Proof step e-64733a2a119dbb75

preserver_image affine, shift 0 → concludes about basis_map_A007318 of Exponential Riordan array (1, x(1+x/2)). JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): Polynomial.Splits.comp_of_degree_le_one

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"affine\",\"slope\":\"1\",\"intercept\":\"1\"}"
}

Premises

• Exponential Riordan array (1, x(1+x/2)). (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "-1" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 5009324dc82ca933ec364e6b480576c6276c5b9c9964bc0b0b1558e918ffea5b, 8,574 bytes (2,372 compressed); download JSON

Cited by

• n-11e2e791fe8625e3 (one_signed_coefficients)
• n-11e2e791fe8625e3 (hadamard_kernel)
• n-11e2e791fe8625e3 (real_rooted)