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| {{Infobox Software
| | The feeling of freedom and self-control that you feel as you drive through the mountain trails can help you forget all the stress and worries of daily life. If you keep winning competitions, you will be invited to bigger and bigger races. Understanding your strengths, and the strengths of your team or business partner can be your best competitive edge this year. Are you in search of a comfort bike, a mountain bike, or a bike that is designed just for cruising and do you prefer a standard road bike or are you looking for an hybrid. Just like coasting, you'll also spend a great deal of time pedaling while standing. <br><br>However, you still have to choose the right Santa Cruz bikes for yourself. In fact, Downhill Mountain biking is the most popular form of competition biking. Every person is different and you should looking for a bike that fit's you best. “Whereas past research emphasized whether or not a relationship existed between bicycle riding on a saddle and erectile dysfunction, Schrader now says that the next step of contemporary research on the subject should focus on intervention. Titanium is very light and gives you an advantage and is usually used in racing bicycles. <br><br>They have great suspension that fits the need of both amateur and professional bikers. That's a level of quality you just don't get from many brands these days. The only way to truly protect yourself against a crash is to ensure that you have the correct safety equipment. Hence, having the bicycle that suits you perfectly is much easier now. We have built a number of thousand semi custom wheels for all kinds of bikes, and will probably be happy to do the exact same for you. <br><br>If you cherished this short article and you would want to get details regarding [http://ikzouhetnietweten.nl/index.php?mod=users&action=view&id=181498 Women mountain bike sizing.] i implore you to pay a visit to our own web site. When discount sales are on, you need to be sure you understand the terms and conditions of your purchase, including warranty information. There are also tires with detailed treads which are very prominent and these are very useful for the biker because of the grip they provide. In the purest sense of the word, a mountain bikes sole mission is to travel "off-road" only. The dedication and solid experience of the experts, it is not difficult to accomplish such goal. I've never been into cycling and wanted to give it a try for exercise. <br><br>In the recent article section, you can find the list of biking related articles with a detailed description present on the official website. Then, the answer is the skeletal frame size that will fit you for a normal bike. One of the main concerns for any cyclist is safety, having the right kit is a must. Many of these trails and stunts are so dangerous that signs are up because of the potential of a serious injury or even death. Which leads me to my favourite materials for hardtails. |
| | name = SymbolicC++
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| | logo =
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| | screenshot =
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| | caption =
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| | developer = Yorick Hardy, Willi-Hans Steeb and Tan Kiat Shi
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| | latest_release_version = 3.35
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| | latest_release_date = {{release date and age|2010|09|15}}
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| | programming language = [[C++]]
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| | operating_system = [[Cross-platform]]
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| | genre = [[Mathematical software]]
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| | license = [[GNU General Public License|GPL]]
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| | website = http://issc.uj.ac.za/symbolic/symbolic.html
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| }}
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| '''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.
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| == Examples ==
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| <source lang="cpp"> | |
| #include <iostream>
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| #include "symbolicc++.h"
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| using namespace std;
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| int main(void)
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| {
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| Symbolic x("x");
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| cout << integrate(x+1, x); // => 1/2*x^(2)+x
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| Symbolic y("y");
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| cout << df(y, x); // => 0
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| cout << df(y[x], x); // => df(y[x],x)
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| cout << df(exp(cos(y[x])), x); // => -sin(y[x])*df(y[x],x)*e^cos(y[x])
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| return 0;
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| }
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| </source>
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| | |
| The following program fragment inverts the matrix
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| <math>
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| \begin{pmatrix}
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| \cos\theta & \sin\theta\\
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| -\sin\theta & \cos\theta
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| \end{pmatrix}
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| </math>
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| symbolically.
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| | |
| <source lang="cpp">
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| Symbolic theta("theta");
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| Symbolic R = ( ( cos(theta), sin(theta) ),
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| ( -sin(theta), cos(theta) ) );
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| cout << R(0,1); // sin(theta)
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| Symbolic RI = R.inverse();
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| cout << RI[ (cos(theta)^2) == 1 - (sin(theta)^2) ];
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| </source>
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| The output is
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| <pre>
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| [ cos(theta) −sin(theta) ]
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| [ sin(theta) cos(theta) ]
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| </pre>
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| 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.
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| | |
| <source lang="cpp"> | |
| #include <iostream>
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| #include "symbolicc++.h"
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| using namespace std;
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| int main(void)
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| {
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| // The operator b is the annihilation operator and bd is the creation operator
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| Symbolic b("b"), bd("bd"), vs("vs");
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| b = ~b; bd = ~bd; vs = ~vs;
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| Equations rules = (b*bd == bd*b + 1, b*vs == 0);
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| | |
| // Example 1
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| Symbolic result1 = b*bd*b*bd;
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| cout << "result1 = " << result1.subst_all(rules) << endl;
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| cout << "result1*vs = " << (result1*vs).subst_all(rules) << endl;
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| // Example 2
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| Symbolic result2 = (b+bd)^4;
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| cout << "result2 = " << result2.subst_all(rules) << endl;
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| cout << "result2*vs = " << (result2*vs).subst_all(rules) << endl;
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| return 0;
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| }
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| </source>
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| Further examples can be found in the books listed below.<ref>
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| Steeb, W.-H. (2010).
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| ''Quantum Mechanics Using Computer Algebra, second edition,'' | |
| World Scientific Publishing, Singapore.
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| </ref><ref>
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| Steeb, W.-H. (2008).
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| ''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,''
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| World Scientific Publishing, Singapore.
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| </ref><ref>
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| Steeb, W.-H. (2007).
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| ''Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra, second edition,''
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| World Scientific Publishing, Singapore.
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| </ref><ref name="symcpp3"/>
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| | |
| == History ==
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| 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
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| * <code>Verylong</code> : An unbounded [[integer]] implementation
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| * <code>Rational</code> : A template class for [[rational number]]s
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| * <code>Quaternion</code> : A template class for [[quaternion]]s
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| * <code>Derive</code> : A template class for [[automatic differentiation]]
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| * <code>Vector</code> : A template class for vectors (see [[vector space]])
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| * <code>Matrix</code> : A template class for matrices (see [[matrix (mathematics)]])
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| * <code>Sum</code> : A template class for symbolic expressions
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| Example:
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| <source lang="cpp">
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| #include <iostream>
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| #include "rational.h"
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| #include "msymbol.h"
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| using namespace std;
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| int main(void)
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| {
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| Sum<int> x("x",1);
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| Sum<Rational<int> > y("y",1);
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| cout << Int(y, y); // => 1/2 yˆ2
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| y.depend(x);
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| cout << df(y, x); // => df(y,x)
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| return 0;
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| }
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| </source>
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| 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.
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| <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.
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| Newer versions are available from the SymbolicC++ [http://issc.uj.ac.za/symbolic/symbolic.html website].
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| ==See also==
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| *[[Comparison of computer algebra systems]]
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| *[[GiNaC]]
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| == References ==
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| <!--- See [[Wikipedia:Footnotes]] on how to create references using <ref></ref> tags which will then appear here automatically -->
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| {{Reflist}}
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| == External links ==
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| * {{Official website|http://issc.uj.ac.za/symbolic/symbolic.html}}
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| * [http://issc.uj.ac.za/downloads/problems/advancedP.pdf Programming exercises in SymbolicC++]
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| {{Computer algebra systems}}
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| {{DEFAULTSORT:Symbolicc}}
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| [[Category:Free computer algebra systems]]
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| [[Category:Free software programmed in C++]]
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| [[Category:C++ libraries]]
| |
The feeling of freedom and self-control that you feel as you drive through the mountain trails can help you forget all the stress and worries of daily life. If you keep winning competitions, you will be invited to bigger and bigger races. Understanding your strengths, and the strengths of your team or business partner can be your best competitive edge this year. Are you in search of a comfort bike, a mountain bike, or a bike that is designed just for cruising and do you prefer a standard road bike or are you looking for an hybrid. Just like coasting, you'll also spend a great deal of time pedaling while standing.
However, you still have to choose the right Santa Cruz bikes for yourself. In fact, Downhill Mountain biking is the most popular form of competition biking. Every person is different and you should looking for a bike that fit's you best. “Whereas past research emphasized whether or not a relationship existed between bicycle riding on a saddle and erectile dysfunction, Schrader now says that the next step of contemporary research on the subject should focus on intervention. Titanium is very light and gives you an advantage and is usually used in racing bicycles.
They have great suspension that fits the need of both amateur and professional bikers. That's a level of quality you just don't get from many brands these days. The only way to truly protect yourself against a crash is to ensure that you have the correct safety equipment. Hence, having the bicycle that suits you perfectly is much easier now. We have built a number of thousand semi custom wheels for all kinds of bikes, and will probably be happy to do the exact same for you.
If you cherished this short article and you would want to get details regarding Women mountain bike sizing. i implore you to pay a visit to our own web site. When discount sales are on, you need to be sure you understand the terms and conditions of your purchase, including warranty information. There are also tires with detailed treads which are very prominent and these are very useful for the biker because of the grip they provide. In the purest sense of the word, a mountain bikes sole mission is to travel "off-road" only. The dedication and solid experience of the experts, it is not difficult to accomplish such goal. I've never been into cycling and wanted to give it a try for exercise.
In the recent article section, you can find the list of biking related articles with a detailed description present on the official website. Then, the answer is the skeletal frame size that will fit you for a normal bike. One of the main concerns for any cyclist is safety, having the right kit is a must. Many of these trails and stunts are so dangerous that signs are up because of the potential of a serious injury or even death. Which leads me to my favourite materials for hardtails.