Closed jasongrout closed 13 years ago
jasongrout
commented
13 years ago This is puzzling that this works, though:
sage: V=(SR^2).subspace_with_basis([[1,1]])
sage: v=V([sqrt(2)/2,sqrt(2)/2])
sage: parent(v)
Vector space of degree 2 and dimension 1 over Symbolic Ring
User basis matrix:
[1 1]
sage: QQ(3)*v
(3/2*sqrt(2), 3/2*sqrt(2))So apparently creating the vector manually (rather than getting it as an eigenvector of a matrix) works okay.
jasongrout
commented
13 years ago jasongrout
commented
13 years ago Tracking this down even more:
sage: V=(QQ^2).span_of_basis([[1,1]])
sage: v=V([1,1])
sage: w=sqrt(2)*v
sage: 3*w
------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component
of Sage has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run Sage under gdb with 'sage -gdb' to debug this.
Sage will now terminate (sorry).
------------------------------------------------------------
Ccing Robert B and Craig Citro, since it looks like it might be a problem in the coercion system, and maybe in how the coercion system builds a module with a user basis:
sage: V=(QQ^2).span_of_basis([[1,1]])
sage: v=V([1,1])
sage: w=v.change_ring(SR)
sage: w.parent()
Vector space of degree 2 and dimension 1 over Symbolic Ring
User basis matrix:
[1 1]
sage: 3*w
(3, 3)
sage: x=sqrt(2)*v # here the coercion system builds the parent of x
sage: x.parent() is w.parent()
False
sage: x.parent()
Vector space of degree 2 and dimension 1 over Symbolic Ring
User basis matrix:
[1 1]
sage: x.parent() == w.parent() # equivalent parents between x and w
True
sage: 3*x # but we get a segfault when multiplying x by something
------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component
of Sage has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run Sage under gdb with 'sage -gdb' to debug this.
Sage will now terminate (sorry).
------------------------------------------------------------
Also, notice that trying to get the coercion system to explain itself also segfaults:
sage: cm = sage.structure.element.get_coercion_model(); cm
<sage.structure.coerce.CoercionModel_cache_maps object at 0x101f3b6b0>
sage: sage: V=(QQ^2).span_of_basis([[1,1]])
sage: v=V([1,1])
sage: x=sqrt(2)*v
sage: cm.explain(3.parent(), x.parent())
------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component
of Sage has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run Sage under gdb with 'sage -gdb' to debug this.
Sage will now terminate (sorry).
------------------------------------------------------------
kcrisman
commented
13 years ago This works in Sage 4.4.4, and doesn't have anything to do with Pynac, as you now suspect.
sage: var('y')
y
sage: get_systems('diff(3*y,y)')
['ginac']but in your example I get
sage: get_systems('3*x')
[]Replying to @kcrisman:
This works in Sage 4.4.4, and doesn't have anything to do with Pynac
Well, yes it does. The backtrace posted above points to the error happening in Ginac.
(gdb) bt
#0 0x00007fff8294a7a2 in __dynamic_cast ()
#1 0x000000010798ffcc in is_a<GiNaC::relational> [inlined] () at /Users/grout/sage-trees/sage-4.6/local/include/pynac/basic.h:939Yes, I saw that. So why don't I get that system as being used? Maybe we are now using Ginac, after the 4.6, and shouldn't be, due to coercion? But I have no idea - sorry.
jasongrout
commented
13 years ago Okay, thanks to John Palmieri testing this out on various versions of Sage, I found that reverting #9502 fixes the issue. I'm CCing the author and reviewer of #9502. In short, #9502 causes a segfault with the following code:
sage: V=(QQ^2).span_of_basis([[1,1]])
sage: v=V([1,1])
sage: x=sqrt(2)*v
sage: 3*x # but we get a segfault when multiplying x by something
------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component
of Sage has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run Sage under gdb with 'sage -gdb' to debug this.
Sage will now terminate (sorry).
------------------------------------------------------------Do you guys that did #9502 know what could have caused this?
jasongrout
commented
13 years ago Now I'm CCing the author/reviewer of #9502. #9502 is causing a segfault now. Please #10250 (this ticket) for details. Do you have any idea of what is happening to cause the segfault?
novoselt
commented
13 years ago I don't, never had issues with segfaults before... I'll look into it, but I am probably not the best person to solve this problem.
vbraun
commented
13 years ago The problem seems to be that the coercion ends up calling __rmul__ (which is inherited) and not _rmul_ (which is directly defined in FreeModuleElement_generic_dense:
sage: x
(sqrt(2), sqrt(2))
sage: x._rmul_(3)
(3*sqrt(2), 3*sqrt(2))
sage: x.__rmul__(3)
------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.For the record, stack backtrace:
#0 __cxxabiv1::__dynamic_cast (src_ptr=0x100000001, src_type=0x7fffd3a02f40,
dst_type=0x7fffd3a090c0, src2dst=0)
at ../../../../libstdc++-v3/libsupc++/dyncast.cc:54
#1 0x00007fffd3224803 in is_a<GiNaC::relational> (__pyx_v_left=0x428c9e0,
__pyx_v_right=0x41b9d70, __pyx_skip_dispatch=<value optimized out>)
at /home/vbraun/Sage/sage/local/include/pynac/basic.h:305
#2 is_a<GiNaC::relational> (__pyx_v_left=0x428c9e0, __pyx_v_right=0x41b9d70,
__pyx_skip_dispatch=<value optimized out>)
at /home/vbraun/Sage/sage/local/include/pynac/ex.h:939
#3 __pyx_f_4sage_8symbolic_10expression_10Expression__mul_ (
__pyx_v_left=0x428c9e0, __pyx_v_right=0x41b9d70,
__pyx_skip_dispatch=<value optimized out>)
at sage/symbolic/expression.cpp:11284
#4 0x00007fffe046a122 in __pyx_f_4sage_7modules_19free_module_element_31FreeModuleElement_generic_dense__rmul_ (__pyx_v_self=0x4289940,
__pyx_v_left=0x428c9e0, __pyx_skip_dispatch=<value optimized out>)
at sage/modules/free_module_element.c:15600
#5 0x00007fffe992212c in __pyx_f_4sage_9structure_14coerce_actions_16LeftModuleAction__call_ (__pyx_v_self=0x72c410, __pyx_v_g=0x428c9e0,
__pyx_v_a=0x4289940, __pyx_skip_dispatch=<value optimized out>)
at sage/structure/coerce_actions.c:5437
#6 0x00007fffe9d4e9a1 in __pyx_pf_4sage_10categories_6action_6Action_act (
__pyx_v_self=0x72c410, __pyx_args=0x412ce18, __pyx_kwds=0x0)
at sage/categories/action.c:2563
#7 0x00007ffff7c7e3b3 in PyObject_Call (func=0x737098,
arg=<value optimized out>, kw=<value optimized out>)
at Objects/abstract.c:2492
#8 0x00007fffe9927764 in __pyx_pf_4sage_9structure_14coerce_actions_12ModuleAction___init__ (__pyx_v_self=0x72c410, __pyx_args=<value optimized out>,
__pyx_kwds=<value optimized out>) at sage/structure/coerce_actions.c:5133
#9 0x00007ffff7cd9f18 in type_call (type=<value optimized out>,
args=0x412d5f0, kwds=0x0) at Objects/typeobject.c:747
#10 0x00007ffff7c7e3b3 in PyObject_Call (func=0x7fffe9b33de0,
arg=<value optimized out>, kw=<value optimized out>)
at Objects/abstract.c:2492
#11 0x00007fffe992a52c in __pyx_pf_4sage_9structure_14coerce_actions_detect_element_action (__pyx_self=<value optimized out>,
__pyx_args=<value optimized out>, __pyx_kwds=<value optimized out>)
at sage/structure/coerce_actions.c:4184
#12 0x00007ffff7c7e3b3 in PyObject_Call (func=0x1042d40,
arg=<value optimized out>, kw=<value optimized out>)
at Objects/abstract.c:2492
#13 0x00007fffeae9d34f in __pyx_f_4sage_9structure_6parent_6Parent_discover_action (__pyx_v_self=0x42d27f0, __pyx_v_S=0x121e8e0, __pyx_v_op=0x1042d40,
__pyx_v_self_on_left=0) at sage/structure/parent.c:14710
#14 0x00007fffeb0c5ecd in __pyx_f_4sage_9structure_10parent_old_6Parent_get_acti---Type <return> to continue, or q <return> to quit---
on_c_impl (__pyx_v_self=0x42d27f0, __pyx_v_S=<value optimized out>,
__pyx_v_op=<value optimized out>,
__pyx_v_self_on_left=<value optimized out>)
at sage/structure/parent_old.c:3254
#15 0x00007fffeb0c7441 in __pyx_pf_4sage_9structure_10parent_old_6Parent_get_action_impl (__pyx_v_self=0x42d27f0, __pyx_args=<value optimized out>,
__pyx_kwds=<value optimized out>) at sage/structure/parent_old.c:3204
#16 0x00007ffff7c7e3b3 in PyObject_Call (func=0x41abfc8,
arg=<value optimized out>, kw=<value optimized out>)
at Objects/abstract.c:2492
#17 0x00007fffeb0cdeb2 in __pyx_f_4sage_9structure_10parent_old_6Parent_get_action_c (__pyx_v_self=0x42d27f0, __pyx_v_S=0x121e8e0, __pyx_v_op=0x78a1b8,
__pyx_v_self_on_left=0, __pyx_skip_dispatch=<value optimized out>)
at sage/structure/parent_old.c:2892
#18 0x00007fffeb0c16c3 in __pyx_f_4sage_9structure_10parent_old_6Parent__get_action_ (__pyx_v_self=0x42d27f0, __pyx_v_other=0x121e8e0,
__pyx_v_op=<value optimized out>,
__pyx_v_self_on_left=<value optimized out>,
__pyx_skip_dispatch=<value optimized out>)
at sage/structure/parent_old.c:6069
#19 0x00007fffeae9ab71 in __pyx_f_4sage_9structure_6parent_6Parent_get_action (
__pyx_v_self=0x42d27f0, __pyx_v_S=0x121e8e0,
__pyx_skip_dispatch=<value optimized out>,
__pyx_optional_args=<value optimized out>) at sage/structure/parent.c:13731
#20 0x00007fffea5bf810 in __pyx_f_4sage_9structure_6coerce_24CoercionModel_cache_maps_discover_action (__pyx_v_self=0x1043350, __pyx_v_R=0x121e8e0,
__pyx_v_S=0x42d27f0, __pyx_v_op=0x78a1b8,
__pyx_skip_dispatch=<value optimized out>) at sage/structure/coerce.c:11909
#21 0x00007fffea5b2aca in __pyx_f_4sage_9structure_6coerce_24CoercionModel_cache_maps_get_action (__pyx_v_self=0x1043350, __pyx_v_R=0x121e8e0,
__pyx_v_S=0x42d27f0, __pyx_v_op=0x78a1b8,
__pyx_skip_dispatch=<value optimized out>) at sage/structure/coerce.c:10837
#22 0x00007fffea5b5417 in __pyx_f_4sage_9structure_6coerce_24CoercionModel_cache_maps_bin_op (__pyx_v_self=0x1043350, __pyx_v_x=0x3296bd0,
__pyx_v_y=0x4289c00, __pyx_v_op=0x78a1b8,
__pyx_skip_dispatch=<value optimized out>) at sage/structure/coerce.c:6080
#23 0x00007fffea7f8c8d in __pyx_pf_4sage_9structure_7element_11RingElement___mul__ (__pyx_v_left=0x3296bd0, __pyx_v_right=0x4289c00)
at sage/structure/element.c:11399
#24 0x00007ffff7c7998a in binary_op1 (v=0x3296bd0, w=0x4289c00, op_slot=16)
at Objects/abstract.c:917
#25 0x00007ffff7c7c788 in PyNumber_Multiply (v=0x3296bd0, w=0x4289c00)
at Objects/abstract.c:1188
#26 0x00007ffff7
throwflag=<value optimized out>) at Python/ceval.c:1118
#27 0x00007ffff7d2072c in PyEval_EvalCodeEx (co=0x6fabe8,
globals=<value optimized out>, locals=<value optimized out>,
args=<value optimized out>, argcount=0, kws=<value optimized out>,
kwcount=0, defs=0x0, defcount=0, closure=0x0) at Python/ceval.c:2968
#28 0x00007ffff7d20802 in PyEval_EvalCode (co=<value optimized out>,
globals=<value optimized out>, locals=<value optimized out>)
at Python/ceval.c:522
#29 0x00007ffff7d1f162 in exec_statement (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:4401
#30 PyEval_EvalFrameEx (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:1717
#31 0x00007ffff7d2072c in PyEval_EvalCodeEx (co=0xb13c60,
globals=<value optimized out>, locals=<value optimized out>,
args=<value optimized out>, argcount=2, kws=<value optimized out>,
kwcount=0, defs=0x0, defcount=0, closure=0x0) at Python/ceval.c:2968
#32 0x00007ffff7d1e8de in fast_function (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:3802
#33 call_function (f=<value optimized out>, throwflag=<value optimized out>)
at Python/ceval.c:3727
#34 PyEval_EvalFrameEx (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:2389
#35 0x00007ffff7d2072c in PyEval_EvalCodeEx (co=0xb13af8,
globals=<value optimized out>, locals=<value optimized out>,
args=<value optimized out>, argcount=3, kws=<value optimized out>,
kwcount=0, defs=0xb730f8, defcount=2, closure=0x0) at Python/ceval.c:2968
#36 0x00007ffff7d1e8de in fast_function (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:3802
#37 call_function (f=<value optimized out>, throwflag=<value optimized out>)
at Python/ceval.c:3727
#38 PyEval_EvalFrameEx (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:2389
#39 0x00007ffff7d1fa7f in fast_function (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:3792
#40 call_function (f=<value optimized out>, throwflag=<value optimized out>)
at Python/ceval.c:3727
#41 PyEval_EvalFrameEx (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:2389
#42 0x00007ffff7d2072c in PyEval_EvalCodeEx (co=0xb13300,
globals=<value optimized out>, locals=<value optimized out>,
args=<value optimized out>, argcount=2, kws=<value optimized out>,
kwcount=0, defs=0xb6c868, defcount=1, closure=0x0) at Python/ceval.c:2968
#43 0x00007ffff7d1e8de in fast_function (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:3802
#44 call_function (f=<value optimized out>, throwflag=<value optimized out>)
at Python/ceval.c:3727
#45 PyEval_EvalFrameEx (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:2389
#46 0x00007ffff7d2072c in PyEval_EvalCodeEx (co=0xb10cd8,
globals=<value optimized out>, locals=<value optimized out>,
args=<value optimized out>, argcount=2, kws=<value optimized out>,
kwcount=0, defs=0xb6c828, defcount=1, closure=0x0) at Python/ceval.c:2968
#47 0x00007ffff7d1e8de in fast_function (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:3802
#48 call_function (f=<value optimized out>, throwflag=<value optimized out>)
at Python/ceval.c:3727
#49 PyEval_EvalFrameEx (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:2389
#50 0x00007ffff7d2072c in PyEval_EvalCodeEx (co=0x931f30,
globals=<value optimized out>, locals=<value optimized out>,
args=<value optimized out>, argcount=1, kws=<value optimized out>,
kwcount=2, defs=0x93d8d8, defcount=2, closure=0x0) at Python/ceval.c:2968
#51 0x00007ffff7d1e8de in fast_function (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:3802
#52 call_function (f=<value optimized out>, throwflag=<value optimized out>)
at Python/ceval.c:3727
#53 PyEval_EvalFrameEx (f=<value optimized out>,
throwflag=<value optimized out>) at Python/ceval.c:2389
#54 0x00007ffff7d2072c in PyEval_EvalCodeEx (co=0x6da378,
globals=<value optimized out>, locals=<value optimized out>,
args=<value optimized out>, argcount=0, kws=<value optimized out>,
kwcount=0, defs=0x0, defcount=0, closure=0x0) at Python/ceval.c:2968
#55 0x00007ffff7d20802 in PyEval_EvalCode (co=<value optimized out>,
globals=<value optimized out>, locals=<value optimized out>)
at Python/ceval.c:522
#56 0x00007ffff7d42600 in run_mod (fp=0x625830,
filename=<value optimized out>, start=<value optimized out>,
globals=0x63c080, locals=0x63c080, closeit=0, flags=0x7fffffffd8b0)
at Python/pythonrun.c:1335
#57 PyRun_FileExFlags (fp=0x625830, filename=<value optimized out>,
start=<value optimized out>, globals=0x63c080, locals=0x63c080, closeit=0,
flags=0x7fffffffd8b0) at Python/pythonrun.c:1321
#58 0x00007ffff7d430cf in PyRun_SimpleFileExFlags (fp=0x625830,
filename=0x7fffffffeac3 "/home/vbraun/Sage/sage/local/bin/sage-ipython",
closeit=0, flags=0x7fffffffd8b0) at Python/pythonrun.c:931
#59 0x00007ffff7d5205b in RunStartupFile (argc=<value optimized out>,
argv=0x7fffffffd9d8) at Modules/main.c:142
#60 Py_Main (argc=<value optimized out>, argv=0x7fffffffd9d8)
at Modules/main.c:558
#61 0x000000381a81ee7d in __libc_start_main (main=0x400710 <main>, argc=2,
ubp_av
fini=<value optimized out>, rtld_fini=<value optimized out>,
stack_end=0x7fffffffd9c8) at libc-start.c:226
#62 0x0000000000400649 in _start ()No, it's deeper than that. __rmul__ should call the right coercion stuff so that _rmul_ is eventually called. So far, I've traced it down to this:
sage: p=x.parent()
sage: p.get_action(3.parent(), operator.mul,False)
------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component
of Sage has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run Sage under gdb with 'sage -gdb' to debug this.
Sage will now terminate (sorry).
------------------------------------------------------------
Actually, I think something is wrong with the parent:
sage: x.parent().an_element()
(1, 1)
sage: x.parent().an_element().__mul__(3)
(0/0, 0/0)I think that the appropriate action is not getting registered (which is a problem with the parent), leading to all sorts of weirdness as the coercion system tries to do things. It can't register the action because when it asks for the action (using the get_action method of the parent), it segfaults.
sage: v.parent().get_action(3.parent(), operator.mul, False)
Left scalar multiplication by Integer Ring on Vector space of degree 2 and dimension 1 over Rational Field
User basis matrix:
[1 1]
sage: x.parent().get_action(3.parent(), operator.mul, False)
------------------------------------------------------------
Unhandled SIGSEGV: A segmentation fault occurred in Sage.
This probably occurred because a *compiled* component
of Sage has a bug in it (typically accessing invalid memory)
or is not properly wrapped with _sig_on, _sig_off.
You might want to run Sage under gdb with 'sage -gdb' to debug this.
Sage will now terminate (sorry).
------------------------------------------------------------
Carefully looking at my patch at #9502, I found that I skipped one conversion. I posted a patch that restores it and gives
sage: sage: V=(QQ^2).span_of_basis([[1,1]])
sage: sage: v=V([1,1])
sage: sage: w=sqrt(2)*v
sage: sage: 3*w
(3*sqrt(2), 3*sqrt(2))But I don't yet understand why the single conversion is not good enough.
jasongrout
commented
13 years ago Yeah, I just found that if you add
if check:
V = ambient.vector_space()
basis = [V(x) for x in basis]right before the if check block, things work. Notice that V is ambient.vector_space() in this case, rather than ambient.ambient_vector_space(). I bet that's the difference.
jasongrout
commented
13 years ago We should also add a doctest to the patch.
novoselt
commented
13 years ago Replying to @jasongrout:
We should also add a doctest to the patch.
I am not sure that this is a satisfactory solution - why converting x into the ambient vector space is not the same as converting it into the spanned vector space and then into the ambient vector space?
jasongrout
commented
13 years ago I think I see the problem. Here is the code in question:
if check:
V = ambient.ambient_vector_space()
for i in range(len(basis)):
x = basis[i]
if x not in V:
try:
basis[i] = V(x)
except TypeError:
raise TypeError("each element of basis must be in "
"the ambient vector space")Notice that a basis element is only converted to V if it's not already in V. The problem is that the test "x in V" may succeed, even if x is not a vector in V. In this case, when you try to construct a basis vector for SR2, you're handed the vector (1,1) as a rational vector. The test "x not in V" fails, since the rational vector (1,1) is in V. So it is put in as a basis vector. You need the initial conversion to first convert vectors to the same type of vectors as live in V, because you need those basis elements to actually be vectors with parent SR2.
I.e., we are handed a basis vector in QQ2, and we fail to convert it to a vector in SR2 because the if statement fails:
sage: (QQ^2)([1,1]) not in (SR^2)
FalseThe initial conversion using ambient.ambient_vector_space is to ensure that the vectors are actually vectors in SR2 (in this case).
novoselt
commented
13 years ago Ah, now I see. Thank you for the clarification, I'll write a proper patch and post it shortly.
novoselt
commented
13 years ago Attachment: trac_10250_fix_conversion_in_submodule_constructor.patch.gz
Apply this patch only.
novoselt
commented
13 years ago Author: Andrey Novoseltsev
novoselt
commented
13 years ago Instead of adding previously removed code I removed some more, now it works and is easier to understand ;-) Didn't run full library tests yet but will do it now and report if there are any issues.
jasongrout
commented
13 years ago Reviewer: Jason Grout
jasongrout
commented
13 years ago I think the new patch looks correct. Thanks for your work on this!
jasongrout
commented
13 years ago Tests pass in the modules/ directory. So if tests pass on the full test suite, please set this to positive review.
Thanks again!
novoselt
commented
13 years ago There will be some delay, as sage.math gets out of memory (not because of this patch ;-))
novoselt
commented
13 years ago OK, all long tests pass on mod.math, so I am switching it to "positive review."
jasongrout
commented
13 years ago Changed author from Andrey Novoseltsev to Andrey Novoseltsev, Jason Grout
jasongrout
commented
13 years ago I think we both came up with the solution independently and worked with each other on authoring and checking each other on this, so I'm putting both of us as authors and reviewers (with Andrey as the primary author and me as the primary reviewer).
jasongrout
commented
13 years ago Changed reviewer from Jason Grout to Jason Grout, Andrey Novoseltsev
jdemeyer
commented
13 years ago Merged: sage-4.6.1.alpha2
This code worked in Sage 4.5.2. I just realized that it now gives a segfault in 4.6. Does anyone know what is going on?
and then:
but here's the problem:
Here is a backtrace using sage -gdb, which indicates a problem in ginac or pynac.
CC: @burcin @rbeezer @craigcitro @robertwb @novoselt @vbraun
Component: linear algebra
Author: Andrey Novoseltsev, Jason Grout
Reviewer: Jason Grout, Andrey Novoseltsev
Merged: sage-4.6.1.alpha2
Issue created by migration from https://trac.sagemath.org/ticket/10250