Proof step e-e470a688ac88b1cf

preserver_image affine, shift 0 → concludes about basis-map coefficients of Riordan array (1+2x,x(1+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\":\"-10\"}"
}

Premises

• Riordan array (1+2x,x(1+x)). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-4, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "6" }, "upper": { "closed": true, "value": "10" } } }
• { "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 00da04cac5cccbb978111d2ca761d00421900d50a7acfa6bbeeb14e7a67d1621, 19,323 bytes (3,774 compressed); download JSON

Cited by

• n-0e6280284de0b3d7 (one_signed_coefficients)
• n-0e6280284de0b3d7 (interlacing)
• n-0e6280284de0b3d7 (real_rooted)