Symja

Symja Library - Java Symbolic Math System for Android calculator

Note: this repository contains the Java 11 sources of the core modules. A minimal Android app example can be found in the symja-example repository :

Try the full-blown Android or iOS apps:

or help testing the latest Android BETA version or the web demo at matheclipse.org.

Read the Symja Manual :blue_book: for the description of the Symja language or browse the available functions :green_book: . We encourage everyone to participate in our Wiki.

• Installation
• Features
• Applications
• Examples
• Maven Usage
• Getting started
• Github GIT
• Contact
• License
• Science and math library dependencies

🔧 Installation

The different kinds of installations are described in the Wiki Installation.

✨ Features

Features of the Symja language:

• arbitrary precision integers, rational and complex numbers. Polynomial, list functions and Associations
• differentiation, integration, equation solving, linear algebra, number theory, combinatorial, logic and polynomial functions...
• unified connectivity and interoperability through Symja functions for open source libraries like Hipparchus, Tablesaw, JGraphT, LogicNG, JAS Java Algebra System, apfloat...

📦 Applications

• Symja.org - test the Symja API

• Appengine web interface symjaweb.appspot.com - available as open source in this Github repository

• Android App Calculator N+ on Google play store - available as open source in this Github repository provides an IDE mode to calculate arbitrary Symja expressions.

• Eclipse EASE extension - use Symja as a REPL in Eclipse with this example Github repository which contains some Symja example scripts.

☕ Examples

Console user interface

HTML notebook interface

To get an idea of the kinds of expressions Symja handles, see the JUnit tests in this file.

Web Examples

Solve({x^2==4,x+y^2==6}, {x,y})

FactorInteger(2^15-5)

D(Sin(x^3), x)

Factor(-1+x^16)

Manipulate(Plot3D(Sin(a * x * y), {x, -1.5, 1.5}, {y, -1.5, 1.5}), {a,1,5})

Plot(Piecewise({{x^2, x < 0}, {x, x >= 0&&x<1},{Cos(x-1), x >= 1}}), {x, -2, 12})

Refine(Abs(n*Abs(m)),n<0)

Inverse({{1,2},{3,4}})

Det({{1,2},{3,4}})

Integrate(Cos(x)^5, x)

JavaForm((x+1)^2+(x+1)^3, Float)

ToExpression("\\frac{x}{\\sqrt{5}}", TeXForm)

A Java usage example:

package org.matheclipse.core.examples;

import org.matheclipse.core.eval.ExprEvaluator;
import org.matheclipse.core.expression.F;
import org.matheclipse.core.interfaces.IAST;
import org.matheclipse.core.interfaces.IExpr;
import org.matheclipse.core.interfaces.ISymbol;
import org.matheclipse.parser.client.SyntaxError;
import org.matheclipse.parser.client.math.MathException;

public class Example {
  public static void main(String[] args) {
    try {
      ExprEvaluator util = new ExprEvaluator(false, (short) 100);

      // Convert an expression to the internal Java form:
      // Note: single character identifiers are case sensitive
      // (the "D()" function identifier must be written as upper case
      // character)
      String javaForm = util.toJavaForm("D(sin(x)*cos(x),x)");
      // prints: D(Times(Sin(x),Cos(x)),x)
      System.out.println("Out[1]: " + javaForm.toString());

      // Use the Java form to create an expression with F.* static
      // methods:
      ISymbol x = F.Dummy("x");
      IAST function = F.D(F.Times(F.Sin(x), F.Cos(x)), x);
      IExpr result = util.eval(function);
      // print: Cos(x)^2-Sin(x)^2
      System.out.println("Out[2]: " + result.toString());

      // An IAST can be read as a java.util.List: index 0 is the head
      // print: [D, Cos(x)*Sin(x), x]
      System.out.println(function.asList());

      // Note "diff" is an alias for the "D" function
      result = util.eval("diff(sin(x)*cos(x),x)");
      // print: Cos(x)^2-Sin(x)^2
      System.out.println("Out[3]: " + result.toString());

      // evaluate the last result (% or $ans contains "last answer")
      result = util.eval("%+cos(x)^2");
      // print: 2*Cos(x)^2-Sin(x)^2
      System.out.println("Out[4]: " + result.toString());

      // evaluate an Integrate[] expression
      result = util.eval("integrate(sin(x)^5,x)");
      // print: 2/3*Cos(x)^3-1/5*Cos(x)^5-Cos(x)
      System.out.println("Out[5]: " + result.toString());

      // set the value of a variable "a" to 10
      // Note: in server mode the variable name must have a preceding '$'
      // character
      result = util.eval("a=10");
      // print: 10
      System.out.println("Out[6]: " + result.toString());

      // do a calculation with variable "a"
      result = util.eval("a*3+b");
      // print: 30+b
      System.out.println("Out[7]: " + result.toString());

      // Do a calculation in "numeric mode" with the N() function
      // Note: single character identifiers are case sensistive
      // (the "N()" function identifier must be written as upper case
      // character)
      result = util.eval("N(sinh(5))");
      // print: 74.20321057778875
      System.out.println("Out[8]: " + result.toString());

      // define a function with a recursive factorial function definition.
      // Note: fac(0) is the stop condition.
      result = util.eval("fac(x_Integer):=x*fac(x-1);fac(0)=1");
      // now calculate factorial of 10:
      result = util.eval("fac(10)");
      // print: 3628800
      System.out.println("Out[9]: " + result.toString());

      function =
          F.Function(F.Divide(F.Gamma(F.Plus(F.C1, F.Slot1)), F.Gamma(F.Plus(F.C1, F.Slot2))));
      // eval function ( Gamma(1+#1)/Gamma(1+#2) ) & [23,20]
      result = util.evalFunction(function, "23", "20");
      // print: 10626
      System.out.println("Out[10]: " + result.toString());
    } catch (SyntaxError e) {
      // catch Symja parser errors here
      System.out.println(e.getMessage());
    } catch (MathException me) {
      // catch Symja math errors here
      System.out.println(me.getMessage());
    } catch (final Exception ex) {
      System.out.println(ex.getMessage());
    } catch (final StackOverflowError soe) {
      System.out.println(soe.getMessage());
    } catch (final OutOfMemoryError oome) {
      System.out.println(oome.getMessage());
    }
    }
}

🔨 Maven Usage

How to use Maven is described in the Maven wiki page.

Getting started

First, you'll need a Java Development Kit (JDK) compatible with Java 11 or later.

The Integrated Development Environment (IDE) Eclipse is shipped with a suitable JDK, so you don't have to install a JDK by yourself. Install and open the latest version of the Eclipse development IDE for Java Developers:

• https://www.eclipse.org/downloads/packages/

Github GIT

a) Fork the Symja repository to use as a starting point.

• Navigate to github.com/axkr/symja_android_library in your browser.
• Click the "Fork" button in the top-right of the page.
• Once your fork is ready, open the new repository's "Settings" by clicking the link in the menu bar on the left.
• Change the repository name to the name of your Library and save your changes.

b) Clone your new repository to your Eclipse workspace.

• Open Eclipse and select the "File -> Import..." menu item.
• Select "Git -> Projects from Git", and click "Next >".
• Select "URI" and click "Next >".
• Enter your repository's clone URL in the "URI" field. The remaining fields in the "Location" and "Connection" groups will get automatically filled in.
• Enter your Github credentials in the "Authentication" group, and click "Next >".
• Select the master branch on the next screen, and click "Next >".
• The default settings on the "Local Configuration" screen should work fine, click "Next >".
• Make sure "Import existing projects" is selected, and click "Next >".
• Eclipse should find and select the symja_android_library automatically, click "Finish".

See this Git version control with Eclipse (EGit) - Tutorial for a general overview.

Contact

If you have any questions about using or developing for this project, send me an email!

License

• the complete Symja system is published under the GNU GENERAL PUBLIC LICENSE Version 3 (GPL) starting with Symja version 2.0.0 parts are published under the Lesser GNU GENERAL PUBLIC LICENSE Version 3 (LGPL).

If you would like to use parts of the system here are some Maven module licenses:

• the maven modules: parser, external, core are published under LGPL license.
• the maven modules: gpl, api, io, astro are published under GPL license.

Here are some of the associated JavaScript licenses:

• the Paul Masson's Math project is published under the MIT license.
• the Paul Masson's MathCell project is published under the MIT license.
• the JSXGraph project is published under the GNU LGPL or MIT license.
• the KaTeX project is published under the MIT license.

Science and math library dependencies by Maven module

The Maven modules below all build on matheclipse-core. A module inherits the dependencies of every module it depends on, so the licenses of matheclipse-core apply everywhere. matheclipse-core itself depends on matheclipse-parser and matheclipse-external; the third-party code vendored inside matheclipse-external is therefore listed together with core.

matheclipse-core

Project	Purpose	License
Hipparchus	linear algebra, ODE solvers, optimization, statistics, FFT, geometry, clustering, curve fitting	Apache License 2.0
apfloat	arbitrary precision arithmetic	MIT License
LogicNG	boolean logic, SAT solving	Apache License 2.0
Choco-solver	constraint programming	BSD 3-Clause License
AdaptiveQuadrature	adaptive Gauss-Kronrod numerical integration	Apache License 2.0
RoaringBitmap	compressed bitsets	Apache License 2.0
MFL	MATLAB .mat file import and export	Apache License 2.0
Paguro	persistent (immutable) collections	Apache License 2.0 or EPL 1.0
JAS Java Algebra System (vendored in matheclipse-external)	polynomial arithmetic, factorization, Groebner bases	LGPL; the Java bytecode is dual licensed under Apache 2.0 to allow usage in Android projects
Diophantine (vendored in matheclipse-external)	solving Diophantine equations

matheclipse-gpl

Project	Purpose	License
java-math-library (vendored as de.tilman_neumann.jml)	integer factorization, prime numbers, partitions, modular arithmetic, quadratic residues	GNU GPL v3

This module is the reason a distribution containing it has to be published under the GPL. No other module depends on it: FactorInteger and the other integer factorization functions use the factorization of matheclipse-core.

matheclipse-graphtheory

Project	Purpose	License
JGraphT	graph data structures and graph algorithms	EPL 2.0 or LGPL 2.1

matheclipse-image

Project	Purpose	License
BoofCV	image processing and computer vision	Apache License 2.0
Hipparchus	numerics and statistics for image operations	Apache License 2.0
JSVG	SVG rendering	MIT License
TwelveMonkeys ImageIO	additional raster image formats (JPEG, BMP, TIFF, WebP, PNM)	BSD 3-Clause License

matheclipse-astro

Project	Purpose	License
Orekit	astronomy and space flight dynamics	Apache License 2.0
Hipparchus	linear algebra and geometry	Apache License 2.0
Night Vision (ported as org.matheclipse.astro.meeus)	Meeus algorithms: planet and Moon positions, nutation, precession, delta T, planet magnitudes, star colours	GNU GPL v3 or later
ASCC-2.5 (via Night Vision's star.db)	star catalogue to magnitude 11, about 1.06 million stars	cited, redistributed as in Night Vision
d3-celestial (data files)	stars to magnitude 8.5, constellations, deep-sky objects, Milky Way	BSD 3-Clause License
Natural Earth (data file)	land outlines for GeoGraphics	public domain

The Night Vision port makes this module GPL. See matheclipse-astro/NOTICE.md.

matheclipse-bio

Project	Purpose	License
BioJava	bioinformatics, sequence alignment, amino acid properties	LGPL 2.1

matheclipse-chem

Project	Purpose	License
Chemistry Development Kit (CDK)	chemoinformatics, molecular formulas, SMILES/SMARTS, structure diagrams	LGPL 2.1 or later

matheclipse-nlp

Project	Purpose	License
ICU4J	Unicode, locale, transliteration and unit data	Unicode License v3

matheclipse-dataset

Project	Purpose	License
Tablesaw (vendored fork)	dataframes and table operations	Apache License 2.0
Apache Arrow	columnar in-memory data format	Apache License 2.0
Apache POI	Excel import and export	Apache License 2.0
fastutil	primitive type collections	Apache License 2.0
RoaringBitmap	compressed bitsets	Apache License 2.0
ICU4J	locale aware parsing and formatting	Unicode License v3
jsoup	HTML table import	MIT License

matheclipse-compile

Project	Purpose	License
Janino	runtime Java compiler	BSD 3-Clause License
JavaPoet	Java source code generation	Apache License 2.0

matheclipse-script

Project	Purpose	License
apfloat	arbitrary precision arithmetic	MIT License

matheclipse-md2html

Project	Purpose	License
commonmark-java	Markdown parsing and HTML rendering	BSD 2-Clause License

matheclipse-discord

Project	Purpose	License
Discord4J	Discord bot client	LGPL 3.0

matheclipse-io

This module aggregates image, nlp, astro, gpl, bio, chem, graphtheory, compile and dataset and therefore inherits all libraries listed above. In addition it bundles the JavaScript libraries listed in the License section, including KaTeX for math typesetting.

<a href = https://github.com/axkr/symja_android_library/graphs/contributors> <img src = https://contrib.rocks/image?repo=axkr/symja_android_library>