{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "4JEDEJRXJW"
    }
  ],
  "body": "\n## Summary\n\nA Siggers term is an idempotent term of arity $6$ that satisfies one fixed identity in three variables, $s(x, y, x, z, y, z) \\approx s(y, x, z, x, z, y)$.\nEvery Siggers term is a [[Taylor term|QEAMRNRJJD]].\nConversely, a finite algebra that has a Taylor term also has a Siggers term, so one explicit identity replaces the whole family of Taylor conditions.\nThis makes the Siggers term a convenient test in the algebraic theory of constraint satisfaction problems.\n\n## Explanations\n\n### L1 human\n\nTaylor terms come in many shapes and arities, which makes them hard to search for.\nA Siggers term has one fixed shape: six inputs and one balanced equation in three letters.\nFor finite algebras, looking for this single shape is enough to decide whether some Taylor term exists.\nFor example, in a semilattice the term $x_1 \\wedge x_2 \\wedge \\cdots \\wedge x_6$ is a Siggers term, because both sides of the identity become $x \\wedge y \\wedge z$.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "08B05",
      "08A70"
    ],
    "name": "Siggers term",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Constraint_satisfaction_problem"
      }
    ],
    "specializes": [
      "QEAMRNRJJD"
    ],
    "tag": "JYW1H3J8SX"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/JYW1H3J8SX/",
  "links": [
    {
      "field": "specializes",
      "target": "QEAMRNRJJD"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/JYW1H3J8SX.md",
  "msc": [
    "08B05",
    "08A70"
  ],
  "name": "Siggers term",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/JYW/JYW1H3J8SX.md",
  "status": null,
  "tag": "JYW1H3J8SX",
  "uri": "m2://JYW1H3J8SX",
  "url": "https://tamnd.github.io/math2/wiki/siggers-term/",
  "writing": {
    "tag": "JYW1H3J8SX",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}
