ToFiniteField
✖
ToFiniteField
converts the integer k to an element of the prime subfield of the finite field ff.
converts the coefficients of the rational expression expr to elements of the finite field ff.
converts the coefficients of the rational expression expr to elements of the finite field ff, with t representing the field generator.
Details

- ToFiniteField replaces integers k with elements ff[{k}] of the prime subfield of ff and replaces t with the field generator ff[{0,1}].
- ToFiniteField goes inside List, Plus, Times and integer Power in expr.
Examples
open allclose allBasic Examples (4)Summary of the most common use cases
Convert an integer to an element of the prime subfield of a finite field:

https://wolfram.com/xid/01yxj57iz4u-783jpd

Use t to represent the field generator:

https://wolfram.com/xid/01yxj57iz4u-z40b4g

Convert the coefficients of a rational expression to elements in the prime subfield of a finite field:

https://wolfram.com/xid/01yxj57iz4u-2p95dg

Use t to represent the field generator:

https://wolfram.com/xid/01yxj57iz4u-g9epn8

Scope (4)Survey of the scope of standard use cases
Convert integers and rational numbers to elements of the prime subfield of a finite field:

https://wolfram.com/xid/01yxj57iz4u-gwbyiv


https://wolfram.com/xid/01yxj57iz4u-bew2ed

Convert a polynomial in t to a a polynomial in the field generator:

https://wolfram.com/xid/01yxj57iz4u-g7w3f1


https://wolfram.com/xid/01yxj57iz4u-h6eu0o


https://wolfram.com/xid/01yxj57iz4u-c2bkmj

Convert the coefficients of a polynomial to elements in the prime subfield of a finite field:

https://wolfram.com/xid/01yxj57iz4u-d8iv40

Convert the coefficients of a rational function, with t used to represent the field generator:

https://wolfram.com/xid/01yxj57iz4u-b63lb


https://wolfram.com/xid/01yxj57iz4u-dress


https://wolfram.com/xid/01yxj57iz4u-gx3iyr

Properties & Relations (2)Properties of the function, and connections to other functions
FromFiniteField converts finite field elements to polynomials in the field generator:

https://wolfram.com/xid/01yxj57iz4u-fy3fo7


https://wolfram.com/xid/01yxj57iz4u-ogsqa5

FromFiniteFieldIndex gives finite field elements with specified indices:

https://wolfram.com/xid/01yxj57iz4u-dgxqzq

ToFiniteField converts integers to elements of the prime subfield:

https://wolfram.com/xid/01yxj57iz4u-e36uhj

Wolfram Research (2024), ToFiniteField, Wolfram Language function, https://reference.wolfram.com/language/ref/ToFiniteField.html.
Text
Wolfram Research (2024), ToFiniteField, Wolfram Language function, https://reference.wolfram.com/language/ref/ToFiniteField.html.
Wolfram Research (2024), ToFiniteField, Wolfram Language function, https://reference.wolfram.com/language/ref/ToFiniteField.html.
CMS
Wolfram Language. 2024. "ToFiniteField." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ToFiniteField.html.
Wolfram Language. 2024. "ToFiniteField." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ToFiniteField.html.
APA
Wolfram Language. (2024). ToFiniteField. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ToFiniteField.html
Wolfram Language. (2024). ToFiniteField. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ToFiniteField.html
BibTeX
@misc{reference.wolfram_2025_tofinitefield, author="Wolfram Research", title="{ToFiniteField}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/ToFiniteField.html}", note=[Accessed: 05-May-2025
]}
BibLaTeX
@online{reference.wolfram_2025_tofinitefield, organization={Wolfram Research}, title={ToFiniteField}, year={2024}, url={https://reference.wolfram.com/language/ref/ToFiniteField.html}, note=[Accessed: 05-May-2025
]}