Proof step e-f9cce4eb6656235e

preserver_image mobius, shift 0 → concludes about basis-map coefficients of A scaled Hermite triangle. JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route fTransform RealRooted.splits_fPolynomial

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"mobius\",\"a\":\"1\",\"b\":\"0\",\"c\":\"1\",\"e\":\"1\",\"schedule\":{\"first_index\":1,\"first_degree\":2,\"step\":1}}"
}

Premises

• basis-map coefficients of A scaled Hermite triangle. (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "lower": { "closed": true, "value": "-1" }, "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 343813c8be6ec49c2e43b8ea9c4305d348b87867701c2bb5cdb3f68a2d6a60cc, 5,238 bytes (1,562 compressed); download JSON

Cited by

• n-5fe240122e98ffb3 (one_signed_coefficients)
• n-5fe240122e98ffb3 (hadamard_kernel)
• n-5fe240122e98ffb3 (real_rooted)