Wyrm.Math

A collection of mathematical methods and algorithms.

Wyrm.Math

Provides double and decimal extensions.

Decimal

Decimal constants E, Pi, and Tau.

Double extensions

Applies all the System.Math methods as extension methods and adds Sqr (square).

Decimal extensions

Replicates the System.Math methods for decimals as extension methods. Abs, Acos, Acosh, Asin, Asinh, Atan, Atanh, Atan2, BitDecrement, BitIncrement, Cbrt, Ceiling, CopySign, Clamp, Cos, Cosh, Exp, Floor, FusedMultiplyAdd, IEEERemainder, ILogB, Log, Log (to base), Log2, Log10, Max, MaxMagnitude, Min, MinMagnitude, Pow, ReciprocalEstimate, ReciprocalSqrtEstimate, Round, Round (to digits), Round (with algorithm), Round (to digits with algorithm), ScaleB, Sign, Sin, SinCos, Sinh, Sqr, Sqrt, Tan, Tanh, Truncate.

Create complex number

Z = N.AsComplex()

Z = N.AsComplex(Ni)

Creates a double or decimal complex number from a value with an optional imaginary part.

Complex Cube Root

Z = N.Cbrti()

Calculates the cube root of a number (either decimal or double) and returns the result as a complex number.

Complex Natural Log

Z = N.Logi()

Calculates the principal natural logarithm of a number (either decimal or double) and returns the result as a complex number.

Complex Square Root

Z = N.Sqrti()

Calculates the square root of a number (either decimal or double) and returns the result as a complex number.

Wyrm.Math.ComplexNumbers

Provides complex number arithmetic.

GeneralComplexNumberDouble

This class allows complex numbers with double values to be created, added, subtracted, multiplied, and divided.

GeneralComplexNumberDecimal

This class allows complex numbers with decimal values to be created, added, subtracted, multiplied, and divided.

Operations

Cast

You can cast a complex number with no imaginary part to a scalar and cast a scalar to a complex number.

Complex Conjugate

Z' = Z.ComplexConjugate()

Calculates the complex conjugate of the complex number.

Abs

|Z| = Z.Abs()

Calculates the absolute value of the complex number.

Argument

P = Z.Argument()

Calculates the argument (or phase) of the complex number.

Inverse

1/Z = Z.Inverse()

Calculates the inverse of the complex number.

Add a scalar

Zv = Z + n

Zv = n + Z

Adds a scalar value to the complex number, creating a new complex number.

Add another complex number

Zv = Z1 + Z2

Adds one complex number to another, creating a new complex number.

Duplicate a complex number

Z = + Z

Duplicates a complex number.

Subtract a scalar

Zv = Z - n

Zv = n - Z

Subtracts a scalar value from a complex number or subtracts a complex number from a scalar, creating a new complex number.

Subtract another complex number

Zv = Z1 - Z2

Subtracts one complex number from another, creating a new complex number.

Negate a complex number

Zv = - Z

Negates the complex number, creating a new complex number.

Multiply by a scalar

Zv = Z * n

Zv = n * Z

Multiplies a scalar value with a complex number, creating a new complex number.

Multiply another complex number

Zv = Z1 * Z2

Multiplies one complex number with another, creating a new complex number.

Divide by a scalar

Zv = Z / n

Zv = n / Z

Divides a scalar value into a complex number or divides a complex number into a scalar, creating a new complex number.

Divide by a complex number

Zv = Z / Zd

Divides complex numbers, creating a new complex number.

Raise to a Power

Z^2 = Z.Sqr()

Z^0.5 = Z.Sqrt()

Z^n = Z.Pow(n)

Z^z = Z.Pow(z)

Raises a complex number by a power either real or complex.

Sine

Zv = Z.Sin()

Returns the sine of a complex number (radians).

Cosine

Zv = Z.Cos()

Returns the cosine of a complex number (radians).

Tangent

Zv = Z.Tan()

Returns the tangent of a complex number (radians).

Arsine

Zv = Z.Asin()

Returns the complex angle (radians) that has the sine.

Arcosine

Zv = Z.Acos()

Returns the complex angle (radians) that has the cosine.

Artangent

Zv = Z.Atan()

Returns the complex angle (radians) that has the tangent.

Hyperbolic Sine

Zv = Z.Sinh()

Returns the hyperbolic sine of a complex number (radians).

Hyperbolic Cosine

Zv = Z.Cosh()

Returns the hyperbolic cosine of a complex number (radians).

Hyperbolic Tangent

Zv = Z.Tanh()

Returns the hyperbolic tangent of a complex number (radians).

Principal Hyperbolic Arsine

Zv = Z.Asinh()

Returns the principal complex angle (radians) that the complex number is a hyperbolic sine of.

Principal Hyperbolic Arcosine

Zv = Z.Acosh()

Returns the principal complex angle (radians) that the complex number is a hyperbolic cosine of.

Principal Hyperbolic Artangent

Zv = Z.Atanh()

Returns the principal complex angle (radians) that the complex number is a hyperbolic tangent of.

Cube Root

Zv = Z.Cbrt()

Returns the complex cube root of a complex number.

Complex Copy Sign

Zv = Zx.CopySign(Zy)

Returns a complex number with the magnitudes of Zx but the signs of Zy. The real part has the magnitude of Zx.Real but the sign of Zy.Real and the imaginary part has the magnitude of Zx.Imaginary but the sign of Zy.Imaginary.

Complex ScaleB

Zv = Z.ScaleB(N)

Returns the result of Zx * 2^N as a complex number.

Exponential

Zv = Z.Exp()

Returns the value of e to the power of a complex number.

Principal Natural Logarithm

Zv = Z.Log()

Returns the principal natural logarithm of a complex number.

Principal Logarithm to Base

Zv = Z.Log(b)

Returns the principal logarithm of a complex number in base b.

Principal Logarithm to complex Base

Zv = Z.Log(Zb)

Returns the principal logarithm of a complex number in complex base Zb.

Principal Logarithm to Base 2

Zv = Z.Log2()

Returns the principal logarithm of a complex number in base 2.

Principal Logarithm to Base 10

Zv = Z.Log10()

Returns the principal logarithm of a complex number in base 10.

Rounding

Zr = Z.Round()

Zr = Z.Round(N)

Zr = Z.Round(MidPointRounding)

Zr = Z.Round(N, MidPointRounding)

Returns a complex number with the real and imaginary parts rounded.

Wyrm.Math.Matrix

Provides matrix arithmetic.

GeneralMatrixDouble

This class allows matrices with double values to be created, added, subtracted, and multiplied.

GeneralMatrixDecimal

This class allows matrices with decimal values to be created, added, subtracted, and multiplied.

Operations

Transpose

{M}' = {M}.Transpose()

Swaps the values of the matrix around the diagonal, creating a new matrix.

Trace

V = {M}.Trace()

Calculates the trace of a matrix.

The matrix must be square.

Determinant

|{M}| = {M}.Determinant()

Calculates the determinant of a matrix using Gaussian Elimination.

The matrix must be square.

Rank

V = {M}.Rank()

Calculates the rank of a matrix using Gaussian Elimination.

Nullity

V = {M}.Nullity()

Calculates the nullity of a matrix using Gaussian Elimination.

This is the number of columns minus the rank.

Inverse

{M}^-1 = {M}.Inverse()

Calculates the inverse of a matrix using Gaussian Elimination.

The matrix must be square and invertible (non-zero determinant).

Add a scalar

{Mv} = {M} + n

{Mv} = n + {M}

Adds a scalar value to every element in a matrix, creating a new matrix.

Add another matrix

{Mv} = {M1} + {M2}

Adds one matrix to another, creating a new matrix.

The matrices must be of the same dimensions.

Duplicate a matrix

{M} = + {M}

Duplicates a matrix.

Subtract a scalar

{Mv} = {M} - n

{Mv} = n - {M}

Subtracts a scalar value from every element in a matrix or subtracts each value in a matrix from a scalar, creating a new matrix.

Subtract another matrix

{Mv} = {M1} - {M2}

Subtracts one matrix from another, creating a new matrix.

The matrices must be of the same dimensions.

Negate a matrix

{Mv} = - {M}

Negates every value in a matrix, creating a new matrix.

Multiply by a scalar

{Mv} = {M} * n

{Mv} = n * {M}

Multiplies a scalar value with every element in a matrix, creating a new matrix.

Multiply another matrix

{Mv} = {M1} * {M2}

Multiplies one matrix with another using the naive algorithm, creating a new matrix.

The number of columns of the first matrix must be the same as the number of rows of the second matrix.

Divide by a scalar

{Mv} = {M} / n

{Mv} = n / {M}

Divides a scalar value into every element in a matrix or divides each value in a matrix into a scalar, creating a new matrix.

Extensions

Create matrix

M = [[],...].AsMatrix()

Creates a matrix from an enumerable of enumerable decimal or double values.