# 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.