Proof step

Geometric basis map (elementary)

Image under a basis map u^k -> P_k A007318

Concludes

Premises

basis_map_A013609 of Triangle of coefficients in expansion of (1+3*x)^n.
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-94d922710a28dcc9 · JSON

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Claims

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

Certificate

basis_map, SHA-256 715cfad3e3d7861d3d492b6f962bfa0a9204de41c7c76d185c55ef5f1b0db8c7, 6,857 bytes (1,388 compressed); download

polytool replayed the certificate when the step was written.

Cited by