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  "body": "\n## Summary\n\nA toric ideal is the ideal of all polynomial relations among a finite set of monomials in Laurent variables.\nIt is a prime ideal generated by binomials, that is, by differences of two monomials.\nIts zero set is an affine toric variety, so toric ideals connect commutative algebra with polyhedral geometry and with integer programming and algebraic statistics.\n\n## Explanations\n\n### L1 human\n\nTake some monomials, such as $s$, $st$ and $st^2$.\nThey satisfy relations: here $s \\cdot st^2 = (st)^2$.\nNaming the monomials $x_1, x_2, x_3$, the relation becomes $x_1 x_3 - x_2^2 = 0$.\nThe toric ideal collects all such relations, and each relation says that two products of the monomials have the same exponent vector.\nSo finding the toric ideal is a question about linear relations among integer vectors.\n",
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