Jason, Thanks for all the suggestions and typos. With this format it is hard sometimes to deal with some of the details. You'll notice I didn't try to explain what symplectic_form() produces. ;-) I thought about the case of not having enough eigenvectors to fill out the matrix as I annotated the command, but I think I now have an idea that might do it in a few words.
Rob On May 9, 11:21 am, Jason Grout <[email protected]> wrote: > Rob Beezer wrote: > > I've put together a quick reference sheet (two pages) for linear > > algebra commands in Sage. I'll do a bit more clean-up on this before > > posting a final copy on the wiki in a couple days, so I know there is > > a bit more work to do. Specifically, I might reorder the sections if > > I come up with a more logical presentation. > > > I'd really like to hear about any glaring omissions, or gross > > misunderstandings of categories, vector spaces, modules, rings and/or > > fields. Draft copy at > > >http://buzzard.ups.edu/sage/quickref-linalg.pdf > > > Thanks, > > Rob > > Nice! > > Comments: > > * The first entry of a vector is not 0! (zero factorial :), but zero. > Unfortunately, it seems like it is always confusing to read mathematics > that has exclamation points. Same comment for the matrix section. > > * u.norm() == u.norm() ? That seems confusing. Do you mean something > like u.norm(2)? > > * A.inverse should have parentheses (i.e., A.inverse() ) > > * under row operations, "e.g." should be followed with a comma > > * You might mention the very powerful and intuitive indexing and setting > available using the bracket notation. See the docstrings of __getitem__ > and __setitem__ in sage/matrix/matrix0.pyx for lots and lots of > examples. This notation puts us roughly on par with octave and matlab > for easy creation of submatrices and setting elements of a submatrix. > > * in eigenmatrix_right/left, P may not have eigenvectors. If the > algebraic multiplicity does not equal the geometric multiplicity for a > particular eigenspace, then P pads the eigenvectors with zero vectors so > that you still have AP=PD (for _right). If A is diagonalizable, then > your statement is correct; the columns of P are eigenvectors of A. > > * Some of the decompositions don't work for all base rings; you might > mention that (e.g., QQ doesn't have SVD) > > * .change_right(R) has unnecessary commas around the last "R" in the > explanation > > Again, very nice! I will probably use this in the next few weeks. > > Thanks, > > Jason --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en -~----------~----~----~----~------~----~------~--~---
