08/15/2007, 08:53 PM

Good, it looks linear, should make it easy to write a function to compute a radius of initial convergence, as well as exactly how many terms of the power series are required to reach a desired level of precision. I plan to stay well within half the radius of initial convergence (probably 1/4th to be safe), so this is useful info.

By the way, have you looked at quarter iterates to make sure there aren't any surprises lurking? I don't think it'll matter (might cause the oscillations to shift, but shouldn't affect the overall linearity too badly), but it'd be good to know. Once I'm up and running with a good math library, I can run these tests myself, of course...

By the way, how do rate PARI/gp versus Sage. Should I just go with Sage? I'm already trying to learn PARI/gp (I'm trying out Gottfried's Paritty interface), but it's slow going.

By the way, have you looked at quarter iterates to make sure there aren't any surprises lurking? I don't think it'll matter (might cause the oscillations to shift, but shouldn't affect the overall linearity too badly), but it'd be good to know. Once I'm up and running with a good math library, I can run these tests myself, of course...

By the way, how do rate PARI/gp versus Sage. Should I just go with Sage? I'm already trying to learn PARI/gp (I'm trying out Gottfried's Paritty interface), but it's slow going.

~ Jay Daniel Fox