- .. WARNING::
-
- This implementation doesn't guarantee that the polynomial
- denominator in the coefficients is not identically zero, so
- theoretically it could crash. The way that this is handled
- in e.g. Faraut and Koranyi is to use a basis that guarantees
- the denominator is non-zero. But, doing so requires knowledge
- of at least one regular element, and we don't even know how
- to do that. The trade-off is that, if we use the standard basis,
- the resulting polynomial will accept the "usual" coordinates. In
- other words, we don't have to do a change of basis before e.g.
- computing the trace or determinant.
+ The resulting polynomial has `n+1` variables, where `n` is the
+ dimension of this algebra. The first `n` variables correspond to
+ the coordinates of an algebra element: when evaluated at the
+ coordinates of an algebra element with respect to a certain
+ basis, the result is a univariate polynomial (in the one
+ remaining variable ``t``), namely the characteristic polynomial
+ of that element.