 A basic example of functional decomposition is expressing the four binary arithmetic operations of addition, subtraction, multiplication, and division in terms of the two binary operations of addition formula_16 and multiplication formula_17 and the two unary operations of additive inversion formula_18 and multiplicative inversion formula_19 Subtraction can then be realized as the composition of addition and additive inversion, formula_20 and division can be realized as the composition of multiplication and multiplicative inverse, formula_21 This simplifies the analysis of subtraction and division, and also makes it easier to axiomatize these operations in the notion of a field, as there are only two binary and two unary operations, rather than four binary operations.Extending these primitive operations, there is a rich literature on the topic of polynomial decomposition.As to "why" the decomposition is valuable, the reason is twofold.