229 lines
6.3 KiB
Python
229 lines
6.3 KiB
Python
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from sympy.core.add import Add
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from sympy.core.expr import unchanged
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from sympy.core.mul import Mul
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from sympy.core.symbol import symbols
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from sympy.core.relational import Eq
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from sympy.concrete.summations import Sum
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from sympy.functions.elementary.complexes import im, re
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from sympy.functions.elementary.piecewise import Piecewise
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from sympy.matrices.immutable import ImmutableDenseMatrix
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from sympy.matrices.expressions.matexpr import MatrixSymbol
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from sympy.matrices.expressions.matadd import MatAdd
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from sympy.matrices.expressions.special import (
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ZeroMatrix, GenericZeroMatrix, Identity, GenericIdentity, OneMatrix)
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from sympy.matrices.expressions.matmul import MatMul
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from sympy.testing.pytest import raises
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def test_zero_matrix_creation():
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assert unchanged(ZeroMatrix, 2, 2)
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assert unchanged(ZeroMatrix, 0, 0)
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raises(ValueError, lambda: ZeroMatrix(-1, 2))
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raises(ValueError, lambda: ZeroMatrix(2.0, 2))
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raises(ValueError, lambda: ZeroMatrix(2j, 2))
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raises(ValueError, lambda: ZeroMatrix(2, -1))
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raises(ValueError, lambda: ZeroMatrix(2, 2.0))
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raises(ValueError, lambda: ZeroMatrix(2, 2j))
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n = symbols('n')
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assert unchanged(ZeroMatrix, n, n)
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n = symbols('n', integer=False)
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raises(ValueError, lambda: ZeroMatrix(n, n))
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n = symbols('n', negative=True)
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raises(ValueError, lambda: ZeroMatrix(n, n))
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def test_generic_zero_matrix():
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z = GenericZeroMatrix()
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n = symbols('n', integer=True)
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A = MatrixSymbol("A", n, n)
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assert z == z
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assert z != A
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assert A != z
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assert z.is_ZeroMatrix
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raises(TypeError, lambda: z.shape)
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raises(TypeError, lambda: z.rows)
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raises(TypeError, lambda: z.cols)
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assert MatAdd() == z
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assert MatAdd(z, A) == MatAdd(A)
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# Make sure it is hashable
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hash(z)
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def test_identity_matrix_creation():
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assert Identity(2)
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assert Identity(0)
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raises(ValueError, lambda: Identity(-1))
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raises(ValueError, lambda: Identity(2.0))
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raises(ValueError, lambda: Identity(2j))
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n = symbols('n')
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assert Identity(n)
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n = symbols('n', integer=False)
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raises(ValueError, lambda: Identity(n))
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n = symbols('n', negative=True)
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raises(ValueError, lambda: Identity(n))
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def test_generic_identity():
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I = GenericIdentity()
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n = symbols('n', integer=True)
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A = MatrixSymbol("A", n, n)
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assert I == I
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assert I != A
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assert A != I
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assert I.is_Identity
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assert I**-1 == I
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raises(TypeError, lambda: I.shape)
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raises(TypeError, lambda: I.rows)
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raises(TypeError, lambda: I.cols)
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assert MatMul() == I
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assert MatMul(I, A) == MatMul(A)
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# Make sure it is hashable
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hash(I)
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def test_one_matrix_creation():
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assert OneMatrix(2, 2)
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assert OneMatrix(0, 0)
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assert Eq(OneMatrix(1, 1), Identity(1))
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raises(ValueError, lambda: OneMatrix(-1, 2))
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raises(ValueError, lambda: OneMatrix(2.0, 2))
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raises(ValueError, lambda: OneMatrix(2j, 2))
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raises(ValueError, lambda: OneMatrix(2, -1))
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raises(ValueError, lambda: OneMatrix(2, 2.0))
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raises(ValueError, lambda: OneMatrix(2, 2j))
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n = symbols('n')
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assert OneMatrix(n, n)
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n = symbols('n', integer=False)
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raises(ValueError, lambda: OneMatrix(n, n))
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n = symbols('n', negative=True)
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raises(ValueError, lambda: OneMatrix(n, n))
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def test_ZeroMatrix():
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n, m = symbols('n m', integer=True)
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A = MatrixSymbol('A', n, m)
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Z = ZeroMatrix(n, m)
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assert A + Z == A
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assert A*Z.T == ZeroMatrix(n, n)
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assert Z*A.T == ZeroMatrix(n, n)
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assert A - A == ZeroMatrix(*A.shape)
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assert Z
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assert Z.transpose() == ZeroMatrix(m, n)
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assert Z.conjugate() == Z
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assert Z.adjoint() == ZeroMatrix(m, n)
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assert re(Z) == Z
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assert im(Z) == Z
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assert ZeroMatrix(n, n)**0 == Identity(n)
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assert ZeroMatrix(3, 3).as_explicit() == ImmutableDenseMatrix.zeros(3, 3)
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def test_ZeroMatrix_doit():
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n = symbols('n', integer=True)
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Znn = ZeroMatrix(Add(n, n, evaluate=False), n)
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assert isinstance(Znn.rows, Add)
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assert Znn.doit() == ZeroMatrix(2*n, n)
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assert isinstance(Znn.doit().rows, Mul)
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def test_OneMatrix():
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n, m = symbols('n m', integer=True)
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A = MatrixSymbol('A', n, m)
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U = OneMatrix(n, m)
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assert U.shape == (n, m)
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assert isinstance(A + U, Add)
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assert U.transpose() == OneMatrix(m, n)
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assert U.conjugate() == U
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assert U.adjoint() == OneMatrix(m, n)
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assert re(U) == U
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assert im(U) == ZeroMatrix(n, m)
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assert OneMatrix(n, n) ** 0 == Identity(n)
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U = OneMatrix(n, n)
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assert U[1, 2] == 1
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U = OneMatrix(2, 3)
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assert U.as_explicit() == ImmutableDenseMatrix.ones(2, 3)
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def test_OneMatrix_doit():
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n = symbols('n', integer=True)
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Unn = OneMatrix(Add(n, n, evaluate=False), n)
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assert isinstance(Unn.rows, Add)
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assert Unn.doit() == OneMatrix(2 * n, n)
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assert isinstance(Unn.doit().rows, Mul)
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def test_OneMatrix_mul():
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n, m, k = symbols('n m k', integer=True)
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w = MatrixSymbol('w', n, 1)
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assert OneMatrix(n, m) * OneMatrix(m, k) == OneMatrix(n, k) * m
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assert w * OneMatrix(1, 1) == w
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assert OneMatrix(1, 1) * w.T == w.T
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def test_Identity():
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n, m = symbols('n m', integer=True)
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A = MatrixSymbol('A', n, m)
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i, j = symbols('i j')
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In = Identity(n)
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Im = Identity(m)
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assert A*Im == A
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assert In*A == A
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assert In.transpose() == In
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assert In.inverse() == In
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assert In.conjugate() == In
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assert In.adjoint() == In
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assert re(In) == In
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assert im(In) == ZeroMatrix(n, n)
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assert In[i, j] != 0
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assert Sum(In[i, j], (i, 0, n-1), (j, 0, n-1)).subs(n,3).doit() == 3
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assert Sum(Sum(In[i, j], (i, 0, n-1)), (j, 0, n-1)).subs(n,3).doit() == 3
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# If range exceeds the limit `(0, n-1)`, do not remove `Piecewise`:
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expr = Sum(In[i, j], (i, 0, n-1))
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assert expr.doit() == 1
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expr = Sum(In[i, j], (i, 0, n-2))
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assert expr.doit().dummy_eq(
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Piecewise(
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(1, (j >= 0) & (j <= n-2)),
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(0, True)
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)
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)
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expr = Sum(In[i, j], (i, 1, n-1))
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assert expr.doit().dummy_eq(
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Piecewise(
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(1, (j >= 1) & (j <= n-1)),
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(0, True)
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)
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)
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assert Identity(3).as_explicit() == ImmutableDenseMatrix.eye(3)
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def test_Identity_doit():
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n = symbols('n', integer=True)
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Inn = Identity(Add(n, n, evaluate=False))
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assert isinstance(Inn.rows, Add)
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assert Inn.doit() == Identity(2*n)
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assert isinstance(Inn.doit().rows, Mul)
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