#14789: Implement hyperplane arrangements
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Reporter: kcrisman | Owner: sage-combinat
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
---------------------------------+-----------------------------
Changes (by dimpase):
* status: needs_review => needs_info
Comment:
This looks like a bug in `num_regions()`:
(stumbled upon this example in a large set of 2d arrangements)
{{{
sage: a=HyperplaneArrangement([[1, 106, 106266],[83, 101, 157866],[111,
110, 186150], [453, 221, 532686], [407, 237, 516882],
[55, 32, 75620], [221, 114, 289346], [452, 115, 474217], [406, 131,
453521], [28, 9, 32446], [287, 19, 271774], [241, 35, 244022],
[231, 1, 210984], [185, 17, 181508], [23, -8, 16609]])
sage: a.num_regions()
---------------------------------------------------------------------------
ValueError Traceback (most recent call
last)
<ipython-input-3-cf364604935f> in <module>()
----> 1 a.num_regions()
/home/dima/sage/sage-5.12.beta4/local/lib/python2.7/site-
packages/sage/geometry/hyperplane_arrangement.pyc in num_regions(self)
2283 if self.base_field().characteristic() != 0:
2284 raise TypeError('base field must have characteristic
zero')
-> 2285 return (-1)**self._dim*self.characteristic_polynomial(-1)
2286
2287 def num_hyperplanes(self):
/home/dima/sage/sage-5.12.beta4/local/lib/python2.7/site-
packages/sage/geometry/hyperplane_arrangement.pyc in
characteristic_polynomial(self, a)
2190 return self._characteristic_polynomial
2191 else:
-> 2192 return self._characteristic_polynomial.subs(x=a)
2193
2194 def poincare_polynomial(self, a=None):
[...]
/home/dima/sage/sage-5.12.beta4/local/lib/python2.7/site-
packages/sage/geometry/hyperplane_arrangement.pyc in restriction(self, H)
3003 for T in new_hyperplanes:
3004 basis = T.linear_part().matrix()
-> 3005 p = H._isomorphism_with_Kn(T.point())
3006 if basis.nrows() == 0:
3007 eqn = [1] + list(p)
/home/dima/sage/sage-5.12.beta4/local/lib/python2.7/site-
packages/sage/geometry/hyperplane_arrangement.pyc in
_isomorphism_with_Kn(self, v)
813 q = q.apply_map(lambda x: QQ(round(RR(x),2)))
814 u = q*G # u is the approximately orthonormalized W
--> 815 return u.solve_left(v-self.point())
816 else: # finite field
817 p = self.point()
/home/dima/sage/sage-5.12.beta4/local/lib/python2.7/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.solve_left
(sage/matrix/matrix2.c:4386)()
/home/dima/sage/sage-5.12.beta4/local/lib/python2.7/site-
packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.solve_right
(sage/matrix/matrix2.c:5242)()
/home/dima/sage/sage-5.12.beta4/local/lib/python2.7/site-
packages/sage/matrix/matrix2.so in
sage.matrix.matrix2.Matrix._solve_right_general
(sage/matrix/matrix2.c:6182)()
ValueError: matrix equation has no solutions
sage:
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/14789#comment:33>
Sage <http://www.sagemath.org>
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