ABS algorithms for integer WZ factorization

Classes of integer abs algorithms have been introduced for solving linear diophantine equations. the algorithms are powerful methods for developing all matrix factorizations. here,we provide the conditions for the existence of the integer wz and zw factorizations of an integer matrix. then,we present algorithms based on the integer abs algorithms for computing the integer wz and zw factorizations of an integer matrix as well as the integer ztxz and wtxw factorizations of a totally unimodular symmetric positives definite matrix.