63 lines
1.9 KiB
Python
63 lines
1.9 KiB
Python
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from sympy.core import S, symbols
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from sympy.matrices import eye, ones, Matrix, ShapeError
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from sympy.matrices.expressions import (
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Identity, MatrixExpr, MatrixSymbol, Determinant,
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det, per, ZeroMatrix, Transpose,
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Permanent
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)
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from sympy.matrices.expressions.special import OneMatrix
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from sympy.testing.pytest import raises
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from sympy.assumptions.ask import Q
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from sympy.assumptions.refine import refine
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n = symbols('n', integer=True)
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A = MatrixSymbol('A', n, n)
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B = MatrixSymbol('B', n, n)
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C = MatrixSymbol('C', 3, 4)
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def test_det():
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assert isinstance(Determinant(A), Determinant)
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assert not isinstance(Determinant(A), MatrixExpr)
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raises(ShapeError, lambda: Determinant(C))
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assert det(eye(3)) == 1
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assert det(Matrix(3, 3, [1, 3, 2, 4, 1, 3, 2, 5, 2])) == 17
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_ = A / det(A) # Make sure this is possible
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raises(TypeError, lambda: Determinant(S.One))
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assert Determinant(A).arg is A
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def test_eval_determinant():
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assert det(Identity(n)) == 1
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assert det(ZeroMatrix(n, n)) == 0
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assert det(OneMatrix(n, n)) == Determinant(OneMatrix(n, n))
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assert det(OneMatrix(1, 1)) == 1
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assert det(OneMatrix(2, 2)) == 0
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assert det(Transpose(A)) == det(A)
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def test_refine():
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assert refine(det(A), Q.orthogonal(A)) == 1
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assert refine(det(A), Q.singular(A)) == 0
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assert refine(det(A), Q.unit_triangular(A)) == 1
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assert refine(det(A), Q.normal(A)) == det(A)
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def test_commutative():
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det_a = Determinant(A)
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det_b = Determinant(B)
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assert det_a.is_commutative
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assert det_b.is_commutative
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assert det_a * det_b == det_b * det_a
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def test_permanent():
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assert isinstance(Permanent(A), Permanent)
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assert not isinstance(Permanent(A), MatrixExpr)
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assert isinstance(Permanent(C), Permanent)
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assert Permanent(ones(3, 3)).doit() == 6
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_ = C / per(C)
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assert per(Matrix(3, 3, [1, 3, 2, 4, 1, 3, 2, 5, 2])) == 103
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raises(TypeError, lambda: Permanent(S.One))
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assert Permanent(A).arg is A
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