# Gröbner Basis Generation on D\_n(Q), n=4, sigma=0.3 (test)

Source: [Gröbner Basis Generation on D\_n(Q), n=4, sigma=0.3 (test)](<https://www.sota2.com/research/sota/gr-bner-basis-generation-on-d_n-q-n-4-sigma-0-3-test>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-02-26T06:02:35.616Z

Evaluation of algorithms for Gröbner Basis Generation on the specific test set configuration of the D\_n(Q) dataset (n=4, sigma=0.3), measured by computational runtime.

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

| Scope | Recorded value |
| --- | --- |
| Task | Gröbner Basis Generation |
| Dataset (including any stated split) | D\_n(Q), n=4, sigma=0.3 (test) |
| Metric | Runtime (s) |
| Unit | TIME |
| Direction | Lower is better |
| Results loaded | 16 of 16 |
| Coverage | All results currently returned for this benchmark |

Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol.

## Metrics

- [Runtime (s)](<https://www.sota2.com/research/sota/gr-bner-basis-generation-on-d_n-q-n-4-sigma-0-3-test.md?metric=Runtime%20(s)>): Lower is better; unit: TIME.

## Recorded results

| Method | Runtime (s) | Result date | Report paper |
| --- | --- | --- | --- |
| F. (STD) | 0.005 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (STD) | 0.006 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (STDFGLM) | 0.008 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (STDFGLM) | 0.008 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (STDFGLM) | 0.008 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (STDFGLM) | 0.015 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (SLIMGB) | 0.018 | Not recorded | 68fa5c8b1e209131ce9d208e |
| Transformer | 0.11 | Not recorded | 68fa5c8b1e209131ce9d208e |
| Transformer | 0.147 | Not recorded | 68fa5c8b1e209131ce9d208e |
| Transformer | 0.238 | Not recorded | 68fa5c8b1e209131ce9d208e |
| Transformer | 0.253 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (SLIMGB) | 100 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (STD) | 100 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (SLIMGB) | 100 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (STD) | 100 | Not recorded | 68fa5c8b1e209131ce9d208e |
| F. (SLIMGB) | 100 | Not recorded | 68fa5c8b1e209131ce9d208e |

### F. (STD)

Runtime (s): 0.005. Result ID: 698bb6767a967eddb770cce3.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"23"}. This record does not assert independent reproduction.

### F. (STD)

Runtime (s): 0.006. Result ID: 698bb6767a967eddb770cceb.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"64"}. This record does not assert independent reproduction.

### F. (STDFGLM)

Runtime (s): 0.008. Result ID: 698bb6767a967eddb770cce5.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"23"}. This record does not assert independent reproduction.

### F. (STDFGLM)

Runtime (s): 0.008. Result ID: 698bb6767a967eddb770cce9.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"49"}. This record does not assert independent reproduction.

### F. (STDFGLM)

Runtime (s): 0.008. Result ID: 698bb6767a967eddb770cced.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"64"}. This record does not assert independent reproduction.

### F. (STDFGLM)

Runtime (s): 0.015. Result ID: 698bb6767a967eddb770ccf1.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"171"}. This record does not assert independent reproduction.

### F. (SLIMGB)

Runtime (s): 0.018. Result ID: 698bb6767a967eddb770cce8.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"49"}. This record does not assert independent reproduction.

### Transformer

Runtime (s): 0.11. Result ID: 698bb6767a967eddb770cce6.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

[Implementation](<https://github.com/HiroshiKERA/transformer-groebner>)

Recorded evaluation configuration: {"Sample ID":"23"}. This record does not assert independent reproduction.

### Transformer

Runtime (s): 0.147. Result ID: 698bb6767a967eddb770ccee.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

[Implementation](<https://github.com/HiroshiKERA/transformer-groebner>)

Recorded evaluation configuration: {"Sample ID":"64"}. This record does not assert independent reproduction.

### Transformer

Runtime (s): 0.238. Result ID: 698bb6767a967eddb770ccf2.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

[Implementation](<https://github.com/HiroshiKERA/transformer-groebner>)

Recorded evaluation configuration: {"Sample ID":"171"}. This record does not assert independent reproduction.

### Transformer

Runtime (s): 0.253. Result ID: 698bb6767a967eddb770ccea.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

[Implementation](<https://github.com/HiroshiKERA/transformer-groebner>)

Recorded evaluation configuration: {"Sample ID":"49"}. This record does not assert independent reproduction.

### F. (SLIMGB)

Runtime (s): 100. Result ID: 698bb6767a967eddb770cce4.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"23"}. This record does not assert independent reproduction.

### F. (STD)

Runtime (s): 100. Result ID: 698bb6767a967eddb770cce7.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"49"}. This record does not assert independent reproduction.

### F. (SLIMGB)

Runtime (s): 100. Result ID: 698bb6767a967eddb770ccec.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"64"}. This record does not assert independent reproduction.

### F. (STD)

Runtime (s): 100. Result ID: 698bb6767a967eddb770ccef.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"171"}. This record does not assert independent reproduction.

### F. (SLIMGB)

Runtime (s): 100. Result ID: 698bb6767a967eddb770ccf0.

[Reporting paper](<https://www.sota2.com/research/paper/68fa5c8b1e209131ce9d208e.md>)

Recorded evaluation configuration: {"Sample ID":"171"}. This record does not assert independent reproduction.

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