mode=value

This option has three settings, full, lazy (the default), and proviso.  mode=full builds a piecewise solution with a branch for all cases of the solution.  mode=lazy builds a piecewise solution with an explicit solution for the most general case, and an inert function call to compute the rest of the solution if needed using the command value.  mode=proviso returns most of the same information as mode=lazy, but formatted as a list with two elements.  The first element is the most general solution, and the second is a set of conditions that must hold for the solution to be valid.

Build a full parametric discussion of the solutions to the equations with respect to the given parameters.

$\mathrm{with}\left(\mathrm{SolveTools}\right)\:$

$\mathrm{Parametric}\left(\left\{ax\right\}\,\left\{x\right\}\,\left\{a\right\}\right)$

$\left\{\begin{array}{cc}\left[\left\{x=x\right\}\right]& a=0\\ \left[\left\{x=0\right\}\right]& a\ne 0\end{array}\right.$

$\mathrm{Parametric}\left(\left\{ax+b\right\}\,\left\{x\right\}\right)$

$\left\{\begin{array}{cc}\left\{\begin{array}{cc}\left[\right]& b\ne 0\\ \left[\left\{x=x\right\}\right]& \mathrm{otherwise}\end{array}\right.& a=0\\ \left[\left\{x=-\frac{b}{a}\right\}\right]& a\ne 0\end{array}\right.$

$\mathrm{Parametric}\left(\left\{ax+b\right\}\,\left\{x\right\}\,\left\{a\right\}\right)$

$\left\{\begin{array}{cc}\left[\right]& a=0\\ \left[\left\{x=-\frac{b}{a}\right\}\right]& a\ne 0\end{array}\right.$

$\mathrm{Parametric}\left(\left\{a{x}^2-\left(b+a\right)x+b\right\}\,\left\{x\right\}\right)$

$\left\{\begin{array}{cc}{\mathrm{SolveTools}}_{\mathrm{Parametric}}\left(\left\{-xb+b\right\}\,\left\{x\right\}\,\left\{b\right\}\right)& a=0\\ \left[\left\{x=1\right\}\,\left\{x=\frac{b}{a}\right\}\right]& a\ne 0\end{array}\right.$

$\mathrm{Parametric}\left(\left\{a{x}^2-\left(b+a\right)x+b\right\}\,\left\{x\right\}\,\mathrm{mode}=\mathrm{proviso}\right)$

$\left[\left[\left\{x=1\right\}\,\left\{x=\frac{b}{a}\right\}\right]\,\left\{a\ne 0\right\}\right]$

$\mathrm{Parametric}\left(\left\{a{x}^2-\left(b+a\right)x+b\right\}\,\left\{x\right\}\,\mathrm{mode}=\mathrm{full}\right)$

$\left\{\begin{array}{cc}\left\{\begin{array}{cc}\left[\left\{x=x\right\}\right]& b=0\\ \left[\left\{x=1\right\}\right]& b\ne 0\end{array}\right.& a=0\\ \left[\left\{x=1\right\}\,\left\{x=\frac{b}{a}\right\}\right]& a\ne 0\end{array}\right.$

The SolveTools[Parametric] command was introduced in Maple 15.

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