BrillhartTests UPΒΆ

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?: (UP, Boolean) -> Boolean

`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?: UP -> Boolean

`brillhartIrreducible?(p)` returns `true` if `p` can be shown to be irreducible by a remark of Brillhart, `false` is inconclusive.

brillhartTrials: () -> NonNegativeInteger

`brillhartTrials()` returns the number of tests in brillhartIrreducible?.

brillhartTrials: NonNegativeInteger -> NonNegativeInteger

`brillhartTrials(n)` sets to `n` the number of tests in brillhartIrreducible? and returns the previous value.

noLinearFactor?: UP -> Boolean

`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.