Feature or bug: Ideal([x*(x-1),y*(y-1)]).reduce(x+y-3)

[Georgi Guninski]

sage: K.<x,y>=QQ[];I=Ideal([x*(x-1),y*(y-1)])
sage: I.reduce(x+y-3) #(1)
x + y - 3
sage: I.reduce(x+y-1) #(2)
x + y - 1

In (1) there is no common solution

[David Roe]

The reduction isn't required to have a common solution; indeed there is no way to add multiples of x(x-1) and y(y-1) to (x+y-3) and change the property of having a common solution.

What would you like to see the answer be for (1)?

David

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