Proof step e-8f18b93eb5dfe7b3

basis_map A013611 → concludes about basis_map_A013611 of Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

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

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^j. (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 d185d232add49818714a22e8bfd036c9ae27925c8239802b95af77b3c8b506a1, 6,917 bytes (1,414 compressed); download JSON

Cited by

• n-f55a7ba0b32633bc (real_rooted)
• n-f55a7ba0b32633bc (one_signed_coefficients)
• n-f55a7ba0b32633bc (hadamard_kernel)