Proof step e-06bdf5b2aa1ff3d5

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Coefficient triangle of certain polynomials N(4; m,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

• Coefficient triangle of certain polynomials N(4; m,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" } } }
• { "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 da40bd0917ad12554e1ec9c7802a06e6301ea67aa411184ff6f2fe8571eb505c, 13,266 bytes (3,127 compressed); download JSON

Cited by

• n-a893b3f9716e8c07 (real_rooted)
• n-a893b3f9716e8c07 (one_signed_coefficients)
• n-a893b3f9716e8c07 (hadamard_kernel)
• n-a893b3f9716e8c07 (interlacing)