Implement __getitem__ and alias weight methods for quasimodular forms

src/sage/modular/quasimodform/element.py

@@ -24,6 +24,7 @@
 from sage.structure.element import ModuleElement
 from sage.structure.richcmp import richcmp, op_NE, op_EQ
 
+from sage.rings.integer import Integer
 from sage.rings.polynomial.polynomial_element import Polynomial
 
 class QuasiModularFormsElement(ModuleElement):
@@ -489,7 +490,8 @@ def weight(self):
  r"""
  Return the weight of the given quasimodular form.
 
- Note that the given form must be homogeneous.
+ Note that the given form must be homogeneous. An alias of this method is
+ ``degree``.
 
  EXAMPLES::
 
@@ -500,6 +502,8 @@ def weight(self):
  6
  sage: QM(1/2).weight()
  0
+ sage: (QM.0).degree()
+ 2
  sage: (QM.0 + QM.1).weight()
  Traceback (most recent call last):
  ...
@@ -510,6 +514,8 @@ def weight(self):
  else:
  raise ValueError("the given graded quasiform is not an homogeneous element")
 
+ degree = weight # alias
+
  def homogeneous_components(self):
  r"""
  Return a dictionary where the values are the homogeneous components of
@@ -538,6 +544,49 @@ def homogeneous_components(self):
  pol_hom_comp = poly_self.homogeneous_components()
  return {k: QM.from_polynomial(pol) for k, pol in pol_hom_comp.items()}
 
+ def __getitem__(self, weight):
+ r"""
+ Return the homogeneous component of the given quasimodular form ring
+ element.
+
+ An alias of this method is ``homogeneous_component``.
+
+ EXAMPLES::
+
+ sage: QM = QuasiModularForms(1)
+ sage: E2, E4, E6 = QM.gens()
+ sage: F = E2 + E4*E6 + E2^3*E6
+ sage: F[2]
+ 1 - 24*q - 72*q^2 - 96*q^3 - 168*q^4 - 144*q^5 + O(q^6)
+ sage: F[10]
+ 1 - 264*q - 135432*q^2 - 5196576*q^3 - 69341448*q^4 - 515625264*q^5 + O(q^6)
+ sage: F[12]
+ 1 - 576*q + 21168*q^2 + 308736*q^3 - 15034608*q^4 - 39208320*q^5 + O(q^6)
+ sage: F[4]
+ 0
+ sage: F.homogeneous_component(2)
+ 1 - 24*q - 72*q^2 - 96*q^3 - 168*q^4 - 144*q^5 + O(q^6)
+
+ TESTS::
+
+ sage: F[x]
+ Traceback (most recent call last):
+ ...
+ KeyError: 'the weight must be an integer'
+ sage: F[-1]
+ Traceback (most recent call last):
+ ...
+ ValueError: the weight must be nonnegative
+ """
+ if not isinstance(weight, (int, Integer)):
+ raise KeyError("the weight must be an integer")
+ if weight < 0:
+ raise ValueError("the weight must be nonnegative")
+ return self.homogeneous_components().get(weight, self.parent().zero())
+
+ homogeneous_component = __getitem__ # alias
+
+
  def serre_derivative(self):
  r"""
  Return the Serre derivative of the given quasimodular form.