On Friday, 24 March 2023 at 13:04:48 UTC-7 William Stein wrote:

The code it suggests next doesn’t work, but to me that seems like a bug in Sage (?). Omitting the P entirely does work.

— William

—

Not a bug in sage, but a more insidious error in the example ChatGPT originally created. It’s basically doing something along the lines:

sage: R.<x,y>=GF(7)[]

sage: P = ProjectiveSpace(2,GF(7))

sage: Curve( P, x^3+y^3-x-y+1)

However, the documentation of Curve says that the *second* argument should be the ambient space (if provided). So:

Curve(x^3+y^3-x-y+1, AffineSpace(R))

does work. The syntactical correction Curve(x^3+y^3-x-y+1,P) still doesn’t work because we have an affine equation and are specifying an unrelated projective space.

I think the conclusion should be that ChatGPT pretends to be a SageMath expert with great confidence but .. gasp … isn’t!

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