Ralf Hemmecke <[email protected]> writes: >>>> For TaylorSeries some results are exact, and it is easier to control >>>> approximation error. > >>> It's still not a Ring. > >> Hm, but when removing "=", it is a ring, no? > > Good. Then tell me what a "ring" is. You can restrict to > "multiplicative monoid" if you like. To clarify what we are talking > about, tell me what "MartinMonoid" is and how it relates to > http://en.wikipedia.org/wiki/Monoid#Definition .
Just that = is not computatble doesn't mean that it's not existent. Thus, associativity in MartinMonoid guarantees that (a*b)*c and a*(b*c) will be equal, but it does not mean that FriCAS can prove this equality. In particular, any algorithm for a MartinMonoid can rely on associativity. I think the determinant for power seris example is quite useful: we have to distinguish between commutative rings where zero can be detected and commutative rings where it cannot. But in both cases we can compute the determinant! (Although with a significant difference concerning performance.) However, we have to rely on commutativity. Martin -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
