I have sent a patch to ticket 8974 that implements this feature.
http://trac.sagemath.org/sage_trac/ticket/8974
It is mixed with the implementation of this functions for
endomorphisms. I hope thats not a problem.
Miguel.
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Reading again this discusion i have noticed that eigenspaces behaviour
is not what i expected:
sage: M=matrix(QQ,[[1,2],[3,4]])
sage: M.eigenspaces()
[
(a0, Vector space of degree 2 and dimension 1 over Number Field in a0
with defining polynomial x^2 - 5*x - 2
User basis matrix:
[ 1 1/3*
David,
All good points.
> I don't agree that this is the most natural result for first year
> calculus or linear algebra. Many will only consider real
> solutions to be valid.
I wish I had my bookshelf of roughly thirty intro linear algebra
textbooks handy, but I'll go out on a limb and suggest
Hi,
Backwards compatibility or not, I consider this either a bad design
or a bug:
sage: M = Matrix([[1,-1],[1,0]])
sage: f = M.minimal_polynomial()
sage: f.roots()
[]
sage: M.eigenvalues()
[0.5? - 0.866025403784439?*I, 0.5? +
0.866025403784439?*I]
First of all, wh
Miguel,
Having read #8974 carefully, I could see the default for endomorphisms
going either way. My main concern is that matrices follow practice
and default to providing eigenvalues (and eigenvectors) outside the
base field. Endomorphisms could default to behave identically to
matrices, or they
On Jun 14, 5:24 pm, mmarco wrote:
> I am OK with keeping the default extend=True. But i would like it to
> be the opposite in the case of endomorphisms (i know it is not a good
> idea to have different default behaviours for matrices and
> endomorphisms, so i won't argue if its decided to keep it
I am OK with keeping the default extend=True. But i would like it to
be the opposite in the case of endomorphisms (i know it is not a good
idea to have different default behaviours for matrices and
endomorphisms, so i won't argue if its decided to keep it alwais true
as default).
My reason to pref
I am happy with that. After all:
sage: a=3
sage: a.sqrt()
sqrt(3)
works like this since the extend parameter defaults to True. Compare:
sage: a.sqrt(extend=False)
...
ValueError: square root of 3 not an integer
John
On 14 June 2010 16:24, William Stein wrote:
> On Mon, Jun 14, 2010 at 8:22 A
On Mon, Jun 14, 2010 at 8:22 AM, Rob Beezer wrote:
> On Jun 14, 6:12 am, mmarco wrote:
>> So, what do you think?
>
> Sure, but can the default remain extend = True and maintain your
> desire for correctness?
It has to. I think it would be a very bad idea to change the default
behavior, since
On Jun 14, 6:12 am, mmarco wrote:
> So, what do you think?
Sure, but can the default remain extend = True and maintain your
desire for correctness?
If a student has to read examples to get complex eigenvalues out of a
real (or rational) matrix, the utility of Sage for teacing
introductory line
I'm happy with the proposed change; as John points out, we already
have a sqrt() function that behaves similarly.
David
On Jun 14, 3:15 pm, mmarco wrote:
> On 14 jun, 15:45, John Cremona wrote:
>
> > I think that sounds a good idea; but can we call the parameter
> > "extend" and not "base_exte
On 14 jun, 15:45, John Cremona wrote:
> I think that sounds a good idea; but can we call the parameter
> "extend" and not "base_extend"? First, as that is less frightening
> for users (who will need examples to show that for a real matrix, if
> you want complex eigenvalues you have to ask for
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