{
 "_provenance": "14x14 rational IBP connection d/ds M = A(d,s) M for the unequal-mass (1,1,2) kite family, built by Kira IBP reduction of this family (exact rational output, vendored here). This is the ANALYTIC FORMULA (exact rational functions of d and s), not any evaluated result. All denominators factor over the alphabet {s, s-1, s-2, s^2-12s+4}.",
 "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 - 4*s)",
   "(d*s + 2*d - 4*s - 4)/(2*s**2 - 4*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 - 4*s)",
   "(d*s**2 - 2*d - 4*s**2 + 3*s + 4)/(s**3 - 3*s**2 + 2*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 - 2*d + 2*s + 4)/(s**3 - 14*s**2 + 28*s - 8)",
   "0",
   "0",
   "0",
   "(-d*s**2 + d*s - 2*d + 2*s**2 - 2*s + 4)/(2*s**4 - 28*s**3 + 56*s**2 - 16*s)",
   "0",
   "0",
   "0",
   "(d*s**3 - 10*d*s**2 - 20*d*s + 8*d - 4*s**3 + 34*s**2 + 16*s - 8)/(2*s**4 - 28*s**3 + 56*s**2 - 16*s)",
   "(9*d*s**2 + 40*d*s - 20*d - 12*s**2 - 60*s + 24)/(4*s**4 - 56*s**3 + 112*s**2 - 32*s)",
   "(-9*d*s + 6*d + 12*s - 8)/(4*s**4 - 56*s**3 + 112*s**2 - 32*s)",
   "0",
   "0",
   "0"
  ],
  [
   "(-d*s + 6*d + 2*s - 12)/(s**2 - 12*s + 4)",
   "0",
   "0",
   "0",
   "(-5*d*s + 6*d + 10*s - 12)/(2*s**3 - 24*s**2 + 8*s)",
   "0",
   "0",
   "0",
   "(-3*s**2 + 8*s - 4)/(s**3 - 12*s**2 + 4*s)",
   "(5*d*s**2 + 12*d - 8*s**2 + 12*s - 8)/(4*s**3 - 48*s**2 + 16*s)",
   "(-3*d*s - 6*d + 4*s + 8)/(4*s**3 - 48*s**2 + 16*s)",
   "0",
   "0",
   "0"
  ],
  [
   "(-d*s**2 + 8*d*s + 20*d + 2*s**2 - 16*s - 40)/(s**2 - 12*s + 4)",
   "0",
   "0",
   "0",
   "(-d*s**2 - 8*d*s + 20*d + 2*s**2 + 16*s - 40)/(2*s**3 - 24*s**2 + 8*s)",
   "0",
   "0",
   "0",
   "(-s**3 + 2*s**2 + 4*s - 8)/(s**3 - 12*s**2 + 4*s)",
   "(d*s**3 + 6*d*s**2 + 28*d*s + 40*d - 36*s**2 + 96*s - 48)/(4*s**3 - 48*s**2 + 16*s)",
   "(d*s**2 - 24*d*s - 20*d + 16*s + 32)/(4*s**3 - 48*s**2 + 16*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 - 3*s**2 + 2*s)",
   "(3*d - 6)/(2*s**3 - 6*s**2 + 4*s)",
   "0",
   "0",
   "0",
   "0",
   "(2 - d)/(2*s**2 - 4*s)",
   "(d*s + 2*d - 4*s - 4)/(2*s**2 - 4*s)",
   "0"
  ],
  [
   "(-d*s**2 + 2*d*s - 8*d + 2*s**2 - 4*s + 16)/(2*s**5 - 34*s**4 + 144*s**3 - 240*s**2 + 160*s - 32)",
   "(d - 2)/(2*s**2 - 6*s + 4)",
   "0",
   "(3 - d)/(s**2 - 3*s + 2)",
   "(-2*d**2*s**3 + 18*d**2*s**2 - 34*d**2*s + 4*d**2 + 9*d*s**3 - 76*d*s**2 + 142*d*s - 12*d - 10*s**3 + 80*s**2 - 148*s + 8)/(4*d*s**6 - 68*d*s**5 + 288*d*s**4 - 480*d*s**3 + 320*d*s**2 - 64*d*s - 12*s**6 + 204*s**5 - 864*s**4 + 1440*s**3 - 960*s**2 + 192*s)",
   "(-d*s**2 + 7*d*s + 2*d + 2*s**2 - 18*s - 4)/(2*s**4 - 8*s**3 + 10*s**2 - 4*s)",
   "(3*d*s + 3*d - 6*s - 6)/(2*s**4 - 8*s**3 + 10*s**2 - 4*s)",
   "(d - 2)/(2*s**2 - 6*s + 4)",
   "(-d*s**4 + 18*d*s**3 - 76*d*s**2 + 24*d*s + 2*s**4 - 48*s**3 + 196*s**2 - 96*s + 16)/(4*s**6 - 68*s**5 + 288*s**4 - 480*s**3 + 320*s**2 - 64*s)",
   "(4*d*s**3 + 5*d*s**2 + 32*d*s - 20*d - 6*s**3 - 60*s + 24)/(4*s**6 - 68*s**5 + 288*s**4 - 480*s**3 + 320*s**2 - 64*s)",
   "(-3*d*s - 6*d + 4*s + 8)/(4*s**5 - 64*s**4 + 224*s**3 - 256*s**2 + 64*s)",
   "(2 - d)/(2*s**3 - 6*s**2 + 4*s)",
   "0",
   "(d*s + 2*d - 6*s - 4)/(2*s**2 - 4*s)"
  ]
 ],
 "vars": "d,s; d=4-2eps; masses^2=(1,1,2); s-derivative d/ds",
 "TOP_idx": 13
}