Proof step e-28a1cf3333f63fa4

preserver_image affine, shift 0 → concludes about A133080 * A007318. JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): Polynomial.Splits.comp_of_degree_le_one

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

Premises

• Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones. (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": { "upper": { "closed": true, "value": "-1" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 389210bfc187a4f16cb67791989fc1d7730310fd933e7cdba59c6a1e55c5af86, 6,439 bytes (1,750 compressed); download JSON

Cited by

• n-d75669a8cd7f9393 (one_signed_coefficients)
• n-d75669a8cd7f9393 (hadamard_kernel)
• n-d75669a8cd7f9393 (real_rooted)