Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver mobius, shift 0

Concludes
basis_map_A013611 of Triangle whose (i,j)-th entry is binomial(i,j)*3^(i-j)*3^j.
Premises
Theorem
polytool ?
Lean
RealRooted route fTransform RealRooted.splits_fPolynomial
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-eb32fd8aed8615f6 · 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\":0,\"first_degree\":0,\"step\":1}}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "lower": {
      "closed": true,
      "value": "-1"
    },
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
preserver_image, SHA-256 a10fb172bdb6f8e933af281c8ed9d7c851e789890dcc1bb514d23ef43f3e5510, 8,192 bytes (2,350 compressed); download
polytool replayed the certificate when the step was written.
Cited by