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https://github.com/mathnet/mathnet-symbolics
Math.NET Symbolics
https://github.com/mathnet/mathnet-symbolics
computer-algebra dotnet fsharp math mathnet symbolic-manipulation
Last synced: 4 months ago
JSON representation
Math.NET Symbolics
- Host: GitHub
- URL: https://github.com/mathnet/mathnet-symbolics
- Owner: mathnet
- License: mit
- Created: 2014-03-29T22:50:41.000Z (over 10 years ago)
- Default Branch: master
- Last Pushed: 2024-01-15T18:54:49.000Z (6 months ago)
- Last Synced: 2024-03-10T20:13:52.049Z (4 months ago)
- Topics: computer-algebra, dotnet, fsharp, math, mathnet, symbolic-manipulation
- Language: F#
- Homepage: http://symbolics.mathdotnet.com
- Size: 80.3 MB
- Stars: 326
- Watchers: 28
- Forks: 65
- Open Issues: 47
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE.md
Lists
- awesome-fsharp - Math.NET Symbolics ★ 203 ⧗ 5 - Math.NET Symbolics is a basic open source computer algebra library for .NET, Silverlight and Mono written entirely in F#. [MIT] (Data Science)
README
Math.NET Symbolics
==================
Math.NET Symbolics is a basic open source **computer algebra library for .NET, Silverlight and Mono** written entirely in F#.
This project does *not* aim to become a full computer algebra system. If you need such a system, have a look at Axiom or Maxima instead, or for proprietary commercial solutions Maple, Mathematica or Wolfram Alpha.
You'll find a large set of expression and algebraic operator examples in the [Unit Tests](src/Symbolics.Tests/Tests.fs) (yes, they're actually very readable). A few examples:
* `(3Q + 2)*4/6` → `10/3`.
* `(a/b/(c*a))*(c*d/a)/d` → `1/(a*b)`
* `(a+b)/(b+a)**2` → `1/(a + b)`
* `Algebraic.expand ((a+b)**3)` → `a^3 + 3*a^2*b + 3*a*b^2 + b^3`
* `Exponential.expand (exp(2*x+y))` → `exp(x)^2*exp(y)`
* `Exponential.contract (exp(x)*(exp(x) + exp(y)))` → `exp(2*x) + exp(x + y)`
* `Exponential.simplify (1/(exp(x)*(exp(y)+exp(-x))) - (exp(x+y)-1)/((exp(x+y))**2-1))` → `0`
* `Trigonometric.expand (sin(2*x))` → `2*sin(x)*cos(x)`
* `Trigonometric.contract (sin(x)**2*cos(x)**2)` → `1/8 - (1/8)*cos(4*x)`
* `Trigonometric.simplify ((cos(x)+sin(x))**4 + (cos(x)-sin(x))**4 + cos(4*x) - 3)` → `0`
* `Polynomial.polynomialDivision x (x**3 - 2*x**2 - 4) (x-3)` → `(3 + x + x^2, 5)`
* `Polynomial.polynomialExpansion x y (x**5 + 11*x**4 + 51*x**3 + 124*x**2 + 159*x + 86) (x**2 + 4*x + 5)` → `1 + x + (2 + x)*y + (3 + x)*y^2`
* `Polynomial.gcd x (x**7 - 4*x**5 - x**2 + 4) (x**5 - 4*x**3 - x**2 + 4)` → `4 - 4*x - x^2 + x^3`
* `Rational.rationalize (1+1/(1+1/x))` → `(1 + 2*x)/(1 + x)`
* `Rational.simplify x ((x**2-1)/(x+1))` → `-1 + x`
```fsharp
let taylor (k:int) symbol x a =
let rec impl n nf acc dxn =
if n = k then acc else
impl (n+1) (nf*(n+1)) (acc + (dxn |> Structure.substitute symbol a)/nf*(symbol-a)**n) (Calculus.differentiate symbol dxn)
impl 0 1 zero x |> Algebraic.expand
taylor 3 x (1/(1-x)) 0Q → 1 + x + x^2
taylor 3 x (1/x) 1Q → 3 - 3*x + x^2
taylor 3 x (ln(x)) 1Q → -3/2 + 2*x - (1/2)*x^2
taylor 4 x (ln(x)) 1Q → -11/6 + 3*x - (3/2)*x^2 + (1/3)*x^3
taylor 4 x (sin(x)+cos(x)) 0Q → 1 + x - (1/2)*x^2 - (1/6)*x^3
```
### Literature
* Computer Algebra and Symbolic Computation - Elementary Algorithms, Joel. S. Cohen
* Computer Algebra and Symbolic Computation - Mathematical Methods, Joel. S. Cohen
* Modern Computer Algebra, Second Edition, Joachim von zur Gathen, Jürgen Gerhard
* Symbolic Integration I - Transcendental Functions, Second Edition, Manuel Bronstein
* Concrete Mathematics, Second Edition, Graham, Knuth, Patashnik
* ... and of course the fundamental theory by Euclid, Newton, Gauss, Fermat and Hilbert.
### Project
Windows (.NET): [](https://ci.appveyor.com/project/cdrnet/mathnet-symbolics)
Maintained by [Christoph Rüegg](https://christoph.ruegg.name/) and part of the [Math.NET initiative](https://www.mathdotnet.com) (see also [Math.NET Numerics](https://numerics.mathdotnet.com/)). It is covered under the terms of the [MIT/X11](https://mathnetnumerics.codeplex.com/license) open source license. See also the [license](LICENSE.md) file in the root folder. **We accept contributions!**
* [**Project Website**](https://symbolics.mathdotnet.com/)
* [Source Code](https://github.com/mathnet/mathnet-symbolics)
* [Release Notes](https://symbolics.mathdotnet.com/ReleaseNotes.html)
* [Documentation](https://symbolics.mathdotnet.com/)
* [Issues & Bugs](https://github.com/mathnet/mathnet-symbolics/issues)
* [Discussions](https://discuss.mathdotnet.com/c/symbolics) | [Stack Overflow](https://stackoverflow.com/questions/tagged/mathdotnet) | [Twitter](https://twitter.com/MathDotNet)