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 derivative of peak
Premises
  • derivative of peak
    sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-542c662300d2bff6 · 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": 1,
  "region": {
    "upper": {
      "closed": true,
      "value": "-1"
    }
  }
}
Certificate
preserver_image, SHA-256 1401ab6168c483f5ac71d4761e69f48353906797da10ef523aa273052caa7922, 8,539 bytes (2,004 compressed); download
polytool replayed the certificate when the step was written.
Cited by