Proof step
Affine, reversal and Möbius substitutions (elementary)
Image under a real-rootedness preserver reversal, shift 0
- Concludes
- reversal of basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*1^j.
- Premises
- basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*1^j.
sequence: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]
- basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*1^j.
- 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-23fe265bb0c329ed· 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-25605dcdf8aa6cd3a9a0cff59ae723c1de28c1dd058aab58a180147d1665c4265c2, 7,936 bytes (2,323 compressed); downloadpolytool replayed the certificate when the step was written.- Cited by
n-3832f5f734db009a(real_rooted)n-3832f5f734db009a(one_signed_coefficients)n-3832f5f734db009a(hadamard_kernel)