Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver affine, shift 0
- Concludes
- shift_x_plus_one of Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
- Premises
- Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
- Theorem
- polytool ?
- Lean
- RealRooted
Polynomial.Splits.comp_of_degree_le_one - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-22ba4ce66cbdf139· 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-256166813dfd265ee05ebc6a803cfe1a4d3d8536fb96a56d6ea85e18cc7df67e9db, 7,786 bytes (2,308 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-0a4cd703d913c76f(real_rooted)n-0a4cd703d913c76f(one_signed_coefficients)n-0a4cd703d913c76f(hadamard_kernel)