Moreover, if we replace the complex group by a real group we may not even get an algebraic set.

The order of operations is a mathematical and algebraic set of rules.

The V stands for variety (a specific type of algebraic set to be defined below).

An algebraic set is called irreducible if it cannot be written as the union of two smaller algebraic sets.

Thus its elements are called the irreducible components of the algebraic set.

An irreducible algebraic set is also called a variety.

The definition of the regular maps apply also to algebraic sets.

Contrarily to the preceding ones, this section concerns only varieties and not algebraic sets.

It follows that the best implementations allow to compute almost routinely with algebraic sets of degree more than 100.

Some are restricted to algebraic varieties while others apply also to any algebraic set.