On Tue, Dec 05, 2023 at 09:06:48PM +0800, Qian Yun wrote:
> I wonder if the current work on figuring out simplified roots
> of degree 4 polynomial is somewhat related to the recent
> "radicalSolve" post on sci.math.symbolic?
Well, one of examples came from this post.
>
> (aka: will this also improve radicalSolve?)
Code that I posted only affects integration, more precisely
transformations of logarithms. I suspect that one could also
do some transformation of special functions, but ATM we do
nothing for them.
There are related issues:
- computation of Galois groups, currently not implemented in
FriCAS
- checking for dependence/independence of roots of Trager
double resultant (important when we want to claim nonintegrability)
- limits of 'rootSum'
- 'radicalSolve'
- TranscendentalSolve
- determining sign
- root simplifiction
It would be nice to share code between various uses, however there
are differences, for example 'radicalSolve' may produce complex
valued radical, for definite integration we want real quantities.
Ideally integrator will make sure that all new roots introduced
during integration are independent, for this we probably should
have "renormalization" pass, that is run computations like
normalization, and use result to eliminate dependencies between
new kernels.
--
Waldek Hebisch
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