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factors

factor a multivariate polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

factors(a)

factors(a, K)

Parameters

a

-

multivariate polynomial

K

-

field extension over which to factor

Description

• 

The factors command computes the factorization of a multivariate polynomial over the rationals, an algebraic number field, and with real or complex numeric coefficients.

• 

Unlike the factor function where the input is any expression and the output is a product of sums in the general case, the input to the factors function must be a polynomial or a rational function, and the output is a data structure more suitable for programming purposes.

• 

The factorization is returned in the form u,f1,m1,...,fn,mn where a=uf1m1...fnmn where each fk (the factor) is a unit normal irreducible polynomial and each mk (its multiplicity) is a positive integer.

• 

The call factors(a) factors over the field implied by the coefficients present: thus, if all the coefficients are rational, then the polynomial is factored over the rationals.

• 

If the second argument K is the keyword real or complex, a floating-point factorization is performed over R and C respectively.  Note, at present this is only implemented for univariate polynomials.

• 

The call factors(a, K) factors the polynomial a 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

factors3x2+6x+3

3,x+1,2

(1)

factorsx44

1,x2+2,1,x22,1

(2)

factorsx44.0

1,x1.41421356237310,1,x+1.41421356237310,1,x2+1.999999999,1

(3)

factorsx44,2

1,x+2,1,x2,1,x2+2,1

(4)

factorsx44,2,I

1,I2+x,1,x+2,1,x2,1,I2+x,1

(5)

aliasα=RootOfx22:

aliasβ=RootOfx2+2:

factorsx44,α

1,x+α,1,x2+2,1,xα,1

(6)

factorsx44,β

1,xβ,1,x+β,1,x22,1

(7)

factorsx44,α,β

1,x+α,1,xβ,1,x+β,1,xα,1

(8)

factorsx44,real

1,x1.41421356237310,1,x+1.41421356237310,1,x2+1.999999999,1

(9)

factorsx44,complex

1,x1.41421356237310,1,x1.414213562I,1,x+1.414213562I,1,x+1.41421356237310,1

(10)

The following is an example that has a rational function as input.

qexpandz1z3expandz2z4

qz24z+3z26z+8

(11)

factorsq

1,z4,1,z2,1,z3,1,z1,1

(12)

See Also

AFactors

factor

Factors

ifactors

PolynomialTools[Split]

roots

sqrfree