# RootReduce

RootReduce[expr]

attempts to reduce expr to a single Root object.

# Details and Options

• If expr consists only of integers and Root and AlgebraicNumber objects combined using algebraic operations, then the result from RootReduce[expr] will always be a single Root object.
• Simple Root objects may in turn automatically evaluate to rational expressions or combinations of radicals.
• RootReduce automatically threads over lists, as well as equations, inequalities, and logic functions.

# Examples

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## Basic Examples(1)

Reduce to a single Root object:

## Scope(2)

Combinations of Root objects:

Reduce any algebraic combination of radicals, Root, and AlgebraicNumber objects:

The result is always a Root object, a quadratic radical expression, or a rational number:

## Options(1)

### Method(1)

By default, RootReduce heuristically selects the method to use:

In this case conversion to AlgebraicNumber objects in a common number field is used:

The other available method recursively performs arithmetic operations:

Here the "Recursive" method is faster:

## Applications(1)

The numeric test used by Equal cannot prove the equality:

RootReduce proves that the two algebraic numbers are equal:

FullSimplify will use RootReduce:

## Properties & Relations(3)

The results given by RootReduce are canonical:

In general the degree of the reduced polynomial will be the product of the degrees:

In exceptional cases the result can have a lower degree:

Root objects can be converted to AlgebraicNumber objects:

RootReduce converts from AlgebraicNumber objects:

Wolfram Research (1996), RootReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/RootReduce.html (updated 2007).

#### Text

Wolfram Research (1996), RootReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/RootReduce.html (updated 2007).

#### CMS

Wolfram Language. 1996. "RootReduce." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/RootReduce.html.

#### APA

Wolfram Language. (1996). RootReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RootReduce.html

#### BibTeX

@misc{reference.wolfram_2023_rootreduce, author="Wolfram Research", title="{RootReduce}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/RootReduce.html}", note=[Accessed: 03-October-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_rootreduce, organization={Wolfram Research}, title={RootReduce}, year={2007}, url={https://reference.wolfram.com/language/ref/RootReduce.html}, note=[Accessed: 03-October-2023 ]}