{
 "_provenance": "14x14 rational IBP connection d/ds M = A(d,s) M for the unequal-mass (1,1,3) kite family (the (1,1,x) line at x = 3: propagator masses^2 (1,0,1,0,3), i.e. the sunrise sub-block (D1,D3,D5) at squared masses (1,1,3)), built by Kira IBP reduction of this family exactly as kite-connection-A14.json was built for (1,1,2) (the same 14 masters in the same order, the same nonzero pattern; only the fifth mass differs).  This is the ANALYTIC FORMULA (exact rational functions of d and s), not any evaluated result.  All denominators factor over the alphabet {d-3, s, s-1, s-3, s^2-14s+1}: singular points s = 0, 1, 3, 7 -/+ 4 sqrt(3); the negative real axis is pole-free.",
 "masters": [
  [
   1,
   0,
   0,
   0,
   1
  ],
  [
   1,
   1,
   0,
   0,
   1
  ],
  [
   1,
   0,
   0,
   1,
   1
  ],
  [
   1,
   1,
   0,
   1,
   1
  ],
  [
   1,
   0,
   1,
   0,
   0
  ],
  [
   0,
   1,
   1,
   1,
   0
  ],
  [
   -1,
   1,
   1,
   1,
   0
  ],
  [
   1,
   0,
   1,
   1,
   0
  ],
  [
   1,
   0,
   1,
   0,
   1
  ],
  [
   1,
   -1,
   1,
   0,
   1
  ],
  [
   1,
   -2,
   1,
   0,
   1
  ],
  [
   0,
   0,
   1,
   1,
   1
  ],
  [
   0,
   1,
   1,
   1,
   1
  ],
  [
   1,
   1,
   1,
   1,
   1
  ]
 ],
 "A": [
  [
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "(2 - d)/(2*s**2 - 6*s)",
   "(d*s + 3*d - 4*s - 6)/(2*s**2 - 6*s)",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "(2 - d)/(2*s**2 - 2*s)",
   "0",
   "(d*s + d - 4*s - 2)/(2*s**2 - 2*s)",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "0",
   "(2 - d)/(2*s**2 - 2*s)",
   "(2 - d)/(2*s**2 - 6*s)",
   "(d*s**2 - 3*d - 4*s**2 + 4*s + 6)/(s**3 - 4*s**2 + 3*s)",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "0",
   "0",
   "0",
   "0",
   "0",
   "(d*s + 3*d - 4*s - 6)/(2*s**2 - 2*s)",
   "(3*d - 6)/(2*s**2 - 2*s)",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "0",
   "0",
   "0",
   "0",
   "0",
   "(d - 2)/s",
   "(d - 2)/s",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "0",
   "0",
   "0",
   "0",
   "(2 - d)/(2*s**2 - 2*s)",
   "0",
   "0",
   "(d*s + d - 4*s - 2)/(2*s**2 - 2*s)",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "(-d*s - 5*d + 2*s + 10)/(s**3 - 17*s**2 + 43*s - 3)",
   "0",
   "0",
   "0",
   "(-d*s**2 + d*s - 2*d + 2*s**2 - 2*s + 4)/(2*s**4 - 34*s**3 + 86*s**2 - 6*s)",
   "0",
   "0",
   "0",
   "(d*s**3 - 11*d*s**2 - 41*d*s + 3*d - 4*s**3 + 40*s**2 + 44*s)/(2*s**4 - 34*s**3 + 86*s**2 - 6*s)",
   "(9*d*s**2 + 62*d*s - 11*d - 12*s**2 - 96*s + 12)/(4*s**4 - 68*s**3 + 172*s**2 - 12*s)",
   "(-9*d*s + 3*d + 12*s - 4)/(4*s**4 - 68*s**3 + 172*s**2 - 12*s)",
   "0",
   "0",
   "0"
  ],
  [
   "(-d*s + 7*d + 2*s - 14)/(s**2 - 14*s + 1)",
   "0",
   "0",
   "0",
   "(-5*d*s + 3*d + 10*s - 6)/(2*s**3 - 28*s**2 + 2*s)",
   "0",
   "0",
   "0",
   "(-3*s**2 + 10*s - 3)/(s**3 - 14*s**2 + s)",
   "(5*d*s**2 - 2*d*s + 9*d - 8*s**2 + 16*s - 8)/(4*s**3 - 56*s**2 + 4*s)",
   "(-3*d*s - 3*d + 4*s + 4)/(4*s**3 - 56*s**2 + 4*s)",
   "0",
   "0",
   "0"
  ],
  [
   "(-d*s**2 + 10*d*s + 27*d + 2*s**2 - 20*s - 54)/(s**2 - 14*s + 1)",
   "0",
   "0",
   "0",
   "(-d*s**2 - 6*d*s + 11*d + 2*s**2 + 12*s - 22)/(2*s**3 - 28*s**2 + 2*s)",
   "0",
   "0",
   "0",
   "(-s**3 + 5*s**2 - 3*s - 9)/(s**3 - 14*s**2 + s)",
   "(d*s**3 + 3*d*s**2 + 35*d*s + 33*d - 36*s**2 + 120*s - 36)/(4*s**3 - 56*s**2 + 4*s)",
   "(d*s**2 - 26*d*s - 11*d + 16*s + 16)/(4*s**3 - 56*s**2 + 4*s)",
   "0",
   "0",
   "0"
  ],
  [
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0",
   "0"
  ],
  [
   "0",
   "0",
   "0",
   "0",
   "0",
   "(d*s + d - 3*s - 2)/(s**3 - 4*s**2 + 3*s)",
   "(3*d - 6)/(2*s**3 - 8*s**2 + 6*s)",
   "0",
   "0",
   "0",
   "0",
   "(2 - d)/(2*s**2 - 6*s)",
   "(d*s + 3*d - 4*s - 6)/(2*s**2 - 6*s)",
   "0"
  ],
  [
   "(-d*s**2 + 2*d*s - 13*d + 2*s**2 - 4*s + 26)/(2*s**5 - 42*s**4 + 228*s**3 - 452*s**2 + 282*s - 18)",
   "(d - 2)/(2*s**2 - 8*s + 6)",
   "0",
   "(3 - d)/(s**2 - 4*s + 3)",
   "(-2*d**2*s**3 + 23*d**2*s**2 - 56*d**2*s - d**2 + 9*d*s**3 - 98*d*s**2 + 237*d*s + 8*d - 10*s**3 + 104*s**2 - 250*s - 12)/(4*d*s**6 - 84*d*s**5 + 456*d*s**4 - 904*d*s**3 + 564*d*s**2 - 36*d*s - 12*s**6 + 252*s**5 - 1368*s**4 + 2712*s**3 - 1692*s**2 + 108*s)",
   "(-d*s**2 + 7*d*s + 2*d + 2*s**2 - 18*s - 4)/(2*s**4 - 10*s**3 + 14*s**2 - 6*s)",
   "(3*d*s + 3*d - 6*s - 6)/(2*s**4 - 10*s**3 + 14*s**2 - 6*s)",
   "(d - 2)/(2*s**2 - 8*s + 6)",
   "(-d*s**4 + 21*d*s**3 - 99*d*s**2 + 7*d*s + 2*s**4 - 54*s**3 + 250*s**2 - 66*s + 12)/(4*s**6 - 84*s**5 + 456*s**4 - 904*s**3 + 564*s**2 - 36*s)",
   "(4*d*s**3 + 5*d*s**2 + 38*d*s - 11*d - 6*s**3 - 78*s + 12)/(4*s**6 - 84*s**5 + 456*s**4 - 904*s**3 + 564*s**2 - 36*s)",
   "(-3*d*s - 3*d + 4*s + 4)/(4*s**5 - 80*s**4 + 376*s**3 - 528*s**2 + 36*s)",
   "(2 - d)/(2*s**3 - 8*s**2 + 6*s)",
   "0",
   "(d*s + 3*d - 6*s - 6)/(2*s**2 - 6*s)"
  ]
 ],
 "vars": "d,s; d=4-2eps; masses^2=(1,1,3); s-derivative d/ds",
 "TOP_idx": 13
}