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 @c{$\sin(2 + x)$}
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

`\`

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):

@begingroup @let@calcindexershow=@calcindexernoshow @let@calcindexersh=@calcindexernoshow @endgroup

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 `\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 section The 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 ``*'`.

Here are some examples of how various Calc formulas are formatted in TeX:

sin(a^2 / b_i) \sin\left( {a^2 \over b_i} \right)

[(3, 4), 3:4, 3 +/- 4, [3 .. inf)] [3 + 4i, {3 \over 4}, 3 \pm 4, [3 \ldots \infty)]

[abs(a), abs(a / b), floor(a), ceil(a / b)] [|a|, \left| a \over b \right|, \lfloor a \rfloor, \left\lceil a \over b \right\rceil]

[sin(a), sin(2 a), sin(2 + a), sin(a / b)] [\sin{a}, \sin{2 a}, \sin(2 + a), \sin\left( {a \over b} \right)]

First with plain `d T`, then with `C-u d T`, then finally with
`C-u - d T` (using the example definition
``\def\foo#1{\tilde F(#1)}'`:

[f(a), foo(bar), sin(pi)] [f(a), foo(bar), \sin{\pi}] [f(a), \hbox{foo}(\hbox{bar}), \sin{\pi}] [f(a), \foo{\hbox{bar}}, \sin{\pi}]

First with ``\def\evalto{}'`, then with ``\def\evalto#1\to{}'`:

2 + 3 => 5 \evalto 2 + 3 \to 5

First with standard `\to`

, then with ``\let\to\Rightarrow'`:

[2 + 3 => 5, a / 2 => (b + c) / 2] [{2 + 3 \to 5}, {{a \over 2} \to {b + c \over 2}}]

Matrices normally, then changing `\matrix`

to `\pmatrix`

:

[ [ a / b, 0 ], [ 0, 2^(x + 1) ] ] \matrix{ {a \over b} & 0 \\ 0 & 2^{(x + 1)} } \pmatrix{ {a \over b} & 0 \\ 0 & 2^{(x + 1)} }

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