Proof step e-a162795980dd8c54

preserver_image reversal, shift 0 → concludes about reversal of A convolution triangle of numbers based on A001906 (even-indexed Fibonacci numbers). 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

• A convolution triangle of numbers based on A001906 (even-indexed Fibonacci numbers). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-5, -1)

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "lower": { "closed": false, "value": "-1" }, "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 87380c2474cfcd7395358977f63a62dd1ed98bbbb3a1dfcc185cf64b722fcad4, 16,998 bytes (3,317 compressed); download JSON

Cited by

• n-c4e1c7f7d91f2e30 (real_rooted)
• n-c4e1c7f7d91f2e30 (one_signed_coefficients)
• n-c4e1c7f7d91f2e30 (hadamard_kernel)