Opened 10 years ago
Closed 10 years ago
#1232 closed defect (fixed)
[with patch, with 2 positive reviews] bug in modular symbols over GF(2)
Reported by: | AlexGhitza | Owned by: | craigcitro |
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Priority: | major | Milestone: | sage-2.9 |
Component: | modular forms | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Running
ModularSymbols(1,6,0,GF(2)).simple_factors()
results in
--------------------------------------------------------------------------- <type 'exceptions.AssertionError'> Traceback (most recent call last) /home/ghitza/sage/<ipython console> in <module>() /opt/sage/local/lib/python2.5/site-packages/sage/modular/modsym/space.py in simple_factors(self) 996 ASSUMPTION: self is a module over the anemic Hecke algebra. 997 """ --> 998 return [S for S,_ in self.factorization()] 999 1000 def star_eigenvalues(self): /opt/sage/local/lib/python2.5/site-packages/sage/modular/modsym/ambient.py in factorization(self) 1064 D = sage.structure.all.Factorization(D, cr=True) 1065 assert r == s, "bug in factorization -- self has dimension %s, but sum of dimensions of factors is %s\n%s"%( -> 1066 r, s, D) 1067 self._factorization = D 1068 return self._factorization <type 'exceptions.AssertionError'>: bug in factorization -- self has dimension 2, but sum of dimensions of factors is 3 (Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 2 for Gamma_0(1) of weight 6 with sign 0 over Finite Field of size 2) * (Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 2 for Gamma_0(1) of weight 6 with sign 0 over Finite Field of size 2) * (Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 2 for Gamma_0(1) of weight 6 with sign 0 over Finite Field of size 2)
Outcome is similar for higher weights, e.g. for weight 100 I get "self has dimension 33, but sum of dimensions of factors is 65".
Attachments (1)
Change History (9)
comment:1 Changed 10 years ago by
- Milestone set to sage-2.8.14
comment:2 Changed 10 years ago by
Changed 10 years ago by
comment:3 Changed 10 years ago by
- Owner changed from was to craigcitro
- Status changed from new to assigned
Added a fix for this. The issue was what I mentioned above, namely the fact that +1 == -1 in characteristic 2. Alex Ghitza offered the following explanation of why this is a mathematically valid fix:
Here's my line of thought: -- in Sage, "simple" means "simple as a module over the anemic Hecke algebra adjoined the star involution *" -- in characteristic 2, the star involution is actually not an involution, but rather the identity map, and so "simple" should just mean "simple as a module over the anemic Hecke algebra", so synonymous to "splittable_anemic" in Sage terminology -- the factorization() aka simple_factors() function for modular symbols uses the HeckeModule_free_module.decomposition() function, which implements an algorithm that breaks up the module as much as possible using the anemic Hecke algebra; therefore the resulting factors are "splittable_anemic", and so "simple" (for char 2).
The attached patch fixes the problem, and adds a doctest or two.
comment:4 Changed 10 years ago by
- Summary changed from bug in modular symbols over GF(2) to [with patch] bug in modular symbols over GF(2)
comment:5 Changed 10 years ago by
- Summary changed from [with patch] bug in modular symbols over GF(2) to [with patch, with positive review] bug in modular symbols over GF(2)
comment:6 Changed 10 years ago by
This is good (ok and better than before). Note however that in a lot of cases simple_factors still won't work (due to the algorithm not really being meant for GF(p) -- instead one should use decomposition):
sage: n = ModularSymbols(54,weight=2,base_ring=GF(2)); n Modular Symbols space of dimension 19 for Gamma_0(54) of weight 2 with sign 0 over Finite Field of size 2 sage: m =n.new_subspace() sage: n.simple_factors() Traceback (most recent call last): ... AssertionError: bug in factorization -- self has dimension 19, but sum of dimensions of factors is 11 (Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 1 for Gamma_0(2) of weight 2 with sign 0 over Finite Field of size 2)^7 * (Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 7 for Gamma_0(27) of weight 2 with sign 0 over Finite Field of size 2)^2 * (Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 19 for Gamma_0(54) of weight 2 with sign 0 over Finite Field of size 2) sage: m.simple_factors() [Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 19 for Gamma_0(54) of weight 2 with sign 0 over Finite Field of size 2, Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 19 for Gamma_0(54) of weight 2 with sign 0 over Finite Field of size 2] sage: f = n.decomposition(5) sage: f [ Modular Symbols subspace of dimension 4 of Modular Symbols space of dimension 19 for Gamma_0(54) of weight 2 with sign 0 over Finite Field of size 2, Modular Symbols subspace of dimension 15 of Modular Symbols space of dimension 19 for Gamma_0(54) of weight 2 with sign 0 over Finite Field of size 2 ]
comment:7 Changed 10 years ago by
- Summary changed from [with patch, with positive review] bug in modular symbols over GF(2) to [with patch, with 2 positive reviews] bug in modular symbols over GF(2)
comment:8 Changed 10 years ago by
- Resolution set to fixed
- Status changed from assigned to closed
Merged in 2.9.rc0.
So the problem here is straightforward to find -- M.factorization() breaks up the cuspidal parts into +1 and -1 eigenspaces; since 1 == -1 mod 2, they all get counted twice (so that the dimension will always be 2*cuspidal part + eisenstein part). The fix is also easy -- if 2 == 0, don't add the minus part in. However, the question is whether the space is still simple in this case, because otherwise we're now producing wrong answers.