Parametric - Maple Help

SolveTools

 Parametric
 solve a set of polynomial equations

 Calling Sequence Parametric(equations, unknowns, mode=value) Parametric(equations, unknowns, parameters, mode=value)

Parameters

 equations - set of polynomial equations unknowns - set of symbols for which to solve parameters - (optional) set of symbols to treat as parameters value - (optional) specify mode (see the Options section)

Options

 • 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.

Description

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

Examples

 > $\mathrm{with}\left(\mathrm{SolveTools}\right):$
 > $\mathrm{Parametric}\left(\left\{ax\right\},\left\{x\right\},\left\{a\right\}\right)$
 $\left\{\begin{array}{cc}\left[\left\{{x}{=}{x}\right\}\right]& {a}{=}{0}\\ \left[\left\{{x}{=}{0}\right\}\right]& {a}{\ne }{0}\end{array}\right\$ (1)
 > $\mathrm{Parametric}\left(\left\{ax+b\right\},\left\{x\right\}\right)$
 $\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\$ (2)
 > $\mathrm{Parametric}\left(\left\{ax+b\right\},\left\{x\right\},\left\{a\right\}\right)$
 $\left\{\begin{array}{cc}\left[\right]& {a}{=}{0}\\ \left[\left\{{x}{=}{-}\frac{{b}}{{a}}\right\}\right]& {a}{\ne }{0}\end{array}\right\$ (3)
 > $\mathrm{Parametric}\left(\left\{a{x}^{2}-\left(b+a\right)x+b\right\},\left\{x\right\}\right)$
 $\left\{\begin{array}{cc}{{\mathrm{Typesetting}}{:-}{\mathrm{_Hold}}{}\left(\left[{\mathrm{%SolveTools}}\right]\right)}_{{\mathrm{Parametric}}}{}\left(\left\{{-}{x}{}{b}{+}{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\$ (4)
 > $\mathrm{Parametric}\left(\left\{a{x}^{2}-\left(b+a\right)x+b\right\},\left\{x\right\},\mathrm{mode}=\mathrm{proviso}\right)$
 $\left[\left[\left\{{x}{=}{1}\right\}{,}\left\{{x}{=}\frac{{b}}{{a}}\right\}\right]{,}\left\{{a}{\ne }{0}\right\}\right]$ (5)
 > $\mathrm{Parametric}\left(\left\{a{x}^{2}-\left(b+a\right)x+b\right\},\left\{x\right\},\mathrm{mode}=\mathrm{full}\right)$
 $\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\$ (6)

Compatibility

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