Add regression tests & mention closed issues

    close sympy/sympy#3112 (MrvAsympt was added in diofant#6)
    close sympy/sympy#9173 (test was added in 5a510ac)
    close sympy/sympy#9808 (fixed in 09e539b)
    close sympy/sympy#9341 (fixed in af98a00)
    close sympy/sympy#9908 (fixed in cc3fa8d)
    close sympy/sympy#6171 (test added in d278031)
    close sympy/sympy#9276 (diagnose_imports.py removed in ab8c535)
    close sympy/sympy#10201 (fixed in 0d0fc5f)
    close sympy/sympy#9057 (test was added in 8290a0c)
    close sympy/sympy#11159 (test was added in ffb76cb)
    close sympy/sympy#2839 (new AST transformers are used, see diofant#278 and diofant#167)
    close sympy/sympy#11081 (see ed01e16 and bb92329)
    close sympy/sympy#10974 (see 73fc425)
    close sympy/sympy#10806 (test in 539929a)
    close sympy/sympy#10801 (test in 2fe3da5)
    close sympy/sympy#9549 (test in 88bdefa)
    close sympy/sympy#4231 (test was added in fb411d5)
    close sympy/sympy#8634 (see 2fcbb58)
    close sympy/sympy#8481 (see 1ef20d3)
    close sympy/sympy#9956 (fixed in a34735f)
    close sympy/sympy#9747 (see e117c60)
    close sympy/sympy#7853 (see 3e4fbed)
    close sympy/sympy#9634 (see 2be03f5)
    close sympy/sympy#8500 (fixed in diofant#104 and finally in diofant#316)
    close sympy/sympy#9192 (see 9bf622f)
    close sympy/sympy#7130 (see e068fa3)
    close sympy/sympy#8514 (see b2d543b)
    close sympy/sympy#9334 (see 90de625)
    close sympy/sympy#8229 (see 9755b89)
    close sympy/sympy#8061 (see 7054f06)
    close sympy/sympy#7872 (tested in diofant#6)
    close sympy/sympy#3496 (tested in test_log_symbolic)
    close sympy/sympy#2929 (see da7db7a)
    close sympy/sympy#8203 (oo is not a real, see diofant#36)
    close sympy/sympy#7649 (0 is imaginary since diofant#8)
    close sympy/sympy#7256 (fixed in c0a4549)
    close sympy/sympy#6783 (see cb28d63)
    close sympy/sympy#5662 (is_integer issue fixed in 6bfa9f8, there is no is_bounded anymore)
    close sympy/sympy#5295 (fixed with diofant#354)
    close sympy/sympy#4856 (we now have flake/pep tests)
    close sympy/sympy#4555 (flake8 enabled after diofant#214)
    close sympy/sympy#5773 (cmp_to_key removed after diofant#164 and c9acbf0)
    close sympy/sympy#5484 (see above)

    Added regression tests:
    from https://groups.google.com/forum/#!topic/sympy/LkTMQKC_BOw
    fixes sympy/sympy#8825 (probably via diofant#209)
    fixes sympy/sympy#8635
    fixes sympy/sympy#8157
    fixes sympy/sympy#7872
    fixes sympy/sympy#7599
    fixes sympy/sympy#6179
    fixes sympy/sympy#5415
    fixes sympy/sympy#2865
    fixes sympy/sympy#5907
    fixes sympy/sympy#11722

    Closes diofant#347

diofant/core/tests/test_cache.py

@@ -1,7 +1,9 @@
 import pytest
 
-from diofant.core.symbol import Symbol
+from diofant.core.compatibility import ordered
+from diofant.core.symbol import Symbol, symbols
 from diofant.core.cache import cacheit, CACHE, print_cache, clear_cache
+from diofant.printing.str import sstr
 
 from diofant.abc import x
 
@@ -68,7 +70,7 @@ def test_nocache(clear_imports, monkeypatch):
     monkeypatch.setenv('DIOFANT_USE_CACHE', 'False')
     from diofant.core.cache import CACHE
     from diofant.core.symbol import Symbol
-    from diofant.functions import sin, sqrt
+    from diofant.functions import sin, sqrt, exp, sinh
 
     # test that we don't use cache
     assert CACHE == []
@@ -82,7 +84,7 @@ def test_nocache(clear_imports, monkeypatch):
     (2*x).is_complex  # not raises
 
     # see commit c459d18
-    sin(x + x)
+    sin(x + x)  # not raises
 
     # see commit 53dd1eb
     mx = -Symbol('x', negative=False)
@@ -96,3 +98,20 @@ def test_nocache(clear_imports, monkeypatch):
     y = Symbol('y')
     result = s.subs(sqrt(x**2), y)
     assert result == 1/y
+
+    # problem from https://groups.google.com/forum/#!topic/sympy/LkTMQKC_BOw
+    # see commit c459d18
+    a = Symbol('a', positive=True)
+    f = exp(x*(-a - 1))
+    g = sinh(x)
+    r = f*g  # not raises
+
+
+def test_issue_8825():
+    import weakref
+    a, b = symbols('a b')
+    d = weakref.WeakKeyDictionary([(a, 1), (b, 2)])
+    assert sstr(list(ordered(d.items()))) == '[(a, 1), (b, 2)]'
+    del a
+    clear_cache()
+    assert sstr(list(ordered(d.items()))) == '[(b, 2)]'

diofant/integrals/tests/test_integrals.py

@@ -874,6 +874,13 @@ def test_issue_5413():
     assert integrate(-a/(a**2 + x**2), x) == I*log(-I*a + x)/2 - I*log(I*a + x)/2
 
 
+def test_issue_5907():
+    a = Symbol('a', real=True)
+    assert (integrate(1/(x**2 + a**2)**2, x) ==
+            x/(2*a**4 + 2*a**2*x**2) + (-I*log(-I*a + x)/4 +
+                                        I*log(I*a + x)/4)/a**3)
+
+
 def test_issue_4892a():
     A = symbols('A')
     c = Symbol('c', nonzero=True)

diofant/series/tests/test_limits.py

@@ -7,7 +7,7 @@
                      acos, ceiling, atan, gamma, Symbol, S, pi, E, Integral,
                      cot, Rational, I, tan, integrate, Sum, sign, Piecewise,
                      Function, subfactorial, PoleError, Integer, Float,
-                     diff, simplify, Matrix)
+                     diff, simplify, Matrix, sinh, polygamma)
 from diofant.series.limits import heuristics
 from diofant.series.order import O
 
@@ -104,6 +104,12 @@ def eval(cls, arg):
                 return S.NaN
     assert limit(my(x), x, oo) == Limit(my(x), x, oo)
 
+    # from https://groups.google.com/forum/#!topic/sympy/LkTMQKC_BOw
+    # fix bisected to ade6d20 and c459d18
+    a = Symbol('a', positive=True)
+    f = exp(x*(-a - 1)) * sinh(x)
+    assert limit(f, x, oo) == 0
+
 
 def test_issue_3885():
     assert limit(x*y + x*z, z, 2) == x*y + 2*x
@@ -501,3 +507,32 @@ def test_issue_11678():
     assert e == Matrix([[Float('0.36363636363636359', prec=15),
                          Float('0.090909090909090898', prec=15),
                          Float('0.54545454545454541', prec=15)]]*3)
+
+
+def test_issue_8635():
+    n = Symbol('n', integer=True, positive=True)
+
+    k = 0
+    assert limit(x**n - x**(n - k), x, oo) == 0
+    k = 1
+    assert limit(x**n - x**(n - k), x, oo) == oo
+    k = 2
+    assert limit(x**n - x**(n - k), x, oo) == oo
+    k = 3
+    assert limit(x**n - x**(n - k), x, oo) == oo
+
+
+def test_issue_8157():
+    n = Symbol('n', integer=True)
+    limit(cos(pi*n), n, oo)  # not raises
+
+
+def test_issue_5415():
+    assert limit(polygamma(2 + 1/x, 3 + exp(-x)), x, oo) == polygamma(2, 3)
+
+
+def test_issue_2865():
+    l1 = limit(O(1/x, (x, oo)), x, 0)
+    assert l1 != 0 and isinstance(l1, Limit)
+    l2 = limit(O(x, (x, oo)), x, 0)
+    assert l2 != 0 and isinstance(l2, Limit)

diofant/series/tests/test_order.py

@@ -1,6 +1,6 @@
 import pytest
 
-from diofant import (Symbol, Rational, exp, ln, log, nan, oo, O, pi, I,
+from diofant import (Symbol, Rational, exp, ln, log, nan, oo, O, pi, I, Add,
                      Integral, sin, cos, sqrt, conjugate, expand, transpose,
                      symbols, Function, Derivative, Integer, digamma)
 
@@ -335,7 +335,8 @@ def test_issue_6753():
 
 
 def test_issue_7872():
-    assert O(x**3).subs(x, exp(-x**2)) == O(exp(-3*x**2), (x, -oo))
+    assert O(x**3).subs(x, exp(-x**2)) in [O(exp(-3*x**2), (x, oo)),
+                                           O(exp(-3*x**2), (x, -oo))]
 
 
 def test_order_at_infinity():
@@ -421,3 +422,8 @@ def test_issue_9351():
 def test_issue_9192():
     assert O(1)*O(1) == O(1)
     assert O(1)**O(1) == O(1)
+
+
+def test_issue_7599():
+    n = Symbol('n', integer=True)
+    assert O(x**n, x) + O(x**2) == Add(O(x**2), O(x**n, x), evaluate=False)

diofant/series/tests/test_series.py

@@ -177,3 +177,18 @@ def test_issue_11407():
     a, b, c = symbols('a, b, c')
     assert sqrt(a + b + c*x).series(x, 0, 1) == sqrt(a + b) + O(x)
     assert sqrt(a + b + c + c*x).series(x, 0, 1) == sqrt(a + b + c) + O(x)
+
+
+def test_issue_6179():
+    assert (sin(x)*log(x)).series(x, 0, 4) == (x*log(x) -
+                                               x**3*log(x)/6 + O(x**4))
+    assert ((x**2*(x**3 + x**2 + 1)*log(x)).series(x, 0, 4) ==
+            x**2*log(x) + x**4*log(x) + O(x**4))
+
+
+@pytest.mark.slow
+def test_issue_11722():
+    t, g = symbols('t g')
+    good = -g**4*t**4/4 + 7*g**3*t**4/3 + g**3*t**3/3 - 27*g**2*t**4/4 - 2*g**2*t**3 - g**2*t**2/2 + 15*g*t**4/2 + 19*g*t**3/6 + 3*g*t**2/2 + g*t + g - 2009*t**4/720 - 13*t**3/9 - 5*t**2/6 - t/2 - (g + log(-t + 1) - 1 + (g + log(-t + 1))/(-1 + 1/t) - 1/(2*(-1 + 1/t)) - (g + log(-t + 1))**2/(2*(-1 + 1/t)**2) + 3*(g + log(-t + 1))/(2*(-1 + 1/t)**2) - 5/(6*(-1 + 1/t)**2) + (g + log(-t + 1))**3/(3*(-1 + 1/t)**3) - 2*(g + log(-t + 1))**2/(-1 + 1/t)**3 + 19*(g + log(-t + 1))/(6*(-1 + 1/t)**3) - 13/(9*(-1 + 1/t)**3) - (g + log(-t + 1))**4/(4*(-1 + 1/t)**4) + 7*(g + log(-t + 1))**3/(3*(-1 + 1/t)**4) - 27*(g + log(-t + 1))**2/(4*(-1 + 1/t)**4) + 15*(g + log(-t + 1))/(2*(-1 + 1/t)**4) - 2009/(720*(-1 + 1/t)**4) + 1/t)/(1 - 1/(g + log(-t + 1) - 1 + (g + log(-t + 1))/(-1 + 1/t) - 1/(2*(-1 + 1/t)) - (g + log(-t + 1))**2/(2*(-1 + 1/t)**2) + 3*(g + log(-t + 1))/(2*(-1 + 1/t)**2) - 5/(6*(-1 + 1/t)**2) + (g + log(-t + 1))**3/(3*(-1 + 1/t)**3) - 2*(g + log(-t + 1))**2/(-1 + 1/t)**3 + 19*(g + log(-t + 1))/(6*(-1 + 1/t)**3) - 13/(9*(-1 + 1/t)**3) - (g + log(-t + 1))**4/(4*(-1 + 1/t)**4) + 7*(g + log(-t + 1))**3/(3*(-1 + 1/t)**4) - 27*(g + log(-t + 1))**2/(4*(-1 + 1/t)**4) + 15*(g + log(-t + 1))/(2*(-1 + 1/t)**4) - 2009/(720*(-1 + 1/t)**4) + 1/t)) + 1/t
+    bad = good.subs(g, log(1/t))
+    assert bad.series(t, x0=0, n=5) == O(t**5)