Scientific Computation MCP

Tools · 26

• create_tensor Creates a new tensor based on a given name, shape, and values, and adds it to the tensor store. For the purposes of this server, tensors are vectors and matrices.
• view_tensor Display the contents of a tensor from the store.
• delete_tensor Deletes a tensor based on its name in the tensor store.
• add_matrices Adds two matrices with the provided names, if compatible.
• subtract_matrices Subtracts two matrices with the provided names, if compatible.
• multiply_matrices Multiplies two matrices with the provided names, if compatible.
• scale_matrix Scales a matrix of the provided name by a certain factor, in-place by default.
• matrix_inverse Computes the inverse of the matrix with the provided name.
• transpose Computes the transpose of the inverse of the matrix of the provided name.
• determinant Computes the determinant of the matrix of the provided name.
• rank Computes the rank (number of pivots) of the matrix of the provided name.
• compute_eigen Calculates the eigenvectors and eigenvalues of the matrix of the provided name.
• qr_decompose Computes the QR factorization of the matrix of the provided name. The columns of Q are an orthonormal basis for the image of the matrix, and R is upper triangular.
• svd_decompose Computes the Singular Value Decomposition of the matrix of the provided name.
• find_orthonormal_basis Finds an orthonormal basis for the matrix of the provided name. The vectors returned are all pair-wise orthogonal and are of unit length.
• change_basis Computes the matrix of the provided name in the new basis.
• vector_project Projects a vector in the tensor store to the specified vector in the same vector space.
• vector_dot_product Computes the dot product of two vectors in the tensor stores based on their provided names.
• vector_cross_product Computes the cross product of two vectors in the tensor stores based on their provided names.
• gradient Computes the gradient of a multivariable function based on the input function. Example call: gradient("x^2 + 2xyz + zy^3"). Do NOT include the function name (like f(x, y, z) = ...).
• curl Computes the curl of a vector field based on the input vector field. The input string must be formatted as a python list. Example call: curl("[3xy, 2z^4, 2y]").
• divergence Computes the divergence of a vector field based on the input vector field. The input string must be formatted as a python list. Example call: divergence("[3xy, 2z^4, 2y]").
• laplacian Computes the laplacian of a scalar function (as the divergence of the gradient) or a vector field (where a component-wise laplacian is computed). If a scalar function is the input, it must be input in the same format as in the gradient tool. If the input is a vector field, it must be input in the same manner as the curl/divergence tools.
• directional_deriv Computes the directional derivative of a function in a given direction u. By default, the tool normalizes u before computing the directional derivative, as specified by the unit parameter.
• plot_vector_field Plots a vector field (specified in the same format as in the curl/divergence functions). Currently, only 3d vector fields are supported. A 2d png perspective image of the vector field is returned. By default, the bounds of the graph are from -1 to 1 on each axis.
• plot_function Plots a function in 2d or 3d (based on the input variables), specified in the same format as in the gradient tool. Only the variables x and y can be used.