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:
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:
DAlgebraicthat transforms an algebraic function into a D-finite.DAlgebraicto allow algebraic elements overDDRing(not only over rational functions).DDRing. This will go on the methodextensionthat comes from the class ring.dpwheredis the order of the D-finite andpthe degree of the algebraic function.