to home


For examination of algorithms on discrete spaces I have developed (circa 2003-2005) software (Lattice software). It runs under Windows, the source code is available (open source).

It was shown that only an a priori finite mathematical model can have an exact equivalent in physical reality. This means that it implies an only finite number of operations on an a priori finite numerical space [1] which can be represented without using irrational numbers. Up to now there is not much experience in this area: Important physical equations are defined on continuous (a priori infinite) sets and often written as partial differential equations. If we want to find the natural finite basis of them, first we have to replace differential calculus by finite difference calculus. This can soon lead to difficult combinatorics, especially in case of interactions across several dimensions. But increasing performance of computers offers new possibilities. The mentioned numerical space can be represented by finite dimensional numerical lattices (sets of numbers defined on finite dimensional point lattices) which can be handled adequately by a computer. So I built as help this program for handling of numerical lattices and for studying the results of numerical algorithms on them. All lattice points are addressed by integer coordinates and the numbers assigned to the points can be complex. Both complex rational and complex floating-point numbers are supported. Graphical representation illustrates the results of algorithms. The aim is to find algorithms whose results correspond to experimental results better and better.
Software Download
It is recommendable to read at first an article which contains a more detailed description. After the download you can unpack the received .zip file into an empty directory and start the program under Windows by clicking on


The program stores all data in files with the ending aa1 . The download contains some examples of them. Due to their standard ASCII format they can be viewed by an usual text editor. If you have created own *.aa1 files, at first don't delete the old program version in case of an update, because the new program version may work with a changed format of those files. You can also
download the source code
to implement and test own algorithms directly without using the *.aa1 files as interface. I used Borland C++ Builder 6, the main code is contained in wqpu1.cpp, the code for the complex rational class is contained in wqpnu.cpp. It is advisable that you write your own code into the separate user file wqpus1.cpp to ensure well defined program structure also in case of further versions.


(1) Nevertheless both can increase without boundary when time increases without boundary (infinite potential).