find_root

THE RISK

High Risk

Why find_root needs a policy

This tool executes a numerical root-finding algorithm within the SageMath environment. It involves running mathematical computations rather than simply reading or writing data. Since the server provides 'full access to SageMath' with 'persistent state across tool calls,' arbitrary expression evaluation could have side effects depending on the input expression passed to the engine.

From the tool's definition Find a numeric root of an expression in a given interval — performs numerical computation via SageMath engine

Risk signalsAdmin/system-level operation

Documented attack patterns abuse exactly the kind of access find_root gives an agent:

POLICY

How to control find_root

PolicyLayer is an MCP gateway — it sits between your AI agents and SageMath MCP Server, and nothing reaches the server without passing your rules. This is the rule we recommend for find_root:

policy.json

{
  "version": "1",
  "default": "deny",
  "tools": {
    "find_root": {
      "limits": [
        {
          "counter": "find_root_rate",
          "window": "minute",
          "max": 10,
          "scope": "grant"
        }
      ]
    }
  }
}

find_root stays usable, but rate-capped — a runaway agent can't fire it dozens of times a minute. Everything else on the server is denied unless you say otherwise.

Create a free account and register SageMath MCP Server — nothing to install.
Add this policy — paste it, or build it visually.
Point your MCP client (Claude, Cursor, anything) at your gateway URL.

RATE-LIMIT THIS TOOL →

Free to start. No card required.

EXPLORE

Related tools and policies

More SageMath MCP Server tools

Destructive reset_sage_session Reset the SageMath session state for the current MCP session Execute cancel_sage_session Cancel any running Sage computation and restart the worker Execute evaluate_sage_streaming Execute SageMath code and stream intermediate print() output Execute boolean_algebra_operation Boolean algebra: operations on boolean polynomials Execute calculate_expression Evaluate a SageMath expression and return numeric/string forms Execute coding_theory_operation Coding theory: construct error-correcting codes Execute combinatorics_operation Combinatorics: binomial, permutations, combinations, partitions, and more Execute differentiate_expression Differentiate an expression with respect to a variable

All 32 SageMath MCP Server tools →

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Go deeper

High-risk tools in SageMath MCP Server → Every high-risk tool this server exposes, in one view.
All high-risk MCP tools → Every high-risk tool across the catalogue, and the policy pattern that contains them.
The MCP Attack Database → Documented attack patterns against MCP deployments — and the policies that stop them.
Agent sandbox → Bounding what an agent can execute and where the boundary should sit.
Least privilege for MCP → Granting agents the minimum tool surface the task needs.
Rate Limiting MCP Tool Calls: A Practical Guide →
MCP Security: Why Prompt Guardrails Aren't Enough →

FAQ

Questions about find_root

What does the find_root tool do? +

Find a numeric root of an expression in a given interval. It is categorised as a Execute tool in the SageMath MCP Server MCP Server, which means it can trigger actions or run processes. Use rate limits and argument validation.

How do I enforce a policy on find_root? +

Register the SageMath MCP Server MCP server in PolicyLayer and add a rule for find_root: allow, deny, rate-limit, or require approval. Point your MCP client at the PolicyLayer proxy URL and the rule is enforced on every call, before it reaches SageMath MCP Server. Nothing to install.

What risk level is find_root? +

find_root is a Execute tool with high risk. Execute tools should be rate-limited and have argument validation enabled.

Can I rate-limit find_root? +

Yes. Add a rate_limit block to the find_root rule in your PolicyLayer policy. For example, setting max: 10 and window: 60 limits the tool to 10 calls per minute. Rate limits are tracked per agent session and reset automatically.

How do I block find_root completely? +

Set action: deny in the PolicyLayer policy for find_root. The AI agent will receive a policy violation error and cannot call the tool. You can also include a reason field to explain why the tool is blocked.

What MCP server provides find_root? +

find_root is provided by the SageMath MCP Server MCP server (xbp-europe/sagemath-mcp). PolicyLayer sits as a proxy in front of this server to enforce policies before tool calls reach the server.

Enforce policy on every SageMath MCP Server tool call.

Start from SageMath MCP Server, add the rest of your stack, and see everything your agents can call. Then put policy on all of it.

CHECK YOUR STACK →