Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver reversal, shift 0

Concludes

reversal of shift_x_plus_one of Triangle read by rows of coefficients of Chebyshev's U(n,x) polynomials (exponents in increasing order).

Premises

shift_x_plus_one of Triangle read by rows of coefficients of Chebyshev's U(n,x) polynomials (exponents in increasing order).
sequence: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

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-8eb9efff82dfd3d1 · JSON

Operation

Image under a real-rootedness preserver

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

Claims

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

Certificate

preserver_image, SHA-256 3d37246072103ecc9f72c96f3a452c7b098ffe905f62dcc22c538723c94507b4, 17,402 bytes (3,163 compressed); download

polytool replayed the certificate when the step was written.

Cited by

n-fbf0c4d004490261 (real_rooted)
n-fbf0c4d004490261 (one_signed_coefficients)
n-fbf0c4d004490261 (hadamard_kernel)