improve conversion from algebraic to differential equations

[mezzarobba]

Currently computing a differential operator annihilating an algebraic function can be done with (x*Dx).annihilator_of_composition(...). However this

• is not easily discoverable,
• is quite slow (compared to gfun),
• tends to return non-minimal annihilators.

[mkauers]

Do you have an example for non-minimal output at hand? I think this should not happen.

[mezzarobba]

I couldn't find the full example, sorry. What I found is a quick note from May 2019 claiming that it happened with "the" generating function of Kreweras walks. However, I just tried again with the equation -64*t^2*K^3 - 16*t*K^2 + (72*t - 1)*K - 54*t + 1 and it works fine. I guess I made a mistake back then, or perhaps I used some variant of the generating function. (With the full generating function, the computation does not finish within a few minutes, so I guess it was not that...)

[fchapoton]

I would appreciate to have a full example somewhere.. Now battling to try to use that on

F^2*u^2*x^2 - 2*F^2*u*x^2 + F*u^2*x^2 - 2*F^2*u*x + F^2*x^2 - 2*F*u*x^2 - 2*F^2*x - 2*F*u*x + F*x^2 - u*x^2 + F^2 - 2*F*x - u*x + F - x