Network operator matrix
Network operator matrix (NOM) is a representation of mathematical expressions in computer memory. NOM is a new approach to the problem of automatic search of mathematical equations. The researcher defines the sets of operations, variables and parameters. The computer program generates a number of mathematical equations that satisfy given restrictions. Then the optimization algorithm finds the structure of appropriate mathematical expression and its parameters. Network operator is a directed graph that corresponds to some mathematical expressions. Every source nodes of the graph are variables or constants of mathematical expression, inner nodes correspond to binary operations and edges  correspond to unary operations. The calculation’s result of mathematical expression is kept in the last sink node. Example. Consider the following mathematical expression The graph for Expression (), is presented in Fig. 1. On the edges we place unary operations formula_1 formula_2 formula_3 formula_4 In the inner and sink nodes we place binary operations formula_5 formula_6 Expression 1 can be presented in the PC memory as a NOM Any mathematical expression can be presented as a network operator matrix. To calculate the mathematical expression by the network operator matrix the node vector is used. Each component of node vector corresponds  to the nodes of the network operator graph. Initially each component is equal to the argument for the given node or the unit element of binary operation. For addition and multiplication the number of operation equals its unit element. For addition it is 0, for multiplication it is 1. The node vector for the given example formula_8 The calculation by matrix formula_9 is performed for nonzero nondiagonal elements formula_10 by formula_11 Follow the rows of the matrix. For the Row 1 we have formula_12, that is formula_13, formula_14, formula_15. Take arguments from formula_8 formula_17, formula_18 then formula_19 Further in Row  1 we have formula_20 formula_21 formula_22 formula_23. As a result after Row 1 we have formula_24. For the Row 2 we have formula_25 formula_26 then follow the rows formula_27 formula_28 formula_29 formula_30 formula_31 formula_32 formula_33 formula_34 formula_35 formula_36.