Proof step e-0bd3c438ff845b55

basis_map A013610 → concludes about basis_map_A013610 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": "A013610",
  "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 d96346603b8490d46465d904e70aa1d072dd718c16bb5104e0742b7400b3593d, 6,929 bytes (1,408 compressed); download JSON

Cited by

• n-c7b786a59ccdf5e9 (real_rooted)
• n-c7b786a59ccdf5e9 (one_signed_coefficients)
• n-c7b786a59ccdf5e9 (hadamard_kernel)