Just to remark that you are referring to Sage 9.4 docs, rather than to the up to date ones, which should be
https://doc.sagemath.org/html/en/reference/functions/sage/functions/transcendental.html#sage.functions.transcendental.DickmanRho (probably no difference here, but just in case) On Mon, Feb 9, 2026 at 10:40 AM Sary Drappeau <[email protected]> wrote: > > Hi, > > Sage currently has a nice implementation of the Dickman rho function 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 : > > 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) > implementing the 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. -- 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/CAAWYfq1ffuTnOmKSM0B32RTe6fqb8Y%2BXtj1g%3DyE_wcixJ_s4Bg%40mail.gmail.com.
