Proof step e-d9920fdddfeeaf81

basis_map A013609 → concludes about basis_map_A013609 of Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013609",
  "operation": "basis_map"
}

Premises

• Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones. (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: basis_map, SHA-256 978849241ae3693c229564fc0b63ea9c837ce4f9f415e0058f4a32d3232756d1, 6,925 bytes (1,406 compressed); download JSON

Cited by

• n-f1bdd4180f3e6ae5 (real_rooted)
• n-f1bdd4180f3e6ae5 (one_signed_coefficients)
• n-f1bdd4180f3e6ae5 (hadamard_kernel)