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Feat: direct quartic extension on koala and baby bears fields #649

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Description

This PR implement the arithmetic of direct quartic extensions on koala and baby bears fields. It might become handy for cross testing and/or hinting in gnark circuit version.

Type of change

  • New feature (non-breaking change which adds functionality)

How has this been tested?

Test between direct and towered extensions implemented.

How has this been benchmarked?

N/A

Checklist:

  • I have performed a self-review of my code
  • I have commented my code, particularly in hard-to-understand areas
  • I have made corresponding changes to the documentation
  • I have added tests that prove my fix is effective or that my feature works
  • I did not modify files generated from templates
  • golangci-lint does not output errors locally
  • New and existing unit tests pass locally with my changes
  • Any dependent changes have been merged and published in downstream modules

@yelhousni yelhousni added this to the v0.10.0 milestone Feb 21, 2025
@yelhousni yelhousni requested a review from gbotrel February 21, 2025 17:54
@yelhousni yelhousni self-assigned this Feb 21, 2025
Base automatically changed from gen/small-fields-extensions to master March 11, 2025 20:50
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