Help me construcing finite field,

  • Thread starter Thread starter Granit_niti
  • Start date Start date
  • Tags Tags
    Field Finite
Granit_niti
Messages
3
Reaction score
0
Help me construcing finite field, please!

I need Construct a finite field with q Elements (10^9<q<10^10) and find
a primitive root. That should be done in mathematica but I should not use Package for Finite Fields.

Any idea how to solve this problem?
 
Physics news on Phys.org
What do you mean by primitive root here?
 
Thread 'Determine whether ##125## is a unit in ##\mathbb{Z_471}##'

Thread 'Determine whether ##125## is a unit in ##\mathbb{Z_471}##'

This is the question, I understand the concept, in ##\mathbb{Z_n}## an element is a is a unit if and only if gcd( a,n) =1. My understanding of backwards substitution, ... i have using Euclidean algorithm, ##471 = 3⋅121 + 108## ##121 = 1⋅108 + 13## ##108 =8⋅13+4## ##13=3⋅4+1## ##4=4⋅1+0## using back-substitution, ##1=13-3⋅4## ##=(121-1⋅108)-3(108-8⋅13)## ... ##= 121-(471-3⋅121)-3⋅471+9⋅121+24⋅121-24(471-3⋅121## ##=121-471+3⋅121-3⋅471+9⋅121+24⋅121-24⋅471+72⋅121##...
View full post »

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Similar threads

MHB Nature and character of Finite Fields of small order
Replies
16
Views
4K
I Need clarification on a theorem about field extensions/isomorphisms
Replies
14
Views
2K
Help me construcing finite field,
Replies
3
Views
2K
Definition of Finite Field: Addition and Multiplication Groups
Replies
1
Views
2K
I Finitely Generated Ideals and Noetherian Rings
Replies
7
Views
3K
I Generators of Galois group of ## X^n - \theta ##
Replies
3
Views
2K
MHB Finitely Generated Ideals and Noetherian Rings
Replies
2
Views
2K
I Decomposition per the Fundamental Theorem of Finite Abelian Groups
Replies
13
Views
3K
I Transforming a Matrix: Elementary Methods for Finite Fields
Replies
8
Views
2K
Finite field is algebraically closed under constraint?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top