Approximate polynomial GCD over integers

Kosaku Nagasaka
2009 ACM SIGSAM Bulletin  
Abs tract Symbolic numeric algorithms for polynomials (He very important, especially for practicul COIllputations since we have to operate with empirical polynomials having numel"ical errors on t heir coefficients. Recently, for those polynomials, lots of a lgorithms have been in troduced, approximate univariate ceo and approximate lIIultivariate factorizat io n for example. However, for polynomials over integers having ooefiicicnts rounded from empir ical data, changing their coefficients over
more » ... r coefficients over Teals docs lIot rcmaill them in the polynomial ring over integers, he,nee we need several a pproximate operations over integers. In this paper, we discuss about computing a polynom ial C GD of unhrdriat.e or multivariate polynomials o\'er integers approximately. Here, "approximately" me1lns that we compute 11 polynomial CCO ovcr in tegers by chang ing their coefficients slightly over integers so that the in put polynomial!; sti ll remain over integers.
doi:10.1145/1504347.1504351 fatcat:elgsflaiwffahnlbukcuooifve