# check_siblings.py  mp.dps = 60

## (a)+(b): original pedal.  c1 size (max over phases) ; spread of A_M/A per M ; spread of c0/A, c2/A
  a=1.3 N= 6 tau=1: |c1| <= 9.33e-61; A_M/A spread: 3.09e-61, 4.36e-61, 3.76e-61, 4.84e-61, 9.72e-61; c0/A 3.09e-61, c2/A 1.03e-60
  a=2.0 N= 6 tau=1: |c1| <= 3.73e-60; A_M/A spread: 5.0e-61, 8.15e-61, 9.54e-61, 5.08e-61, 1.17e-60; c0/A 5.0e-61, c2/A 2.01e-60
  a=3.5 N=10 tau=3: |c1| <= 1.72e-59; A_M/A spread: 1.74e-59, 1.29e-59, 8.6e-59, 1.31e-59, 2.51e-59; c0/A 1.74e-59, c2/A 1.85e-59
  a=2.0 N=10 tau=1: |c1| <= 1.56e-60; A_M/A spread: 4.39e-61, 2.58e-61, 4.38e-61, 2.33e-61, 3.55e-61; c0/A 4.39e-61, c2/A 1.3e-60
  a=2.0 N=14 tau=3: |c1| <= 5.6e-60; A_M/A spread: 1.27e-60, 1.46e-60, 1.62e-60, 2.1e-60, 1.64e-60; c0/A 1.27e-60, c2/A 3.49e-60
  a=2.0 N= 8 tau=1: |c1| <= 1.87e-60; A_M/A spread: 0.00162, 0.00162, 0.00162, 0.00162, 0.00162; c0/A 0.00162, c2/A 0.00162
  a=2.0 N=12 tau=5: |c1| <= 8.19e-57; A_M/A spread: 0.0142, 0.0142, 0.0142, 0.0142, 0.0142; c0/A 0.0142, c2/A 0.0142
  a=2.0 N= 5 tau=1: |c1| <= 0.0511; A_M/A spread: 0.000592, 0.0153, 0.0332, 0.0144, 0.0251; c0/A 0.000592, c2/A 0.000592

## (b) residue of A at a vertex pole u0 = iK' - j h  vs  formula  (i a b (dn h - 1)/(k^2 sn h)) * (2 if N even else 1)
  a=2.0 N=6 tau=1: eps*A(u0+eps) = (-1.98775572933552e-30 - 2.51415744421884j), (4.81676098859949e-37 - 2.51415744421884j); formula = (0.0 - 2.51415744421884j)
  a=2.0 N=8 tau=3: eps*A(u0+eps) = (-9.97637829278593e-31 - 3.46263162515201j), (-1.71686619985115e-33 - 3.46263162515201j); formula = (0.0 - 3.46263162515201j)
  a=2.0 N=5 tau=1: eps*A(u0+eps) = (-2.81706382161281e-30 - 1.42287158133796j), (6.43630335788282e-37 - 1.42287158133796j); formula = (0.0 - 1.42287158133796j)
  a=1.3 N=12 tau=1: eps*A(u0+eps) = (-4.08112175853317e-30 - 0.743547876630693j), (3.81465914802796e-37 - 0.743547876630693j); formula = (0.0 - 0.743547876630693j)

## (c) outer polygon: spread of A'*A'_M and of A'/A'_M along the family (5 points M)
  a=1.3 N= 4 tau=1: M0: prod 0.0606 ratio 4.67e-61 | M1: prod 0.0606 ratio 9.33e-61 | M2: prod 0.0606 ratio 1.79e-60 | M3: prod 0.0606 ratio 1.0e-59 | M4: prod 0.0606 ratio 1.01e-60
  a=2.0 N= 8 tau=1: M0: prod 0.00162 ratio 2.95e-61 | M1: prod 0.00162 ratio 3.27e-61 | M2: prod 0.00162 ratio 3.51e-61 | M3: prod 0.00162 ratio 4.6e-61 | M4: prod 0.00162 ratio 4.28e-61
  a=2.0 N= 8 tau=3: M0: prod 0.287 ratio 1.77e-58 | M1: prod 0.287 ratio 2.91e-58 | M2: prod 0.287 ratio 2.27e-57 | M3: prod 0.287 ratio 3.04e-58 | M4: prod 0.287 ratio 2.27e-58
  a=3.5 N=12 tau=5: M0: prod 0.0221 ratio 1.07e-53 | M1: prod 0.0221 ratio 1.35e-53 | M2: prod 0.0221 ratio 1.06e-53 | M3: prod 0.0221 ratio 1.8e-53 | M4: prod 0.0221 ratio 1.21e-53
  a=2.0 N=16 tau=1: M0: prod 6.29e-8 ratio 2.7e-61 | M1: prod 6.29e-8 ratio 4.1e-61 | M2: prod 6.29e-8 ratio 7.36e-61 | M3: prod 6.29e-8 ratio 4.65e-61 | M4: prod 6.29e-8 ratio 5.03e-61
  a=1.3 N= 6 tau=1: M0: prod 4.84e-61 ratio 0.00132 | M1: prod 2.83e-61 ratio 0.00132 | M2: prod 4.73e-61 ratio 0.00132 | M3: prod 7.48e-61 ratio 0.00132 | M4: prod 6.6e-61 ratio 0.00132
  a=2.0 N=10 tau=3: M0: prod 2.29e-60 ratio 0.00963 | M1: prod 3.4e-60 ratio 0.00963 | M2: prod 2.17e-59 ratio 0.00963 | M3: prod 4.65e-60 ratio 0.00963 | M4: prod 3.67e-60 ratio 0.00963
  a=2.0 N= 5 tau=1: M0: prod 3.83e-61 ratio 0.000592 | M1: prod 0.0157 ratio 0.0153 | M2: prod 0.0398 ratio 0.0399 | M3: prod 0.0199 ratio 0.0203 | M4: prod 0.023 ratio 0.0234
  a=2.0 N= 7 tau=2: M0: prod 1.81e-60 ratio 0.000261 | M1: prod 0.0104 ratio 0.0102 | M2: prod 0.0747 ratio 0.0757 | M3: prod 0.0242 ratio 0.0242 | M4: prod 0.0132 ratio 0.0133

  check A'(u) - (dnD/cn^2D) A(u+D) = 0.0
