Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- reversal of hadamard_factor parent of Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
- Premises
- hadamard_factor parent of Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- hadamard_factor parent of Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
- 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-fbcfcbb1806b4823· 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-256fe2c1cc2b951a2f8d41bbf1565e59d0bf011d0b0c95f3f36b2bb4d88230328a9, 7,251 bytes (2,108 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-11817a9d1f935606(real_rooted)n-11817a9d1f935606(one_signed_coefficients)n-11817a9d1f935606(hadamard_kernel)