Proof step e-d847ca7730038c3c

preserver_image affine, shift 0 → concludes about shift_x_plus_one of chebyshev_u 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

• chebyshev_u (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-1, 1)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-2" }, "upper": { "closed": false, "value": "0" } } }
• { "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 614890d289ef3efce8dd134f3a5fdf0db9ed3a2cdcbd3a28b3b2a6696af21d74, 18,069 bytes (3,173 compressed); download JSON

Cited by

• n-a2f149315d09c809 (real_rooted)
• n-a2f149315d09c809 (one_signed_coefficients)
• n-a2f149315d09c809 (hadamard_kernel)
• n-a2f149315d09c809 (interlacing)