Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes

Premises

shift_x_plus_one of Triangle of B-analogs of Stirling numbers of 2nd kind.
sequence: Every row P_n, n >= 0, 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-a2e7c85a22952f73 · 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 8a910b73aea65ee34f00494dd620cfa32f4e48bfc13a2ceb77c4d0ea811f624f, 26,450 bytes (4,521 compressed); download

polytool replayed the certificate when the step was written.

Cited by