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In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [1] —hence the method may be referred to as the FOIL method. The word FOIL is an acronym for the four terms of the product: First ("first" terms of each binomial are multiplied together)
For binomial multiplication, distribution is sometimes referred to as the FOIL Method [2] (First terms , Outer , Inner , and Last ) such as: (+) (+) = + + +. In all semirings , including the complex numbers , the quaternions , polynomials , and matrices , multiplication distributes over addition: u ( v + w ) = u v + u w , ( u + v ) w = u w + v ...
Like the ID3 algorithm, FOIL hill climbs using a metric based on information theory to construct a rule that covers the data. Unlike ID3, however, FOIL uses a separate-and-conquer method rather than divide-and-conquer, focusing on creating one rule at a time and collecting uncovered examples for the next iteration of the algorithm. [citation ...
As a search of the Web will confirm, the FOIL idea is discussed at many educational sites (some training teachers) and incorporated into textbooks. Two objections are: (1) this introduces a new isolated fact to memorize rather than relying on the already-learned distributive law, and (2) it only applies to a product of binomials.
[1] [2] When n = 2, it is easy to see why this is incorrect: (x + y) 2 can be correctly computed as x 2 + 2xy + y 2 using distributivity (commonly known by students in the United States as the FOIL method). For larger positive integer values of n, the correct result is given by the binomial theorem.
Binomial coefficient, numbers appearing in the expansions of powers of binomials; Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition; Binomial theorem, a theorem about powers of binomials; Binomial type, a property of sequences of polynomials; Binomial series, a mathematical series
The initial idea is usually attributed to the work of Hardy with Srinivasa Ramanujan a few years earlier, in 1916 and 1917, on the asymptotics of the partition function.It was taken up by many other researchers, including Harold Davenport and I. M. Vinogradov, who modified the formulation slightly (moving from complex analysis to exponential sums), without changing the broad lines.
The Octave programming language provides a pseudoinverse through the standard package function pinv and the pseudo_inverse() method. In Julia (programming language) , the LinearAlgebra package of the standard library provides an implementation of the Moore–Penrose inverse pinv() implemented via singular-value decomposition.