This paper presents an algorithm and its implementation in the software package <ExternalRef> <RefSource> <Emphasis FontCategory="NonProportional">NCSOStools </RefSource> <RefTarget Address="http://ncsostools.fis.unm.si/" TargetType="URL"/> </ExternalRef> for finding sums of Hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of the classical Gram matrix method and...</emphasis></refsource></externalref>

In this paper we provide a generalization of a Positivstellensatz by Pólya [Pólya in Naturforsch Ges Zürich 73:141–145 <CitationRef CitationID="CR18">1928</CitationRef>]. We show that if a homogeneous polynomial is positive over the intersection of the non-negative orthant and a given basic semialgebraic cone (excluding the origin),...</citationref>