SymbolicC++

SymbolicC++

Developer(s)	Yorick Hardy, Willi-Hans Steeb and Tan Kiat Shi
Stable release	3.24 / May 27, 2009 (2009-05-27)
Written in	C++
Operating system	Cross-platform
Type	Mathematical software
License	GPL
Website	http://issc.uj.ac.za/symbolic/symbolic.html

SymbolicC++ is a general purpose computer algebra system embedded in the programming language C++. It is free software released under the terms of the GNU General Public License. SymbolicC++ can be used by simply including a C++ header file or by linking against a library.

Examples

#include <iostream>
#include "symbolicc++.h"

using namespace std;

int main(void)
{
 Symbolic x("x");
 cout << integrate(x, x); // => 1/2 xˆ2
 Symbolic y("y");
 cout << df(y, x);        // => 0
 cout << df(y[x], x);     // => df(y[x],x)
 return 0;
}

The following program fragment inverts the matrix ${\begin{pmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{pmatrix}}$ symbolically.

Symbolic theta("theta");
Symbolic R = ( (  cos(theta), sin(theta) ),
               ( -sin(theta), cos(theta) ) );
cout << R(0,1); // sin(theta)
Symbolic RI = R.inverse();
cout << RI[ (cos(theta)^2) == 1 - (sin(theta)^2) ];

The output is

[ cos(theta) −sin(theta) ]
[ sin(theta) cos(theta)  ]

Further examples can be found in the books listed below.

History

SymbolicC++ is described in a series of books on computer algebra. The first book described the first version of SymbolicC++. In this version the main data type for symbolic computation was the Sum class. The list of available classes included

• Verylong  : An unbounded integer implementation
• Rational  : A tempate class for rational numbers
• Quaternion : A template class for quaternions
• Derive  : A template class for automatic differentiation
• Vector  : A template class for vectors (see vector space)
• Matrix  : A template class for matrices (see matrix (mathematics))
• Sum  : A template class for symbolic expressions

Example:

#include <iostream.h>
#include "rational.h"
#include "msymbol.h"

int main(void)
{
 Sum<int> x("x",1);
 Sum<Rational<int> > y("y",1);
 cout << Int(y, y);       // => 1/2 yˆ2
 y.depend(x);
 cout << df(y, x);        // => df(y,x)
 return 0;
}

The second version of SymbolicC++ featured new classes such as the Polynomial class and initial support for simple integration. Subsequently support for Gröbner bases was added. The third version features a complete rewrite of SymbolicC++ and was released in 2008. This version encapsulates all symbolic expressions in the Symbolic class.

Newer versions are available from the SymbolicC++ website.

See also

• Comparison of computer algebra systems
• GiNaC

External links

• SymbolicC++