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)

Category for operations needed by Taylor expansions.

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

applyTaylor(g, f) applies g to f

apply_taylor : (UTS, PS) -> PS

apply_taylor(g, f) applies g to f

taylor_via_deriv : (Coef, List(PS), List(Mapping(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(Mapping(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