Eqn Language Mode
-----------------

"Eqn" is another popular formatter for math formulas.  It is designed
for use with the TROFF text formatter, and comes standard with many
versions of Unix.  The `d E' (`calc-eqn-language') command selects
"eqn" notation.

The "eqn" language's main idiosyncrasy is that whitespace plays a
significant part in the parsing of the language.  For example, `sqrt
x+1 + y' treats `x+1' as the argument of the `sqrt' operator.  "Eqn"
also understands more conventional grouping using curly braces:
`sqrt{x+1} + y'.  Braces are required only when the argument contains
spaces.

In Calc's "eqn" mode, however, curly braces are required to delimit
arguments of operators like `sqrt'.  The first of the above examples
would treat only the `x' as the argument of `sqrt', and in fact `sin
x+1' would be interpreted as `sin * x + 1', because `sin' is not a
special operator in the "eqn" language.  If you always surround the
argument with curly braces, Calc will never misunderstand.

Calc also understands parentheses as grouping characters.  Another
peculiarity of "eqn"'s syntax makes it advisable to separate words
with spaces from any surrounding characters that aren't curly braces,
so Calc writes `sin ( x + y )' in "eqn" mode.  (The spaces around
`sin' are important to make "eqn" recognize that `sin' should be
typeset in a roman font, and the spaces around `x' and `y' are a good
idea just in case the "eqn" document has defined special meanings for
these names, too.)

Powers and subscripts are written with the `sub' and `sup' operators,
respectively.  Note that the caret symbol `^' is treated the same as a
space in "eqn" mode, as is the `~' symbol (these are used to introduce
spaces of various widths into the typeset output of "eqn").

As in TeX mode, Calc's formatter omits parentheses around the
arguments of functions like `ln' and `sin' if they are
"simple-looking"; in this case Calc surrounds the argument with
braces, separated by a `~' from the function name: `sin~{x}'.

Font change codes (like `roman X') and positioning codes (like `~' and
`down N X') are ignored by the "eqn" reader.  Also ignored are the
words `left', `right', `mark', and `lineup'.  Quotation marks in "eqn"
mode input are treated the same as curly braces: `sqrt "1+x"' is
equivalent to `sqrt {1+x}'; this is only an approximation to the true
meaning of quotes in "eqn", but it is good enough for most uses.

Accent codes (`X dot') are handled by treating them as
function calls (`dot(X)') internally.  See TeX Language Mode for a table of these accent functions.  The `prime' accent
is treated specially if it occurs on a variable or function name:
`f prime prime ( x prime )' is stored internally as
`f''(x')'.  For example, taking the derivative of `f(2 x)'
with `a d x' will produce `2 f'(2 x)', which "eqn" mode
will display as `2 f prime ( 2 x )'.

Assignments are written with the `<-' (left-arrow) symbol, and
`evalto' operators are written with `->' or `evalto ... ->' (*Note TeX
Language Mode::, for a discussion of this).  The regular Calc symbols
`:=' and `=>' are also recognized for these operators during reading.

Vectors in "eqn" mode use regular Calc square brackets, but matrices
are formatted as `matrix { ccol { a above b } ... }'.  The words
`lcol' and `rcol' are recognized as synonyms for `ccol' during input,
and are generated instead of `ccol' if the matrix justification mode
so specifies.