complex_analysis_suite
Convert complex numbers, calculate residues, perform analytic continuation, and visualize complex planes. Supports arithmetic, contour integration, series expansion, and more.
Instructions
Brief description:
Powerful complex analysis and complex function tool, supporting complex number form conversion, residue calculation, analytic continuation, complex plane visualization, and other advanced features.
Examples:
complex_analysis_suite(operation='convert_form', complex_number='3+4i')
complex_analysis_suite(operation='function_evaluation', function_expression='z**2 + 1', complex_number='1+i')
complex_analysis_suite(operation='residue_calculation', function_expression='1/(z**2 + 1)', singularities=['i', '-i'])
Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| operation | Yes | Complex analysis operation. Supports: 'arithmetic', 'complex_functions', 'contour_integration', 'residue_calculation', 'series_expansion', 'visualization' | |
| complex_number | No | Single complex number (string or complex type) | |
| complex_numbers | No | List of complex numbers for operations | |
| function_expression | No | Complex function expression | |
| variable | No | Complex variable symbol | z |
| contour_points | No | Contour points for integration | |
| singularities | No | List of function singularities | |
| center | No | Center point for expansion | |
| radius | No | Radius for convergence | |
| order | No | Order of expansion or pole | |
| x_range | No | Real axis range for visualization | |
| y_range | No | Imaginary axis range for visualization | |
| resolution | No | Plot resolution | |
| colormap | No | Colormap for visualization | hsv |
| filename | No | Output filename for plots | |
| plot_type | No | Visualization type. Supports: 'domain_coloring', 'contour_plot', 'surface_plot' | domain_coloring |
| series_terms | No | Number of series terms | |
| branch_cut | No | Branch cut specification | |
| method | No | Calculation method | auto |