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  "body": "\n## Summary\n\nThe Witt group of a field $F$ of characteristic not $2$ is an abelian group built from the nondegenerate [[quadratic forms|0RBQS1JJCR]] over $F$.\nTwo forms give the same element when they differ only by hyperbolic planes, and the group operation is the orthogonal sum.\nIt collects the essential information about quadratic forms over $F$ into one algebraic object.\nWith the tensor product of forms it becomes a ring, the Witt ring.\n\n## Explanations\n\n### L1 human\n\nQuadratic forms can be added by placing them side by side in separate variables.\nSome forms, the hyperbolic ones such as $x^2 - y^2$, carry no interesting information, so they are treated as zero.\nAfter this, every form has a negative, namely the form with all signs reversed, and one gets a group.\nFor the real numbers, the class of a form is given by its signature, the number of plus signs minus the number of minus signs.\nSo the Witt group of $\\R$ is $\\Z$.\n",
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