gh-35025: Implement __getitem__ and alias weight methods for quasimod…

…ular forms

    
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This PR implements a `__getitem__` method for quasimodular forms ring
elements to access their components of a fixed degree. Moreover, the PR
defines the alias `degree = weight` (which is the right nomenclature for
elements of a graded algebra, as discussed with @fchapoton).

@videlec

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URL: #35025
Reported by: David Ayotte
Reviewer(s):

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
 from sage.rings.integer_ring import ZZ
 
@@ -506,7 +507,8 @@ 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::
 
@@ -517,6 +519,8 @@ 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):
             ...
@@ -529,6 +533,8 @@ def weight(self):
             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
@@ -574,6 +580,49 @@ def homogeneous_components(self):
                         components[ZZ(k + 2*i)] = QM(forms[k]*(E2**i))
         return components
 
+    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.