StreamExponentialSeriesOperations CoefΒΆ

expps.spad line 23 [edit on github]

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, () -> 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.