Real Algebraic and Analytic Geometry
homepages: http://www.uam.es/josefrancisco.fernando, http://www.mat.ucm.es/~jesusr
Submission: 2003, April 14.
We show that: (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number 2 if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive semide.nite analytic function germs.
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