PSLQ

[Han]

(11-30-2017 02:16 AM)AlexFekken Wrote:  [b]But, as a sanity check, from a mathematical perspective these special types of numbers have measure zero, i.e. the probability that a randomly picked real number (within a given range, say between 0 and 1) belongs to one of these special types is 0, rather than close to 1. So mathematically your expectation that these functions will be useful when working with arbirtrary numbers should be 0 too.

I suppose it depends on whether you are looking at pure measure, or "relative measure" -- in the sense that most students are given problems in which the answers are generally not from the set of reals, but instead from the set of algebraic numbers. (I.e. they are guaranteed with probability 1.)

But even for folks such as physicists are interested in these "nice" numbers because they show up as constants in various "important" physics equations. In fact, there is an entire field of study devoted to finding the "identity" of various constants all due to the advent of more efficient algorithms for integer coefficients such as PSLQ.

http://www2.lbl.gov/Science-Articles/Arc...rithm.html