Fixing some details and a few slight doc tweaks.

src/sage/algebras/down_up_algebra.py

@@ -1,20 +1,20 @@
-"""
+r"""
 Down-Up Algebras
 
 AUTHORS:
 
 - Travis Scrimshaw (2023-4): initial version
 """
 
-#*****************************************************************************
-# Copyright (C) 2023 Travis Scrimshaw <tcscrims at gmail.com>
+# ****************************************************************************
+#  Copyright (C) 2023 Travis Scrimshaw <tcscrims at gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
-# http://www.gnu.org/licenses/
-#*****************************************************************************
+# https://www.gnu.org/licenses/
+# ****************************************************************************
 
 from sage.misc.cachefunc import cached_method
 from sage.categories.algebras import Algebras
@@ -461,11 +461,9 @@ def degree_on_basis(self, m):
 
  def verma_module(self, la):
  r"""
- Return the Verma module `V(\lambda)` of ``self``.
-
- .. SEEALSO::
-
- :class:`~sage.algebras.down_up_algebra.VermaModule`
+ Return the :class:`Verma module
+ <sage.algebras.down_up_algebra.VermaModule>`
+ `V(\lambda)` of ``self``.
 
  EXAMPLES::
 
@@ -647,7 +645,8 @@ def _latex_(self):
 
  def highest_weight_vector(self):
  r"""
- Return the highest weight vector of ``self``.
+ Return the highest weight vector of ``self`` that generates
+ ``self`` as a down-up module.
 
  EXAMPLES::
 
@@ -729,6 +728,9 @@ def _action_on_basis(self, m, n):
  return self.term(n - m[2] + m[0], coeff)
 
  class Element(CombinatorialFreeModule.Element):
+ r"""
+ An element of a Verma module of a down-up algebra.
+ """
  def _acted_upon_(self, scalar, self_on_left):
  r"""
  Return the action of ``scalar`` (an element of the base ring or
@@ -749,6 +751,12 @@ def _acted_upon_(self, scalar, self_on_left):
  True
  sage: 5 * V.basis()[3]
  5*v[3]
+ sage: V.basis()[0] * d
+ Traceback (most recent call last):
+ ...
+ TypeError: unsupported operand parent(s) for *:
+ 'Verma module of weight a of Down-Up algebra ...'
+ and 'Down-Up algebra ...'
  """
  ret = super()._acted_upon_(scalar, self_on_left)
  if ret is not None:
@@ -765,7 +773,7 @@ def _acted_upon_(self, scalar, self_on_left):
  for n, nc in self._monomial_coefficients.items())
 
  def is_weight_vector(self):
- """
+ r"""
  Return if ``self`` is a weight vector.
 
  EXAMPLES::