sage.structure.element: Introduce ABC InfinitePolynomial

src/sage/rings/polynomial/infinite_polynomial_element.py

@@ -91,10 +91,9 @@
 
 from sage.rings.integer_ring import ZZ
 from sage.rings.integer import Integer
-from sage.structure.element import RingElement
 from sage.structure.richcmp import richcmp
 from sage.misc.cachefunc import cached_method
-from sage.structure.element import MPolynomial
+from sage.structure.element import RingElement, MPolynomial, InfinitePolynomial as InfinitePolynomial_base
 import copy
 
 
@@ -206,7 +205,7 @@ def InfinitePolynomial(A, p):
     return InfinitePolynomial_sparse(A, p)
 
 
-class InfinitePolynomial_sparse(RingElement):
+class InfinitePolynomial_sparse(InfinitePolynomial_base):
     """
     Element of a sparse Polynomial Ring with a Countably Infinite Number of Variables.
 

src/sage/structure/element.pyx

@@ -4295,7 +4295,10 @@ cdef class CommutativeAlgebraElement(CommutativeRingElement):
 
 cdef class CommutativePolynomial(CommutativeAlgebraElement):
     r"""
-    Abstract base class, common base for :class:`Polynomial` and :class:`MPolynomial`
+    Abstract base class for commutative polynomials in any number of variables
+
+    It is a common base for :class:`Polynomial`, :class:`MPolynomial`, and
+    :class:`InfinitePolynomial`.
     """
 
     pass
@@ -4320,6 +4323,15 @@ cdef class MPolynomial(CommutativePolynomial):
 
     ##############################################
 
+cdef class InfinitePolynomial(CommutativePolynomial):
+    r"""
+    Abstract base class for :class:`~sage.rings.polynomial.infinite_polynomial_element.InfinitePolynomial_sparse`
+    """
+
+    pass
+
+    ##############################################
+
 def is_InfinityElement(x):
     """
     Return ``True`` if x is of type InfinityElement.