curl --request POST \
--url https://api.fincept.in/quantlib/numerical/roots/find-nd \
--header 'Content-Type: application/json' \
--header 'X-API-Key: <api-key>' \
--data '
{
"system": "nonlinear_2x2",
"x0": [
1.5,
1
],
"method": "newton",
"tol": 1e-10
}
'import requests
url = "https://api.fincept.in/quantlib/numerical/roots/find-nd"
payload = {
"system": "nonlinear_2x2",
"x0": [1.5, 1],
"method": "newton",
"tol": 1e-10
}
headers = {
"X-API-Key": "<api-key>",
"Content-Type": "application/json"
}
response = requests.post(url, json=payload, headers=headers)
print(response.text)const options = {
method: 'POST',
headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
body: JSON.stringify({system: 'nonlinear_2x2', x0: [1.5, 1], method: 'newton', tol: 1e-10})
};
fetch('https://api.fincept.in/quantlib/numerical/roots/find-nd', options)
.then(res => res.json())
.then(res => console.log(res))
.catch(err => console.error(err));<?php
$curl = curl_init();
curl_setopt_array($curl, [
CURLOPT_URL => "https://api.fincept.in/quantlib/numerical/roots/find-nd",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "POST",
CURLOPT_POSTFIELDS => json_encode([
'system' => 'nonlinear_2x2',
'x0' => [
1.5,
1
],
'method' => 'newton',
'tol' => 1e-10
]),
CURLOPT_HTTPHEADER => [
"Content-Type: application/json",
"X-API-Key: <api-key>"
],
]);
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}package main
import (
"fmt"
"strings"
"net/http"
"io"
)
func main() {
url := "https://api.fincept.in/quantlib/numerical/roots/find-nd"
payload := strings.NewReader("{\n \"system\": \"nonlinear_2x2\",\n \"x0\": [\n 1.5,\n 1\n ],\n \"method\": \"newton\",\n \"tol\": 1e-10\n}")
req, _ := http.NewRequest("POST", url, payload)
req.Header.Add("X-API-Key", "<api-key>")
req.Header.Add("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/numerical/roots/find-nd")
.header("X-API-Key", "<api-key>")
.header("Content-Type", "application/json")
.body("{\n \"system\": \"nonlinear_2x2\",\n \"x0\": [\n 1.5,\n 1\n ],\n \"method\": \"newton\",\n \"tol\": 1e-10\n}")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.fincept.in/quantlib/numerical/roots/find-nd")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n \"system\": \"nonlinear_2x2\",\n \"x0\": [\n 1.5,\n 1\n ],\n \"method\": \"newton\",\n \"tol\": 1e-10\n}"
response = http.request(request)
puts response.read_body{
"success": true,
"data": {
"root": [
1.7320508,
0.5773503
],
"iterations": 5,
"converged": true
}
}{
"detail": "Invalid API key"
}{
"detail": "Endpoint requires Basic tier or higher"
}Find Root of System of Equations
Find a solution to a system of nonlinear equations F(x) = 0 where F and x are vectors. Supports built-in systems: linear_2x2 (system of two linear equations), nonlinear_2x2 (nonlinear system like x^2 + y^2 = 4, xy = 1). Methods: newton (multidimensional Newton-Raphson with Jacobian), broyden (quasi-Newton method, approximates Jacobian). Essential for finding equilibrium points, solving nonlinear systems in economics, and multi-asset calibration. [Tier: BASIC, Credits: 1]
curl --request POST \
--url https://api.fincept.in/quantlib/numerical/roots/find-nd \
--header 'Content-Type: application/json' \
--header 'X-API-Key: <api-key>' \
--data '
{
"system": "nonlinear_2x2",
"x0": [
1.5,
1
],
"method": "newton",
"tol": 1e-10
}
'import requests
url = "https://api.fincept.in/quantlib/numerical/roots/find-nd"
payload = {
"system": "nonlinear_2x2",
"x0": [1.5, 1],
"method": "newton",
"tol": 1e-10
}
headers = {
"X-API-Key": "<api-key>",
"Content-Type": "application/json"
}
response = requests.post(url, json=payload, headers=headers)
print(response.text)const options = {
method: 'POST',
headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
body: JSON.stringify({system: 'nonlinear_2x2', x0: [1.5, 1], method: 'newton', tol: 1e-10})
};
fetch('https://api.fincept.in/quantlib/numerical/roots/find-nd', options)
.then(res => res.json())
.then(res => console.log(res))
.catch(err => console.error(err));<?php
$curl = curl_init();
curl_setopt_array($curl, [
CURLOPT_URL => "https://api.fincept.in/quantlib/numerical/roots/find-nd",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "POST",
CURLOPT_POSTFIELDS => json_encode([
'system' => 'nonlinear_2x2',
'x0' => [
1.5,
1
],
'method' => 'newton',
'tol' => 1e-10
]),
CURLOPT_HTTPHEADER => [
"Content-Type: application/json",
"X-API-Key: <api-key>"
],
]);
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}package main
import (
"fmt"
"strings"
"net/http"
"io"
)
func main() {
url := "https://api.fincept.in/quantlib/numerical/roots/find-nd"
payload := strings.NewReader("{\n \"system\": \"nonlinear_2x2\",\n \"x0\": [\n 1.5,\n 1\n ],\n \"method\": \"newton\",\n \"tol\": 1e-10\n}")
req, _ := http.NewRequest("POST", url, payload)
req.Header.Add("X-API-Key", "<api-key>")
req.Header.Add("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/numerical/roots/find-nd")
.header("X-API-Key", "<api-key>")
.header("Content-Type", "application/json")
.body("{\n \"system\": \"nonlinear_2x2\",\n \"x0\": [\n 1.5,\n 1\n ],\n \"method\": \"newton\",\n \"tol\": 1e-10\n}")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.fincept.in/quantlib/numerical/roots/find-nd")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n \"system\": \"nonlinear_2x2\",\n \"x0\": [\n 1.5,\n 1\n ],\n \"method\": \"newton\",\n \"tol\": 1e-10\n}"
response = http.request(request)
puts response.read_body{
"success": true,
"data": {
"root": [
1.7320508,
0.5773503
],
"iterations": 5,
"converged": true
}
}{
"detail": "Invalid API key"
}{
"detail": "Endpoint requires Basic tier or higher"
}Authorizations
API key for authentication. Get your key at https://api.fincept.in/auth/register
Body
System of equations to solve
linear_2x2, nonlinear_2x2 "nonlinear_2x2"
Initial guess for the solution (number of elements = number of equations)
[1.5, 1]
Solution method
newton, broyden "newton"
Convergence tolerance
1e-10
System-specific parameters (for linear_2x2: [a,b,c,d,e,f] for ax+by+c=0, dx+ey+f=0)
[1, 1, -3, 2, -1, -1]
