AgentSkillsCN

asymptotic-notation-calculator

自动化推导与简化算法分析中的大O、大Ω与大Θ表达式

SKILL.md
--- frontmatter
name: asymptotic-notation-calculator
description: Automated derivation and simplification of Big-O, Big-Omega, and Big-Theta expressions for algorithm analysis
allowed-tools:
  - Bash
  - Read
  - Write
  - Edit
  - Glob
  - Grep
metadata:
  specialization: computer-science
  domain: science
  category: algorithm-analysis
  phase: 6

Asymptotic Notation Calculator

Purpose

Provides expert guidance on analyzing, simplifying, and comparing asymptotic complexity expressions for algorithm analysis.

Capabilities

  • •Parse and simplify asymptotic expressions
  • •Compare complexity classes
  • •Identify dominant terms
  • •Handle logarithmic, polynomial, and exponential factors
  • •Generate LaTeX-formatted notation
  • •Prove asymptotic relationships

Usage Guidelines

  1. •Expression Analysis: Parse complexity expressions into canonical forms
  2. •Simplification: Apply dominance rules to simplify nested expressions
  3. •Comparison: Determine ordering between complexity classes
  4. •Documentation: Generate properly formatted asymptotic notation
  5. •Verification: Prove Big-O, Big-Omega, and Big-Theta relationships

Tools/Libraries

  • •SymPy
  • •Symbolic computation
  • •LaTeX rendering