I use sympy only via sympy.physics.mechanics to set up symbolic equations
of motion for rigid body systems. Some of them may take quite some time be
be set up.
I would imagine, that a 'faster sympy' may make this process faster, too.
( I personally only play around with this, but I am sure there are real
world applications using sympy.physics.mechanics)

On Sat 19. Aug 2023 at 23:52, David Bailey <d...@dbailey.co.uk> wrote:

> On 16/08/2023 16:13, Oscar Benjamin wrote:
> > Hi all,
> >
> > I have written a blog post about recent work on SymPy and what I think
> > should be future development plans:
> >
> > https://oscarbenjamin.github.io/blog/czi/post1.html
> >
> > This is the first in a series of posts and in this one I describe what
> > I think are the core parts of SymPy and outline from a high level what
> > I think should be done going forwards. Subsequent posts will describe
> > specific components in more detail.
> >
> > Oscar
> >
> I do wonder slightly if pushing for higher speed in symbolic operations
> is worth it if it causes a lot of disruption, or distracts from other
> work that might be more useful.
>
> Symbolic calculations are wonderful in the right circumstances, however,
> the cost of symbolic calculations grows pretty steeply with the size of
> the problem.
>
> Everything becomes clumsier, for example fractional coefficients get
> much more complicated  after a few mathematical steps.
>
> That means that multiplying the raw computational speed by 10 (say) may
> only expand the pool of problems that can be solved in a reasonable time
> very slightly.
>
> There is also the problem that complicated symbolic results are often
> not very useful. For example the solutions of a quadratic equation are
> well known and very useful. However, the corresponding solutions for
> cubic or quartic equations are really only of theoretical interest.  It
> is even possible to get solutions for quintic equations (so I am told)
> by using theta functions. My point is, that these are of no practical use.
>
> Do you have some motivational examples of what can be achieved by moving
> from SymPy to SymEngine? (I just use SymEngine for comparison purposes)
>
> David
>
>
>
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-- 
Best regards,

Peter Stahlecker

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