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[14] and whose period is the least common multiple of the component periods. Although the periods will share a common divisor of 2, the moduli can be chosen so that is the only common divisor and the resultant period is (m 1 − 1)(m 2 − 1)···(m k − 1)/2 k−1. [2]: 744 One example of this is the Wichmann–Hill generator.
A least common multiple of a and b is a common multiple that is minimal, in the sense that for any other common multiple n of a and b, m divides n. In general, two elements in a commutative ring can have no least common multiple or more than one. However, any two least common multiples of the same pair of elements are associates. [10]
One method of producing a longer period is to sum the outputs of several LCGs of different periods having a large least common multiple; the Wichmann–Hill generator is an example of this form. (We would prefer them to be completely coprime, but a prime modulus implies an even period, so there must be a common factor of 2, at least.) This can ...
The results of multiple LCG algorithms are combined through the CLCG algorithm to create pseudo-random numbers with a longer period than is achievable with the LCG method by itself. [ 3 ] The period of a CLCG is the least common multiple of the periods of the individual generators, which are one less than the moduli.
Equivalently, g(n) is the largest least common multiple (lcm) of any partition of n, or the maximum number of times a permutation of n elements can be recursively applied to itself before it returns to its starting sequence. For instance, 5 = 2 + 3 and lcm(2,3) = 6. No other partition of 5 yields a bigger lcm, so g(5) = 6.
Tools. Tools. move to sidebar hide ... Download as PDF; Printable version; ... Greatest common divisor, also known as the greatest common factor; Least common multiple;
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The Unscrambler – free-to-try commercial multivariate analysis software for Windows; Unistat – general statistics package that can also work as Excel add-in; WarpPLS – statistics package used in structural equation modeling; Wolfram Language [8] – the computer language that evolved from the program Mathematica. It has similar ...