KP-1.19 run 2: sanity checks of formulas (these are not proofs)
A  Lemma 3.2 in lattice coordinates (exact rational arithmetic)
   point groups found: square 8, rectangular 4, hexagonal 12, rhombic 4, centred rectangular 4, oblique 2
   configurations (lattice, A, m, b) with A m = +-m: 1792  (eps=+1: 896, eps=-1: 896)
   orders of sigma|T that occur: [1, 2, 4, 6, 8, 10, 14, 15, 28, 30, 56]
   tests: 156632
B1 circle action on L(p,q), exact: commutes with the deck group, effective with period 2 pi
   pairs (p,q): [(2, 1), (3, 1), (5, 2), (7, 3), (8, 3), (12, 5), (13, 5)];  tests: 1016
B2 differential of R_theta at the fixed point = rotation by theta about an axis: 12 tests (finite differences)
B3 lift of the rotation loop to the unit quaternions (end point . start point):
   one turn, one turn with a smooth step, two turns, one turn backwards: (-1.0, -1.0, 1.0, -1.0); (-1.0, -1.0, 1.0, -1.0); (-1.0, -1.0, 1.0, -1.0)
   (-1 means the loop generates pi_1(SO(3)) = Z/2; +1 means it is null-homotopic)
B4 the isotopy H_r of Lemma 4.2(a) on the shell: 800 tests
C  property (*) in the figure-eight knot group <x,y>, x=[[1,1],[0,1]], y=[[1,0],[-omega,1]] (exact, Z[omega])
   relation w x = y w with w = x^-1 y x y^-1 holds: True
   reduced words of length <= 10: 118097;  elements fixing infinity among them: 31
   all of these are +-[[1,t],[0,1]] (parabolic or trivial): True;  t in Z + Z(2+4 omega): True;  they commute: True
   a shortest word with t not in Z: yXYxxYXy (length 8), t = 2 + 4 omega
   (*) with a = x: delta x delta^-1 fixes infinity only if delta does: True (118096 words)
   (*) with a = that second element: True (13120 words)
D  collar formula of Step 4 (exact rational arithmetic, four families u_tau): 1680 tests
   includes v in Z^2, where u_1 = id on T and kappa_0 is a twist of the collar that is the identity on both ends
ALL CHECKS PASSED
