Proof step e-7157ac2ddeb657bf

preserver_image affine, shift 0 → concludes about A127733 * A007318 as infinite lower triangular matrices. 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: n-th row is n^2 preceded by (n-1) zeros. (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 3ccb4c20b6500b24a3060454661eef947c38670d9ad41920ec46c45269156df8, 9,271 bytes (2,636 compressed); download JSON

Cited by

• n-375ba152c4aebf61 (one_signed_coefficients)
• n-375ba152c4aebf61 (hadamard_kernel)
• n-375ba152c4aebf61 (real_rooted)