gh-37107: Added is_isomorphic() for rational quaternion algebras

Added `QuaternionAlgebra_ab.is_isomorphic()` to conveniently check
whether two rational quaternion algebras are isomorphic.

TODO (future work):
- [] Extend isomorphism check to quaternion algebras over number fields.

#sd123

URL: #37107
Reported by: Sebastian Spindler
Reviewer(s): Peter Bruin

Author: Release Manager

build/pkgs/configure/checksums.ini

@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
-sha1=1041fee1d3ed5dc9c6c428668a895fb7109a48e5
-md5=e254e55345074cd0959cb21c8e4716ca
-cksum=1271538328
+sha1=16fe5aaba9a760dd8a2e66736a117cea46ee6e91
+md5=375511ae93e27dce742292d0c7557d75
+cksum=2150430088

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-c6bf497a0fd0f29c721481b52afaf49969c0cef8
+ab5b59acc27408b89ef07ab0e6c654364fceafe6

src/sage/algebras/quatalg/quaternion_algebra.py

@@ -1074,6 +1074,31 @@ def ramified_primes(self):
         # TODO: more examples
         return [f[0] for f in factor(self.discriminant())]
 
+    def is_isomorphic(self, A) -> bool:
+        r"""
+        Return ``True`` if ``self`` and ``A`` are isomorphic quaternion algebras over Q.
+
+        INPUT:
+
+        - ``A`` -- a quaternion algebra defined over the rationals Q
+
+        EXAMPLES::
+
+            sage: B = QuaternionAlgebra(-46, -87)
+            sage: A = QuaternionAlgebra(-58, -69)
+            sage: B.is_isomorphic(A)
+            True
+            sage: A == B
+            False
+        """
+        if not isinstance(A, QuaternionAlgebra_ab):
+            raise TypeError("A must be a quaternion algebra of the form (a,b)_K")
+
+        if self.base_ring() != QQ or A.base_ring() != QQ:
+            raise NotImplementedError("isomorphism check only implemented for rational quaternion algebras")
+
+        return self.discriminant() == A.discriminant()
+
     def _magma_init_(self, magma):
         """
         Return Magma version of this quaternion algebra.