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  "body": "\n## Summary\n\nLet $V$ be a finite-dimensional space of functions.\nA set of points is unisolvent for $V$ when each choice of values at the points is taken by exactly one function in $V$.\nIt is the condition under which an interpolation problem has a unique answer.\nIn one variable, any $n + 1$ distinct points are unisolvent for the polynomials of degree at most $n$, which is the basis of [[polynomial interpolation|SS1YMS2NPC]].\nIn several variables the position of the points matters, and choosing unisolvent sets is a central problem of [[multivariate interpolation|BM703GV34G]].\n\n## Explanations\n\n### L1 human\n\nA space of functions with $N$ free parameters needs $N$ conditions to fix one function.\nValues at $N$ points give $N$ conditions, but they only work when the points are in a good position.\nThe affine functions $a + bx + cy$ on the plane have three parameters.\nThree points that form a triangle fix such a function, so they are unisolvent.\nThree points on one line are not: the function $x - y$ is zero at $(0, 0)$, $(1, 1)$ and $(2, 2)$, and so it can be added to any solution.\nThe [[definition|681HPCS6G6]] makes this precise.\n",
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  "msc": [
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  "name": "Unisolvent point set",
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