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 On Thu, Jun 26, 2025 at 4:47 AM Georgi Guninski <[email protected]> wrote: > 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 > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/sage-devel/CAGUWgD9HsrEkxgm6C-9rzAMbmtgDvC%3DQZzpNXTg%2Bh7qVa3cUbw%40mail.gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/sage-devel/CAChs6_myNUNAf4xjwJNSBEmstvFJsCx%3Dd9BiNEL1etQs7YKjAA%40mail.gmail.com.
