add test for trace in free_module_tensor

Author: tobiasdiez

src/sage/manifolds/differentiable/tensorfield_paral_test.py

@@ -0,0 +1,15 @@
+# pylint: disable=missing-function-docstring,missing-class-docstring
+import pytest
+
+from sage.manifolds.differentiable.examples.euclidean import EuclideanSpace
+from sage.manifolds.differentiable.manifold import DifferentiableManifold
+
+
+class TestR3VectorSpace:
+    @pytest.fixture
+    def manifold(self):
+        return EuclideanSpace(3)
+
+    def test_trace_using_metric_works(self, manifold: DifferentiableManifold):
+        metric = manifold.metric('g')
+        assert metric.trace(using=metric) == manifold.scalar_field(3)

src/sage/tensor/modules/free_module_tensor.py

@@ -2515,7 +2515,7 @@ def trace(
 
         The contraction on two slots having the same tensor type cannot occur::
 
-            sage: b =  M.tensor((2,0), name='b') ; b
+            sage: b = M.tensor((2,0), name='b') ; b
             Type-(2,0) tensor b on the Rank-3 free module M over the Integer Ring
             sage: b[:] = [[1,2,3], [4,5,6], [7,8,9]]
             sage: b.trace(0,1)