`Install-Package DelSquared.Radicals -Version 1.1.0`
`dotnet add package DelSquared.Radicals --version 1.1.0`
`<PackageReference Include="DelSquared.Radicals" Version="1.1.0" />`
For projects that support PackageReference, copy this XML node into the project file to reference the package.
`paket add DelSquared.Radicals --version 1.1.0`

## Documentation

### Overview

.NET implementation of
where the radicand is a rational number and the index is a positive integer.
Enables arithmetic and string formatting of radical expressions, and can
handle rational radicands of arbitrary precision (see dependencies).
Seamlessly integrates with other numeric types such as int, long, and BigInteger.

NuGet package for this library is published here.

### Usage

This library provides three structures to enable radical expression arithmetic:

integer index:

``````var sqrt2 = Radical.Sqrt(2);                        // Sqrt(2)
var sqrt_1_3 = Radical.Sqrt((Rational)1/3);         // Sqrt(1/3)    = (1/3)*Sqrt(3)
var root_3_1_2 = Radical.NthRoot((Rational)1/2, 3); // Root[3](1/2) = (1/2)*Root[3](4)
``````

Note - see dependencies section for information on the Rational structure

The structure automatically simplifies radicals to simplest form, as described here.

``````var result1 = Radical.Sqrt(2) * Radical.Sqrt(3/4);  // Sqrt(2) * Sqrt(3/4)       = (1/2)*Sqrt(6)
var result2 = result1 * Radical.Sqrt(2);            // (1/2)*Sqrt(6)*Sqrt(2)     = Sqrt(3)
var result3 = result2 / result1;                    // Sqrt(3) / [(1/2)*Sqrt(6)] = Sqrt(2)
var result4 = result3 / Radical.Sqrt(5);            // Sqrt(2) / Sqrt(5)         = (1/5)*Sqrt(10)
``````

They can also be multiplied and divided by most numeric types, returning new Radicals:

``````var result1 = Radical.Sqrt(2) * 3;                  // 3 * Sqrt(2)
var result2 = 4 * result1;                          // 4 * 3 * Sqrt(2)   = 12 * Sqrt(2)
var result3 = result2 / 3;                          // 12 * Sqrt(2) / 3  = 4 * Sqrt(2)
var result4 = 5 / result3;                          // 5 / (4 * Sqrt(2)) = (5/8)*Sqrt(2)
``````

``````var result1 = Radical.Sqrt(2)
* Radical.NthRoot(2,3);                         // Sqrt(2) * Root[3](2)     = Root[6](32)
var result2 = result1 / Root[3](5);                 // Root[6](32) / Root[3](5) = (1/5)*Root[6](20000)
``````

Radicals can also be added and subtracted from each other. However, unless they have
identical indices and radicands, the simplest form result is not another radical, but

``````var result1 = Radical.Sqrt(2) + Radical.Sqrt(3);    // Sqrt(2) + Sqrt(3)
var result2 = result1 + Radical.Sqrt(2);            // [Sqrt(2) + Sqrt(3)] + Sqrt(2) = 2*Sqrt(2) + Sqrt(3)
var result3 = result1 - Radical.NthRoot(5,3);       // 2*Sqrt(2) + Sqrt(3) + (-1)*Root[3](5)
var result4 = result3 + 11;                         // 11 + 2*Sqrt(2) + Sqrt(3) + (-1)*Root[3](5)
``````

``````var result1 =
* Radical.Sqrt(2);                          // [Sqrt(2) + Sqrt(3)] * Sqrt(2) = 2 + Sqrt(6)
var result2 =
result1
* (Radical.Sqrt(5) + Radical.Sqrt(7));      // [2 + Sqrt(6)] * [Sqrt(5) + Sqrt(7)]
// = 2*Sqrt(5) + 2*Sqrt(7) + Sqrt(30) + Sqrt(35)

var result3 = result2 * 3;                          // 6*Sqrt(5) + 6*Sqrt(7) + 3*Sqrt(30) + 3*Sqrt(35)
``````

...as well as divided by most numeric types and Radicals to return new RadicalSums:

``````var result4 = result3 / 2;                          // 3*Sqrt(5) + 3*Sqrt(7) + (3/2)*Sqrt(30) + (3/2)*Sqrt(35)
var result5 = result4 / Radical.Sqrt(2);            // (3/2)*Sqrt(10) + (3/2)*Sqrt(14) + (3/2)*Sqrt(15) + (3/4)*Sqrt(70)
``````

RadicalSums can also be divided by other RadicalSums. However the result is not

``````var result1 =
// -----------------
// Sqrt(2) - Sqrt(3)
``````

### Performance

This project was intended as a small fun side project. As such, I haven't put much
effort or thought into optimization. While it suited my needs and should be okay for
most casual implementations, don't expect optimal performance and use at your own
risk!
Of course, I'm always open to suggestions and improvements. :-)

### Background

The original inspiration for this project came from working on a program that recursively calculates
Clebsch-Gordan coefficients. While
this succeeded in generating the coefficients in decimal form, I wanted it to present them in radical
form similarly to how they're usually presented in tables (e.g.,
here). I created this
library to enable radical expression arithmetic during the calculation of the coefficients, and to
format the result as usually presented in tables.

My Clebsch-Gordan coefficient calculator utilizing the Radicals package can be found
here.

### Dependencies

This project is dependent on the following NuGet packages:

Rationals: Encapsulates rational numbers of theoretically
arbitrary precision. Based on BigInteger.

Open.Numeric.Primes: Provides methods to get
prime factorization of BigInteger values.

### Overview

.NET implementation of
where the radicand is a rational number and the index is a positive integer.
Enables arithmetic and string formatting of radical expressions, and can
handle rational radicands of arbitrary precision (see dependencies).
Seamlessly integrates with other numeric types such as int, long, and BigInteger.

NuGet package for this library is published here.

### Usage

This library provides three structures to enable radical expression arithmetic:

integer index:

``````var sqrt2 = Radical.Sqrt(2);                        // Sqrt(2)
var sqrt_1_3 = Radical.Sqrt((Rational)1/3);         // Sqrt(1/3)    = (1/3)*Sqrt(3)
var root_3_1_2 = Radical.NthRoot((Rational)1/2, 3); // Root[3](1/2) = (1/2)*Root[3](4)
``````

Note - see dependencies section for information on the Rational structure

The structure automatically simplifies radicals to simplest form, as described here.

``````var result1 = Radical.Sqrt(2) * Radical.Sqrt(3/4);  // Sqrt(2) * Sqrt(3/4)       = (1/2)*Sqrt(6)
var result2 = result1 * Radical.Sqrt(2);            // (1/2)*Sqrt(6)*Sqrt(2)     = Sqrt(3)
var result3 = result2 / result1;                    // Sqrt(3) / [(1/2)*Sqrt(6)] = Sqrt(2)
var result4 = result3 / Radical.Sqrt(5);            // Sqrt(2) / Sqrt(5)         = (1/5)*Sqrt(10)
``````

They can also be multiplied and divided by most numeric types, returning new Radicals:

``````var result1 = Radical.Sqrt(2) * 3;                  // 3 * Sqrt(2)
var result2 = 4 * result1;                          // 4 * 3 * Sqrt(2)   = 12 * Sqrt(2)
var result3 = result2 / 3;                          // 12 * Sqrt(2) / 3  = 4 * Sqrt(2)
var result4 = 5 / result3;                          // 5 / (4 * Sqrt(2)) = (5/8)*Sqrt(2)
``````

``````var result1 = Radical.Sqrt(2)
* Radical.NthRoot(2,3);                         // Sqrt(2) * Root[3](2)     = Root[6](32)
var result2 = result1 / Root[3](5);                 // Root[6](32) / Root[3](5) = (1/5)*Root[6](20000)
``````

Radicals can also be added and subtracted from each other. However, unless they have
identical indices and radicands, the simplest form result is not another radical, but

``````var result1 = Radical.Sqrt(2) + Radical.Sqrt(3);    // Sqrt(2) + Sqrt(3)
var result2 = result1 + Radical.Sqrt(2);            // [Sqrt(2) + Sqrt(3)] + Sqrt(2) = 2*Sqrt(2) + Sqrt(3)
var result3 = result1 - Radical.NthRoot(5,3);       // 2*Sqrt(2) + Sqrt(3) + (-1)*Root[3](5)
var result4 = result3 + 11;                         // 11 + 2*Sqrt(2) + Sqrt(3) + (-1)*Root[3](5)
``````

``````var result1 =
* Radical.Sqrt(2);                          // [Sqrt(2) + Sqrt(3)] * Sqrt(2) = 2 + Sqrt(6)
var result2 =
result1
* (Radical.Sqrt(5) + Radical.Sqrt(7));      // [2 + Sqrt(6)] * [Sqrt(5) + Sqrt(7)]
// = 2*Sqrt(5) + 2*Sqrt(7) + Sqrt(30) + Sqrt(35)

var result3 = result2 * 3;                          // 6*Sqrt(5) + 6*Sqrt(7) + 3*Sqrt(30) + 3*Sqrt(35)
``````

...as well as divided by most numeric types and Radicals to return new RadicalSums:

``````var result4 = result3 / 2;                          // 3*Sqrt(5) + 3*Sqrt(7) + (3/2)*Sqrt(30) + (3/2)*Sqrt(35)
var result5 = result4 / Radical.Sqrt(2);            // (3/2)*Sqrt(10) + (3/2)*Sqrt(14) + (3/2)*Sqrt(15) + (3/4)*Sqrt(70)
``````

RadicalSums can also be divided by other RadicalSums. However the result is not

``````var result1 =
// -----------------
// Sqrt(2) - Sqrt(3)
``````

### Performance

This project was intended as a small fun side project. As such, I haven't put much
effort or thought into optimization. While it suited my needs and should be okay for
most casual implementations, don't expect optimal performance and use at your own
risk!
Of course, I'm always open to suggestions and improvements. :-)

### Background

The original inspiration for this project came from working on a program that recursively calculates
Clebsch-Gordan coefficients. While
this succeeded in generating the coefficients in decimal form, I wanted it to present them in radical
form similarly to how they're usually presented in tables (e.g.,
here). I created this
library to enable radical expression arithmetic during the calculation of the coefficients, and to
format the result as usually presented in tables.

My Clebsch-Gordan coefficient calculator utilizing the Radicals package can be found
here.

### Dependencies

This project is dependent on the following NuGet packages:

Rationals: Encapsulates rational numbers of theoretically
arbitrary precision. Based on BigInteger.

Open.Numeric.Primes: Provides methods to get
prime factorization of BigInteger values.

## Used By

### NuGet packages

This package is not used by any NuGet packages.

### GitHub repositories

This package is not used by any popular GitHub repositories.