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

David Carlisle davidc at nag.co.uk
Mon May 20 17:52:49 CEST 2002

> It is not
>   so useful if have two computer algebra systems at your disposal
> and they do different things with cosine.

The point is that refering to (a particular edition of) A&S  ties down
such details as branch cuts etc. So if you are implementing a phrasebook
to a system that has different choices then you know you have to make
the appropriate transfomation. The author of the phrasebook mapping to
the CA system needs to be aware of that, the author of the OM object
need not be.

> 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)"

This is unspecified, if you have an OM application that is a front end
to TeX It doesn't make sense. If it's a numerical library it will
probably get evaluated as a double. If it's a symbolic package it may
get stored as an exact expression cos(1/3). But the fact that a numeric
library will evaluate an expression to some finite precision does not
mean that the openmath object itself is imprecise, it just means that
the application is taking some reasonable approximation to the abstract
object before working on it. this is always the case.

>  When I say Cos[x]  I mean exactly what
> Mathematica means.

In what way (other than choice of reference) is that different from
fixing on an arbitrary book. You are just fixing on an arbitrary CA
system.

> 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.

Maybe you just want to do something different because that doesn't look
useful to me, it looks essentially unusable for any of the uses I have
in mind for OM or MathML. The whole point is that you should be able to
refer to mathematical concepts in a platform neutral way. Someone else
may at some other time map those concepts to some system that I know
nothing about. The idea that I should lump in one place the definition
in every conceivable system appears totally unworkable to me.

David

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