49 lines
1.6 KiB
Python
49 lines
1.6 KiB
Python
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from sympy.core.expr import unchanged
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from sympy.core.symbol import Symbol, symbols
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from sympy.matrices.immutable import ImmutableDenseMatrix
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from sympy.matrices.expressions.companion import CompanionMatrix
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from sympy.polys.polytools import Poly
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from sympy.testing.pytest import raises
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def test_creation():
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x = Symbol('x')
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y = Symbol('y')
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raises(ValueError, lambda: CompanionMatrix(1))
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raises(ValueError, lambda: CompanionMatrix(Poly([1], x)))
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raises(ValueError, lambda: CompanionMatrix(Poly([2, 1], x)))
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raises(ValueError, lambda: CompanionMatrix(Poly(x*y, [x, y])))
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assert unchanged(CompanionMatrix, Poly([1, 2, 3], x))
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def test_shape():
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c0, c1, c2 = symbols('c0:3')
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x = Symbol('x')
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assert CompanionMatrix(Poly([1, c0], x)).shape == (1, 1)
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assert CompanionMatrix(Poly([1, c1, c0], x)).shape == (2, 2)
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assert CompanionMatrix(Poly([1, c2, c1, c0], x)).shape == (3, 3)
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def test_entry():
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c0, c1, c2 = symbols('c0:3')
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x = Symbol('x')
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A = CompanionMatrix(Poly([1, c2, c1, c0], x))
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assert A[0, 0] == 0
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assert A[1, 0] == 1
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assert A[1, 1] == 0
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assert A[2, 1] == 1
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assert A[0, 2] == -c0
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assert A[1, 2] == -c1
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assert A[2, 2] == -c2
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def test_as_explicit():
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c0, c1, c2 = symbols('c0:3')
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x = Symbol('x')
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assert CompanionMatrix(Poly([1, c0], x)).as_explicit() == \
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ImmutableDenseMatrix([-c0])
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assert CompanionMatrix(Poly([1, c1, c0], x)).as_explicit() == \
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ImmutableDenseMatrix([[0, -c0], [1, -c1]])
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assert CompanionMatrix(Poly([1, c2, c1, c0], x)).as_explicit() == \
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ImmutableDenseMatrix([[0, 0, -c0], [1, 0, -c1], [0, 1, -c2]])
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