solve a set of polynomial equations - Maple Help

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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)

Description

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

Examples

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