cas.js•2.96 kB
/**
* Validation schemas for CAS (Computer Algebra System) tools
*/
import { z } from 'zod';
import { ExpressionSchema, SymbolSchema, VariablesSchema } from './common.js';
/**
* CAS action types
*/
export const CASActionSchema = z.enum([
'evaluate',
'diff',
'integrate',
'solve_equation',
'solve_ode',
'propagate_uncertainty'
]).describe('CAS operation to perform');
/**
* Base CAS input schema
*/
export const CASBaseSchema = z.object({
action: CASActionSchema
});
/**
* Evaluate expression schema
*/
export const CASEvaluateSchema = CASBaseSchema.extend({
action: z.literal('evaluate'),
expr: ExpressionSchema,
vars: VariablesSchema.optional().describe('Variables to substitute')
});
/**
* Differentiation schema
*/
export const CASDiffSchema = CASBaseSchema.extend({
action: z.literal('diff'),
expr: ExpressionSchema,
symbol: SymbolSchema.describe('Variable to differentiate with respect to'),
order: z.number().int().positive().default(1).describe('Order of differentiation')
});
/**
* Integration schema
*/
export const CASIntegrateSchema = CASBaseSchema.extend({
action: z.literal('integrate'),
expr: ExpressionSchema,
symbol: SymbolSchema.describe('Variable to integrate with respect to'),
bounds: z.tuple([z.number(), z.number()]).optional()
.describe('Integration bounds [lower, upper] for definite integral')
});
/**
* Equation solving schema
*/
export const CASSolveEquationSchema = CASBaseSchema.extend({
action: z.literal('solve_equation'),
equation: z.string().min(1, 'Equation cannot be empty')
.describe('Equation to solve (e.g., "x^2 - 4 = 0")'),
symbol: SymbolSchema.describe('Variable to solve for')
});
/**
* ODE solving schema
*/
export const CASSolveODESchema = CASBaseSchema.extend({
action: z.literal('solve_ode'),
ode: z.string().min(1, 'ODE cannot be empty')
.describe('Differential equation (e.g., "y\'\' + y = 0")'),
symbol: SymbolSchema.describe('Independent variable'),
func: SymbolSchema.describe('Dependent function name (e.g., "y")'),
ics: z.record(z.string(), z.number()).optional()
.describe('Initial conditions for ODE')
});
/**
* Uncertainty propagation schema
*/
export const CASPropagateUncertaintySchema = CASBaseSchema.extend({
action: z.literal('propagate_uncertainty'),
expr: ExpressionSchema,
vars: z.record(z.string(), z.object({
value: z.number().describe('Variable value'),
unit: z.string().optional().describe('Physical unit'),
sigma: z.number().positive().describe('Standard uncertainty')
})).describe('Variables with uncertainties')
});
/**
* Complete CAS input schema (union of all actions)
*/
export const CASInputSchema = z.discriminatedUnion('action', [
CASEvaluateSchema,
CASDiffSchema,
CASIntegrateSchema,
CASSolveEquationSchema,
CASSolveODESchema,
CASPropagateUncertaintySchema
]);