TaylorSeriesExpansion(Coef, Expon, Var, PS, UTS)

serexp.spad line 1 [edit on github]

• Coef: Algebra Fraction Integer

• Expon: OrderedAbelianMonoid

• Var: OrderedSet

• PS: PowerSeriesCategory(Coef, Expon, Var)

• UTS: UnivariateTaylorSeriesCategory Coef

Author: Waldek Hebisch

apply_taylor: (UTS, PS) -> PS

apply_taylor(g, f) applies g to f

applyTaylor: (UTS -> UTS, PS) -> PS

applyTaylor(g, f) applies g to f

taylor_via_deriv: (Coef, List PS, List(Coef -> Coef)) -> PS

taylor_via_deriv(f, [x1, ..., xn], [D1, ..., Dn]) expands f into Taylor series at (x1, …, xn) using D1, …, Dn as partial derivatives

taylor_via_deriv: (PS, List PS, List(Coef -> Coef)) -> PS

taylor_via_deriv(f, [x1, ..., xn], [D1, ..., Dn]) expands f into Taylor series at (x1, …, xn) using D1, …, Dn as partial derivatives

taylor_via_lode: (List UTS, PS, List Coef) -> PS

taylor_via_lode([a0, ..., ak], z, [c0, ..., ck]) expands into Taylor series solution of the linear ordinary differential equation