From a627ce685f4ac30ba9660f66b24fae246209c5d1 Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Thu, 28 Jul 2022 19:04:22 -0700
Subject: [PATCH 1/4] src/sage/rings/qqbar.py
 (AlgebraicNumber_base._maxima_init_): New

---
 src/sage/rings/qqbar.py | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index 7db32272b26..3c0830c23c7 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -4710,6 +4710,35 @@ def radical_expression(self):
             roots = candidates
             interval_field = interval_field.to_prec(interval_field.prec() * 2)
 
+    def _maxima_init_(self, I=None):
+        r"""
+        EXAMPLES::
+
+            sage: maxima(QQbar(sqrt(5/2)))
+            sqrt(5)/sqrt(2)
+            sage: maxima(AA(-sqrt(5)))
+            -sqrt(5)
+            sage: QQbar(sqrt(-2))._maxima_init_()
+            Traceback (most recent call last):
+            ...
+            NotImplementedError: conversion implemented only for square roots of nonnegative rationals
+        """
+        try:
+            return self._rational_()._maxima_init_(I)
+        except ValueError:
+            pass
+        try:
+            square_QQ = (self ** 2)._rational_()
+        except ValueError:
+            raise NotImplementedError('conversion implemented only for square roots of nonnegative rationals')
+        else:
+            if square_QQ < 0:
+                raise NotImplementedError('conversion implemented only for square roots of nonnegative rationals')
+            if self >= 0:
+                return 'sqrt(' + square_QQ._maxima_init_() + ')'
+            else:
+                return '-sqrt(' + square_QQ._maxima_init_() + ')'
+
 
 class AlgebraicNumber(AlgebraicNumber_base):
     r"""

From 6204a76d0ec2cbc3cd350cd82f77b2b3ec8088c0 Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Thu, 28 Jul 2022 21:22:39 -0700
Subject: [PATCH 2/4] src/sage/rings/qqbar.py
 (AlgebraicNumber_base._maxima_init_): Fixup

---
 src/sage/rings/qqbar.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index 3c0830c23c7..eadc0689385 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -4724,7 +4724,7 @@ def _maxima_init_(self, I=None):
             NotImplementedError: conversion implemented only for square roots of nonnegative rationals
         """
         try:
-            return self._rational_()._maxima_init_(I)
+            return self._rational_()._maxima_init_()
         except ValueError:
             pass
         try:

From 3e560cf5b30377da9d3122427f81f9b0ef93c5c4 Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Thu, 28 Jul 2022 21:25:00 -0700
Subject: [PATCH 3/4] src/sage/rings/qqbar.py: Add doctest

---
 src/sage/rings/qqbar.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index eadc0689385..7da3e3fa415 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -4714,6 +4714,8 @@ def _maxima_init_(self, I=None):
         r"""
         EXAMPLES::
 
+            sage: maxima(AA(7))
+            7
             sage: maxima(QQbar(sqrt(5/2)))
             sqrt(5)/sqrt(2)
             sage: maxima(AA(-sqrt(5)))

From 58f4cd1c63b7d7a8aee04de5d8c53a7fac27d061 Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Thu, 28 Jul 2022 22:55:42 -0700
Subject: [PATCH 4/4] src/sage/rings/qqbar.py
 (AlgebraicNumber_base._maxima_init_): Generalize using radical_expression

---
 src/sage/rings/qqbar.py | 25 +++++++++++--------------
 1 file changed, 11 insertions(+), 14 deletions(-)

diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index 7da3e3fa415..9e865493bf9 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -4717,29 +4717,26 @@ def _maxima_init_(self, I=None):
             sage: maxima(AA(7))
             7
             sage: maxima(QQbar(sqrt(5/2)))
-            sqrt(5)/sqrt(2)
+            sqrt(10)/2
             sage: maxima(AA(-sqrt(5)))
             -sqrt(5)
-            sage: QQbar(sqrt(-2))._maxima_init_()
+            sage: maxima(QQbar(sqrt(-2)))
+            sqrt(2)*%i
+            sage: maxima(AA(2+sqrt(5)))
+            sqrt(5)+2
+            sage: maxima(QQ[x](x^7 - x - 1).roots(AA, False)[0])
             Traceback (most recent call last):
             ...
-            NotImplementedError: conversion implemented only for square roots of nonnegative rationals
+            NotImplementedError: cannot find radical expression
         """
         try:
             return self._rational_()._maxima_init_()
         except ValueError:
             pass
-        try:
-            square_QQ = (self ** 2)._rational_()
-        except ValueError:
-            raise NotImplementedError('conversion implemented only for square roots of nonnegative rationals')
-        else:
-            if square_QQ < 0:
-                raise NotImplementedError('conversion implemented only for square roots of nonnegative rationals')
-            if self >= 0:
-                return 'sqrt(' + square_QQ._maxima_init_() + ')'
-            else:
-                return '-sqrt(' + square_QQ._maxima_init_() + ')'
+        rad = self.radical_expression()
+        if isinstance(rad.parent(), sage.rings.abc.SymbolicRing):
+            return rad._maxima_init_()
+        raise NotImplementedError('cannot find radical expression')
 
 
 class AlgebraicNumber(AlgebraicNumber_base):