Proof step e-ad91514e27294b92

preserver_image affine, shift 0 → concludes about Exponential Riordan array [x*exp(x),x]. 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

• Triangle read by rows: row n consists of n zeros followed by n+1. (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": { "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 234d97ad497ab0ed76bfdfcda382ebd1e77eb974b9a1deb8e3811fc838ee3aaf, 8,340 bytes (2,425 compressed); download JSON

Cited by

• n-308cf60736924b4c (real_rooted)
• n-308cf60736924b4c (one_signed_coefficients)
• n-308cf60736924b4c (hadamard_kernel)