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evalr

evaluate an expression using range arithmetic

shake

compute a bounding interval

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

evalr(expr)

shake(expr, ampl)

Parameters

expr

-

expression

ampl

-

(optional) positive integer

Description

• 

The evalr(expr) function evaluates an expression containing ranges written INTERVAL(a..b) with a<=b, sequences of ranges written INTERVAL(a..b, c..d, ...), or bounded variables written INTERVAL(x, a..b). By default a variable x is converted to INTERVAL(x, -infinity ..infinity). The result of evalr in this case can be a sequence of ranges, or an expression if both sides of the resulting range are equal. The imprecise variables INTERVAL(x, -infinity..infinity) are converted back to x if the result is the same for all values of x.

• 

The function evalr can be called with an expression without a range. In this case, the decision functions min, max, abs and Signum are evaluated using range arithmetic. Thus, evalr(Signum(expr)) can return FAIL.

• 

The shake(expr, ampl) function replaces the constants at the leaves of the expression tree by an interval of width Float(10, -ampl), then uses evalr to propagate these intervals bottom-up. If ampl is not specified, the current value of Digits is used.

Examples

evalrmin2&comma;3

3

(1)

evalrsinINTERVAL2..7

INTERVAL1..sin2

(2)

evalrx

INTERVALINTERVALx&comma;0..&infin;&comma;INTERVALx&comma;&infin;..0

(3)

shake&pi;&comma;3

INTERVAL3.1102..3.1730

(4)

See Also

abs

Digits

evalrC

max

min

signum

solve

 


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