/**
* 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;
}
include 'Math/PolynomialOp.php';
echo "<br />-- Algebra --<br />";
$p = new Math_Polynomial('3x^2 + 2x');
$q = new Math_Polynomial('4x + 1');
echo 'P is: ' . $p->toString() . "<br />";
echo 'Q is: ' . $q->toString() . "<br />";
$mul = Math_PolynomialOp::mul($p, $q);
// Multiply p by q
echo 'P multiplied by Q is: ' . $mul->toString() . "<br />";
// Print string representation
echo 'The degree of that result is: ' . $mul->degree() . "<br />";
echo 'That result evaluated at x = 10 is: ' . number_format(Math_PolynomialOp::evaluate($mul, 10)) . "<br />";
$sub = Math_PolynomialOp::sub($p, $q);
echo 'P minus Q is: ' . $sub->toString() . "<br />";
$r = new Math_Polynomial('3x^3 - 5x^2 + 10x-3');
$s = new Math_Polynomial('3x+1');
$remainder = new Math_Polynomial();
echo 'R is: ' . $r->toString() . "<br />";
echo 'S is: ' . $s->toString() . "<br />";
$div = Math_PolynomialOp::div($r, $s, $remainder);
echo 'R divided by S is: ' . $div->toString() . ' ( remainder of: ' . $remainder->toString() . ' )' . "<br />";
echo "<br />-- Creating Polynomials --<br />";
$roots = Math_PolynomialOp::createFromRoots(1, 2, -3);
echo 'Here is a polynomial with the roots 1, 2, and -3: ' . $roots->toString() . "<br />";
echo "<br />-- Derivatives --<br />";
echo 'f(x) is: ' . $p->toString() . "<br />";
$der1 = Math_PolynomialOp::getDerivative($p);
echo 'f\'(x) is: ' . $der1->toString() . ' (first derivative)' . "<br />";
$der2 = Math_PolynomialOp::getDerivative($p, 2);
echo 'f\'\'(x) is: ' . $der2->toString() . ' (second derivative)' . "<br />";
echo "<br />";
function testParamConstness()
{
$p1 = new Math_Polynomial('3x + 1');
$p2 = '4x^2 + 2x + 1';
$res = Math_PolynomialOp::add($p1, $p2);
$this->assertEquals('4x^2 + 2x + 1', $p2);
}
