Re: Embellished operators

I hope I'm stating this correctly:  the embellished operator rules are
clear with the exception of the case of an mrow that contains an
embellished operator and space-like elements (the last rule in
http://www.w3.org/TR/MathML3/chapter3.html#id.3.2.5.7.3).

So for your two less trivial vertical stretching rules:

1.  the first should have the arrow stretch to 200px because it is part of
the inner munder. and the other part of the outer mover is smaller.

2.   the second is slightly trickier.  The inner munder's initial width is
100px, but because the arrow is at the "core" and is hence an embellished
operator, laying out the outer mover means that it needs to stretch to
cover the 200px.  Hence this too should be 200px.  This is based on the
following from the spec for *horizontal* stretching:  "...the mo element at
its core, should stretch to cover the width of the other direct
sub-expressions in the given element..."


For the vertical case, it is clear that if there was only one mrow, then
the maximum size would be used (200px).  But that's not the case.  As your
analysis in a subsequent email demonstrated,  the inner mrow should cause
that mrow to be 200px.  But since it should act as an embellished operator,
it is subject to further stretching.

There are two possibilities:
1.  We ignore the stretching caused by the inner mrow and consider the
"normal" height to be be that of the unstretched "|".  In this case, the
answer should be that the result is 100px because it should stretch to the
height f the space in the outer mrow.

2.  We consider the stretched height of "|" caused by the inner mrow's
stretching to be the normal height of the operator.  In this case, the
outer mrow doesn't stretch it further, so the answer is 200px.  If the
outer mrow had a larger stretch than the inner one, than the largest value
should be used.

The spec is silent on what to do here (AFAIK) -- the rule mentioned for
horizontal stretching is not listed as part of the vertical stretching
rules.  I'm leaning towards '1' as being the correct interpretation, so the
result should be 100px.

I haven't looked at the code, but I suspect that MathPlayer chooses the
inner one (even if the outer one is larger) because it doesn't implement
the "mrow whose arguments consist (in any order) of one embellished
operator and zero or more space-like elements" rule.

I tried Mathematica and it behaves like MathPlayer (I didn't implement this
part of the code in MathPlayer, but did in Mathematica).  So both are doing
it wrong (probably because they didn't implement this rule).

Based on what you reported, it sounds like MathJax is doing it wrong under
option '1' above, but correct under '2'.  Firefox sounds is doing the
opposite:  correct under option '1', but wrong under '2'.

If there is a clear consensus on what should happen, we can add an errata
to the spec to clear up this case.

Neil Soiffer
Senior Scientist
Design Science, Inc.
www.dessci.com
~ Makers of MathType, MathFlow, MathPlayer, MathDaisy, Equation Editor ~


On Thu, Feb 23, 2012 at 1:02 AM, Frédéric WANG <fred.wang@free.fr> wrote:

>  Hi all,
>
> I'm thinking again about the rules for embellished operators and it seems
> to me that some elements are particular. For example if we ask how to
> determine the stretching of something like:
>
> <math>
> <mover>
> <mo>&#x2192;</mo>
> <mtext>over</mtext>
> </mover>
> </math>
>
> The obvious answer is that the arrow should stretch to cover the over
> script. OK. However one can also say that the <mover> is an embellished
> element as a whole. Since is has no siblings, the arrow should have its
> default size.
>
> To give slightly less trivial examples, what should be the size of the
> arrows (100px or 200px?) in these examples:
>
> <math>
> <mover>
> <mspace width="100px"/>
> <munder>
> <mo>&#x2192;</mo>
> <mspace width="200px"/>
> </munder>
> </mover>
> </math>
>
> and
>
> <math>
> <mover>
> <mspace width="200px"/>
> <munder>
> <mo>&#x2192;</mo>
> <mspace width="100px"/>
> </munder>
> </mover>
> </math>
>
> An example with vertical stretching rules:
>
> <math>
> <mrow>
> <mspace height="50px" depth="50px"/>
> <mrow>
> <mo>|</mo>
> <mspace height="100px" depth="100px"/>
> </mrow>
> </mrow>
> </math>
>
> (I wonder if an attribute like embellishedop = "false" could help to
> prevent this kind of ambiguity?)
>
> I noticed this because implementing the complete embellished op rules
> caused a regression in Mozilla with MathML code generated by MathJax:
> https://bugzilla.mozilla.org/show_bug.cgi?id=687807
>
>