Private/Test-Polynomial.ps1
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.SYNOPSIS Evaluates a polynomial at a given point over a finite field. .DESCRIPTION Evaluates a polynomial at a given point over a finite field using Horner's method for efficient calculation. .PARAMETER Polynomial An array of coefficients representing the polynomial. .PARAMETER PointToEval The point at which to evaluate the polynomial. .PARAMETER Prime The prime modulus of the finite field. .OUTPUTS The value of the polynomial at the given point. .EXAMPLE Evaluate the polynomial x^2 + 2x + 1 at point 3 over the field modulo 7: $Polynomial = @(1, 2, 1) $PointToEval = 3 $Prime = 7 Test-Polynomial -Polynomial $Polynomial -PointToEval $PointToEval -Prime $Prime #> Function Test-Polynomial { param ( [bigint[]]$Polynomial, [bigint]$PointToEval, [bigint]$Prime ) $Accumulator = 0 # Iterate over the coefficients in reverse order for ($i = $Polynomial.Length - 1; $i -ge 0; $i--) { $Accumulator *= $PointToEval $Accumulator += $Polynomial[$i] $Accumulator %= $Prime } return $Accumulator } |