The a r
(calc-rewrite) [rewrite] command makes
substitutions in a formula according to a specified pattern or
patterns known as rewrite rules. Whereas a
b (calc-substitute) matches literally, so that
substituting ‘sin(x)’ with ‘cos(x)’ matches only the
sin function applied to the variable x,
rewrite rules match general kinds of formulas; rewriting using
the rule ‘sin(x) :=
cos(x)’ matches sin of any
argument and replaces it with cos of that same
argument. The only significance of the name x is
that the same name is used on both sides of the rule.
Rewrite rules rearrange formulas already in Calc's memory. See Syntax Tables, to read about syntax rules, which are similar to algebraic rewrite rules but operate when new algebraic entries are being parsed, converting strings of characters into Calc formulas.