Bill Page wrote:
>
> Is it not possible to consistently and indefinitely delay the choice
> of branch or branch-cuts? What problems could result from producing
>
> x*sqrt(x^2)/2
>
> and similar results in other cases? Then in a give context such as
> definite integral, draw and limit the choice of branch or branch-cut
> could be made explicitly.
For roots the method I outlined can do that. More precisely,
"useless" roots means that we have ring with zero divisors.
As long as we have finite nomber of root this ring is
isomorphic to direct sum of fields. Consequently we
can do computations on coordinates using algorithms for
fields.
To do this on larger scale we have problem that most of
our algebraic routines assume that we work inside
integral domain. For example, polynomial GCD routines
assume base ring is GCD domain and in particular
integral domain.
--
Waldek Hebisch
[email protected]
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