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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 | |