On 8/21/06, Ralf Hemmecke <[EMAIL PROTECTED]> wrote:
On 08/21/2006 07:18 PM, Martin Rubey wrote:
> (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) Looking at this thing I would say that if you take R = Q[s,c] -- polynomial ring in two variables over rationals I = (s^2+c^2-1)R -- ideal in R A = R/I -- factor structure S = A[[x]] -- formal power series then S would be a perfect candidate for the result type of the above expression. And there is no "Expression Integer". While constructing the result of "series", Axiom should try hard to get a reasonable (in some sense minimal) type for the result.
That is in deed a very nice way to characterize the coefficients of of this power series. But how exactly would you coax Axiom into producing a power series with coefficients of this type starting with sin(x+y)? It'd also be nice if the variables s and c printed as sin(y) and cos(y) and behaved the same under operations like, say, taking derivatives with respect to y. Igor _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math
