Re: Mathematical selection

> Neil Soiffer wrote:
>>
>> I assume that by the dual operator "*", you mean "*" in a superscript 
>> position such as in x^*.  In such a position, it has no arguments and 
>> precedence is meaningless so I don't understand what you are 
>> asking/commenting on. 
>>
> Well... we're getting down to where it shouldn't get... the appearance 
> of character.
> The * symbol in all the fonts I used every day is high so I'd write V* 
> without an exponent. Would such a shape be part of Unicode spec ?

In all typeset books I've seen, "*" is clearly in a superscript position.  I would claim you are making a mistake in your use and copy editors are likely to do the same.  The spec however, isn't as judgemental as I am.


<snip>

> Another usage of * which is not a multiplication but a binary operator 
> is the pull-back (much used in categories, topology, and differential 
> geometry, I agree we leave K-12 here ;-)) or the convolution (which at 
> least many electrical engineers use).
> 
> Do these all have the same precedence ? Not sure.
> I fear Darwinism should suppresses species!

Again, I think pullback is used in a superscript position.  Convolution uses "*" as an infix operator that does have the same (or very close to the same) precedence as multiplication.  Notations are re-used in different contexts with different meanings.  The remarkable thing is that for at least commonly used notations and operators, people seem to have come to agreement as to their relative precedence and grouping -- it makes understanding the new use easier.

The MathML spec does recommend proper nesting of mrows to reflect the structure of the expression.  This aids in linebreaking and indenting expressions.  Proper nesting also aids in writing transformations of MathML to whatever.  Unfortunately, proper nesting is not the norm.  However, this does mean that applications can distinguish themselves by inferring the proper mrow structure.  They do so at the very minor risk that the generating application really did want a flat mrow.

Neil Soiffer
Senior Scientist
Design Science, Inc.
neils@dessci.com
www.dessci.com
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