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MCP compliance, safety and math fixes; English tool docs; symbolic dsolve

Browse Source 
Fork of https://github.com/thinkitpossible/CalcMCP with:
- tools/list now publishes inputSchema (upstream used non-standard 'params'
  key, leaving clients with no parameter information)
- tool descriptions and parameter docs rewritten in English with examples
- JSON-RPC notifications are no longer answered; tool failures set isError
- raw eval() of tool arguments removed (json.loads/ast.literal_eval for
  matrices, sympy.lambdify for the numeric ODE right-hand side)
- complex eigenvalues serialize as 'a+bi' strings instead of crashing
- solve accepts '=' equations; ttest accepts {"popmean": ...} params
- new symbolic_tool operation 'dsolve' for symbolic ODE solutions

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
This commit is contained in:
Michal
2026-10-03 01:27:21 +01:00
parent a17b0c8017
commit e4b5ea649f
3 changed files with 159 additions and 80 deletions
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19
README.md
View File

@@ -1,9 +1,26 @@
# Scientific Calculator MCP Server
> A production-ready Model Context Protocol (MCP) server providing advanced mathematical calculation capabilities for AI models. Supports symbolic math (SymPy), numerical computing (NumPy/SciPy), data analysis (pandas), and image processing.
> A Model Context Protocol (MCP) server providing advanced mathematical calculation capabilities for AI models. Supports symbolic math (SymPy), numerical computing (NumPy/SciPy), data analysis (pandas), and image processing.
[![License: MIT](https://img.shields.io/badge/License-MIT-yellow.svg)](https://opensource.org/licenses/MIT)
> **Fork notice** — this is a patched fork of
> [thinkitpossible/CalcMCP](https://github.com/thinkitpossible/CalcMCP).
> Changes relative to upstream:
>
> - **MCP compliance**: tools are published with a proper `inputSchema` (upstream used a
> non-standard `params` key, so clients saw no parameters at all); JSON-RPC notifications
> (`notifications/initialized`) are no longer answered with an error; tool failures set
> `isError: true` on the result.
> - **Tool descriptions rewritten in English**, with per-parameter docs and inline examples.
> - **Security**: removed all raw `eval()` of tool arguments (matrix inputs now parse via
> `json.loads`/`ast.literal_eval`, the numeric-ODE right-hand side via `sympy.lambdify`).
> - **Bug fixes**: eigenvalue/eigenvector results with complex values no longer crash JSON
> serialization (rendered as `a+bi` strings); `solve` accepts equations written with `=`;
> one-sample t-test accepts `params` as `{"popmean": ...}` or a bare number.
> - **New**: `symbolic_tool` operation `dsolve` — symbolic ODE solving
> (e.g. `Derivative(y(x), x, 2) + y(x) = 0` → `y(x) = C1*sin(x) + C2*cos(x)`).
## Quick Start
### 1. Install Dependencies

73
calculator.py
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@@ -13,8 +13,18 @@ except Exception:
from scipy.integrate import odeint
from scipy.fftpack import fft, rfft
from typing import Optional
import ast
import json
def _json_default(obj):
"""JSON fallback for numpy/complex values (eigenvalues are often complex)."""
if isinstance(obj, complex):
return obj.real if obj.imag == 0 else f"{obj.real}{obj.imag:+}i"
if hasattr(obj, "item"):
return _json_default(obj.item())
return str(obj)
# ============================================================================
# SYMBOLIC MATHEMATICS (SymPy)
# ============================================================================
@@ -91,9 +101,14 @@ def symbolic_limit(expression: str, variable: str, point: str) -> str:
def solve_equation(equation: str, variable: str) -> str:
"""解方程"""
"""Solve an equation. Accepts 'expr' (treated as expr = 0), 'lhs = rhs' or 'lhs == rhs'."""
try:
expr = sp.sympify(equation)
eq_str = equation.replace("==", "=")
if "=" in eq_str:
lhs, rhs = eq_str.split("=", 1)
expr = sp.Eq(sp.sympify(lhs), sp.sympify(rhs))
else:
expr = sp.sympify(eq_str)
var = sp.Symbol(variable)
result = sp.solve(expr, var)
return str(result)
@@ -101,6 +116,22 @@ def solve_equation(equation: str, variable: str) -> str:
return f"Error: {str(e)}"
def symbolic_dsolve(equation: str, variable: str = "x") -> str:
"""Solve an ODE symbolically. Unknown function must be written as y(x),
e.g. 'Derivative(y(x), x, 2) + y(x) = 0' -> y(x) = C1*sin(x) + C2*cos(x)."""
try:
eq_str = equation.replace("==", "=")
if "=" in eq_str:
lhs, rhs = eq_str.split("=", 1)
eq = sp.Eq(sp.sympify(lhs), sp.sympify(rhs))
else:
eq = sp.sympify(eq_str)
result = sp.dsolve(eq)
return str(result)
except Exception as e:
return f"Error: {str(e)}"
def taylor_series(expression: str, variable: str, point: str, n: int) -> str:
"""泰勒级数展开"""
try:
@@ -185,8 +216,8 @@ def numpy_linear_algebra(matrix_a, operation: str, matrix_b=None) -> str:
if isinstance(matrix_a, str):
try:
mat1 = np.array(json.loads(matrix_a), dtype=float)
except:
mat1 = np.array(eval(matrix_a), dtype=float)
except Exception:
mat1 = np.array(ast.literal_eval(matrix_a), dtype=float)
else:
mat1 = np.array(matrix_a, dtype=float)
@@ -195,27 +226,19 @@ def numpy_linear_algebra(matrix_a, operation: str, matrix_b=None) -> str:
if isinstance(matrix_b, str):
try:
mat2 = np.array(json.loads(matrix_b), dtype=float)
except:
mat2 = np.array(eval(matrix_b), dtype=float)
except Exception:
mat2 = np.array(ast.literal_eval(matrix_b), dtype=float)
else:
mat2 = np.array(matrix_b, dtype=float)
# 执行操作
if operation == "eigenvalues":
if operation in ("eigenvalues", "eigenvectors"):
eigenvalues, eigenvectors = np.linalg.eig(mat1)
result = {
"eigenvalues": eigenvalues.tolist(),
"eigenvectors": eigenvectors.tolist()
}
return json.dumps(result, ensure_ascii=False)
elif operation == "eigenvectors":
eigenvalues, eigenvectors = np.linalg.eig(mat1)
result = {
"eigenvalues": eigenvalues.tolist(),
"eigenvectors": eigenvectors.tolist()
}
return json.dumps(result, ensure_ascii=False)
return json.dumps(result, ensure_ascii=False, default=_json_default)
elif operation == "determinant":
result = float(np.linalg.det(mat1))
@@ -434,19 +457,15 @@ def scipy_solve_ode(expression: str, initial_conditions: str, t_values: str, var
else:
reverse_order = False
# 评估 ODE 函数表达式
try:
# 尝试作为 lambda 函数字符串
ode_func = eval(expression)
except:
# 如果失败，尝试作为符号表达式
var_list = [sp.Symbol(v.strip()) for v in variables.split(",")]
# Parse dy/dt = f(t, y) as a SymPy expression (no eval of raw Python)
var_list = [sp.Symbol(v.strip()) for v in (variables or "y").split(",")]
t_sym = sp.Symbol('t')
expr = sp.sympify(expression)
if len(var_list) == 1:
ode_func = sp.lambdify([t_sym, var_list[0]], expr, modules=['numpy'])
ode_func_wrapped = lambda y, t: ode_func(t, y)
f = sp.lambdify([t_sym, var_list[0]], expr, modules=['numpy'])
# odeint calls func(y, t)
ode_func = lambda y, t: f(t, y)
else:
return "Error: System ODEs not yet fully supported"
@@ -489,6 +508,8 @@ def scipy_statistics(operation: str, data: str, params: Optional[str] = None) ->
return str(float(np.std(data_arr)))
elif operation == "ttest":
popmean = json.loads(params) if params else 0
if isinstance(popmean, dict):
popmean = popmean.get("popmean", 0)
result = stats.ttest_1samp(data_arr, popmean)
return f"statistic={result.statistic}, pvalue={result.pvalue}"
elif operation == "pearsonr" and params:
@@ -560,6 +581,8 @@ def symbolic_tool(
return symbolic_limit(expression, variable, point or point_value)
if op in ("solve", "solve_equation"):
return solve_equation(equation or expression, variable)
if op in ("dsolve", "ode", "solve_ode", "differential_equation"):
return symbolic_dsolve(equation or expression, variable or "x")
if op in ("taylor", "taylor_series"):
return taylor_series(expression, variable, point or "0", order)
if op in ("matrix", "symbolic_matrix_operations"):

125
mcp_server.py
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@@ -58,55 +58,85 @@ class MCPCalculatorServer:
# Consolidated tool definitions (3 tools)
tool_definitions = {
"symbolic_tool": {
"description": "统一符号计算入口：simplify/expand/factor/derivative/integral/limit/solve/taylor/matrix",
"description": (
"Exact symbolic math (SymPy). Set operation to one of: simplify, expand, factor, "
"derivative, integral, limit, solve, dsolve, taylor, matrix. "
"Write expressions in Python/SymPy syntax, e.g. 'x**2 * exp(-x)'; use 'oo' for infinity. "
"integral: optional lower_limit/upper_limit for definite integrals. "
"solve: pass the equation, '=' is allowed (e.g. 'x**2 = 4' or 'x**3 - 6*x**2 + 11*x - 6'). "
"dsolve: solves an ODE symbolically — write the unknown function as y(x), "
"e.g. equation='Derivative(y(x), x, 2) + y(x) = 0'. "
"taylor: expression + variable + point + order. "
"matrix: matrix_data (JSON) with variable=determinant|inverse|rank|trace. "
"Results are exact (e.g. '2', 'E', 'C1*sin(x) + C2*cos(x)')."
),
"params": [
{"name": "operation", "type": "string", "description": "操作类型，如 derivative, integral, solve 等"},
{"name": "expression", "type": "string", "description": "表达式", "optional": True},
{"name": "variable", "type": "string", "description": "变量", "optional": True},
{"name": "order", "type": "integer", "description": "阶数（导数/泰勒）", "optional": True},
{"name": "lower_limit", "type": "string", "description": "积分下限", "optional": True},
{"name": "upper_limit", "type": "string", "description": "积分上限", "optional": True},
{"name": "equation", "type": "string", "description": "方程", "optional": True},
{"name": "point", "type": "string", "description": "极限或泰勒展开点", "optional": True},
{"name": "matrix_data", "type": "string", "description": "符号矩阵（JSON）", "optional": True}
{"name": "operation", "type": "string", "description": "One of: simplify, expand, factor, derivative, integral, limit, solve, dsolve, taylor, matrix"},
{"name": "expression", "type": "string", "description": "Expression in SymPy syntax, e.g. 'sin(x)/x'", "optional": True},
{"name": "variable", "type": "string", "description": "Variable name, e.g. 'x' (for matrix: the operation name)", "optional": True},
{"name": "order", "type": "integer", "description": "Order for derivative/taylor (default 1 / 5)", "optional": True},
{"name": "lower_limit", "type": "string", "description": "Lower bound for definite integral, e.g. '0'", "optional": True},
{"name": "upper_limit", "type": "string", "description": "Upper bound for definite integral, e.g. 'oo'", "optional": True},
{"name": "equation", "type": "string", "description": "Equation for solve/dsolve; '=' allowed", "optional": True},
{"name": "point", "type": "string", "description": "Point for limit/taylor, e.g. '0' or 'oo'", "optional": True},
{"name": "matrix_data", "type": "string", "description": "Matrix as JSON, e.g. '[[1,2],[3,4]]'", "optional": True}
]
},
"numpy_tool": {
"description": "统一 NumPy 入口：数组归约、线性代数、三角、多项式",
"description": (
"Numeric arrays and linear algebra (NumPy). Set operation to one of: "
"sum, mean, std, max, min (array_data, optional axis); "
"eigenvalues, eigenvectors, determinant, inverse, solve, norm, rank, trace, "
"svd, qr, cholesky, matmul, dot, hadamard (matrix_a, and matrix_b where two matrices are needed); "
"sin, cos, tan, arcsin, arccos, arctan, sinh, cosh, tanh (values, optional use_degrees); "
"poly_eval, poly_derivative, poly_integral (coefficients highest-degree first, optional x_values). "
"All array/matrix inputs are JSON strings, e.g. matrix_a='[[2,1],[1,2]]'. Results are numeric."
),
"params": [
{"name": "operation", "type": "string", "description": "操作类型，如 eigenvalues, sum, poly_eval 等"},
{"name": "array_data", "type": "string", "description": "数组数据（JSON）", "optional": True},
{"name": "axis", "type": "string", "description": "轴参数", "optional": True},
{"name": "matrix_a", "type": "string", "description": "矩阵A（JSON）", "optional": True},
{"name": "matrix_b", "type": "string", "description": "矩阵B（JSON）", "optional": True},
{"name": "values", "type": "string", "description": "三角函数输入（JSON）", "optional": True},
{"name": "use_degrees", "type": "boolean", "description": "角度制", "optional": True},
{"name": "coefficients", "type": "string", "description": "多项式系数（JSON）", "optional": True},
{"name": "x_values", "type": "string", "description": "多项式自变量数组（JSON）", "optional": True}
{"name": "operation", "type": "string", "description": "Operation name, e.g. 'eigenvalues', 'matmul', 'mean', 'poly_eval'"},
{"name": "array_data", "type": "string", "description": "Array as JSON, e.g. '[1,2,3]' or '[[1,2],[3,4]]'", "optional": True},
{"name": "axis", "type": "string", "description": "Axis for reductions: '0' or '1'", "optional": True},
{"name": "matrix_a", "type": "string", "description": "First matrix as JSON", "optional": True},
{"name": "matrix_b", "type": "string", "description": "Second matrix as JSON (solve/matmul/dot/hadamard)", "optional": True},
{"name": "values", "type": "string", "description": "Input values for trig functions as JSON, e.g. '[0, 90, 180]'", "optional": True},
{"name": "use_degrees", "type": "boolean", "description": "Treat trig inputs as degrees (default radians)", "optional": True},
{"name": "coefficients", "type": "string", "description": "Polynomial coefficients as JSON, highest degree first", "optional": True},
{"name": "x_values", "type": "string", "description": "x values for poly_eval as JSON", "optional": True}
]
},
"scipy_tool": {
"description": "统一 SciPy 入口：积分、优化、插值、特殊函数、ODE、统计、FFT、特征分解",
"description": (
"Numerical methods (SciPy). Set operation to one of: "
"integrate (numeric definite integral: expression, variable, lower, upper); "
"optimize_minimize, optimize_root (expression, initial_value, optional method); "
"interpolate_linear, interpolate_cubic, interpolate_spline (x_data, y_data, x_eval); "
"special (function name + parameters JSON, e.g. gamma, besselj); "
"solve_ode (NUMERIC simulation of dy/dt = f(t,y): expression e.g. '-2*y + t', "
"initial_conditions, t_values; for exact general solutions use symbolic_tool with operation='dsolve'); "
"statistics ops mean, std, describe, ttest, pearsonr (function + data, optional params); "
"fft, rfft (data_series or data); matrix_eigensystem (matrix_a). "
"All list inputs are JSON strings. Results are numeric."
),
"params": [
{"name": "operation", "type": "string", "description": "操作类型，如 integrate, optimize_minimize, fft 等"},
{"name": "expression", "type": "string", "description": "表达式/函数", "optional": True},
{"name": "variable", "type": "string", "description": "变量", "optional": True},
{"name": "lower", "type": "string", "description": "积分下限", "optional": True},
{"name": "upper", "type": "string", "description": "积分上限", "optional": True},
{"name": "initial_value", "type": "string", "description": "初值/起点", "optional": True},
{"name": "method", "type": "string", "description": "算法方法", "optional": True},
{"name": "x_data", "type": "string", "description": "插值 x 数据（JSON）", "optional": True},
{"name": "y_data", "type": "string", "description": "插值 y 数据（JSON）", "optional": True},
{"name": "x_eval", "type": "string", "description": "插值求值点（JSON）", "optional": True},
{"name": "function", "type": "string", "description": "特殊函数名/统计操作名", "optional": True},
{"name": "parameters", "type": "string", "description": "特殊函数参数（JSON）", "optional": True},
{"name": "initial_conditions", "type": "string", "description": "ODE 初值（JSON）", "optional": True},
{"name": "t_values", "type": "string", "description": "ODE 时间点（JSON）", "optional": True},
{"name": "variables", "type": "string", "description": "ODE 变量名", "optional": True},
{"name": "data", "type": "string", "description": "统计或 FFT 数据（JSON）", "optional": True},
{"name": "params", "type": "string", "description": "统计附加参数（JSON）", "optional": True},
{"name": "data_series", "type": "string", "description": "FFT 数据（JSON）", "optional": True},
{"name": "matrix_a", "type": "string", "description": "矩阵（JSON）用于特征分解", "optional": True}
{"name": "operation", "type": "string", "description": "Operation name, e.g. 'integrate', 'optimize_minimize', 'solve_ode', 'fft'"},
{"name": "expression", "type": "string", "description": "Expression/function of the variable, e.g. 'x**2 * exp(-x)'", "optional": True},
{"name": "variable", "type": "string", "description": "Variable name, e.g. 'x'", "optional": True},
{"name": "lower", "type": "string", "description": "Lower integration bound (number)", "optional": True},
{"name": "upper", "type": "string", "description": "Upper integration bound (number or 'oo')", "optional": True},
{"name": "initial_value", "type": "string", "description": "Starting point for optimization/root finding", "optional": True},
{"name": "method", "type": "string", "description": "Algorithm, e.g. 'BFGS', 'brentq'", "optional": True},
{"name": "x_data", "type": "string", "description": "Interpolation x data as JSON", "optional": True},
{"name": "y_data", "type": "string", "description": "Interpolation y data as JSON", "optional": True},
{"name": "x_eval", "type": "string", "description": "Points to evaluate the interpolant at, JSON", "optional": True},
{"name": "function", "type": "string", "description": "Special-function or statistics operation name", "optional": True},
{"name": "parameters", "type": "string", "description": "Special-function parameters as JSON", "optional": True},
{"name": "initial_conditions", "type": "string", "description": "ODE initial value(s) as JSON, e.g. '[1.0]'", "optional": True},
{"name": "t_values", "type": "string", "description": "ODE time points as JSON, e.g. '[0, 0.1, 0.2]'", "optional": True},
{"name": "variables", "type": "string", "description": "ODE dependent variable name, default 'y'", "optional": True},
{"name": "data", "type": "string", "description": "Statistics/FFT data as JSON", "optional": True},
{"name": "params", "type": "string", "description": "Extra statistics parameter as JSON: for ttest the population mean ('2.3' or '{\"popmean\": 2.3}'), for pearsonr the second data series", "optional": True},
{"name": "data_series", "type": "string", "description": "FFT data as JSON", "optional": True},
{"name": "matrix_a", "type": "string", "description": "Matrix as JSON for matrix_eigensystem", "optional": True}
]
},
}
@@ -116,7 +146,7 @@ class MCPCalculatorServer:
tools.append({
"name": tool_name,
"description": definition["description"],
"params": {
"inputSchema": {
"type": "object",
"properties": {
param["name"]: {
@@ -171,6 +201,10 @@ class MCPCalculatorServer:
params = request_dict.get("params", {})
req_id = request_dict.get("id")
# JSON-RPC notifications (no id) must not be answered
if req_id is None and isinstance(method, str) and method.startswith("notifications/"):
return None
# 处理特殊方法
if method == "initialize":
return {
@@ -201,6 +235,9 @@ class MCPCalculatorServer:
result = self.call_tool(tool_name, tool_params)
is_error = isinstance(result, str) and result.startswith(
("Error", "Parameter Error", "Execution Error")
)
return {
"jsonrpc": "2.0",
"result": {
@@ -209,7 +246,8 @@ class MCPCalculatorServer:
"type": "text",
"text": result
}
]
],
"isError": is_error
},
"id": req_id
}
@@ -253,7 +291,8 @@ class MCPCalculatorServer:
request = json.loads(line)
response = self.handle_rpc_request(request)
# 写入 JSON-RPC 响应到标准输出
# Notifications return None — nothing must be written back
if response is not None:
sys.stdout.write(json.dumps(response, ensure_ascii=False) + '\n')
sys.stdout.flush()