Proof step e-8bdfc53769ec9007

preserver_image affine, shift 0 → concludes about basis_map_A007318 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\":\"1\"}"
}

Premises

• Riordan array (1, 2+2x). (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 7b6e77b5bd9bf21706d448a48fbd4439e38a22c341edcdf70c979f9f6368b6b7, 9,403 bytes (2,510 compressed); download JSON

Cited by

• n-002f74523f94b1c9 (hadamard_kernel)
• n-002f74523f94b1c9 (real_rooted)
• n-002f74523f94b1c9 (one_signed_coefficients)