random polynomial over a finite field - Maple Help

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Randpoly - random polynomial over a finite field

Randprime - random monic prime polynomial over a finite field

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&plus;x

(1)

Randprime4&comma;xmod2

x4&plus;x&plus;1

(2)

alias&alpha;&equals;RootOfy2&plus;y&plus;1&colon;

f:=Randpoly2&comma;x&comma;&alpha;mod2

f:=x2&plus;&alpha;&plus;x

(3)

Factorfmod2

x2&plus;&alpha;&plus;x

(4)

g:=Randprime2&comma;x&comma;&alpha;mod2

g:=&alpha;x&plus;x2&plus;1

(5)

Irreducgmod2

true

(6)

See Also

alias, Factor, Irreduc, Nextpoly, Nextprime, RootOf


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