add max_degree, max and filter operator

16 files changed, 770 insertions, 0 deletions

diff --git a/test_polymatrix/test_expression/__init__.py b/test_polymatrix/test_expression/__init__.py
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/test_polymatrix/test_expression/__init__.py
diff --git a/test_polymatrix/test_expression/test_addition.py b/test_polymatrix/test_expression/test_addition.py
new file mode 100644
index 0000000..623b13f
--- /dev/null
+++ b/test_polymatrix/test_expression/test_addition.py
@@ -0,0 +1,64 @@
+import unittest
+
+from polymatrix.expression.init.initadditionexpr import init_addition_expr
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+
+
+class TestAddition(unittest.TestCase):
+
+    def test_1(self):
+        left_terms = {
+            (0, 0): {
+                tuple(): 1.0,
+                ((0, 1),): 1.0,
+            }, 
+            (1, 0): {
+                ((0, 2),): 1.0,
+            },
+        }
+
+        right_terms = {
+            (0, 0): {
+                tuple(): 3.0,
+                ((1, 1),): 2.0,
+            },
+            (1, 1): {
+                tuple(): 1.0,
+            },
+        }
+
+        left = init_from_terms_expr(
+            terms=left_terms,
+            shape=(2, 2),
+        )
+
+        right = init_from_terms_expr(
+            terms=right_terms,
+            shape=(2, 2),
+        )
+
+        expr = init_addition_expr(
+            left=left,
+            right=right,
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictContainsSubset({
+            tuple(): 4.0,
+            ((0, 1),): 1.0,
+            ((1, 1),): 2.0,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictContainsSubset({
+            ((0, 2),): 1.0,
+        }, data)
+
+        data = val.get_poly(1, 1)
+        self.assertDictContainsSubset({
+            tuple(): 1.0,
+        }, data)
diff --git a/test_polymatrix/test_expression/test_blockdiag.py b/test_polymatrix/test_expression/test_blockdiag.py
new file mode 100644
index 0000000..69141a4
--- /dev/null
+++ b/test_polymatrix/test_expression/test_blockdiag.py
@@ -0,0 +1,58 @@
+import unittest
+
+from polymatrix.expression.init.initblockdiagexpr import init_block_diag_expr
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+
+
+class TestBlockDiag(unittest.TestCase):
+
+    def test_1(self):
+        terms1 = {
+            (0, 0): {
+                ((1, 1),): 1.0,
+            }, 
+            (1, 0): {
+                tuple(): 2.0,
+            },
+        }
+
+        terms2 = {
+            (0, 0): {
+                tuple(): 3.0,
+            },
+            (1, 1): {
+                tuple(): 4.0,
+            },
+        }
+
+        expr = init_block_diag_expr(
+            underlying=(
+                init_from_terms_expr(terms=terms1, shape=(2, 2),), 
+                init_from_terms_expr(terms=terms2, shape=(2, 2),),
+            ),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            ((1, 1),): 1.0,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictEqual({
+            tuple(): 2.0,
+        }, data)
+
+        data = val.get_poly(2, 2)
+        self.assertDictEqual({
+            tuple(): 3.0,
+        }, data)
+
+        data = val.get_poly(3, 3)
+        self.assertDictEqual({
+            tuple(): 4.0,
+        }, data)
+
diff --git a/test_polymatrix/test_expression/test_derivative.py b/test_polymatrix/test_expression/test_derivative.py
new file mode 100644
index 0000000..a4fc6f6
--- /dev/null
+++ b/test_polymatrix/test_expression/test_derivative.py
@@ -0,0 +1,52 @@
+import unittest
+from polymatrix.expression.init.initderivativeexpr import init_derivative_expr
+from polymatrix.expression.init.initdivergenceexpr import init_divergence_expr
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initlinearinexpr import init_linear_in_expr
+
+
+class TestDerivative(unittest.TestCase):
+
+    def test_1(self):
+        underlying_terms = {
+            (0, 0): {
+                ((0, 1),): 2.0,
+                ((1, 2),): 3.0,
+            },
+            (1, 0): {
+                tuple(): 5.0,
+                ((0, 1), (2, 3)): 4.0,
+            },
+        }
+
+        expr = init_derivative_expr(
+            underlying=init_from_terms_expr(terms=underlying_terms, shape=(2, 1)),
+            variables=(0, 1, 2),
+        )
+
+        state = init_expression_state(n_param=3)
+        state, val = expr.apply(state)
+
+        self.assertTupleEqual(val.shape, (2, 3))
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            tuple(): 2.0,
+        }, data)
+
+        data = val.get_poly(0, 1)
+        self.assertDictEqual({
+            ((1, 1),): 6.0,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictEqual({
+            ((2, 3),): 4.0,
+        }, data)
+
+        data = val.get_poly(1, 2)
+        self.assertDictEqual({
+            ((0, 1), (2, 2)): 12.0,
+        }, data)
diff --git a/test_polymatrix/test_expression/test_divergence.py b/test_polymatrix/test_expression/test_divergence.py
new file mode 100644
index 0000000..412dcca
--- /dev/null
+++ b/test_polymatrix/test_expression/test_divergence.py
@@ -0,0 +1,39 @@
+import unittest
+from polymatrix.expression.init.initdivergenceexpr import init_divergence_expr
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initlinearinexpr import init_linear_in_expr
+
+
+class TestDivergence(unittest.TestCase):
+
+    def test_1(self):
+        underlying_terms = {
+            (0, 0): {
+                ((0, 1),): 2.0,
+                ((1, 1),): 3.0,
+            },
+            (1, 0): {
+                tuple(): 5.0,
+                ((0, 1),): 3.0,
+            },
+            (2, 0): {
+                ((0, 1),): 2.0,
+                ((1, 1), (2, 3)): 3.0,
+            },
+        }
+
+        expr = init_divergence_expr(
+            underlying=init_from_terms_expr(terms=underlying_terms, shape=(3, 1)),
+            variables=(0, 1, 2),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            tuple(): 2.0,
+            ((1, 1), (2, 2)): 9.0,
+        }, data)
diff --git a/test_polymatrix/test_expression/test_eval.py b/test_polymatrix/test_expression/test_eval.py
new file mode 100644
index 0000000..662322a
--- /dev/null
+++ b/test_polymatrix/test_expression/test_eval.py
@@ -0,0 +1,41 @@
+import unittest
+
+from polymatrix.expression.init.initevalexpr import init_eval_expr
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+
+
+class TestEval(unittest.TestCase):
+
+    def test_1(self):
+        terms = {
+            (0, 0): {
+                ((0, 1), (2, 1)): 2.0,
+                ((0, 1), (1, 1), (3, 1)): 3.0,
+            }, (1, 0):{
+                tuple(): 1.0,
+                ((1, 2),): 1.0,
+                ((2, 1),): 1.0,
+            },
+        }
+
+        expr = init_eval_expr(
+            underlying=init_from_terms_expr(terms=terms, shape=(2, 1)),
+            variables=(0, 1),
+            values=(2.0, 3.0),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            ((2, 1),): 4.0,
+            ((3, 1),): 18.0,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictEqual({
+            tuple(): 10.0,
+            ((2, 1),): 1,
+        }, data)
diff --git a/test_polymatrix/test_expression/test_linearin.py b/test_polymatrix/test_expression/test_linearin.py
new file mode 100644
index 0000000..67f2c3d
--- /dev/null
+++ b/test_polymatrix/test_expression/test_linearin.py
@@ -0,0 +1,50 @@
+import unittest
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initlinearinexpr import init_linear_in_expr
+
+
+class TestLinearIn(unittest.TestCase):
+
+    def test_1(self):
+        underlying_terms = {
+            (0, 0): {
+                ((0, 1),): 2.0,
+                ((1, 1),): 3.0,
+            },
+        }
+
+        monomial_terms = {
+            (0, 0): {
+                ((0, 1),): 1.0,
+            },
+            (1, 0): {
+                ((2, 1),): 1.0,
+            },
+            (2, 0): {
+                ((1, 1),): 1.0,
+            },
+            (3, 0): {
+                ((3, 1),): 1.0,
+            },
+        }
+
+        expr = init_linear_in_expr(
+            underlying=init_from_terms_expr(terms=underlying_terms, shape=(2, 1)),
+            monomials=init_from_terms_expr(terms=monomial_terms, shape=(4, 1),),
+            variables=(0, 1),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            tuple(): 2.0,
+        }, data)
+
+        data = val.get_poly(0, 2)
+        self.assertDictEqual({
+            tuple(): 3.0,
+        }, data)
diff --git a/test_polymatrix/test_expression/test_matrixmult.py b/test_polymatrix/test_expression/test_matrixmult.py
new file mode 100644
index 0000000..6facb48
--- /dev/null
+++ b/test_polymatrix/test_expression/test_matrixmult.py
@@ -0,0 +1,64 @@
+import unittest
+from polymatrix.expression.init.initadditionexpr import init_addition_expr
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initmatrixmultexpr import init_matrix_mult_expr
+
+
+class TestMatrixMult(unittest.TestCase):
+
+    def test_1(self):
+        left_terms = {
+            (0, 0): {
+                tuple(): 1.0,
+                ((0, 1),): 1.0,
+            },
+            (0, 1): {
+                ((0, 1),): 1.0,
+            }, 
+            (1, 1): {
+                ((0, 2),): 1.0,
+            },
+        }
+
+        right_terms = {
+            (0, 0): {
+                tuple(): 3.0,
+                ((1, 1),): 2.0,
+            },
+            (1, 0): {
+                tuple(): 1.0,
+            },
+        }
+
+        left = init_from_terms_expr(
+            terms=left_terms,
+            shape=(2, 2),
+        )
+
+        right = init_from_terms_expr(
+            terms=right_terms,
+            shape=(2, 1),
+        )
+
+        expr = init_matrix_mult_expr(
+            left=left,
+            right=right,
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            tuple(): 3.0,
+            ((0, 1),): 4.0,
+            ((1, 1),): 2.0,
+            ((0, 1), (1, 1),): 2.0,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictEqual({
+            ((0, 2),): 1.0,
+        }, data)
diff --git a/test_polymatrix/test_expression/test_quadraticin.py b/test_polymatrix/test_expression/test_quadraticin.py
new file mode 100644
index 0000000..c340d7f
--- /dev/null
+++ b/test_polymatrix/test_expression/test_quadraticin.py
@@ -0,0 +1,62 @@
+import unittest
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initquadraticinexpr import init_quadratic_in_expr
+
+
+class TestQuadraticIn(unittest.TestCase):
+
+    def test_1(self):
+        underlying_terms = {
+            (0, 0): {
+                ((0, 1),): 1.0,  # x1
+                ((0, 1), (2, 1)): 2.0,  # x1 
+                ((0, 2), (3, 1)): 3.0,  # x1 x1
+                ((0, 2), (1, 2), (4, 1)): 4.0,  # x1 x1 x2 x2
+                ((0, 2), (1, 1), (5, 1)): 5.0,  # x1 x1 x2
+            }
+        }
+
+        monomial_terms = {
+            (0, 0): {
+                tuple(): 1.0,
+            },
+            (1, 0): {
+                ((0, 1),): 1.0,
+            },
+            (2, 0): {
+                ((0, 1), (1, 1)): 1.0,
+            },
+        }
+
+        expr = init_quadratic_in_expr(
+            underlying=init_from_terms_expr(terms=underlying_terms, shape=(1, 1)),
+            monomials=init_from_terms_expr(terms=monomial_terms, shape=(3, 1)),
+            variables=(0, 1),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 1)
+        self.assertDictContainsSubset({
+            tuple(): 1.0,
+            ((2, 1),): 2.0,
+        }, data)
+
+        data = val.get_poly(1, 1)
+        self.assertDictContainsSubset({
+            ((3, 1),): 3.0,
+        }, data)
+
+        data = val.get_poly(2, 2)
+        self.assertDictContainsSubset({
+            ((4, 1),): 4.0,
+        }, data)
+
+        data = val.get_poly(1, 2)
+        self.assertDictContainsSubset({
+            ((5, 1),): 5.0,
+        }, data)
+    
\ No newline at end of file
diff --git a/test_polymatrix/test_expression/test_substitude.py b/test_polymatrix/test_expression/test_substitude.py
new file mode 100644
index 0000000..9a6e875
--- /dev/null
+++ b/test_polymatrix/test_expression/test_substitude.py
@@ -0,0 +1,43 @@
+import unittest
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initsubstituteexpr import init_substitute_expr
+
+
+class TestEval(unittest.TestCase):
+
+    def test_1(self):
+        terms = {
+            (0, 0): {
+                tuple(): 2.0,
+                ((0, 2),): 3.0,
+                ((1, 1),): 1.0,
+                ((2, 2),): 1.0,
+            },
+        }
+
+        substitution = {
+            (0, 0): {
+                ((1, 1),): 1.0,
+                ((2, 1),): 1.0,
+            },
+        }
+
+        expr = init_substitute_expr(
+            underlying=init_from_terms_expr(terms=terms, shape=(1, 1)),
+            variables=(0,),
+            substitutions=(init_from_terms_expr(terms=substitution, shape=(1, 1)),),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            tuple(): 2.0,
+            ((1, 1),): 1.0,
+            ((1, 2),): 3.0,
+            ((1, 1), (2, 1)): 6.0,
+            ((2, 2),): 4.0
+        }, data)
diff --git a/test_polymatrix/test_expression/test_subtractmonomials.py b/test_polymatrix/test_expression/test_subtractmonomials.py
new file mode 100644
index 0000000..f80f76a
--- /dev/null
+++ b/test_polymatrix/test_expression/test_subtractmonomials.py
@@ -0,0 +1,55 @@
+import unittest
+from polymatrix.expression.init.initderivativeexpr import init_derivative_expr
+from polymatrix.expression.init.initdivergenceexpr import init_divergence_expr
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initlinearinexpr import init_linear_in_expr
+from polymatrix.expression.init.initsubtractmonomialsexpr import init_subtract_monomials_expr
+
+
+class TestDerivative(unittest.TestCase):
+
+    def test_1(self):
+        monomials1 = {
+            (0, 0): {
+                ((0, 1),): 1.0,
+            },
+            (1, 0): {
+                ((0, 1), (1, 2)): 1.0,
+            },
+        }
+
+        monomials2 = {
+            (0, 0): {
+                ((0, 1),): 1.0,
+            },
+            (1, 0): {
+                ((1, 1),): 1.0,
+            },
+        }
+
+        expr = init_subtract_monomials_expr(
+            underlying=init_from_terms_expr(terms=monomials1, shape=(2, 1)),
+            monomials=init_from_terms_expr(terms=monomials2, shape=(2, 1)),
+        )
+
+        state = init_expression_state(n_param=3)
+        state, val = expr.apply(state)
+
+        self.assertTupleEqual(val.shape, (3, 1))
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            tuple(): 1.0,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictEqual({
+            ((1, 2),): 1.0,
+        }, data)
+
+        data = val.get_poly(2, 0)
+        self.assertDictEqual({
+            ((0, 1), (1, 1)): 1.0,
+        }, data)
diff --git a/test_polymatrix/test_expression/test_sum.py b/test_polymatrix/test_expression/test_sum.py
new file mode 100644
index 0000000..48ae073
--- /dev/null
+++ b/test_polymatrix/test_expression/test_sum.py
@@ -0,0 +1,35 @@
+import unittest
+
+from polymatrix.expression.init.initevalexpr import init_eval_expr
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initsumexpr import init_sum_expr
+
+
+class TestSum(unittest.TestCase):
+
+    def test_1(self):
+        terms = {
+            (0, 0): {
+                tuple(): 2.0,
+                ((0, 1),): 3.0,
+            }, 
+            (0, 1):{
+                tuple(): 1.0,
+                ((0, 2),): 1.0,
+            },
+        }
+
+        expr = init_sum_expr(
+            underlying=init_from_terms_expr(terms=terms, shape=(1, 2)),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            tuple(): 3.0,
+            ((0, 1),): 3.0,
+            ((0, 2),): 1.0,
+        }, data)
diff --git a/test_polymatrix/test_expression/test_symmetric.py b/test_polymatrix/test_expression/test_symmetric.py
new file mode 100644
index 0000000..ac5eba6
--- /dev/null
+++ b/test_polymatrix/test_expression/test_symmetric.py
@@ -0,0 +1,53 @@
+import unittest
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initquadraticinexpr import init_quadratic_in_expr
+from polymatrix.expression.init.initsymmetricexpr import init_symmetric_expr
+
+
+class TestQuadraticIn(unittest.TestCase):
+
+    def test_1(self):
+        terms = {
+            (0, 0): {
+                ((0, 1),): 1.0,
+            },
+            (1, 0): {
+                ((1, 1),): 1.0,
+            },
+            (0, 1): {
+                ((1, 1),): 1.0,
+                ((2, 1),): 1.0,
+            },
+        }
+
+        underlying = init_from_terms_expr(
+            terms=terms,
+            shape=(2, 2),
+        )
+
+        expr = init_symmetric_expr(
+            underlying=underlying,
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictContainsSubset({
+            ((0, 1),): 1.0,
+        }, data)
+
+        data = val.get_poly(0, 1)
+        self.assertDictContainsSubset({
+            ((1, 1),): 1.0,
+            ((2, 1),): 0.5,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictContainsSubset({
+            ((1, 1),): 1.0,
+            ((2, 1),): 0.5,
+        }, data)
+    
\ No newline at end of file
diff --git a/test_polymatrix/test_expression/test_toconstant.py b/test_polymatrix/test_expression/test_toconstant.py
new file mode 100644
index 0000000..784aeec
--- /dev/null
+++ b/test_polymatrix/test_expression/test_toconstant.py
@@ -0,0 +1,46 @@
+import unittest
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initquadraticinexpr import init_quadratic_in_expr
+from polymatrix.expression.init.initsymmetricexpr import init_symmetric_expr
+from polymatrix.expression.init.inittoconstantexpr import init_to_constant_expr
+from polymatrix.expression.init.inittruncateexpr import init_truncate_expr
+
+
+class TestToConstant(unittest.TestCase):
+
+    def test_1(self):
+        terms = {
+            (0, 0): {
+                tuple(): 2.0,
+                ((0, 1),): 1.0,
+            },
+            (1, 0): {
+                ((0, 2), (1, 1)): 1.0,
+                ((0, 3), (1, 1)): 1.0,
+            },
+            (0, 1): {
+                tuple(): 5.0,
+                ((0, 2), (2, 1),): 1.0,
+                ((3, 1),): 1.0,
+            },
+        }
+
+        expr = init_to_constant_expr(
+            underlying=init_from_terms_expr(terms=terms, shape=(2, 2)),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            tuple(): 2.0,
+        }, data)
+
+        data = val.get_poly(0, 1)
+        self.assertDictEqual({
+            tuple(): 5.0,
+        }, data)
+    
\ No newline at end of file
diff --git a/test_polymatrix/test_expression/test_truncate.py b/test_polymatrix/test_expression/test_truncate.py
new file mode 100644
index 0000000..e944229
--- /dev/null
+++ b/test_polymatrix/test_expression/test_truncate.py
@@ -0,0 +1,50 @@
+import unittest
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initquadraticinexpr import init_quadratic_in_expr
+from polymatrix.expression.init.initsymmetricexpr import init_symmetric_expr
+from polymatrix.expression.init.inittruncateexpr import init_truncate_expr
+
+
+class TestTruncate(unittest.TestCase):
+
+    def test_1(self):
+        terms = {
+            (0, 0): {
+                ((0, 1),): 1.0,  # x1 x1
+            },
+            (1, 0): {
+                ((0, 2), (1, 1)): 1.0,  # x1 x1 x2
+                ((0, 3), (1, 1)): 1.0,  # x1 x1 x1 x2
+            },
+            (0, 1): {
+                ((0, 2), (2, 1),): 1.0,  # x1 x1
+                ((3, 1),): 1.0,
+            },
+        }
+
+        expr = init_truncate_expr(
+            underlying=init_from_terms_expr(terms=terms, shape=(2, 2)),
+            variables=(0, 1),
+            degrees=(1, 2),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            ((0, 1),): 1.0,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictEqual(
+            {}, data
+        )
+
+        data = val.get_poly(0, 1)
+        self.assertDictEqual({
+            ((0, 2), (2, 1)): 1.0,  # x1 x1
+        }, data)
+    
\ No newline at end of file
diff --git a/test_polymatrix/test_expression/test_vstack.py b/test_polymatrix/test_expression/test_vstack.py
new file mode 100644
index 0000000..a50267f
--- /dev/null
+++ b/test_polymatrix/test_expression/test_vstack.py
@@ -0,0 +1,58 @@
+import unittest
+
+from polymatrix.expression.init.initexpressionstate import init_expression_state
+from polymatrix.expression.init.initfromtermsexpr import init_from_terms_expr
+from polymatrix.expression.init.initvstackexpr import init_v_stack_expr
+
+
+class TestVStack(unittest.TestCase):
+
+    def test_1(self):
+        terms1 = {
+            (0, 0): {
+                ((1, 1),): 1.0,
+            }, 
+            (1, 0): {
+                tuple(): 2.0,
+            },
+        }
+
+        terms2 = {
+            (0, 0): {
+                tuple(): 3.0,
+            },
+            (1, 1): {
+                tuple(): 4.0,
+            },
+        }
+
+        expr = init_v_stack_expr(
+            underlying=(
+                init_from_terms_expr(terms=terms1, shape=(2, 2),), 
+                init_from_terms_expr(terms=terms2, shape=(2, 2),),
+            ),
+        )
+
+        state = init_expression_state(n_param=2)
+        state, val = expr.apply(state)
+
+        data = val.get_poly(0, 0)
+        self.assertDictEqual({
+            ((1, 1),): 1.0,
+        }, data)
+
+        data = val.get_poly(1, 0)
+        self.assertDictEqual({
+            tuple(): 2.0,
+        }, data)
+
+        data = val.get_poly(2, 0)
+        self.assertDictEqual({
+            tuple(): 3.0,
+        }, data)
+
+        data = val.get_poly(3, 1)
+        self.assertDictEqual({
+            tuple(): 4.0,
+        }, data)
+