Proof step e-5582917b7b4067c2

basis_map A013609 → concludes about basis_map_A013609 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": "A013609",
  "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 85cdec31f1a22e456437d4c0bcb8d438e39dd8f199a471d4824391e703a72af7, 6,929 bytes (1,411 compressed); download JSON

Cited by

• n-a5617eda68ae335d (real_rooted)
• n-a5617eda68ae335d (one_signed_coefficients)
• n-a5617eda68ae335d (hadamard_kernel)