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
Nextprime(f, x, alpha) mod p
Prevprime(f, x, alpha) mod p
Nextpoly(f, x, alpha) mod p
Prevpoly(f, x, alpha) mod p
f
-
polynomial over a finite field
x
name
alpha
(optional) RootOf
p
integer
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.
f≔x4
Nextpolyf,xmod2
x4+1
Nextprimef,xmod2
x4+x+1
Prevpolyf,xmod2
x3+x2+x+1
Prevprimef,xmod2
x3+x2+1
aliasα=RootOfy2+y+1:
Nextpolyf,x,αmod2
Nextprimef,x,αmod2
x4+αx+x2+1
Prevpolyf,x,αmod2
αx3+αx2+x3+αx+x2+α+x+1
Prevprimef,x,αmod2
αx3+αx2+x3+αx+x2+α+x
See Also
alias
nextprime
Randpoly
Randprime
RootOf
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