\START92\
\COMMENT=
\NAME=p3exact
\FILE=P3EXACT.89F
(poly)
Func
\(C)\{a3,a2,a1,a0}:Func
Local  a2,a1,a0,p,q,u,v,r
If  when(poly[1]=0,true,false,false):Return  cZeros(polyEval(poly,x),x)
poly[2]/(poly[1])\->\a2
poly[3]/(poly[1])\->\a1
poly[4]/(poly[1])\->\a0
a1-a2^2/3\->\p
a0-a1*a2/3+2/27*a2^3\->\q
(\(-)\q/2+\root\(q^2/4+p^3/27)+0*\i\)^(1/3)\->\u
If when(u=0,true,false,false) Then
(\(-)\q/2-\root\(q^2/4+p^3/27)+0*\i\)^(1/3)\->\v
Else
\(-)\p/(3*u)\->\v
EndIf
{u+v,(\(-)\1/2+\i\*\root\(3)/2)*u+(\(-)\1/2-\i\*\root\(3)/2)*v,(\(-)\1/2-\i\*\root\(3)/2)*u+(\(-)\1/2+\i\*\root\(3)/2)*v}-a2/3
EndFunc

\STOP92\