Symja is a pure Java library for symbolic mathematics. It was forked from the MathEclipse project.

>>> Try the Symja online calculator on Google App Engine <<< (Getting started)

• Features
• Usage
• License

Features

• arbitrary precision integers, rationals and complex numbers
• polynomials
• differentiation
• pattern matching
• linear algebra

Usage

Examples in the console application:

org.matheclipse.core.eval.Console [options]

Program arguments: 
  -h or -help                  print this message
  -f or -file <filename>       use given file as input script
  -d or -default <filename>    use given textfile for system rules
To stop the program type: 
exit<RETURN>
To continue an input line type '\' at the end of the line.
****+****+****+****+****+****+****+****+****+****+****+****+
>>> a+a+4*b^2+3*b^2
In [1]: a+a+4*b^2+3*b^2
Out[1]: 2*a+7*b^2
>>> FactorInteger[2^15-5]
In [2]: FactorInteger[2^15-5]
Out[2]: {{3,1},{67,1},{163,1}}
>>> D[Sin[x^3],x]
In [3]: D[Sin[x^3],x]
Out[3]: 3*Cos[x^3]*x^2
>>> Factor[-1+x^16]
In [4]: Factor[-1+x^16]
Out[4]: (-1+x)*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)
>>> Factor[5+x^12,Modulus->7]
In [5]: Factor[5+x^12,Modulus->7]
Out[5]: (2+x^3)*(4+x^6)*(5+x^3)
>>> Expand[(-1+x)*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)]
In [6]: Expand[(-1+x)*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)]
Out[6]: -1+x^16
>>> Inverse[{{1,2},{3,4}}]
In [7]: Inverse[{{1,2},{3,4}}]
Out[7]: {{-2,1},
 {3/2,-1/2}}
>>> Det[{{1,2},{3,4}}]
In [8]: Det[{{1,2},{3,4}}]
Out[8]: -2
>>> Roots[4+x^2+2*x+3*x^3]
In [9]: Roots[4+x^2+2*x+3*x^3]
Out[9]: {-1,1/6*(I*44^(1/2)+2),1/6*(-I*44^(1/2)+2)}
>>> Apart[(x)/(x^2-1)]
In [10]: Apart[(x)/(x^2-1)]
Out[10]: 1/2*(x+1)^(-1)+1/2*(x-1)^(-1)
>>> $x=10
In [11]: $x=10
Out[11]: 10
>>> $x+$x
In [12]: $x+$x
Out[12]: 20
>>> Integrate[(10 x^2 - 63 x + 29)/(x^3 - 11 x^2 + 40 x -48),x]
In [13]: Integrate[(10 x^2 - 63 x + 29)/(x^3 - 11 x^2 + 40 x -48),x]
Out[13]: 63*(x-4)^(-1)-70*Log[x-3]+80*Log[x-4]
>>> Solve[{x+2*y==10,3*x+y==20},{x,y}]
In [14]: Solve[{x+2*y==10,3*x+y==20},{x,y}]
Out[14]: {{x->6,y->2}}
>>> 

See the JUnit test cases for more syntax examples.

License

• the complete system (Symja Swing GUI and Android GUI) is published under the GNU GENERAL PUBLIC LICENSE

Some parts are published under more liberal licenses:

• the underlying libraries (Symja core and generic libraries) are published under the LESSER GNU GENERAL PUBLIC LICENSE
• the parser (and simple numeric evaluators) are published under the APACHE LICENSE Version 2.0.
• for the licenses of the used libraries see UsedLibraries.