Please support Dual Numbers arithmetic

[ytrezq]

Problem Description

I would like to test and modify https://www.sciencedirect.com/science/article/pii/S0022314X08000486

Proposed Solution

Not only SageMath don t support Elliptic Curves over duals numbers, but Dual Number arithmetic isn t supported at all.

Alternatives Considered

Impossible. Everything need to be written from scratch.

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.

[r-mb]

Hello! What is wrong in using dual numbers as follows?

K = GF(5) # choose K as you wish
P.<e> = K[]
L = K.extension (e^2)

And then working with elliptic curves over L as explained here?

[ytrezq]

@r-mb but then how I declare a curve resulting from a curve mapped from a finite field as described in the paper?

[r-mb]

I am sorry, it is not clear from your question which part of the paper you are referring to. Could you please give more details on what you are trying to achieve?
With my previous answer I was replying to the two problems mentioned on this PR: both dual numbers, and elliptic curves over them, seem to be implemented. Am I missing something?

[maxale]

It looks like a question for sage-support group or ask.sagemath.org website than an issue in Sage.