Nextpoly - Maple Help
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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

Parameters

Description

Examples

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 .  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 .

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

See Also

alias

nextprime

Randpoly

Randprime

RootOf

 


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