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  • Sum of squares decompositio...
    Laplagne, Santiago

    Journal of pure and applied algebra, July 2024, 2024-07-00, Letnik: 228, Številka: 7
    Journal Article

    We present an example of a strictly positive polynomial with rational coefficients that can be decomposed as a sum of squares of polynomials over R but not over Q. This answers an open question by C. Scheiderer posed as the second question in 14, Section 5.1. We verify that the example we construct defines a nonsingular projective hypersurface, giving also a positive answer to the third question posed in that section.