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  "body": "\n## Summary\n\nThe Alexander polynomial is a [[knot invariant|GZQ5ZE3X6G]] that assigns to each [[knot|QYEAZTYGPT]] a Laurent polynomial with integer coefficients.\nIt was the first polynomial knot invariant, found by James Waddell Alexander II in the 1920s.\nIt can be computed from a Seifert matrix, from a knot diagram, or from the homology of the infinite cyclic cover of the knot complement.\nIt detects many knots but not all; some nontrivial knots have Alexander polynomial $1$.\n\n## Explanations\n\n### L1 human\n\nThe Alexander polynomial turns a knot into a polynomial such as $t - 1 + t^{-1}$.\nIf two knots have different polynomials, they are different knots.\nThe [[unknot|1TQ06R4Q66]] has polynomial $1$, while the [[trefoil knot|VYTYSVHN4A]] has $t - 1 + t^{-1}$, so the trefoil is really knotted.\nThe polynomial records how the loops on a surface bounded by the knot wind around each other.\n",
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