This paper revisits the real symmetrizer equation in the literature to transform it into a reduced symmetrizer equation. This reduction can be accomplished by decomposing the symmetrizer of the equation. The reduced equation has a diagonal matrix as its symmetrizer and can be further decomposed into more such equations. These reduced equations are coexisting and synchronized with the original symmetrizer equation. Associated results concerning the reduced symmetrizer equation are introduced. A numerical algorithm for symmetrizer computation is developed based on these results. Typical symmetrizer problems in the literature are solved using the algorithm and the results are presented.