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In the newest documentation https://reference.wolfram.com/language/ref/PolynomialSumOfSquaresList.html I read that

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However, on Mathematica 14.1.0 I tested the same code and it didn't fail

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Is the documentation wrong?

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Clearly the documentation is wrong. Please report to WRI [email protected]

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The point that the documentation is making is still valid, namely PolynomialSumOfSquaresList uses machine-precision numeric algorithms, so it may fail even if a sum of squares representation exists. Giving specific examples where this happens is a moving target. As the numeric algorithms get improved, examples that didn't work may start working. It looks like we need new documentation examples...

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