/**
* Find and return the roots of a Quartic Polynomial (degree 4) with the Quartic formula
*
* @see Math_PolynomialOp::getRoots()
*
* @access public
*
* @param object $p
* @return array
*/
function getRootsQuartic($p)
{
if (!is_a($p, 'Math_Polynomial')) {
$p = new Math_Polynomial($p);
}
if ($p->degree() == 4) {
$arr = array();
// Array of roots
// Simplify it a bit first
$a_term = $p->getTerm(0);
$p = Math_PolynomialOp::div($p, $a_term->getCoefficient());
$a = 0;
$b = 0;
$c = 0;
$d = 0;
$e = 0;
$num_terms = $p->numTerms();
for ($i = 0; $i < $num_terms; $i++) {
$term = $p->getTerm($i);
if ($term->getExponent() == 4) {
$a = $term->getCoefficient();
} else {
if ($term->getExponent() == 3) {
$b = $term->getCoefficient();
} else {
if ($term->getExponent() == 2) {
$c = $term->getCoefficient();
} else {
if ($term->getExponent() == 1) {
$d = $term->getCoefficient();
} else {
if ($term->getExponent() == 0) {
$e = $term->getCoefficient();
}
}
}
}
}
}
$f = $c - 3 * $b * $b / 8;
$g = $d + pow($b, 3) / 8 - $b * $c / 2;
$h = $e - 3 * pow($b, 4) / 256 + $b * $b * ($c / 16) - $b * $d / 4;
$cubic = new Math_Polynomial('x^3 + ' . $f / 2 . 'x^2 + ' . (pow($f, 2) - 4 * $h) / 16 . 'x - ' . pow($g, 2) / 64);
$p = 0;
$q = 0;
foreach (Math_PolynomialOp::getRootsCubic($cubic) as $p_or_q) {
if ($p == 0 && $p_or_q != 0) {
$p = sqrt($p_or_q);
} else {
if ($q == 0 && $p_or_q != 0) {
$q = sqrt($p_or_q);
}
}
}
if ($p != 0 && $q != 0) {
$r = -1 * $g / (8 * $p * $q);
$s = $b / (4 * $a);
$arr[] = $p + $q + $r - $s;
$arr[] = $p - $q - $r - $s;
$arr[] = -1 * $p + $q - $r - $s;
$arr[] = -1 * $p - $q + $r - $s;
}
return Math_PolynomialOp::_round($arr);
} else {
return PEAR::raiseError('Parameter to Math_PolynomialOp::getRootsQuartic() is not quartic.');
}
}
function testGetRootsCubic()
{
$p = new Math_Polynomial('x - 6');
$p = Math_PolynomialOp::mul($p, 'x + 1');
$p = Math_PolynomialOp::mul($p, 'x - 3');
$roots = Math_PolynomialOp::getRootsCubic($p);
$this->assertEquals(array(6, -1, 3), $roots);
}