AngouriMath

Symbolics for .NET


Table of contents

AngouriMath

Navigation
Home Quick start Wiki Almanac Research What's new Try Use Angouri.org GitHub Report a bug Donate Contacts

IntervalArithmetic

← Back to list of classes

Description

Summary

The image of an interval under a function that is monotone on it, and the product and
quotient of two intervals: what ln((0; 1)), e^[0; 1], [1; 2]^2 and
(1; 2) * (3; 4) are as sets.

Remarks

A function that is monotone on an interval maps it to the interval between the images of
its ends, in the same order when it is increasing and the reverse when it is decreasing,
each end attained exactly when the end it comes from is -- so the openness travels with
the end. An end whose image is infinite is never attained: ln((0; 1)) is
(-oo; 0), and ln([0; 1)) is the same set, since ln(0) is not a
value. That is the whole of the method, and the only question for each function is on
which intervals it is monotone, which is answered here for the ones the library has
nodes for and declined for the rest: a sine over an interval longer than half a period
is not an interval between two images, and a sign that cannot be read is not guessed.
 Only numeric ends are read. An interval with a symbolic end could be handled by the same
rule under a condition on the end, and is left as written instead: the answer would be
a piecewise over the sign of something, which is not what a caller asking for a set
wants back.
 A product of two intervals is the interval between the least and the greatest of the
four products of ends, an end attained where both its factors are, and a quotient is a
product by the reciprocal, which is an interval exactly when the divisor does not
contain zero.
https://github.com/asc-community/AngouriMath/issues/322

Members

























Angouri © 2019-2023 · Project's repo · Site's repo · Octicons · Transparency · 4378 pages online