denominator

Function: denominator
Section: conversions
C-Name: denominator
Prototype: GDG
Help: denominator(f,{D}): denominator of f.
Doc:
 denominator of $f$. The meaning of this is clear when $f$ is a rational number
 or function. If $f$ is an integer or a polynomial, it is treated as a rational
 number or function, respectively, and the result is equal to $1$. For
 polynomials, you probably want to use
 \bprog
 denominator( content(f) )
 @eprog\noindent instead. As for modular objects, \typ{INTMOD} and \typ{PADIC}
 have denominator $1$, and the denominator of a \typ{POLMOD} is the
 denominator of its lift.

 If $f$ is a recursive structure, for instance a vector or matrix, the lcm
 of the denominators of its components (a common denominator) is computed.
 This also applies for \typ{COMPLEX}s and \typ{QUAD}s.

 \misctitle{Warning} Multivariate objects are created according to variable
 priorities, with possibly surprising side effects ($x/y$ is a polynomial, but
 $y/x$ is a rational function). See \secref{se:priority}.

 The optional argument $D$ allows to control over which ring we compute the
 denominator and get a more predictable behaviour:

 \item $1$: we only consider the underlying $\Q$-structure and the
 denominator is a (positive) rational integer

 \item a simple variable, say \kbd{'x}: all entries as rational functions
 in $K(x)$ and the denominator is a polynomial in $x$.

 \bprog
 ? f = x + 1/y + 1/2;
 ? denominator(f) \\ a t_POL in x
 %2 = 1
 ? denominator(f, 1) \\ Q-denominator
 %3 = 2
 ? denominator(f, x) \\ as a t_POL in x, seen above
 %4 = 1
 ? denominator(f, y) \\ as a rational function in y
 %5 = 2*y
 @eprog
Variant: Also available are
 \fun{GEN}{denom}{GEN x}  which implements the not very useful default
 behaviour ($D$ is \kbd{NULL}) and \fun{GEN}{Q_denom}{GEN x} ($D = 1$).