Real-rooted atlas

Proof step

Affine-current basis map theorem

Image under a basis map u^k -> P_k A008288

Concludes
basis_map_A008288 of basis_map_A013611 of Triangle read by rows. T(n, k) = RisingFactorial(n + 1, n) / (k! * (n - k)!).
Premises
Theorem
polytool RealRooted orderTwoConstants_nonneg_iff ?
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-73b47dbe092b389d · JSON
Operation
Image under a basis map u^k -> P_k
{
  "map": "A008288",
  "operation": "basis_map"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "lower": {
      "closed": true,
      "exact": {
        "radicand": "2",
        "rational_part": "-3",
        "sqrt_coefficient": "-2"
      },
      "value": "-1564556493/268435456"
    },
    "upper": {
      "closed": true,
      "exact": {
        "radicand": "2",
        "rational_part": "-3",
        "sqrt_coefficient": "2"
      },
      "value": "-46056243/268435456"
    }
  }
}
Certificate
basis_map, SHA-256 973574566caf299fd4b72b2f06f1bf2f55e3ddbb12a51e6f0a9a48132459d341, 19,183 bytes (3,262 compressed); download
polytool replayed the certificate when the step was written.
Cited by