Updates:
Status: Fixed
Comment #8 on issue 1890 by [email protected]: Quartic equation solution
probably not correct
http://code.google.com/p/sympy/issues/detail?id=1890
This equation now raises an error. Bu we also have the Euler form for
applicable quartics which can give a much smaller solution. e.g. For jdU=2
the op-count of all solutions is 297:
EQN2.subs(jdU,2)
-2*x**4 - x**3/2 + x**2 + 1
aa=roots(_,x)
aa
{-1/16 + sqrt(-23/(72*(-611/13824 + sqrt(128001)/4608)**(1/3)) + 67/192 +
2*(-61
1/13824 + sqrt(128001)/4608)**(1/3))/2 -
sqrt(-33/(256*sqrt(-23/(72*(-611/13824
+ sqrt(128001)/4608)**(1/3)) + 67/192 + 2*(-611/13824 +
sqrt(128001)/4608)**(1/3
))) - 2*(-611/13824 + sqrt(128001)/4608)**(1/3) + 67/96 +
23/(72*(-611/13824 + s
qrt(128001)/4608)**(1/3)))/2: 1, -1/16 - sqrt(-23/(72*(-611/13824 +
sqrt(128001)
/4608)**(1/3)) + 67/192 + 2*(-611/13824 + sqrt(128001)/4608)**(1/3))/2 +
sqrt(-2
*(-611/13824 + sqrt(128001)/4608)**(1/3) + 67/96 + 23/(72*(-611/13824 +
sqrt(128
001)/4608)**(1/3)) + 33/(256*sqrt(-23/(72*(-611/13824 +
sqrt(128001)/4608)**(1/3
)) + 67/192 + 2*(-611/13824 + sqrt(128001)/4608)**(1/3))))/2: 1, -1/16 +
sqrt(-2
3/(72*(-611/13824 + sqrt(128001)/4608)**(1/3)) + 67/192 + 2*(-611/13824 +
sqrt(1
28001)/4608)**(1/3))/2 + sqrt(-33/(256*sqrt(-23/(72*(-611/13824 +
sqrt(128001)/4
608)**(1/3)) + 67/192 + 2*(-611/13824 + sqrt(128001)/4608)**(1/3))) -
2*(-611/13
824 + sqrt(128001)/4608)**(1/3) + 67/96 + 23/(72*(-611/13824 +
sqrt(128001)/4608
)**(1/3)))/2: 1, -sqrt(-2*(-611/13824 + sqrt(128001)/4608)**(1/3) + 67/96 +
23/(
72*(-611/13824 + sqrt(128001)/4608)**(1/3)) +
33/(256*sqrt(-23/(72*(-611/13824 +
sqrt(128001)/4608)**(1/3)) + 67/192 + 2*(-611/13824 +
sqrt(128001)/4608)**(1/3)
)))/2 - 1/16 - sqrt(-23/(72*(-611/13824 + sqrt(128001)/4608)**(1/3)) +
67/192 +
2*(-611/13824 + sqrt(128001)/4608)**(1/3))/2: 1}
count_ops(_)
297
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