WOLFRAM

Wolfram Language & System Documentation Center

$MaxRootDegree

specifies the maximum degree of polynomial to allow in Root objects.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
See Also
Related Guides
History
Cite this Page

$MaxRootDegree

$MaxRootDegree

specifies the maximum degree of polynomial to allow in Root objects.

Details

Examples

open all close all

Basic Examples  (1)

Evaluation of Root objects with high degree minimal polynomials may be slow:

Wolfram Language code: Root[# ^ 1000 - 123# ^ 777 + 211# ^ 356 - 127# ^ 123 + 888# ^ 11 - 2&, 1]//Timing

The result is a valid algebraic number with minimal polynomial proven irreducible:

Wolfram Language code: NumericQ[%[[2]]]

Root does not attempt factoring polynomials with degrees higher than $MaxRootDegree:

Wolfram Language code: $MaxRootDegree
Wolfram Language code: Root[# ^ 1001 - 123# ^ 777 + 211# ^ 356 - 127# ^ 123 + 888# ^ 11 - 2&, 1]//Timing

The result is not a valid algebraic number:

Wolfram Language code: NumericQ[%[[2]]]

Scope  (2)

The degree of the sum of two Root objects may be as high as the product of their degrees:

Wolfram Language code: RootReduce[Root[# ^ 10 - 9# + 7&, 10] + Root[# ^ 11 + 3# - 5&, 2]]

This prevents the Wolfram Language from creating Root objects with degrees greater than 100:

Wolfram Language code: $MaxRootDegree = 100

Root objects already created are cached; this removes the cached results:

Wolfram Language code: ClearSystemCache[]

Now RootReduce is not allowed to create a Root object with degree 110:

Wolfram Language code: RootReduce[Root[# ^ 10 - 9# + 7&, 10] + Root[# ^ 11 + 3# - 5&, 2]]

This resets $MaxRootDegree to the default value:

Wolfram Language code: $MaxRootDegree = 1000;

By default, the Wolfram Language does not use Root objects with degrees exceeding 1000:

Wolfram Language code: Root[# ^ 1001 - 2# + 3&, 1]

Increasing the value of $MaxRootDegree allows the Wolfram Language to create the algebraic number:

Wolfram Language code: $MaxRootDegree = 1001;
Wolfram Language code: r = Root[# ^ 1001 - 2# + 3&, 1]

Since this Root object is real, computing its numeric approximation is reasonably fast:

Wolfram Language code: N[r, 20]
Wolfram Research (1996), $MaxRootDegree, Wolfram Language function, https://reference.wolfram.com/language/ref/$MaxRootDegree.html.

Text

Wolfram Research (1996), $MaxRootDegree, Wolfram Language function, https://reference.wolfram.com/language/ref/$MaxRootDegree.html.

CMS

Wolfram Language. 1996. "$MaxRootDegree." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/$MaxRootDegree.html.

APA

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

BibTeX

@misc{reference.wolfram_2026_$maxrootdegree, author="Wolfram Research", title="{$MaxRootDegree}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/$MaxRootDegree.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_$maxrootdegree, organization={Wolfram Research}, title={$MaxRootDegree}, year={1996}, url={https://reference.wolfram.com/language/ref/$MaxRootDegree.html}, note=[Accessed: 13-June-2026]}