From Mathematics to Generic Programming by Alexander A. Stepanov & Daniel E. Rose

Author:Alexander A. Stepanov & Daniel E. Rose [Stepanov, Alexander A.]
Language: eng
Format: epub, mobi
Publisher: Pearson Education
Published: 2014-11-13T08:00:00+00:00

Let’s extend our table from Section 6.8 to include the new structures we introduced in this chapter. Note that every row of the table includes all the axioms from earlier rows. (In the case of semirings and rings, the “times” operation inherits all the axioms from monoids, while the “plus” operation inherits the axioms from abelian groups.) To illustrate this, we’ve grayed out operations, elements, and axioms that appeared previously in the table.

As we did before, we can also define some other structures more concisely in terms of others:

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