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

[Richard Fateman]

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
> 
> 
> 
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