SAGE code for computing flow matrix for exp(z)-1

[jaydfox]

You may also use the powerseries package that was an outcome/branch of some effort of Andrew and me to put together sage routines for hyperoperations.

Very cool, I've perused through the code a bit and will take a better look when I can dedicate the time. Interestingly, calculating the 101x101 (i.e., size=100) matrix with my code takes about 8 seconds and comsumes negligible RAM (<10 MB), and it takes about 160 seconds for a 201x201 matrix (and perhaps 40-50 MB of RAM). So there seems to be a lot of overhead involved somewhere in the formal power series ring.

On the other hand, the matrix system is nowhere near as flexible; it's specially built for one purpose. Memory-wise 1GB of RAM should be sufficient to calculate somewhere between 600 and 1000 terms (probably close to the low end of that estimate).

Update: 400 terms took 2800 seconds to calculate the parabolic_idm function, and 960 seconds to calculate the "fma" matrix of lagrangian polynomials. Memory usage was about 410 MB (on top of the roughly 130 MB used by SAGE itself). Based on the growth rate, it would seem that 1 GB would only be good enough for about 500 terms, perhaps slightly more. For 600 terms, one would need at least 1.5 GB, perhaps slightly more.