#10563: improve jordan_form over univariate rational expressions
------------------------------+---------------------------------------------
Reporter: zimmerma | Owner: jason, was
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.6.1
Component: linear algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
------------------------------+---------------------------------------------
Comment(by rbeezer):
Even with a quick-hacked `.is_finite()` method, this still fails. Getting
eigenvalues over an exact ring requires factoring or root-finding, neither
of which seems to be implemented over this fraction field. The following
uses the same matrix `A` as above, but with the finiteness check added in:
{{{
sage: A.jordan_form()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call
last)
/home/sage/sage-4.6.1.rc1/devel/sage-main/<ipython console> in <module>()
/sage/sage-4.6.1.rc1/local/lib/python2.6/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.jordan_form
(sage/matrix/matrix2.c:32626)()
/sage/sage-4.6.1.rc1/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial.roots
(sage/rings/polynomial/polynomial_element.c:31330)()
NotImplementedError: root finding for this polynomial not implemented
sage: A.eigenvalues()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call
last)
/home/sage/sage-4.6.1.rc1/devel/sage-main/<ipython console> in <module>()
/sage/sage-4.6.1.rc1/local/lib/python2.6/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.eigenvalues
(sage/matrix/matrix2.c:22130)()
/sage/sage-4.6.1.rc1/local/lib/python2.6/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.fcp
(sage/matrix/matrix2.c:10516)()
/sage/sage-4.6.1.rc1/local/lib/python2.6/site-
packages/sage/rings/polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial.factor
(sage/rings/polynomial/polynomial_element.c:23007)()
NotImplementedError:
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10563#comment:2>
Sage <http://www.sagemath.org>
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