6 files changed, 66 insertions, 1 deletions
diff --git a/polymatrix/__init__.py b/polymatrix/__init__.py
index 4df9a81..1c072b4 100644
--- a/polymatrix/__init__.py
+++ b/polymatrix/__init__.py
@@ -20,7 +20,6 @@ from polymatrix.statemonad.mixins.statemonadmixin import StateMonadMixin
 from polymatrix.expression.utils.monomialtoindex import monomial_to_index
 from polymatrix.expressionstate.init.initexpressionstate import init_expression_state as original_init_expression_state
 
-
 def init_expression_state():
     return original_init_expression_state()
 
diff --git a/polymatrix/expression/impl/traceexprimpl.py b/polymatrix/expression/impl/traceexprimpl.py
new file mode 100644
index 0000000..19efeeb
--- /dev/null
+++ b/polymatrix/expression/impl/traceexprimpl.py
@@ -0,0 +1,8 @@
+import dataclass_abc
+from polymatrix.expression.traceexpr import TraceExpr 
+
+from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin 
+
+@dataclass_abc.dataclass_abc(frozen=True)
+class TraceExprImpl(TraceExpr):
+	underlying: ExpressionBaseMixin
diff --git a/polymatrix/expression/init/inittraceexpr.py b/polymatrix/expression/init/inittraceexpr.py
new file mode 100644
index 0000000..9069ee6
--- /dev/null
+++ b/polymatrix/expression/init/inittraceexpr.py
@@ -0,0 +1,10 @@
+from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
+from polymatrix.expression.impl.traceexprimpl import TraceExprImpl
+
+
+def init_trace_expr(
+		underlying: ExpressionBaseMixin,
+):
+	return TraceExprImpl(
+		underlying=underlying,
+)
diff --git a/polymatrix/expression/mixins/expressionmixin.py b/polymatrix/expression/mixins/expressionmixin.py
index 4afa44f..43b1e41 100644
--- a/polymatrix/expression/mixins/expressionmixin.py
+++ b/polymatrix/expression/mixins/expressionmixin.py
@@ -33,6 +33,7 @@ from polymatrix.expression.init.initsumexpr import init_sum_expr
 from polymatrix.expression.init.initsymmetricexpr import init_symmetric_expr
 from polymatrix.expression.init.inittoconstantexpr import init_to_constant_expr
 from polymatrix.expression.init.inittoquadraticexpr import init_to_quadratic_expr
+from polymatrix.expression.init.inittraceexpr import init_trace_expr
 from polymatrix.expression.init.inittransposeexpr import init_transpose_expr
 from polymatrix.expression.init.inittruncateexpr import init_truncate_expr
 
@@ -446,6 +447,14 @@ class ExpressionMixin(
             ),
         )
 
+    def trace(self):
+        return dataclasses.replace(
+            self, 
+            underlying=init_trace_expr(
+                underlying=self.underlying,
+            ),
+        )
+
     def truncate(self, variables: tuple, degrees: tuple[int]):
         return dataclasses.replace(
             self, 
diff --git a/polymatrix/expression/mixins/traceexprmixin.py b/polymatrix/expression/mixins/traceexprmixin.py
new file mode 100644
index 0000000..fa46967
--- /dev/null
+++ b/polymatrix/expression/mixins/traceexprmixin.py
@@ -0,0 +1,35 @@
+import abc
+import dataclass_abc
+
+from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
+from polymatrix.expressionstate.mixins.expressionstatemixin import ExpressionStateMixin
+from polymatrix.polymatrix.mixins.polymatrixmixin import PolyMatrixMixin
+
+class TraceExprMixin(ExpressionBaseMixin):
+    @property
+    @abc.abstractclassmethod
+    def underlying(self) -> ExpressionBaseMixin:
+        ...
+
+    # overwrites abstract method of `ExpressionBaseMixin`
+    def apply(
+        self, 
+        state: ExpressionStateMixin,
+    ) -> tuple[ExpressionStateMixin, PolyMatrixMixin]:
+
+        state, underlying = self.underlying.apply(state)
+
+        assert underlying.shape[0] == underlying.shape[1], f'{underlying.shape=}'
+
+        @dataclass_abc.dataclass_abc(frozen=True)
+        class TracePolyMatrix(PolyMatrixMixin):
+            underlying: PolyMatrixMixin
+            shape: tuple[int, int]
+
+            def get_poly(self, row: int, _) -> dict[tuple[int, ...], float]:
+                return self.underlying.get_poly(row, row)
+
+        return state, TracePolyMatrix(
+            underlying=underlying,
+            shape=(underlying.shape[0], 1),
+        )
+\ No newline at end of file
diff --git a/polymatrix/expression/traceexpr.py b/polymatrix/expression/traceexpr.py
new file mode 100644
index 0000000..f35bbca
--- /dev/null
+++ b/polymatrix/expression/traceexpr.py
@@ -0,0 +1,4 @@
+from polymatrix.expression.mixins.traceexprmixin import TraceExprMixin 
+
+class TraceExpr(TraceExprMixin):
+	pass