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  "body": "\n## Summary\n\nA polynomial operation of an algebra is a [[term operation|N9M2N27END]] in which some arguments are fixed to constant elements of the algebra.\nFor a commutative ring, the polynomial operations are the [[polynomial functions|1G0B73WPX8]] in several variables, which explains the name.\nPolynomial operations describe the congruences of an algebra: an equivalence relation is a congruence exactly when it is preserved by all unary polynomial operations.\n\n## Explanations\n\n### L1 human\n\nTerm operations may use only the operations that the algebra comes with.\nPolynomial operations may also use any element of the algebra as a fixed constant.\nIn the group $(\\Z, +)$, the map $x \\mapsto 2x$ is a term operation, while $x \\mapsto 2x + 5$ is a polynomial operation that is not a term operation.\nIn a ring, $x \\mapsto 3x^2 + 7$ is a polynomial operation, matching the usual polynomial.\n",
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