Symja Library - Java Symbolic Math System

Note: this repository contains the Java 8 version of the project. The NCalc and Natural Calc projects maintains a Java 7 branch based on Retrolambda.

• Quick start
• Features
• Demos
• Examples
• Maven Usage
• Getting started
• Github GIT
• Contact
• License

Quick start

Read the Symja Manual for the description of the Symja language. We encourage everyone to participate in our Wiki.

Features

Features of the Symja language:

• arbitrary precision integers, rational and complex numbers
• differentiation, integration, equation solving, polynomial and linear algebra functions...
• a general purpose Term Rewriting System and Pattern Matching engine
• use human readable math expression strings or the internal abstract syntax tree (AST) representation to code in Java. See the Unit test examples
• two REPLs are available in the library a Console.java for standard math input and a MMAConsole.java for Mathematica like syntax input.
• Symja can also be used interactively in the Java jshell

Demos

• 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.

Examples

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

>>> 24/60
2/5

>>> N(24/60)
0.4

>>> sin(30*degree)
1/2

>>> sin(pi/2)
1

>>> a+a+4*b^2+3*b^2
2*a+7*b^2

>>> solve({x^2-11==y, x+y==-9}, {x,y})
{{x->-2,y->-7},{x->1,y->-10}}

>>> dsolve({y'(x)==y(x)+2,y(0)==1},y(x), x)
{{y(x)->-2+3*E^x}}

>>> integrate(cos(x)^5, x)
-2/3*Sin(x)^3+Sin(x)^5/5+Sin(x)

>>> D(sin(x^3), x)
3*x^2*Cos(x^3)

>>> factor(-1+x^16)
(-1+x)*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)

>>> factor(5+x^12, Modulus->7)
(2+x^3)*(4+x^6)*(5+x^3)

>>> expand((-1+x)*(1+x)*(1+x^2)*(1+x^4)*(1+x^8))
-1+x^16

>>> det({{1,2},{3,4}})
-2

>>> inverse({{1,2},{3,4}})
{{-2,1},
 {3/2,-1/2}}

>>> factorinteger(2^15-5)
{{3,1},{67,1},{163,1}}

>>> refine(abs(n*abs(m)), n<0)
-n*Abs(m)

Maven Usage

Using Maven, add the following to your pom.xml

<dependencies>
  <dependency>
    <groupId>org.matheclipse</groupId>
      <artifactId>matheclipse-core</artifactId>
	  <version>1.0.0-SNAPSHOT</version>
    </dependency>
</dependencies>

<repositories> 
  <repository>
    <id>snapshots-repo</id>
    <url>https://oss.sonatype.org/content/repositories/snapshots</url>
    <releases>
      <enabled>false</enabled>
    </releases>
    <snapshots>
      <enabled>true</enabled>
    </snapshots>
  </repository>
</repositories>

and run

mvn clean install

With the following command you can run the Symja console from the command line

mvn exec:java -pl matheclipse-core

With the following command you can run a symja console with a Mathematica-compatible syntax and functions

mvn exec:java@mma -pl matheclipse-core 

With the following command you can build a fat jar which contains all needed classes

mvn assembly:single -pl matheclipse-core

The Excelsior JET Maven Plugin provides Maven users with an easy way to compile their applications down to optimized native Windows, OS X, or Linux executables with Excelsior JET.

mvn jet:build -pl matheclipse-core

Getting started

First, you'll need a Java Development Kit compatible with Java 8 or later.

You can find JDK installers at:

• http://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-2133151.html

If you're unsure how to install the JDK, you can find instructions for all operating systems here:

• https://docs.oracle.com/javase/8/docs/technotes/guides/install/install_overview.html

Pay careful attention to anything about setting up your PATH or CLASSPATH.

Install and open the latest version of the Eclipse development IDE for Java Developers:

• http://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.

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

• the JAS Java Algebra System is published under the (LESSER) GNU GENERAL PUBLIC LICENSE licence. The Java bytecode is dual licenced also under the Apache 2.0 licence to allow usage in Android projects.
• the apfloat project is published under the (LESSER) GNU GENERAL PUBLIC LICENSE licence.
• the LogicNG project is published under the Apache software licence
• the Hipparchus Mathematics Library is published under the Apache software licence
• the Symja parser libraries (org.matheclipse.parser* packages) are published under the APACHE LICENSE Version 2.0.