Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- reversal of theta_plus_one_squared of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by…
- Premises
- theta_plus_one_squared of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros fol…
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- theta_plus_one_squared of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros fol…
- Theorem
- polytool ?
- Lean
- RealRooted
route
reversedRealRooted.X_pow_mul_reverse_eq_zero_or_splits,RealRooted.reflect_eq_zero_or_splits - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-580fa37ebb3c55ee· JSON- Operation
- Image under a real-rootedness preserver
{ "index_shift": 0, "operation": "preserver_image", "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }- Certificate
preserver_image, SHA-2567774cb4b72d62501ad3345c4eb4f4b49373626718777b4e8e7288a9419ee7a10, 8,278 bytes (2,388 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-68128ecab2720b7c(real_rooted)n-68128ecab2720b7c(one_signed_coefficients)n-68128ecab2720b7c(hadamard_kernel)