Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver mobius, shift 0

Concludes
mobius_x_over_x_plus_one of basis_map_A007318 of Triangle read by rows: T(n, k) = binomial(n+k-1, 2*k-1).
Premises
Theorem
polytool ?
Lean
RealRooted route fTransform RealRooted.splits_fPolynomial
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-a5dfd8e2836f7669 · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"mobius\",\"a\":\"1\",\"b\":\"0\",\"c\":\"1\",\"e\":\"1\",\"schedule\":{\"first_index\":1,\"first_degree\":0,\"step\":1}}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 1,
  "region": {
    "lower": {
      "closed": true,
      "value": "-1"
    },
    "upper": {
      "closed": false,
      "value": "-1/2"
    }
  }
}
Certificate
preserver_image, SHA-256 b59fe0be9b1819ee447c6b11237fd58ebedcc54ff27109d4f4e7eee659414a28, 17,230 bytes (3,301 compressed); download
polytool replayed the certificate when the step was written.
Cited by