[Do Not Merge] RuntimeError if SYMPY_USE_CACHE='no'

[pzrq]

I do not want this merged as is, this is just a point to start the discussion on how to fix it as it makes it a lot harder to debug other issues I am trying to resolve.

Basically I have used the following file, which turns off the SymPy cache and runs a test from the existing solution:
https://gist.github.com/pzrq/05a5d1a16c63e7485110

The commit messages indicate the detected results in that I at least (Mac OSX, Python 2.7) am seeing stack traces that result in:
RuntimeError: maximum recursion depth exceeded

The first one seems to be attempting something like zero -> algebraic -> imaginary -> negative [then always recursively loops back to negative, the exact route depends on a shuffle].

I have not looked in detail at the second one, just ran the gist. Usage was just a variation on python test.py, fed into git bisect or other commands as needed.

[pzrq]

Reproduced on master with no additional test files, just a console:

In [1]: import os

In [2]: os.environ['SYMPY_USE_CACHE'] = 'no'

In [3]: import sympy

In [4]: sympy.test('sympy/integrals/tests/test_integrals', kw='test_issue_4737')
=========================================== test process starts ============================================
executable:         /Users/pzrq/.virtualenvs/sympy/bin/python  (2.7.6-final-0) [CPython]
architecture:       64-bit
cache:              no
ground types:       python 
random seed:        41546754
hash randomization: on (PYTHONHASHSEED=2660920852)

sympy/integrals/tests/test_integrals.py[1] E                                                          [FAIL]

____________________________________________________________________________________________________________
_________________________ sympy/integrals/tests/test_integrals.py:test_issue_4737 __________________________
  File "/users/pzrq/projects/sympy/sympy/integrals/tests/test_integrals.py", line 964, in test_issue_4737
    assert integrate(sin(x)/x, (x, -oo, oo)) == pi
  File "sympy/utilities/decorator.py", line 35, in threaded_func
    return func(expr, *args, **kwargs)
  File "sympy/integrals/integrals.py", line 1254, in integrate
    risch=risch, manual=manual)
  File "sympy/integrals/integrals.py", line 390, in doit
    if self.is_zero:
  File "sympy/core/assumptions.py", line 245, in getit
    return _ask(fact, self)
  File "sympy/core/assumptions.py", line 288, in _ask
    a = evaluate(obj)
  File "sympy/integrals/integrals.py", line 109, in _eval_is_zero
    if self.function.is_zero:
  File "sympy/core/assumptions.py", line 245, in getit
    return _ask(fact, self)
  File "sympy/core/assumptions.py", line 288, in _ask
    a = evaluate(obj)
  File "sympy/core/mul.py", line 993, in _eval_is_zero
    z = a.is_zero
  File "sympy/core/assumptions.py", line 245, in getit
    return _ask(fact, self)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 288, in _ask
    a = evaluate(obj)
  File "sympy/core/power.py", line 983, in _eval_is_algebraic
    if self.base.is_zero or (self.base - 1).is_zero:
  File "sympy/core/assumptions.py", line 245, in getit
    return _ask(fact, self)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 288, in _ask
    a = evaluate(obj)
  File "sympy/core/add.py", line 469, in _eval_is_imaginary
    r = _fuzzy_group(a.is_real for a in iargs)
  File "sympy/core/logic.py", line 52, in _fuzzy_group
    for a in args:
  File "sympy/core/add.py", line 469, in <genexpr>
    r = _fuzzy_group(a.is_real for a in iargs)
  File "sympy/core/assumptions.py", line 245, in getit
    return _ask(fact, self)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 288, in _ask
    a = evaluate(obj)
  File "sympy/core/mul.py", line 1008, in _eval_is_integer
    is_rational = self.is_rational
  File "sympy/core/assumptions.py", line 245, in getit
    return _ask(fact, self)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 288, in _ask
    a = evaluate(obj)
  File "sympy/core/mul.py", line 1150, in _eval_is_negative
    return (-self).is_positive
  File "sympy/core/assumptions.py", line 245, in getit
    return _ask(fact, self)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 288, in _ask
    a = evaluate(obj)
  File "sympy/core/mul.py", line 1150, in _eval_is_negative
    return (-self).is_positive
  File "sympy/core/assumptions.py", line 245, in getit
    return _ask(fact, self)
  File "sympy/core/assumptions.py", line 300, in _ask
    _ask(pk, obj)
  File "sympy/core/assumptions.py", line 288, in _ask
    a = evaluate(obj)
  File "sympy/core/mul.py", line 1150, in _eval_is_negative
    return (-self).is_positive

< Removed lots more output for readability>

RuntimeError: maximum recursion depth exceeded while calling a Python object

========================= tests finished: 0 passed, 1 exceptions, in 0.23 seconds ==========================
DO *NOT* COMMIT!
Out[4]: False

[pzrq]

Generalised on #8266