While I'm waiting for this massive script to run, I was hoping to get a comparison of the speed of the matrix solvers in the various libraries. Andrew, since you seem to have a copy of Mathematica, Maple, and SAGE, could you generate comparison solver times for various matrix sizes (e.g., 50 to 250 by multiples of 50) for each library. One set of times with rational matrices, and one set with integer?
By integer, I mean don't divide through by the factorial, which means you will have to multiply the "-1" terms (the first subdiagonal) by the factorial to compensate. For bases with where 1/ln(b) is non-integer, this will introduce rationals, so I don't mean "integer" in the general case, but... Anyway, Andrew, could you generate these numbers for comparison? If, as I'm beginning to strongly believe, your solution is the "unique" solution for bases greater than eta (I've only tested e so far), then it would be good to know the quickest way to compute it in each library, as well as sample expected times, etc.
By integer, I mean don't divide through by the factorial, which means you will have to multiply the "-1" terms (the first subdiagonal) by the factorial to compensate. For bases with where 1/ln(b) is non-integer, this will introduce rationals, so I don't mean "integer" in the general case, but... Anyway, Andrew, could you generate these numbers for comparison? If, as I'm beginning to strongly believe, your solution is the "unique" solution for bases greater than eta (I've only tested e so far), then it would be good to know the quickest way to compute it in each library, as well as sample expected times, etc.
~ Jay Daniel Fox
