6 files changed, 67 insertions, 2 deletions
diff --git a/polymatrix/__init__.py b/polymatrix/__init__.py
index ad11c70..de3f9f3 100644
--- a/polymatrix/__init__.py
+++ b/polymatrix/__init__.py
@@ -483,6 +483,7 @@ def to_matrix_repr(
                         continue
                     
                     for monomial, value in underlying_terms.items():
+                        
                         def gen_new_monomial():
                             for var, count in monomial:
                                 try:
diff --git a/polymatrix/expression/impl/tosortedvariablesimpl.py b/polymatrix/expression/impl/tosortedvariablesimpl.py
new file mode 100644
index 0000000..249e55e
--- /dev/null
+++ b/polymatrix/expression/impl/tosortedvariablesimpl.py
@@ -0,0 +1,8 @@
+import dataclass_abc
+from polymatrix.expression.tosortedvariables import ToSortedVariables 
+
+from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin 
+
+@dataclass_abc.dataclass_abc(frozen=True)
+class ToSortedVariablesImpl(ToSortedVariables):
+	underlying: ExpressionBaseMixin
diff --git a/polymatrix/expression/init/inittosortedvariables.py b/polymatrix/expression/init/inittosortedvariables.py
new file mode 100644
index 0000000..5d669c9
--- /dev/null
+++ b/polymatrix/expression/init/inittosortedvariables.py
@@ -0,0 +1,10 @@
+from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
+from polymatrix.expression.impl.tosortedvariablesimpl import ToSortedVariablesImpl
+
+
+def init_to_sorted_variables(
+		underlying: ExpressionBaseMixin,
+):
+	return ToSortedVariablesImpl(
+		underlying=underlying,
+)
diff --git a/polymatrix/expression/mixins/expressionmixin.py b/polymatrix/expression/mixins/expressionmixin.py
index b828d6a..622db34 100644
--- a/polymatrix/expression/mixins/expressionmixin.py
+++ b/polymatrix/expression/mixins/expressionmixin.py
@@ -36,6 +36,7 @@ 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.initdiagexpr import init_diag_expr
+from polymatrix.expression.init.inittosortedvariables import init_to_sorted_variables
 from polymatrix.expression.init.inittransposeexpr import init_transpose_expr
 from polymatrix.expression.init.inittruncateexpr import init_truncate_expr
 
@@ -454,10 +455,18 @@ class ExpressionMixin(
             ),
         )
 
-    def to_quadratic(self) -> 'ExpressionMixin':
+    # def to_quadratic(self) -> 'ExpressionMixin':
+    #     return dataclasses.replace(
+    #         self, 
+    #         underlying=init_to_quadratic_expr(
+    #             underlying=self.underlying,
+    #         ),
+    #     )
+
+    def to_sorted_variables(self) -> 'ExpressionMixin':
         return dataclasses.replace(
             self, 
-            underlying=init_to_quadratic_expr(
+            underlying=init_to_sorted_variables(
                 underlying=self.underlying,
             ),
         )
diff --git a/polymatrix/expression/mixins/tosortedvariablesmixin.py b/polymatrix/expression/mixins/tosortedvariablesmixin.py
new file mode 100644
index 0000000..490604d
--- /dev/null
+++ b/polymatrix/expression/mixins/tosortedvariablesmixin.py
@@ -0,0 +1,33 @@
+
+import abc
+from polymatrix.expression.utils.getvariableindices import get_variable_indices_from_variable
+
+from polymatrix.polymatrix.init.initpolymatrix import init_poly_matrix
+from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
+from polymatrix.polymatrix.polymatrix import PolyMatrix
+from polymatrix.expressionstate.expressionstate import ExpressionState
+
+
+class ToSortedVariablesMixin(ExpressionBaseMixin):
+    @property
+    @abc.abstractmethod
+    def underlying(self) -> ExpressionBaseMixin:
+        ...
+
+    # overwrites abstract method of `ExpressionBaseMixin`
+    def apply(
+        self, 
+        state: ExpressionState,
+    ) -> tuple[ExpressionState, PolyMatrix]:
+        state, variable_indices = get_variable_indices_from_variable(state, self.underlying)
+
+        def gen_sorted_vector():
+            for row, index in enumerate(sorted(variable_indices)):
+                yield (row, 1), {(index, 1): 1}
+        
+        poly_matrix = init_poly_matrix(
+            terms=dict(gen_sorted_vector()),
+            shape=(len(variable_indices), 1),
+        )
+
+        return state, poly_matrix   
diff --git a/polymatrix/expression/tosortedvariables.py b/polymatrix/expression/tosortedvariables.py
new file mode 100644
index 0000000..89ca315
--- /dev/null
+++ b/polymatrix/expression/tosortedvariables.py
@@ -0,0 +1,4 @@
+from polymatrix.expression.mixins.tosortedvariablesmixin import ToSortedVariablesMixin 
+
+class ToSortedVariables(ToSortedVariablesMixin):
+	pass