To match a particular formula x with a particular rewrite rule
`` old := new'`, Calc compares the structure of x with
the structure of

If a given meta-variable appears more than once in `old`, the
corresponding sub-formulas of x must be identical. Thus
the pattern ``f(x,x)'` would match ``f(12, 12)'` and
``f(a+1, a+1)'` but not ``f(12, a+1)'` or ``f(a+b, b+a)'`.
(See section Conditional Rewrite Rules, for a way to match the latter.)

Things other than variables must match exactly between the pattern
and the target formula. To match a particular variable exactly, use
the pseudo-function ``quote(v)'` in the pattern. For example, the
pattern ``x+quote(y)'` matches ``x+y'`, ``2+y'`, or
``sin(a)+y'`.

The special variable names ``e'`, ``pi'`, ``i'`, ``phi'`,
``gamma'`, ``inf'`, ``uinf'`, and ``nan'` always match
literally. Thus the pattern ``sin(d + e + f)'` acts exactly like
``sin(d + quote(e) + f)'`.

If the `old` pattern is found to match a given formula, that
formula is replaced by `new`, where any occurrences in `new`
of meta-variables from the pattern are replaced with the sub-formulas
that they matched. Thus, applying the rule ``f(x,y) := g(y+x,x)'`
to ``f(12, a+1)'` would produce ``g(a+13, 12)'`.

The normal `a r` command applies rewrite rules over and over
throughout the target formula until no further changes are possible
(up to a limit of 100 times). Use `C-u 1 a r` to make only one
change at a time.

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