FromFiniteField
FromFiniteField[a,ff]
converts the element a of the prime subfield of the finite field ff to an integer.
FromFiniteField[expr,ff,t]
converts the elements of the finite field ff in the coefficients of the rational expression expr to polynomials in t, where t represents the field generator.
Details
- FromFiniteField replaces elements
of ff, where α=ff[{0,1}] is the field generator, with polynomials 
. - FromFiniteField goes inside List, Plus, Times and integer Power in expr.
Examples
open all close allBasic Examples (4)
Convert an element of the prime subfield of a finite field to an integer:
ff = FiniteField[5, 2];
a = ff[3]FromFiniteField[a, ff]Convert an element of a finite field to a polynomial in a variable representing the field generator:
ff = FiniteField[7, 3];
a = ff[123]FromFiniteField[a, ff, t]Convert prime field coefficients in a rational expression to integers:
ff = FiniteField[19];
expr = ff[7]x + ff[12]y / (ff[17] + ff[15]x)FromFiniteField[expr, ff]Convert finite field coefficients in a rational expression to polynomials in the field generator:
ff = FiniteField[11, 3];
expr = ff[123]x + ff[234] / (ff[345]x + ff[456]y)FromFiniteField[expr, ff, t]Scope (3)
Convert an element of the prime subfield of a finite field to an integer:
ff = FiniteField[19, 4];
a = ff[16]FromFiniteField[a, ff]b is not an element of the prime subfield:
b = ff[123]FromFiniteField[b, ff]
Convert an element of a finite field to a polynomial in a variable representing the field generator:
ff = FiniteField[5, 5];
a = ff[1234]FromFiniteField[a, ff, t]% /. t -> ff[{0, 1}]Convert finite field coefficients in a rational expression to polynomials in the field generator:
ff = FiniteField[29, 3];
expr = ff[123](ff[234]x ^ 2 + ff[345]y ^ 2) / (ff[456] + ff[678]x ^ 3 + ff[789]y ^ 3)FromFiniteField[expr, ff, t]% /. t -> ff[{0, 1}]Properties & Relations (2)
ToFiniteField converts coefficients to finite field elements, with t representing the field generator:
ToFiniteField[(2 + 3t)x + (4 + t ^ 2)y, FiniteField[7, 3], t]FromFiniteField[%, FiniteField[7, 3], t]FiniteFieldIndex gives indices of field elements:
a = FiniteField[5, 4][99];
FiniteFieldIndex[{a, a ^ 77, a ^ 156}]FromFiniteField gives integers only for elements of the prime subfield:
FromFiniteField[{a, a ^ 77, a ^ 156}, FiniteField[5, 4], t]Text
Wolfram Research (2024), FromFiniteField, Wolfram Language function, https://reference.wolfram.com/language/ref/FromFiniteField.html.
CMS
Wolfram Language. 2024. "FromFiniteField." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FromFiniteField.html.
APA
Wolfram Language. (2024). FromFiniteField. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FromFiniteField.html