# How to minimize or maximize a function over a finite field in WolframAlpha?

Is it possible to ask WolframAlpha to minimize or maximize a function with variables in a finite field?

Let's take a stupid example: how do I ask WolframAlpha to maximize $x_1+x_2$ with $x_1, x_2\in\mathbb{Z}_2$?

Thanks!

Edit: let's consider, in $\mathbb{Z}_2$, the order $[0]<[1]$.

• Finite fields have no order! There is no meaning in "maximizing" or "minimizing" over a finite field. – Crostul Jun 23 '18 at 8:12
• Maximizing something implies that you have some ordering on the finite field. However, as finite fields have positive characteristic, they are not ordered fields. I'm not aware of any nice ordering on a finite field, as none respect the field structure itself. – user571438 Jun 23 '18 at 8:13
• @Poecilia $\mathbb{Z}/2\mathbb{Z}$ is a set of equivalence classes modulo 2. If I instead wrote $\mathbb{Z}/2\mathbb{Z} = \{[1000], [1]\}$, where $[a]$ denotes the equivalence class modulo 2, which element would you now choose as the maximum? – user571438 Jun 23 '18 at 8:15
• For $\Bbb{F}_2$ we can maximize, taking the order of the standard representatives in the integers. But take $\Bbb{F}_4$. This is not $\Bbb{Z}/4$. Try to compare the elements with respect to $\le$. – Dietrich Burde Jun 23 '18 at 8:16
• @DietrichBurde thanks, this is what I meant. I want to maximize taking the order of the standard representatives in the integers. – Poecilia Jun 23 '18 at 8:19