is an
*abbreviation* of the name of another method should actually be the *same*
method. Anything else is hugely confusing to a user. Both the
functionalities described are, of course, useful, but giving them such
similar names has a times certainly confused me.
Francis Clarke
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Looks like a linbox problem:
sage: J = jordan_block(0, 31).change_ring(QQ)
sage: (J^2).charpoly(algorithm='generic')
x^31
sage: (J^2).charpoly(algorithm='linbox') # the default
x^16
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This (slightly fixed) output from sage -grep shows what needs to be done:
$ sage -grep -n 'def submatrix'
sage/matrix/matrix1.pyx:1810:def submatrix(self, Py_ssize_t row=0,
Py_ssize_t col=0,
Py_ssize_t nrows=-1,
Py_ssize_t ncols=-1):
this is correct. Similarly omitting unnecessary checks gives rise
to significant improvements in speed at
http://trac.sagemath.org/sage_trac/ticket/10843 (still waiting for review
after two years).
Francis Clarke
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I think you want
sage: V.direct_sum(W)
Vector space of degree 200 and dimension 2 over Rational Field
Basis matrix:
2 x 200 dense matrix over Rational Field
Francis
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hours), and make ptestlong gave rise to no failures at
all. In particular,
sage -t --long -force_lib devel/sage/sage/rings/polynomial/pbori.pyx
[7.0 s]
--
All tests passed!
Total time for all tests: 7.0 seconds
Francis Clarke
On Jul 7, 8:55 am, Francis Clarke francis.w.cla...@gmail.com wrote:
Hermite Normal Forms (HNFs) exist for matrices over Bezout
rings and are unique up to multiplication by units over PIDs.
Correction: they're unique modulo units over Euclidean domains.
Francis
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On Jul 6, 9:45 am, John Cremona john.crem...@gmail.com wrote:
I think it is too much to expect general PIDs to have unique
(canonical) echelon forms, since that would, as a special case, mean a
canonical generator for each principal ideal. Of course there are
PIDs (such as Z) where there is
On Jun 30, 2:26 am, Rob Beezer goo...@beezer.cotse.net wrote:
sage: V = GF(3)^3
sage: W = QQ^2
sage: H = Hom(V, W)
sage: m = matrix(3, 2, range(6))
sage: f = H(m)
This makes no sense at all; the function is not a homomorphism:
sage: v = [V.random_element() for i in range(2)]
sage: l =
The following article has interesting remarks on this question,
particularly pages 407--408:
\bib{MR1163629}{article}{
author={Knuth, Donald E.},
title={Two notes on notation},
journal={Amer. Math. Monthly},
volume={99},
date={1992},
number={5},
pages={403--422},
}
Among
On May 13, 5:06 pm, William Stein [EMAIL PROTECTED] wrote:
I really want to fix *every* single bug in the notebook that can be reliably
replicated (non-replicatable system-specific bugs are really hard to fix).
If you know of any please please report them.
A subtle problem with %latex cells
I've set the delay at 250, and
it's working well with both Firefox and Safari.
My setup is
Mac OS X 10.4.11
2 GHz Intel Core 2 Duo
Sage 2.10.2
Firefox 2.0.0.12
Safari 3.0.4
thanks again
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Francis Clarke
Department of Mathematics
Swansea University
Swansea
SA2 8PP
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