The ordp command computes the p-adic order of the p-adic number a (evalp(a, p) in the 2-argument case), which is the degree of the leading term.

The valuep command computes the p-adic valuation of the p-adic number a (evalp(a, p) in the 2-argument case), which is 1/p^ordp(a).

For an explanation of the representation of p-adic numbers in Maple, see padic[evalp].

$\mathrm{with}\left(\mathrm{padic}\right)\:$

$a≔234234234975$

$a≔234234234975$

$\mathrm{ordp}\left(a\,5\right)$

$2$

$\mathrm{evalp}\left(a\,5\,7\right)$

$45^2+45^3+5^6+35^7+O\left(5^8\right)$

$a≔\mathrm{evalp}\left(a\,5\right)$

$a≔45^2+45^3+5^6+35^7+45^8+25^9+25^{11}+45^{12}+5^{13}+35^{14}+25^{15}+5^{16}$

$b≔\mathrm{evalp}\left(-\frac{1}{a^2}\,5\right)$

$b≔45^{\mathrm{-4}}+45^{\mathrm{-3}}+25^{\mathrm{-2}}+45^{\mathrm{-1}}+4+25+45^3$

$\mathrm{ordp}\left(a\right)$

$2$

$\mathrm{ordp}\left(b\right)$

$\mathrm{-4}$

$\mathrm{ordp}\left(ab\,5\right)$

$\mathrm{-2}$

$\mathrm{valuep}\left(ab\right)$

$5^2$

$\mathrm{valuep}\left(\frac{a}{b}\,5\right)$

$5^{\mathrm{-6}}$

$\mathrm{ordp}\left(x-y^2\,5\right)$

$\mathrm{ordp}\left(-y^2+x\,5\right)$

$\mathrm{valuep}\left(x{y}^2\,5\right)$

$\mathrm{valuep}\left(x{y}^2\,5\right)$