On Mon, Jul 21, 2008 at 10:17 PM, Ondrej Certik <[EMAIL PROTECTED]> wrote: > > 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. > > > Do you have some FEM code in Python? > > We develope sfepy (CCing sfepy-devel): > > http://code.google.com/p/sfepy/ > > and we'd like to hook symbolic capabilities to it, so that you can do > this kind of things symbolically. We just started to use SymPy for > checking the numerical solutions symbolically and my secret plan is to > be able to just write an equation in SymPy or Sage, optionally specify > some boundary conditions and get it solved using FEM.
I just want to quickly mention in case the originally poster doesn't know that (1) sympy is part of Sage, and (2) Ondrej is the lead sympy developer. > Do you have some pointers to the manipulations in Mathematica? Let's > implement the same in Sage using the same or similar syntax. > I don't think it is difficult. > > Ondrej > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
