StreamExponentialSeriesOperations(Coef)

expps.spad line 22 [edit on github]

• Coef : CommutativeRing

StreamExponentialSeriesOperations implements arithmetic of exponential power series, where a power series is represented by a stream of its coefficients.

* : (Stream(Coef), Stream(Coef)) -> Stream(Coef)

a * b returns the power series (Cauchy) product of a and b: [a0, a1, ...] * [b0, b1, ...] = [c0, c1, ...] where ck = sum(i + j = k, binomial(k, i) * ai * bj).

deriv : Stream(Coef) -> Stream(Coef)

deriv(f) is the derivative, which simply coincides with left shift

exp0 : Stream(Coef) -> Stream(Coef)

exp0(f) returns the exponential of the power series represented by cons(0, f), i.e. assuming zero constant term and therefore transcendentality is not involved.

integrate : (Coef, Stream(Coef)) -> Stream(Coef)

integrate(c, f) integrates with constant term c, this is simply the right shift

lazyIntegrate : (Coef, Mapping(Stream(Coef))) -> Stream(Coef)

lazyIntegrate(c, f) integrates with constant term c, this is simply the right shift

log1 : Stream(Coef) -> Stream(Coef)

log1(f) returns the logarithm of the power series represented by cons(1, f), i.e. assuming that the constant term is 1 and therefore transcendentality is not involved.