5 files changed, 74 insertions, 32 deletions
diff --git a/polymatrix/expression/expression.py b/polymatrix/expression/expression.py
index 9d910db..a7e2025 100644
--- a/polymatrix/expression/expression.py
+++ b/polymatrix/expression/expression.py
@@ -2,7 +2,6 @@ from __future__ import annotations
 
 import dataclasses
 import typing
-import itertools
 import numpy as np
 
 from abc import ABC, abstractmethod
@@ -18,9 +17,8 @@ import polymatrix.expression.init
 from polymatrix.utils.getstacklines import get_stack_lines
 
 from polymatrix.polymatrix.abc import PolyMatrix
-from polymatrix.polymatrix.init import init_poly_matrix
-from polymatrix.polymatrix.typing import PolyMatrixDict, PolyDict, MonomialIndex, VariableIndex
 from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
+from polymatrix.expression.mixins.variablemixin import VariableMixin
 from polymatrix.expression.op import (
     diff,
     integrate,
@@ -508,7 +506,7 @@ class ExpressionImpl(Expression):
     def __repr__(self) -> str:
         return self.underlying.__repr__()
 
-    def copy(self, underlying: ExpressionBaseMixin) -> "Expression":
+    def copy(self, underlying: ExpressionBaseMixin) -> Expression:
         return dataclasses.replace(
             self,
             underlying=underlying,
@@ -528,39 +526,32 @@ class VariableExpression(Expression, Variable):
     Expression that is a polynomial variable, i.e. an expression that cannot be
     reduced further.
     """
-    @property
-    @override
-    def underlying(self):
-        return None
-
-    @override
-    def apply(self, state: ExpressionState) -> tuple[ExpressionState, PolyMatrix]:
-        # Since there is no underlying this class directly does the job of
-        # creating a polymatrix
 
-        state, indices = state.index(self) 
-        p = PolyMatrixDict()
+    def __hash__(self):
+        return self.underlying.__hash__()
 
-        rows, cols = self.shape
-        for (row, col), index in zip(itertools.product(range(rows), range(cols)), indices):
-            p[row, col] = PolyDict({
-                # Create monomial with variable to the first power
-                # with coefficient of one
-                MonomialIndex((VariableIndex(index, power=1),)): 1.
-            })
+    @override
+    @property
+    def name(self):
+        return self.underlyng.name
 
-        return state, init_poly_matrix(p, self.shape)
+    @override
+    @property
+    def shape(self):
+        return self.underlyng.shape
 
 
 @dataclassabc(frozen=True)
 class VariableExpressionImpl(VariableExpression):
-    name: str
-    shape: tuple[int, int]
+    underlying: ExpressionBaseMixin
+
+    def __repr__(self) -> str:
+        return self.underlying.__repr__()
+
+    def copy(self, underlying: ExpressionBaseMixin) -> Expression:
+        return init_expression(underlying)
 
-    @override
-    def copy(self, underlying: ExpressionBaseMixin) -> "Expression":
-        return self
 
+def init_variable_expression(underlying: VariableMixin):
+    return VariableExpressionImpl(underlying)
 
-def init_variable_expression(name: str, shape: tuple[int, int] = (1, 1)):
-    return VariableExpressionImpl(name, shape)
diff --git a/polymatrix/expression/from_.py b/polymatrix/expression/from_.py
index 6fdb672..a1303a3 100644
--- a/polymatrix/expression/from_.py
+++ b/polymatrix/expression/from_.py
@@ -35,8 +35,9 @@ def from_(
 
 def from_names(names: str, shape: tuple[int, int] = (1,1)) -> tuple[VariableExpression] | VariableExpression:
     """ Construct one or multiple variables from comma separated a list of names. """
-    variables = tuple(init_variable_expression(name.strip(), shape)
-                      for name in names.split(","))
+    variables = tuple(init_variable_expression(
+                        underlying=polymatrix.expression.init.init_variable_expr(name.strip(), shape))
+                            for name in names.split(","))
 
     if len(variables) == 1:
         return variables[0]
diff --git a/polymatrix/expression/impl.py b/polymatrix/expression/impl.py
index 8551fc5..119d8c7 100644
--- a/polymatrix/expression/impl.py
+++ b/polymatrix/expression/impl.py
@@ -1,5 +1,6 @@
 import numpy.typing
 import sympy
+from typing_extensions import override
 
 import dataclassabc
 from polymatrix.expression.mixins.integrateexprmixin import IntegrateExprMixin
@@ -65,6 +66,7 @@ from polymatrix.expression.mixins.tosymmetricmatrixexprmixin import (
 )
 from polymatrix.expression.mixins.transposeexprmixin import TransposeExprMixin
 from polymatrix.expression.mixins.truncateexprmixin import TruncateExprMixin
+from polymatrix.expression.mixins.variablemixin import VariableMixin
 from polymatrix.expression.mixins.vstackexprmixin import VStackExprMixin
 from polymatrix.expression.mixins.tosortedvariablesmixin import (
     ToSortedVariablesExprMixin,
@@ -375,5 +377,11 @@ class TruncateExprImpl(TruncateExprMixin):
 
 
 @dataclassabc.dataclassabc(frozen=True)
+class VariableImpl(VariableMixin):
+    name: str
+    shape: tuple[int, int]
+
+
+@dataclassabc.dataclassabc(frozen=True)
 class VStackExprImpl(VStackExprMixin):
     underlying: tuple
diff --git a/polymatrix/expression/init.py b/polymatrix/expression/init.py
index 0e6faf9..131dd82 100644
--- a/polymatrix/expression/init.py
+++ b/polymatrix/expression/init.py
@@ -15,6 +15,7 @@ from polymatrix.utils.getstacklines import get_stack_lines
 from polymatrix.expression.utils.formatsubstitutions import format_substitutions
 from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
 from polymatrix.expression.impl import AdditionExprImpl
+from polymatrix.expression.expression import VariableExpression
 
 
 def init_addition_expr(
@@ -174,6 +175,9 @@ def init_from_sympy_expr(data: sympy.Expr | sympy.Matrix | tuple[tuple[sympy.Exp
 def init_from_expr_or_none(
     data: FromDataTypes,
 ) -> ExpressionBaseMixin | None:
+    if isinstance(data, VariableExpression):
+        return data
+
     if isinstance(data, str):
         return init_parametrize_expr(
             underlying=init_from_expr_or_none(1), # FIXME: typing
@@ -529,3 +533,7 @@ def init_truncate_expr(
         degrees=degrees,
         inverse=inverse,
     )
+
+
+def init_variable_expr(name: str, shape: tuple[int, int]):
+    return polymatrix.expression.impl.VariableImpl(name, shape)
diff --git a/polymatrix/expression/mixins/variablemixin.py b/polymatrix/expression/mixins/variablemixin.py
new file mode 100644
index 0000000..01968e4
--- /dev/null
+++ b/polymatrix/expression/mixins/variablemixin.py
@@ -0,0 +1,34 @@
+from __future__ import annotations
+
+import typing
+import itertools
+from typing_extensions import override
+
+if typing.TYPE_CHECKING:
+    from polymatrix.expressionstate.mixins import ExpressionStateMixin
+
+from polymatrix.expression.mixins.expressionbasemixin import ExpressionBaseMixin
+from polymatrix.polymatrix.abc import PolyMatrix
+from polymatrix.polymatrix.init import init_poly_matrix
+from polymatrix.polymatrix.typing import PolyMatrixDict, PolyDict, MonomialIndex, VariableIndex
+from polymatrix.variable.abc import Variable
+
+
+class VariableMixin(ExpressionBaseMixin, Variable):
+    """ Underlying object for VariableExpression """
+
+    @override
+    def apply(self, state: ExpressionStateMixin) -> tuple[ExpressionStateMixin, PolyMatrixMixin]:
+        state, indices = state.index(self) 
+        p = PolyMatrixDict()
+
+        rows, cols = self.shape
+        for (row, col), index in zip(itertools.product(range(rows), range(cols)), indices):
+            p[row, col] = PolyDict({
+                # Create monomial with variable to the first power
+                # with coefficient of one
+                MonomialIndex((VariableIndex(index, power=1),)): 1.
+            })
+
+        return state, init_poly_matrix(p, self.shape)
+