Ralf Hemmecke <[EMAIL PROTECTED]> writes: > Well, but how can you tell this to Axiom? It should be impossible to construct > the domain UnivariateTaylorSeries(Expression Integer,x,0). > I guess the Axiom designers thought that returning that domain for taylor x > would be reasonable. I must say, I question that. > UTS(Fraction Integer, x, 0) would have been sufficient and you wouldn't have > the trouble.
No, I disagree. As long as we don't have domains UnivariateExpression and MultivariateExpression that take variables as parameters, things like UTS(EXPR INT, x, 0) are necessary. Otherwise you cannot create series like (67) -> series(sin(y+x), x=0) (67) sin(y) 2 cos(y) 3 sin(y) 4 cos(y) 5 sin(y) + cos(y)x - ------ x - ------ x + ------ x + ------ x 2 6 24 120 + sin(y) 6 cos(y) 7 sin(y) 8 cos(y) 9 sin(y) 10 11 - ------ x - ------ x + ------ x + ------ x - ------- x + O(x ) 720 5040 40320 362880 3628800 Type: UnivariatePuiseuxSeries(Expression Integer,x,0) I agree that taking EXPR INT as the default domain is a bad idea though. I think there is one important point for MMA, Maple and MuPAD to make: as long as the mathematics of a particular topic is unclear, good expression domains are useful and sometimes maybe even necessary. Of course, once the mathematics is well understood, for example, as is the case with DFinite functions (as is the case with sin(x+y), an appropriate domain should be created and used. But for the discovery, I believe that "insecure" domains are very useful. In my opinion, especially MuPAD got this very right. By the way, just today I was led to use the domain SUP SUP INT. (In code, of course) As soon as one realizes that different things may generate the same output (printed representation), most of the problems go away. I had very long discusssions with William Sit about that topic on this list, and I have to admit that I now agree with him :-) Martin _______________________________________________ Axiom-math mailing list Axiom-math@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-math