#15390: roots of polynomials and eigenvalues of matrices over finite fields
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: number theory | Resolution:
Keywords: sage-days55 | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues: wait for dependency
Branch: | Commit:
u/vdelecroix/15390 | 42c5808ea1a7961a9dd22de18a36f587aacc5e03
Dependencies: #14990, #16509 | Stopgaps:
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Comment (by vdelecroix):
Hey
The two things are equivalent in an algebraically closed field, right? And
from the coding point of view, it is more natural the other way around. If
you look at the part of the code which actually does the computation, I do
not see where it looks more like a factorisation rather than a computation
of roots
{{{
roots = [] # a list of pair (root,multiplicity)
for g,m in P(new_coeffs).factor():
if g.degree() == 1:
r = phi(-g.constant_coefficient())
roots.append((r,m))
else:
ll = l * g.degree()
psi = self.inclusion(l, ll)
FF, pphi = self.subfield(ll)
gg = PolynomialRing(FF, 'x')(map(psi, g))
for r,_ in gg.roots(): # note: we know that multiplicity is 1
roots.append((pphi(r),m))
}}}
If you have an alternative proposition, propose it, but I really do not
see what you mean. The only `factor` which appears above is over the field
where are defined the coefficients.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/15390#comment:23>
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