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The FOIL algorithm is as follows: Input List of examples and predicate to be learned Output A set of first-order Horn clauses FOIL(Pred, Pos, Neg) Let Pos be the positive examples Let Pred be the predicate to be learned Until Pos is empty do: Let Neg be the negative examples Set Body to empty Call LearnClauseBody Add Pred ← Body to the rule
The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
FOIL is sufficient to expand this product if you creatively combine it with associativity and recursion. It might be instructive to include this tidbit to show how one could apply FOIL to expanding the product with two multiplicands with three summands each. (And, btw, thanks KSmrq for adding the tableau.) Lunch 00:21, 1 May 2007 (UTC)
A Cabtaxi number is the smallest positive number that can be expressed as a sum of two integer cubes in n ways, allowing the cubes to be negative or zero as well as positive. The smallest cabtaxi number after Cabtaxi(1) = 0, is Cabtaxi(2) = 91, [ 5 ] expressed as:
The Klee–Minty cube or Klee–Minty polytope (named after Victor Klee and George J. Minty) is a unit hypercube of variable dimension whose corners have been perturbed. Klee and Minty demonstrated that George Dantzig 's simplex algorithm has poor worst-case performance when initialized at one corner of their "squashed cube".
The notation is also used to denote the characteristic function in convex analysis, which is defined as if using the reciprocal of the standard definition of the indicator function.
Geometric constraint solving is constraint satisfaction in a computational geometry setting, which has primary applications in computer aided design. [1] A problem to be solved consists of a given set of geometric elements and a description of geometric constraints between the elements, which could be non-parametric (tangency, horizontality, coaxiality, etc) or parametric (like distance, angle ...
for the 3-cube is rotations of a 2-polytope (square) in 2-space = 4; for the 2-cube is rotations of a 1-polytope in 1-space = 1; In other words, the 2D puzzle cannot be scrambled at all if the same restrictions are placed on the moves as for the real 3D puzzle. The moves actually given to the 2D Magic Cube are the operations of reflection.