;; July 25, 2009: physics matrix from Manocha paper, p. 114. ;; takes from 1.9 to 6 secs by various methods. 10 meg (i.e. virtually 0.) That would translate to maybe 19 to 60 secs on his computer. He gets ;; 94 secs. Even multiplying by 20 gives 38 to 120 secs. ;; best is with for i=1,32 do Fin(i,i);DC;Pre;KD;DC;N with &u=2. &u=5 also good. Fin(1,32) is bad! ;; On substituted matrix, get from .458 secs to .8 secs. He gets 21 minutes. about 250 times faster, after hardware allowance. ;; Maple 12, white Imac, crashed after 870 secs, used 700 meg. (plenty more was available) ;; Mathematica 6.0, same Imac, 6 mins 25 secs, 190 meg. ;; June 14, 2010: 1.4 sec with &u=5. ;; Oct 18: .917 with &u=2, new laptop and fer64. ;; Dec 2014: fastest time is &D=3 with Det of non sparse version. ;; Sep 2015: fastest in 0.823 secs. Others are less than 1.2 secs. &(e = 1); &(m = 1); &(a = 1); &(D = 10); &(t = 1); &(J=jj); &(J=ee); &(J=rr); &(J=ka); &(J=al); &(J=be); &(J=ga); &(J=de); &(J=et); &(J=e1); &(J=e2); &(J=e3); &(J=e4); d := de; k := ka; g := ga; e := et; b := be; [m] := [[ e1, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, 0, 0, 0, 0, 0, e1, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, al, 0, 0, 0, 0, 0, 0, 0, 0, e2, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, 0, 0, 0, 0, 0, e2, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, be, 0, 0, 0, 0, de, 0, et, 0, ga, 0, et, 0, de, 0, et, 0, de, 0, et, 0, de, 0, et, 0, de, 0, et, 0, 0, 0, 0, 0, de, 0, et, 0, 0, de, 0, -et, 0, ga, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, 0, 0, 0, 0, de, 0, -et, -et, 0, de, 0, -et, 0, ga, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, de, 0, 0, 0, 0, 0, -et, 0, de, 0, 0, et, 0, de, 0, et, 0, ga, 0, et, 0, de, 0, et, 0, de, 0, et, 0, de, 0, et, 0, de, 0, 0, 0, 0, 0, et, 0, de, de, 0, 0, ka, de, 0, 0, ka, ga, 0, 0, ka, de, 0, 0, ka, de, 0, 0, ka, 0, 0, 0, 0, de, 0, 0, ka, de, 0, 0, ka, 0, de, -ka, 0, 0, de, -ka, 0, 0, ga, -ka, 0, 0, de, -ka, 0, 0, de, -ka, 0, 0, 0, 0, 0, 0, de, -ka, 0, 0, de, -ka, 0, 0, -ka, de, 0, 0, -ka, de, 0, 0, -ka, ga, 0, 0, -ka, de, 0, 0, -ka, de, 0, 0, 0, 0, 0, 0, -ka, de, 0, 0, -ka, de, 0, ka, 0, 0, de, ka, 0, 0, de, ka, 0, 0, ga, ka, 0, 0, de, ka, 0, 0, de, 0, 0, 0, 0, ka, 0, 0, de, ka, 0, 0, de, de, 0, 0, et, de, 0, 0, et, de, 0, 0, et, ga, 0, 0, et, 0, 0, 0, 0, de, 0, 0, et, de, 0, 0, et, de, 0, 0, et, 0, de, et, 0, 0, de, et, 0, 0, de, et, 0, 0, ga, et, 0, 0, 0, 0, 0, 0, de, et, 0, 0, de, et, 0, 0, de, et, 0, 0, -et, de, 0, 0, -et, de, 0, 0, -et, de, 0, 0, -et, ga, 0, 0, 0, 0, 0, 0, -et, de, 0, 0, -et, de, 0, 0, -et, de, 0, -et, 0, 0, de, -et, 0, 0, de, -et, 0, 0, de, -et, 0, 0, ga, 0, 0, 0, 0, -et, 0, 0, de, -et, 0, 0, de, -et, 0, 0, de, de, 0, 0, -et, de, 0, 0, -et, de, 0, 0, -et, 0, 0, 0, 0, de + 1, 0, 0, -et, de, 0, 0, -et, de, 0, 0, -et, de, 0, 0, -et, 0, de, -et, 0, 0, de, -et, 0, 0, de, -et, 0, 0, 0, 0, 0, 0, ga, -et, 0, 0, de, -et, 0, 0, de, -et, 0, 0, de, -et, 0, 0, et, de, 0, 0, et, de, 0, 0, et, de, 0, 0, 0, 0, 0, 0, et, ga, 0, 0, et, de, 0, 0, et, de, 0, 0, et, de, 0, et, 0, 0, de, et, 0, 0, de, et, 0, 0, de, 0, 0, 0, 0, et, 0, 0, ga, et, 0, 0, de, et, 0, 0, de, et, 0, 0, de, de, 0, 0, -ka, de, 0, 0, -ka, 0, 0, 0, 0, de, 0, 0, -ka, de, 0, 0, -ka, ga, 0, 0, -ka, de, 0, 0, -ka, de, 0, 0, -ka, 0, de, ka, 0, 0, de, ka, 0, 0, 0, 0, 0, 0, de, ka, 0, 0, de, ka, 0, 0, ga, ka, 0, 0, de, ka, 0, 0, de, ka, 0, 0, ka, de, 0, 0, ka, de, 0, 0, 0, 0, 0, 0, ka, de, 0, 0, ka, de, 0, 0, ka, ga, 0, 0, ka, de, 0, 0, ka, de, 0, -ka, 0, 0, de, -ka, 0, 0, de, 0, 0, 0, 0, -ka, 0, 0, de, -ka, 0, 0, de, -ka, 0, 0, ga, -ka, 0, 0, de, -ka, 0, 0, de, de, 0, -et, 0, 0, 0, 0, 0, de, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, ga, 0, -et, 0, de, 0, -et, 0, 0, de, 0, et, 0, 0, 0, 0, 0, de, 0, et, 0, de, 0, et, 0, de, 0, et, 0, de, 0, et, 0, ga, 0, et, 0, de, 0, et, et, 0, de, 0, 0, 0, 0, 0, et, 0, de, 0, et, 0, de, 0, et, 0, de, 0, et, 0, de, 0, et, 0, ga, 0, et, 0, de, 0, 0, -et, 0, de, 0, 0, 0, 0, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, de, 0, -et, 0, ga, 0, -et, 0, de, 0, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3 + 1, 0, 0, 0, 0, 0, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3, 0, 0, 0, e3 + 1, 0, 0, 0, 0, 0, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4 + 1, 0, 0, 0, 0, 0, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4, 0, 0, 0, e4 + 1 ]]; &x;