arccoshp - Maple Help

 Calling Sequence sinp(ex, p, s)  or  evalp(sin(ex, p, s)) sinp(ex, p)  or  evalp(sin(ex, p)) sinp(ex) ...

Parameters

 ex - expression of rational numbers and p-adic numbers p - prime number or positive integer s - positive integer

Description

 • The following functions evaluate the p-adic version of the corresponding real-valued function (obtained by dropping the final p from the name).

 sinp cosp tanp cscp secp cotp sinhp coshp tanhp cschp sechp cothp arcsinp arccosp arctanp arccscp arcsecp arccotp arcsinhp arccoshp arctanhp arccschp arcsechp arccothp expp logp sqrtp

 • sinp is a short form for evalp@sin, and similarly for each of the other functions above.
 • 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.
 • The expression ex can contain any of the operations +, -, *, /, ^, and any of the functions defined in the padic package.
 • If the second and third arguments are omitted, then the expression ex must be a p-adic number.
 • If the result of the computation is not convergent in the p-adic field, then the routine returns FAIL.
 • See padic[evalp] for an explanation of the representation of p-adic numbers in Maple.
 • These functions are part of the padic package, and so can only be used after performing the command with(padic) or with(padic,).

Examples

 > $\mathrm{with}\left(\mathrm{padic}\right):$
 > $\mathrm{cosp}\left(3,3\right)$
 ${1}{+}{{3}}^{{2}}{+}{2}{}{{3}}^{{4}}{+}{{3}}^{{6}}{+}{2}{}{{3}}^{{7}}{+}{{3}}^{{8}}{+}{O}{}\left({{3}}^{{9}}\right)$ (1)
 > $\mathrm{cosp}\left(3+,3\right)$
 ${\mathrm{FAIL}}$ (2)
 > $\mathrm{cos}\left(3\right)$
 ${\mathrm{cos}}{}\left({3}\right)$ (3)
 > $\mathrm{evalf}\left(\right)$
 ${-0.9899924966}$ (4)
 > $\mathrm{evalp}\left(,3\right)$
 ${1}{+}{{3}}^{{2}}{+}{2}{}{{3}}^{{4}}{+}{{3}}^{{6}}{+}{2}{}{{3}}^{{7}}{+}{{3}}^{{8}}{+}{O}{}\left({{3}}^{{9}}\right)$ (5)
 > $\mathrm{Digitsp}≔8$
 ${\mathrm{Digitsp}}{≔}{8}$ (6)
 > $\mathrm{evalp}\left({ⅇ}^{3},3\right)$
 ${1}{+}{3}{+}{{3}}^{{2}}{+}{2}{}{{3}}^{{3}}{+}{2}{}{{3}}^{{4}}{+}{{3}}^{{6}}$ (7)
 > $\mathrm{logp}\left(\right)$
 ${3}{+}{O}{}\left({{3}}^{{8}}\right)$ (8)
 > $\mathrm{arctanp}\left(x,p,10\right)$
 ${\mathrm{arctanp}}{}\left({x}{,}{p}{,}{10}\right)$ (9)
 > $\mathrm{eval}\left(,\left[x=6,p=3\right]\right)$
 ${2}{}{3}{+}{{3}}^{{2}}{+}{2}{}{{3}}^{{4}}{+}{2}{}{{3}}^{{8}}$ (10)
 > $\mathrm{op}\left(\right)$
 ${\mathrm{p_adic}}{}\left({3}{,}{1}{,}\left[{2}{,}{1}{,}{0}{,}{2}{,}{0}{,}{0}{,}{0}{,}{2}{,}{0}{,}{0}\right]\right)$ (11)
 > $\mathrm{evalp}\left(\right)$
 ${2}{}{3}{+}{{3}}^{{2}}{+}{2}{}{{3}}^{{4}}{+}{2}{}{{3}}^{{8}}$ (12)