Function: variable
Section: conversions
C-Name: gpolvar
Prototype: DG
Help: variable({x}): main variable of object x. Gives p for p-adic x, 0
if no variable can be attached to x. Returns the list of user variables if
x is omitted.
Description:
(pol):var:parens:copy $var:1
(gen):gen gpolvar($1)
Doc:
gives the main variable of the object $x$ (the variable with the highest
priority used in $x$), and $p$ if $x$ is a $p$-adic number. Return $0$ if
$x$ has no variable attached to it.
\bprog
? variable(x^2 + y)
%1 = x
? variable(1 + O(5^2))
%2 = 5
? variable([x,y,z,t])
%3 = x
? variable(1)
%4 = 0
@eprog\noindent The construction
\bprog
if (!variable(x),...)
@eprog\noindent can be used to test whether a variable is attached to $x$.
If $x$ is omitted, returns the list of user variables known to the
interpreter, by order of decreasing priority. (Highest priority is initially
$x$, which come first until \tet{varhigher} is used.) If \kbd{varhigher}
or \kbd{varlower} are used, it is quite possible to end up with different
variables (with different priorities) printed in the same way: they
will then appear multiple times in the output:
\bprog
? varhigher("y");
? varlower("y");
? variable()
%4 = [y, x, y]
@eprog\noindent Using \kbd{v = variable()} then \kbd{v[1]}, \kbd{v[2]},
etc.~allows to recover and use existing variables.
Variant: However, in library mode, this function should not be used for $x$
non-\kbd{NULL}, since \tet{gvar} is more appropriate. Instead, for
$x$ a $p$-adic (type \typ{PADIC}), $p$ is $gel(x,2)$; otherwise, use
\fun{long}{gvar}{GEN x} which returns the variable number of $x$ if
it exists, \kbd{NO\_VARIABLE} otherwise, which satisfies the property
$\kbd{varncmp}(\kbd{NO\_VARIABLE}, v) > 0$ for all valid variable number
$v$, i.e. it has lower priority than any variable.