evaluation of polynomials mod 8

[John Cremona]

Am I doing something stupid here, or is this a bug?

sage: R = Integers(8)
sage: RXY.<X,Y> = R[]
sage: F = X^3-X^2*Y+X*Y^2+Y^3
sage: F([4,2])
6
sage: 4^3-4^2*2+4*2^2+2^3
56
sage: (4^3-4^2*2+4*2^2+2^3) % 8
0


Why does F not evaluate to 0 mod 8 at X=4, Y=2? Rather obviously, each
of the terms in F(4,2) is 0 mod 8.

John

[Vincent Delecroix]

The iterated subs turns out to be correct

sage: F.subs(X=4).subs(Y=2)
0
sage: F.subs(Y=2).subs(X=4)
0

But not the one shot version (which is supposedly equivalent to the evaluation)

sage: F.subs(X=4, Y=2)
6

There is definitely something wrong!!

Vincent

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[David Joyner]

On Tue, Sep 27, 2022 at 4:46 AM John Cremona <john.c...@gmail.com> wrote:
>
> Am I doing something stupid here, or is this a bug?
>
> sage: R = Integers(8)
> sage: RXY.<X,Y> = R[]
> sage: F = X^3-X^2*Y+X*Y^2+Y^3
> sage: F([4,2])
> 6
> sage: 4^3-4^2*2+4*2^2+2^3
> 56
> sage: (4^3-4^2*2+4*2^2+2^3) % 8
> 0
>

Even after coercion it doesn't evaluate in ZZ/8ZZ:

sage: ZZ8 = IntegerModRing(8)
sage: R.<x,y> = PolynomialRing(ZZ8, "x,y")
sage: f = x^3-x^2*y+x*y^2+y^3
sage: x0 = ZZ8(4)
sage: y0 = ZZ8(2)
sage: x0^3-x0^2*y0+x0*y0^2+y0^3
0
sage: f(x0,y0)
6
sage: f(4,2)
6

>
> Why does F not evaluate to 0 mod 8 at X=4, Y=2? Rather obviously, each
> of the terms in F(4,2) is 0 mod 8.
>
> John
>

[Kwankyu]

This bug is tracked now in 

https://trac.sagemath.org/ticket/34591

[John Cremona]

Thanks!