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private void Calculate_Click(object sender, EventArgs e)
        {
            string functioninput, saveinput;
            functioninput = Input.Text; // Abspeichern der Eingabe
            if (functioninput.Trim() == "") 
            {
                functioninput = "0";
            }
            saveinput = functioninput.Replace("+1x", "+x").Replace("-1x", "-x").Replace("f(x)", "").Replace("=", ""); //Ausgabekopie
            functioninput = MakeStringReadable(functioninput);//Lesbarmachen des Strings, inklusive umrechnen der Konfortoptionen
            functioninput = functioninput.Replace("-", "+-"); //Einfacherer Splitvorgang durch Anwendung der Operatorenregel
            string[] singleaddends = functioninput.Trim().Split(new[] { "+" }, StringSplitOptions.RemoveEmptyEntries); //Auftrennen der einzelnen Addenden
            for (int i = 0; i < singleaddends.Length; i++)
            {
                if (!singleaddends[i].Contains("x^"))
                {
                    singleaddends[i] = singleaddends[i] + "x^0"; //umrechnen der Konfortoptionen
                }
            }
            double[,] factorexponent = new double[2, singleaddends.Length]; // Anlegen der zweidimensionalen Funktionsarrays
            for (int i = 0; i < singleaddends.Length; i++)
            {
                string[] ram = singleaddends[i].Split(new[] { "x^" }, StringSplitOptions.RemoveEmptyEntries);
                factorexponent[0, i] = Convert.ToDouble(ram[0]); //Auftrennen der einzelnen Addenden
                factorexponent[1, i] = Convert.ToDouble(ram[1]);
            }
            /////
            double[,] f1arr = new double[2, factorexponent.Length]; //Funktionsspeicher für Albleitungen und Stammfunktion
            double[,] f2arr = new double[2, factorexponent.Length];
            double[,] f3arr = new double[2, factorexponent.Length];
            double[,] Farr = new double[2, factorexponent.Length];
            ////
            Farr = Sortieren(Stammfunktion(factorexponent));
            f1arr = Sortieren(Ableiten(factorexponent, 1));
            f2arr = Sortieren(Ableiten(factorexponent, 2));
            f3arr = Sortieren(Ableiten(factorexponent, 3));
            GradLabel.Text = "Es liegt eine Funktion " + Grade(factorexponent) + ". Grades vor.\n";
            StammfunktionLabel.Text = StammfunktionToString(Farr);
            InputFunction.Text = "f(x) = " + saveinput;
            A1Label.Text = AbleitungsfunktionToString(f1arr, 1);
            A2Label.Text = AbleitungsfunktionToString(f2arr, 2);
            A3Label.Text = AbleitungsfunktionToString(f3arr, 3);
        }

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 static string MakeStringReadable(string functioninput)
        {
            functioninput = functioninput.Replace("f(x)", "");
            functioninput = functioninput.Replace("=", "");
            functioninput = functioninput.Trim();
            functioninput = functioninput.Replace(" ", "");
            functioninput = "Beginn:" + functioninput;
            functioninput = functioninput.Replace("Beginn:x", "1x");
            functioninput = functioninput.Replace("+x", "+1x");
            functioninput = functioninput.Replace("-x", "-1x");
            functioninput = functioninput.Replace("Beginn:", "");
            for (int i = 0; i < functioninput.Length; i++)
            {
                if ((functioninput[i] == Convert.ToChar("x")) && (i + 1 == functioninput.Length))
                {
                    functioninput = functioninput.Remove(i, 1);
                    functioninput = functioninput.Insert(i, "x^1");
                }
                else
                {
                    if ((functioninput[i] == Convert.ToChar("x")) && (functioninput[i + 1] != Convert.ToChar("^")))
                    {
                        functioninput = functioninput.Remove(i, 1);
                        functioninput = functioninput.Insert(i, "x^1");
                    }
                }
            }
            return functioninput;
        } //Bearbeitung des Stringinputs zur besseren Verarbeitung - Ausgabe String

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static double[,] Ableiten(double[,] function, int times)
        {
            double[,] output = new double[2, function.GetLength(1)];
            for (int i = 0; i < function.GetLength(1); i++)
            {
                if (function[1, i] == 0)
                {
                    output[0, i] = 0;
                    function[1, i] = 0;
                }
                else
                {
                    output[0, i] = function[0, i] * function[1, i];
                    output[1, i] = function[1, i] - 1;
                }
            }
            if (times > 1)
            {
                return Ableiten(output, times - 1);
            }
            else
            {
                return output;
            }
        } //Rekursiver Algorithmus zur Bildung der Ableitungsfunktion n. Grades - Ausgabe double[,]

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static double[,] Stammfunktion(double[,] function)
        {
            double[,] output = new double[2, function.GetLength(1)];
            for (int i = 0; i < function.GetLength(1); i++)
            {
                output[0, i] = function[0, i] / (function[1, i] + 1);
                output[1, i] = function[1, i] + 1;
            }
            output = Zusammenfassen(output);
            return output;
        } // Algorithmus zur Bildung der Stammfunktion - Ausgabe double[,]

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static int Grade(double[,] function)
        {
            int counter = Convert.ToInt32(function[1, 0]);
            for (int i = 1; i < function.GetLength(1); i++)
            {
                if (function[1, i] > counter)
                {
                    counter = Convert.ToInt32(function[1, i]);
                }
            }
            return counter;
        } //Bestimmt Grad der Funktion - Ausgabe Integer

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static double[,] Zusammenfassen(double[,] function)
        {
            int count = 1;
            int size = function.GetLength(1);
            for (int i = 0; i < size; i++)
            {
                for (int j = count; j < size; j++)
                {
                    if (function[1, i] == function[1, j])
                    {
                        function[0, i] = function[0, i] + function[0, j];
                        function[0, j] = 0;
                        function[1, j] = 0;
                    }
                }
                count = count + 1;
            }
            return function;
        } //Fasst Addenden mit gleichem Exponenten zusammen -> Vereinfachung der Ausgabefunktion - Ausgabe double[,]

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static double[,] Sortieren(double[,] function)
        {
            double[,] output = new double[2, function.GetLength(1)];
            double[] exp = new double[function.GetLength(1)];
            double[] bases = new double[function.GetLength(1)];
            for (int i = 0; i < function.GetLength(1); i++)
            {
                exp[i] = function[1, i];
            }
            Array.Sort(exp);
            Array.Reverse(exp);
            for (int i = 0; i < function.GetLength(1); i++)
            {
                for (int j = 0; j < function.GetLength(1); j++)
                {
                    if (exp[i] == function[1, j])
                    {
                        bases[i] = function[0, j];
                    }
                }
            }
            for (int i = 0; i < function.GetLength(1); i++)
            {
                output[0, i] = bases[i];
                output[1, i] = exp[i];
            }
            return output;
        } // Sortiert Addenden nach Höhe ihrer Exponenten -> Konfortableres Ausgabeformat - Ausgabe double[,]

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static string AbleitungsfunktionToString(double[,] arr, int grad)
        {
            string strich = new String(Convert.ToChar("\'"), grad);
            string output = "f" + strich + "(x) = ";
            arr = Zusammenfassen(arr);
            for (int i = 0; i < arr.GetLength(1); i++)
            {
                output += "+" + Math.Round(arr[0, i], 2) + "x^" + Math.Round(arr[1, i], 2);
            }
            output = output.Replace("+1x", "+x");
            output = output.Replace("-1x", "-x");
            output = output.Replace("x^0", "");
            output = output.Replace("x^1", "x");
            output = output.Replace("+0", "");
            output = output.Replace("-0", "");
            output = output.Replace("+-", "-");
            output = output.Replace(" +", " ");
            output = output.TrimEnd('-', '+');
            if (output == "f" + strich + "(x) = ")
            {
                output = output + "0";
            }
            return output;
        } //Ausgabe der Ableitungsfunktionen im Stringformat - Ausgabe String

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static string StammfunktionToString(double[,] arr)
        {
            string output = "F(x) = ";
            for (int i = 0; i < arr.GetLength(1); i++)
            {
                output += "+" + Math.Round(arr[0, i], 2) + "x^" + Math.Round(arr[1, i], 2);
            }
            output = output.Replace("+1x", "+x");
            output = output.Replace("-1x", "-x");
            output = output.Replace("+0x", "");
            output = output.Replace("-0x", "");
            output = output.Replace("+-", "-");
            output = output.Replace(" +", " ");
            output = output.Replace("x^1", "x");
            output = output.Replace("x^0", "");
            output = output.Replace("^0", "");
            return output;
        }   //Ausgabe der Stammfunktion im Stringformat - Ausgabe String

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private void Clear_Click(object sender, EventArgs e)
        {
            Input.Text = "";
            StammfunktionLabel.Text = "";
            A1Label.Text = "";
            A2Label.Text = "";
            A3Label.Text = "";
            InputFunction.Text = "";
            GradLabel.Text = "";
        }

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private void Form1_Load(object sender, EventArgs e)
        {
            Input.Focus();
        }

        private void Abbrechen_Click(object sender, EventArgs e)
        {
            Application.Exit();
        }