Find or inspect public Jacobian MCP operations.

Forms:

• query: describe one local mathematical need in ordinary language. namespace, limit, cursor, and search_mode are optional search controls. Preserve established mathematical names from the task, the supplied objects and constraints, the requested computation or decision, the full scalar, batch, or exhaustive scope, and whether the requested result is a value, witness, certificate, obstruction, profile, or complete enumeration. Do not replace a supplied named property only with its expanded definition, translate the need into catalog tags, or submit the surrounding proof goal.

• operation_id: pass one exact operation ID to receive its authoritative input and output schemas, operator-authored examples, and current optional backend availability. Matches expose static runtime_requirements; inspection checks these runtimes in the server environment.

For matching, use namespace only when the primary operation-ID namespace is already known with high confidence. Matching returns 10 candidates by default; request up to 20 when a wider first page is useful. Follow next_cursor with the same query, namespace, and search_mode to continue; the limit may change. Ordered matches are deterministic retrieval candidates, not applicability claims; inspect a promising operation before math.run. Read operation://catalog only when the complete bulk catalog is genuinely needed.

An unknown operation ID returns kind: "error" with error.code: "UNKNOWN_OPERATION"; inspect kind even when MCP isError is false. Search with query to find an installed operation, then inspect its exact ID. Zero matches is a successful search.

Examples:

• {"query":"exact determinant of a rational matrix","namespace":"matrix","limit":3}

• {"operation_id":"polynomial.compute.gcd"}

Run one installed math tool by ID with its typed payload. A successful call returns the operation-owned canonical mathematical value in output; a later inspected operation may accept that complete value unchanged. Read its fields to determine what the calculation established. MCP reports malformed payloads, unknown IDs, and host failures as tool errors, not as mathematical results. If the payload shape is unknown, inspect the exact operation with math.find. When it publishes an examples item, copy and adapt that item's input object as the payload; otherwise, form the payload from the input schema and its field descriptions. Do not call math.run with an empty payload merely to discover required fields; inspection is authoritative.

Timeout, incomplete search, and missing witnesses appear only in the concrete domain result that owns them; none is a mathematical conclusion by itself.

Examples:

• {"operation_id":"integer.compute.extended_gcd","payload":{"left":"84","right":"30"}}