gh-37896: Deprecate `is_FreeAlgebra`, `is_QuaternionAlgebra`, `is_SymmetricFunctionAlgebra`
    
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- Fixes #32738

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URL: #37896
Reported by: Matthias Köppe
Reviewer(s): Kwankyu Lee, Travis Scrimshaw

Author: Release Manager

src/sage/algebras/free_algebra.py

@@ -376,6 +376,10 @@ def is_FreeAlgebra(x) -> bool:
 
         sage: from sage.algebras.free_algebra import is_FreeAlgebra
         sage: is_FreeAlgebra(5)
+        doctest:warning...
+        DeprecationWarning: the function is_FreeAlgebra is deprecated;
+        use 'isinstance(..., (FreeAlgebra_generic, FreeAlgebra_letterplace))' instead
+        See https://github.com/sagemath/sage/issues/37896 for details.
         False
         sage: is_FreeAlgebra(ZZ)
         False
@@ -387,6 +391,8 @@ def is_FreeAlgebra(x) -> bool:
         ....:                            degrees=list(range(1,11))))
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(37896, "the function is_FreeAlgebra is deprecated; use 'isinstance(..., (FreeAlgebra_generic, FreeAlgebra_letterplace))' instead")
     return isinstance(x, (FreeAlgebra_generic, FreeAlgebra_letterplace))
 
 
@@ -742,7 +748,7 @@ def _coerce_map_from_(self, R):
             return True
 
         # free algebras in the same variable over any base that coerces in:
-        if is_FreeAlgebra(R):
+        if isinstance(R, (FreeAlgebra_generic, FreeAlgebra_letterplace)):
             if R.variable_names() == self.variable_names():
                 return self.base_ring().has_coerce_map_from(R.base_ring())
         if isinstance(R, PBWBasisOfFreeAlgebra):

src/sage/algebras/free_algebra_quotient.py

@@ -60,13 +60,16 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.algebras.free_algebra import is_FreeAlgebra
+from sage.algebras.free_algebra import FreeAlgebra_generic
 from sage.algebras.free_algebra_quotient_element import FreeAlgebraQuotientElement
 from sage.categories.algebras import Algebras
+from sage.misc.lazy_import import lazy_import
 from sage.modules.free_module import FreeModule
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.parent import Parent
 
+lazy_import('sage.algebras.letterplace.free_algebra_letterplace', 'FreeAlgebra_letterplace')
+
 
 class FreeAlgebraQuotient(UniqueRepresentation, Parent):
     @staticmethod
@@ -153,7 +156,7 @@ def __init__(self, A, mons, mats, names):
 
             sage: TestSuite(H2).run()
         """
-        if not is_FreeAlgebra(A):
+        if not isinstance(A, (FreeAlgebra_generic, FreeAlgebra_letterplace)):
             raise TypeError("argument A must be a free algebra")
         R = A.base_ring()
         n = A.ngens()

src/sage/algebras/quatalg/quaternion_algebra.py

@@ -307,10 +307,16 @@ def is_QuaternionAlgebra(A):
     EXAMPLES::
 
         sage: sage.algebras.quatalg.quaternion_algebra.is_QuaternionAlgebra(QuaternionAlgebra(QQ,-1,-1))
+        doctest:warning...
+        DeprecationWarning: the function is_QuaternionAlgebra is deprecated;
+        use 'isinstance(..., QuaternionAlgebra_abstract)' instead
+        See https://github.com/sagemath/sage/issues/37896 for details.
         True
         sage: sage.algebras.quatalg.quaternion_algebra.is_QuaternionAlgebra(ZZ)
         False
     """
+    from sage.misc.superseded import deprecation
+    deprecation(37896, "the function is_QuaternionAlgebra is deprecated; use 'isinstance(..., QuaternionAlgebra_abstract)' instead")
     return isinstance(A, QuaternionAlgebra_abstract)
 
 

src/sage/combinat/sf/sfa.py

@@ -246,6 +246,10 @@ def is_SymmetricFunctionAlgebra(x):
 
         sage: from sage.combinat.sf.sfa import is_SymmetricFunctionAlgebra
         sage: is_SymmetricFunctionAlgebra(5)
+        doctest:warning...
+        DeprecationWarning: the function is_SymmetricFunctionAlgebra is deprecated;
+        use 'isinstance(..., SymmetricFunctionAlgebra_generic)' instead
+        See https://github.com/sagemath/sage/issues/37896 for details.
         False
         sage: is_SymmetricFunctionAlgebra(ZZ)
         False
@@ -258,6 +262,8 @@ def is_SymmetricFunctionAlgebra(x):
         sage: is_SymmetricFunctionAlgebra(SymmetricFunctions(FractionField(QQ['q','t'])).macdonald().P())
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(37896, "the function is_SymmetricFunctionAlgebra is deprecated; use 'isinstance(..., SymmetricFunctionAlgebra_generic)' instead")
     return isinstance(x, SymmetricFunctionAlgebra_generic)