Function: taylor
Section: polynomials
C-Name: tayl
Prototype: GnDP
Help: taylor(x,t,{d=seriesprecision}): taylor expansion of x with respect to
t, adding O(t^d) to all components of x.
Doc: Taylor expansion around $0$ of $x$ with respect to
the simple variable $t$. $x$ can be of any reasonable type, for example a
rational function. Contrary to \tet{Ser}, which takes the valuation into
account, this function adds $O(t^d)$ to all components of $x$.
\bprog
? taylor(x/(1+y), y, 5)
%1 = (y^4 - y^3 + y^2 - y + 1)*x + O(y^5)
? Ser(x/(1+y), y, 5)
*** at top-level: Ser(x/(1+y),y,5)
*** ^----------------
*** Ser: main variable must have higher priority in gtoser.
@eprog