Proof step e-2abd4179002ed34f

preserver_image affine, shift 0 → concludes about shift_x_plus_one of Triangle of coefficients of cos(x)^n in polynomial for cos(nx). 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 cos(x)^n in polynomial for cos(nx). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": {} }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 d06bd6f1e12d56347919818fdf2ab0a2fbf76170fa4be74ccdd1a108c0f1ba1e, 12,701 bytes (2,497 compressed); download JSON

Cited by

• n-e0e035772684cc42 (real_rooted)