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Ability to represent curve groups #40350

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@whoami730

Description

@whoami730

Problem Description

I want to be able to create groups over general curves akin to Elliptic Curves.
As an example, consider the equation x^2 - y^2 = 1 modulo p for prime p. This is a hyperbolic equation, and we should be able to both represent groups of points on this curve as well as experiment on the structure of this curve - as an example, I wanted to know what would the abelian_group function provide for such a curve.

Proposed Solution

Maybe something like - Curve(Zp, x**2 - y**2 - 1) could be used to represent this.

Alternatives Considered

Really couldn't find anything similar.

Additional Information

No response

Is there an existing issue for this?

  • I have searched the existing issues for a bug report that matches the one I want to file, without success.

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