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{{Infobox Software
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| name = SymbolicC++
| logo =
| screenshot =
| caption =
| developer = Yorick Hardy, Willi-Hans Steeb and Tan Kiat Shi
| latest_release_version = 3.35
| latest_release_date = {{release date and age|2010|09|15}}
| programming language = [[C++]]
| operating_system = [[Cross-platform]]
| genre = [[Mathematical software]]
| license = [[GNU General Public 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++ is used by including a C++ header file or by linking against a library.
 
== Examples ==
<source lang="cpp">
#include <iostream>
#include "symbolicc++.h"
using namespace std;
 
int main(void)
{
Symbolic x("x");
cout << integrate(x+1, x);    // => 1/2*x^(2)+x
Symbolic y("y");
cout << df(y, x);              // => 0
cout << df(y[x], x);          // => df(y[x],x)
cout << df(exp(cos(y[x])), x); // => -sin(y[x])*df(y[x],x)*e^cos(y[x])
return 0;
}
</source>
 
The following program fragment inverts the matrix
<math>
\begin{pmatrix}
\cos\theta & \sin\theta\\
-\sin\theta & \cos\theta
\end{pmatrix}
</math>
symbolically.
 
<source lang="cpp">
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) ];
</source>
 
The output is
 
<pre>
[ cos(theta) −sin(theta) ]
[ sin(theta) cos(theta)  ]
</pre>
 
The next program illustrates non-commutative symbols in SymbolicC++.  Here <code>b</code> is a Bose [[annihilation operator]] and <code>bd</code> is a Bose [[creation operator]].  The variable <code>vs</code> denotes the [[vacuum state]] <math>|0\rangle</math>. The <code>~</code> operator toggles the commutativity of a variable, i.e. if <code>b</code> is commutative that <code>~b</code> is non-commutative and if <code>b</code> is non-commutative <code>~b</code> is commutative.
 
<source lang="cpp">
#include <iostream>
#include "symbolicc++.h"
using namespace std;
 
int main(void)
{
// The operator b is the annihilation operator and bd is the creation operator
Symbolic b("b"), bd("bd"), vs("vs");
 
b = ~b; bd = ~bd; vs = ~vs;
 
Equations rules = (b*bd == bd*b + 1, b*vs == 0);
 
// Example 1
Symbolic result1 = b*bd*b*bd;
cout << "result1 = " << result1.subst_all(rules) << endl;
cout << "result1*vs = " << (result1*vs).subst_all(rules) << endl;
 
// Example 2
Symbolic result2 = (b+bd)^4;
cout << "result2 = " << result2.subst_all(rules) << endl;
cout << "result2*vs = " << (result2*vs).subst_all(rules) << endl;
 
return 0;
}
</source>
 
Further examples can be found in the books listed below.<ref>
Steeb, W.-H. (2010).
''Quantum Mechanics Using Computer Algebra, second edition,''
World Scientific Publishing, Singapore.
</ref><ref>
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.
</ref><ref>
Steeb, W.-H. (2007).
''Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra, second edition,''
World Scientific Publishing, Singapore.
</ref><ref name="symcpp3"/>
 
== History ==
SymbolicC++ is described in a series of books on [[computer algebra]].  The first book<ref>Tan Kiat Shi and Steeb, W.-H. (1997). ''SymbolicC++: An introduction to Computer Algebra Using Object-Oriented Programming'' Springer-Verlag, Singapore.</ref> described the first version of SymbolicC++. In this version the main data type for symbolic computation was the <code>Sum</code> class. The list of available classes included
 
* <code>Verylong</code>  : An unbounded [[integer]] implementation
* <code>Rational</code>  : A template class for [[rational number]]s
* <code>Quaternion</code> : A template class for [[quaternion]]s
* <code>Derive</code>    : A template class for [[automatic differentiation]]
* <code>Vector</code>    : A template class for vectors (see [[vector space]])
* <code>Matrix</code>    : A template class for matrices (see [[matrix (mathematics)]])
* <code>Sum</code>        : A template class for symbolic expressions
 
Example:
<source lang="cpp">
#include <iostream>
#include "rational.h"
#include "msymbol.h"
using namespace std;
 
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;
}
</source>
 
The second version<ref>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.</ref> of SymbolicC++ featured new classes such as the <code>Polynomial</code> class and initial support for simple integration. Support for the algebraic computation of [[Clifford algebras]] was described in using SymbolicC++ in 2002.<ref>Fletcher, J.P. (2002). Symbolic Processing of Clifford Numbers in C++ <br>in Doran C., Dorst L. and Lasenby J. (eds.) ''Applied Geometrical Algebras in computer Science and Engineering AGACSE 2001'', Birkhauser, Basel.
<br>http://www.ceac.aston.ac.uk/research/staff/jpf/papers/paper25/index.php</ref> Subsequently support for Gröbner bases was added.<ref>Kruger, P.J.M (2003). ''Gröbner bases with Symbolic C++'', M. Sc. Dissertation, Rand Afrikaans University.</ref>
The third version<ref name="symcpp3">Hardy, Y, Tan Kiat Shi and Steeb, W.-H. (2008). ''Computer Algebra with SymbolicC++'', World Scientific Publishing, Singapore.</ref> features a complete rewrite of SymbolicC++ and was released in 2008. This version encapsulates all symbolic expressions in the <code>Symbolic</code> class.
 
Newer versions are available from the SymbolicC++ [http://issc.uj.ac.za/symbolic/symbolic.html website].
 
==See also==
*[[Comparison of computer algebra systems]]
*[[GiNaC]]
 
== References ==
<!--- See [[Wikipedia:Footnotes]] on how to create references using <ref></ref> tags which will then appear here automatically -->
{{Reflist}}
 
== External links ==
* {{Official website|http://issc.uj.ac.za/symbolic/symbolic.html}}
* [http://issc.uj.ac.za/downloads/problems/advancedP.pdf Programming exercises in SymbolicC++]
 
{{Computer algebra systems}}
 
{{DEFAULTSORT:Symbolicc}}
[[Category:Free computer algebra systems]]
[[Category:Free software programmed in C++]]
[[Category:C++ libraries]]

Revision as of 00:34, 19 February 2014

Therefore, we all are needed to consider each area of writing accurately to be sufficient our desire. People who work in custom writing industry are usually professional freelance writers with undergraduate or graduate degree and some years of experience in academic writing. All our customers are guaranteed of non plagiarized papers of the highest quality. The introduction also needs to generate sufficient interest to entice the reader into the main body of the essay. s students are taught that how to write an effective essay but the problem is this that when they reach to the final stage I mean to say that when they are up to the age of writing an essay then the problem comes that they are not enough capable to write it more perfectly as they want to get the perfect marks.

Definition essay- A definition essay defines a particular term. We have brilliant experts who have the required skills in essay writing. Custom essay writing services today can produce anything ranging from originally researched and written term papers, theses and essays to articles and blogs for people, organizations, websites and individuals based on their needs and requirements. However, the fact is completely different from this myth, which is writing a research paper thesis is not at all an easy business; rather it is a crucial activity because it requires time and effort to come up with proficient answers and explanation to queries, best suiting to the sense of question. This can be a time consuming and tedious task, and having an experienced writing service that can do that part of the work for you can ensure that you do it properly and turn in an accurate bibliography for the research you used in your essay.

If one wants to write an essay, but one does not know how to write one, one can take essay writing help from an expert. We ensure that our writers use diverse resource to gather information for the papers. So,it is wise to explore lacking sides in your essay writing task by indulging more into the process. Now, you have to revise your paper and find out mistakes. ll have to negotiate a deadline with your professor, or plan using this service in advance.

Papers are evaluated and judged based on your organization and development of ideas, supporting evidences or examples that you quote in your essay, understanding the intended audience, incorporating audiences needs in your essay, attaining the goal of your assigned task, and off course skilful use of language, correctness in using grammar. Do they specify that the work needs to be double-spaced. Qualified Essay Writers Custom well prepared essays are not essay to get because most companies do not have the required sources of information. In the Academy of Art New Delhi the students have the opportunities to get the educational degrees in Interior designing, retail designing and visual merchandising. You can also improve your academic performance by buying a custom essay.

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