Bug in roots()?
Hi guys, I might have found a bug in the roots method. Below is some (ugly) polynomial of degree 4 over a fraction field of a polynomial ring over a finite extension of GF(11). The roots() method returns 0 as a root which it is not. If i do the same thing over QQ instead of GF(11) "Not implemented" is returned. Sry i couldn't come up with a shorter example.
sage: K0=GF(11)
sage: #K0=QQ
sage: R0.<b>=K0[]
sage: K.<b>=K0.extension(b^5+4)
sage: R1.<z3>=K[]
sage: L=FractionField(R1)
sage: R.<x>=L[]
sage: f=(x^4 + ((3*b^3*z3^24 + 9*b^4*z3^23 + 8*z3^22 + 7*b*z3^21 + 9*b^2*z3^20 + 4*b^3*z3^19 + 4*b^4*z3^18 + 10*z3^17 + 6*b*z3^16 + 4*b^2*z3^15 + 6*b^3*z3^14 + 4*b^4*z3^13 + 5*z3^12 + 2*b*z3^11 + 3*b^2*z3^10 + b^3*z3^9 + b^4*z3^8 + 9*z3^7 + 2*b*z3^6 + 4*b^2*z3^5 + b^4*z3^3 + 2*z3^2 + 9*b*z3 + 10*b^2)/(b^4*z3^24 + 7*z3^23 + 7*b*z3^22 + 2*b^2*z3^21 + b^3*z3^20 + 5*b^4*z3^19 + 9*z3^18 + 7*b*z3^17 + 2*b^3*z3^15 + 8*b^4*z3^14 + 2*z3^13 + 7*b*z3^12 + 6*b^3*z3^10 + 6*b^4*z3^9 + 4*z3^8 + b*z3^7 + 8*b^3*z3^5 + 5*b^4*z3^4))*x^3 + ((5*b^3*z3^26 + 9*b^4*z3^25 + 8*z3^24 + 10*b*z3^23 + 3*b^2*z3^22 + 8*b^3*z3^21 + 8*b^4*z3^20 + 6*z3^19 + 4*b*z3^18 + 7*b^2*z3^17 + 9*b^4*z3^15 + 7*z3^14 + b*z3^13 + 5*b^2*z3^12 + 10*b^3*z3^11 + 6*z3^9 + 4*b*z3^8 + 3*b^2*z3^7 + 8*b^3*z3^6 + 2*b^4*z3^5 + 4*z3^4 + 6*b*z3^3 + 2*b^2*z3^2 + 5*b^3*z3 + 10*b^4)/(b^4*z3^27 + 7*z3^26 + 7*b*z3^25 + 2*b^2*z3^24 + b^3*z3^23 + 5*b^4*z3^22 + 9*z3^21 + 7*b*z3^20 + 2*b^3*z3^18 + 8*b^4*z3^17 + 2*z3^16 + 7*b*z3^15 + 6*b^3*z3^13 + 6*b^4*z3^12 + 4*z3^11 + b*z3^10 + 8*b^3*z3^8 + 5*b^4*z3^7))*x^2 + ((9*b^3*z3^28 + b^4*z3^27 + 8*z3^26 + 4*b*z3^25 + 3*b^3*z3^23 + 7*b^4*z3^22 + 2*z3^21 + 6*b*z3^20 ...
Seems to be a bug in the Singular interface. For
f._singular_()
returnsx^4