asymptotic-notation-calculator

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}
graph	{"domains":["domain:computer-science"],"specializations":["specialization:theoretical-computer-science"],"skillAreas":["skill-area:np-hard-heuristics","skill-area:mathematical-reasoning","skill-area:dynamic-programming"],"workflows":["workflow:research-grant-lifecycle"],"roles":["role:computational-scientist","role:research-engineer"]}

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