I have updated some basic requirements for a generic mathematical

markup language for scientific requirements at the next link.

[http://canonicalscience.blogspot.com...nonml-is.html]

Some requirements fit into the XML model and could be considered for

debate for the future mathML specifications. Other requirements do not

fit and will be developed in alternative mathematical approaches to

those from the w3c from the Center for CANONICAL |SCIENCE).

Some requirements were presented in the past

[http://canonicalscience.blogspot.com...anonmath.html]

but that document will be updated.

=== Basic requirements =============

Data optimisation

--------------------------------

MathML is unnaturally verbose and redundant. Whereas in practice this

is not a serious problem for encoding simple formulae as E=mc^2, it is

a problem for scientific databases and for computation or interchange

of information.

In shorthand notation, the Redfield equation reads

(partial rho) / (partial t) = (L + R) rho

where R is the Redfield tensor. But equation stored for a small

physicochemical system of current interest needs of the order of 7 GB

of memory.

Taking an x10 verbosity factor, we would need 70 Gb in MathML for the

same equation.

The Redfield equation is an ultrasimplified version of more general

equations.

For example, following MathML 2.0 specification matrix

0 1 0

0 0 1

1 0 0

is encoded as

<matrix>

<matrixrow>

<cn>0</cn><cn>1</cn><cn>0</cn>

</matrixrow>

<matrixrow>

<cn>0</cn><cn>0</cn><cn>1</cn>

</matrixrow>

<matrixrow>

<cn>1</cn><cn>0</cn><cn>0</cn>

</matrixrow>

</matrix>

but can I use this ultraverbose encoding for Detour matrices of

scientific interest? Detour matrices are N x N ones. In mathematical

chemistry, N is of the order of the size of a chemical compound.

I do not consider elegant and coherent encoding big (N = 1000) Detour

matrices using MathML. Is it?

Encoding of non-hierarchical structures

-----------------------------------------------------------------

This may be useful on quantum mechanical models.

Extensibility

------------------------

Currently MathML presentational markup is not, and not all people agree

on extensibility of Content MathML.

Backward compatibility

---------------------------------------

Language would be more close possible to popular existent systems. I

mean: TeX, LaTeX, Mathematica, Maple, Fortran, Lisp, C, ISO 12083, AAP

Math, some scientific DTD (Elsevier one), etc.

This also includes compatibility with CSS, HTML and others.

Formal language

-----------------------------

For example, SXML is directly based in SEXPR and permit us to exploit

formal structure for abstraction layers.

I agree with mathematician Chaitin on the possibilities of computerized

versions of set theory.

Simplicity

------------------

The good and concise is twice good!

The language would be directly manipulated and encoded by humans.

Another "advanced" site where (ds)^2 is being incorrectly served as

2s ds is Distler's blog MUSSINGS.

If you rely on tools and you are trained to never see the underlying

code (MathML is popularly presented as a kind of hidden mathematical

postscript) you do not know you are encoding.

MathML ultraverbose code

<mrow>

<semantics>

<mrow>

<msubsup>

<mo>∫</mo>

<mn>1</mn>

<mi>t</mi>

</msubsup>

<mfrac>

<mrow>

<mo>ⅆ</mo>

<mi>x</mi>

</mrow>

<mi>x</mi>

</mfrac>

</mrow>

<annotation-xml encoding="MathM L-Content">

<apply>

<int/>

<bvar><ci>x</ci></bvar>

<lowlimit><cn>1 </cn></lowlimit>

<uplimit><ci> t</ci></uplimit>

<apply>

<divide/>

<cn>1</cn>

<ci>x</ci>

</apply>

</apply>

</annotation-xml>

</semantics>

</mrow>

for \int_1^t \frac{dx}{x} may be avoided. Difficulty of the encoding

would be of same order than in TeX.

Juan R.

Center for CANONICAL |SCIENCE)