Proof step e-d8ead6c583c2763e

basis_map A013611 → concludes about basis_map_A013611 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": "A013611",
  "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 a85d8be5fba42abd9c76c3ae4bdcc2964f539709be87955b99472d3e344bf0d6, 6,927 bytes (1,407 compressed); download JSON

Cited by

• n-c322146fd9758ee0 (real_rooted)
• n-c322146fd9758ee0 (one_signed_coefficients)
• n-c322146fd9758ee0 (hadamard_kernel)