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FiniteFieldIndex[u]

gives the index of the FiniteFieldElement object u.

Details
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Examples  
Basic Examples  
Scope  
Properties & Relations  
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FiniteFieldIndex

FiniteFieldIndex[u]

gives the index of the FiniteFieldElement object u.

Details

  • FiniteFieldIndex has the Listable attribute.
  • FiniteFieldIndex[u] is equivalent to u["Index"].
  • If u is an element of FiniteField[p,f,"Polynomial"], then , where α is the field generator and d is the degree of f. The index ind of u satisfies IntegerDigits[ind,p,d]=={ud-1,…,u0}.
  • If u is a nonzero element of FiniteField[p,f,"Exponential"], then , with , where α is the field generator and d is the degree of f. The index ind of u satisfies ind==k+1. The index of the field zero is 0.

Examples

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Basic Examples  (1)

Create a matrix of finite field elements:

Wolfram Language code: (m = FromFiniteFieldIndex[{{11, 12}, {21, 22}}, FiniteField[5, 2]])//MatrixForm

Find the indices of matrix elements:

Wolfram Language code: FiniteFieldIndex[m]//MatrixForm

Scope  (3)

Find the index of a finite field element:

Wolfram Language code: FiniteFieldIndex[FiniteField[11, 3][{1, 2, 3}]]

Use a finite field in the exponential representation:

Wolfram Language code: FiniteFieldIndex[FiniteField[11, 3, "Exponential"][{1, 2, 3}]]

Find indices of a vector and a matrix of finite field elements:

Wolfram Language code: a = FiniteField[7, 5][{0, 1}]; FiniteFieldIndex[{a, a ^ 2, a ^ 3}]
Wolfram Language code: FiniteFieldIndex[{{a, 2a, 3a}, {1 / a, 2 / a, 3 / a}}]//MatrixForm

Properties & Relations  (3)

For a single field element, FiniteFieldIndex[u] is equivalent to u["Index"]:

Wolfram Language code: u = FiniteField[11, 3][1234]; FiniteFieldIndex[u] === u["Index"]

FiniteFieldIndex can be applied to lists of elements:

Wolfram Language code: FiniteFieldIndex[{u, u ^ 2, u ^ 3}]
Wolfram Language code: FiniteFieldIndex[Table[i u ^ j + k, {i, 3}, {j, 3}, {k, 3}]]

Use FromFiniteFieldIndex to get field elements with specified indices:

Wolfram Language code: FromFiniteFieldIndex[{123, 234, 345}, FiniteField[19, 2]]
Wolfram Language code: FiniteFieldIndex[%]

Convert elements of a finite field to polynomials in a variable representing the field generator:

Wolfram Language code: a = FiniteField[5, 4][99]; FromFiniteField[{a, a ^ 77, a ^ 156}, FiniteField[5, 4], t]
Wolfram Research (2024), FiniteFieldIndex, Wolfram Language function, https://reference.wolfram.com/language/ref/FiniteFieldIndex.html.

Text

Wolfram Research (2024), FiniteFieldIndex, Wolfram Language function, https://reference.wolfram.com/language/ref/FiniteFieldIndex.html.

CMS

Wolfram Language. 2024. "FiniteFieldIndex." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FiniteFieldIndex.html.

APA

Wolfram Language. (2024). FiniteFieldIndex. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FiniteFieldIndex.html

BibTeX

@misc{reference.wolfram_2026_finitefieldindex, author="Wolfram Research", title="{FiniteFieldIndex}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/FiniteFieldIndex.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_finitefieldindex, organization={Wolfram Research}, title={FiniteFieldIndex}, year={2024}, url={https://reference.wolfram.com/language/ref/FiniteFieldIndex.html}, note=[Accessed: 13-June-2026]}