Proof step e-9b0d1368ced4486d

preserver_image affine, shift 0 → concludes about basis_map_A007318 of Riordan array (1, 3+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

• Riordan array (1, 3+x). (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 3a93e5df2b81347dfa54155073f1081b0c125b19938eb9324a638ff34324d33f, 9,402 bytes (2,497 compressed); download JSON

Cited by

• n-a9307f854ca152e2 (one_signed_coefficients)
• n-a9307f854ca152e2 (hadamard_kernel)
• n-a9307f854ca152e2 (real_rooted)