/NerdSharp.Net_Studio/NerdSharp_UberNet/Science/Math/Utils/GeneralMath.cs

using System;

using System.Collections.Generic;

using System.Linq;

using System.Text;

using System.Numerics;

using M = System.Math;

using NerdSharp.Net_Studio.NerdSharp_UberNet.Science.Math.TypeLibrary.Numeric;

using NerdSharp.Net_Studio.NerdSharp_UberNet.Science.Math.TypeLibrary.Equation;

using E = NerdSharp.Net_Studio.NerdSharp_UberNet.Science.Math.TypeLibrary.Equation.EquationSide;

using System.Threading;



namespace NerdSharp.Net_Studio.NerdSharp_UberNet.Science.Math.Utils

{

    public class Math

    {

        public enum Signs

        {

            plus,

            minus,

            times,

            divide,

            pow

        }



        public static ulong[] primeNumbers = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 

                                                 31, 37, 41, 43, 43, 47, 53, 61, 67, 

                                                 71, 73, 79, 83, 89, 97, 101, 103, 107, 

                                                 109, 113, 127, 131, 137, 139, 149, 151, 157, 

                                                 163, 167, 173, 179, 181, 191, 193, 197, 199, 

                                                 211, 223, 227, 229, 233, 239, 241, 251, 257, 

        263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 

        379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 

        491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 

        617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 

        743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 

        877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 

        1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 

        1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 

        1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 

        1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 

        1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 

        1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 

        1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 

        1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 

        1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 

        2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 

        2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 

        2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 

        2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 

        2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 

        2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707,

        2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803,

        2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939,

        2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067,

        3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,

        3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329,

        3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461,

        3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559,

        3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677,

        3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803,

        3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 

        3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 

        4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 

        4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 

        4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 

        4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 

        4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 

        4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 

        4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 

        4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 

        5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 

        5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 

        5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 

        5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 

        5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 

        5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 

        5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 

        6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 

        6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 

        6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 

        6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 

        6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 

        6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 

        6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 

        6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 

        7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 

        7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 

        7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 

        7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 

        7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 

        7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 

        7877, 7879, 7883, 7901, 7907, 7919 };



        #region linear



        public static double yMXBFormula(double slope, double x, double b)

        {

            return (slope * x) + b;

        }



        public static List<double> yMXBFormula(double slope, List<double> x, double b)

        {

            List<double> yListAnswer = new List<double>();

            for (int i = 0; i < x.Count; i++)

            {

                yListAnswer.Add((slope * x[i]) + b);

            }

            return yListAnswer;

        }



        public static double findSlopeM(double x1, double x2, double y1, double y2)

        {

            return (y2 - y1) / (x2 - x1);

        }



        #endregion



        public static List<double> FindYArrayPolynom(List<double> coefficients, List<double> x)

        {

            List<double> yAnswers = new List<double>();

            for (int i = 0; i < x.Count; i++)

            {

                for (int j = 0; j < coefficients.Count; j++)

                {



                }

            }

            return yAnswers;

        }



        public static object[] xQuadratic(double a, double b, double c)

        {

            object[] answer = new object[2];

            double x1 = 0.0d;

            double x2 = 0.0d;

            double sqrtCheck = (System.Math.Pow(b, 2)) - (4 * a * c);

            if (sqrtCheck < 0)

            {

                sqrtCheck = -1.0d * sqrtCheck;

                Complex twoComplex = new Complex(2.0d, 0.0d);

                Complex complex = new Complex(0.0d, M.Sqrt(sqrtCheck));

                Complex aComplex = new Complex(a, 0.0d);

                Complex bComplex = new Complex(b, 0.0d);

                Complex cComplex = new Complex(c, 0.0d);

                Complex x1complex = new Complex();

                Complex x2complex = new Complex();

                x1complex = ((-bComplex) + complex) / (twoComplex * aComplex);

                x2complex = ((-bComplex) - complex) / (twoComplex * aComplex);

                answer[0] = x1complex;

                answer[1] = x2complex;

                return answer;

            }

            else

            {



                x1 = ((-1.0d * b) + M.Sqrt(sqrtCheck)) / (2 * a);

                x2 = ((-1.0d * b) - M.Sqrt(sqrtCheck)) / (2 * a);

                answer[0] = x1;

                answer[1] = x2;

                return answer;

            }

        }



        public static List<ulong> PrimeFactorization(ulong number)

        {

            //http://www.amby.com/educate/math/2-1_fact.html

            //uses division by primes

            List<ulong> primeFactAnswer = new List<ulong>();

            ulong quotientAfterDivByPrime = number;

            ulong currentPrimeCount = 1;



            while (quotientAfterDivByPrime != 1)

            {

                ulong currentPrime = primeNumbers[currentPrimeCount];

                ulong ulongComparison = quotientAfterDivByPrime / currentPrime;

                if (IsDivisibleBy(quotientAfterDivByPrime, currentPrime))

                {

                    quotientAfterDivByPrime = ulongComparison;

                    primeFactAnswer.Add(currentPrime);

                }

                else if (!IsDivisibleBy(quotientAfterDivByPrime, currentPrime))

                {

                    currentPrimeCount++;

                }

            }

            return primeFactAnswer;

        }



        #region Divisibility



        public static List<ulong> FindDivisibility(ulong number)

        {

            List<ulong> answer = new List<ulong>();

            for (ulong i = 2; i < number + 1; i++)

            {

                ulong ulongComparison = number / i;

                double doubleCmparison = Convert.ToDouble(number) / Convert.ToDouble(i);

                if (Convert.ToDouble(ulongComparison) == doubleCmparison)

                {

                    answer.Add(i);

                }

            }

            return answer;

        }



        public static bool IsDivisibleBy(ulong dividend, ulong divisor)

        {

            ulong ulongComparison = dividend / divisor;

            double doubleCmparison = Convert.ToDouble(dividend) / Convert.ToDouble(divisor);

            if (Convert.ToDouble(ulongComparison) == doubleCmparison)

            {

                return true;

            }

            else

            {

                return false;

            }

            return false;

        }



        #endregion



        public static void DoNothing() { }



        public static float InternalAnglePolygon(float side)

        {

            return (side - 2) * 180 / side;

        }



        public static double Sumation(double[] numbers)

        {

            double sumOfnums = 0.0d;

            for (int i = 0; i < numbers.Length; i++)

            {

                sumOfnums += numbers[i];

            }

            return sumOfnums;

        }



        public static double Summation(E equationSide)

        {

            return 0;

        }



        #region Cubic



        public static double CubicRootX1(double a, double b, double c, double d)

        {

            //first two parts of the innermost root of part one

            double firstInnerRoot_0 = System.Math.Pow((2 * System.Math.Pow(b, 3) - 9 * a * b * c + 27 * System.Math.Pow(a, 2) * d), 2);

            double firstInnerRoot_1 = 4 * System.Math.Pow((System.Math.Pow(b, 2) - 3 * a * c), 3);

            double innerRoot = System.Math.Sqrt(firstInnerRoot_0 - firstInnerRoot_1);

            double outerRoot_0 = 2 * System.Math.Pow(b, 3) - 9 * a * b * c + 27 * System.Math.Pow(a, 2) * d;

            double outerRoot = NthRoot((innerRoot + outerRoot_0) / 2, 3);

            double firstPart = (-(1 / 3 * a)) * outerRoot;

            //secondPart

            double secondOuterRoot = NthRoot((innerRoot - outerRoot_0) / 2, 3);

            double secondPart = (-(1 / 3 * a)) * secondOuterRoot;



            return ((-b) / 3 * a) - firstPart - secondPart;

        }



        public static Complex CubicRootX2(double a, double b, double c, double d)

        {

            //makes ready answer and turns nums in form needed

            Complex i = new Complex(0, 1);

            Complex realOne = new Complex(1, 0);

            Complex answer = new Complex();

            //firstPart

            Complex firstPiece = new Complex(((-b) / 3 * a), 0);

            //secondPart

            Complex secondPiece = i * realOne;

            Complex innerRoot = new Complex();

            //thirdPart

            Complex thirdPiece = new Complex();

            Complex outerRoot = new Complex();

            //completes the final answer

            answer = firstPiece + secondPiece + thirdPiece;

            return answer;

        }



        public static double CubicRootX3(double a, double b, double c, double d)

        {

            return ((-b) / 3 * a);

        }



        public static object[] FindCubicsXVal(double a, double b, double c, double d, bool useMultiThreading)

        {

            object[] answer = new object[3];

            if (useMultiThreading)

            {

                ThreadStart job = new ThreadStart(X1Job);

                Thread t = new Thread(job);



                return answer;

            }

            else

            {

                answer[0] = CubicRootX1(a, b, c, d);

                //answer[1] = CubicRootX2(a, b, c, d);

                answer[2] = CubicRootX3(a, b, c, d);

                return answer;

            }

        }



        public static void X1Job()

        {



        }



        public static double CubicRootX1Monic(double a, double b, double c)

        {



            double firstRoot;

            double secondRoot;

            return -(a / 3);

        }



        public static object[] CubicYVals(object[] xVals)

        {

            object[] answer = new object[3];

            for (int i = 0; i < answer.Length; i++)

            {



            }

            return answer;

        }



        #endregion



        public static double NthRoot(double x, double index)

        {

            if (index == 0)

            {

                throw new DivideByZeroException("The zeroth root is the same as dividing by zero. Cannot perform operation.");

            }

            else

            {

                return System.Math.Pow(x, 1 / index);

            }

            return double.NaN;

        }



        public static double Product(double[] input)

        {

            double answer = 1.0d;

            for (int i = 0; i < input.Length; i++)

            {

                answer *= input[i];

            }

            return answer;

        }



        public static double NewtonsMethod(Function function, double x0, long iterations)

        {

            double xn = x0;

            for (int i = 0; i < iterations; i++)

            {



            }

            return xn;

        }



        public static BigDecimal E(BigInteger iterations)

        {

            BigDecimal answer = new BigDecimal();



            return answer;

        }



        public static long Factorial(long n)

        {

            long answer = 1;

            for (long i = n; i > 1; i--)

            {

                answer *= i;

            }

            return answer;

        }



        public static BigInteger Factorial(BigInteger n)

        {

            BigInteger answer = 1;

            for (BigInteger i = n; i > 1; i--)

            {

                answer *= i;

            }

            return answer;

        }



        public static long BinomialCoeffecient(long n, long k)

        {

            if (k <= 0)

            {

                throw new ArgumentException("");

            }

            if (n <= k)

            {

                throw new ArgumentException("");

            }

            return Factorial(n) / (Factorial(k) * Factorial(n - k));

        }



        public static BigInteger BinomialCoeffecient(BigInteger n, BigInteger k)

        {

            if (k <= 0)

            {

                throw new ArgumentException("");

            }

            if (n <= k)

            {

                throw new ArgumentException("");

            }

            return Factorial(n) / (Factorial(k) * Factorial(n - k));

        }

    }

}