#5642 closed enhancement (fixed)
[with patch, positive review] Overconvergent modular forms for genus 0 primes
Reported by: | davidloeffler | Owned by: | davidloeffler |
---|---|---|---|
Priority: | major | Milestone: | sage-3.4.1 |
Component: | modular forms | Keywords: | |
Cc: | Merged in: | 3.4.1.rc0 | |
Authors: | David Loeffler | Reviewers: | William Stein |
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
I have written some code that computes approximations to the q-expansions of overconvergent p-adic modular forms of tame level 1, when p is one of the primes {2, 3, 5, 7, 13} (so X_0(p) has genus 0). See the notes of my talk at the Heilbronn Institute for background:
http://www.dpmms.cam.ac.uk/~dl267/maths/lecturenotes/overconvergent_lecture.pdf.
Attachments (2)
Change History (11)
Changed 12 years ago by
comment:1 Changed 12 years ago by
- Status changed from new to assigned
- Summary changed from Overconvergent modular forms for genus 0 primes to [with patch, needs review] Overconvergent modular forms for genus 0 primes
comment:2 Changed 12 years ago by
- Summary changed from [with patch, needs review] Overconvergent modular forms for genus 0 primes to [with patch, needs work] Overconvergent modular forms for genus 0 primes
REFEREE REPORT:
- Could we rename
WeightSpace
topAdicWeightSpace
? I say that only because Sage is so broad and in combinatorics/representation theoryWeightSpace
could have some completely different meaning. - Could
WeightSpace?
give more useful documentation? - I'm very happy with how good
OverconvergentModularForms
docstring is, but there should be doctests that illustrate all of the options to theOverconvergentModularForms
function. Right now the doctests don't at all test/illustratebase_ring
orprec
. - Here's a bug. This was *literally* the first random thing I tried:
sage: M = OverconvergentModularForms(3, 0, 1/2) sage: w = M.weight() sage: w.Lvalue() --------------------------------------------------------------------------- NameError Traceback (most recent call last) /scratch/wstein/sage/temp/sage.math.washington.edu/30657/_scratch_wstein_sage_init_sage_0.py in <module>() /scratch/wstein/build/sage-3.4.1.alpha0/local/lib/python2.5/site-packages/sage/modular/overconvergent/weightspace.pyc in Lvalue(self) 457 return -self.chi.bernoulli(self.k)/self.k 458 if self.is_trivial(): --> 459 return Infinity 460 else: 461 raise NotImplementedError, "Don't know how to compute value of this L-function" NameError: global name 'Infinity' is not defined
- Continuing the above example, the second thing I tried also fails:
sage: w.base_extend(QQ) --------------------------------------------------------------------------- AttributeError Traceback (most recent call last) ... AttributeError: 'WeightSpace_class' object has no attribute 'base_extend'
- The third thing I tried gives nonsense. Shouldn't w.base_ring() either raise an error, or return a ring?
sage: w.base_ring() sage: w.base_ring() is None True
- Do you really want that I can just change the attribute k (the weight) of the p-adic Weight space like this?
sage: w.k = 10 sage: w 10 sage: M.weight() # that can't be good 10
- This is pretty weird:
sage: w.n() init_coerce() for <class 'sage.modular.overconvergent.weightspace.WeightSpace_class'> --------------------------------------------------------------------------- ZeroDivisionError Traceback (most recent call last) ZeroDivisionError: hello
- I'm unhappy that one_over_Lvalue() outputs a Python int. I would rather get a Sage Integer or a Rational or p-adic or something.
sage: w.one_over_Lvalue() 0 sage: type(w.one_over_Lvalue()) <type 'int'>
- This isn't good, and is why I would never ever expose attributes like this. It's best to use self.prime and make a method or use the Python "properties" protocol.
sage: w.prime = 6 sage: w.prime 6 sage: w.parent() Space of 3-adic weight-characters
- Moving back to
M=OverconvergentModularForms(3, 0, 1/2)
, and going through some of the methods, the first one I try is broken. I realize this is broken because a function in the abstract base class for Hecke modules assumes certain things and you wrote code that doesn't satisfy those assumption. But we have to find a way to make this all work. Half the functions in the abstract base class assume there is a functionM.hecke_matrix(n)
that works, so if you doM.<tab>
and try things, you'll find a whole bunch of functions that don't work.sage: M.hecke_polynomial(2) --------------------------------------------------------------------------- TypeError Traceback (most recent call last) 1028 OUTPUT: a polynomial 1029 """ -> 1030 return self.hecke_operator(n).charpoly(var) 1031 1032 def is_simple(self): TypeError: hecke_operator() takes exactly 3 arguments (2 given)
- Here's another bug, which I realize is probably actually a bug in code I wrote long ago but it would be cool if you fixed it :-)
sage: M.zero_submodule() --------------------------------------------------------------------------- AttributeError Traceback (most recent call last) /scratch/wstein/sage/temp/sage.math.washington.edu/30657/_scratch_wstein_sage_init_sage_0.py in <module>() /scratch/wstein/build/sage-3.4.1.alpha0/local/lib/python2.5/site-packages/sage/modular/hecke/module.pyc in zero_submodule(self) 1248 Modular Forms subspace of dimension 0 of Modular Forms space of dimension 4 for Congruence Subgroup Gamma0(11) of weight 4 over Rational Field 1249 """ -> 1250 return self.submodule(self.free_module().zero_submodule(), check=False) 1251 1252 AttributeError: 'PowerSeriesRing_over_field' object has no attribute 'zero_submodule'
- That one can do this is *not* good, IMHO:
sage: M.q q sage: M.q = 10 sage: M.q 10 sage: M=OverconvergentModularForms(3, 0, 1/2) sage: M.q 10 (so I restart -- there should be maybe a use_cache=False option to the constructor...)
- This could be more graceful:
sage: M.list() --------------------------------------------------------------------------- TypeError Traceback (most recent call last) /scratch/wstein/sage/temp/sage.math.washington.edu/31166/_scratch_wstein_sage_init_sage_0.py in <module>() /scratch/wstein/build/sage-3.4.1.alpha0/local/lib/python2.5/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.list (sage/structure/parent.c:5211)() /scratch/wstein/build/sage-3.4.1.alpha0/local/lib/python2.5/site-packages/sage/structure/gens_py.pyc in abelian_iterator(M) 48 def abelian_iterator(M): 49 from sage.rings.all import infinity ---> 50 G = M.gens() 51 if len(G) == 0: 52 yield M(0) /scratch/wstein/build/sage-3.4.1.alpha0/local/lib/python2.5/site-packages/sage/structure/parent_gens.so in sage.structure.parent_gens.ParentWithGens.gens (sage/structure/parent_gens.c:2749)() TypeError: an integer is required
- This "M.gsr" thing is 100% totally cryptic and confusing, and again can easily lead to brokeness (same with M.qsr):
sage: M.gsr Power Series Ring in g over Rational Field sage: M.gsr = 10 # badness
- Here's another problem
sage: M.new_submodule() --------------------------------------------------------------------------- AttributeError Traceback (most recent call last) /scratch/wstein/sage/temp/sage.math.washington.edu/31246/_scratch_wstein_sage_init_sage_0.py in <module>() /scratch/wstein/build/sage-3.4.1.alpha0/local/lib/python2.5/site-packages/sage/modular/hecke/ambient_module.pyc in new_submodule(self, p) 538 f = 1 539 else: --> 540 f = eps.conductor() 541 if p == None: 542 D = arith.prime_divisors(N) AttributeError: 'AlgebraicWeight' object has no attribute 'conductor'
Anyway, as you can see, I hope you could take each of the main new objects that this code introduces, try each method, and fix the issues. You can probably clean this all up pretty quickly.
Please don't take the above in too negative away. This is frickin' *awesome* code, and I'm very very happy and excited to finally see a real implementation of overconvergent p-adic modular forms in Sage. This is wonderful!
comment:3 Changed 12 years ago by
Most of these are plain stupidity on my part and I will fix them, and add doctests to prove that they are fixed. I will also hide some more attributes.
comment:4 Changed 12 years ago by
- Summary changed from [with patch, needs work] Overconvergent modular forms for genus 0 primes to [with new patch, needs review] Overconvergent modular forms for genus 0 primes
Here's a new version. Overconvergent spaces + elements now inherit from Module and ModuleElement, not HeckeModule and HeckeModuleElement, which is a pity, but leads to fewer meaningless inherited methods. I've also hidden lots of things away out of sight of the user, and improved the documentation somewhat.
comment:5 Changed 12 years ago by
- Summary changed from [with new patch, needs review] Overconvergent modular forms for genus 0 primes to [with new patch, positive review] Overconvergent modular forms for genus 0 primes
OK, this is now very good. Excellent! Thanks!!
comment:6 Changed 12 years ago by
- Milestone changed from sage-feature to sage-3.4.1
comment:7 Changed 12 years ago by
- Summary changed from [with new patch, positive review] Overconvergent modular forms for genus 0 primes to [with patch, positive review] Overconvergent modular forms for genus 0 primes
comment:8 Changed 12 years ago by
- Resolution set to fixed
- Status changed from assigned to closed
Merged both patches in Sage 3.4.1.rc0.
Cheers,
Michael
comment:9 Changed 12 years ago by
- Merged in set to 3.4.1.rc0
- Reviewers set to William Stein
patch against 3.4.1.alpha0