RootOf - Maple Help

convert/RootOf

convert radicals and I to RootOf notation

 Calling Sequence convert(expr, RootOf) convert(expr, RootOf, form=selector)

Parameters

 expr - expression form=selector - selector could be one of the three values: index, interval, or numeric; this is an option to convert between RootOf selectors, namely range/interval selector, numeric selector, and the index selector. For information on these selectors, see RootOf.

Description

 • The convert/RootOf function changes all occurrences of radicals (may be algebraic constants or functions), to indexed RootOf notation.
 • Usually, the radical ${A}^{\frac{p}{m}}$, for integers p < m, is transformed into the expression RootOf(_Z^m-A,index=1)^p.
 • I is replaced by RootOf(_Z^2+1,index=1)
 • This function is mapped recursively over expressions. In particular, nested radicals are converted. If the input expression is an unnamed table then the conversion routine is mapped onto the elements of the table.
 • This function uses radfield to convert radicals into independent RootOfs.
 • To convert RootOf notation to I and radicals (where possible) use convert(expr, radical).
 • To convert RootOf notation between different selectors, use form=selector to select the target selector format.

Examples

 > $\mathrm{convert}\left({2}^{\frac{1}{5}},\mathrm{RootOf}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{5}}{-}{2}{,}{\mathrm{index}}{=}{1}\right)$ (1)
 > $\mathrm{convert}\left({\left(1+{2}^{\frac{1}{2}}\right)}^{\frac{1}{3}}I,\mathrm{RootOf}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{+}{1}{,}{\mathrm{index}}{=}{1}\right){}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{-}{1}{-}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{-}{2}{,}{\mathrm{index}}{=}{1}\right){,}{\mathrm{index}}{=}{1}\right)$ (2)
 > $\mathrm{convert}\left(\left(1+{2}^{\frac{1}{2}}\right)I,\mathrm{RootOf}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{+}{1}{,}{\mathrm{index}}{=}{1}\right){}\left({1}{+}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{-}{2}{,}{\mathrm{index}}{=}{1}\right)\right)$ (3)
 > $\mathrm{convert}\left({2}^{\frac{1}{4}}+{2}^{\frac{1}{3}},\mathrm{RootOf}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{4}}{-}{2}{,}{\mathrm{index}}{=}{1}\right){+}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{-}{2}{,}{\mathrm{index}}{=}{1}\right)$ (4)
 > $\mathrm{convert}\left({\left({x}^{2}+2x+1\right)}^{\frac{1}{2}},\mathrm{RootOf}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{2}}{-}{{x}}^{{2}}{-}{2}{}{x}{-}{1}{,}{\mathrm{index}}{=}{1}\right)$ (5)
 > $\mathrm{convert}\left({\left({x}^{3}-6{x}^{2}-6x-7\right)}^{\frac{1}{2}},\mathrm{RootOf}\right)$
 ${\mathrm{RootOf}}{}\left({-}{{x}}^{{3}}{+}{{\mathrm{_Z}}}^{{2}}{+}{6}{}{{x}}^{{2}}{+}{6}{}{x}{+}{7}{,}{\mathrm{index}}{=}{1}\right)$ (6)
 > $\mathrm{convert}\left(,\mathrm{radical}\right)$
 $\sqrt{{{x}}^{{3}}{-}{6}{}{{x}}^{{2}}{-}{6}{}{x}{-}{7}}$ (7)
 > $a≔\mathrm{RootOf}\left({x}^{3}-x-1,\mathrm{index}=1\right)$
 ${a}{≔}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{-}{\mathrm{_Z}}{-}{1}{,}{\mathrm{index}}{=}{1}\right)$ (8)
 > $\mathrm{convert}\left(a,'\mathrm{RootOf}',\mathrm{form}=\mathrm{interval}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{-}{\mathrm{_Z}}{-}{1}{,}\frac{{10349359}}{{7812500}}{..}\frac{{662358981}}{{500000000}}\right)$ (9)
 > $\mathrm{convert}\left(a,'\mathrm{RootOf}',\mathrm{form}=\mathrm{numeric}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{3}}{-}{\mathrm{_Z}}{-}{1}{,}{1.324717957}\right)$ (10)
 > $b≔\mathrm{RootOf}\left({\mathrm{_Z}}^{5}-\mathrm{_Z}-1,1\right)$
 ${b}{≔}{\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{5}}{-}{\mathrm{_Z}}{-}{1}{,}{1}\right)$ (11)
 > $\mathrm{convert}\left(b,'\mathrm{RootOf}',\mathrm{form}=\mathrm{index}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{5}}{-}{\mathrm{_Z}}{-}{1}{,}{\mathrm{index}}{=}{1}\right)$ (12)
 > $\mathrm{convert}\left(b,'\mathrm{RootOf}',\mathrm{form}=\mathrm{interval}\right)$
 ${\mathrm{RootOf}}{}\left({{\mathrm{_Z}}}^{{5}}{-}{\mathrm{_Z}}{-}{1}{,}\frac{{1167303973}}{{1000000000}}{..}\frac{{1167303983}}{{1000000000}}\right)$ (13)

Compatibility

 • The convert/RootOf command was updated in Maple 18.
 • The form parameter was introduced in Maple 18.
 • For more information on Maple 18 changes, see Updates in Maple 18.