Proof step e-7ddc15d309ad2a75

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Triangle of coefficients of Chebyshev's S(n,x-2) = U(n,x/2-1) 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-2) = U(n,x/2-1) polynomials (exponents of x in increasing order). (sequence)
  uses: Every row P_n, n >= 1, is zero or real-rooted with all roots in (0, 4)

Claims

• { "claim": "real_rooted", "from_index": 1, "region": { "lower": { "closed": false, "value": "-1" }, "upper": { "closed": false, "value": "3" } } }
• { "claim": "interlacing", "from_index": 2, "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 3daff7e5b2fdadecd801855b63777a5bb1642e0ca5e64619982562ccb1902f3d, 18,146 bytes (3,200 compressed); download JSON

Cited by

• n-2de752bc9bc14cd4 (interlacing)
• n-2de752bc9bc14cd4 (real_rooted)