{"product_id":"an-elementary-recursive-bound-for-effective-positivstellensatz-and-hilberts-17th-problem-9781470441081","title":"An Elementary Recursive Bound for Effective","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe authors prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely they express a nonnegative polynomial as a sum of squares of rational functions and obtain as degree estimates for the numerators and denominators the following tower of five exponentials $ 2^{ 2^{ 2^{d^{4^{k}}} } } $.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eWeak inference and weak existence\u003c\/li\u003e\n\u003cli\u003eIntermediate value theorem \u003c\/li\u003e\n\u003cli\u003eFundamental theorem of algebra\u003c\/li\u003e\n\u003cli\u003eHermite's theory \u003c\/li\u003e\n\u003cli\u003eElimination of one variable\u003c\/li\u003e\n\u003cli\u003eProof of the main theorems\u003c\/li\u003e\n\u003cli\u003eBibliography\/References.\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50041328468311,"sku":"9781470441081","price":67.5,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470441081.jpg?v=1740182503","url":"https:\/\/bookcurl.com\/products\/an-elementary-recursive-bound-for-effective-positivstellensatz-and-hilberts-17th-problem-9781470441081","provider":"Book Curl","version":"1.0","type":"link"}