residues

Name: residues
Availability: InStock
Author: parcadei

Compute residues of complex functions and evaluate contour integrals via the Residue Theorem.

3.9k|296|Updated Dec 23, 2025

Search Tags:#calculus #complex analysis #sympy #singularity #residues #contour integral

Ready to run

npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill residues-parcadei

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: residues
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/complex-analysis/residues
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill residues-parcadei

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires sympy, z3-solver, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides a structured approach to solving problems involving residues in complex analysis, including computation, classification of singularities, and application of the Residue Theorem.

Core Features & Use Cases

Residue Computation: Calculates residues for simple poles, poles of higher order, and essential singularities.
Singularity Identification: Helps in classifying singularities (poles, essential, removable).
Residue Theorem Application: Assists in evaluating contour integrals using the Residue Theorem.
Use Case: Given a complex function f(z) and a contour C, this skill can compute the residues of f(z) at its poles inside C and then evaluate the contour integral of f(z) along C.

Quick Start

Use the residues skill to compute the residue of the function 1/((z-1)*(z-2)) at z=1.

Frequently Asked Questions about residues

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I compute residues of complex functions using SymPy?▼

This Skill evaluates contour integrals by applying the Residue Theorem, calculating the residues of a complex function at its poles within the given contour. It uses SymPy for symbolic computation and Z3 for verifying theorem application.

Can I classify singularities of a complex function automatically?▼

Yes, you can classify singularities of a complex function automatically. This Skill identifies and classifies singularities into poles, essential singularities, and removable singularities to determine the appropriate residue calculation method.

What's the best way to evaluate contour integrals with the Residue Theorem?▼

The best way to evaluate contour integrals with the Residue Theorem is to identify the enclosed poles, compute their residues, and apply the theorem directly. This Skill automates that workflow using SymPy for calculation and Z3 for verification.

Do I need Z3 to calculate residues for higher-order poles?▼

You need Z3 to verify calculations and theorem application, while SymPy handles the symbolic computation for higher-order pole residues. Z3 acts as a theorem prover to ensure the mathematical steps and limits are correctly applied.

When should I use Laurent series instead of limits for residue calculation?▼

You should use Laurent series instead of limits for residue calculation when dealing with essential singularities where limit formulas are insufficient. This Skill implements both methods to systematically compute residues across different singularity types.