The solve command with the parametric option solves a system of polynomial equations with parameters.

It builds a full parametric discussion of the solutions to the equations with respect to the parameters in the equations using a piecewise expression. By default, an efficient approach is used that returns the result as a lazily evaluated piecewise expression.  That is, the piecewise solution contains inert function calls in some branches of the form %SolveTools[Parametric].  To compute an answer in one of these cases, use the value command. The intention behind this output format is to do as little computation as possible but to make it easy to compute the answer in non-general cases, if needed.

Currently only polynomial equations are supported.

If the real option is given, the SolveTools[SemiAlgebraic] command is called on the equations.  In this case, only a full case discussion on non-variable symbols is available.

The parametric option can also be given as an equation parametric=lazy, parametric=full or parametric=proviso which will return answers in the corresponding modes for SolveTools[Parametric].  (The default is parametric=lazy.)

The parameters option can be used to specify that only a subset of the non-variable symbols in the equations should be treated as parameters.

$\mathrm{solve}\left(\left\{y=mx+b\,y=nx+c\right\}\,\left\{x\,y\right\}\,'\mathrm{parametric}'\right)$

$\left\{\begin{array}{cc}{\mathrm{SolveTools}}_{\mathrm{Parametric}}\left(\left\{-mx-b+y\,-mx-c+y\right\}\,\left\{x\,y\right\}\,\left\{b\,c\,m\right\}\right)& m-n=0\\ \left[\left\{x=-\frac{b-c}{m-n}\,y=-\frac{bn-cm}{m-n}\right\}\right]& m-n\ne 0\end{array}\right.$

$\mathrm{solve}\left(\left\{y=mx+b\,y=nx+c\right\}\,\left\{x\,y\right\}\,'\mathrm{parametric}'='\mathrm{full}'\,'\mathrm{parameters}'=\left\{m\,n\right\}\right)$

$\left\{\begin{array}{cc}\left[\right]& m-n=0\\ \left[\left\{x=-\frac{b-c}{m-n}\,y=-\frac{bn-cm}{m-n}\right\}\right]& m-n\ne 0\end{array}\right.$

$\mathrm{solve}\left(\left\{y<nx+c\&comma;mx+b<y\right\}\&comma;\left\{x\&comma;y\right\}\&comma;'\mathrm{parametric}'\&comma;'\mathrm{real}'\right)$

$\left\{\begin{array}{cc}\left[\left[x=x\&comma;xn+b<y\&comma;y<xn+c\right]\right]& m=n\wedge b<c\\ \left[\left[-\frac{b-c}{m-n}<x\&comma;xm+b<y\&comma;y<xn+c\right]\right]& m<n\\ \left[\left[x<-\frac{b-c}{m-n}\&comma;xm+b<y\&comma;y<xn+c\right]\right]& n<m\\ \left[\right]& \mathrm{otherwise}\end{array}\right.$

The solve/parametric command was introduced in Maple 15.

The parametric option was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.

The real option was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.