# Polynomials over Finite Fields

The functions in this section are available for univariate polynomials over finite fields only.

## `PrimePolynomials(R, d): RngUPol, RngIntElt -> SeqEnum[ RngUPolElt ]`

## `PrimePolynomials(R, d, n): RngUPol, RngIntElt, RngIntElt -> SeqEnum[ RngUPolElt ]`

A sequence of all monic prime polynomials of $R$ of degree $d$, resp. a sequence of $n$ monic prime polynomials of $R$ of degree $d$.

## `RandomPrimePolynomial(R, d): RngUPol, RngIntElt -> RngUPolElt`

A random monic prime polynomial of $R$ of degree $d$.

## `NumberOfPrimePolynomials(q, d): RngIntElt, RngIntElt -> RngIntElt`

## `NumberOfPrimePolynomials(K, d): FldFin, RngIntElt -> RngIntElt`

## `NumberOfPrimePolynomials(R, d): RngUPol, RngIntElt -> RngIntElt`

The number of monic prime polynomials of degree $d$ over the respective finite field.

## `JacobiSymbol(a, b): RngUPol, RngUPol -> RngIntElt`

The Jacobi symbol (a/b) of the two polynomials $a,b \in {\mathbb{F}}_q[x]$ where $q$ must be odd. If $b$ is irreducible, the symbol equals $0$ if $b$ divides $a$. It equals $1$ if $a$ is a square mod $b$ and $-1$ otherwise. The symbol then extends multiplicatively to all non-constant polynomials $b$.