About the Taylor Center
Dedicated to Teaching and Research of the Foundations of Automatic
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
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
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
completion, every such project will assist the teaching process in the
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
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
Examples of applications and
articles in scientific Delphi with a teaching potential
Pascal to Delphi to Object
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,
4. Recursion Excursion.
Delphi Informant Magazine,
No. 8, pp. 30-38 (2000).
5. A Recursive Journey
to the Problem of Three Bodies. Delphi
Informant Magazine. Vol. 8, No. 3, pp.
6. 3D Delphi:
Stereo Vision on Your Home PC. Delphi
Informant Magazine. Vol. 10, No. 1, pp.
7. 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