45 lines
1.4 KiB
Plaintext
45 lines
1.4 KiB
Plaintext
function det-perm ($array) {
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if($array) {
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$size = $array.Count
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function prod($A) {
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$prod = 1
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if($A) { $A | foreach{$prod *= $_} }
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$prod
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}
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function generate($sign, $n, $A) {
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if($n -eq 1) {
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$i = 0
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$prod = prod @($A | foreach{$array[$i++][$_]})
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[pscustomobject]@{det = $sign*$prod; perm = $prod}
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}
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else{
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for($i = 0; $i -lt ($n - 1); $i += 1) {
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generate $sign ($n - 1) $A
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if($n % 2 -eq 0){
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$i1, $i2 = $i, ($n-1)
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$A[$i1], $A[$i2] = $A[$i2], $A[$i1]
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}
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else{
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$i1, $i2 = 0, ($n-1)
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$A[$i1], $A[$i2] = $A[$i2], $A[$i1]
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}
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$sign *= -1
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}
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generate $sign ($n - 1) $A
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}
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}
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$det = $perm = 0
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generate 1 $size @(0..($size-1)) | foreach{
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$det += $_.det
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$perm += $_.perm
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}
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[pscustomobject]@{det = "$det"; perm = "$perm"}
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} else {Write-Error "empty array"}
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}
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det-perm 5
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det-perm @(@(1,0,0),@(0,1,0),@(0,0,1))
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det-perm @(@(0,0,1),@(0,1,0),@(1,0,0))
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det-perm @(@(4,3),@(2,5))
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det-perm @(@(2,5),@(4,3))
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det-perm @(@(4,4),@(2,2))
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