APPARATUS, METHOD, AND PROGRAM FOR EVALUATING TOLERANCE LIMIT WITH RESPECT TO COEFFICIENT OF SIMULTANEOUS ALGEBRAIC EQUATION

摘要

PROBLEM TO BE SOLVED: To provide a technology of evaluating a limit of permissible error ensuring that simultaneous equation ~f(x, y)=~g(x, y)=0 is solvable, from the bottom.;SOLUTION: A bivariate polynomial f(x, y), g(x, y)E*K[x, y] over a field K is written as follows (E* is a set symbol and represents "belong"): f(x, y)=a_d(y)x^d+ ... +a₁(y)x+a₀(y), g(x, y)=b_e(y)x^e+ ... +b₁(y)x+b₀(y), wherein a_d(y) and b_e(y) are not a constant 0. If both a requirement 1 [a_d(y) and b_e(y) have no common zero] and a requirement 2 [Res_x(f, g) is not a constant] are satisfied, f(x, y)=g(x, y)=0 has a solution (over a field of complex numbers). Res_x(f, g) is a resultant of f(x, y) and g(x, y) for x. The proved fact is applied to the bivariate polynomial ~f(x, y), ~g(x, y) including an error in a coefficient.;COPYRIGHT: (C)2011,JPO&INPIT