SymbolicC++ explained

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

1. include
2. include "symbolicc++.h"

using namespace std;

int main(void)

The following program fragment inverts the matrix

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)  ]

. 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.

1. include
2. include "symbolicc++.h"

using namespace std;

int main(void)

Further examples can be found in the books listed below.^{[1] [2] [3]}

History

SymbolicC++ is described in a series of books on computer algebra. The first book^[4] 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:

1. include
2. include "rational.h"
3. include "msymbol.h"

using namespace std;

int main(void)

The second version^[5] 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.^[6] Subsequently, support for Gröbner bases was added.^[7] The third version^[8] 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

• • Programming exercises in SymbolicC++

Notes and References

1. Steeb, W.-H. (2010).Quantum Mechanics Using Computer Algebra, second edition,World Scientific Publishing, Singapore.
2. Steeb, W.-H. (2008).The Nonlinear Workbook: Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithm, Gene Expression Programming, Wavelets, Fuzzy Logic with C++, Java and SymbolicC++ Programs, fourth edition,World Scientific Publishing, Singapore.
3. Steeb, W.-H. (2007).Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra, second edition,World Scientific Publishing, Singapore.
4. Tan Kiat Shi and Steeb, W.-H. (1997). SymbolicC++: An introduction to Computer Algebra Using Object-Oriented Programming Springer-Verlag, Singapore.
5. Tan Kiat Shi, Steeb, W.-H. and Hardy, Y (2000). SymbolicC++: An Introduction to Computer Algebra using Object-Oriented Programming, 2nd extended and revised edition, Springer-Verlag, London.
6. Fletcher, J.P. (2002). Symbolic Processing of Clifford Numbers in C++
   in Doran C., Dorst L. and Lasenby J. (eds.) Applied Geometrical Algebras in computer Science and Engineering AGACSE 2001, Birkhauser, Basel.
   http://www.ceac.aston.ac.uk/research/staff/jpf/papers/paper25/index.php
7. Kruger, P.J.M (2003). Gröbner bases with Symbolic C++, M. Sc. Dissertation, Rand Afrikaans University.
8. Hardy, Y, Tan Kiat Shi and Steeb, W.-H. (2008). Computer Algebra with SymbolicC++, World Scientific Publishing, Singapore.