Proof step e-18c37bd14c5a739f

preserver_image reversal, shift 0 → concludes about reversal of Riordan array (1/((1-x)(1-3x)),x/((1-x)(1-3x))). 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

• Riordan array (1/((1-x)(1-3x)),x/((1-x)(1-3x))). (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 af4c2b3a825b56641b6e9884d9f383038a220bbd549d331efc108ae35c54fd4f, 16,765 bytes (3,230 compressed); download JSON

Cited by

• n-940e4d08e5526f20 (real_rooted)
• n-940e4d08e5526f20 (one_signed_coefficients)
• n-940e4d08e5526f20 (hadamard_kernel)