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  • Reference request: APPLICATIONS of computer algebra

    From David Stork@21:1/5 to All on Sat Mar 4 11:06:49 2023
    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.

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  • From Richard Fateman@21:1/5 to David Stork on Sun Apr 9 13:13:09 2023
    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.

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  • From Dr Huang (DrHuang.com)@21:1/5 to David Stork on Sun Oct 1 15:32:02 2023
    On Sunday, 5 March 2023 at 06:06:50 UTC+11, 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).

    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.

    May I suggest you try MathHandbook?
    What is mathHandbook?
    the Math Handbook Calculator has the function of machine learning. It is unique in the world to solve the function of any order (such as 0.5 order) differential equations. Enter mathematical formulas on the Mathematics Handbook website, click
    continuously to calculate calculus, solve equations, give analytical solutions and numerical solutions and diagrams, interactively zoom in the drawing, and zoom in with the mouse wheel. You can use it on your mobile phone to learn computing and
    development anytime, anywhere.

    http://mathhand.com
    http://mathhandbook.com

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