An integer relation between a set of real numbers x1, x2, ..., xn is a set of integers a1, a2, ..., an, not all 0, such that
- π. PSLQ has also helped find new identities involving multiple zeta functions and their appearance in quantum field theory; and in identifying bifurcation points of the logistic map. For example, where B4 is the logistic map's fourth bifurcation point, the constant α = −B4(B4 − 2) is a root of a 120th-degree polynomial whose largest coefficient is 257. Integer relation algorithms are combined with tables of high precision mathematical constants and heuristic search methods in applications such as the Inverse Symbolic Calculator or Plouffe's Inverter.
Integer relation finding can be used to factor polynomials of high degree.
Weisstein, Eric W. "HJLS Algorithm". MathWorld.
- ↑ Johan Håstad, Bettina Just, Jeffrey Lagarias, Claus-Peter Schnorr: Polynomial time algorithms for finding integer relations among real numbers. Preliminary version: STACS 1986 (Symposium Theoret. Aspects Computer Science) Lecture Notes Computer Science 210 (1986), p. 105–118. SIAM J. Comput., Vol. 18 (1989), pp. 859–881
- ↑