Function: Ser
Section: conversions
C-Name: gtoser
Prototype: GDnDP
Help: Ser(s,{v='x},{d=seriesprecision}): convert s into a power series with
 variable v and precision d, starting with the constant coefficient.
Doc: transforms the object $s$ into a power series with main variable $v$
 ($x$ by default) and precision (number of significant terms) equal to
 $d$ (= the default \kbd{seriesprecision} by default). If $s$ is a
 scalar, this gives a constant power series in $v$ with precision \kbd{d}.
 If $s$ is a polynomial, the polynomial is truncated to $d$ terms if needed
 \bprog
 ? Ser(1, 'y, 5)
 %1 = 1 + O(y^5)
 ? Ser(x^2,, 5)
 %2 = x^2 + O(x^7)
 ? T = polcyclo(100)
 %3 = x^40 - x^30 + x^20 - x^10 + 1
 ? Ser(T, 'x, 11)
 %4 = 1 - x^10 + O(x^11)
 @eprog\noindent The function is more or less equivalent with multiplication by
 $1 + O(v^d)$ in theses cases, only faster.

 If $s$ is a vector, on the other hand, the coefficients of the vector are
 understood to be the coefficients of the power series starting from the
 constant term (as in \tet{Polrev}$(x)$), and the precision $d$ is ignored:
 in other words, in this case, we convert \typ{VEC} / \typ{COL} to the power
 series whose significant terms are exactly given by the vector entries.
 Finally, if $s$ is already a power series in $v$, we return it verbatim,
 ignoring $d$ again. If $d$ significant terms are desired in the last two
 cases, convert/truncate to \typ{POL} first.
 \bprog
 ? v = [1,2,3]; Ser(v, t, 7)
 %5 = 1 + 2*t + 3*t^2 + O(t^3)  \\ 3 terms: 7 is ignored!
 ? Ser(Polrev(v,t), t, 7)
 %6 = 1 + 2*t + 3*t^2 + O(t^7)
 ? s = 1+x+O(x^2); Ser(s, x, 7)
 %7 = 1 + x + O(x^2)  \\ 2 terms: 7 ignored
 ? Ser(truncate(s), x, 7)
 %8 = 1 + x + O(x^7)
 @eprog\noindent
 The warning given for \kbd{Pol} also applies here: this is not a substitution
 function.