About the Taylor Center
Dedicated to Teaching and Research of the Foundations of Automatic Differentiation and ODEs

The goals

This organization is established in order to create a home and lasting future for a private software project - the advance ODE solver called the Taylor Center. However, along with preservation of the legacy and further development of this software, a few more appropriate goals for such an organization have emerged, as explained below.

1) The software proper, the sophisticated Taylor solver running under Windows, was developed and first presented in the beginning of the 2000s. It was designed in the Borland's Delphi environment as a GUI-intensive professional application with unique graphic features, capitalizing on the ingenuity and power of the so called Visual Component model and Library (VCL) – the trademark of Borland (now Embarcadero).  Since then this ODE solver grew acquiring more and more powerful features, being smoothly ported through every new version of Windows and the respective new versions of the Delphi compilers up to the current (2016). Such a track record of smoothness in the process of transfer to new upgraded versions of the OS promises a long life of this software and the algorithms implemented in it: Perhaps for several decades more. This implies however that somebody must preserve and maintain this software legacy, to upgrade it for every future OS environment, and possibly to enhance the features. This would be the first goal of this organization which
will therefore need at least one professional or an associated bright student familiar with Delphi and the modern Taylor method (Automatic Differentiation).          

The other goals are closely associated with this primary goal.

2) Research in the purely mathematical aspects of Automatic Differentiation, i.e. in the Unifying View on ODEs and AD. The final goal will be to fill in the gap in this theory – the unresolved Conjecture. If its solution is not obtained in the near future, it is important to keep this unsolved problem in a focus of the mathematical community, and to collect the related researches for an indefinitely long time.   

3) Teaching courses of scientific programming based on Delphi and the Borland Visual Component model as regular programming curriculums in universities. It is assumed, that teaching a Pascal based object oriented language is methodologically a right thing to do, while an opportunity to easily build sophisticated GUI-intensive applications is both a fun and professionally useful skill.  

It is also assumed, that a vast list of small programming projects well illustrating particular models in Physics and Mathematics may be worked out and offered as the course works for bright students (as an example see the Appendix below). After completion, every such project will assist the teaching process in the future.

4) Currently the Delphi environment offers a negligibly small mathematical library (the Math unit), covering only the basic needs. Yet Delphi language (an extended object Pascal) offers powerful features for scientific and numeric programming such as the Dynamic arrays. As benchmarks have proved, multidimensional dynamic arrays (i.e. a run-time structure) are implemented so efficiently, that the access time to dynamic arrays elements is near the same as for the Pascal static arrays (when the access is programmed in a compile time). Another crucial advantage of Delphi for numeric and scientific programming is that Delphi implements the native Intel 10 byte real type extended based on the 63 bit mantissa. Keeping the most of the significant digits is indispensable in any non-trivial numeric algorithms.

That is why it makes sense to gradually develop an advanced library of the fundamental mathematical routines in a form of a Delphi library with a final goal to compete with the commercial Math-oriented environments. A highly efficient Delphi compiler coupled with the VCL and the vast mathematical library promises the most powerful environment for developing professional math-intensive applications: Better than under MathLab or other mathematical tools. Meanwhile only the Taylor Center is ready as a kernel of such a professional library. However, when this library grows, it will finally surpass the other similar products enabling a transfer to a commercial activity and commercial status of the organization.

Examples of applications and articles in scientific Delphi with a teaching potential

1. From Pascal to Delphi to Object Pascal-2000. ACM SIGPLAN Notices, Vol. 36, No. 6, pp. 38-49 (2001).
2. Object vs. Class: Fewer Pointers, Less Double Thinking. Delphi Informant Magazine, Vol. 5, No. 7, pp. 47-52 (1999).
3. Dynamic Arrays. Delphi Informant Magazine, Vol. 6, No. 2,  (2000).
4. Recursion Excursion. Delphi Informant Magazine, Vol. 6, No. 8, pp. 30-38 (2000).
5. A Recursive Journey to the Problem of Three Bodies. Delphi Informant Magazine. Vol. 8, No. 3, pp. 44-49, (2002)
3D Delphi: Stereo Vision on Your Home PC. Delphi Informant Magazine. Vol. 10, No. 1, pp. 8-15, (2004)
Do-It-Yourself 3D. Delphi Informant Magazine. Vol. 10, No. 8, pp. 17-22, (2004)
8. Applications of the Taylor Center software for teaching and research