Help me construcing finite field,

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Homework Help Overview

The discussion revolves around constructing a finite field with a specified number of elements, specifically within the range of \(10^9 < q < 10^{10}\). The original poster seeks guidance on how to achieve this using Mathematica without relying on any packages for finite fields.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the concept of finite fields and the conditions necessary for their construction, including the relationship between prime numbers and the number of elements in the field. Questions arise regarding the specific requirements for constructing a field, such as the use of irreducible polynomials and the nature of the elements involved.

Discussion Status

The discussion is ongoing, with participants providing hints and asking clarifying questions. Some guidance has been offered regarding the need for prime numbers and irreducible polynomials, but there is no explicit consensus on the best approach or method to construct the finite field.

Contextual Notes

There is a noted uncertainty regarding the understanding of finite fields and the specific steps required for their construction. The original poster expresses a lack of confidence in their knowledge of fields, which may affect the direction of the discussion.

Granit_niti
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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?
 
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What do you know about fields?
Do you have any examples of fields?
 
I don’t think this is pre-calc, but:

Can you think of a number p and n where

10^9 < p^n < 10^10

you should know how to construct a field with p^n elements.

Hint: It involves Z_p and a irreducible polynomial of order n (check your class notes!)


Edit: p must be prime of course
 
Last edited:
Thank you very much!

Could you refer me to any tutorial for constructing field with p^n elements the?
I am not good with fields at all!

When I construct the field do I have to take all polynomials possible of n degree in Z/Zp or only one irreducible or all irreducible ones?

I don't have clear what is the finite field. What do I have to find in order to construct finite field?
 
Last edited:

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