Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A013610

Concludes

Premises

basis_map_A013610 of Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Theorem

polytool ?

Checked

polytool replayed · Lean not attempted

Technical details

Step id

e-49f0aab7e0fe6198 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A013610",
  "operation": "basis_map"
}

Claims

{
  "claim": "real_rooted",
  "from_index": 0,
  "region": {
    "upper": {
      "closed": true,
      "value": "0"
    }
  }
}

Certificate

basis_map, SHA-256 6b510411371cb17c9d8ab1de168f5e68886d3d6fc4a1eb27ee3959ded27c7f7a, 6,860 bytes (1,390 compressed); download

polytool replayed the certificate when the step was written.

Cited by