Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
- Premises
- reversal of 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]
- reversal of Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
- 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-0956702acf3e3a5b· 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-2564102caff67dcfccc3b38f1aae9a1050f9ca2ae20afbd4638f496f9ddf7bd247e, 12,549 bytes (2,961 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-5fa21c8779d2bdd1(one_signed_coefficients)n-5fa21c8779d2bdd1(hadamard_kernel)n-5fa21c8779d2bdd1(real_rooted)