Proof step
Geometric basis map (elementary)
Image under a basis map u^k -> P_k A007318
- Concludes
- shift_x_plus_one of theta_plus_one of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical opera…
- Premises
- theta_plus_one of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical opera…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- theta_plus_one of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical opera…
- Theorem
- polytool ?
- Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-90ca7fc405d18dfa· 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-2568ac0d66ae0a0d25a0f554f903aa5c93d9118f4b2a1a41868f67ec3c537faa2c9, 13,236 bytes (2,500 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-32ac941c8532b0d4(hadamard_kernel)n-32ac941c8532b0d4(real_rooted)n-32ac941c8532b0d4(one_signed_coefficients)