On Sun, Jul 19, 2009 at 10:58 AM, Tim Lahey<tim.la...@gmail.com> wrote: > > > > > On Jul 19, 2009, at 12:08 PM, Golam Mortuza Hossain wrote: > >> >> Hi, >> >> I have spent considerable amount of time in last one month >> working with new symbolics. Overall, I am impressed with >> it. >> >> However, my experience with new derivative makes me >> wonder whether the pynac "fderivative" construct is really >> worth the efforts! >> >> While implementing functional derivative and integration >> algorithm for generalized function using new symbolics, I >> have been brought to near a dead end because of new >> derivative. >> >> It.... >> >> (1) Breaks substitution: >> >> Arguments of derivative can't be substituted >> >> http://trac.sagemath.org/sage_trac/ticket/6480 >> > > This is a really big problem. I know I need to be able to > do this all the time. >> >> >> (2) Nightmare for writing integration algorithm: >> >> If h = f(g(x)).diff(x) then integrate(h, x) is trivial. However, in >> new symbolics to do so, one needs compute >> >> integrate( D[0](f)(g(x, y))*D[0](g)(x, y), x) >> >> Let me claim: Integrating an expression involving new symbolic >> derivative >> is at best EQUAL and often MORE computationally EXPENSIVE than its >> "diff" >> counterpart. >> >> > > It's also a mess. > >> >> (4) Causes Maxima interface to break: >> >> http://trac.sagemath.org/sage_trac/ticket/6376 >> > > Since there are many useful calculus-related routines, that's a problem. > >> >> >> (4) Gives mathematically non-sensical results: >> >> http://trac.sagemath.org/sage_trac/ticket/6465 >> > > That's more of a problem that it doesn't know about integration, which > is > quite annoying. > >> >> >> (5) Looses information irrecoverably: >> >> From "D[0](f)(x-a)" its not possible to decide whether original >> variable of differentiation was "x" as in f(x-a).diff(x) or "a" >> as in -f(x-a).diff(a). This again affects integration algorithm. >> > > This is one of the reasons I hate this notation. It may be compact, > but it hides information that may be useful and makes it difficult to > unravel. > > >> >> (6) Compact? >> >> It is true that this format is sometime compact but consider >> the counter example: >> ------ >> sage: f( g(x) + h(x) ).diff(x) >> (D[0](g)(x) + D[0](h)(x))*D[0](f)(g(x) + h(x)) >> ------ >> >> In old symbolics it takes less space to print >> ----- >> sage: f( g(x) + h(x) ).diff(x) >> diff(f(h(x) + g(x)), x, 1) >> ----- >> > > The first appears to be an expansion. I'd much rather see the second. > >> >> (7) Printing issues: >> >> We are still debating on this in separate thread. > > I need to have standard partial derivative notation as an option at > least > in LaTeX form. There is no way I'm going to re-write the from this > notation > to standard notation hundreds of equations. > > I've basically stopped working with Sage because of this notation. I > can see > what's going on much simpler with something like > > \left.\frac{\partial f}{\partial x}(x,y)\right_{x=x-a} > > than the equivalent in the D notation. Sure, it isn't as compact, but > from long > experience, I know exactly what it means. More importantly, my > supervisor and my > committee members know what it means. I thought there was going to be an > option of not using the D notation? > > Note that I've been discussing specifically the LaTeX output. That's > what's most > important for me, but I'd prefer using notation that's consistent. > This D notation > may be internally consistent, but it doesn't work with the rest of Sage. > > >> >> >> My question now is it really worth solving all of the >> above issue to keep working with fderivative of pynac? >> >> Or should we just restore old "diff" by simply sub-classing it >> from SFunction like what is being done for "integration" >> and others?
At first glance doing this sounds like a really good idea. How hard would it be for you to make a mock-up prototype of this to more clearly demonstrate it? I'm definitely not opposed. William >> >> Cheers, >> Golam >> > > > Also, Maple has a useful feature of letting you present partial > derivatives in > the form f,x,x,x for a triple partial derivative with respect to x. > Note the variables > of f aren't show. They're implicit. However, this is just a nice > display feature, but they > do have a similar input feature. See PDETools and DETools. > > Like I said above, this D notation has basically guaranteed I won't > use Sage > for my work. > > Cheers, > > Tim. > > --- > Tim Lahey > PhD Candidate, Systems Design Engineering > University of Waterloo > http://www.linkedin.com/in/timlahey > > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
