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C++ is programming language characterized with simple syntax, efficiency of compilers and the resulting executable files.

C++ is extension of the previously developed language C, that allows to deal with complex numbers and has many other advantages.

The most of figures in TORI are generated with C++ codes.


The C++ compilers are available for free. In particular, the compiler comes together with the Linux distribution and it is included in the X-code for Macintosh. There may be some problems with Microsoft products, but in many cases, the C++ can be installed even for the Microsoft Windows operational system.

The C++ programs are highly portable, in the most of cases, the program written in one computer can be compiled at another computer without any adjustment. In this sense, the C++ is highly conservative; once some function is implemented in C++, it can be used for a long time as a tool. For this reasons, in TORI, the C++ codes generating pictures are stored in the descriptions.

C++ is important tool for any serious research. In any case, even if the rigorous mathematica proof is suggested, the examples of application of such a tool should be provided. Following the First of the TORI Axioms, it worth to demonstrate, that the new concept can be applied, and to make the C++ implementation is good way to provide the example of the application.

Structure of program

The C++ program should begin with "head", that includes the service and routine. The main program should follow the head.

There exist tutorials [1][2], and there is no reason to repeat them here.

The structure of codes in C++ is similar to that of Fortran and Matlab. Everyone who has any ideas about programming may just download the examples of pics from TORI, compile them, play them and learn how to use the basic C++ tools even without to read the manual. However, the abilities of C++ greatly exceed the needs to generation of figures; to, the looking into the manuals is still recommended.

C++ in TORI

Codes in C++ are used to generate figures for TORI in format EPS. Then figures are converted to PDF, supplied with necessary labels in Latex and then converted to PNG or to JPG for the loading. Unfortunately, yet, the mediawiki installed does not allow to use figures in PDF format.

In order to follow the descriptions of functions and to reproduce and to modify the figures suggested, the installing of C++ is strongly recommended. Some expressions in C++ can be generated with Mathematica and then copypasted or exported to the C++ code.

There are two graphical routines specific for TORI.

Routine ado.cin generates the header of an EPS file. This header is small and is almost the same for all figures.

Routine conto.cin generates the contour plots; and in particular, the complex maps of functions of compex variables (mainly those of holomorphic functions). One may generate some complex maps with codes suggested in TORI (see any figure in category Complex map), and then try to reproduce the map of similar quality with some GNUplot, or Mathematica, or Matlab, or Maple, and see, that in order to avoid troubles, one should writhe in C++ or, at least, in "C" [3].


  1. http://www.cplusplus.com/doc/tutorial/ C++ Language Tutorial
  2. http://www.cprogramming.com/tutorial/c++-tutorial.html C++ Tutorial
  3. http://www.youtube.com/watch?v=H4YRPdRXKFs Leonardo Yamasaki on Oct 13, 2011. Dennis Ritchie - Write in C.



Mathematica, Maple,.