Linear System

{
  "asOf": "2026-10-11T08:51:18.857Z",
  "degraded": false,
  "determinant": -1,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "equations": 3,
  "maxResidual": 0,
  "notChecked": [
    "ill-conditioning: a nearly singular system can give very inaccurate results (the determinant is reported so you can judge)",
    "exact rational answers (results are decimals)"
  ],
  "rankOfMatrix": 3,
  "reasons": [
    "Gauss-Jordan elimination with partial pivoting.",
    "Check: largest residual |Ax - b| = 0.00e+0."
  ],
  "solution": {
    "x1": 2,
    "x2": 3,
    "x3": -1
  },
  "solutionVector": [
    2,
    3
  ],
  "source": "computed locally",
  "summary": "x1 = 2, x2 = 3, x3 = -1.",
  "unknowns": 3,
  "verdict": "UNIQUE_SOLUTION"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://math-geometry.x402tookit.com/linear-system?constants=8%2C-11%2C-3&matrix=2%2C1%2C-1%3B-3%2C-1%2C2%3B-2%2C1%2C2'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://math-geometry.x402tookit.com/linear-system?constants=8%2C-11%2C-3&matrix=2%2C1%2C-1%3B-3%2C-1%2C2%3B-2%2C1%2C2' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fmath-geometry.x402tookit.com%2Flinear-system
const res = await pay("https://math-geometry.x402tookit.com/linear-system?constants=8%2C-11%2C-3&matrix=2%2C1%2C-1%3B-3%2C-1%2C2%3B-2%2C1%2C2");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://math-geometry.x402tookit.com/linear-system?constants=8%2C-11%2C-3&matrix=2%2C1%2C-1%3B-3%2C-1%2C2%3B-2%2C1%2C2")
    print(res.status_code, res.text)