Proof step e-318674696f0c0931

preserver_image reversal, shift 0 → concludes about reversal of Triangle read by rows, (n-1) zeros followed by (2n, 1). JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}

Premises

• Triangle read by rows, (n-1) zeros followed by (2n, 1). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 442fccadcfec02155479d765d9b49ce7f2afc29ea1bd2e1a4e856136c02e87ac, 10,415 bytes (2,719 compressed); download JSON

Cited by

• n-61e4be490bff1d89 (real_rooted)
• n-61e4be490bff1d89 (one_signed_coefficients)
• n-61e4be490bff1d89 (hadamard_kernel)