# Tensor Index Contraction Engine for math. AI Agent Connect

> Tensor Index Contraction Engine gives your AI agent the ability to process multi-dimensional arrays with mathematical precision. It handles the heavy lifting for tensor products, axis permutations, index contractions, and Einstein summation notation. Instead of guessing shapes, your agent uses these tools to calculate exact index mappings and resulting structures for any given tensor operation.

## Overview
- **Category:** science
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_vDuTlV8hzFXn3UPsU3O9gbNlhM8Wz4dKGYfDXc9L/ai-agent-connect
- **Tags:** tensor, linear-algebra, einstein-notation, physics, matrix-calculus

## Description

You can stop manually tracking tensor shapes and index mappings. This MCP provides the mathematical backbone your AI client needs to solve multi-dimensional array problems accurately. Whether you are working with physics simulations, machine learning architectures, or complex linear algebra, your agent can now execute precise operations that require strict adherence to index rules.

When you need to reduce the rank of a tensor, the MCP calculates the exact resulting shape and index mapping. If you are working with Einstein summation, the engine parses your notation strings to determine the final structure. It handles the logic of axis permutations and outer products, ensuring that the index transformations remain consistent. This moves the burden of dimensional bookkeeping from your prompts to a dedicated mathematical tool, preventing the common errors AI agents make when calculating high-dimensional transformations.

## Tools

### apply_permutation
This tool calculates the new shape and index mapping after you permute a tensor's axes.

### calculate_tensor_product
Use this to find the resulting shape and index mapping for a tensor outer product.

### evaluate_einstein_notation
This tool parses Einstein summation strings to determine the resulting tensor structure.

### perform_contraction
This tool calculates the resulting shape and index mapping after summing over specific indices to reduce tensor rank.

## Prompt Examples

**Prompt:** 
```
What is the result of the Einstein notation 'ij,jk->ik' for two tensors with shapes [2,3] and [3,4] and indices 'ij' and 'jk'?
```

**Response:** 
```
The resulting tensor has a shape of [2,4] with indices 'ik'.
```

**Prompt:** 
```
Calculate the outer product of a tensor with shape [2,2] and indices 'ab' and a tensor with shape [3,3] and indices 'cd'.
```

**Response:** 
```
The resulting tensor has a shape of [2,2,3,3] and indices 'abcd'.
```

**Prompt:** 
```
How does the shape change if I apply a permutation [1,0] to a tensor with shape [5,10] and indices 'xy'?
```

**Response:** 
```
The new shape is [10,5] and the new indices are 'yx'.
```

## Capabilities

### Einstein Summation
Your agent parses compact summation strings to find the final tensor structure.

### Tensor Contraction
The MCP reduces tensor rank by summing over specified indices.

### Axis Permutation
It calculates how shapes and indices shift when you reorder axes.

### Outer Products
The engine determines the resulting shape and index mapping for tensor products.

## Use Cases

### Tensor Shape Verification
Check if a specific permutation or contraction will result in the expected tensor dimensions.

### Physics Notation Parsing
Convert complex Einstein summation strings into predictable tensor shapes.

### Linear Algebra Automation
Let your agent calculate outer products and contractions for large-scale matrix math.

### Algorithm Debugging
Verify the mathematical correctness of tensor transformations in your code.

## Benefits

- Eliminates manual index tracking errors in your AI prompts.
- Provides exact shape and index mapping for every operation.
- Translates compact Einstein notation into concrete tensor structures.
- Handles rank reduction through precise index contraction.

## How It Works

The MCP connects your AI client to a specialized mathematical engine.

1. Connect your preferred MCP-compatible client to Vinkius.
2. Your agent identifies the need for a tensor operation.
3. The agent calls a specific tool like evaluate_einstein_notation.
4. The MCP calculates the exact shape and index mapping.
5. The result is returned to your agent to continue the task.

## Frequently Asked Questions

**What can this MCP do with Einstein notation?**
It uses the evaluate_einstein_notation tool to parse summation strings and determine the resulting tensor structure and shape.

**How does it handle tensor contractions?**
The perform_contraction tool calculates the new shape and index mapping after summing over specific indices to reduce the tensor rank.

**Can I use this with Claude or Cursor?**
Yes, you can connect this MCP to any MCP-compatible client including Claude, Cursor, and Windsurf.

**Does it calculate the actual tensor values?**
This MCP focuses on the mathematical structure, calculating the resulting shapes and index mappings for operations like permutations and products.

**What is an outer product in this context?**
The calculate_tensor_product tool determines the resulting shape and index mapping when performing a tensor outer product.