Hi, Sage currently has a nice implementation of the Dickman rho function <https://sagemath.gitlab.io/documentation/html/en/reference/functions/sage/functions/transcendental.html> which is a solution to a specific differential delay equation (DDE). In the context of ongoing work with integrals from sieve theory, I'm considering proposing two minor changes :
1. allowing dickman_rho to return a rigorously proven RIF value (easy). As it stands, it seems the precision is a constant multiple of abs_prec for small values of the argument (for large values of the argument using saddle-point method, the relative precision is O(1/x) but the constant is non-explicit as far as I know, I don't intend to work this out) 2. implementing the Buchstab function <https://en.wikipedia.org/wiki/Buchstab_function>, which is another solution to a differential delay equation, or more general solutions to DDE of the type x f'(x) + a f(x) + b f(x-1) = 0 using the same method as in dickman_rho (Marsaglia-Zaman-Marsaglia). Regarding 2. I'm not sure where this should belong: by default I'll propose a builtin "number theoretic function" with parameters a, b, in the same file as dickman_rho, but perhaps it should be part of a specific class, "DDESolution" ? === Sary -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/sage-devel/e906ac8f-2caa-4133-92f9-5b26b7b654abn%40googlegroups.com.
