High-risk tools in SageMath MCP Server
31 of the 32 tools in SageMath MCP Server are classified as high risk. This page profiles those tools specifically, with recommended policy actions and the attack patterns that target them.
Every operation listed below is an action PolicyLayer recommends controlling at the transport layer. Open any tool to see the full profile, risk score, and YAML policy snippet.
Tools at high risk
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cancel_sage_sessionExecuteCancel any running Sage computation and restart the worker
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evaluate_sage_streamingExecuteExecute SageMath code and stream intermediate print() output
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boolean_algebra_operationExecuteBoolean algebra: operations on boolean polynomials
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calculate_expressionExecuteEvaluate a SageMath expression and return numeric/string forms
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coding_theory_operationExecuteCoding theory: construct error-correcting codes
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combinatorics_operationExecuteCombinatorics: binomial, permutations, combinations, partitions, and more
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differentiate_expressionExecuteDifferentiate an expression with respect to a variable
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distribution_operationExecuteProbability distribution operations: PDF, CDF, quantile, mean, variance, sampling
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elliptic_curve_operationExecuteElliptic curve operations: rank, torsion,
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expand_expressionExecuteExpand a mathematical expression
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factor_expressionExecuteFactor a mathematical expression or integer
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find_rootExecuteFind a numeric root of an expression in a given interval
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geometry_operationExecuteGeometry: distances, areas, volumes, convex hulls
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group_operationExecuteGroup theory: construct groups and query properties
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integrate_expressionExecuteIntegrate an expression (indefinite or definite with bounds)
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limit_expressionExecuteCompute the limit of an expression
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matrix_multiplyExecuteMultiply two matrices and return the result as nested lists
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matrix_operationExecutePerform a matrix operation (det, inverse, eigenvalues, ...)
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number_theory_operationExecuteNumber theory operations: is_prime, factor_integer, next_prime, gcd, lcm
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plot_expressionExecutePlot an expression and return a base64-encoded PNG image
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plot_multi_expressionExecutePlot multiple expressions overlaid on a single 2D graph
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plot3d_expressionExecutePlot a 3D surface of a two-variable expression as base64 PNG
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polynomial_ring_operationExecutePolynomial ring operations: construct rings
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series_expansionExecuteCompute a Taylor/Laurent series expansion
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simplify_expressionExecuteSimplify a mathematical expression
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solve_equationExecuteSolve an equation or system of equations
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solve_odeExecuteSolve an ordinary differential equation
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statistics_summaryExecuteCompute descriptive statistics for a dataset
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symbolic_sumExecuteCompute a symbolic sum or product over an index variable
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vector_calculus_operationExecuteVector calculus operations: gradient, divergence, curl, laplacian
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graph_operationExecuteGraph theory: create named graphs and compute properties
Attacks that target this class
High-risk tools in any server share these documented attack patterns. Each links to the full case and the defensive policy.