Compute complex function residues and apply the Residue Theorem.
npx skills add https://github.com/scooter-lacroix/Maestro --skill residues
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
This Skill provides strategies and tools for calculating residues of complex functions, classifying singularities, and applying the Residue Theorem for contour integration.
Use the residues skill to compute the residue of the function 1/((z-1)*(z-2)) at z=1.
High-intent search queries and answers about installing and using this skill.
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.
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.
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.
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.
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.
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.
hxk622Perform symbolic math computations with SymPy in Python.
scooter-lacroixSolve contour integral problems using the residue theorem and Python scripts.
parcadeiCompute residues of complex functions and evaluate contour integrals via the Residue Theorem.
scooter-lacroixVerify analyticity with Cauchy-Riemann equations and compute power series using Sympy.
