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Roots

roots of a polynomial mod n

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Roots(a)

Roots(a, K)

Parameters

a

-

univariate polynomial

K

-

RootOf

Description

• 

The Roots function is a placeholder for representing the roots of the univariate polynomial a. The roots are returned as a list of pairs of the form [[r1,m1],...,[rn,mn]] where rk is a root and mk its multiplicity, that is, xrkmk divides a.

• 

The call Roots(a) mod n computes the roots of the polynomial a modulo n.

• 

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

• 

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

Examples

Rootsx3xmod6

0,1,1,1,2,1,3,1,4,1,5,1

(1)

Rootsx31mod2

1,1

(2)

aliasα=RootOfx2+x+1:

Rootsx31,αmod2

1,1,α,1,α+1,1

(3)

See Also

Factors

mod

modp1

msolve

root

RootOf

roots

Student[Calculus1][Roots]

Student[NumericalAnalysis][Roots]

 


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