20.67 WITH: Local Switch Settings

Author: Francis Wright

The operator withallows an expression to be evaluated and its value displayed subject to switch settings that apply only locally during the evaluation and display of this expression. Its syntax is

where on/off is either onor off, and switches is a single switch name or a comma-separated sequence of switch names (as for the onand offcommands). It is intended primarily for interactive use and provides a convenient way to experiment with the effects of different switches. Messages about changes of domain mode are suppressed.

Here are some examples, assuming default switch settings:

(a+b)^2/2 with off exp, on div;

 1         2
---*(a + b)
 2

pi with on rounded;

3.14159265359

fix(sqrt 10) with on rounded;

3

The withoperator has precedence immediately above :=, so withbinds tighter than :=but looser than almost every other infix operator. Therefore,

x := pi + e with on rounded;

parses as

x := ((pi + e) with on rounded);

Hence,

x := pi + e with on rounded;

5.85987448205

x;

 103088002085129
-----------------
 17592186044416

x with on rounded;

5.85987448205

In the above example, \(x\) is assigned a floating-point number, but it is displayed as a rational number when the default switch settings are in effect.

The keywords onand offcan appear as many times as desired in the right operand of with. If a switch already has the setting specified in the right operand then it is not changed, but if it has the opposite setting then it is changed before the left operand is evaluated, and displayed if required, and changed back afterwards. Repeated identical switch settings are ignored but conflicting settings cause an error. The order of switch settings is preserved.

Not all switches work sensibly locally, but for example

int(sin x, x) with on trint;

turns on integration tracing temporarily.

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