TeX Language Mode
-----------------

The `d T' (`calc-tex-language') command selects the conventions of
"math mode" in the TeX typesetting language, by Donald Knuth.
Formulas are entered and displayed in TeX notation, as in `\sin\left(
a \over b \right)'.  Math formulas are usually enclosed by `$ $' signs
in TeX; these should be omitted when interfacing with Calc.  To Calc,
the `$' sign has the same meaning it always does in algebraic formulas
(a reference to an existing entry on the stack).

Complex numbers are displayed as in `3 + 4i'.  Fractions and quotients
are written using `\over'; binomial coefficients are written with
`\choose'.  Interval forms are written with `\ldots', and error forms
are written with `\pm'.  Absolute values are written as in `|x + 1|',
and the floor and ceiling functions are written with `\lfloor',
`\rfloor', etc.  The words `\left' and `\right' are ignored when
reading formulas in TeX mode.  Both `inf' and `uinf' are written as
`\infty'; when read, `\infty' always translates to `inf'.

Function calls are written the usual way, with the function name
followed by the arguments in parentheses.  However, functions for
which TeX has special names (like `\sin') will use curly braces
instead of parentheses for very simple arguments.  During input, curly
braces and parentheses work equally well for grouping, but when the
document is formatted the curly braces will be invisible.  Thus the
printed result is `sin 2x' but `sin(2 + x)'.

Function and variable names not treated specially by TeX are simply
written out as-is, which will cause them to come out in italic letters
in the printed document.  If you invoke `d T' with a positive numeric
prefix argument, names of more than one character will instead be
written `\hbox{NAME}'.  The `\hbox{ }' notation is ignored during
reading.  If you use a negative prefix argument, such function names
are written `\NAME', and function names that begin with `\' during
reading have the `\' removed.  (Note that in this mode, long variable
names are still written with `\hbox'.  However, you can always make an
actual variable name like `\bar' in any TeX mode.)

During reading, text of the form `\matrix{ ... }' is replaced by `[
... ]'.  The same also applies to `\pmatrix' and `\bmatrix'.  The
symbol `&' is interpreted as a comma, and the symbols `\cr' and `\\'
are interpreted as semicolons.  During output, matrices are displayed
in `\matrix{ a & b \\ c & d}' format; you may need to edit this
afterwards to change `\matrix' to `\pmatrix' or `\\' to `\cr'.

Accents like `\tilde' and `\bar' translate into function calls
internally (`tilde(x)', `bar(x)').  The `\underline' sequence is
treated as an accent.  The `\vec' accent corresponds to the function
name `Vec', because `vec' is the name of a built-in Calc function.
The following table shows the accents in Calc, TeX, and "eqn"
(described in the next section):

     Calc      TeX           eqn
     ----      --           --
     acute     \acute
     bar       \bar          bar
     breve     \breve
     check     \check
     dot       \dot          dot
     dotdot    \ddot         dotdot
     dyad                    dyad
     grave     \grave
     hat       \hat          hat
     Prime                   prime
     tilde     \tilde        tilde
     under     \underline    under
     Vec       \vec          vec

The `=>' (evaluates-to) operator appears as a `\to' symbol: `{A \to
B}'.  TeX defines `\to' as an alias for `\rightarrow'.  However, if
the `=>' is the top-level expression being formatted, a slightly
different notation is used: `\evalto A \to B'.  The `\evalto' word is
ignored by Calc's input routines, and is undefined in TeX.  You will
typically want to include one of the following definitions at the top
of a TeX file that uses `\evalto':

     \def\evalto{}
     \def\evalto#1\to{}

The first definition formats evaluates-to operators in the usual
way.  The second causes only the B part to appear in the
printed document; the A part and the arrow are hidden.
Another definition you may wish to use is `\let\to=\Rightarrow'
which causes `\to' to appear more like Calc's `=>' symbol.
See Evaluates-To Operator, for a discussion of `evalto'.

The complete set of TeX control sequences that are ignored during
reading is:

     \hbox  \mbox  \text  \left  \right
     \,  \>  \:  \;  \!  \quad  \qquad  \hfil  \hfill
     \displaystyle  \textstyle  \dsize  \tsize
     \scriptstyle  \scriptscriptstyle  \ssize  \ssize
     \rm  \bf  \it  \sl  \roman  \bold  \italic  \slanted
     \cal  \mit  \Cal  \Bbb  \frak  \goth
     \evalto

Note that, because these symbols are ignored, reading a TeX formula
into Calc and writing it back out may lose spacing and font
information.

Also, the "discretionary multiplication sign" `\*' is read the same as
`*'.

The TeX version of this manual includes some printed examples at the
end of this section.