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Intervals are generally coded as lower bound and upper bound connected by the operator ‘..’, usually associated to a variable in an equation. E.g.
x= (2.5 .. 3.5)
means that the variable x is taken in the range from 2.5 up to 3.5. Note, that the bounds can be algebraic expressions, which, however, must evaluate to numeric results. In cases where an interval is returned as the result, the lower and upper bounds can be extracted by the part operator as the first and second part respectively. A starting point is specified by an equation with a numeric righthand side, e.g.
x=3.0
If for multivariate applications several coordinates must be specified by intervals or as a starting point, these specifications can be collected in one parameter (which is then a list) or they can be given as separate parameters alternatively. The list form is more appropriate when the parameters are built from other REDUCE calculations in an automatic style, while the flat form is more convenient for direct interactive input.
The keyword parameters accuracy=\(\langle \)a\(\rangle \) and iterations=\(\langle \)i\(\rangle \), where \(\langle \)a\(\rangle \) and \(\langle \)i\(\rangle \) must be positive integer numbers, control the iterative algorithms: the iteration is continued until the local error is below \(10^{-a}\); if that is impossible within \(\langle \)i\(\rangle \) steps, the iteration is terminated with an error message. The values reached so far are then returned as the result.
Normally the algorithms produce only a minimum of printed output during their operation. In cases of an unsuccessful or unexpected long operation a trace of the iteration can be printed by setting
on trnumeric;
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