円内接八角形の外接円半径公式の計算結果について (Computer Algebra --Theory and its Applications)

Abstract

This paper reports the results of computing the circumradius formula for cyclic octagons given by the lengths of the sides. Continuing with the author's recent paper in 2018, we have finally succeeded in computing all the coefficients of the octagon formula, which has 845, 027 terms in the form of elementary symmetric polynomials. In this study, we have newly applied the method of numerical interpolation, adding to the method of elimination by resultants. We have found out that traditional modular algorithms are also effective in our problems for solving system of linear equations over the integers.