eliminate - Maple Help

eliminate

eliminate some variables from a set or list of equations

 Calling Sequence eliminate (eqnset, varset)

Parameters

 eqnset - set or list of equations varset - variable, or set or list of variables to eliminate from the equations

Description

 • eliminate eliminates the given variables from a set or list of equations.
 • The result of this elimination is an expression sequence of lists.  Each list represents a possible elimination of the given variables.
 • The first component of each solution is a set of equations, where the left-hand side of these equations is a variable (one of the variables in varset) and the right-hand side is its corresponding value.  The second component of each solution is the set of remaining equations once the varset have been eliminated.

Examples

Eliminate the variable x from a list of equations.

 > $\mathrm{eliminate}\left(\left\{{x}^{3}-{y}^{2}x+xy-3,{x}^{2}+{y}^{2}-1\right\},x\right)$
 $\left[\left\{{x}{=}\frac{{3}}{{-}{2}{}{{y}}^{{2}}{+}{y}{+}{1}}\right\}{,}\left\{{4}{}{{y}}^{{6}}{-}{4}{}{{y}}^{{5}}{-}{7}{}{{y}}^{{4}}{+}{6}{}{{y}}^{{3}}{+}{4}{}{{y}}^{{2}}{-}{2}{}{y}{+}{8}\right\}\right]$ (1)
 > $\mathrm{eliminate}\left(\left[x+\mathrm{sin}\left(y\right),3\mathrm{cos}\left(x\right)+xy\right],x\right)$
 $\left[\left\{{x}{=}{-}{\mathrm{sin}}{}\left({y}\right)\right\}{,}\left\{{3}{}{\mathrm{cos}}{}\left({\mathrm{sin}}{}\left({y}\right)\right){-}{\mathrm{sin}}{}\left({y}\right){}{y}\right\}\right]$ (2)
 > $\mathrm{eliminate}\left(\left\{3\mathrm{sin}\left(y\right)z+5xy,3y{z}^{2}x+\mathrm{cos}\left(x\right)z,\mathrm{exp}\left(x+z\right)\right\},x\right)$
 $\left[\left\{{x}{=}{-}\frac{{3}{}{\mathrm{sin}}{}\left({y}\right){}{z}}{{5}{}{y}}\right\}{,}\left\{{z}{}\left({-}{9}{}{\mathrm{sin}}{}\left({y}\right){}{{z}}^{{2}}{+}{5}{}{\mathrm{cos}}{}\left(\frac{{3}{}{\mathrm{sin}}{}\left({y}\right){}{z}}{{5}{}{y}}\right)\right){,}{{ⅇ}}^{{-}\frac{{z}{}\left({3}{}{\mathrm{sin}}{}\left({y}\right){-}{5}{}{y}\right)}{{5}{}{y}}}\right\}\right]$ (3)

Eliminate the variables x and y from a list of equations.

 > $\mathrm{eliminate}\left(\left\{x+z,3{y}^{2}z+5xy,5z+3y{z}^{2}+xy\right\},\left\{x,y\right\}\right)$
 $\left[\left\{{x}{=}{-}{z}{,}{y}{=}{-}\frac{{5}}{{3}{}{z}{-}{1}}\right\}{,}\left\{{25}{}{z}{}\left({2}{+}{3}{}{z}\right)\right\}\right]$ (4)