Proof step e-07e3ff75f72fdf91

preserver_image affine, shift 0 → concludes about Triangle whose (i,j)-th entry is binomial(i,j)*2^i. 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

• Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Tri… (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 6792d8449b1ec9e9bb0884f1c8b7341432c76f6a1e9b8b437db479789cfec1f0, 4,877 bytes (1,539 compressed); download JSON

Cited by

• n-d28ad9841fc73317 (one_signed_coefficients)
• n-d28ad9841fc73317 (hadamard_kernel)
• n-d28ad9841fc73317 (real_rooted)