Derive recurrences and closed forms for sequences using formal power series in Lean 4.
npx skills add https://github.com/bneb/perqed --skill generating-functions
Please help me install this Agent Skill. Skill: generating_functions Source: https://github.com/bneb/perqed/tree/main/.agents/skills/generating_functions Command: npx skills add https://github.com/bneb/perqed --skill generating-functions
Encode a sequence as a formal power series and use algebraic operations to derive recurrences, closed forms, and identities.
Provide a sequence and ask the system to derive its generating function and the associated recurrence or closed form.
High-intent search queries and answers about installing and using this skill.
Encode the sequence as a formal power series F(x), apply algebraic operations and partial fractions, then extract coefficients to derive the associated recurrence relation or closed form.
Translate the integer sequence into a generating function and apply standard power series manipulation techniques like partial fractions to solve for a closed-form expression.
Yes, this approach integrates with Lean 4 and mathlib4 to formalize generating functions, relying on formal power series manipulation to validate algebraic identities and extract coefficients within the proof environment.
Generating function manipulation works for proving algebraic identities in mathlib4 by encoding sequences as power series and using coefficient extraction to formally verify the identity within the proof assistant.
Manipulate the generating functions algebraically and apply the coefficient extraction logic supported by mathlib4 to isolate the specific sequence terms from the convolution.
fmhallGenerate roundtrip theorems for Lean 4 PNG encoding and decoding.
bnebConstruct explicit δ(ε) or N witnesses for Lean 4 / mathlib4 limit proofs.
r-irbeFormalize nonlinear dynamical systems and stability proofs in Lean 4.
AndrewK404Coordinate empirical testing and formal proof generation for iterative mathematical functions.
