Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver affine, shift 0
- Concludes
- shift_x_plus_one of theta_plus_one_squared of Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
- Premises
- theta_plus_one_squared 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]
- theta_plus_one_squared 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-e8df69c2a72251af· 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-25669f327af376765bd4be7c46ce66e2352f939b6be24a8b0cc7a9b7f6b135f17e0, 9,412 bytes (2,157 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-52a557efbe1a7c54(real_rooted)n-52a557efbe1a7c54(one_signed_coefficients)n-52a557efbe1a7c54(hadamard_kernel)