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irreduc

polynomial irreducibility test

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

irreduc(a)

irreduc(a, K)

Parameters

a

-

multivariate polynomial

K

-

(optional) algebraic number field extension

Description

• 

The irreduc function tests whether a multivariate polynomial over an algebraic number field is irreducible.  It returns true if a is irreducible, false otherwise.  Note that a constant polynomial by convention is reducible.

• 

The call irreduc(a) tests for irreducibility over the field implied by the coefficients present; if all the coefficients are rational, then the irreducibility test is over the rationals.

• 

The call irreduc(a, K) tests for irreducibility over the algebraic number field defined by K. K must be a single RootOf, a list or set of RootOfs, a single radical, or a list or set of radicals.

Examples

irreduc2

false

(1)

irreducx3+5

true

(2)

irreducx3+5,513

false

(3)

factorx3+5,513

52/3x51/3+x2x+51/3

(4)

aliasα=RootOfx35:

irreducx3+5,α

false

(5)

factorx3+5,α

α2xα+x2x+α

(6)

See Also

evala/AIrreduc

factor

Irreduc

isprime

PolynomialTools[Split]

RootOf

roots

 


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