To efficiently compute the determinants of symbolic matrices arising in science and engineering fields, based on dimension decreasing algorithm and parallel computation of symbolic determinant, a hybrid algorithm,which can convert the computation of a given multivariate determinant to the computation of a univariate determinant,was presented. In addition, the degree of parallelism was enhanced greatly. Experimental results showed that this new algorithm can effectively reduce the intermediate expression swell and deal with some symbolic determinants with polynomial entries in many variables.
