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

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