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csgn

sign function for real and complex expressions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

csgn(x)

csgn(1, x)

csgn(0, x, y)

Parameters

x

-

any algebraic expression

y

-

any algebraic expression

Description

• 

The csgn function is used to determine in which half-plane ("left" or "right") the complex-valued expression or number x lies. With the exception described in the next bullet point, it is defined by

csgnx=10<xorx=0and0<x−1x<0orx=0andx<0

• 

For the case of a complex number in which the real component is one of the floating point values -0. or +0., csgn returns the sign of the real part.  For more information, see Numeric Computation in Maple.

• 

The value of csgn(0) is controlled by the environment variable _Envsignum0.  The 3-argument calling sequence csgn(0, x, y) sets _Envsignum0 = y for the duration of the call to csgn. See signum for further information.

• 

The decision of whether or not to perform many of the automatic symmetry transformations in maple is based on the value of csgn. For example, if csgn(x) = -1, the transformation sinxsinx is done.

• 

csgn uses signum to determine the signs of x and x.

• 

The derivative of csgn is denoted by csgn(1, x).  This is 0 for all non-purely-imaginary numbers, and is undefined otherwise.

• 

For mathematical consistency, the value of csgn(0), as determined either by the value of _Envsignum0 or by the third argument to csgn, should be either 0 (the default) or one of 1, -1, or undefined.

Examples

csgn12I3

1

(1)

csgn12I3

−1

(2)

csgn1&plus;2I3

−1

(3)

csgn1&plus;2I3

1

(4)

csgn2PiI3

−1

(5)

csgn&ExponentialE;2PiI3

−1

(6)

csgnPi

1

(7)

&DifferentialD;&DifferentialD;xcsgnx

csgn1&comma;x

(8)

&DifferentialD;2&DifferentialD;x2csgnx

csgn1&comma;x

(9)

csgn1&comma;3&plus;I

0

(10)

csgn0

0

(11)

csgn0&comma;0&comma;1

−1

(12)

The following illustrates the exception for floating point complex numbers with real part equal to -0. or +0.:

csgn0&plus;I

1

(13)

csgn0.&plus;1.I

−1

(14)

csgn0I

−1

(15)

csgn0.1.I

1

(16)

See Also

assume

evalc

initialfunctions

sign

signum