non-principal root function - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : Numbers : Integer Functions : surd

surd - non-principal root function

Calling Sequence

surd(x, n)

Parameters

x

-

any algebraic expression

n

-

any algebraic expression, understood to be an integer

Description

• 

For a complex number x and integer n, surd(x, n) computes the nth root of x whose (complex) argument is closest to that of x.  Ties are broken in such a way that the function x -> surd(x,n) is  continuous in a counter-clockwise manner onto its branch cuts (that is, continuous in the direction of increasing complex argument).

• 

In particular, if n is odd then if x>=0 then surd(x,n) = x^(1/n) and if x<0 then surd(x,n) = -(-x)^(1/n).

Examples Using surd

surd(-1, 3);

1

(1)

surd( 8, 3);

2

(2)

surd(-8, 3);

2

(3)

surd(-1, 2);

I

(4)

surd(1+2*I,3);

1&plus;2I1&sol;3

(5)

surd( x, n);

xn

(6)

convert((6), power);

x1n

(7)
  

Maple simplifies the expression before converting. Constants will still be written with fractional exponents.

convert((9*x)^(1/3), surd);

32&sol;3x3

(8)

convert(3^(1/3)*x^(1/2)*a^b+f((-2)^(1/5)*x^(1/n)), surd);

31&sol;3xab&plus;f21&sol;5x1n

(9)

int(surd(x^2,3)*(3*x^3-2*x^2+x-1), x=-2..2);

6125522&sol;3

(10)
  

Note the differences among the outputs of the surd, ^, and root commands.

(8)^(1/3); root(8, 3); surd(8, 3);

81&sol;3

2

2

(11)

(8.0)^(1/3); root(8.0, 3); surd(8.0, 3);

2.000000000

2.000000000

2.000000000

(12)

(-8)^(1/3); root(-8, 3); surd(-8, 3);

81&sol;3

211&sol;3

2

(13)

(-8.0)^(1/3); root(-8.0, 3); surd(-8.0, 3);

1.000000000&plus;1.732050807I

1.000000000&plus;1.732050807I

2.000000000

(14)

See Also

^, convert, RealDomain, root


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam