Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes
reversal of theta_plus_one_squared of Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded in increas…
Premises
Theorem
polytool ?
Lean
RealRooted route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-d1176f2212d235c9 · JSON
Operation
Image under a real-rootedness preserver
{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}
Claims
{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}
Certificate
preserver_image, SHA-256 4e4012631d247f480ef14b4f1156724942b1b9b9dc1b929b3dafc6b42c57a695, 8,739 bytes (2,250 compressed); download
polytool replayed the certificate when the step was written.
Cited by