I've tackled #1 on my original list, the subject of the most
discussion here. Found a variety of bugs in the process - caching
mistakes and the problem with matrices over QQbar discussed elsewhere.
My approach to eigenspaces and Galois conjugates was to introduce a
"format" keyword with possible
On Jun 24, 11:48 am, Rob Beezer wrote:
> I am just now about to implement optionally promoting a QQ matrix to a
> QQbar matrix when the eigenvalues lie outside QQ, to obtain an
> alternate format for output, as described above. I don't think there
> will be any disagreement with making that avail
On Fri, Jun 24, 2011 at 7:48 PM, Rob Beezer wrote:
> Hi Gonzalo,
>
> Thanks for your comments.
>
> On Jun 24, 8:06 am, Gonzalo Tornaria wrote:
>> What's wrong with:
>
> Nothing - except there are no vector spaces in sight. I'd like to
> retain the exposure to vector spaces (eigenspaces) without
Hi Gonzalo,
Thanks for your comments.
On Jun 24, 8:06 am, Gonzalo Tornaria wrote:
> What's wrong with:
Nothing - except there are no vector spaces in sight. I'd like to
retain the exposure to vector spaces (eigenspaces) without going as
far as Galois theory. They are a nice lead-in to invaria
On Thu, Jun 23, 2011 at 4:49 PM, Rob Beezer wrote:
> Proposal: For matrices over QQ (or implicitly ZZ) with eigenvalues
> outside QQ, make the default output like the second example above,
> while retaining the current output as optional behavior via a keyword.
What's wrong with:
sage: B = matr
On 6/23/11 2:49 PM, Rob Beezer wrote:
Proposal: For matrices over QQ (or implicitly ZZ) with eigenvalues
outside QQ, make the default output like the second example above,
while retaining the current output as optional behavior via a keyword.
I'd be okay with that. So +epsilon. Or maybe +2*e
On Jun 23, 4:37 am, Dima Pasechnik wrote:
> Don't they at least know about complex numbers?!
> Or are we talking about some dark ages situation when complex numbers
> were considered
> a heresy? :–)
> I don't thing Sage should suffer from bad decisions made by designers
> of stupidifying curricula
> Given that we talk about
> A = matrix([[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]]) # no field
> explicitly specified
> do you suggest that Sage should restrict itself to eigenvalues in Z,
> which is the base ring of A?
> Do you suggest that Sage should check whether we create a proper
> extensi
>
> > > Dima
>
> > If you are talking about vector spaces over a field, what makes sense
> > is to consider only the eigenvalues that lie in that field. If you
> > talk about plain matrices, that's another stuff (the same matrix may
> > represent an endomorphism of different vector spaces). But con
On Jun 23, 5:35 pm, mmarco wrote:
> > Over R? Over C?
> > From my limited experience in tutoring linear algebra to undergrads, I
> > only saw confusion when
> > eigenvalues were required to be in R.
> > I would never go for this in any class I teach myself; I would always
> > say that we allow a
> Over R? Over C?
> From my limited experience in tutoring linear algebra to undergrads, I
> only saw confusion when
> eigenvalues were required to be in R.
> I would never go for this in any class I teach myself; I would always
> say that we allow any root of
> det(A-xI) to occur, not only real o
On Jun 22, 4:44 pm, John H Palmieri wrote:
> On Wednesday, June 22, 2011 7:37:11 AM UTC-7, Dima Pasechnik wrote:
>
> > On Jun 21, 9:59 pm, Rob Beezer wrote:
> > > I think I have one more big push left in me as I try to tidy up linear
> > > algebra in Sage to make it even more useful for student
Thanks, Dima, John, mmarco and Jason, for the very helpful comments.
Dima - had not thought about using QQbar! That pretty much gives the
output I would like to have as the default, other than the reference
to the "Algebraic Field" in the output. John sees my dilemma
exactly. The less I have to
On 6/21/11 3:59 PM, Rob Beezer wrote:
1. Eigenspaces
sage: A = matrix(QQ, [[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]])
sage: A.eigenspaces_right()
[
(a0, Vector space of degree 4 and dimension 2 over Number Field in a0
with defining polynomial x^2 + 1
User basis matrix:
[ 1 -a0 0 0]
[ 0
On Wednesday, June 22, 2011 7:37:11 AM UTC-7, Dima Pasechnik wrote:
>
>
>
> On Jun 21, 9:59 pm, Rob Beezer wrote:
> > I think I have one more big push left in me as I try to tidy up linear
> > algebra in Sage to make it even more useful for students studying the
> > subject for the first time
On Jun 21, 9:59 pm, Rob Beezer wrote:
> I think I have one more big push left in me as I try to tidy up linear
> algebra in Sage to make it even more useful for students studying the
> subject for the first time. Eigen-stuff is on my radar. Some
> behaviors that I find problematic, most vexing
I faced that kind of decissions when i implemented the eigen-stuff
for endomorphisms (see ticket 8974).
My opinion was to stick to the base field, and only look for
extensions when directly requested. David Loefler argued that, for
consistency reasons, it would be preferable to continue with the s
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