From e320299c7e507eed242b43c98f92e6a6991fde6b Mon Sep 17 00:00:00 2001
From: Matthias Koeppe <mkoeppe@math.ucdavis.edu>
Date: Thu, 30 May 2024 14:25:38 -0700
Subject: [PATCH] src/sage/structure/coerce.pyx (is_mpmath_type,
 py_scalar_parent): Handle mpmath types without Sage backend

---
 src/sage/structure/coerce.pyx | 44 +++++++++++++++++++++++------------
 1 file changed, 29 insertions(+), 15 deletions(-)

diff --git a/src/sage/structure/coerce.pyx b/src/sage/structure/coerce.pyx
index 26b9ee77cd7..9a6645421da 100644
--- a/src/sage/structure/coerce.pyx
+++ b/src/sage/structure/coerce.pyx
@@ -143,6 +143,13 @@ cpdef py_scalar_parent(py_type):
         Real Double Field
         sage: py_scalar_parent(gmpy2.mpc)                                               # needs sage.rings.complex_double
         Complex Double Field
+
+        sage: # needs mpmath
+        sage: import mpmath
+        sage: py_scalar_parent(mpmath.mpf)
+        Real Double Field
+        sage: py_scalar_parent(mpmath.mpc)                                              # needs sage.rings.complex_double
+        Complex Double Field
     """
     if issubclass(py_type, int):
         import sage.rings.integer_ring
@@ -150,39 +157,46 @@ cpdef py_scalar_parent(py_type):
     if py_type is FractionType:
         import sage.rings.rational_field
         return sage.rings.rational_field.QQ
-    elif issubclass(py_type, float):
+    if issubclass(py_type, float):
         import sage.rings.real_double
         return sage.rings.real_double.RDF
-    elif issubclass(py_type, complex):
+    if issubclass(py_type, complex):
         import sage.rings.complex_double
         return sage.rings.complex_double.CDF
-    elif is_numpy_type(py_type):
+    if is_numpy_type(py_type):
         import numpy
         if issubclass(py_type, numpy.integer):
             import sage.rings.integer_ring
             return sage.rings.integer_ring.ZZ
-        elif issubclass(py_type, numpy.floating):
+        if issubclass(py_type, numpy.floating):
             import sage.rings.real_double
             return sage.rings.real_double.RDF
-        elif issubclass(py_type, numpy.complexfloating):
+        if issubclass(py_type, numpy.complexfloating):
             import sage.rings.complex_double
             return sage.rings.complex_double.CDF
-        else:
-            return None
-    elif issubclass(py_type, gmpy2.mpz):
+        return None
+    if issubclass(py_type, gmpy2.mpz):
         import sage.rings.integer_ring
         return sage.rings.integer_ring.ZZ
-    elif issubclass(py_type, gmpy2.mpq):
+    if issubclass(py_type, gmpy2.mpq):
         import sage.rings.rational_field
         return sage.rings.rational_field.QQ
-    elif issubclass(py_type, gmpy2.mpfr):
+    if issubclass(py_type, gmpy2.mpfr):
         import sage.rings.real_double
         return sage.rings.real_double.RDF
-    elif issubclass(py_type, gmpy2.mpc):
+    if issubclass(py_type, gmpy2.mpc):
         import sage.rings.complex_double
         return sage.rings.complex_double.CDF
-    else:
+    if is_mpmath_type(py_type):
+        import mpmath
+        if issubclass(py_type, mpmath.mpf):
+            from sage.rings.real_double import RDF
+            return RDF
+        if issubclass(py_type, mpmath.mpc):
+            from sage.rings.complex_double import CDF
+            return CDF
         return None
+    return None
 
 cpdef py_scalar_to_element(x):
     """
@@ -468,10 +482,10 @@ cpdef bint is_numpy_type(t) noexcept:
         return True
     return False
 
+
 cpdef bint is_mpmath_type(t) noexcept:
     r"""
-    Check whether the type ``t`` is a type whose name starts with either
-    ``mpmath.`` or ``sage.libs.mpmath.``.
+    Check whether the type ``t`` is a type whose name starts with ``mpmath.``
 
     EXAMPLES::
 
@@ -488,7 +502,7 @@ cpdef bint is_mpmath_type(t) noexcept:
         True
     """
     return isinstance(t, type) and \
-           strncmp((<PyTypeObject*>t).tp_name, "sage.libs.mpmath.", 17) == 0
+           t.__module__.startswith("mpmath.")
 
 
 cdef class CoercionModel: