Function: math[symmetry] - determines symmetry of a function in one real variable

Calling Sequence:

symmetry(f);

Parameters:

f - an algebraic expression

Description:

symmetry determines whether a function (an expression) in one real is either even, odd, or neither even nor odd.

A function is even, i.e. symmetric about the y-axis if f(-a) = f(+a), it is odd if -f(-a) = f(a), i.e. f is symmetric about the origin; and neither even nor odd if it does not satisfy the above mentioned conditions.

The return is either the sequences "true, `even`", "true, `odd`" or "false, `neither even nor odd`" (w/o the double quotes), i.e. a Boolean value and a string.

Internally symmdiff uses type/evenfunc and type/oddfunc.

This function is part of the math package, and so can be used only after performing the command with(math) or with(math, symmetry).

Examples:

> with(math):

> symmetry(x^2);

[Maple Math]

> symmetry(x^5-x^3);

[Maple Math]

> symmetry(exp(x));

[Maple Math]

See Also:

type/evenfunc .

Version History:

Version 1.00 - May 13, 1997