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Add and refine algebraic elements #21

@Antonio-JP

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@Antonio-JP

The current implementation of algebraic elements is not well developed.

The computation of the solutions of the system seems to be quite old-fashioned and do not follow the main guidelines of the latest implementations in the package. For example, the computing of the differential equation for an algebraic function do not use the linear solvers implemented in the package misc.

In addition, we found more examples of D-finite functions: exponentials of integrals of algebraic functions.

This progress requires a reworking of the lazy computations.

The goals of this issue are the following:

  • Change and update the implementation of method DAlgebraic that transforms an algebraic function into a D-finite.
  • Improve the method DAlgebraic to allow algebraic elements over DDRing (not only over rational functions).
  • Implement an algebraic extension of a DDRing. This will go on the method extension that comes from the class ring.
  • Add example of exponentials of integral of algebraic functions.
  • Try to generalize to any D-finite function (instead of simply exponentials): it should work the same with a bound dp where d is the order of the D-finite and p the degree of the algebraic function.

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