User defined recursion – not limited

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The tutorial consists of more than 180 live examples from 40 sections. Each of the examples can be copied and run on your own environment. In addition, mXparser provides an extensive collection of over 500 built-in math functions, expressions and symbols. Familiarize yourself with the scope and the syntax. Live testing is the best way to learn. Good luck! 🙂

Tutorial Math Collection API spec Download

Below is the code for JAVA, the code for C# is almost identical.

Case 1: Fibonacci numbers using user defined recursive function

import org.mariuszgromada.math.mxparser.*;
...
Function fib = new Function("fib(n) = if( n>1, fib(n-1)+fib(n-2), if(n>0, 1, 0) )");
Expression e = new Expression("fib(10)", fib);

mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());
mXparser.consolePrintln("Res 2: fib(11) = " + fib.calculate(11));
[mXparser-v.5.0.0] Res 1: fib(10) = 55.0
[mXparser-v.5.0.0] Res 2: fib(11) = 89.0

Case 2: Number of recursive parameters is not limited – binomial coefficient definition using user defined recursive function

import org.mariuszgromada.math.mxparser.*;
...
Function Cnk = new Function("Cnk(n,k) = if( k>0, if( k<n, Cnk(n-1,k-1)+Cnk(n-1,k), 1), 1)");
Expression e = new Expression("Cnk(10,3) - C(10,3)", Cnk);

mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());
mXparser.consolePrintln("Res 2: Cnk(10,3) = " + Cnk.calculate(10,3));
[mXparser-v.5.0.0] Res 1: Cnk(10,3) - C(10,3) = 0.0
[mXparser-v.5.0.0] Res 2: Cnk(10,3) = 120.0

Case 3: Mixing function parameters – part causing recursive calls, other part as ‘typical’ parameter. Below example is presenting definition of Chebyshev polynomial using recursive function

import org.mariuszgromada.math.mxparser.*;
...
Function T = new Function("T(n,x) = if(n>1, 2*x*T(n-1,x)-T(n-2,x), if(n>0, x, 1) )");
Argument k = new Argument("k = 5");
Argument x = new Argument("x = 2");

Expression e = new Expression("T(k,x) - ( (x + sqrt(x^2-1))^k + (x - sqrt(x^2-1))^k)/2", T, k, x);
mXparser.consolePrintln("Res : " + e.getExpressionString() + " = " + e.calculate());
[mXparser-v.5.0.0] Res : T(k,x) - ( (x + sqrt(x^2-1))^k + (x - sqrt(x^2-1))^k)/2 = 1.0E-13

Case 4: Indirect recursion – approximating sin(x) and cos(x)

import org.mariuszgromada.math.mxparser.*;
...
Constant a = new Constant("a = 0.0001");
Function s = new Function("s(x) = if( abs(x) < a, x, 2*s(x/2)*c(x/2) )", a);
Function c = new Function("c(x) = if( abs(x) < a, 1, c(x/2)^2-s(x/2)^2 )", a);
/*
 * Functions s and c must point to each other,
 * i.e. references should be added only after
 * they have been created
 */
s.addDefinitions(c);
c.addDefinitions(s);

Expression e1 = new Expression("sin(5)-s(5)", s);
Expression e2 = new Expression("cos(5)-c(5)", c);

mXparser.consolePrintln("Res 1: " + e1.getExpressionString() + " = " + e1.calculate());
mXparser.consolePrintln("Res 2: " + e2.getExpressionString() + " = " + e2.calculate());
[mXparser-v.5.0.0] Res 1: sin(5)-s(5) = 1.829204866182E-4
[mXparser-v.5.0.0] Res 2: cos(5)-c(5) = -5.410012369295E-5
Nuget – Package Manager

Install-Package MathParser.org-mXparser -Version 5.1.0

Nuget – .NET CLI

dotnet add package MathParser.org-mXparser --version 5.1.0

Nuget – Package Reference

<PackageReference Include="MathParser.org-mXparser" Version="5.1.0"/>

Maven – Dependency

<dependency>
<groupid>
org.mariuszgromada.math</groupid>
<artifactid>
MathParser.org-mXparser</artifactid>
<version>
5.1.0</version>
</dependency>

Maven – Gradle

implementation 'org.mariuszgromada.math:MathParser.org-mXparser:5.1.0'

Maven – Gradle (Kotlin)

implementation("org.mariuszgromada.math:MathParser.org-mXparser:5.1.0")

GitHub

git clone https://github.com/mariuszgromada/MathParser.org-mXparser

OTHER DOWNLOAD OPTIONS

Download latest release – v.5.1.0 Libris: .NET bin onlyDownload latest release – v.5.1.0 Libris: JAVA bin onlyDownload latest release – v.5.1.0 Libris: bin + doc

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SOURCE CODE

Source code .zipSource code .tar.gz
View on GitHubMathSpace.pl

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