Computing the multiplicity structure of an isolated singular solution: Case of breadth one

摘要

We present an explicit algorithm to compute a closed basis of the local dual space of I = (f_1,... ,f_t) at a given isolated singular solution x = (x_1,..., x_s) when the Jacobian matrix J(x) has corank one. The algorithm is efficient both in time and memory use. Moreover, it can be modified to compute an approximate basis if the coefficients of f_1,... ,f_t and x are only known with limited accuracy.