fact: Fixpoint find_coeff α {R : ring α} {K : field R} {acf : algeb_closed_field K} max_iter npow m f L i := match max_iter with | 0%nat => 0%K | S mx => if ps_zerop _ (ps_poly_nth 0 f) then 0%K else match Nat.compare npow i with | Eq => ac_root (Φq f L) | Lt => let c₁ := ac_root (Φq f L) in let f₁ := next_pol f (β L) (γ L) c₁ in let L₁ := option_get phony_ns (newton_segments f₁) in let npow₁ := next_pow npow L₁ m in find_coeff mx npow₁ m f₁ L₁ i | Gt => 0%K end end.
imports: Utf8 QArith NPeano Sorting Misc Field2 Fpolynomial Fsummation Newton ConvexHull Power_series Puiseux_series Ps_add Ps_mul Ps_div PSpolynomial Puiseux_base AlgCloCharPol CharactPolyn F1Eq F1Prop Q_field PosOrder QbarM