{"passport":{"unfragile":{"@version":"1.0","version":"2026-05","artifact":{"id":"smithery_aman-amith-shastry-scientific-computation","slug":"aman-amith-shastry-scientific-computation","name":"Scientific Computing","type":"mcp","url":"https://github.com/Aman-Amith-Shastry/scientific_computation_mcp","page_url":"https://unfragile.ai/aman-amith-shastry-scientific-computation","categories":["mcp-servers","rag-knowledge"],"tags":["mcp","model-context-protocol","smithery:Aman-Amith-Shastry/scientific_computation"],"pricing":{"model":"open_source","free":true,"starting_price":null},"status":"active","verified":false},"capabilities":[{"id":"smithery_aman-amith-shastry-scientific-computation__cap_0","uri":"capability://data.processing.analysis.tensor.creation.and.manipulation","name":"tensor-creation-and-manipulation","description":"Create and manage multi-dimensional tensor objects with support for initialization from lists, numpy arrays, or symbolic expressions. The MCP server exposes tensor construction via standardized tools that handle shape validation, dtype inference, and memory layout optimization. Tensors serve as the foundational data structure for all downstream linear algebra and calculus operations.","intents":["I need to create a matrix or higher-dimensional array to work with in linear algebra computations","I want to initialize tensors from existing data structures and validate their shapes before operations","I need to manipulate tensor dimensions through reshaping, transposing, or slicing operations"],"best_for":["researchers building numerical computing workflows in LLM-augmented environments","developers integrating scientific computing into Claude-based agents","teams prototyping mathematical simulations with AI assistance"],"limitations":["No built-in GPU acceleration — all computations run on CPU, limiting scalability for large tensors (>1GB)","Tensor persistence requires external serialization; MCP server maintains state only during session","No automatic differentiation tracking — gradients computed symbolically, not via autograd"],"requires":["MCP client compatible with Claude or other LLM platforms","Python 3.8+ runtime for the MCP server","NumPy or SymPy installed for underlying tensor operations"],"input_types":["list of numbers","nested lists (for multi-dimensional arrays)","numpy array objects","symbolic expressions"],"output_types":["tensor object reference","shape metadata","dtype information"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_1","uri":"capability://data.processing.analysis.matrix.decomposition.analysis","name":"matrix-decomposition-analysis","description":"Perform QR decomposition, Singular Value Decomposition (SVD), and other matrix factorizations through MCP tools that return decomposed components and analysis metadata. The server wraps scipy.linalg and numpy.linalg functions, exposing decomposition results as structured outputs that include singular values, eigenvectors, and reconstruction information for validation.","intents":["I need to decompose a matrix into orthogonal and upper-triangular components for numerical stability","I want to find the rank, condition number, and singular values of a matrix to understand its properties","I need to solve least-squares problems or analyze matrix invertibility through decomposition"],"best_for":["numerical analysts building AI-assisted matrix analysis workflows","engineers solving systems of linear equations with LLM guidance","researchers exploring matrix properties interactively through Claude"],"limitations":["Decomposition results are computed eagerly and returned as dense arrays — no lazy evaluation or streaming for very large matrices","No incremental updates — recomputing full decomposition if matrix changes slightly","Numerical stability depends on input conditioning; ill-conditioned matrices may produce inaccurate results"],"requires":["MCP server with scipy and numpy installed","Matrix input must be 2-dimensional and numeric (float or complex)","Python 3.8+ for underlying linear algebra libraries"],"input_types":["2D tensor/matrix","numeric array (float or complex)"],"output_types":["decomposed component matrices","singular values array","rank information","condition number","reconstruction error metrics"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_10","uri":"capability://data.processing.analysis.symbolic.equation.solving","name":"symbolic-equation-solving","description":"Solve algebraic and transcendental equations symbolically using SymPy's equation solver, exposed as MCP tools that accept equations and variables, returning exact symbolic solutions or numerical approximations. The server supports systems of equations, polynomial equations, and transcendental equations with multiple solution branches.","intents":["I need to find critical points of a function by solving gradient equations symbolically","I want to solve a system of nonlinear equations to find equilibrium points","I need to find roots of a polynomial or transcendental equation analytically"],"best_for":["mathematicians solving equations analytically","control systems engineers finding equilibrium points","optimization researchers analyzing critical point structure"],"limitations":["Symbolic equation solving is computationally expensive for high-degree polynomials (>4) or transcendental equations","Solutions may be expressed in terms of special functions or radicals that are difficult to interpret","No guarantee of finding all solutions — some transcendental equations may have infinitely many solutions"],"requires":["MCP server with SymPy installed","Equation(s) as symbolic expressions","Variable(s) to solve for","Python 3.8+ runtime"],"input_types":["symbolic equation (SymPy Eq or expression)","list of variables to solve for"],"output_types":["solution(s) (symbolic or numerical)","solution set (for systems)","solution multiplicity information"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_11","uri":"capability://data.processing.analysis.matrix.equation.solving","name":"matrix-equation-solving","description":"Solve linear matrix equations (Ax = b, AXB = C) and Lyapunov/Sylvester equations using scipy.linalg solvers exposed as MCP tools. The server handles dense and sparse matrices, supports multiple right-hand sides, and returns solutions with condition number and residual information for numerical validation.","intents":["I need to solve a linear system Ax = b for x given matrix A and vector b","I want to solve Lyapunov or Sylvester equations for control system analysis","I need to solve least-squares problems when the system is overdetermined"],"best_for":["control systems engineers solving Lyapunov equations for stability analysis","numerical analysts solving linear systems in scientific computing","researchers analyzing matrix equations in optimization and control"],"limitations":["Dense matrix solvers scale as O(n³) — inefficient for large systems; sparse solvers required for >10k×10k matrices","Solution accuracy depends on matrix conditioning — ill-conditioned systems produce inaccurate results despite correct algorithm","No built-in iterative refinement — single-pass solution may accumulate rounding errors"],"requires":["MCP server with scipy and numpy installed","Matrix A (square for standard linear systems, rectangular for least-squares)","Right-hand side vector(s) or matrix B","Python 3.8+ runtime"],"input_types":["coefficient matrix A","right-hand side vector or matrix B","optional: equation type (standard, Lyapunov, Sylvester)"],"output_types":["solution vector or matrix X","residual norm","condition number","rank information (for least-squares)"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_12","uri":"capability://tool.use.integration.mcp.tool.integration.interface","name":"mcp-tool-integration-interface","description":"Expose all scientific computing capabilities through the Model Context Protocol (MCP) as standardized tools that Claude and other LLM clients can invoke. The MCP server implements tool schemas with input validation, error handling, and structured JSON responses, enabling seamless integration of scientific computing into LLM-augmented workflows without direct code execution.","intents":["I need to integrate scientific computing capabilities into Claude-based agents for mathematical reasoning","I want to expose tensor operations and linear algebra as callable tools in an LLM context","I need to build a scientific computing assistant that can perform calculations and visualizations through natural language"],"best_for":["LLM application developers building scientific computing agents","teams integrating Claude with numerical computing workflows","researchers building AI-assisted mathematical analysis systems"],"limitations":["MCP tool invocation adds latency (~100-500ms per call) compared to direct library usage","Tool schemas must be predefined — dynamic tool generation based on runtime data not supported","Error handling and validation occur at MCP layer, potentially obscuring underlying numerical errors"],"requires":["MCP-compatible LLM client (Claude, etc.)","MCP server running with Python 3.8+ and scientific libraries","Network connectivity between client and server (local or remote)"],"input_types":["JSON-formatted tool arguments","tensor/matrix data as nested lists or base64-encoded arrays","symbolic expressions as strings"],"output_types":["JSON-structured tool results","numeric arrays as nested lists","symbolic expressions as strings","visualization data as base64-encoded images"],"categories":["tool-use-integration","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_2","uri":"capability://data.processing.analysis.eigenvalue.eigenvector.computation","name":"eigenvalue-eigenvector-computation","description":"Compute eigenvalues and eigenvectors for square matrices through MCP tools that return sorted eigenvalue spectra and corresponding eigenvector bases. The implementation uses numpy.linalg.eig and scipy eigensolvers, with optional sorting and filtering by magnitude or real/imaginary components, enabling spectral analysis of linear transformations.","intents":["I need to find the eigenvalues and eigenvectors of a matrix to understand its spectral properties","I want to analyze the stability of a dynamical system by examining eigenvalue magnitudes","I need to identify principal directions or modes of a system through eigenvector analysis"],"best_for":["control systems engineers analyzing system stability with AI assistance","researchers studying dynamical systems and bifurcations","data scientists performing dimensionality reduction via spectral methods"],"limitations":["Eigenvalue computation for non-symmetric matrices may produce complex eigenvalues; numerical precision depends on matrix conditioning","No generalized eigenvalue problem support (Ax = λBx) — only standard eigenvalue problems","Large sparse matrices (>10k×10k) require external sparse eigensolvers not included in this MCP"],"requires":["MCP server with numpy and scipy installed","Square matrix input (n×n)","Python 3.8+ runtime"],"input_types":["square 2D tensor/matrix","numeric array (float or complex)"],"output_types":["eigenvalue array (sorted by magnitude or real part)","eigenvector matrix","spectral radius","condition number of eigenvector matrix"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_3","uri":"capability://data.processing.analysis.determinant.and.matrix.properties","name":"determinant-and-matrix-properties","description":"Compute matrix determinants, traces, ranks, and condition numbers through MCP tools that return scalar properties and numerical stability metrics. The server wraps numpy.linalg functions to provide quick analysis of matrix invertibility, volume scaling factors, and numerical conditioning without full decomposition.","intents":["I need to check if a matrix is invertible by computing its determinant","I want to understand the numerical stability of a matrix through its condition number","I need to compute the trace or rank of a matrix for system analysis"],"best_for":["numerical analysts checking matrix properties before solving linear systems","engineers validating system matrices for stability and invertibility","researchers analyzing matrix conditioning in optimization problems"],"limitations":["Determinant computation via LU decomposition is numerically unstable for ill-conditioned matrices; use log-determinant for better stability","Rank computation uses SVD with default tolerance — may misidentify rank for nearly-singular matrices","Condition number computation is expensive for large matrices (O(n³) complexity)"],"requires":["MCP server with numpy installed","Square matrix for determinant and trace; any matrix for rank","Python 3.8+ runtime"],"input_types":["2D tensor/matrix","numeric array (float or complex)"],"output_types":["determinant (scalar)","trace (scalar)","rank (integer)","condition number (scalar)","numerical stability assessment"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_4","uri":"capability://data.processing.analysis.vector.projection.and.orthogonalization","name":"vector-projection-and-orthogonalization","description":"Compute vector projections, orthogonal complements, and orthonormal bases using Gram-Schmidt orthogonalization and projection formulas exposed as MCP tools. The server implements projection onto subspaces, orthogonal decomposition (v = v_parallel + v_perpendicular), and basis transformation, enabling geometric analysis of vector spaces.","intents":["I need to project a vector onto a subspace or another vector for geometric analysis","I want to decompose a vector into parallel and perpendicular components relative to a subspace","I need to construct an orthonormal basis from a set of vectors for numerical stability"],"best_for":["computational geometers working with vector spaces and subspaces","engineers analyzing projections in signal processing or control systems","researchers building orthogonal decompositions for numerical algorithms"],"limitations":["Gram-Schmidt orthogonalization is numerically unstable for nearly-dependent vectors; modified Gram-Schmidt or Householder reflections recommended for ill-conditioned bases","Projection onto high-dimensional subspaces requires storing full basis matrix — memory-intensive for large dimensions","No support for weighted projections or projections in non-Euclidean metrics"],"requires":["MCP server with numpy installed","Vector(s) and subspace basis as tensor inputs","Python 3.8+ runtime"],"input_types":["1D vector array","2D matrix (columns as basis vectors)","multiple vectors for orthogonalization"],"output_types":["projected vector","orthogonal component","orthonormal basis matrix","projection coefficients"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_5","uri":"capability://data.processing.analysis.basis.change.and.coordinate.transformation","name":"basis-change-and-coordinate-transformation","description":"Transform vectors and matrices between different coordinate bases using change-of-basis matrices computed from basis vectors. The MCP tools accept a vector/matrix and two bases (old and new), computing the transformation matrix and applying it to convert coordinates, enabling analysis in natural or convenient coordinate systems.","intents":["I need to transform a vector from one coordinate system to another using a change-of-basis matrix","I want to express a matrix in a different basis to simplify analysis or computation","I need to convert between Cartesian, polar, or other coordinate systems for problem-specific analysis"],"best_for":["physicists and engineers working with multiple coordinate systems","researchers analyzing systems in natural or principal coordinate bases","developers building coordinate-agnostic numerical algorithms"],"limitations":["Basis vectors must be linearly independent; no automatic detection of rank-deficient bases","Transformation accuracy depends on conditioning of basis matrix — ill-conditioned bases amplify numerical errors","No support for non-orthogonal bases or weighted coordinate transformations"],"requires":["MCP server with numpy installed","Two sets of basis vectors (old and new bases)","Vector or matrix to transform","Python 3.8+ runtime"],"input_types":["vector to transform","matrix to transform","old basis (matrix with basis vectors as columns)","new basis (matrix with basis vectors as columns)"],"output_types":["change-of-basis matrix","transformed vector","transformed matrix","condition number of transformation"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_6","uri":"capability://data.processing.analysis.symbolic.gradient.computation","name":"symbolic-gradient-computation","description":"Compute gradients of scalar functions symbolically using SymPy's differentiation engine, exposed as MCP tools that accept symbolic expressions and return gradient vectors or Jacobian matrices. The server supports partial derivatives, directional derivatives, and automatic simplification of symbolic results for analytical insight.","intents":["I need to compute the gradient of a function symbolically to understand its behavior analytically","I want to find critical points by setting the gradient to zero and solving symbolically","I need to compute Jacobian matrices for nonlinear system analysis or optimization"],"best_for":["mathematicians and researchers analyzing functions analytically","optimization engineers building symbolic optimization algorithms","control systems designers analyzing nonlinear system dynamics"],"limitations":["Symbolic differentiation is slow for complex expressions — exponential complexity in expression tree depth","Automatic simplification may fail for highly nonlinear or transcendental functions, returning unsimplified expressions","No support for implicit differentiation or differentiation of integrals (Leibniz rule requires manual setup)"],"requires":["MCP server with SymPy installed","Symbolic expression input (using SymPy symbols)","Python 3.8+ runtime"],"input_types":["symbolic expression (SymPy Expr)","list of variables to differentiate with respect to"],"output_types":["gradient vector (list of partial derivatives)","Jacobian matrix","simplified symbolic expressions"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_7","uri":"capability://data.processing.analysis.divergence.curl.and.laplacian.computation","name":"divergence-curl-and-laplacian-computation","description":"Compute divergence, curl, and Laplacian operators on vector and scalar fields using symbolic differentiation via SymPy, exposed as MCP tools that accept field expressions and return operator results. The server supports 2D and 3D fields with automatic coordinate system handling and symbolic simplification.","intents":["I need to compute the divergence of a vector field to analyze flux and source/sink behavior","I want to find the curl of a vector field to understand rotational properties","I need to compute the Laplacian of a scalar field for PDE analysis or heat equation problems"],"best_for":["physicists and engineers analyzing vector fields in fluid dynamics or electromagnetism","PDE researchers studying Laplacian operators and harmonic functions","computational scientists building symbolic PDE solvers"],"limitations":["Symbolic computation of curl and divergence is slow for complex field expressions","No support for non-Cartesian coordinate systems (cylindrical, spherical) — requires manual Jacobian adjustment","Laplacian computation assumes Euclidean metric; no support for Riemannian manifolds"],"requires":["MCP server with SymPy installed","Symbolic vector or scalar field expression","Coordinate variables (x, y, z) defined as SymPy symbols","Python 3.8+ runtime"],"input_types":["symbolic vector field (list of 2-3 symbolic expressions)","symbolic scalar field (single symbolic expression)","coordinate variables"],"output_types":["divergence (scalar expression)","curl (vector expression in 3D)","Laplacian (scalar expression)","simplified symbolic results"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_8","uri":"capability://image.visual.function.and.vector.field.visualization","name":"function-and-vector-field-visualization","description":"Generate 2D and 3D visualizations of scalar functions and vector fields using matplotlib and numpy, exposed as MCP tools that produce plots saved as image files or returned as base64-encoded data. The server supports surface plots, contour plots, quiver plots for vector fields, and streamline visualizations with customizable styling.","intents":["I need to visualize a scalar function to understand its behavior and identify critical points or regions","I want to plot a vector field to see flow patterns, singularities, and field structure","I need to validate numerical results by comparing computed fields against expected visualizations"],"best_for":["researchers exploring function behavior interactively through Claude","engineers validating numerical simulations visually","educators building interactive mathematical demonstrations"],"limitations":["Visualization is static — no interactive 3D rotation or zooming; requires regeneration for different views","High-resolution plots are memory-intensive; large grids (>1000×1000) may cause performance issues","Vector field visualization with quiver plots becomes cluttered for high-density fields; requires manual downsampling"],"requires":["MCP server with matplotlib and numpy installed","Function or field expression (numerical or symbolic)","Domain specification (x/y/z ranges)","Python 3.8+ runtime"],"input_types":["scalar function (numerical or symbolic)","vector field (list of 2-3 components)","domain bounds (min/max for each axis)","grid resolution parameters"],"output_types":["PNG image file","base64-encoded image data","plot metadata (axis labels, title, colorbar range)"],"categories":["image-visual","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0},{"id":"smithery_aman-amith-shastry-scientific-computation__cap_9","uri":"capability://data.processing.analysis.numerical.integration.and.quadrature","name":"numerical-integration-and-quadrature","description":"Compute definite integrals of scalar functions using numerical quadrature methods (Simpson's rule, Gaussian quadrature) exposed as MCP tools. The server wraps scipy.integrate functions to provide adaptive integration with error estimation, supporting 1D and multi-dimensional integrals with customizable tolerance and method selection.","intents":["I need to compute a definite integral numerically when symbolic integration is intractable","I want to integrate a function over a domain with error bounds for validation","I need to compute arc length, area, or volume integrals for geometric analysis"],"best_for":["numerical analysts computing integrals in scientific workflows","engineers solving problems requiring numerical integration","researchers validating symbolic integration results numerically"],"limitations":["Adaptive quadrature may fail for highly oscillatory functions or functions with singularities near integration bounds","Multi-dimensional integration (>3D) becomes exponentially expensive; requires specialized sparse-grid methods not included","Singular integrals require manual transformation or regularization; no built-in singularity handling"],"requires":["MCP server with scipy and numpy installed","Integrand function (numerical or callable)","Integration bounds (finite or infinite)","Python 3.8+ runtime"],"input_types":["scalar function (numerical or callable)","integration bounds (lower, upper)","tolerance parameters (optional)"],"output_types":["integral value (scalar)","error estimate","number of function evaluations"],"categories":["data-processing-analysis","scientific-computing"],"confidence":0.5,"matches":0,"success_rate":0}],"trust":{"score":37,"verified":false,"data_access_risk":"moderate","permissions":["MCP client compatible with Claude or other LLM platforms","Python 3.8+ runtime for the MCP server","NumPy or SymPy installed for underlying tensor operations","MCP server with scipy and numpy installed","Matrix input must be 2-dimensional and numeric (float or complex)","Python 3.8+ for underlying linear algebra libraries","MCP server with SymPy installed","Equation(s) as symbolic expressions","Variable(s) to solve for","Python 3.8+ runtime"],"failure_modes":["No built-in GPU acceleration — all computations run on CPU, limiting scalability for large tensors (>1GB)","Tensor persistence requires external serialization; MCP server maintains state only during session","No automatic differentiation tracking — gradients computed symbolically, not via autograd","Decomposition results are computed eagerly and returned as dense arrays — no lazy evaluation or streaming for very large matrices","No incremental updates — recomputing full decomposition if matrix changes slightly","Numerical stability depends on input conditioning; ill-conditioned matrices may produce inaccurate results","Symbolic equation solving is computationally expensive for high-degree polynomials (>4) or transcendental equations","Solutions may be expressed in terms of special functions or radicals that are difficult to interpret","No guarantee of finding all solutions — some transcendental equations may have infinitely many solutions","Dense matrix solvers scale as O(n³) — inefficient for large systems; sparse solvers required for >10k×10k matrices","builder identity is not verified yet","no observed match outcomes yet"],"rank_breakdown":{"adoption":0.05,"quality":0.6,"ecosystem":0.5900000000000001,"match_graph":0.25,"freshness":0.52,"weights":{"adoption":0.25,"quality":0.25,"ecosystem":0.15,"match_graph":0.23,"freshness":0.12}},"observed_outcomes":{"matches":0,"success_rate":0,"avg_confidence":0,"top_intents":[],"last_matched_at":null},"maintenance":{"status":"active","updated_at":"2026-05-24T12:16:25.635Z","last_scraped_at":"2026-05-03T15:19:16.961Z","last_commit":null},"community":{"stars":null,"forks":null,"weekly_downloads":null,"model_downloads":null,"model_likes":null}},"distribution":{"claim_url":"https://unfragile.ai/submit?claim=aman-amith-shastry-scientific-computation","compare_url":"https://unfragile.ai/compare?artifact=aman-amith-shastry-scientific-computation"}},"signature":"+LNLL8upWeO83y0uQtZbv5J01ovuM53cwD1IPxMDk2MSlZ3qtiRZULh2K8eSeaD+8GORyUbz6PfYCsfVJ4gkCg==","signedAt":"2026-06-21T00:42:30.848Z","signedBy":"unfragile.ai","version":1},"_links":{"self":"https://unfragile.ai/api/v1/passport/aman-amith-shastry-scientific-computation","artifact":"https://unfragile.ai/aman-amith-shastry-scientific-computation","verify":"https://unfragile.ai/api/v1/verify?slug=aman-amith-shastry-scientific-computation","publicKey":"https://unfragile.ai/api/v1/trust-passport-public-key","spec":"https://unfragile.ai/trust","schema":"https://unfragile.ai/schema.json","docs":"https://unfragile.ai/docs"}}