Trac #31153: Fix latex of elements of multivariate polynomial quotien…

…t ring

Following an initial report by Ask Sage user "Road" at

- [https://ask.sagemath.org/question/54375 Ask Sage question 54375]

Define a polynomial ring and its generators:
{{{
sage: R = PolynomialRing(QQ, 'a, b, c')
sage: a, b, c = R.gens()
}}}
The generators display well:
{{{
sage: latex(a)  # good
a
}}}
Now define a quotient of that ring modulo an ideal:
{{{
sage: I = R.ideal(a**2 + a + 1)
sage: S = R.quotient(I, names=R.variable_names()).fraction_field()
sage: a, b, c = S.gens()
}}}
The generators display poorly:
{{{
sage: latex(a)  # should be same as above
\text{\texttt{a}}
}}}

Adding a `_latex_` method in `sage/rings/quotient_ring_element.py`
addresses the issue.

This is done in this ticket.

URL: https://trac.sagemath.org/31153
Reported by: slelievre
Ticket author(s): Frédéric Chapoton
Reviewer(s): Samuel Lelièvre

src/sage/rings/quotient_ring_element.py

@@ -224,6 +224,31 @@ def _repr_(self):
         with localvars(R, P.variable_names(), normalize=False):
             return str(self.__rep)
 
+    def _latex_(self):
+        """
+        Return the LaTeX representation as a string.
+
+        EXAMPLES::
+
+            sage: R = PolynomialRing(QQ, 'a, b, c')
+            sage: a = R.gen(0)
+            sage: I = R.ideal(a**2 + a + 1)
+            sage: S = R.quotient(I, names=R.variable_names())
+            sage: a = S.gen(0)
+            sage: latex(a)
+            a
+        """
+        from sage.structure.parent_gens import localvars
+        P = self.parent()
+        R = P.cover_ring()
+        # see _repr_ above for the idea
+        try:
+            P.variable_names()
+        except ValueError:
+            return self.__rep._latex_()
+        with localvars(R, P.variable_names(), normalize=False):
+            return self.__rep._latex_()
+
     def __pari__(self):
         """
         The Pari representation of this quotient element.