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 radical expressions:

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_2025_rootreduce, author="Wolfram Research", title="{RootReduce}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/RootReduce.html}", note=[Accessed: 26-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_rootreduce, organization={Wolfram Research}, title={RootReduce}, year={2007}, url={https://reference.wolfram.com/language/ref/RootReduce.html}, note=[Accessed: 26-July-2025 ]}