I think it's great that you are doing this. Does a patch exist yet? I'd like to try it out.
On Sat, Jul 19, 2008 at 11:06 AM, Jason Grout <[EMAIL PROTECTED]> wrote: > > I've been working on writing eigenvalue/eigenvector functions, as > mentioned here: > http://groups.google.com/group/sage-devel/browse_thread/thread/c8d2001f2b19a9bc/2585039efd2fbd2f?lnk=gst&q=kernel#2585039efd2fbd2f > > Here is the interface as it now stands. Does anyone have any comments > or questions? > > * eigenspaces_left, eigenspaces_right: Like the current eigenspaces > function, but returns the algebraic multiplicity of the eigenvalue as > well in tuples like: (eigenvalue, eigenspace, algebraic multiplicity). > This way, existing code that depends on the first two elements of a > returned tuple being what they are still works. In the future, we might > consider using a dictionary like {"eigenvalue": eigenvaxill works. It > prints a deprecation warning and then calls eigenspaces_left. > > Also, the even_if_inexact argument is deprecated. Instead, a warning > message is printed if the function is called with an inexact base ring. > > Note that the eigenspace functions still return the eigenvalues up to > Galois conjugation, and the algebraic multiplicity applies to each > galois conjugate of the returned eigenvalue (at least, I think that's > how the math should work, right?) > > * eigenvalues: This function returns all the eigenvalues as elements of > QQbar: i.e., it returns all the galois conjugates of eigenvalues > returned in eigenspaces_left. For an nxn matrix, it returns n > eigenvalues, so the algebraic multiplicity is not explicitly returned, > but is implicit in the list. > > * eigenvectors_left, eigenvectors_right: These functions return tuples > of the form: (eigenvalue, list of eigenvectors, algebraic multiplicity). > The eigenvalues are elements of QQbar and are all distinct > eigenvalues. The list of eigenvectors is found by taking the basis of > the space returned in eigenspaces_* and then mapping it to QQbar^n by > the map that takes the eigenvalue to a particular galois conjugate. > > * eigenmatrix_left, eigenmatrix_right: This mimics the eig command in > Matlab: it returns a matrix D and a matrix P, where D is a diagonal > matrix of eigenvalues and P is a matrix of rows or columns corresponding > eigenvectors or zero vectors so that AP=PD or PA=DP (depending on left > or right). > > I'm also trying to get the kernel and image and other functions that > depend on left/right notions to signify they side they are computing. > Right now I changed them to *_left and *_right (instead of left_* and > right_*) and deprecating the left_* and right_* functions. I realize > that the *_left/right functions don't read as naturally as left/right_* > functions, but they make a lot more sense in tab completion; if someone > is looking to compute the kernel of a matrix, then it's harder to find > the function if it is called left/right_kernel than if it is called > kernel_left/right. For tab completion, I think it's better in general > to do an index-style noun_modifier than modifier_noun (as would be more > naturally spoken). > > Also, to address another point: there would be a lot functions with the > above changes. I'm following the philosophy expressed, I believe, by > Nick: that each function should clearly indicate what it is returning > and that arguments should not change the mathematical content of what is > being returned. I see left eigenvectors and right eigenvectors as > fundamentally different things, i.e., I wouldn't ever want to confuse > the two (well, I guess unless the matrix was symmetric :). That's why I > have two different functions instead of one eigenvectors(left=True) or > eigenvectors(right=True). > > I'm trying hard to get this done for 3.0.6 in time for an AIM workshop > on undergraduate linear algebra research that is introducing the > participants to Sage. Otherwise, I'm afraid that Sage won't be very > suitable for the workshop, not having an eigenvalues function, for example. > > Thanks, > > Jason > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@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-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
