# Rational Interpolation Engine for data modeling. AI Agent Connect

> Rational Interpolation Engine lets your AI client model data using ratios of polynomials. You can specify numerator and denominator degrees to handle complex behaviors like singularities. It provides the math needed to fit functions, evaluate coordinates, check error rates, and locate poles or zeros directly within your existing AI workflow.

## Overview
- **Category:** mathematics
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_gAUvmOw51Y8MKPCjq7SsiPPBCfSrXK57BpsQyr8c/ai-agent-connect
- **Tags:** interpolation, polynomials, rational-functions, data-fitting, mathematical-modeling

## Description

You can use this MCP to build mathematical models that standard polynomial regression might miss. By using ratios of polynomials, you can account for singularities and more complex data behaviors. You simply tell your AI client the degrees you want for the numerator and denominator, and it handles the heavy lifting of fitting the function to your points. Once the model is built, you can use it to predict values at specific coordinates or check how well the model actually matches your original data. It is a specialized tool for when your data doesn't follow a simple curve and requires the flexibility of rational functions to get an accurate fit.

## Tools

### analyze_fit_quality
This tool provides a statistical summary of how well your fitted model represents the input data.

### find_function_singularities
Use this to locate all poles and zeros within a specific rational function.

### fit_rational_function
This tool fits a rational function to your data points based on the degrees you specify.

### get_function_value
This tool evaluates your fitted rational function at any specific coordinate you provide.

## Prompt Examples

**Prompt:** 
```
Fit a rational function to these points: (1, 2), (2, 4), (3, 8) with numerator degree 1 and denominator degree 1.
```

**Response:** 
```
The fitted rational function has coefficients: numerator [0, 2], denominator [1, -1].
```

**Prompt:** 
```
Find the poles for a function with numerator [1, 0] and denominator [1, -2].
```

**Response:** 
```
The pole is located at x = 2.
```

**Prompt:** 
```
Evaluate the function with numerator [1, 1] and denominator [1, 0] at x = 5.
```

**Response:** 
```
The value at x = 5 is 1.5.
```

## Capabilities

### Rational Function Fitting
Your agent uses this to create models from data points using custom polynomial degrees.

### Singularity Detection
The AI identifies the exact locations of poles and zeros in your functions.

### Coordinate Evaluation
Your client calculates specific values for a fitted function at any given point.

### Statistical Error Reporting
The tool generates summaries to show how accurately a model represents your data.

## Use Cases

### Modeling Singularities
Use the tool when your data contains points that approach infinity or other singular behaviors.

### Advanced Curve Fitting
Fit rational functions to datasets where a simple ratio of polynomials is required for accuracy.

### Function Analysis
Quickly find the zeros and poles of a known rational function.

### Data Validation
Check the statistical quality of a model to ensure it is a reliable fit for your data.

## Benefits

- Handles complex data behaviors that standard polynomials cannot model.
- Provides direct access to singularity locations like poles and zeros.
- Allows for custom control over numerator and denominator degrees.
- Integrates mathematical computation directly into your AI client.

## How It Works

The process moves from data input to a fully evaluated mathematical model.

1. Connect your AI client to the Vinkius hosted MCP.
2. Provide your data points and desired polynomial degrees to the agent.
3. The agent calls the fitting tool to generate the rational function.
4. Use the resulting model to evaluate points or check for singularities.

## Frequently Asked Questions

**What is a rational function?**
A rational function is a function that can be expressed as the ratio of two polynomial functions.

**How do I use this with Claude or Cursor?**
You connect your client to the Vinkius hosted MCP once, and then you can call the mathematical tools directly in your chat or editor.

**Can I specify the complexity of the model?**
Yes, you can specify the degrees for both the numerator and the denominator when fitting the function.

**How do I know if the fit is accurate?**
You can use the analyze_fit_quality tool to get a statistical summary of the model's performance.

**Does this MCP handle singularities?**
Yes, it includes a specific tool to find the locations of poles and zeros in your functions.

**What is the difference between exact and numerical modes?**
Exact mode forces the function to pass through every data point, while numerical mode performs a least-squares fit to minimize residuals in noisy datasets.

**How can I check if my model is accurate?**
You can use the `analyze_fit_quality` tool to receive a detailed report including mean squared error and maximum residuals.

**What happens if the system is underdetermined?**
If the provided degrees and data points do not allow for a unique solution, the `fit_rational_function` tool will return an `isRankDeficient` flag as true.