SolveTools[Inequality] - Maple Programming Help

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SolveTools[Inequality]

 LinearUnivariateSystem
 solve a system of linear inequalities with respect to one variable

 Calling Sequence LinearUnivariateSystem(sys, var)

Parameters

 sys - system of inequalities var - variable name

Description

 • The LinearUnivariateSystem command solves a system of linear inequalities with respect to one variable.
 • The LinearUnivariateSystem command returns a set describing the interval of possible values of the variable or a piecewise function of such sets depending on parameters

Examples

 > $\mathrm{with}\left(\mathrm{SolveTools}[\mathrm{Inequality}]\right):$
 > $\mathrm{LinearUnivariateSystem}\left(\left\{0
 $\left\{\frac{{1}}{{2}}{<}{x}\right\}$ (1)
 > $\mathrm{LinearUnivariateSystem}\left(\left\{0
 $\left\{{-}{1}{<}{x}{,}{x}{<}\frac{{1}}{{2}}\right\}$ (2)
 > $\mathrm{LinearUnivariateSystem}\left(\left\{x+1<0,2x-1<0\right\},x\right)$
 $\left\{{x}{<}{-}{1}\right\}$ (3)
 > $\mathrm{LinearUnivariateSystem}\left(\left\{x+1<0,0<2x-1\right\},x\right)$
 $\left\{{}\right\}$ (4)
 > $\mathrm{LinearUnivariateSystem}\left(\left\{x+a<0,0<2x-1\right\},x\right)$
 ${{}\begin{array}{cc}\left\{\frac{{1}}{{2}}{<}{x}{,}{x}{<}{-}{a}\right\}& {a}{<}{-}\frac{{1}}{{2}}\\ \left\{{}\right\}& {\mathrm{otherwise}}\end{array}$ (5)
 > $\mathrm{LinearUnivariateSystem}\left(\left\{2x+a\le 0,0\le 2x-b\right\},x\right)$
 ${{}\begin{array}{cc}\left\{{x}{\le }{-}\frac{{1}}{{2}}{}{a}{,}\frac{{1}}{{2}}{}{b}{\le }{x}\right\}& {a}{\le }{-}{b}\\ \left\{{}\right\}& {\mathrm{otherwise}}\end{array}$ (6)
 > $\mathrm{LinearUnivariateSystem}\left(\left\{ax+2\le 0,0\le 2x-b\right\},x\right)$
 ${{}\begin{array}{cc}\left\{{x}{\le }{-}\frac{{2}}{{a}}{,}\frac{{1}}{{2}}{}{b}{\le }{x}\right\}& {\mathrm{And}}{}\left({0}{<}{a}{,}\frac{{1}}{{2}}{}{b}{\le }{-}\frac{{2}}{{a}}\right)\\ \left\{{-}\frac{{2}}{{a}}{\le }{x}\right\}& {\mathrm{And}}{}\left({a}{<}{0}{,}\frac{{1}}{{2}}{}{b}{<}{-}\frac{{2}}{{a}}\right)\\ \left\{\frac{{1}}{{2}}{}{b}{\le }{x}\right\}& {\mathrm{And}}{}\left({a}{<}{0}{,}{-}\frac{{2}}{{a}}{\le }\frac{{1}}{{2}}{}{b}\right)\\ \left\{{}\right\}& {a}{=}{0}\\ \left\{{}\right\}& {\mathrm{otherwise}}\end{array}$ (7)
 > $\mathrm{LinearUnivariateSystem}\left(\left\{ax+b<0,0\le cx+d\right\},x\right)$
 ${{}\begin{array}{cc}\left\{{x}{\le }{-}\frac{{d}}{{c}}\right\}& {\mathrm{And}}{}\left({0}{<}{a}{,}{c}{<}{0}{,}{-}\frac{{d}}{{c}}{<}{-}\frac{{b}}{{a}}\right)\\ \left\{{x}{<}{-}\frac{{b}}{{a}}\right\}& {\mathrm{And}}{}\left({0}{<}{a}{,}{c}{<}{0}{,}{-}\frac{{b}}{{a}}{\le }{-}\frac{{d}}{{c}}\right)\\ \left\{{-}\frac{{d}}{{c}}{\le }{x}{,}{x}{<}{-}\frac{{b}}{{a}}\right\}& {\mathrm{And}}{}\left({0}{<}{a}{,}{0}{<}{c}{,}{-}\frac{{d}}{{c}}{<}{-}\frac{{b}}{{a}}\right)\\ \left\{{x}{<}{-}\frac{{b}}{{a}}\right\}& {\mathrm{And}}{}\left({0}{<}{a}{,}{c}{=}{0}{,}{0}{\le }{d}\right)\\ \left\{{}\right\}& {\mathrm{And}}{}\left({0}{<}{a}{,}{c}{=}{0}{,}{d}{<}{0}\right)\\ \left\{{x}{\le }{-}\frac{{d}}{{c}}{,}{-}\frac{{b}}{{a}}{<}{x}\right\}& {\mathrm{And}}{}\left({a}{<}{0}{,}{c}{<}{0}{,}{-}\frac{{b}}{{a}}{<}{-}\frac{{d}}{{c}}\right)\\ \left\{{-}\frac{{d}}{{c}}{\le }{x}\right\}& {\mathrm{And}}{}\left({a}{<}{0}{,}{0}{<}{c}{,}{-}\frac{{b}}{{a}}{<}{-}\frac{{d}}{{c}}\right)\\ \left\{{-}\frac{{b}}{{a}}{<}{x}\right\}& {\mathrm{And}}{}\left({a}{<}{0}{,}{0}{<}{c}{,}{-}\frac{{d}}{{c}}{\le }{-}\frac{{b}}{{a}}\right)\\ \left\{{-}\frac{{b}}{{a}}{<}{x}\right\}& {\mathrm{And}}{}\left({a}{<}{0}{,}{c}{=}{0}{,}{0}{\le }{d}\right)\\ \left\{{}\right\}& {\mathrm{And}}{}\left({a}{<}{0}{,}{c}{=}{0}{,}{d}{<}{0}\right)\\ \left\{{x}{\le }{-}\frac{{d}}{{c}}\right\}& {\mathrm{And}}{}\left({a}{=}{0}{,}{b}{<}{0}{,}{c}{<}{0}\right)\\ \left\{{-}\frac{{d}}{{c}}{\le }{x}\right\}& {\mathrm{And}}{}\left({a}{=}{0}{,}{b}{<}{0}{,}{0}{<}{c}\right)\\ \left\{{x}\right\}& {\mathrm{And}}{}\left({a}{=}{0}{,}{b}{<}{0}{,}{c}{=}{0}{,}{0}{\le }{d}\right)\\ \left\{{}\right\}& {\mathrm{And}}{}\left({a}{=}{0}{,}{b}{<}{0}{,}{c}{=}{0}{,}{d}{<}{0}\right)\\ \left\{{}\right\}& {\mathrm{And}}{}\left({a}{=}{0}{,}{0}{\le }{b}\right)\end{array}$ (8)