residues

Compute complex function residues and apply the Residue Theorem.

8|1|Updated Jan 4, 2026

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

Ready to run

npx skills add https://github.com/scooter-lacroix/Maestro --skill residues

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: residues
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/complex-analysis/residues
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill residues

SYSTEM DOCUMENTATION & REQUIREMENTS

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

What problem does it solve?

This Skill provides strategies and tools for calculating residues of complex functions, classifying singularities, and applying the Residue Theorem for contour integration.

Core Features & Use Cases

Residue Computation: Calculate residues for simple poles, poles of higher order, and essential singularities.
Singularity Classification: Identify the type and order of singularities of a complex function at a given point.
Residue Theorem Application: Evaluate contour integrals using the sum of residues inside the contour.
Use Case: You need to evaluate the integral of a complex function around a closed curve. This Skill can help you find the poles inside the curve, compute their residues, and apply the Residue Theorem to find the integral's value.

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 for contour integration?▼

To compute residues of complex functions for contour integration, you can use this Skill to calculate residues at simple poles, higher-order poles, and essential singularities. It leverages sympy for symbolic computation to find the values needed for contour integrals.

What is the Residue Theorem and how does it evaluate contour integrals?▼

The Residue Theorem evaluates contour integrals by summing the residues of all singularities inside a closed contour. This Skill applies the theorem by identifying poles within the curve, computing their residues, and summing them to find the integral's value.

How do I classify singularities and find the order of poles in complex analysis?▼

To classify singularities and find the order of poles in complex analysis, this Skill identifies the type and order of singularities at a given point. It supports Laurent series expansion to characterize function behavior around these points.

Can I use sympy and z3 to verify pole locations relative to integration contours?▼

Yes, you can use sympy and z3 to verify pole locations relative to integration contours. This Skill uses sympy for symbolic residue computation and z3 for proof verification, ensuring correct poles inside the contour are included in the calculation.

Does this approach work for essential singularities and Laurent series expansion?▼

Yes, this approach works for essential singularities and Laurent series expansion. The Skill computes residues for essential singularities and expands functions into Laurent series to analyze complex function behavior around the singularity.

What are the limitations of using symbolic computation for complex analysis problems?▼

Limitations of using symbolic computation for complex analysis problems include difficulties with highly abstract functions or non-standard contours lacking closed-form representations. The z3 proof verification may also face constraints with complex pole location logic.