#11889: Power series exp fails uninformatively when base ring has nonzero
characteristic
-----------------------------+----------------------------------------------
   Reporter:  davidloeffler  |          Owner:  AlexGhitza
       Type:  defect         |         Status:  new       
   Priority:  trivial        |      Milestone:  sage-4.7.2
  Component:  algebra        |       Keywords:            
Work_issues:                 |       Upstream:  N/A       
   Reviewer:                 |         Author:            
     Merged:                 |   Dependencies:            
-----------------------------+----------------------------------------------
 {{{
 sage: R.<x> = GF(2)[[]]
 sage: f = x + x^2 + O(x^5)
 sage: exp(f)
 ---------------------------------------------------------------------------
 ZeroDivisionError                         Traceback (most recent call
 last)

 /home/masiao/<ipython console> in <module>()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/functions/log.pyc in __call__(self, x, coerce, hold, prec,
 dont_call_method_on_arg)
     128             return x.n(prec)
     129         return GinacFunction.__call__(self, x, coerce=coerce,
 hold=hold,
 --> 130                 dont_call_method_on_arg=dont_call_method_on_arg)
     131
     132 exp = Function_exp()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/symbolic/function.so in
 sage.symbolic.function.GinacFunction.__call__
 (sage/symbolic/function.cpp:6652)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/rings/power_series_ring_element.so in
 sage.rings.power_series_ring_element.PowerSeries.exp
 (sage/rings/power_series_ring_element.c:11024)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/rings/power_series_ring_element.so in
 sage.rings.power_series_ring_element.PowerSeries.solve_linear_de
 (sage/rings/power_series_ring_element.c:10857)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/rings/power_series_ring_element.so in
 sage.rings.power_series_ring_element._solve_linear_de
 (sage/rings/power_series_ring_element.c:12441)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/rings/power_series_ring_element.so in
 sage.rings.power_series_ring_element._solve_linear_de
 (sage/rings/power_series_ring_element.c:12656)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/rings/power_series_ring_element.so in
 sage.rings.power_series_ring_element._solve_linear_de
 (sage/rings/power_series_ring_element.c:12379)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/structure/element.so in
 sage.structure.element.RingElement.__div__
 (sage/structure/element.c:12803)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/structure/coerce.so in
 sage.structure.coerce.CoercionModel_cache_maps.bin_op
 (sage/structure/coerce.c:6436)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/site-
 packages/sage/structure/element.so in
 sage.structure.element.RingElement.__div__
 (sage/structure/element.c:12777)()

 /usr/local/sage/sage-4.7.1/local/lib/python2.6/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:19299)()

 ZeroDivisionError: Inverse does not exist.
 }}}

 There's no way of making this work in a mathematically meaningful way, but
 it could certainly be made to fail a bit more gracefully!

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11889>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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