Thanks for the references. I suppose the follow are also relevant: A Normal Form for Function Rings of Piecewise Functions MARTIN VON MOHRENSCHILDT
http://www.cas.mcmaster.ca/~mohrens/JSC.pdf Integration of the signum, piecewise and related functions D.J. Jeffrey, G. Labahn, M. v. Mohrenschildt and A.D. Rich https://cs.uwaterloo.ca/~glabahn/Papers/issac99-2.pdf But the Maple documentation http://www.maplesoft.com/support/help/Maple/view.aspx?path=dsolve/piecewise says: "The solutions are found in terms of distribution theory and translated into a piecewise expression." and "The theory is based on the dissertation Martin von Mohrenschildt. "Symbolic Solutions of Discontinuous Differential Equations." Swiss Federal Institute of Technology ETHZ No. 10768" which at least from the abstract unless I misunderstand, seems perhaps contradictory. No? In particular it is not clear to me that this provides any representation of Dirac delta function. On 5 July 2014 09:45, someone <[email protected]> wrote: > Hi, > > >> What would be required to support derivatives like this (and other >> related functions such as Dirac delta and Heaviside step function)? > > It might be an idea to look at the work of Martin von Mohrenschildt[1,2]. > He did some interesting extensions and implemented that in Maple[3]. It > might be not that difficult to implement the PPDR (piecewise polynomial > differential ring) in Axiom. I'm not sure if this exactly matches your > initial question. It would in any way be nice to make such computations > in Axiom. > > > Citing the abstract of the paper: > > In this paper we generalize the basic notations of the > Liouville-Ritt-Risch > theory of closed-form solutions to discontinuous field extensions. Our aim > is to extend the theory of differential fields such that the “classical > algorithm” > like the Risch structure theorem and the algorithm solving the Risch > differential > equation can be extended to handle discontinuous extensions. > > > [1]: http://e-collection.library.ethz.ch/view/eth:39463?lang=de > [2]: http://link.springer.com/chapter/10.1007%2F978-1-4612-4268-0_7 > [3]: > http://www.maplesoft.com/support/helpJP/Maple/view.aspx?path=dsolve/piecewise > > -- > You received this message because you are subscribed to the Google Groups > "FriCAS - computer algebra system" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/fricas-devel. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
