User defined recursion - not limited - mXparser - Math Expressions Parser for JAVA, C#, C++, Kotlin, Android, .NET/MONO/Xamarin - Mathematical Formula Parser / Evaluator Library

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The tutorial consists of more than 200 live examples from 50 sections given separately for JAVA, C# and C++. 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, C# (the code for C# is almost identical) and C++. To copy the code, double-click inside the frame.

Case 1: Fibonacci numbers using user defined recursive function

Java/C# code

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using 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));

C++ code

#include "org/mariuszgromada/math/mxparser.hpp"
// ...

Code result

[mXparser-v.5.2.1] Res 1: fib(10) = 55.0
[mXparser-v.5.2.1] Res 2: fib(11) = 89.0

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

Java/C# code

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using 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));

C++ code

#include "org/mariuszgromada/math/mxparser.hpp"
// ...
FunctionPtr Cnk = new_Function("Cnk(n,k) = if( k>0, if( k<n, Cnk(n-1,k-1)+Cnk(n-1,k), 1), 1)");

ExpressionPtr 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));

Code result

[mXparser-v.5.2.1] Res 1: Cnk(10,3) - C(10,3) = 0.0
[mXparser-v.5.2.1] 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

Java/C# code

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using 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());

C++ code

#include "org/mariuszgromada/math/mxparser.hpp"
// ...
FunctionPtr T = new_Function("T(n,x) = if(n>1, 2*x*T(n-1,x)-T(n-2,x), if(n>0, x, 1) )");

ArgumentPtr k = new_Argument("k = 5");
ArgumentPtr x = new_Argument("x = 2");

ExpressionPtr 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());

Code result

[mXparser-v.5.2.1] Res : T(k,x) - ( (x + sqrt(x^2-1))^k + (x - sqrt(x^2-1))^k)/2 = 0.0

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

Java/C# code

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using 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());

C++ code

#include "org/mariuszgromada/math/mxparser.hpp"
// ...
ConstantPtr a = new_Constant("a = 0.0001");

FunctionPtr s = new_Function("s(x) = if( abs(x) < a, x, 2*s(x/2)*c(x/2) )", a);
FunctionPtr 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);

ExpressionPtr e1 = new_Expression("sin(5)-s(5)", s);
ExpressionPtr e2 = new_Expression("cos(5)-c(5)", c);

mXparser::consolePrintln("Res 1: " + e1->getExpressionString() + " = " + e1->calculate());
mXparser::consolePrintln("Res 2: " + e2->getExpressionString() + " = " + e2->calculate());

Code result

[mXparser-v.5.2.1] Res 1: sin(5)-s(5) = 1.829204866182E-4
[mXparser-v.5.2.1] Res 2: cos(5)-c(5) = -5.410012369295E-5

Nuget – Package Manager (C#, F#, Visual Basic, …)

Install-Package MathParser.org-mXparser-Version 6.1.1

Nuget – .NET CLI

dotnet add package MathParser.org-mXparser--version 6.1.1

Nuget – Package Reference

<PackageReference Include="MathParser.org-mXparser"Version="6.1.1"/>

Maven – Dependency (Java, Kotlin, Scala, Groovy, …)

<dependency> <groupid>org.mariuszgromada.math</groupid> <artifactid>MathParser.org-mXparser</artifactid> <version>6.1.1</version> </dependency>

Maven – Gradle

implementation 'org.mariuszgromada.math:MathParser.org-mXparser:6.1.1'

CMake – Dependency / FetchContent (C++, MSVC, LLVM/Clang, GNU/GCC, MinGW, MSYS2, WSL, Windows, Linux, Unix, MacOS)

include(FetchContent) FetchContent_Declare(MathParserOrgMxParserGIT_REPOSITORYhttps://github.com/mariuszgromada/MathParser.org-mXparser.gitGIT_TAGv.6.1.1SOURCE_SUBDIR CURRENT/cpp/lib ) FetchContent_MakeAvailable(MathParserOrgMxParser) mxparser_link(YourExecutable)