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Automated derivation and simplification of Big-O, Big-Omega, and Big-Theta expressions for algorithm analysis
--- name: asymptotic-notation-calculator-f8306b39dc61 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--- name: asymptotic-notation-calculator-f8306b39dc61 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
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