On Thu, May 15, 2008 at 8:16 AM, kcrisman <[EMAIL PROTECTED]> wrote: > > > > On May 15, 10:55 am, "William Stein" <[EMAIL PROTECTED]> wrote: >> On Thu, May 15, 2008 at 7:48 AM, Jason Grout >> >> >> >> <[EMAIL PROTECTED]> wrote: >> >> > Jason Grout wrote: >> >> Based on some conversations with linear algebra people and classroom >> >> demonstrations in a linear algebra class, people are confused that when >> >> they create a matrix with matrix(3, range(9)), for example, that the >> >> echelon_form is not the rref output that they get from most any other >> >> program they have ever used, and certainly not what is taught in an >> >> undergrad linear algebra class. There is additional confusion if the >> >> entries specified have a fraction in them; then the matrix defaults to >> >> being over QQ, and the echelon_form functino gives the expected naive >> >> rref! The problem, of course, lies in the matrix defaulting to having >> >> base_ring == ZZ (i.e., non-field). >> >> >> What do people think about making the default ring for matrices QQ? >> >> Additionally, if the ring R is determined from the elements provided, >> >> then the matrix would be over R.fraction_field(). Of course, the >> >> documentation for matrix() would clearly indicate what is happening if >> >> the ring is not specified. >> >> > More concisely, this proposal could be worded: >> >> > What do people think of making matrix() return a matrix over a field by >> > default, unless a ring is explicitly specified. The default field would >> > either be the fraction field of the ring containing the specified >> > elements, or would be QQ if no elements are specified. This logic would >> > *only* be applied if a ring is not specified. The documentation of >> > matrix() would also be changed accordingly. >> >> +1 >> >> I suggested this idea. I would never do this is Sage were "just for me", >> but Sage isn't. Please keep that in mind when reading the above proposal... >> >> -- William > > I was just discussing this very issue with my chair yesterday. He had > created some wrappers to make using the elementary operations a little > easier for linear algebra students (though I think ended up sticking > with Octave for this semester for unrelated reasons), and then noticed > this with scaling rows under his first implementation. > > What happens if you start with something like matrix(3, range(9)), but > then want to turn it into a complex matrix and scale a row by (say) i/ > 2?
That would work fine. What you're really asking about is making the function rescale row on an *integer* or rational matrix automatically change the base ring to complex. I think that is very reasonable and would be fine with that. It is somewhat orthogonal to Jason's proposal though. > Under the current scaling code, this happens: > > sage: N.rescale_col(2,i/2) > --------------------------------------------------------------------------- > <type 'exceptions.TypeError'> Traceback (most recent call > last) > <snip> > <type 'exceptions.TypeError'>: unable to convert I/2 to a rational > > I certainly have no problem with matrices starting off as rational > ones - a great idea! But it doesn't directly affect this sort of > issue - one could still start with a matrix over ZZ and then want to > multiply it later on by 1/2 without using change_ring(). Yep, this is orthogonal. You're just suggesting that scale_row be improved. > > What I am wondering is whether throwing an exception of TypeError > under the current code should be replaced by a try statement first > attempting N.changering(??) . The problem is I have no idea what to > use for ??, because unfortunately i/2 lives in Symbolic Ring, not in > CC, so I can't just put in ??=parent(i/2). The Sequence constructor is the canonical answer to this question. Given any list v of Sage object it will find a canonical place to put them all: sage: v = [3, I/2] sage: w = Sequence(v) sage: w [3, I/2] sage: w.universe() Symbolic Ring > It would sort of be beside > of the point of making Sage easier to use in the linear algebra > classroom if we had to explicitly type CC(i/2) everytime we wanted to > use i/2. > > In any case, what "should" happen in the scaling context when scaling > by something mathematically legitimate, but not in the ring the matrix > is defined over in Sage? > > - kcrisman > > (By the way, the wrapper code is nice and well-documented, at > https://sage.math.gordon.edu/home/pub/1/) --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
