Thanks, Mateusz. I ran into another expression and tried
extension=True but it failed with an error. q should factor neatly
into (x+sqrt(2)/2)*(x-sqrt(3)/3). Whatever is the solution to get that
to factor should probably be applied in the solving routine so
solutions come back in a simple form. Here I am trying to solve the
expanded form of the above for x:
>>> var('x');q=S('6**(1/2)/6 - x*2**(1/2)/2 + x*3**(1/2)/3 - x**2');solve(q,x)
x
[-2**(1/2)*(3 + (15 + 6*6**(1/2))**(1/2) - 6**(1/2))/12, -2**(1/2)*(3
- 6**(1/2) - (15 + 6*6**(1/2))**(1/2))/12]
>>> [nsimplify(w) for w in _]
[-2**(1/2)/2, 3**(1/2)/3]
Now here is the failed extension=True factoring of the same:
>>> q
6**(1/2)/6 - x*2**(1/2)/2 + x*3**(1/2)/3 - x**2
>>> factor(q, extension=True)
Traceback (most recent call last):
File "<interactive input>", line 1, in <module>
File "C:\Documents and Settings\chris\sympy\sympy\polys
\polytools.py", line 2245, in factor
coeff, factors = _factor(f)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\polytools.py", line 2237, in _factor
(coeff, factors), result = F.factor_list(**args), S.One
File "C:\Documents and Settings\chris\sympy\sympy\polys
\polytools.py", line 1387, in factor_list
result = f.rep.factor_list(**args)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\polyclasses.py", line 1497, in factor_list
result = dmp_factor_list(f.rep, f.lev, f.dom, **args)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\factortools.py", line 1139, in dmp_factor_list
return dup_factor_list(f, K0, **args)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\factortools.py", line 1061, in dup_factor_list
coeff, factors = dup_ext_factor(f, K0)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\factortools.py", line 1016, in dup_ext_factor
h, _, g = dup_inner_gcd(h, g, K)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\densetools.py", line 1253, in dup_inner_gcd
return dup_ff_prs_gcd(f, g, K)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\densetools.py", line 887, in dup_ff_prs_gcd
h = dup_monic(h, K)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\densetools.py", line 1408, in dup_monic
return dup_quo_ground(f, lc, K)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\densearith.py", line 144, 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 508, in quo
return a / b
File "C:\Documents and Settings\chris\sympy\sympy\polys
\polyclasses.py", line 2230, in __div__
return f.exquo(g)
File "C:\Documents and Settings\chris\sympy\sympy\polys
\polyclasses.py", line 2153, in quo
return per(dup_rem(dup_mul(F, dup_invert(G, mod, dom), dom), mod,
dom))
File "C:\Documents and Settings\chris\sympy\sympy\polys
\densetools.py", line 367, in dup_invert
raise NotInvertible("zero divisor")
NotInvertible: zero divisor
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