ordp - Maple Help

 ordp
 the order of a p-adic number
 valuep

 Calling Sequence ordp(a, p) ordp(a) valuep(a, p) valuep(a)

Parameters

 a - rational number (2-argument case) or p-adic number (1-argument case) p - prime number or positive integer greater than $1$

Description

 • 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].

Examples

 > $\mathrm{with}\left(\mathrm{padic}\right):$
 > $a≔234234234975$
 ${a}{≔}{234234234975}$ (1)
 > $\mathrm{ordp}\left(a,5\right)$
 ${2}$ (2)
 > $\mathrm{evalp}\left(a,5,7\right)$
 ${4}{}{{5}}^{{2}}{+}{4}{}{{5}}^{{3}}{+}{{5}}^{{6}}{+}{3}{}{{5}}^{{7}}{+}{O}{}\left({{5}}^{{8}}\right)$ (3)
 > $a≔\mathrm{evalp}\left(a,5\right)$
 ${a}{≔}{4}{}{{5}}^{{2}}{+}{4}{}{{5}}^{{3}}{+}{{5}}^{{6}}{+}{3}{}{{5}}^{{7}}{+}{4}{}{{5}}^{{8}}{+}{2}{}{{5}}^{{9}}{+}{2}{}{{5}}^{{11}}{+}{4}{}{{5}}^{{12}}{+}{{5}}^{{13}}{+}{3}{}{{5}}^{{14}}{+}{2}{}{{5}}^{{15}}{+}{{5}}^{{16}}$ (4)
 > $b≔\mathrm{evalp}\left(-\frac{1}{{a}^{2}},5\right)$
 ${b}{≔}{4}{}{{5}}^{{-4}}{+}{4}{}{{5}}^{{-3}}{+}{2}{}{{5}}^{{-2}}{+}{4}{}{{5}}^{{-1}}{+}{4}{+}{2}{}{5}{+}{4}{}{{5}}^{{3}}$ (5)
 > $\mathrm{ordp}\left(a\right)$
 ${2}$ (6)
 > $\mathrm{ordp}\left(b\right)$
 ${-4}$ (7)
 > $\mathrm{ordp}\left(ab,5\right)$
 ${-2}$ (8)
 > $\mathrm{valuep}\left(ab\right)$
 ${{5}}^{{2}}$ (9)
 > $\mathrm{valuep}\left(\frac{a}{b},5\right)$
 ${{5}}^{{\mathrm{-6}}}$ (10)
 > $\mathrm{ordp}\left(x-{y}^{2},5\right)$
 ${\mathrm{ordp}}{}\left({-}{{y}}^{{2}}{+}{x}{,}{5}\right)$ (11)
 > $\mathrm{valuep}\left(x{y}^{2},5\right)$
 ${\mathrm{valuep}}{}\left({x}{}{{y}}^{{2}}{,}{5}\right)$ (12)