Comment #46 on issue 1598 by smichr: New polynomials manipulation module
http://code.google.com/p/sympy/issues/detail?id=1598

Also, perhaps roots_cubic and roots_quartic should use the monic function  
rather than
the monic method for reasons discussed in comment 41:

###
>>> var('x');p=Poly(3*x**3+5*x**2+7*x+11)
x
>>> roots(p)
Traceback (most recent call last):
   File "<interactive input>", line 1, in <module>
   File "C:\Documents and Settings\chris\sympy\sympy\polys\polyroots.py",  
line 417, in
roots
     result = _try_decompose(f)
   File "C:\Documents and Settings\chris\sympy\sympy\polys\polyroots.py",  
line 337, in
_try_decompose
     for r in _try_heuristics(h):
   File "C:\Documents and Settings\chris\sympy\sympy\polys\polyroots.py",  
line 380, in
_try_heuristics
     result += roots_cubic(f)
   File "C:\Documents and Settings\chris\sympy\sympy\polys\polyroots.py",  
line 36, in
roots_cubic
     one, a, b, c = f.monic().all_coeffs()
   File "C:\Documents and Settings\chris\sympy\sympy\polys\polytools.py",  
line 1053,
in monic
     result = f.rep.monic()
   File "C:\Documents and Settings\chris\sympy\sympy\polys\polyclasses.py",  
line 1400,
in monic
     return f.per(dmp_ground_monic(f.rep, f.lev, f.dom))
   File "C:\Documents and Settings\chris\sympy\sympy\polys\densetools.py",  
line 1391,
in dmp_ground_monic
     return dup_monic(f, K)
   File "C:\Documents and Settings\chris\sympy\sympy\polys\densetools.py",  
line 1385,
in dup_monic
     return dup_quo_ground(f, lc, K)
   File "C:\Documents and Settings\chris\sympy\sympy\polys\densearith.py",  
line 143,
in dup_quo_ground
     return [ K.quo(cf, c) for cf in f ]
   File "C:\Documents and Settings\chris\sympy\sympy\polys\algebratools.py",  
line 400,
in quo
     raise ExactQuotientFailed('%s does not divide %s in %s' % (b, a, self))
ExactQuotientFailed: 3 does not divide 5 in ZZ


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