/**
* Get the end behavior of a Polynomial
*
* The end behaviors are determined by the degree of the Polynomial and
* whether or not the coefficient is positive or negative. The values
* returned correspond to the MATH_POLYNOMIAL_QUADRANT_* constants for the
* cartesian coordinate system:
* <pre>
* Quad 2 | Quad 1
* ---------------
* Quad 3 | Quad 4
* </pre>
*
* Returns an array containing two elements:
* <code>
* $end_behaviors = Math_PolynomialOp::getEndBehavior('x^2 + 1');
* print_r($end_behaviors);
*
* // prints:
* Array
* (
* [0] => MATH_POLYNOMAIL_QUADRANT_2 // This is the left-end behavior
* [1] => MATH_POLYNOMIAL_QUADRANT_1 // This is the right-end behavior
* )
* </code>
*
* @see Math_PolynomialOp::getRightEndBehavior()
* @see Math_PolynomialOp::getLeftEndBehavior()
*
* @access public
* @static
*
* @param object $p
* @return array
*/
function getEndBehavior($p)
{
if (!is_a($p, 'Math_Polynomial')) {
$p = new Math_Polynomial($p);
}
$term = $p->getTerm(0);
if ($term->getCoefficient() > 0) {
// Positive leading coefficient
if ($p->degree() % 2) {
// Odd degree
return array(MATH_POLYNOMIAL_QUADRANT_3, MATH_POLYNOMIAL_QUADRANT_1);
} else {
// Even degree
return array(MATH_POLYNOMIAL_QUADRANT_2, MATH_POLYNOMIAL_QUADRANT_1);
}
} else {
// Negative leading coefficient
if ($p->degree() % 2) {
// Odd degree
return array(MATH_POLYNOMIAL_QUADRANT_2, MATH_POLYNOMIAL_QUADRANT_4);
} else {
// Even degree
return array(MATH_POLYNOMIAL_QUADRANT_3, MATH_POLYNOMIAL_QUADRANT_4);
}
}
}
