#11457: Witt Vectors
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Reporter: tdupu | Owner: roed
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.7
Component: padics | Resolution:
Keywords: witt vectors, padic, rings | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Taylor Dupuy, David Roe | Merged in:
Dependencies: | Stopgaps:
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Comment (by tdupu):
There is a problem in the division by p in characteristic p.
{{{
sage: a = pWittElement({0:GF(3)(1), 1:GF(3)(2), 2:GF(3)(2)}, Wp)
sage: Wp=pWittVectors(GF(3),3)
sage: a = pWittElement({0:GF(3)(1), 1:GF(3)(2), 2:GF(3)(2)}, Wp)
sage: a^2 + a
---------------------------------------------------------------------------
ZeroDivisionError Traceback (most recent call
last)
/home/tdupu/sage-5.6/devel/sage-oms/<ipython console> in <module>()
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__pow__
(sage/structure/element.c:14627)()
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.generic_power_c (sage/structure/element.c:26200)()
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__mul__
(sage/structure/element.c:14096)()
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement._mul_
(sage/structure/element.c:14222)()
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/rings/padics/witt.pyc in _mul_(self, other)
219 a = self.dict
220 b = other.dict
--> 221 return C(wittprod(self.p,a,b), self.parent() )
222
223 def frob(self):
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/rings/padics/witt.pyc in wittprod(p, x, y)
116 prod[0] = x[0]*y[0]
117 for j in range(1,m):
--> 118 prod[j] = ( witt(p,j,x)*witt(p,j,y) -
witt(p,j-1,frob(p,prod)) )/p**j
119 return prod
120
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__div__
(sage/structure/element.c:14855)()
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/structure/coerce.so in
sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:6832)()
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/structure/element.so in
sage.structure.element.RingElement.__div__
(sage/structure/element.c:14834)()
/home/tdupu/sage-5.6/local/lib/python2.7/site-
packages/sage/rings/finite_rings/integer_mod.so in
sage.rings.finite_rings.integer_mod.IntegerMod_int._div_
(sage/rings/finite_rings/integer_mod.c:21514)()
ZeroDivisionError: Inverse does not exist.
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11457#comment:4>
Sage <http://www.sagemath.org>
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