I am done

rl/Lib/site-packages/sympy/solvers/tests/test_decompogen.py

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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]
+
+
+@XFAIL
+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