Ferguson-Forcade Algorithm
A practical algorithm for determining if there exist integers 
for given real numbers 
such that
or else establish bounds within which no such Integer Relation can exist (Ferguson and Forcade 1979). Anonrecursive variant of the original algorithm was subsequently devised by Ferguson (1987). The Ferguson-Forcadealgorithm has shown that there are no algebraic equations of degree
with integer coefficients having Euclideannorms below certain bounds for 
, 
, 
, 
, 
, 
, 
, and 
,where e is the base for the Natural Logarithm, 
is Pi, and is theEuler-Mascheroni Constant (Bailey 1988).| Constant | Bound |
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References
Bailey, D. H. ``Numerical Results on the Transcendence of Constants Involving Ferguson, H. R. P. ``A Short Proof of the Existence of Vector Euclidean Algorithms.'' Proc. Amer. Math. Soc. 97, 8-10, 1986. Ferguson, H. R. P. ``A Non-Inductive GL( Ferguson, H. R. P. and Forcade, R. W. ``Generalization of the Euclidean Algorithm for Real Numbers to All Dimensions Higher than Two.'' Bull. Amer. Math. Soc. 1, 912-914, 1979., 
, and Euler's Constant.'' Math. Comput. 50, 275-281, 1988.
) Algorithm that Constructs Linear Relations for 
-Linearly Dependent Real Numbers.'' J. Algorithms 8, 131-145, 1987.
- Sheaf (Topology)
- Shear
- Shear Matrix
- Shephard's Problem
- Sheppard's Correction
- Sherman-Morrison Formula
- Shi
- Shift
- Shift Property
- Shimura-Taniyama Conjecture
- Shimura-Taniyama-Weil Conjecture
- Shoemaker's Knife
- Shoe Surface
- Shortening
- Shuffle
- Siamese Dodecahedron
- Siamese Method
- Sibling
- Sicherman Dice
- Sici Spiral
- Side
- Sidon Sequence
- Siegel Disk Fractal
- Siegel Modular Function
- Siegel's Paradox