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45 lines
1.5 KiB
45 lines
1.5 KiB
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) # cannot simplify with 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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