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Randpoly

random polynomial over a finite field

Randprime

random monic prime polynomial over a finite field

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Randpoly(n, x) mod p

Randpoly(n, x, alpha) mod p

Randprime(n, x) mod p

Randprime(n, x, alpha) mod p

Parameters

n

-

non-negative integer

x

-

name

alpha

-

RootOf

p

-

integer

Description

• 

Randpoly(n, x) mod p returns a polynomial of degree n in the variable x whose coefficients are selected at random from the integers mod p.

• 

Randprime(n, x) mod p returns a random monic irreducible polynomial of degree 0<n in the variable x over the integers mod p where p must be a prime integer.

• 

The optional third argument alpha specifies a representation for the finite field GFpk.  The field extension alpha is specified by a RootOf a monic univariate polynomial of degree k which must be irreducible.

• 

Thus Randprime(n, x, alpha) mod p creates a random monic irreducible polynomial of degree 0<n in the variable x over GFpk.

Examples

Randpoly4&comma;xmod2

x4+x

(1)

Randprime4&comma;xmod2

x4+x+1

(2)

aliasα=RootOfy2+y+1&colon;

fRandpoly2&comma;x&comma;αmod2

fx2+α+x

(3)

Factorfmod2

x2+α+x

(4)

gRandprime2&comma;x&comma;αmod2

gαx+x2+1

(5)

Irreducgmod2

true

(6)

See Also

alias

Factor

Irreduc

Nextpoly

Nextprime

RootOf