Equations and Inequalities, =, <>, <, <=, >, >=

Description


•

An equation is represented externally using the binary operator =. An expression which is an equation has two operands, the lefthand side and the righthand side. The names = and equation are known to the type function.

•

There are three internal data types for inequalities, corresponding to the operators <>, <, and <=. Inequalities involving the operators > and >= are converted to the latter two cases for purposes of representation. An inequality has two operands, the lefthand side and the righthand side. The names <>, <, <= are known to the type function.

•

Comparisons of numeric values are carried out in the corresponding numeric computation environment. For example, the test 3.141 < 3.142 is evaluated by subtraction in the floatingpoint environment determined by Digits. Hence, if Digits > 3, this returns true. If Digits <= 3, this test returns false.

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These operators are viewed as relational operators in a Boolean context or by the evalb function. For more information, see boolean.



Thread Safety


•

The equation and inequality operators are thread safe as of Maple 15.

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The Equations and Inequalities, =, <>, <, <=, >, >= command is threadsafe as of Maple 15.



Examples


${e}{\u2254}{a}{=}{b}$
 (1) 
>

$\mathrm{type}\left(e\,\'\mathrm{equation}\'\right)$

>

$e\u2254f\left(x\right)<g\left(x\right)$

${e}{\u2254}{f}{}\left({x}\right){<}{g}{}\left({x}\right)$
 (3) 
>

$\mathrm{type}\left(e\,\'\mathrm{equation}\'\right)$

>

$\mathrm{type}\left(e\,\mathrm{`<`}\right)$

>

$\mathrm{lhs}\left(e\right)$

${f}{}\left({x}\right)$
 (6) 
>

$\mathrm{rhs}\left(e\right)$

${g}{}\left({x}\right)$
 (7) 
>

$\mathrm{eqs}\u2254\left\{\mathrm{a1}\=\mathrm{b1}\,\mathrm{a2}\=\mathrm{b2}\,\mathrm{a3}\=\mathrm{b3}\right\}$

${\mathrm{eqs}}{\u2254}\left\{{\mathrm{a1}}{=}{\mathrm{b1}}{\,}{\mathrm{a2}}{=}{\mathrm{b2}}{\,}{\mathrm{a3}}{=}{\mathrm{b3}}\right\}$
 (8) 
>

$\mathrm{map}\left(\mathrm{lhs}\,\mathrm{eqs}\right)$

$\left\{{\mathrm{a1}}{\,}{\mathrm{a2}}{\,}{\mathrm{a3}}\right\}$
 (9) 
>

$\mathrm{assign}\left(\right)$






