Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver affine, shift 0
- Concludes
- shift_x_plus_one of basis_map_A013609 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0.
- Premises
- basis_map_A013609 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013609 of Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0.
- Theorem
- polytool ?
- Lean
- RealRooted
Polynomial.Splits.comp_of_degree_le_one - Checked
- polytool replayed · Lean not attempted
Technical details
- Step id
e-24823b2466a4ed25· 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-256bfdb4c4d07cdcee0c365fbe3d7f67d0b2419ad13ca29b5ef8d5d892fde8dc3c6, 7,457 bytes (2,065 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-fbfc2c564a29cf31(real_rooted)n-fbfc2c564a29cf31(one_signed_coefficients)n-fbfc2c564a29cf31(hadamard_kernel)