The available means of ordering and sorting in some important sections of discrete mathematics and computer science are studied, namely: in the set theory, classical mathematical logic, proof theory, graph theory, POST method, system of algorithmic algebras, algorithmic languages of object-oriented and assembly programming. The Cartesian product of sets, ordered pairs and ordered n-s, the description by means of set theory of an ordered pair, which are performed by Wiener, Hausdorff and Kuratowski, are presented. The requirements as for the relations that order sets are described.
In expanding the known classical algebra algorithms received meaningful input operations elimination, introduced a new extension. At the level of innovation is the introduction of the alphabet in special unitermiv, what are the signs uniterm return cycle and conditional uniterm cycle. At the level of innovation definitions of operations is an axiom uniterma input and output in the region of the operation cyclic sequencing, axiom input and output uniterma in scope and with the operationcyclic elimination, input and output axioms uniterma in scope and operation cyclic paralleling.
There DATABASE of the modified algorithms algebra for constructing mathematical models of patterns of relational databases is grounded. Mathematical models of abstract database schemes with one or many relations and abstract schema data warehouse are constructed.