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| github: HamletTanyavong | ||
| patreon: HamletTanyavong |
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| <h1 align="center">Mathematics.NET</h1> | ||
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| <p align="center">Mathematics.NET is a C# class library that provides tools for solving mathematical problems.</p> | ||
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| [](https://github.com/HamletTanyavong/Mathematics.NET) | ||
| [](https://github.com/HamletTanyavong/Mathematics.NET/stargazers) | ||
| [](https://www.nuget.org/packages/Physics.NET.Mathematics) | ||
| [](https://www.nuget.org/packages/Physics.NET.Mathematics) | ||
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| ## Documentation | ||
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| Please visit the [documentation site](https://mathematics.hamlettanyavong.com) for detailed information. |
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| # Numeric Types | ||
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| There are three numeric types that can be used to represent complex, real, and rational numbers in Mathematics.NET. | ||
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| All Mathematics.NET numbers implement the [IComplex<T, U>](https://mathematics.hamlettanyavong.com/api/Mathematics.NET.Core.IComplex-2.html) interface. Particularly useful is the fact that, unlike .NET runtime's [INumberBase\<T\>](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Numerics/INumberBase.cs), `IComplex<T, U>` defines the `Conjugate` method; this is incredibly helpful in avoiding code duplication for calculations involving complex and real numbers. | ||
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| ## Floating-Point Types | ||
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| Floating-point Mathematics.NET numbers may be backed any number that implements [IFloatingPointIee754\<T\>](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Numerics/IFloatingPointIeee754.cs) and [IMinMaxValue\<T\>](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Numerics/IMinMaxValue.cs), or more specifically, [float](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Single.cs), [double](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Double.cs), and [decimal](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Decimal.cs). | ||
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| ### Complex Numbers | ||
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| To create a complex number, we choose a backing type, in this case `double`, and write | ||
| ```csharp | ||
| Complex<double> z = new(3, 4); | ||
| ``` | ||
| This represents the number $ z = 3+i4 $. We can also specify only one number to create a complex number with no imaginary part | ||
| ```csharp | ||
| Complex<double> z = 3; | ||
| ``` | ||
| which represents $ z = 3 $. | ||
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| ### Real Numbers | ||
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| Likewise, to create a real number, write | ||
| ```csharp | ||
| Real<double> z = 1; | ||
| ``` | ||
| With real numbers, we can also get maximum and minimum values which will depend on the backing type. | ||
| ```csharp | ||
| Console.WriteLine("Max value with float backing type: {0}", Real<float>.MaxValue); | ||
| Console.WriteLine("Max value with double backing type: {0}", Real<double>.MaxValue); | ||
| ``` | ||
| This will output `Max value with float backing type: 3.4028235E+38` | ||
| and `Max value with double backing type: 1.7976931348623157E+308`. | ||
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| ## Binary Types | ||
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| Rational numbers are the only Mathematics.NET type in this category. | ||
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| ### Rational Numbers | ||
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| Rational numbers require two backing types, one that implements [IBinaryInteger\<T\>](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Numerics/IBinaryInteger.cs) and one that implements both [IFloatingPointIee754\<T\>](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Numerics/IFloatingPointIeee754.cs) and [IMinMaxValue\<T\>](https://github.com/dotnet/runtime/blob/main/src/libraries/System.Private.CoreLib/src/System/Numerics/IMinMaxValue.cs). | ||
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| With this information, we can create the following rational numbers: | ||
| ```csharp | ||
| Rational<int, double> a = 2; | ||
| Rational<byte, float> b = new(2, 3); | ||
| Rational<BigInteger, double> c = new(3, 4); | ||
| ``` | ||
| which represent $ a = 2 $, $ b = 2/3 $, and $ c = 3/4 $. | ||
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| The first type parameter indicates that the constructor only accepts values of that type. In these cases, `a` must be an int, `b` must be a byte, and `c` must be a BigInteger. The second parameter indicates the desired floating-point type with which we want to represent the rational number. We can get this value in two ways, e.g. | ||
| ```csharp | ||
| Console.WriteLine(b.Value); | ||
| Console.WriteLine((float)b); | ||
| ``` | ||
| which will both output `0.6666667`. | ||
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| > [!CAUTION] | ||
| > The floating-point representation of rational numbers may not be accurate in all cases. | ||
| We can also convert a floating-point number into a rational number with an explicit cast | ||
| ```csharp | ||
| Console.WriteLine((Rational<int, double>)3.14); | ||
| ``` | ||
| > [!NOTE] | ||
| > The conversion conversion is not guaranteed to create the "best" fraction; for instance, the value $ 0.3333333333333333 $ will not produce $ 1/3 $ but instead produce $ 8333333333333331 / 25000000000000000 $. | ||
| Be aware that there are performance penalties with converting rationals to and from real numbers. An overflow exception will also be thrown if a value being converted cannot be represented by the target type. |
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| # Installation | ||
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| Mathematics.NET is available to download from [nuget](https://www.nuget.org). | ||
| Mathematics.NET is available to download from [nuget](https://www.nuget.org/packages/Physics.NET.Mathematics). | ||
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| ## Polyglot Notebooks | ||
| # [Package Reference](#tab/package-reference) | ||
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| To use Mathematics.NET in you project, add the following line to your .csproj file: | ||
| ```xml | ||
| <PackageReference Include="Physics.NET.Mathematics" Version="" /> | ||
| ``` | ||
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| # [Polyglot Notebooks](#tab/polyglot-notebooks) | ||
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| Please have [Visual Studio Code](https://code.visualstudio.com/) installed as well as the [Polyglot Notebooks](https://marketplace.visualstudio.com/items?itemName=ms-dotnettools.dotnet-interactive-vscode) extension installed to begin using Mathematics.NET. When that is complete, create a new .ipynb file and add the following line to import the package: | ||
| ```csharp | ||
| #r "nuget: Mathematics.NET" | ||
| #r "nuget: Physics.NET.Mathematics" | ||
| ``` | ||
| To get a specific version of Mathematics.NET, use, for example, | ||
| ```csharp | ||
| #r "nuget: Mathematics.NET, 1.0.0" | ||
| #r "nuget: Physics.NET.Mathematics, 0.1.0-alpha.1" | ||
| ``` |
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| // <copyright file="Extensions.cs" company="Mathematics.NET"> | ||
| // Mathematics.NET | ||
| // https://github.com/HamletTanyavong/Mathematics.NET | ||
| // | ||
| // MIT License | ||
| // | ||
| // Copyright (c) 2023 Hamlet Tanyavong | ||
| // | ||
| // Permission is hereby granted, free of charge, to any person obtaining a copy | ||
| // of this software and associated documentation files (the "Software"), to deal | ||
| // in the Software without restriction, including without limitation the rights | ||
| // to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | ||
| // copies of the Software, and to permit persons to whom the Software is | ||
| // furnished to do so, subject to the following conditions: | ||
| // | ||
| // The above copyright notice and this permission notice shall be included in all | ||
| // copies or substantial portions of the Software. | ||
| // | ||
| // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | ||
| // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | ||
| // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | ||
| // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | ||
| // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | ||
| // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | ||
| // SOFTWARE. | ||
| // </copyright> | ||
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| using System.Numerics; | ||
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| namespace Mathematics.NET.Core; | ||
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| public static class Extensions | ||
| { | ||
| public static Rational<T, U> Reduce<T, U>(this Rational<T, U> r) | ||
| where T : IBinaryInteger<T> | ||
| where U : IFloatingPointIeee754<U>, IMinMaxValue<U> | ||
| => Rational<T, U>.Reduce(r); | ||
| } |
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