Symbolic and Digital Mathematics - Productivity

Question

Do significant mathematical calculations (especially for solving non-linear polynomial systems) cause tremendous performance (speed of speed calculation) compared to numerical calculations? Is there any reference data / data about this?

Found a related question: https://scicomp.stackexchange.com/questions/21754/symbolic-computation-vs-numerical-computation

One more: Computational efficiency of automatic forward mode versus numerical and symbol differentiation

Answer 1

This is not a direct answer to the question, but the proposed course correction.

Although mathematical expressions can be evaluated in purely numerical terms or in purely symbolic means, a hybrid approach can also be used.

This is known as Symbolic Numerical Computation.

Maple is one software package with this ability.
Note. I have never used Maple, so I can not add more.

Package Search

I find that I get better results when searching for mathematical packages using symbolic-numeric calculations by searching for the package name in combination with alphanumeric computing, for example

symbolic numerical calculation of tungsten

Case study related to neural networks

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Answer 2

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