Summation & Product iterated operators

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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: SIGMA summation operator

$$\sum_{i=k}^{n}f(x_1,x_2,,\ldots,i)$$

Java/C# code

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Expression e1 = new Expression("sum(i, 1, 10, 2*i)");
mXparser.consolePrintln("Res 1: " + e1.getExpressionString() + " = " + e1.calculate());
         
/* Iteration can be done by not necessarily whole increment */
Expression e2 = new Expression("sum(i, 1, 10, i, 0.5)");
mXparser.consolePrintln("Res 2: " + e2.getExpressionString() + " = " + e2.calculate());

C++ code

#include "org/mariuszgromada/math/mxparser.hpp"
// ...
ExpressionPtr e1 = new_Expression("sum(i, 1, 10, 2*i)");
mXparser::consolePrintln("Res 1: " + e1->getExpressionString() + " = " + e1->calculate());

/* Iteration can be done by not necessarily whole increment */
ExpressionPtr e2 = new_Expression("sum(i, 1, 10, i, 0.5)");
mXparser::consolePrintln("Res 2: " + e2->getExpressionString() + " = " + e2->calculate());

Code result

[mXparser-v.5.2.1] Res 1: sum(i, 1, 10, 2*i) = 110.0
[mXparser-v.5.2.1] Res 2: sum(i, 1, 10, i, 0.5) = 104.5

Case 2: PI product operator

$$\prod_{i=k}^{n}f(x_1,x_2,,\ldots,i)$$

Java/C# code

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

/* factorial */
Expression e1 = new Expression("prod(i, 1, 5, i)");
mXparser.consolePrintln("Res 1: " +  e1.getExpressionString() + " = " + e1.calculate());
         
/* Iteration can be done by not necessarily whole increment */
/* Here different form of 10! */
Expression e2 = new Expression("prod(i, 1, 5, 2*i, 0.5)");
mXparser.consolePrintln("Res 2: " + e2.getExpressionString() + " = " + e2.calculate());

C++ code

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

/* factorial */
ExpressionPtr e1 = new_Expression("prod(i, 1, 5, i)");
mXparser::consolePrintln("Res 1: " +  e1->getExpressionString() + " = " + e1->calculate());

/* Iteration can be done by not necessarily whole increment */
/* Here different form of 10! */
ExpressionPtr e2 = new_Expression("prod(i, 1, 5, 2*i, 0.5)");
mXparser::consolePrintln("Res 2: " + e2->getExpressionString() + " = " + e2->calculate());

Code result

[mXparser-v.5.2.1] Res 1: prod(i, 1, 5, i) = 120.0
[mXparser-v.5.2.1] Res 2: prod(i, 1, 5, 2*i, 0.5) = 3628800.0

Case 3: SIGMA summation operator – Approximating sin(x) by Taylor series

Java/C# code

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Argument x = new Argument("x = 2*pi");
Argument n = new Argument("n = 3");
Expression e = new Expression("sin(x) - sum(k, 0, n, (-1)^k*(x^(2*k+1))/(2*k+1)! )", x, n);
mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());
 
/* Increasing polynomial order ... */
n.setArgumentValue(5);
mXparser.consolePrintln("Res 2: " + e.getExpressionString() + " = " + e.calculate());
 
/* Increasing polynomial order ... */
n.setArgumentValue(10);     
mXparser.consolePrintln("Res 3: " + e.getExpressionString() + " = " + e.calculate());
         
/* Increasing polynomial order ... */
n.setArgumentValue(20);     
mXparser.consolePrintln("Res 4: " + e.getExpressionString() + " = " + e.calculate());
         
/* Checking other point closer to '0' */
x.setArgumentValue(2);
mXparser.consolePrintln("Res 5: " + e.getExpressionString() + " = " + e.calculate());

C++ code

#include "org/mariuszgromada/math/mxparser.hpp"
// ...
ArgumentPtr x = new_Argument("x = 2*pi");
ArgumentPtr n = new_Argument("n = 3");
ExpressionPtr e = new_Expression("sin(x) - sum(k, 0, n, (-1)^k*(x^(2*k+1))/(2*k+1)! )", x, n);
mXparser::consolePrintln("Res 1: " + e->getExpressionString() + " = " + e->calculate());

/* Increasing polynomial order ... */
n->setArgumentValue(5);
mXparser::consolePrintln("Res 2: " + e->getExpressionString() + " = " + e->calculate());

/* Increasing polynomial order ... */
n->setArgumentValue(10);
mXparser::consolePrintln("Res 3: " + e->getExpressionString() + " = " + e->calculate());

/* Increasing polynomial order ... */
n->setArgumentValue(20);     
mXparser::consolePrintln("Res 4: " + e->getExpressionString() + " = " + e->calculate());

/* Checking other point closer to '0' */
x->setArgumentValue(2);
mXparser::consolePrintln("Res 5: " + e->getExpressionString() + " = " + e->calculate());

Code result

[mXparser-v.5.2.1] Res 1: sin(x) - sum(k, 0, n, (-1)^k*(x^(2*k+1))/(2*k+1)! ) = 30.159127410206484
[mXparser-v.5.2.1] Res 2: sin(x) - sum(k, 0, n, (-1)^k*(x^(2*k+1))/(2*k+1)! ) = 3.195076042131831
[mXparser-v.5.2.1] Res 3: sin(x) - sum(k, 0, n, (-1)^k*(x^(2*k+1))/(2*k+1)! ) = -8.27409522186923E-5
[mXparser-v.5.2.1] Res 4: sin(x) - sum(k, 0, n, (-1)^k*(x^(2*k+1))/(2*k+1)! ) = 0.0
[mXparser-v.5.2.1] Res 5: sin(x) - sum(k, 0, n, (-1)^k*(x^(2*k+1))/(2*k+1)! ) = 0.0

Case 4: SIGMA summation operator – Approximating pi value by integrating sqrt(1-x^2)

Java/C# code

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Argument d = new Argument("d",0.1);
Expression e = new Expression("2 * sum(x, -1, 1, d*sqrt(1-x^2), d)", d);
mXparser.consolePrintln("Res 1: d = " + d.getArgumentValue() + ", " + e.getExpressionString() + " = " + e.calculate());
d.setArgumentValue(0.01);
mXparser.consolePrintln("Res 2: d = " + d.getArgumentValue() + ", " + e.getExpressionString() + " = " + e.calculate());

C++ code

#include "org/mariuszgromada/math/mxparser.hpp"
// ...
ArgumentPtr d = new_Argument("d",0.1);
ExpressionPtr e = new_Expression("2 * sum(x, -1, 1, d*sqrt(1-x^2), d)", d);
mXparser_consolePrintln("Res 1: d = " + d->getArgumentValue() + ", " + e->getExpressionString() + " = " + e->calculate());
d->setArgumentValue(0.01);
mXparser_consolePrintln("Res 2: d = " + d->getArgumentValue() + ", " + e->getExpressionString() + " = " + e->calculate());

Code result

[mXparser-v.5.2.1] Res 1: d = 0.1, 2 * sum(x, -1, 1, d*sqrt(1-x^2), d) = 3.1045183304630037
[mXparser-v.5.2.1] Res 2: d = 0.01, 2 * sum(x, -1, 1, d*sqrt(1-x^2), d) = 3.1404170317790436

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

Install-Package MathParser.org-mXparser -Version 6.1.0

Nuget – .NET CLI

dotnet add package MathParser.org-mXparser --version 6.1.0

Nuget – Package Reference

<PackageReference Include="MathParser.org-mXparser" Version="6.1.0"/>

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

<dependency> <groupid>org.mariuszgromada.math</groupid> <artifactid>MathParser.org-mXparser</artifactid> <version>6.1.0</version> </dependency>

Maven – Gradle

implementation 'org.mariuszgromada.math:MathParser.org-mXparser:6.1.0'

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.6.1.0SOURCE_SUBDIR CURRENT/cpp/lib ) FetchContent_MakeAvailable(MathParserOrgMxParser) target_link_libraries(YourExecutableMathParserOrgMxParser)

GitHub

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

OTHER DOWNLOAD OPTIONS

Download latest release – v.6.1.0 Sagitara: .NET bin only Download latest release – v.6.1.0 Sagitara: JAVA bin only Download latest release – v.6.1.0 Sagitara: bin + doc

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SOURCE CODE

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mXparser – Math Expressions Parser for JAVA, C#, C++, Kotlin, Android, .NET/MONO/Xamarin – Mathematical Formula Parser / Evaluator Library

JAVA, C#, C++, Kotlin, Android, and all .NET platforms (Supports .NET Framework, .NET Core, .NET Standard, Xamarin, MONO and more, common Language Specification Compliant: VB, F#, C++/CLI). Available via Nuget, Maven, CMake, GitHub.

TO SUPPORT MY WORK, ORDER A COMMERCIAL LICENSE

THANK YOU!

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: SIGMA summation operator

Java/C# code

C++ code

Code result

Case 2: PI product operator

Java/C# code

C++ code

Code result

Case 3: SIGMA summation operator – Approximating sin(x) by Taylor series

Java/C# code

C++ code

Code result

Case 4: SIGMA summation operator – Approximating pi value by integrating sqrt(1-x^2)

Java/C# code

C++ code

Code result

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

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

Maven – Gradle

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

GitHub

OTHER DOWNLOAD OPTIONS

NEWS FROM MATHPARSER.ORG

SOURCE CODE

My other creative spaces

DONATION

Scalar is a powerful math engine and math scripting language powered by the MathParser.org-mXparser

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I wish you all the best 🙂

I wish you all the best 🙂