Proof step e-651850b9e78a2c19

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

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 (-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 15dd33ca8510452b5b6e1c4a3deb1a4857e0bd74aafc545e77dfc617a07d95ff, 9,299 bytes (2,458 compressed); download JSON

Cited by

• n-fb2cd7d8c683bee9 (real_rooted)
• n-fb2cd7d8c683bee9 (one_signed_coefficients)
• n-fb2cd7d8c683bee9 (hadamard_kernel)