WOLFRAM

Wolfram Language & System Documentation Center

MaxRoots

is an option for NSolve and related functions that specifies the maximum number of roots that should be returned in the solution for a system of algebraic or transcendental equations.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Possible Issues  
See Also
History
Cite this Page

MaxRoots

MaxRoots

is an option for NSolve and related functions that specifies the maximum number of roots that should be returned in the solution for a system of algebraic or transcendental equations.

Details

  • Possible settings include:
  • Automaticautomatically decide how many roots to return
    Infinityreturn all roots
    nreturn at most n roots

Examples

open all close all

Basic Examples  (3)

Find three roots of a polynomial equation:

Wolfram Language code: NSolve[x ^ 100 - x == 1, x, MaxRoots -> 3]

With the default Automatic setting, all 100 roots are returned:

Wolfram Language code: NSolve[x ^ 100 - x == 1, x]//Length

Find three roots of a transcendental equation:

Wolfram Language code: NSolve[Sin[x] == x + 1, x, MaxRoots -> 3]

With the default Automatic setting, 16 roots are returned:

Wolfram Language code: NSolve[Sin[x] == x + 1, x]//Length

Find five exact roots of a transcendental equation:

Wolfram Language code: Solve[Sin[Cos[x]] == Sin[x] + Cos[x], x, MaxRoots -> 5]

Scope  (6)

Find two roots of a system of polynomial equations:

Wolfram Language code: NSolve[x ^ 3 + y ^ 3 == x y - 1 && x ^ 7 - y ^ 7 == x + y + 3, {x, y}, MaxRoots -> 2]

With the default Automatic setting, all 21 roots are returned:

Wolfram Language code: NSolve[x ^ 3 + y ^ 3 == x y - 1 && x ^ 7 - y ^ 7 == x + y + 3, {x, y}]//Length

Find five roots of a system of transcendental equations:

Wolfram Language code: NSolve[x == Sin[x y] - 1 && y ^ 2 == Cos[x - y] + 2, {x, y}, MaxRoots -> 5]

With the default Automatic setting, 16 roots are returned:

Wolfram Language code: NSolve[x == Sin[x y] - 1 && y ^ 2 == Cos[x - y] + 2, {x, y}]//Length

Find 100 roots:

Wolfram Language code: NSolve[x == Sin[x y] - 1 && y ^ 2 == Cos[x - y] + 2, {x, y}, MaxRoots -> 100]//Length

Find five roots of a polynomial of a high degree:

Wolfram Language code: Solve[x ^ 1234567 + 9x ^ 2 + 7x - 1 == 0, x, MaxRoots -> 5]

Find three roots of an unrestricted complex transcendental equation:

Wolfram Language code: SolveValues[Sin[FresnelS[x] + BesselJ[3, x ^ 3 - 2]] == 2 ^ Cos[x] - 5, x, MaxRoots -> 3]

Find three out of a trillion roots of a polynomial system:

Wolfram Language code: SolveValues[x ^ 10000 == y ^ 2 + 3y + 2 && y ^ 10000 == z ^ 2 + 3z + 2 && z ^ 10000 == x ^ 2 + 3x + 2, {x, y, z}, MaxRoots -> 3]

Find five solutions of a transcendental system:

Wolfram Language code: Solve[Sin[x + y] == x y + 1 && Cos[x - y] == AiryAi[x y] / 2, {x, y}, MaxRoots -> 5]

Possible Issues  (1)

The setting of MaxRoots is ignored when solutions depend on symbolic parameters:

Wolfram Language code: NSolve[x ^ 2 == a x + 1 && Abs[x] < 2, x, Reals, MaxRoots -> 1]
Wolfram Research (2024), MaxRoots, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxRoots.html.

Text

Wolfram Research (2024), MaxRoots, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxRoots.html.

CMS

Wolfram Language. 2024. "MaxRoots." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MaxRoots.html.

APA

Wolfram Language. (2024). MaxRoots. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaxRoots.html

BibTeX

@misc{reference.wolfram_2026_maxroots, author="Wolfram Research", title="{MaxRoots}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/MaxRoots.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_maxroots, organization={Wolfram Research}, title={MaxRoots}, year={2024}, url={https://reference.wolfram.com/language/ref/MaxRoots.html}, note=[Accessed: 12-June-2026]}