# Numora Nonlinear Equation Solver

> Numora Nonlinear Equation Solver is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.05/call, status unknown (last checked 2026-09-14).

Finds the numerical root of a nonlinear single-variable equation given a function expression and an initial guess

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/solve/nonlinear
- Price: $0.05/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-nonlinear-equation-solver-7ff3dfe8
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_ripjrs3_rmfGTqPVZ0lZl

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-nonlinear-equation-solver-7ff3dfe8 -d '<json body>'
```

Example prompt: Can you solve the nonlinear equation x^3 - 2x - 5 = 0 for me numerically, starting with an initial guess of x = 2?

## When to prefer this

Use this endpoint when you need to numerically solve a single-variable nonlinear equation (polynomial, transcendental, or mixed) and can provide a reasonable initial guess. Prefer this over symbolic solvers when an approximate numerical answer is sufficient and speed matters. Not suitable for systems of equations or when an exact closed-form solution is required.

## Known failure modes

- Function expression is syntactically invalid — likely returns error or success:false
- Initial guess is too far from any real root, causing divergence or non-convergence
- Division by zero or singularity encountered during iteration
- Function has no real roots — solver may fail to converge
- Malformed request body missing required fn or guess fields — 400 error
- Payment not fulfilled via x402 — 402 Payment Required response

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with a boolean success flag, a result object containing the computed root value, and a human-readable computation string describing what was solved.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn",
  "guess"
 ],
 "properties": {
  "fn": {
   "type": "string",
   "description": "Function expression (e.g., 'x^2 - 4')"
  },
  "guess": {
   "type": "number"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-nonlinear-equation-solver-7ff3dfe8/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)