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Complex arithmetic using the float complex and double complex primitive data types was added in the C99 standard, via the _Complex keyword and complex convenience macro. In C++, complex arithmetic can be performed using the complex number class, but the two methods are not code-compatible.
Here b is a Bose annihilation operator and bd is a Bose creation operator. The variable vs denotes the vacuum state | 0 {\displaystyle |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.
Note that C99 and C++ do not implement complex numbers in a code-compatible way – the latter instead provides the class std:: complex. All operations on complex numbers are defined in the <complex.h> header. As with the real-valued functions, an f or l suffix denotes the float complex or long double complex variant of the function.
Java does not have a standard complex number class, but there exist a number of incompatible free implementations of a complex number class: The Apache Commons Math library provides complex numbers for Java with its Complex class. The JScience library has a Complex number class. The JAS library allows the use of complex numbers.
The builder pattern is a design pattern that provides a flexible solution to various object creation problems in object-oriented programming.The builder pattern separates the construction of a complex object from its representation.
[8] GMP is part of the GNU project (although its website being off gnu.org may cause confusion), and is distributed under the GNU Lesser General Public License (LGPL). GMP is used for integer arithmetic in many computer algebra systems such as Mathematica [9] and Maple. [10] It is also used in the Computational Geometry Algorithms Library (CGAL).
Perhaps the most well-known example is C++, an object-oriented extension of the C programming language. Due to the design requirements to add the object-oriented paradigm on to an existing procedural language, message passing in C++ has some unique capabilities and terminologies. For example, in C++ a method is known as a member function.
An interface to the Python language is available through the PyArmadillo package, [4] which facilitates prototyping of algorithms in Python followed by relatively straightforward conversion to C++. Armadillo is a core dependency of the mlpack machine learning library [ 5 ] and the ensmallen C++ library for numerical optimization.