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# -*- coding: utf-8 -*-
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from sympy.core.function import (Derivative, Function)
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from sympy.core.numbers import oo
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from sympy.core.symbol import symbols
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from sympy.functions.elementary.exponential import exp
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from sympy.functions.elementary.trigonometric import cos
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from sympy.integrals.integrals import Integral
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from sympy.functions.special.bessel import besselj
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from sympy.functions.special.polynomials import legendre
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from sympy.functions.combinatorial.numbers import bell
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from sympy.printing.conventions import split_super_sub, requires_partial
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from sympy.testing.pytest import XFAIL
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def test_super_sub():
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assert split_super_sub("beta_13_2") == ("beta", [], ["13", "2"])
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assert split_super_sub("beta_132_20") == ("beta", [], ["132", "20"])
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assert split_super_sub("beta_13") == ("beta", [], ["13"])
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assert split_super_sub("x_a_b") == ("x", [], ["a", "b"])
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assert split_super_sub("x_1_2_3") == ("x", [], ["1", "2", "3"])
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assert split_super_sub("x_a_b1") == ("x", [], ["a", "b1"])
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assert split_super_sub("x_a_1") == ("x", [], ["a", "1"])
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assert split_super_sub("x_1_a") == ("x", [], ["1", "a"])
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assert split_super_sub("x_1^aa") == ("x", ["aa"], ["1"])
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assert split_super_sub("x_1__aa") == ("x", ["aa"], ["1"])
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assert split_super_sub("x_11^a") == ("x", ["a"], ["11"])
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assert split_super_sub("x_11__a") == ("x", ["a"], ["11"])
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assert split_super_sub("x_a_b_c_d") == ("x", [], ["a", "b", "c", "d"])
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assert split_super_sub("x_a_b^c^d") == ("x", ["c", "d"], ["a", "b"])
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assert split_super_sub("x_a_b__c__d") == ("x", ["c", "d"], ["a", "b"])
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assert split_super_sub("x_a^b_c^d") == ("x", ["b", "d"], ["a", "c"])
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assert split_super_sub("x_a__b_c__d") == ("x", ["b", "d"], ["a", "c"])
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assert split_super_sub("x^a^b_c_d") == ("x", ["a", "b"], ["c", "d"])
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assert split_super_sub("x__a__b_c_d") == ("x", ["a", "b"], ["c", "d"])
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assert split_super_sub("x^a^b^c^d") == ("x", ["a", "b", "c", "d"], [])
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assert split_super_sub("x__a__b__c__d") == ("x", ["a", "b", "c", "d"], [])
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assert split_super_sub("alpha_11") == ("alpha", [], ["11"])
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assert split_super_sub("alpha_11_11") == ("alpha", [], ["11", "11"])
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assert split_super_sub("w1") == ("w", [], ["1"])
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assert split_super_sub("w𝟙") == ("w", [], ["𝟙"])
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assert split_super_sub("w11") == ("w", [], ["11"])
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assert split_super_sub("w𝟙𝟙") == ("w", [], ["𝟙𝟙"])
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assert split_super_sub("w𝟙2𝟙") == ("w", [], ["𝟙2𝟙"])
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assert split_super_sub("w1^a") == ("w", ["a"], ["1"])
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assert split_super_sub("ω1") == ("ω", [], ["1"])
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assert split_super_sub("ω11") == ("ω", [], ["11"])
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assert split_super_sub("ω1^a") == ("ω", ["a"], ["1"])
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assert split_super_sub("ω𝟙^α") == ("ω", ["α"], ["𝟙"])
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assert split_super_sub("ω𝟙2^3α") == ("ω", ["3α"], ["𝟙2"])
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assert split_super_sub("") == ("", [], [])
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def test_requires_partial():
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x, y, z, t, nu = symbols('x y z t nu')
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n = symbols('n', integer=True)
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f = x * y
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assert requires_partial(Derivative(f, x)) is True
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assert requires_partial(Derivative(f, y)) is True
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## integrating out one of the variables
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assert requires_partial(Derivative(Integral(exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False
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## bessel function with smooth parameter
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f = besselj(nu, x)
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assert requires_partial(Derivative(f, x)) is True
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assert requires_partial(Derivative(f, nu)) is True
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## bessel function with integer parameter
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f = besselj(n, x)
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assert requires_partial(Derivative(f, x)) is False
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# this is not really valid (differentiating with respect to an integer)
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# but there's no reason to use the partial derivative symbol there. make
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# sure we don't throw an exception here, though
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assert requires_partial(Derivative(f, n)) is False
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## bell polynomial
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f = bell(n, x)
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assert requires_partial(Derivative(f, x)) is False
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# again, invalid
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assert requires_partial(Derivative(f, n)) is False
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## legendre polynomial
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f = legendre(0, x)
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assert requires_partial(Derivative(f, x)) is False
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f = legendre(n, x)
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assert requires_partial(Derivative(f, x)) is False
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# again, invalid
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assert requires_partial(Derivative(f, n)) is False
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f = x ** n
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assert requires_partial(Derivative(f, x)) is False
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assert requires_partial(Derivative(Integral((x*y) ** n * exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False
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# parametric equation
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f = (exp(t), cos(t))
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g = sum(f)
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assert requires_partial(Derivative(g, t)) is False
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f = symbols('f', cls=Function)
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assert requires_partial(Derivative(f(x), x)) is False
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assert requires_partial(Derivative(f(x), y)) is False
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assert requires_partial(Derivative(f(x, y), x)) is True
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assert requires_partial(Derivative(f(x, y), y)) is True
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assert requires_partial(Derivative(f(x, y), z)) is True
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assert requires_partial(Derivative(f(x, y), x, y)) is True
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@XFAIL
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def test_requires_partial_unspecified_variables():
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x, y = symbols('x y')
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# function of unspecified variables
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f = symbols('f', cls=Function)
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assert requires_partial(Derivative(f, x)) is False
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assert requires_partial(Derivative(f, x, y)) is True
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