Reference request: APPLICATIONS of computer algebra

[David Stork]

For a class lecture, I'd like to present research results from science, technology, or mathematics that use large-scale simulations involving SYMBOLIC (not numerical) computations. One ideal case would involve a problem where a large number of coupled differential equations were solved analytically (again, not NUMERICALLY).

Citations would be greatly appreciated.

Nor am I (here) interested in research that increases the power or accuracy of computer algebra, such as the nice work on deep networks to enhance the scope and accuracy of symbolic integration or solving differential equations.

Thanks in advance.

[Richard Fateman]

On Saturday, March 4, 2023 at 11:06:50 AM UTC-8, David Stork wrote:
> For a class lecture, I'd like to present research results from science, technology, or mathematics that use large-scale simulations involving SYMBOLIC (not numerical) computations. One ideal case would involve a problem where a large number of coupled differential equations were solved analytically (again, not NUMERICALLY).

Frankly, I would be surprised if anyone bothered to try such problems symbolically, give
the vast quantity and quality of work solving such problems ( which are
usually intractable symbolically.)

Here's an example that might appeal to you, though not of the "ideal case" you are hoping for.
https://people.eecs.berkeley.edu/~fateman/papers/vortex.pdf
which was published here:
R. J. Fateman, "Symbolic computation of turbulence and energy dissipation in the Taylor vortex model," Intl. J. Modern Physics C, vol. 9, no. 3, pp. 509-525, May 1998.

>
> Citations would be greatly appreciated.
>
> Nor am I (here) interested in research that increases the power or accuracy of computer algebra, such as the nice work on deep networks to enhance the scope and accuracy of symbolic integration or solving differential equations.

I am aware of some activities using machine learning to do symbolic mathematics. While someone in
the ML community might characterize this work as "nice" from the computer algebra standpoint
the papers border on fraudulent.
RJF

>
> Thanks in advance.

[Dr Huang (DrHuang.com)]

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