Proof step e-73dd335e950d1f81

preserver_image reversal, shift 0 → concludes about reversal of Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order). JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

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}}"
}

Premises

• Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-6, -2)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-1/2" }, "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 f1cf545ca8d704eebec03aaf59102be1f188fe9b0e4041f67fd6d7c1c20e60ac, 17,085 bytes (3,337 compressed); download JSON

Cited by

• n-8ac1223942f7b8c5 (real_rooted)
• n-8ac1223942f7b8c5 (one_signed_coefficients)
• n-8ac1223942f7b8c5 (hadamard_kernel)