surd

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

surd(x, n)

Description

For a complex number x and integer n, surd(x, n) returns the n-th root of x whose (complex) argument is closest to that of x.

If x is a positive real number, surd(x, n) coincides with x^(1/n). If x is a negative real number and n is odd, then surd(x, n) coincides with -|x|^(1/n).

surd(x, n) returns that complex solution y of yn = x with polar angle closest to that of x; among two equally distant y's, the one with smaller argument is chosen. In contrast, x^(1/n) represents the solution with the smallest absolute value of the polar angle in the range .

If n is a numerical value, it must be a non-zero integer. If it is symbolic, it is understood to represent a non-zero integer.

surd(x, 2) is mathematically equivalent to sqrt(x). Unlike sqrt, however, surd may return an unevaluated symbolic call.

Environment Interactions

When called with a floating-point argument, the function is sensitive to the environment variable DIGITS which determines the numerical working precision.

Examples

Example 1

If n is odd and x is real, then surd(x, n) is real, too. On the other hand, x^(1/n) is not real if x is negative:

surd(-27, 3), surd(-27.0, 3), (-27)^(1/3), (-27.0)^(1/3)

Example 2

surd may be called with symbolic arguments:

surd(3, n)

Sometimes, surd returns an unevaluated function call:

surd(x, 3), surd(x, n^2 + n)

Return Values

Arithmetical expression.

See Also

MuPAD Functions

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