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  "body": "\n## Definition\n\nLet $A$ be a nonempty set.\nThe *ternary discriminator* on $A$ is the following [[ternary operation|WC47MFR6GW]] $t \\colon A^3 \\to A$.\n$$t(x, y, z) = \\begin{cases} z \u0026 \\text{if } x = y, \\\\ x \u0026 \\text{if } x \\neq y. \\end{cases}$$\nA term $s(x, y, z)$ is a *discriminator term* for an algebra $A$ if its term operation on $A$ is the ternary discriminator on $A$.\n\n## Remarks\n\nExample: on a field $F$ with $q$ elements, the polynomial $s(x, y, z) = x + (z - x)\\bigl(1 - (x - y)^{q - 1}\\bigr)$ gives the discriminator.\nCheck: if $x = y$ then $(x - y)^{q - 1} = 0$ and $s = z$; if $x \\neq y$ then $(x - y)^{q - 1} = 1$ and $s = x$.\nNon-example: on $\\set{0, 1}$ the lattice term $(x \\wedge y) \\vee (y \\wedge z) \\vee (x \\wedge z)$ is not the discriminator, since at $(0, 1, 1)$ it gives $1$ while the discriminator gives $0$.\nThe discriminator satisfies $t(x, y, y) = x$, $t(x, x, y) = y$ and $t(x, y, x) = x$, so it is a [[Pixley term|5C91SFVTY7]] operation.\n",
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