 solvefor - Maple Help

solvefor

solve for one or more of the variables found in a set of equations Calling Sequence solvefor(eqn_1, eqn_2, ... ) solvefor[varseq](eqnset) Parameters

 eqn_1, eqn_2, ... - equation or a set of equations to be solved collectively varseq - expression sequence of variables to be placed on the left-side of the equations forming a solution eqnset - expression sequence; one or more equations to be solved collectively Description

 • Important: The solvefor command has been deprecated.  Use the superseding command solve instead.
 • The solvefor command isolates specified variables (if any) from a set of equations on the left-hand side of a reduced set of equations. If no variables are specified it is essentially equivalent to a call to solve. Answer are returned in a form suitable for use in other commands such as subs and eval.
 • The original set of equations is formed by collecting the arguments to solvefor into a set of equations. The solve command is applied to the resulting system to produce 0 or more solutions.
 • If no solution is found this is indicated by an empty list. If more than one solution is found then they are returned as a list of solutions.
 • Each solution is returned as an equation, or (if more than one equation is involved) as a set of equations in which the variables on the left-hand side do not appear on the right hand side.
 • Variables may be specified as an index to the procedure name, as in solvefor[x](...).  This indicates that the solutions must include the indicated variables on the left-hand side of the solution equations. Examples

Important: The solvefor command has been deprecated.  Use the superseding command solve instead.

 > $\mathrm{solvefor}\left(\left\{{x}^{3}-{y}^{2}x+xy=3,{x}^{2}+{y}^{2}=1\right\}\right)$
 Warning, solvefor is deprecated. Please use solve command.
 $\left[\left\{{x}{=}{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{1}\right){,}{y}{=}{-}\frac{{4}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{1}\right)}^{{5}}}{{3}}{+}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{1}\right)}^{{3}}{+}{2}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{1}\right)}^{{2}}{-}{1}\right\}{,}\left\{{x}{=}{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{2}\right){,}{y}{=}{-}\frac{{4}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{2}\right)}^{{5}}}{{3}}{+}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{2}\right)}^{{3}}{+}{2}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{2}\right)}^{{2}}{-}{1}\right\}{,}\left\{{x}{=}{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{3}\right){,}{y}{=}{-}\frac{{4}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{3}\right)}^{{5}}}{{3}}{+}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{3}\right)}^{{3}}{+}{2}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{3}\right)}^{{2}}{-}{1}\right\}{,}\left\{{x}{=}{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{4}\right){,}{y}{=}{-}\frac{{4}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{4}\right)}^{{5}}}{{3}}{+}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{4}\right)}^{{3}}{+}{2}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{4}\right)}^{{2}}{-}{1}\right\}{,}\left\{{x}{=}{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{5}\right){,}{y}{=}{-}\frac{{4}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{5}\right)}^{{5}}}{{3}}{+}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{5}\right)}^{{3}}{+}{2}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{5}\right)}^{{2}}{-}{1}\right\}{,}\left\{{x}{=}{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{6}\right){,}{y}{=}{-}\frac{{4}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{6}\right)}^{{5}}}{{3}}{+}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{6}\right)}^{{3}}{+}{2}{}{{\mathrm{RootOf}}{}\left({4}{}{{\mathrm{_Z}}}^{{6}}{-}{3}{}{{\mathrm{_Z}}}^{{4}}{-}{12}{}{{\mathrm{_Z}}}^{{3}}{+}{6}{}{\mathrm{_Z}}{+}{9}{,}{\mathrm{index}}{=}{6}\right)}^{{2}}{-}{1}\right\}\right]$ (1)
 > $\mathrm{solvefor}\left[t\right]\left(x+y=1,x-y+zt=3\right)$
 $\left\{{t}{=}{-}\frac{{2}{}\left({x}{-}{2}\right)}{{z}}{,}{y}{=}{-}{x}{+}{1}\right\}$ (2)
 > $\mathrm{solvefor}\left[y\right]\left(x+y=1,x-y+zt=3\right)$
 $\left\{{x}{=}{-}\frac{{z}{}{t}}{{2}}{+}{2}{,}{y}{=}\frac{{z}{}{t}}{{2}}{-}{1}\right\}$ (3)
 > $\mathrm{solvefor}\left[z\right]\left(x+y=1,x-y+zt=3\right)$
 $\left\{{y}{=}{-}{x}{+}{1}{,}{z}{=}{-}\frac{{2}{}\left({x}{-}{2}\right)}{{t}}\right\}$ (4)