Пример #1
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def test_diff():
    x = Symbol("x")
    y = Symbol("y")
    f = Function("f")
    g = Function("g")
    assert simplify(g(x).diff(x)*f(x).diff(x) - f(x).diff(x)*g(x).diff(x)) == 0
    assert simplify(2*f(x)*f(x).diff(x) - diff(f(x)**2, x)) == 0
    assert simplify(diff(1/f(x), x) + f(x).diff(x)/f(x)**2) == 0
    assert simplify(f(x).diff(x, y) - f(x).diff(y, x)) == 0
Пример #2
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def test_diff():
    x = Symbol("x")
    y = Symbol("y")
    f = Function("f")
    g = Function("g")
    assert simplify(g(x).diff(x)*f(x).diff(x) - f(x).diff(x)*g(x).diff(x)) == 0
    assert simplify(2*f(x)*f(x).diff(x) - diff(f(x)**2, x)) == 0
    assert simplify(diff(1/f(x), x) + f(x).diff(x)/f(x)**2) == 0
    assert simplify(f(x).diff(x, y) - f(x).diff(y, x)) == 0
Пример #3
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def test_simplify_function_inverse():
    x, y = symbols('x, y')
    g = Function('g')

    class f(Function):
        def inverse(self, argindex=1):
            return g

    assert simplify(f(g(x))) == x
    assert simplify(f(g(sin(x)**2 + cos(x)**2))) == 1
    assert simplify(f(g(x, y))) == f(g(x, y))
Пример #4
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def test_simplify_function_inverse():
    x, y = symbols('x, y')
    g = Function('g')

    class f(Function):
        def inverse(self, argindex=1):
            return g

    assert simplify(f(g(x))) == x
    assert simplify(f(g(sin(x)**2 + cos(x)**2))) == 1
    assert simplify(f(g(x, y))) == f(g(x, y))
Пример #5
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def test_simplify_function_inverse():
    # "inverse" attribute does not guarantee that f(g(x)) is x
    # so this simplification should not happen automatically.
    # See issue #12140
    x, y = symbols('x, y')
    g = Function('g')

    class f(Function):
        def inverse(self, argindex=1):
            return g

    assert simplify(f(g(x))) == f(g(x))
    assert inversecombine(f(g(x))) == x
    assert simplify(f(g(x)), inverse=True) == x
    assert simplify(f(g(sin(x)**2 + cos(x)**2)), inverse=True) == 1
    assert simplify(f(g(x, y)), inverse=True) == f(g(x, y))
    assert simplify(2 * asin(sin(3 * x)), inverse=True) == 6 * x
Пример #6
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def test_simplify_function_inverse():
    # "inverse" attribute does not guarantee that f(g(x)) is x
    # so this simplification should not happen automatically.
    # See issue #12140
    x, y = symbols('x, y')
    g = Function('g')

    class f(Function):
        def inverse(self, argindex=1):
            return g

    assert simplify(f(g(x))) == f(g(x))
    assert inversecombine(f(g(x))) == x
    assert simplify(f(g(x)), inverse=True) == x
    assert simplify(f(g(sin(x)**2 + cos(x)**2)), inverse=True) == 1
    assert simplify(f(g(x, y)), inverse=True) == f(g(x, y))
    assert simplify(2*asin(sin(3*x)), inverse=True) == 6*x
Пример #7
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def test_simplify_function_inverse():
    # "inverse" attribute does not guarantee that f(g(x)) is x
    # so this simplification should not happen automatically.
    # See issue #12140
    x, y = symbols("x, y")
    g = Function("g")

    class f(Function):
        def inverse(self, argindex=1):
            return g

    assert simplify(f(g(x))) == f(g(x))
    assert inversecombine(f(g(x))) == x
    assert simplify(f(g(x)), inverse=True) == x
    assert simplify(f(g(sin(x)**2 + cos(x)**2)), inverse=True) == 1
    assert simplify(f(g(x, y)), inverse=True) == f(g(x, y))
    assert unchanged(asin, sin(x))
    assert simplify(asin(sin(x))) == asin(sin(x))
    assert simplify(2 * asin(sin(3 * x)), inverse=True) == 6 * x
    assert simplify(log(exp(x))) == log(exp(x))
    assert simplify(log(exp(x)), inverse=True) == x
    assert simplify(log(exp(x), 2), inverse=True) == x / log(2)
    assert simplify(log(exp(x), 2, evaluate=False), inverse=True) == x / log(2)