SageMath MCP Server

A mathematics Model Context Protocol (MCP) server that gives LLM clients a sandboxed mathematical subset of SageMath --- one of the most comprehensive open-source mathematics systems available. Built on FastMCP 3.x, the server maintains a dedicated SageMath process for each MCP session so variables, functions, and assumptions persist across tool calls. Caller code is deny-by-default: the full breadth of Sage mathematics is reachable, but imports, the external CAS interfaces, and the file/display/persistence primitives are not (see Security Sandbox).

Whether the task is symbolic calculus, number theory, linear algebra, differential equations, plotting, combinatorics, graph theory, group theory, or basic arithmetic, the server provides 40 MCP tools --- the math tools backed by the SageMath engine, plus evaluate_sage_streaming (streaming wrapper) and HTTP /health and /ready endpoints.

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Table of Contents

• Features at a Glance
• Architecture Overview
• Quick Start
• Detailed Tool Reference
  • evaluate_sage --- Open-Ended Execution
  • Calculus Tools
  • Algebra & Simplification Tools
  • Linear Algebra Tools
  • Differential Equations
  • Number Theory
  • Statistics
  • Visualization
  • Session Management & Observability
• Security Sandbox
• LLM Client Configuration
• Deployment
• Configuration Reference
• CLI Reference
• Development
• CLI Integration Testing
• Project Layout
• Technology Stack
• Changelog
• Roadmap
• Contributing

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Features at a Glance

Category	Tools	Backend	Capabilities
Core execution	evaluate_sage, evaluate_sage_streaming	Sage	Run SageMath code (the mathematical subset the sandbox permits) with persistent state, LaTeX output, stdout capture, progress heartbeats, per-call timeouts, and line-by-line streaming
Calculus	differentiate_expression, integrate_expression, limit_expression, series_expansion	Sage	Derivatives of any order, indefinite & definite integrals, one-sided limits, Taylor/Laurent series
Algebra	solve_equation, simplify_expression, expand_expression, factor_expression, calculate_expression	Sage	Single equations & systems, symbolic simplification, expansion, factoring, numeric evaluation
Symbolic sums	symbolic_sum	Sage	Symbolic summation and products (finite and infinite series)
Linear algebra	matrix_multiply, matrix_operation	Sage	Matrix products, determinants, inverses, eigenvalues, rank, RREF, transpose
Differential equations	solve_ode	Sage	First- and higher-order ODEs via Sage's desolve()
Number theory	number_theory_operation	Sage	Primality testing, integer factorization, next prime, GCD, LCM
Combinatorics	combinatorics_operation	Sage	Binomial, permutations, combinations, partitions, factorial, Catalan, Fibonacci, Bell numbers
Graph theory	graph_operation	Sage	Named graphs including parameterised constructors (CompleteGraph(4)) and adjacency dicts; chromatic number, connectivity, planarity, diameter, shortest path
Group theory	group_operation	Sage	Symmetric, dihedral, cyclic, alternating groups; order, abelian/cyclic test, center, exponent
Elliptic curves	elliptic_curve_operation	Sage	Rank, torsion, discriminant, j-invariant, conductor, generators
Coding theory	coding_theory_operation	Sage	Hamming and generalized Reed-Solomon codes; length, dimension, minimum distance, generator matrix, rate
Polynomial rings	polynomial_ring_operation	Sage	Groebner bases, ideal dimension/variety, reduction, Groebner test
Boolean algebra	boolean_algebra_operation	Sage	Boolean polynomial ring, addressed as x, y, z or x0, x1, x2; evaluate, variables, degree, zero/one test
Geometry	geometry_operation	Sage	Distance, polygon area, polytope volume, convex hull, compactness via Polyhedron
Statistics	statistics_summary	Sage	Mean, median, population & sample variance/std dev, min, max
Probability	distribution_operation	Sage	Normal, exponential, Poisson, chi-squared, Student-t, uniform, beta, gamma; PDF, CDF, quantile, analytic mean/variance, sampling
Visualization	plot_expression, plot3d_expression, plot_multi_expression	Sage	2D plots, 3D surface plots, multi-function overlays, returned as rendered images (PNG or SVG) the client displays
Numeric methods	find_root	Sage	Numeric root-finding in an interval via Sage's find_root(), from an expression or an equation
Verification	verify_claim	Sage	Independently re-check a stated claim through a proof ladder; answers proved, refuted, supported or undecided, always with its evidence
Vector calculus	vector_calculus_operation	Sage	Gradient, divergence, curl, Laplacian on scalar/vector fields
Session control	reset_sage_session, interrupt_sage_session, cancel_sage_session	Worker	Clear state, or stop a computation with or without keeping variables
Named workspaces	start_sage_session, list_sage_sessions, stop_sage_session	Worker	Several independent variable namespaces per client
Diagnostics	check_sage_health, lookup_sage_doc	Worker/Server	MCP-level readiness probe (evaluates 1+1, reports latency); doc links for a Sage name plus whether this server offers it to caller code
Infrastructure	/health and /ready endpoints, 3 MCP resources	Server	Liveness (process up) and readiness (evaluates 1+1 on the backend), session snapshots, aggregated metrics, documentation links

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Architecture Overview