Re: Stretchy Operators

• To: rminer@geom.umn.edu, w3c-math-erb@w3.org
• Subject: Re: Stretchy Operators
• From: ion@math.ams.org (Patrick D. F. Ion)
• Date: Wed, 03 Jul 1996 17:56:37 -0400
• From ion@math.ams.org Wed Jul 3 17: 53:10 1996
• Message-Id: <v02130507ae0092d7c699@[130.44.25.36]>
• X-Sender: ion@mr4.mr.ams.org

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My personal position on the aesthetics of growing matching fences has
always been very conservative.  For instance I feel that the surrounding
parentheses in
x + 1
( ----- )
x - 1

should indeed have enough height to cover the numerator and denominator.
The display list you have looks right to me.

However, I think it is just an algorithmic hack to decide that the fence
heights _always_ have to exceed the highest and lowest excursions of
numerator and denominator, as in something like

___ oo
x +  a | |      B (x)  + C(x) + D
i=1    i
( --------------------------------- )
x - 1

or a worse case with an integral that I can't readily do in ASCII.  There are
expressions in high-energy physics that I don't think used to have matching
vast
parens before algorithmic typsetting took over from visually oriented.

For instance, in the case ||x-a| sin(b)| the important thing is probably
that the outer vert pair be associated together and not be confused with
the inner.  So we have a case here of a modulus of a product of a modulus
by something signed.  A similar example could be constructed with norms
instead of the presumed absolute values using double (or triple, or
subscripted) verts.  Personally I don't think the outer modulus here needs
to be displayed larger at all.

If you want always to size fences automatically increasingly outward then
one method has got to be a pairing of fences, and a rule such as alluded to
above about covering the extreme excursions of any expression nested
within.  But that leads to things like the TeX dummy \. fences to allow
balancing, and to difficulties when an "bracketed expression" continues
over a line.   In addition there are constructions like the semi-open
interval notation [a,b) which might have to have explicit pairings added.

Patrick

```

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