---
license: apache-2.0
tags:
- math
- reasoning
- dynamic-analysis
- bode-plot
- llm-evaluation
- systems-of-linear-equations
pretty_name: "MathBode-LinearSystem"
size_categories:
- "1K<n<10K"
---

# MathBode-LinearSystem: Systems of Linear Equations Domain

Linear system solving problems from the MathBode benchmark.

This dataset is part of the **MathBode** benchmark, which evaluates the dynamic reasoning capabilities of large language models (LLMs) by treating parametric math problems as dynamic systems. Instead of testing static accuracy on fixed problems, MathBode sinusoidally varies a parameter and measures the model's response in terms of **gain** (amplitude tracking) and **phase** (reasoning lag), analogous to a Bode plot in control theory.

## About This Domain

This dataset contains **Systems of Linear Equations** problems specifically, with approximately 9,408 prompts covering:

- **3 question variants** with different constants
- **Sinusoidal parameter sweeps** at 5 frequencies (1, 2, 4, 8, 16 cycles)
- **3 phase offsets** (0°, 120°, 240°) for statistical robustness
- **3 amplitude scales** (0.5x, 1.0x, 2.5x) for non-linearity testing
- **Chirp signal validation** with continuous frequency sweeps

## Dataset Structure

| Column | Description |
|--------|-------------|
| `family` | Problem family name (always `linear_system` for this dataset) |
| `question_id` | Question variant ID (0, 1, or 2) |
| `signal_type` | Type of parameter variation (`sinusoid` or `chirp`) |
| `amplitude_scale` | Scaling factor for parameter variation amplitude |
| `frequency_cycles` | Frequency of parameter variation in cycles per sweep |
| `phase_deg` | Starting phase of sinusoidal signal in degrees |
| `time_step` | Step index within the sweep |
| `p_value` | The dynamic parameter value for this time step |
| `prompt` | The complete prompt text for the model |
| `ground_truth` | The correct numerical answer |
| `symbolic_baseline_answer` | Answer from perfect symbolic solver |

## Usage

```python
from datasets import load_dataset

# Load this specific domain
dataset = load_dataset("cognitive-metrology-lab/MathBode-LinearSystem")

# Access the data
print(dataset['train'][0])
```

## Related Datasets

- [MathBode](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode) - Complete benchmark with all families
- [MathBode-LinearSolve](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-LinearSolve)
- [MathBode-RatioSaturation](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-RatioSaturation)
- [MathBode-ExponentialInterest](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-ExponentialInterest)
- [MathBode-LinearSystem](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-LinearSystem)
- [MathBode-SimilarTriangles](https://huggingface.co/datasets/cognitive-metrology-lab/MathBode-SimilarTriangles)

## Citation

If you use this dataset, please cite our work (citation to be added).