Proof step e-78e2985691766434

preserver_image mobius, shift 0 → concludes about mobius_x_over_x_plus_one of Even-numbered rows of Pascal's 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\":0,\"first_degree\":0,\"step\":2}}"
}

Premises

• Even-numbered rows of Pascal's triangle. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "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 a4e61d07ddca107159f0fe6e046d66beb627885f68b3c2364cc76164d254b46a, 5,243 bytes (1,572 compressed); download JSON

Cited by

• n-d66b602a2fc4bda7 (real_rooted)
• n-d66b602a2fc4bda7 (one_signed_coefficients)
• n-d66b602a2fc4bda7 (hadamard_kernel)