inert factors function - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : Inert Functions : Factors

Factors - inert factors function

Calling Sequence

Factors(a, K)

Parameters

a

-

multivariate polynomial

K

-

optional specification for an algebraic extension

Description

• 

The Factors function is a placeholder for representing the factorization of the multivariate polynomial a over U, a unique factorization domain. The construct Factors(a) produces a data structure of the form [u,[[f1,ⅇ1],...,[fn,ⅇn]]] such that a=uf1ⅇ1...fnⅇn, where each f[i] is a primitive irreducible polynomial.

• 

The difference between the Factors function and the Factor function is only the form of the result.  The Factor function, if defined, returns a Maple sum of products more suitable for interactive display and manipulation.

• 

The call Factors(a) mod p computes the factorization of a over the integers modulo p, a prime integer. The polynomial a must have rational coefficients or coefficients over a finite field specified by RootOfs.

• 

The call Factors(a, K) mod p computes the factorization over the finite field defined by K, an algebraic extension of the integers mod p where K is a RootOf.

• 

The call modp1(Factors(a),p) computes the factorization of the polynomial a in the modp1 representation modulo p a prime integer.

• 

The call evala(Factors(a, K)) computes the factorization of the polynomial a over an algebraic number (or function) field defined by the extension K, which is specified as a RootOf or a set of RootOfs. The polynomial a must have algebraic number (or function) coefficients. The factors are monic for the ordering of the variables chosen by Maple.

Examples

Factors2x2+6x+6mod7

2,x+6,1,x+4,1

(1)

Factorsx5+1mod2

1,x4+x3+x2+x+1,1,x+1,1

(2)

aliasα=RootOfx2+x+1

α

(3)

Factorsx5+1,αmod2

1,x+1,1,αx+x2+x+1,1,αx+x2+1,1

(4)

aliassqrt2=RootOfx22:

evalaFactors2x21,sqrt2

2,x+12sqrt2,1,x12sqrt2,1

(5)

aliassqrtx=RootOfy2x,y:

evalaFactorsxy21,sqrtx

x,ysqrtxx,1,y+sqrtxx,1

(6)

expandx3+y5+2xy2+3mod7

xy7+x4y2+3y5+3x3+2xy2+6

(7)

Factorsmod7

1,y5+x3+2,1,xy2+3,1

(8)

Factorsx2+2xy+y2+1+x+y,αmod5

1,y+x+4α,1,y+x+α+1,1

(9)

Factorsx2y+xy2+2αxy+αx2+4αx+y+αmod5

1,αx+xy+1,1,y+x+α,1

(10)

See Also

AFactor, AFactors, Expand, Factor, factors, ifactors, Irreduc, mod, modp1, Sqrfree


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam