On the Pythagoras number for polynomials of degree 4 in 5 variables

2023/06/09 by Santiago Laplagne, Laplagne, Santiago
Mathematics · Engineering · #Mathematics and Applications #Advanced Numerical Analysis Techniques #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.2306.05959

Abstract

We give an example of a polynomial of degree 4 in 5 variables that is the sum of squares of 8 polynomials and cannot be decomposed as the sum of 7 squares. This improves the current existing lower bound of 7 polynomials for the Pythagoras number p(5,4).

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