public PolynomialX Differentiate()
{
PolynomialX polynomial = new PolynomialX(Coefficients.Length - 1);
for (int i = 1; i < Coefficients.Length; i++)
{
polynomial[i - 1] = i * this[i];
}
return(polynomial);
}
public static bool Verify(IntX[] output, PolynomialX poly, InputTypes type, int startingValue = -1, bool verify = false)
{
IntX[] input = GenerateInput(output, type, startingValue);
for (int i = 0; i < output.Length; i++)
{
if (output[i] != poly.F(input[i]))
{
return(false);
}
}
return(true);
}
public PolynomialX DivideOutRoot(FractionX root)
{
var copy = Copy();
PolynomialX result = new PolynomialX(Coefficients.Length - 1);
FractionX last = Coefficients[Coefficients.Length - 1];
result[result.Coefficients.Length - 1] = last;
for (int i = Coefficients.Length - 3; i >= 0; i--)
{
copy[i + 1] += root * last;
result[i] = last = copy[i + 1];
}
return(result);
}
public static string[] BuildMessage(string output, InputTypes type, PolynomialX poly, TextFormat format, char functionVariable = 'x', string functionName = "f", int startingValue = -1)
{
string exportMessage;
switch (type)
{
case InputTypes.Primes:
exportMessage = "Input the first " + output.Length + " consecutive primes to get the message ASCII values for the string: \"" + output + "\".";
break;
case InputTypes.Recursive:
exportMessage = "Input " + startingValue +
" into the following function and put the output into the function and repeat the recursive process to get the first "
+ output.Length + " outputs which will corrospond to the ASCII values for the string: \"" + output + "\".";
break;
case InputTypes.RecursivePrimes:
exportMessage = "Input " + startingValue +
" into the following function and multiply the output by the first prime number" +
", then put that product into the function, repeat with the next output and the second consecutive prime prime" +
"and so on until "
+ output.Length + " output values have been obtained. These values will corospond to the ASCII values which give the following string: \"" + output + "\".";
break;
case InputTypes.PreviousProduct:
exportMessage = "Input " + startingValue +
" into the following function and multiply the output by the previous input and put that into the function a total of "
+ (output.Length - 1) + " times to get a total of " + output.Length + " output values will corrospond to the ASCII values for the string: \"" + output + "\".";
break;
default:
throw new ArgumentOutOfRangeException();
}
return(new string[]
{
exportMessage,
functionName + "(" + functionVariable + ") = " + poly.ToString(functionVariable, format)
});
}
public static PolynomialX Generate(IntX[] input, IntX[] output)
{
if (input.Length != output.Length)
{
return(null);
}
MatrixX A = new MatrixX(input.Length, input.Length);
MatrixX column = new MatrixX(1, input.Length);
for (int i = 0; i < input.Length; i++)
{
IntX prod = 1;
for (int j = 0; j < input.Length; j++)
{
A[j, i] = prod;
prod *= input[i];
}
column[0, i] = output[i];
}
var det = A.Determinant();
if (det == 0)
{
return(null);
}
var adjoint = A.GetAdjointMatrix();
PolynomialX poly = new PolynomialX(input.Length);
var result = adjoint * column;
for (int i = 0; i < input.Length; i++)
{
poly.Coefficients[i] = (FractionX)result[i, 0] / det;
}
return(poly);
}
public static void Export(string path, string output, InputTypes type, PolynomialX poly, TextFormat format, char functionVariable = 'x', string functionName = "f", int startingValue = -1) => File.WriteAllLines(path, BuildMessage(output, type, poly, format, functionVariable, functionName, startingValue));