ecterrab

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These are replies submitted by ecterrab

Hi, > 1. Will the differential geometry package subsume the functionality of the tensor and/or differential forms package s? Yes, in that DifferentialGeometry (DG) turns obsolete these other package you mention, though not entirely in Maple 11. > 2. Will there be any major changes and/or upgrades to the group package? Any new (abstract) algebra functionality? I am not sure what you mean by abstract algebra and some of that I believe is already in DG. Could you be more precise? > 3. Is the new differential equations package a successor to the DETools package? There is no new differential equations package, though PDEtools duplicated its size with a new module for symmetries for PDEs, and DEtools has a module for symmetries since 1997, so I guess you are asking whether the new PDE symmetries routines are replacing the old ones in DEtools? If so, the answer is: no. The old symmetry routines - only for ODEs, not PDEs - have sophistications that will take some years to implement in the PDE sector. Even that day I believe there would be no reason to remove them because they are specialized and fast in a way it would be difficult to achieve with more general routines. Edgardo S. Cheb-Terrab Ph.D. Theoretical Physics, Maplesoft
Hi, Although it would be interesting to have a Maple plug-in, especially for helpfiles, note that the existing GDS plug-ins by Larry Gaeda (from Ontario), allow you to index Maple worksheets and also windows help-files; I wouldn't be surprised if he finds a simple way to extend his plug-in to also index Maple help databases (hdb files) or perhaps his plug-ins already work OK with these files. The links to Larry's plug-ins are: http://desktop.google.ca/plugins/i/indexitall.html http://desktop.google.ca/plugins/i/indexthechm.html In connection with installing these plug-ins, you may want to re-index or do alike operations, for which the following plug-in is relevant: http://desktop.google.ca/plugins/i/tweakgds.html Finally this other plug-in is helpful in narrowing searches in typical ways which are not possible with the standard GDS http://desktop.google.ca/plugins/i/airbeargdsuite.html Edgardo S. Cheb-Terrab Research Fellow, Maplesoft
Hi, It is true that in general these problems are tough. There are Maple commands to treat them though. I mean: "Given a system of equations, differential or not, linear or not, involving inequations or not, depending on some parameters, say {a,b,c,...}, such that a solution exists only for some particular values of these parameters, compute all these solutions as well as the different values of the parameters {a,b,c,...} such that these solutions exist". By the way, among the existing computer algebra systems, Maple is the only one able to handle such a general problem. The Maple packages handling these probelms are diffalg and RIF. They can do this type of computation since Maple R5 (diffalg) and Maple 6 (RIF), and both work rather efficiently, in my opinion RIF performs better on average problems. The computation using diffalg/RIF in Maple is also simplified and extended, by means of the PDEtools[casesplit] and PDEtools[dpolyform] commands, in order to handle basically all the mathematical functions. That is, to perform types of (maybe differential) Grobner basis elimination on systems not just rational in the unknowns and the independent variables. Despite being in PDEtools, casesplit handles the same way systems of equations not involving derivatives. To see some examples of how this works see ?PDEtools[casesplit] and PDEtools[dpolyform]. Edgardo S. Cheb-Terrab Research Fellow, Maplesoft Editor for Computer Algebra, Computer Physics Communications
Hi, It is true that in general these problems are tough. There are Maple commands to treat them though. I mean: "Given a system of equations, differential or not, linear or not, involving inequations or not, depending on some parameters, say {a,b,c,...}, such that a solution exists only for some particular values of these parameters, compute all these solutions as well as the different values of the parameters {a,b,c,...} such that these solutions exist". By the way, among the existing computer algebra systems, Maple is the only one able to handle such a general problem. The Maple packages handling these probelms are diffalg and RIF. They can do this type of computation since Maple R5 (diffalg) and Maple 6 (RIF), and both work rather efficiently, in my opinion RIF performs better on average problems. The computation using diffalg/RIF in Maple is also simplified and extended, by means of the PDEtools[casesplit] and PDEtools[dpolyform] commands, in order to handle basically all the mathematical functions. That is, to perform types of (maybe differential) Grobner basis elimination on systems not just rational in the unknowns and the independent variables. Despite being in PDEtools, casesplit handles the same way systems of equations not involving derivatives. To see some examples of how this works see ?PDEtools[casesplit] and PDEtools[dpolyform]. Edgardo S. Cheb-Terrab Research Fellow, Maplesoft Editor for Computer Algebra, Computer Physics Communications
Hi, You question is about aspects of a numerical solution, assuming that
> ... for this problem no closed-form...
So maybe this is of help: in Maple 9.5 and 10 (perhaps also in previous versions), dsolve can compute a closed-form solution for this problem: > dsolve([diff(s(t),t) = A - A * rho^((1 - r^(theta * t)) * x) - v, diff(f(t),t)=((c - s(t)) / l) * m + x, diff(h(t),t) = x, f(0) = 0, s(0) = 0, h(0) = 0]);
                           x          (theta t)
                      A rho  Ei(1, x r          ln(rho))
  {h(t) = x t, s(t) = ----------------------------------
                                 theta ln(r)

                                                          t
                x                                        /
           A rho  Ei(1, x ln(rho))                      |   m c
         - ----------------------- + (A - v) t, f(t) =  |   ---
                 theta ln(r)                            |    l
                                                       /
                                                         0

                            x          (theta _z1)
           m A _z1   m A rho  Ei(1, x r            ln(rho))   m v _z1
         - ------- - -------------------------------------- + -------
              l                  l theta ln(r)                   l

                  x
           m A rho  Ei(1, x ln(rho))
         + ------------------------- + x d_z1}
                 l theta ln(r)
Edgardo S. Cheb-Terrab Research Fellow, Maplesoft
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