Petr R. Ivankov, Nicolay P. Ivankov.
Engineering and research in common are boundless areas and development those universal software seems hopeless. However if we develop robust architecture and provide ability to extend soft, including user interface then the problem is realizable. Authors of this paper realized software that can to solve following tasks.
1) Physical optics.
2) Boundary elements method.
3) Simulation of transmitting/receiving antennas with arbitrary complex vector polarization directional diagrams.
4) 6D dynamics of rigid body.
5) Transformation of 3D shapes.
6) Bar centric split of figures.
7) Simulation of electric circuits
8) Space navigation
9) Navigation by video images
10) Electric circuits parameters identification
11) Interaction with external devices
12) Nonlinear regression
13) 3D Visualization.
These tasks do not exist separately. They can interoperate.
The software had been appeared as development of devoted to category theory  program. Now foundations of mathematics are based on this theory. Recently the category theory found applications for computer science . Basic notions of the category theory are object and arrow. In this software objects are aircrafts, antennas, ordinary differential equation systems, recursive elements, video cameras etc. Arrows are geometric links, information links, links between antennas and electric circuits. In the program each type of object implements a number of interfaces. For example aircraft implements following interfaces: target of electromagnetic radiation, source of electromagnetic radiation, object with geometric motion, object of 3D visualization. A video camera implements interfaces: object with geometric motion, source of information for navigation by video images.
Another important feature is formula editor. This can operate with real, Boolean, vector parameters etc. This editor is used even for Galois fields.
Fig 1. Formula editor
The editor is used for motion equation, reflective properties of material, directional diagrams etc. If your browser supports Java applets you can try this editor on www.orc.ru/~ipro .
Software contains a set of dispatchers. Each dispatcher is responsible for definite kind of physical processes : kinematical, electromagnetic, informational. Now we consider a few samples of this software.
This sample is represented in fig 2.
Fig 2. Radiation
Big squares are objects and little ones are arrows. We have kinematics arrow which links radar and aircraft, radar, receiver, processor of received data, rigid geometric link between receiver antenna and radar. This picture shows typical situations in radar.
Formula editor permits to specify anisotropy absorption layer properties. The fig 3 illustrate effective current densities of sphere with 3 types of absorption layer
Fig 3. Absorption layers.
The red color corresponds to maximal current density and purple color to minimal one.
The logics of this sample is shown in fig 4.
Fig 4. Identification of transient parameters.
It contains a general linear method component, graph indicator and some auxiliary components.
The result of identification is shown on fig. 5.
Fig 5. Aperiodic link transient (Red – real transient, blue – identification result)
a) large scale
To show the universality and robustness of this approach we show exotic sample of its application to modern math.
Now the following list of functionality is realized.
1) Checking of diagrams commutative.
2) Calculation of functors.
3) Definitions of unknown morphisms in diagrams
4) Calculations of Im, Ker, Coker in abelian categories.
5) Homology and cohomology calculations.
6) Direct and inverse finite limits calculation.
Realized modules over Euclidean domain. Finite fields. Following functors
HomA(M, -), HomA(-, M), HomF(V, -), HomF(-, V), - ÄA M , *AM, Ext(M,-), Ext(-,M);
1. Carl Faith. Algebra : Rings, Modules and Categories. Springer – Verlag, Berlin – Heidelberg – New York 1973.
2) Steve Easterbrook An introduction to category theory for software engineers. Tutorial given at ASE'98 (Oct 1998). http://www.cs.toronto.edu/~sme/presentations/cat101.pdf