1. The method for detecting reduction variables in a source code program loop to enable execution parallelization, comprising the steps of: a. recasting the expression on the right hand side (RHS) of each assignment statement of the source code program loop into a reduced form, b. determining for each said assignment statement its corresponding left hand side (LHS) variable and creating a corresponding variable search string for the said LHS variable to enable a search for the said LHS variable as a factor in a recast expression, c. creating a corresponding reciprocal variable search string for the reciprocal of the LHS variable to enable a search for the reciprocal of the LHS variable as a factor in a recast expression, d. searching in the recast RHS expression of each said assignment statement for a variable search string corresponding to a LHS variable, e. searching in the recast RHS expression of each said assignment statement for a reciprocal variable search string corresponding to the reciprocal of a LHS variable, f. inserting references to LHS variables and their corresponding assignment statements in a reduction table based on pre-determined conditions, g. deleting references to LHS variables and their corresponding assignment statements from the reduction table based on predetermined conditions, and h. determining for each assignment statement referenced in the reduction table its corresponding associative operator and associative operand.