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PolynomialTools

  

Splits

  

find a complete factorization of a polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Splits(a, x, b)

Parameters

a

-

polynomial with algebraic number or polynomial coefficients

x

-

variable

b

-

(optional) name

Description

• 

The Splits(a, x) function computes the complete factorization of the univariate polynomial a in x.

• 

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

• 

If the third argument b is specified, it is assigned a set of elements {t1,...,tm} such that the polynomial a splits over K=Qt1,...,tm, where Q denotes the field of rational numbers.

• 

This function is part of the PolynomialTools package, and so it can be used in the form Splits(..) only after executing the command with(PolynomialTools). However, it can always be accessed through the long form of the command by using PolynomialTools[Splits](..).

Examples

withPolynomialTools:

Splitsx2+x+1,x

1,x+1+RootOf_Z2+_Z+1,1,xRootOf_Z2+_Z+1,1

(1)

Splitsx2+yx+1+y2,x,'b'

1,xRootOf_Z2+_Zy+y2+1,1,x+y+RootOf_Z2+_Zy+y2+1,1

(2)

b

RootOf_Z2+_Zy+y2+1

(3)

See Also

AFactor

PolynomialTools[Split]

RootOf

 


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