automatic list maintenance software at majordomo at openmath.org
Mail om-owner at openmath.org for assistance with any problems



More information about the Om mailing list