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| from sympy.solvers.decompogen import decompogen, compogen | |
| from sympy.core.symbol import symbols | |
| from sympy.functions.elementary.complexes import Abs | |
| from sympy.functions.elementary.exponential import exp | |
| from sympy.functions.elementary.miscellaneous import sqrt, Max | |
| from sympy.functions.elementary.trigonometric import (cos, sin) | |
| from sympy.testing.pytest import XFAIL, raises | |
| x, y = symbols('x y') | |
| def test_decompogen(): | |
| assert decompogen(sin(cos(x)), x) == [sin(x), cos(x)] | |
| assert decompogen(sin(x)**2 + sin(x) + 1, x) == [x**2 + x + 1, sin(x)] | |
| assert decompogen(sqrt(6*x**2 - 5), x) == [sqrt(x), 6*x**2 - 5] | |
| assert decompogen(sin(sqrt(cos(x**2 + 1))), x) == [sin(x), sqrt(x), cos(x), x**2 + 1] | |
| assert decompogen(Abs(cos(x)**2 + 3*cos(x) - 4), x) == [Abs(x), x**2 + 3*x - 4, cos(x)] | |
| assert decompogen(sin(x)**2 + sin(x) - sqrt(3)/2, x) == [x**2 + x - sqrt(3)/2, sin(x)] | |
| assert decompogen(Abs(cos(y)**2 + 3*cos(x) - 4), x) == [Abs(x), 3*x + cos(y)**2 - 4, cos(x)] | |
| assert decompogen(x, y) == [x] | |
| assert decompogen(1, x) == [1] | |
| assert decompogen(Max(3, x), x) == [Max(3, x)] | |
| raises(TypeError, lambda: decompogen(x < 5, x)) | |
| u = 2*x + 3 | |
| assert decompogen(Max(sqrt(u),(u)**2), x) == [Max(sqrt(x), x**2), u] | |
| assert decompogen(Max(u, u**2, y), x) == [Max(x, x**2, y), u] | |
| assert decompogen(Max(sin(x), u), x) == [Max(2*x + 3, sin(x))] | |
| def test_decompogen_poly(): | |
| assert decompogen(x**4 + 2*x**2 + 1, x) == [x**2 + 2*x + 1, x**2] | |
| assert decompogen(x**4 + 2*x**3 - x - 1, x) == [x**2 - x - 1, x**2 + x] | |
| def test_decompogen_fails(): | |
| A = lambda x: x**2 + 2*x + 3 | |
| B = lambda x: 4*x**2 + 5*x + 6 | |
| assert decompogen(A(x*exp(x)), x) == [x**2 + 2*x + 3, x*exp(x)] | |
| assert decompogen(A(B(x)), x) == [x**2 + 2*x + 3, 4*x**2 + 5*x + 6] | |
| assert decompogen(A(1/x + 1/x**2), x) == [x**2 + 2*x + 3, 1/x + 1/x**2] | |
| assert decompogen(A(1/x + 2/(x + 1)), x) == [x**2 + 2*x + 3, 1/x + 2/(x + 1)] | |
| def test_compogen(): | |
| assert compogen([sin(x), cos(x)], x) == sin(cos(x)) | |
| assert compogen([x**2 + x + 1, sin(x)], x) == sin(x)**2 + sin(x) + 1 | |
| assert compogen([sqrt(x), 6*x**2 - 5], x) == sqrt(6*x**2 - 5) | |
| assert compogen([sin(x), sqrt(x), cos(x), x**2 + 1], x) == sin(sqrt( | |
| cos(x**2 + 1))) | |
| assert compogen([Abs(x), x**2 + 3*x - 4, cos(x)], x) == Abs(cos(x)**2 + | |
| 3*cos(x) - 4) | |
| assert compogen([x**2 + x - sqrt(3)/2, sin(x)], x) == (sin(x)**2 + sin(x) - | |
| sqrt(3)/2) | |
| assert compogen([Abs(x), 3*x + cos(y)**2 - 4, cos(x)], x) == \ | |
| Abs(3*cos(x) + cos(y)**2 - 4) | |
| assert compogen([x**2 + 2*x + 1, x**2], x) == x**4 + 2*x**2 + 1 | |
| # the result is in unsimplified form | |
| assert compogen([x**2 - x - 1, x**2 + x], x) == -x**2 - x + (x**2 + x)**2 - 1 | |