3.4.3 Continuing work

The macros described above are currently being used by the authors with apparent success. Yet, the macros do not quite reduce ambiguities to the desired extent, particularly regarding powers and derivatives using superscripts, and the status of parentheses is somewhat uncomfortable. The main extension being developed is that an optional @ sign will be taken as introducing the argument list (with the mnemonic `function evaluated at a point'). Thus,

$$\verb\vert\BesselJ{\nu}@{z}\vert \rightarrow J_{\nu}(z).$$

Further, authors often wish to incorporate operations, particularly powers and derivatives between the function and its arguments. We must recognize the semantic import, while still accepting the presentational hint. We extend the syntax by allowing a primes (or a backprime taking a macro argument), which applied to a mathematical function, is taken as signifying single (or multiple) derivative; the caret is then reserved solely for powers. Inclusion of other declared operators needs also be considered (eg. transpose, conjugation, etc.).

Thus the following markup could be employed

$$\verb\vert\BesselJ{\nu}''@{z}\vert \rightarrow J''_{\nu}(z)$$

or

$$\verb\vert\HypergeoF^{2}@{a,b}{c}{z}\vert \rightarrow F^{2}\left({a,b\atop c};z\right).$$

This additional markup seems only slightly `odd' (from a L^ATEX point of view), while significantly clarifying the author's intent.

At the same time, it still supports good presentation. It preserves the author's flexibility in choosing whether to write derivatives with embedded primes or as a prefix operation; similarly with powers. Standardized presentation of function arguments is also provided.

The special function macros also serve as a starting point for type inference, but further declarations will be needed to handle variables and operators, at least.