component

Function: component
Section: conversions
C-Name: compo
Prototype: GL
Help: component(x,n): the n'th component of the internal representation of
 x. For vectors or matrices, it is simpler to use x[]. For list objects such
 as nf, bnf, bnr or ell, it is much easier to use member functions starting
 with ".".
Description:
 (error,small):gen     err_get_compo($1, $2)
 (gen,small):gen       compo($1,$2)
Doc: extracts the $n^{\text{th}}$-component of $x$. This is to be understood
 as follows: every PARI type has one or two initial \idx{code words}. The
 components are counted, starting at 1, after these code words. In particular
 if $x$ is a vector, this is indeed the $n^{\text{th}}$-component of $x$, if
 $x$ is a matrix, the $n^{\text{th}}$ column, if $x$ is a polynomial, the
 $n^{\text{th}}$ coefficient (i.e.~of degree $n-1$), and for power series,
 the $n^{\text{th}}$ significant coefficient.

 For polynomials and power series, one should rather use \tet{polcoeff}, and
 for vectors and matrices, the \kbd{[$\,$]} operator. Namely, if $x$ is a
 vector, then \tet{x[n]} represents the $n^{\text{th}}$ component of $x$. If
 $x$ is a matrix, \tet{x[m,n]} represents the coefficient of row \kbd{m} and
 column \kbd{n} of the matrix, \tet{x[m,]} represents the $m^{\text{th}}$
 \emph{row} of $x$, and \tet{x[,n]} represents the $n^{\text{th}}$
 \emph{column} of $x$.

 Using of this function requires detailed knowledge of the structure of the
 different PARI types, and thus it should almost never be used directly.
 Some useful exceptions:
 \bprog
     ? x = 3 + O(3^5);
     ? component(x, 2)
     %2 = 81   \\ p^(p-adic accuracy)
     ? component(x, 1)
     %3 = 3    \\ p
     ? q = Qfb(1,2,3);
     ? component(q, 1)
     %5 = 1
 @eprog