Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes

reversal of basis_map_A007318 of Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section.

Premises

basis_map_A007318 of Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-5, -1)

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-c8e1c16005fade80 · JSON

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":0,\"first_degree\":2,\"step\":1}}"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "lower": {
      "closed": false,
      "value": "-1"
    },
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

preserver_image, SHA-256 2129c8a08be0d41dfe97961e4035b6f069dfdbce4574dc5e303bed68fa48e425, 25,727 bytes (6,970 compressed); download

polytool replayed the certificate when the step was written.

Cited by

n-4a8b92b99ec82596 (one_signed_coefficients)
n-4a8b92b99ec82596 (hadamard_kernel)
n-4a8b92b99ec82596 (real_rooted)