Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes
shift_x_plus_one of shift_x_plus_one of Triangle read by rows: T(n,k) is k-th entry of the gamma-vector of the n-dimensional cyclohedron, 0 <= k <= floor(n/2).
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-7608435acb15ec98 · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "-1"
    }
  }
}
Certificate
preserver_image, SHA-256 4797dcb082a683028a67ee136db9958d05c1e36e7b0bf687e3444f77e9291484, 27,238 bytes (4,796 compressed); download
polytool replayed the certificate when the step was written.
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