Real-rooted atlas

Proof step

Affine, reversal and Möbius substitutions (elementary)

Image under a real-rootedness preserver affine, shift 0

Concludes
basis_map_A007318 of Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section.
Premises
Theorem
polytool ?
Lean
RealRooted Polynomial.Splits.comp_of_degree_le_one
Checked
polytool replayed · Lean not attempted
Technical details
Step id
e-23e971f1ed1ce0e7 · 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": {
    "lower": {
      "closed": false,
      "value": "-5"
    },
    "upper": {
      "closed": false,
      "value": "-1"
    }
  }
}
{
  "claim": "interlacing",
  "from_index": 1,
  "kind": "weak",
  "orientation": "unordered"
}
Certificate
preserver_image, SHA-256 736518b7c50d469dd877b209beba02a746910b5e8f20ed3f93488c0829795380, 24,971 bytes (6,081 compressed); download
polytool replayed the certificate when the step was written.
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