function testSubtract()
{
$p = new Math_Polynomial('3x^2 - 2x + 1');
$q = new Math_Polynomial('2x^2 + 2x');
$res = Math_PolynomialOp::sub($p, $q);
$this->assertEquals('x^2 - 4x + 1', $res->toString());
}
//header('Content-type: text/plain');
include 'Math/Polynomial.php';
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 />";
/**
* Divide one Polynomial by another, returning the result
*
* Divide the first polynomial by another polynomial object or a string
* represention of another polynomial. Optionally, you can pass another
* Polynomial object by reference to store the remainder of the division
* operator.
*
* <code>
* $a = new Polynomial("4x^2 + 2x");
* $b = new Polynomial("2x");
* $remainder = new Polynomial();
* $result = PolynomialOp::div($a, $b, $remainder);
* print("A divided by B is: " . $result->toString() . " with a remainder of " . $remainder->toString() . "\n");
* </code>
*
* @access public
*
* @param object $p1
* @param object $p2
* @param object $rem
* @return object
*/
function &div($p1, $p2, &$rem = null)
{
if (!is_a($p1, 'Math_Polynomial')) {
$p1 = new Math_Polynomial($p1);
}
if (!is_a($p2, 'Math_Polynomial')) {
$p2 = new Math_Polynomial($p2);
}
if (Math_PolynomialOp::isZero($p2)) {
$err = PEAR::raiseError('Divide by zero error in Math_PolynomialOp::div().');
return $err;
}
if (is_null($rem)) {
$remain = new Math_Polynomial();
} else {
if (!is_a($rem, 'Math_Polynomial')) {
$err = PEAR::raiseError('Reference remainder parameter must be a Math_Polynomial object.');
return $err;
} else {
$remain =& $rem;
}
}
$res = new Math_Polynomial();
// Copy terms in $p1 over to the remainder Polynomial
$count = $p1->numTerms();
for ($i = 0; $i < $count; $i++) {
$remain->addTerm($p1->getTerm($i));
}
/*
* Method here is for each term in $p1, find out what we'd need to mult.
* the first term in $p2 by to get $p1. That term goes into the result,
* do the multiplication and subtract that from $p1. That gets rid of
* the terms 1 by 1 until we're done.
*/
while (true) {
$term_remain = $remain->getTerm(0);
// This will change on each loop as we subtract stuff out of $remain
$term_p2 = $p2->getTerm(0);
// This should stay constant, we're not changing $p2
if ($term_p2->getExponent() > $remain->degree()) {
// If the degree of b is larger than degree of a, there's no way b can be a factor...
break;
}
// Next three lines could be shortened a bit...
$div = new Math_PolynomialTerm($term_remain->getCoefficient() / $term_p2->getCoefficient(), $term_remain->getExponent() - $term_p2->getExponent());
$div_poly = new Math_Polynomial();
$div_poly->addTerm($div);
$step_poly = Math_PolynomialOp::mul($p2, $div_poly);
$remain = Math_PolynomialOp::sub($remain, $step_poly);
$res->addTerm($div);
if (Math_PolynomialOp::isZero($remain)) {
break;
}
}
return $res;
}
