FiniteFieldIndex

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]=={u_d-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.

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Create a matrix of finite field elements:

Find the indices of matrix elements:

Find the index of a finite field element:

Use a finite field in the exponential representation:

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

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

FiniteFieldIndex can be applied to lists of elements:

Use FromFiniteFieldIndex to get field elements with specified indices:

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

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