SIRD:An Algorithm for Simultaneous Integer Relations Detection

In order to reduce the hyperplane matrix when detecting simultaneous integer relations for several real vectors,a generalized Hermite reduction was presented.Based on generalized Hermite reduction and patial sum-lower trapezoidal orthogonal decomposition(PSLQ) algorithm,the algorithm of simultaneous integer relations detection(SIRD) was proposed.SIRD was implemented in computer algebra system Maple in two different routes of software float-point data type "sfloat" and hardware float point data type "hfloat".The SIRD was compared with HJLS,and the results showed that SIRD is better.Furthermore,SIRD was applied to get a complete method for finding the minimal polynomial of an unknown complex algebraic number from its approximation.