Proof step e-dbf8101c811237e4

preserver_image affine, shift 0 → concludes about Triangle of coefficients of Chebyshev's S(n,x+5) polynomials (exponents of x in increasing order). 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 Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-6, -2)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-7" }, "upper": { "closed": false, "value": "-3" } } }
• { "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 6edbc44f21a0fab62a3930d02e57cd2262fcebb9990026356de3a032a58f84b4, 18,350 bytes (3,646 compressed); download JSON

Cited by

• n-c2b7c74f8491f01b (hadamard_kernel)
• n-c2b7c74f8491f01b (real_rooted)
• n-c2b7c74f8491f01b (interlacing)
• n-c2b7c74f8491f01b (one_signed_coefficients)