`s` * `t`

The operator `*`

evaluates to the product of the two monoid elements `s`
and `t`. The operands must of course lie in a common parent monoid,
otherwise an error is signaled.

`s` ^ `i`

The powering operator `^`

returns the `i`-th power of a monoid element
`s` and a positive integer `i`. If `i` is zero the identity of a parent
monoid of `s` is returned.

`list` * `s``s` * `list`

In this form the operator `*`

returns a new list where each entry is the
product of `s` and the corresponding entry of `list`. Of course
multiplication must be defined between `s` and each entry of `list`.