function simplextoarray($sm)
{
for ($r = 0; $r < count($sm); $r++) {
for ($c = 0; $c < count($sm[0]); $c++) {
$sm[$r][$c] = fractionparse($sm[$r][$c]);
}
}
return $sm;
}
function matrixreduce($A, $rref = false, $frac = false)
{
include_once "fractions.php";
// number of rows
$N = count($A);
$M = count($A[0]);
$pivots = array();
if ($N > 10) {
global $myrights;
if ($myrights > 10) {
echo "You really shouldn't use matrixreduce for matrices bigger than 10 rows.";
}
}
for ($r = 0; $r < $N; $r++) {
for ($c = 0; $c < $M; $c++) {
$A[$r][$c] = fractionparse($A[$r][$c]);
}
}
$r = 0;
$c = 0;
while ($r < $N && $c < $M) {
if ($A[$r][$c][0] == 0) {
//swap only if there's a 0 entry
$max = $p;
for ($i = $r + 1; $i < $N; $i++) {
if (abs($A[$i][$c][0] / $A[$i][$c][1]) > abs($A[$max][$c][0] / $A[$max][$c][1])) {
$max = $i;
}
}
if ($max != $p) {
$temp = $A[$r];
$A[$r] = $A[$max];
$A[$max] = $temp;
}
}
if (abs($A[$r][$c][0] / $A[$r][$c][1]) <= 1.0E-10) {
$c++;
continue;
}
//scale pivot row
if ($rref) {
$divisor = $A[$r][$c];
for ($j = $c; $j < $M; $j++) {
$A[$r][$j] = fractiondivide($A[$r][$j], $divisor);
}
}
for ($i = $rref ? 0 : $r + 1; $i < $N; $i++) {
if ($i == $r) {
continue;
}
$mult = fractiondivide($A[$i][$c], $A[$r][$c]);
if ($mult[0] == 0) {
continue;
}
for ($j = $c; $j < $M; $j++) {
//echo "Entry $i,$j: ".fractionreduce($A[$i][$j]).' - '.fractionreduce( $mult).'*'.fractionreduce($A[$r][$j]).'<br/>';
$A[$i][$j] = fractionsubtract($A[$i][$j], fractionmultiply($mult, $A[$r][$j]));
}
}
$r++;
$c++;
}
for ($r = 0; $r < $N; $r++) {
for ($c = 0; $c < $M; $c++) {
if ($frac) {
$A[$r][$c] = fractionreduce($A[$r][$c]);
} else {
$A[$r][$c] = $A[$r][$c][0] / $A[$r][$c][1];
}
}
}
return $A;
}
function fractionroot($f, $root = 2)
{
if (!is_array($f)) {
$f = fractionparse($f);
}
include_once "radicals.php";
return reduceradicalfrac(1, $f[0] * $f[1], $f[1]);
}