coefficients for QuasiModularFormsElement

[seewoo5]

This patch implements _compute and coefficients methods to QuasiModularFormsElement, which already exists in ModularFormsElement. I made this for my own usage.
(This is my first PR for Sage, so comments are welcome!)

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[mantepse]

I am not familiar with modular forms, but wouldn't it be nice to return a (lazy) power series, analogous to molien_series?

            sage: S3 = MatrixGroup(SymmetricGroup(3))
            sage: mol = S3.molien_series(prec=oo); mol
            1 + t + 2*t^2 + 3*t^3 + 4*t^4 + 5*t^5 + 7*t^6 + O(t^7)
            sage: mol.parent()
            Lazy Taylor Series Ring in t over Integer Ring
            sage: mol[100]
            884

With this, it is very natural (and efficient) to get any particular coefficient.

[seewoo5]

I am not familiar with modular forms, but wouldn't it be nice to return a (lazy) power series, analogous to molien_series?

            sage: S3 = MatrixGroup(SymmetricGroup(3))
            sage: mol = S3.molien_series(prec=oo); mol
            1 + t + 2*t^2 + 3*t^3 + 4*t^4 + 5*t^5 + 7*t^6 + O(t^7)
            sage: mol.parent()
            Lazy Taylor Series Ring in t over Integer Ring
            sage: mol[100]
            884

With this, it is very natural (and efficient) to get any particular coefficient.

Thank you for letting me know. My code is actually almost a copy & paste of the same methods of ModularFormsElement, where I updated docs & tests with different examples (see the below code). I also don't understand the detailed implementation of q_expansion method well.

sage/src/sage/modular/modform/element.py

Lines 309 to 373 in 80f6d77

	def _compute(self, X):
	"""
	Compute the coefficients of `q^n` of the power series of self,
	for `n` in the list `X`. The results are not cached. (Use
	coefficients for cached results).
	EXAMPLES::
	sage: f = ModularForms(18,2).1
	sage: f.q_expansion(20)
	q + 8*q^7 + 4*q^10 + 14*q^13 - 4*q^16 + 20*q^19 + O(q^20)
	sage: f._compute([10,17])
	[4, 0]
	sage: f._compute([])
	[]
	"""
	if not isinstance(X, list) or not X:
	return []
	bound = max(X)
	q_exp = self.q_expansion(bound + 1)
	return [q_exp[i] for i in X]
	def coefficients(self, X):
	"""
	The coefficients a_n of self, for integers n>=0 in the list
	X. If X is an Integer, return coefficients for indices from 1
	to X.
	This function caches the results of the compute function.
	TESTS::
	sage: e = DirichletGroup(11).gen()
	sage: f = EisensteinForms(e, 3).eisenstein_series()[0]
	sage: f.coefficients([0,1])
	[15/11*zeta10^3 - 9/11*zeta10^2 - 26/11*zeta10 - 10/11,
	1]
	sage: f.coefficients([0,1,2,3])
	[15/11*zeta10^3 - 9/11*zeta10^2 - 26/11*zeta10 - 10/11,
	1,
	4*zeta10 + 1,
	-9*zeta10^3 + 1]
	sage: f.coefficients([2,3])
	[4*zeta10 + 1,
	-9*zeta10^3 + 1]
	Running this twice once revealed a bug, so we test it::
	sage: f.coefficients([0,1,2,3])
	[15/11*zeta10^3 - 9/11*zeta10^2 - 26/11*zeta10 - 10/11,
	1,
	4*zeta10 + 1,
	-9*zeta10^3 + 1]
	"""
	try:
	self.__coefficients
	except AttributeError:
	self.__coefficients = {}
	if isinstance(X, Integer):
	X = list(range(1, X + 1))
	Y = [n for n in X if n not in self.__coefficients]
	v = self._compute(Y)
	for i in range(len(v)):
	self.__coefficients[Y[i]] = v[i]
	return [self.__coefficients[x] for x in X]

[seewoo5]

@DavidAyotte Could you check this one (or any suggestions)?

[DavidAyotte]

@DavidAyotte Could you check this one (or any suggestions)?

Absolutely, I will check it in a couple days!

[DavidAyotte]

Hello Seewoo, overall it looks good! I have minor docstring recommendation. Thank you for implementing this.

[DavidAyotte]

@mantepse Hello Martin! Yes I think it would be feasible and interesting to use the Lazy power series framework for $q$-expansion of modular forms. It would probably require a bit of factoring, but I'm think of something like:

sage: M = ModularForms(1, 12)
sage: f = M.0
sage: f.q_expansion(prec=oo)
# Lazy power series

I will probably open a PR about this soon.

[seewoo5]

Updated all the docstrings!

[DavidAyotte]

Thank you! I do have more minor comments.

[DavidAyotte]

Suggested change

	TESTS::
	EXAMPLES::

If you use the "TESTS" block, the doctests will not appear in the reference manual.

[seewoo5]

But it would be still tested, right? (is TESTS:: legacy?)

[DavidAyotte]

Yes both TESTS and EXAMPLES run the doctests, however TESTS block does not show any examples in the Sage reference manual and I think that it is the only difference. I personally think that it is a good thing to present some examples in the manual so the user can better understand how to use the method.

[DavidAyotte]

To add to my previous reply, even though it is a good practice to present some examples, sometimes some doctests aren't that useful for the user (technical or internal doctest) so you might want to hide them. But in your case the doctests are all relevant so that is why I suggested to use the EXAMPLES block.

[seewoo5]

Thanks, I didn't know that examples would be also tested. Just updated!

[DavidAyotte]

Thank you Seewoo for the changes.

@mkoeppe can you approve the workflows for this PR? Thanks!

[github-actions]

Documentation preview for this PR (built with commit f055a04; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[DavidAyotte]

Hello sorry for the delay, but I wanted to see the build jobs before setting this to postive review. There's a single doctest that does not pass and I believe it is not related with this PR, so I'm setting this to postive review. Thank you for this contribution!