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- from itertools import product
- from sympy.core.power import Pow
- from sympy.core.symbol import symbols
- from sympy.functions.elementary.exponential import exp, log
- from sympy.functions.elementary.trigonometric import cos
- from sympy.core.numbers import pi
- from sympy.codegen.scipy_nodes import cosm1, powm1
- x, y, z = symbols('x y z')
- def test_cosm1():
- cm1_xy = cosm1(x*y)
- ref_xy = cos(x*y) - 1
- for wrt, deriv_order in product([x, y, z], range(3)):
- assert (
- cm1_xy.diff(wrt, deriv_order) -
- ref_xy.diff(wrt, deriv_order)
- ).rewrite(cos).simplify() == 0
- expr_minus2 = cosm1(pi)
- assert expr_minus2.rewrite(cos) == -2
- assert cosm1(3.14).simplify() == cosm1(3.14) # cannot simplify with 3.14
- assert cosm1(pi/2).simplify() == -1
- assert (1/cos(x) - 1 + cosm1(x)/cos(x)).simplify() == 0
- def test_powm1():
- cases = {
- powm1(x, y): x**y - 1,
- powm1(x*y, z): (x*y)**z - 1,
- powm1(x, y*z): x**(y*z)-1,
- powm1(x*y*z, x*y*z): (x*y*z)**(x*y*z)-1
- }
- for pm1_e, ref_e in cases.items():
- for wrt, deriv_order in product([x, y, z], range(3)):
- der = pm1_e.diff(wrt, deriv_order)
- ref = ref_e.diff(wrt, deriv_order)
- delta = (der - ref).rewrite(Pow)
- assert delta.simplify() == 0
- eulers_constant_m1 = powm1(x, 1/log(x))
- assert eulers_constant_m1.rewrite(Pow) == exp(1) - 1
- assert eulers_constant_m1.simplify() == exp(1) - 1
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