"Igor Khavkine" <[EMAIL PROTECTED]> writes: > Can someone explain the following behavior of Taylor series in Axiom? > > (113) -> y := taylor x > (113) x > Type: UnivariateTaylorSeries(Expression Integer,x,0) > (114) -> x*y > (114) x x > Type: UnivariateTaylorSeries(Expression Integer,x,0) > (115) -> coefficient(%,1) > (115) x > Type: Expression Integer
The reason is that Axiom cannot really know whether you meant x in (114) to be an element of the coefficient Ring EXPR INT, or to be a univariate Taylor series. In case of doubt, it usually chooses the wrong possibility :-) Thus, you should help Axiom by saying monomial(1,1)$UTS(EXPR INT,x,0) * y > I've been trying to write a routine that takes some expression f(x,y), but > possibly containing other symbolic constants, and then solves the implicit > equation f(x,y)=0 for y as a Taylor series in x. The above behavior has > proved to be an obstacle. I think such a routine already exists - at least if f(x, y) involves only powers and derivatives of y. Look at seriesSolve. If you need more help or examples, ask again. If I'm wrong, tell me so :-) Martin _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math
