Comment #7 on issue 2133 by asmeurer: Merge new polynomials manipulation module
http://code.google.com/p/sympy/issues/detail?id=2133

Regarding the intervals thing, if I apply the patch:

diff --git a/sympy/polys/tests/test_polytools.py b/sympy/polys/tests/test_polytools.py
index 61e0576..0bce56c 100644
--- a/sympy/polys/tests/test_polytools.py
+++ b/sympy/polys/tests/test_polytools.py
@@ -1836,8 +1836,9 @@ def test_intervals():

     assert intervals([x**5 - 200, x**5 - 201], fast=True) == \
         [((S(75)/26, S(101)/35), {0: 1}), ((S(283)/98, S(26)/9), {1: 1})]
-
-    assert intervals([x**2 - 200, x**2 - 201]) == \
+    a = intervals([x**2 - 200, x**2 - 201])
+    print a
+    assert a == \
[((-S(71)/5, -S(85)/6), {1: 1}), ((-S(85)/6, -14), {0: 1}), ((14, S(85)/6), {0: 1}), ((S(85)/6, S(71)/5), {1: 1})]

     assert intervals([x+1, x+2, x-1, x+1, 1, x-1, x-1, (x-2)**2]) == \

I get (with SYMPY_GROUND_TYPES=python bin/test sympy/polys/tests/test_polytools.py -k intervals)

============================= test process starts ==============================
executable:   /sw/bin/python  (2.7.1-final-0)
ground types: python

sympy/polys/tests/test_polytools.py[1] [((-71/5, -85/6), {1: 1}), ((-99/7, -113/8), {0: 1}), ((113/8, 99/7), {0: 1}), ((85/6, 71/5), {1: 1})]
F                                  [FAIL]

________________________________________________________________________________
______________ sympy/polys/tests/test_polytools.py:test_intervals ______________ File "/users/aaronmeurer/documents/python/sympy/sympy/sympy/polys/tests/test_polytools.py", line 1842, in test_intervals [((-S(71)/5, -S(85)/6), {1: 1}), ((-S(85)/6, -14), {0: 1}), ((14, S(85)/6), {0: 1}), ((S(85)/6, S(71)/5), {1: 1})]
AssertionError

============= tests finished: 0 passed, 1 failed, in 1.56 seconds ==============
DO *NOT* COMMIT!

but it doesn't seem to be reproducible in the interpreter.

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