#5642: [with patch, needs work] Overconvergent modular forms for genus 0 primes
---------------------------+------------------------------------------------
Reporter: davidloeffler | Owner: davidloeffler
Type: enhancement | Status: assigned
Priority: major | Milestone: sage-feature
Component: modular forms | Keywords:
---------------------------+------------------------------------------------
Comment(by was):
REFEREE REPORT:
1. Could we rename {{{WeightSpace}}} to {{{pAdicWeightSpace}}}? I say
that only because Sage is so broad and in combinatorics/representation
theory {{{WeightSpace}}} could have some completely different meaning.
1. Could {{{WeightSpace?}}} give more useful documentation?
1. I'm very happy with how good {{{OverconvergentModularForms}}}
docstring is, but there should be doctests that illustrate all of the
options to the {{{OverconvergentModularForms}}} function. Right now the
doctests don't at all test/illustrate {{{base_ring}}} or {{{prec}}}.
1. 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
}}}
1. 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'
}}}
1. 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
}}}
1. 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
}}}
1. 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
}}}
1. 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'>
}}}
1. 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
}}}
1. 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
function {{{M.hecke_matrix(n)}}} that works, so if you do {{{M.<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)
}}}
1. 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'
}}}
1. 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...)
}}}
1. 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
}}}
1. 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
}}}
1. 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!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5642#comment:2>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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