ineq - Maple Help

solve/ineqs

solve inequalities

 Calling Sequence solve(ineqs, vars)

Parameters

 ineqs - inequalities ( $<$, $<=$, $>$, or $>=$ ) vars - variables (as in solve)

Description

 • The solve function can solve many types of inequalities and systems of inequalities in one or more variables.
 • In general, variables and parameters will automatically be assumed to be real-valued in the context of one or more inequalities.
 • Systems of linear, parametric inequalities are fully supported.  Univariate inequalities can be solved if their points of equality can be sorted into strictly increasing order.  In other cases, solve may return solutions involving the signum function.
 • Some parametric inequalities may have conditional solutions that are invalid for some values of the parameters.  In some cases, Maple will return these solutions in the form of piecewise functions whose conditions depend upon the values of the parameters.  To prevent solve from returning conditional solutions, set the environment variable _EnvConditionalSolutions := false.

Examples

 > $\mathrm{solve}\left(0\le {x}^{2},x\right)$
 ${x}$ (1)
 > $\mathrm{solve}\left(0
 $\left({0}{,}{\mathrm{\infty }}\right)$ (2)
 > $\mathrm{solve}\left(\left(x-1\right)\left(x-2\right)\left(x-3\right)<0,x\right)$
 $\left({-}{\mathrm{\infty }}{,}{1}\right){,}\left({2}{,}{3}\right)$ (3)
 > $\mathrm{solve}\left(\left(x-1+a\right)\left(x-2+a\right)\left(x-3+a\right)<0,\left[x\right]\right)$
 $\left[\left[{x}{<}{3}{-}{a}{,}{2}{-}{a}{<}{x}\right]{,}\left[{x}{<}{1}{-}{a}\right]\right]$ (4)
 > $\mathrm{solve}\left(x+1<\mathrm{exp}\left(x\right)\right)$
 $\left({-}{\mathrm{\infty }}{,}{0}\right){,}\left({0}{,}{\mathrm{\infty }}\right)$ (5)
 > $\mathrm{solve}\left(ax
 $\left\{\begin{array}{cc}\left[\left[{x}{=}{x}\right]\right]& {a}{=}{0}{\wedge }{0}{<}{b}\\ \left[\left[{x}{<}\frac{{b}}{{a}}\right]\right]& {0}{<}{a}\\ \left[\left[\frac{{b}}{{a}}{<}{x}\right]\right]& {a}{<}{0}\\ \left[\right]& {\mathrm{otherwise}}\end{array}\right\$ (6)

This inequality has only conditional solutions, so NULL is returned if _EnvConditionalSolutions is set to false.

 > $\mathrm{_EnvConditionalSolutions}≔\mathrm{false}$
 ${\mathrm{_EnvConditionalSolutions}}{≔}{\mathrm{false}}$ (7)
 > $\mathrm{solve}\left(ax