Proof step e-a9568ed3b8022fa1

preserver_image affine, shift 0 → concludes about basis_map_A007318 of Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section. 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

• Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section. (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": "-5" }, "upper": { "closed": false, "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 070aa523b47c59ec0d0f289e80621ee50f788e20eb7a846d2bfdc9631df82722, 24,836 bytes (6,043 compressed); download JSON

Cited by

• n-dd70177049267f47 (one_signed_coefficients)
• n-dd70177049267f47 (hadamard_kernel)
• n-dd70177049267f47 (interlacing)
• n-dd70177049267f47 (real_rooted)