On Mon, Jul 21, 2008 at 10:12 PM, Tim Lahey <[EMAIL PROTECTED]> wrote: > > > On Jul 21, 2008, at 3:41 PM, Gary Furnish wrote: > >> >> On Mon, Jul 21, 2008 at 10:00 AM, William Stein <[EMAIL PROTECTED]> >> wrote: >>> On Mon, Jul 21, 2008 at 6:28 PM, <[EMAIL PROTECTED]> wrote: >>>> >>>> Hello all, >>>> >>>> I have a simple question about the capabilities of Sage that I have >>>> not been able to resolve by looking at the documentation. I often >>>> find myself manipulating somewhat complex functions that take vector >>>> arguments. I then need to derive gradients, hessians, etc. I >>>> need to >>>> do this with out knowing the dimensions of the vectors. So for >>>> example, what I would like to do is something like the following. >>>> First, I would define the function f(x)=.5 * x' * A * x + b, perhaps >>>> something like: >>>> >>>> A = matrix(); >>>> x = vector(); >>>> b = vector(); >>>> f = function( x' * A * x + b); >>>> >>>> Then, I would like Sage to do the calculus for me, something like, >>>> say: >>>> >>>> f.gradient() >>>> sage) 2*A*x >>>> f.hessian() >>>> sage) A >>>> >>>> (Of course, I wouldn't bother using a computer algebra system for >>>> such >>>> a simple function, but you get the idea.) My question is: can >>>> Sage do >>>> things like this? I would like to avoid specifying the dimensions >>>> of >>>> x, or giving the entries of A when I define the function. >>> >> >> My system does not currently support this, and I have no plans to >> implement this, but it could be done pretty easily if there was a >> dimensionless vectorspace and matrixspace object, but I'm not >> completely convinced I see the point. If one wanted to do this they >> could just choose an arbitrary dimension, and as long as they don't do >> anything that depends on the dimension it should still give the same >> answer (in my system, not the current one). > > The purpose for this is computations like this come up in Finite Element > Analysis when you are deriving the system of equations (and probably > elsewhere). > The reason for not specifying the dimensions is that you don't know the > length of the vectors in advance since it is dependent upon the number > of > elements you choose. They have a definite structure, so once the size is > specified, you can then fill in the vectors, but you don't specify the > size > in advance. The most you would do is say that A is n by n and x is n > by 1. > > Maxima and Maple can't do these calculations (I've tried), but > Mathematica > can. I had to go through a lot of effort to figure out an alternative > to use > in Maple for deriving Finite Element equations, although I haven't > been able > to convert it into Sage. > > Cheers, > > Tim Lahey
Well I want Sage to be able to nicely do what you want. Any chance you could make up a slightly nontrivial example in Sage vapor-code, which would illustrate the sort of functionality you enjoy in Mathematica and perhaps wish Sage had? -- William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
