The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring elementary, i.e. we can express with elementary ones in unique way. does not extend directly to semirings, but do have analogous results for some special example, the tropical, extended and supertropical semirings. These all fall into larger class upper-bound In this...

An explicit a priori bound for the condition number associated to each of the following problems is given: general linear equation solving, least squares, non-symmetric eigenvalue problems, solving univariate polynomials, and solving systems of multivariate polynomials. It is assumed that the input has integer coefficients and is not on the degeneracy locus of the respective problem (i.e., the ...