" Factoring Integers with the Self-Initializing Quadratic Sieve ", M.A. In Number Theoretic and Algebraic Methods in Computer Science, Proc. "Implementing the Self Initializing Quadratic Sieve on a Distributed Network.
#MAPLE IFACTOR CODE#
The implementation of the Multiple Polynomial Quadratic Sieve is based on code by Paul Zimmermann and Scott Contini, and it is described in the following articles.Īlford, W. It increases the efficiency of the method when one of the factors is of the form k m + 1. The pollard base method accepts an additional optional integer k : ifactor ( n, pollard, k ). iFactor is an excellent way to have some challenging, strategic fun while practicing multiplication. You try to get four-in-a-row before your opponent by multiplying two factors together. If the 'easyfunc' option is chosen, the result of the ifactor call will be a product of the factors that were easy to compute, and one or more functions of the form _c_k ( m ) where the k is an integer which preserves the uniqueness of this composite, and m is the composite number itself. The board is populated with the all the products of the numbers 1 through 9. If the 'easy' option is chosen, the result of the ifactor call will be a product of the factors that were easy to compute, and one or more names of the form _c||m_k indicating an m -digit composite number that was not factored where the k is an integer which preserves (but does not imply) the uniqueness of this composite. which does no further work, and provides the computed factors. I do see mserver using 100 of a single core. I ran ifactor with a 100 digit input and do not see mserver using multiple cores in top. 'morrbril' and 'pollard' (default for Maple 11 and earlier) Mohsin Ali at the University of Ontario, he says that ifactor uses multiple threads and presents a graph of measured results. Shanks' undocumented square-free factorization Morrison and Brillhart's continued fraction method Multiple Polynomial Quadratic Sieve method By default, a mixed method that primarily uses the multiple polynomial quadratic sieve method ( 'mpqsmixed' ) is used as the base method. If a second parameter is specified, the named method will be used when the front-end code fails to achieve the factorization. The expand function may be applied to cause the factors to be multiplied together again. Maple is a powerful mathematical calculator, often called a computer algebra system (CAS) or symbolic mathematics program, because unlike most calculators it can do alge- bra and calculus symbolically. , e m are their multiplicities (negative in the case of the denominator of a rational). , f m are the distinct prime factors of n, and e 1. Ifactor returns the complete integer factorization of n. One of our healthcare providers will review your request and respond in minutes. (optional) additional arguments specific to base method How it works 1 Describe your symptoms through our app Open the app and click the Get care button. (optional) name of base method for factoring
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