gives the real-valued root of x.
- Surd[x,n] returns the real-valued root of real-valued x for odd n.
- Surd[x,n] returns the principal root for non-negative real-valued x and even n.
- For symbolic x in Surd[x,n], x is assumed to be real valued.
- Surd can be evaluated to arbitrary numerical precision.
- Surd automatically threads over lists.
- In StandardForm, Surd[x,n] formats as .
- can be entered as surd, and moves between the fields.
- Surd can be used with Interval and CenteredInterval objects. »
Examplesopen allclose all
Basic Examples (5)
Numerical Evaluation (5)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
Surd threads elementwise over lists and matrices:
Surd can be used with Interval and CenteredInterval objects:
Specific Values (4)
Plot the Surd function for various orders:
Visualize the absolute value and argument (sign) of for odd n:
The function has the same absolute value but a different argument for :
Compare the real and imaginary parts of and for even n:
Function Properties (8)
Surd[x,n] is defined for all real x when n is a positive, odd integer:
For positive, even n, it is defined for non-negative x:
For negative n, 0 is removed from the domain:
Surd is not defined for nonreal complex values:
Surd[x,n] achieves all non-negative real values when n is a positive even integer:
For positive odd n, its range is the whole real line:
For negative n, 0 is removed from the range:
Surd[x,n] is not an analytic function of x for any integer n:
Decreasing for negative even :
And it is surjective onto for odd, positive , but not other values of :
It is non-negative on its real domain for even :
in general has both singularities and discontinuities at zero:
However, for positive odd it is continuous at the origin:
is neither convex nor concave for odd :
On its domain of definition, it is concave for positive even and convex of negative even :
Compute the indefinite integral using Integrate:
Series Expansions (4)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
General term in the series expansion using SeriesCoefficient:
The first-order Fourier series:
Properties & Relations (3)
Possible Issues (1)
Neat Examples (1)
Plot a composition of Surd:
Wolfram Research (2012), Surd, Wolfram Language function, https://reference.wolfram.com/language/ref/Surd.html.
Wolfram Language. 2012. "Surd." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Surd.html.
Wolfram Language. (2012). Surd. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Surd.html