Proof step e-541f0d63dcdb93da

basis_map A013611 → concludes about basis_map_A013611 of Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,...] DELTA [3,-2,-1,0,0,0,0,0,0,...] where DELTA is the operator … JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013611",
  "operation": "basis_map"
}

Premises

• Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,...] DELTA [3,-2,-1,0,0,0,0,0,0,...] where DELTA is the operator d… (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 a5773a335d72b5fb06c982fce58671669aae56d2e2bcfac2cead84f89a527cbf, 6,931 bytes (1,409 compressed); download JSON

Cited by

• n-899fb13ecc891703 (real_rooted)
• n-899fb13ecc891703 (one_signed_coefficients)
• n-899fb13ecc891703 (hadamard_kernel)