What is the way of integer representation of an element in $GF(3^{15})$

For each integer $i$ there is an polynomial representation in $GF(3^{15})$ by

for i in srange(F.cardinality()):
    print(i, '=>', F(i.digits(3)))

As for example $4 \implies x + 1$. What is the reverses way that is, $ x + 1\implies 4$

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The alternative solution from an answer to a previous question applies:

sage: F.<x> = GF(3^15)
sage: i = 231
sage: a = F(i.digits(3))
sage: ZZ(list(vector(a)),base=3)
231

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Asked: 2020-04-03 13:46:54 +0100

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Last updated: Apr 03 '20