Fermat

Perform symbolic mathematical operations including equation solving, polynomial manipulation, and algebraic simplification using SymPy's computer algebra system. The MCP server exposes SymPy's symbolic expression API, allowing clients to define variables, construct equations, and request symbolic solutions without numerical approximation. Operations are executed server-side and results returned as symbolic expressions or simplified forms.

Execute numerical computations using NumPy arrays and linear algebra operations, including matrix operations, statistical calculations, and numerical transformations. The server wraps NumPy's vectorized operations and exposes them through MCP function calls, handling array serialization/deserialization and returning results as JSON-compatible numeric structures. Supports batch operations on multi-dimensional arrays.

Customizes plot appearance through Matplotlib's styling API, supporting color schemes, line styles, markers, fonts, legends, grid options, and axis formatting. Accepts plot objects and styling specifications, applies Matplotlib formatting functions, and returns styled plots. Supports both programmatic styling and predefined style templates.

Compute derivatives, integrals, limits, and series expansions using SymPy for symbolic calculus and NumPy for numerical differentiation/integration. The server routes requests to appropriate backends based on operation type — symbolic operations use SymPy's calculus module, while numerical integration uses scipy.integrate. Results include both symbolic expressions and numerical evaluations where applicable.

Perform statistical computations including descriptive statistics (mean, median, variance, skewness), correlation analysis, hypothesis testing, and probability distributions using NumPy and SciPy.stats. The server accepts datasets as arrays and returns statistical summaries, correlation matrices, and test results with p-values. Supports both parametric and non-parametric statistical tests.

Generate 2D plots including line plots, scatter plots, histograms, bar charts, and heatmaps using Matplotlib. The server accepts plot specifications (data, axes labels, plot type) and returns rendered images as PNG or SVG. Supports customization of colors, markers, legends, and styling. Generated plots are serialized as base64-encoded images or file paths for client consumption.

Generate 3D surface plots, scatter plots, and wireframe visualizations using Matplotlib's mplot3d toolkit. The server accepts 3D data specifications and returns rendered 3D plots as images with configurable viewing angles and projections. Supports surface plots from function definitions or data grids, and 3D scatter plots for point cloud visualization.

Expose all mathematical and plotting operations through the Model Context Protocol (MCP) as callable functions with typed schemas. The server implements MCP's tool/function interface, allowing LLM clients to discover available operations, inspect parameter schemas, and invoke computations with automatic argument validation and error handling. Results are returned as structured JSON responses compatible with LLM processing.

Execute multiple mathematical operations in sequence or parallel through a single MCP request, with support for chaining results between operations. The server accepts a batch specification defining operation order, data dependencies, and parameter mappings, then executes the batch and returns all results in a single response. Enables complex multi-step mathematical workflows without repeated MCP round-trips.

Provide detailed error messages, computation diagnostics, and fallback strategies when mathematical operations fail or produce unexpected results. The server catches computation errors (e.g., singular matrices, convergence failures) and returns structured error responses with diagnostic information, suggested corrections, and alternative approaches. Includes warnings for numerical instability or precision loss.

Solves equations and finds roots of functions using SymPy's symbolic solver and numerical root-finding methods. Accepts equations (symbolic or string format), variable specifications, and optional initial guesses, then applies appropriate solving algorithms. Returns exact symbolic solutions when available, with numerical fallbacks for transcendental equations. Supports systems of equations and polynomial root finding.