Mathematical notation

Functions and tuples

In this work, a user-defined $n$-ary operation $f(a_0, a_1, \cdots, a_{n-1})$ is equivalently expressed as $f(\boldsymbol{a})$, where $\boldsymbol{a}$ is an $n$-tuple representing the ordered sequence of elements $(a_0, a_1, \cdots, a_{n-1})$.

Sequences

The documentation provided here uses a form of sequence notation:

$(\boldsymbol{a}_i)_{i=0}^{n-1}$ ,

which corresponds to the sequence of $n$ elements $\boldsymbol{a}_0, \boldsymbol{a}_1, \cdots, \boldsymbol{a}_{n-1}$. When no ambiguity is present, we will use the abbreviation:

$(\boldsymbol{a})_n := (\boldsymbol{a}_i)_{i=0}^{n-1}$ .