Integer Relation
A set of Real Numbers 
, ..., 
is said to possess an integer relation if there exist integers 
such that
with not all
. An interesting example of such a relation is the 17-Vector (1, 
, 
, ..., 
)with 
, which has an integer relation (1, 0, 0, 0, 
, 0, 0, 0, 
, 0, 0, 0, 
, 0, 0, 0,1), i.e.,
This is a special case of finding the polynomial of degree
satisfied by 
.Algorithms for finding integer relations include the Ferguson-Forcade Algorithm, HJLS Algorithm, LLLAlgorithm, PSLQ Algorithm, PSOS Algorithm, and the algorithm of Lagarias and Odlyzko (1985). Perhaps the simplest(and unfortunately most inefficient) such algorithm is the Greedy Algorithm. Plouffe's ``Inverse Symbolic Calculator''site includes a huge database of 54 million Real Numbers which are algebraically related to fundamentalmathematical constants.
See also Constant Problem, Ferguson-Forcade Algorithm, Greedy Algorithm, Hermite-Lindemann Theorem,HJLS Algorithm, Lattice Reduction, LLL Algorithm, PSLQ Algorithm, PSOS Algorithm, RealNumber, Lindemann-Weierstraß Theorem
References
Bailey, D. and Plouffe, S. ``Recognizing Numerical Constants.'' http://www.cecm.sfu.ca/organics/papers/bailey/. Lagarias, J. C. and Odlyzko, A. M. ``Solving Low-Density Subset Sum Problems.'' J. ACM 32, 229-246, 1985. Plouffe, S. ``Inverse Symbolic Calculator.'' http://www.cecm.sfu.ca/projects/ISC/.
- Steenrod Algebra
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