**numeric arithmetic**

- normally inexact
- usually produces some sort of answer (may suffer loss of accuracy, fail to converge, etc.)
- arithmetic relatively cheap
- zeroes usually not given special treatment except to avoid computational singularities
- zero detection: number sufficiently small?
- maximize size of pivots to promote stability

- always exact
- frequently cannot produce an answer (problem is intractable, expression swell, etc.)
- arithmetic often expensive
- zeroes can greatly simplify calculations by making some of them unnecessary
- zero detection: expression equivalent to zero?
- minimize complexity of

pivots to stunt expression growth

Richard Liska