10.11.1 Entering Rewrite Rules

Rewrite rules normally use the “assignment” operator ‘old := new’. This operator is equivalent to the function call ‘assign(old, new)’. The assign function is undefined by itself in Calc, so an assignment formula such as a rewrite rule will be left alone by ordinary Calc commands. But certain commands, like the rewrite system, interpret assignments in special ways.

For example, the rule ‘sin(x)^2 := 1-cos(x)^2’ says to replace every occurrence of the sine of something, squared, with one minus the square of the cosine of that same thing. All by itself as a formula on the stack it does nothing, but when given to the a r command it turns that command into a sine-squared-to-cosine-squared converter.

To specify a set of rules to be applied all at once, make a vector of rules.

When a r prompts you to enter the rewrite rules, you can answer in several ways:

1. With a rule: f(x) := g(x) RET.
2. With a vector of rules: [f1(x) := g1(x), f2(x) := g2(x)] RET. (You can omit the enclosing square brackets if you wish.)
3. With the name of a variable that contains the rule or rules vector: myrules RET.
4. With any formula except a rule, a vector, or a variable name; this will be interpreted as the old half of a rewrite rule, and you will be prompted a second time for the new half: f(x) RET g(x) RET.
5. With a blank line, in which case the rule, rules vector, or variable will be taken from the top of the stack (and the formula to be rewritten will come from the second-to-top position).

If you enter the rules directly (as opposed to using rules stored in a variable), those rules will be put into the Trail so that you can retrieve them later. See Trail Commands.

It is most convenient to store rules you use often in a variable and invoke them by giving the variable name. The s e (calc-edit-variable) command is an easy way to create or edit a rule set stored in a variable. You may also wish to use s p (calc-permanent-variable) to save your rules permanently; see Other Operations on Variables.

Rewrite rules are compiled into a special internal form for faster matching. If you enter a rule set directly it must be recompiled every time. If you store the rules in a variable and refer to them through that variable, they will be compiled once and saved away along with the variable for later reference. This is another good reason to store your rules in a variable.

Calc also accepts an obsolete notation for rules, as vectors ‘[old, new]’. But because it is easily confused with a vector of two rules, the use of this notation is no longer recommended.