Rounding coefficients and artificially underflowing terms in non-numeric expressions

Abstract

This article takes an analytical viewpoint to address the following questions: 1. How can we justifiably beautify an input or result sum of non-numeric terms that has some approximate coefficients by deleting some terms and/or rounding some coefficients to simpler floating-point or rational numbers? 2. When we add two expressions, how can we justifiably delete more non-zero result terms and/or round some result coefficients to even simpler floating-point, rational or irrational numbers? The methods considered in this paper provide a justifiable scale-invariant way to attack these problems for subexpressions that are multivariate sums of monomials with real exponents.