sagemathgh-38303: Fix DrinfeldModule is_isomorphic method absolutely'…

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Fixes sagemath#38276.

@xcaruso @DavidAyotte @ymusleh

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URL: sagemath#38303
Reported by: Antoine Leudière
Reviewer(s): Travis Scrimshaw, Xavier Caruso

src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py

@@ -1292,9 +1292,9 @@ def is_isomorphic(self, other, absolutely=False):
 
         INPUT:
 
-        - ``absolutely`` -- a boolean (default: ``False``); if ``True``,
+        - ``absolutely`` -- a boolean (default: ``False``); if ``False``,
           check the existence of an isomorphism defined on the base
-          field; if ``False``, check over an algebraic closure.
+          field; if ``True``, check over an algebraic closure.
 
         EXAMPLES::
 
@@ -1328,6 +1328,18 @@ def is_isomorphic(self, other, absolutely=False):
             sage: phi.is_isomorphic(psi, absolutely=True)
             True
 
+        In particular, two Drinfeld modules may have the same
+        `j`-invariant, while not being isomorphic on the base field::
+
+            sage: phi = DrinfeldModule(A, [z, 0, 1])
+            sage: psi = DrinfeldModule(A, [z, 0, z])
+            sage: phi.j_invariant() == psi.j_invariant()
+            True
+            sage: phi.is_isomorphic(psi)
+            False
+            sage: phi.is_isomorphic(psi, absolutely=True)
+            True
+
         On certain fields, testing isomorphisms over the base field may
         fail::