Proof step e-b9371054cfe1d371

preserver_image affine, shift 0 → concludes about basis-map coefficients of Riordan array (1, 2+2x). 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\":\"-9\"}"
}

Premises

• Riordan array (1, 2+2x). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-2, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "7" }, "upper": { "closed": true, "value": "9" } } }
• { "claim": "interlacing", "from_index": 1, "kind": "weak", "orientation": "unordered" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 19a84d8f33423ebc1b1a94e7c2e83ad60c2aa873240d6a7d2322e9b0e5cfefcb, 19,348 bytes (3,765 compressed); download JSON

Cited by

• n-192a0153bc9ffe91 (real_rooted)
• n-192a0153bc9ffe91 (one_signed_coefficients)
• n-192a0153bc9ffe91 (interlacing)