Algo Math Structurer

algo-math-structurer

Transform Python algorithm code into formal mathematical documents with proofs, exported as LaTeX and compiled to PDF.

Description

algo-math-structurer is a Claude Cowork plugin that bridges the gap between implementation and formal mathematics. It takes Python algorithm code - search, sort, graph, optimization, dynamic programming, clustering - and produces rigorously structured mathematical documents complete with definitions, theorems, proofs by recurrence, and complexity analysis.

The output is a LaTeX document compiled to PDF, suitable for academic papers, technical documentation, or educational materials.

Skills

Skill	Description
algorithm-formalization	Analyzes Python algorithm implementations and generates formal mathematical specifications: preconditions, postconditions, loop invariants, recurrence relations, and proofs.

Commands

Command	Description
/algo-math:generate-proof	Full proof generation: reads Python code, produces complete LaTeX document with definitions, theorems, proofs, and complexity analysis. Compiles to PDF.
/algo-math:analyze-complexity	Big-O complexity analysis only. Extracts time and space complexity from the algorithm's control flow and recursion structure.
/algo-math:extract-properties	Extracts formal properties: preconditions, postconditions, loop invariants, and termination conditions. No proof generation.

Setup Instructions

1. Install from marketplace: In Claude Cowork, type /plugin, choose Add marketplace, and select this repository. Then install algo-math-structurer.

2. Local development: If you are testing the plugin directly from disk, copy the algo-math-structurer/ directory into your Claude Cowork plugins folder:

   cp -r algo-math-structurer ~/.claude-cowork/plugins/
   

3. Verify installation: Restart Claude Cowork. The three /algo-math:* commands should appear in the command palette.

4. LaTeX dependency: Ensure pdflatex (or xelatex) is installed on your system for PDF compilation:

   # macOS
   brew install --cask mactex
   
   # Ubuntu/Debian
   sudo apt install texlive-full
   

Packaging

• algo-math-structurer/ is the source tree you edit locally.
• algo-math-structurer.plugin is the packaged archive ready to distribute or import.
• Both contain the same plugin contents, including .claude-plugin/plugin.json, commands/, skills/, and .mcp.json.

Usage Examples

Exponentiation Rapide

Input (algorithms/exponentiation.py):

def puissance(a, n):
    if n == 0: return 1
    elif n % 2 == 0: return puissance(a * a, n // 2)
    else: return a * puissance(a * a, (n - 1) // 2)

Run: /algo-math:generate-proof

Output — PDF containing:

• Definition: Recursive binary exponentiation function $f: \mathbb{R} \times \mathbb{N} \to \mathbb{R}$
• Theorem: For all $a \in \mathbb{R}, n \in \mathbb{N}$, $f(a, n) = a^n$
• Proof by recurrence: Base case $n=0$, even case $n=2k$, odd case $n=2k+1$
• Complexity analysis: $O(\log n)$ time, $O(\log n)$ stack space

Complexity Analysis Only

Run: /algo-math:analyze-complexity on a merge sort implementation.

Output: Time $O(n \log n)$, Space $O(n)$, with derivation from recurrence $T(n) = 2T(n/2) + O(n)$.

Limitations

• Language: Python only. No TypeScript, Java, C++, or other languages.
• Algorithm scope: Classical algorithms — search, sort, graph traversal, optimization, dynamic programming, clustering.
• Excluded: Neural network training loops, reinforcement learning, generative models, heuristic black-box algorithms.
• Proof depth: Proofs are formal but not machine-checked. No Coq, Lean, or Isabelle output.
• Interactive refinement: No iterative proof refinement loop. Single-pass generation.

Customization Tips

• Extend algorithm coverage: Add new algorithm patterns to the algorithm-formalization skill's reference library in skills/algorithm-formalization/SKILL.md.
• Adjust proof style: Modify the LaTeX template sections in the skill to change theorem formatting, notation conventions, or proof structure.
• Add complexity templates: For new algorithm families, add recurrence relation templates to the skill's complexity analysis section.
• Custom LaTeX preamble: Edit the skill's LaTeX preamble to include your institution's style, custom macros, or bibliography format.