A method is presented for computing all higher-order partial derivatives of a multivariate function R~n → R. This method works by evaluating the function under a nonstandard interpretation, lifting reals to multivariate power series. Multivariate power series, with potentially an infinite number of terms with nonzero coefficients, are represented using a lazy data structure constructed out of linear terms. A complete implementation of this method in Scheme is presented, along with a straightforward exposition, based on Taylor expansions, of the method's correctness.
展开▼
