## New answers tagged computer-algebra

2
votes

### Alternate descriptions of finite fields

Instead of having a single polynomial-quotient (aka “rupture”) step $\mathbb{F}_p[X]/(P)$ with $P \in \mathbb{F}_p[X]$ irreducible, you can also construct finite fields in several steps, i.e., ...

0
votes

### Alternate descriptions of finite fields

The field of $p^n$ elements is the splitting field of $x^{p^n}-x$ over the field of $p$ elements.

1
vote

### Alternate descriptions of finite fields

Another way of representing finite fields that is sometimes used on computational algebra is via Zech logarithms: basically you represent all non-zero elements as powers of a fixed primitive root $\...

1
vote

### Alternate descriptions of finite fields

An alternate description that works for every finite field is the matrix representation: any finite field of order $q^m$ can be represented by a matrix algebra $\mathbb F_q[M]$ where $M$ is a $m\times ...

Top 50 recent answers are included

#### Related Tags

computer-algebra × 370ag.algebraic-geometry × 75

ac.commutative-algebra × 66

rt.representation-theory × 33

nt.number-theory × 30

polynomials × 30

algorithms × 27

gr.group-theory × 26

linear-algebra × 26

ra.rings-and-algebras × 22

reference-request × 21

co.combinatorics × 20

groebner-bases × 20

magma × 20

computational-geometry × 16

computational-number-theory × 16

computational-complexity × 15

mathematical-software × 15

sage × 15

gap × 13

matrices × 12

computer-science × 12

finite-groups × 11

finite-fields × 11

lo.logic × 10