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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
"read between the symbols".

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
meanings and can handle polymorphism and overloading of operators. So
the trick is not to lose such information once an expression is sent to
the display handler.


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