#17740 closed defect (fixed)
Division of modules by basering elements should not pass to the fraction field.
Reported by:  robertwb  Owned by:  

Priority:  major  Milestone:  sage6.5 
Component:  coercion  Keywords:  
Cc:  Merged in:  
Authors:  Robert Bradshaw  Reviewers:  Vincent Delecroix 
Report Upstream:  N/A  Work issues:  
Branch:  2075e2e (Commits, GitHub, GitLab)  Commit:  
Dependencies:  Stopgaps: 
Description (last modified by )
sage: cm = sage.structure.element.get_coercion_model() sage: cm.bin_op(GF(5)['x'].gen(), 7, operator.div).parent() Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5
The problem is that we are not finding the inverse because we are passing to the fraction field of ZZ before coercing to GF(5).
Change History (33)
comment:1 Changed 7 years ago by
 Description modified (diff)
comment:2 Changed 7 years ago by
 Branch set to u/robertwb/coercediv
comment:3 Changed 7 years ago by
 Commit set to 6a507b79f14c7db4f28ac841996cc2ef3d1ba71d
comment:4 Changed 7 years ago by
 Status changed from new to needs_review
It was probably added because coercion simply didn't used to do the right thing. I've filed #17741 about removing the redundant div which may uncover surprises.
comment:5 Changed 7 years ago by
My main concern is that your solution ignore iteration
sage: cm.get_action(GF(5)['x']['y'], ZZ, operator.div) Right inverse action by Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5 on Univariate Polynomial Ring in y over Univariate Polynomial Ring in x over Finite Field of size 5 with precomposition on right by Composite map: From: Integer Ring To: Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5 Defn: Natural morphism: From: Integer Ring To: Finite Field of size 5 then Polynomial base injection morphism: From: Finite Field of size 5 To: Univariate Polynomial Ring in x over Finite Field of size 5 then Ring Coercion morphism: From: Univariate Polynomial Ring in x over Finite Field of size 5 To: Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5
I think that GF(5)['x,y']
and GF(5)['x']['y']
should behave similarly.
Vincent
comment:6 Changed 7 years ago by
Yes, I've actually been thinking about that as well, and I'm not sure exactly how best to handle this. GF(5)x?y? is a GF(5)module but represented as a GF(5)x?module. Or, put otherwise, (most) elements of ZZ have an inverse in GF(5); we want to take the most conservative inverse possible.
I used to be very against partial coercions like QQ > GF(p), but I'm not as sure anymore.
comment:7 Changed 7 years ago by
Note that this behavior is not new
sage: parent(GF(5)['x']['y'].gen() / 2) Univariate Polynomial Ring in y over Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5
More generally, given an Rmodule M and an element in R0 such that R0 > R1 > ... > Rn > R, where along this chain should the multiplicative inverse be calculated? Maybe the first (last?) Ri that is already field? Starts to feel a bit adhoc...
comment:8 Changed 7 years ago by
 Commit changed from 6a507b79f14c7db4f28ac841996cc2ef3d1ba71d to 1e88c72687b89713e3ca79e435c509c0d99bece2
comment:9 Changed 7 years ago by
OK, I've implemented the above behavior.
comment:10 Changed 7 years ago by
 Branch changed from u/robertwb/coercediv to u/vdelecroix/17440
 Commit changed from 1e88c72687b89713e3ca79e435c509c0d99bece2 to 96c1a0348964c4edbd42f3fc52e93b9e76f26156
 Status changed from needs_review to needs_info
I wrote trivial commits while I was reading the code. One thing to mention: in the documentation you should use :trac:`17440`
instead of #17440
.
One last question: in coerce.pyx
, you wrote
try: return ~right_mul except TypeError: # action may not be invertible self._record_exception()
Shouldn't we catch only CoercionException
?
New commits:
a60134c  trac #17740: review 1 (documentation)

728811d  trac #17740: review 2 (clean Errors)

96c1a03  trac #17740: review 3 (less in try/except block)

comment:11 followup: ↓ 12 Changed 7 years ago by
 Status changed from needs_info to needs_work
And something is broken:
sage t schemes/toric/divisor.py ********************************************************************** File "schemes/toric/divisor.py", line 35, in sage.schemes.toric.divisor Failed example: (1/2)*Dx + Dy/3  Dz Exception raised: Traceback (most recent call last): ... TypeError: unsupported operand parent(s) for '/': 'Group of toric ZZWeil divisors on 2d CPRFano toric variety covered by 6 affine patches' and 'Integer Ring' ********************************************************************** File "schemes/toric/divisor.py", line 40, in sage.schemes.toric.divisor Failed example: (Dx/2).parent() Exception raised: Traceback (most recent call last): ... TypeError: unsupported operand parent(s) for '/': 'Group of toric ZZWeil divisors on 2d CPRFano toric variety covered by 6 affine patches' and 'Integer Ring' ********************************************************************** File "schemes/toric/divisor.py", line 866, in sage.schemes.toric.divisor.ToricDivisor_generic.is_Weil Failed example: (D/2).is_Weil() Exception raised: Traceback (most recent call last): ... TypeError: unsupported operand parent(s) for '/': 'Group of toric ZZWeil divisors on 2d CPRFano toric variety covered by 3 affine patches' and 'Integer Ring' ********************************************************************** File "schemes/toric/divisor.py", line 893, in sage.schemes.toric.divisor.ToricDivisor_generic.is_QQ_Weil Failed example: (D/2).is_QQ_Weil() Exception raised: Traceback (most recent call last): ... TypeError: unsupported operand parent(s) for '/': 'Group of toric ZZWeil divisors on 2d CPRFano toric variety covered by 3 affine patches' and 'Integer Ring' ********************************************************************** 3 items had failures: 2 of 42 in sage.schemes.toric.divisor 1 of 5 in sage.schemes.toric.divisor.ToricDivisor_generic.is_QQ_Weil 1 of 5 in sage.schemes.toric.divisor.ToricDivisor_generic.is_Weil [363 tests, 4 failures, 2.53 s]  sage t schemes/toric/divisor.py # 4 doctests failed 
comment:12 in reply to: ↑ 11 Changed 7 years ago by
Replying to vdelecroix:
And something is broken:
sage t schemes/toric/divisor.py
The problematic line is module_action = type(self)(K, self.codomain())
in coerce_action.pyx
sage: dP6 = toric_varieties.dP6() sage: Dx,Du,Dy,Dv,Dz,Dw = dP6.toric_divisor_group().gens() sage: A = RightModuleAction(ZZ, Dx.parent()) sage: ~A Traceback (most recent call last): ... 472 print "self.codomain = {}".format(self.codomain()) > 473 module_action = type(self)(K, self.codomain()) 474 connecting = K.coerce_map_from(self.G) ... CoercionException: No common base
comment:13 Changed 7 years ago by
 Branch changed from u/vdelecroix/17440 to u/robertwb/17440
comment:14 Changed 7 years ago by
 Commit changed from 96c1a0348964c4edbd42f3fc52e93b9e76f26156 to 2cb51c095e0e3375dead95c194febd5873ba5e06
Fixed these failing tests.
Also, no, we don't want to only catch CoercionException
there.
New commits:
2cb51c0  Reintroduce action of fraction field as fallback for division action.

comment:15 Changed 7 years ago by
Still some failing doctests... (the last one only concerns the more recent 65.rc0)
File rings/quotient_ring_element.py
line 360, in sage.rings.quotient_ring_element.QuotientRingElement._div_ Failed example: 1/cuberoot Exception raised: Traceback (most recent call last): ... TypeError: self must be an integral domain. ********************************************************************** line 362, in sage.rings.quotient_ring_element.QuotientRingElement._div_ Failed example: 1/a Exception raised: Traceback (most recent call last): ... TypeError: self must be an integral domain. ********************************************************************** File "src/sage/rings/quotient_ring_element.py", line 370, in sage.rings.quotient_ring_element.QuotientRingElement._div_ Failed example: 1 / S(x1 + x2) Expected: Traceback (most recent call last): ... ArithmeticError: Division failed. The numerator is not a multiple of the denominator. Got: Traceback (most recent call last): ... TypeError: self must be an integral domain.
File rings/padics/local_generic_element.pyx
line 63, in sage.rings.padics.local_generic_element.LocalGenericElement._div_ Failed example: R = Zp(7, 4, 'fixedmod'); 1/R(7) Expected: Traceback (most recent call last): ... ValueError: cannot invert nonunit Got: Traceback (most recent call last): ... TypeError: This implementation of the padic ring does not support fields of fractions.
File rings/padics/padic_ZZ_pX_FM_element.pyx
line 88, in sage.rings.padics.padic_ZZ_pX_FM_element Failed example: 1/a Exception raised: Traceback (most recent call last): ... TypeError: This implementation of the padic ring does not support fields of fractions. ********************************************************************** line 875, in sage.rings.padics.padic_ZZ_pX_FM_element.pAdicZZpXFMElement._div_ Failed example: 1 / W(14) == ~W(14) Exception raised: Traceback (most recent call last): ... TypeError: This implementation of the padic ring does not support fields of fractions. ********************************************************************** line 877, in sage.rings.padics.padic_ZZ_pX_FM_element.pAdicZZpXFMElement._div_ Failed example: 1 / w Expected: Traceback (most recent call last): ... ValueError: cannot invert nonunit Got: Traceback (most recent call last): ... TypeError: This implementation of the padic ring does not support fields of fractions. ********************************************************************** line 885, in sage.rings.padics.padic_ZZ_pX_FM_element.pAdicZZpXFMElement._div_ Failed example: 1/(t+t^2) Exception raised: Traceback (most recent call last): ... TypeError: This implementation of the padic ring does not support fields of fraction.
In modular/modform_hecketriangle/graded_ring_element.py
:
sage t long src/sage/modular/modform_hecketriangle/graded_ring_element.py ********************************************************************** line 887, in sage.modular.modform_hecketriangle.graded_ring_element.FormsRingElement._div_ Failed example: ((E4.as_ring_element())^(2)).parent() == (E4^(2)).parent() Exception raised: Traceback (most recent call last): ... NotImplementedError: No way to prove that ModularFormsRing(n=8) over Integer Ring is an integral domain! ********************************************************************** line 889, in sage.modular.modform_hecketriangle.graded_ring_element.FormsRingElement._div_ Failed example: (MR(x)^(3)).parent() Exception raised: Traceback (most recent call last): ... NotImplementedError: No way to prove that QuasiMeromorphicModularFormsRing(n=8) over Integer Ring is an integral domain!
comment:16 Changed 7 years ago by
 Branch changed from u/robertwb/17440 to u/vdelecroix/17740
 Commit changed from 2cb51c095e0e3375dead95c194febd5873ba5e06 to d1fc166516e7574fceda32a828402c31586bed01
comment:17 Changed 7 years ago by
 Status changed from needs_work to needs_review
comment:18 Changed 7 years ago by
 Reviewers set to Vincent Delecroix
comment:19 Changed 7 years ago by
 Branch changed from u/vdelecroix/17740 to u/robertwb/17740
comment:20 Changed 7 years ago by
 Commit changed from d1fc166516e7574fceda32a828402c31586bed01 to bff474b33f681de5d51ebf1be5c95dc7ac7f2f03
I don't think self is the right thing to return by default, but here's a similar fix.
New commits:
bff474b  Better _pseudo_fraction_field default implementation.

comment:21 Changed 7 years ago by
 Status changed from needs_review to positive_review
comment:22 Changed 7 years ago by
 Status changed from positive_review to needs_info
Now, I am not sure anymore that your solution is better. The implementation of division_parent
tries to execute ~parent.one()
. But the default implementation of __invert__
of an element x
in sage.structure.element
is precisely to call 1/x
(and soonly x.parent().one()/x
with #17692). Hence using division_parent
should lead to some infinite recursions that we curiously do not see here. No?
EDIT: This is fine, because in x.parent().one()/x
the numerator and denominator have the same type... and so no coercion is involved and __div__
is called directly.
comment:23 Changed 7 years ago by
 Status changed from needs_info to positive_review
comment:24 Changed 7 years ago by
Yes, indeed this should go in with #17692 to prevent possible infinite recursion. Thanks for the review!
comment:25 Changed 7 years ago by
 Status changed from positive_review to needs_work
Merge conflict, possibly #17694
comment:26 Changed 7 years ago by
 Branch changed from u/robertwb/17740 to u/vdelecroix/17740
 Commit changed from bff474b33f681de5d51ebf1be5c95dc7ac7f2f03 to 52cc62d92f8bed38aab6e2a9a8cfb785493a69bf
 Status changed from needs_work to needs_review
Hi Robert,
There was only a trivial conflict in sage/rings/ring.pyx
. I did merge with sage6.6.beta0 in my last commit. I let you set the positive review if this is fine.
Vincent
New commits:
52cc62d  trac #17740: merge sage6.6.beta0

comment:27 Changed 7 years ago by
 Commit changed from 52cc62d92f8bed38aab6e2a9a8cfb785493a69bf to 9c970ae1c2ef9516f61a3c6cc737e6d0c644565e
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
9c970ae  trac #17740: merge sage6.6.beta1

comment:28 Changed 7 years ago by
 Status changed from needs_review to positive_review
All long tests pass. Put back in positive review.
comment:29 Changed 7 years ago by
 Status changed from positive_review to needs_work
I'm getting this on OSX:
sage t long src/sage/structure/coerce_actions.pyx ********************************************************************** File "src/sage/structure/coerce_actions.pyx", line 419, in sage.structure.coerce_actions.ModuleAction.__invert__ Failed example: A = ~RightModuleAction(ZZ, GF(5)['x']); A Exception raised: Traceback (most recent call last): File "/Users/buildslavesage/slave/sage_git/build/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 488, in _run self.compile_and_execute(example, compiler, test.globs) File "/Users/buildslavesage/slave/sage_git/build/local/lib/python2.7/sitepackages/sage/doctest/forker.py", line 850, in compile_and_execute exec(compiled, globs) File "<doctest sage.structure.coerce_actions.ModuleAction.__invert__[10]>", line 1, in <module> A = ~RightModuleAction(ZZ, GF(Integer(5))['x']); A File "sage/structure/coerce_actions.pyx", line 464, in sage.structure.coerce_actions.ModuleAction.__invert__ (build/cythonized/sage/structure/coerce_actions.c:7385) module_action = type(self)(K, self.codomain()) File "sage/structure/coerce_actions.pyx", line 376, in sage.structure.coerce_actions.ModuleAction.codomain (build/cythonized/sage/structure/coerce_actions.c:6711) return self.underlying_set() File "sage/categories/action.pyx", line 186, in sage.categories.action.Action.underlying_set (build/cythonized/sage/categories/action.c:4087) raise RuntimeError, "This action acted on a set that became garbage collected" RuntimeError: This action acted on a set that became garbage collected ********************************************************************** File "src/sage/structure/coerce_actions.pyx", line 424, in sage.structure.coerce_actions.ModuleAction.__invert__ Failed example: A(x, 2) Expected: 3*x Got: 1/2*x ********************************************************************** 1 item had failures: 2 of 15 in sage.structure.coerce_actions.ModuleAction.__invert__ [90 tests, 2 failures, 0.47 s]
In all these doctests you need to hold domain/codomain explicitly alive.
comment:30 Changed 7 years ago by
 Commit changed from 9c970ae1c2ef9516f61a3c6cc737e6d0c644565e to 2075e2e68f6e6fc981096948ad4ffc61c47cfa46
Branch pushed to git repo; I updated commit sha1. New commits:
2075e2e  trac #17740: avoid parent deaths

comment:31 Changed 7 years ago by
 Status changed from needs_work to positive_review
Right. We should not kill our parents ;)
It is strange that I did not get these in the first place... All doctest pass.
Vincent
comment:32 Changed 7 years ago by
 Branch changed from u/vdelecroix/17740 to 2075e2e68f6e6fc981096948ad4ffc61c47cfa46
 Resolution set to fixed
 Status changed from positive_review to closed
comment:33 Changed 7 years ago by
 Commit 2075e2e68f6e6fc981096948ad4ffc61c47cfa46 deleted
Thanks for following up on this. Looks good to me.
Can we also address here why asking the coercion system to do this operation does not lead to the same result as when we just do the computation?
There may be good reasons for this (performance?) so I'm not immediately suggesting that we change the code to use the same path in both cases, but we should document that and why we're not.
New commits:
Better inversion of module actions for correct division coercions.