Heuristic detection of relations between real numbers
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misc::pslq(numberlist, precision) returns
a list of integers
[k1, ..., kn] such that —
denoting the elements of
..., an — the absolute value of
is less than
Euclidean norm of
such integers could not be detected.
This method can be used to get an idea about linear dependencies, before proving them.
misc::pslq is not affected
by the current value of
DIGITS. Numerical computations are carried
out with more significant digits such that the output meets the specification
Does π satisfy a polynomial equation of degree at most 2 ?
misc::pslq([1, PI, PI^2], 20)
Having forgotten the relation between sine and cosine, we can try the heuristic way.
misc::pslq([1, sin(0.32), sin(0.32)^2, cos(0.32), cos(0.32)^2], 10)
List of real numbers or objects that can be converted to real
numbers by the function
List of integers, or
This function has been written by Raymond Manzoni.
The algorithm has been taken from Bailey and Plouffe, Recognizing numerical constants. See also Helaman R.P. Ferguson and David Bailey, A Polynomial Time, Numerically Stable Integer Relation Algorithm, RNR Technical Report RNR-92-032.