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from itertools import product |
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from sympy.core.power import Pow |
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from sympy.core.symbol import symbols |
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from sympy.functions.elementary.exponential import exp, log |
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from sympy.functions.elementary.trigonometric import cos |
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from sympy.core.numbers import pi |
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from sympy.codegen.scipy_nodes import cosm1, powm1 |
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x, y, z = symbols('x y z') |
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def test_cosm1(): |
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cm1_xy = cosm1(x*y) |
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ref_xy = cos(x*y) - 1 |
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for wrt, deriv_order in product([x, y, z], range(3)): |
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assert ( |
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cm1_xy.diff(wrt, deriv_order) - |
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ref_xy.diff(wrt, deriv_order) |
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).rewrite(cos).simplify() == 0 |
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expr_minus2 = cosm1(pi) |
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assert expr_minus2.rewrite(cos) == -2 |
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assert cosm1(3.14).simplify() == cosm1(3.14) |
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assert cosm1(pi/2).simplify() == -1 |
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assert (1/cos(x) - 1 + cosm1(x)/cos(x)).simplify() == 0 |
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def test_powm1(): |
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cases = { |
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powm1(x, y): x**y - 1, |
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powm1(x*y, z): (x*y)**z - 1, |
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powm1(x, y*z): x**(y*z)-1, |
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powm1(x*y*z, x*y*z): (x*y*z)**(x*y*z)-1 |
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} |
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for pm1_e, ref_e in cases.items(): |
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for wrt, deriv_order in product([x, y, z], range(3)): |
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der = pm1_e.diff(wrt, deriv_order) |
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ref = ref_e.diff(wrt, deriv_order) |
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delta = (der - ref).rewrite(Pow) |
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assert delta.simplify() == 0 |
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eulers_constant_m1 = powm1(x, 1/log(x)) |
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assert eulers_constant_m1.rewrite(Pow) == exp(1) - 1 |
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assert eulers_constant_m1.simplify() == exp(1) - 1 |
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