next irreducible polynomial over a finite field - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Algebra : Polynomials : Nextpoly

Nextprime - next irreducible polynomial over a finite field

Prevprime - previous irreducible polynomial over a finite field

Nextpoly - next polynomial over a finite field

Prevpoly - previous polynomial over a finite field

Calling Sequence

Nextprime(f, x, alpha) mod p

Prevprime(f, x, alpha) mod p

Nextpoly(f, x, alpha) mod p

Prevpoly(f, x, alpha) mod p

Parameters

f

-

polynomial over a finite field

x

-

name

alpha

-

(optional) RootOf

p

-

integer

Description

• 

Nextpoly(f, x) mod p returns the next polynomial from f in x in lexicographical order over the integers modulo p. Similarly, Prevpoly(f, x) mod p returns the previous polynomial from f in x in lexicographical order over the integers modulo p.

• 

Nextprime(f, x) mod p returns the next irreducible polynomial from f in x in lexicographical order over the integers modulo p. Similarly, Prevprime(f, x) mod p returns the previous irreducible polynomial from f in x in lexicographical order over the integers modulo p.

• 

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, Nextprime(f, x, alpha) mod p computes the next irreducible polynomial from f in lexicographical order over GFpk.

Examples

f:=x4

f:=x4

(1)

Nextpolyf,xmod2

x4+1

(2)

Nextprimef,xmod2

x4+x+1

(3)

Prevpolyf,xmod2

x3+x2+x+1

(4)

Prevprimef,xmod2

x3+x2+1

(5)

aliasα=RootOfy2+y+1:

Nextpolyf,x,αmod2

x4+1

(6)

Nextprimef,x,αmod2

x4+αx+x2+1

(7)

Prevpolyf,x,αmod2

αx3+αx2+x3+αx+x2+α+x+1

(8)

Prevprimef,x,αmod2

αx3+αx2+x3+αx+x2+α+x

(9)

See Also

alias, Randpoly, Randprime, RootOf


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