Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver affine, shift 0
- Concludes
- shift_x_plus_one 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
Polynomial.Splits.comp_of_degree_le_one - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-55eebf3098e53f1f· JSON- Operation
- Image under a real-rootedness preserver
{ "index_shift": 0, "operation": "preserver_image", "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}" } - Claims
{ "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "-1" } } }- Certificate
preserver_image, SHA-25617c0eb7c5e4a89a40795ee6480427bc4bb44732887c71a8a5a0b1c02cacce0cf, 7,066 bytes (2,064 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-f365acd4f1e97c97(real_rooted)n-f365acd4f1e97c97(one_signed_coefficients)n-f365acd4f1e97c97(hadamard_kernel)