Modify primitive_poly() to use the database

src/galois/_polys/_primitive.py

@@ -9,7 +9,7 @@
 
 from typing_extensions import Literal
 
-from .._databases import ConwayPolyDatabase
+from .._databases import ConwayPolyDatabase, PrimitivePolyDatabase
 from .._domains import _factory
 from .._helper import export, verify_isinstance
 from .._prime import is_prime, is_prime_power
@@ -96,8 +96,15 @@ def primitive_poly(order: int, degree: int, method: Literal["min", "max", "rando
     if not method in ["min", "max", "random"]:
         raise ValueError(f"Argument 'method' must be in ['min', 'max', 'random'], not {method!r}.")
 
+    field = _factory.FIELD_FACTORY(order)
+
     if method == "min":
-        poly = next(primitive_polys(order, degree))
+        try:
+            db = PrimitivePolyDatabase()
+            degrees, coeffs = db.fetch(order, degree)
+            poly = Poly.Degrees(degrees, coeffs, field=field)
+        except LookupError:
+            poly = next(primitive_polys(order, degree))
     elif method == "max":
         poly = next(primitive_polys(order, degree, reverse=True))
     else: