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Re: [Texmacs-dev] Re: [Axiom-developer] RE: [xml-litprog-l] Re:noweb,pa

 From: William Sit Subject: Re: [Texmacs-dev] Re: [Axiom-developer] RE: [xml-litprog-l] Re:noweb,pamphlets, and TeXmacs Date: Wed, 27 Nov 2002 16:39:02 -0500

```address@hidden wrote:
>
> Hello William,
>
> > A TeX expression does not have
> > an unambiguous mathematical meaning. MathML tags define a unique
> > mathematical meaning to a subclass of mathematical expression.
>
> Sorry I don't see exactly what you mean, could you develop a little your
> arguments? In what sense is \$x_i\$ for example ambiguous?

Tim Daly wrote:
>
> Michel,
>
> The expression \$x_i\$ is ambiguous for many reasons. You don't know the
> type of x. It could be a vector so x_i is an element. It could be a
> symbol so x_i is a symbol. It could be a matrix so x_i could be a
> vector, etc.
>
> Without knowing the type of x (and, by the way, of i) and the domain
> of discourse x_i says nothing.
>
> Tim

Thanks, Tim. In fact, in typesetting, the meaning of the expression
\$x_i\$ also depends on its surrounding environment. Mathematicians and
physicists create their own notations, typically these are adopted
"universally" IN THE SUBAREA. Physicists typically write \$a_{ij} x_i\$ to
mean summation as \$i\$ runs through its range. So even if we know the
domain of both \$x\$ and of \$i\$, and the "operator" \$\_\$ (subscript, which
IS a unary operator with lots of different meanings, for example, \$x_i\$
could mean the partial derivative of \$x\$ with respect to the \$i\$-th
independent variable, or the order \$i\$ derivative with respect to some
notationally unspecified independent variable), we still won't know what
\$x_i\$ means in context. Only the human mathematician or physicist can

This, is one reason I say MathML and OpenML are only partial solutions
to the content problem. Fortunately, in computer algebra systems, as in
contrast to typesetting or display, the systems require more precise