Function: valuation
Section: conversions
C-Name: gpvaluation
Prototype: GG
Help: valuation(x,p): valuation of x with respect to p.
Doc:
 computes the highest
 exponent of $p$ dividing $x$. If $p$ is of type integer, $x$ must be an
 integer, an intmod whose modulus is divisible by $p$, a fraction, a
 $q$-adic number with $q=p$, or a polynomial or power series in which case the
 valuation is the minimum of the valuation of the coefficients.

 If $p$ is of type polynomial, $x$ must be of type polynomial or rational
 function, and also a power series if $x$ is a monomial. Finally, the
 valuation of a vector, complex or quadratic number is the minimum of the
 component valuations.

 If $x=0$, the result is \kbd{+oo} if $x$ is an exact object. If $x$ is a
 $p$-adic numbers or power series, the result is the exponent of the zero.
 Any other type combinations gives an error.

Variant: Also available is
 \fun{long}{gvaluation}{GEN x, GEN p}, which returns \tet{LONG_MAX} if $x = 0$
 and the valuation as a \kbd{long} integer.