Rank integer factorization for prime-power queries

src/jacobian/math/number_theory/_factorization.py

@@ -121,7 +121,10 @@ def _operation[RequestT: StrictModel, ResultT: StrictModel](
     _operation(
         operation_id="integer.compute.prime_factorization",
         title="Factor an integer",
-        description="Compute a complete prime-power factorization.",
+        description=(
+            "Factor an integer into prime powers and return the complete "
+            "prime-power factorization."
+        ),
         request_model=NonzeroFactorizationRequest,
         result_model=PrimeFactorizationResult,
         implementation=_compute_prime_factorization,

tests/catalog/test_catalog.py

@@ -122,6 +122,32 @@ def fail_descriptor(*_args: object) -> None:
     assert browse.operations
 
 
+def test_natural_prime_power_query_ranks_factorization_before_prime_navigation() -> (
+    None
+):
+    catalog = Catalog.open()
+
+    result = catalog.search(
+        OperationDiscoveryRequest(
+            query="factor an integer into prime powers",
+            limit=5,
+        )
+    )
+    positions = {
+        match.operation_id: index for index, match in enumerate(result.matches)
+    }
+
+    assert all(
+        positions["integer.compute.prime_factorization"]
+        < positions[prime_navigation_id]
+        for prime_navigation_id in (
+            "integer.compute.next_prime",
+            "integer.compute.nth_prime",
+            "integer.compute.previous_prime",
+        )
+    )
+
+
 def test_search_finds_lattice_hnf_in_matrix_domain() -> None:
     catalog = Catalog.open()