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  "body": "\n## Summary\n\nA Colombeau algebra is an algebra of generalized functions that contains the distributions and in which any two elements can be multiplied.\nIts elements are classes of families of smooth functions indexed by a small parameter, with bounds that are polynomial in the inverse of the parameter.\nIt keeps the product of smooth functions and has a derivative obeying the Leibniz rule.\nIt is used for nonlinear equations with singular data.\n\n## Explanations\n\n### L1 human\n\nThe delta function cannot be squared as a distribution.\nA Colombeau algebra replaces the delta by the whole family of narrower and narrower spikes that approximate it.\nFamilies can be multiplied term by term, so products such as the square of the delta make sense.\nFamilies that become small faster than any power of the parameter are treated as zero.\n",
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