rootp
 find all roots of a polynomial with rational coefficients in a p-adic number field

 Calling Sequence rootp (pol, p, s)  or  evalp (RootOf(pol),p, s) rootp (pol, p)  or  evalp(RootOf(pol), p)

Parameters

 pol - polynomial with rational coefficients p - prime number or positive integer s - (optional) positive integer

Description

 • This function computes all roots in the given p-adic number field of the polynomial pol.
 • The parameter s sets the size of the resulting expression, where "size" means the number of terms of the p-adic number which will be printed.  If omitted, it defaults to the value of the global variable Digitsp, which is initially assigned the value 10.
 • See padic[evalp] for an explanation of the representation of p-adic numbers in Maple.
 • The command with(padic,rootp) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{padic}\right):$
 > $\mathrm{rootp}\left({x}^{25}-1,5\right)$
 ${1}$ (1)
 > $\mathrm{rootp}\left({x}^{2}+1,5\right)$
 ${3}{+}{3}{}{5}{+}{2}{}{{5}}^{{2}}{+}{3}{}{{5}}^{{3}}{+}{{5}}^{{4}}{+}{2}{}{{5}}^{{6}}{+}{{5}}^{{7}}{+}{4}{}{{5}}^{{8}}{+}{\mathrm{O}}\left({{5}}^{{9}}\right){,}{2}{+}{5}{+}{2}{}{{5}}^{{2}}{+}{{5}}^{{3}}{+}{3}{}{{5}}^{{4}}{+}{4}{}{{5}}^{{5}}{+}{2}{}{{5}}^{{6}}{+}{3}{}{{5}}^{{7}}{+}{\mathrm{O}}\left({{5}}^{{9}}\right)$ (2)
 > $\mathrm{rootp}\left({x}^{2}+1,3\right)$
 > $f≔75{x}^{3}+3{x}^{2}+8x+3$
 ${f}{≔}{75}{}{{x}}^{{3}}{+}{3}{}{{x}}^{{2}}{+}{8}{}{x}{+}{3}$ (3)
 > $\mathrm{evalp}\left(\mathrm{RootOf}\left(f\right),5,15\right)$
 ${4}{}{{5}}^{{-}{2}}{+}{4}{}{{5}}^{{-}{1}}{+}{2}{}{5}{+}{3}{}{{5}}^{{2}}{+}{3}{}{{5}}^{{4}}{+}{3}{}{{5}}^{{5}}{+}{{5}}^{{6}}{+}{3}{}{{5}}^{{7}}{+}{4}{}{{5}}^{{8}}{+}{2}{}{{5}}^{{9}}{+}{2}{}{{5}}^{{10}}{+}{4}{}{{5}}^{{11}}$ (4)