Physics MCP Server

import { z } from 'zod'; // Base operation types export const GraphingCalculatorOperation = z.enum([ // Basic arithmetic and functions 'evaluate', 'simplify', 'expand', 'factor', // Equation solving 'solve_equation', 'solve_system', 'find_roots', // Calculus operations 'derivative', 'integral', 'limit', 'series', // Graphing operations 'plot_function', 'plot_parametric', 'plot_polar', 'plot_implicit', 'plot_inequality', 'plot_data', // Matrix operations 'matrix_add', 'matrix_multiply', 'matrix_determinant', 'matrix_inverse', 'matrix_eigenvalues', 'matrix_rref', // Statistics operations 'stats_descriptive', 'stats_regression', 'stats_distribution', 'stats_hypothesis_test', // Data operations 'create_list', 'list_operations', 'table_values', // Programming operations 'store_variable', 'recall_variable', 'define_function', 'execute_program', // Unit conversions 'convert_units', // Financial calculations 'financial_calc' ]); // Common parameter schemas export const ExpressionSchema = z.object({ expression: z.string().describe('Mathematical expression to process'), variables: z.record(z.union([z.number(), z.string()])).optional().describe('Variable substitutions') }); export const GraphingSchema = z.object({ function: z.string().describe('Function to graph (e.g., "x^2 + 2*x + 1")'), x_range: z.tuple([z.number(), z.number()]).optional().describe('X-axis range [min, max]'), y_range: z.tuple([z.number(), z.number()]).optional().describe('Y-axis range [min, max]'), resolution: z.number().optional().default(1000).describe('Number of points to plot'), style: z.enum(['line', 'points', 'both']).optional().default('line').describe('Plot style'), color: z.string().optional().describe('Plot color'), title: z.string().optional().describe('Graph title'), grid: z.boolean().optional().default(true).describe('Show grid'), axes_labels: z.object({ x: z.string().optional(), y: z.string().optional() }).optional().describe('Axis labels') }); export const MatrixSchema = z.object({ matrix: z.array(z.array(z.number())).describe('Matrix as 2D array'), matrix_b: z.array(z.array(z.number())).optional().describe('Second matrix for operations') }); export const StatisticsSchema = z.object({ data: z.array(z.number()).describe('Data array for statistical analysis'), data_y: z.array(z.number()).optional().describe('Y-data for bivariate analysis'), confidence_level: z.number().optional().default(0.95).describe('Confidence level for intervals'), distribution: z.enum(['normal', 'binomial', 'poisson', 't', 'chi_square', 'f']).optional().describe('Probability distribution'), parameters: z.record(z.number()).optional().describe('Distribution parameters') }); export const ListSchema = z.object({ list_name: z.string().describe('Name of the list'), data: z.array(z.number()).describe('List data'), operation: z.enum(['sum', 'mean', 'median', 'std', 'var', 'min', 'max', 'sort', 'reverse']).optional().describe('Operation to perform on list') }); export const VariableSchema = z.object({ name: z.string().describe('Variable name'), value: z.union([z.number(), z.string(), z.array(z.number())]).describe('Variable value'), type: z.enum(['number', 'expression', 'list', 'matrix', 'function']).optional().describe('Variable type') }); export const FinancialSchema = z.object({ calculation_type: z.enum(['present_value', 'future_value', 'payment', 'interest_rate', 'periods']).describe('Type of financial calculation'), present_value: z.number().optional().describe('Present value'), future_value: z.number().optional().describe('Future value'), payment: z.number().optional().describe('Payment amount'), interest_rate: z.number().optional().describe('Interest rate (as decimal)'), periods: z.number().optional().describe('Number of periods'), compounding: z.enum(['annual', 'semi_annual', 'quarterly', 'monthly', 'daily']).optional().default('annual').describe('Compounding frequency') }); // Main graphing calculator schema export const GraphingCalculatorSchema = z.object({ operation: GraphingCalculatorOperation.describe('Calculator operation to perform'), // Expression-based operations expression: z.string().optional().describe('Mathematical expression'), variable: z.string().optional().describe('Variable for calculus operations'), variables: z.record(z.union([z.number(), z.string()])).optional().describe('Variable substitutions'), // Equation solving equation: z.string().optional().describe('Equation to solve (e.g., "x^2 - 4 = 0")'), equations: z.array(z.string()).optional().describe('System of equations'), solve_for: z.array(z.string()).optional().describe('Variables to solve for'), // Calculus parameters point: z.number().optional().describe('Point for limit evaluation'), order: z.number().optional().default(1).describe('Order of derivative'), bounds: z.tuple([z.number(), z.number()]).optional().describe('Integration bounds'), // Graphing parameters function: z.string().optional().describe('Function to graph'), x_function: z.string().optional().describe('X-component for parametric plots'), y_function: z.string().optional().describe('Y-component for parametric plots'), r_function: z.string().optional().describe('R-component for polar plots'), x_range: z.tuple([z.number(), z.number()]).optional().describe('X-axis range'), y_range: z.tuple([z.number(), z.number()]).optional().describe('Y-axis range'), t_range: z.tuple([z.number(), z.number()]).optional().describe('Parameter range'), theta_range: z.tuple([z.number(), z.number()]).optional().describe('Theta range for polar'), resolution: z.number().optional().default(1000).describe('Plot resolution'), // Matrix operations matrix: z.array(z.array(z.number())).optional().describe('Matrix A'), matrix_b: z.array(z.array(z.number())).optional().describe('Matrix B'), // Statistics data: z.array(z.number()).optional().describe('Data for statistical analysis'), data_x: z.array(z.number()).optional().describe('X-data for regression'), data_y: z.array(z.number()).optional().describe('Y-data for regression'), regression_type: z.enum(['linear', 'quadratic', 'cubic', 'exponential', 'logarithmic', 'power', 'sinusoidal']).optional().describe('Regression type'), distribution: z.enum(['normal', 'binomial', 'poisson', 't', 'chi_square', 'f']).optional().describe('Probability distribution'), // List operations list_name: z.string().optional().describe('List identifier'), list_data: z.array(z.number()).optional().describe('List data'), list_operation: z.enum(['sum', 'mean', 'median', 'std', 'var', 'min', 'max', 'sort', 'reverse']).optional().describe('List operation'), // Variable storage var_name: z.string().optional().describe('Variable name'), var_value: z.union([z.number(), z.string(), z.array(z.number())]).optional().describe('Variable value'), // Function definition func_name: z.string().optional().describe('Function name'), func_expression: z.string().optional().describe('Function expression'), func_variables: z.array(z.string()).optional().describe('Function parameters'), // Unit conversion from_unit: z.string().optional().describe('Source unit'), to_unit: z.string().optional().describe('Target unit'), value: z.number().optional().describe('Value to convert'), // Financial calculations financial_type: z.enum(['present_value', 'future_value', 'payment', 'interest_rate', 'periods']).optional().describe('Financial calculation type'), present_value: z.number().optional().describe('Present value'), future_value: z.number().optional().describe('Future value'), payment: z.number().optional().describe('Payment amount'), interest_rate: z.number().optional().describe('Interest rate (as decimal)'), periods: z.number().optional().describe('Number of periods'), compounding: z.enum(['annual', 'semi_annual', 'quarterly', 'monthly', 'daily']).optional().describe('Compounding frequency'), // Output options format: z.enum(['exact', 'decimal', 'fraction']).optional().default('decimal').describe('Output format'), precision: z.number().optional().default(6).describe('Decimal precision'), plot_style: z.enum(['line', 'points', 'both']).optional().default('line').describe('Plot style'), plot_color: z.string().optional().describe('Plot color'), show_grid: z.boolean().optional().default(true).describe('Show grid on plots'), plot_title: z.string().optional().describe('Plot title'), export_data: z.boolean().optional().default(false).describe('Export plot data as CSV') });