residues

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.

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.

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.

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.

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.