# Testing Polynomial Equality

DevFeed: [Testing Polynomial Equality](<https://devfeed.tech/articles/testing-polynomial-equality-40409.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2017/04/24/testing-polynomial-equality/>)

Published: 2017-04-24T09:00:14Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Testing](<https://devfeed.tech/topics/testing.md>), [function](<https://devfeed.tech/topics/function.md>)

Tags: [field](<https://devfeed.tech/tags/field.md>), [function](<https://devfeed.tech/tags/function.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>), [random](<https://devfeed.tech/tags/random.md>), [roots](<https://devfeed.tech/tags/roots.md>), [testing](<https://devfeed.tech/tags/testing.md>), [variables](<https://devfeed.tech/tags/variables.md>)

## AI overview

The article explains how to test whether two multivariable polynomial expressions represent the same function. It presents randomized evaluation over a finite subset of a field and uses the Schwartz-Zippel lemma to bound the probability of an incorrect equality judgment.

## Source excerpt

Problem: Determine if two polynomial expressions represent the same function. Specifically, if $ p(x_1, x_2, \dots, x_n)$ and $ q(x_1, x_2, \dots, x_n)$ are a polynomial with inputs, outputs and coefficients in a field $ F$, where $ |F|$ is sufficiently large, then the problem is to determine if $ p(\mathbf{x}) = q(\mathbf{x})$ for every $ x \in F$, in time polynomial in the number of bits required to write down $ p$ and $ q$.