SymbolicC++
# SymbolicC++

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

## Examples

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

The output is

The next program illustrates non-commutative symbols in SymbolicC++. Here b is a Bose annihilation operator and bd is a Bose creation operator. The variable vs denotes the vacuum state $|0\rangle$. The ~ operator toggles the commutativity of a variable, i.e. if b is commutative that ~b is non-commutative and if b is non-commutative ~b is commutative.

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 template 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:

The second version of SymbolicC++ featured new classes such as the Polynomial class and initial support for simple integration. Support for the algebraic computation of Clifford algebras was described in using SymbolicC++ in 2002. 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.

