Mathematical Markup Language (MathML)

Peter Murray-Rust Peter at
Fri May 16 13:26:36 BST 1997

[To xml-dev, crossposted to CLIC and CHEMIME and Patrick Ion, AMS.
Patrick, please feel free to circulate this to HTML-Math-WG.
This posting is being addressed to both XML-DEV and the Chemical Informatics
community, so please excuse any confusions :-).]

The first draft of MathML was published on May 15th and is enormously
exciting.  It is written to be compatible with XML and to evolve as that
spec evolves, so that we have one of the very first DTDs that has been 
developed in that way.  Since math is common to a very large number of
vertical markets in the ScientificTechnicalMedical market (and many
others) MathML will highlight how domain-specific DTDs and documents can
be re-used in a variety of contexts.

The draft (long, impressive, and in several sections) is at:
Could the authors provide a tar.gz or similar file so that all the sections
including the gifs can be downloaded?  Also could the appendices have names
unique under 8.3 format.  TIA :-)

Note that the Math-WG has addressed the two key aspects of encoding
maths - presentation (cf. TeX) and content (cf. symbolic algebra, 
plotting packages, etc.).  The current document addresses both of these and
having had very useful discussions with Patrick Ion, Martin and Roy Pike and 
Steve Buswell I'm very confident that MathML will cater for a wide range 
of chemical requirements.  Certainly I hope to explore its use for
plotting graphs, extracting functions, using symbolic variables within
chemical discourse and tables, and much more.  In principle it should be
possible to (say) extract a set of force-field equations from a 
molecular mechanics paper and directly manipulate them into a computer

The publication of MathML coincides with the XML-ERB's request for discussion
on multiple namespaces, and the very large emphasis at SGML97 on Information
Objects.  The XML community is now clearly working as fast as possible to
develop the spec so that an XML document can be composed of a variety
of fragments/subdocuments/objects - various names are chosen.  Chemical
Markup Language is being developed along some of the same lines as MathML 
- to be XML-compatible, to use common semantics where appropriate, and
to avoid namespace collisions.  Whatever syntactic mechanism is chosen it
will allow subcomponents of a document to be linked to the appropriate
DTD - very probably distributed over the WWW - and for appropriate semantics
and behaviour to be applied.

The math proposal has enormous implications for technical publications and
documents.  In CML a space has been deliberately left called 'MATH' and now
can be replaced by 'MathML', e.g. as:

<!Entity % mathml.dtd SYSTEM "">

<!Element CML (lots|of|elements|%mol)*>  <!-- note NOT math -->

<!Element XLIST ANY>   <!-- CML's generic container -->

and in a document instance something like:

<P>The <A HREF="#fn1" XML-LINK="simple" ACTUATE="AUTO" SHOW="EMBED">
function</A> relating...</P>
<XLIST TITLE="Equations in the text">
<EXPR ID="fn1" TITLE="quadratic"><MI>x</MI><POWER/><MN>2</MN></EXPR>

would now insert the expression x^2 at the appropropriate part of the
text.  Note that this use of XML-LINK avoids the complexity of tailoring
the parent DTD to accommodate infinitely variable content models.  Note
that the document suggested above *can be validated* if required, since all
the DTDs involved are included.  Of course this is only possible because
CML and Math have no namespace collisions, and this mechanism will not
be generally applicable.  (MathML has some very short GIs (have I got the
terminology right this time? :-) and is therefore likely to collide with
an arbitrarily chosen DTD).

I'd welcome comments from the chemical community on this and suggest that
posting them to chemime at would be the most appropriate (please 
*don't* post directly to the math group!).   On the more general question
of interoperability of information objects we may need to wait a week
or two to see how the XML-WG discussions take that, but I'm very keen to
start trying to get an implementation of math in CML.


Peter Murray-Rust, domestic net connection
Virtual School of Molecular Sciences

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