- The usual way to do this is to check if the determinant is
- zero, but we need the characteristic polynomial for the
- determinant. The minimal polynomial is a lot easier to get,
- so we use Corollary 2 in Chapter V of Koecher to check
- whether or not the parent algebra's zero element is a root
- of this element's minimal polynomial.
-
- That is... unless the coefficients of our algebra's
- "characteristic polynomial of" function are already cached!
- In that case, we just use the determinant (which will be fast
- as a result).
-
- Beware that we can't use the superclass method, because it
- relies on the algebra being associative.
+ If computing my determinant will be fast, we do so and compare
+ with zero (Proposition II.2.4 in Faraut and
+ Koranyi). Otherwise, Proposition II.3.2 in Faraut and Koranyi
+ reduces the problem to the invertibility of my quadratic
+ representation.