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