Proof step e-0ca777a455cc19d8

preserver_image affine, shift 0 → concludes about basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a triangle. shifted by 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\":\"0\"}"
}

Premises

• basis-map coefficients of Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a tr… (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": { "lower": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 a3d7705439d8377f792fd9671cd9759727d5dab41a4d1e592e271351d6fee0ef, 4,897 bytes (1,538 compressed); download JSON

Cited by

• n-cdb0db4ad473ee28 (real_rooted)
• n-cdb0db4ad473ee28 (one_signed_coefficients)