Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- reversal of Coefficient table for Chebyshev's U(2*n,x) polynomial expanded in decreasing powers of (-4*(1-x^2)).
- Premises
- Coefficient table for Chebyshev's U(2*n,x) polynomial expanded in decreasing powers of (-4*(1-x^2)).
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- Coefficient table for Chebyshev's U(2*n,x) polynomial expanded in decreasing powers of (-4*(1-x^2)).
- 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-8890424cdb87cb36· 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-256d0e81ed003f5458d3b2d6ab5905a6a179f38204e23859d5ffa28175dfa7ffc46, 12,920 bytes (3,175 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-fe40873ed3cfd4a4(real_rooted)n-fe40873ed3cfd4a4(one_signed_coefficients)n-fe40873ed3cfd4a4(hadamard_kernel)