Randpoly
random polynomial over a finite field
Randprime
random monic prime polynomial over a finite field
Calling Sequence
Parameters
Description
Examples
Randpoly(n, x) mod p
Randpoly(n, x, alpha) mod p
Randprime(n, x) mod p
Randprime(n, x, alpha) mod p
n
-
non-negative integer
x
name
alpha
RootOf
p
integer
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.
Randpoly4,xmod2
x4+x
Randprime4,xmod2
x4+x+1
aliasα=RootOfy2+y+1:
f≔Randpoly2,x,αmod2
f≔x2+α+x
Factorfmod2
x2+α+x
g≔Randprime2,x,αmod2
g≔αx+x2+1
Irreducgmod2
true
See Also
alias
Factor
Irreduc
Nextpoly
Nextprime
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