fact: Fixpoint lowest_with_zero_1st_const_coeff n f L := match n with | O => O | S n' => if ps_zerop _ (ps_poly_nth 0 f) then O else let f₁ := next_pol f (β L) (γ L) (ac_root (Φq f L)) in let L₁ := option_get phony_ns (newton_segments f₁) in S (lowest_with_zero_1st_const_coeff n' f₁ L₁) 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