Heuristic detection of relations between real numbers
This functionality does not run in MATLAB.
misc::pslq(numberlist
, precision
)
misc::pslq(numberlist, precision)
returns
a list of integers [k1, ..., kn]
such that —
denoting the elements of numberlist
by a1,
..., an
— the absolute value of
is less than
times the
Euclidean norm of numberlist
, or FAIL
if
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
given above.
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 

Positive integer 
List of integers, or FAIL
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 RNR92032.