Science & Education

Signal Flow Graph Mason Gain Rule Feedback Loop Solver

Solve control-system signal flow graphs with Mason's gain formula: forward paths, loops, non-touching combinations, Δ/Δk determinants and the exact transfer function.

html· HTML resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/signal-flow-graph-mason-gain-rule-feedback-loop-solver' \
  -H 'Content-Type: application/json' \
  -d '{"edges":"R -> n1 = 1\nn1 -> n2 = G1\nn2 -> n3 = G2\nn3 -> out = 1\nn1 -> n4 = G3\nn4 -> n3 = G4\nn2 -> n2 = H1\nn4 -> n4 = H2","inputNode":"R","outputNode":"out"}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/signal-flow-graph-mason-gain-rule-feedback-loop-solver

Parameters

Name	Type	Required	Description
edges	textarea	Yes	—
inputNode	text	Yes	—
outputNode	text	Yes	—

Response format

HTML result

JSON

{
  "result": "<div>Processed HTML content</div>",
  "error": "Error message (optional)",
  "message": "Notification message (optional)",
  "metadata": {
    "key": "value"
  }
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-signal-flow-graph-mason-gain-rule-feedback-loop-solver": {
      "name": "signal-flow-graph-mason-gain-rule-feedback-loop-solver",
      "description": "Solve control-system signal flow graphs with Mason's gain formula: forward paths, loops, non-touching combinations, Δ/Δk determinants and the exact transfer function.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=signal-flow-graph-mason-gain-rule-feedback-loop-solver",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "signal-flow-graph-mason-gain-rule-feedback-loop-solver",
    "arguments": {
  "edges": "R -> n1 = 1\nn1 -> n2 = G1\nn2 -> n3 = G2\nn3 -> out = 1\nn1 -> n4 = G3\nn4 -> n3 = G4\nn2 -> n2 = H1\nn4 -> n4 = H2",
  "inputNode": "R",
  "outputNode": "out"
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Browse tools Open tool

curl -X POST 'https://api.elysiatools.com/en/api/tools/signal-flow-graph-mason-gain-rule-feedback-loop-solver' \ -H 'Content-Type: application/json' \ -d '{"edges":"R -> n1 = 1\nn1 -> n2 = G1\nn2 -> n3 = G2\nn3 -> out = 1\nn1 -> n4 = G3\nn4 -> n3 = G4\nn2 -> n2 = H1\nn4 -> n4 = H2","inputNode":"R","outputNode":"out"}'

Name

Type

Required

Description

edges

textarea

Yes

—

inputNode

text

Yes

—

outputNode

text

Yes

—

{ "mcpServers": { "elysiatools-signal-flow-graph-mason-gain-rule-feedback-loop-solver": { "name": "signal-flow-graph-mason-gain-rule-feedback-loop-solver", "description": "Solve control-system signal flow graphs with Mason's gain formula: forward paths, loops, non-touching combinations, Δ/Δk determinants and the exact transfer function.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=signal-flow-graph-mason-gain-rule-feedback-loop-solver", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "signal-flow-graph-mason-gain-rule-feedback-loop-solver", "arguments": { "edges": "R -> n1 = 1\nn1 -> n2 = G1\nn2 -> n3 = G2\nn3 -> out = 1\nn1 -> n4 = G3\nn4 -> n3 = G4\nn2 -> n2 = H1\nn4 -> n4 = H2", "inputNode": "R", "outputNode": "out" } } }