# BrillhartTests UP¶

Author: Frederic Lehobey, James H. Davenport Date Created: 28 June 1994 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart, Note on Irreducibility Testing, Mathematics of Computation, vol. 35, num. 35, Oct. 1980, 1379-1381 [2] James Davenport, On Brillhart Irreducibility. To appear. [3] John Brillhart, On the Euler and Bernoulli polynomials, J. Reine Angew. Math., v. 234, (1969), pp. 45-64
brillhartIrreducible?(p, noLinears) returns true if p can be shown to be irreducible by a remark of Brillhart, false else. If noLinears is true, we are being told p has no linear factors false does not mean that p is reducible.
brillhartIrreducible?(p) returns true if p can be shown to be irreducible by a remark of Brillhart, false is inconclusive.
brillhartTrials() returns the number of tests in brillhartIrreducible?.
brillhartTrials(n) sets to n the number of tests in brillhartIrreducible? and returns the previous value.
noLinearFactor?(p) returns true if p can be shown to have no linear factor by a theorem of Lehmer, false else. I insist on the fact that false does not mean that p has a linear factor.