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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

 > with(SolveTools):
 > Parametric({a*x}, {x}, {a});
 $\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)
 > Parametric({a*x+b}, {x});
 $\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)
 > Parametric({a*x+b}, {x}, {a});
 $\left\{\begin{array}{cc}\left[\right]& {a}{=}{0}\\ \left[\left\{{x}{=}{-}\frac{{b}}{{a}}\right\}\right]& {a}{\ne }{0}\end{array}\right\$ (3)
 > Parametric({a*x^2-(b+a)*x+b}, {x});
 $\left\{\begin{array}{cc}{{?}}_{{\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)
 > Parametric({a*x^2-(b+a)*x+b}, {x}, mode=proviso);
 $\left[\left[\left\{{x}{=}{1}\right\}{,}\left\{{x}{=}\frac{{b}}{{a}}\right\}\right]{,}\left\{{a}{\ne }{0}\right\}\right]$ (5)
 > Parametric({a*x^2-(b+a)*x+b}, {x}, mode=full);
 $\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.