#16453: Cythonize quiver paths
-------------------------------------+-------------------------------------
Reporter: SimonKing | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Simon King | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/SimonKing/cythonize_quiver_paths | f60c7c1e2dafa1930ef23319d8d3917003ad7c9a
Dependencies: #15820 | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by SimonKing):
* status: needs_review => needs_work
Comment:
Needs work. I just found the following totally wrong answer of
`poincare_series()`:
{{{
sage: S = DiGraph({0:{1:['a'], 2:['b']}, 1:{0:['c'], 1:['d']},
2:{0:['e'],2:['f']}}).path_semigroup()
sage: S.inject_variables()
Defining e_0, e_1, e_2, a, b, c, d, e, f
sage: S.poincare_series((e*b, b*f, f*f, c*a, d*c, a*d, f*e, d*d*d*d,
a*c*b*e, c*b*e*a*c, b*e*a*c*b))[0,0]
(948568795032094272909893509191171341133987714380927500611236528192824358010355712*t^6
-
474284397516047136454946754595585670566993857190463750305618264096412179005177856*t^5
+
1422853192548141409364840263786757011700981571571391250916854792289236537015533568*t^4
-
1422853192548141409364840263786757011700981571571391250916854792289236537015533568*t^3
+
1897137590064188545819787018382342682267975428761855001222473056385648716020711424*t^2
-
948568795032094272909893509191171341133987714380927500611236528192824358010355712*t
+
474284397516047136454946754595585670566993857190463750305618264096412179005177856)/(-474284397516047136454946754595585670566993857190463750305618264096412179005177856*t^11
+
1422853192548141409364840263786757011700981571571391250916854792289236537015533568*t^10
-
1897137590064188545819787018382342682267975428761855001222473056385648716020711424*t^9
+
3319990782612329955184627282169099693968957000333246252139327848674885253036244992*t^8
-
2371421987580235682274733772977928352834969285952318751528091320482060895025889280*t^7
+
1897137590064188545819787018382342682267975428761855001222473056385648716020711424*t^6
+
2371421987580235682274733772977928352834969285952318751528091320482060895025889280*t^5
-
2371421987580235682274733772977928352834969285952318751528091320482060895025889280*t^4
+
1422853192548141409364840263786757011700981571571391250916854792289236537015533568*t^3
+
948568795032094272909893509191171341133987714380927500611236528192824358010355712*t^2
-
948568795032094272909893509191171341133987714380927500611236528192824358010355712*t
+
474284397516047136454946754595585670566993857190463750305618264096412179005177856)
}}}
It is correct that we have a polynomial (what we have here is obtained
from the principal 2-block of Mathieu group M11, which is finite), but of
course it it complete nonsense to have negative coefficients when we are
supposed to count paths. And the constant coefficient should just be 1
(since there is precisely one path of length zero from vertex 0 to vertex
0). I need to check the underlying maths, probably I got something wrong
there.
--
Ticket URL: <http://trac.sagemath.org/ticket/16453#comment:26>
Sage <http://www.sagemath.org>
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