/**
* Get the nth derivative of a Math_Polynomial
*
* Returns the nth derivative of the Polynomial. Derivatives are commonly
* used in calculus as they represent slopes or acceleration. To get the
* first derivative, the second parameter should be a 1. For the second
* derivative parameter should be a two, etc. etc.
*
* @see PolynomialOp::getAntiDerivative()
*
* @access public
*
* @param object $p The Polynomial object
* @param integer $der_num The derivative you want (1 = 1st, 2 = 2nd, etc.)
*
* @return object A polynomial object representing the nth derivative
*/
function &getDerivative($p, $n = 1)
{
if (!is_a($p, 'Math_Polynomial')) {
$p = new Math_Polynomial($p);
}
$result = new Math_Polynomial();
// This will store the Polynomial's derivative
$count = $p->numTerms();
for ($i = 0; $i < $count; $i++) {
// For each term, multiply coefficient by exponent, subtract 1 from exponent
$term = $p->getTerm($i);
$der_term = new Math_PolynomialTerm($term->getCoefficient() * $term->getExponent(), $term->getExponent() - 1);
$result->addTerm($der_term);
}
for ($i = 0; $i < $n - 1; $i++) {
// If we want other than the 1st derivative, keep going...
$result = Math_PolynomialOp::getDerivative($result);
if (Math_PolynomialOp::isZero($result)) {
// If derivative is ever zero, every derivative thereafter is also 0
return $result;
}
}
return $result;
}